question
stringlengths 37
38.8k
| group_id
stringlengths 2
6
| sentence_embeddings
sequencelengths 768
768
|
|---|---|---|
<p>I understand that the black-and-white images you see looking through a household telescope are only like that due to the intensity of the light that reaches us, and that most of the astronomy images we find online have some color modification. But if we were to eventually travel between galaxies, how would those galaxies appear to the naked eye? How close to the false color images would they be, and how accurately do we know this?</p> | g1217 | [
-0.03321056067943573,
0.024072473868727684,
0.0043228971771895885,
-0.056275345385074615,
0.03482498601078987,
-0.02142895944416523,
-0.06446298956871033,
-0.014906689524650574,
-0.00672108493745327,
0.013188613578677177,
0.06533757597208023,
0.02883320301771164,
0.059924207627773285,
0.02580776810646057,
0.025515418499708176,
-0.005144675727933645,
-0.032026518136262894,
-0.02969437651336193,
0.004567599855363369,
-0.012799235992133617,
-0.020564928650856018,
-0.0046283891424536705,
0.022290358319878578,
-0.05750291422009468,
-0.11377040296792984,
-0.016394902020692825,
-0.023824423551559448,
-0.026209602132439613,
0.009811735711991787,
-0.028072306886315346,
0.06439663469791412,
-0.04452793672680855,
0.014586947858333588,
-0.03903960809111595,
-0.014092914760112762,
0.08376571536064148,
0.02295810729265213,
0.06524541974067688,
0.059122297912836075,
0.004569595213979483,
-0.000910823349840939,
0.02712688408792019,
-0.026179106906056404,
-0.0011638258583843708,
0.021559374406933784,
-0.00015115643327590078,
0.0010665092850103974,
0.003530857851728797,
0.03281324729323387,
0.05114732310175896,
-0.039464328438043594,
0.05715538188815117,
-0.025763504207134247,
0.0733603984117508,
-0.03764324262738228,
-0.033882588148117065,
0.04072108492255211,
-0.02689579874277115,
0.038872506469488144,
0.00534871406853199,
-0.046157363802194595,
-0.013137543573975563,
-0.0036496382672339678,
-0.01542367972433567,
0.026846641674637794,
0.028234204277396202,
-0.05348534137010574,
0.044525619596242905,
0.0941552072763443,
0.011966545134782791,
-0.04512416943907738,
0.037773944437503815,
-0.04666605964303017,
0.0063808374106884,
-0.0053021558560431,
0.021926162764430046,
0.025691330432891846,
-0.014991363510489464,
-0.015740619972348213,
0.05658702179789543,
0.011135822162032127,
-0.006020542234182358,
-0.005029643885791302,
0.014146501198410988,
0.0017078184755519032,
-0.030589116737246513,
-0.019540777429938316,
-0.03105669654905796,
0.020709944888949394,
0.03546379879117012,
0.020619196817278862,
0.020424194633960724,
0.0035609384067356586,
-0.0002513827639631927,
0.06252741813659668,
-0.02289765514433384,
-0.03888518363237381,
0.07208661735057831,
-0.017834844067692757,
-0.006459048017859459,
-0.035546064376831055,
0.019893376156687737,
0.053627368062734604,
-0.02746545895934105,
-0.03831930086016655,
0.01248876005411148,
0.06877762079238892,
0.04432756081223488,
0.007022099103778601,
0.0006779495161026716,
-0.061231598258018494,
-0.042757466435432434,
0.03745560720562935,
0.008129309862852097,
-0.05973304808139801,
0.01471201702952385,
-0.027408864349126816,
0.043098434805870056,
0.05054984986782074,
0.09827650338411331,
0.06547122448682785,
0.05512097105383873,
-0.030686205253005028,
-0.03791253641247749,
0.010194940492510796,
-0.07389287650585175,
-0.04161488264799118,
-0.055994149297475815,
-0.02847718447446823,
-0.03311185911297798,
0.021103717386722565,
0.04973400756716728,
0.016112225130200386,
0.052922800183296204,
0.008567803539335728,
0.025869907811284065,
0.04167678579688072,
-0.015538952313363552,
-0.05046067386865616,
0.0176357664167881,
0.04972212761640549,
-0.030248885974287987,
-0.01683839038014412,
0.0020659726578742266,
0.017260879278182983,
-0.0000830337157822214,
0.007589370012283325,
0.0152366254478693,
0.041413821280002594,
-0.012141764163970947,
-0.004193571861833334,
-0.005276248790323734,
0.03844407945871353,
0.0023833620361983776,
-0.04281524568796158,
-0.0455779954791069,
0.016894999891519547,
0.024443428963422775,
0.002814745996147394,
-0.03908132016658783,
0.050812169909477234,
-0.06978503614664078,
0.05960448086261749,
0.03206527233123779,
0.003525329753756523,
-0.05933075398206711,
0.020774755626916885,
-0.06060617044568062,
0.04915912076830864,
-0.007002202793955803,
0.03111489675939083,
0.04071599990129471,
-0.008531812578439713,
0.03729035332798958,
0.05785096064209938,
-0.04701228812336922,
0.028260458260774612,
-0.00672773877158761,
-0.034174930304288864,
0.003988228272646666,
-0.03887350112199783,
-0.018561145290732384,
-0.0116541413590312,
-0.019485412165522575,
0.029397359117865562,
-0.0748634859919548,
-0.050277139991521835,
-0.06638245284557343,
0.06222052127122879,
0.047783300280570984,
0.017250550910830498,
-0.04809056594967842,
0.06055592745542526,
0.05901716277003288,
0.008367760106921196,
-0.03322425112128258,
0.005406595300883055,
-0.021619906648993492,
-0.0277627594769001,
0.006918872240930796,
0.03652620688080788,
0.06720800697803497,
0.042267438024282455,
0.02458404377102852,
0.017735203728079796,
-0.05791731923818588,
-0.01479873526841402,
-0.02250032126903534,
0.01048897672444582,
-0.0651354044675827,
-0.0396500900387764,
-0.01144441869109869,
0.053658582270145416,
-0.0022034798748791218,
-0.016624154523015022,
0.05124819278717041,
-0.03494057431817055,
0.012913967482745647,
-0.00565384142100811,
-0.01119162142276764,
0.01941419020295143,
-0.044063933193683624,
0.044730495661497116,
-0.051658615469932556,
0.039794281125068665,
-0.038387756794691086,
-0.05981270968914032,
-0.016249971464276314,
0.03088517114520073,
0.042440079152584076,
-0.02137005887925625,
-0.02697083167731762,
0.032409243285655975,
0.008031921461224556,
0.0024534855037927628,
-0.0018167942762374878,
0.007908597588539124,
-0.008049081079661846,
0.04766068235039711,
0.017659436911344528,
0.0413820743560791,
-0.022550681605935097,
-0.03580930083990097,
0.06674961000680923,
-0.029424775391817093,
-0.011428957805037498,
-0.0001922852243296802,
-0.04694167152047157,
-0.05482745170593262,
0.05198809877038002,
0.007506356108933687,
0.029042281210422516,
-0.04858250170946121,
-0.012788298539817333,
-0.04283011332154274,
0.031022025272250175,
-0.004692563321441412,
0.037557102739810944,
-0.05189305543899536,
0.04790448397397995,
-0.0020113149657845497,
-0.030637983232736588,
-0.03996403142809868,
-0.02024441957473755,
0.032135527580976486,
-0.030742811039090157,
-0.03655483201146126,
0.03180752694606781,
-0.03288542851805687,
0.011793886311352253,
0.029910670593380928,
0.011728446930646896,
0.008799382485449314,
-0.04859621077775955,
0.008104612119495869,
0.009586114436388016,
0.0043073189444839954,
0.01295909471809864,
-0.028920412063598633,
-0.002486096927896142,
-0.020274607464671135,
0.012134311720728874,
-0.06132514402270317,
0.015677455812692642,
-0.00889069214463234,
-0.037093982100486755,
0.005513561889529228,
0.02215217798948288,
0.01981424167752266,
0.00627173762768507,
-0.05194056034088135,
0.025129923596978188,
0.02042338065803051,
0.03918560594320297,
-0.022106589749455452,
-0.013598199002444744,
0.05664665997028351,
0.03280173987150192,
-0.01913231797516346,
-0.013669859617948532,
-0.043460797518491745,
-0.010362919420003891,
0.05118594691157341,
0.04676785692572594,
-0.012191985733807087,
0.010609155520796776,
-0.06138373166322708,
-0.0034804276656359434,
-0.007034321315586567,
-0.033345744013786316,
0.012308270670473576,
0.010924862697720528,
0.018391847610473633,
0.03811459243297577,
0.00322311301715672,
0.013572382740676403,
-0.04021091014146805,
0.03569992259144783,
-0.0009983584750443697,
0.03890366107225418,
-0.021908806636929512,
-0.007131335791200399,
-0.017286868765950203,
-0.015947513282299042,
0.029923273250460625,
0.007023118436336517,
0.005808230489492416,
-0.03301076591014862,
-0.06365209072828293,
0.026144837960600853,
-0.007768740877509117,
0.016795268282294273,
-0.0315621979534626,
-0.009139509871602058,
-0.014845489524304867,
0.0391252264380455,
-0.02065119706094265,
-0.031393732875585556,
0.04220853000879288,
-0.021744504570961,
0.05646827444434166,
-0.021746721118688583,
-0.04445958882570267,
0.00393241411074996,
0.006298639811575413,
-0.036640942096710205,
0.007695600390434265,
-0.052855413407087326,
-0.014707906171679497,
-0.041454486548900604,
0.018696030601859093,
-0.02227262780070305,
0.03985060006380081,
-0.05726958438754082,
0.01336029265075922,
-0.008472291752696037,
-0.010106094181537628,
0.057633135467767715,
0.09449325501918793,
-0.018616551533341408,
0.05952872335910797,
0.03402359411120415,
0.01108643226325512,
-0.04778759181499481,
-0.005900417920202017,
-0.1111874133348465,
0.04455971345305443,
-0.03803325444459915,
0.01254494208842516,
0.01476885937154293,
-0.02381388284265995,
0.03425101563334465,
-0.03185996413230896,
0.015601190738379955,
0.014072787947952747,
-0.0010426613735035062,
0.000501948525197804,
0.03443572297692299,
0.05035313963890076,
0.0343809612095356,
-0.04607386514544487,
0.041130997240543365,
0.0530330128967762,
0.002761900657787919,
0.027600044384598732,
-0.020264098420739174,
-0.020643405616283417,
-0.05733134597539902,
0.0015591656556352973,
-0.05580223351716995,
0.007560991682112217,
-0.0405823290348053,
-0.024652400985360146,
-0.044575031846761703,
0.018454035744071007,
-0.04925670474767685,
0.01029987446963787,
-0.005816739052534103,
0.06872227787971497,
0.003374183550477028,
0.022705232724547386,
0.08836665004491806,
0.036876410245895386,
-0.023609334602952003,
-0.0328451506793499,
-0.04679829999804497,
-0.04494939744472504,
-0.0028982297517359257,
-0.023047734051942825,
-0.015730921179056168,
-0.04208557680249214,
-0.03937729820609093,
0.014380832202732563,
-0.05533098429441452,
0.018805326893925667,
0.02248157188296318,
0.015509194694459438,
-0.017215117812156677,
-0.0007672901265323162,
0.02344570681452751,
0.01648835837841034,
-0.0159909687936306,
-0.026022789999842644,
0.013532676734030247,
-0.034315288066864014,
0.06489533185958862,
-0.008074386976659298,
-0.035549312829971313,
0.01555621437728405,
0.02683679200708866,
0.07224225997924805,
0.012697415426373482,
0.016787363216280937,
0.10030488669872284,
-0.049373429268598557,
0.009906420484185219,
0.02464938908815384,
0.04619171842932701,
0.014473703689873219,
-0.04475836455821991,
0.04029998183250427,
-0.03135770559310913,
0.05313644930720329,
0.00851371604949236,
-0.003832698566839099,
0.08136249333620071,
-0.03839017450809479,
-0.002456418704241514,
0.007809776347130537,
-0.024462800472974777,
-0.014975668862462044,
-0.0011259770253673196,
-0.045966193079948425,
0.005865402519702911,
-0.03777706250548363,
0.016438495367765427,
-0.028295541182160378,
-0.01936669833958149,
0.02062286250293255,
0.007665413431823254,
0.013961119577288628,
0.047282613813877106,
0.012701157480478287,
0.026231853291392326,
-0.0017287074588239193,
0.008299494162201881,
-0.03202981501817703,
-0.038299135863780975,
0.0011167339980602264,
0.025171346962451935,
-0.09857729822397232,
0.013609321787953377,
0.04315034672617912,
-0.0022140834480524063,
0.0024215374141931534,
0.03544241562485695,
0.0024484682362526655,
0.006859736517071724,
-0.01676192507147789,
0.0049422737210989,
-0.030694369226694107,
-0.02766350656747818,
0.09688230603933334,
-0.025400104001164436,
-0.05189118534326553,
0.03335568681359291,
-0.03991364315152168,
0.03210444003343582,
0.04083452746272087,
-0.0060355328023433685,
0.02685089223086834,
-0.03939971700310707,
-0.02089121751487255,
0.002064555184915662,
-0.053345974534749985,
-0.018931427970528603,
-0.02173592522740364,
-0.035117171704769135,
0.02529895305633545,
0.0806216150522232,
0.00806335173547268,
0.06566376984119415,
0.05316625162959099,
-0.003064463846385479,
-0.0017209240468218923,
0.053265221416950226,
0.01541195996105671,
-0.09455578029155731,
0.006412323098629713,
0.05791430547833443,
-0.018533853814005852,
-0.032445278018713,
-0.03198770061135292,
0.04269006848335266,
0.02447163499891758,
-0.03689412400126457,
-0.0633637085556984,
0.002973488997668028,
0.030717991292476654,
-0.017539113759994507,
-0.049220919609069824,
-0.019179031252861023,
0.04122479632496834,
0.050794340670108795,
0.038080986589193344,
-0.0068944594822824,
0.025937341153621674,
0.07310285419225693,
0.039299674332141876,
-0.026802120730280876,
0.01692158356308937,
0.00029666407499462366,
0.018304742872714996,
-0.008172198198735714,
0.0005087012541480362,
0.016044732183218002,
0.03439238294959068,
0.0005723306676372886,
0.00978302862495184,
0.04953600466251373,
0.005078268237411976,
0.030668308958411217,
-0.013126280158758163,
0.047484371811151505,
0.013883455656468868,
-0.022412028163671494,
0.027469316497445107,
0.02166716195642948,
0.009448990225791931,
-0.0013050995767116547,
-0.0039194668643176556,
-0.0006897255079820752,
-0.018698619678616524,
0.05464940890669823,
-0.029046855866909027,
0.027874726802110672,
0.056362200528383255,
-0.04071640595793724,
-0.003513708943501115,
-0.021401407197117805,
0.025969229638576508,
-0.009524615481495857,
-0.05524752289056778,
0.008892656303942204,
0.06383070349693298,
-0.03411196917295456,
-0.009511350654065609,
-0.036874473094940186,
0.04064705967903137,
-0.01853902079164982,
-0.032882217317819595,
-0.038997042924165726,
0.03369155898690224,
-0.014251367188990116,
-0.007331968750804663,
-0.025898095220327377,
-0.003907500300556421,
-0.004064222797751427,
-0.06954694539308548,
-0.019947974011301994,
0.04618123173713684,
-0.002138111274689436,
-0.03067990206182003,
0.020407259464263916,
-0.020704245194792747,
0.027119934558868408,
-0.0021584341302514076,
0.002842710353434086,
0.027331819757819176,
-0.025644458830356598,
0.04448092728853226,
-0.04673129692673683,
0.003923427779227495,
-0.031829584389925,
-0.001712964498437941,
-0.06292414665222168,
-0.013002537190914154,
0.04023880138993263,
-0.054777566343545914,
0.020966174080967903,
-0.03635680675506592,
-0.02860051579773426,
0.018436718732118607,
0.021821893751621246,
0.005317005794495344,
-0.010288702324032784,
-0.03020658530294895,
0.036964308470487595,
0.10950738936662674,
-0.01659386046230793,
0.03521209955215454,
0.02485683746635914,
0.015908189117908478,
-0.00868492666631937,
-0.00608333433046937,
-0.008040402084589005,
-0.02662966400384903,
-0.06709039956331253,
-0.019292043522000313,
0.015552856028079987,
-0.004624396096915007,
-0.029199231415987015,
-0.02886597439646721,
0.018845776095986366,
-0.007300405763089657,
0.025764290243387222,
-0.035151079297065735,
0.06280265003442764,
0.023470619693398476,
-0.0019902384374290705,
-0.013632092624902725,
0.00004736382106784731,
0.07129506766796112,
0.02216176874935627,
0.018597517162561417,
-0.03751648589968681,
-0.07252562046051025,
0.00047240525600500405,
0.007564363069832325,
-0.030769042670726776,
0.004588766023516655,
-0.00537688797339797,
0.028799574822187424,
-0.019555939361453056,
0.029770080000162125,
0.015825780108571053,
0.017318395897746086,
-0.046483900398015976,
-0.02767994813621044,
-0.002561932196840644,
0.016505902633070946,
-0.09040451794862747,
0.004090372938662767,
-0.02942708693444729,
-0.055082499980926514,
0.024743175134062767,
-0.002871214644983411,
0.017176082357764244,
-0.0253825131803751,
-0.03704911470413208,
0.015489024110138416,
0.006361306179314852,
-0.11705063283443451,
0.03139559179544449,
0.03615625947713852,
-0.020364752039313316,
0.054200656712055206,
-0.03975698724389076,
-0.02229355461895466,
0.057982537895441055,
0.018801206722855568,
-0.03605108708143234,
-0.033469364047050476,
0.061521317809820175,
-0.012779665179550648,
-0.07937300205230713,
-0.061546690762043,
0.02800137735903263,
0.0707465410232544,
-0.043881144374608994,
-0.0024775173515081406,
0.032803259789943695,
0.047982051968574524,
0.08197067677974701,
-0.006780866999179125,
0.02623901143670082,
-0.043325360864400864,
-0.03483947366476059,
-0.03540019318461418,
-0.008275759406387806,
-0.06724941730499268,
-0.05937757343053818,
-0.03372186794877052,
-0.025112686678767204,
0.0023770967964082956,
-0.03989211469888687,
0.019919773563742638,
-0.016405535861849785,
0.03984040021896362,
-0.0038101605605334044,
-0.026750953868031502,
0.008163612335920334,
-0.007275971584022045,
-0.05230773240327835,
0.031184270977973938,
-0.061716411262750626,
-0.009254018776118755,
0.0020888601429760456,
-0.03998010233044624,
0.015577047131955624,
0.0704738050699234,
0.04446830973029137,
-0.0068986183032393456,
0.007969709113240242,
0.002968201180920005,
-0.08719942718744278,
0.005891354288905859,
-0.06871789693832397,
-0.018045051023364067,
0.02775905840098858,
0.003057820023968816,
-0.0018072796519845724,
0.06127198785543442,
0.011389833875000477,
0.061985645443201065,
0.05016879364848137,
0.014225748367607594,
-0.006858098320662975,
-0.015563467517495155,
-0.03312087431550026,
-0.01947074756026268,
0.030490126460790634,
0.021380111575126648,
0.003164048306643963,
-0.06173669919371605,
0.03613476827740669,
-0.023572849109768867,
0.003427009331062436,
0.0007861240883357823,
-0.03300463780760765,
-0.05492690950632095,
-0.00887458398938179,
-0.036540377885103226,
-0.0554320402443409,
0.005921832285821438,
0.008368059992790222,
0.02353791892528534,
0.008584435097873211,
0.03398648649454117,
-0.005457069259136915,
0.025484777987003326,
0.02896929159760475,
0.062310848385095596,
0.041828956454992294,
0.024905530735850334,
0.009981413371860981,
-0.06840178370475769,
-0.06806938350200653,
-0.04105302318930626,
0.039022158831357956,
-0.031748637557029724,
-0.009703273884952068,
-0.0038034855388104916,
0.011204088106751442,
-0.053183116018772125,
-0.03395623713731766,
-0.0335996113717556,
0.004685295280069113
] |
<p>I understand the mathematical derivation of the Tully Fisher relation from basic physics formulas, as shown on <a href="http://www.jca.umbc.edu/~george/html/courses/glossary/tully_fisher.html" rel="nofollow">this site</a>. However, after using the physics equations, it seems that several assumptions are made from this point on.</p>
<p>First are statistical assumptions. There are statistical errors because the observable, luminous mass of the galaxy is less than the actual mass of the galaxy, and the mass of the galaxy is assumed to be only the observed mass, not the actual mass. Second, this relationship seems to assume that all galaxies are perfectly circular (with negligible thickness).</p>
<p>So, with all these assumptions necessary for the Tully-Fisher relation, how is the relationship derived, how can corrections be made for the assumptions when attempting calculations using this relationship, and why is the Tully-Fisher relation generally accepted by the astrophysics community?</p> | g1218 | [
0.025884082540869713,
-0.05863797664642334,
-0.010015604086220264,
-0.04867503419518471,
0.056482698768377304,
0.01886787824332714,
0.003676164895296097,
0.013537358492612839,
-0.034928854554891586,
-0.01299305073916912,
0.04954344406723976,
-0.06913811713457108,
0.009121552109718323,
0.07638607919216156,
0.02383788675069809,
-0.008595130406320095,
0.023730972781777382,
0.03190406784415245,
-0.00192417879588902,
0.011949173174798489,
-0.030044088140130043,
0.004692563321441412,
0.013077011331915855,
0.013482783921062946,
-0.005726320203393698,
-0.005915927235037088,
-0.0005274956929497421,
0.017261937260627747,
-0.013407658785581589,
-0.024978429079055786,
0.07354322820901871,
0.008087711408734322,
0.042306214570999146,
-0.08152177929878235,
-0.06211685761809349,
-0.030768124386668205,
-0.041748177260160446,
0.06635140627622604,
0.022188309580087662,
0.012947755865752697,
0.014516605995595455,
0.07731060683727264,
0.022360248491168022,
0.04316892474889755,
-0.03133663907647133,
0.02804655022919178,
-0.014169537462294102,
0.03512760251760483,
0.013125383295118809,
0.022898096591234207,
-0.015466665849089622,
-0.00949159450829029,
0.0005577787524089217,
0.04262428358197212,
-0.02498330920934677,
0.008590694516897202,
0.06851426512002945,
-0.05533212795853615,
0.01596541330218315,
0.032910965383052826,
0.011049661785364151,
0.010873865336179733,
-0.028550174087285995,
0.01972748339176178,
0.007216475438326597,
0.011353770270943642,
-0.019335901364684105,
-0.04696229472756386,
0.06885882467031479,
-0.07270443439483643,
0.012364222668111324,
-0.024671778082847595,
-0.040911655873060226,
-0.034302834421396255,
-0.0034777384717017412,
-0.014360290952026844,
0.023142937570810318,
-0.014167513698339462,
-0.038520894944667816,
-0.01611962914466858,
-0.02474159374833107,
-0.020304856821894646,
0.01917886547744274,
0.050627700984478,
0.02390381507575512,
-0.011799633502960205,
-0.014165066182613373,
0.04601884260773659,
-0.012894406914710999,
0.05446755513548851,
-0.017937829717993736,
0.07750082015991211,
0.05512235686182976,
-0.04737824946641922,
0.01579350046813488,
-0.0068593332543969154,
-0.03831399604678154,
0.013601346872746944,
0.03512514755129814,
0.031174371019005775,
-0.029890017583966255,
0.04953297972679138,
0.019294362515211105,
0.0009718569344840944,
0.027149271219968796,
0.019988272339105606,
-0.017664536833763123,
0.05989322438836098,
-0.025417480617761612,
0.023748811334371567,
-0.1296575516462326,
-0.01851739175617695,
0.027528690174221992,
-0.033782221376895905,
-0.05269550159573555,
-0.08099997788667679,
0.06730980426073074,
0.007442300207912922,
0.07308635115623474,
0.06016221642494202,
0.02123130112886429,
-0.001984208822250366,
-0.039838243275880814,
0.09119787067174911,
-0.028590291738510132,
-0.04376368224620819,
-0.0416557602584362,
0.024985337629914284,
-0.023439085111021996,
-0.0020922331605106592,
0.021488718688488007,
0.004878748208284378,
0.03702080249786377,
0.03285301849246025,
0.04218757897615433,
-0.024445703253149986,
-0.030311452224850655,
0.011109529063105583,
-0.005621922202408314,
-0.027121640741825104,
0.005745475180447102,
0.001515256823040545,
0.040356941521167755,
-0.026519376784563065,
-0.08825021982192993,
0.08496464788913727,
-0.005820743273943663,
-0.008759417571127415,
0.08724730461835861,
0.023385774344205856,
0.08392368257045746,
0.046863242983818054,
-0.02518964372575283,
-0.03457900509238243,
-0.0036250550765544176,
-0.00813775509595871,
0.043560612946748734,
-0.06151508912444115,
0.00276770512573421,
-0.0681808814406395,
0.052242059260606766,
-0.03373014181852341,
0.10123251378536224,
-0.03518293797969818,
-0.023783782497048378,
-0.024706466123461723,
-0.013646991923451424,
-0.08087287098169327,
-0.04888645559549332,
-0.03884955868124962,
-0.047341201454401016,
0.03478018194437027,
0.00759819895029068,
0.050944890826940536,
-0.012477553449571133,
-0.012706991285085678,
0.027943920344114304,
-0.015507735311985016,
-0.07693994790315628,
0.0425252839922905,
0.011003865860402584,
-0.023600876331329346,
0.03896072134375572,
-0.027198217809200287,
-0.005339223425835371,
-0.054321251809597015,
0.043005526065826416,
-0.06179371848702431,
-0.02990718185901642,
0.05130353197455406,
0.003029590006917715,
-0.006277548149228096,
0.007209561765193939,
0.029338255524635315,
-0.007941740565001965,
0.031199326738715172,
0.013479234650731087,
0.04039040952920914,
-0.01746535114943981,
0.03940435126423836,
-0.0738753154873848,
0.05235185846686363,
0.015291162766516209,
0.032920338213443756,
0.016837935894727707,
0.03485877439379692,
-0.03140576183795929,
0.006585272494703531,
0.020234735682606697,
-0.010548725724220276,
-0.07598640769720078,
-0.021324506029486656,
-0.016025952994823456,
0.029866496101021767,
0.020000960677862167,
0.008700951002538204,
-0.04358267784118652,
0.02105209231376648,
-0.002509214449673891,
-0.020185327157378197,
-0.012421135790646076,
-0.031896378844976425,
0.028187323361635208,
-0.0004656215896829963,
-0.0013471337733790278,
-0.052582066506147385,
-0.013756612315773964,
0.009920129552483559,
0.005229468457400799,
-0.0014289611717686057,
-0.041012637317180634,
-0.0019300761632621288,
-0.010046928189694881,
0.05835382267832756,
0.0361146405339241,
0.026776254177093506,
-0.001206091372296214,
-0.016112957149744034,
0.023115163668990135,
0.0776696726679802,
-0.029909733682870865,
-0.007822091691195965,
-0.0020908445585519075,
0.014302763156592846,
0.01601794734597206,
-0.01720499061048031,
0.08037357777357101,
-0.08134192228317261,
-0.009357660077512264,
0.02358498051762581,
0.020276518538594246,
0.03686495125293732,
0.020536452531814575,
-0.07714174687862396,
0.020558085292577744,
-0.027422918006777763,
-0.0036769940052181482,
0.05423968657851219,
-0.03646475449204445,
0.014521613717079163,
0.03573969006538391,
-0.07382266223430634,
-0.008854580111801624,
-0.032787200063467026,
-0.04113345220685005,
-0.03728413209319115,
-0.08134704828262329,
0.03706218674778938,
-0.023604996502399445,
-0.013647915795445442,
0.01558228675276041,
0.024289580062031746,
0.002280198270455003,
0.012174800969660282,
-0.00513354642316699,
0.05062110722064972,
-0.01603095419704914,
-0.031338926404714584,
0.07981830835342407,
0.0007313305395655334,
-0.00856450293213129,
0.008511179126799107,
-0.07238566875457764,
0.00909480918198824,
0.0005031191976740956,
-0.030532412230968475,
-0.01223171316087246,
-0.022000452503561974,
0.00890127383172512,
0.018196983262896538,
-0.03219524770975113,
-0.0085940882563591,
-0.019194383174180984,
-0.027817239984869957,
0.007861491292715073,
0.00840553268790245,
0.047204840928316116,
0.0075584412552416325,
-0.0664999783039093,
0.004325310233980417,
0.029087599366903305,
0.0426553450524807,
0.009452635422348976,
-0.01022986602038145,
-0.005746913608163595,
0.09419876337051392,
-0.0007668153266422451,
-0.04041942209005356,
-0.029803400859236717,
-0.017002537846565247,
-0.0034783671144396067,
0.051938753575086594,
0.02414383552968502,
0.004823760595172644,
-0.03528445586562157,
-0.016197873279452324,
-0.001977794338017702,
0.012813043780624866,
0.002557898871600628,
-0.01267239823937416,
-0.0626455694437027,
-0.0007813023403286934,
-0.04009650647640228,
-0.05847803130745888,
0.0936005488038063,
-0.0014598437119275331,
-0.03595468029379845,
-0.021049179136753082,
-0.04178430885076523,
-0.01972225494682789,
0.03268192335963249,
-0.025219153612852097,
0.018942292779684067,
-0.01631522737443447,
-0.11197081953287125,
-0.009441623464226723,
-0.0023121570702642202,
-0.012038903310894966,
-0.011392803862690926,
0.018811054527759552,
0.00467674620449543,
0.0015150746330618858,
-0.02482743002474308,
-0.008593350648880005,
-0.029846493154764175,
0.025077665224671364,
-0.034424565732479095,
-0.009231391362845898,
0.001257469761185348,
-0.05849379673600197,
0.004371857736259699,
0.01760617271065712,
0.05819110944867134,
0.04920194298028946,
0.003638141555711627,
-0.014747299253940582,
-0.01584441028535366,
0.04428008198738098,
0.04495810344815254,
0.04907950013875961,
0.035154011100530624,
-0.00035306878271512687,
-0.00923665426671505,
-0.01105667557567358,
-0.00021239295892883092,
0.009380137547850609,
0.04341549053788185,
0.03752245381474495,
0.04259348660707474,
-0.04535269737243652,
-0.048393189907073975,
-0.0029339257162064314,
-0.013340582139790058,
-0.029942495748400688,
0.031408410519361496,
0.010635537095367908,
0.08297860622406006,
0.04077579081058502,
-0.01607062667608261,
0.040324389934539795,
0.047394320368766785,
0.055595532059669495,
0.028622403740882874,
-0.013578374870121479,
0.06721647828817368,
-0.03046272322535515,
-0.04636208340525627,
0.0020574366208165884,
0.008201424032449722,
-0.00025079637998715043,
0.060362309217453,
-0.05764201655983925,
0.013701104559004307,
-0.010927877388894558,
0.04333551228046417,
-0.06843050569295883,
-0.007106035016477108,
0.01984105072915554,
0.0341179296374321,
0.01806493103504181,
-0.03617561608552933,
0.03911740705370903,
0.020374057814478874,
-0.01967056654393673,
0.011233935132622719,
0.027872473001480103,
-0.0060286810621619225,
-0.05082644522190094,
-0.03265395388007164,
-0.0005613320390693843,
0.008432059548795223,
-0.06311521679162979,
0.02917301468551159,
-0.012280494906008244,
-0.0008815208566375077,
0.004533913917839527,
0.0171616580337286,
-0.05832711607217789,
-0.024849161505699158,
0.014258209615945816,
0.011272859759628773,
-0.02388574182987213,
-0.004812675528228283,
-0.02695932425558567,
0.02072025090456009,
0.03216887265443802,
0.01563289761543274,
-0.020472584292292595,
0.005741704721003771,
-0.018798278644680977,
0.047204453498125076,
-0.006546318996697664,
0.044141873717308044,
0.033397890627384186,
-0.06761468946933746,
0.016953276470303535,
-0.028090912848711014,
0.06354762613773346,
0.055805083364248276,
-0.0864158570766449,
0.021810777485370636,
0.008996475487947464,
0.0007698472472839057,
-0.019209034740924835,
0.00044535970664583147,
0.07182207703590393,
-0.048906467854976654,
-0.02867037057876587,
-0.05769403278827667,
-0.03132999315857887,
-0.009477974846959114,
0.013435587286949158,
-0.061600212007761,
-0.00749044306576252,
0.013835837133228779,
-0.003326346166431904,
-0.007559077814221382,
0.0613948218524456,
0.010223795659840107,
-0.04128902778029442,
0.0011161864968016744,
0.02093449793756008,
0.03320523351430893,
-0.007094881497323513,
0.058184754103422165,
0.00913994386792183,
-0.011955827474594116,
-0.05566415935754776,
-0.035719603300094604,
0.047639019787311554,
-0.07870271056890488,
0.029696626588702202,
0.009256027638912201,
0.020653171464800835,
-0.019724683836102486,
0.027511825785040855,
0.025706492364406586,
-0.022246910259127617,
-0.032265812158584595,
-0.0030301474034786224,
-0.017430219799280167,
-0.025321200489997864,
0.04456918314099312,
0.03384057432413101,
-0.03107486478984356,
0.06515476852655411,
0.010265620425343513,
-0.04744715616106987,
0.0009542700136080384,
0.03963899984955788,
-0.02357010543346405,
-0.05374453589320183,
0.024111907929182053,
0.02028791233897209,
-0.024151252582669258,
-0.03868559002876282,
0.05123387649655342,
-0.03686373680830002,
0.004398411605507135,
-0.0268083568662405,
-0.06409168988466263,
0.005480644758790731,
0.007771936245262623,
0.026377884671092033,
-0.015200157649815083,
0.019679678604006767,
0.027125032618641853,
-0.04265546053647995,
0.0035566703882068396,
0.014728439971804619,
0.03872821107506752,
0.025058314204216003,
0.06031601503491402,
0.015741882845759392,
0.0036915920209139585,
0.0103674978017807,
0.002060230355709791,
0.02098289132118225,
0.06903437525033951,
0.014031276106834412,
-0.0011119506089016795,
-0.016298960894346237,
0.02923799678683281,
-0.03662353754043579,
0.012413056567311287,
-0.019575143232941628,
0.023927781730890274,
0.023961827158927917,
0.0373925119638443,
-0.042155634611845016,
-0.0009868353372439742,
0.027431556954979897,
0.034904953092336655,
0.006682621780782938,
-0.013446617871522903,
0.03951697051525116,
0.03942441940307617,
-0.006252937484532595,
0.030451741069555283,
0.03520933538675308,
-0.0011651351815089583,
0.000009081662028620485,
0.008004614152014256,
0.032987628132104874,
0.030501430854201317,
0.02193130925297737,
0.04303565248847008,
-0.017719291150569916,
0.04567268118262291,
-0.03566441312432289,
-0.029854977503418922,
-0.0005478352541103959,
0.028954988345503807,
0.041520074009895325,
0.01950256898999214,
-0.004607724491506815,
-0.012173573486506939,
-0.007849193178117275,
-0.0229357797652483,
-0.004679033532738686,
-0.005283156875520945,
0.03863505646586418,
-0.0008375978213734925,
0.014110679738223553,
0.03071555122733116,
-0.015777016058564186,
-0.010285208001732826,
-0.045113686472177505,
-0.0005985791212879121,
0.01963997259736061,
-0.0061339037492871284,
-0.02425491251051426,
-0.0029918518848717213,
0.02476509101688862,
0.044041622430086136,
0.011628909036517143,
-0.0437464714050293,
-0.003093517618253827,
-0.06226706504821777,
-0.026179427281022072,
0.028266724199056625,
-0.011960937641561031,
0.012114092707633972,
-0.0971723347902298,
-0.01957044191658497,
-0.04252754896879196,
-0.036460720002651215,
0.031689904630184174,
0.002664996776729822,
-0.009390272200107574,
-0.02815410867333412,
0.022923437878489494,
-0.029047273099422455,
-0.010100663639605045,
-0.032378148287534714,
-0.04401537775993347,
0.03863120451569557,
0.02764890156686306,
-0.05061785876750946,
-0.041878871619701385,
-0.0185606200248003,
-0.02214786596596241,
0.04377451911568642,
0.03607194498181343,
0.03200346231460571,
-0.03163284808397293,
-0.0388236828148365,
0.06465285271406174,
0.014254500158131123,
-0.0059476736932992935,
-0.06865260004997253,
0.03492559492588043,
0.041211314499378204,
-0.007703869137912989,
0.004204766359180212,
-0.013570527546107769,
-0.03664037585258484,
0.0004925536341033876,
-0.051289938390254974,
0.00741588557139039,
-0.04764507710933685,
-0.0676700547337532,
0.01214729342609644,
0.025355499237775803,
0.025280997157096863,
0.015234261751174927,
-0.06162179633975029,
0.06818290054798126,
0.0033859917894005775,
-0.05972318723797798,
-0.01251633558422327,
0.0013684191508218646,
0.03996904194355011,
0.026874544098973274,
0.04689502716064453,
0.021089978516101837,
-0.04149875417351723,
0.0007884513470344245,
0.04599222168326378,
-0.020897168666124344,
-0.05063461884856224,
0.021371519193053246,
0.02973608858883381,
0.022009123116731644,
-0.04795210063457489,
-0.03669436275959015,
-0.009652378037571907,
-0.04276200383901596,
-0.09776227176189423,
0.024120191112160683,
-0.013735209591686726,
-0.034287866204977036,
-0.022133082151412964,
0.010662629269063473,
-0.03385799378156662,
-0.02486119046807289,
-0.029676910489797592,
0.01849708892405033,
0.06176082789897919,
-0.0039252848364412785,
-0.008756112307310104,
0.0009613513830117881,
-0.005404179450124502,
0.0022727118339389563,
-0.019641974940896034,
-0.02135651558637619,
0.0499526709318161,
-0.05816512182354927,
0.02585773915052414,
0.014509323053061962,
0.044427044689655304,
-0.009020878933370113,
-0.02613646723330021,
-0.03549902141094208,
-0.00942161213606596,
-0.012033089064061642,
-0.02703060768544674,
-0.024726957082748413,
0.03489673510193825,
0.005613677203655243,
-0.03411188721656799,
0.06075529381632805,
-0.009309849701821804,
0.04260748624801636,
-0.009371759369969368,
0.032965727150440216,
-0.016405906528234482,
-0.027908796444535255,
0.019515763968229294,
0.025452367961406708,
-0.0729760229587555,
0.00048018310917541385,
-0.017297927290201187,
-0.028096390888094902,
-0.02791418321430683,
0.049120500683784485,
0.07766415923833847,
0.010193279944360256,
0.014442449435591698,
0.02158079482614994,
-0.04428187012672424,
-0.09054882079362869,
-0.008706573396921158,
-0.047571733593940735,
0.08462633192539215,
-0.012532640248537064,
-0.03286454454064369,
0.011076671071350574,
-0.05795580521225929,
-0.023986104875802994,
0.07318471372127533,
-0.023256275802850723,
-0.007257447112351656,
0.007807066664099693,
0.026952676475048065,
0.00009308508015237749,
-0.06785286962985992,
-0.01912544295191765,
-0.03486768528819084,
0.011159993708133698,
0.001064671203494072,
0.008173438720405102,
0.058637458831071854,
-0.06011407449841499,
0.03026915341615677,
-0.0371936596930027,
0.003884881269186735,
-0.04508735239505768,
-0.005012053065001965,
-0.01766527257859707,
-0.02783360704779625,
0.0507439561188221,
-0.011216693557798862,
-0.010943840257823467,
-0.017057685181498528,
-0.005980089772492647,
0.027327939867973328,
-0.015533163212239742,
-0.020242860540747643,
0.004054801072925329,
0.023405076935887337,
-0.0057496847584843636,
0.03566605970263481,
-0.06298086792230606,
-0.02043212577700615,
-0.037129465490579605,
-0.024923786520957947,
0.0789082869887352,
0.01389017328619957,
-0.01776937209069729,
0.014542895369231701,
0.12630218267440796,
-0.009444517083466053,
0.06005747988820076,
0.023789668455719948,
-0.06762942671775818,
-0.025022614747285843,
-0.06194554269313812,
-0.02923637628555298,
-0.010157875716686249,
0.002858443185687065,
0.004008153453469276,
-0.025989793241024017,
0.0004924837849102914,
0.01831246167421341,
-0.00864593405276537,
-0.05168246477842331,
0.06054165959358215
] |
<p>How can I prove Thevenin's and Norton's theorem? <a href="http://en.wikipedia.org/wiki/Th%C3%A9venin%27s_theorem" rel="nofollow">Thévenin's theorem</a> can be used to convert any circuit's sources and impedances to a Thévenin equivalent.</p> | g1219 | [
0.03887549415230751,
0.009629573673009872,
0.0076270997524261475,
-0.09018592536449432,
0.0355231836438179,
-0.05543428659439087,
0.0013327281922101974,
0.030122477561235428,
0.0044114599004387856,
0.03227917477488518,
-0.022829925641417503,
0.028546152636408806,
-0.07964605838060379,
0.03932370990514755,
0.024801142513751984,
0.030374426394701004,
0.02978702448308468,
0.0074998680502176285,
0.05652368813753128,
0.013150984421372414,
-0.020946143195033073,
0.015612231567502022,
-0.0313415601849556,
-0.07556115835905075,
0.020744454115629196,
-0.009911068715155125,
-0.02632119506597519,
-0.03811422362923622,
-0.04592468589544296,
0.030096523463726044,
0.013761559501290321,
-0.06043028086423874,
0.1015419289469719,
0.006974765099585056,
0.015286433510482311,
0.01940038986504078,
-0.019198058173060417,
0.02561390958726406,
0.027620578184723854,
-0.0010018639732152224,
0.0041834465228021145,
0.03926682472229004,
-0.003954294603317976,
0.022804725915193558,
-0.05230123922228813,
0.008401241153478622,
-0.04793091118335724,
0.005197899416089058,
-0.03727897256612778,
-0.04375162720680237,
0.04462529718875885,
0.002761810552328825,
0.011731715872883797,
0.017284782603383064,
-0.023624977096915245,
-0.0056251781061291695,
0.05954379215836525,
0.018044140189886093,
0.03926205635070801,
-0.007504287175834179,
-0.023465415462851524,
0.040003612637519836,
-0.018452439457178116,
0.022535137832164764,
0.05515257269144058,
-0.023258067667484283,
0.0225539430975914,
0.014844195917248726,
-0.01102534681558609,
0.06695038825273514,
0.026868756860494614,
-0.027916045859456062,
0.013494356535375118,
-0.0044103581458330154,
0.041341688483953476,
0.014208687469363213,
0.08481134474277496,
-0.0015666276449337602,
0.0033172115217894316,
-0.011991768144071102,
-0.045190345495939255,
-0.059024665504693985,
0.019636744633316994,
-0.0006734287017025054,
0.044848714023828506,
-0.08786332607269287,
0.06898532807826996,
-0.058535072952508926,
0.02643340826034546,
0.0018640841590240598,
-0.004403314087539911,
0.04046331346035004,
0.0745549350976944,
0.01854759268462658,
-0.007305706385523081,
-0.039381105452775955,
0.028089843690395355,
0.03595637157559395,
0.012651560828089714,
-0.014484921470284462,
-0.0579351969063282,
0.011676234193146229,
0.002737997565418482,
-0.013864437118172646,
-0.0015091944951564074,
0.03391614183783531,
0.01564360223710537,
-0.02390568144619465,
0.009529868140816689,
-0.02593548409640789,
-0.06758328527212143,
-0.10266351699829102,
-0.0013705891324207187,
0.052792128175497055,
-0.03274884819984436,
0.008003116585314274,
-0.008023640140891075,
0.04960211366415024,
-0.008660725317895412,
0.0986684039235115,
-0.017461853101849556,
-0.010359544306993484,
-0.03961799666285515,
0.04031657055020332,
0.010371902957558632,
0.04345770925283432,
0.004768542014062405,
0.015995502471923828,
0.026981735602021217,
-0.00326362531632185,
0.03451554849743843,
0.0019312880467623472,
-0.0747189000248909,
-0.020864669233560562,
0.05650685355067253,
-0.0036088875494897366,
0.014777121134102345,
-0.01171015202999115,
-0.004934723023325205,
0.022223331034183502,
-0.0349915474653244,
-0.06846145540475845,
-0.0325690358877182,
-0.005702430382370949,
-0.01618497632443905,
0.018733054399490356,
0.022482242435216904,
-0.014193697832524776,
-0.06064149737358093,
0.04596517235040665,
0.03020489402115345,
0.08645879477262497,
0.011763252317905426,
-0.05168982222676277,
-0.022777097299695015,
-0.02798965387046337,
-0.01522243581712246,
-0.016769975423812866,
-0.05622514337301254,
-0.032253991812467575,
-0.03524174913764,
0.032898109406232834,
0.008202852681279182,
0.015646547079086304,
-0.03530445322394371,
-0.04345017299056053,
0.002392771188169718,
-0.029516180977225304,
-0.061713721603155136,
-0.02417108602821827,
-0.04206404089927673,
0.04735061898827553,
0.032853689044713974,
0.04502013698220253,
-0.0052423374727368355,
0.011458257213234901,
-0.08258511126041412,
0.004909109324216843,
0.02975762076675892,
-0.032597266137599945,
-0.0027452781796455383,
-0.0044670444913208485,
0.05625864490866661,
-0.00980084203183651,
-0.011985746212303638,
0.014216156676411629,
-0.010675426572561264,
-0.029690654948353767,
-0.0577394962310791,
-0.026156822219491005,
-0.07550586760044098,
0.03312230110168457,
-0.04112597927451134,
0.037756312638521194,
-0.01657896302640438,
-0.011943983845412731,
0.013925068080425262,
-0.04398700222373009,
0.04257871210575104,
0.004918262828141451,
0.043973326683044434,
-0.036148231476545334,
0.05004915967583656,
-0.007521231658756733,
-0.01727965474128723,
0.037598319351673126,
-0.039400745183229446,
-0.0056292032822966576,
0.04210280254483223,
-0.029426617547869682,
-0.0127486577257514,
-0.030342228710651398,
0.03933548182249069,
0.008245608769357204,
-0.009757040068507195,
0.011856906116008759,
-0.05070238187909126,
-0.06382045149803162,
-0.016663137823343277,
-0.02682788297533989,
0.009244979359209538,
-0.045252736657857895,
0.07386083155870438,
-0.039340291172266006,
-0.0108964703977108,
0.043055493384599686,
-0.00863719079643488,
0.018022892996668816,
-0.004850039724260569,
-0.016423717141151428,
0.0028920446056872606,
-0.021685471758246422,
-0.03389158099889755,
-0.04558837413787842,
0.0171652901917696,
0.07168372720479965,
-0.001724065630696714,
-0.009053901769220829,
0.010795188136398792,
0.03725331649184227,
-0.0074522350914776325,
-0.05749277397990227,
0.03780406713485718,
0.03439364582300186,
-0.0009566789376549423,
-0.10686951130628586,
0.04347452148795128,
-0.010189168155193329,
0.06715721637010574,
-0.003092031227424741,
-0.04658161476254463,
-0.01533111184835434,
-0.019740993157029152,
0.029659707099199295,
-0.031566984951496124,
-0.011373302899301052,
0.05353785306215286,
0.01923086680471897,
-0.022344069555401802,
-0.042419783771038055,
-0.013404992409050465,
-0.0489034503698349,
0.006096251774579287,
0.0709952637553215,
-0.08710093051195145,
-0.008753531612455845,
-0.019888583570718765,
0.0016575552290305495,
0.022154200822114944,
-0.010005585849285126,
-0.02438291907310486,
0.06098943203687668,
0.018131377175450325,
-0.020050382241606712,
-0.0003444865287747234,
-0.01795228198170662,
0.022667650133371353,
0.03125526383519173,
0.008260282687842846,
-0.004866205621510744,
-0.0525304414331913,
0.01342627964913845,
-0.07142279297113419,
-0.018933888524770737,
-0.02195245772600174,
-0.015310349874198437,
-0.0187959223985672,
-0.06337324529886246,
-0.02220957726240158,
0.06405384093523026,
-0.04767255857586861,
-0.0336427167057991,
0.024640025570988655,
-0.00028637683135457337,
-0.024873511865735054,
0.0334363728761673,
0.04859255626797676,
-0.04871083423495293,
0.016986455768346786,
0.0038230258505791426,
-0.03451399877667427,
0.016863759607076645,
-0.010476252995431423,
-0.015692753717303276,
0.029068367555737495,
0.056092940270900726,
-0.02582176774740219,
-0.017839092761278152,
0.01849445514380932,
0.02368590235710144,
0.009371016174554825,
0.021902943029999733,
-0.003162636421620846,
-0.02988516166806221,
0.072751984000206,
0.030471954494714737,
0.07741981744766235,
0.07182659953832626,
0.10559824109077454,
-0.010443720035254955,
-0.04704194515943527,
-0.07022865861654282,
0.028622936457395554,
-0.06448738276958466,
0.04939677566289902,
-0.008127829991281033,
0.0030493775848299265,
0.007416234351694584,
0.025366833433508873,
-0.033233191817998886,
0.0005653554107993841,
-0.0009820262202993035,
-0.017491552978754044,
0.006743574980646372,
-0.014710919931530952,
-0.04118875786662102,
0.0065826112404465675,
0.056984737515449524,
0.005408899858593941,
0.021277595311403275,
0.002009161515161395,
0.0008555862586945295,
-0.08972375094890594,
0.044528741389513016,
-0.00970947090536356,
0.004365143831819296,
-0.004547773860394955,
0.06022077426314354,
0.02753518521785736,
-0.04164368286728859,
0.022956395521759987,
0.012486811727285385,
0.07749450206756592,
0.05600311979651451,
-0.06250794976949692,
0.0006825989112257957,
0.00451213913038373,
0.04690631851553917,
-0.02269827574491501,
0.020134015008807182,
0.006281017791479826,
-0.010016586631536484,
0.07886609435081482,
-0.00531828124076128,
-0.008468309417366982,
0.031248731538653374,
-0.014085435308516026,
0.06268728524446487,
-0.03429572284221649,
-0.05780970677733421,
0.024379083886742592,
-0.006714046001434326,
0.058891262859106064,
-0.013832305558025837,
0.0083862179890275,
-0.04673347622156143,
-0.023934034630656242,
0.020667288452386856,
-0.06455741077661514,
0.05860450491309166,
-0.013020595535635948,
0.05107396841049194,
0.04727676883339882,
0.011140981689095497,
0.04781878739595413,
-0.07911574095487595,
-0.05140700563788414,
0.020474646240472794,
-0.0036388561129570007,
-0.09044363349676132,
0.00007417710003210232,
-0.003831843612715602,
-0.002242696238681674,
-0.0011525441659614444,
0.004722693469375372,
-0.008099495433270931,
0.011913727037608624,
-0.035161033272743225,
-0.00640349555760622,
0.033027153462171555,
0.015339856036007404,
0.03107777237892151,
0.023620786145329475,
-0.01866196095943451,
0.019710950553417206,
-0.013768335804343224,
0.016383862122893333,
-0.010708664543926716,
-0.033968109637498856,
0.03560485690832138,
-0.040956154465675354,
-0.042503561824560165,
0.059956613928079605,
0.03557148575782776,
-0.011149785481393337,
0.0036544848699122667,
0.05661681294441223,
-0.04933517426252365,
0.0893765464425087,
-0.003842839738354087,
-0.043856579810380936,
0.03781318664550781,
-0.06538153439760208,
-0.05181802436709404,
-0.010371667332947254,
0.04637078195810318,
0.0019504207884892821,
-0.02925669401884079,
0.003541412763297558,
0.0029670654330402613,
-0.011896217241883278,
-0.010974044911563396,
0.020480014383792877,
-0.000057883142289938405,
-0.026224607601761818,
-0.02021435648202896,
-0.035224031656980515,
0.09210211038589478,
-0.011478678323328495,
0.009750154800713062,
0.01784391701221466,
-0.028024230152368546,
-0.004455645103007555,
-0.015936728566884995,
-0.02410922758281231,
0.05183966085314751,
-0.025561513379216194,
-0.03516135364770889,
-0.03374439477920532,
-0.04296204447746277,
0.0017464536940678954,
0.01384980883449316,
-0.019922427833080292,
-0.0506926067173481,
-0.0182156041264534,
0.02651640586555004,
0.0036779188085347414,
-0.009477373212575912,
0.029074018821120262,
-0.019478455185890198,
-0.03221932426095009,
0.0074867005459964275,
0.011791960336267948,
-0.008931232616305351,
-0.004900581203401089,
0.014828250743448734,
-0.016933580860495567,
0.0035647766198962927,
0.0033128869254142046,
-0.006704226136207581,
0.04600362479686737,
-0.021689128130674362,
-0.04545415937900543,
0.05449214205145836,
0.05465672165155411,
-0.02937888354063034,
0.04072977975010872,
-0.00625811330974102,
-0.033464111387729645,
-0.010019103065133095,
-0.023826228454709053,
-0.02622358500957489,
-0.008807407692074776,
0.02050871029496193,
0.017719347029924393,
0.017336778342723846,
0.006983843632042408,
0.013329829089343548,
-0.02072475291788578,
-0.013308608904480934,
-0.024986859411001205,
0.027167053893208504,
0.032001763582229614,
0.005029420834034681,
-0.019800715148448944,
-0.005568396765738726,
0.012998306192457676,
-0.0022981874644756317,
-0.0786982998251915,
0.034394554793834686,
-0.06088469550013542,
0.051829587668180466,
-0.04332957789301872,
0.004910856951028109,
-0.02552163414657116,
0.03394509106874466,
-0.043635569512844086,
0.040935222059488297,
-0.03804027661681175,
-0.020001215860247612,
-0.012237664312124252,
-0.04256919026374817,
-0.016156930476427078,
-0.01893647573888302,
0.014277306385338306,
0.06801564991474152,
-0.06690197438001633,
-0.0311565101146698,
-0.05597398802638054,
-0.04105337709188461,
0.06095030903816223,
-0.005164943169802427,
0.019545897841453552,
-0.017055509611964226,
-0.08001472055912018,
0.0281418077647686,
-0.06189466640353203,
-0.05295368283987045,
0.08703307807445526,
0.026669375598430634,
0.0018214592710137367,
-0.02095952443778515,
-0.05937527120113373,
-0.012682885862886906,
-0.010189003311097622,
0.036169007420539856,
-0.004284151829779148,
-0.016370784491300583,
-0.01135883666574955,
0.025448910892009735,
-0.01683490350842476,
-0.02977515570819378,
0.07782598584890366,
0.03730731084942818,
-0.019518472254276276,
-0.010927979834377766,
-0.03251206502318382,
-0.03992316126823425,
0.04168938472867012,
-0.05200634151697159,
0.0035331184044480324,
0.036274876445531845,
-0.010570952668786049,
0.02076917514204979,
0.06542180478572845,
-0.01069023460149765,
-0.013053148984909058,
-0.027206603437662125,
-0.00008910932228900492,
-0.019555795937776566,
0.043573033064603806,
0.0574328787624836,
-0.03293678164482117,
-0.019104335457086563,
-0.03201223164796829,
-0.01886080391705036,
0.0009700021473690867,
0.06826714426279068,
-0.03389320522546768,
0.011290639638900757,
-0.025560026988387108,
-0.022548144683241844,
-0.0014340735506266356,
-0.008248201571404934,
0.03822162747383118,
-0.002728991210460663,
0.028666343539953232,
-0.04694730043411255,
0.024923335760831833,
-0.04860473796725273,
0.010787485167384148,
0.022632546722888947,
0.01796061545610428,
-0.02969820238649845,
-0.02712191268801689,
0.014634591527283192,
-0.0416509248316288,
-0.0266403891146183,
0.02595933899283409,
0.010319065302610397,
-0.0008552681538276374,
-0.008848973549902439,
-0.016194207593798637,
0.050214171409606934,
0.006059625651687384,
-0.02647867240011692,
0.017398783937096596,
0.009909328073263168,
0.021275999024510384,
0.07843603193759918,
-0.007516157813370228,
-0.015135454013943672,
0.04507693275809288,
-0.010909242555499077,
-0.0021964972838759422,
0.014718610793352127,
0.043876759707927704,
-0.009895432740449905,
-0.017506320029497147,
-0.02879679761826992,
0.02317284420132637,
0.04275491088628769,
-0.026756955310702324,
0.018404413014650345,
0.032915469259023666,
-0.013062291778624058,
-0.010764685459434986,
-0.04419265314936638,
-0.018904224038124084,
0.07522357255220413,
0.030411604791879654,
0.012719888240098953,
-0.010537071153521538,
0.04959489032626152,
-0.07268331199884415,
0.05560427904129028,
-0.00939685758203268,
0.019707996398210526,
0.05676565691828728,
0.007717942353338003,
-0.03990643098950386,
0.025033388286828995,
0.0068616862408816814,
-0.04414943978190422,
-0.03251739591360092,
0.03051372617483139,
0.014104093424975872,
-0.05517461895942688,
0.016435174271464348,
0.09428246319293976,
-0.0068275462836027145,
0.001648900331929326,
-0.02192743308842182,
0.01115455199033022,
-0.0017913555493578315,
0.029011240229010582,
0.017855852842330933,
-0.011996771208941936,
-0.03251589462161064,
0.038103651255369186,
0.037718553096055984,
-0.004391318187117577,
-0.02093530260026455,
0.04558265209197998,
-0.04812799021601677,
0.021512353792786598,
0.010248793289065361,
0.021441416814923286,
0.007430261466652155,
0.026907283812761307,
-0.03427157178521156,
-0.01874149590730667,
0.09983640164136887,
-0.01947229541838169,
0.023665104061365128,
-0.016144774854183197,
0.018147628754377365,
-0.0716596469283104,
0.020924489945173264,
0.003872219007462263,
0.021106230095028877,
-0.06667546182870865,
0.014040626585483551,
-0.02982175163924694,
0.000778363726567477,
-0.015730764716863632,
0.0077369785867631435,
0.04848116263747215,
-0.0068854717537760735,
0.0010634532663971186,
-0.03228488564491272,
0.006514093838632107,
0.023099524900317192,
-0.005075308959931135,
0.0018392485799267888,
-0.03753899782896042,
-0.07460284233093262,
-0.04183385521173477,
0.05556529760360718,
0.0352361761033535,
0.021183911710977554,
-0.003437318606302142,
0.001180667313747108,
-0.0397583469748497,
0.027161085978150368,
0.028641970828175545,
-0.0458478108048439,
0.020318372175097466,
-0.002500159665942192,
-0.023527545854449272,
0.02030668407678604,
0.021751271560788155,
-0.02992101199924946,
0.04460764303803444,
-0.07055532932281494,
-0.07845303416252136,
-0.05964963138103485,
-0.020157521590590477,
-0.04844729229807854,
0.007559686433523893,
0.03975642845034599,
0.014081405475735664,
-0.009397219866514206,
0.03902605548501015,
0.06258979439735413,
-0.006516589783132076,
-0.02654472552239895,
-0.018206452950835228,
-0.015991730615496635,
0.0648033395409584,
0.07306613028049469,
-0.04940292239189148,
0.026960227638483047,
-0.025881484150886536,
0.015570585615932941,
-0.003783879801630974,
0.03077699989080429,
-0.022538838908076286,
-0.005036721471697092,
0.02111615613102913,
0.0035258193966001272,
-0.017965426668524742,
0.05997829884290695,
0.02042732946574688,
-0.05814513564109802,
0.006333380471915007,
0.003627425292506814,
-0.003619022434577346,
-0.01662665233016014,
0.013354363851249218,
0.005380590911954641,
-0.040267154574394226,
-0.03874798119068146,
-0.0697740912437439,
-0.007315570954233408,
-0.03616883605718613,
-0.029976751655340195,
0.04655629023909569,
-0.020960140973329544,
-0.0016287264879792929,
0.02395356260240078,
0.01843576319515705,
0.007915336638689041,
-0.007633773144334555,
0.05242312327027321,
-0.029850926250219345,
0.032453350722789764,
0.045661937445402145,
0.10875025391578674,
0.033133454620838165,
0.00952853262424469,
0.04559134319424629,
0.03974314033985138,
0.05346112325787544,
-0.061667006462812424,
-0.019748864695429802,
-0.02705751545727253,
-0.018939925357699394
] |
<p>I'm doing simulations of copper, where the temperature can reach up to ~1300 K.</p>
<p>Some calculations depend on the mean free path (MFP) of copper. The only value I've found for it is 39nm and it's always accompanied with the clause of "at room temperature".</p>
<p>Can anybody tell me (or provide some references), how does the MFP depend on temperature?</p>
<p>Copper's resistivity dependence on temperature is known to me, can that be used to derive the mean free path dependence in the following way?</p>
<p>So we got the conductivity $\sigma(T)$ and that can be related to the relaxation time as</p>
<p>$\sigma = \frac{n e^{2}}{m} \tau$</p>
<p>And the relation between the mean free path and relaxation time is $\Lambda = v_F \tau$, where $v_F$ is the Fermi velocity (is this an approximation?).</p>
<p>Thus we get</p>
<p>$\Lambda(T) = \frac{v_F m}{n e^{2}} \sigma(T)$</p>
<p>Is this a valid way of finding the dependence of the mean free path of copper on temperature?</p> | g1220 | [
0.02474234439432621,
0.034804023802280426,
0.004212072119116783,
0.031040111556649208,
0.007095579989254475,
-0.00009326431609224528,
-0.0038789825048297644,
0.0020711321849375963,
-0.02238093875348568,
0.037985388189554214,
-0.019947310909628868,
0.03152379393577576,
-0.031674910336732864,
0.017964020371437073,
0.031378161162137985,
0.006469163112342358,
0.022888528183102608,
0.0056729125790297985,
0.022907081991434097,
-0.0483207032084465,
0.0061157140880823135,
-0.004409732762724161,
0.020103828981518745,
-0.0013345279730856419,
0.028381850570440292,
0.01392956543713808,
-0.002489459700882435,
-0.034780941903591156,
-0.06618619710206985,
0.05028090998530388,
-0.010312139987945557,
-0.017560336738824844,
0.03807626664638519,
-0.014091096818447113,
-0.06157873570919037,
0.03255704790353775,
0.024888252839446068,
0.014420359395444393,
0.054613012820482254,
0.0028273011557757854,
-0.0004677243414334953,
-0.043214164674282074,
0.03661094978451729,
0.0331948958337307,
0.03487042337656021,
0.040665145963430405,
-0.004149561747908592,
-0.0670752078294754,
-0.05032753199338913,
-0.009919132106006145,
0.0006234605680219829,
0.042187925428152084,
0.014707556925714016,
0.005004824139177799,
-0.04795333743095398,
-0.050787556916475296,
-0.010686121881008148,
-0.024641944095492363,
0.00038903875974938273,
0.06954358518123627,
0.049535151571035385,
0.03744468837976456,
-0.08624719083309174,
-0.014741437509655952,
0.022902635857462883,
0.0699230283498764,
-0.043045517057180405,
0.013987332582473755,
-0.02440919727087021,
-0.02322036400437355,
0.011668617837131023,
-0.01622861623764038,
-0.0856848806142807,
-0.10165906697511673,
-0.02270621806383133,
-0.009174146689474583,
0.03525274991989136,
-0.03337578475475311,
0.05358642339706421,
-0.03168288990855217,
-0.03811168298125267,
0.015028146095573902,
-0.006499424576759338,
0.05461690574884415,
-0.006748974323272705,
-0.05992614105343819,
-0.014691184274852276,
0.04820819944143295,
-0.01724325120449066,
0.028243085369467735,
-0.03782407194375992,
-0.03542491793632507,
0.017303749918937683,
0.008748369291424751,
0.044667452573776245,
0.028303800150752068,
-0.021459531038999557,
0.015577992424368858,
0.0336555540561676,
0.030424971133470535,
-0.019186167046427727,
0.008613010868430138,
0.029769597575068474,
0.02802366204559803,
-0.05959751084446907,
-0.0131478700786829,
-0.007709146942943335,
0.0647483840584755,
0.007760313339531422,
-0.013095704838633537,
0.012290322221815586,
-0.02168024145066738,
-0.0467543862760067,
0.07233460247516632,
-0.007220652420073748,
0.04277240112423897,
-0.007933099754154682,
-0.07481862604618073,
0.07635798305273056,
-0.028294140473008156,
-0.020445922389626503,
-0.025482656434178352,
-0.03694045543670654,
0.05656867474317551,
0.006899458821862936,
0.03733488544821739,
-0.011122766882181168,
-0.012942947447299957,
-0.0006308794254437089,
0.07089581340551376,
0.012257748283445835,
-0.0020566945895552635,
-0.04162003844976425,
0.07078476995229721,
-0.008814551867544651,
-0.012163112871348858,
-0.011506497859954834,
0.05559048801660538,
-0.03382905572652817,
0.022129299119114876,
-0.007411201484501362,
-0.04743286594748497,
0.0012808387400582433,
-0.00805127713829279,
-0.016688089817762375,
0.009566154330968857,
-0.028436893597245216,
-0.09229199588298798,
0.07836786657571793,
-0.02012890949845314,
0.041937701404094696,
0.0530841201543808,
-0.01856400817632675,
-0.008880428038537502,
-0.04974094405770302,
-0.08024853467941284,
-0.020285189151763916,
-0.034192878752946854,
0.017228107899427414,
-0.018877103924751282,
-0.0018764151027426124,
-0.002708438551053405,
0.05055200681090355,
-0.007823866792023182,
-0.012915332801640034,
0.00870442483574152,
-0.018750546500086784,
-0.004654730670154095,
0.01296296063810587,
-0.06355146318674088,
-0.044380009174346924,
-0.032083965837955475,
0.006570319179445505,
0.09322046488523483,
-0.04421663656830788,
-0.05751592293381691,
0.010414771735668182,
-0.009982398711144924,
-0.0016989503055810928,
-0.01278167124837637,
0.014378603547811508,
0.027890389785170555,
0.056082822382450104,
-0.07792671769857407,
-0.01215448323637247,
0.01598634570837021,
0.01632220856845379,
0.022925835102796555,
-0.035732198506593704,
-0.01589161902666092,
-0.01731754094362259,
-0.04761575534939766,
-0.010288001969456673,
0.03313043713569641,
0.04852169007062912,
0.004521212074905634,
-0.011324017308652401,
-0.04293389245867729,
-0.007717848289757967,
-0.005078441463410854,
0.003431767225265503,
-0.002731196815147996,
-0.010067873634397984,
-0.008273784071207047,
0.008304722607135773,
0.017677728086709976,
-0.08543770015239716,
0.018273718655109406,
0.0074177333153784275,
-0.014496365562081337,
0.006690140347927809,
0.048221223056316376,
-0.01593223214149475,
0.08087452501058578,
0.028087299317121506,
0.020434273406863213,
0.00932511780411005,
-0.029025400057435036,
0.01114697102457285,
0.026847366243600845,
0.05322268605232239,
-0.0461299791932106,
0.01771089993417263,
-0.006682162173092365,
0.001363479532301426,
0.004969486966729164,
-0.031524159014225006,
0.02384101040661335,
0.0051928432658314705,
0.03578909859061241,
-0.049429282546043396,
0.00535607198253274,
0.0017257147701457143,
0.013589790090918541,
0.01080302707850933,
0.024035098031163216,
0.03483859822154045,
0.010647098533809185,
-0.027415763586759567,
0.027852894738316536,
0.005704908166080713,
-0.01544435229152441,
-0.05321728065609932,
-0.014202279038727283,
-0.0005245038191787899,
0.0041496288031339645,
-0.004380231723189354,
0.03316321596503258,
0.009428804740309715,
0.0018070043297484517,
0.04139013960957527,
0.03095659241080284,
0.033736251294612885,
0.008207272738218307,
-0.0538610965013504,
0.040826816111803055,
-0.04556293413043022,
0.013174263760447502,
-0.03226291388273239,
-0.03338053822517395,
0.008912621065974236,
-0.02839551866054535,
-0.013671508990228176,
0.0015110168606042862,
0.013023949228227139,
0.04311779886484146,
0.0071348100900650024,
-0.01805008016526699,
-0.029791245236992836,
0.010286221280694008,
0.00521761504933238,
0.04902547597885132,
-0.0065206503495574,
0.06007201224565506,
0.05880245938897133,
-0.05118052661418915,
0.047984879463911057,
0.04331827908754349,
0.06244843080639839,
-0.02089247666299343,
-0.01586432382464409,
-0.030833007767796516,
-0.04788873717188835,
0.009825702756643295,
0.022135373204946518,
-0.03320527449250221,
-0.024293415248394012,
0.017505448311567307,
0.018290912732481956,
-0.03523177653551102,
0.019219493493437767,
0.00536329997703433,
-0.016837218776345253,
0.0272433590143919,
-0.019922897219657898,
0.01620865799486637,
0.06633229553699493,
-0.10312401503324509,
-0.02524043433368206,
0.029934417456388474,
0.020451920107007027,
0.017529835924506187,
-0.014781033620238304,
0.07072463631629944,
-0.019265562295913696,
0.04610534757375717,
0.005343732424080372,
-0.06846901029348373,
0.00923890806734562,
-0.07109574228525162,
0.03936353325843811,
0.08704838901758194,
0.02033638209104538,
-0.06134191155433655,
-0.03174331411719322,
0.00938569474965334,
-0.04930368810892105,
0.049408089369535446,
0.04834888130426407,
-0.08260483294725418,
-0.02836259827017784,
-0.09291629493236542,
-0.020302940160036087,
-0.024505598470568657,
-0.009540524333715439,
-0.004152457229793072,
0.025309862568974495,
-0.05211898684501648,
-0.027708841487765312,
0.031407430768013,
0.06944017857313156,
0.054057180881500244,
0.0009368009632453322,
-0.03484527766704559,
-0.03583746775984764,
-0.039742205291986465,
0.08483808487653732,
0.03180494159460068,
0.023469261825084686,
0.018482426181435585,
-0.012173889204859734,
-0.05150018632411957,
-0.07330388575792313,
0.007645673118531704,
-0.015206574462354183,
-0.007969730533659458,
-0.015113970264792442,
0.028208015486598015,
0.007612936198711395,
0.010652667842805386,
0.06266079843044281,
-0.012141685001552105,
-0.06618636846542358,
0.04416153207421303,
-0.037524014711380005,
0.0647159293293953,
0.0050855036824941635,
-0.013788176700472832,
-0.0328579805791378,
0.04141251742839813,
-0.005767718888819218,
-0.05679521709680557,
-0.014272153377532959,
-0.0019529463024809957,
-0.04495137557387352,
-0.026611268520355225,
0.02712656557559967,
0.059397049248218536,
0.0671289712190628,
-0.09057194739580154,
-0.024062329903244972,
-0.010308928787708282,
-0.0092405304312706,
0.02648049406707287,
0.0004014745354652405,
0.05736112594604492,
-0.0007788237417116761,
0.021032510325312614,
0.00955332349985838,
0.07538221031427383,
-0.013807360082864761,
-0.058676786720752716,
0.00649616215378046,
0.00327878980897367,
0.03690028935670853,
0.0031116539612412453,
-0.001472978387027979,
0.005421041045337915,
-0.07228223979473114,
-0.045808639377355576,
-0.009749691002070904,
-0.04441412538290024,
0.007294204086065292,
0.06231149658560753,
0.02207646705210209,
-0.010393458418548107,
0.06738162785768509,
0.06909551471471786,
0.025335608050227165,
-0.026982832700014114,
0.06577149033546448,
-0.03352255001664162,
0.019394075497984886,
0.05437231436371803,
-0.034001145511865616,
0.022671781480312347,
-0.03048202022910118,
-0.07113122940063477,
-0.011905902996659279,
-0.03577275574207306,
-0.057156044989824295,
-0.035985369235277176,
0.0006009635981172323,
-0.004481891635805368,
0.0023402299266308546,
-0.06942246854305267,
0.009021959267556667,
-0.07098760455846786,
-0.01559953298419714,
0.02044842578470707,
-0.02027805708348751,
-0.05461471900343895,
0.023710256442427635,
-0.0466792918741703,
0.011222085915505886,
0.019584493711590767,
0.019983869045972824,
0.037647951394319534,
-0.013461651280522346,
-0.03513769805431366,
-0.02630685642361641,
0.03844493627548218,
-0.05050123855471611,
-0.006391807459294796,
-0.055194027721881866,
0.020745011046528816,
0.0251779742538929,
-0.010726457461714745,
-0.0181837547570467,
0.028276095166802406,
-0.014752907678484917,
0.03800090402364731,
0.021460916846990585,
-0.009623202495276928,
-0.02757224254310131,
-0.0026217736303806305,
-0.01421061810106039,
-0.003933778963983059,
-0.010215028189122677,
-0.03811800852417946,
0.04418744519352913,
0.018402231857180595,
-0.04607604444026947,
0.05465563014149666,
0.020586002618074417,
-0.045377571135759354,
-0.022150574252009392,
0.032421648502349854,
0.059697456657886505,
0.027705783024430275,
-0.01751095987856388,
-0.042201075702905655,
-0.008254683576524258,
0.007935822941362858,
-0.058022160083055496,
-0.01645839959383011,
0.03136400878429413,
-0.011097406968474388,
-0.028485970571637154,
0.06843928247690201,
-0.0036469704937189817,
0.013334245420992374,
0.04019249230623245,
0.06049610301852226,
0.019752413034439087,
0.0011807559058070183,
0.009294791147112846,
0.014464191161096096,
-0.017032722011208534,
-0.007589458022266626,
-0.01508597657084465,
0.01359698735177517,
0.04484376683831215,
0.028952976688742638,
0.018279772251844406,
0.0002258670429000631,
-0.05854767560958862,
-0.010414290241897106,
-0.000616877747233957,
-0.06358413398265839,
0.05043496936559677,
-0.0007759791915304959,
-0.004173900932073593,
0.0176578089594841,
-0.027205513790249825,
-0.014794941991567612,
-0.01973574049770832,
0.03345085307955742,
0.06649700552225113,
-0.06486749649047852,
0.0029142596758902073,
0.0031343738082796335,
0.03188513591885567,
-0.008054787293076515,
0.0034112141001969576,
0.02838531695306301,
0.017672237008810043,
-0.02939913049340248,
-0.04369578883051872,
-0.01026434451341629,
0.05861271917819977,
0.016457123681902885,
0.01835966482758522,
-0.023229647427797318,
0.020018892362713814,
-0.0017845539841800928,
-0.021273043006658554,
-0.0272905882447958,
-0.0033297587651759386,
0.009831400588154793,
0.06211051344871521,
0.000455821689683944,
0.0647539347410202,
-0.0129936458542943,
-0.015514490194618702,
0.05139726400375366,
-0.005757863167673349,
-0.05977528169751167,
0.055713724344968796,
-0.014114848338067532,
-0.007803868968039751,
-0.032509949058294296,
0.03932875022292137,
-0.014421801082789898,
-0.026922985911369324,
-0.0002004641864914447,
0.005819970741868019,
0.0018352270126342773,
-0.062815822660923,
-0.02587002143263817,
0.030773520469665527,
-0.038788896054029465,
0.03983592614531517,
-0.0022768047638237476,
-0.003208423964679241,
0.027685683220624924,
0.07227026671171188,
-0.019486427307128906,
0.020474569872021675,
-0.015514258295297623,
-0.005357217043638229,
-0.037306781858205795,
-0.009176698513329029,
-0.028480783104896545,
-0.010733217932283878,
0.04447762295603752,
-0.009649962186813354,
-0.015473475679755211,
-0.013676651753485203,
0.015331640839576721,
0.0357840396463871,
-0.034561313688755035,
0.030730213969945908,
0.009359152056276798,
0.005871318746358156,
-0.06364236772060394,
-0.050024181604385376,
0.00940610095858574,
0.02272825688123703,
0.053475264459848404,
-0.007460986264050007,
-0.006041727028787136,
-0.0320860892534256,
0.004717870149761438,
-0.013028481043875217,
0.03132491558790207,
-0.008181228302419186,
-0.042350977659225464,
0.012933687306940556,
-0.008247279562056065,
0.006592956837266684,
0.015759678557515144,
-0.0019294206285849214,
0.03425784781575203,
-0.07357659935951233,
0.06529372930526733,
0.043888770043849945,
0.013643108308315277,
-0.00032150602783076465,
-0.004865521565079689,
-0.03767036646604538,
-0.031517185270786285,
0.0507512129843235,
-0.01083935797214508,
0.03420587256550789,
-0.009991774335503578,
-0.019314413890242577,
-0.09553825110197067,
0.005385007709264755,
0.05134906992316246,
0.007982345297932625,
0.012097980827093124,
0.007239507976919413,
-0.054470181465148926,
0.07240205258131027,
0.012620746158063412,
0.03527836501598358,
0.020669899880886078,
0.02436451055109501,
0.06550335139036179,
0.023020928725600243,
-0.00287076598033309,
0.07931670546531677,
0.031056633219122887,
-0.060388125479221344,
0.004166111350059509,
0.00022892089327797294,
0.032506462186574936,
-0.05061349645256996,
0.02724420465528965,
0.03520023450255394,
-0.010192789137363434,
-0.013851972296833992,
-0.039630595594644547,
0.0072849104180932045,
0.045717742294073105,
-0.009362352080643177,
0.05522492155432701,
0.05725696682929993,
-0.06690368801355362,
0.014514584094285965,
-0.005580395460128784,
-0.0076543474569916725,
0.04029658064246178,
-0.013091961853206158,
0.02347898855805397,
-0.013100828975439072,
-0.0010001420741900802,
-0.01670612208545208,
0.03835110738873482,
-0.023909708485007286,
-0.053875382989645004,
-0.021806465461850166,
-0.018241561949253082,
-0.009153016842901707,
0.0187700055539608,
0.05308454856276512,
0.06441927701234818,
-0.06667681783437729,
-0.013338684104382992,
0.0007748827338218689,
-0.03471338003873825,
-0.029305249452590942,
0.04446842521429062,
0.019893193617463112,
-0.030052991583943367,
-0.04078558459877968,
0.0040349639020860195,
0.03819768875837326,
-0.017536351457238197,
-0.08664888888597488,
-0.017377818003296852,
-0.06036199629306793,
0.019194429740309715,
0.06570564955472946,
0.040761448442935944,
-0.007545909844338894,
-0.011205242946743965,
0.04885808005928993,
-0.10421803593635559,
0.00629937369376421,
0.032927725464105606,
0.0008956408710218966,
0.042704831808805466,
0.001957481261342764,
-0.04066844284534454,
-0.026715824380517006,
0.03650843724608421,
-0.056482017040252686,
-0.011791294440627098,
0.003699799068272114,
-0.04586155340075493,
0.027885328978300095,
-0.04046674817800522,
0.014391292817890644,
0.009186196140944958,
-0.030104342848062515,
-0.033223092555999756,
-0.040300872176885605,
-0.019155073910951614,
-0.08596932142972946,
0.023275770246982574,
0.01459183543920517,
-0.04860176146030426,
-0.006968311034142971,
0.03672415390610695,
0.02116142213344574,
0.041519299149513245,
0.09998411685228348,
0.017824236303567886,
-0.005369789898395538,
-0.039508648216724396,
0.013122797012329102,
0.016787920147180557,
0.01492164097726345,
0.030064355581998825,
-0.0748818963766098,
-0.006128789857029915,
-0.06219307705760002,
-0.005318810231983662,
0.051710549741983414,
0.0382724292576313,
-0.008134393952786922,
-0.006275224033743143,
-0.01494121178984642,
-0.021320369094610214,
-0.01828194409608841,
-0.04181021451950073,
-0.005276493728160858,
0.015458958223462105,
0.023985879495739937,
-0.01280273124575615,
0.04462563619017601,
0.00817824061959982,
0.023081351071596146,
-0.05333889275789261,
-0.0715177059173584,
0.012940517626702785,
0.0033812602050602436,
-0.05078192427754402,
0.03334638476371765,
-0.03402939438819885,
0.02149011380970478,
-0.030950495973229408,
0.0069745443761348724,
0.07082545757293701,
0.022593392059206963,
0.08543290197849274,
-0.01997479796409607,
0.038162197917699814,
-0.004915568977594376,
0.007702573202550411,
0.007099303882569075,
0.03513328358530998,
-0.053922705352306366,
-0.0018947137286886573,
-0.02732587233185768,
0.005830628797411919,
0.014345673844218254,
-0.011289839632809162,
-0.007595711853355169,
0.015017340891063213,
-0.06928642094135284,
0.008737497963011265,
-0.07734247297048569,
-0.01759498007595539,
0.009141708724200726,
0.02221963182091713,
0.0007324385805986822,
0.0045230938121676445,
-0.04656617343425751,
-0.06905170530080795,
-0.006747187580913305,
0.08549877256155014,
0.01928919181227684,
0.005009475164115429,
-0.02277417853474617,
0.01461033709347248
] |
<ol>
<li><p>What does a <a href="http://en.wikipedia.org/wiki/Quantum_state" rel="nofollow">"STATE"</a> exactly mean in <a href="http://en.wikipedia.org/wiki/Quantum_mechanics" rel="nofollow">quantum mechanics</a>? </p></li>
<li><p>What is the equivalence of "STATE" in classical mechanics?</p></li>
<li><p>If we have a wave function $\Psi$ , its absolute square $|\Psi|^2$ is the probability density of finding the particle somewhere in the space, and I know it can be written as $\langle \Psi |\Psi \rangle$. But what is the physical meaning of $\langle \Phi | \Psi \rangle$, where $\Phi$ and $\Psi$ are two different wave functions. Why we need to take inner product of two different wave functions. </p></li>
</ol> | g1221 | [
0.010280530899763107,
-0.0052063059993088245,
0.0039007433224469423,
-0.07409126311540604,
0.05209663137793541,
-0.00159350351896137,
-0.004606050904840231,
0.04497521370649338,
-0.022808166220784187,
0.0004734493268188089,
0.0010447206441313028,
-0.008475711569190025,
0.001979753142222762,
-0.03779945522546768,
0.028038153424859047,
-0.015743564814329147,
0.09900687634944916,
0.024542752653360367,
0.03577757254242897,
-0.028898561373353004,
-0.019597288221120834,
0.011205271817743778,
-0.02273271232843399,
-0.03192966803908348,
0.04912678524851799,
-0.030326060950756073,
-0.01218500081449747,
-0.0336446575820446,
-0.04607556015253067,
0.044708721339702606,
0.0024737059138715267,
-0.017411520704627037,
0.03622770681977272,
-0.06194435432553291,
0.004516582936048508,
0.0103805186226964,
0.06501436978578568,
0.045625265687704086,
-0.009419085457921028,
-0.007269035093486309,
-0.041234713047742844,
0.003568873507902026,
0.011387025937438011,
-0.04029916971921921,
0.04821407422423363,
0.011293475516140461,
-0.017484301701188087,
0.0012218765914440155,
-0.029668938368558884,
0.003158241743221879,
-0.0049173529259860516,
0.013110687024891376,
0.07068739831447601,
0.04852287471294403,
0.08634798228740692,
0.027538156136870384,
0.02447783388197422,
-0.036106985062360764,
0.04570662975311279,
0.0349491611123085,
0.05089704692363739,
-0.008992195129394531,
0.030017774552106857,
-0.003616524860262871,
0.033107370138168335,
-0.023278726264834404,
-0.0026543682906776667,
0.020824288949370384,
-0.003236911492422223,
0.0072618694975972176,
-0.005689484067261219,
-0.09620284289121628,
-0.02077358029782772,
-0.007553735747933388,
-0.025524865835905075,
-0.028276875615119934,
0.010523197241127491,
-0.010714199393987656,
0.04312977194786072,
0.028638029471039772,
-0.035006314516067505,
-0.06490689516067505,
0.05531987175345421,
-0.01776798442006111,
0.018541350960731506,
0.014493847265839577,
-0.027153434231877327,
-0.03327001631259918,
-0.02945011295378208,
0.061276596039533615,
0.011396675370633602,
0.009515522047877312,
0.08678792417049408,
0.023149870336055756,
-0.08979382365942001,
-0.037619493901729584,
-0.0457780584692955,
0.048193495720624924,
-0.013272174634039402,
0.04357670620083809,
-0.048479609191417694,
-0.016842057928442955,
0.06711413711309433,
-0.006404865998774767,
0.02072191797196865,
-0.00669842679053545,
0.045184697955846786,
0.013211162760853767,
-0.043740857392549515,
0.020188242197036743,
-0.027830390259623528,
0.02677968703210354,
0.011320547200739384,
-0.04985565319657326,
-0.04733237251639366,
0.014338758774101734,
0.029379673302173615,
-0.050636377185583115,
-0.031383197754621506,
0.06736652553081512,
0.033075980842113495,
0.07120323181152344,
0.0520162396132946,
0.019402755424380302,
0.006739632226526737,
-0.03228481486439705,
0.029414817690849304,
-0.017085403203964233,
0.017896706238389015,
0.011924128979444504,
0.06176717206835747,
0.01352257002145052,
-0.029941849410533905,
-0.000754569482523948,
-0.03308332711458206,
-0.012371882796287537,
0.0034941942431032658,
-0.02448844723403454,
0.0049533662386238575,
-0.021315880119800568,
-0.013491208665072918,
-0.010743371210992336,
0.03295670077204704,
0.0036371571477502584,
0.019308151677250862,
-0.05171336978673935,
-0.05614262819290161,
-0.03353683277964592,
-0.024538390338420868,
0.02382604405283928,
0.020071228966116905,
0.0010549441212788224,
-0.020610466599464417,
-0.0015792872291058302,
0.012763747945427895,
0.013046089559793472,
-0.004978582728654146,
0.02929675579071045,
-0.019233277067542076,
0.017918802797794342,
0.025335978716611862,
0.006314599886536598,
0.020158492028713226,
0.03703019395470619,
-0.04657625034451485,
0.027217717841267586,
0.04563680663704872,
-0.07572603225708008,
0.030927931889891624,
-0.03481577709317207,
0.039069630205631256,
-0.0151505246758461,
-0.06681706756353378,
0.03045453503727913,
-0.00808139331638813,
0.05853011831641197,
-0.04186031594872475,
-0.017034929245710373,
0.030153708532452583,
0.0013185144634917378,
-0.02178926020860672,
-0.02732088603079319,
0.030541209504008293,
0.009892956353724003,
-0.06289085000753403,
-0.010516236536204815,
0.006595278158783913,
-0.0065256101079285145,
-0.07276786863803864,
0.044544532895088196,
-0.057895462960004807,
-0.020037153735756874,
-0.0018164465436711907,
0.04847942292690277,
-0.008696413598954678,
-0.0027553606778383255,
-0.00058747612638399,
-0.030157433822751045,
-0.04888593405485153,
0.00650674756616354,
-0.010937714949250221,
0.01925837993621826,
0.01127867866307497,
-0.009849773719906807,
-0.012042547576129436,
0.04961938410997391,
0.02038566954433918,
-0.03635020554065704,
-0.007367541082203388,
-0.03373696655035019,
0.04853427782654762,
-0.053695064038038254,
0.018970247358083725,
0.03745768591761589,
-0.013001985847949982,
0.023177463561296463,
0.012411586940288544,
0.0008661600877530873,
-0.04045643284916878,
-0.01627950742840767,
-0.027881687507033348,
-0.02500671148300171,
0.05722062662243843,
0.007226038258522749,
0.006824825890362263,
0.04750240221619606,
-0.07829506695270538,
-0.009214446879923344,
-0.020985957235097885,
0.05765616521239281,
-0.05362726002931595,
-0.031248582527041435,
-0.009298671968281269,
0.031016606837511063,
0.03838681802153587,
0.09002161026000977,
-0.02504773437976837,
0.05165460333228111,
0.04261466860771179,
0.0037281769327819347,
0.020445460453629494,
0.024351680651307106,
-0.060585636645555496,
0.0588049553334713,
0.026865096762776375,
0.010408062487840652,
-0.0035878289490938187,
-0.023086730390787125,
-0.03393365070223808,
0.025172287598252296,
-0.039088744670152664,
-0.014422193169593811,
-0.060807883739471436,
-0.004239201080054045,
0.029538609087467194,
-0.029308607801795006,
0.01751427724957466,
-0.014882697723805904,
-0.0388655886054039,
-0.03882930427789688,
0.002695201663300395,
0.020146973431110382,
-0.01037193089723587,
0.030071323737502098,
-0.03059435449540615,
-0.012956543825566769,
0.017633851617574692,
0.031868983060121536,
-0.016671553254127502,
-0.024920575320720673,
0.01591753214597702,
0.11537126451730728,
-0.021664036437869072,
0.0002241629990749061,
0.0026935418136417866,
-0.05736430361866951,
-0.034959856420755386,
-0.027248414233326912,
-0.005412517115473747,
-0.0401233546435833,
-0.016588667407631874,
0.030111145228147507,
-0.03715699911117554,
0.045342400670051575,
0.033155135810375214,
-0.10407016426324844,
0.01621355675160885,
0.060184795409440994,
-0.005775489378720522,
0.016305141150951385,
0.01991058699786663,
0.060274846851825714,
-0.004786312114447355,
-0.004988386295735836,
-0.04526339843869209,
0.03626934438943863,
-0.030975358560681343,
-0.04432247206568718,
0.0350496880710125,
0.03237101435661316,
0.011850140057504177,
-0.026231329888105392,
-0.03629973158240318,
-0.02542557194828987,
0.0008002019603736699,
0.025325868278741837,
-0.04314586520195007,
-0.010637786239385605,
-0.050188563764095306,
0.019270645454525948,
0.004820362199097872,
0.05825313925743103,
-0.038654446601867676,
-0.016938477754592896,
-0.02681838348507881,
0.008664742112159729,
-0.02978367917239666,
-0.00423350278288126,
0.022627081722021103,
-0.01181954424828291,
-0.0387343168258667,
-0.04213494062423706,
0.027543533593416214,
0.002390190027654171,
0.03631899133324623,
0.013680484145879745,
-0.038791678845882416,
0.022988898679614067,
-0.035639986395835876,
-0.07411804795265198,
0.01450266968458891,
0.002648062538355589,
-0.042164746671915054,
-0.02780042216181755,
-0.04104804992675781,
-0.01609732210636139,
-0.02500850148499012,
-0.000345563079463318,
0.05376787111163139,
-0.006545642390847206,
0.055342815816402435,
-0.0008933630888350308,
-0.03265124931931496,
0.058922819793224335,
-0.017542904242873192,
-0.034324705600738525,
-0.03468691185116768,
-0.002907578367739916,
0.058291178196668625,
-0.013540784828364849,
-0.038473859429359436,
0.033903464674949646,
0.03727467730641365,
0.018911831080913544,
-0.03368036821484566,
0.019366873428225517,
0.05519474297761917,
-0.02070780098438263,
0.06016016751527786,
-0.00011327430547680706,
0.005690522491931915,
-0.05151408910751343,
0.06482522934675217,
-0.0078518595546484,
-0.020234327763319016,
0.004248340148478746,
0.0071334317326545715,
-0.016218706965446472,
0.03478072211146355,
-0.05014946684241295,
-0.01948346011340618,
-0.011222714558243752,
0.0022327685728669167,
0.002139923395588994,
0.025746788829565048,
-0.04557104781270027,
-0.013461662456393242,
-0.04422489553689957,
-0.07952825725078583,
-0.022872529923915863,
0.022386625409126282,
0.035431526601314545,
0.042527079582214355,
0.0001624622818781063,
0.0660683885216713,
-0.03143567591905594,
-0.012851355597376823,
0.03454519063234329,
0.0501583032310009,
-0.002745971782132983,
0.01617623306810856,
-0.03935321420431137,
-0.07421259582042694,
0.027249353006482124,
0.03035527467727661,
0.06476344168186188,
0.055368635803461075,
-0.0046179043129086494,
-0.0508677214384079,
0.04182010516524315,
-0.03196776285767555,
-0.03268063813447952,
0.004873131401836872,
0.0003659748181235045,
-0.016741130501031876,
-0.009352248162031174,
0.07005441188812256,
-0.05923238396644592,
-0.02565624564886093,
-0.06001734361052513,
0.01019332092255354,
0.020800692960619926,
0.03931821137666702,
-0.04486788064241409,
-0.03933429718017578,
0.07029461860656738,
0.00462118536233902,
-0.07302946597337723,
-0.009981774725019932,
0.039822835475206375,
-0.023601138964295387,
0.042552776634693146,
0.038776274770498276,
0.032115787267684937,
0.029332254081964493,
0.026481419801712036,
0.0774453803896904,
0.06259725987911224,
-0.0162062905728817,
-0.07494241744279861,
0.008794020861387253,
0.01958945393562317,
0.039488453418016434,
0.03624638915061951,
-0.0677175298333168,
-0.03421055153012276,
-0.09929592907428741,
-0.004511747509241104,
0.021759033203125,
0.0145108075812459,
0.03541859984397888,
-0.011995917186141014,
-0.04704073444008827,
0.017304319888353348,
0.006313169375061989,
0.008199797011911869,
-0.023180536925792694,
-0.03841937333345413,
-0.041455503553152084,
-0.06137058511376381,
-0.0014371395809575915,
0.018912019208073616,
-0.007742119487375021,
-0.07846181094646454,
0.021693982183933258,
0.006767619866877794,
0.009053299203515053,
0.004170910455286503,
-0.010175012983381748,
0.026075948029756546,
-0.033086832612752914,
0.044272683560848236,
0.011919939890503883,
-0.0535883828997612,
0.011488155461847782,
0.020344426855444908,
-0.10793085396289825,
0.006546960677951574,
-0.10452453047037125,
-0.05015392601490021,
0.029588917270302773,
-0.026467330753803253,
0.037124067544937134,
-0.034429602324962616,
0.04749591276049614,
0.0003551506670191884,
-0.022629177197813988,
-0.03899034857749939,
-0.021455807611346245,
-0.06245312839746475,
-0.013132571242749691,
-0.0039609577506780624,
0.012125212699174881,
0.02303338050842285,
0.013185972347855568,
0.008806430734694004,
-0.009777356870472431,
-0.02316373772919178,
-0.026455475017428398,
-0.03621537983417511,
0.05116850510239601,
0.021967319771647453,
0.046353720128536224,
0.009989115409553051,
0.043988414108753204,
0.013365703634917736,
-0.0007192937773652375,
-0.019252581521868706,
-0.020891806110739708,
0.035710953176021576,
-0.05831635743379593,
0.022193579003214836,
0.012840532697737217,
0.04851437732577324,
-0.02001049555838108,
0.008194789290428162,
0.03337406367063522,
0.014371377415955067,
0.004311430733650923,
-0.0028796184342354536,
0.02300453931093216,
-0.011242677457630634,
-0.04594380408525467,
-0.03594835847616196,
0.03286728262901306,
0.013879828155040741,
0.011754457838833332,
0.05277901142835617,
-0.006550239864736795,
-0.007352052256464958,
0.012679745443165302,
0.004645295441150665,
0.010480985045433044,
-0.029272479936480522,
-0.021281415596604347,
0.02615337446331978,
-0.025641299784183502,
-0.0353814959526062,
0.016950136050581932,
0.09902118891477585,
-0.01116554532200098,
0.028378693386912346,
0.03228605538606644,
-0.0059439740143716335,
-0.03414482995867729,
-0.037383075803518295,
-0.041528236120939255,
-0.017176499590277672,
0.053263064473867416,
0.058502525091171265,
-0.02565447986125946,
-0.020084848627448082,
-0.03406805917620659,
0.01799614727497101,
-0.00923397671431303,
0.029995962977409363,
-0.020287979394197464,
-0.025565622374415398,
0.01573428139090538,
-0.00873794686049223,
0.006187039893120527,
-0.01987290009856224,
-0.008881349116563797,
-0.04040279984474182,
0.0707017034292221,
0.016672389581799507,
0.0026062247343361378,
0.013962404802441597,
-0.016121406108140945,
-0.016337189823389053,
0.05292907729744911,
0.04007018357515335,
0.00990889873355627,
0.021134771406650543,
0.03665938228368759,
-0.03843667358160019,
-0.005350625608116388,
-0.006228841841220856,
0.02286761999130249,
-0.01020284928381443,
0.015324851498007774,
0.015568962320685387,
-0.003375857602804899,
-0.010907626710832119,
0.0264965258538723,
0.020582016557455063,
-0.05739805847406387,
-0.0609392412006855,
-0.025267943739891052,
0.030117833986878395,
-0.022319044917821884,
0.0011428273282945156,
0.015180268324911594,
-0.04891642555594444,
-0.07523103058338165,
0.056326724588871,
0.0221429243683815,
-0.08052658289670944,
0.07919280230998993,
0.058681994676589966,
-0.021372418850660324,
-0.03133583068847656,
-0.03269203007221222,
0.024373212829232216,
-0.0389246828854084,
0.026866581290960312,
-0.02112402766942978,
-0.008479401469230652,
0.007338953670114279,
0.021758530288934708,
-0.006309883669018745,
0.0010673531796783209,
0.03418678417801857,
-0.03629402071237564,
0.01962180808186531,
0.032264046370983124,
-0.04590258374810219,
-0.05404586344957352,
-0.07387974113225937,
0.01649073325097561,
-0.052689775824546814,
-0.02253412827849388,
-0.05780390277504921,
-0.003424137132242322,
0.019902534782886505,
-0.06420030444860458,
0.00020802856306545436,
0.0598791129887104,
-0.03710158169269562,
-0.013101328164339066,
0.08127856254577637,
-0.0027867837343364954,
0.00994473323225975,
-0.014157302677631378,
0.04546414315700531,
0.04463394358754158,
-0.027149995788931847,
0.022715456783771515,
0.07005073130130768,
-0.006097802426666021,
0.003411407582461834,
-0.051837414503097534,
0.03566586598753929,
0.05877775698900223,
-0.02814590558409691,
0.0030852239578962326,
-0.025138190016150475,
-0.02477787248790264,
0.06849798560142517,
-0.016766786575317383,
-0.01978476531803608,
0.00985776912420988,
0.10644607245922089,
-0.023335369303822517,
-0.11392244696617126,
-0.014855857007205486,
0.03797542676329613,
-0.037196602672338486,
-0.07135370373725891,
0.015420098789036274,
-0.02929501235485077,
0.007227792404592037,
-0.03943997994065285,
-0.032114360481500626,
-0.015542237088084221,
0.05143081024289131,
0.05095250904560089,
0.029549991711974144,
-0.024509018287062645,
-0.0749826654791832,
0.007301733363419771,
-0.007150363177061081,
-0.017009617760777473,
0.0244731642305851,
0.005265611223876476,
0.04760807752609253,
-0.014085115864872932,
-0.07463253289461136,
-0.0013306394685059786,
-0.040662731975317,
0.032207466661930084,
-0.0084761967882514,
-0.07167305797338486,
-0.03135320544242859,
0.002168519888073206,
0.03320203348994255,
0.0285934004932642,
0.021323518827557564,
-0.009689467959105968,
-0.02099144272506237,
0.006476586684584618,
0.03831744194030762,
-0.034507423639297485,
0.010688700713217258,
-0.034577760845422745,
0.008674739859998226,
-0.0047106207348406315,
0.009321356192231178,
-0.010507123544812202,
0.010154127143323421,
0.017314840108156204,
-0.01797822117805481,
-0.020711282268166542,
-0.021791061386466026,
0.013322102837264538,
0.03851008415222168,
0.07770399749279022,
0.07101389765739441,
0.019781501963734627,
-0.006134471856057644,
0.0138930082321167,
0.006605932489037514,
-0.01349475234746933,
-0.0015999932074919343,
0.038252539932727814,
-0.03136499971151352,
0.019733697175979614,
-0.011831443756818771,
-0.026633920148015022,
0.030397459864616394,
0.039174288511276245,
-0.006100490689277649,
0.02108653634786606,
0.019801950082182884,
0.044614169746637344,
-0.02751903049647808,
-0.0032506391871720552,
0.03341512009501457,
0.015013907104730606,
-0.03530757129192352,
0.04763927683234215,
0.01560227945446968,
-0.026907887309789658,
-0.02134985662996769,
-0.029584554955363274,
0.0031053766142576933,
0.009253403171896935,
0.0052363197319209576,
-0.02131379023194313,
0.024282345548272133,
-0.030157038941979408,
0.02599390223622322,
0.0007706604665145278,
0.04097413644194603,
-0.03240048512816429,
0.04375464841723442,
0.014895128086209297,
0.05876617506146431,
0.026134690269827843,
0.04672878608107567,
0.030154360458254814,
-0.045838646590709686,
-0.018849121406674385,
0.025842174887657166,
-0.06711290031671524,
-0.015780393034219742,
0.0030072624795138836,
0.035893384367227554,
0.04866863042116165,
-0.026498282328248024,
-0.0010798197472468019,
0.034259133040905,
-0.0552753210067749,
0.09218969196081161,
0.023761199787259102,
-0.08193367719650269,
0.03999439626932144,
0.031981151551008224,
0.0652545690536499,
0.014237858355045319,
0.04558015614748001,
-0.004459884483367205,
-0.01934991218149662,
-0.05086108669638634,
-0.0441758930683136,
-0.03684398904442787,
-0.007703196723014116,
0.02113557606935501
] |
<p>If I drop a ball in a train moving at a constant speed, will it land on the spot I aimed it at or a little away as the train has moved while it was in air? If it lands away, will the observer not know that he is in a moving frame of reference? If it lands on the intended spot, how did the ball know it is inside a train? </p> | g1222 | [
-0.00279696611687541,
-0.032634228467941284,
0.030512211844325066,
0.008047170005738735,
0.04676143079996109,
0.06890367716550827,
0.04204719886183739,
0.04109556972980499,
-0.09312441945075989,
-0.05034426599740982,
-0.039363667368888855,
-0.03467204421758652,
0.07714660465717316,
-0.05579139664769173,
-0.02478053607046604,
-0.036881592124700546,
0.033765606582164764,
-0.01995733007788658,
0.024128127843141556,
-0.004555272404104471,
0.07082106173038483,
0.02388148196041584,
0.0166240893304348,
-0.010055547580122948,
-0.034336790442466736,
-0.010077618062496185,
0.005891963839530945,
-0.053419824689626694,
-0.0395062156021595,
-0.019109563902020454,
0.011409247294068336,
-0.040524229407310486,
-0.02926758863031864,
-0.04344204440712929,
0.03504687175154686,
-0.058621447533369064,
0.010038534179329872,
-0.017262613400816917,
0.0020337023306638002,
0.004452014807611704,
0.009349662810564041,
-0.000627806584816426,
-0.038474421948194504,
-0.018334178254008293,
0.05886147916316986,
0.037681788206100464,
-0.002918344922363758,
-0.0046155452728271484,
0.0009836585959419608,
-0.03280796483159065,
-0.026968037709593773,
0.04824884608387947,
-0.02648288384079933,
0.027532855048775673,
0.012555905617773533,
0.022627169266343117,
-0.009347537532448769,
-0.011146405711770058,
-0.005486707668751478,
-0.02270372211933136,
-0.013167545199394226,
-0.032852064818143845,
-0.037666551768779755,
-0.023329703137278557,
0.0423382967710495,
-0.00003967698648921214,
-0.08028363436460495,
-0.025465726852416992,
-0.04282369464635849,
-0.029906149953603745,
0.007083963602781296,
0.01360087189823389,
-0.06914892047643661,
0.013215095736086369,
-0.03635932505130768,
-0.021407460793852806,
0.013598348014056683,
-0.050294823944568634,
-0.02900375798344612,
0.03143348544836044,
-0.0062925866805016994,
-0.0012664314126595855,
0.061987295746803284,
0.014665133319795132,
0.06971579045057297,
0.01547089871019125,
0.004325899761170149,
0.019573092460632324,
-0.03206236660480499,
-0.017518015578389168,
0.01136777177453041,
-0.04004031419754028,
0.11777552962303162,
0.0824943408370018,
-0.031219637021422386,
-0.015218902379274368,
-0.037535928189754486,
0.023037390783429146,
0.03473768010735512,
0.009551970288157463,
-0.03470834717154503,
-0.03157307207584381,
0.007164826616644859,
-0.04269517585635185,
0.034118976444005966,
-0.017993386834859848,
0.026743760332465172,
0.014135039411485195,
-0.023789729923009872,
-0.06185983866453171,
0.008799783885478973,
-0.049414511770009995,
-0.03460618108510971,
0.0040349471382796764,
-0.07720930129289627,
-0.002377316588535905,
0.054841406643390656,
0.045808665454387665,
0.019953273236751556,
0.02287159115076065,
-0.0014269546372815967,
0.06323149800300598,
0.011807930655777454,
0.06394156813621521,
-0.013983461074531078,
0.00523144006729126,
-0.02247420698404312,
-0.023724591359496117,
-0.03929717093706131,
0.019949330016970634,
-0.022590748965740204,
-0.007459666114300489,
0.047120705246925354,
-0.02634604461491108,
-0.08655449002981186,
0.02180955745279789,
0.029166100546717644,
-0.048706185072660446,
0.006794374901801348,
0.03499076887965202,
0.08859692513942719,
0.04924442619085312,
-0.005219711922109127,
-0.057307418435811996,
-0.03101552277803421,
0.04878516495227814,
-0.018502742052078247,
0.004413702059537172,
0.04601718857884407,
0.01844964548945427,
0.01137826219201088,
-0.007461084984242916,
-0.004023732151836157,
-0.07107534259557724,
0.05797630548477173,
-0.05192320793867111,
-0.014278805814683437,
-0.01170500461012125,
0.027606746181845665,
-0.0009205706301145256,
0.0924815908074379,
-0.02205529808998108,
0.02656010538339615,
0.017260080203413963,
-0.045833438634872437,
-0.006274281069636345,
0.003196300007402897,
-0.035041648894548416,
0.015994030982255936,
-0.030838387086987495,
-0.04525122418999672,
0.023504802957177162,
0.0350765623152256,
0.04420718178153038,
-0.024614999070763588,
-0.004380182363092899,
0.030254386365413666,
-0.0435790941119194,
-0.007024249993264675,
-0.01986170932650566,
0.023940663784742355,
-0.009991184808313847,
-0.02996860258281231,
-0.05282043665647507,
-0.0022953625302761793,
0.01915903389453888,
0.005555026698857546,
-0.04720670357346535,
-0.056439436972141266,
-0.015668481588363647,
-0.03117438778281212,
-0.05676449090242386,
-0.025957124307751656,
0.06468265503644943,
-0.017089277505874634,
0.004173413384705782,
0.02302742376923561,
-0.03174549341201782,
-0.03927243500947952,
-0.0008144222665578127,
0.00013469060650095344,
0.0030041944701224566,
0.008077382110059261,
0.022931300103664398,
-0.006387263536453247,
-0.023337872698903084,
0.05368233844637871,
0.008339058607816696,
-0.03655994310975075,
-0.020640600472688675,
0.03956542909145355,
-0.01360497996211052,
0.025997241958975792,
0.0021171034313738346,
0.03300109878182411,
0.04047785699367523,
0.014806977473199368,
0.0021141692996025085,
0.0043590073473751545,
0.02000463381409645,
0.007457811385393143,
0.03789805620908737,
0.006443837657570839,
-0.04251355677843094,
-0.04419589415192604,
-0.03781810775399208,
-0.062021173536777496,
-0.024125313386321068,
0.04877624660730362,
0.049655552953481674,
-0.043346334248781204,
0.0276622511446476,
-0.00216436549089849,
0.042602524161338806,
0.002283788751810789,
0.011363886296749115,
0.006018987391144037,
-0.029426025226712227,
0.041801221668720245,
-0.04082547500729561,
0.0028076183516532183,
0.003192044561728835,
0.012048077769577503,
-0.014561629854142666,
-0.03951346501708031,
-0.013985036872327328,
0.05877053737640381,
-0.030724208801984787,
0.02451317012310028,
0.01526155136525631,
-0.010756298899650574,
0.0443248376250267,
-0.01454461831599474,
0.0007449230179190636,
-0.038008321076631546,
-0.010524879209697247,
-0.061981700360774994,
-0.009146928787231445,
-0.06779875606298447,
-0.008135117590427399,
-0.021437814459204674,
-0.0477542020380497,
-0.011427340097725391,
-0.01650984212756157,
0.02334386482834816,
0.010783765465021133,
0.02409711666405201,
0.04589586704969406,
-0.011009997688233852,
-0.00043110339902341366,
-0.03935650363564491,
0.0735856294631958,
0.005666520446538925,
0.041237782686948776,
-0.011155528947710991,
-0.035200946033000946,
-0.009088266640901566,
-0.046066924929618835,
0.0020347030367702246,
-0.00755572272464633,
-0.03799014538526535,
0.04371693730354309,
-0.07677147537469864,
-0.015424801968038082,
0.01667182520031929,
-0.0894966647028923,
0.012099134735763073,
0.028927747160196304,
0.0019115636823698878,
-0.04046874865889549,
-0.016924027353525162,
0.07071655243635178,
0.057981859892606735,
0.04001464694738388,
-0.04065229743719101,
0.047505564987659454,
0.009916515089571476,
-0.00827445462346077,
-0.040943071246147156,
0.06565455347299576,
-0.013219652697443962,
-0.017572147771716118,
-0.006611920427531004,
0.0004886651877313852,
0.02557549439370632,
0.04181692376732826,
-0.03205586224794388,
-0.015456809662282467,
0.022617442533373833,
-0.028821153566241264,
0.002953298855572939,
0.0687485784292221,
0.00262384838424623,
-0.029247039929032326,
-0.04834575206041336,
-0.023221449926495552,
0.0008389090071432292,
0.02783699333667755,
-0.04028373584151268,
0.0641910657286644,
0.07969793677330017,
0.05149112269282341,
-0.005578693468123674,
-0.0299370214343071,
0.07562325894832611,
0.002278850646689534,
0.04200326278805733,
-0.0066039771772921085,
0.009262551553547382,
-0.01631845161318779,
-0.002272429410368204,
-0.016797734424471855,
-0.01618008315563202,
-0.018348274752497673,
0.024326138198375702,
-0.013158556073904037,
-0.02568289265036583,
0.0012509394437074661,
0.04359036684036255,
-0.027376625686883926,
0.04703658074140549,
0.00213306094519794,
-0.0035472826566547155,
-0.05822831019759178,
0.04704063758254051,
0.012434485368430614,
0.005109298508614302,
0.0008058733073994517,
-0.023892482742667198,
-0.040859341621398926,
0.09224849939346313,
-0.06540343910455704,
-0.023149318993091583,
-0.05372477322816849,
-0.037264056503772736,
-0.012555399909615517,
-0.003204065840691328,
0.04134095832705498,
-0.031315915286540985,
0.014944838359951973,
-0.027030985802412033,
-0.017907965928316116,
-0.0009064585901796818,
0.050156865268945694,
0.026155313476920128,
-0.06840182095766068,
-0.05332452058792114,
-0.013902420178055763,
0.03316577151417732,
0.004442964680492878,
-0.03223477303981781,
0.0006360835977829993,
-0.050434425473213196,
0.040420811623334885,
0.004453522618860006,
-0.022174151614308357,
0.028548119589686394,
-0.02394331619143486,
-0.07187904417514801,
-0.018069138750433922,
-0.008704639039933681,
0.05289136618375778,
-0.0034188597928732634,
0.005320040043443441,
0.06385531276464462,
0.03634181618690491,
-0.021896591410040855,
-0.020179197192192078,
0.05568787828087807,
-0.0033919927664101124,
0.01428387500345707,
-0.031361211091279984,
-0.006623081862926483,
-0.020621515810489655,
0.02281893603503704,
-0.008049643598496914,
-0.010676704347133636,
-0.02618277072906494,
0.0321793369948864,
0.05396932736039162,
0.020281312987208366,
0.03530467301607132,
-0.06845986098051071,
-0.027982516214251518,
0.001185499015264213,
0.02084510587155819,
0.006230884697288275,
-0.011576644144952297,
-0.017990242689847946,
-0.011612728238105774,
-0.04618879035115242,
0.013471253216266632,
-0.06917628645896912,
-0.060975659638643265,
0.0032123273704200983,
0.049413569271564484,
-0.020796915516257286,
0.04667282849550247,
-0.06723753362894058,
-0.00005508678805199452,
0.03797166422009468,
0.01006365567445755,
0.056503016501665115,
-0.04642608016729355,
-0.02984968200325966,
0.03392617776989937,
0.010191606357693672,
-0.01946783810853958,
-0.021784888580441475,
-0.009248282760381699,
0.017072590067982674,
-0.020817559212446213,
0.039163440465927124,
0.07927479594945908,
-0.004171888809651136,
0.04517833888530731,
-0.015898777171969414,
-0.01037514302879572,
0.07801221311092377,
-0.029633494094014168,
0.052953850477933884,
0.03672252967953682,
-0.03289042413234711,
0.0018056505359709263,
-0.05514936149120331,
0.06340572983026505,
-0.054733969271183014,
0.008166465908288956,
-0.01797529123723507,
0.0033462962601333857,
-0.007229539565742016,
0.01674036495387554,
-0.019175110384821892,
-0.008988861925899982,
-0.010882820002734661,
-0.004238208290189505,
-0.05777578428387642,
-0.03320961073040962,
-0.01236347109079361,
-0.021771246567368507,
0.035250429064035416,
-0.034159258008003235,
-0.040824729949235916,
-0.00015971303218975663,
-0.03570078685879707,
-0.0036510431673377752,
0.043401505798101425,
-0.023270543664693832,
-0.04124930500984192,
-0.037557534873485565,
-0.02644549123942852,
0.02750875987112522,
0.0032198335975408554,
0.05727637559175491,
0.05161439999938011,
-0.0004719733551610261,
0.036365218460559845,
-0.032928381115198135,
0.0738486498594284,
-0.043326880782842636,
-0.05892225354909897,
0.0008468308369629085,
0.018134891986846924,
0.024630628526210785,
-0.033796556293964386,
-0.00822467915713787,
-0.0011945561273023486,
0.03351254388689995,
0.04567812755703926,
-0.03193999081850052,
0.052915431559085846,
-0.0419175960123539,
-0.023176804184913635,
0.0030517708510160446,
-0.0835132896900177,
-0.06827050447463989,
-0.016485702246427536,
-0.0017412028973922133,
-0.00854027085006237,
0.01776181161403656,
-0.08519336581230164,
-0.0027890573255717754,
0.05118809640407562,
0.040166061371564865,
-0.0016173030016943812,
0.0396750308573246,
0.04127568379044533,
-0.018197758123278618,
-0.04727109521627426,
0.09556843340396881,
-0.00504670524969697,
0.06404406577348709,
-0.02191566303372383,
-0.007111500483006239,
-0.02776786871254444,
-0.02369624748826027,
-0.0028417916037142277,
0.0005385682452470064,
-0.046794988214969635,
0.0305947232991457,
0.01876978576183319,
-0.005450086668133736,
-0.012844225391745567,
0.03496074676513672,
-0.05009133741259575,
0.015888022258877754,
-0.025742705911397934,
0.007193571887910366,
-0.005250371061265469,
0.038442984223365784,
0.03398717939853668,
-0.0027085079345852137,
0.040891584008932114,
-0.003566865809261799,
-0.039846453815698624,
0.0269280057400465,
0.00766325369477272,
-0.04519249498844147,
0.04220442473888397,
0.05802156403660774,
-0.0328994020819664,
-0.000600513769313693,
-0.041081663221120834,
0.07874171435832977,
0.034852467477321625,
-0.052185967564582825,
-0.04413730651140213,
0.04027735814452171,
0.09592245519161224,
-0.030025359243154526,
-0.011843523941934109,
0.08263804763555527,
-0.06376835703849792,
0.042755573987960815,
-0.04651564732193947,
0.040299657732248306,
0.003682253183797002,
0.03279919549822807,
-0.01190638355910778,
-0.03989021107554436,
0.02498345822095871,
-0.004924887791275978,
0.04847310855984688,
0.005120817106217146,
-0.013861088082194328,
0.048533037304878235,
-0.018840931355953217,
0.002399169374257326,
0.039231617003679276,
0.004200681112706661,
0.015275546349585056,
-0.0014604137977585196,
-0.03965749591588974,
-0.033448476344347,
0.005175026133656502,
0.008456667885184288,
-0.056052107363939285,
-0.03414164111018181,
-0.07041946798563004,
0.052853211760520935,
0.021944204345345497,
-0.02619674988090992,
-0.007021111901849508,
-0.044385045766830444,
0.013003749772906303,
0.013888451270759106,
-0.013571372255682945,
-0.010738793760538101,
0.02402491495013237,
-0.005271147470921278,
-0.0061464253813028336,
-0.03220852464437485,
0.012046695686876774,
-0.037605706602334976,
-0.04722369834780693,
-0.05304490029811859,
-0.038434963673353195,
0.007115516811609268,
-0.053774844855070114,
0.04242165759205818,
-0.029758857563138008,
-0.03963875398039818,
0.05763719603419304,
-0.00778838200494647,
-0.04319993034005165,
0.06750836223363876,
0.04632505029439926,
-0.05413714423775673,
-0.0020559143740683794,
0.013062850572168827,
-0.007356091868132353,
0.03294207155704498,
0.015271402895450592,
0.05276184156537056,
-0.02297051064670086,
-0.003686686046421528,
0.03540104255080223,
-0.03308901563286781,
-0.033839695155620575,
-0.07664315402507782,
0.013596744276583195,
0.0005663602496497333,
-0.02110252156853676,
0.006467387080192566,
0.0349465049803257,
0.004348422400653362,
-0.026635227724909782,
0.021809354424476624,
0.018093518912792206,
0.016481678932905197,
0.021236373111605644,
0.02168004773557186,
-0.06520406156778336,
-0.002600242616608739,
-0.0007024432998150587,
0.09147149324417114,
0.06509818881750107,
0.04750807583332062,
0.003962571732699871,
-0.008123479783535004,
-0.0032850911375135183,
0.05986396595835686,
-0.02821141481399536,
0.008674218319356441,
-0.02042344957590103,
0.03532160446047783,
0.020539293065667152,
0.021846730262041092,
-0.013405052945017815,
0.042981721460819244,
-0.03353430703282356,
-0.039204422384500504,
-0.014594103209674358,
0.031515251845121384,
-0.0044220080599188805,
0.044401731342077255,
0.008206197060644627,
0.07894959300756454,
0.015397798269987106,
-0.011976299807429314,
-0.0549137257039547,
-0.08217781037092209,
-0.0315549373626709,
0.009842448867857456,
-0.02090703509747982,
0.02242901548743248,
0.0557665191590786,
-0.06792081892490387,
-0.04673917591571808,
0.03949578106403351,
0.03224078565835953,
-0.02378244511783123,
0.029202286154031754,
0.04628131166100502,
0.05703100934624672,
0.02617320790886879,
-0.0756022110581398,
0.020660705864429474,
-0.0003969611134380102,
0.00025349765201099217,
-0.016082659363746643,
0.06212369352579117,
0.022113783285021782,
-0.012574590742588043,
-0.022582365199923515,
0.0396624356508255,
-0.00583629310131073,
-0.04915885627269745,
0.05581025034189224,
-0.11475787311792374,
0.022616107016801834,
0.06500702351331711,
0.0360182486474514,
-0.02303902804851532,
-0.016290297731757164,
-0.051352888345718384,
0.05888599529862404,
0.004324886482208967,
0.02647511288523674,
0.008116904646158218,
-0.009293759241700172,
0.008607359603047371,
0.04451655596494675,
0.03569858521223068,
0.017645565792918205,
-0.0010968676069751382,
-0.027657510712742805,
0.043673038482666016,
0.0058045294135808945,
0.06375996023416519,
0.036118168383836746,
0.017155909910798073,
0.08123956620693207,
0.010095319710671902,
-0.04886201024055481,
-0.005485660396516323,
-0.020563166588544846,
0.005266469903290272,
0.043415628373622894,
0.009029857814311981,
-0.0048922523856163025,
0.04952486976981163,
0.0014427413698285818,
-0.018187113106250763,
0.029331088066101074,
0.04750146344304085,
0.019127801060676575,
0.04051763936877251,
0.0061761923134326935,
-0.04000626876950264,
-0.0008346522809006274,
0.05497031658887863,
-0.05020253732800484,
0.027213919907808304,
0.009130006656050682,
-0.01767297275364399,
0.01741558127105236,
0.015483721159398556,
-0.04212027043104172,
-0.0030322836246341467,
-0.007860601879656315,
-0.07939258217811584,
0.04317153990268707,
0.0035221846774220467,
-0.0034365742467343807,
-0.018048405647277832,
0.028863733634352684,
0.004493781365454197,
-0.006664362736046314,
-0.003186715068295598,
0.015358059667050838,
0.012113941833376884,
-0.030231259763240814,
0.049104295670986176,
0.05062692612409592,
-0.04536499083042145,
-0.015077049843966961,
-0.019657358527183533,
-0.010994051583111286,
-0.0028041766490787268,
0.0019130302825942636,
-0.006537706591188908,
0.008986306376755238,
-0.0010174402268603444,
-0.02875153161585331,
-0.006586871109902859,
-0.02287120558321476,
0.019315339624881744
] |
<p>I'm struggling with the notion of an inertial frame of reference. I suspect my difficulty lies with the difference between Newtonian and relativistic inertial frames, but I can't see it. </p>
<p>I've read that Newton's laws apply in any non accelerating frame of reference, which are called inertial frames. So, if I play pool on a train moving with uniform velocity, the balls behave in the same way as if I were playing pool in a pool hall. So the train is (to a good approximation, ignoring forces caused by the Earth's rotation and movement around the Sun etc) an inertial frame. </p>
<p>I've also read that in an inertial frame, Newton's first law is satisfied. So, if I slide a rock on a sheet of ice and I could somehow eliminate the frictional forces between the rock and the ice, the rock would carry on sliding for ever, as predicted by Newton's first law. </p>
<p>Question 1 - is the sheet of ice also therefore a good approximation to an inertial frame?</p>
<p>Question 2 - are these two definitions of inertial frames saying the same thing in different ways?</p>
<p>Both these examples occur in gravitation fields, which doesn't seem to matter as both the train and the ice sheet are presumably good approximations to inertial frames.</p>
<p>Question 3 - is gravity irrelevant when defining these two inertial frames?</p>
<p>In special relativity, I've read (Foster and Nightingale) that an inertial frame is also one where Newton's first law holds. But as it's special relativity there cannot be an inertial frame if there's a gravitational field, so I'm assuming the above two examples are not inertial frames in special relativity.</p>
<p>Question 4 - how come you can use the same definition of an inertial frame (satisfied Newton's first law) but in the case of special relativity, the train and the ice sheet aren't inertial frames. Is this to do with not being able to synchronize clocks in a gravitational field?</p>
<p>In general relativity, I've read (Schutz) that a freely falling frame is (on Earth) the only possible (and local) inertial frame. So again the first two examples would not be inertial frames in general relativity.</p>
<p>Question 5 - am I right to think that my two examples aren't even approximate approximations to an inertial frame in relativity?</p>
<p>Question 6 - have I missed anything else that might be useful?</p>
<p>Many thanks</p>
<p>Edit. On reflection, am I right in thinking that because Newtonian mechanics assumes universal, absolute time we don't need to worry about synchronizing clocks in a Newtonian inertial frame. Therefore we don't need to worry about gravity in a Newtonian inertial frame, because in such a frame gravity does not affect time.</p>
<p>This is not the case in spacetime, as here gravity does affect time and the only way to have synchronized clocks in an inertial frame in spacetime is:
1. have no gravitational field, or
2. use a local, freely falling frame.</p>
<p>Am I on the right track here? </p> | g285 | [
0.04049628973007202,
0.018632730469107628,
0.02107509970664978,
0.030726764351129532,
0.09756148606538773,
-0.0009740945533849299,
0.08104795962572098,
0.007053811103105545,
-0.0863763615489006,
0.003282883670181036,
0.006496982648968697,
-0.04002049192786217,
-0.022615382447838783,
0.0018723454559221864,
-0.030605077743530273,
-0.04426051676273346,
0.07867132127285004,
0.040175437927246094,
0.027117878198623657,
0.022770237177610397,
0.09429669380187988,
0.016530731692910194,
0.013788250274956226,
-0.033954523503780365,
-0.004982904065400362,
0.04219533130526543,
0.03655487298965454,
-0.04312000051140785,
-0.011120802722871304,
-0.014164106920361519,
0.0049329656176269054,
-0.037869833409786224,
-0.033330269157886505,
-0.015014562755823135,
0.06875762343406677,
0.008834018371999264,
0.048251014202833176,
0.03844138979911804,
0.016837196424603462,
0.0008179890573956072,
0.016076216474175453,
-0.00602234061807394,
0.0269691813737154,
-0.04283453896641731,
0.05976986885070801,
0.04752287641167641,
-0.010969247668981552,
-0.024155108258128166,
0.024097952991724014,
-0.013706783764064312,
0.033838849514722824,
0.06078599393367767,
-0.012996425852179527,
0.0014437882928177714,
-0.02255394123494625,
0.02619527466595173,
0.008946774527430534,
0.022592030465602875,
0.05334310606122017,
0.04434490576386452,
-0.0006693080067634583,
-0.03525000810623169,
0.004116202238947153,
-0.022678317502141,
0.012975028716027737,
0.0415765605866909,
0.02439745143055916,
-0.030133454129099846,
-0.017171159386634827,
-0.014187220484018326,
0.026335934177041054,
-0.021603267639875412,
-0.0071966927498579025,
-0.007169164717197418,
-0.05720967426896095,
0.0008512101485393941,
-0.03482251614332199,
-0.00889456458389759,
-0.0018911274382844567,
0.0378827229142189,
-0.010928630828857422,
0.03979850560426712,
0.03324480727314949,
0.00019003638590220362,
0.07238283008337021,
0.042839303612709045,
-0.0017004109686240554,
0.054728131741285324,
-0.035463329404592514,
0.004549918230623007,
0.0005638048169203103,
-0.011192811653017998,
0.07978080958127975,
0.017696714028716087,
-0.027346616610884666,
-0.01833471655845642,
-0.0420316644012928,
0.05966823548078537,
0.08278914541006088,
0.08051826804876328,
-0.0470978207886219,
-0.07198432087898254,
0.025382474064826965,
-0.03672473132610321,
0.058952655643224716,
-0.02292652055621147,
-0.012194313108921051,
0.0535842590034008,
-0.046004194766283035,
-0.068097785115242,
-0.02647330053150654,
-0.028249291703104973,
0.022116398438811302,
-0.05187760293483734,
-0.07140535116195679,
-0.0025936122983694077,
0.03896310552954674,
-0.0014235201524570584,
0.0427071787416935,
-0.005525064188987017,
-0.0170779787003994,
0.06724393367767334,
0.02284156158566475,
0.09097649157047272,
-0.05297732353210449,
-0.01268304605036974,
-0.011644651181995869,
-0.009516258724033833,
-0.014067504554986954,
-0.036050502210855484,
-0.0023775058798491955,
0.02914493903517723,
0.024086158722639084,
-0.014057345688343048,
-0.04939870163798332,
-0.006699053570628166,
0.015144282020628452,
-0.04217500984668732,
0.001407061005011201,
-0.0269041508436203,
0.051706619560718536,
-0.03454478457570076,
-0.006235860288143158,
-0.01117307972162962,
0.034257348626852036,
0.058410633355379105,
-0.0679389089345932,
0.024201927706599236,
0.06038747355341911,
0.030667193233966827,
-0.02111523225903511,
0.057646553963422775,
-0.017557714134454727,
-0.05067364498972893,
0.08490733057260513,
0.01913168653845787,
0.024170469492673874,
-0.03135502710938454,
-0.005946412682533264,
0.004861019551753998,
0.10585200786590576,
-0.027385029941797256,
0.015348561108112335,
0.0061998795717954636,
-0.016857054084539413,
0.04897283762693405,
-0.02597464621067047,
-0.042671605944633484,
0.04765549674630165,
-0.06916075199842453,
-0.06585139036178589,
-0.01227006409317255,
-0.02078479900956154,
0.05015791952610016,
-0.058659106492996216,
-0.01697235368192196,
0.04276507720351219,
-0.06953275203704834,
-0.020189212635159492,
-0.06478998810052872,
0.008623790927231312,
-0.06574449688196182,
-0.010159325785934925,
-0.029313882812857628,
-0.033619120717048645,
0.02694314904510975,
0.03581170737743378,
-0.006517562549561262,
-0.04645385593175888,
-0.0006528642843477428,
-0.017391541972756386,
-0.06291228532791138,
-0.02074906788766384,
-0.045858241617679596,
-0.0677090585231781,
0.028763387352228165,
0.026910757645964622,
0.01974274218082428,
-0.029126320034265518,
0.027352983132004738,
-0.025984439998865128,
-0.01753794215619564,
-0.08334366977214813,
0.02957576885819435,
-0.01930316351354122,
-0.005751673597842455,
-0.008120468817651272,
0.03293278068304062,
-0.006221605930477381,
0.022153129801154137,
0.060015492141246796,
-0.027844903990626335,
-0.020208366215229034,
-0.0024965021293610334,
-0.03747182339429855,
-0.00297592394053936,
0.03493870049715042,
0.012894422747194767,
-0.04712994396686554,
0.03137875720858574,
-0.02669098600745201,
-0.02622167207300663,
-0.009448923170566559,
-0.04003431275486946,
-0.03553146868944168,
-0.05645361170172691,
-0.07939247786998749,
0.0203684214502573,
0.050675079226493835,
-0.003792779054492712,
-0.06698647141456604,
0.05202078819274902,
-0.07601946592330933,
0.004158578347414732,
0.03566683456301689,
-0.003053939202800393,
0.04434051364660263,
-0.051566194742918015,
0.05272717773914337,
-0.02952979877591133,
-0.034045156091451645,
0.05759572982788086,
-0.01728467456996441,
-0.012124921195209026,
0.005777444690465927,
-0.04271664470434189,
0.023796681314706802,
-0.04863417521119118,
-0.00016224449791479856,
0.02136283554136753,
-0.02752978913486004,
-0.0042097968980669975,
-0.06339482218027115,
0.012466161511838436,
0.0679178535938263,
0.03039264865219593,
0.019309699535369873,
-0.02160353772342205,
-0.06988068670034409,
-0.006926691625267267,
0.05724465101957321,
-0.06660887598991394,
-0.05544893816113472,
0.048043690621852875,
-0.05437606945633888,
0.025933463126420975,
-0.014404493384063244,
0.05397026240825653,
-0.008054033853113651,
-0.011137048713862896,
-0.05034435912966728,
0.0032899233046919107,
-0.016491612419486046,
0.04727428779006004,
0.012745920568704605,
-0.04152686893939972,
-0.03878908231854439,
-0.02647581696510315,
-0.05236644670367241,
-0.05554589629173279,
0.028295809403061867,
0.039494313299655914,
-0.042901139706373215,
-0.033109813928604126,
0.05894362926483154,
-0.06902656704187393,
-0.01732276752591133,
0.014813614077866077,
-0.028048932552337646,
-0.0017222355818375945,
0.027055013924837112,
0.07988469302654266,
-0.02489841915667057,
0.07120943814516068,
-0.030574442818760872,
0.044085439294576645,
-0.027130266651511192,
-0.01452531386166811,
-0.05447607859969139,
0.03229135274887085,
0.02655734308063984,
0.023006673902273178,
0.03846810758113861,
0.044274263083934784,
0.029330383986234665,
0.02299126796424389,
-0.05519156903028488,
-0.0038271520752459764,
-0.00935318786650896,
-0.027061888948082924,
-0.024133313447237015,
0.06235948204994202,
0.006707018706947565,
0.002697819611057639,
-0.04936959967017174,
0.0016197318909689784,
-0.008513296023011208,
-0.05060773342847824,
0.023455236107110977,
-0.018399136140942574,
-0.004752264358103275,
0.004265249706804752,
0.023199116811156273,
-0.007826275192201138,
0.00709159392863512,
0.0719299167394638,
0.010269347578287125,
-0.023516586050391197,
-0.008141769096255302,
-0.011098317801952362,
-0.03073820099234581,
0.005220490042120218,
-0.008144858293235302,
0.02057822234928608,
-0.040736354887485504,
-0.001826667576096952,
-0.020845739170908928,
-0.02205035462975502,
0.042560726404190063,
0.005559687968343496,
0.042614616453647614,
0.036681920289993286,
-0.003181754844263196,
0.019154639914631844,
0.014986678957939148,
0.05115950107574463,
0.004140953067690134,
0.018863748759031296,
-0.06694363802671432,
-0.02329712174832821,
0.06960088759660721,
-0.07438486069440842,
0.017659828066825867,
-0.002194915898144245,
-0.020950671285390854,
0.0520118772983551,
0.022978555411100388,
0.036260031163692474,
-0.042764391750097275,
-0.013472557067871094,
0.02104504406452179,
0.010219897143542767,
0.019221846014261246,
0.08776336163282394,
-0.00008187988714780658,
0.011364036239683628,
0.02984171360731125,
-0.01153782568871975,
-0.030449021607637405,
-0.017214374616742134,
0.019574135541915894,
0.02705417387187481,
-0.013109677471220493,
-0.04582333192229271,
0.024136727675795555,
-0.09157905727624893,
0.034913185983896255,
-0.0007556725176982582,
0.045755308121442795,
-0.009670602157711983,
0.013550844974815845,
-0.00968624372035265,
-0.01825757697224617,
0.021606940776109695,
0.11562054604291916,
0.01083655096590519,
0.009455060586333275,
-0.03661061078310013,
0.043492432683706284,
-0.0036783867981284857,
-0.03454573079943657,
-0.003642688039690256,
-0.034935690462589264,
-0.0370783656835556,
0.021733520552515984,
0.009299618192017078,
0.04252597689628601,
0.012710721231997013,
-0.0011207059724256396,
-0.031002236530184746,
-0.002982709091156721,
0.01695830561220646,
-0.026267055422067642,
0.009222190827131271,
-0.02386774867773056,
0.04482337832450867,
0.04819336533546448,
-0.041640158742666245,
-0.0498746819794178,
-0.01838761754333973,
-0.012240919284522533,
0.03565632551908493,
-0.05759521946310997,
-0.04855305701494217,
0.05886361375451088,
0.011266286484897137,
-0.008420614525675774,
-0.025633936747908592,
0.012131408788263798,
0.016462083905935287,
0.04257652908563614,
0.06498631089925766,
0.017049847170710564,
-0.07073107361793518,
0.024663401767611504,
0.092068150639534,
0.037380483001470566,
-0.0006183655932545662,
0.02300114929676056,
-0.0011142697185277939,
0.03670451045036316,
-0.030287528410553932,
0.06937367469072342,
0.008070935495197773,
-0.012244810350239277,
0.040999505668878555,
0.004678139928728342,
-0.015639442950487137,
0.06273091584444046,
-0.013159369118511677,
0.03276611119508743,
0.04219295084476471,
0.020013174042105675,
0.011860206723213196,
-0.0031270100735127926,
0.05654910206794739,
-0.027561621740460396,
0.0035709645599126816,
-0.0384792722761631,
0.008572708815336227,
0.011230891570448875,
0.027469728142023087,
-0.06461909413337708,
0.006101533304899931,
-0.014933515340089798,
-0.016436994075775146,
-0.059168193489313126,
0.07067432254552841,
-0.04837552458047867,
0.026194144040346146,
0.007052020635455847,
0.029176535084843636,
0.009346545673906803,
-0.01878463663160801,
-0.04245486482977867,
0.037456367164850235,
-0.04578671604394913,
-0.02865283563733101,
-0.07964566349983215,
-0.008975477889180183,
0.030785303562879562,
-0.011395727284252644,
-0.05795099958777428,
-0.020210154354572296,
0.057745013386011124,
0.002198456320911646,
0.0567765086889267,
0.01634061709046364,
0.0032969412859529257,
-0.06357903778553009,
-0.07786854356527328,
-0.007780850864946842,
0.02452172338962555,
0.06044088304042816,
0.028483282774686813,
-0.01357321161776781,
-0.024306900799274445,
0.006117168813943863,
-0.011905492283403873,
-0.03243056312203407,
-0.01567336730659008,
-0.029161851853132248,
-0.020910529419779778,
-0.025715835392475128,
-0.020277438685297966,
0.04340902343392372,
-0.00871451199054718,
-0.007213039789348841,
-0.017638204619288445,
0.005695102270692587,
-0.044749122112989426,
0.002838353393599391,
0.013869494199752808,
0.014246711507439613,
0.03203751891851425,
-0.006220764480531216,
0.013659481890499592,
0.024106649681925774,
-0.03597307205200195,
0.003527785884216428,
0.03072035126388073,
0.02521400898694992,
-0.047586552798748016,
0.016942165791988373,
0.0378388836979866,
-0.015752732753753662,
0.0035405626986175776,
-0.03239062428474426,
-0.0030799908563494682,
-0.030554872006177902,
0.018615102395415306,
-0.017639169469475746,
0.018466085195541382,
0.03417946398258209,
-0.046348314732313156,
0.04601144790649414,
-0.009272768162190914,
-0.034485794603824615,
-0.010584866628050804,
-0.005786211229860783,
0.001285242848098278,
-0.07640030980110168,
0.024369731545448303,
-0.008695212192833424,
0.0029822385404258966,
0.013057173229753971,
-0.011686551384627819,
-0.031284574419260025,
0.061284102499485016,
0.051422469317913055,
-0.03589373081922531,
-0.005550103262066841,
0.023087944835424423,
0.0032979559618979692,
-0.016291271895170212,
0.027581768110394478,
0.008392175659537315,
0.046059176325798035,
0.034874044358730316,
-0.03189065679907799,
-0.05483867600560188,
-0.0023104348219931126,
0.01324404589831829,
-0.01961161009967327,
-0.02413243241608143,
-0.0039005985017865896,
0.02413010783493519,
0.002314991783350706,
-0.017899522557854652,
-0.0031437287107110023,
-0.003706802846863866,
0.005547661334276199,
0.03496895357966423,
0.01800595410168171,
-0.007090468425303698,
0.05507180094718933,
0.000814208120573312,
-0.09051571041345596,
0.0024565402418375015,
-0.024273881688714027,
0.02143213152885437,
-0.0274269450455904,
-0.03323623165488243,
-0.010950216092169285,
-0.02599315531551838,
0.0030979507137089968,
-0.07024671137332916,
0.0445602685213089,
-0.054069750010967255,
-0.009710758924484253,
0.007794230245053768,
0.0033168902155011892,
0.011240687221288681,
-0.03250811621546745,
-0.041977882385253906,
-0.015649011358618736,
0.00926008727401495,
0.02527668885886669,
-0.018554983660578728,
-0.009244243614375591,
0.0014548356411978602,
-0.01824660785496235,
-0.03798140212893486,
-0.036489032208919525,
-0.09014894813299179,
-0.0057000755332410336,
-0.00741688534617424,
0.011392253451049328,
-0.017546867951750755,
0.04103877767920494,
-0.03305164724588394,
0.0006837599794380367,
0.03586544841527939,
-0.055289607495069504,
0.0024930026847869158,
0.044346295297145844,
-0.02475825697183609,
0.0015618111938238144,
0.01379393320530653,
0.014528307132422924,
-0.024563049897551537,
0.002388780238106847,
0.0013733101077377796,
0.036767419427633286,
-0.013108927756547928,
0.0327434167265892,
-0.029778311029076576,
-0.001060520182363689,
0.05143837630748749,
-0.07719625532627106,
0.02981606312096119,
-0.02552633546292782,
0.030144814401865005,
-0.01329269353300333,
0.037470199167728424,
0.0047894436866045,
-0.06608998775482178,
0.08216037601232529,
0.004911880008876324,
-0.0291706845164299,
-0.016394643113017082,
-0.03743206709623337,
-0.0402558296918869,
0.08362223953008652,
0.03677442669868469,
0.028049014508724213,
0.02364811860024929,
-0.0034545084927231073,
0.0218762569129467,
0.024860311299562454,
-0.03823240101337433,
-0.04084012657403946,
-0.014274245128035545,
0.044390592724084854,
-0.040130969136953354,
-0.02294800616800785,
0.04437867924571037,
-0.04694171994924545,
-0.01116111222654581,
0.028554892167448997,
-0.047925010323524475,
-0.01911569945514202,
-0.0063589951023459435,
0.04785998538136482,
-0.0324268564581871,
0.009868970140814781,
0.02092224918305874,
0.00126188388094306,
0.0404914952814579,
-0.05539663881063461,
-0.019759340211749077,
0.013616264797747135,
-0.01262863352894783,
-0.03146239370107651,
-0.04824882000684738,
0.02107023075222969,
-0.04337592050433159,
-0.013354059308767319,
-0.04546500742435455,
0.04675321280956268,
0.02022865042090416,
0.005895950831472874,
0.039400212466716766,
0.03456646203994751,
0.02581840008497238,
0.022620758041739464,
-0.031397171318531036,
-0.02674941159784794,
-0.03604545444250107,
-0.0719454288482666,
-0.006879071239382029,
0.020053556188941002,
-0.0020983656868338585,
0.01891716569662094,
0.010140743106603622,
0.0752662792801857,
0.08753296732902527,
-0.002854498801752925,
-0.013512765988707542,
-0.022394180297851562,
-0.030282942578196526,
0.05540044978260994,
0.01985293999314308,
-0.02279427833855152,
0.021295808255672455,
-0.0177229605615139,
0.05433041602373123,
0.036383889615535736,
-0.037911295890808105,
-0.03540679067373276,
-0.057847511023283005,
-0.019688434898853302,
-0.005244716070592403,
0.038107894361019135,
0.007517698686569929,
-0.005168442148715258,
-0.02038527838885784,
-0.0003792621719185263,
-0.022639881819486618,
0.01256050355732441,
0.02006092667579651,
0.01798708364367485,
0.03129127621650696,
-0.002302127657458186,
0.008520277217030525,
0.001657828688621521,
-0.03168870881199837,
-0.004636901896446943,
-0.026983093470335007,
-0.03693876788020134,
0.005459698382765055,
0.04689004644751549,
-0.0013766067568212748,
-0.04042981564998627,
0.006404200568795204,
0.04738476127386093,
0.008049432188272476,
0.0010996810160577297,
-0.03191881626844406,
-0.07000606507062912,
-0.0487564280629158,
0.041522569954395294,
-0.032291773706674576,
0.03948257863521576,
-0.01863224431872368,
0.040331028401851654,
0.03210955858230591,
-0.04347526282072067,
-0.015102294273674488,
0.01002878975123167,
-0.024597756564617157,
-0.03135184198617935,
-0.031721390783786774,
-0.02313903346657753,
-0.005160145461559296,
-0.028692051768302917,
0.07408368587493896,
-0.03143637627363205,
-0.033212583512067795,
0.023390300571918488,
-0.049920398741960526,
0.06929066777229309,
0.0008421820239163935,
0.03397306799888611,
0.05331428721547127,
-0.01259789988398552,
-0.02271255850791931,
0.02162177488207817,
-0.011906977742910385,
0.028733080253005028,
-0.029244085773825645,
0.009125635959208012,
0.02866375260055065,
-0.019469786435365677,
-0.02085801772773266,
0.000339950667694211,
-0.018908251076936722,
0.03724277392029762
] |
<p>Example of pendulum is inertial frame of reference or non inertial frame of reference?
because if pendulum starts moving its continuously moves without changing there period of time but is changes its velocity with there motion... </p> | g1223 | [
0.06513020396232605,
-0.029368028044700623,
0.01898849941790104,
-0.031535323709249496,
0.05239737778902054,
0.003200992476195097,
0.06064353883266449,
-0.025675320997834206,
0.010040121152997017,
-0.017368044704198837,
-0.02795892022550106,
-0.005699370987713337,
-0.03229258954524994,
-0.00957073736935854,
-0.015368963591754436,
-0.031949516385793686,
0.05176427587866783,
0.013593905605375767,
0.034947074949741364,
0.02815062180161476,
0.04548941180109978,
0.041616544127464294,
-0.029224224388599396,
-0.012183851562440395,
-0.04814442992210388,
0.02380920574069023,
0.01816108077764511,
-0.04426448419690132,
0.010592382401227951,
-0.006424375344067812,
0.010624518617987633,
-0.014040203765034676,
-0.005010467488318682,
-0.012005237862467766,
0.01148441806435585,
-0.0161212719976902,
0.04928974807262421,
0.018522050231695175,
0.043261442333459854,
0.011049789376556873,
0.02821575105190277,
0.013673871755599976,
0.003248182125389576,
0.021596968173980713,
0.027083955705165863,
0.02099565789103508,
0.07524929940700531,
0.0010254767257720232,
-0.01814866065979004,
-0.04721175879240036,
-0.0220734104514122,
0.05882902070879936,
-0.011836688965559006,
0.015382228419184685,
-0.014546996913850307,
0.03448329493403435,
0.08381384611129761,
0.018213078379631042,
0.015903588384389877,
0.039694491773843765,
0.01074343454092741,
-0.030263958498835564,
0.04768815636634827,
0.015297329984605312,
0.02332933619618416,
0.0047662388533353806,
-0.031478289514780045,
-0.04009026288986206,
-0.024681473150849342,
0.0031992143485695124,
0.008646542206406593,
-0.040104616433382034,
-0.03717292100191116,
0.019832953810691833,
-0.05112346261739731,
0.011520682834088802,
0.018519246950745583,
-0.022753596305847168,
-0.026886023581027985,
-0.0077273244969546795,
-0.048259928822517395,
0.03711928054690361,
0.02150535024702549,
0.02937842346727848,
0.14167185127735138,
0.00041235992102883756,
-0.012205248698592186,
0.03052954189479351,
-0.002358238212764263,
-0.014100641943514347,
-0.02366235852241516,
-0.061041925102472305,
0.06536513566970825,
0.02034725807607174,
-0.013415548950433731,
-0.01008281297981739,
-0.10274717956781387,
0.07643353193998337,
0.046102818101644516,
0.0575355589389801,
-0.03489963710308075,
-0.04302363097667694,
-0.012430350296199322,
-0.05620100721716881,
0.053723014891147614,
-0.02469637244939804,
0.027424225583672523,
-0.03275056183338165,
-0.041445523500442505,
-0.08413523435592651,
0.010873089544475079,
-0.0136730270460248,
0.009438867680728436,
0.008115221746265888,
-0.05822967365384102,
0.009456878527998924,
0.08002058416604996,
-0.008310257457196712,
0.05489898845553398,
0.021442748606204987,
0.020883871242403984,
-0.009509352035820484,
0.006418090313673019,
0.06656187027692795,
-0.027215585112571716,
-0.028444403782486916,
-0.004564689006656408,
0.0021507202181965113,
0.0025684568099677563,
-0.07276678085327148,
0.03701703995466232,
0.044045303016901016,
-0.01617383025586605,
0.013268728740513325,
0.019247639924287796,
0.0020600478164851665,
0.07813579589128494,
-0.058267705142498016,
-0.011234845034778118,
0.04760408774018288,
0.054727233946323395,
-0.0005334954475983977,
0.050185102969408035,
-0.04352344200015068,
-0.00579226715490222,
0.051054321229457855,
0.03860188275575638,
-0.0191077571362257,
0.027700580656528473,
0.07122998684644699,
-0.021874375641345978,
0.04924938455224037,
-0.021645156666636467,
-0.06075247377157211,
0.05931675434112549,
-0.04825888201594353,
-0.007444287650287151,
0.037909090518951416,
0.0351303406059742,
-0.010826717130839825,
0.046931713819503784,
-0.011902015656232834,
0.02287866547703743,
-0.01729636825621128,
-0.06633161753416061,
-0.011678439565002918,
-0.007578630931675434,
0.003155532293021679,
-0.01299443282186985,
-0.061006274074316025,
-0.08069320768117905,
0.003187449648976326,
-0.007542754523456097,
0.05175161734223366,
0.05793946981430054,
0.023869328200817108,
0.026529790833592415,
-0.04782966896891594,
-0.006558162625879049,
-0.057210687547922134,
0.025960460305213928,
-0.015867596492171288,
-0.022565165534615517,
-0.039580196142196655,
-0.06796442717313766,
0.09712554514408112,
0.04168493673205376,
0.02586759440600872,
-0.06052142009139061,
-0.031068991869688034,
0.011713520623743534,
-0.08188565075397491,
-0.02355382964015007,
-0.011846796609461308,
-0.03457753732800484,
0.0014017500216141343,
-0.029074745252728462,
-0.01596636138856411,
-0.05264519900083542,
0.003823576495051384,
0.03651006892323494,
-0.00691426545381546,
0.016135677695274353,
0.030937302857637405,
-0.023180436342954636,
-0.05618941783905029,
0.02523491345345974,
-0.05422412231564522,
0.008183982223272324,
-0.0006797172827646136,
0.04170360043644905,
0.013527394272387028,
-0.013776827603578568,
0.07598421722650528,
0.005942476447671652,
0.0020228519570082426,
0.03766520321369171,
0.0014292702544480562,
-0.021530592814087868,
0.0011480096727609634,
-0.004834992811083794,
0.008264643140137196,
-0.008697428740561008,
-0.026668962091207504,
0.014058359898626804,
-0.05590653792023659,
-0.0478438176214695,
-0.014763794839382172,
0.05992292985320091,
0.049972787499427795,
-0.04932240769267082,
-0.04239024221897125,
-0.04727676883339882,
-0.00690981512889266,
0.04707825556397438,
0.005680933594703674,
0.04079221561551094,
-0.015164317563176155,
0.0005917761009186506,
-0.03383994475007057,
0.023243265226483345,
0.00950759556144476,
0.012039675377309322,
-0.05030545964837074,
-0.02003639005124569,
-0.08438640832901001,
0.010904479771852493,
0.01552586443722248,
0.006248438265174627,
0.033226270228624344,
-0.004130188375711441,
-0.017543837428092957,
-0.06879211217164993,
0.03906656801700592,
0.015134196728467941,
0.008012792095541954,
-0.010996588505804539,
-0.009278022684156895,
-0.05066922679543495,
-0.00708807772025466,
0.026410330086946487,
-0.08985171467065811,
0.009208910167217255,
0.013168668374419212,
-0.013743855990469456,
-0.010180406272411346,
0.040519505739212036,
0.04970284551382065,
-0.049144670367240906,
-0.003914028871804476,
0.018382471054792404,
0.035597171634435654,
0.014846626669168472,
0.03267858922481537,
-0.026631882414221764,
0.022921046242117882,
0.02854335680603981,
-0.05091195926070213,
0.0013720494462177157,
-0.07785159349441528,
0.005934638902544975,
0.0179961659014225,
-0.013880875892937183,
0.058555420488119125,
0.0664864033460617,
-0.042637571692466736,
-0.019032752141356468,
-0.008099745959043503,
-0.07645254582166672,
-0.0192403644323349,
-0.02205202542245388,
0.044479869306087494,
-0.017834801226854324,
0.022895004600286484,
-0.0502387210726738,
0.04460573196411133,
-0.006485189311206341,
-0.033433783799409866,
0.014197168871760368,
0.03341513127088547,
0.017239738255739212,
0.020730219781398773,
0.0038264303002506495,
0.05356337130069733,
0.07635843753814697,
-0.006566853262484074,
0.011998402886092663,
0.013582119718194008,
0.016855591908097267,
-0.026689350605010986,
0.005489459726959467,
0.030730577185750008,
-0.00851755402982235,
0.037177544087171555,
-0.08188574016094208,
0.02680380269885063,
0.0019213819177821279,
0.007304562255740166,
-0.012569630518555641,
0.015986301004886627,
-0.003983627539128065,
-0.05114533752202988,
0.0176443662494421,
-0.02807549573481083,
0.005022512748837471,
0.05991814658045769,
0.021009033545851707,
-0.020282715559005737,
-0.032130468636751175,
-0.06333932280540466,
-0.014296349138021469,
0.00018558677402324975,
-0.015148329548537731,
0.004754605703055859,
0.011478542350232601,
-0.04647934064269066,
-0.019160913303494453,
0.005551357287913561,
0.0540294386446476,
0.030986333265900612,
0.0418391078710556,
0.031612738966941833,
-0.04000747576355934,
-0.008646782487630844,
0.0025932714343070984,
0.07767864316701889,
0.0554727241396904,
-0.010415738448500633,
-0.007762607652693987,
0.012522530741989613,
0.05976729840040207,
-0.0011788924457505345,
0.0004989776061847806,
-0.027549749240279198,
-0.013760803267359734,
-0.0010083098895847797,
0.03451471030712128,
0.04547657445073128,
-0.080637626349926,
-0.030514225363731384,
0.004865286406129599,
-0.007768912240862846,
0.01559788454324007,
0.08271355926990509,
0.028452789410948753,
0.03464125096797943,
0.02105194516479969,
0.007840019650757313,
0.012862549163401127,
-0.024941658601164818,
-0.015392007306218147,
-0.0339873805642128,
0.023090295493602753,
-0.041329629719257355,
0.03290421888232231,
-0.044404346495866776,
0.012463000603020191,
0.008879106491804123,
-0.02625505067408085,
-0.021028965711593628,
0.002483729738742113,
-0.06395649164915085,
-0.009048637934029102,
-0.01118086464703083,
0.018857533112168312,
0.01562853902578354,
0.04123428836464882,
-0.0016046008095145226,
0.029110165312886238,
-0.08677774667739868,
0.036804504692554474,
0.04048028588294983,
0.005166622344404459,
-0.034529197961091995,
0.05695745721459389,
-0.01986544020473957,
0.05014617368578911,
0.013843247666954994,
0.030840547755360603,
-0.0030951129738241434,
-0.00479555269703269,
0.026399405673146248,
-0.059854332357645035,
0.04723867028951645,
0.015091252513229847,
0.06061936169862747,
0.024043070152401924,
-0.06294386833906174,
-0.029602715745568275,
0.028605682775378227,
-0.03086920455098152,
0.0182818416506052,
-0.019059140235185623,
-0.05297555401921272,
-0.007437631022185087,
0.017987197265028954,
0.029973603785037994,
-0.029968753457069397,
0.013116185553371906,
0.030762214213609695,
-0.003294094232842326,
0.09214980900287628,
0.03025367483496666,
0.056695159524679184,
0.021863337606191635,
0.012034709565341473,
0.034284185618162155,
0.03366324305534363,
-0.0011663933983072639,
-0.03071671724319458,
0.004062882158905268,
0.025661222636699677,
0.049482837319374084,
0.004588198382407427,
-0.023654108867049217,
0.031725287437438965,
-0.003913248889148235,
-0.0018534284317865968,
0.010957243852317333,
-0.04065846651792526,
0.02517191879451275,
0.08239422738552094,
-0.056990429759025574,
-0.005253204144537449,
-0.01754353754222393,
0.05283694341778755,
0.020849252119660378,
-0.049723170697689056,
0.012765566818416119,
-0.019834743812680244,
-0.06586796045303345,
0.049846943467855453,
-0.042846065014600754,
-0.007003762759268284,
-0.023710865527391434,
-0.061396948993206024,
-0.043066538870334625,
0.005446008872240782,
-0.06404870748519897,
0.04690941795706749,
-0.03855883702635765,
-0.038002487272024155,
-0.06064974144101143,
0.023793097585439682,
-0.01550829503685236,
0.00004675700984080322,
-0.00593534205108881,
-0.07522893697023392,
-0.038830917328596115,
-0.004049449693411589,
0.010894937440752983,
-0.03089757077395916,
-0.05904436483979225,
0.011938788928091526,
0.036405984312295914,
-0.012947297655045986,
0.08903816342353821,
0.0056486576795578,
0.02936054952442646,
-0.039154473692178726,
-0.025079524144530296,
-0.019484365358948708,
0.018306707963347435,
0.00014203682076185942,
0.017139848321676254,
-0.0295669287443161,
-0.015851953998208046,
-0.009419100359082222,
0.025437114760279655,
0.006086038425564766,
-0.00009968921222025529,
0.038469791412353516,
0.023086637258529663,
-0.0559513196349144,
-0.03278568387031555,
-0.014047852717339993,
-0.01772936061024666,
0.010787349194288254,
-0.007981794886291027,
-0.010310826823115349,
-0.055801160633563995,
0.03911450132727623,
0.0018165827495977283,
-0.03840995207428932,
-0.004748847335577011,
0.050444573163986206,
0.03783028572797775,
0.056447017937898636,
-0.025320636108517647,
0.07470715790987015,
0.02637624740600586,
0.0023496481589972973,
-0.043637465685606,
0.021779919043183327,
-0.007749522570520639,
-0.022871199995279312,
0.04245316982269287,
-0.04308925196528435,
-0.019498273730278015,
0.010901427827775478,
0.036252398043870926,
-0.033128801733255386,
0.03043220192193985,
-0.005420770030468702,
-0.007092408835887909,
0.03995346277952194,
0.01067326683551073,
-0.006964752916246653,
-0.02169458381831646,
0.0598318912088871,
0.013808243907988071,
-0.03114880993962288,
0.05099531263113022,
-0.01567251607775688,
-0.020648352801799774,
0.024480754509568214,
-0.013433041051030159,
0.018174415454268456,
0.015398154966533184,
0.026726718991994858,
-0.06624642759561539,
-0.03274807706475258,
0.061669398099184036,
0.011241445317864418,
0.011030678637325764,
0.011623593047261238,
0.006502170115709305,
0.014363836497068405,
-0.010385609231889248,
-0.04595249891281128,
-0.013630076311528683,
0.0559842474758625,
-0.033705536276102066,
-0.039776116609573364,
-0.051329780369997025,
0.01677451841533184,
0.04761257767677307,
-0.011513885110616684,
-0.06767413765192032,
-0.028780890628695488,
0.007849563844501972,
-0.005969544406980276,
0.07352741062641144,
-0.03920945152640343,
-0.036219388246536255,
-0.012384563684463501,
-0.04883513227105141,
-0.07455729693174362,
0.010426006279885769,
0.004272765479981899,
-0.04836482182145119,
-0.03133513405919075,
-0.106831394135952,
-0.018632998690009117,
0.00008156658441293985,
0.021927576512098312,
-0.07245588302612305,
-0.019773371517658234,
-0.027709607034921646,
-0.04419560730457306,
-0.009473301470279694,
0.007704727817326784,
-0.009529792703688145,
-0.02267221361398697,
-0.045498091727495193,
0.02775956131517887,
0.013786476105451584,
0.039569925516843796,
-0.03246879205107689,
0.05895432084798813,
-0.05283273383975029,
0.009569678455591202,
-0.05601068586111069,
-0.04847857356071472,
-0.0011542007559910417,
0.037437424063682556,
-0.06553906202316284,
0.010773865506052971,
0.03558427095413208,
-0.0006962089682929218,
-0.020479736849665642,
-0.028840072453022003,
0.02887653186917305,
-0.01452934555709362,
-0.028389299288392067,
0.059508439153432846,
0.0483490489423275,
-0.009602893143892288,
0.0345255546271801,
0.04149094596505165,
0.018539151176810265,
-0.013180086389183998,
0.08115538209676743,
-0.0045104855671525,
-0.05417643114924431,
-0.004842786118388176,
-0.03756128251552582,
0.0065101878717541695,
-0.009314844384789467,
-0.02557678334414959,
-0.009137501940131187,
-0.06988980621099472,
0.029561147093772888,
0.024510987102985382,
0.04004928842186928,
0.09077153354883194,
-0.10146593302488327,
0.03267686814069748,
0.01872122287750244,
-0.06728093326091766,
-0.038987547159194946,
0.00852054450660944,
-0.05894310772418976,
0.0571097657084465,
-0.031221088021993637,
0.03687190264463425,
-0.015203545801341534,
0.02030758187174797,
0.05299560725688934,
0.010268048383295536,
0.020826049149036407,
0.0063042426481842995,
0.0033994056284427643,
-0.012308604083955288,
-0.0010368794901296496,
-0.026621054857969284,
0.03819723054766655,
-0.022676534950733185,
-0.04065410792827606,
0.030594000592827797,
-0.04486767202615738,
-0.017091937363147736,
-0.011026240885257721,
0.05477441847324371,
-0.04477214440703392,
0.058769285678863525,
0.055860042572021484,
-0.00578024797141552,
-0.02184407040476799,
-0.030377255752682686,
-0.022571928799152374,
-0.008306710049510002,
-0.025220410898327827,
0.008250275626778603,
-0.014704321511089802,
0.03545951470732689,
-0.03904353454709053,
-0.058747466653585434,
-0.05295877903699875,
0.02593318186700344,
0.013831309042870998,
-0.008145401254296303,
0.036810580641031265,
0.018262213096022606,
-0.025432495400309563,
0.050250254571437836,
0.04075149819254875,
-0.04949827492237091,
-0.02795085310935974,
-0.0542614683508873,
0.01782696694135666,
0.04201732575893402,
0.05736207589507103,
-0.011364513076841831,
-0.028788933530449867,
0.04696310684084892,
0.04097849875688553,
-0.02749846689403057,
0.008690179325640202,
-0.04075445234775543,
-0.007600156124681234,
0.10385754704475403,
0.014521315693855286,
-0.04686868190765381,
-0.036959342658519745,
-0.017116347327828407,
0.024240439757704735,
-0.022655826061964035,
-0.02262715995311737,
0.0000447192469437141,
-0.02184484899044037,
-0.0217201616615057,
-0.018496079370379448,
0.01987021416425705,
0.02479013055562973,
0.013205735012888908,
0.026973240077495575,
0.00917980819940567,
-0.07213670760393143,
0.04079275578260422,
0.003775662975385785,
0.022154144942760468,
0.03581632301211357,
0.010761208832263947,
-0.013678919523954391,
0.038830023258924484,
0.007974114269018173,
0.014956574887037277,
0.029731685295701027,
-0.01531736645847559,
-0.0032239092979580164,
0.016164932399988174,
-0.009266810491681099,
-0.040466345846652985,
-0.054726772010326385,
0.02047606371343136,
-0.004850044380873442,
-0.017551647499203682,
-0.05183691158890724,
-0.007850081659853458,
-0.03277051821351051,
0.031653713434934616,
-0.03889589011669159,
0.038877811282873154,
-0.0467359758913517,
0.02721104770898819,
0.008683882653713226,
-0.018063511699438095,
0.0251512099057436,
0.023498838767409325,
0.00870449934154749,
-0.05027741193771362,
-0.012593720108270645,
-0.015448822639882565,
0.01796160824596882,
0.010555571876466274,
0.032960195094347,
-0.029895002022385597,
0.015032575465738773,
0.01432138029485941,
-0.02329305000603199,
0.0033753258176147938,
-0.0023316561710089445,
0.0355798602104187,
0.010088657028973103,
0.001268279505893588,
-0.021471135318279266,
-0.013813347555696964,
-0.011969409883022308,
0.014051687903702259,
-0.013300653547048569,
-0.009520973078906536,
0.03596219792962074,
-0.03270415961742401,
-0.01042239274829626,
-0.00746105145663023,
-0.07390637695789337,
0.01218430232256651
] |
<p>Let $\rho = \begin{bmatrix}\ 1&0 \\ 0&0 \end{bmatrix}$, $\rho' = \begin{bmatrix}\ 0&0 \\ 0&1 \end{bmatrix}$, $\rho'' = \dfrac{1}{2}\begin{bmatrix}\ 1&1 \\ 1&1 \end{bmatrix}$ (all density operators).</p>
<p>Consider a physical operation $\phi$ such that $\phi(\rho) = \rho$, $\phi(\rho') = \rho'$, $\phi(\rho'') = \dfrac{1}{5}\begin{bmatrix}\ 4&2 \\ 2&1 \end{bmatrix}$.</p>
<p>Why is $\phi$ not a realisable physical operation? It certainly preserves trace and positivity...</p> | g1224 | [
0.042162004858255386,
0.010625390335917473,
0.009595240466296673,
0.0005788209964521229,
0.07721426337957382,
-0.03554920852184296,
0.04711681604385376,
0.018598614260554314,
-0.058604903519153595,
0.011810882948338985,
-0.002020678948611021,
0.01268377248197794,
-0.023729780688881874,
-0.01024662982672453,
-0.022151771932840347,
0.00939132459461689,
-0.031174873933196068,
-0.015232199802994728,
-0.001663861214183271,
0.018339361995458603,
-0.11193057894706726,
0.029387816786766052,
0.05790434405207634,
-0.024208052083849907,
0.05387355014681816,
-0.052945297211408615,
0.07720425724983215,
-0.026757806539535522,
-0.045096565037965775,
-0.045372042804956436,
0.05674808472394943,
0.011028624139726162,
0.05378080904483795,
-0.027622930705547333,
-0.04959825053811073,
-0.011778220534324646,
0.04705538600683212,
-0.0017104133730754256,
0.02613019198179245,
-0.006262341979891062,
-0.00517188711091876,
-0.03487776219844818,
0.010746722109615803,
-0.021761339157819748,
-0.04863864928483963,
0.04118496552109718,
-0.041988883167505264,
-0.022929713129997253,
-0.01141590066254139,
-0.022594785317778587,
-0.02130841091275215,
0.07252226769924164,
-0.006139299366623163,
0.0036697036121040583,
-0.0014442966785281897,
0.013963330537080765,
0.046239640563726425,
-0.003912217449396849,
-0.007888667285442352,
-0.03311144560575485,
-0.001342884497717023,
-0.012117494828999043,
0.03823568671941757,
0.014449543319642544,
-0.010315686464309692,
-0.04544619098305702,
0.006000959314405918,
-0.03847523033618927,
-0.024233167991042137,
0.02789752185344696,
-0.031079238280653954,
-0.036244869232177734,
0.04761829227209091,
0.01608908362686634,
0.029790358617901802,
0.0021916674450039864,
-0.007668517529964447,
-0.005590388085693121,
0.00025835211272351444,
-0.021607154980301857,
-0.051327895373106,
-0.03837445750832558,
0.027395499870181084,
0.09454439580440521,
0.011907268315553665,
0.04260214418172836,
0.027704361826181412,
-0.08133216947317123,
0.013223813846707344,
0.0269311610609293,
0.004011805169284344,
-0.007208088878542185,
0.03314783051609993,
0.08506916463375092,
-0.015282265841960907,
-0.0382193885743618,
-0.021334119141101837,
0.031549159437417984,
-0.005113425198942423,
-0.008841760456562042,
0.033926039934158325,
0.005772818345576525,
0.007468074560165405,
-0.002935520838946104,
0.007419211324304342,
-0.02284717746078968,
0.06816268712282181,
0.04118257015943527,
-0.005486895330250263,
0.036860860884189606,
0.034407228231430054,
0.010188042186200619,
-0.011514783836901188,
-0.04465920478105545,
0.0469515323638916,
0.0007785183843225241,
0.008224550634622574,
-0.0675332322716713,
-0.06259651482105255,
0.08396594971418381,
0.04818165674805641,
-0.027434468269348145,
0.07831329852342606,
-0.0009350953623652458,
-0.0268040020018816,
-0.028724009171128273,
-0.0225115604698658,
0.02034415304660797,
0.041620656847953796,
-0.04741000756621361,
0.045493610203266144,
0.005124665796756744,
-0.004027101211249828,
0.05812862515449524,
-0.036199502646923065,
-0.018831485882401466,
-0.03638593479990959,
0.03504149243235588,
0.027914488688111305,
-0.06051618233323097,
-0.018624503165483475,
0.0058939456939697266,
-0.04410947859287262,
-0.0002747644030023366,
0.011937057599425316,
0.018548356369137764,
0.01762804202735424,
-0.013956593349575996,
0.03795716166496277,
0.047463010996580124,
-0.02565908618271351,
0.06692732870578766,
-0.025826632976531982,
0.006338398437947035,
0.032786209136247635,
0.01034670788794756,
0.07253044098615646,
-0.007718981709331274,
-0.01899956353008747,
0.04697762057185173,
0.06767076998949051,
0.0076681459322571754,
0.020056331530213356,
0.019390342757105827,
0.0025596357882022858,
-0.058943748474121094,
0.006392172537744045,
-0.10638251900672913,
-0.0027411654591560364,
-0.0811370462179184,
-0.01808018423616886,
0.03291063755750656,
0.014131028205156326,
0.04522474855184555,
-0.018853839486837387,
-0.030042137950658798,
-0.0031724635045975447,
0.029309337958693504,
0.08073589950799942,
0.009099526330828667,
-0.05515747517347336,
-0.012896234169602394,
0.024692511186003685,
-0.018016597256064415,
0.024759577587246895,
-0.055054884403944016,
-0.013514990918338299,
0.0057066953741014,
-0.08470679819583893,
-0.011203068308532238,
0.009616384282708168,
0.03099258989095688,
-0.03364161029458046,
0.05667303875088692,
-0.005852879490703344,
-0.07450710237026215,
0.0064339404925704,
0.0055715483613312244,
0.010769420303404331,
0.0007056343602016568,
0.017063360661268234,
-0.02385040931403637,
0.056056633591651917,
0.0018211741698905826,
0.038568057119846344,
-0.01520584523677826,
-0.00983328465372324,
-0.041086480021476746,
-0.03911576047539711,
0.019679037854075432,
0.022491471841931343,
-0.057159122079610825,
0.044421881437301636,
-0.03427742421627045,
0.0025436219293624163,
-0.04967941343784332,
-0.0006145540392026305,
0.01173589937388897,
-0.02954181283712387,
-0.02305820770561695,
-0.10096064954996109,
-0.023155653849244118,
0.03175370395183563,
0.03624303638935089,
-0.08188214153051376,
0.013803927227854729,
0.019825343042612076,
-0.01555197685956955,
-0.02343856170773506,
-0.04136083647608757,
-0.013310343958437443,
0.03911346569657326,
-0.005983126815408468,
0.012089037336409092,
-0.012155267409980297,
0.04002942144870758,
0.0013390725944191217,
-0.000046326931624207646,
0.01271381787955761,
0.03090514987707138,
-0.00022515231103170663,
-0.002926329616457224,
-0.02010040357708931,
0.030899927020072937,
0.016270836815238,
-0.0507633313536644,
0.021894006058573723,
0.047280699014663696,
0.008907776325941086,
0.03323807567358017,
-0.00861475057899952,
-0.009135324507951736,
0.02063589356839657,
-0.014952858909964561,
0.04751765355467796,
-0.018571393564343452,
-0.009473050013184547,
-0.0313543900847435,
0.024293525144457817,
0.002754556480795145,
-0.03760899230837822,
0.030846185982227325,
0.016836410388350487,
-0.007392393425107002,
-0.03351588174700737,
0.02641507238149643,
-0.0561789833009243,
0.007872658781707287,
-0.005262515973299742,
0.05966300144791603,
0.03432893380522728,
0.037813834846019745,
0.025414224714040756,
0.018716348335146904,
-0.0336979515850544,
0.02200714498758316,
-0.028061235323548317,
0.006952333729714155,
0.03213140368461609,
0.018147876486182213,
0.02477446012198925,
0.030367352068424225,
-0.04096567630767822,
0.012178475968539715,
-0.011899007484316826,
-0.026424052193760872,
0.005555680952966213,
-0.008960466831922531,
-0.004937571473419666,
0.04385031387209892,
-0.013528408482670784,
0.03572745621204376,
0.005834799725562334,
-0.01805230788886547,
-0.045847728848457336,
0.0070407334715127945,
0.01916436478495598,
-0.027760164812207222,
0.05195053666830063,
0.06265608221292496,
-0.021938052028417587,
0.016339270398020744,
-0.018900996074080467,
0.039420828223228455,
0.007072328589856625,
0.049188144505023956,
-0.08425269275903702,
0.007190301548689604,
0.0021275999024510384,
-0.025673892349004745,
0.06863577663898468,
0.03961874172091484,
-0.057854898273944855,
-0.03134506568312645,
0.03800231218338013,
-0.05366018787026405,
-0.02094421349465847,
0.007384154479950666,
0.004448815248906612,
-0.009932850487530231,
-0.030196228995919228,
-0.028079770505428314,
-0.00150400516577065,
-0.017177216708660126,
0.034653615206480026,
0.003017992014065385,
-0.06433534622192383,
0.04493122920393944,
0.0031707759480923414,
-0.015399486757814884,
-0.011594517156481743,
0.0066079325042665005,
0.0353250727057457,
-0.0032316436991095543,
-0.0712529718875885,
-0.03678683936595917,
-0.040567975491285324,
-0.006432774476706982,
-0.016377383843064308,
0.004797979723662138,
-0.008409139700233936,
-0.022123396396636963,
-0.030027922242879868,
-0.02340536192059517,
-0.003389759687706828,
0.003919263835996389,
0.005621173419058323,
-0.032795652747154236,
0.07885417342185974,
0.005309200845658779,
0.025674480944871902,
-0.0022303913719952106,
0.05924993380904198,
-0.03207310289144516,
-0.04531735181808472,
0.0329027958214283,
0.03333708643913269,
0.020167525857686996,
0.020765084773302078,
-0.00016948174743447453,
-0.041768647730350494,
-0.011036541312932968,
-0.04509314149618149,
-0.020820600911974907,
0.003989245742559433,
0.02233886532485485,
-0.0006508922670036554,
0.07855604588985443,
-0.001138511230237782,
0.014718545600771904,
-0.009060530923306942,
0.01812671311199665,
0.050642527639865875,
0.05904161185026169,
-0.023101313039660454,
-0.03077761083841324,
-0.03679060563445091,
0.00915241427719593,
0.007845820859074593,
0.08005528897047043,
0.01583726331591606,
0.026958180591464043,
0.027850456535816193,
0.015786677598953247,
-0.021701384335756302,
-0.017056595534086227,
-0.002289729192852974,
-0.023161280900239944,
0.02399805374443531,
-0.00729834521189332,
-0.03570692986249924,
0.031404197216033936,
0.016720382496714592,
0.03068179450929165,
0.017316410318017006,
-0.012998423539102077,
0.0018449317431077361,
-0.03924105688929558,
-0.018533295020461082,
0.00907628983259201,
-0.043231502175331116,
-0.06033696234226227,
0.008779260329902172,
-0.04461472108960152,
-0.015507717616856098,
-0.03619905188679695,
-0.0007250478374771774,
0.04189429059624672,
0.06421098113059998,
-0.05279584601521492,
-0.020093707367777824,
-0.03645579516887665,
0.035005904734134674,
0.012615412473678589,
0.038791198283433914,
-0.0032192992512136698,
0.006752035580575466,
0.044237252324819565,
0.016313085332512856,
0.0025087364483624697,
0.0026159239932894707,
0.06323584169149399,
0.004048461560159922,
-0.007914800196886063,
0.006116793025285006,
0.06779062747955322,
0.05372963473200798,
-0.03630942106246948,
0.027428625151515007,
-0.01701350323855877,
0.023616289719939232,
0.010015695355832577,
0.05983436107635498,
0.030497277155518532,
-0.08731494843959808,
0.013353940099477768,
-0.09943006187677383,
0.05728989839553833,
-0.0569399930536747,
-0.01417193841189146,
-0.027392126619815826,
-0.06091956049203873,
0.015024400316178799,
-0.021978192031383514,
0.023327961564064026,
-0.023107921704649925,
0.020809143781661987,
-0.059679724276065826,
-0.08256838470697403,
0.04713773354887962,
0.008707602508366108,
-0.021158112213015556,
0.021975500509142876,
-0.06141126900911331,
0.020641809329390526,
0.007061240263283253,
-0.014189769513905048,
-0.026119882240891457,
0.015835098922252655,
-0.0006139680044725537,
-0.02197638526558876,
0.020277151837944984,
0.006595666520297527,
0.008094385266304016,
-0.04188656806945801,
0.013299208134412766,
-0.058974530547857285,
0.03746812790632248,
-0.028098823502659798,
0.05380295217037201,
0.004813331179320812,
0.0220011156052351,
0.07432441413402557,
0.03687508776783943,
0.04125324264168739,
0.0257301963865757,
-0.053727712482213974,
0.01783464103937149,
-0.059730999171733856,
0.0017545040464028716,
-0.037595484405756,
0.018549442291259766,
-0.004735584370791912,
0.04685201123356819,
0.006408690940588713,
0.07078219950199127,
0.0068520959466695786,
-0.024657806381583214,
-0.045574989169836044,
0.011824008077383041,
0.040959715843200684,
0.05528253689408302,
0.06584082543849945,
0.04307610169053078,
0.0017236601561307907,
-0.07246967405080795,
-0.002409779466688633,
0.06312412023544312,
-0.047664374113082886,
0.02235526405274868,
-0.04647613689303398,
-0.05806709825992584,
0.012050431221723557,
0.01588091067969799,
-0.02908448688685894,
0.020727984607219696,
0.0795276015996933,
-0.0022663231939077377,
0.005034749396145344,
-0.03499021381139755,
-0.009765684604644775,
0.06697849184274673,
0.03972283750772476,
0.03564092144370079,
-0.015649180859327316,
-0.027204938232898712,
0.029934382066130638,
0.025561587885022163,
-0.046644292771816254,
-0.06988268345594406,
0.025159815326333046,
-0.005893552675843239,
0.02304888516664505,
-0.015545802190899849,
0.06341373920440674,
0.04465874284505844,
-0.055864568799734116,
-0.028508426621556282,
0.019963335245847702,
0.06756243854761124,
0.0323333777487278,
-0.03180259093642235,
0.03839636221528053,
-0.07941555976867676,
-0.11527865380048752,
-0.0511070154607296,
-0.017576070502400398,
-0.022719737142324448,
0.02601456828415394,
0.006793110631406307,
-0.006847957614809275,
0.04797626659274101,
-0.01737223193049431,
0.05602283775806427,
0.012002341449260712,
-0.0042929151095449924,
-0.031886570155620575,
-0.020960500463843346,
-0.04009963572025299,
-0.025638191029429436,
-0.0017693863483145833,
0.02052779495716095,
-0.0456244982779026,
-0.026461713016033173,
0.030998293310403824,
-0.0005544199957512319,
-0.030635105445981026,
-0.030909482389688492,
-0.004303969908505678,
0.011518090963363647,
-0.04263998568058014,
0.04186779260635376,
-0.031990982592105865,
0.08471192419528961,
0.025462279096245766,
-0.045514557510614395,
0.0404595285654068,
0.04110785946249962,
-0.0042846109718084335,
0.030201956629753113,
-0.041954170912504196,
-0.026807179674506187,
-0.0007057728944346309,
0.03749390318989754,
0.0424850657582283,
0.031131349503993988,
-0.031323716044425964,
-0.05995629355311394,
0.021418806165456772,
-0.017695220187306404,
0.016561998054385185,
-0.01789465732872486,
0.0035107829608023167,
-0.034359827637672424,
0.021180959418416023,
-0.0006620248313993216,
-0.06861752271652222,
-0.021260064095258713,
0.02826382964849472,
-0.008258855901658535,
-0.014795689843595028,
0.029527489095926285,
-0.07647065818309784,
-0.03891981020569801,
-0.03370700404047966,
0.009829813614487648,
-0.032636020332574844,
0.021007811650633812,
-0.022740280255675316,
-0.02812102437019348,
0.016251428052783012,
0.05814917013049126,
0.004955126903951168,
-0.0398704968392849,
-0.060456376522779465,
0.018744289875030518,
-0.038449667394161224,
0.020696362480521202,
-0.03386213630437851,
0.007011008448898792,
-0.048378992825746536,
0.04336569830775261,
-0.09038113802671432,
-0.024660635739564896,
0.014236006885766983,
0.015744784846901894,
0.034515973180532455,
0.051481571048498154,
0.021314168348908424,
0.0012087440118193626,
-0.028436435386538506,
0.01874401979148388,
-0.0022977024782449007,
-0.055488403886556625,
0.017095321789383888,
0.0001473194279242307,
0.057826925069093704,
-0.012729492038488388,
-0.0007366714417003095,
0.035234782844781876,
-0.007587755564600229,
0.040978047996759415,
-0.028104383498430252,
0.06655469536781311,
0.03022930584847927,
0.06033198907971382,
-0.024753818288445473,
0.03720520809292793,
0.047190845012664795,
0.02384108677506447,
0.004578066989779472,
0.03247319534420967,
0.03235207870602608,
-0.003945444244891405,
-0.06533502042293549,
-0.009327859617769718,
0.04316247999668121,
0.015558423474431038,
-0.10902773588895798,
0.01333586871623993,
0.04770471528172493,
0.04617294296622276,
-0.040646471083164215,
-0.053194645792245865,
-0.06364186853170395,
-0.02586199901998043,
-0.05153138190507889,
0.04248984903097153,
-0.025044206529855728,
-0.044968508183956146,
-0.0024077631533145905,
-0.023609720170497894,
0.025454500690102577,
0.01138817984610796,
0.061919666826725006,
-0.030048655346035957,
-0.007203774061053991,
-0.027625488117337227,
0.04094022512435913,
-0.050739943981170654,
0.03901464119553566,
0.0025019049644470215,
-0.006322128232568502,
0.036681823432445526,
0.03134746104478836,
0.0005727184470742941,
0.050164029002189636,
0.0039664278738200665,
-0.029715776443481445,
0.022795945405960083,
-0.020915202796459198,
-0.014602826908230782,
-0.013906411826610565,
-0.0008351473952643573,
-0.004724991507828236,
0.041613489389419556,
-0.05629535764455795,
0.0012888084165751934,
0.07258400321006775,
0.02586943842470646,
0.015159178525209427,
-0.014722280204296112,
0.022439509630203247,
0.03930748254060745,
0.010232754051685333,
0.004227977246046066,
0.005550547502934933,
0.03788488358259201,
0.020681075751781464,
0.03906697779893875,
0.018961213529109955,
-0.014996700920164585,
0.015334274619817734,
-0.042464178055524826,
0.03688723221421242,
-0.008871191181242466,
-0.0092776482924819,
-0.05384417250752449,
-0.004009139724075794,
0.060471076518297195,
-0.03932042792439461,
-0.005137091502547264,
-0.030962767079472542,
-0.017810551449656487,
0.01899191364645958,
-0.0255175419151783,
-0.043376583606004715,
-0.016715366393327713,
-0.016730356961488724,
-0.029752878472208977,
0.007032229099422693,
-0.02128634788095951,
-0.05662975832819939,
-0.032383233308792114,
-0.04735307767987251,
-0.012831936590373516,
-0.04972129315137863,
-0.03493805602192879,
-0.015918245539069176,
0.04822894185781479,
-0.0041978927329182625,
-0.08324572443962097,
-0.01889742910861969,
0.026432981714606285,
-0.012601986527442932,
0.006339389830827713,
0.005519844125956297,
0.01588531583547592,
0.02551986090838909,
0.00174445821903646,
-0.04210412874817848,
-0.042577505111694336,
-0.04527604952454567,
0.02737434208393097,
0.03536033630371094,
0.006316265556961298,
-0.0520155131816864,
0.0741259977221489,
0.031127916648983955,
0.03169029578566551,
-0.02895164303481579,
0.004983782768249512,
-0.06363744288682938,
0.01593133993446827,
-0.030327947810292244,
0.018418554216623306,
0.022517241537570953,
-0.005316463764756918,
0.0771062970161438,
0.03102077730000019,
0.02864142879843712,
-0.05421992391347885,
0.011357874609529972,
-0.05764509364962578,
-0.04744186997413635,
-0.031606078147888184,
0.030176078900694847,
-0.027380144223570824
] |
<p>I remember considering in class in college, the case of a photon gas trapped in a d-dimensional box as a subject of interest, whose energy distribution, heat capacity, etc. should be calculated. </p>
<p>This momentum/energy distribution was then related to that emitted by a black body - that up to a constant factor, they are one in the same.</p>
<p>I could understand the argument that making a small hole in such a box would constitute a "black body", as the hole can't reflect back light impinging on it, but I can't see how to make the conclusion that this is the exact same distribution. Shouldn't the atomic structure of matter be brought into account as well, or is it considered "hollow" on sufficiently large scales? </p> | g1225 | [
0.012270117178559303,
0.015614531002938747,
0.00010636733350111172,
-0.03693539649248123,
0.028278952464461327,
0.030769409611821175,
0.01117650605738163,
0.02273819036781788,
-0.013519988395273685,
-0.049441833049058914,
0.025611013174057007,
0.02035635896027088,
0.049469687044620514,
-0.049395546317100525,
-0.04581121727824211,
-0.03770272433757782,
0.026476290076971054,
-0.0017769898986443877,
0.0006877559935674071,
0.010389270260930061,
-0.008222678676247597,
0.01660996675491333,
0.01179057639092207,
-0.04355347901582718,
-0.04329240322113037,
-0.02245507203042507,
-0.012678559869527817,
-0.014093529433012009,
-0.006652451120316982,
-0.05681664124131203,
0.02109363302588463,
0.035879410803318024,
0.06520407646894455,
-0.014549536630511284,
-0.08459188789129257,
0.01441273558884859,
0.05785202980041504,
0.03348671272397041,
0.03191003203392029,
0.022088680416345596,
0.027316851541399956,
-0.05900445580482483,
-0.034717075526714325,
0.010197069495916367,
-0.030820582062005997,
-0.0006607829127460718,
-0.01839684695005417,
0.0016025648219510913,
0.030471930280327797,
0.05669904500246048,
-0.00005592542220256291,
0.04627213627099991,
0.07219360768795013,
-0.009854128584265709,
0.028646130114793777,
0.0017295553116127849,
-0.043288469314575195,
0.007704401854425669,
0.05024096742272377,
0.03362666442990303,
-0.03599067032337189,
0.011383186094462872,
-0.049750667065382004,
0.03792259097099304,
0.06770998984575272,
0.009202306158840656,
-0.04165977984666824,
0.01388387568295002,
-0.040015313774347305,
-0.04153276979923248,
0.03493416681885719,
-0.031083235517144203,
0.015790557488799095,
0.0015275439945980906,
-0.0469837412238121,
0.01054031029343605,
-0.040534839034080505,
0.06804332882165909,
0.004271723795682192,
-0.027242416515946388,
-0.03402727097272873,
0.002304928144440055,
0.05113296955823898,
0.014176481403410435,
0.05018683522939682,
-0.015171867795288563,
-0.015463675372302532,
-0.03939244523644447,
-0.0009740490349940956,
0.05763818696141243,
0.06283546984195709,
0.05963313579559326,
0.06214152276515961,
-0.026213591918349266,
0.05428575351834297,
0.031886618584394455,
-0.004777140449732542,
0.08292470872402191,
-0.0461132675409317,
0.035050321370363235,
-0.031125273555517197,
0.047061365097761154,
-0.05911846458911896,
0.01983039267361164,
-0.020918535068631172,
-0.02420186996459961,
-0.04927567020058632,
-0.008295533247292042,
-0.01239408552646637,
0.02815490961074829,
-0.04888911917805672,
-0.049270838499069214,
-0.06881347298622131,
-0.060791853815317154,
-0.013592402450740337,
-0.050882142037153244,
0.07761207967996597,
-0.07775826752185822,
0.004871404729783535,
0.12195051461458206,
0.018834922462701797,
-0.011960918083786964,
0.020832514390349388,
-0.000050034926971420646,
-0.017574407160282135,
-0.0000850499200168997,
-0.036227550357580185,
0.02016623131930828,
-0.03332376480102539,
-0.043628230690956116,
0.050916630774736404,
-0.03364560380578041,
-0.00985168106853962,
0.061977677047252655,
0.027031248435378075,
0.05917510390281677,
-0.009415763430297375,
-0.019837722182273865,
0.011480572633445263,
0.013981854543089867,
0.013907773420214653,
0.020367078483104706,
-0.05670472979545593,
0.035318803042173386,
-0.012997139245271683,
0.028241420164704323,
-0.035531893372535706,
-0.021590329706668854,
0.020347580313682556,
0.043561242520809174,
0.026794860139489174,
0.09752027690410614,
-0.0026251135859638453,
-0.012660921551287174,
0.013245737180113792,
0.02378975786268711,
0.05174160376191139,
0.01872529275715351,
-0.013075672090053558,
0.0016510288696736097,
0.039103034883737564,
0.06938689947128296,
0.020109672099351883,
-0.00866287387907505,
-0.03876678645610809,
-0.05063489079475403,
-0.03404200077056885,
-0.09972559660673141,
0.0023716094437986612,
-0.07581440359354019,
0.00916613545268774,
0.004594525787979364,
-0.015279385261237621,
0.0781342163681984,
-0.0157476793974638,
0.03818894177675247,
0.04414081573486328,
-0.05544733628630638,
0.04697804898023605,
-0.0029172254726290703,
0.030650554224848747,
0.02327774092555046,
0.04785529524087906,
-0.03896766155958176,
0.026345036923885345,
-0.01910381205379963,
0.059454433619976044,
0.0023837671615183353,
0.015068920329213142,
-0.02015807293355465,
-0.011208941228687763,
-0.03519218787550926,
0.051904745399951935,
0.014263158664107323,
0.009793349541723728,
-0.04755711182951927,
0.02464309334754944,
-0.016651513054966927,
0.005268506705760956,
-0.009113441221415997,
-0.06873530149459839,
0.04914763942360878,
-0.007233649026602507,
0.011046890169382095,
0.09924251586198807,
0.04980562627315521,
-0.058073099702596664,
-0.004410340916365385,
0.018396802246570587,
0.03020596317946911,
0.012277345173060894,
-0.018852954730391502,
0.017702853307127953,
0.04284532368183136,
0.016106711700558662,
0.016381127759814262,
-0.1061338558793068,
0.06486719101667404,
0.0034217950887978077,
-0.02547137625515461,
-0.09303313493728638,
-0.03682797774672508,
-0.038464680314064026,
-0.05876069888472557,
0.02039780095219612,
0.014589902944862843,
-0.09189216792583466,
-0.02367924340069294,
0.024220185354351997,
0.0021765276324003935,
-0.06347186863422394,
-0.019397974014282227,
-0.02565118670463562,
-0.010303137823939323,
0.012295869179069996,
0.03822152316570282,
-0.039901603013277054,
-0.0523197166621685,
-0.012854105792939663,
0.026842501014471054,
0.01991785503923893,
-0.05633487552404404,
-0.059789493680000305,
-0.045583389699459076,
0.04308118298649788,
-0.0064458842389285564,
-0.016278360038995743,
-0.00975092127919197,
-0.012157777324318886,
0.019558360800147057,
-0.03740694746375084,
-0.00035920742084272206,
-0.023256026208400726,
-0.017566045746207237,
0.017148520797491074,
-0.00043820898281410336,
0.028542760759592056,
0.014192475005984306,
-0.05209430307149887,
-0.05904090031981468,
0.04063289240002632,
-0.09024973958730698,
-0.05462786927819252,
0.018139783293008804,
-0.0982610210776329,
-0.054893821477890015,
-0.013242160901427269,
-0.019909892231225967,
-0.004676330368965864,
0.012345120310783386,
-0.019604694098234177,
0.07370231300592422,
0.02932322584092617,
-0.012858242727816105,
0.08619976043701172,
0.024775154888629913,
-0.02643868699669838,
-0.03519516438245773,
0.043646860867738724,
-0.035010818392038345,
-0.016951778903603554,
0.012527179904282093,
-0.08176766335964203,
-0.005309556145220995,
-0.00551137700676918,
-0.056055936962366104,
-0.015072934329509735,
-0.0133013054728508,
-0.010121887549757957,
0.026448700577020645,
0.0214295145124197,
0.04494881629943848,
-0.053118690848350525,
0.10180449485778809,
-0.024987798184156418,
0.048813994973897934,
0.059580396860837936,
0.013509311713278294,
-0.01013894286006689,
0.04434753209352493,
-0.02582305297255516,
-0.01807064563035965,
0.013063330203294754,
-0.002127020852640271,
0.029742229729890823,
0.029754463583230972,
-0.04332771897315979,
-0.023900838568806648,
-0.03858378157019615,
0.018078317865729332,
-0.03319313004612923,
-0.01594928279519081,
0.024557368829846382,
0.04439982771873474,
-0.032824475318193436,
-0.014817208051681519,
-0.0208541639149189,
-0.006906312890350819,
0.03333441540598869,
-0.03088831715285778,
-0.029709283262491226,
0.02211480215191841,
0.04900943487882614,
-0.0326373465359211,
0.06445924937725067,
0.022340359166264534,
-0.04627353698015213,
-0.029209014028310776,
-0.007755669299513102,
-0.003442204324528575,
-0.005222167354077101,
-0.02525484561920166,
-0.030780086293816566,
0.04343019798398018,
-0.014761646278202534,
-0.014292832463979721,
-0.020091883838176727,
-0.017103100195527077,
0.02676561288535595,
-0.004090297035872936,
-0.02040920779109001,
-0.04372227564454079,
-0.00775198545306921,
-0.008714578114449978,
-0.004049434792250395,
0.015061370097100735,
-0.0035138148814439774,
0.010885752737522125,
-0.0174573827534914,
-0.012462340295314789,
-0.014107447117567062,
-0.0245195385068655,
0.03621712327003479,
0.04416404291987419,
-0.006716967560350895,
0.045567821711301804,
0.019525514915585518,
0.0017587223555892706,
0.055271197110414505,
0.026658231392502785,
-0.01104920543730259,
-0.04276648163795471,
0.0811024159193039,
-0.038151275366544724,
-0.005809481721371412,
-0.04252813756465912,
-0.004099099896848202,
-0.011671885848045349,
0.01855093240737915,
0.013034647330641747,
-0.019193777814507484,
0.022860422730445862,
0.002206431468948722,
0.02006671018898487,
0.031681034713983536,
-0.04115990921854973,
0.012357517145574093,
0.0026419954374432564,
-0.02170717529952526,
-0.016120070591568947,
-0.009617507457733154,
0.004407061263918877,
0.008541636168956757,
0.01997198536992073,
-0.01538087148219347,
0.029645439237356186,
-0.027351057156920433,
-0.00857128668576479,
0.04310895502567291,
-0.013925253413617611,
-0.06146080791950226,
-0.035694293677806854,
-0.08441087603569031,
-0.010183519683778286,
-0.013387693092226982,
0.014728222973644733,
-0.007376152090728283,
-0.045107271522283554,
0.02118246629834175,
0.001042249146848917,
0.055586766451597214,
0.029827533289790154,
0.023104267194867134,
-0.017438989132642746,
0.029145361855626106,
0.040790289640426636,
0.06023474037647247,
-0.035417817533016205,
-0.026594145223498344,
-0.03098425455391407,
0.009623218327760696,
0.004069096874445677,
0.010222590528428555,
-0.014078638516366482,
0.026956306770443916,
-0.031136296689510345,
0.01904287002980709,
0.0217050202190876,
0.0006848562625236809,
0.046038080006837845,
0.015354206785559654,
0.01612097956240177,
0.053656335920095444,
0.004102819599211216,
0.0004331141826696694,
0.04229765385389328,
0.037739161401987076,
0.03951680287718773,
-0.03796757757663727,
-0.009763325564563274,
0.02575284242630005,
0.003879682859405875,
0.017754700034856796,
0.025377091020345688,
-0.08723387867212296,
0.01492325309664011,
-0.04317769408226013,
-0.009546301327645779,
0.04165206477046013,
0.05759185180068016,
0.08081873506307602,
0.008583691902458668,
0.048138029873371124,
-0.038117989897727966,
-0.014768562279641628,
0.05037896707653999,
-0.013388427905738354,
-0.004543699324131012,
-0.03320278599858284,
0.03822851553559303,
-0.007055219262838364,
-0.02012786455452442,
-0.010637081228196621,
-0.09399080276489258,
-0.007127242628484964,
-0.027841106057167053,
-0.04858613759279251,
-0.005459899548441172,
0.01903201825916767,
0.01880367286503315,
-0.06338387727737427,
-0.019811492413282394,
0.01726558431982994,
0.0451347641646862,
0.02299894392490387,
-0.04944370687007904,
-0.01970495842397213,
0.025040358304977417,
-0.0006128567038103938,
-0.031234003603458405,
-0.007523814681917429,
0.023123588413000107,
-0.005299518816173077,
-0.005101195070892572,
0.021821802482008934,
0.008709424175322056,
-0.029076004400849342,
-0.05742039158940315,
-0.017098747193813324,
-0.011786410585045815,
-0.02055775746703148,
-0.022233810275793076,
0.06399025768041611,
0.012313100509345531,
-0.02439202554523945,
0.02526727505028248,
-0.054083116352558136,
0.04442881792783737,
-0.0369645394384861,
0.014077393338084221,
-0.012414512224495411,
0.039079271256923676,
0.01110866479575634,
-0.012375627644360065,
0.0021057226695120335,
0.004677290562540293,
0.050031982362270355,
0.012530552223324776,
-0.035796210169792175,
0.0716441348195076,
-0.07110753655433655,
0.012006258592009544,
0.024665474891662598,
-0.02581159584224224,
0.023340536281466484,
0.021592192351818085,
0.03370628505945206,
0.01584256812930107,
0.026963049545884132,
-0.03465135395526886,
-0.02829468995332718,
0.0035817045718431473,
0.018966365605592728,
0.0471767857670784,
0.015913160517811775,
-0.033596258610486984,
-0.001904105069115758,
0.03187185898423195,
-0.024876484647393227,
0.017753880470991135,
0.04651547223329544,
0.003627122612670064,
0.008511644788086414,
-0.011472733691334724,
0.028971826657652855,
0.02607814595103264,
-0.0443948395550251,
-0.07406991720199585,
-0.013371657580137253,
0.038724154233932495,
0.05904785916209221,
0.02602376602590084,
0.00627728970721364,
-0.03243791311979294,
-0.06177714094519615,
-0.018688710406422615,
-0.0006153425201773643,
0.08213336020708084,
0.03844738006591797,
-0.03648436814546585,
-0.010099688544869423,
-0.04427105188369751,
-0.0334232896566391,
-0.0017147292383015156,
0.012368826195597649,
-0.014159535989165306,
0.04358736425638199,
-0.025056593120098114,
0.0025800808798521757,
-0.039612073451280594,
-0.007566171232610941,
0.013539827428758144,
-0.040377743542194366,
0.0035691573284566402,
0.025685638189315796,
0.006545993033796549,
-0.003218586789444089,
0.021699942648410797,
-0.008378316648304462,
-0.012013761326670647,
0.021033015102148056,
0.047828949987888336,
0.014822565019130707,
-0.00802508182823658,
-0.010046371258795261,
-0.017996802926063538,
-0.03388313204050064,
-0.051669228821992874,
-0.006072133779525757,
-0.05241171270608902,
-0.050788067281246185,
0.021325664594769478,
0.042402613908052444,
0.017485536634922028,
-0.0098135219886899,
0.0362139455974102,
0.02372073382139206,
0.008498506620526314,
-0.02428356744349003,
0.02815159037709236,
0.04306970164179802,
0.027368690818548203,
0.07577399909496307,
0.01344266813248396,
-0.019096963107585907,
0.0845898911356926,
-0.04488696530461311,
0.04267806559801102,
0.020465800538659096,
0.0004850833211094141,
-0.004500639624893665,
0.04066389799118042,
-0.02094973810017109,
-0.011026039719581604,
-0.07191237062215805,
-0.022771377116441727,
0.006857599131762981,
-0.017699413001537323,
-0.03553178906440735,
-0.013195356354117393,
0.017949558794498444,
-6.591817509615794e-7,
-0.02925269864499569,
-0.027684088796377182,
0.019756445661187172,
0.04759126529097557,
-0.032505784183740616,
0.008239513263106346,
-0.044234953820705414,
0.02163325995206833,
-0.01011497899889946,
0.011633326299488544,
-0.05037425458431244,
-0.0051355306059122086,
0.01428174041211605,
-0.05064994469285011,
-0.020795464515686035,
0.0036544508766382933,
0.00653126509860158,
0.021185334771871567,
0.012440722435712814,
-0.006570903118699789,
-0.00838390365242958,
-0.04238821566104889,
0.07777334749698639,
0.08592186123132706,
-0.1041429415345192,
0.07674602419137955,
0.043067943304777145,
0.029196709394454956,
-0.02827276475727558,
0.01618369296193123,
-0.00951737817376852,
0.020110642537474632,
-0.010670197196304798,
0.054258573800325394,
-0.04716723784804344,
0.033468976616859436,
0.005541193764656782,
-0.028193293139338493,
-0.013994810171425343,
-0.012645591050386429,
0.05247125029563904,
0.03844478353857994,
-0.036913156509399414,
0.04400419071316719,
0.030176114290952682,
0.01425696350634098,
-0.06571269035339355,
0.005095691420137882,
-0.050662245601415634,
-0.0720721036195755,
-0.03536596894264221,
-0.023950614035129547,
-0.02914239652454853,
-0.023942438885569572,
-0.020674027502536774,
0.011533241719007492,
0.016629498451948166,
-0.10642104595899582,
0.006848784163594246,
0.000005963575404166477,
-0.007613503374159336,
-0.032268792390823364,
0.005110824014991522,
0.020083613693714142,
0.018689269199967384,
-0.04254399240016937,
0.016471054404973984,
0.004755652975291014,
0.028326746076345444,
-0.017923610284924507,
-0.06224123761057854,
0.013169019483029842,
-0.027745166793465614,
-0.01362996082752943,
0.006656917743384838,
0.08719310164451599,
0.014851017855107784,
0.018817922100424767,
0.028009718284010887,
0.03941504284739494,
-0.03205673396587372,
0.002232704544439912,
-0.018983792513608932,
0.010925937443971634,
-0.07205075025558472,
-0.017813790589571,
-0.000848215539008379,
-0.0019280165433883667,
-0.0018700698856264353,
0.005599022377282381,
-0.04275408759713173,
-0.036647114902734756,
-0.021560950204730034,
0.027096707373857498,
0.0742967426776886,
0.05230197310447693,
0.014252354390919209,
-0.028738753870129585,
0.0013733612140640616,
-0.0030862234998494387,
0.0005343625089153647,
-0.04574015736579895,
0.03336484730243683,
-0.012898704037070274,
0.034765902906656265,
0.01431246753782034,
-0.04276200756430626,
-0.032334983348846436,
0.10338856279850006,
0.014230209402740002,
0.05096789076924324,
0.007470392622053623,
0.00492088682949543,
-0.020874466747045517,
-0.040244314819574356,
-0.0032974828500300646,
0.007681901101022959,
-0.0365871898829937,
0.02842487022280693,
0.04523639380931854,
-0.02881593629717827,
0.024419454857707024,
0.04168963059782982,
-0.034870393574237823,
0.00934787280857563,
-0.005585367325693369,
-0.009100142866373062,
-0.012806873768568039,
-0.01133560948073864,
0.006847488693892956,
-0.0016084351809695363,
-0.014523178339004517,
0.03266637772321701,
-0.0039013109635561705,
-0.04671645537018776,
0.002842094749212265,
0.04533303156495094,
-0.01890592835843563,
0.0007528259884566069,
-0.028532633557915688,
0.010961740277707577,
-0.012105144560337067,
-0.008925034664571285,
-0.0339914970099926,
-0.07213519513607025,
0.050799429416656494,
0.05152837187051773,
0.061034392565488815,
-0.0387415774166584,
0.006569691933691502,
-0.00031631122692488134,
0.025303760543465614,
0.059825606644153595,
-0.0727461501955986,
-0.026038039475679398,
0.014234370552003384,
-0.0184192918241024,
0.017756622284650803,
-0.04589306563138962,
0.04381846636533737,
-0.009097802452743053,
-0.036522164940834045,
-0.009831585921347141,
-0.0336095355451107,
0.04534667357802391,
0.007362503092736006
] |
<p>There are some definitions and properties for <a href="http://en.wikipedia.org/wiki/Pauli_matrices" rel="nofollow">Pauli matrices</a> and their combinations:</p>
<p>$$
\varepsilon^{\alpha \beta } = \varepsilon^{\dot {\alpha} \dot {\beta} } = \begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}_{\alpha \beta }, \quad \varepsilon_{\dot {\alpha} \dot {\beta}} = \varepsilon_{\alpha \beta} = -\varepsilon^{\alpha \beta },
$$
$$
(\sigma^{\mu})_{\alpha \dot {\alpha} } = (\hat {\mathbf E} , \hat {\mathbf \sigma})^{\mu}_{\alpha \dot {\alpha}}, \quad (\tilde {\sigma}^{\mu})^{\dot {\beta } \beta } = \varepsilon^{\alpha \beta}\varepsilon^{\dot {\alpha }\dot {\beta }}(\sigma^{\mu})_{\alpha \dot {\alpha}} = (\hat {\mathbf E}, -\hat {\mathbf \sigma})^{\mu , \dot {\beta }\beta },
$$
$$
(\sigma^{\mu \nu})_{\alpha \beta} = -\frac{1}{4}\left( (\sigma^{\mu} \tilde {\sigma}^{\nu})_{\alpha \beta } - (\sigma^{\nu} \tilde {\sigma}^{\mu})_{\alpha \beta }\right), \quad (\tilde {\sigma}^{\mu \nu})_{\dot {\alpha }\dot {\beta }} = -\frac{1}{4}\left( (\tilde{\sigma}^{\mu} \sigma^{\nu})_{\dot {\alpha} \dot {\beta} } - (\tilde {\sigma}^{\nu} \sigma^{\mu})_{\dot {\alpha} \dot {\beta} }\right),
$$
$$
(\tilde {\sigma}^{\mu})^{\dot {\alpha }\alpha}(\sigma_{\mu})_{\beta \dot {\beta }} = 2\delta^{\dot {\alpha}}_{\dot {\beta}}\delta^{\alpha}_{\beta}.
$$
How to show, that
$$
(\sigma^{\alpha \beta})_{a b }(\tilde {\sigma}^{\mu \nu})_{\dot {c} \dot {d}}g_{\alpha \mu} = 0?
$$
(It helps to show, that spinor irreducible representation of the generators of Lorentz group expands on two spinor subgroups).</p>
<p><strong>My attempt</strong>.</p>
<p>I tried to show this, but only got following.
$$
(\sigma^{\alpha \beta})_{a b }(\tilde {\sigma}^{\mu \nu})_{\dot {c} \dot {d}}g_{\alpha \mu} = \frac{1}{16}\left( (\sigma^{\alpha})_{a \dot {n}}(\tilde {\sigma}^{\beta })^{ \dot {n}}_{\quad b}(\tilde {\sigma}^{\mu})_{\dot {c}}^{\quad m }(\sigma^{\nu })_{m \dot {d}} - (\sigma^{\alpha})_{a \dot {n}}(\tilde {\sigma}^{\beta })^{ \dot {n}}_{\quad b}(\tilde {\sigma}^{\nu})_{\dot {c}}^{ \quad m}(\sigma^{\mu })_{m \dot {d}}\right)
$$
$$
+ \frac{1}{16}\left(-(\sigma^{\beta })_{a \dot {n}}(\tilde {\sigma}^{\alpha })^{ \dot {n}}_{\quad b}(\tilde {\sigma}^{\mu})_{\dot {c}}^{\quad m}(\sigma^{\nu })_{m \dot {d}} + (\sigma^{\beta })_{a \dot {n}}(\tilde {\sigma}^{\alpha })^{ \dot {n}}_{\quad b}(\tilde {\sigma}^{\nu})_{\dot {c}}^{\quad m }(\sigma^{\mu })_{m \dot {d}} \right)g_{\alpha \mu}
$$
After that I transformed each summand like
$$
(\sigma^{\alpha})_{a \dot {n}}(\tilde {\sigma}^{\beta })^{ \dot {n}}_{\quad b}(\tilde {\sigma}^{\mu})_{\dot {c}}^{\quad m }(\sigma^{\nu })_{m \dot {d}}g_{\alpha \mu} = (\sigma^{\alpha})_{a \dot {n}}(\tilde {\sigma}_{\alpha})_{\dot {c}}^{\quad m }(\tilde {\sigma}^{\beta })^{ \dot {n}}_{\quad b}(\sigma^{\nu })_{m \dot {d}} =
$$
$$
= \varepsilon_{\dot {c}\dot {\gamma}}(\sigma^{\alpha})_{a \dot {n}}(\tilde {\sigma}_{\alpha})^{\dot {\gamma} m }(\tilde {\sigma}^{\beta })^{ \dot {n}}_{\quad b}(\sigma^{\nu })_{m \dot {d}} = 2\varepsilon_{\dot {c}\dot {\gamma }}\delta^{\dot {\gamma}}_{\dot {m}}\delta^{n}_{a}(\tilde {\sigma}^{\beta })^{ \dot {n}}_{\quad b}(\sigma^{\nu })_{m \dot {d}} =
$$
$$
2\varepsilon_{\dot {c}\dot {m}}(\tilde {\sigma}^{\beta })^{ \dot {m}}_{\quad b}(\sigma^{\nu })_{a \dot {d}} = 2(\sigma^{\beta } )_{b \dot {c}}(\sigma^{\nu })_{a \dot {d}}.
$$
Finally, I got
$$
(\sigma^{\alpha \beta})_{a b }(\tilde {\sigma}^{\mu \nu})_{\dot {c} \dot {d}}g_{\alpha \mu} = \frac{1}{8}\left( (\sigma^{\beta})_{b\dot {c}}(\sigma^{\nu})_{a\dot {d}} + (\sigma^{\beta })_{b \dot {d}}(\sigma^{\nu})_{a \dot {c}} + (\sigma^{\beta })_{a \dot {c}}(\sigma^{\nu})_{b \dot {d}} + (\sigma^{\beta})_{a \dot {d}}(\sigma^{\nu})_{b \dot {c}}\right).
$$
What to do next?</p> | g1226 | [
0.0019919623155146837,
-0.01909884624183178,
-0.027275174856185913,
-0.03353266417980194,
0.005500797647982836,
-0.028660297393798828,
0.03538857400417328,
0.008899156004190445,
-0.028103390708565712,
0.011547592468559742,
-0.019401244819164276,
0.07014774531126022,
-0.008261223323643208,
0.014231101609766483,
0.0230051688849926,
0.02221560850739479,
0.10043390095233917,
0.009576385840773582,
0.053904712200164795,
-0.011066298000514507,
0.0010299377609044313,
0.05030630901455879,
-0.02849729359149933,
-0.010138292796909809,
0.10190855711698532,
-0.01304618176072836,
0.008620792999863625,
0.03718065842986107,
0.0059440527111291885,
-0.05206703767180443,
-0.00884088221937418,
0.06733784079551697,
0.017554301768541336,
-0.03344760835170746,
-0.013900630176067352,
-0.030136115849018097,
0.018166813999414444,
-0.0429517924785614,
0.02034725621342659,
-0.010840768925845623,
-0.011014003306627274,
-0.025592012330889702,
0.03848044201731682,
0.014669068157672882,
-0.02032635733485222,
-0.03416922688484192,
-0.015956874936819077,
-0.023152565583586693,
0.005183897912502289,
0.019928449764847755,
0.03968428075313568,
-0.021561305969953537,
0.07545459270477295,
-0.0109619852155447,
0.04267466813325882,
0.0048782071098685265,
0.011973408982157707,
0.013860126957297325,
0.05648580193519592,
0.012394648045301437,
0.032760050147771835,
-0.02135423570871353,
0.04753190651535988,
-0.027655044570565224,
0.025095732882618904,
-0.017169365659356117,
0.014875080436468124,
-0.007476037368178368,
0.014130670577287674,
0.004344762768596411,
-0.020585305988788605,
0.03377559408545494,
0.1409209966659546,
-0.01912013813853264,
-0.02016921527683735,
-0.02559645287692547,
-0.004384294617921114,
0.023641562089323997,
0.028326362371444702,
0.0012564464705064893,
-0.01240201760083437,
0.009461760520935059,
-0.029899412766098976,
-0.003128621494397521,
0.03481949120759964,
-0.0010158936493098736,
-0.019589925184845924,
0.01956077292561531,
-0.021155839785933495,
0.01590834930539131,
0.026214100420475006,
0.02481059543788433,
-0.008952098898589611,
0.045154985040426254,
-0.017719320952892303,
-0.025554627180099487,
0.02556891366839409,
0.049310918897390366,
-0.03303249552845955,
-0.02979392372071743,
0.010018509812653065,
0.05265804007649422,
0.03318864852190018,
0.019763140007853508,
-0.00108466821257025,
0.026327598839998245,
-0.034718796610832214,
-0.056820835918188095,
-0.042900826781988144,
0.014130388386547565,
-0.06808504462242126,
-0.027431586757302284,
0.024687398225069046,
-0.026329804211854935,
-0.03820153698325157,
-0.005673693958669901,
-0.00208419281989336,
0.006769836414605379,
0.005347398575395346,
0.014456831850111485,
0.0008279071189463139,
-0.040267638862133026,
0.013727803714573383,
-0.01181166060268879,
0.005586207844316959,
0.018480423837900162,
-0.019596748054027557,
-0.03834330290555954,
0.06772683560848236,
-0.09423546493053436,
-0.006508151069283485,
0.00730177853256464,
0.07542165368795395,
0.08130091428756714,
0.006818897090852261,
-0.019804343581199646,
-0.029546568170189857,
0.03022894635796547,
-0.0239451602101326,
0.020296316593885422,
-0.04772724583745003,
-0.04526520520448685,
-0.02738058939576149,
0.013746471144258976,
0.01779036968946457,
-0.047163523733615875,
0.0061509679071605206,
-0.04103010892868042,
-0.017960695549845695,
0.046149324625730515,
0.0029893172904849052,
0.04037277027964592,
0.0003087598306592554,
0.02086472511291504,
0.019075585529208183,
0.013928304426372051,
0.060004670172929764,
0.011784556321799755,
-0.03411880508065224,
-0.00004193456334178336,
0.025104910135269165,
-0.04988199099898338,
-0.021452350541949272,
-0.014619954861700535,
-0.003435830119997263,
0.0005767365219071507,
0.02045651711523533,
-0.013341718353331089,
0.020670661702752113,
0.023556765168905258,
-0.026340989395976067,
-0.014363917522132397,
-0.006690792739391327,
0.00340555259026587,
0.020649999380111694,
0.0318513922393322,
-0.030709873884916306,
0.0019383467733860016,
0.05373109504580498,
0.020373042672872543,
-0.046840496361255646,
-0.04326401278376579,
-0.025758566334843636,
-0.028392869979143143,
0.00912664458155632,
-0.006896354258060455,
0.008534351363778114,
0.06880781054496765,
-0.09440296143293381,
0.05050722509622574,
0.022113917395472527,
0.03275756537914276,
0.047096144407987595,
0.03507988899946213,
0.005777127109467983,
0.011644373647868633,
0.05848238989710808,
-0.10373766720294952,
-0.020352596417069435,
0.028879616409540176,
-0.028912736102938652,
0.060008704662323,
0.0006031174561940134,
-0.02774461731314659,
-0.008214565925300121,
0.051514193415641785,
-0.011495937593281269,
0.033029042184352875,
-0.012488007545471191,
0.030259503051638603,
-0.0009168453398160636,
0.02486652508378029,
0.005989230703562498,
-0.005327239166945219,
-0.0022669772151857615,
-0.019010132178664207,
0.028782835230231285,
-0.01957729086279869,
-0.023066667839884758,
0.0718536376953125,
0.025351911783218384,
-0.005820974241942167,
-0.03244787082076073,
0.05733447149395943,
-0.01636582985520363,
0.05926728993654251,
-0.021773304790258408,
0.01018377486616373,
-0.004595512989908457,
0.0317404605448246,
-0.04241722822189331,
0.03286582976579666,
-0.0416947603225708,
0.0294216126203537,
0.007479376159608364,
-0.05056995525956154,
-0.020239204168319702,
0.022695478051900864,
0.023830121383070946,
-0.01579814963042736,
0.06292840093374252,
-0.04310839995741844,
0.030387630686163902,
-0.01287226751446724,
0.013037723489105701,
-0.010838109068572521,
0.009897114709019661,
-0.02724536880850792,
-0.004903178662061691,
0.016552254557609558,
-0.012477105483412743,
-0.018661869689822197,
-0.025244001299142838,
0.041003964841365814,
0.05634972080588341,
0.00495498301461339,
0.0045453752391040325,
0.020920157432556152,
-0.03240476921200752,
-0.0017380437348037958,
-0.026150710880756378,
0.0120274368673563,
-0.05831556022167206,
0.07565438747406006,
-0.017757972702383995,
0.01017671637237072,
-0.059890612959861755,
-0.09599466621875763,
0.024461081251502037,
0.011707687750458717,
-0.05431356281042099,
0.07472972571849823,
0.04988107085227966,
-0.0033271093852818012,
-0.028553958982229233,
-0.01009753905236721,
-0.0015458195703104138,
0.07549472153186798,
-0.019786886870861053,
0.04366034269332886,
0.009887834079563618,
0.055338308215141296,
-0.0007826360524632037,
0.0008930943440645933,
-0.014636735431849957,
-0.04689136892557144,
0.029996613040566444,
0.04042883589863777,
-0.011592444963753223,
0.06940019875764847,
-0.02718164771795273,
0.04041100665926933,
0.05923568829894066,
-0.00945241004228592,
-0.05917016416788101,
0.006189713720232248,
0.010430417954921722,
-0.10920574516057968,
-0.011329210363328457,
0.07255849987268448,
0.028595933690667152,
-0.006901259999722242,
0.008168859407305717,
-0.02615802176296711,
0.03900881111621857,
-0.04040060564875603,
-0.075531505048275,
-0.03484801948070526,
-0.03360147774219513,
-0.01369383279234171,
-0.034850455820560455,
-0.03703813999891281,
0.050204891711473465,
-0.05133797228336334,
-0.000021152869521756656,
0.003607821650803089,
0.024936527013778687,
-0.03824590519070625,
-0.011115397326648235,
-0.07369765639305115,
-0.04385845363140106,
-0.03976266831159592,
0.024357082322239876,
0.030175046995282173,
0.01985839381814003,
-0.006082759238779545,
-0.06128866225481033,
-0.007467170245945454,
-0.021425137296319008,
0.01715398207306862,
-0.02437775768339634,
-0.023414326831698418,
0.03492963686585426,
0.02272038348019123,
-0.07609322667121887,
0.011858206242322922,
-0.05850255489349365,
0.04272543638944626,
-0.008570699021220207,
-0.02363697625696659,
-0.015960847958922386,
-0.023006409406661987,
0.012313918210566044,
0.03937951847910881,
-0.003858117153868079,
0.015167406760156155,
0.02710825763642788,
-0.022092821076512337,
0.032936859875917435,
-0.0010185845894739032,
-0.04563688114285469,
0.050879303365945816,
-0.0034723253920674324,
-0.04075027257204056,
0.011984835378825665,
0.03080114535987377,
-0.008781453594565392,
0.017561759799718857,
-0.026872528716921806,
-0.01606641709804535,
0.03768712282180786,
-0.0073415497317910194,
-0.028202371671795845,
0.02171085774898529,
-0.0276802908629179,
0.01856904849410057,
0.03719547018408775,
-0.00526111014187336,
0.00337910745292902,
0.011966678313910961,
0.0483001209795475,
0.012333875522017479,
-0.011416198685765266,
0.0486285574734211,
-0.01043839380145073,
-0.02067956142127514,
-0.005488099996000528,
-0.029966842383146286,
0.010119429789483547,
0.060958705842494965,
-0.011535724624991417,
-0.030635366216301918,
0.029478423297405243,
0.03115912713110447,
0.024070093408226967,
-0.025185009464621544,
0.022979728877544403,
0.02189207822084427,
0.019162854179739952,
0.01824229396879673,
0.009742137975990772,
-0.006643758155405521,
0.03369803726673126,
-0.040725547820329666,
0.03513655066490173,
-0.04598638415336609,
-0.02006499283015728,
0.03778848052024841,
-0.009152413345873356,
-0.009310895577073097,
-0.07609187811613083,
-0.006710448767989874,
0.05395416170358658,
-0.05159399285912514,
0.004297009203583002,
-0.03099057823419571,
-0.046779803931713104,
0.05283684283494949,
0.04641945660114288,
0.02411939576268196,
-0.012993970885872841,
-0.01377096213400364,
0.04665942117571831,
-0.03582168370485306,
0.02399544231593609,
0.06835119426250458,
0.039999183267354965,
-0.013546030037105083,
-0.0021208850666880608,
-0.017528198659420013,
-0.04198487475514412,
0.0367814265191555,
0.020644735544919968,
0.007878756150603294,
0.05643598735332489,
-0.0021183183416724205,
-0.02756122499704361,
-0.01053474098443985,
-0.013386065140366554,
-0.05913563817739487,
-0.009883992373943329,
0.0045682392083108425,
-0.022345609962940216,
-0.0916604995727539,
-0.05882611870765686,
-0.033158041536808014,
-0.03235901892185211,
0.05178271606564522,
-0.010611340403556824,
0.036519963294267654,
0.04286067560315132,
0.06432643532752991,
0.07397554069757462,
-0.005059156101197004,
-0.06062999367713928,
-0.016132669523358345,
-0.012711068615317345,
-0.0329536572098732,
0.008226166479289532,
-0.033082734793424606,
-0.05295797809958458,
-0.00430656410753727,
0.013199372217059135,
-0.02614087052643299,
-0.0022477018646895885,
0.022025946527719498,
-0.006381816230714321,
0.07683886587619781,
-0.011684739030897617,
0.025206873193383217,
-0.01690310798585415,
0.01843404583632946,
-0.024377621710300446,
0.008568021468818188,
-0.061729252338409424,
0.010389886796474457,
-0.02586432732641697,
0.009656194597482681,
0.04161398485302925,
0.01448468491435051,
0.030825885012745857,
0.04983449727296829,
0.016147781163454056,
-0.08354002982378006,
0.030138324946165085,
0.009645895101130009,
-0.037977010011672974,
-0.008939606137573719,
-0.027755841612815857,
-0.02222445048391819,
0.016841568052768707,
-0.012761169113218784,
0.07245545834302902,
-0.0247945599257946,
0.006946883164346218,
0.023998413234949112,
0.009997088462114334,
0.012893632985651493,
-0.0432797446846962,
-0.07521609961986542,
-0.024616174399852753,
0.02945653907954693,
-0.018774723634123802,
-0.029988331720232964,
-0.05512003228068352,
-0.017475292086601257,
0.007924485951662064,
-0.002360713202506304,
0.015046801418066025,
0.0063345408998429775,
0.040109023451805115,
0.03220171108841896,
0.015671882778406143,
-0.025213686749339104,
-0.026800068095326424,
0.01973101682960987,
0.006630615796893835,
-0.0037077779415994883,
0.01511429250240326,
0.054962899535894394,
0.018536711111664772,
0.008077197708189487,
0.0340820774435997,
-0.08741167187690735,
-0.04149194061756134,
0.01872490905225277,
0.01049910206347704,
-0.024885091930627823,
-0.05535443499684334,
-0.061053670942783356,
0.047451768070459366,
-0.03885186091065407,
0.023747216910123825,
-0.07777324318885803,
0.014119012281298637,
0.03147336468100548,
-0.01854066550731659,
-0.041997380554676056,
0.0023414134047925472,
0.04051459953188896,
0.001305252779275179,
-0.04723668098449707,
-0.005661096889525652,
-0.024661865085363388,
0.03329929709434509,
-0.0547468326985836,
0.024548903107643127,
-0.04399660974740982,
-0.012757014483213425,
-0.0039536007679998875,
0.005598217714577913,
-0.046975310891866684,
0.004734473768621683,
0.03721940517425537,
0.013305057771503925,
0.012966690585017204,
0.009574267081916332,
-0.011468688026070595,
0.016441939398646355,
0.033254534006118774,
0.0055982922203838825,
-0.0598350428044796,
-0.027548670768737793,
0.005486029200255871,
0.021943993866443634,
0.00915648601949215,
-0.01801234856247902,
-0.02846468612551689,
0.042444679886102676,
0.028591180220246315,
0.04111258685588837,
-0.06113336607813835,
-0.024422824382781982,
-0.025240037590265274,
-0.055477555841207504,
-0.030712904408574104,
0.016560086980462074,
-0.009599626995623112,
0.005087139550596476,
0.032281890511512756,
-0.013540592975914478,
0.03210893273353577,
0.021290088072419167,
0.041032321751117706,
0.027806125581264496,
0.029306326061487198,
-0.022779272869229317,
-0.02495955303311348,
-0.0062394458800554276,
0.01563940942287445,
-0.017381856217980385,
0.030719317495822906,
-0.014760923571884632,
0.07994016259908676,
-0.0862138420343399,
-0.02223314344882965,
-0.03219882398843765,
-0.047953877598047256,
0.02533312886953354,
0.009792884811758995,
-0.06662183254957199,
0.03756622597575188,
-0.030378179624676704,
-0.04972599819302559,
0.038252029567956924,
0.016824845224618912,
0.0011521399719640613,
0.015975957736372948,
0.015485748648643494,
0.012021626345813274,
0.028364380821585655,
0.008493076078593731,
0.03923933580517769,
0.08174113929271698,
0.026742039248347282,
0.0005868193111382425,
-0.09408725053071976,
-0.05327454209327698,
0.010182038880884647,
0.037082377821207047,
-0.008577990345656872,
0.00859400350600481,
-0.02418556436896324,
0.11538776010274887,
0.06023580953478813,
0.0005408723372966051,
-0.005044109653681517,
0.0003392676590010524,
-0.057513706386089325,
0.06788315623998642,
0.04296626150608063,
-0.0015500345034524798,
-0.017113247886300087,
-0.03201747685670853,
0.006193246692419052,
0.07418631762266159,
-0.029555846005678177,
-0.0011771529680117965,
0.02507302351295948,
-0.04365240037441254,
0.010801435448229313,
0.003149083349853754,
-0.008971575647592545,
0.03354359045624733,
-0.009595620445907116,
-0.0066902837716042995,
-0.06650614738464355,
0.04606430232524872,
0.04292549192905426,
0.11592665314674377,
-0.022687429562211037,
-0.02865932509303093,
0.023244693875312805,
0.019298167899250984,
-0.02380182407796383,
-0.018546607345342636,
-0.03707698732614517,
0.021053513512015343,
-0.12339220196008682,
0.02150505781173706,
0.05770100653171539,
0.023249706253409386,
0.008216743357479572,
0.023989226669073105,
-0.03258082643151283,
-0.02132585644721985,
0.029109321534633636,
-0.030942516401410103,
0.024813229218125343,
-0.012978142127394676,
-0.06699354946613312,
-0.0072540235705673695,
0.00969272293150425,
-0.028316766023635864,
0.015213006176054478,
0.057734694331884384,
-0.01237131841480732,
0.061728786677122116,
-0.002582387998700142,
-0.011845413595438004,
-0.06434834748506546,
-0.04529895633459091,
-0.04032563045620918,
-0.003909288439899683,
0.008197925984859467,
-0.04190123826265335,
0.018037885427474976,
0.024957267567515373,
-0.060053154826164246,
-0.03903234004974365,
-0.012396194040775299,
-0.019475094974040985,
-0.02027134783565998,
0.02236156538128853,
0.047465573996305466,
-0.016773592680692673,
-0.00023247369972523302,
0.08376408368349075,
0.010902761481702328,
0.045826785266399384,
-0.015175449661910534,
0.026088042184710503,
-0.007812555879354477,
0.010168883018195629,
-0.05135875195264816,
0.009750655852258205,
-0.05009686201810837,
0.0016385779017582536,
0.004619857296347618,
0.028490714728832245,
-0.055426742881536484,
-0.07429803162813187,
-0.030134784057736397,
0.0010667472379282117,
-0.012956884689629078,
0.021297061815857887,
-0.05015641450881958,
0.03526013717055321,
-0.04569707065820694,
-0.0810241848230362,
-0.04459964483976364,
-0.027632853016257286,
-0.03772906959056854,
0.024167079478502274,
0.022129464894533157,
0.004663901403546333,
-0.028634171932935715,
0.021705351769924164,
0.05252547934651375,
0.028180517256259918,
0.06739611178636551,
-0.00016149472503457218,
-0.06846560537815094,
-0.058024778962135315,
-0.051096633076667786,
-0.06188146024942398,
0.029991667717695236,
0.0058140880428254604,
0.042914390563964844,
-0.00455511175096035,
-0.050353240221738815,
0.006189127452671528,
-0.05110331252217293,
0.04230397939682007,
-0.03709836304187775,
0.016977284103631973,
0.006482877302914858,
-0.08386615663766861,
0.009026492945849895,
0.052078112959861755,
-0.05586286261677742,
-0.01564813405275345,
0.02780577354133129,
0.014212697744369507,
-0.0005534238298423588,
-0.04330221191048622,
-0.09007300436496735,
0.03184989467263222,
-0.0024307870771735907,
-0.017833871766924858,
-0.03295953944325447,
0.06532694399356842,
0.009343123063445091,
0.048327308148145676,
0.02330058626830578,
0.020315418019890785,
-0.009671968407928944,
0.006007674150168896,
0.07272011786699295,
0.00449821911752224,
-0.007336287759244442,
-0.0030619960743933916,
-0.06304603070020676,
0.03402945026755333,
0.012543106451630592,
-0.012413118965923786,
-0.02043275348842144,
-0.0389946848154068
] |
<p>I'm curious if you have a radiator or say a block of metal (lets say it's copper since it has the highest thermal conductivity) and on one side is a processor producing heat.</p>
<p>At idle the processor heats the block to 50°C, and the block is 120mm x 120mm. The ambient room temp is 22.2°C. You put a fan on the block (120mm x 120mm @ 1000RPM) and it cools the block to 40°C. Now drop the ambient temp 2 degrees C to 20.2°C.</p>
<p>Would the full change in ambient temp take effect upon the aluminum block? Would it have less effect due to the blocks efficiency? The processor's heat is constant and the fan blowing on the block is constant.</p> | g1227 | [
0.0912298932671547,
0.010258510708808899,
0.03131368011236191,
0.01049769390374422,
-0.0077776298858225346,
-0.01998625136911869,
-0.010981054976582527,
0.05099450424313545,
-0.04595424607396126,
0.05295905843377113,
0.008215445093810558,
0.09559336304664612,
-0.02992313541471958,
-0.00037093000719323754,
0.04403961822390556,
0.03406466916203499,
0.00003712188117788173,
-0.032407645136117935,
0.04443206638097763,
0.05776391550898552,
-0.00781139824539423,
-0.05289316177368164,
-0.01300795003771782,
-0.012585051357746124,
0.008454508148133755,
-0.007594973314553499,
0.0017806956311687827,
-0.039184413850307465,
-0.09072396159172058,
0.019012222066521645,
-0.07112666219472885,
0.04440098628401756,
-0.01627708040177822,
0.024277620017528534,
-0.04788685217499733,
0.03385200724005699,
0.09788279980421066,
0.024373028427362442,
-0.03285835683345795,
-0.01984783448278904,
-0.006717310752719641,
0.0008400955703109503,
0.03501540422439575,
0.014029668644070625,
-0.015206195414066315,
0.02989594265818596,
-0.02203710563480854,
-0.023386036977171898,
-0.09631406515836716,
-0.012210793793201447,
-0.0021317587234079838,
-0.05758709833025932,
0.014607951045036316,
0.014496642164885998,
0.011523489840328693,
-0.03654726594686508,
-0.03885313495993614,
0.034724507480859756,
0.044234756380319595,
0.019960055127739906,
0.003911974374204874,
0.04479266330599785,
-0.0030425717122852802,
-0.06759975105524063,
-0.047104574739933014,
-0.009146850556135178,
0.03654409945011139,
0.00438215397298336,
0.007480524946004152,
0.053505029529333115,
0.012990567833185196,
-0.002563498681411147,
-0.006596332881599665,
-0.042379457503557205,
0.010710028931498528,
-0.006196537520736456,
-0.015210793353617191,
-0.03550506383180618,
0.04708079993724823,
0.08379504829645157,
0.008542810566723347,
-0.05343974381685257,
0.05899861082434654,
0.007022653240710497,
0.014787049032747746,
0.016539815813302994,
-0.05388053134083748,
0.012484005652368069,
-0.03907088190317154,
0.015666445717215538,
-0.004273829981684685,
0.017535608261823654,
0.04528886079788208,
0.014606412500143051,
0.057592544704675674,
0.050207946449518204,
0.006511983461678028,
0.011669684201478958,
-0.04062167555093765,
0.00018435801030136645,
-0.012410508468747139,
0.011379564180970192,
0.09119077771902084,
0.018807323649525642,
-0.035427071154117584,
-0.026703447103500366,
0.001457855338230729,
-0.011282693594694138,
-0.03353988379240036,
0.015427387319505215,
0.028642931953072548,
-0.04706593230366707,
-0.08633087575435638,
-0.04743103310465813,
-0.05981896072626114,
-0.014434312470257282,
0.08211017400026321,
0.03581823408603668,
-0.046473514288663864,
0.020514260977506638,
0.037322964519262314,
0.020662423223257065,
-0.019289426505565643,
-0.01643751561641693,
0.059204261749982834,
-0.005734370555728674,
-0.02102690376341343,
0.009468670934438705,
0.03304734826087952,
0.006290515884757042,
0.03669310733675957,
0.06678669899702072,
-0.05175720155239105,
0.011529829353094101,
0.02842380292713642,
0.0013986623380333185,
0.011423474177718163,
-0.016954723745584488,
-0.008568552322685719,
-0.05154626816511154,
0.012936816550791264,
0.02874939888715744,
-0.04473244026303291,
-0.009371502324938774,
-0.05828278884291649,
0.06281477212905884,
-0.03845082223415375,
-0.014458518475294113,
-0.015216391533613205,
-0.007063360419124365,
0.020010925829410553,
-0.01506213191896677,
0.009294409304857254,
-0.03999732434749603,
-0.016261614859104156,
0.024858135730028152,
-0.049136579036712646,
-0.013312997296452522,
0.01252114400267601,
0.010947621427476406,
0.01321355253458023,
-0.005191591568291187,
0.035269055515527725,
-0.019277241080999374,
-0.10282250493764877,
0.0016092404257506132,
-0.032983239740133286,
0.0201580673456192,
0.002572433091700077,
-0.0550953671336174,
-0.024617696180939674,
0.03840300440788269,
-0.05425260215997696,
-0.004833810962736607,
-0.020867781713604927,
-0.0012237197952345014,
0.06937006860971451,
-0.0024616967421025038,
0.02794414572417736,
-0.031225034967064857,
-0.054304543882608414,
0.010296294465661049,
0.02131825126707554,
-0.04967085272073746,
0.009024592116475105,
0.013624358922243118,
0.0075131673365831375,
-0.010635167360305786,
-0.03684770688414574,
0.02358930930495262,
-0.06558020412921906,
-0.015996301546692848,
0.051886849105358124,
0.030034098774194717,
-0.021277517080307007,
0.022037068381905556,
-0.05519485101103783,
-0.02838708646595478,
-0.016320940107107162,
0.00848465971648693,
0.03599223494529724,
0.03983938694000244,
-0.0029106028378009796,
0.005430341698229313,
0.019722934812307358,
0.0935625359416008,
-0.03634284436702728,
0.0029673660174012184,
0.02819361910223961,
-0.045011505484580994,
0.0298435240983963,
0.05509086325764656,
0.0395110584795475,
0.036313097923994064,
0.026308570057153702,
0.04831691458821297,
-0.0314236581325531,
0.0318707637488842,
-0.025900866836309433,
0.032695472240448,
0.04247013479471207,
0.029796795919537544,
-0.02395102195441723,
0.01907958835363388,
-0.009864438325166702,
-0.06328415125608444,
-0.0331386923789978,
-0.0056239343248307705,
-0.008941027335822582,
0.031245391815900803,
-0.05456504225730896,
0.006033527664840221,
0.04506215453147888,
-0.03659719601273537,
-0.007883032783865929,
0.017078842967748642,
0.02678496204316616,
0.07820966094732285,
0.0148610919713974,
-0.03591812402009964,
-0.01756974868476391,
-0.0031096285674721003,
-0.07016562670469284,
0.00753757543861866,
0.015502272173762321,
-0.054370760917663574,
-0.019456056877970695,
0.005942794028669596,
0.005693687591701746,
-0.026722710579633713,
-0.008190096355974674,
0.01996362954378128,
-0.04476645961403847,
0.019028939306735992,
-0.038489483296871185,
-0.02616037428379059,
-0.055787231773138046,
0.017807552590966225,
0.05269135162234306,
0.0005624121404252946,
-0.014476822689175606,
-0.062208157032728195,
-0.025619538500905037,
0.05091270059347153,
0.013187488541007042,
0.022017454728484154,
-0.020606061443686485,
-0.012974852696061134,
0.01852426677942276,
0.07865010201931,
0.034410543739795685,
0.0364936888217926,
0.009353606030344963,
0.0061675733886659145,
-0.06631605327129364,
-0.03267718851566315,
-0.01536140963435173,
-0.057836417108774185,
-0.011687571182847023,
-0.004704069346189499,
0.030792735517024994,
0.009355018846690655,
-0.06414563953876495,
0.028733981773257256,
0.0429457388818264,
-0.021943116560578346,
-0.04520807042717934,
0.0353308729827404,
0.004144913516938686,
-0.04718499258160591,
-0.014512480236589909,
0.006213851738721132,
0.017782067880034447,
-0.030814120545983315,
0.04020952060818672,
0.01235415693372488,
-0.002983999438583851,
0.015787167474627495,
-0.018590472638607025,
0.02909606508910656,
0.0021758603397756815,
-0.05620822682976723,
-0.07143928855657578,
0.009401187300682068,
0.01740354672074318,
0.03112485073506832,
-0.08539633452892303,
-0.002904699882492423,
0.018716590479016304,
-0.01657259277999401,
-0.01527947187423706,
0.02791927382349968,
0.03271077200770378,
0.019093457609415054,
-0.04621068760752678,
0.004279077053070068,
-0.04420500993728638,
-0.04941385239362717,
-0.0234995037317276,
-0.005841020029038191,
-0.0021423378493636847,
-0.03279469907283783,
0.007875856943428516,
0.01808764785528183,
0.004984049126505852,
0.05862169712781906,
0.055575672537088394,
0.023477448150515556,
-0.024503488093614578,
0.018916450440883636,
-0.06729985773563385,
-0.015450038947165012,
-0.0644352063536644,
-0.026473890990018845,
-0.026021244004368782,
0.0401400551199913,
0.016369612887501717,
0.029844168573617935,
-0.02842903323471546,
-0.020912233740091324,
0.012645662762224674,
-0.012860333546996117,
0.008998334407806396,
0.005354989320039749,
0.018941348418593407,
0.03403634577989578,
0.016128597781062126,
-0.01860860176384449,
-0.03168894723057747,
0.041451141238212585,
0.0744679719209671,
-0.05019273981451988,
-0.0029141174163669348,
0.003612038679420948,
-0.0687798336148262,
-0.026421792805194855,
-0.010668198578059673,
0.02713930234313011,
-0.05119030177593231,
0.01997830718755722,
-0.010557261295616627,
-0.018206380307674408,
0.02451869659125805,
-0.05732124298810959,
-0.0010071833385154605,
0.061623960733413696,
-0.012276064604520798,
-0.007938804104924202,
0.016801344230771065,
-0.005774755962193012,
0.025785433128476143,
0.030636264011263847,
-0.06989477574825287,
0.02767769806087017,
0.028618277981877327,
0.04232897236943245,
0.031827859580516815,
0.03870927542448044,
-0.0021320469677448273,
0.04518936574459076,
-0.032285090535879135,
0.009190087206661701,
0.027692345902323723,
0.0013549431459978223,
-0.045558009296655655,
0.009428110904991627,
-0.035169567912817,
0.04247942939400673,
-0.043388206511735916,
-0.07830697298049927,
-0.02218826860189438,
0.01039869338274002,
0.006501924712210894,
0.042434390634298325,
-0.00020818185294046998,
-0.009632185101509094,
-0.00718059204518795,
-0.0448329821228981,
0.029148302972316742,
0.022645937278866768,
0.04457729682326317,
0.044419270008802414,
0.042045287787914276,
-0.022667285054922104,
0.005381698254495859,
-0.06956325471401215,
0.03573478385806084,
-0.0009945648489519954,
-0.04568519815802574,
-0.0162583626806736,
-0.014847972430288792,
-0.07009073346853256,
-0.02033837139606476,
0.03179037943482399,
0.03452634438872337,
0.002097147749736905,
-0.0019126578699797392,
0.061905913054943085,
0.02638479694724083,
-0.020055286586284637,
-0.09595388919115067,
-0.06326960027217865,
-0.02691733092069626,
-0.008890911005437374,
0.022323481738567352,
0.010776784271001816,
0.006882627960294485,
-0.06355155259370804,
-0.029919350519776344,
-0.008271846920251846,
-0.02227354235947132,
0.030835319310426712,
-0.06976516544818878,
0.0036826927680522203,
-0.003630751743912697,
0.07587039470672607,
-0.01817898266017437,
0.049137044697999954,
0.034231998026371,
-0.023629801347851753,
0.01705724000930786,
-0.0030241594649851322,
-0.01650112122297287,
0.0651039183139801,
-0.04043016955256462,
0.06211674585938454,
-0.00284840096719563,
-0.023582905530929565,
0.031090490520000458,
-0.020294727757573128,
-0.06269101798534393,
0.030347608029842377,
-0.06310894340276718,
0.003559091128408909,
-0.011711971834301949,
0.002171360421925783,
-0.004995179362595081,
0.031817540526390076,
0.04975485801696777,
0.05466397479176521,
-0.035168543457984924,
-0.006467615719884634,
0.010563967749476433,
0.02795501798391342,
-0.06366811692714691,
-0.019039545208215714,
0.049986839294433594,
-0.01479626540094614,
-0.09232116490602493,
0.04838895425200462,
0.037019867449998856,
0.05990394204854965,
0.013535376638174057,
0.06765598058700562,
0.05031938478350639,
0.06843949854373932,
0.025601385161280632,
-0.017678964883089066,
0.019365446642041206,
-0.0043782941065728664,
-0.01408375520259142,
-0.0018119936576113105,
0.025993747636675835,
-0.01382098626345396,
0.01960848830640316,
-0.02790651097893715,
-0.07245806604623795,
0.020889604464173317,
0.025673193857073784,
-0.037919409573078156,
-0.010672777891159058,
0.009366418235003948,
-0.028419043868780136,
0.01979789324104786,
-0.04999936744570732,
0.004542263690382242,
-0.015069665387272835,
-0.02859494276344776,
0.05149456858634949,
-0.026515807956457138,
0.010494654066860676,
0.040057748556137085,
-0.003234059549868107,
-0.04058827459812164,
-0.03202948346734047,
0.04077416658401489,
-0.042726825922727585,
-0.03155706077814102,
-0.01499076560139656,
-0.002505991840735078,
-0.018778512254357338,
0.02611020766198635,
-0.01869409717619419,
0.019203003495931625,
0.04641309380531311,
-0.04813208803534508,
-0.03753216937184334,
-0.035568058490753174,
-0.03507279232144356,
-0.015042450278997421,
0.009163223206996918,
-0.03064461424946785,
0.027353975921869278,
0.045517340302467346,
0.004240058828145266,
0.032264333218336105,
-0.07131421566009521,
0.031371258199214935,
-0.06478983163833618,
0.04184101149439812,
0.0099269337952137,
0.01535471435636282,
0.02241632342338562,
0.004151700064539909,
0.0013115550391376019,
-0.02693811245262623,
-0.012243397533893585,
-0.004246645141392946,
0.04953319579362869,
0.04677436500787735,
0.025820432230830193,
0.00911161582916975,
0.03872125968337059,
0.03677964210510254,
0.028865348547697067,
-0.0009350085165351629,
0.0035972222685813904,
0.02385871484875679,
0.052974436432123184,
-0.04316885769367218,
0.035769131034612656,
0.004865027964115143,
0.0032974679488688707,
0.0014824384124949574,
0.024170642718672752,
0.007950329221785069,
0.05526565760374069,
0.010441495105624199,
0.03073125146329403,
-0.03390936180949211,
-0.03459763526916504,
-0.0219474695622921,
0.05141708254814148,
-0.02214732952415943,
0.00003385446689208038,
-0.07085304707288742,
-0.03587966784834862,
-0.014965766109526157,
0.05184183642268181,
0.01930672489106655,
0.08754570037126541,
-0.033318500965833664,
0.01820024661719799,
-0.08208005875349045,
0.009123383089900017,
0.002244201023131609,
-0.0861716940999031,
0.0043832166120409966,
0.00859221164137125,
0.01643626019358635,
-0.024569401517510414,
-0.008848659694194794,
0.0030096827540546656,
0.030139505863189697,
0.049202725291252136,
0.029990432783961296,
-0.024175604805350304,
0.03778264671564102,
0.03365163132548332,
0.04810028150677681,
-0.03652671352028847,
-0.04836135730147362,
0.03161872178316116,
0.04863440617918968,
0.00696793757379055,
-0.00372405257076025,
-0.07477305829524994,
0.0020736136939376593,
0.006886644754558802,
-0.03280826658010483,
0.035567060112953186,
0.0009105530334636569,
-0.012817987240850925,
-0.10143321007490158,
-0.014392922632396221,
0.018740512430667877,
0.008981946855783463,
-0.006613016128540039,
0.03382517397403717,
-0.003640526905655861,
-0.044689226895570755,
0.0037306854501366615,
0.06372613459825516,
-0.015793751925230026,
0.037651777267456055,
-0.02216389775276184,
0.011351185850799084,
-0.039051707834005356,
-0.013992203399538994,
0.017993655055761337,
0.026059294119477272,
-0.031193075701594353,
0.02885567955672741,
-0.08802793174982071,
-0.027713539078831673,
0.07213366776704788,
-0.007090037688612938,
0.0010737446136772633,
0.021634066477417946,
0.00696590868756175,
-0.02450193092226982,
0.005868054926395416,
-0.04593846946954727,
0.007861653342843056,
-0.005906650796532631,
0.03933289274573326,
0.0010202834382653236,
0.011285052634775639,
-0.01859387196600437,
0.07823368906974792,
-0.012206735089421272,
0.0020500721875578165,
-0.021247945725917816,
0.025873035192489624,
-0.0270663071423769,
-0.01564083993434906,
0.03857427462935448,
0.029097069054841995,
-0.04130558669567108,
0.013162387534976006,
-0.015798920765519142,
-0.020709224045276642,
-0.05314479023218155,
0.06069225072860718,
0.01150042936205864,
0.0016464133514091372,
-0.05344255268573761,
0.030325070023536682,
-0.02581831067800522,
0.0020477124489843845,
-0.05927792564034462,
-0.04027703404426575,
0.012006006203591824,
0.12000979483127594,
0.010916761122643948,
0.010506776161491871,
0.044449582695961,
-0.004865151364356279,
0.025560373440384865,
-0.08425572514533997,
-0.02543860673904419,
-0.04047595337033272,
0.003665363881736994,
0.00656058918684721,
0.06332716345787048,
0.0275135301053524,
-0.009845966473221779,
-0.05534196272492409,
-0.023467982187867165,
-0.025657810270786285,
0.03001377172768116,
0.00024926045443862677,
-0.034341420978307724,
-0.028491640463471413,
-0.0033762336242944,
0.014946555718779564,
-0.06427275389432907,
-0.007086936850100756,
0.024629054591059685,
-0.07901885360479355,
-0.023865990340709686,
0.011304877698421478,
0.009636038914322853,
-0.01405318919569254,
-0.07431095093488693,
0.0815543457865715,
0.040481582283973694,
-0.012042361311614513,
-0.01541976723819971,
-0.02966180257499218,
-0.010355030186474323,
-0.004652503412216902,
0.023176707327365875,
-0.001715514692477882,
0.013312915340065956,
0.016192937269806862,
0.04677233472466469,
0.06101016327738762,
-0.028710851445794106,
0.058066874742507935,
0.04415042698383331,
0.018203798681497574,
0.05448925867676735,
-0.010648945346474648,
-0.03509615361690521,
-0.03908601775765419,
-0.04314442351460457,
-0.006201242562383413,
-0.010056106373667717,
0.07275081425905228,
-0.03284803032875061,
-0.0016585212433710694,
0.031716905534267426,
-0.025804752483963966,
0.019055627286434174,
-0.00777019327506423,
0.023915797472000122,
-0.008775414898991585,
0.04867325723171234,
-0.06636161357164383,
0.020073693245649338,
0.03356550633907318,
-0.01873811148107052,
-0.03522640839219093,
0.021150218322873116,
-0.001106463372707367,
0.034693606197834015,
0.029780752956867218,
0.006878491956740618,
0.003970955032855272,
-0.016279634088277817,
0.018946800380945206,
-0.023685801774263382,
0.00895287748426199,
0.006403624080121517,
-0.017853252589702606,
-0.041411805897951126,
0.031645163893699646,
-0.006750892382115126,
0.0041114394553005695,
-0.08486717939376831,
0.04449668526649475,
-0.06596105545759201,
-0.026478635147213936,
-0.005741259083151817,
0.04557715728878975,
-0.07496064901351929,
0.03038034774363041,
-0.004457398783415556,
0.0012442797888070345,
0.005474881734699011,
0.02289951778948307,
-0.054065730422735214,
-0.022873008623719215,
0.014354610815644264,
0.018454967066645622,
0.02745923213660717,
-0.005381659604609013
] |
<p>If I have two balls with masses and charges $m_1, q_1^{+}$, $m_2, q_2^{+}$, initially held at distance $d$, and then released, how can I know the kinetic energies of each of the balls at infinite distance between them? I'm quite stuck on that, because they both have the same potential energy at the beginning, and it decreases not in the same pattern, as if one of the balls was stationary. So it not only falls like $1/R$, because at the same time, the other ball that is causing this potential energy, is also being repelled. So how can I really find out the energies? I tried to apply the conservation of energy law, because I know that at infinite distance from each other they'll have zero potential energy, thus all the initial was transformed into kinetic form, however I'm stuck with the initial potential energy (they both have it, so should I put $2U_p$?), and even so, I can't find their kinetic energies separately, without having another equation.</p> | g1228 | [
0.06621494144201279,
-0.035473085939884186,
0.0017811161233112216,
-0.02894308976829052,
0.07292795926332474,
0.032520685344934464,
-0.0032477308996021748,
0.05315307155251503,
-0.05059938505291939,
0.00225983839482069,
-0.04810705408453941,
0.0028717401437461376,
0.021203940734267235,
-0.01884075626730919,
-0.009796163998544216,
-0.001086326315999031,
0.09554722160100937,
-0.038271352648735046,
-0.03655032068490982,
0.01682402566075325,
-0.024623220786452293,
-0.014798738993704319,
0.01272605825215578,
-0.012305318377912045,
-0.025640135630965233,
0.0013656264636665583,
-0.000037063724448671564,
0.01995273493230343,
-0.04218539968132973,
-0.043611206114292145,
0.00007340872252825648,
-0.004265885334461927,
0.043428849428892136,
-0.026270922273397446,
0.005423710215836763,
-0.009199649095535278,
0.08714792877435684,
-0.10671351104974747,
-0.03726775571703911,
-0.012801602482795715,
0.03223530203104019,
-0.03283179923892021,
0.05987770855426788,
0.005446029826998711,
0.012654634192585945,
-0.0322074256837368,
-0.005110110621899366,
0.02145475149154663,
-0.012464644387364388,
-0.008193864487111568,
0.042852845042943954,
0.09075431525707245,
-0.01061897911131382,
0.01468346081674099,
-0.009594590403139591,
0.002465856494382024,
-0.013663053512573242,
-0.05143757537007332,
0.0779685229063034,
0.05125528946518898,
0.07184872031211853,
-0.01503751240670681,
-0.01118526142090559,
-0.018569493666291237,
0.0565270259976387,
-0.049326878041028976,
-0.07306328415870667,
0.0015850658528506756,
-0.04326049983501434,
0.02299947291612625,
0.0010603353148326278,
0.021312229335308075,
-0.017054405063390732,
0.020975112915039062,
0.028889480978250504,
-0.042993322014808655,
0.04424913972616196,
-0.00438650231808424,
0.040440633893013,
-0.004922839347273111,
-0.05130298063158989,
0.04026772081851959,
0.07955819368362427,
-0.009116291999816895,
0.04741944372653961,
0.010495735332369804,
-0.02288210578262806,
0.014425371773540974,
-0.0789073035120964,
0.027005398645997047,
0.021984320133924484,
-0.015457101166248322,
0.05095066502690315,
0.015590284951031208,
-0.027096403762698174,
-0.04902490973472595,
-0.01672741211950779,
0.04284628853201866,
0.01639794185757637,
-0.026637159287929535,
-0.0003129015676677227,
0.006904805079102516,
0.052889954298734665,
0.003100881353020668,
-0.0077837686985731125,
0.013247579336166382,
0.0011033645132556558,
0.01758909970521927,
0.0058618937619030476,
0.029341693967580795,
0.0073668016120791435,
-0.033237800002098083,
-0.027027571573853493,
-0.0034905888605862856,
-0.02680973894894123,
-0.05626337230205536,
0.0499269962310791,
-0.023554155603051186,
-0.027137162163853645,
0.04718171805143356,
0.025143995881080627,
0.046037402004003525,
0.0010714964009821415,
-0.00013233507343102247,
0.028227580711245537,
0.0068006254732608795,
-0.011504435911774635,
-0.01228567585349083,
0.01848818175494671,
-0.018657000735402107,
-0.020208057016134262,
-0.03368481993675232,
0.05155535414814949,
-0.02140054851770401,
-0.07435983419418335,
0.041608575731515884,
0.013547594659030437,
0.021911125630140305,
0.004291990771889687,
0.005042960401624441,
0.006589123513549566,
-0.030282793566584587,
0.029030686244368553,
-0.019666915759444237,
-0.020542794838547707,
0.04511931911110878,
0.01273596752434969,
-0.04241974279284477,
0.03515852615237236,
0.055772945284843445,
0.04776567220687866,
0.023661550134420395,
0.003724663518369198,
-0.015455054119229317,
0.07433570921421051,
-0.062233611941337585,
0.042605310678482056,
-0.004398403223603964,
-0.02979622222483158,
-0.015171714127063751,
0.06114991009235382,
0.016214819625020027,
0.0895676538348198,
-0.022894421592354774,
-0.0055241938680410385,
0.03444240614771843,
0.040486324578523636,
-0.006892700679600239,
-0.004608774557709694,
-0.04226682707667351,
-0.060557372868061066,
-0.040843665599823,
0.03133538365364075,
0.04535793513059616,
-0.04090602695941925,
0.0459328256547451,
-0.009578916244208813,
-0.01558280922472477,
0.01568283885717392,
0.036359354853630066,
0.01169340219348669,
0.007755296770483255,
0.03621496632695198,
0.021076064556837082,
0.017516933381557465,
0.04520044103264809,
-0.030204100534319878,
0.07555993646383286,
-0.013566945679485798,
-0.018973078578710556,
0.008692008443176746,
0.003979196771979332,
-0.007007261272519827,
-0.0033244118094444275,
0.022814931347966194,
0.04259495437145233,
0.05253586173057556,
-0.026784002780914307,
-0.02647867053747177,
0.029093729332089424,
-0.04813678562641144,
0.015606756322085857,
0.0008920719265006483,
0.016308089718222618,
0.00808264221996069,
0.0007968387217260897,
0.0365036278963089,
0.0020793648436665535,
0.034832436591386795,
-0.03159835934638977,
-0.01638847589492798,
-0.05131947994232178,
-0.02908034808933735,
0.021529946476221085,
0.0012858585687354207,
0.01922057941555977,
-0.031126035377383232,
0.007269342429935932,
-0.022572077810764313,
-0.013278252445161343,
-0.08784864842891693,
0.03689239174127579,
0.04021051526069641,
0.0005120644345879555,
-0.023720283061265945,
0.005330848507583141,
-0.06123053655028343,
0.000838306441437453,
-0.03437713161110878,
0.03267251327633858,
-0.041999492794275284,
0.04756368324160576,
0.0019761379808187485,
0.02342289499938488,
0.0382077619433403,
0.003341472940519452,
-0.04326487332582474,
-0.002975091803818941,
0.012904403731226921,
0.00021555201965384185,
0.005700268782675266,
-0.04914052039384842,
0.02717982605099678,
0.028011605143547058,
0.014115304686129093,
-0.03817484527826309,
0.05031795799732208,
0.03365074843168259,
0.032708801329135895,
0.012207240797579288,
0.008695846423506737,
0.0175810307264328,
0.0005755441379733384,
0.008784487843513489,
-0.01634538732469082,
-0.0023992371279746294,
-0.017923101782798767,
-0.023128550499677658,
-0.05237356573343277,
-0.07553203403949738,
0.002402703743427992,
-0.018316907808184624,
-0.0015160390175879002,
0.002021841937676072,
0.0027639325708150864,
-0.05699438601732254,
0.017747769132256508,
0.042814772576093674,
-0.007295872550457716,
0.004017081577330828,
-0.05203275382518768,
0.08756598085165024,
0.02937408722937107,
0.014783401973545551,
0.015436012297868729,
-0.037356212735176086,
0.033250842243433,
-0.04143696278333664,
0.01576158031821251,
-0.006505639757961035,
0.016655998304486275,
-0.006609233096241951,
-0.04824008792638779,
0.01681380718946457,
0.06202445179224014,
-0.07118479907512665,
0.008212544023990631,
0.03934842720627785,
0.06723061949014664,
-0.031091226264834404,
-0.02231234312057495,
0.07141636312007904,
0.13710494339466095,
-0.04096154496073723,
-0.044497739523649216,
0.0475287102162838,
0.037968285381793976,
-0.024656597524881363,
-0.03521279990673065,
-0.03959454968571663,
0.01578710973262787,
-0.029323749244213104,
0.02826553024351597,
0.024401646107435226,
0.05619462952017784,
0.09698862582445145,
-0.04465019702911377,
0.02678360603749752,
0.06346974521875381,
-0.03412949666380882,
-0.014707517810165882,
0.03371541202068329,
0.03960033506155014,
0.03642024099826813,
-0.04722852632403374,
-0.0026730401441454887,
0.0005264402134343982,
-0.009221462532877922,
-0.012165220454335213,
-0.015002112835645676,
-0.006906754802912474,
-0.005897742696106434,
0.08277032524347305,
0.023502955213189125,
0.02213292010128498,
0.014227895066142082,
-0.03861655667424202,
-0.008971510455012321,
-0.011951166205108166,
-0.017218470573425293,
-0.001955213723704219,
0.049444641917943954,
0.049626149237155914,
-0.06495317071676254,
0.02341356873512268,
-0.05951092019677162,
-0.014095515012741089,
-0.00422716373577714,
0.016823410987854004,
0.022380273789167404,
-0.005998623091727495,
0.07099156826734543,
-0.08288739621639252,
-0.005794053431600332,
-0.02408907376229763,
-0.0022225556895136833,
-0.0200594961643219,
-0.03411594405770302,
-0.02782941795885563,
-0.06440127640962601,
0.019831139594316483,
-0.0062635852955281734,
0.029852744191884995,
0.007726145908236504,
-0.018518537282943726,
-0.053598228842020035,
-0.025538191199302673,
0.010187449865043163,
-0.01520842220634222,
-0.01608404517173767,
0.010491336695849895,
-0.022812213748693466,
-0.014762776903808117,
-0.002044862834736705,
-0.013996904715895653,
-0.05165402591228485,
-0.08501963317394257,
-0.06652050465345383,
0.0173550583422184,
-0.029011227190494537,
-0.06396130472421646,
0.006197498179972172,
-0.028354156762361526,
0.009188134223222733,
-0.021408066153526306,
-0.032484255731105804,
0.032900985330343246,
-0.01682896353304386,
-0.054408878087997437,
-0.022754907608032227,
-0.010899701155722141,
-0.021538157016038895,
-0.02076525241136551,
0.014703053049743176,
0.011564245447516441,
0.10290835052728653,
-0.01937362737953663,
-0.02093537338078022,
0.019815951585769653,
-0.00415456248447299,
-0.019243182614445686,
-0.009868397377431393,
-0.012349404394626617,
0.005972170736640692,
0.011872765608131886,
-0.03638394922018051,
0.032997872680425644,
-0.05817459523677826,
0.03809753805398941,
0.03967318311333656,
-0.057845693081617355,
0.011774079874157906,
-0.029151445254683495,
-0.056510332971811295,
0.015062117949128151,
-0.050580982118844986,
0.03145992010831833,
-0.025490211322903633,
0.033131733536720276,
0.0038312720134854317,
-0.014988432638347149,
-0.05225006863474846,
0.047348786145448685,
-0.03633459284901619,
-0.04861901327967644,
-0.004238255321979523,
-0.05234287306666374,
-0.01781645230948925,
-0.04134161397814751,
0.007975481450557709,
0.015928218141198158,
-0.010902747511863708,
-0.024708429351449013,
-0.04515299201011658,
-0.01482479553669691,
0.0919869914650917,
0.05465662106871605,
-0.0007079831557348371,
-0.021106453612446785,
-0.02779233455657959,
0.029341772198677063,
0.04255622625350952,
-0.027501793578267097,
0.0007369124796241522,
-0.0905766561627388,
-0.013229192234575748,
-0.0013768011704087257,
-0.019426332786679268,
0.018160229548811913,
0.041249193251132965,
0.09798949211835861,
0.04792996123433113,
-0.025411678478121758,
0.005139033775776625,
0.007057773880660534,
0.045502614229917526,
-0.0010302279843017459,
0.013166142627596855,
-0.04079144820570946,
-0.06736121326684952,
0.0017628914210945368,
0.017340991646051407,
-0.06460616737604141,
-0.033986423164606094,
0.04385032877326012,
0.01283351518213749,
-0.02663799561560154,
0.010639368556439877,
0.01681016944348812,
0.001581915421411395,
0.02531289868056774,
0.01844104938209057,
0.017899880185723305,
-0.03767011687159538,
-0.022696513682603836,
-0.019073475152254105,
0.0206396896392107,
-0.014583120122551918,
-0.008710102178156376,
-0.04580661281943321,
0.026329534128308296,
0.012789483182132244,
-0.01386323757469654,
-0.039068471640348434,
0.011628611013293266,
-0.03675444796681404,
-0.0062212636694312096,
-0.02931467816233635,
0.07279866188764572,
-0.08093095570802689,
-0.06113138049840927,
0.037923019379377365,
-0.04407263547182083,
0.05621688812971115,
-0.024248739704489708,
0.026501810178160667,
0.01807829923927784,
0.01076532993465662,
0.06567167490720749,
0.05172878876328468,
0.015345281921327114,
0.034032948315143585,
-0.01705220900475979,
0.0001635230437386781,
0.010285777971148491,
-0.027659917250275612,
0.035023827105760574,
0.036466363817453384,
0.003533431328833103,
0.06148659810423851,
0.008636830374598503,
-0.013628209009766579,
0.02552618645131588,
0.01895270310342312,
0.0033043590374290943,
0.0433683879673481,
0.061509955674409866,
-0.04027828574180603,
0.01764003187417984,
0.008939974941313267,
-0.06586288660764694,
0.05398257076740265,
0.01425943709909916,
0.028825407847762108,
0.025246214121580124,
0.02075839415192604,
-0.0007162001566030085,
0.007907094433903694,
-0.009517937898635864,
-0.0021937969140708447,
0.058653827756643295,
-0.01151993777602911,
0.0336630679666996,
0.018086088821291924,
-0.0017241702880710363,
0.02295236848294735,
-0.05085955932736397,
0.016068914905190468,
-0.038858696818351746,
0.0719926506280899,
-0.0033577810972929,
-0.06103162094950676,
-0.07266199588775635,
-0.05142915993928909,
-0.03406236693263054,
-0.010341881774365902,
0.01339358277618885,
-0.047400690615177155,
0.01077505387365818,
-0.009812196716666222,
0.045419421046972275,
-0.05778879299759865,
0.01730949804186821,
0.019355395808815956,
0.0006336307269521058,
-0.021733563393354416,
-0.05076396465301514,
-0.07627550512552261,
0.0566449873149395,
-0.04290125146508217,
0.007394750136882067,
0.014092938974499702,
0.014310394413769245,
-0.011799423955380917,
0.020862450823187828,
0.062354687601327896,
-0.004559013526886702,
-0.01491403579711914,
-0.08232139050960541,
0.0196975190192461,
0.02108016051352024,
0.01258054468780756,
-0.00029691835516132414,
0.058799222111701965,
0.03497672080993652,
-0.007622133009135723,
-0.027783457189798355,
-0.044227439910173416,
0.05148199573159218,
0.03876500576734543,
0.039403174072504044,
-0.012426556088030338,
0.0030150983948260546,
-0.007193438243120909,
0.04670173302292824,
-0.022480422630906105,
0.01375535037368536,
-0.019653383642435074,
-0.04507382959127426,
-0.03165215253829956,
0.012543203309178352,
0.0001050790524459444,
0.006634663324803114,
-0.021682042628526688,
0.0034750979393720627,
0.07862361520528793,
0.010788384824991226,
-0.05529564246535301,
0.06418493390083313,
-0.05497299134731293,
0.026955386623740196,
-0.027845049276947975,
0.021178074181079865,
-0.03834736719727516,
-0.017730936408042908,
0.0012087892973795533,
-0.004046689718961716,
-0.0018487361958250403,
0.0027401873376220465,
0.026176944375038147,
0.0047325799241662025,
-0.01183543261140585,
0.00282297027297318,
-0.024614330381155014,
0.0319671668112278,
-0.008875948376953602,
-0.04735904932022095,
0.0016731052892282605,
-0.02447431907057762,
-9.108851486416825e-7,
-0.08393175899982452,
0.010052531957626343,
-0.03444915637373924,
-0.0036628672387450933,
-0.03327208384871483,
-0.0030926126055419445,
0.003462395863607526,
0.054958928376436234,
-0.09016264975070953,
-0.056025393307209015,
0.01654653251171112,
0.025542326271533966,
0.002944628708064556,
0.023994863033294678,
0.0757075697183609,
0.007567348890006542,
-0.025947747752070427,
0.054885562509298325,
0.04281600937247276,
-0.0011047726729884744,
0.006453636568039656,
0.016355611383914948,
0.039568010717630386,
0.049518078565597534,
0.017074376344680786,
0.043467506766319275,
0.0035965517163276672,
0.05091288313269615,
0.005961363669484854,
-0.03896401450037956,
-0.008123205974698067,
0.021498795598745346,
0.0568842850625515,
0.05476674810051918,
0.0021311831660568714,
-0.04311266541481018,
0.04482961446046829,
0.01559801772236824,
-0.009765570051968098,
-0.01044660247862339,
-0.02466559037566185,
-0.06552503257989883,
-0.009428351186215878,
0.01046694815158844,
-0.0372563861310482,
-0.0030769826844334602,
-0.026259077712893486,
-0.020316675305366516,
0.011331749148666859,
-0.05477399006485939,
0.02120201103389263,
-0.0314105786383152,
0.0017613678937777877,
-0.017734665423631668,
-0.010077317245304585,
0.05320345610380173,
0.009934816509485245,
-0.029830623418092728,
-0.0014786202227696776,
-0.03415992110967636,
0.01440359652042389,
-0.04713284596800804,
-0.05892994999885559,
-0.00007756538252579048,
-0.023701002821326256,
-0.0005333190783858299,
0.038483671844005585,
0.027950644493103027,
-0.017026301473379135,
-0.028265533968806267,
-0.020556116476655006,
0.024846598505973816,
-0.07783833146095276,
-0.003005319507792592,
-0.020745085552334785,
0.07392299175262451,
-0.014061378315091133,
-0.007568138651549816,
-0.027012541890144348,
0.025707297027111053,
-0.046781089156866074,
-0.007631982211023569,
0.022592486813664436,
-0.003794582560658455,
-0.00849322322756052,
-0.029834454879164696,
0.03930378332734108,
0.02295692451298237,
0.032856736332178116,
-0.021832378581166267,
0.01538186613470316,
-0.025247620418667793,
0.06093288213014603,
0.018335534259676933,
0.0033620381727814674,
-0.002116369316354394,
-0.07642118632793427,
-0.039073389023542404,
-0.01917966455221176,
0.002211781218647957,
-0.0034174611791968346,
0.013305896893143654,
0.012733891606330872,
0.0006983666098676622,
0.04029056057333946,
-0.0067992364056408405,
-0.05193132162094116,
0.06564487516880035,
0.019352054223418236,
0.02586018666625023,
-0.01919756643474102,
0.01847533881664276,
0.04191212356090546,
-0.08650036156177521,
0.02556280605494976,
-0.01898108795285225,
-0.013793622143566608,
0.06327532976865768,
-0.03414997458457947,
-0.009772428311407566,
-0.010341845452785492,
-0.030392462387681007,
-0.026900602504611015,
0.0018180663464590907,
0.01586049608886242,
-0.004245416726917028,
0.0041712140664458275,
-0.015423636883497238,
0.006288763601332903,
0.005186597816646099,
-0.046218473464250565,
-0.09892571717500687,
-0.02892366424202919,
-0.014839010313153267,
-0.04216781258583069,
-0.03383989259600639,
-0.005543889012187719,
0.053984105587005615,
0.0669216513633728,
-0.027732089161872864,
0.0728817731142044,
-0.08286888897418976,
-0.06098424270749092,
0.07694811373949051,
0.04046067222952843,
-0.07718603312969208,
0.00930198933929205,
0.02343100681900978,
-0.05251046642661095,
-0.012646593153476715,
-0.016641253605484962,
0.001911049010232091,
-0.0064345370046794415,
0.01820315606892109,
0.011590443551540375,
-0.048547353595495224,
-0.00781452190130949,
0.0013951370492577553
] |
<p>Or: can it be proved that anti-matter definitely is nót matter going backwards in time?</p>
<p><a href="http://en.wikipedia.org/wiki/Antimatter" rel="nofollow">From wikipedia</a>:</p>
<blockquote>
<p><em>There is considerable speculation as to why the observable universe is apparently almost entirely matter [...] the apparent asymmetry of matter and antimatter in the visible universe is one of the greatest unsolved problems in physics.</em></p>
</blockquote>
<p>Couldn't the concept of reversal in time contribute to the explanation of this problem?</p>
<p>Measurements that reveal reversal in time must be rare and exceptional, just like anti-matter.</p> | g420 | [
0.042559344321489334,
0.0509028285741806,
0.016889002174139023,
-0.01335484255105257,
0.06301526725292206,
0.03832753375172615,
-0.015461070463061333,
-0.0019719586707651615,
-0.019590523093938828,
0.04316548630595207,
0.057258255779743195,
0.024887515231966972,
0.020499587059020996,
0.03227043151855469,
-0.034021440893411636,
0.018026569858193398,
0.05486263334751129,
0.004462964832782745,
0.004269817844033241,
0.04702099785208702,
0.008222878910601139,
-0.012939250096678734,
-0.007632601074874401,
-0.05657336115837097,
-0.028076613321900368,
0.005680219270288944,
0.0027151554822921753,
-0.04858599975705147,
0.003987077623605728,
0.005418403539806604,
0.09265764057636261,
-0.05715027078986168,
0.004510059021413326,
-0.033300161361694336,
0.004088227637112141,
-0.037124957889318466,
0.04047393053770065,
-0.0080631198361516,
0.0275108739733696,
0.0013271468924358487,
0.012439255602657795,
-0.007347357925027609,
0.03513389080762863,
0.0704856589436531,
0.041320595890283585,
0.06393922120332718,
-0.026750249788165092,
0.04731037840247154,
-0.010208487510681152,
-0.07292359322309494,
-0.0007828290108591318,
-0.003719588275998831,
0.05951919034123421,
0.07601862400770187,
-0.05177481845021248,
-0.03544082120060921,
0.018648536875844002,
-0.012562396004796028,
0.11272916942834854,
0.019579196348786354,
-0.06137464568018913,
-0.011419395916163921,
-0.0033915594685822725,
0.03499289229512215,
0.050199564546346664,
-0.023144125938415527,
-0.04081173986196518,
0.007945066317915916,
0.04427170008420944,
0.031845953315496445,
0.05131086707115173,
-0.011956162750720978,
-0.02838101238012314,
0.028796076774597168,
-0.0067841606214642525,
0.038548197597265244,
0.04550658166408539,
-0.025582484900951385,
0.027666840702295303,
0.0009755917126312852,
-0.061662256717681885,
-0.010478902608156204,
0.01699616014957428,
0.07703032344579697,
0.06608119606971741,
-0.04400108382105827,
0.01326385885477066,
-0.011411323212087154,
-0.01054401509463787,
0.06142376363277435,
-0.02039021998643875,
0.012926054187119007,
0.018589429557323456,
-0.06308604031801224,
0.020543966442346573,
-0.030903879553079605,
-0.028648700565099716,
-0.0127940122038126,
-0.08060215413570404,
0.05299936980009079,
-0.06470806896686554,
-0.005662241484969854,
0.005309589672833681,
0.008562798611819744,
0.006781083531677723,
-0.03838333860039711,
0.06078619137406349,
-0.07938765734434128,
-0.04080415889620781,
0.01288868859410286,
-0.024690883234143257,
-0.04121680557727814,
-0.09948620945215225,
0.011158374138176441,
-0.023887012153863907,
0.013981467112898827,
0.03733731433749199,
-0.004538635723292828,
-0.015751272439956665,
0.04598618298768997,
-0.028579186648130417,
0.03469111770391464,
-0.020897602662444115,
0.014237719587981701,
-0.05112822353839874,
0.006757599767297506,
0.0181396696716547,
-0.017188262194395065,
0.040765535086393356,
-0.011576427146792412,
-0.026236021891236305,
0.0492929071187973,
-0.0023601537104696035,
0.022389797493815422,
0.02070513926446438,
0.003744982648640871,
0.016090570017695427,
-0.009380689822137356,
-0.0025765742175281048,
-0.038658514618873596,
0.014841381460428238,
-0.022260256111621857,
0.011102121323347092,
-0.0059683979488909245,
-0.04216785356402397,
0.014014973305165768,
-0.04186186566948891,
0.053401898592710495,
-0.033241402357816696,
0.026524066925048828,
0.028699366375803947,
0.05698905885219574,
-0.02019309438765049,
-0.018479960039258003,
-0.030024945735931396,
-0.037765681743621826,
0.04527058079838753,
0.03772438317537308,
-0.009073294699192047,
0.004490185528993607,
0.035108353942632675,
0.04627959057688713,
-0.047661393880844116,
-0.013842832297086716,
-0.006615417543798685,
0.017312390729784966,
-0.06373506784439087,
-0.01384144090116024,
-0.014205214567482471,
-0.08564311265945435,
-0.08912677317857742,
0.023030627518892288,
-0.0007858255412429571,
0.034171562641859055,
0.024948032572865486,
-0.020072290673851967,
0.02606865018606186,
-0.03001912496984005,
-0.05009262636303902,
-0.04067160561680794,
0.016188714653253555,
0.0030097090639173985,
-0.02613869309425354,
0.019011132419109344,
-0.0003982518974225968,
0.026526225730776787,
0.030011039227247238,
0.03807616978883743,
-0.07428789883852005,
-0.0005111338687129319,
0.04629367217421532,
0.004229079466313124,
-0.04735301807522774,
0.039187002927064896,
0.08314618468284607,
-0.04728953540325165,
-0.013692514970898628,
0.030929140746593475,
0.01087189931422472,
-0.0017120123375207186,
0.006035143975168467,
-0.024180905893445015,
0.03763274475932121,
-0.035047534853219986,
0.05792504921555519,
0.01711530238389969,
-0.02049945294857025,
-0.006109998095780611,
0.06595756858587265,
-0.003989218734204769,
0.058195244520902634,
0.07305866479873657,
-0.008332381956279278,
-0.031230365857481956,
-0.02073593996465206,
0.04869109392166138,
-0.04130282253026962,
0.03593454137444496,
0.005999305751174688,
0.041491471230983734,
-0.04776254668831825,
-0.005005762912333012,
-0.05500246584415436,
-0.04973778501152992,
0.007723045069724321,
0.0250712838023901,
-0.027770226821303368,
-0.012688996270298958,
-0.044603779911994934,
-0.029260214418172836,
-0.059915974736213684,
0.035328563302755356,
-0.013061515055596828,
-0.03404337540268898,
0.0714661031961441,
-0.01813209243118763,
0.041543055325746536,
0.023537689819931984,
0.04276755079627037,
-0.03438720479607582,
-0.02061069943010807,
-0.0010717731202021241,
-0.07493846118450165,
0.01696331799030304,
0.0341770313680172,
-0.061045024544000626,
0.04030761495232582,
-0.030484233051538467,
-0.005612354725599289,
-0.011564835906028748,
0.07333848625421524,
0.007240142673254013,
-0.04094934090971947,
-0.019926665350794792,
0.021907230839133263,
0.004585388582199812,
0.04297642409801483,
0.04125245288014412,
-0.08350315690040588,
0.0313560776412487,
0.026883479207754135,
-0.00985880196094513,
0.02786032296717167,
-0.003279278287664056,
0.0019461449701339006,
-0.024430010467767715,
-0.06746414303779602,
0.04030518978834152,
-0.03485223650932312,
0.05233227461576462,
0.008402002044022083,
0.005527419038116932,
0.015513991005718708,
0.01091338973492384,
-0.047783538699150085,
0.04049839451909065,
-0.022193439304828644,
-0.05688554421067238,
0.07431500405073166,
0.016040552407503128,
-0.06783352792263031,
0.018893875181674957,
-0.008309628814458847,
-0.01840379275381565,
-0.021963266655802727,
0.0008964409935288131,
-0.014437766745686531,
-0.04628245159983635,
0.02993159368634224,
0.016326066106557846,
-0.04594094306230545,
0.016262147575616837,
0.03851711004972458,
-0.011385840363800526,
-0.006665252149105072,
0.056777603924274445,
0.05731524899601936,
-0.0032319508027285337,
-0.022939395159482956,
-0.0180473905056715,
-0.009195717051625252,
-0.02712610550224781,
0.01539362408220768,
-0.015489219687879086,
0.049522385001182556,
-0.0066372305154800415,
-0.007342484313994646,
0.014602519571781158,
0.005856984760612249,
-0.01767185889184475,
-0.007339492905884981,
0.06090721860527992,
-0.02442372776567936,
0.020318422466516495,
0.023338809609413147,
0.007132596801966429,
-0.008469820953905582,
-0.023927688598632812,
0.006663275882601738,
0.03419710323214531,
-0.029024729505181313,
0.029133548960089684,
0.01537948939949274,
0.0029444287065416574,
0.04302934557199478,
-0.0680256113409996,
-0.046601779758930206,
-0.012780150398612022,
-0.0749819278717041,
-0.020703859627246857,
0.0001280777796637267,
-0.027939125895500183,
0.05401255190372467,
0.02521727792918682,
-0.08377212285995483,
-0.0007923490484245121,
0.020823892205953598,
0.019496435299515724,
-0.007583072874695063,
0.03890039399266243,
-0.020188182592391968,
-0.03381488099694252,
0.020874708890914917,
0.005428663920611143,
0.0031202700920403004,
0.05690809339284897,
-0.05678046494722366,
-0.027823705226182938,
0.013266378082334995,
0.06420133262872696,
0.02921609953045845,
0.033333033323287964,
0.09199339151382446,
-0.006491000764071941,
0.045440368354320526,
0.0013570301234722137,
0.06974305212497711,
0.07117079943418503,
0.037224914878606796,
-0.06523415446281433,
-0.03375997021794319,
-0.010375394485890865,
0.032286129891872406,
-0.05816895514726639,
0.03331504762172699,
0.013484969735145569,
0.004785674158483744,
0.019220633432269096,
0.005838971119374037,
-0.022072089836001396,
0.03997465968132019,
-0.040440745651721954,
0.021552009508013725,
0.000960634439252317,
0.04492778331041336,
-0.015193164348602295,
0.01305736880749464,
0.05241573229432106,
0.02735663577914238,
0.05486597120761871,
0.01906651072204113,
-0.0337105356156826,
-0.02127307653427124,
-0.05281699448823929,
0.014677954837679863,
0.029728930443525314,
-0.030553000047802925,
-0.02986302226781845,
-0.04443977773189545,
-0.08348988741636276,
0.016052130609750748,
0.04629264026880264,
0.013539058156311512,
-0.005130448844283819,
-0.07174511253833771,
0.00015648755652364343,
0.033195022493600845,
-0.02825777418911457,
0.023635338991880417,
-0.030484076589345932,
0.014164361171424389,
0.02642328478395939,
-0.035837311297655106,
0.030956771224737167,
0.01082982774823904,
-0.006425405386835337,
0.0409855954349041,
-0.056630074977874756,
0.003926733508706093,
-0.014854444190859795,
-0.0324755497276783,
0.034349169582128525,
-0.04351086914539337,
-0.061194855719804764,
-0.003055074717849493,
0.02147500030696392,
0.01348500419408083,
0.03575752303004265,
0.03583386912941933,
-0.017448440194129944,
0.08119145035743713,
0.04775204882025719,
-0.023166147992014885,
0.03071378543972969,
0.015536876395344734,
0.06422796845436096,
0.009319442324340343,
0.007811792194843292,
-0.03505153954029083,
-0.024784982204437256,
0.042748887091875076,
0.009007050655782223,
-0.011943616904318333,
0.046249017119407654,
-0.018798543140292168,
0.020462991669774055,
0.0448450967669487,
0.06633368879556656,
0.03757985308766365,
-0.014607044868171215,
0.04471913352608681,
-0.03396754711866379,
0.01598312519490719,
-0.062116581946611404,
-0.029964962974190712,
0.06450190395116806,
-0.03146001324057579,
-0.015403348952531815,
0.0053197056986391544,
0.0016074312152341008,
-0.04528773948550224,
-0.0009195258026011288,
-0.000569198455195874,
-0.019571250304579735,
-0.07810615748167038,
-0.041971515864133835,
0.0009594748844392598,
0.014190019108355045,
-0.026570037007331848,
0.0704583078622818,
-0.028494050726294518,
-0.012234818190336227,
0.05193573236465454,
0.037130121141672134,
0.009314880706369877,
0.018105609342455864,
-0.011970484629273415,
-0.014128169044852257,
-0.007367303594946861,
0.02045547217130661,
-0.06497424095869064,
0.05627774819731712,
-0.040147144347429276,
0.024920672178268433,
0.001033338950946927,
-0.007334765512496233,
-0.030917976051568985,
-0.03277623653411865,
-0.000589260074775666,
0.010867780074477196,
-0.061924394220113754,
0.01523168571293354,
0.06774609535932541,
-0.028518514707684517,
-0.07050235569477081,
0.08486419171094894,
-0.026356274262070656,
0.06739365309476852,
-0.02705530636012554,
-0.09625338017940521,
-0.005317839793860912,
-0.032065827399492264,
0.03512542322278023,
-0.06752131879329681,
0.0031171771697700024,
0.022003043442964554,
-0.006717471871525049,
0.04360905662178993,
-0.06256558746099472,
-0.012675028294324875,
0.0035293647088110447,
0.02526596188545227,
-0.015204659663140774,
-0.018586602061986923,
-0.004763716831803322,
0.02123669721186161,
-0.0035786146763712168,
0.02961362525820732,
-0.0666206106543541,
-0.04540809988975525,
-0.02021939493715763,
-0.024442514404654503,
-0.012707249261438847,
0.05921344459056854,
0.02185080759227276,
-0.02998306415975094,
-0.027045708149671555,
-0.023226359859108925,
0.03634475916624069,
-0.08542536944150925,
-0.080115906894207,
0.03848782926797867,
0.04035917669534683,
-0.023236921057105064,
-0.028714273124933243,
-0.04258149117231369,
-0.01003984920680523,
0.0241344403475523,
-0.027390778064727783,
-0.024313965812325478,
0.0014148360351100564,
0.022577090188860893,
0.02959064021706581,
-0.07074874639511108,
-0.017663585022091866,
0.02376631647348404,
-0.00206043035723269,
0.02863156981766224,
0.024665825068950653,
-0.006217924412339926,
-0.045351866632699966,
-0.01673010177910328,
0.033887941390275955,
0.03107447549700737,
-0.030047835782170296,
0.009221004322171211,
-0.038610730320215225,
-0.029308585450053215,
0.04944326728582382,
-0.0376330204308033,
0.0012428777990862727,
0.037536170333623886,
-0.028377404436469078,
-0.018204109743237495,
0.016616588458418846,
0.024190260097384453,
-0.0012795988004654646,
-0.03056490048766136,
-0.038705527782440186,
-0.031137915328145027,
0.01696731150150299,
0.037134286016225815,
0.016881540417671204,
0.029103800654411316,
-0.048492513597011566,
-0.04200848191976547,
-0.014337902888655663,
-0.014625395648181438,
0.0043233041651546955,
-0.00046534271677955985,
0.04428378492593765,
0.038144804537296295,
-0.01157121080905199,
0.0055576045997440815,
-0.0018994706915691495,
-0.009104101918637753,
-0.007421855349093676,
-0.061580073088407516,
-0.012607146054506302,
-0.015265134163200855,
0.0635710060596466,
-0.05145459249615669,
0.030667763203382492,
0.003677134169265628,
0.05531776323914528,
-0.022135483101010323,
-0.050275277346372604,
0.050547901540994644,
0.007309150416404009,
-0.003180447965860367,
-0.023362809792160988,
0.010904831811785698,
-0.04039282724261284,
-0.018740426748991013,
-0.012337769381701946,
0.0011088837636634707,
-0.04750040918588638,
-0.0033519132994115353,
-0.05842999368906021,
-0.024683967232704163,
-0.0380697101354599,
0.007672631181776524,
0.02496754564344883,
-0.02292788401246071,
0.04861679673194885,
0.014795584604144096,
0.0018661122303456068,
0.06005573645234108,
0.08594881743192673,
-0.01528486330062151,
0.01383035909384489,
0.014116359874606133,
0.004417411517351866,
0.08118688315153122,
-0.02465391531586647,
-0.011656096205115318,
0.009162120521068573,
-0.015500042587518692,
-0.05169518664479256,
0.0025361613370478153,
0.05816256254911423,
0.047939904034137726,
-0.027956627309322357,
-0.034898389130830765,
-0.04201067239046097,
0.05144817382097244,
-0.012611104175448418,
0.04664378613233566,
0.05525817349553108,
0.01589018478989601,
-0.02142474055290222,
-0.005443035624921322,
0.009921789169311523,
0.008557996712625027,
-0.01599111780524254,
-0.023366540670394897,
0.0013033332070335746,
0.025487219914793968,
-0.032629430294036865,
-0.025615818798542023,
-0.006090088747441769,
-0.003244167659431696,
-0.03714493289589882,
-0.004837383981794119,
-0.021856559440493584,
0.04304008558392525,
0.02891037054359913,
-0.008893018588423729,
-0.029964493587613106,
-0.0068211848847568035,
0.023411033675074577,
-0.02367199957370758,
-0.02519010379910469,
0.020872121676802635,
-0.03819548711180687,
0.01708410307765007,
0.0073898229748010635,
0.05882915481925011,
0.059293877333402634,
-0.08427146822214127,
-0.02537108212709427,
-0.04863819107413292,
-0.033683668822050095,
0.016304954886436462,
-0.030858924612402916,
-0.005406288430094719,
-0.004684289451688528,
-0.04604104906320572,
0.038057927042245865,
-0.03589724004268646,
-0.013517270796000957,
-0.007289980538189411,
-0.006446764804422855,
-0.013238800689578056,
0.01972811110317707,
-0.02591351792216301,
0.016282420605421066,
0.003042851807549596,
0.04235945641994476,
0.017141127958893776,
0.01738343946635723,
0.05441718548536301,
-0.021551331505179405,
0.015201018191874027,
-0.002852000994607806,
0.03376011550426483,
-0.056394532322883606,
0.011212493292987347,
-0.06391210108995438,
-0.015854869037866592,
-0.0017936303047463298,
0.026142526417970657,
-0.042597681283950806,
-0.005790554452687502,
0.005115718115121126,
0.00349085358902812,
0.0837482362985611,
0.016538716852664948,
-0.03920556604862213,
-0.06219280883669853,
-0.005028348881751299,
0.019100120291113853,
-0.01084273960441351,
-0.005690551362931728,
-0.018968235701322556,
-0.030215559527277946,
-0.0072922538965940475,
0.0014861616073176265,
-0.08436467498540878,
0.0038847317919135094,
-0.016000378876924515,
0.060795750468969345,
-0.009111485444009304,
-0.0045113330706954,
0.045611243695020676,
-0.003926618490368128,
-0.06240652874112129,
-0.05034933611750603,
0.006163420621305704,
-0.0512731671333313,
-0.01225984562188387,
0.01837281696498394,
-0.011649713851511478,
-0.05788448452949524,
-0.05757203325629234,
0.00410543754696846,
0.0068891895934939384,
0.0007231552735902369,
0.021965740248560905,
-0.009464937262237072,
0.027087436988949776,
0.03358990326523781,
0.00537086371332407,
-0.011404150165617466,
-0.018424006178975105,
0.013445290736854076,
0.035634707659482956,
0.009503602050244808,
-0.05404619500041008,
-0.012299700640141964,
0.010272554121911526,
-0.000032218635169556364,
-0.04325955733656883,
0.006860438734292984,
0.025451339781284332,
-0.0557367317378521,
-0.009845687076449394,
0.022856518626213074,
-0.01579589582979679,
-0.07693628966808319,
0.05947832390666008,
0.033850640058517456,
-0.023062361404299736,
-0.023207111284136772,
0.08453796803951263,
0.0557873472571373,
0.01728135161101818,
-0.02511027455329895,
0.006541950162500143,
0.03778628632426262,
0.008854836225509644,
-0.056710947304964066,
-0.02521815337240696,
0.0009527928195893764,
0.013868751935660839,
0.011612124741077423,
-0.025672655552625656,
0.002905358327552676
] |
<p><strong>Short question</strong></p>
<p>Given any Lagrangian density of fields one could possibly conceive, is it the case that after one has performed a Legendre transformation, if the Hamiltonian is then expressed in terms of the original fields, will it contain all of the terms originally in the Lagrangian but with the signs of the potentials 'flipped'? Or are there cases when terms will be dropped in the transformation? Or is my statement altogether wrong. This question is inspired by the long version of my question below, relating to a problem I am currently working on.</p>
<p><strong>Long, specific question</strong></p>
<p>Given the Lagrangian density</p>
<p><img src="http://i.stack.imgur.com/bIVKZ.png" alt="enter image description here"></p>
<p>I have derived (several times to check for errors) using a Legendre transformation, the Hamiltonian density:</p>
<p><img src="http://i.stack.imgur.com/pZJVT.png" alt="enter image description here"></p>
<p>which is basically the Lagrangian density with a few sign flips <em>apart</em> from that it is missing the two terms outside the brackets in the Lagrangian density $\frac{1}{4\pi c}\frac{\partial\vec{A}}{\partial t}\cdot \nabla\phi + \frac{1}{c}\vec{A}\cdot\frac{\partial \vec{P}}{\partial t}$.</p>
<p>This worries me, as naively I expected to obtain a Hamiltonian very similar looking to the Lagrangian with all the same terms but some of the signs flipped. However I noticed that the 'missing' terms are the only ones which contain non-squared time derivatives so thought that might have something to do with it.</p> | g1229 | [
0.08810160309076309,
0.017798779532313347,
0.010432067327201366,
-0.06721096485853195,
0.004514342173933983,
-0.021575476974248886,
0.047709137201309204,
0.01973920315504074,
-0.04025965929031372,
0.006767138373106718,
-0.021113956347107887,
0.015703270211815834,
0.01667044125497341,
-0.018795344978570938,
0.026904849335551262,
0.052984852343797684,
0.04900379106402397,
0.03837965056300163,
0.029501240700483322,
-0.00023303097987081856,
-0.06625887006521225,
0.02087622880935669,
0.02015417255461216,
-0.021634114906191826,
-0.028994817286729813,
-0.060374077409505844,
-0.0353688970208168,
-0.017792830243706703,
-0.01449075061827898,
-0.046356916427612305,
0.012892107479274273,
0.01777450181543827,
0.026125693693757057,
-0.010698502883315086,
-0.027859484776854515,
-0.02672089822590351,
0.08025000244379044,
-0.015939582139253616,
0.02836131490767002,
-0.0031759028788655996,
0.0500960536301136,
-0.016107065603137016,
0.035142190754413605,
0.028167724609375,
-0.027064919471740723,
0.062255583703517914,
-0.03039260394871235,
0.035233523696660995,
-0.004224385134875774,
-0.020885152742266655,
0.08185552805662155,
-0.0017426700796931982,
-0.003647824749350548,
0.03356980159878731,
-0.030835937708616257,
0.04187560826539993,
0.06555692106485367,
0.0283038467168808,
0.039573293179273605,
0.013020076788961887,
0.007186755537986755,
-0.07782553136348724,
-0.048807643353939056,
-0.002098297933116555,
0.02499239519238472,
-0.041263602674007416,
-0.0033328256104141474,
-0.002611086005344987,
0.0038872805889695883,
-0.057469844818115234,
-0.03413887694478035,
-0.031889572739601135,
0.03227405622601509,
-0.040719594806432724,
0.06426361203193665,
0.02805177867412567,
0.012404820881783962,
0.04529314860701561,
0.006492736283689737,
0.00021374622883740813,
-0.06836043298244476,
-0.07103876024484634,
-0.056557659059762955,
0.05089074373245239,
0.06566929072141647,
0.017132500186562538,
0.04972464218735695,
0.017780493944883347,
-0.019147347658872604,
0.04555180296301842,
0.020165152847766876,
0.044726669788360596,
0.0644526556134224,
0.005523966159671545,
-0.06826077401638031,
-0.025311477482318878,
0.012877866625785828,
0.014406807720661163,
-0.0467117615044117,
-0.030830062925815582,
-0.047343745827674866,
-0.007492449600249529,
-0.0019433321431279182,
-0.0427178218960762,
-0.013730903156101704,
-0.0029448652639985085,
0.021455660462379456,
-0.057467784732580185,
-0.049722615629434586,
-0.029875870794057846,
-0.012261157855391502,
0.012720548547804356,
0.049096494913101196,
0.043700460344552994,
-0.08396999537944794,
-0.047301050275564194,
0.044208671897649765,
0.04416902735829353,
-0.056132275611162186,
0.05526323989033699,
-0.009258211590349674,
0.00661106500774622,
0.06459508091211319,
0.01889873296022415,
0.07362867891788483,
-0.014795319177210331,
-0.025538304820656776,
0.05267226696014404,
0.014322015456855297,
-0.032786548137664795,
-0.015462961047887802,
0.05400919169187546,
0.03938741981983185,
0.054238636046648026,
0.005676379892975092,
0.005800199694931507,
0.03615652397274971,
0.07062695920467377,
0.09050071239471436,
0.009087295271456242,
0.0704110637307167,
-0.04595014825463295,
0.06282118707895279,
-0.041250601410865784,
-0.005721233319491148,
-0.02167746052145958,
0.013207013718783855,
-0.040731582790613174,
0.002097807824611664,
-0.018504148349165916,
-0.0505208782851696,
-0.007178781554102898,
-0.007819805294275284,
-0.006476107053458691,
0.04153750091791153,
0.03111618384718895,
-0.004692666232585907,
0.028717152774333954,
0.03067789413034916,
-0.02676135115325451,
0.036394473165273666,
-0.036351412534713745,
0.05149295553565025,
-0.0010787643259391189,
0.0031836528796702623,
0.028646424412727356,
0.004420741926878691,
-0.01649138703942299,
-0.050236158072948456,
-0.01737022213637829,
-0.005455790087580681,
0.02646196074783802,
-0.011690962128341198,
0.035129621624946594,
0.02430313639342785,
0.004054123070091009,
0.018332602456212044,
0.017057053744792938,
-0.015893831849098206,
0.03395756706595421,
-0.059527117758989334,
-0.028633195906877518,
-0.020960520952939987,
-0.008281391113996506,
0.04270317777991295,
-0.036222800612449646,
0.026938851922750473,
0.04179878905415535,
-0.01479924563318491,
0.026277313008904457,
0.0077886637300252914,
0.04018479585647583,
-0.07390539348125458,
0.0266112107783556,
0.00923883356153965,
-0.0037728548049926758,
0.05606794357299805,
-0.060951486229896545,
0.026725519448518753,
-0.026558464393019676,
0.03042946197092533,
0.02049827203154564,
0.0029816937167197466,
-0.003020056989043951,
-0.017589127644896507,
-0.023332035169005394,
-0.031615953892469406,
0.001962837064638734,
0.03592872992157936,
-0.051832474768161774,
0.01555926725268364,
-0.03897281363606453,
-0.04104912653565407,
0.018757803365588188,
-0.061859749257564545,
-0.024442436173558235,
-0.01682358607649803,
0.08684609085321426,
-0.027147913351655006,
-0.0021177763119339943,
-0.04558410495519638,
0.024562757462263107,
-0.023552531376481056,
-0.000034044900530716404,
-0.020510094240307808,
0.012301277369260788,
0.014167173765599728,
-0.0017755680019035935,
-0.044048696756362915,
-0.023441217839717865,
-0.01725735142827034,
-0.014579658396542072,
-0.03333882987499237,
-0.05800807848572731,
-0.016583947464823723,
0.03919154033064842,
-0.024469686672091484,
0.0004690357600338757,
0.0818658396601677,
0.02505621686577797,
-0.03377655893564224,
-0.015697238966822624,
0.04587578400969505,
-0.0409054160118103,
0.03349073603749275,
0.018433332443237305,
0.03475189581513405,
0.0005185377667658031,
0.0010361496824771166,
-0.0060362741351127625,
0.0006671615410596132,
0.03881567716598511,
-0.005746133625507355,
0.02931303344666958,
-0.02385721355676651,
0.0083991764113307,
0.012754316441714764,
-0.02842777781188488,
0.028490055352449417,
-0.02578185498714447,
0.006628517061471939,
0.02117406390607357,
-0.06075827777385712,
0.04667828977108002,
-0.04958657920360565,
-0.022653833031654358,
-0.008654741570353508,
-0.0623495876789093,
0.004992966540157795,
0.013980760239064693,
-0.04508022218942642,
0.10814021527767181,
0.05205180123448372,
0.0653066486120224,
-0.011722007766366005,
-0.022983569651842117,
-0.04540714994072914,
-0.01332890521734953,
0.03085831180214882,
-0.00555235892534256,
0.039141129702329636,
-0.0008612039964646101,
-0.004006956238299608,
0.07089594006538391,
-0.04504859820008278,
-0.06414749473333359,
-0.027992891147732735,
-0.03647567704319954,
-0.021069452166557312,
0.07095539569854736,
0.010445081628859043,
0.03373279795050621,
0.09296886622905731,
-0.040581461042165756,
-0.07506481558084488,
0.023371810093522072,
-0.030406663194298744,
-0.043338343501091,
-0.04869190603494644,
-0.0019091840367764235,
-0.00321974721737206,
-0.007894206792116165,
0.051702890545129776,
0.05043704807758331,
0.05176882818341255,
0.006643959321081638,
-0.03329090401530266,
-0.0033794348128139973,
-0.02799728885293007,
-0.07808800041675568,
-0.03203369304537773,
0.005201423075050116,
0.008717706426978111,
-0.032068729400634766,
-0.02560875378549099,
-0.033009059727191925,
-0.01635211706161499,
-0.013014676980674267,
0.062442559748888016,
-0.047720812261104584,
-0.043246399611234665,
-0.026941899210214615,
0.003571701468899846,
0.018678132444620132,
0.028483374044299126,
0.0005676174187101424,
-0.03386200591921806,
-0.006986057851463556,
-0.06476186960935593,
-0.04616258293390274,
-0.018243849277496338,
-0.02942306362092495,
-0.01655130833387375,
-0.006505862344056368,
-0.054824478924274445,
0.01886574923992157,
-0.07635156810283661,
0.009824453853070736,
0.006588024087250233,
-0.013735445216298103,
-0.05368369445204735,
-0.022897234186530113,
-0.04936686530709267,
0.0017507870215922594,
0.020585523918271065,
-0.02682381682097912,
-0.01682622730731964,
-0.008697967045009136,
0.01928774081170559,
0.010083870030939579,
-0.05189279466867447,
-0.04800023138523102,
0.09949023276567459,
-0.01977999322116375,
0.024726727977395058,
-0.030312906950712204,
0.03724467754364014,
0.018724529072642326,
0.04300551861524582,
-0.03146348148584366,
-0.036597251892089844,
-0.05569655820727348,
0.01256810687482357,
0.04443223401904106,
0.014860447496175766,
-0.0017797325272113085,
-0.010388488881289959,
-0.044862475246191025,
0.04131435602903366,
-0.012551282532513142,
0.05758723244071007,
-0.001559744356200099,
-0.01980791985988617,
0.030800551176071167,
0.024681420996785164,
0.007357119116932154,
-0.0101221464574337,
0.017149770632386208,
-0.008395181968808174,
0.027925092726945877,
0.017536990344524384,
0.021689265966415405,
0.0024455501697957516,
0.00404699519276619,
0.0674590989947319,
0.02041308581829071,
-0.026218481361865997,
-0.003921401686966419,
-0.013647559098899364,
-0.01671396568417549,
-0.032383713871240616,
0.03883303701877594,
0.020457196980714798,
0.021835733205080032,
-0.01622384786605835,
-0.06504622846841812,
0.029455671086907387,
-0.00544164190068841,
0.02205539122223854,
0.011533807031810284,
-0.058679088950157166,
-0.007503509055823088,
0.05410246178507805,
-0.009229747578501701,
0.06449040025472641,
-0.05612306669354439,
0.09001532942056656,
-0.014581933617591858,
-0.023607579991221428,
-0.06913907080888748,
-0.02327442355453968,
-0.024125423282384872,
0.008571000769734383,
-0.02275339514017105,
-0.04479925334453583,
-0.045249104499816895,
-0.02094443328678608,
-0.0636327788233757,
-0.019988615065813065,
-0.027177229523658752,
0.05190441384911537,
0.04766133055090904,
0.03484933823347092,
0.05949947610497475,
0.043245695531368256,
0.03465946391224861,
0.10450208187103271,
-0.029923610389232635,
-0.02403225190937519,
-0.04295671358704567,
-0.0575275719165802,
-0.02327510342001915,
0.038191113620996475,
-0.049486152827739716,
-0.060485124588012695,
-0.04492582380771637,
-0.05558468773961067,
0.02221241220831871,
0.019739985466003418,
-0.029089344665408134,
0.04340878501534462,
-0.02874048240482807,
0.041554514318704605,
-0.013829979114234447,
-0.043854087591171265,
0.013467153534293175,
-0.018378404900431633,
-0.03207331523299217,
0.0039881933480501175,
-0.0071326969191432,
-0.005434692371636629,
0.01718818210065365,
-0.016351040452718735,
0.002076205797493458,
0.006815718486905098,
-0.00041665148455649614,
-0.007273551542311907,
-0.007197599392384291,
-0.053709983825683594,
-0.045477598905563354,
-0.012183618731796741,
-0.010139995254576206,
-0.016750788316130638,
0.0035991405602544546,
0.05472380667924881,
-0.03249874338507652,
-0.008106780238449574,
0.03125898912549019,
-0.045246466994285583,
-0.08900605142116547,
0.055489681661129,
-0.059325914829969406,
0.0071736834943294525,
-0.02666001208126545,
-0.008138549514114857,
-0.01813049428164959,
0.011942734941840172,
0.0221534613519907,
-0.0035779401659965515,
-0.03837565332651138,
-0.03119906596839428,
-0.024926044046878815,
-0.023542821407318115,
0.05308632180094719,
-0.04604416340589523,
0.05979709327220917,
0.046640194952487946,
-0.04079221561551094,
-0.02598995342850685,
-0.03712115436792374,
0.021542342379689217,
-0.023371485993266106,
-0.04204336926341057,
0.028151553124189377,
-0.019995253533124924,
-0.02882644161581993,
-0.04427998512983322,
-0.011327007785439491,
-0.056065309792757034,
0.021829307079315186,
-0.06389431655406952,
0.047884657979011536,
-0.027005665004253387,
0.015677912160754204,
-0.027411650866270065,
0.050765104591846466,
0.02036919631063938,
0.04000366851687431,
-0.05989353731274605,
0.002328877802938223,
0.005745389964431524,
-0.017275160178542137,
-0.029458284378051758,
0.027104554697871208,
-0.00950046256184578,
-0.04199524596333504,
-0.04053113982081413,
0.00141487258952111,
0.013856622390449047,
-0.04604337736964226,
0.016556579619646072,
0.012933803722262383,
0.0289215836673975,
-0.038817062973976135,
0.011479748412966728,
0.035875104367733,
-0.02779894694685936,
-0.08801094442605972,
-0.027883440256118774,
0.05233616381883621,
-0.029803123325109482,
0.06552526354789734,
0.03220730647444725,
-0.016277853399515152,
-0.013591473922133446,
-0.003906644880771637,
0.004780452232807875,
-0.005010240711271763,
-0.00024245404347311705,
0.03769354149699211,
0.028364306315779686,
0.011994159780442715,
0.005560976453125477,
0.033455852419137955,
-0.02375725284218788,
0.00911725964397192,
0.002010551281273365,
-0.019344571977853775,
0.0104484548792243,
-0.016853857785463333,
-0.01834844797849655,
0.01415807195007801,
-0.041883405297994614,
0.020358577370643616,
-0.030994078144431114,
-0.009598108008503914,
-0.006484230048954487,
-0.0032270136289298534,
0.03377106413245201,
0.022265706211328506,
0.014762986451387405,
-0.03096691705286503,
0.009345239959657192,
-0.006234289146959782,
-0.030303874984383583,
0.0528365895152092,
0.03235141932964325,
-0.0063361916691064835,
0.03634008392691612,
0.052816834300756454,
0.05073408782482147,
0.00034692540066316724,
-0.001428318559192121,
-0.01912166364490986,
0.06366892158985138,
0.007067323196679354,
-0.01678740791976452,
-0.032358214259147644,
-0.03130749240517616,
0.012785491533577442,
-0.058600377291440964,
-0.013452469371259212,
-0.0017297278391197324,
-0.08563010394573212,
-0.06268375366926193,
-0.021727019920945168,
0.0010907634859904647,
-0.01898602396249771,
-0.016445303335785866,
0.05864863097667694,
-0.03726562112569809,
0.019245227798819542,
-0.014050992205739021,
0.001202126732096076,
-0.015131615102291107,
0.014697007834911346,
-0.01798924431204796,
-0.005150351673364639,
-0.006440744735300541,
0.004455939866602421,
0.01615176908671856,
0.0013853179989382625,
0.05278946831822395,
0.009881074540317059,
0.03672303259372711,
0.013246376067399979,
0.015183866955339909,
0.051681604236364365,
-0.0027399708051234484,
-0.006631434429436922,
0.058214884251356125,
-0.10164138674736023,
0.00566656980663538,
-0.018186258152127266,
0.04969329386949539,
-0.02404196932911873,
0.023757386952638626,
0.04308990016579628,
-0.03167565166950226,
0.07820817828178406,
0.01832999289035797,
-0.006005007307976484,
-0.0672144740819931,
-0.006747828330844641,
-0.015420404262840748,
0.008189400658011436,
-0.012895527295768261,
0.01862046681344509,
0.07708201557397842,
-0.0014081494882702827,
0.03678528964519501,
0.07264680415391922,
-0.01952863298356533,
0.009099308401346207,
0.03232108801603317,
0.03037377819418907,
-0.05296683311462402,
0.002681067446246743,
0.07154853641986847,
-0.05973507836461067,
-0.014089364558458328,
0.03813577815890312,
0.05264035612344742,
-0.04123317077755928,
-0.01986246183514595,
0.022838205099105835,
-0.03482310473918915,
-0.07568679004907608,
-0.07050696015357971,
-0.004970695823431015,
0.015128348022699356,
0.019664136692881584,
-0.032962895929813385,
-0.006857071537524462,
0.06324347108602524,
-0.02974325604736805,
0.03745312988758087,
0.07229861617088318,
-0.03031545877456665,
-0.01111719198524952,
-0.02699047513306141,
-0.009981370531022549,
0.025564398616552353,
0.012725520879030228,
-0.0177624449133873,
0.024632113054394722,
0.03978145867586136,
-0.012013522908091545,
0.03663045912981033,
0.025404073297977448,
0.06269588321447372,
0.049974799156188965,
-0.032919742166996,
-0.008277155458927155,
0.03686590865254402,
0.019437842071056366,
0.009984789416193962,
0.009908311069011688,
0.025054682046175003,
0.015683205798268318,
-0.02887655794620514,
0.017695559188723564,
-0.015244539827108383,
-0.00006455848051700741,
0.012307656928896904,
0.04171617701649666,
-0.02614477090537548,
-0.041338175535202026,
-0.019030766561627388,
0.05887581408023834,
-0.013863123022019863,
-0.0032134370412677526,
0.03194870427250862,
0.043486934155225754,
-0.03813120722770691,
-0.0015665541868656874,
0.053676802664995193,
0.03124719299376011,
0.017488298937678337,
0.02183055877685547,
0.005609504878520966,
0.007862872444093227,
-0.03884036839008331,
0.013096734881401062,
0.03173892945051193,
-0.016911517828702927,
0.04500836506485939,
-0.03250769153237343,
-0.03400512784719467,
0.04672034829854965,
-0.03195558115839958,
0.04399726912379265,
0.008360335603356361,
-0.02804543823003769,
0.07025592029094696,
0.038450248539447784,
0.012501214630901814,
-0.0249080341309309,
0.010474443435668945,
-0.034705668687820435,
-0.0011636927956715226,
-0.03963889181613922,
-0.09110420197248459,
-0.02177039161324501,
0.054783616214990616,
0.0077112698927521706,
-0.024380115792155266,
0.00783123355358839,
-0.015608876012265682,
0.0516357384622097,
-0.010894304141402245,
-0.022372566163539886,
-0.007721711415797472,
0.01672571897506714,
-0.02422660030424595,
-0.04367198050022125,
-0.045181676745414734,
0.009809044189751148,
0.034687288105487823,
-0.02817934937775135,
-0.049993887543678284,
-0.0752207338809967,
0.04770369082689285,
-0.018358834087848663,
-0.015578612685203552,
0.027718057855963707,
-0.0019920540507882833,
0.012068122625350952,
0.004024600610136986,
0.0118382778018713,
0.014907650649547577,
0.07495690882205963,
-0.03612197935581207,
0.0147545812651515,
0.009814209304749966,
0.02841624617576599,
-0.041514720767736435,
0.010292276740074158,
0.030736597254872322,
0.0005024714628234506,
-0.026651134714484215,
-0.008306576870381832,
0.025029011070728302,
-0.023926544934511185,
-0.026104364544153214,
-0.01630447246134281,
0.037626683712005615,
0.0614435076713562
] |
<p>I have a set of trajectories of three particles and their instantaneous velocities. I would like to compute the 3 components of the angular velocity pseudovector of the fictive triangle formed by these three particles. How can I proceed for that?</p> | g1230 | [
0.0215129554271698,
-0.007245421875268221,
0.0006935657584108412,
-0.0567350760102272,
0.05811160430312157,
-0.07426750659942627,
-0.0015503618633374572,
-0.01513341348618269,
-0.005525708198547363,
0.031539637595415115,
-0.005427470896393061,
0.015475823543965816,
0.052801646292209625,
-0.009561669081449509,
-0.02616768889129162,
0.006795416120439768,
-0.021595116704702377,
0.014937572181224823,
0.04129466041922569,
0.07333208620548248,
-0.012099775485694408,
0.008357472717761993,
0.017144523561000824,
0.020955607295036316,
0.04896162450313568,
-0.03387874364852905,
0.012629755772650242,
-0.059822630137205124,
-0.060977522283792496,
0.05444369092583656,
0.0486205592751503,
0.007096633780747652,
-0.029621737077832222,
0.010222699493169785,
-0.009856779128313065,
-0.050938140600919724,
0.06943334639072418,
0.01265840232372284,
0.008865530602633953,
0.021197667345404625,
-0.027818309143185616,
0.00119048822671175,
0.05981731042265892,
-0.021977869793772697,
-0.010158922523260117,
-0.022000752389431,
0.001954312901943922,
-0.023949917405843735,
-0.09347278624773026,
0.04256387799978256,
-0.028437213972210884,
0.03853660449385643,
-0.015474485233426094,
-0.049661535769701004,
-0.024295810610055923,
0.03765377402305603,
0.0033640966285020113,
-0.03373807296156883,
0.03084874525666237,
0.05534375458955765,
-0.02677292563021183,
-0.05983946472406387,
-0.03178860619664192,
-0.010729224421083927,
0.04588373377919197,
-0.000018485485270502977,
-0.019208082929253578,
0.030654363334178925,
-0.02207917533814907,
-0.0065284608863294125,
0.0345577709376812,
-0.009641937911510468,
0.050867415964603424,
-0.017387520521879196,
-0.059866342693567276,
-0.013967558741569519,
-0.03981465846300125,
-0.02898329496383667,
0.013141797855496407,
0.03385378420352936,
-0.006362000480294228,
0.002467287937179208,
0.017233144491910934,
-0.04417043551802635,
0.015432202257215977,
-0.003519997466355562,
0.015320210717618465,
-0.0047270809300243855,
-0.04733337461948395,
-0.048949871212244034,
-0.04613380506634712,
0.003980959299951792,
0.008530336432158947,
-0.013855385594069958,
-0.00384103087708354,
-0.02881748415529728,
-0.06681254506111145,
0.054877638816833496,
0.017738811671733856,
-0.012162922881543636,
0.024451380595564842,
0.012562059797346592,
-0.012288224883377552,
-0.04353756830096245,
-0.01887373998761177,
-0.10091080516576767,
0.011397061869502068,
0.06316672265529633,
0.038925301283597946,
-0.014894818887114525,
-0.05022706836462021,
-0.06167599931359291,
-0.021720588207244873,
0.0016814899863675237,
-0.00024379037495236844,
-0.03234073892235756,
0.029432905837893486,
0.0033195936121046543,
0.02595175802707672,
0.07104624062776566,
-0.035858530551195145,
0.02396038919687271,
-0.008307654410600662,
0.07611959427595139,
0.015762412920594215,
0.0096062570810318,
-0.041104383766651154,
-0.015004418790340424,
0.05364132300019264,
-0.022791290655732155,
0.032497722655534744,
-0.03365300968289375,
-0.0041498951613903046,
-0.025659121572971344,
-0.040249865502119064,
0.04797208309173584,
-0.02146831899881363,
-0.0076250433921813965,
-0.015335152857005596,
0.05454927310347557,
0.0060572498477995396,
-0.011919422075152397,
-0.01490755658596754,
0.002341863699257374,
0.017240146175026894,
-0.019248293712735176,
-0.07268532365560532,
-0.05249393731355667,
-0.017455507069826126,
-0.018701860681176186,
0.010189646854996681,
0.050884053111076355,
0.024988029152154922,
-0.007574999239295721,
-0.02007587067782879,
0.0148527966812253,
0.05689892917871475,
-0.04500485211610794,
0.00985481683164835,
0.001514958101324737,
0.06665344536304474,
-0.04013197496533394,
0.054493337869644165,
0.01357330847531557,
0.015968726947903633,
0.044671107083559036,
-0.014997689984738827,
-0.03165814280509949,
-0.04089389741420746,
-0.010564438998699188,
-0.0008154893293976784,
-0.004170994274318218,
-0.009789763949811459,
0.00018187033128924668,
0.01878170855343342,
0.014979362487792969,
-0.0788421556353569,
-0.036027777940034866,
-0.005582271609455347,
0.030253274366259575,
0.0181558970361948,
0.008119957521557808,
0.054426610469818115,
0.06942522525787354,
0.022033466026186943,
0.020355693995952606,
-0.04821772500872612,
0.029346849769353867,
-0.062074556946754456,
0.05014893785119057,
0.024855412542819977,
0.023655006662011147,
0.001508630346506834,
0.046767231076955795,
0.006217006593942642,
-0.035499658435583115,
0.026371996849775314,
-0.03291640058159828,
-0.05331495776772499,
-0.020262116566300392,
-0.02177073061466217,
0.03673592582345009,
0.08107165992259979,
0.05405057966709137,
0.04447829723358154,
0.014077304862439632,
-0.010221945121884346,
-0.010656552389264107,
0.020266592502593994,
0.06062319874763489,
0.06850706785917282,
0.035284873098134995,
-0.011877547018229961,
0.004546291194856167,
0.016215838491916656,
-0.011340580880641937,
0.02235197089612484,
-0.013392538763582706,
0.03061135858297348,
-0.011997625231742859,
-0.04097365215420723,
-0.01904495432972908,
-0.03260857239365578,
-0.03733065351843834,
-0.025100497528910637,
0.0033616849686950445,
-0.0016716176178306341,
-0.013325347565114498,
0.014130436815321445,
0.0026590710040181875,
0.012237349525094032,
-0.01629841886460781,
-0.00588550791144371,
-0.019477495923638344,
0.052608564496040344,
-0.005982290953397751,
-0.008044927380979061,
0.004697548691183329,
0.012961217202246189,
0.0015983973862603307,
0.064505934715271,
0.03954261168837547,
0.09690270572900772,
-0.006494149565696716,
0.04110477864742279,
-0.051158640533685684,
0.007724160328507423,
-0.01982489600777626,
0.0011461277026683092,
-0.022915208712220192,
-0.021914571523666382,
-0.03619981184601784,
-0.05537060648202896,
0.07639351487159729,
-0.022469475865364075,
0.017980238422751427,
0.03296809270977974,
0.05604267120361328,
-0.0015380209079012275,
0.007146297488361597,
-0.026458607986569405,
0.008194472640752792,
0.01600613445043564,
0.040581099689006805,
-0.04487895965576172,
0.011401188559830189,
0.026668332517147064,
-0.01251727994531393,
0.0015070034423843026,
0.009678994305431843,
-0.014770854264497757,
-0.04245031252503395,
0.06215854734182358,
0.008083319291472435,
-0.029049251228570938,
-0.011043103411793709,
0.03293727710843086,
0.00029077293584123254,
-0.07031051814556122,
0.012026611715555191,
-0.04870123043656349,
-0.011749288998544216,
0.01301282923668623,
0.03771473467350006,
0.042951181530952454,
-0.08203699439764023,
0.03851454704999924,
0.07756190001964569,
-0.01537487655878067,
0.023099254816770554,
-0.01629498414695263,
0.027193276211619377,
-0.051689956337213516,
-0.011729427613317966,
-0.004149758256971836,
0.00962956715375185,
0.00611695135012269,
0.007646156940609217,
0.018861930817365646,
0.015771064907312393,
0.037781886756420135,
0.014564561657607555,
0.0035322322510182858,
-0.01730967126786709,
0.03466438874602318,
-0.010420722886919975,
-0.0080550666898489,
0.014155986718833447,
0.0239349864423275,
-0.0008001101086847484,
-0.0404011495411396,
-0.03196908161044121,
-0.020100627094507217,
0.02201847918331623,
0.016150733456015587,
0.023056011646986008,
-0.04897153005003929,
0.0718865841627121,
-0.03867071494460106,
0.046147421002388,
-0.08252579718828201,
-0.027463898062705994,
-0.0491015762090683,
-0.018186070024967194,
0.06997263431549072,
0.007057840470224619,
0.03565886244177818,
-0.03063468262553215,
0.03659740835428238,
-0.0020167985931038857,
-0.013623131439089775,
-0.019747255370020866,
0.04030880331993103,
0.010410823859274387,
0.00565575435757637,
-0.07364469766616821,
-0.07567562162876129,
0.055176544934511185,
-0.027006424963474274,
-0.0913006141781807,
0.01911650411784649,
0.006333867087960243,
-0.06258020550012589,
-0.047460127621889114,
0.0007775690173730254,
0.022132769227027893,
0.020272253081202507,
0.005383508279919624,
-0.017696620896458626,
-0.00792159978300333,
-0.019187532365322113,
-0.01593964360654354,
0.017088089138269424,
-0.02497035078704357,
0.042723432183265686,
0.006958417594432831,
-0.01372409425675869,
0.015767022967338562,
-0.014743426814675331,
0.003378356574103236,
-0.007084503769874573,
-0.05573227256536484,
-0.02644769474864006,
0.03932990878820419,
0.037737391889095306,
0.022684136405587196,
-0.005288328044116497,
0.055669527500867844,
-0.0056812758557498455,
0.06892948597669601,
0.03145533800125122,
-0.07090224325656891,
-0.03114604391157627,
-0.026903854683041573,
-0.0908963605761528,
0.005455636419355869,
0.03408446162939072,
0.007715863641351461,
-0.024476444348692894,
-0.015916893258690834,
0.034147705882787704,
0.05677467957139015,
0.0654270201921463,
0.02387635037302971,
0.047835662961006165,
0.04940184950828552,
-0.029270486906170845,
0.013549812138080597,
0.00826198048889637,
-0.03385385870933533,
0.0019055658485740423,
-0.012840758077800274,
-0.03354622796177864,
-0.07426349073648453,
-0.017361581325531006,
-0.09055858105421066,
0.025220470502972603,
-0.010467244312167168,
-0.009174095466732979,
0.05340719595551491,
-0.0400480218231678,
0.01843642257153988,
0.004504052922129631,
-0.02608235739171505,
-0.00959303043782711,
0.03103858046233654,
-0.02438964694738388,
0.003480176907032728,
0.019781608134508133,
-0.0162624754011631,
-0.02268693409860134,
-0.015194162726402283,
0.08703742921352386,
-0.018296340480446815,
-0.03945261240005493,
0.01818992756307125,
-0.00953859556466341,
-0.02036910131573677,
-0.024176770821213722,
-0.024582961574196815,
0.01007242314517498,
-0.019448332488536835,
-0.020458457991480827,
-0.028566477820277214,
0.00045281913480721414,
0.05074884369969368,
0.028172360733151436,
-0.03047623112797737,
-0.022045468911528587,
0.0012187587562948465,
0.026959532871842384,
0.033095214515924454,
-0.015934068709611893,
0.027660654857754707,
-0.022633777931332588,
0.04730488732457161,
0.011864138767123222,
0.030744336545467377,
-0.003674305509775877,
-0.01563365012407303,
-0.005871375557035208,
0.02086355723440647,
-0.05356087163090706,
-0.03106682002544403,
0.005623261909931898,
0.06956280767917633,
-0.04275570437312126,
-0.029855864122509956,
0.04968123137950897,
0.01664334535598755,
0.033822230994701385,
0.010413388721644878,
-0.0351560115814209,
-0.010590856894850731,
-0.006636418867856264,
0.019819973036646843,
-0.003495402866974473,
-0.008850017562508583,
0.009484353475272655,
0.02811703085899353,
-0.04422268271446228,
0.025422783568501472,
-0.043430592864751816,
0.022893009707331657,
-0.011930489912629128,
-0.001478005200624466,
-0.04641188681125641,
0.025212809443473816,
0.05149608105421066,
-0.059207409620285034,
0.030298754572868347,
0.02308535948395729,
-0.010071085765957832,
0.009544389322400093,
0.026914343237876892,
-0.057630881667137146,
0.01317725982517004,
0.053579047322273254,
-0.06476850807666779,
-0.029118860140442848,
-0.010507251136004925,
0.013738596811890602,
-0.04201662167906761,
0.015177794732153416,
0.045111283659935,
-0.07187072187662125,
-0.00483373086899519,
-0.08199708163738251,
0.009350434876978397,
-0.01655653305351734,
0.0025327573530375957,
0.055676884949207306,
-0.009544458240270615,
0.04960836470127106,
0.006814205087721348,
-0.0496443510055542,
0.006866422016173601,
0.003601865377277136,
0.026776107028126717,
0.032320037484169006,
-0.049566708505153656,
-0.01191333495080471,
0.0024600806646049023,
0.012721344828605652,
-0.014366116374731064,
0.0661492869257927,
0.02936393767595291,
-0.004731725435703993,
-0.032109856605529785,
0.049638744443655014,
0.05894520878791809,
0.011267184279859066,
0.042733293026685715,
-0.031793128699064255,
-0.08433780074119568,
0.07940290868282318,
0.03310466185212135,
-0.011202394030988216,
-0.011131820268929005,
0.02154393307864666,
0.10322670638561249,
0.032514214515686035,
-0.05155940353870392,
-0.0038458541966974735,
0.0071429600939154625,
0.02246832847595215,
-0.020481867715716362,
-0.07267493009567261,
0.0044335913844406605,
0.029883025214076042,
-0.055345140397548676,
-0.042400144040584564,
-0.02963448502123356,
-0.01207156665623188,
-0.029808130115270615,
-0.01046538446098566,
0.022268667817115784,
-0.0402040109038353,
0.05986323580145836,
-0.0021192184649407864,
-0.07321268320083618,
-0.031211011111736298,
-0.003125356277450919,
0.02506347745656967,
-0.03165901452302933,
0.012611156329512596,
0.034857310354709625,
0.018036864697933197,
0.016229823231697083,
-0.0007055861060507596,
-0.04620800167322159,
0.015034561045467854,
0.025746788829565048,
-0.12348715215921402,
0.012301541864871979,
0.014942064881324768,
-0.011700074188411236,
-0.030513877049088478,
-0.03625771775841713,
-0.018747478723526,
0.026031315326690674,
-0.007259774953126907,
0.0376107394695282,
-0.012058457359671593,
-0.04426508769392967,
0.00712908711284399,
0.005088892299681902,
0.03758953884243965,
-0.006117658689618111,
-0.0036915987730026245,
-0.03225164860486984,
-0.06365948915481567,
0.0004495010362006724,
0.009581118822097778,
0.060005877166986465,
-0.008892490528523922,
0.026169637218117714,
-0.06340602785348892,
0.001130316057242453,
0.09673605114221573,
0.007119410205632448,
0.017356643453240395,
-0.007858360186219215,
0.05925162881612778,
0.04431222751736641,
-0.01805361546576023,
-0.020550115033984184,
0.007015514653176069,
-0.03327515348792076,
-0.04879685118794441,
-0.0020568999461829662,
0.027195176109671593,
-0.05001162365078926,
-0.057802606374025345,
-0.02119510807096958,
0.02163773775100708,
0.017992611974477768,
0.03928796574473381,
0.0170910507440567,
0.017200397327542305,
0.04156113788485527,
-0.008469508029520512,
-0.04781774431467056,
-0.054655540734529495,
0.018326260149478912,
-0.006372552365064621,
0.005229688249528408,
0.04502212628722191,
-0.03572151064872742,
-0.0119899557903409,
0.028175966814160347,
0.06498588621616364,
0.007352078799158335,
0.03439543768763542,
0.04956451803445816,
-0.0036996991839259863,
0.005440044216811657,
-0.03308902308344841,
0.014324929565191269,
-0.051247235387563705,
0.04962771758437157,
-0.010325024835765362,
-0.01606713980436325,
0.007190512493252754,
0.005857438780367374,
-0.0158111322671175,
-0.008246314711868763,
0.036383140832185745,
-0.033575449138879776,
0.07402388006448746,
0.07780010253190994,
-0.07645206153392792,
0.04322371631860733,
0.002070641377940774,
0.07635952532291412,
-0.00878581777215004,
-0.03727087005972862,
0.04870358854532242,
0.008585639297962189,
0.09576951712369919,
0.020753394812345505,
0.05063813179731369,
-0.05178505554795265,
-0.005275283474475145,
-0.0406033992767334,
-0.04194752499461174,
0.07070502638816833,
-0.009581218473613262,
-0.0068084802478551865,
-0.014876271598041058,
0.004043094348162413,
-0.0408647246658802,
0.051232244819402695,
0.06007392704486847,
-0.04104340821504593,
-0.07552240788936615,
0.028692079707980156,
0.0004497183836065233,
0.0029937741346657276,
-0.010651321150362492,
-0.05367575213313103,
-0.05755610391497612,
0.034482453018426895,
-0.024058828130364418,
-0.0013696696842089295,
0.02958093024790287,
-0.010280554182827473,
-0.008990309201180935,
0.01891457848250866,
-0.011792057193815708,
-0.050201330333948135,
-0.021383142098784447,
-0.057997800409793854,
0.004289859440177679,
0.022201145067811012,
-0.029021810740232468,
-0.006378076039254665,
0.021276351064443588,
0.0067368545569479465,
-0.025230929255485535,
0.03403095155954361,
0.02472967840731144,
-0.02633500285446644,
-0.01645730994641781,
-0.02665286883711815,
0.003403975861147046,
-0.039823032915592194,
-0.022598562762141228,
0.03532932698726654,
-0.012179863639175892,
-0.017546337097883224,
0.09111962467432022,
0.029894500970840454,
-0.0898875966668129,
-0.002432445762678981,
-0.023963095620274544,
0.0004258233238942921,
0.0014665768248960376,
-0.011480669490993023,
0.009739463217556477,
-0.03585045784711838,
-0.003083587158471346,
0.06268464773893356,
-0.004411657340824604,
-0.03966459631919861,
0.009054158814251423,
-0.017183339223265648,
-0.01194320060312748,
-0.01099653635174036,
0.0186080951243639,
-0.06711632013320923,
-0.014120497740805149,
0.008127852343022823,
-0.014559888280928135,
-0.04761814698576927,
0.008476083166897297,
-0.008841552771627903,
0.09199749678373337,
0.022805336862802505,
0.03638691455125809,
-0.030894320458173752,
-0.05012502148747444,
-0.03848106786608696,
-0.06815019994974136,
-0.012536673806607723,
-0.06227978318929672,
-0.023570751771330833,
0.04502907022833824,
0.07355894148349762,
-0.03708488494157791,
-0.0006437628180719912,
0.035200249403715134,
-0.07235059887170792,
0.07210276275873184,
-0.030244609341025352,
0.016602883115410805,
0.025842836126685143,
-0.04268934577703476,
0.03318840637803078,
0.04864325001835823,
-0.016949215903878212,
-0.021504849195480347,
0.03995797410607338,
-0.05349119380116463,
0.05113891139626503,
-0.020918527618050575,
0.01471627689898014,
0.05311521515250206,
0.054941143840551376,
0.0008248141384683549,
0.019378041848540306,
-0.019464407116174698,
-0.023795483633875847,
-0.009188270196318626,
-0.0003239657962694764,
0.02672100067138672,
-0.016558440402150154,
0.04532226175069809,
0.0016040619229897857,
-0.04901299998164177,
-0.06080751493573189,
0.01403365470468998,
0.006873222533613443,
0.03194130212068558,
0.014412520453333855,
0.012280627153813839,
-0.0366034060716629,
0.04125342145562172
] |
<p>Several different sources online state that the average temperature of interstellar space (or the universe in general) is around 2-3K.</p>
<p>I learned that temperature is basically the wiggling of matter, and I find it somewhat counterintuitive that the wiggling of so few particles can cause a temperature of 2-3K. Is there a (order-of-magnitude) calculation which can show that this average temperature estimation is correct, using an estimation of the average density of interstellar space (or the universe in general)?</p> | g1231 | [
0.01861480064690113,
-0.016250329092144966,
0.009956888854503632,
-0.01357375830411911,
-0.025410141795873642,
0.01458354014903307,
-0.02372753620147705,
0.0787372961640358,
-0.030020402744412422,
0.06241270899772644,
0.05899663269519806,
0.02306879311800003,
0.020149055868387222,
0.027113132178783417,
-0.014989638701081276,
0.027416273951530457,
-0.018340306356549263,
-0.026889102533459663,
0.01570909284055233,
0.025123771280050278,
0.015708977356553078,
-0.052462149411439896,
0.028397656977176666,
-0.024800879880785942,
-0.01855657808482647,
0.007905544713139534,
-0.03101528249680996,
0.005366833880543709,
0.0073627326637506485,
0.002541018882766366,
0.030976925045251846,
0.037780728191137314,
0.002129883272573352,
-0.03183416649699211,
0.002938796766102314,
-0.035226911306381226,
0.0007159954402595758,
0.010875620879232883,
-0.00396724883466959,
-0.0468464121222496,
-0.04019489884376526,
-0.04835762456059456,
0.05291576683521271,
0.023411419242620468,
0.05594455078244209,
0.04742533713579178,
-0.042189113795757294,
0.05509992316365242,
-0.006705425679683685,
0.013990508392453194,
-0.06248851493000984,
-0.008296160027384758,
0.02542024664580822,
0.03203778713941574,
-0.04079478979110718,
-0.006257805973291397,
-0.025522589683532715,
-0.061659615486860275,
0.038345180451869965,
0.0513320118188858,
0.013621114194393158,
-0.011060962453484535,
-0.042345475405454636,
-0.05418288707733154,
-0.02176559530198574,
0.056820061057806015,
-0.039240822196006775,
0.0008302942733280361,
0.06564069539308548,
-0.08149956166744232,
-0.01143574807792902,
-0.010226655751466751,
-0.0047567784786224365,
-0.03170764818787575,
-0.15075384080410004,
0.020293785259127617,
-0.031695835292339325,
0.013942155987024307,
0.013875983655452728,
0.019649311900138855,
0.01195988617837429,
-0.0012519701849669218,
-0.017275039106607437,
0.04671652242541313,
0.01014807540923357,
-0.05394897609949112,
-0.0016488560941070318,
0.02434111014008522,
-0.01212488953024149,
0.0452650785446167,
-0.0024776298087090254,
0.08365847170352936,
0.046274334192276,
-0.04214617982506752,
0.022464554756879807,
-0.028938904404640198,
0.007435408886522055,
-0.011895167641341686,
-0.015091469511389732,
0.03115834854543209,
-0.024209819734096527,
-0.018030863255262375,
0.0043920609168708324,
-0.049218252301216125,
-0.008552774786949158,
-0.0230316873639822,
-0.01113920845091343,
-0.007269653957337141,
-0.020428985357284546,
-0.011514436453580856,
-0.046747807413339615,
-0.025146659463644028,
-0.004126009996980429,
-0.006278777960687876,
-0.0143745681270957,
-0.012201023288071156,
-0.01095491275191307,
0.027293246239423752,
0.029942862689495087,
0.06817422062158585,
-0.007820432074368,
0.0664035826921463,
-0.031368620693683624,
0.029867660254240036,
-0.008182685822248459,
-0.06994490325450897,
-0.026456620544195175,
-0.0004513249732553959,
-0.06024859473109245,
0.004285263828933239,
-0.02684883028268814,
-0.0021193029824644327,
-0.014846482314169407,
0.003044550074264407,
-0.06601466983556747,
-0.022475698962807655,
0.001803779974579811,
-0.0017870613373816013,
-0.02652679570019245,
0.013836575672030449,
0.02280031144618988,
0.025924475863575935,
0.07264301925897598,
-0.03163363039493561,
-0.04764221981167793,
0.04512424021959305,
-0.07429854571819305,
-0.01579265110194683,
0.04249386489391327,
0.01614079438149929,
0.04387208819389343,
0.01952304318547249,
0.05297000706195831,
-0.033189620822668076,
-0.026627248153090477,
0.0301772803068161,
0.034283604472875595,
0.04261790215969086,
0.029439276084303856,
0.04055069386959076,
0.03136485815048218,
-0.08159466087818146,
0.06159568578004837,
0.04395420476794243,
-0.04808161407709122,
0.0004375242569949478,
-0.02688208781182766,
-0.051825862377882004,
-0.043605271726846695,
-0.005741920787841082,
-0.02947123348712921,
0.02542056143283844,
0.032433412969112396,
0.009745731949806213,
-0.005285699386149645,
-0.03518344834446907,
0.07099463045597076,
-0.0063764601945877075,
-0.029025062918663025,
-0.020696941763162613,
0.033701661974191666,
0.0001881135394796729,
0.04461796209216118,
-0.048354730010032654,
-0.010739225894212723,
-0.040464166551828384,
-0.008972744457423687,
-0.030181176960468292,
0.004370464477688074,
0.015272043645381927,
0.009185275994241238,
-0.009774604812264442,
0.06479544937610626,
0.021405166015028954,
0.04666002094745636,
0.008156080730259418,
0.052794814109802246,
-0.009705008007586002,
-0.01000011432915926,
0.007521262392401695,
0.010937399230897427,
0.011227025650441647,
-0.047531355172395706,
-0.048284225165843964,
0.04122723266482353,
0.02020227164030075,
-0.027290550991892815,
0.005009803920984268,
-0.003590031061321497,
0.02975599281489849,
0.038306962698698044,
-0.011247662827372551,
-0.004970245063304901,
0.037934768944978714,
0.04072786867618561,
0.09654884040355682,
-0.030008912086486816,
0.0011032001348212361,
-0.008216649293899536,
0.012441045604646206,
-0.023096108809113503,
0.013576691970229149,
0.025112833827733994,
-0.040904633700847626,
0.02875254862010479,
-0.03389349952340126,
-0.06551696360111237,
0.0124522615224123,
0.015178607776761055,
0.021116673946380615,
-0.07991401851177216,
-0.001658010296523571,
-0.07404628396034241,
0.007146293763071299,
0.01007771398872137,
0.050435133278369904,
0.02564297802746296,
-0.01393602229654789,
0.0719318762421608,
0.05940514802932739,
0.015153855085372925,
0.018662789836525917,
-0.034486833959817886,
0.017691662535071373,
0.004593945574015379,
-0.015269043855369091,
0.010675580240786076,
-0.08458422869443893,
-0.004035960417240858,
-0.01739479787647724,
0.03352976590394974,
-0.004556626547127962,
0.03774697706103325,
-0.05986117944121361,
-0.005370159633457661,
-0.01134458463639021,
-0.05518084391951561,
0.055750198662281036,
-0.02091793157160282,
-0.03668258711695671,
0.0574069507420063,
-0.03582431748509407,
-0.007284051738679409,
-0.04849119111895561,
-0.003813120536506176,
-0.08236989378929138,
0.011152058839797974,
-0.024555809795856476,
-0.027877721935510635,
0.06114279106259346,
0.045401837676763535,
-0.04249304533004761,
-0.029546843841671944,
0.016008460894227028,
-0.014963305555284023,
0.014105439186096191,
0.02014441229403019,
0.0014852427411824465,
0.030479097738862038,
-0.03312896937131882,
-0.0006671868613921106,
-0.0070193372666835785,
-0.10595197975635529,
0.03962850198149681,
0.01445557177066803,
-0.08293356746435165,
-0.0376376174390316,
0.03862939029932022,
0.03488617762923241,
-0.008493498899042606,
0.037610381841659546,
-0.011888353154063225,
-0.04816817492246628,
0.06754588335752487,
0.06084955111145973,
0.03309328481554985,
0.017339592799544334,
-0.0020478100050240755,
-0.01859399490058422,
-0.029629893600940704,
0.0430782251060009,
-0.06521493196487427,
0.042099274694919586,
-0.04280385747551918,
-0.02271955832839012,
0.013770202174782753,
-0.015314655378460884,
-0.021944914013147354,
-0.013180536217987537,
-0.04354594275355339,
0.011910682544112206,
0.0032233919482678175,
0.01186691876500845,
0.06386160850524902,
-0.06625184416770935,
-0.00035420755739323795,
0.019639447331428528,
0.021677302196621895,
0.0356258861720562,
0.03252348303794861,
0.03383219242095947,
-0.006883372087031603,
-0.005872880574315786,
-0.04206622764468193,
0.05467604473233223,
0.039567138999700546,
-0.02698027342557907,
-0.08140908926725388,
-0.025286413729190826,
-0.010148917324841022,
-0.004670689348131418,
-0.07914122194051743,
-0.013883755542337894,
0.031153198331594467,
-0.015460997819900513,
-0.054852474480867386,
0.012194397859275341,
-0.04780508205294609,
0.021143073216080666,
0.016031531617045403,
-0.0017817359184846282,
0.014448589645326138,
-0.02974928542971611,
-0.015345151536166668,
-0.03350207954645157,
0.04377317801117897,
-0.001089728088118136,
-0.03288532793521881,
-0.033592838793992996,
-0.006124218925833702,
0.01995731145143509,
-0.03440753370523453,
0.029157496988773346,
-0.019075745716691017,
0.009702724404633045,
0.01684773899614811,
0.0031147957779467106,
0.02606254443526268,
0.044313617050647736,
-0.0433078370988369,
0.021281078457832336,
-0.05097819119691849,
0.022591138258576393,
-0.028353702276945114,
0.014279262162744999,
-0.04185644909739494,
-0.015897594392299652,
0.062491998076438904,
0.00878903828561306,
0.011816250160336494,
-0.06635168194770813,
0.010847555473446846,
-0.05843498557806015,
0.015452769584953785,
0.04198632761836052,
0.01022305153310299,
0.07271147519350052,
-0.01164762582629919,
0.009765100665390491,
0.05972309783101082,
0.03560091555118561,
0.08737263083457947,
0.018328189849853516,
0.03961721435189247,
-0.002541963243857026,
-0.006545242853462696,
-0.037272050976753235,
0.014381558634340763,
0.014630495570600033,
-0.05844015255570412,
0.08509452641010284,
-0.06020918861031532,
0.06739799678325653,
0.019887445494532585,
0.015423308126628399,
-0.05692585930228233,
0.04663196951150894,
0.02219979092478752,
0.02403508871793747,
0.007008868735283613,
0.03234267979860306,
-0.07249566912651062,
0.08757993578910828,
-0.014057040214538574,
0.019720716401934624,
0.0011956357629969716,
0.02093103528022766,
-0.05177290365099907,
-0.004635956604033709,
0.0064012156799435616,
-0.01221488881856203,
0.05348815768957138,
-0.0390455536544323,
0.007986783050000668,
-0.010780607350170612,
-0.011538093909621239,
0.008223011158406734,
-0.06423284858465195,
0.04439753666520119,
0.0353613942861557,
-0.022587038576602936,
0.03786944970488548,
-0.026141058653593063,
0.008342881686985493,
-0.04227421060204506,
0.052784088999032974,
0.05790463462471962,
0.014706007204949856,
-0.009023244492709637,
-0.003111842554062605,
0.03948826342821121,
-0.004756066482514143,
-0.040713511407375336,
0.1045486330986023,
-0.012630818411707878,
-0.021840766072273254,
-0.01780550740659237,
0.07230553776025772,
-0.058370303362607956,
-0.037319548428058624,
-0.025533201172947884,
0.013770170509815216,
-0.010547512210905552,
0.07498671859502792,
-0.03556189686059952,
0.05184460058808327,
-0.03998732566833496,
-0.03653471916913986,
-0.0643739327788353,
0.03225052356719971,
0.039473749697208405,
0.004648842383176088,
-0.06684789061546326,
0.04479217529296875,
-0.033759381622076035,
0.02345310151576996,
-0.04812132194638252,
0.051532674580812454,
0.001829197397455573,
0.037772975862026215,
-0.04474157094955444,
0.0241834819316864,
0.016979260370135307,
0.06335005164146423,
0.022829951718449593,
0.024728547781705856,
-0.0024680227506905794,
-0.030621608719229698,
0.054508525878190994,
0.021230319514870644,
-0.002381369471549988,
0.053307563066482544,
-0.029246900230646133,
-0.011015759781002998,
0.014571367762982845,
0.027583492919802666,
-0.009952872060239315,
-0.029379384592175484,
-0.05870773643255234,
0.060098227113485336,
-0.0372190847992897,
0.020170442759990692,
0.06845693290233612,
0.03197364881634712,
0.01058193389326334,
0.010771275497972965,
-0.02750716358423233,
0.022514240816235542,
0.0100714061409235,
-0.010048518888652325,
-0.001530392444692552,
-0.0037935529835522175,
0.009153592400252819,
0.015043827705085278,
-0.05889518931508064,
-0.020332925021648407,
-0.001340140006504953,
-0.05789969861507416,
0.00620752340182662,
0.05451098456978798,
0.009209658019244671,
0.04249785095453262,
0.004514299798756838,
-0.03104960173368454,
-0.03010457195341587,
-0.03442355617880821,
-0.019550146535038948,
-0.007176861632615328,
-0.05736645683646202,
0.012453394941985607,
0.014089128002524376,
0.04277927801012993,
0.04366358369588852,
-0.008683976717293262,
0.011334373615682125,
-0.03999960422515869,
0.032499875873327255,
0.011105254292488098,
0.042975448071956635,
-0.03717895969748497,
0.012001077644526958,
-0.018201002851128578,
0.033271197229623795,
0.004293722566217184,
0.00055508385412395,
0.03693307191133499,
-0.03247302398085594,
0.002473024418577552,
-0.0026357986498624086,
-0.05999087542295456,
-0.0068622468970716,
0.008860002271831036,
0.008515887893736362,
-0.07608697563409805,
0.0011749217519536614,
0.02687211148440838,
-0.005430515855550766,
0.016562025994062424,
0.026865122839808464,
0.05265498161315918,
-0.04870427027344704,
-0.00404075812548399,
0.007391004357486963,
-0.02137380838394165,
0.0363960862159729,
0.015865502879023552,
-0.03272567316889763,
0.0055169309489429,
0.07011225074529648,
-0.0364454947412014,
-0.00874071940779686,
0.017166484147310257,
0.006871577352285385,
-0.07961146533489227,
0.0009621580829843879,
0.04787048324942589,
-0.012532848864793777,
-0.027427608147263527,
0.004816933069378138,
0.044619932770729065,
-0.006692968774586916,
-0.013975890353322029,
0.043019358068704605,
0.011787636205554008,
-0.09203682839870453,
-0.025831671431660652,
-0.000029370694392127916,
-0.029896531254053116,
0.030869388952851295,
0.01855110377073288,
-0.019609257578849792,
0.058238089084625244,
-0.016197385266423225,
-0.028810713440179825,
0.09375819563865662,
0.016493957489728928,
-0.0022408098448067904,
-0.03892561420798302,
-0.022912466898560524,
0.0074640968814492226,
-0.046038106083869934,
-0.0003923218755517155,
-0.01017528772354126,
0.011223473586142063,
-0.01980862393975258,
0.021271279081702232,
-0.06004294380545616,
0.038483187556266785,
0.002802284201607108,
-0.02808261476457119,
-0.016209430992603302,
-0.009432608261704445,
-0.0044704885222017765,
-0.014858421869575977,
-0.01705470122396946,
-0.04429941624403,
-0.036778222769498825,
-0.02118070423603058,
-0.01864274963736534,
0.052160441875457764,
0.05025215074419975,
0.015833547338843346,
0.03172917291522026,
-0.02319403924047947,
0.04140697047114372,
-0.040229082107543945,
-0.02288803644478321,
0.03931865096092224,
0.04291579872369766,
0.01098170131444931,
-0.05820982903242111,
0.0025064852088689804,
-0.01212306972593069,
-0.002444119192659855,
0.0191953144967556,
-0.022747157141566277,
0.01970645599067211,
0.058028195053339005,
-0.023283865302801132,
-0.018842771649360657,
-0.027428332716226578,
0.00083901610923931,
-0.012633775360882282,
-0.019658515229821205,
-0.005179110914468765,
0.017259513959288597,
-0.042353857308626175,
0.04597966745495796,
0.030227066949009895,
-0.03429184854030609,
0.008759694173932076,
-0.042908765375614166,
-0.005422128364443779,
0.008984644897282124,
0.0019758185371756554,
-0.03772654011845589,
-0.046623244881629944,
-0.0003519896708894521,
-0.03688591346144676,
0.056988660246133804,
-0.0193551704287529,
-0.0875004306435585,
-0.013913428410887718,
-0.013624493032693863,
-0.03634938225150108,
0.004445728380233049,
-0.024285171180963516,
0.013771564699709415,
-0.02845562808215618,
-0.009318415075540543,
-0.03269781917333603,
-0.03867146000266075,
-0.011814807541668415,
0.036668334156274796,
0.002798832021653652,
0.054847147315740585,
0.02864167094230652,
0.0006341006373986602,
0.03133920580148697,
-0.013883659616112709,
-0.0101460637524724,
-0.0474652498960495,
0.006317165680229664,
0.011014746502041817,
-0.025106463581323624,
0.012141472660005093,
0.005457793828099966,
-0.022816378623247147,
0.03281109780073166,
-0.07518899440765381,
0.03456142917275429,
0.009466816671192646,
-0.10321139544248581,
-0.03346756100654602,
0.02053813822567463,
-0.027629544958472252,
-0.002301642904058099,
-0.00005017458533984609,
0.04331745207309723,
0.014392537996172905,
0.0022409060038626194,
0.0321802981197834,
0.012514214031398296,
0.03316567838191986,
-0.012085710652172565,
0.09580836445093155,
-0.013575129210948944,
-0.016445951536297798,
0.009799923747777939,
0.005931597203016281,
-0.05714893713593483,
-0.009244076907634735,
-0.04648236185312271,
-0.09091028571128845,
-0.01883634179830551,
0.08148239552974701,
0.07774750143289566,
0.005423630587756634,
0.026611389592289925,
0.02795613929629326,
-0.004412822891026735,
-0.01878511719405651,
-0.04504211246967316,
-0.009410740807652473,
0.030985726043581963,
0.049035970121622086,
-0.005892677698284388,
0.007381931412965059,
-0.02543686516582966,
-0.07026238739490509,
0.05569365248084068,
0.000026401521608931944,
0.062382981181144714,
0.06857822835445404,
0.018771111965179443,
-0.04177829623222351,
-0.02588476426899433,
-0.029980434104800224,
-0.020671486854553223,
-0.023153074085712433,
0.013153751380741596,
0.007086977828294039,
0.047972969710826874,
-0.011288891546428204,
0.03171037137508392,
-0.014027697965502739,
0.01894252374768257,
-0.018232539296150208,
0.034677695482969284,
-0.024585487321019173,
0.0315881222486496,
0.02771257795393467,
0.030612289905548096,
0.023378465324640274,
-0.05893652141094208,
0.030396126210689545,
0.026768678799271584,
0.006108388304710388,
0.020855413749814034,
0.0476454496383667,
0.006037147715687752,
0.03286809101700783,
0.027744939550757408,
-0.04700389504432678,
-0.007288873661309481,
-0.01916973665356636,
-0.005904714111238718,
0.040822628885507584,
0.004681856371462345,
-0.01986660622060299,
0.008997851051390171,
0.05155899375677109,
-0.02670479007065296,
0.018034329637885094,
0.039679769426584244,
0.00958983600139618,
-0.06527183949947357,
-0.05227771773934364,
-0.060788594186306,
0.004648336675018072,
-0.0641152635216713,
-0.06819811463356018,
0.018879374489188194,
-0.020751560106873512,
0.012595917098224163,
0.007235337980091572,
-0.007738426327705383,
0.006383455358445644
] |
<p>Is it possible to write down a partition function for a <a href="http://en.wikipedia.org/wiki/Microcanonical_ensemble" rel="nofollow">microcanonical ensemble</a>?</p> | g1232 | [
-0.03462273254990578,
-0.03299250826239586,
-0.024889569729566574,
-0.10164840519428253,
-0.012530018575489521,
-0.08904151618480682,
-0.008446434512734413,
0.045992836356163025,
-0.09889872372150421,
0.006878073792904615,
-0.00752214016392827,
0.016797536984086037,
0.03665011376142502,
0.06376184523105621,
-0.025710957124829292,
0.04004343971610069,
0.04671479016542435,
0.028831034898757935,
0.03551725298166275,
0.03055248223245144,
0.008643442764878273,
0.01641000621020794,
0.011513832025229931,
0.0007305878680199385,
0.07877463102340698,
0.031126776710152626,
0.058203037828207016,
-0.01940622739493847,
-0.03400633484125137,
-0.0013386807404458523,
0.0032934776972979307,
0.03483206778764725,
-0.004696079064160585,
0.05898023396730423,
0.03970853239297867,
0.07823780179023743,
0.017626332119107246,
-0.06646620482206345,
0.0021032814402133226,
-0.04145883023738861,
0.04434400424361229,
0.04934266209602356,
-0.0035301586613059044,
-0.016171416267752647,
0.029285438358783722,
0.03962871432304382,
0.04375568404793739,
-0.024493055418133736,
-0.0717705488204956,
-0.04720800742506981,
0.05998790264129639,
0.00006185082020238042,
-0.007735094521194696,
-0.018489815294742584,
0.026860985904932022,
0.016173969954252243,
0.0403207503259182,
-0.05949750542640686,
0.011004244908690453,
0.03927147760987282,
0.013789958320558071,
-0.006498116068542004,
-0.0233792494982481,
0.033823899924755096,
0.03941471502184868,
-0.008288566954433918,
-0.021484673023223877,
-0.012229792773723602,
-0.05385301634669304,
-0.03839108347892761,
0.0316840298473835,
0.029782800003886223,
0.04374183341860771,
-0.023837566375732422,
-0.049460649490356445,
-0.01593330316245556,
0.051228202879428864,
-0.007637768983840942,
0.02552141807973385,
0.05668305233120918,
-0.022949695587158203,
0.031936630606651306,
0.027673818171024323,
-0.016899213194847107,
-0.018781056627631187,
-0.036663878709077835,
0.05039643123745918,
-0.06206759810447693,
-0.012860124930739403,
0.07018335908651352,
0.026420958340168,
0.008608859963715076,
0.02585107460618019,
0.01072741113603115,
0.03212737664580345,
0.0004711207584477961,
-0.0820714458823204,
-0.000766868470236659,
-0.08030794560909271,
0.02837376296520233,
0.014583509415388107,
-0.01972893252968788,
0.02624186873435974,
-0.027801048010587692,
0.032612886279821396,
-0.057854220271110535,
0.010958581231534481,
0.0033908274490386248,
-0.029698967933654785,
0.004553052131086588,
0.055150292813777924,
0.013894758187234402,
-0.09511052817106247,
0.0047870962880551815,
-0.04182164743542671,
-0.031314510852098465,
0.0036350421141833067,
-0.09423451870679855,
-0.033062394708395004,
0.0033361169043928385,
0.028592949733138084,
-0.0327456034719944,
0.00991848111152649,
-0.02539237029850483,
-0.02590968646109104,
0.0035817238967865705,
-0.0028869847301393747,
0.029036663472652435,
-0.010953136719763279,
-0.07635009288787842,
0.020941488444805145,
0.014583664946258068,
0.003643149510025978,
0.0038504248950630426,
0.022413145750761032,
0.019443325698375702,
-0.014758029952645302,
0.007689859252423048,
-0.08298920094966888,
0.01291676051914692,
0.012625519186258316,
-0.007334268651902676,
0.002687455154955387,
0.0016427768860012293,
0.0306720994412899,
-0.023808807134628296,
-0.000002657508957781829,
-0.01620962657034397,
0.002538457280024886,
0.031047897413372993,
0.0053700548596680164,
0.02222413197159767,
0.0014042970724403858,
-0.012974778190255165,
-0.0012059570290148258,
0.060766272246837616,
0.01276138424873352,
-0.006074552424252033,
-0.019105909392237663,
-0.02860962599515915,
-0.03193363547325134,
0.03435463458299637,
0.053073134273290634,
-0.04193415120244026,
-0.08836733549833298,
0.0007708249613642693,
-0.016337020322680473,
0.007358454633504152,
-0.04046644642949104,
-0.03322267904877663,
0.0194645207375288,
0.03719095140695572,
0.03452928736805916,
0.034701745957136154,
0.015192721039056778,
0.051676321774721146,
-0.00046375239617191255,
0.02237747237086296,
-0.0004970834124833345,
-0.004288134165108204,
0.03588962182402611,
0.0031530919950455427,
-0.00752811087295413,
-0.03416000306606293,
-0.0007659167167730629,
-0.039763566106557846,
0.006205798126757145,
0.0419929213821888,
0.015205666422843933,
-0.05183875560760498,
0.01872239075601101,
0.05604349076747894,
0.05335595831274986,
-0.08020078390836716,
0.02760535664856434,
-0.046403251588344574,
-0.06834552437067032,
0.0004557674692478031,
-0.006938989739865065,
-0.03612861409783363,
0.04807800054550171,
0.03969650715589523,
0.008953532204031944,
-0.012353278696537018,
0.032184701412916183,
-0.01355904620140791,
-0.01984829269349575,
-0.06925204396247864,
-0.020591452717781067,
-0.041865311563014984,
0.07269006967544556,
0.00008753497240832075,
-0.010756729170680046,
-0.0022611464373767376,
-0.012742200866341591,
-0.02415558695793152,
0.01415045466274023,
-0.049502573907375336,
0.04623839631676674,
-0.05564622953534126,
-0.06722904741764069,
-0.014097338542342186,
0.013301776722073555,
0.048533447086811066,
0.029793204739689827,
0.01338824164122343,
0.009995509870350361,
0.040333304554224014,
-0.04111996293067932,
-0.006151054985821247,
-0.026763275265693665,
-0.027913475409150124,
-0.008330320939421654,
-0.041874904185533524,
0.006632019765675068,
0.014731652103364468,
-0.008054250851273537,
0.00028756223036907613,
-0.01697101816534996,
0.026005949825048447,
-0.014034227468073368,
-0.053581397980451584,
0.011117247864603996,
-0.018483242020010948,
-0.027010969817638397,
-0.0509202815592289,
-0.03468246012926102,
-0.009971490129828453,
0.03221997246146202,
0.005033324472606182,
-0.04725303128361702,
-0.025877051055431366,
0.03051205538213253,
0.042116813361644745,
-0.03298568353056908,
-0.04375500604510307,
-0.003898533061146736,
-0.008771953172981739,
0.004885636270046234,
0.0061943791806697845,
0.04618007317185402,
0.023923641070723534,
-0.02726694568991661,
-0.02807769924402237,
0.034264128655195236,
-0.05965223163366318,
-0.04361485689878464,
-0.0026502027176320553,
-0.01218697614967823,
0.04632778465747833,
-0.028392519801855087,
-0.016694262623786926,
0.006218864582479,
0.025478068739175797,
0.01658693701028824,
-0.011041484773159027,
-0.012243187986314297,
0.0071014463901519775,
0.015637051314115524,
-0.026227619498968124,
-0.028542764484882355,
0.013136029243469238,
-0.02870677039027214,
-0.023898255079984665,
0.010556533001363277,
-0.030157141387462616,
-0.010772811248898506,
0.00022617938520852476,
0.024321695789694786,
0.01481102965772152,
-0.0020827390253543854,
0.054740387946367264,
0.07386438548564911,
0.02656315453350544,
0.017082147300243378,
-0.05830356106162071,
0.01697194203734398,
-0.01494809240102768,
0.009650846011936665,
0.017781857401132584,
-0.009518698789179325,
-0.0345148965716362,
0.05815904587507248,
0.009271274320781231,
-0.03834384307265282,
0.012673713266849518,
0.01359600480645895,
-0.005036907270550728,
0.05044860765337944,
-0.01567992754280567,
0.025026241317391396,
0.03138463944196701,
-0.05625762417912483,
-0.002496860921382904,
-0.008281613700091839,
0.053326092660427094,
0.05429663881659508,
-0.012461206875741482,
0.003268721280619502,
-0.09822176396846771,
-0.02552621439099312,
-0.04976004362106323,
0.025420282036066055,
0.04320520535111427,
0.026933718472719193,
0.0303510595113039,
-0.02463364601135254,
-0.046424027532339096,
0.02031402289867401,
0.04477931559085846,
-0.011531565338373184,
0.022260596975684166,
0.028297489508986473,
0.015735307708382607,
-0.011308345943689346,
0.022119801491498947,
-0.04319290816783905,
-0.05632752552628517,
-0.01689484529197216,
0.0004990902380086482,
0.004000546410679817,
-0.005082570947706699,
-0.03163045272231102,
0.0141648780554533,
-0.04578453674912453,
0.008862697519361973,
0.03662803769111633,
0.012335415929555893,
0.028717005625367165,
-0.00834106095135212,
-0.01169524621218443,
-0.03954658284783363,
0.02457692287862301,
-0.027209458872675896,
0.031330402940511703,
-0.019762320443987846,
0.06403713673353195,
-0.08954533189535141,
-0.04391023889183998,
0.08240810036659241,
-0.012875320389866829,
-0.0544244609773159,
0.07701779901981354,
0.012867474928498268,
0.011311814188957214,
0.024039966985583305,
-0.011272051371634007,
0.07833442091941833,
-0.021761218085885048,
0.03151250630617142,
0.037739839404821396,
-0.010751968249678612,
-0.030700158327817917,
-0.024937011301517487,
-0.02101118117570877,
-0.04630402475595474,
0.009214756079018116,
0.010840252041816711,
-0.013059087097644806,
0.002181664574891329,
0.03652536869049072,
-0.013036597520112991,
0.10519391298294067,
-0.00394862936809659,
-0.029197145253419876,
-0.0055639417842030525,
-0.04245396703481674,
0.012839624658226967,
0.001351708546280861,
0.03389570489525795,
-0.013346237130463123,
0.002697673859074712,
-0.08315470069646835,
0.00924050621688366,
-0.05251650884747505,
0.01730428636074066,
-0.04449969157576561,
-0.03170013427734375,
-0.05003494396805763,
0.0660359114408493,
0.018781952559947968,
-0.04523804411292076,
0.004783462733030319,
-0.010070235468447208,
0.051852643489837646,
-0.015367567539215088,
0.007684352342039347,
-0.007465045899152756,
0.007439223118126392,
-0.03842060640454292,
0.0003810842172242701,
-0.02485715225338936,
0.031735364347696304,
0.002655223710462451,
-0.024647530168294907,
-0.031970757991075516,
0.06251106411218643,
0.009315790608525276,
0.01571265235543251,
0.018345322459936142,
-0.09827951341867447,
-0.01892661675810814,
-0.06148182228207588,
0.02528599090874195,
-0.07311695069074631,
-0.0018961390014737844,
-0.02485017664730549,
-0.017106622457504272,
0.0014716414734721184,
0.010344354435801506,
0.02950086072087288,
0.03150178864598274,
0.0311179980635643,
-0.012146016582846642,
0.00018698666826821864,
-0.07467134296894073,
-0.028407158330082893,
-0.054355438798666,
0.0127699701115489,
-0.014539964497089386,
-0.029976528137922287,
0.008677386678755283,
-0.009764735586941242,
0.04162108525633812,
-0.008587853983044624,
0.028286386281251907,
-0.044842928647994995,
-0.005118560045957565,
-0.040658172219991684,
-0.02233101613819599,
0.0744379460811615,
0.022352397441864014,
-0.02541452832520008,
-0.0013115608599036932,
0.06223944574594498,
0.03827003389596939,
-0.030717728659510612,
-0.03944820910692215,
0.04815131798386574,
-0.0170636847615242,
0.0119539275765419,
0.030322933569550514,
0.01190219633281231,
-0.008390435017645359,
0.02785312570631504,
0.02932729572057724,
-0.06074942648410797,
0.03571053594350815,
-0.02864726074039936,
0.050402216613292694,
0.06295376271009445,
-0.0018109376542270184,
-0.026003630831837654,
-0.01697443053126335,
-0.020223483443260193,
-0.01421526912599802,
0.000517501262947917,
-0.012664424255490303,
0.053054243326187134,
0.020191393792629242,
-0.010029468685388565,
0.0244196318089962,
-0.03132973983883858,
-0.010520746000111103,
0.0835394486784935,
0.00037479560705833137,
-0.011856392957270145,
-0.041102245450019836,
-0.022891277447342873,
0.021410999819636345,
-0.004508949816226959,
0.004980573896318674,
0.016870979219675064,
-0.0019303919980302453,
0.08249740302562714,
-0.03832332417368889,
0.040277957916259766,
-0.05233999341726303,
0.043438710272312164,
-0.046303894370794296,
0.045628610998392105,
-0.016901588067412376,
0.027357997372746468,
0.009797702543437481,
0.011282335966825485,
0.027416713535785675,
-0.009547186084091663,
0.03192462399601936,
-0.006488129962235689,
0.08445852249860764,
0.022898048162460327,
0.017275536432862282,
0.00045511696953326464,
0.029355693608522415,
0.043171510100364685,
-0.022374678403139114,
-0.008517520502209663,
0.03522643446922302,
-0.015119872987270355,
-0.0003559916513040662,
-0.018806390464305878,
0.022592058405280113,
-0.02380223013460636,
0.02824120968580246,
0.004939403850585222,
-0.019487356767058372,
-0.009312446229159832,
-0.028203072026371956,
0.021575231105089188,
0.06612085551023483,
-0.03652258589863777,
-0.009609585627913475,
-0.03554223105311394,
-0.003447888186201453,
0.016908418387174606,
-0.06594748795032501,
-0.01682298071682453,
0.02855471521615982,
0.046560466289520264,
0.044298309832811356,
0.011081338860094547,
-0.03499123826622963,
-0.062037330120801926,
-0.04387972503900528,
-0.016091924160718918,
-0.01072790939360857,
-0.03979203477501869,
0.07720962166786194,
0.0566018708050251,
0.008253349922597408,
-0.04292914643883705,
0.005066398996859789,
-0.047480762004852295,
-0.05511869862675667,
-0.01667797937989235,
0.023556862026453018,
-0.04481516778469086,
-0.0010287286713719368,
0.04292900860309601,
0.0053384918719530106,
-0.01894417777657509,
-0.05199965462088585,
0.014281874522566795,
-0.04842759296298027,
-0.05927225574851036,
-0.06268256157636642,
0.0006306578870862722,
0.013847935944795609,
-0.017017200589179993,
-0.05129481852054596,
0.01750604622066021,
-0.08001554757356644,
-0.019015586003661156,
0.036173947155475616,
0.004766023252159357,
-0.04545707628130913,
0.01968580298125744,
0.0743282213807106,
0.03407064825296402,
-0.05183415114879608,
-0.011368289589881897,
-0.039260439574718475,
0.04205017909407616,
0.03163513168692589,
-0.0027970843948423862,
0.04938914254307747,
-0.0036872720811516047,
-0.03347135707736015,
-0.020659221336245537,
0.017130447551608086,
0.00023333047283813357,
0.03183403238654137,
-0.02869468927383423,
0.045905496925115585,
-0.012916582636535168,
0.00019658055680338293,
-0.025389017537236214,
0.07520244270563126,
0.00467574642971158,
-0.0029741886537522078,
0.01798064447939396,
0.013931957073509693,
0.011181931011378765,
-0.08453693985939026,
0.004057629499584436,
0.04861338064074516,
-0.06645042449235916,
0.06191258877515793,
0.03834556043148041,
0.002078794874250889,
-0.07000912725925446,
0.05407646298408508,
0.0673270970582962,
-0.033446043729782104,
0.0139777148142457,
-0.017325948923826218,
0.010529513470828533,
-0.03357579559087753,
-0.022279130294919014,
0.024379491806030273,
0.10051743686199188,
-0.06736765056848526,
-0.006315387319773436,
-0.03788754343986511,
0.005063061136752367,
0.04538348689675331,
-0.04609237238764763,
0.008208096027374268,
0.010310918092727661,
-0.013749871402978897,
-0.013369559310376644,
0.004383477848023176,
-0.048307087272405624,
0.016999099403619766,
-0.010109142400324345,
0.032820284366607666,
-0.08785375207662582,
-0.037509411573410034,
0.04659244418144226,
-0.002465202473104,
-0.08057481795549393,
0.06464526802301407,
0.06358231604099274,
0.016023926436901093,
0.030619440600275993,
0.020454933866858482,
0.03206276521086693,
0.0035321065224707127,
-0.007982355542480946,
-0.06404533982276917,
0.056039661169052124,
-0.021476924419403076,
0.04932648688554764,
0.010573260486125946,
-0.04303732141852379,
0.05170118063688278,
-0.02826150320470333,
-0.01978709176182747,
-0.018794506788253784,
0.03205641731619835,
0.010963075794279575,
0.012690157629549503,
-0.02040449157357216,
-0.026370657607913017,
0.014641115441918373,
0.04034000262618065,
0.040175314992666245,
0.042773306369781494,
-0.016291484236717224,
-0.027611156925559044,
0.01258417684584856,
0.0036556844133883715,
-0.009360547177493572,
0.0007864381186664104,
0.027502432465553284,
-0.015935439616441727,
-0.019210660830140114,
0.031645238399505615,
0.04765850305557251,
0.020228566601872444,
-0.021777978166937828,
-0.06985756009817123,
0.007907933555543423,
-0.05785149335861206,
-0.0014292586129158735,
-0.058138273656368256,
-0.007399473339319229,
0.002649192698299885,
0.013050170615315437,
-0.020777199417352676,
0.0010242171119898558,
-0.00027049455093219876,
-0.0021593680139631033,
-0.03030817024409771,
-0.015697499737143517,
0.02417113073170185,
0.006465085782110691,
-0.011773529462516308,
0.023863451555371284,
0.044435545802116394,
-0.021177079528570175,
-0.035232800990343094,
0.049742598086595535,
-0.049602895975112915,
-0.038356103003025055,
-0.02585374005138874,
-0.017090346664190292,
0.034524448215961456,
0.01879223808646202,
-0.09849583357572556,
0.004031040705740452,
0.08708623051643372,
-0.0896952897310257,
-0.021346522495150566,
0.048369381576776505,
0.009668007493019104,
-0.08285129070281982,
-0.04016128182411194,
-0.00018557655857875943,
-0.021376958116889,
-0.0375572107732296,
0.013797839172184467,
0.05114896968007088,
0.0013689622282981873,
0.0033118959981948137,
-0.029806368052959442,
-0.010111801326274872,
0.05131690204143524,
0.03936336562037468,
-0.025003349408507347,
0.02641226351261139,
0.04371720924973488,
0.04109160229563713,
0.000006361025953083299,
0.00798048172146082,
0.018740523606538773,
-0.01921577751636505,
0.03693030774593353,
0.03471594303846359,
0.028284097090363503,
-0.052377816289663315,
0.026657896116375923,
0.014506664127111435,
0.0020393054001033306,
0.06008636951446533,
0.026118317618966103,
-0.04990452527999878,
-0.03136139363050461,
0.02823266014456749,
0.02720090001821518,
0.0033075790852308273,
-0.05430639162659645,
0.040526390075683594,
-0.03479216992855072,
0.026156751438975334,
0.034804027527570724,
0.08709345012903214,
0.06136452034115791,
0.02305477485060692,
0.004588523413985968,
-0.0018096108688041568,
0.03333291411399841,
-0.004544239956885576,
-0.004048326518386602,
0.008194019086658955,
-0.0003868736093863845,
0.03734708949923515,
0.0006402612198144197
] |
<p>I am very curious if an easy calculable formula for the bremstrahlung radiation of deeply relativistic, charged particles exists, if they are moving on circular orbit:</p>
<p>$P(E,m_0,Q,r)=?$</p>
<p>...where</p>
<ul>
<li>$P$ is the power of the Bremstrahlung radiation;</li>
<li>$E$ is the total kinetic energy of the particles (we are in deeply relativistic case, thus $E\gg{m_0}c^2$);</li>
<li>$m_0$ is the total rest mass of the particles;</li>
<li>$Q$ is the total charge of the particles;</li>
<li>and $r$ is the radius of the orbit.</li>
</ul>
<p>If a such clean, trivial formula doesn't exist, a link were also okay, where it can be found.</p> | g1233 | [
0.03956858813762665,
0.033366862684488297,
0.0005741541972383857,
-0.004170636646449566,
0.03861194849014282,
-0.008005496114492416,
-0.04373415187001228,
0.018642010167241096,
-0.024512270465493202,
0.06188322603702545,
0.005936679430305958,
0.11059746891260147,
0.0004154047346673906,
-0.012975812889635563,
-0.03766390308737755,
-0.053278882056474686,
0.0715201124548912,
-0.005190020892769098,
-0.010710923932492733,
0.05086357519030571,
0.023144053295254707,
-0.03071175329387188,
0.0008503546705469489,
-0.022729475051164627,
-0.014889474958181381,
0.05712484195828438,
-0.010833097621798515,
0.00013073947047814727,
-0.01686210185289383,
-0.049534913152456284,
0.01594281569123268,
-0.01797088049352169,
-0.01302491407841444,
-0.025311781093478203,
0.054155249148607254,
-0.0900394544005394,
0.0225254874676466,
0.03272759169340134,
-0.0152833117172122,
0.02793782763183117,
0.011021679267287254,
-0.03255088999867439,
0.05334022268652916,
0.02198152430355549,
-0.008548956364393234,
0.010020740330219269,
-0.026333685964345932,
0.026895301416516304,
-0.04090907424688339,
-0.018065374344587326,
-0.07843778282403946,
0.015350949950516224,
0.025590771809220314,
-0.005762926768511534,
0.00430492777377367,
-0.03812097758054733,
-0.05910804122686386,
-0.057122960686683655,
0.024586370214819908,
0.04080132395029068,
0.009169153869152069,
-0.011388540267944336,
-0.02245139889419079,
-0.058379385620355606,
0.02619384415447712,
0.01027904823422432,
-0.02550080418586731,
0.037615224719047546,
-0.013161423616111279,
-0.028719456866383553,
0.041474904865026474,
-0.014869293197989464,
-0.019507000222802162,
-0.06209229677915573,
0.035021767020225525,
0.005178235471248627,
0.0037326542660593987,
-0.020259356126189232,
0.0049191731959581375,
-0.027227314189076424,
-0.032743677496910095,
-0.0032707659993320704,
0.007933489046990871,
-0.02738202176988125,
0.039282992482185364,
-0.06546176970005035,
-0.013598361983895302,
0.013704448938369751,
-0.009834401309490204,
-0.07254016399383545,
0.0026885061524808407,
-0.04279365763068199,
0.024717651307582855,
-0.0711868554353714,
0.025205180048942566,
-0.06603538990020752,
0.003224420128390193,
0.042072709649801254,
-0.05507393181324005,
-0.026725009083747864,
0.010253207758069038,
0.011957724578678608,
-0.06184885650873184,
0.050541795790195465,
0.04142395034432411,
-0.05609869584441185,
0.02451225370168686,
-0.025853361934423447,
0.0194321870803833,
-0.03255442529916763,
0.003377453191205859,
-0.07236826419830322,
0.03894251957535744,
-0.0064167361706495285,
-0.07298560440540314,
0.042291443794965744,
0.07260429859161377,
-0.058774542063474655,
-0.012281850911676884,
0.06628026068210602,
0.046684447675943375,
0.028021609410643578,
-0.016148803755640984,
0.06406844407320023,
-0.01155833713710308,
0.0028713291976600885,
-0.03483423590660095,
0.005675214342772961,
0.05284155160188675,
0.05200730264186859,
-0.020992757752537727,
0.006096465978771448,
0.03512544557452202,
-0.004802503623068333,
-0.007854212075471878,
-0.002631537150591612,
-0.009070642292499542,
0.027573436498641968,
-0.0034663418773561716,
-0.06954126805067062,
0.013189585879445076,
-0.02153291553258896,
0.028411448001861572,
0.011862421408295631,
-0.057065002620220184,
0.022259050980210304,
-0.04269484430551529,
-0.057751771062612534,
0.04408140480518341,
0.02591993287205696,
0.02075682021677494,
0.03501142933964729,
0.02582669071853161,
-0.0475931353867054,
0.016023093834519386,
0.003212437266483903,
-0.018172916024923325,
-0.009152835234999657,
-0.051044873893260956,
0.08425667136907578,
0.027917124330997467,
0.02078583650290966,
0.016245024278759956,
-0.03346312791109085,
-0.0262069683521986,
0.06428103148937225,
-0.041858553886413574,
-0.046107690781354904,
-0.07101355493068695,
-0.062188971787691116,
-0.03136388212442398,
0.010547593235969543,
0.019568482413887978,
0.006629550829529762,
0.017932722344994545,
0.00820119772106409,
0.06939002871513367,
0.011439750902354717,
-0.015202837996184826,
0.0033764452673494816,
-0.01819687895476818,
0.01339017879217863,
0.04442510008811951,
0.033319924026727676,
0.013036340475082397,
-0.03714602440595627,
-0.02743358537554741,
-0.00487367482855916,
-0.0190472062677145,
-0.0310895424336195,
0.012762673199176788,
0.03498586639761925,
0.02578488178551197,
0.023271841928362846,
-0.02914072759449482,
0.003589480184018612,
-0.029551981016993523,
0.03995390236377716,
-0.00867962185293436,
0.008435018360614777,
0.009636767208576202,
0.04180733487010002,
0.005544770509004593,
-0.014854692853987217,
0.04263012483716011,
0.04396788403391838,
-0.017347073182463646,
0.03366900607943535,
0.03774018958210945,
0.022917388007044792,
0.007355086039751768,
-0.030541667714715004,
0.015552866272628307,
0.029456421732902527,
-0.0013903792714700103,
-0.01838923804461956,
-0.05237194523215294,
0.019259124994277954,
-0.035255804657936096,
0.022518282756209373,
-0.0798564925789833,
-0.042633529752492905,
0.005319235380738974,
0.020084744319319725,
0.012358667328953743,
-0.014856526628136635,
-0.03940064460039139,
-0.009599922224879265,
0.06522035598754883,
0.03152758628129959,
0.018993696197867393,
0.052114568650722504,
-0.017216822132468224,
-0.0070284889079630375,
0.014834621921181679,
0.02104610577225685,
-0.046849485486745834,
-0.02431320957839489,
0.08584654331207275,
0.021085575222969055,
-0.03035924956202507,
-0.029938487336039543,
-0.01444603968411684,
-0.013450678437948227,
0.034620001912117004,
-0.026598777621984482,
0.0604521669447422,
0.018524708226323128,
0.03980381041765213,
0.003286314196884632,
-0.009673131629824638,
-0.048648398369550705,
-0.061553288251161575,
0.0014213224640116096,
-0.0047994027845561504,
0.0381784550845623,
-0.0878659039735794,
0.03792957961559296,
-0.04059801623225212,
-0.00020987039897590876,
-0.0339265838265419,
-0.01243501901626587,
0.05081230774521828,
0.025215942412614822,
-0.0012998990714550018,
-0.012492157518863678,
0.009245911613106728,
0.04719910770654678,
0.055046066641807556,
0.03240685164928436,
-0.025758013129234314,
0.10062894970178604,
0.024668049067258835,
-0.0018477243138477206,
0.006867891643196344,
-0.05049026384949684,
0.013676060363650322,
-0.030018692836165428,
-0.010687046684324741,
-0.011204253882169724,
0.028546031564474106,
0.0012192954309284687,
0.015455822460353374,
0.05408572033047676,
-0.02026989869773388,
-0.08967345952987671,
-0.031609173864126205,
0.041531432420015335,
0.01720886491239071,
-0.043285202234983444,
0.02636287733912468,
0.01531235221773386,
0.09427936375141144,
-0.00842867698520422,
-0.01958134025335312,
0.0516938753426075,
0.04493052139878273,
-0.004674937110394239,
-0.012141848914325237,
0.05181709676980972,
0.011368912644684315,
-0.05550796538591385,
0.02836654894053936,
0.024639301002025604,
-0.04503364488482475,
0.053088366985321045,
-0.04203691706061363,
-0.02828979305922985,
0.02472323179244995,
0.0141758369281888,
-0.02284853532910347,
0.03731958940625191,
0.00230933609418571,
0.03059788979589939,
0.04064026102423668,
-0.052728816866874695,
-0.021192770451307297,
-0.009463094174861908,
0.04098408296704292,
0.016701510176062584,
0.0067701698280870914,
-0.02231781743466854,
0.014794482849538326,
-0.030997542664408684,
0.015536089427769184,
0.02547479420900345,
-0.06408552080392838,
-0.008903414942324162,
-0.005125462543219328,
-0.015501444227993488,
0.0010258530965074897,
0.03259506821632385,
0.03832012787461281,
0.038535501807928085,
-0.0026403022930026054,
-0.03694600611925125,
-0.014369972050189972,
0.043458301573991776,
0.03074808418750763,
0.01941102370619774,
0.04114852473139763,
0.009406639263033867,
-0.05430128425359726,
0.049962230026721954,
-0.017154758796095848,
0.015458641573786736,
-0.005641906522214413,
-0.019741399213671684,
-0.03605156019330025,
-0.041395895183086395,
-0.024789394810795784,
0.03388276696205139,
0.00022399716544896364,
-0.01874973438680172,
-0.0639050081372261,
-0.01488629262894392,
-0.007587752304971218,
0.01915799081325531,
0.06165362522006035,
0.02513030357658863,
0.010413768701255322,
-0.0008677438599988818,
-0.020568108186125755,
0.034616634249687195,
0.02148212492465973,
-0.03147195652127266,
-0.056662000715732574,
-0.022033244371414185,
0.02104228362441063,
-0.05153873562812805,
-0.040681105107069016,
-0.03368932008743286,
0.035494331270456314,
-0.05655400827527046,
-0.0198071226477623,
-0.005809264723211527,
0.01275001559406519,
0.02697579935193062,
-0.05755660682916641,
-0.02843078225851059,
-0.01751643791794777,
0.0323633998632431,
0.009090585634112358,
0.06044767424464226,
-0.011916271410882473,
0.028121478855609894,
-0.05007125437259674,
-0.029694166034460068,
-0.021818408742547035,
-0.017903827130794525,
0.01778293028473854,
-0.052230045199394226,
-0.016437187790870667,
-0.029552960768342018,
0.007270898669958115,
-0.0636492371559143,
0.06623340398073196,
0.006387821398675442,
0.027265312150120735,
0.01947888545691967,
0.013650476932525635,
-0.013511624187231064,
0.02609975077211857,
-0.006299400702118874,
0.025884848088026047,
0.0020219534635543823,
0.023557692766189575,
-0.00644020177423954,
0.02402443066239357,
0.058161936700344086,
-0.0013514049351215363,
-0.018482141196727753,
0.019438501447439194,
0.014464541338384151,
0.022839615121483803,
0.0019982727244496346,
-0.0480814054608345,
-0.059293899685144424,
-0.003690545680001378,
0.007065785117447376,
-0.03723097965121269,
0.017996789887547493,
0.04537511244416237,
-0.011329288594424725,
-0.07010763883590698,
0.11560898274183273,
0.04756806418299675,
0.011372312903404236,
0.0008856728672981262,
-0.007853737100958824,
0.041201382875442505,
0.027109315618872643,
-0.06235220283269882,
-0.01541429664939642,
0.006652127485722303,
0.005703519564121962,
-0.035501353442668915,
0.04272717237472534,
0.04062444716691971,
0.045401521027088165,
-0.004460437223315239,
0.025073310360312462,
0.0756763145327568,
0.0291032325476408,
-0.03547237440943718,
0.0854981318116188,
-0.03738030046224594,
-0.025304146111011505,
-0.05497260019183159,
-0.03534414619207382,
0.005294156260788441,
0.011264997534453869,
-0.041861988604068756,
0.007260328158736229,
-0.021232139319181442,
-0.006629047449678183,
-0.017504872754216194,
0.007877523079514503,
0.038500308990478516,
0.004514801315963268,
-0.06782633066177368,
0.028789842501282692,
0.07301949709653854,
0.0060026212595403194,
0.04555520415306091,
0.016545267775654793,
-0.08125194907188416,
0.005015579517930746,
-0.03180072456598282,
-0.026663213968276978,
-0.011670528911054134,
0.006795521359890699,
0.041097242385149,
-0.052288416773080826,
-0.07020824402570724,
-0.057466693222522736,
-0.025805825367569923,
0.011215884238481522,
-0.024122146889567375,
0.011946693994104862,
-0.052291497588157654,
-0.022801216691732407,
-0.03701447322964668,
0.005592424888163805,
-0.030215060338377953,
0.06261114031076431,
-0.0353141687810421,
0.08525647968053818,
-0.0008815525216050446,
-0.04920676350593567,
-0.024080650880932808,
0.011719765141606331,
-0.017641445621848106,
-0.05100221559405327,
0.028898578137159348,
0.0036739036440849304,
-0.00877166073769331,
-0.03330526873469353,
0.014635134488344193,
0.02702019177377224,
-0.025826426222920418,
0.0022968638222664595,
0.0020805636886507273,
-0.00917693693190813,
0.009889134205877781,
0.04294193163514137,
0.014894790947437286,
0.012788662686944008,
0.006381154526025057,
-0.004444373305886984,
0.019394515082240105,
0.020109398290514946,
0.012323505245149136,
-0.05092211812734604,
-0.029368771240115166,
0.004384622909128666,
-0.07933346182107925,
0.040702708065509796,
0.00998078566044569,
-0.021360225975513458,
0.010998772457242012,
0.03369119390845299,
0.030458640307188034,
0.01006062887609005,
0.041459064930677414,
-0.029633203521370888,
-0.05434058606624603,
-0.016208911314606667,
0.019422942772507668,
0.05052954703569412,
-0.018569424748420715,
-0.04262373596429825,
-0.027398107573390007,
-0.041230905801057816,
-0.033837657421827316,
-0.01682216115295887,
0.07093758881092072,
0.008080336265265942,
0.014719267375767231,
-0.014844100922346115,
0.03576965630054474,
0.03620995208621025,
-0.011745376512408257,
0.02109902910888195,
0.009408954530954361,
0.02624516375362873,
-0.03953784331679344,
0.006357789039611816,
0.020734775811433792,
-0.050027213990688324,
0.031036289408802986,
-0.006499784532934427,
0.04135977104306221,
-0.052520573139190674,
-0.02610088139772415,
0.013032106682658195,
0.045340411365032196,
-0.029409091919660568,
-0.0023056010250002146,
-0.01800845004618168,
0.02286248281598091,
-0.03628283739089966,
0.06004302203655243,
-0.006801823154091835,
0.007509248331189156,
0.029388926923274994,
0.01566545106470585,
-0.061767470091581345,
0.08473104238510132,
-0.005387997720390558,
-0.008934782817959785,
0.042233776301145554,
-0.04489988088607788,
-0.02851363644003868,
0.0354284904897213,
-0.06299164146184921,
0.030335556715726852,
-0.02038838528096676,
-0.03767870366573334,
0.009426713921129704,
0.05935497209429741,
0.003930721897631884,
0.06379348039627075,
0.001959199784323573,
-0.07520513236522675,
0.00030514999525621533,
-0.012688101269304752,
0.05489077791571617,
-0.011402884498238564,
0.046753063797950745,
0.00625698221847415,
-0.025333398953080177,
-0.02286960743367672,
-0.04504447430372238,
-0.009216336533427238,
-0.002923529362305999,
0.01969979889690876,
-0.010791375301778316,
0.017476117238402367,
0.0440644770860672,
-0.020517727360129356,
-0.0025146619882434607,
-0.01901322416961193,
0.008468138054013252,
0.09959854930639267,
-0.0335102453827858,
-0.027971982955932617,
-0.0183876920491457,
-0.015577055513858795,
0.05205141380429268,
-0.02619171515107155,
0.03249087929725647,
-0.031318556517362595,
-0.01908160001039505,
-0.03531328961253166,
0.03197022154927254,
0.003219632664695382,
0.06083867326378822,
-0.0005133291124366224,
-0.01296806987375021,
0.021903550252318382,
-0.03368956595659256,
-0.016078900545835495,
-0.05239557474851608,
0.03337454795837402,
-0.04035639762878418,
0.0010282770963385701,
0.033857692033052444,
0.003942770883440971,
0.0031103019136935472,
0.03645438700914383,
-0.0381995365023613,
-0.011722488328814507,
0.04206696152687073,
0.0635979026556015,
0.01586175709962845,
0.007400680799037218,
0.015454339794814587,
-0.06650106608867645,
0.015187334269285202,
-0.0004528217250481248,
-0.03729328513145447,
0.05754019692540169,
-0.019955633208155632,
-0.13002343475818634,
-0.07911931723356247,
0.021139979362487793,
0.03863990679383278,
-0.040542569011449814,
0.007879411801695824,
0.0121916513890028,
-0.01802222616970539,
0.0201735757291317,
-0.022311074659228325,
-0.02353282831609249,
-0.05740516632795334,
-0.05214664340019226,
0.01956704445183277,
-0.030709419399499893,
-0.052793942391872406,
0.042638253420591354,
-0.03185761347413063,
0.04132935032248497,
-0.012508329004049301,
0.024030018597841263,
-0.015680106356739998,
-0.008914158679544926,
0.017580140382051468,
0.05516032129526138,
-0.05410606786608696,
-0.006701568141579628,
0.020235275849699974,
-0.07694534212350845,
-0.006120985373854637,
0.009564066305756569,
0.030166303738951683,
-0.019667455926537514,
0.031730059534311295,
-0.052381306886672974,
0.0003698742075357586,
-0.010904341004788876,
0.007002705242484808,
-0.0428500734269619,
0.0271598007529974,
-0.029028749093413353,
0.017120011150836945,
-0.014859937131404877,
-0.00323590449988842,
0.05479065701365471,
0.047094378620386124,
-0.013025173917412758,
0.04484234377741814,
0.04750511795282364,
-0.06290891766548157,
-0.025672905147075653,
0.02503511868417263,
0.0697256401181221,
0.0050392006523907185,
0.1065516546368599,
-0.026512447744607925,
0.010876189917325974,
0.013926315121352673,
0.002875223523005843,
-0.020274171605706215,
-0.014542536810040474,
0.059039827436208725,
-0.0312343779951334,
0.016522863879799843,
-0.034311503171920776,
0.048027727752923965,
0.007225239649415016,
0.028898756951093674,
-0.01733573153614998,
-0.02498052455484867,
-0.006254186388105154,
-0.03463101387023926,
-0.022023238241672516,
0.08650068938732147,
0.00746114132925868,
-0.009286681190133095,
-0.053418997675180435,
0.01316531840711832,
0.01621212810277939,
-0.010339470580220222,
0.06045442074537277,
-0.03787964582443237,
-0.05186077952384949,
-0.06772247701883316,
0.023599950596690178,
-0.016947511583566666,
0.026281053200364113,
0.016541553661227226,
-0.05327942967414856,
0.04517309367656708,
0.016301395371556282,
-0.049585770815610886,
-0.025194859132170677,
-0.0460008904337883,
0.0353495292365551,
0.04499654471874237,
0.01670900359749794,
-0.05560477823019028,
-0.027959279716014862,
0.0031028124503791332,
-0.00615721894428134,
0.005690110381692648,
0.006536043249070644,
-0.011624094098806381,
0.09817417711019516,
-0.0063214958645403385,
-0.00724652037024498,
0.029171917587518692,
-0.020762849599123,
0.04433530941605568,
0.08413747698068619,
-0.056794874370098114,
0.047143589705228806,
-0.016242755576968193,
-0.011111929081380367,
0.013592644594609737,
0.0005969501798972487,
0.00016404154303018004,
0.026878874748945236,
0.008325513452291489,
0.018541574478149414,
-0.05067266896367073,
-0.030030405148863792,
0.01735673099756241
] |
<p>I came across the notion of complex energy while studying instanton method to study the unstable state. Unstable states are those which have energy with an imaginary part. But as we know Hamiltonian is a Hermitian operator. So how can the energy be imaginary?</p> | g1234 | [
0.00974122155457735,
0.023761188611388206,
0.018218835815787315,
-0.01125355064868927,
-0.005643636919558048,
-0.022207584232091904,
-0.02614125795662403,
0.066832035779953,
-0.03249401971697807,
0.008968929760158062,
-0.026569092646241188,
-0.02491196244955063,
0.034554097801446915,
-0.020424136891961098,
0.032329484820365906,
-0.009373812936246395,
0.0378827340900898,
0.05981417000293732,
0.036153074353933334,
0.016047846525907516,
-0.035927124321460724,
-0.00576511025428772,
0.039849016815423965,
-0.015307789668440819,
0.0012624618830159307,
-0.04087129980325699,
0.014645624905824661,
-0.042986515909433365,
-0.009306575171649456,
-0.03667253628373146,
0.05216702073812485,
-0.013298391364514828,
0.05218656733632088,
0.01048869825899601,
-0.03111310489475727,
0.012730027548968792,
0.061599038541316986,
0.04491344839334488,
0.09192139655351639,
-0.029579544439911842,
-0.024670112878084183,
-0.00390189909376204,
-0.012351502664387226,
-0.07043369859457016,
-0.05028565600514412,
0.01940179616212845,
-0.003415652783587575,
-0.02180502563714981,
-0.016992567107081413,
0.006414337083697319,
0.006934214383363724,
0.0038297001738101244,
0.09426594525575638,
0.02460922859609127,
0.035176731646060944,
-0.011093911714851856,
-0.023044535890221596,
-0.03246167674660683,
0.04991428926587105,
0.05859073996543884,
0.04135529324412346,
-0.04926152154803276,
0.007609557826071978,
0.05648711323738098,
0.04597974941134453,
-0.00977883581072092,
0.010289674624800682,
-0.012312401086091995,
-0.00016879869508557022,
0.0036034625954926014,
0.02068340592086315,
-0.08367232233285904,
0.04060542583465576,
-0.00688547920435667,
0.02492382936179638,
0.004802027717232704,
0.05431976541876793,
-0.06278549134731293,
0.01567414216697216,
0.030922163277864456,
0.006445865146815777,
-0.010158073157072067,
0.000338968908181414,
-0.060232874006032944,
0.06935736536979675,
-0.008829271420836449,
0.01940322108566761,
-0.02910381369292736,
-0.0012983226915821433,
-0.00980974081903696,
-0.026946090161800385,
0.07559139281511307,
0.03839842975139618,
-0.006592268124222755,
0.0018992149271070957,
-0.036269333213567734,
-0.052418943494558334,
0.06450261920690536,
-0.01953795738518238,
0.04695219174027443,
-0.03958559036254883,
-0.042368847876787186,
0.05306801199913025,
-0.02718367800116539,
0.013558254577219486,
-0.002264939248561859,
-0.045446883887052536,
-0.07599253207445145,
0.019052136689424515,
0.022109124809503555,
-0.024693692103028297,
0.01876450516283512,
-0.016372069716453552,
-0.02855520136654377,
0.058106936514377594,
0.010055274702608585,
-0.0017640903824940324,
-0.0684359073638916,
0.02219507284462452,
0.04922245815396309,
0.04995391517877579,
0.01357901282608509,
0.021923284977674484,
0.04471391439437866,
-0.01643020287156105,
0.022006500512361526,
0.030334392562508583,
-0.031877655535936356,
0.029244916513562202,
-0.05801347643136978,
0.0010933222947642207,
-0.030167419463396072,
0.009817581623792648,
-0.06262785196304321,
0.008907844312489033,
-0.01643943414092064,
-0.03494942560791969,
-0.02868950180709362,
-0.0005084438598714769,
0.025466909632086754,
0.027597567066550255,
-0.02067520283162594,
0.006229612044990063,
-0.04991442710161209,
0.006692045833915472,
0.009393641725182533,
-0.029704483225941658,
-0.029690520837903023,
-0.02892383188009262,
0.005013823509216309,
0.0362941138446331,
0.06348300725221634,
0.022030068561434746,
-0.057504747062921524,
0.037640370428562164,
0.0005452478653751314,
0.046350471675395966,
0.02359898015856743,
-0.030613495036959648,
0.011005566455423832,
-0.02295888029038906,
0.0018619380425661802,
0.02080482244491577,
0.008736463263630867,
0.026012327522039413,
0.03506322577595711,
0.01605357974767685,
-0.03223361819982529,
-0.014947792515158653,
-0.0008736563031561673,
0.05783889442682266,
-0.017977632582187653,
-0.008580151945352554,
0.03743534907698631,
0.03602670133113861,
0.05343865975737572,
-0.04741012305021286,
0.016079526394605637,
0.0204081479460001,
-0.019010215997695923,
-0.018524980172514915,
0.0013919086195528507,
0.020257851108908653,
-0.03455755114555359,
0.025290891528129578,
0.058385010808706284,
0.028999101370573044,
0.01387109886854887,
-0.005743993446230888,
0.0011562877334654331,
0.021096238866448402,
0.021396184340119362,
0.05165097862482071,
0.015018646605312824,
0.018938714638352394,
-0.01984478160738945,
0.04476405307650566,
-0.07385517656803131,
0.003414881881326437,
-0.046412885189056396,
0.035542525351047516,
0.010601986199617386,
-0.04242102429270744,
0.005509409587830305,
0.0029716873541474342,
0.03591596335172653,
0.019841482862830162,
0.0008053583442233503,
-0.057636361569166183,
-0.01787531189620495,
0.028505679219961166,
-0.0034189228899776936,
0.03814293071627617,
0.05071437358856201,
0.003920475486665964,
0.005566148553043604,
0.03644236922264099,
-0.03944314271211624,
-0.01876792497932911,
0.029470259323716164,
-0.04823683574795723,
0.02002875879406929,
0.06125669181346893,
0.017833838239312172,
0.03191857039928436,
0.022725336253643036,
-0.08995969593524933,
-0.002602766966447234,
-0.04795341566205025,
-0.013442154042422771,
-0.055408719927072525,
0.03068104386329651,
0.056984223425388336,
0.035597678273916245,
0.03282198682427406,
0.03481651842594147,
-0.028505410999059677,
0.033071063458919525,
0.00467647984623909,
0.0019654203206300735,
-0.019628189504146576,
-0.025454560294747353,
0.037285808473825455,
-0.040070582181215286,
0.014850395731627941,
-0.0039175041019916534,
0.08368761837482452,
0.006669371388852596,
-0.0368194542825222,
-0.021449189633131027,
0.020686769858002663,
0.028920140117406845,
-0.02368742972612381,
0.0022831859532743692,
-0.03699913248419762,
0.0023498577065765858,
0.03172019124031067,
0.03115527331829071,
-0.00018372370686847717,
-0.002864886075258255,
0.029079098254442215,
-0.009603415615856647,
0.026744546368718147,
0.05499252304434776,
-0.000010928421943390276,
-0.02081926167011261,
0.010576455853879452,
-0.03552934527397156,
-0.08759245276451111,
0.009784260764718056,
-0.03668225184082985,
0.07304425537586212,
-0.001137563376687467,
0.001076267333701253,
-0.0011304692598059773,
-0.008337493054568768,
-0.0345386378467083,
-0.04811632260680199,
0.07249286025762558,
-0.0949716791510582,
-0.05889809876680374,
0.04518566280603409,
-0.045576244592666626,
0.05350086838006973,
-0.0262837465852499,
-0.08638063818216324,
0.046872448176145554,
0.08670295029878616,
0.018125589936971664,
-0.06330066919326782,
-0.03836950287222862,
0.0033331536687910557,
-0.044497665017843246,
-0.038827184587717056,
-0.08917366713285446,
0.01664154790341854,
0.014442935585975647,
-0.01112364511936903,
0.009408711455762386,
0.0828409418463707,
0.04697147384285927,
0.016723860055208206,
-0.025730106979608536,
0.01805145852267742,
0.025582965463399887,
-0.01598929427564144,
-0.04278299957513809,
-0.009532909840345383,
-0.025916261598467827,
-0.007259360048919916,
-0.04964897409081459,
-0.02941226027905941,
0.0019220904214307666,
0.0429660826921463,
-0.004556417930871248,
0.06126873940229416,
-0.06303292512893677,
0.004678432364016771,
0.04570728912949562,
-0.05899824947118759,
-0.03769528120756149,
0.04874303191900253,
-0.02830336056649685,
0.02280346490442753,
-0.01511416770517826,
-0.0035549593158066273,
-0.09237157553434372,
-0.04238829389214516,
-0.06197064742445946,
-0.020262494683265686,
0.0011053512571379542,
-0.027563517913222313,
-0.027191249653697014,
0.014040227048099041,
-0.0178708266466856,
-0.046127695590257645,
-0.014891584403812885,
0.0241958387196064,
0.01368665974587202,
0.0063330125994980335,
0.04357779026031494,
0.0017802651273086667,
-0.017213817685842514,
-0.058098454028367996,
-0.0072424644604325294,
0.028137212619185448,
-0.026453234255313873,
-0.06518884748220444,
-0.024245107546448708,
-0.05170091986656189,
-0.008496561087667942,
0.005108408164232969,
0.015394316986203194,
-0.061327554285526276,
-0.014773796312510967,
0.020960571244359016,
0.018882526084780693,
0.03359226882457733,
-0.001862421166151762,
-0.02319934591650963,
-0.014405649155378342,
-0.033455923199653625,
0.016453949734568596,
-0.025035440921783447,
-0.012067845091223717,
-0.01336002442985773,
0.007507753558456898,
0.0013924557715654373,
0.026855913922190666,
-0.011658326722681522,
0.006605370435863733,
-0.014482781291007996,
0.03237270936369896,
-0.027552321553230286,
0.031383853405714035,
-0.01569291017949581,
-0.03548588976264,
0.007463167887181044,
-0.024459050968289375,
-0.004339814186096191,
0.02014022320508957,
-0.07622568309307098,
0.05424520745873451,
0.05743195116519928,
0.04286931827664375,
0.042124193161726,
-0.017077812924981117,
0.016154184937477112,
0.04233245179057121,
0.014198441989719868,
0.03226965665817261,
-0.10341599583625793,
0.003304916201159358,
0.001576617476530373,
0.026311218738555908,
0.004775606095790863,
0.029353616759181023,
-0.01381677109748125,
-0.017403950914740562,
0.03876243531703949,
0.0011337029282003641,
-0.009639212861657143,
0.016019055619835854,
0.012356596998870373,
0.02300751581788063,
0.01838294230401516,
0.0668635368347168,
-0.016602588817477226,
0.004395029507577419,
-0.07536263763904572,
0.03256210312247276,
-0.026870734989643097,
0.05826056748628616,
-0.05469440296292305,
-0.05275534465909004,
-0.03611190244555473,
0.030642639845609665,
-0.03813397139310837,
-0.028054771944880486,
-0.009667796082794666,
0.024734405800700188,
0.008956821635365486,
-0.0030448883771896362,
0.005282457917928696,
-0.03658945485949516,
0.031120862811803818,
0.050256047397851944,
-0.06063830852508545,
-0.08766891807317734,
-0.00961209274828434,
0.0021618404425680637,
-0.02845877967774868,
0.0010783551260828972,
-0.014375357888638973,
-0.0817306637763977,
-0.03477974608540535,
-0.03763804957270622,
-0.055539216846227646,
0.027556655928492546,
0.03121880628168583,
0.08430741727352142,
0.05655481293797493,
0.030512582510709763,
0.0323152132332325,
0.005893494933843613,
0.023412222042679787,
-0.04084465652704239,
-0.02906259335577488,
-0.027172911912202835,
-0.03384657949209213,
-0.019776325672864914,
0.02787327952682972,
0.004863942041993141,
-0.038934558629989624,
-0.009756948798894882,
-0.04498955234885216,
-0.02496870793402195,
0.0015896648401394486,
-0.03525085747241974,
0.019597593694925308,
0.006675491575151682,
-0.06600973755121231,
-0.0350445881485939,
0.02371891215443611,
0.028049487620592117,
-0.025688014924526215,
-0.06569445133209229,
0.011554555967450142,
-0.06673221290111542,
0.015029343776404858,
0.05524389445781708,
-0.0077952006831765175,
0.015331481583416462,
-0.01273125596344471,
0.05027259141206741,
-0.05824406445026398,
-0.02635296806693077,
-0.07620427012443542,
0.01704062707722187,
-0.03495273366570473,
-0.005507925525307655,
0.013709650374948978,
0.01755370758473873,
0.07949090003967285,
-0.03479819372296333,
0.02042902633547783,
0.024055086076259613,
0.03608489781618118,
0.023306163027882576,
0.011491728015244007,
0.00907029490917921,
0.006640514824539423,
-0.010400008410215378,
0.0009056095732375979,
0.024100471287965775,
-0.009754554368555546,
-0.038011062890291214,
-0.014878008514642715,
0.011530430987477303,
0.0019351086812093854,
-0.015676399692893028,
-0.007577113341540098,
-0.07420317828655243,
0.05538829788565636,
-0.007842474617064,
0.022223465144634247,
0.06213941425085068,
-0.05901891365647316,
-0.024094972759485245,
0.031078245490789413,
0.001764702145010233,
-0.009897561743855476,
-0.039968933910131454,
0.012626593001186848,
0.05143054574728012,
-0.002885952591896057,
-0.03540363535284996,
-0.014477724209427834,
-0.013413511216640472,
0.001952458987943828,
0.05031637102365494,
0.030337516218423843,
-0.019735734909772873,
-0.05407525226473808,
-0.0026048633735626936,
0.04216878488659859,
-0.037975866347551346,
-0.07819680124521255,
-0.013954839669167995,
0.041860781610012054,
-0.005742938257753849,
0.032293371856212616,
-0.041866958141326904,
-0.012811368331313133,
-0.06844215095043182,
0.013277750462293625,
-0.026934253051877022,
0.008921942673623562,
0.02843514084815979,
0.03551728278398514,
0.03293963521718979,
-0.007557725999504328,
-0.03355366364121437,
0.0716789960861206,
0.027854952961206436,
0.004694297444075346,
-0.009119468741118908,
0.015005718916654587,
0.04005192592740059,
-0.03373507782816887,
0.003853385103866458,
-0.019955160096287727,
-0.040102723985910416,
-0.025066616013646126,
0.05476289987564087,
0.030081797391176224,
-0.004610434640198946,
-0.03514725714921951,
-0.0366656668484211,
0.02677350491285324,
-0.02595704421401024,
-0.0033916388638317585,
-0.023308085277676582,
0.006243627984076738,
0.07830535620450974,
-0.03365251421928406,
-0.04362493380904198,
0.0178837887942791,
-0.023440895602107048,
0.013269499875605106,
0.007209710776805878,
0.0289817713201046,
0.02380412630736828,
0.01587170548737049,
0.017903871834278107,
-0.020192783325910568,
0.029719153419137,
-0.03228040039539337,
-0.07280087471008301,
-0.02761482447385788,
-0.028620831668376923,
0.015978800132870674,
0.07930810004472733,
-0.000898680358659476,
-0.006307113915681839,
-0.009220333769917488,
0.008471953682601452,
-0.02078375034034252,
0.07378611713647842,
0.04506849870085716,
-0.059568747878074646,
0.03996072709560394,
-0.05897432193160057,
-0.03412269055843353,
-0.03466181457042694,
0.06518425792455673,
0.041704196482896805,
0.005329237785190344,
-0.013449043035507202,
-0.003786846762523055,
0.005582637619227171,
-0.010259566828608513,
-0.057415496557950974,
0.00019244039140176028,
-0.005788816604763269,
0.05754487216472626,
-0.009061947464942932,
0.014522646553814411,
-0.06311732530593872,
0.0226972084492445,
0.0005415129708126187,
-0.019231991842389107,
0.019314734265208244,
-0.0045074173249304295,
0.01681542582809925,
-0.017459668219089508,
0.008351804688572884,
0.07552773505449295,
0.01822231337428093,
0.0044155907817184925,
0.03539424017071724,
-0.03913967311382294,
0.09153084456920624,
-0.0038271830417215824,
0.03995330631732941,
0.013654139824211597,
-0.017821460962295532,
0.08509142696857452,
0.02722000889480114,
-0.02259393408894539,
0.03419679030776024,
0.06617695093154907,
-0.006790915969759226,
0.06466520577669144,
0.047092780470848083,
0.028713254258036613,
-0.08572307229042053,
-0.039564963430166245,
0.030050529167056084,
0.03824997320771217,
-0.021023256704211235,
0.03201328590512276,
0.0655745342373848,
-0.0035050574224442244,
-0.08485355228185654,
0.020733868703246117,
-0.048073917627334595,
-0.01942392997443676,
0.024170346558094025,
0.02762848325073719,
0.06417415291070938,
-0.042417533695697784,
-0.021965671330690384,
-0.028568370267748833,
-0.013804414309561253,
-0.028940901160240173,
0.004157808609306812,
-0.030032606795430183,
-0.00469720596447587,
-0.0883350670337677,
-0.016021858900785446,
0.023528650403022766,
0.022547615692019463,
0.024041686207056046,
0.01931079290807247,
0.08771739900112152,
-0.01963449828326702,
-0.03811381384730339,
-0.009121988900005817,
-0.022949758917093277,
0.020573778077960014,
-0.017076442018151283,
-0.07767055928707123,
-0.04223693534731865,
-0.04030728340148926,
-0.04490821436047554,
0.03801063075661659,
0.026737581938505173,
0.005857591051608324,
0.028262851759791374,
0.008635997772216797,
0.0551014244556427,
0.03883231803774834,
-0.014176599681377411,
-0.006970921065658331,
0.03672942519187927,
-0.028175832703709602,
0.05067487806081772,
-0.0039905402809381485,
0.03571796044707298,
0.018717238679528236,
0.03179740905761719,
-0.013709918595850468,
0.019727934151887894,
-0.020865608006715775,
0.0010068770498037338,
0.025158723816275597,
0.011254392564296722,
0.04726333171129227,
-0.0025286776944994926,
0.00083878543227911,
-0.048329923301935196,
0.047606613487005234,
0.005106757394969463,
-0.021797386929392815,
0.009122808463871479,
0.022400319576263428,
-0.04518899694085121,
-0.05089450255036354,
0.07730820775032043,
0.012256214395165443,
0.012168901041150093,
0.02991197630763054,
0.01919584907591343,
-0.005773322656750679,
0.024576377123594284,
0.0055945501662790775,
0.04585817828774452,
-0.020880600437521935,
-0.026774108409881592,
-0.02324032224714756,
-0.030367745086550713,
-0.03570855036377907,
0.02468835934996605,
0.03280826658010483,
-0.04764297977089882,
-0.007303261198103428,
-0.003956666681915522,
-0.020165665075182915,
0.011034720577299595,
-0.031477976590394974,
0.05018646642565727,
-0.001659932779148221,
0.027808446437120438,
-0.03362440690398216,
0.01093568466603756,
-0.031642697751522064,
-0.04846002161502838,
0.03786969184875488,
0.008249705657362938,
0.040718600153923035,
-0.06620161235332489,
0.005042582284659147,
-0.045365817844867706,
0.02334626205265522,
-0.034332361072301865,
-0.05113277956843376,
0.011074017733335495,
0.027666086331009865,
-0.01931706815958023,
-0.052482686936855316,
0.06381993740797043,
-0.057149872183799744,
0.014929051510989666,
0.04577869921922684,
-0.027543606236577034,
-0.043355025351047516,
-0.023825138807296753,
0.017446985468268394,
0.041207510977983475,
0.002530843485146761,
0.021098626777529716,
-0.04055620729923248,
-0.04420877993106842,
-0.05576961860060692,
-0.05098387971520424,
-0.003721049753949046,
0.004216092638671398
] |
<p>Where do the terms <a href="http://en.wikipedia.org/wiki/Microcanonical_ensemble" rel="nofollow">microcanonical</a>, <a href="http://en.wikipedia.org/wiki/Canonical_ensemble" rel="nofollow">canonical</a> and <a href="http://en.wikipedia.org/wiki/Grand_canonical_ensemble" rel="nofollow">grand canonical</a> (ensemble) come from?</p>
<p>When were they coined and by whom? Is there any reason for the names or are they historical accidents?</p> | g1235 | [
-0.0055500357411801815,
-0.004557117819786072,
-0.01353833544999361,
-0.06592594087123871,
0.02365436777472496,
-0.00883683655411005,
0.0547543503344059,
0.03695296123623848,
-0.06611620634794235,
-0.002551574492827058,
-0.029255496338009834,
0.0516359843313694,
0.05171554535627365,
0.054573167115449905,
0.006026510149240494,
-0.01689881645143032,
-0.028832970187067986,
0.1007528007030487,
0.0251908078789711,
0.04488300532102585,
-0.05419674888253212,
-0.03065747395157814,
0.0031184214167296886,
-0.025427188724279404,
0.04257655516266823,
-0.05916859209537506,
0.006553573999553919,
-0.03093872219324112,
0.006290464196354151,
-0.05369909852743149,
-0.029237104579806328,
0.018269013613462448,
0.062104612588882446,
0.053267743438482285,
0.04333912581205368,
0.03508991003036499,
-0.0040859654545784,
0.003907645586878061,
0.03522739186882973,
0.006697259843349457,
0.036668892949819565,
0.031363245099782944,
-0.040084611624479294,
0.009712452068924904,
0.008557761088013649,
0.030928265303373337,
-0.0407278873026371,
-0.05592169612646103,
-0.0038845399394631386,
-0.0532328225672245,
0.08573421835899353,
0.0384870208799839,
-0.00593572435900569,
0.03965001180768013,
0.014317749068140984,
0.01664000190794468,
0.04082825407385826,
-0.03848319873213768,
0.008786644786596298,
0.028419101610779762,
0.005175081081688404,
-0.0055265603587031364,
0.015382139012217522,
0.044655535370111465,
0.04869445040822029,
-0.0038199464324861765,
0.02880875952541828,
0.03618675470352173,
0.05747130140662193,
0.004700837191194296,
-0.005402243696153164,
-0.08771885931491852,
0.008996231481432915,
0.06680666655302048,
0.002074230695143342,
-0.009522632695734501,
-0.0065598622895777225,
0.021701227873563766,
0.04057883098721504,
-0.008191782049834728,
0.006905040238052607,
-0.022191209718585014,
0.04579716548323631,
0.032525960355997086,
0.037549376487731934,
0.014952448196709156,
-0.02723502926528454,
-0.041029561311006546,
-0.022896304726600647,
0.04233615845441818,
0.004445248283445835,
-0.05693896859884262,
0.04167845472693443,
-0.014195164665579796,
0.000025053133867913857,
-0.016144027933478355,
-0.04409986734390259,
0.037417057901620865,
-0.03508862853050232,
0.018755018711090088,
0.024853728711605072,
-0.04473189264535904,
0.014710620976984501,
-0.009731817059218884,
-0.03000219725072384,
0.04509923607110977,
0.022097142413258553,
-0.026255302131175995,
-0.11891394108533859,
0.02559170126914978,
-0.033214446157217026,
0.06555242091417313,
-0.050063688308000565,
-0.02252097986638546,
-0.006593869999051094,
-0.0055661448277533054,
0.0038193820510059595,
-0.03821753337979317,
0.022699913010001183,
0.014598621986806393,
-0.027187207713723183,
-0.07725214213132858,
-0.009836291894316673,
0.014617722481489182,
-0.06468380242586136,
-0.0034238689113408327,
0.023139553144574165,
0.023526789620518684,
-0.0088557880371809,
-0.06806561350822449,
-0.0058086044155061245,
-0.012721030041575432,
-0.016346724703907967,
-0.028989795595407486,
0.040121302008628845,
0.025530554354190826,
-0.055808376520872116,
-0.03376733511686325,
0.004366573877632618,
0.02512115053832531,
-0.0319916270673275,
-0.03145046532154083,
0.05302000045776367,
-0.06650051474571228,
0.06114785745739937,
-0.08177345246076584,
-0.02154443971812725,
-0.031192682683467865,
0.027072889730334282,
0.0631306916475296,
-0.013091404922306538,
0.056104425340890884,
0.03936857357621193,
-0.014579747803509235,
-0.031121034175157547,
0.06974579393863678,
-0.02790132723748684,
0.011927666142582893,
-0.03646203130483627,
-0.03862018138170242,
-0.04075470566749573,
-0.002826702082529664,
-0.004948082845658064,
-0.00961847323924303,
-0.04971112310886383,
0.02029917947947979,
0.0366235114634037,
-0.032614514231681824,
-0.03661137446761131,
-0.0011541476706042886,
-0.0018643243238329887,
0.04851894825696945,
-0.015051509253680706,
0.04225477576255798,
0.03285901993513107,
0.05964590236544609,
0.06737601011991501,
-0.05095957964658737,
-0.0016378144500777125,
-0.039375290274620056,
-0.024668077006936073,
-0.0773448720574379,
0.0035942750982940197,
-0.01865755207836628,
-0.0240939948707819,
-0.02976742945611477,
-0.014765195548534393,
0.014288708567619324,
-0.03068174421787262,
-0.03186136484146118,
-0.012582956813275814,
0.005126423202455044,
0.048981692641973495,
-0.0507630929350853,
-0.022534087300300598,
-0.002089062239974737,
-0.08708217740058899,
-0.02059834450483322,
-0.04158136621117592,
-0.007221420761197805,
0.011688461527228355,
-0.010992462746798992,
0.004048941191285849,
0.0006843180162832141,
0.011309901252388954,
0.039421241730451584,
0.016036035493016243,
-0.0074074710719287395,
-0.003491355339065194,
-0.025973545387387276,
0.0031041193287819624,
-0.028452789410948753,
-0.0052015520632267,
0.03792688250541687,
-0.05302352085709572,
-0.04445280134677887,
-0.021979060024023056,
-0.038770101964473724,
0.0249305609613657,
-0.028467996045947075,
-0.04288482666015625,
-0.008390654809772968,
0.023203641176223755,
0.03638371452689171,
0.06404104083776474,
0.018352173268795013,
0.03544020280241966,
-0.008530044928193092,
-0.010784628801047802,
-0.0013264225563034415,
-0.06497490406036377,
-0.04415537416934967,
-0.031160349026322365,
-0.053600676357746124,
-0.009732682257890701,
0.003999043721705675,
0.022467756643891335,
-0.0046751732006669044,
-0.02023639716207981,
0.036910660564899445,
0.03690856322646141,
-0.043224871158599854,
0.0003562777419574559,
-0.022819146513938904,
-0.013771846890449524,
-0.06257852166891098,
-0.04977808892726898,
-0.01081202644854784,
0.011836863122880459,
0.029770445078611374,
-0.040418386459350586,
0.015294015407562256,
-0.04584847763180733,
0.004510141909122467,
0.0037902859039604664,
-0.0013743924209848046,
-0.0026160837151110172,
0.004893716424703598,
-0.057525284588336945,
0.05197010561823845,
0.037575963884592056,
-0.014956166036427021,
-0.025875644758343697,
-0.023715240880846977,
0.0345616489648819,
-0.03453567624092102,
-0.032444726675748825,
0.019399933516979218,
-0.061701562255620956,
0.03774234652519226,
-0.03388804569840431,
0.010935173369944096,
0.025610242038965225,
-0.04336545988917351,
0.016308706253767014,
0.029350731521844864,
-0.009352317079901695,
0.002344076754525304,
-0.028198247775435448,
0.02372884750366211,
-0.02164635621011257,
0.05681315064430237,
-0.0020717221777886152,
-0.0193378496915102,
0.03747938945889473,
-0.0036142522003501654,
-0.024879349395632744,
-0.0008744606166146696,
-0.01882234215736389,
-0.033438920974731445,
-0.012959555722773075,
0.02189498022198677,
0.06259717047214508,
-0.0008580368012189865,
0.019016819074749947,
-0.038062699139118195,
-0.04005574434995651,
0.04542095959186554,
-0.027551209554076195,
0.0705542042851448,
0.024742159992456436,
-0.0041114650666713715,
0.06903206557035446,
0.026140674948692322,
0.01206646766513586,
0.03644080087542534,
0.02503982186317444,
-0.031047355383634567,
0.05604010075330734,
-0.023761460557579994,
-0.030542882159352303,
0.02692820318043232,
-0.027829306200146675,
0.016554519534111023,
0.019361166283488274,
0.027036892250180244,
-0.01551323477178812,
0.018620086833834648,
-0.0004062108346261084,
-0.08519387990236282,
-0.019370444118976593,
-0.03069138154387474,
-0.010453486815094948,
-0.02272089757025242,
0.012736636213958263,
0.01571725122630596,
-0.06322634965181351,
-0.059235189110040665,
0.05384325608611107,
-0.012633902952075005,
-0.013107458129525185,
-0.019464004784822464,
-0.012689781375229359,
0.009953872300684452,
-0.016284726560115814,
-0.041047725826501846,
-0.050588104873895645,
-0.04170333594083786,
-0.03445172309875488,
-0.005407094024121761,
-0.02252448908984661,
0.03923195227980614,
-0.035071175545454025,
-0.005996019579470158,
-0.02844923920929432,
0.05051208660006523,
0.04387920722365379,
0.0036247647367417812,
-0.03463980555534363,
-0.017871331423521042,
-0.04741619527339935,
0.00047209643526002765,
-0.008693755604326725,
0.01891031488776207,
-0.0520441047847271,
0.00006233511521713808,
-0.032229188829660416,
-0.04217257723212242,
0.028867267072200775,
0.035944290459156036,
-0.007534955628216267,
-0.0011145101161673665,
-0.022162945941090584,
0.024919304996728897,
0.0410439632833004,
0.04010475426912308,
-0.00437093386426568,
0.06659269332885742,
0.0065374006517231464,
-0.00004191491461824626,
-0.002250414341688156,
0.05089252442121506,
-0.05852153152227402,
0.007487823721021414,
-0.015458056703209877,
-0.013022947125136852,
-0.00013106681581120938,
0.09697724133729935,
-0.02889503911137581,
-0.028950707986950874,
0.013056746684014797,
-0.00011874425399582833,
0.04377514496445656,
0.010781621560454369,
0.02136983536183834,
-0.027062715962529182,
-0.030736804008483887,
-0.014331848360598087,
-0.033070728182792664,
-0.01917838305234909,
-0.008377382531762123,
0.061794254928827286,
-0.02298157848417759,
-0.05901439115405083,
-0.03950062394142151,
0.03688402846455574,
0.0015792235499247909,
0.004766060039401054,
0.019096622243523598,
0.021599551662802696,
0.059025753289461136,
-0.03672942891716957,
0.02163340337574482,
0.02697526291012764,
0.03681693971157074,
0.04835348203778267,
0.0050841281190514565,
-0.010878280736505985,
0.01332789659500122,
0.024884743615984917,
0.05054989829659462,
0.05975111573934555,
0.02217530831694603,
-0.023586351424455643,
0.013027968816459179,
-0.010310483165085316,
0.0613010972738266,
-0.012834404595196247,
-0.00003873617242788896,
0.04532644897699356,
-0.05259639769792557,
-0.004608691204339266,
0.03532863408327103,
-0.011678212322294712,
0.0389331690967083,
0.027465274557471275,
0.009957118891179562,
-0.004044193308800459,
-0.003633559448644519,
0.029590290039777756,
-0.00847627967596054,
0.015335043892264366,
0.006376694887876511,
0.016771022230386734,
0.030911393463611603,
-0.046773869544267654,
-0.06269810348749161,
-0.044955234974622726,
0.03192361071705818,
0.025610167533159256,
0.03802116587758064,
-0.015436019748449326,
-0.04759112745523453,
-0.02006656490266323,
-0.01248150784522295,
0.038812752813100815,
0.02309873327612877,
0.01596272923052311,
-0.08495091646909714,
-0.02985045313835144,
0.06324563920497894,
0.024610554799437523,
0.03412989526987076,
-0.010753181762993336,
0.07770600914955139,
0.017832865938544273,
-0.027921359986066818,
-0.07136110961437225,
0.014400428161025047,
0.018622275441884995,
-0.029385624453425407,
0.024919705465435982,
-0.05645972862839699,
0.037839122116565704,
0.06992529332637787,
-0.0019711742643266916,
-0.08552947640419006,
-0.026750808581709862,
-0.08608818799257278,
0.024023041129112244,
0.007628952618688345,
0.022771604359149933,
-0.047868866473436356,
0.01607966423034668,
0.0019034508150070906,
-0.00976010411977768,
0.020244289189577103,
0.021838922053575516,
0.005391155369579792,
0.00952173862606287,
-0.026604454964399338,
-0.02949044294655323,
-0.09213507920503616,
-0.049473803490400314,
0.0684279277920723,
0.03585383668541908,
0.05293804034590721,
-0.019016051664948463,
0.026819946244359016,
-0.010239173658192158,
0.014663906767964363,
-0.07163818180561066,
0.03630141541361809,
-0.001261608093045652,
0.0223537664860487,
0.02058664709329605,
-0.030238348990678787,
0.027727235108613968,
0.057282060384750366,
-0.04726656526327133,
0.0004667633620556444,
0.0485701747238636,
0.013105717487633228,
0.03212442249059677,
0.046254757791757584,
0.08952376246452332,
0.07364165782928467,
-0.004602018278092146,
0.04418689385056496,
0.052203550934791565,
0.019411858171224594,
0.02322741597890854,
-0.006091926712542772,
0.014861381612718105,
0.03925059363245964,
0.02464963309466839,
0.04258542135357857,
-0.029500875622034073,
0.00463334284722805,
0.00017263430345337838,
-0.055918917059898376,
0.007630074396729469,
-0.02061920240521431,
0.050031960010528564,
-0.007415986619889736,
0.0015904342290014029,
0.0013644309947267175,
-0.018701421096920967,
0.055154263973236084,
0.04488154128193855,
-0.050389159470796585,
-0.012647788040339947,
0.03584039583802223,
0.019033603370189667,
-0.009331933222711086,
-0.0005871235043741763,
-0.06113489344716072,
0.013937743380665779,
0.032331787049770355,
0.003913620486855507,
-0.053118858486413956,
-0.06942944973707199,
-0.030879464000463486,
-0.03992660716176033,
0.004266928415745497,
0.024005673825740814,
0.0783287063241005,
0.07406437397003174,
0.052733078598976135,
0.0011446885764598846,
-0.007245139684528112,
-0.009301959536969662,
-0.015850240364670753,
-0.04046455770730972,
-0.026474367827177048,
0.04536137729883194,
-0.059044476598501205,
-0.008808406069874763,
-0.09109343588352203,
-0.016570622101426125,
-0.0025163909886032343,
0.022345589473843575,
-0.01693214476108551,
-0.10742126405239105,
-0.007859484292566776,
-0.01420400571078062,
-0.03911854699254036,
-0.005428462289273739,
0.0305164884775877,
0.04250656068325043,
0.04268718883395195,
-0.09393182396888733,
0.03474055975675583,
0.02343251369893551,
0.013742480427026749,
0.01583787612617016,
-0.03265325725078583,
-0.0006119264871813357,
-0.01997988298535347,
-0.04359009861946106,
0.019693834707140923,
-0.0488833412528038,
0.003878610208630562,
-0.04538629576563835,
-0.07954134792089462,
0.014613009057939053,
0.016787929460406303,
-0.021741122007369995,
-0.019217271357774734,
0.05364860221743584,
0.06127477064728737,
0.014728439040482044,
-0.06311918050050735,
0.039986636489629745,
-0.05787201598286629,
-0.02839396893978119,
-0.008926085196435452,
0.0830644965171814,
-0.031123870983719826,
-0.0005296115996316075,
-0.0017288171220570803,
-0.01020457036793232,
0.004027299117296934,
-0.028224295005202293,
0.09535717219114304,
0.002333587035536766,
-0.020014405250549316,
0.095409095287323,
0.011515798978507519,
0.041727859526872635,
-0.034270480275154114,
0.05875945836305618,
0.01496189832687378,
-0.04686302691698074,
-0.035626646131277084,
-0.029338499531149864,
-0.03706317022442818,
0.008400416001677513,
-0.021048713475465775,
0.03960919752717018,
0.0060286992229521275,
-0.04932648688554764,
-0.010010799393057823,
0.009256533347070217,
0.020045578479766846,
0.06042343005537987,
-0.051366209983825684,
0.0018210968701168895,
0.04575025290250778,
-0.0061193532310426235,
-0.03890278562903404,
0.0009979999158531427,
-0.008943643420934677,
-0.004333291668444872,
-0.03258994221687317,
0.0002747683320194483,
-0.06741014122962952,
-0.041361041367053986,
0.07734476029872894,
-0.03363148495554924,
-0.024795319885015488,
0.009437133558094501,
0.05731235072016716,
0.002472145715728402,
0.066150963306427,
-0.026503195986151695,
0.03957517072558403,
-0.00856738816946745,
0.0065719629637897015,
-0.0725673958659172,
-0.026117676869034767,
-0.0512128546833992,
0.04879680275917053,
0.051478590816259384,
-0.0389997698366642,
0.04092080146074295,
0.04062872380018234,
0.024536052718758583,
-0.020033657550811768,
-0.02827940136194229,
-0.03192180022597313,
0.02780214697122574,
0.027735430747270584,
0.03470148518681526,
0.0025173001922667027,
-0.011797559447586536,
0.028828106820583344,
-0.08107833564281464,
-0.0017505160067230463,
-0.003180345054715872,
0.03148068115115166,
0.021279944106936455,
0.02869022823870182,
-0.0374588705599308,
0.0188121497631073,
-0.009088058024644852,
0.010670296847820282,
0.03264087066054344,
0.04255545139312744,
0.01569373346865177,
-0.010013977065682411,
0.002085187239572406,
0.0028210438322275877,
-0.06523369252681732,
-0.028722528368234634,
-0.05276961997151375,
-0.031628210097551346,
0.008123068138957024,
-0.035678599029779434,
-0.039797380566596985,
0.02351163513958454,
-0.05176776275038719,
-0.012083279900252819,
0.024686988443136215,
0.0033792946487665176,
-0.004251621663570404,
0.003051348961889744,
0.01944694295525551,
-0.011923584155738354,
-0.019250500947237015,
0.017219871282577515,
-0.010431262664496899,
-0.021802732720971107,
-0.007052676752209663,
0.001517440308816731,
0.005550001282244921,
0.024437913671135902,
0.04774988070130348,
-0.016248032450675964,
-0.051148150116205215,
-0.05793669819831848,
0.018964402377605438,
-0.044312186539173126,
0.02045631594955921,
-0.0002937565732281655,
0.007144795265048742,
0.0000684373953845352,
-0.0353713259100914,
-0.005564722698181868,
0.024213142693042755,
-0.009023499675095081,
-0.028364064171910286,
0.04051023721694946,
-0.07227171957492828,
-0.03204628452658653,
0.01522117666900158,
0.045914050191640854,
-0.004514412023127079,
-0.03000928834080696,
0.022701088339090347,
-0.040238458663225174,
-0.009862354025244713,
0.021740566939115524,
0.05009355768561363,
-0.01929011195898056,
0.011765285395085812,
0.015861956402659416,
0.035715628415346146,
0.053923092782497406,
0.021519483998417854,
-0.030878538265824318,
0.04339434579014778,
0.004960506688803434,
0.027555065229535103,
0.03557691350579262,
0.008429192006587982,
0.014361279085278511,
-0.012007880955934525,
-0.011237110011279583,
-0.0291435606777668,
-0.025342794135212898,
0.01731121353805065,
0.05372988060116768,
0.016261836513876915,
0.03806249424815178,
0.03598973527550697,
0.06171606853604317,
0.08328306674957275,
0.049971919506788254,
0.028594955801963806,
-0.011458944529294968,
-0.020914586260914803,
0.01555639412254095,
-0.01602793112397194,
-0.04155892878770828,
-0.012943274341523647,
0.0029888253193348646,
-0.017038796097040176
] |
<p>Trying to understand <a href="https://en.wikipedia.org/wiki/Limits_to_computation" rel="nofollow">the physical limits to computation</a>, I notice that among these we have two types of limits that constrain the minimum allowable energy for a computation.</p>
<ul>
<li>Limits that constrain <strong>the product of energy and time taken</strong>, which include <a href="https://en.wikipedia.org/wiki/Bremermann%27s_limit" rel="nofollow">Bremermann's limit</a> and <a href="https://en.wikipedia.org/wiki/Margolus%E2%80%93Levitin_theorem" rel="nofollow">Margolus-Levitin</a>. These two laws pretty much state the same thing as far as I can tell, with the only difference being a constant which doesn't concern me since only order of magnitude matters for my own purposes.</li>
<li>Limits that constrain <strong>only energy</strong> required for computation, notably <a href="https://en.wikipedia.org/wiki/Landauer%27s_principle" rel="nofollow">Landauer's principle</a>.</li>
</ul>
<p>So let's just write these. I'll utilize the Bremermann's limit since it seems to be more commonly referenced.</p>
<p>$$ E \ge \frac{ 2 \pi \hbar }{ \Delta t } $$</p>
<p>$$ E \ge k T \ln{(2)} $$</p>
<p>If you believe what these two equations are telling you literally, then obviously there is a certain time range where the energy-time limit will be more restrictive and a range where the energy-alone limit will be more restrictive. With trivial algebra, we set the RHS equal to each other and find the time for computation where the crossover happens. I used the temperature of space here. For room temperature, it is much smaller/faster.</p>
<p>$$ \Delta t = \frac{ 2 \pi \hbar }{ k T \ln{(2)} } \approx 2 \times 10^{-13} s $$</p>
<p>If we're considering serial computations, this would leave us in the $\text{THz}$ range. It's not anywhere near Planck time or anything like that, but it also doesn't seem like much of a practical limitation.</p>
<p>Is the energy-time limitation only discussed for academic purposes, with the understanding that it will be swamped by the more restrictive limit? Or is there some deeper reason why it should matter?</p> | g1236 | [
0.023822935298085213,
0.10484454035758972,
0.02612697333097458,
0.040753889828920364,
-0.025568455457687378,
-0.017323313280940056,
0.01575656421482563,
-0.0022187153808772564,
-0.0927099660038948,
-0.00261859642341733,
0.04357754439115524,
0.053635936230421066,
-0.025130968540906906,
0.022792350500822067,
-0.020178761333227158,
-0.03671002760529518,
0.022969398647546768,
-0.04295981675386429,
0.022660009562969208,
0.03078334964811802,
-0.03838648647069931,
0.03290947526693344,
0.010581077076494694,
-0.02812640555202961,
-0.019152099266648293,
-0.013297517783939838,
0.018125347793102264,
-0.013950131833553314,
-0.038938600569963455,
-0.020571863278746605,
0.04385864734649658,
-0.002100293291732669,
0.05494464933872223,
-0.042848438024520874,
-0.029840627685189247,
-0.04594861716032028,
0.03536928445100784,
-0.04089312627911568,
0.0614599883556366,
0.0012354166246950626,
-0.008153699338436127,
-0.016199860721826553,
-0.007156794425100088,
-0.030145354568958282,
-0.047350432723760605,
0.011140041053295135,
-0.06757787615060806,
-0.044989701360464096,
0.021217530593276024,
-0.0359899140894413,
0.016239192336797714,
0.048456624150276184,
-0.019098903983831406,
-0.04250936210155487,
0.01448539923876524,
-0.056934330612421036,
-0.031863272190093994,
-0.004406411200761795,
0.03387057036161423,
-0.0036118756979703903,
0.07229536026716232,
0.008504277095198631,
-0.0229683518409729,
-0.024974651634693146,
0.028578588739037514,
-0.010113149881362915,
-0.02087431214749813,
-0.020922688767313957,
0.029838500544428825,
0.04088805243372917,
-0.0028535122983157635,
-0.056701961904764175,
-0.030625687912106514,
-0.09329263865947723,
0.05030876398086548,
-0.0163598470389843,
0.031400274485349655,
-0.008191370405256748,
0.04851299896836281,
0.010363752953708172,
-0.03273552656173706,
-0.03748468682169914,
-0.024368517100811005,
0.016176853328943253,
0.03527780994772911,
0.027721155434846878,
-0.028254520148038864,
-0.027170276269316673,
0.017658859491348267,
0.03214544802904129,
-0.059454869478940964,
-0.019470112398266792,
0.033225465565919876,
-0.029148684814572334,
0.007231643423438072,
0.005681315902620554,
0.04491805285215378,
0.04182283952832222,
-0.031200945377349854,
0.008784953504800797,
-0.011539891362190247,
0.007942534051835537,
0.037377532571554184,
-0.029063666239380836,
-0.04525592550635338,
-0.04890775308012962,
-0.004851476289331913,
-0.012514691799879074,
-0.005729335360229015,
-0.05377206951379776,
-0.02661481313407421,
0.0358722098171711,
-0.05743565410375595,
-0.06609029322862625,
-0.033885907381772995,
0.004344673361629248,
0.022571271285414696,
-0.01628020405769348,
0.014242402277886868,
0.045521944761276245,
-0.006867965217679739,
-0.05918819084763527,
0.02973788231611252,
0.037211716175079346,
-0.05010354518890381,
0.025057591497898102,
-0.04699632525444031,
-0.018220357596874237,
0.02548287622630596,
-0.04200339317321777,
0.0570608489215374,
-0.017921360209584236,
-0.04449070245027542,
0.04269516468048096,
-0.03218287229537964,
-0.005363060161471367,
-0.011566651985049248,
0.022863617166876793,
0.01494405884295702,
-0.014988379552960396,
0.007223134860396385,
-0.07494870573282242,
-0.05595182627439499,
-0.05513933673501015,
-0.04744752123951912,
0.04638153687119484,
-0.02506488375365734,
0.015407158993184566,
0.00598943792283535,
0.03138893097639084,
-0.014793450944125652,
0.05748673900961876,
0.0009809705661609769,
-0.019144926220178604,
0.03174817934632301,
0.017555855214595795,
0.025705421343445778,
-0.014852956868708134,
-0.0224996879696846,
0.04083910956978798,
0.03811414912343025,
0.03207595273852348,
0.0021113345865160227,
-0.006179437506943941,
-0.08663208037614822,
0.027534494176506996,
0.002006055787205696,
-0.015369352884590626,
0.04088309407234192,
-0.05068879574537277,
-0.07818271219730377,
-0.017566734924912453,
-0.031185826286673546,
0.02289416827261448,
-0.020512089133262634,
0.024469099938869476,
0.03543022274971008,
-0.006738622207194567,
0.007417791988700628,
0.015744883567094803,
-0.06160161644220352,
-0.017700720578432083,
-0.01344254519790411,
0.0186064001172781,
0.009008240886032581,
0.03329344838857651,
-0.008066870272159576,
0.05047563090920448,
-0.010218561626970768,
-0.011199354194104671,
-0.02117551490664482,
-0.004840362351387739,
0.039365414530038834,
0.03708120062947273,
-0.06309718638658524,
-0.009244212880730629,
0.00993107259273529,
-0.014137106016278267,
-0.03184337541460991,
-0.014851000159978867,
-0.004780416842550039,
0.0015302944229915738,
0.04071442782878876,
0.018348675221204758,
0.06847869604825974,
0.035011328756809235,
-0.04465702548623085,
0.028811339288949966,
0.026442432776093483,
0.0024210449773818254,
0.010157630778849125,
0.017727570608258247,
0.04695196449756622,
0.03226850554347038,
0.042111728340387344,
-0.030843375250697136,
-0.02411757782101631,
-0.001872232649475336,
0.016182195395231247,
0.04453132301568985,
0.022466696798801422,
-0.03611037880182266,
0.03935219720005989,
0.0006619393243454397,
-0.03639088571071625,
-0.014906950294971466,
-0.04386073723435402,
-0.04953355714678764,
0.006002605427056551,
0.018106691539287567,
-0.0436001680791378,
0.05498136952519417,
-0.011019503697752953,
-0.03407474607229233,
0.006352044176310301,
-0.02811511792242527,
0.0018285466358065605,
-0.004118516109883785,
0.039135776460170746,
0.036050911992788315,
0.014321809634566307,
-0.010693572461605072,
-0.02503666654229164,
0.04480944573879242,
-0.014017700217664242,
-0.07687404006719589,
0.007078817114233971,
-0.05872863158583641,
-0.013046788051724434,
-0.00022156369232106954,
0.00731028662994504,
-0.024661919102072716,
-0.05630418285727501,
0.05953819677233696,
-0.025990145280957222,
0.008940235711634159,
0.010152160190045834,
-0.013004844076931477,
-0.023974621668457985,
-0.008414724841713905,
0.057221394032239914,
0.0191141776740551,
0.028577925637364388,
0.0725889652967453,
-0.02769618295133114,
0.0023017923813313246,
-0.0759681910276413,
-0.000019754224922508,
0.019663935527205467,
-0.0004893328296020627,
0.028140023350715637,
0.13332051038742065,
0.03054780140519142,
0.07520349323749542,
0.012316199019551277,
-0.022546114400029182,
0.009006783366203308,
-0.030444610863924026,
0.04725314676761627,
0.005440023262053728,
-0.02796284295618534,
-0.07221019268035889,
-0.02652915194630623,
0.09977482259273529,
0.009912543930113316,
-0.041190117597579956,
-0.035238102078437805,
0.011892062611877918,
-0.0563303641974926,
0.0321507565677166,
0.02313598431646824,
0.06232030689716339,
-0.029706323519349098,
0.0015889760106801987,
-0.017010526731610298,
-0.009604579769074917,
-0.01248206477612257,
-0.0185034591704607,
-0.052652209997177124,
0.07380590587854385,
0.058704715222120285,
-0.015068682841956615,
-0.0032407736871391535,
0.08754011988639832,
-0.008595199324190617,
0.02938205935060978,
-0.07109569758176804,
-0.04668474197387695,
-0.06200999766588211,
-0.0032196631655097008,
0.05111096799373627,
-0.008727876469492912,
0.024915574118494987,
-0.0037521100603044033,
-0.0077243950217962265,
-0.007575967349112034,
-0.02910921908915043,
0.03366713970899582,
0.004274702165275812,
-0.023375824093818665,
-0.008528415113687515,
-0.019818328320980072,
-0.0048431456089019775,
-0.040748998522758484,
0.013196349143981934,
0.002272950951009989,
-0.03618159145116806,
0.004085148684680462,
-0.08893519639968872,
-0.010042225942015648,
-0.01474386639893055,
0.004947967827320099,
0.007923870347440243,
-0.03193039819598198,
-0.05601358413696289,
-0.019081778824329376,
0.025850264355540276,
0.001798407407477498,
0.04047888144850731,
-0.00338850193656981,
-0.046862129122018814,
0.0421220101416111,
-0.05254465714097023,
0.057049717754125595,
0.05762246251106262,
0.018672851845622063,
-0.060954175889492035,
0.02500852569937706,
-0.0006019524880684912,
-0.025809409096837044,
0.002774854889139533,
0.05081213265657425,
0.016170090064406395,
0.04633000120520592,
0.03681261092424393,
0.024934660643339157,
-0.03517903760075569,
0.07108520716428757,
-0.0012053392129018903,
-0.006154961884021759,
-0.01695031113922596,
0.026618922129273415,
-0.014291183091700077,
-0.06931503862142563,
-0.029037902131676674,
-0.018938472494482994,
0.007358234375715256,
0.038172099739313126,
0.026128645986318588,
-0.017972754314541817,
0.022230416536331177,
-0.006077588070183992,
0.06561922281980515,
0.024214409291744232,
0.054303936660289764,
-0.006745839957147837,
0.0583210214972496,
0.023331789299845695,
0.017395658418536186,
0.05943520739674568,
-0.016153141856193542,
-0.00602139625698328,
0.005633460823446512,
0.01687869243323803,
-0.004001663066446781,
-0.021577633917331696,
-0.03500492498278618,
-0.008902378380298615,
0.0057040853425860405,
-0.04732420668005943,
-0.037237346172332764,
-0.05894146114587784,
-0.03877457603812218,
-0.014384330250322819,
0.005781082436442375,
-0.0015197863103821874,
0.01933220401406288,
-0.003265266539528966,
0.01878621242940426,
0.06690751761198044,
0.02391587197780609,
0.03236842155456543,
-0.01781652495265007,
0.01767881028354168,
-0.007253674324601889,
-0.04034590721130371,
0.019299853593111038,
0.03288232162594795,
-0.001835675910115242,
-0.07910599559545517,
-0.012341853231191635,
-0.045023366808891296,
0.010550403967499733,
-0.004289414267987013,
-0.009453512728214264,
-0.0849691778421402,
-0.03599913790822029,
-0.033497489988803864,
0.015360930934548378,
0.03527313470840454,
0.0008110826602205634,
0.005467731039971113,
-0.014919915236532688,
-0.008020931854844093,
-0.01076040230691433,
0.039270687848329544,
-0.006905979942530394,
-0.030702287331223488,
-0.048659659922122955,
0.019270261749625206,
-0.00992265623062849,
0.044213809072971344,
0.00740561680868268,
0.0008681938052177429,
0.006676133722066879,
-0.004333147779107094,
0.006757841911166906,
0.04232964292168617,
-0.013857859186828136,
0.05106713995337486,
0.03797397017478943,
-0.03397776186466217,
0.02038196288049221,
0.04300010949373245,
0.011507858522236347,
0.02963242493569851,
-0.020326662808656693,
-0.08599001169204712,
0.004460562951862812,
-0.007015624083578587,
-0.011654726229608059,
0.03737578168511391,
0.03476063162088394,
-0.006395434029400349,
0.005827661603689194,
-0.021588673815131187,
-0.04138588905334473,
0.04849821329116821,
0.025591250509023666,
0.011004538275301456,
-0.03454847261309624,
-0.026877805590629578,
-0.048329710960388184,
-0.006946181412786245,
0.05463670194149017,
0.05020231381058693,
-0.0301497969776392,
-0.021197395399212837,
-0.04553362354636192,
-0.004021432716399431,
0.05721241235733032,
0.07155032455921173,
0.02343553677201271,
0.06650378555059433,
0.004541889298707247,
-0.0730627104640007,
0.037675146013498306,
-0.006147886626422405,
-0.02102322317659855,
-0.029759299010038376,
-0.0000981933408183977,
0.0031749759800732136,
0.021241003647446632,
0.0854991152882576,
0.0196590144187212,
0.04436317831277847,
-0.011717196553945541,
-0.0036553149111568928,
0.007121779024600983,
-0.01853429339826107,
0.014112110249698162,
0.015934329479932785,
0.023015910759568214,
0.04351885989308357,
-0.013966917060315609,
0.0751076340675354,
0.008130066096782684,
0.022128837183117867,
-0.012033826671540737,
0.026546945795416832,
0.03276831656694412,
0.021818585693836212,
0.00879600178450346,
-0.031638432294130325,
-0.04425198584794998,
0.013825739733874798,
0.03514502942562103,
-0.04352302476763725,
-0.005417216569185257,
0.007610969245433807,
-0.036892157047986984,
0.044835980981588364,
0.019574908539652824,
-0.0013327393680810928,
0.02384447492659092,
0.01741873472929001,
-0.003927863668650389,
0.005069647450000048,
-0.05109967663884163,
-0.0832144245505333,
0.03132666274905205,
-0.004872818011790514,
0.07597912847995758,
-0.004265641327947378,
-0.0028202258981764317,
-0.012810317799448967,
-0.005719778593629599,
-0.03955646604299545,
-0.014828379265964031,
0.08004426211118698,
0.016706500202417374,
0.03239203616976738,
-0.051663704216480255,
0.001782355597242713,
-0.030363213270902634,
-0.0026807067915797234,
-0.03231414034962654,
-0.013278723694384098,
-0.010440944693982601,
-0.00997424777597189,
0.0581950806081295,
-0.004436913412064314,
-0.00691731134429574,
0.05454611778259277,
0.0009704335243441164,
0.017306307330727577,
0.023307517170906067,
-0.015767771750688553,
-0.0142670888453722,
-0.10679548978805542,
-0.015787320211529732,
-0.0387299470603466,
0.015061810612678528,
-0.02721799723803997,
0.06951044499874115,
0.057348210364580154,
0.030287284404039383,
-0.002654413226991892,
-0.04505801945924759,
0.026568982750177383,
0.048637788742780685,
0.02960457280278206,
0.022070232778787613,
-0.005308075342327356,
0.02863740548491478,
-0.05485650897026062,
0.011214920319616795,
-0.027887718752026558,
-0.03888050839304924,
0.01927887462079525,
0.07560056447982788,
0.012198537588119507,
0.035890839993953705,
0.009655572474002838,
0.03100038692355156,
0.019428450614213943,
-0.05082528293132782,
-0.07140028476715088,
-0.02099231258034706,
-0.04425399750471115,
0.0014506207080557942,
-0.020065240561962128,
-0.04582619294524193,
-0.015954267233610153,
-0.009076672606170177,
0.016106275841593742,
-0.03262564539909363,
0.015242169611155987,
0.020773954689502716,
-0.0429048091173172,
-0.02089576981961727,
-0.0420110858976841,
0.040724050253629684,
-0.0056710923090577126,
0.004847204312682152,
-0.019331319257616997,
-0.028494443744421005,
-0.07186917215585709,
-0.08034861832857132,
0.04631952568888664,
0.028421243652701378,
0.005108095705509186,
0.03149029240012169,
0.03188978135585785,
-0.007871928624808788,
0.07430661469697952,
-0.05657293647527695,
0.008903125301003456,
0.007905768230557442,
0.035070180892944336,
-0.0823783352971077,
-0.01782824844121933,
0.06521979719400406,
0.031229685992002487,
-0.03110245242714882,
-0.015442807227373123,
-0.06505520641803741,
-0.023443026468157768,
-0.065672867000103,
-0.041432011872529984,
0.03421355038881302,
-0.00006075395504012704,
0.0005684170755557716,
-0.030265003442764282,
0.007972276769578457,
0.0517948754131794,
-0.045367248356342316,
0.049947600811719894,
0.02779529057443142,
0.0030804548878222704,
0.041769761592149734,
-0.01520371064543724,
-0.004951384849846363,
0.07651203125715256,
0.03571188822388649,
0.008011603727936745,
-0.08220735192298889,
-0.016329724341630936,
0.02024937979876995,
-0.00593279954046011,
0.029659684747457504,
0.011368079110980034,
0.023806218057870865,
0.02465454488992691,
-0.00039375023334287107,
0.00772363506257534,
0.012372770346701145,
0.014814991503953934,
-0.06504298001527786,
-0.0442059189081192,
0.018970081582665443,
-0.003245566040277481,
-0.08857373148202896,
-0.045135367661714554,
-0.03216076269745827,
-0.053465068340301514,
-0.01885547861456871,
-0.03901166468858719,
0.03684971109032631,
-0.03810940310359001,
-0.010530958883464336,
0.015543523244559765,
0.012123842723667622,
0.01875726878643036,
0.04156646504998207,
0.042746953666210175,
-0.021463649347424507,
-0.042895715683698654,
-0.005408382508903742,
-0.08426464349031448,
0.02786804549396038,
-0.026478517800569534,
-0.03327930346131325,
-0.014589093625545502,
0.045871637761592865,
-0.0008751688292250037,
-0.03221124783158302,
-0.0017286754446104169,
-0.0068245031870901585,
0.009320197626948357,
-0.005379778798669577,
-0.005257222801446915,
-0.05445956438779831,
-0.029029015451669693,
0.02901112101972103,
-0.014474851079285145,
-0.05785148963332176,
0.055422019213438034,
0.042291611433029175,
0.0018978273728862405,
0.02246738411486149,
0.0174819678068161,
0.09828394651412964,
0.0025612255558371544,
-0.013601521030068398,
-0.01679452322423458,
0.029806392267346382,
0.0464487224817276,
0.08362520486116409,
0.034027405083179474,
-0.03878635913133621,
-0.01479633804410696,
0.00023218904971145093,
0.027204351499676704,
-0.004784009885042906,
0.03230571746826172,
-0.0017176225082948804,
-0.026440542191267014,
-0.047734007239341736,
-0.024291105568408966,
0.020062433555722237,
0.05743265524506569,
-0.04529241845011711,
0.02387499064207077,
0.07751615345478058,
-0.019574003294110298,
-0.005172824487090111,
-0.03377564996480942,
-0.037025995552539825,
0.012025278992950916,
0.06810039281845093,
-0.011897207237780094,
-0.03367946296930313,
-0.0372919887304306,
-0.028437113389372826,
0.014014942571520805,
-0.011575587093830109,
-0.01999630779027939,
0.004835324827581644,
-0.03499149531126022,
-0.014873577281832695,
-0.03497811779379845,
0.004268744960427284,
0.016134146600961685,
-0.09071577340364456,
0.03819653391838074,
-0.035088494420051575,
0.0620216503739357,
0.04064665362238884,
-0.019026683643460274,
0.0044305347837507725,
0.03523213416337967,
-0.07208876311779022,
0.03819437697529793,
0.0019599427469074726,
-0.008486881852149963,
-0.07277635484933853,
-0.013708696700632572,
0.08658690750598907,
0.02442944049835205,
-0.010890702717006207,
0.005018795374780893,
-0.002253891434520483,
0.04205349087715149,
0.03505222871899605,
-0.010790604166686535,
0.025146668776869774,
0.058276161551475525,
0.012594805099070072,
0.07059259712696075,
0.0031879162415862083,
-0.0062387012876570225,
0.03593942150473595,
0.04587940126657486,
0.006340758875012398,
-0.005731028970330954,
0.026759512722492218,
-0.033438149839639664
] |
<p>By reading <a href="http://www.sciencedirect.com/science/article/pii/0550321388904555" rel="nofollow">an article</a>, I found a partition function that, according to the author, describes an interacting with random variables as coupling constant.</p>
<p>$$Z =\int \mathrm{d} \lambda_i e^{i(K^{ij}\lambda_i\lambda_j + V^{ijk}\lambda_i\lambda_j\lambda_k)}\mathrm{exp}(e^{iS_{eff}(\lambda)})$$</p>
<p>This expression is totally unfamiliar to me. Could someone show me how to derive that, providing a reference (online course, textbook, etc.) if necessary?</p> | g1237 | [
0.045318860560655594,
-0.043645989149808884,
-0.014554760418832302,
-0.09735692292451859,
-0.006200728937983513,
-0.015486576594412327,
0.0270603708922863,
0.029409606009721756,
0.02521839737892151,
0.013832761906087399,
-0.0504179447889328,
0.04132235422730446,
-0.01944412849843502,
0.04750584810972214,
-0.014243174344301224,
-0.04842980578541756,
0.017523040995001793,
0.016862312331795692,
-0.03186687082052231,
-0.0252592284232378,
-0.0032336488366127014,
-0.023936957120895386,
-0.02317718043923378,
-0.017391828820109367,
0.0775371864438057,
-0.013323593884706497,
0.025116177275776863,
0.023468930274248123,
-0.030664609745144844,
-0.03660595044493675,
-0.01245204173028469,
0.02933346852660179,
0.02704973705112934,
0.00656545627862215,
-0.04528634622693062,
0.028124498203396797,
0.009479239583015442,
0.0038438921328634024,
0.0025464489590376616,
-0.03199366107583046,
-0.04298551008105278,
0.05144037306308746,
0.024972138926386833,
0.048568353056907654,
0.0022603501565754414,
0.03985903412103653,
-0.019439952448010445,
0.02766481786966324,
-0.026016822084784508,
0.041260767728090286,
-0.031480129808187485,
0.05745939165353775,
0.01299307681620121,
-0.029947826638817787,
0.02248276211321354,
-0.018227899447083473,
0.00999951921403408,
-0.010231487452983856,
-0.01404249481856823,
0.050858594477176666,
0.06416201591491699,
-0.00853248406201601,
-0.04333845153450966,
-0.02688080631196499,
0.11031965166330338,
0.04177572578191757,
0.030210884287953377,
0.0030889175832271576,
-0.023096635937690735,
0.0021540136076509953,
-0.025787945836782455,
0.03958822041749954,
0.020757107064127922,
-0.0476754792034626,
-0.04284585267305374,
0.02204037830233574,
0.09405414015054703,
0.009463968686759472,
-0.028359856456518173,
0.04342181608080864,
-0.02871556393802166,
0.05564044788479805,
0.049864597618579865,
0.023316416889429092,
0.03412912040948868,
0.012600085698068142,
-0.015731314197182655,
-0.03223799541592598,
-0.04407450556755066,
-0.02881738729774952,
0.04378683120012283,
0.03141017630696297,
-0.007898191921412945,
-0.019681401550769806,
0.009206129238009453,
-0.054636042565107346,
-0.05414806678891182,
0.010467558167874813,
-0.04163267835974693,
-0.014117108657956123,
0.03937935829162598,
-0.0031379167921841145,
0.057613175362348557,
0.016369875520467758,
-0.050902098417282104,
-0.023509712889790535,
0.023717869073152542,
0.0091349296271801,
0.012754264287650585,
0.009339459240436554,
-0.009384002536535263,
0.08627455681562424,
-0.024647288024425507,
-0.0546320378780365,
-0.011235526762902737,
0.01146100927144289,
0.02575143240392208,
-0.03902198001742363,
-0.02614912949502468,
0.00978660024702549,
0.0490390807390213,
0.04579688236117363,
-0.04472984001040459,
0.03382421284914017,
-0.026768546551465988,
-0.03807792440056801,
-0.007795228622853756,
-0.017752841114997864,
-0.012566424906253815,
-0.006470239255577326,
0.011019036173820496,
-0.004566367715597153,
0.03716680780053139,
0.03213813155889511,
-0.01182134635746479,
0.018113918602466583,
-0.014822130091488361,
-0.023377086967229843,
-0.048415761440992355,
0.07578746974468231,
0.045549530535936356,
-0.023198772221803665,
-0.02817774936556816,
-0.024572055786848068,
-0.08657720685005188,
0.029818527400493622,
0.029857594519853592,
-0.07176821678876877,
-0.03790942579507828,
-0.030877819284796715,
0.016664935275912285,
0.07316058874130249,
-0.06799671798944473,
-0.006423605605959892,
-0.044965703040361404,
0.01900286227464676,
0.029720444232225418,
-0.08133728802204132,
0.01695287600159645,
-0.01430430542677641,
0.05148816108703613,
0.022291621193289757,
0.007239785511046648,
-0.0027769107837229967,
-0.027008000761270523,
-0.010710494592785835,
0.028767049312591553,
-0.07415740191936493,
-0.04568788409233093,
0.013846326619386673,
-0.06304555386304855,
0.030652303248643875,
0.005985955707728863,
0.03637316823005676,
-0.033564262092113495,
0.04522930085659027,
-0.018699808046221733,
-0.014014446176588535,
-0.010066221468150616,
-0.04989323019981384,
0.055459488183259964,
-0.06476621329784393,
0.05181581526994705,
-0.07522163540124893,
-0.047398731112480164,
-0.05485386401414871,
-0.004369682166725397,
0.020725233480334282,
-0.0018957071006298065,
-0.03479570895433426,
-0.027004538103938103,
-0.02292981743812561,
-0.0016922281356528401,
-0.07735106348991394,
-0.02939220704138279,
-0.037292659282684326,
0.02517150714993477,
-0.07597026228904724,
-0.012278217822313309,
-0.033342767506837845,
-0.018256569281220436,
0.014510364271700382,
0.02394339255988598,
-0.00140885089058429,
0.036118511110544205,
-0.040035467594861984,
-0.04450851306319237,
-0.022574709728360176,
-0.030088191851973534,
0.04796035587787628,
0.003857148578390479,
-0.045414574444293976,
0.003172624623402953,
0.015499509871006012,
0.0565059632062912,
-0.008338098414242268,
0.04079745337367058,
-0.01453046128153801,
0.021168146282434464,
0.007468205876648426,
-0.00031072364072315395,
-0.03554403781890869,
0.04204515367746353,
0.07991556078195572,
0.0008832330931909382,
0.015378378331661224,
-0.021900463849306107,
0.05111255496740341,
-0.007176626473665237,
0.012062141671776772,
-0.0436197929084301,
0.0216516200453043,
0.019394414499402046,
0.05382658913731575,
0.02628129906952381,
0.03137801215052605,
0.0004679052799474448,
0.045318227261304855,
-0.04894407093524933,
0.020945755764842033,
-0.028273647651076317,
0.025647640228271484,
-0.035852257162332535,
0.052465908229351044,
-0.009606881998479366,
0.0403301864862442,
-0.005175824277102947,
-0.01092296838760376,
-0.04077596589922905,
-0.01866699755191803,
0.025208337232470512,
0.0032957664225250483,
0.035197895020246506,
-0.004151215776801109,
-0.009229235351085663,
-0.07400019466876984,
0.040009755641222,
0.022411027923226357,
-0.030750850215554237,
-0.03320346027612686,
0.02128179371356964,
-0.027113230898976326,
0.03267798200249672,
0.04950081557035446,
0.027117261663079262,
-0.07100733369588852,
0.02305392175912857,
0.013228063471615314,
0.003418904962018132,
-0.001963299000635743,
-0.017680563032627106,
0.03215356916189194,
-0.002689740154892206,
0.02966369315981865,
0.035980578511953354,
-0.07040026783943176,
-0.019129853695631027,
-0.01706291362643242,
0.031185148283839226,
-0.07447139918804169,
0.021384647116065025,
-0.010500992648303509,
0.0010044334921985865,
0.02659079246222973,
0.02854922227561474,
-0.03846229240298271,
0.0491039864718914,
0.011326112784445286,
0.02034362591803074,
-0.012930340133607388,
-0.03123088926076889,
0.004585513845086098,
-0.07281013578176498,
-0.030731279402971268,
-0.01315062865614891,
-0.016894323751330376,
0.04012422263622284,
-0.03073165751993656,
0.006171738263219595,
0.020271137356758118,
0.022231094539165497,
-0.0012939306907355785,
0.028605083003640175,
-0.0017518234672024846,
-0.09811292588710785,
-0.0034182597883045673,
-0.018589772284030914,
0.0041628647595644,
-0.036179330199956894,
0.004472339991480112,
-0.039849262684583664,
-0.013671333901584148,
0.0038211201317608356,
0.028741009533405304,
-0.052688829600811005,
0.0753122866153717,
0.050735943019390106,
-0.012010135687887669,
0.01662672869861126,
-0.04810477793216705,
-0.02343807741999626,
-0.0414702408015728,
0.09810151904821396,
-0.010820728726685047,
-0.010577451437711716,
-0.0005316887400113046,
-0.00797346793115139,
-0.03435099497437477,
-0.023172467947006226,
0.05301513150334358,
0.0045448788441717625,
0.02286812663078308,
0.03260692209005356,
-0.031593628227710724,
-0.006210618186742067,
0.007621901109814644,
-0.04559064283967018,
-0.00816420465707779,
-0.0005461398395709693,
-0.02233509160578251,
0.021270250901579857,
-0.01916147582232952,
-0.024579208344221115,
-0.02973836474120617,
-0.07072022557258606,
0.046135567128658295,
0.012978240847587585,
-0.007691790349781513,
0.07265634834766388,
-0.018816951662302017,
-0.024908490478992462,
0.04128927364945412,
0.0023939714301377535,
-0.04736856743693352,
-0.006076383870095015,
-0.01442102249711752,
0.01135930698364973,
-0.053605154156684875,
-0.04042999818921089,
0.03561258688569069,
0.036411624401807785,
-0.09814555943012238,
-0.005023820325732231,
0.0054608783684670925,
-0.009487779811024666,
-0.041296083480119705,
-0.00736998300999403,
0.08904050290584564,
-0.01563955284655094,
-0.028012292459607124,
0.027298230677843094,
0.013467568904161453,
0.02482013590633869,
0.031541626900434494,
0.033883992582559586,
-0.06369493156671524,
0.0322079062461853,
0.027890941128134727,
-0.027765067294239998,
0.015199724584817886,
0.010287300683557987,
0.04429788514971733,
0.008972342126071453,
0.11446800827980042,
0.07882386445999146,
0.008667388930916786,
0.012492367997765541,
0.04439524933695793,
0.0400417223572731,
-0.013963933102786541,
0.03564532473683357,
0.013707193545997143,
0.00471808947622776,
0.03026464767754078,
0.022251125425100327,
0.04482634738087654,
-0.08251334726810455,
0.022115973755717278,
-0.010876324027776718,
-0.02452191710472107,
-0.002532496815547347,
-0.04044191166758537,
-0.0009061492746695876,
-0.0635567158460617,
0.00030337809585034847,
-0.010844970121979713,
-0.018151110038161278,
-0.03143376484513283,
0.05115840956568718,
-0.023683084174990654,
-0.005137961823493242,
0.06328161805868149,
0.05282518267631531,
-0.035711679607629776,
0.008759272284805775,
0.010376593098044395,
0.061624735593795776,
-0.005160181783139706,
-0.0012178377946838737,
-0.0019380043959245086,
-0.05742723494768143,
-0.048160653561353683,
-0.028096003457903862,
0.018592702224850655,
0.017742639407515526,
0.040697772055864334,
-0.0012809832114726305,
0.04057694971561432,
0.013029089197516441,
-0.060193512588739395,
-0.04660502076148987,
0.034539517015218735,
-0.011810600757598877,
-0.0154004180803895,
-0.07414751499891281,
0.021128052845597267,
-0.006300598848611116,
0.01335881557315588,
-0.024917811155319214,
0.015206266194581985,
0.017991844564676285,
-0.014521123841404915,
-0.023755811154842377,
0.03969300538301468,
0.014987782575190067,
0.01557187084108591,
-0.029989995062351227,
-0.0337819941341877,
0.033486366271972656,
-0.04750726744532585,
0.03877862170338631,
0.021001970395445824,
-0.02932715229690075,
0.02058158814907074,
0.019890258088707924,
-0.022615963593125343,
0.01692880503833294,
0.016729308292269707,
0.027209198102355003,
0.010844551958143711,
-0.08349088579416275,
0.003329208120703697,
0.03677602857351303,
-0.007277729455381632,
0.01863144524395466,
0.006604204885661602,
-0.006910914089530706,
-0.01381680741906166,
0.04117945209145546,
0.0877685621380806,
0.0019430823158472776,
0.03586525470018387,
0.024793999269604683,
-0.007789975963532925,
0.018550021573901176,
-0.01931259036064148,
0.001933535560965538,
0.026977896690368652,
-0.0203873123973608,
-0.04145626723766327,
0.003028680570423603,
-0.018631573766469955,
-0.02678651735186577,
-0.0002835608902387321,
0.009590186178684235,
0.016744667664170265,
0.008315719664096832,
-0.013760725036263466,
-0.05058442801237106,
0.03233323618769646,
-0.009896298870444298,
-0.01411259826272726,
0.07199526578187943,
0.02387506701052189,
0.007776488084346056,
-0.04725509509444237,
0.012877128086984158,
-0.08861585706472397,
0.05296480283141136,
-0.0158314798027277,
-0.022858448326587677,
-0.03652626648545265,
-0.07500156760215759,
0.027189213782548904,
-0.05876576155424118,
0.03347599133849144,
0.00690173776820302,
-0.0046705761924386024,
-0.0029203793965280056,
0.07742176949977875,
0.047109510749578476,
0.001403571106493473,
0.07929042726755142,
-0.023264558985829353,
-0.027019258588552475,
0.004838886205106974,
-0.04380583018064499,
-0.008760782890021801,
-0.006129128392785788,
-0.02319733425974846,
0.02714313380420208,
-0.0008209702791646123,
-0.040515802800655365,
-0.02607589028775692,
-0.06081234663724899,
-0.022250695154070854,
0.008941230364143848,
0.054471250623464584,
-0.04395940899848938,
0.014672740362584591,
-0.008156323805451393,
0.010241121985018253,
-0.06007499247789383,
-0.032076120376586914,
0.035982172936201096,
-0.04635369032621384,
-0.02753935568034649,
0.012628820724785328,
-0.0064763352274894714,
0.01116508711129427,
0.007200746797025204,
-0.0075407554395496845,
-0.03475756198167801,
0.016958829015493393,
-0.05295204371213913,
0.031471092253923416,
-0.007501200772821903,
0.039197973906993866,
0.04389309883117676,
-0.02973324805498123,
0.03310908377170563,
0.02535342052578926,
-0.00035705618211068213,
0.08588287234306335,
0.06161058694124222,
-0.018302608281373978,
0.02979426644742489,
0.013268415816128254,
-0.01812823675572872,
-0.01740333065390587,
-0.03417085483670235,
0.04481875151395798,
0.023620445281267166,
0.04664824530482292,
-0.011592501774430275,
-0.07316245138645172,
0.029697271063923836,
-0.02377212420105934,
-0.010237742215394974,
0.06010478362441063,
-0.00955462921410799,
-0.013316630385816097,
0.02884972281754017,
0.05317303165793419,
0.013911126181483269,
-0.004132312256842852,
-0.003132514888420701,
0.027753055095672607,
-0.032574113458395004,
0.013167418539524078,
0.018424494192004204,
0.011826512403786182,
0.02254188247025013,
-0.03915282338857651,
-0.06732248514890671,
0.035385530441999435,
-0.016723686829209328,
-0.024888411164283752,
-0.039048030972480774,
0.035154666751623154,
-0.024940771982073784,
-0.0019012556876987219,
-0.01687169447541237,
-0.06545144319534302,
0.010036223568022251,
-0.029892006888985634,
0.02581636607646942,
0.036430276930332184,
0.012238703668117523,
-0.042131535708904266,
-0.03662298992276192,
0.008837250992655754,
0.021495480090379715,
-0.04363306984305382,
-0.003534735878929496,
0.04616141691803932,
-0.02305879071354866,
-0.013761098496615887,
0.02859644405543804,
-0.01092316210269928,
-0.023348689079284668,
0.0456521175801754,
0.03605327010154724,
0.07896117120981216,
0.034235578030347824,
-0.02571031078696251,
-0.013788712210953236,
0.043267861008644104,
-0.010656042955815792,
0.020313309505581856,
-0.008302420377731323,
0.02500285767018795,
0.0018358079250901937,
-0.03518060967326164,
0.031203938648104668,
0.02136876806616783,
-0.032709408551454544,
-0.04554877430200577,
-0.007821773178875446,
-0.06648662686347961,
-0.02635379135608673,
-0.012504324316978455,
0.018942762166261673,
0.009921806864440441,
-0.060694221407175064,
0.046367693692445755,
-0.07318637520074844,
0.03739466890692711,
0.06910993158817291,
0.05713966116309166,
-0.020001938566565514,
0.06450258940458298,
0.04577263817191124,
0.032949190586805344,
-0.04548927769064903,
0.006993661634624004,
0.06543907523155212,
0.047125570476055145,
-0.08126050978899002,
0.03331179544329643,
0.00048107796465046704,
0.009395093657076359,
-0.005035909824073315,
-0.005975269712507725,
0.0010880173649638891,
0.05083462595939636,
0.016099050641059875,
-0.03130469471216202,
0.015931658446788788,
0.004954775329679251,
-0.029726216569542885,
0.006256001070141792,
-0.038317807018756866,
-0.01871897093951702,
0.009131675586104393,
0.019467078149318695,
0.0182455163449049,
0.028485102578997612,
0.0212671160697937,
-0.049502208828926086,
-0.03234181925654411,
-0.08989870548248291,
-0.043792590498924255,
-0.002530018799006939,
-0.01183340698480606,
0.030281653627753258,
-0.01462519634515047,
0.033051081001758575,
0.013575151562690735,
-0.02779444120824337,
-0.018584217876195908,
-0.0015580430626869202,
-0.0320877842605114,
-0.01502250600606203,
-0.055532585829496384,
-0.01994798332452774,
0.0007461557979695499,
-0.017529208213090897,
0.03132703900337219,
0.07328249514102936,
-0.04141815006732941,
0.004766094032675028,
0.061348386108875275,
-0.03565869852900505,
-0.01252792403101921,
0.05253704637289047,
0.0031623891554772854,
0.0134331239387393,
0.030874397605657578,
0.10397813469171524,
0.016144396737217903,
-0.0356876440346241,
0.03302149102091789,
-0.0687679648399353,
0.03654341772198677,
0.0055080861784517765,
-0.04445391520857811,
-0.08391130715608597,
0.02739178203046322,
-0.02283550798892975,
-0.01364018302410841,
0.007732439786195755,
-0.03590478003025055,
-0.011049746535718441,
-0.010650710202753544,
0.017741095274686813,
-0.013638896867632866,
0.036111019551754,
0.01329139806330204,
-0.011156564578413963,
0.0028170861769467592,
-0.01837119087576866,
0.02751915715634823,
-0.0038719556760042906,
-0.045693278312683105,
-0.06253749132156372,
-0.02489582635462284,
-0.00913028884679079,
0.04938437417149544,
0.0018075197003781796,
-0.009886526502668858,
-0.006085983477532864,
-0.02614963799715042,
0.029173005372285843,
-0.022715643048286438,
0.018636910244822502,
0.005055819172412157,
0.053845908492803574,
-0.004983123391866684,
0.02807459980249405,
-0.02965022437274456,
-0.05048512667417526,
0.042398951947689056,
0.03962118178606033,
0.050127677619457245,
-0.022457627579569817,
-0.01989620178937912,
0.04317557439208031,
0.06418497115373611,
0.009468370117247105,
-0.0064653134904801846,
-0.053853005170822144,
-0.0537140928208828,
0.014953813515603542,
0.08640144765377045,
-0.0763208195567131,
-0.022703230381011963,
0.0639231726527214,
-0.012101302854716778,
-0.027457885444164276,
-0.0558842308819294,
-0.04038890823721886,
-0.01615467667579651,
0.030873514711856842,
0.01936206966638565,
0.00168321852106601,
0.02687656693160534,
0.04037971422076225
] |
<p>I'm studying optics at the moment and I am wondering how the refractive index changes when a liquid is in super critical state?</p>
<p>Thank you.</p> | g1238 | [
-0.003515668213367462,
-0.0018823343561962247,
0.017033100128173828,
0.003473889082670212,
0.005249134264886379,
0.038225237280130386,
-0.042307138442993164,
0.046990565955638885,
0.005961623042821884,
0.008350030519068241,
0.00937589816749096,
0.023383235558867455,
0.029180623590946198,
-0.021952960640192032,
0.02160722203552723,
-0.031081900000572205,
0.015405518002808094,
-0.006954814773052931,
-0.013672834262251854,
-0.00396008649840951,
-0.023636018857359886,
-0.03206703066825867,
-0.04994387552142143,
-0.05230144038796425,
0.02985152043402195,
0.01335565373301506,
0.029060322791337967,
-0.03421095013618469,
-0.03043236956000328,
0.060443464666604996,
-0.016208065673708916,
-0.04432808235287666,
0.008850347250699997,
-0.06043800711631775,
0.057850565761327744,
0.007656304631382227,
0.018659517168998718,
0.05199166759848595,
0.05257358029484749,
-0.029520126059651375,
-0.042818255722522736,
0.01559553574770689,
-0.03457357734441757,
-0.0636889860033989,
-0.007759395055472851,
-0.038490571081638336,
-0.016109930351376534,
-0.030454330146312714,
-0.0320877805352211,
-0.023352716118097305,
0.05603631213307381,
0.0838886946439743,
-0.0030674918089061975,
0.007412418257445097,
0.012650715187191963,
0.046977698802948,
-0.08654852956533432,
0.042841069400310516,
0.07290172576904297,
-0.00026982426061294973,
0.013753139413893223,
-0.026772763580083847,
0.021282264962792397,
-0.002097907941788435,
0.06247234717011452,
-0.0013962623197585344,
0.004409550689160824,
0.004549760837107897,
-0.011544663459062576,
-0.016451822593808174,
-0.015108329243957996,
-0.027580002322793007,
-0.06263181567192078,
-0.012092158198356628,
-0.039648931473493576,
-0.0077163162641227245,
0.0009242030791938305,
-0.020098306238651276,
-0.02072473056614399,
0.01353167463093996,
0.0004240004054736346,
-0.06947020441293716,
0.027239620685577393,
-0.005404874682426453,
-0.056192152202129364,
0.023558951914310455,
0.009835020639002323,
-0.03235138952732086,
-0.0005090778577141464,
-0.007808155380189419,
0.025842705741524696,
-0.006904138717800379,
0.045069366693496704,
0.047236133366823196,
0.09516119956970215,
0.02934577874839306,
0.006653432734310627,
0.025213226675987244,
-0.03149206563830376,
-0.027621330693364143,
0.029273565858602524,
-0.061015382409095764,
0.001230392255820334,
-0.03208070620894432,
-0.0363386869430542,
0.032531335949897766,
0.05985358729958534,
-0.0056295813992619514,
0.04661135375499725,
0.006966929417103529,
-0.06278416514396667,
-0.07658840715885162,
-0.05355129763484001,
0.006821380462497473,
-0.04662816599011421,
0.018351489678025246,
0.06260821223258972,
-0.009956436231732368,
0.03724390268325806,
-0.05086352303624153,
0.06345784664154053,
0.05178111046552658,
-0.017018530517816544,
0.07054605334997177,
0.03125566616654396,
0.04334310069680214,
0.06175108253955841,
0.009146281518042088,
0.052927542477846146,
0.01372284721583128,
0.00018285012629348785,
-0.004685965366661549,
-0.020801562815904617,
-0.049380019307136536,
-0.03412943705916405,
0.04880145192146301,
0.008007210679352283,
-0.018403925001621246,
-0.014910673722624779,
-0.06262419372797012,
0.0016221782425418496,
0.06676242500543594,
0.043422553688287735,
0.030304277315735817,
-0.00042327542905695736,
-0.09856569766998291,
-0.01731511950492859,
-0.010861880145967007,
0.021041836589574814,
-0.02975461259484291,
0.027064215391874313,
0.0061989761888980865,
0.0005567071493715048,
-0.06362012028694153,
-0.005058417562395334,
0.02428884245455265,
0.03368127718567848,
0.001149161602370441,
0.002690055873245001,
-0.006852741353213787,
0.016536979004740715,
-0.04727637395262718,
-0.014064807444810867,
0.08364847302436829,
-0.05966617539525032,
0.01428117323666811,
0.023848125711083412,
-0.042583223432302475,
0.017454378306865692,
-0.02320322021842003,
-0.025714203715324402,
-0.007231820374727249,
-0.007506170775741339,
0.07468456774950027,
0.05910978838801384,
0.05860156938433647,
0.0317293144762516,
0.04743179678916931,
-0.030402472242712975,
0.06608274579048157,
-0.017061056569218636,
0.013648285530507565,
0.04791092500090599,
-0.06110116466879845,
0.03354859724640846,
0.016108263283967972,
0.006540108472108841,
-0.028374630957841873,
-0.0592525377869606,
-0.03697562962770462,
-0.03780202567577362,
0.007931272499263287,
0.002994702197611332,
0.005943467374891043,
0.000730891537386924,
-0.015860090032219887,
0.01179854478687048,
-0.045595232397317886,
-0.051592424511909485,
-0.023031244054436684,
-0.04050979018211365,
-0.020486006513237953,
0.002719087526202202,
0.05070575326681137,
-0.031067075207829475,
0.016304561868309975,
-0.008075702004134655,
0.05967433378100395,
-0.03465542569756508,
0.017027543857693672,
0.01616310328245163,
0.04341227561235428,
-0.0018904120661318302,
-0.030320612713694572,
-0.012617111206054688,
0.10604400187730789,
0.002974982373416424,
-0.011869646608829498,
0.004492421168833971,
0.06841976195573807,
0.00862944032996893,
0.02759598009288311,
-0.0044994293712079525,
0.05219491198658943,
-0.016260311007499695,
-0.005663549527525902,
-0.032431136816740036,
0.023855028674006462,
0.12696516513824463,
-0.0010027261450886726,
0.01717955991625786,
0.02846483699977398,
0.004271277226507664,
-0.018204089254140854,
-0.05103955417871475,
0.05734412372112274,
-0.025615591555833817,
0.07994052767753601,
-0.006652044132351875,
0.005675324238836765,
-0.026944560930132866,
0.02779204212129116,
-0.005596401169896126,
0.038065485656261444,
-0.0491027906537056,
0.0045868149027228355,
0.021481823176145554,
0.004438247997313738,
-0.03508008271455765,
0.04624093323945999,
0.03945401683449745,
-0.00459319818764925,
-0.013592817820608616,
0.0360705628991127,
-0.025926973670721054,
0.029531052336096764,
-0.010789411142468452,
0.1064266487956047,
-0.010061798617243767,
0.004597955849021673,
-0.016619203612208366,
0.008649558760225773,
-0.0069279978051781654,
-0.05927140638232231,
-0.004133610986173153,
-0.0012468761997297406,
0.007256928365677595,
0.009072329849004745,
0.0306793674826622,
0.010818611830472946,
-0.0025590965524315834,
0.07675537467002869,
0.01505813654512167,
0.023760031908750534,
0.02295038104057312,
-0.05394371971487999,
-0.05531016364693642,
0.016474924981594086,
0.07607909291982651,
-0.05387117713689804,
-0.0714360848069191,
-0.022496044635772705,
-0.05039992555975914,
0.005821567960083485,
0.0073721883818507195,
-0.04244023561477661,
0.042258717119693756,
0.04023692011833191,
-0.025308430194854736,
-0.052819058299064636,
-0.025369351729750633,
0.015291979536414146,
-0.036071039736270905,
-0.03751154616475105,
-0.020214444026350975,
0.005232831928879023,
0.08762608468532562,
-0.01043753232806921,
0.029591405764222145,
0.013926348648965359,
-0.012536847032606602,
-0.010483602061867714,
-0.0020145478192716837,
0.04572572931647301,
0.0734398141503334,
0.054442983120679855,
-0.032843176275491714,
-0.04271102324128151,
-0.021916115656495094,
0.00018591196567285806,
-0.06391318887472153,
0.025936907157301903,
-0.017257921397686005,
0.056469596922397614,
0.0055673997849226,
0.04400055110454559,
-0.029241172596812248,
0.04859870299696922,
-0.004670914728194475,
-0.00346184941008687,
-0.07361602038145065,
0.00362725299783051,
0.03856108710169792,
0.012308209203183651,
-0.0017165588214993477,
-0.05480653792619705,
-0.005977432243525982,
-0.020449498668313026,
-0.03831993415951729,
0.03627883642911911,
-0.04016197845339775,
-0.015347215346992016,
-0.050838109105825424,
0.001999822910875082,
-0.03119780123233795,
0.05202674865722656,
-0.06800772994756699,
0.000680032535456121,
0.04356525465846062,
0.027133602648973465,
0.07312187552452087,
-0.021207600831985474,
0.01329900324344635,
-0.011492551304399967,
0.01828499138355255,
0.010013611055910587,
0.0037417197600007057,
-0.0385851226747036,
0.03787458688020706,
-0.015601146966218948,
0.0027941446751356125,
0.006219179835170507,
-0.0028049321845173836,
-0.038050390779972076,
-0.04558616504073143,
0.04224193096160889,
-0.01290060579776764,
-0.008918673731386662,
0.022757383063435555,
-0.00615874445065856,
0.010189134627580643,
-0.049550220370292664,
0.029519906267523766,
0.0009956207359209657,
-0.016083279624581337,
0.018336817622184753,
0.030375167727470398,
-0.02242487110197544,
-0.05828814208507538,
0.0058432272635400295,
-0.014947310090065002,
-0.03344540670514107,
0.020331066101789474,
0.004830026533454657,
-0.0589916817843914,
0.016760041937232018,
-0.05531657487154007,
-0.02524331770837307,
-0.040493790060281754,
0.008451802656054497,
-0.005653874948620796,
-0.020845292136073112,
0.02588074468076229,
-0.04993400722742081,
-0.03193221241235733,
-0.04738881066441536,
0.0024519560392946005,
-0.015181860886514187,
0.007648995146155357,
-0.052086468786001205,
0.03199245035648346,
-0.06943336129188538,
0.015051069669425488,
-0.018261423334479332,
0.007114333100616932,
0.05375880002975464,
0.033867791295051575,
0.027034753933548927,
0.009404241107404232,
0.029794426634907722,
0.012439260259270668,
0.08334796875715256,
0.028517931699752808,
-0.014851024374365807,
-0.003373212879523635,
-0.023429831489920616,
0.03975290432572365,
0.03423537686467171,
-0.07967501878738403,
0.005038036964833736,
0.04278780147433281,
0.04117332026362419,
-0.024631083011627197,
-0.06962090730667114,
-0.026346780359745026,
0.06601420789957047,
0.05179819464683533,
-0.04025740176439285,
0.018802601844072342,
-0.029285209253430367,
0.00338038825429976,
-0.052325714379549026,
-0.021467300131917,
-0.015098913572728634,
-0.029316041618585587,
0.0049069831147789955,
-0.02398718148469925,
-0.0703679695725441,
0.015888305380940437,
-0.05152542516589165,
0.023552503436803818,
0.028621777892112732,
0.006180154159665108,
0.04460027441382408,
0.02995952032506466,
0.028980663046240807,
0.020920731127262115,
-0.04582304507493973,
-0.01843409053981304,
-0.008764192461967468,
0.058187760412693024,
-0.0034064040519297123,
-0.0024823423009365797,
-0.010243488475680351,
0.014751618728041649,
0.006035199388861656,
0.02966923452913761,
-0.0016645259456709027,
-0.017030715942382812,
-0.037306539714336395,
-0.04854162782430649,
0.007831837981939316,
0.001314725843258202,
-0.03679591417312622,
-0.06991203874349594,
-0.0858813002705574,
-0.005049888510257006,
0.0430041141808033,
-0.00496551301330328,
0.0016031243139877915,
-0.030457470566034317,
0.0020604124292731285,
-0.0020193099044263363,
-0.022171150892972946,
0.0513770766556263,
0.02853318862617016,
0.0060228570364415646,
-0.06663621217012405,
0.006840029265731573,
-0.01294906809926033,
0.019069798290729523,
-0.05786266550421715,
0.01755642518401146,
0.011494842357933521,
0.054960377514362335,
-0.008434916846454144,
-0.03802892565727234,
-0.014402327127754688,
0.08600883930921555,
-0.019441604614257812,
-0.008216867223381996,
-0.007803008891642094,
0.08594150841236115,
-0.014182613231241703,
0.016962818801403046,
-0.022122444584965706,
0.0009619031334295869,
0.03103700838983059,
-0.0010410743998363614,
-0.013570141978561878,
-0.010948849841952324,
0.00583984050899744,
0.022220924496650696,
-0.004098276142030954,
0.030174046754837036,
-0.05085145682096481,
0.03828859329223633,
-0.029063986614346504,
-0.0024804275017231703,
-0.01118413358926773,
-0.03783702850341797,
-0.026658521965146065,
-0.019739467650651932,
0.00817803479731083,
-0.042865071445703506,
0.03895634412765503,
0.000248684489633888,
-0.011822376400232315,
0.06362531334161758,
0.05464203283190727,
-0.03086734749376774,
0.00725840637460351,
0.017499562352895737,
-0.023938609287142754,
-0.0003291166212875396,
-0.048401933163404465,
-0.02017630822956562,
0.00791482999920845,
-0.02591511979699135,
-0.022256841883063316,
-0.021332766860723495,
-0.008049455471336842,
-0.022350294515490532,
0.019216617569327354,
-0.016141239553689957,
0.008404701016843319,
-0.06511206924915314,
0.020730776712298393,
0.07534325867891312,
-0.06073951721191406,
-0.012928890995681286,
0.04232661798596382,
0.03151428699493408,
0.002768678590655327,
0.01763983629643917,
-0.02920743264257908,
-0.0023428506683558226,
0.0055851140059530735,
-0.016159290447831154,
0.04784606397151947,
-0.058715056627988815,
0.09283368289470673,
-0.002384169027209282,
0.03506537899374962,
0.008332476951181889,
-0.029614554718136787,
-0.02811950072646141,
0.01730046048760414,
-0.00983175914734602,
-0.015629805624485016,
0.014930034056305885,
0.013898035511374474,
0.022640444338321686,
0.030699994415044785,
0.04437877982854843,
0.026009172201156616,
-0.0030916749965399504,
-0.026723472401499748,
-0.030181754380464554,
-0.04535413533449173,
0.03145866096019745,
0.0335867740213871,
-0.032659437507390976,
-0.029827458783984184,
0.03074890375137329,
-0.06963425874710083,
-0.008518499322235584,
0.024109607562422752,
0.026279937475919724,
-0.0035890783183276653,
-0.07850106060504913,
0.010671454481780529,
-0.06392566859722137,
-0.05315861105918884,
0.029284177348017693,
-0.0036773383617401123,
-0.03573698177933693,
0.02925373800098896,
0.018111562356352806,
-0.04933786764740944,
0.03753669932484627,
0.02878332883119583,
0.03337317332625389,
0.009342472068965435,
-0.07286582887172699,
-0.005309028550982475,
0.0024634459987282753,
0.049872856587171555,
0.060091327875852585,
-0.014311150647699833,
-0.023478081449866295,
0.013006188906729221,
-0.005394504405558109,
-0.007376532070338726,
0.058845825493335724,
-0.006918337661772966,
-0.0408351756632328,
0.06216421350836754,
-0.02466057799756527,
0.02858036383986473,
-0.007768877316266298,
-0.01910373754799366,
-0.020661722868680954,
-0.006938938982784748,
-0.01872391253709793,
-0.03032122738659382,
0.028589807450771332,
0.020695367828011513,
0.05090383067727089,
0.008555472828447819,
0.029496924951672554,
-0.009899988770484924,
0.04040505364537239,
-0.01024993322789669,
-0.0008781565702520311,
-0.06114981696009636,
0.031061705201864243,
0.01892622373998165,
-0.024012813344597816,
-0.01730848103761673,
-0.017793558537960052,
-0.04983749985694885,
0.002059331163764,
-0.041402559727430344,
-0.0210303645581007,
0.029491310939192772,
-0.004233889747411013,
-0.06340385228395462,
0.02174454927444458,
-0.020872613415122032,
0.05972874537110329,
-0.029478246346116066,
0.05181010439991951,
0.04741816595196724,
-0.002998080337420106,
0.017463482916355133,
-0.05218588188290596,
0.028949355706572533,
-0.0023055144120007753,
-0.007857699878513813,
0.09984735399484634,
0.009972861036658287,
0.024858493357896805,
-0.029407527297735214,
-0.019040940329432487,
0.04264084994792938,
0.015264764428138733,
-0.0571630485355854,
-0.06669947504997253,
-0.009915138594806194,
-0.020445361733436584,
-0.07862253487110138,
-0.0487419031560421,
0.06961268186569214,
-0.016286976635456085,
0.08504815399646759,
-0.02867249958217144,
0.030872078612446785,
0.006403795443475246,
-0.004936915822327137,
-0.014902048744261265,
-0.021329272538423538,
0.012202061712741852,
-0.008807006292045116,
0.03940686956048012,
0.02843312732875347,
0.06082102283835411,
-0.06167266517877579,
0.012102830223739147,
-0.007155977189540863,
0.0475638210773468,
-0.0020434188190847635,
-0.010624973103404045,
0.005366648081690073,
0.012662012130022049,
-0.04556075856089592,
-0.06943638622760773,
0.056715227663517,
0.02981693483889103,
0.015336528420448303,
0.0010502906516194344,
0.018479274585843086,
0.03438371792435646,
-0.09447617828845978,
-0.05120411515235901,
-0.00019640885875560343,
0.006076373625546694,
0.039819229394197464,
0.08812902867794037,
-0.03798629716038704,
0.005501536186784506,
-0.10265811532735825,
-0.02727099135518074,
0.017106372863054276,
-0.007504946552217007,
-0.03861561045050621,
0.03493151441216469,
0.039822760969400406,
0.07237133383750916,
-0.04315581172704697,
-0.02481323480606079,
-0.007602481637150049,
-0.058420561254024506,
-0.0020262631587684155,
-0.02314121462404728,
0.009401284158229828,
-0.030628250911831856,
-0.045417629182338715,
0.009302640333771706,
0.03828778117895126,
-0.004394919145852327,
0.009447173215448856,
0.04269403591752052,
-0.03910677507519722,
0.007260750513523817,
0.014691370539367199,
0.034341953694820404,
-0.0039369892328977585,
-0.041790299117565155,
0.031463343650102615,
-0.05746112018823624,
-0.006889089476317167,
0.007613605819642544,
-0.02804490737617016,
-0.011448378674685955,
0.0002179691509809345,
0.013620760291814804,
0.03509341552853584,
-0.04024553298950195,
-0.009013167582452297,
-0.027884026989340782,
0.019728360697627068,
-0.07003659754991531,
0.00005665062053594738,
0.00870213471353054,
0.04714960232377052,
0.027302786707878113,
-0.007227233611047268,
0.03847896680235863,
0.03371046856045723,
-0.015446376986801624,
-0.02767437882721424,
0.009107289835810661,
-0.02659478411078453,
0.06319818645715714,
-0.04572311416268349,
-0.014471671544015408,
-0.008255158551037312,
0.012498140335083008,
-0.01596982218325138,
-0.025969406589865685,
-0.014148913323879242,
0.05892043188214302,
0.04551493749022484,
-0.0048165954649448395,
-0.01772148534655571,
-0.03015616349875927,
-0.0445859432220459,
0.029307179152965546,
-0.039222508668899536,
-0.011162525974214077,
0.027351107448339462,
0.006122012622654438,
-0.008257841691374779,
0.0005761503707617521,
-0.03453758358955383,
-0.020532989874482155,
0.02093128301203251
] |
<p>I recently learnt that the conservation laws are a consequence of the symmetries of space and time (the Lagrangian in Newton mechanics). Since space-time change in a black hole wouldn't quantum mechanics also change?</p>
<p>Let me give an example by what I mean: <br>
In classical space: <br>
$$x' = x + e \\
L(x') = L(x)$$</p>
<p>But the above transformation is not true in relativistic space. Hence, the conservation of momentum changes in special relativity (i.e momentum is not $mv$). So similarly shouldn't all the conservation laws change for a black hole and therefore it's action? </p>
<p>Side note: the reason I was thinking of a black-hole was that the incoming particle of mass will not drastically affect the space-time (due to the heavy centre) </p> | g1239 | [
0.009837056510150433,
-0.04300881549715996,
0.015828998759388924,
0.006932156626135111,
0.026436064392328262,
0.030154595151543617,
0.03464873507618904,
0.06879108399152756,
-0.0355730876326561,
0.04634450003504753,
0.01978517696261406,
-0.024933623149991035,
-0.0045292251743376255,
0.02575113996863365,
-0.02174670808017254,
-0.016402753069996834,
0.04248356819152832,
0.010577535256743431,
-0.021808886900544167,
0.003497176570817828,
-0.018345190212130547,
-0.05151508376002312,
-0.008444524370133877,
-0.04938995838165283,
-0.011906095780432224,
0.01955672726035118,
0.05283831059932709,
-0.021283291280269623,
-0.042581673711538315,
0.03746304288506508,
0.04266396909952164,
0.03820411488413811,
-0.025569908320903778,
-0.03728180751204491,
0.029025953263044357,
-0.044508785009384155,
0.04168805480003357,
-0.015835778787732124,
0.06763831526041031,
0.048335473984479904,
0.026258384808897972,
-0.023024914786219597,
-0.015240916982293129,
-0.028554268181324005,
0.0055700913071632385,
-0.0933377593755722,
-0.003444897709414363,
-0.0442880354821682,
-0.005350054707378149,
0.02308603562414646,
0.04335441067814827,
-0.03050869330763817,
0.027540992945432663,
0.0425744354724884,
0.03909091651439667,
0.010777579620480537,
0.016511637717485428,
0.014154335483908653,
0.01514583919197321,
0.017201628535985947,
-0.05919799208641052,
-0.035528331995010376,
0.05263429135084152,
0.08347396552562714,
0.028944874182343483,
-0.027115188539028168,
-0.013830320909619331,
-0.05758009850978851,
-0.03144514933228493,
0.03242051228880882,
0.024450600147247314,
-0.0011774675222113729,
0.001876196009106934,
0.03449082374572754,
0.04815530404448509,
0.040580056607723236,
-0.04785744473338127,
0.053189683705568314,
-0.022533519193530083,
-0.09468607604503632,
-0.06737607717514038,
-0.032990939915180206,
0.06015771999955177,
0.024783547967672348,
0.08677742630243301,
-0.001360244699753821,
-0.041158903390169144,
-0.001604596502147615,
-0.0499165914952755,
-0.023277807980775833,
0.01527940109372139,
-0.036210622638463974,
0.0744447335600853,
0.026049599051475525,
-0.020713744685053825,
0.0016215319046750665,
0.013187184929847717,
0.0448223352432251,
0.01085630338639021,
0.005392823833972216,
-0.05493050068616867,
0.00015128965605981648,
-0.014553988352417946,
-0.009768376126885414,
-0.0006695353658869863,
0.010020960122346878,
-0.02041020058095455,
0.050998907536268234,
-0.03673940151929855,
-0.0009974604472517967,
0.019751176238059998,
-0.10640446841716766,
-0.031755704432725906,
0.001800711383111775,
-0.055214084684848785,
-0.04064960032701492,
0.042807694524526596,
-0.037422023713588715,
0.023107169196009636,
0.03786766156554222,
-0.00592870032414794,
0.02494061551988125,
0.05397028848528862,
-0.00872136652469635,
0.0020042574033141136,
-0.03940257430076599,
-0.045349445194005966,
0.03204509988427162,
0.06478071212768555,
-0.006397359073162079,
-0.013953872956335545,
0.03511194512248039,
-0.058318838477134705,
0.07704612612724304,
-0.026495153084397316,
0.001925080199725926,
0.02235781028866768,
0.013819911517202854,
0.01796337403357029,
-0.0610051304101944,
-0.008898478001356125,
0.009106893092393875,
0.053407274186611176,
0.015805624425411224,
-0.002327041933313012,
-0.027138665318489075,
-0.05197575315833092,
-0.015336899086833,
0.01369448471814394,
-0.014025802724063396,
0.0014315888984128833,
0.08231672644615173,
-0.030132228508591652,
0.035107772797346115,
0.006578081287443638,
0.02423687092959881,
0.0022959269117563963,
0.04946714639663696,
-0.03445618972182274,
0.016273152083158493,
0.07280318439006805,
-0.03334207832813263,
0.02368132397532463,
0.019314855337142944,
-0.06092973053455353,
0.023910939693450928,
-0.03969605267047882,
-0.06458194553852081,
-0.012433554977178574,
-0.020507264882326126,
-0.02831459417939186,
0.022600462660193443,
-0.030896907672286034,
0.0628274530172348,
0.018176652491092682,
0.020502232015132904,
-0.005937006790190935,
0.008333864621818066,
0.035385895520448685,
0.010174788534641266,
-0.033909671008586884,
-0.011969047598540783,
0.016236208379268646,
-0.04070365056395531,
0.01680695079267025,
0.05079064890742302,
0.07438767701387405,
0.008696343749761581,
-0.06342892348766327,
0.006614633835852146,
-0.03350269794464111,
0.005536073353141546,
0.02972344495356083,
0.04278557002544403,
0.01599026843905449,
0.043923165649175644,
-0.022587815299630165,
-0.010350155644118786,
-0.024549121037125587,
0.08956580609083176,
-0.020817570388317108,
0.024079445749521255,
0.016931092366576195,
-0.013044883497059345,
-0.018775010481476784,
-0.0011337778996676207,
-0.030767029151320457,
0.0345817431807518,
0.014691302552819252,
-0.026410486549139023,
0.05846382677555084,
-0.033937811851501465,
0.013854637742042542,
-0.0114882942289114,
-0.022941162809729576,
0.026749899610877037,
-0.06100469455122948,
0.055170394480228424,
-0.023337028920650482,
0.03722408786416054,
-0.05150272697210312,
-0.03637322038412094,
0.0022416100837290287,
0.004509248770773411,
-0.04290224239230156,
0.010010977275669575,
-0.049085576087236404,
-0.04788433387875557,
-0.013731311075389385,
0.019949648529291153,
-0.04893749952316284,
0.05241511017084122,
-0.02858869545161724,
0.017984595149755478,
0.014900179579854012,
0.07466607540845871,
0.030698280781507492,
-0.015055535361170769,
0.05660263076424599,
0.010965896770358086,
0.049562033265829086,
0.0014886653516441584,
-0.02303716167807579,
-0.029011771082878113,
0.08436129987239838,
0.007128886412829161,
0.004052319563925266,
-0.017943250015378,
-0.012220987118780613,
-0.011432470753788948,
-0.0031527220271527767,
-0.03027050569653511,
-0.03237219527363777,
-0.0362737663090229,
-0.001841514720581472,
-0.01621105521917343,
0.06620607525110245,
-0.01575271226465702,
-0.07195134460926056,
-0.014073324389755726,
0.01155174896121025,
0.015592134557664394,
-0.02398792840540409,
0.06748605519533157,
-0.03450901806354523,
0.011616242118179798,
0.003921706695109606,
0.03606703132390976,
-0.014993724413216114,
0.020116087049245834,
-0.04158148542046547,
0.07057936489582062,
0.007963285781443119,
0.03522593155503273,
-0.011623320169746876,
-0.04242321476340294,
-0.03786468878388405,
-0.010526949539780617,
0.024479767307639122,
-0.045713383704423904,
-0.03352423757314682,
0.0062534864991903305,
-0.06799978762865067,
-0.004781286232173443,
0.04380577802658081,
-0.0505998469889164,
-0.03323902189731598,
-0.03735116869211197,
-0.04572600498795509,
-0.001445902744308114,
0.007903380319476128,
0.08659635484218597,
0.0005345034878700972,
0.02140922285616398,
0.01605578325688839,
0.048017457127571106,
-0.023555876687169075,
-0.068306565284729,
-0.08063472807407379,
0.0351669080555439,
-0.013378218747675419,
-0.017996257171034813,
0.012704198248684406,
0.07639148086309433,
0.01895676553249359,
0.0438050851225853,
-0.04505753144621849,
-0.024806028231978416,
0.042309969663619995,
-0.03210281953215599,
-0.03935840353369713,
0.01866951771080494,
-0.05406599119305611,
0.022505290806293488,
-0.013180178590118885,
-0.025470847263932228,
-0.0003778619284275919,
-0.023596277460455894,
-0.005476158577948809,
-0.01575852930545807,
-0.03873569890856743,
-0.012190261855721474,
-0.0038699908182024956,
-0.0005791314761154354,
0.06837998330593109,
0.03220536932349205,
-0.033811863511800766,
-0.018171781674027443,
-0.023609600961208344,
-0.0023567986208945513,
-0.01602432318031788,
0.012015430256724358,
0.026262717321515083,
-0.004489339422434568,
-0.06438049674034119,
0.03535821661353111,
-0.0037731067277491093,
-0.050588008016347885,
0.001333905616775155,
-0.033825188875198364,
0.03153963014483452,
-0.013573816046118736,
0.005347806960344315,
0.10024908185005188,
0.029567915946245193,
0.02022230066359043,
0.04007486253976822,
-0.03271668404340744,
-0.03706221282482147,
0.02477436326444149,
-0.00020727772789541632,
-0.04314562678337097,
0.06292575597763062,
-0.007397257257252932,
-0.017026666551828384,
0.015848932787775993,
0.02233966439962387,
0.03895561769604683,
0.015337508171796799,
0.0006586189847439528,
-0.014464570209383965,
-0.015383588150143623,
-0.03220416232943535,
0.01323612779378891,
-0.022559743374586105,
0.02535758726298809,
0.027269797399640083,
-0.0741562694311142,
0.05188986659049988,
0.003805706975981593,
0.09115006774663925,
0.03421977162361145,
-0.004671476781368256,
-0.0008061437983997166,
-0.009443010203540325,
-0.0478651225566864,
0.06660240888595581,
0.013747721910476685,
0.012438081204891205,
-0.018210945650935173,
0.020974302664399147,
-0.04348472133278847,
0.01656290516257286,
0.031135402619838715,
0.024285543709993362,
0.018711522221565247,
-0.016234396025538445,
0.021785292774438858,
0.03147425502538681,
-0.024087386205792427,
-0.029466524720191956,
-0.0086145531386137,
0.05988549441099167,
-0.08478110283613205,
0.013854625634849072,
0.04401156306266785,
0.019230812788009644,
-0.04277563840150833,
-0.0012757837539538741,
-0.02196473255753517,
-0.009575583040714264,
0.06075785681605339,
0.016005877405405045,
0.031102411448955536,
0.04498395696282387,
-0.004949773196130991,
0.0513705275952816,
-0.009475779719650745,
-0.04078876972198486,
-0.02735595963895321,
0.016765475273132324,
-0.014508068561553955,
0.011180886998772621,
0.008958128280937672,
-0.04035758599638939,
0.02043945901095867,
-0.04292309656739235,
-0.05684370920062065,
-0.00858752429485321,
0.023477347567677498,
0.06023477390408516,
0.006030069664120674,
0.012046278454363346,
-0.0035088122822344303,
0.06814578175544739,
0.03188779950141907,
0.024661825969815254,
0.00548614002764225,
0.0038878831546753645,
-0.019358722493052483,
-0.003897784510627389,
-0.029076743870973587,
0.01409924402832985,
-0.01938607543706894,
-0.09400663524866104,
0.04753909632563591,
-0.06527736037969589,
-0.03166864439845085,
0.005785105749964714,
0.03185972198843956,
0.08277149498462677,
0.021912988275289536,
0.002461305819451809,
-0.04964476451277733,
-0.040119100362062454,
0.046713028103113174,
0.035704605281353,
-0.005369877442717552,
-0.008602903224527836,
-0.02481033466756344,
-0.034746747463941574,
0.048045091331005096,
0.012756580486893654,
-0.052897922694683075,
-0.024580257013440132,
0.014949590899050236,
-0.020015470683574677,
0.018324878066778183,
0.007535007782280445,
0.03846203535795212,
-0.0887468159198761,
-0.023067984730005264,
0.018743207678198814,
0.0005536044482141733,
-0.003992501180619001,
-0.034579746425151825,
-0.050648033618927,
0.015366299077868462,
-0.028530992567539215,
-0.023290956392884254,
0.024607885628938675,
-0.018352244049310684,
-0.016610875725746155,
0.0013568467693403363,
0.018054218962788582,
0.021738780662417412,
-0.014424021355807781,
-0.0010498169576749206,
0.022882698103785515,
-0.06365464627742767,
-0.001449785428121686,
-0.03696242347359657,
0.0655866339802742,
0.04759352654218674,
0.023125026375055313,
0.039483025670051575,
-0.01756378635764122,
0.04642152041196823,
0.01419677585363388,
-0.040031589567661285,
0.011006779968738556,
0.010431921109557152,
-0.008106095716357231,
-0.010705338791012764,
0.0303601436316967,
0.036679212003946304,
-0.020509595051407814,
-0.008437078446149826,
0.015192175284028053,
-0.008417265489697456,
-0.07790398597717285,
0.01963948644697666,
0.04698949679732323,
-0.04152603819966316,
-0.024389194324612617,
0.004934624303132296,
-0.02273162081837654,
0.060343433171510696,
-0.044801015406847,
0.03262685611844063,
0.00854441151022911,
0.009121818467974663,
-0.01956786960363388,
0.039280738681554794,
0.06425492465496063,
-0.03484008461236954,
-0.005393801722675562,
-0.03403611481189728,
0.0042245578952133656,
-0.03734572231769562,
-0.009489132091403008,
-0.004741456359624863,
0.06676685065031052,
0.05021371692419052,
0.022477416321635246,
0.0552925281226635,
-0.05281538516283035,
0.0013325109612196684,
0.02876666560769081,
0.02544482611119747,
0.012563352473080158,
0.010036511346697807,
0.04118151590228081,
-0.017126986756920815,
-0.011018333956599236,
-0.033266764134168625,
-0.004427221138030291,
0.03048548474907875,
0.05045140162110329,
-0.0007071106811054051,
0.015736129134893417,
-0.021592892706394196,
0.020453082397580147,
0.01893937587738037,
0.022418370470404625,
0.029812173917889595,
-0.06361249834299088,
-0.02752443216741085,
-0.013411722145974636,
-0.07029610127210617,
-0.04325633868575096,
0.009314238093793392,
-0.06624280661344528,
-0.001689663389697671,
-0.033348944038152695,
0.03993716835975647,
0.01155512873083353,
-0.017199669033288956,
-0.004126178100705147,
-0.04569888114929199,
0.04844863340258598,
0.030619816854596138,
-0.003949853125959635,
-0.012132116593420506,
0.015658313408493996,
-0.006236419081687927,
0.012675686739385128,
-0.040836308151483536,
0.07765406370162964,
0.040476612746715546,
-0.04663631692528725,
0.04081941768527031,
0.00326181179843843,
-0.00524850795045495,
0.009654278866946697,
0.0034162576775997877,
-0.01950080879032612,
-0.014038462191820145,
-0.07692543417215347,
-0.04272376000881195,
0.01787780411541462,
-0.041363079100847244,
0.035544123500585556,
-0.08601931482553482,
-0.07690753042697906,
0.003750853007659316,
0.0016440724721178412,
0.013741561211645603,
0.043854646384716034,
0.0745258554816246,
-0.02721920795738697,
0.007441139314323664,
0.008417702279984951,
0.029149331152439117,
0.00009535985736874864,
0.018352456390857697,
-0.008187903091311455,
-0.002879916690289974,
0.0114439120516181,
-0.019290685653686523,
0.003795188618823886,
0.03346652910113335,
0.001035394612699747,
-0.024778535589575768,
-0.0036295545287430286,
0.05197613686323166,
-0.08962491899728775,
-0.0014586296165362,
0.07239101082086563,
0.013941299170255661,
-0.006426415406167507,
-0.0007525188848376274,
-0.06578036397695541,
0.03141967952251434,
0.016202569007873535,
0.017847998067736626,
-0.043361105024814606,
0.015961937606334686,
-0.015168668702244759,
-0.03767964616417885,
0.016970666125416756,
0.05947602540254593,
-0.060982976108789444,
-0.015936650335788727,
0.019234713166952133,
0.027724532410502434,
-0.06918548792600632,
0.05192175880074501,
0.06238086149096489,
0.033207427710294724,
-0.0027990462258458138,
0.01082103606313467,
-0.028927594423294067,
0.03992626443505287,
0.004106832202523947,
-0.0056328061036765575,
-0.034916579723358154,
0.009732493199408054,
0.00394395412877202,
-0.038228362798690796,
-0.0008113670046441257,
-0.0264899842441082,
0.02771001122891903,
0.027751952409744263,
-0.058850906789302826,
0.020555274561047554,
0.021862855181097984,
-0.027887580916285515,
-0.10883331298828125,
0.022764351218938828,
-0.006828200537711382,
-0.041733287274837494,
-0.10491489619016647,
0.008313565514981747,
-0.021241487935185432,
-0.05313742160797119,
-0.01632825657725334,
0.011883575469255447,
-0.0008903535781428218,
-0.09990101307630539,
-0.012588003650307655,
-0.0050154635682702065,
-0.036082323640584946,
-0.007006275467574596,
0.08447065204381943,
0.0033818462397903204,
0.03365056589245796,
-0.007325654849410057,
0.03740253299474716,
-0.006201484706252813,
-0.005907795391976833,
-0.002951171016320586,
-0.023010700941085815,
0.024427998811006546,
0.00017354177543893456,
-0.01478530839085579,
0.00512298010289669,
0.04188624024391174,
-0.05789657309651375,
0.057095762342214584,
0.008910301141440868,
-0.005107405129820108,
-0.044192392379045486,
0.00917770154774189,
-0.030372343957424164,
-0.003731470089405775,
-0.015985708683729172,
0.015416323207318783,
0.012470784597098827,
0.006870620418339968,
-0.027254531159996986,
-0.03667616844177246,
-0.022523121908307076,
-0.022829467430710793,
0.004173554480075836,
0.0010688244365155697,
0.1192643865942955,
0.02508390322327614,
-0.040727708488702774,
-0.06978870928287506,
-0.021336045116186142,
-0.03899529203772545,
-0.015885701403021812,
-0.01142368745058775,
-0.0047975583001971245,
0.006308741867542267,
-0.008624585345387459,
-0.06178310886025429,
-0.05332540348172188,
0.04303480312228203,
-0.009366939775645733,
-0.006820193491876125,
0.0362677164375782,
-0.015730077400803566,
0.036118485033512115,
-0.021727798506617546,
0.005288772750645876,
-0.03168722614645958,
-0.02208443358540535,
-0.051545400172472,
0.014595289714634418,
0.02148623764514923,
-0.035215556621551514,
-0.1062900498509407,
-0.023143276572227478,
-0.010211119428277016,
0.02131476067006588,
-0.022761238738894463,
0.02001716010272503,
-0.015287434682250023,
-0.03010149672627449,
0.0067158895544707775,
-0.044896043837070465,
0.022623611614108086,
0.018030347302556038,
0.002803451381623745,
0.03898254781961441,
-0.004574085120111704,
-0.02768586203455925,
0.03467090427875519,
0.004571286495774984,
-0.05542193353176117,
0.037698742002248764,
0.03187862038612366,
-0.0049108341336250305,
-0.04164010286331177,
0.05952690914273262,
-0.026279110461473465,
0.020502189174294472,
0.014616577886044979,
0.04419432207942009,
0.03908136114478111,
-0.018738120794296265,
0.013472381979227066,
0.007529531605541706,
-0.02511756680905819,
-0.012714603915810585,
-0.04530944302678108,
-0.02106356807053089,
0.043778982013463974,
-0.00800591241568327,
0.0640408992767334,
0.00043286947766318917,
-0.04057306796312332,
-0.03304886072874069,
-0.03327755257487297,
0.03615428879857063,
0.05272713676095009
] |
<p>I'm trying to calculate the spin and color averaged gg->gg cross section, and I am stumbling upon gauge invariance:</p>
<p>Must the amplitude not be invariant under replacements $\epsilon_i \to \epsilon_i + \kappa_i p_i$ where $p_i\cdot\epsilon_i=0$ and $\kappa_i$ is arbitrary? For me it is not :/</p>
<p>I have summed the 4-gluon diagram and s,t,u-channel diagrams with two 3-gluon vertices each.</p>
<p>When I square the amplitude and carry out the spin averaged polarization sum in axial gauge, the extra "n"-vector does not vanish.</p>
<p>Am I missing something trivial? Can someone point me to some resource? I do not want to calculate the amplitude with spinor helicity formalism. I am thankful for any hints because I've been sitting on this problem with a collegue for quite a while.</p>
<p>Thanks, Tobias</p> | g1240 | [
-0.039520565420389175,
-0.04230419918894768,
-0.018631307408213615,
-0.07024059444665909,
0.003784392960369587,
0.035200245678424835,
0.04127566143870354,
0.08348585665225983,
-0.040853917598724365,
0.0624905601143837,
0.05901088938117027,
-0.03687547892332077,
0.010162590071558952,
-0.0033346465788781643,
0.04674207791686058,
0.03542628511786461,
0.010275943204760551,
0.03991878405213356,
0.04269229248166084,
-0.030690642073750496,
-0.032729391008615494,
0.025869697332382202,
-0.00040387935587204993,
-0.06419096142053604,
0.09662362933158875,
-0.0112596545368433,
-0.0018517103744670749,
-0.014529828913509846,
-0.018488723784685135,
0.009027003310620785,
-0.021670250222086906,
0.011322221718728542,
0.016444683074951172,
-0.046677350997924805,
-0.010771230794489384,
0.03930564224720001,
0.04369659721851349,
0.04452476650476456,
0.022870272397994995,
0.023451533168554306,
0.040629833936691284,
0.023417610675096512,
0.004943082109093666,
0.010359999723732471,
0.00912733655422926,
0.03151564300060272,
0.04559869319200516,
0.016646765172481537,
-0.02398587018251419,
-0.004836925771087408,
-0.07505372166633606,
0.014433973468840122,
0.12877577543258667,
-0.02768373116850853,
-0.04409864544868469,
0.05047830566763878,
-0.007963527925312519,
0.019321754574775696,
-0.0033954516984522343,
0.05546437203884125,
0.04938192665576935,
0.0054059214890003204,
-0.0020204721949994564,
0.004787962418049574,
0.03780916705727577,
-0.06851822882890701,
-0.031376201659440994,
0.009711702354252338,
0.005648482125252485,
-0.00039671786362305284,
-0.0012710554292425513,
-0.013227419927716255,
0.057874660938978195,
0.03346744179725647,
-0.07324287295341492,
-0.0040680477395653725,
-0.004599621519446373,
0.040189288556575775,
0.05176493525505066,
0.0012908552307635546,
-0.0628090426325798,
-0.002803277224302292,
-0.020401109009981155,
-0.041948433965444565,
0.02023002877831459,
-0.0801088809967041,
0.01086733490228653,
0.008940012194216251,
-0.05644451081752777,
0.013981685973703861,
0.04793628305196762,
-0.01845107413828373,
-0.018336882814764977,
0.0031646816059947014,
0.00028036226285621524,
-0.026715880259871483,
-0.01254394743591547,
0.03954850509762764,
-0.0027062075678259134,
0.0331764742732048,
-0.026012761518359184,
0.013282731175422668,
-0.020463481545448303,
0.004531686659902334,
-0.003481870051473379,
0.015531565062701702,
0.023209000006318092,
-0.039149124175310135,
-0.0211398433893919,
-0.009322423487901688,
-0.06313123553991318,
-0.010350208729505539,
-0.007391560357064009,
-0.009405619464814663,
-0.03557463735342026,
-0.0734068974852562,
0.07267428934574127,
-0.02157127484679222,
-0.012635395862162113,
-0.011135152541100979,
0.03697182238101959,
0.04229836165904999,
-0.044700510799884796,
0.04899488389492035,
0.0007789643714204431,
0.07583755999803543,
-0.011510271579027176,
0.03046230971813202,
0.07455944269895554,
0.00011335487215546891,
0.036585643887519836,
-0.04751930758357048,
0.013623889535665512,
0.06946610659360886,
0.03806508705019951,
-0.06558286398649216,
0.06554114818572998,
0.020721571519970894,
0.028982212767004967,
-0.0031600631773471832,
-0.044062476605176926,
-0.013674995861947536,
-0.018354816362261772,
-0.02700956165790558,
0.06939494609832764,
0.005817039404064417,
0.021334301680326462,
-0.09472081065177917,
0.06810269504785538,
-0.03917304798960686,
0.0645253136754036,
0.03232797235250473,
0.03420060873031616,
-0.058883294463157654,
0.018065983429551125,
-0.040941059589385986,
0.008059630170464516,
-0.004647614434361458,
0.017206422984600067,
0.007762370631098747,
0.04991835728287697,
-0.05507715418934822,
0.014810328371822834,
0.010463876649737358,
-0.01636868715286255,
-0.022087467834353447,
0.006250153295695782,
-0.031745292246341705,
-0.03762391582131386,
-0.05081286281347275,
-0.007760812994092703,
0.021863309666514397,
0.048752784729003906,
-0.0018807519227266312,
0.032118894159793854,
0.07540466636419296,
0.007304506842046976,
-0.05705367773771286,
0.040646668523550034,
-0.0143424142152071,
-0.004106433596462011,
0.032513584941625595,
0.043779563158750534,
-0.02936823107302189,
0.005789482966065407,
-0.018920863047242165,
0.04011250287294388,
0.020470639690756798,
-0.010820087976753712,
0.027801163494586945,
0.02511240914463997,
0.06843909621238708,
-0.02258490025997162,
0.04227631539106369,
0.000681254779919982,
-0.006017777137458324,
0.0599183551967144,
-0.017962507903575897,
-0.04773573949933052,
0.07208117097616196,
0.006504890974611044,
-0.015703387558460236,
0.00016952393343672156,
-0.017698945477604866,
0.007033476606011391,
0.0007411605911329389,
-0.019873103126883507,
-0.01080296840518713,
0.02877834253013134,
-0.016604101285338402,
0.029760165140032768,
0.04678693413734436,
0.0026281431782990694,
0.020820854231715202,
-0.036223605275154114,
-0.030962420627474785,
0.02022639475762844,
-0.006177132949233055,
-0.05101797729730606,
0.02290312573313713,
-0.025903483852744102,
-0.023975495249032974,
-0.03207535296678543,
0.03749249875545502,
-0.02283773012459278,
0.030883286148309708,
-0.005732972174882889,
-0.014370879158377647,
-0.0340433269739151,
-0.038718532770872116,
-0.042414888739585876,
0.014098632149398327,
-0.04162735491991043,
-0.08052397519350052,
-0.024087976664304733,
0.004263236653059721,
-0.031027210876345634,
-0.01815659925341606,
0.018302027136087418,
-0.0318443737924099,
0.024271439760923386,
0.07188402861356735,
0.01407771185040474,
0.03325846791267395,
0.053680144250392914,
0.028237994760274887,
0.013533416204154491,
0.002381452126428485,
-0.0011319983750581741,
0.05973577871918678,
0.050661779940128326,
0.023237401619553566,
0.036450617015361786,
-0.052523043006658554,
0.002387793967500329,
0.0063536511734128,
0.05087880417704582,
-0.0021367112640291452,
-0.036583222448825836,
0.032839588820934296,
-0.009758338332176208,
-0.040366802364587784,
-0.012363334186375141,
0.03135800361633301,
-0.09644731879234314,
-0.007135198451578617,
0.06398112326860428,
-0.04832048714160919,
-0.026955321431159973,
-0.019997289404273033,
-0.07422331720590591,
0.019189821556210518,
-0.043920669704675674,
0.010506125167012215,
-0.005506773479282856,
-0.03427140787243843,
-0.02800002321600914,
0.007873507216572762,
-0.020306777209043503,
-0.048806723207235336,
0.006721039768308401,
-0.011297703720629215,
-0.011527861468493938,
-0.01590193808078766,
0.03252631425857544,
-0.04733787477016449,
0.06297741085290909,
0.018903911113739014,
-0.005564739927649498,
0.070999875664711,
-0.027459019795060158,
-0.011415866203606129,
-0.028013627976179123,
-0.0019586572889238596,
-0.05927194654941559,
-0.0465753935277462,
-0.019324274733662605,
-0.012732945382595062,
0.03422568738460541,
0.05529196932911873,
0.0422917939722538,
-0.001690224395133555,
-0.03215460479259491,
-0.009467856027185917,
0.0448923259973526,
-0.025644585490226746,
-0.06021082401275635,
-0.03212374821305275,
0.0406213216483593,
0.060146480798721313,
-0.017190488055348396,
0.0085653867572546,
-0.02738768979907036,
0.048125971108675,
0.03886852040886879,
-0.031265921890735626,
-0.023117629811167717,
-0.019013239070773125,
-0.026948045939207077,
-0.03717971220612526,
-0.0504927821457386,
-0.004115563351660967,
0.030827932059764862,
0.045480359345674515,
-0.022906439378857613,
-0.005309672094881535,
-0.07645559310913086,
0.011743217706680298,
0.03254871442914009,
-0.005725385621190071,
-0.009492144919931889,
-0.023143330588936806,
-0.008325202390551567,
0.09688301384449005,
0.02988635003566742,
-0.03782167658209801,
-0.010903085581958294,
0.010979645885527134,
-0.02393367514014244,
0.03774749115109444,
-0.020123133435845375,
-0.06963971257209778,
-0.028548797592520714,
-0.07795294374227524,
-0.028144199401140213,
-0.016527820378541946,
-0.03039204515516758,
-0.005636157933622599,
-0.020970413461327553,
0.048055972903966904,
-0.028212638571858406,
0.06873442232608795,
0.04086218774318695,
-0.014928347431123257,
-0.014745500870049,
-0.02802644670009613,
0.005382950883358717,
0.028067929670214653,
0.012780050747096539,
-0.020563993602991104,
0.040365345776081085,
-0.006127818953245878,
-0.03103146329522133,
-0.013748418539762497,
-0.018473679199814796,
0.0059096538461744785,
-0.021526623517274857,
0.013270515948534012,
0.0705443024635315,
0.046858783811330795,
0.03479475900530815,
0.04134879261255264,
0.02215145155787468,
-0.01792086474597454,
0.04035506024956703,
-0.05891120061278343,
0.037535760551691055,
-0.0030762148089706898,
-0.04004136100411415,
-0.004320609383285046,
-0.0016818722942844033,
-0.0019765833858400583,
0.05517471581697464,
0.007047347258776426,
0.0075604114681482315,
-0.011534263379871845,
-0.0079812528565526,
0.04859607666730881,
-0.053206633776426315,
-0.02695128321647644,
0.0025554827880114317,
0.0022997877094894648,
0.006964223459362984,
0.019773894920945168,
0.021973108872771263,
-0.05777004733681679,
0.024712638929486275,
-0.04408041760325432,
-0.039637889713048935,
0.013730655424296856,
0.01197521761059761,
0.03328144550323486,
0.03523850440979004,
-0.04252432659268379,
-0.00760566396638751,
-0.0021965180058032274,
-0.010451066307723522,
0.006755214184522629,
-0.01967577449977398,
0.027123205363750458,
-0.01576404646039009,
0.031900860369205475,
0.014858979731798172,
-0.023778965696692467,
-0.0033345252741128206,
0.006423493847250938,
-0.01585070975124836,
-0.06002786010503769,
-0.008823459967970848,
-0.029739560559391975,
0.051784686744213104,
0.024010049179196358,
0.04855112358927727,
-0.019175009801983833,
0.021587247028946877,
0.029650401324033737,
-0.010747030377388,
-0.010436983779072762,
-0.01355071272701025,
-0.01786847598850727,
0.024255352094769478,
-0.03180333226919174,
-0.04365278035402298,
0.014944512397050858,
-0.028427699580788612,
0.06820851564407349,
-0.08439422398805618,
0.0026537589728832245,
0.03610914200544357,
-0.015445862896740437,
0.046065978705883026,
-0.0031583504751324654,
0.06450962275266647,
-0.056796085089445114,
-0.010424387641251087,
0.021609991788864136,
0.00036543505848385394,
-0.05423654988408089,
0.013389830477535725,
0.003463256172835827,
0.021386612206697464,
-0.05023057758808136,
-0.0064018964767456055,
0.000567504670470953,
-0.04383024573326111,
0.06253013014793396,
-0.020896214991807938,
0.06749886274337769,
0.015455519780516624,
0.037891753017902374,
-0.029366496950387955,
-0.013786579482257366,
-0.07518060505390167,
-0.027595287188887596,
-0.022002587094902992,
0.0059575969353318214,
-0.0583309605717659,
0.08289407938718796,
0.024654241278767586,
-0.03200393542647362,
0.026951706036925316,
-0.0029613531660288572,
0.010762921534478664,
-0.04821150004863739,
-0.021983465179800987,
0.043102819472551346,
0.014514269307255745,
0.037905704230070114,
-0.03178826719522476,
0.00010509681305848062,
-0.05022391304373741,
-0.04939338564872742,
0.017022185027599335,
0.00770142488181591,
-0.0364929623901844,
0.027039533481001854,
0.003232905175536871,
-0.017413165420293808,
-0.014585549011826515,
-0.03410166874527931,
0.004567778669297695,
-0.015367495827376842,
0.02332433871924877,
-0.02349022403359413,
0.015920378267765045,
0.005375952459871769,
0.04349373281002045,
-0.003870538668707013,
-0.029371198266744614,
-0.01692730188369751,
-0.012161022052168846,
0.02365051954984665,
-0.019442902877926826,
0.000010449763976794202,
-0.04403546452522278,
0.047641780227422714,
0.04456239193677902,
-0.019692637026309967,
0.04300532117486,
0.049633391201496124,
-0.011300169862806797,
-0.05038691312074661,
0.07926950603723526,
0.028920896351337433,
-0.012936352752149105,
-0.011676591821014881,
0.007320732809603214,
-0.04764246940612793,
-0.024704867973923683,
-0.04302270710468292,
0.047633249312639236,
0.01672174595296383,
-0.06411899626255035,
-0.05170894414186478,
0.02188126929104328,
0.0506993867456913,
-0.02353731356561184,
-0.01319922786206007,
0.05659109354019165,
0.020106038078665733,
0.07158542424440384,
-0.042764030396938324,
-0.04788852855563164,
0.00041163110290654004,
0.008564498275518417,
-0.03529318422079086,
-0.04952077567577362,
-0.05602022260427475,
0.0037880123127251863,
0.010217930190265179,
-0.00949100311845541,
0.01883758045732975,
0.014933896251022816,
0.04885488748550415,
-0.062111418694257736,
-0.006670343689620495,
-0.04428853467106819,
-0.0395292267203331,
-0.0480169951915741,
-0.009835714474320412,
-0.08164965361356735,
-0.023055825382471085,
0.04896136000752449,
-0.016578538343310356,
-0.014171364717185497,
-0.027694642543792725,
-0.03800543397665024,
-0.052551038563251495,
0.0025900844484567642,
-0.004260263871401548,
0.028167158365249634,
-0.027036817744374275,
0.03435991331934929,
-0.00853407196700573,
0.0011393449967727065,
0.02206764928996563,
-0.02937491238117218,
-0.07557407766580582,
0.018248220905661583,
0.06305596232414246,
-0.006846301723271608,
-0.011505164206027985,
-0.04400806128978729,
0.0478239469230175,
0.022031914442777634,
0.02942660078406334,
-0.017070356756448746,
-0.05210547149181366,
0.009693491272628307,
0.0017110351473093033,
0.03173366189002991,
0.01072882954031229,
0.011168859899044037,
-0.027881942689418793,
-0.02586490474641323,
-0.01129090040922165,
-0.05972275882959366,
-0.018206417560577393,
0.011821157298982143,
0.02232266217470169,
-0.035761743783950806,
0.0038320093881338835,
0.010811233893036842,
0.05634559318423271,
0.0028459939640015364,
-0.02626802958548069,
-0.01709177903831005,
0.0005680610775016248,
0.018850022926926613,
-0.04253110662102699,
0.029860883951187134,
-0.03021458350121975,
0.04784880951046944,
-0.0005888814921490848,
0.054330576211214066,
0.04160744696855545,
-0.06918597966432571,
-0.023080484941601753,
-0.04799607768654823,
-0.0034663155674934387,
0.04694265499711037,
0.05043904110789299,
-0.0035651051439344883,
0.04478660225868225,
0.030046729370951653,
-0.0164902675896883,
-0.0629294216632843,
0.016264265403151512,
0.05330543592572212,
0.03368300572037697,
0.04878560081124306,
0.030912145972251892,
0.016851220279932022,
-0.01432891096919775,
0.056309010833501816,
0.06266193091869354,
0.025439748540520668,
0.040787119418382645,
0.02964477613568306,
-0.05735570192337036,
0.003052003215998411,
0.019832702353596687,
-0.050781771540641785,
-0.021070878952741623,
-0.002254374325275421,
-0.012284629046916962,
-0.01858477108180523,
0.03969014436006546,
0.052267417311668396,
0.07373751699924469,
-0.011843331158161163,
0.006761849857866764,
0.043390318751335144,
-0.013334083370864391,
0.00989384576678276,
0.03225551173090935,
-0.04599761590361595,
-0.07943505793809891,
-0.050688959658145905,
0.022510217502713203,
-0.0022299617994576693,
-0.007820556871592999,
0.043448224663734436,
0.04273286461830139,
-0.04433748871088028,
-0.00584603613242507,
0.06598544120788574,
0.044381044805049896,
0.03886377438902855,
-0.004291355609893799,
-0.02523626945912838,
-0.023617787286639214,
-0.033296722918748856,
-0.017809083685278893,
-0.037288255989551544,
0.01961636170744896,
0.000011892632755916566,
-0.09377209842205048,
0.06037469208240509,
-0.019034042954444885,
-0.02343399077653885,
-0.06638548523187637,
-0.027351778000593185,
0.03924096003174782,
0.0022806748747825623,
-0.0595787838101387,
-0.026506558060646057,
0.001377369393594563,
-0.023294080048799515,
0.013835914433002472,
-0.023763956502079964,
-0.04605445638298988,
0.003933114465326071,
0.04184303805232048,
0.02277938649058342,
0.008409978821873665,
-0.0236753448843956,
-0.002632394665852189,
-0.01809666119515896,
0.04159945994615555,
-0.03969132900238037,
0.020657341927289963,
-0.01969790644943714,
0.004419395234435797,
-0.007781564723700285,
0.047515619546175,
-0.06282658874988556,
0.012311611324548721,
-0.01931283064186573,
0.009830928407609463,
0.04781504347920418,
-0.09454529732465744,
-0.0032846301328390837,
-0.04864325746893883,
0.042877137660980225,
-0.025045238435268402,
-0.0004147041472606361,
-0.052770376205444336,
-0.03429429605603218,
-0.004612641874700785,
-0.001043068477883935,
0.03916727006435394,
0.0035400849301368,
0.0626082792878151,
0.06549767404794693,
0.0002147340856026858,
-0.06118646636605263,
-0.06824655830860138,
0.02874087728559971,
0.036504440009593964,
-0.04127700254321098,
-0.010425513610243797,
0.006971972994506359,
-0.02349567599594593,
-0.005476178135722876,
-0.02361971326172352,
-0.005542442202568054,
-0.010163349099457264,
0.08578808605670929,
0.04044058173894882,
-0.01621181331574917,
0.0025890846736729145,
-0.08194105327129364,
0.022114083170890808,
-0.0077854241244494915,
0.03893519192934036,
-0.030293159186840057,
-0.028108365833759308,
0.008858470246195793,
0.03425266966223717,
0.04063660651445389,
-0.07018980383872986,
0.012495571747422218,
0.008569512516260147,
-0.026939554139971733,
0.08726149052381516,
0.01727519929409027,
-0.010042618960142136,
0.015506965108215809,
-0.009772077202796936,
0.008136818185448647,
-0.00623840419575572,
0.058829788118600845,
0.024466993287205696,
0.018081119284033775,
-0.04030214250087738,
0.00987208355218172,
-0.0066559575498104095,
-0.00566449761390686,
0.04575616866350174,
0.008768870495259762,
0.009765236638486385,
-0.038658492267131805,
-0.008331019431352615,
-0.013602383434772491,
-0.03171204403042793,
-0.01842767931520939,
-0.00710166385397315
] |
<p>Squeezed electromagnetic vacuum does have a renormalized energy density smaller than the vacuum. So it makes it in my opinion a inconspicuous candidate for a dark energy carrier.</p>
<p>Are there observatories at the moment attempting to detect squeezed radiation from astrophysical and cosmic background sources? If not, What sort of equipment do you need to measure squeezed vacuum radiation?</p> | g1241 | [
-0.021662505343556404,
0.011437000706791878,
0.005223107058554888,
-0.0528857447206974,
0.010677313432097435,
0.06164390966296196,
-0.05897224321961403,
0.019752314314246178,
-0.010676044970750809,
-0.018303880468010902,
0.04638780653476715,
0.04406844079494476,
-0.028570689260959625,
-0.03816361352801323,
0.02983194962143898,
0.01756245829164982,
0.01982695795595646,
-0.018910899758338928,
0.03178909048438072,
-0.024498820304870605,
0.005873420741409063,
-0.013535150326788425,
0.02545853517949581,
-0.052047260105609894,
-0.03834916651248932,
0.026349343359470367,
0.02878352627158165,
-0.02675555646419525,
-0.005895944777876139,
-0.05431687831878662,
0.03249103203415871,
-0.013101913034915924,
0.09862852841615677,
0.011919810436666012,
0.009817000478506088,
0.0015400158008560538,
0.028492402285337448,
0.048838112503290176,
-0.03936166688799858,
0.014673984609544277,
-0.0031513215508311987,
-0.003479305189102888,
-0.0431026816368103,
0.031385160982608795,
-0.009207642637193203,
0.035735853016376495,
-0.025775443762540817,
0.05576296150684357,
0.05428525060415268,
0.013480759225785732,
0.021756373345851898,
-0.009095361456274986,
0.059915296733379364,
0.056489497423172,
0.03511404991149902,
-0.06113898754119873,
-0.07105752825737,
-0.013231969438493252,
0.04654684662818909,
-0.03596784174442291,
-0.04671194404363632,
-0.018501581624150276,
0.02842782251536846,
0.014139632694423199,
0.014183706603944302,
0.024824179708957672,
-0.034843508154153824,
-0.04981619119644165,
0.01015087403357029,
-0.03186248987913132,
0.040086500346660614,
-0.041409481316804886,
-0.029555082321166992,
0.03225097432732582,
0.005905816797167063,
-0.03240044042468071,
-0.004846490919589996,
-0.05814104899764061,
-0.0035020760260522366,
0.007543918676674366,
-0.016313420608639717,
-0.03112882748246193,
-0.009968303143978119,
-0.02777191810309887,
0.06612009555101395,
-0.046088214963674545,
-0.03217208757996559,
-0.004466669633984566,
0.04727314040064812,
-0.006896830163896084,
0.02528720535337925,
0.0001239066623384133,
0.026728248223662376,
-0.03145041689276695,
0.07223706692457199,
0.04553217440843582,
0.026924315840005875,
0.06669958680868149,
-0.050102926790714264,
-0.03545809164643288,
0.015971671789884567,
0.02086813747882843,
-0.03759828954935074,
-0.011951836757361889,
0.0437447763979435,
-0.020078981295228004,
-0.06175444647669792,
-0.03505101054906845,
0.013333186507225037,
-0.016542280092835426,
-0.02914973348379135,
-0.027247821912169456,
0.011082319542765617,
0.002251268830150366,
-0.06527315825223923,
-0.026977894827723503,
-0.012323805131018162,
-0.04161602258682251,
-0.01618300750851631,
0.06948862969875336,
-0.0007905520033091307,
0.05065876245498657,
-0.019459255039691925,
0.03056439198553562,
0.011669964529573917,
0.03448411449790001,
-0.0037576465401798487,
0.007728095166385174,
-0.0064407228492200375,
0.0001849059626692906,
0.0023856854531913996,
-0.0075921970419585705,
-0.0399533174932003,
-0.03473648428916931,
-0.03484237939119339,
0.029876701533794403,
-0.01796918362379074,
0.0007326283375732601,
0.011823560111224651,
0.03110508807003498,
0.03061668761074543,
-0.002123634796589613,
-0.03257979825139046,
0.021213367581367493,
0.06116210296750069,
-0.011891531758010387,
-0.019645245745778084,
0.04251129552721977,
0.03596452996134758,
0.03245458006858826,
0.012771056033670902,
0.0349411703646183,
0.048438459634780884,
-0.011390098370611668,
-0.0150008425116539,
0.003561995457857847,
0.03658508509397507,
0.001658319728448987,
0.018600216135382652,
0.014071191661059856,
0.016649235039949417,
-0.0006406144239008427,
0.01336476020514965,
0.029938751831650734,
0.06207236647605896,
-0.015173627063632011,
0.006208797451108694,
-0.03747983276844025,
0.04142633453011513,
-0.0015599618200212717,
-0.03974366560578346,
-0.009828422218561172,
0.02518681436777115,
-0.012008809484541416,
-0.013182471506297588,
0.0517091304063797,
0.05947723239660263,
-0.0198176559060812,
0.006012534722685814,
-0.009069515392184258,
0.010508588515222073,
-0.04046015441417694,
0.03731610253453255,
-0.03641403466463089,
0.02290930785238743,
-0.041140735149383545,
-0.06630976498126984,
-0.019157566130161285,
0.016206761822104454,
-0.016896570101380348,
0.027340732514858246,
-0.025689953938126564,
0.004335405305027962,
0.062877357006073,
-0.021250423043966293,
-0.031041281297802925,
0.003381115850061178,
-0.03826426342129707,
0.00890025682747364,
0.0535600446164608,
-0.010876311920583248,
0.04593798890709877,
0.07879677414894104,
0.053886186331510544,
0.028393756598234177,
0.028742559254169464,
-0.02318531833589077,
-0.02565118856728077,
0.051315028220415115,
-0.012924136593937874,
0.027194581925868988,
-0.008860268630087376,
0.048730842769145966,
-0.02965938299894333,
-0.04555623233318329,
0.0694475844502449,
-0.04764938727021217,
-0.016991091892123222,
-0.008388878777623177,
0.024113671854138374,
-0.04477827996015549,
-0.015054609626531601,
0.04124514013528824,
0.00656066695228219,
0.01875673234462738,
0.009499474428594112,
-0.09605710953474045,
0.028372986242175102,
0.04204213619232178,
-0.0064142001792788506,
-0.003236605552956462,
0.017433812841773033,
-0.022379890084266663,
0.03398893028497696,
0.004396857228130102,
0.017769264057278633,
-0.05104479566216469,
-0.04933809116482735,
0.00326991337351501,
0.018031319603323936,
-0.019560284912586212,
-0.0027777852956205606,
-0.013082234188914299,
0.03026496432721615,
0.020692991092801094,
-0.04240395128726959,
0.005159981548786163,
0.03335382416844368,
0.07864361256361008,
-0.0633072555065155,
-0.00477101095020771,
0.019214848056435585,
0.002247275086119771,
-0.00696090841665864,
-0.018768124282360077,
0.03090658038854599,
-0.006889414042234421,
0.027915995568037033,
-0.07092366367578506,
-0.03409365192055702,
0.045349135994911194,
0.004542676266282797,
0.02067740447819233,
0.013061832636594772,
0.015167190693318844,
-0.010731491260230541,
0.009069827385246754,
0.0447242446243763,
-0.02757488191127777,
-0.01860116794705391,
-0.011788660660386086,
0.048338811844587326,
-0.0018623447977006435,
-0.06895241141319275,
0.0493631437420845,
0.010272137820720673,
-0.03878229111433029,
0.0097800949588418,
0.04727080836892128,
-0.08430132269859314,
-0.0006406483589671552,
0.0014854823239147663,
0.0030469270423054695,
-0.03588974103331566,
-0.05893692374229431,
-0.0641983225941658,
-0.052396856248378754,
-0.05584889277815819,
-0.01220564916729927,
-0.03201223164796829,
-0.004920594859868288,
0.0031008783262223005,
-0.021817700937390327,
0.012472538277506828,
-0.027700748294591904,
-0.008983741514384747,
0.019010035321116447,
0.041174232959747314,
0.00996523816138506,
0.022802967578172684,
0.010102000087499619,
-0.10242391377687454,
0.008955875411629677,
0.004192572087049484,
0.025224022567272186,
-0.0052599431946873665,
-0.026978857815265656,
-0.028310103341937065,
0.00950932502746582,
0.06202283129096031,
-0.03452400863170624,
0.05031449347734451,
0.022029360756278038,
0.025954807177186012,
0.005691809579730034,
-0.06874211877584457,
0.007953593507409096,
-0.005771607626229525,
-0.02530592493712902,
0.019767839461565018,
0.08299073576927185,
0.03847743570804596,
0.027292771264910698,
-0.038538962602615356,
0.08673422038555145,
0.040116045624017715,
-0.019613875076174736,
0.0065940567292273045,
-0.024248525500297546,
-0.005660761147737503,
0.008895108476281166,
-0.02155398391187191,
0.006211958359926939,
-0.0018000314012169838,
-0.04041697457432747,
-0.010362787172198296,
-0.059099484235048294,
0.057238105684518814,
0.06423389166593552,
-0.009193996898829937,
-0.004534904379397631,
0.024656491354107857,
-0.016818419098854065,
0.02985076792538166,
-0.005141708068549633,
0.02736111730337143,
-0.004110316745936871,
0.0080301808193326,
0.05192142724990845,
-0.07514261454343796,
0.0010403050109744072,
-0.002740418305620551,
0.07230600714683533,
0.00877365842461586,
0.01566799357533455,
0.021532822400331497,
-0.02576257288455963,
-0.011613266542553902,
0.05086169019341469,
-0.028568685054779053,
-0.011419682763516903,
-0.010481245815753937,
0.0319395437836647,
-0.10675328969955444,
-0.022057274356484413,
-0.06634682416915894,
-0.013952511362731457,
0.0007766280323266983,
-0.027178339660167694,
0.05955749377608299,
0.014775683172047138,
-0.011626580730080605,
0.006191419903188944,
0.06078631803393364,
0.026453780010342598,
-0.014485041610896587,
-0.01067164447158575,
-0.0037407539784908295,
0.007849329151213169,
0.004184979945421219,
-0.0010423155035823584,
0.03707042708992958,
-0.00962560810148716,
-0.007211589254438877,
0.0008486300939694047,
-0.012121962383389473,
-0.03736964985728264,
0.025192122906446457,
0.016658930107951164,
-0.07408023625612259,
0.022786488756537437,
-0.005213025026023388,
-0.03707285225391388,
0.015605146996676922,
-0.01154898852109909,
-0.05011334642767906,
0.10683673620223999,
-0.03718351945281029,
0.04432564601302147,
0.036670781672000885,
0.009086724370718002,
0.03929007798433304,
0.06008712947368622,
-0.018634194508194923,
-0.02055252157151699,
0.008449536748230457,
0.007137881126254797,
0.05400402471423149,
-0.02369055151939392,
-0.018135912716388702,
0.014406383968889713,
-0.01564319059252739,
-0.04232752323150635,
-0.0003088675148319453,
0.018063295632600784,
-0.06732672452926636,
0.00014248206571210176,
-0.020369060337543488,
0.04443279281258583,
-0.007435076870024204,
0.008393856696784496,
0.026788441464304924,
0.02616710588335991,
0.00018780468963086605,
-0.08512356132268906,
0.0820087119936943,
0.05607897788286209,
-0.0045162383466959,
-0.010419500060379505,
0.009468925185501575,
0.0552065372467041,
-0.01863270252943039,
0.035065434873104095,
0.04299335554242134,
0.05572701618075371,
0.020832862704992294,
-0.027139974758028984,
-0.04620245471596718,
0.050547413527965546,
-0.006071958690881729,
0.09182658791542053,
-0.08851451426744461,
-0.0023982804268598557,
0.011752326041460037,
-0.005262468941509724,
0.0592767558991909,
-0.0013314695097506046,
-0.024485165253281593,
-0.006953550968319178,
0.030076680704951286,
0.003345190081745386,
-0.02862057462334633,
-0.03571411222219467,
-0.010830710642039776,
0.057718317955732346,
-0.017083657905459404,
0.035516805946826935,
0.006131727714091539,
0.05668695271015167,
0.023599274456501007,
-0.03387600556015968,
0.0026496860664337873,
0.08406417071819305,
-0.030178338289260864,
0.01604035124182701,
0.00558451097458601,
-0.07904338091611862,
0.006117986049503088,
0.006137805990874767,
-0.0301656611263752,
-0.041444551199674606,
0.0030625842045992613,
0.003971310332417488,
-0.03240007534623146,
-0.05055324360728264,
-0.010905522853136063,
-0.02768329344689846,
-0.00849534198641777,
-0.028678180649876595,
0.009690812788903713,
-0.010737704113125801,
0.0030596607830375433,
-0.031021665781736374,
-0.013230709359049797,
-0.02230561524629593,
0.052765555679798126,
-0.05457991361618042,
-0.00122102873865515,
-0.05159137770533562,
-0.012441221624612808,
0.033799659460783005,
0.03234976902604103,
0.004214020445942879,
-0.021716469898819923,
-0.034690506756305695,
0.035147588700056076,
-0.036526791751384735,
-0.022142209112644196,
-0.030821463093161583,
-0.034502435475587845,
-0.014716783538460732,
-0.027959950268268585,
-0.02023204043507576,
0.008842146955430508,
-0.007145645562559366,
-0.027737515047192574,
0.006333875935524702,
0.009631766006350517,
0.061929620802402496,
0.05227440595626831,
-0.041414774954319,
-0.0009152756538242102,
-0.054224174469709396,
0.022849567234516144,
0.01316571794450283,
0.02654636837542057,
-0.03508532792329788,
0.03317292034626007,
-0.02068660594522953,
-0.08184678852558136,
-0.04961714148521423,
0.035084694623947144,
0.07694949954748154,
0.00568920373916626,
0.01380958128720522,
-0.014145638793706894,
0.006175484508275986,
0.09261219203472137,
-0.04333648458123207,
-0.05264183133840561,
0.03256819769740105,
-0.012837649323046207,
0.02890900894999504,
-0.036511220037937164,
-0.009735824540257454,
0.011906369589269161,
0.035710565745830536,
0.03426145762205124,
0.018165845423936844,
0.008135813288390636,
-0.012654958292841911,
-0.02317511849105358,
-0.0640726387500763,
0.04926526919007301,
0.005910893902182579,
0.03526119515299797,
-0.03757552430033684,
0.04098329693078995,
-0.0029772226698696613,
-0.052630338817834854,
-0.03435705974698067,
-0.0276845283806324,
-0.009445755742490292,
0.007184018846601248,
-0.02803087793290615,
-0.05978398770093918,
-0.012430842034518719,
0.012703376822173595,
-0.07420097291469574,
0.018275540322065353,
-0.007383313961327076,
-0.03288772329688072,
0.03786437213420868,
-0.0051374309696257114,
-0.031281985342502594,
-0.027301495894789696,
0.027298687025904655,
-0.054919302463531494,
-0.012643812224268913,
-0.010748242028057575,
-0.06506825238466263,
0.05115164816379547,
-0.022524025291204453,
-0.02154070883989334,
0.02528221160173416,
-0.09741845726966858,
0.04392894729971886,
-0.024243559688329697,
-0.019467458128929138,
-0.045466598123311996,
0.09398007392883301,
0.015355079434812069,
0.09359676390886307,
-0.01982899196445942,
-0.010224704630672932,
0.04383450746536255,
-0.02928345277905464,
0.029517000541090965,
-0.015461661852896214,
0.01364334486424923,
0.024234024807810783,
0.03389609605073929,
0.013622010126709938,
-0.05537799745798111,
-0.0692170187830925,
-0.011173094622790813,
-0.034689243882894516,
0.04206714406609535,
-0.02015727199614048,
0.03283630684018135,
0.01334154698997736,
-0.006379198748618364,
-0.055344004184007645,
-0.015828046947717667,
0.019902527332305908,
-0.04384458437561989,
-0.010598242282867432,
0.017924020066857338,
0.04502424970269203,
0.014478136785328388,
-0.05966439098119736,
0.014081916771829128,
-0.05889040231704712,
0.006811265368014574,
-0.012923386879265308,
-0.03807060793042183,
0.02551022358238697,
0.008903094567358494,
0.014203345403075218,
-0.02075979672372341,
-0.00380505807697773,
-0.0064836046658456326,
-0.06660842150449753,
0.011772758327424526,
-0.018499063327908516,
0.03565571457147598,
-0.03290446102619171,
-0.03510762006044388,
0.0730966180562973,
-0.01156177744269371,
0.025479871779680252,
-0.012080786749720573,
0.035679928958415985,
-0.022210657596588135,
0.010476906783878803,
0.03698389604687691,
-0.000337119767209515,
0.012458114884793758,
0.014005792327225208,
-0.041636426001787186,
0.01366700790822506,
-0.02326219156384468,
-0.02528272196650505,
0.0230593029409647,
0.011319903656840324,
0.06634106487035751,
0.03015037439763546,
0.028246326372027397,
0.04938090592622757,
-0.040339987725019455,
-0.01864716038107872,
-0.02667768858373165,
0.022349314764142036,
-0.01731732487678528,
-0.07417281717061996,
0.11238671094179153,
0.010385232977569103,
-0.025250837206840515,
-0.04001125693321228,
-0.11332512646913528,
0.044645149260759354,
-0.06047855690121651,
-0.06264137476682663,
0.006048991810530424,
-0.013298960402607918,
-0.029166826978325844,
-0.037197526544332504,
-0.04182438924908638,
0.014996235258877277,
-0.027269748970866203,
0.03239990398287773,
-0.00962133426219225,
-0.062248051166534424,
-0.028931381180882454,
0.014504192396998405,
-0.08175847679376602,
-0.010998297482728958,
-0.04097245633602142,
0.030506517738103867,
0.0037733453791588545,
-0.04783078655600548,
0.011478553526103497,
-0.004486359655857086,
0.01958097517490387,
0.021814808249473572,
0.07682137936353683,
-0.03582931309938431,
-0.05782792344689369,
0.05234652757644653,
-0.004051923751831055,
-0.032453253865242004,
-0.026089638471603394,
0.015965435653924942,
-0.047358304262161255,
0.007644870784133673,
-0.013299851678311825,
0.02641916461288929,
0.02789846621453762,
-0.02597174420952797,
-0.051766764372587204,
-0.06034794822335243,
0.04460786283016205,
0.025492368265986443,
0.0017404556274414062,
-0.003521524602547288,
0.021857239305973053,
0.05100655183196068,
-0.013078499585390091,
-0.04853742569684982,
0.06488785147666931,
0.010909766890108585,
-0.017093252390623093,
-0.03743769973516464,
0.044761840254068375,
0.028873156756162643,
0.014209690503776073,
-0.0584956556558609,
0.041271667927503586,
0.029228905215859413,
-0.07275771349668503,
0.03898065164685249,
0.005662707146257162,
0.020671486854553223,
0.011310882866382599,
0.02497883513569832,
-0.003823705017566681,
0.007573456969112158,
0.01887795515358448,
0.009726854972541332,
-0.0451190248131752,
0.05555930361151695,
0.007187928073108196,
0.04363435506820679,
-0.02698543667793274,
-0.013513470068573952,
-0.011527705937623978,
0.0006346675218082964,
0.05912068858742714,
0.038949158042669296,
0.031892694532871246,
-0.0090035330504179,
-0.04261366277933121,
-0.04809124395251274,
-0.039378613233566284,
0.060255102813243866,
-0.02762196771800518,
-0.02355847880244255,
-0.03250405192375183,
0.04650339484214783,
-0.005033234134316444,
0.0050576175563037395,
-0.032581061124801636,
-0.001910272752866149,
0.04984758049249649,
-0.003027835162356496,
-0.010825233533978462,
0.017815664410591125,
-0.03445415943861008,
-0.030745625495910645,
0.024576321244239807,
0.09366889297962189,
0.049488648772239685,
0.011994276195764542,
-0.03957529366016388,
-0.06298325955867767,
0.0022028484381735325,
0.026507990434765816,
0.03552565351128578
] |
<p>If the atmosphere is filled with electromagnetic waves all oscillating at different wavelengths and speeds how is it that they don’t all interfere with each other? For example turning on your light seems to have no effect on the sound coming from your radio. </p> | g1242 | [
0.06926631927490234,
-0.017526494339108467,
0.01463993638753891,
0.0394730269908905,
0.06377402693033218,
0.06383275240659714,
0.025967711582779884,
0.008079118095338345,
-0.01941193826496601,
-0.041047606617212296,
0.04946335405111313,
-0.027484703809022903,
-0.03585238382220268,
0.054565493017435074,
-0.03505812585353851,
0.004285168368369341,
-0.03021945245563984,
0.004368414171040058,
-0.013391113840043545,
0.02997693046927452,
0.01975375972688198,
-0.025034695863723755,
-0.019916335120797157,
-0.056158434599637985,
-0.06690768152475357,
0.0003620977804530412,
0.05281528830528259,
-0.08662478625774384,
-0.048177607357501984,
-0.01307147927582264,
-0.028090761974453926,
-0.027790533378720284,
0.05184883996844292,
0.004330224357545376,
-0.05288553237915039,
-0.03932750225067139,
-0.013603249564766884,
0.03568541631102562,
-0.012138208374381065,
0.06224578619003296,
0.020022470504045486,
0.0071556419134140015,
0.013168520294129848,
-0.005127526354044676,
0.015283661894500256,
-0.05646602809429169,
-0.02463177591562271,
0.024775519967079163,
-0.0115875955671072,
-0.03487662225961685,
-0.039787136018276215,
-0.05296998471021652,
-0.01380408089607954,
0.05735970661044121,
0.02464296482503414,
-0.009759939275681973,
0.0390382818877697,
-0.0276274885982275,
0.026694927364587784,
0.037291280925273895,
-0.009503585286438465,
0.004673625808209181,
-0.001686458708718419,
0.05779913440346718,
-0.023136192932724953,
-0.029753707349300385,
-0.015117495320737362,
-0.06593448668718338,
0.06103374436497688,
-0.00823813583701849,
0.019641684368252754,
-0.04350285977125168,
-0.0854453444480896,
-0.01560195628553629,
0.013086742721498013,
0.08538452535867691,
0.022150075063109398,
0.07488726079463959,
0.04832238703966141,
0.04916952922940254,
-0.02409943751990795,
-0.022929131984710693,
0.01282696146517992,
0.00030028921901248395,
-0.006691244430840015,
-0.01646869257092476,
0.008693528361618519,
-0.0361611433327198,
-0.0006348942406475544,
-0.03592366352677345,
0.04341588541865349,
-0.07494599372148514,
0.023575184866786003,
0.0039281114004552364,
-0.004502380266785622,
-0.016177775338292122,
-0.011301220394670963,
0.06363293528556824,
0.03413394093513489,
0.006673872005194426,
-0.025775743648409843,
-0.03133031353354454,
0.003159173531457782,
0.016529273241758347,
0.011425766162574291,
0.008154753595590591,
-0.02278956025838852,
0.004236407577991486,
-0.016000140458345413,
-0.004454331938177347,
-0.04606562852859497,
-0.002675844356417656,
-0.04426157474517822,
0.00813696626573801,
-0.03971952572464943,
-0.02468004636466503,
0.04106486216187477,
-0.008348338305950165,
0.016179967671632767,
0.036097753793001175,
0.035654034465551376,
0.03671121224761009,
-0.0299781896173954,
-0.009327159263193607,
-0.009815632365643978,
0.004925217013806105,
0.008043322712182999,
-0.007128182332962751,
0.023409830406308174,
-0.06738913059234619,
-0.0060004498809576035,
0.06004966422915459,
-0.018023919314146042,
0.023800790309906006,
-0.01717819646000862,
-0.04774243384599686,
0.04739117994904518,
-0.014829209074378014,
0.02512134611606598,
-0.012874767184257507,
0.042101603001356125,
-0.006203754805028439,
0.0670243576169014,
-0.030600596219301224,
-0.036017511039972305,
-0.003981437999755144,
-0.008057685568928719,
-0.05000507831573486,
0.02323540486395359,
-0.031008131802082062,
-0.007606700994074345,
0.05287553742527962,
0.04215438291430473,
0.002670582849532366,
-0.059938184916973114,
-0.004075754899531603,
-0.013491874560713768,
0.0046443575993180275,
0.00018478004494681954,
0.013159985654056072,
0.03560274839401245,
0.024684354662895203,
-0.00806304719299078,
0.06138041615486145,
-0.026002373546361923,
0.04442330449819565,
-0.03245488181710243,
-0.033476218581199646,
-0.0043141888454556465,
0.04922442510724068,
-0.06658782064914703,
-0.0034038859885185957,
-0.030643511563539505,
0.04110702499747276,
-0.0028166999109089375,
0.06717674434185028,
0.08891485631465912,
-0.03167867287993431,
0.012771058827638626,
0.019026979804039,
-0.007085474207997322,
-0.044998280704021454,
-0.07173296064138412,
-0.09659411758184433,
-0.02749716304242611,
0.00626671127974987,
-0.01350440364331007,
-0.0403292216360569,
-0.08514520525932312,
-0.006323841400444508,
0.002914055483415723,
-0.0439002625644207,
-0.05753699317574501,
-0.028249889612197876,
0.02426106482744217,
-0.04501805081963539,
-0.06037268415093422,
-0.002157077193260193,
-0.0052582873031497,
-0.002319467021152377,
-0.0032644113525748253,
0.032404325902462006,
0.06024964526295662,
0.0072348942048847675,
0.018322840332984924,
-0.010858642868697643,
-0.008881529793143272,
-0.029629679396748543,
0.05568387731909752,
0.0275424737483263,
0.03098975121974945,
0.016348691657185555,
0.0557582788169384,
0.04837590083479881,
-0.016804054379463196,
0.007130294572561979,
-0.05118178576231003,
-0.003209970658645034,
0.003078313311561942,
-0.015681171789765358,
-0.0009979686001315713,
0.001683708862401545,
-0.03103611059486866,
-0.05206814035773277,
-0.02741003967821598,
-0.05153505131602287,
-0.05590441823005676,
0.00030676438473165035,
-0.026026399806141853,
0.0013609116431325674,
0.02244834043085575,
-0.020876023918390274,
0.0016523058293387294,
-0.034124042838811874,
-0.014010659419000149,
0.03278645500540733,
0.008448188193142414,
-0.0038885455578565598,
-0.028488369658589363,
-0.028403375297784805,
0.004381015431135893,
-0.02659974806010723,
-0.018390590324997902,
0.038612209260463715,
-0.0071057830937206745,
-0.07622450590133667,
-0.020774925127625465,
-0.011482780799269676,
-0.03587470203638077,
0.006089426577091217,
0.04358173534274101,
0.04886389151215553,
-0.033321261405944824,
0.002493765205144882,
-0.004809391684830189,
-0.05132044106721878,
-0.030462276190519333,
0.012456303462386131,
-0.03343139588832855,
-0.0038703721947968006,
-0.004796525463461876,
-0.004107162822037935,
0.03551897779107094,
-0.042113397270441055,
-0.004814517218619585,
-0.0018616941524669528,
-0.012449147179722786,
0.03581937029957771,
-0.0023925399873405695,
-0.03386318311095238,
-0.029588308185338974,
0.00442902697250247,
-0.02079063095152378,
-0.00839952751994133,
-0.003947632387280464,
-0.002159863943234086,
-0.002216071356087923,
0.021689515560865402,
0.0353255569934845,
0.03842976689338684,
-0.028177674859762192,
-0.007805662229657173,
-0.06663647294044495,
-0.03878554701805115,
0.05182182043790817,
-0.07356416434049606,
0.02032448537647724,
0.005364986602216959,
-0.003759159008041024,
-0.012985884211957455,
-0.030466455966234207,
0.02662196196615696,
0.040527839213609695,
0.04475072771310806,
-0.05834402143955231,
0.04524847865104675,
0.033322181552648544,
-0.051638636738061905,
-0.03577159345149994,
0.019937727600336075,
0.056639935821294785,
0.025139492005109787,
0.020179681479930878,
-0.0020141243003308773,
0.012074196711182594,
-0.012645267881453037,
-0.04513995349407196,
-0.00005870936729479581,
0.002685207175090909,
-0.0038833036087453365,
-0.010879619978368282,
0.05149107053875923,
-0.05395074933767319,
0.015359039418399334,
-0.024058353155851364,
0.027284853160381317,
-0.0474795438349247,
0.005185899790376425,
0.07886122167110443,
0.024223536252975464,
-0.046627312898635864,
0.0009812549687922,
0.02685578726232052,
-0.06668046116828918,
-0.023608727380633354,
-0.03290384262800217,
0.06399933993816376,
0.043238211423158646,
-0.038723092526197433,
0.02653820626437664,
-0.019801214337348938,
0.0034458632580935955,
-0.04447805881500244,
-0.019602803513407707,
-0.03137032687664032,
0.0059509919956326485,
0.04533933475613594,
-0.03794410824775696,
-0.0111508434638381,
0.056902140378952026,
0.017921950668096542,
-0.05000555142760277,
-0.009817852638661861,
-0.04070345312356949,
-0.08190992474555969,
0.04770592227578163,
-0.00538067938759923,
0.005560640711337328,
-0.020749961957335472,
-0.012141005136072636,
0.005471436772495508,
0.049436043947935104,
-0.0448303259909153,
-0.014596205204725266,
-0.044004689902067184,
0.04214908555150032,
0.02933688275516033,
0.054783422499895096,
0.034479666501283646,
-0.023004326969385147,
0.012318693101406097,
0.028235627338290215,
-0.0015185184311121702,
-0.005468974821269512,
0.012772055342793465,
0.025583121925592422,
0.017116805538535118,
0.05790531262755394,
0.039325810968875885,
0.020458951592445374,
0.0208774171769619,
0.026950063183903694,
-0.04529433697462082,
0.03609268739819527,
0.03136204928159714,
-0.0174543634057045,
0.022868996486067772,
0.05289498344063759,
0.021789951249957085,
0.05961417406797409,
-0.02721438556909561,
0.019238265231251717,
-0.01567523367702961,
-0.05058255419135094,
0.018149476498365402,
-0.02249930426478386,
0.017322003841400146,
0.013400212861597538,
-0.027130985632538795,
-0.042401738464832306,
-0.029116027057170868,
-0.015890540555119514,
-0.006098420824855566,
0.02936050109565258,
0.0392877534031868,
-0.06338691711425781,
0.004035969264805317,
-0.021374620497226715,
0.049910590052604675,
0.06966451555490494,
0.07400211691856384,
0.013251147232949734,
-0.037128206342458725,
-0.04099898412823677,
-0.01344224251806736,
0.04491782560944557,
0.020287994295358658,
0.023910334333777428,
-0.015851112082600594,
-0.04545535892248154,
-0.03128441423177719,
0.02383173070847988,
-0.05096776783466339,
-0.05647977069020271,
0.031951967626810074,
0.0579136461019516,
0.041159737855196,
-0.03427257761359215,
0.06875850260257721,
0.006079141050577164,
-0.013749808073043823,
0.045904215425252914,
-0.016133395954966545,
0.0050124721601605415,
-0.0034908363595604897,
0.030727539211511612,
0.08909329771995544,
-0.02446887455880642,
-0.054307982325553894,
-0.021571381017565727,
-0.037349849939346313,
-0.02563430741429329,
-0.037283554673194885,
-0.006741452496498823,
-0.0034146911930292845,
-0.005094246007502079,
-0.04385073482990265,
0.0036356153432279825,
0.05591937154531479,
0.040330346673727036,
0.03819594159722328,
-0.043960973620414734,
0.021044982597231865,
-0.0020057186484336853,
0.0037397730629891157,
0.08073914796113968,
0.012330968864262104,
-0.020240552723407745,
-0.005504859145730734,
0.03424197807908058,
-0.025940418243408203,
0.021064231172204018,
-0.07746229320764542,
-0.05098807066679001,
-0.02212161384522915,
0.012257583439350128,
-0.01668795384466648,
-0.011295237578451633,
0.1045294851064682,
-0.020469263195991516,
-0.05293954163789749,
-0.03225317597389221,
0.0258954968303442,
0.02000916190445423,
0.040666159242391586,
-0.024549992755055428,
-0.019980110228061676,
-0.001545669510960579,
-0.12562225759029388,
0.022203881293535233,
0.05855708569288254,
0.010602917522192001,
-0.006982348393648863,
0.056267280131578445,
0.022406794130802155,
0.0063889529556035995,
-0.0723264291882515,
0.00240177265368402,
-0.010042384266853333,
-0.0459379106760025,
0.02654813975095749,
-0.03374364972114563,
-0.008182295598089695,
0.05305156111717224,
-0.02001231350004673,
0.03504665195941925,
-0.003840457880869508,
0.009017216973006725,
-0.018354125320911407,
-0.05075377970933914,
0.06459252536296844,
0.060287438333034515,
-0.008141090162098408,
-0.016875531524419785,
-0.03703797236084938,
-0.003210740862414241,
0.03544427827000618,
-0.03534158691763878,
-0.02696344256401062,
-0.11313911527395248,
0.021910712122917175,
-0.034571655094623566,
-0.07243064790964127,
-0.02703751064836979,
-0.00898163951933384,
0.025294922292232513,
0.031378038227558136,
0.012419373728334904,
-0.003226179163902998,
0.0409834198653698,
-0.014953920617699623,
-0.05251240357756615,
-0.03056349977850914,
0.08716745674610138,
0.031377747654914856,
-0.05161420255899429,
-0.03308646380901337,
0.04744582250714302,
-0.014908147044479847,
-0.03799411654472351,
-0.014569654129445553,
-0.018609357997775078,
0.0025602770037949085,
-0.00207888032309711,
0.02597939595580101,
0.0017665927298367023,
-0.03232991322875023,
0.011963777244091034,
0.019496923312544823,
0.004211616236716509,
-0.02816714346408844,
0.07507660239934921,
0.03902058303356171,
-0.004346110858023167,
0.0903732106089592,
-0.05548148602247238,
0.07056352496147156,
-0.003751311916857958,
0.038560498505830765,
0.07325351983308792,
-0.007516044192016125,
-0.008746067993342876,
0.03987112641334534,
0.050346340984106064,
0.007091652136296034,
0.011797132901847363,
0.0005225029890425503,
0.08836223185062408,
0.029308972880244255,
0.0410865917801857,
0.010272420011460781,
0.041230686008930206,
0.005041584372520447,
0.049315113574266434,
-0.007362590171396732,
-0.008358482271432877,
0.014072787016630173,
0.03467611223459244,
0.028253844007849693,
-0.035291559994220734,
0.06201566383242607,
0.033552613109350204,
0.042351171374320984,
-0.032899923622608185,
0.007973708212375641,
-0.01896953210234642,
-0.020694749429821968,
0.024750888347625732,
-0.01641998626291752,
0.0303366519510746,
-0.010473985224962234,
0.015229773707687855,
-0.01272174995392561,
-0.006265491247177124,
-0.002760808216407895,
0.01659715175628662,
0.011959090828895569,
-0.017031967639923096,
-0.008302307687699795,
-0.023074038326740265,
0.036455828696489334,
-0.02734336629509926,
-0.007970147766172886,
-0.026144517585635185,
0.02721349522471428,
-0.015860071405768394,
0.036820679903030396,
0.0073409429751336575,
0.04744815453886986,
-0.0027323290705680847,
-0.034929659217596054,
-0.060679953545331955,
-0.008166207000613213,
-0.019421473145484924,
0.018762309104204178,
-0.13197140395641327,
0.014934835024178028,
0.0263151116669178,
0.036907996982336044,
0.040833380073308945,
0.09877508133649826,
-0.03802094981074333,
0.01581358164548874,
0.026221545413136482,
-0.011717787943780422,
-0.0051734670996665955,
-0.03462976962327957,
-0.04867728799581528,
0.020526869222521782,
0.01736847311258316,
-0.05349836125969887,
-0.013187368400394917,
0.0411943718791008,
-0.03228607401251793,
-0.037567611783742905,
-0.044332634657621384,
-0.030713623389601707,
-0.03354847803711891,
0.01847922056913376,
0.004323137458413839,
-0.040991321206092834,
-0.014326058328151703,
-0.06074137985706329,
-0.020429005846381187,
0.013831808231770992,
-0.019620435312390327,
0.029595253989100456,
-0.07386437803506851,
0.03889377787709236,
-0.01454897690564394,
0.013843543827533722,
0.024891674518585205,
0.03812248259782791,
0.007219433318823576,
0.02533118799328804,
0.002124803839251399,
0.029475800693035126,
-0.0679902583360672,
-0.020704463124275208,
0.005048811435699463,
0.07061243802309036,
0.06149620562791824,
0.05997774377465248,
0.07751751691102982,
-0.000523836410138756,
0.048135921359062195,
0.07115690410137177,
-0.05314023792743683,
-0.01738882064819336,
0.006902358029037714,
-0.059947237372398376,
-0.050917863845825195,
0.010225691832602024,
0.04071090370416641,
0.018819713965058327,
0.018965505063533783,
-0.06806900352239609,
0.0027434113435447216,
-0.001559809548780322,
-0.02426481433212757,
-0.03219778090715408,
-0.03201308473944664,
-0.02449873648583889,
0.023235702887177467,
0.052004147320985794,
0.027846815064549446,
0.03843800723552704,
-0.07684805989265442,
-0.054875265806913376,
0.031712498515844345,
-0.017632808536291122,
-0.04219444468617439,
-0.007124876603484154,
-0.004224096890538931,
0.004140312783420086,
-0.024474799633026123,
-0.048855796456336975,
-0.015017244964838028,
-0.0003763253625947982,
-0.03165466710925102,
0.0406707264482975,
-0.017328601330518723,
0.0031884820200502872,
-0.00055198825430125,
0.03587965667247772,
0.05510636419057846,
-0.01218041218817234,
0.023366354405879974,
0.03499118983745575,
-0.10084212571382523,
-0.00516242440789938,
0.04702126607298851,
0.030121102929115295,
-0.02555224299430847,
-0.013219788670539856,
-0.0015121953329071403,
0.022703923285007477,
0.041105128824710846,
-0.033512841910123825,
0.023020219057798386,
-0.022376909852027893,
0.009593215771019459,
0.020540427416563034,
-0.023415716364979744,
0.045541711151599884,
0.025899667292833328,
0.07330846786499023,
-0.007842246443033218,
-0.009436064399778843,
-0.006967276334762573,
-0.04079122468829155,
0.04173477366566658,
0.04832698032259941,
0.006423186976462603,
0.0017343142535537481,
-0.015245122835040092,
-0.014698472805321217,
0.05950571224093437,
0.0302851852029562,
-0.00968267023563385,
-0.008225598372519016,
-0.039338693022727966,
0.0002282249479321763,
-0.011149533092975616,
0.0005710687837563455,
0.016171764582395554,
0.029807517305016518,
-0.06525043398141861,
0.02499398961663246,
-0.043236035853624344,
0.004034325480461121,
0.04959212616086006,
0.002533569000661373,
0.0006170516717247665,
0.0031403987668454647,
0.017850393429398537,
0.007119952235370874,
0.020857077091932297,
-0.028911719098687172,
-0.02492956817150116,
0.02902287244796753,
0.023108549416065216,
-0.05697910115122795,
0.0282675139605999,
-0.0012007573386654258,
0.0006004402530379593,
-0.0396827831864357,
-0.007918300107121468,
0.042487118393182755,
-0.004617828875780106,
-0.02781980112195015,
0.0331844836473465,
-0.05149489641189575,
0.05383939668536186,
0.05902697518467903,
-0.04093156382441521,
-0.005983956158161163,
-0.024319637566804886,
0.016766972839832306,
0.01668134331703186,
0.02769879437983036,
0.028000369668006897,
-0.014622027985751629,
-0.03870388865470886,
-0.01906951330602169,
-0.020936526358127594,
-0.01750962994992733,
-0.018550874665379524
] |
<p>Does time exist in space or does space exist in time?</p>
<p>Alternatively, perhaps both are independent existences?</p>
<p>Another possibility is that this question is beyond the capacities of the human mind.</p> | g11 | [
0.055435869842767715,
0.044258713722229004,
0.03374046832323074,
0.004735997412353754,
-0.02008878067135811,
0.04500889405608177,
-0.012208891101181507,
0.006425891537219286,
0.0029595568776130676,
0.024326937273144722,
0.032243452966213226,
-0.045995425432920456,
0.0027317022904753685,
0.048156652599573135,
-0.027109520509839058,
-0.009372086264193058,
0.06348893791437149,
-0.02050727978348732,
0.014617576263844967,
0.01083972305059433,
0.02019522339105606,
0.009528842754662037,
0.013730029575526714,
0.018031015992164612,
0.011874586343765259,
-0.06390207260847092,
0.0283631794154644,
-0.021303949877619743,
0.0017497653607279062,
-0.044739093631505966,
0.0273921899497509,
0.042052868753671646,
0.0006334987701848149,
-0.03979038819670677,
0.0028109210543334484,
-0.05143563449382782,
-0.005444988142699003,
0.01015058346092701,
0.018480591475963593,
0.0001259222044609487,
-0.037591710686683655,
-0.029691440984606743,
-0.023962538689374924,
-0.025414111092686653,
0.012496213428676128,
0.08817284554243088,
-0.027362598106265068,
0.050200726836919785,
0.05247469246387482,
-0.04373834282159805,
-0.013526408933103085,
0.05416847765445709,
0.03630838543176651,
0.022211967036128044,
0.007196034770458937,
-0.03688739240169525,
0.05672372132539749,
0.013972818851470947,
0.043761566281318665,
0.046744510531425476,
-0.0026689493097364902,
0.024552559480071068,
0.025339573621749878,
0.08241404592990875,
0.0730256512761116,
-0.013776098378002644,
-0.025229990482330322,
0.0006880812579765916,
0.05051941052079201,
-0.07170828431844711,
0.04101049154996872,
-0.05538221821188927,
-0.003474155440926552,
0.0069553181529045105,
-0.024238288402557373,
0.06151142343878746,
0.06332258135080338,
0.04705246165394783,
0.017618341371417046,
0.04384450241923332,
-0.0003925966448150575,
-0.030616741627454758,
-0.012861203402280807,
-0.044372860342264175,
0.025616126134991646,
-0.03679794818162918,
-0.013247188180685043,
-0.08048601448535919,
-0.008638576604425907,
0.07718704640865326,
-0.0010378763545304537,
0.06042898818850517,
0.08389294147491455,
0.040922585874795914,
-0.02156243659555912,
-0.05225469172000885,
-0.009871476329863071,
0.06546716392040253,
-0.024738777428865433,
0.02511252462863922,
-0.06441201269626617,
-0.02216387167572975,
-0.03159768879413605,
-0.047021493315696716,
0.08443591743707657,
-0.070305235683918,
-0.015725433826446533,
-0.02543691173195839,
-0.09546619653701782,
-0.020753227174282074,
-0.019129205495119095,
-0.03446712717413902,
-0.03164377436041832,
0.01540310401469469,
0.024752318859100342,
-0.00831525307148695,
0.032820940017700195,
-0.021106785163283348,
0.007655448280274868,
0.01623385213315487,
-0.010384232737123966,
0.018272295594215393,
0.0020303961355239153,
0.013955465517938137,
-0.028285156935453415,
0.05131088197231293,
0.02627408131957054,
-0.05559103935956955,
0.006154860369861126,
0.013728603720664978,
-0.029389092698693275,
0.04833037033677101,
0.02883373387157917,
0.03504738584160805,
-0.050294794142246246,
-0.021706953644752502,
-0.035390570759773254,
-0.010889400728046894,
-0.07236453145742416,
0.019896430894732475,
0.0022451102267950773,
-0.014688191935420036,
0.033975765109062195,
0.0006638229824602604,
-0.04747587814927101,
0.02033582143485546,
-0.01064597349613905,
-0.005644362885504961,
-0.05111270770430565,
0.012015819549560547,
0.006085411179810762,
0.04524813964962959,
0.004661265294998884,
-0.003370055928826332,
-0.0007372163236141205,
-0.004822766408324242,
-0.0010841090697795153,
0.034646399319171906,
0.020375793799757957,
0.0004059945931658149,
0.026958391070365906,
0.015887776389718056,
0.02115173637866974,
0.0035035598557442427,
-0.02178364060819149,
-0.00047644670121371746,
0.0003182519576512277,
-0.054643984884023666,
0.015479457564651966,
-0.08788023144006729,
-0.04914550483226776,
-0.05380760505795479,
0.02144349180161953,
0.04880611598491669,
0.0513235442340374,
-0.030649516731500626,
0.006175266578793526,
-0.006832543294876814,
-0.04700232297182083,
-0.011183476075530052,
0.00044179699034430087,
-0.04239436611533165,
-0.05447392538189888,
-0.04951520264148712,
0.0009574485011398792,
0.012930587865412235,
0.047895390540361404,
-0.01156197302043438,
-0.08623474091291428,
-0.0016322359442710876,
-0.022601541131734848,
-0.04758119955658913,
0.03936177119612694,
0.057649847120046616,
0.01820090413093567,
0.014976156875491142,
0.029546022415161133,
0.025363897904753685,
0.03277454152703285,
0.04188322648406029,
-0.009595106355845928,
-0.05020582675933838,
0.0350518599152565,
0.025621717795729637,
0.005677273962646723,
0.00855241995304823,
-0.05452413111925125,
-0.006401007063686848,
0.05387454852461815,
-0.05611323565244675,
0.002266369527205825,
0.013577822595834732,
0.006296807434409857,
0.03456735983490944,
0.011522783897817135,
-0.025826599448919296,
0.011310405097901821,
0.01851026900112629,
-0.04366791993379593,
0.012200891971588135,
0.08640646934509277,
-0.02511517144739628,
0.004692418500781059,
-0.040709804743528366,
0.0006185051752254367,
-0.050900839269161224,
-0.07286559790372849,
-0.016801083460450172,
0.0036079317796975374,
0.034075308591127396,
0.0026903494726866484,
-0.01785905659198761,
0.04067562520503998,
-0.019260838627815247,
-0.0026651150546967983,
0.04935068637132645,
0.06466013938188553,
0.024988193064928055,
-0.043423790484666824,
0.012454761192202568,
-0.03724655136466026,
-0.01104152761399746,
-0.0041705346666276455,
0.013002035208046436,
0.018123898655176163,
-0.058781906962394714,
0.001403947127982974,
-0.05802606791257858,
0.019564397633075714,
0.01827811263501644,
-0.019107859581708908,
-0.00518778758123517,
-0.0587136372923851,
-0.05545849725604057,
-0.036943625658750534,
-0.01350752729922533,
0.026841210201382637,
0.07661750912666321,
-0.16380570828914642,
-0.02718563936650753,
-0.0306182149797678,
0.018691150471568108,
-0.028255894780158997,
0.0585656464099884,
-0.019815290346741676,
-0.05688811093568802,
-0.04452831670641899,
0.006677861791104078,
0.0008414493058808148,
-0.01986892707645893,
0.05289256572723389,
0.016874166205525398,
-0.00824652798473835,
-0.010963897220790386,
-0.0030687798280268908,
0.040713053196668625,
-0.03025553934276104,
-0.0035742884501814842,
0.042234666645526886,
0.015032893046736717,
0.01234191469848156,
0.003444010391831398,
-0.03423062339425087,
0.09009544551372528,
0.011985770426690578,
-0.023505819961428642,
-0.022797107696533203,
0.002312246011570096,
-0.022248374298214912,
0.03135708346962929,
-0.016291419044137,
0.07525902986526489,
-0.0006745635764673352,
-0.03975221887230873,
-0.047147613018751144,
0.06634004414081573,
-0.029804624617099762,
-0.024648237973451614,
-0.0008361468208022416,
-0.07620714604854584,
0.04107005149126053,
-0.019267739728093147,
0.06607653200626373,
0.05299834907054901,
0.04793627932667732,
-0.025465479120612144,
-0.03839567303657532,
-0.026653341948986053,
0.00251045823097229,
-0.02581368200480938,
0.027345528826117516,
0.07161018252372742,
-0.01782737672328949,
0.03966749459505081,
-0.00659954734146595,
0.07626697421073914,
-0.05059105157852173,
-0.017687654122710228,
-0.007651719730347395,
-0.02125965617597103,
0.007902375422418118,
0.0183047354221344,
-0.01988823339343071,
-0.0074590775184333324,
-0.0018473195377737284,
-0.055565591901540756,
0.0007677284302189946,
-0.05217355489730835,
-0.025488583371043205,
0.008085486479103565,
-0.09035521000623703,
-0.060347963124513626,
-0.024105792865157127,
-0.012748409993946552,
-0.029851434752345085,
-0.034981340169906616,
-0.029328742995858192,
0.012289231643080711,
0.004601596854627132,
0.010614444501698017,
0.014549712650477886,
0.060477737337350845,
0.012588195502758026,
0.02745421975851059,
0.03754127025604248,
0.09482379257678986,
-0.006597267463803291,
0.032131098210811615,
0.010646187700331211,
0.018369702622294426,
0.06579937040805817,
0.03628988936543465,
0.052505236119031906,
-0.009581281803548336,
0.016849996522068977,
0.008452638983726501,
-0.01590876094996929,
0.07721398025751114,
0.008046535775065422,
-0.04137030243873596,
0.0072173625230789185,
-0.012875854969024658,
0.0464184433221817,
-0.02803226001560688,
0.022957192733883858,
-0.03477403149008751,
0.02280375361442566,
0.016062552109360695,
0.06402458250522614,
0.010033909231424332,
0.06634006649255753,
0.03237691894173622,
0.02915658801794052,
-0.01282909233123064,
0.13373591005802155,
-0.057961538434028625,
-0.012392476201057434,
-0.009886656887829304,
0.0329563282430172,
0.002610385650768876,
-0.005051684100180864,
-0.04222210496664047,
0.0071564107201993465,
-0.019070200622081757,
0.04180378466844559,
-0.013715190812945366,
-0.003717011073604226,
-0.03514224290847778,
-0.041164323687553406,
-0.07339829206466675,
0.0386081226170063,
-0.004557776264846325,
-0.055500783026218414,
-0.05324220284819603,
0.00938828382641077,
-0.0012961752945557237,
0.021399088203907013,
0.01983203925192356,
-0.02002233825623989,
-0.07323317974805832,
0.04850510507822037,
0.020047593861818314,
-0.002319877967238426,
0.0027541732415556908,
0.015228761360049248,
0.0362597219645977,
0.03285969793796539,
-0.08983425796031952,
0.004930473398417234,
-0.024605445563793182,
-0.01594880409538746,
-0.004963321145623922,
-0.021975327283143997,
0.005673326086252928,
0.0032225623726844788,
-0.01197192445397377,
-0.001717344275675714,
-0.01725715957581997,
0.040084224194288254,
0.042447738349437714,
0.04960381239652634,
0.07693332433700562,
-0.01148390956223011,
0.013475043699145317,
0.04303410276770592,
0.07541880756616592,
-0.02593492716550827,
0.005871254950761795,
-0.02252449095249176,
0.029693633317947388,
-0.027971912175416946,
0.013714039698243141,
0.007396644912660122,
0.04665978625416756,
-0.0052899643778800964,
0.014176853932440281,
-0.003882466582581401,
0.008224745281040668,
0.0371270515024662,
-0.00395826855674386,
0.018842920660972595,
-0.011289373971521854,
0.01622447930276394,
0.007164053153246641,
-0.01727324351668358,
0.028334027156233788,
-0.003909528721123934,
-0.04086340591311455,
-0.06982029974460602,
-0.046009037643671036,
-0.03794002905488014,
0.0028976609464734793,
-0.03802723065018654,
-0.03367508947849274,
-0.05803676322102547,
-0.015090233646333218,
-0.007947943173348904,
-0.025444265455007553,
-0.021113216876983643,
0.04069780185818672,
-0.034330323338508606,
-0.026347599923610687,
0.02011733502149582,
0.07029162347316742,
0.03928428515791893,
-0.019985085353255272,
0.004510931670665741,
-0.020710203796625137,
-0.01855287328362465,
-0.006070342846214771,
-0.0056312428787350655,
0.025133930146694183,
0.0007184665300883353,
-0.024059541523456573,
0.0007331126253120601,
0.007039755582809448,
-0.031069384887814522,
-0.03990785405039787,
-0.02680203504860401,
0.015144704841077328,
-0.027643872424960136,
-0.01013097818940878,
0.017963653430342674,
0.00044655767851509154,
0.023351604118943214,
0.05408754199743271,
-0.04808051884174347,
0.028445495292544365,
0.013075741939246655,
-0.05543616786599159,
0.014297183603048325,
0.009421535767614841,
-0.0015952024841681123,
0.01789635233581066,
-0.02624858170747757,
-0.0429643914103508,
-0.0589139461517334,
0.027787266299128532,
-0.05843648687005043,
-0.003751545213162899,
-0.0023843615781515837,
-0.02064012736082077,
-0.014859371818602085,
-0.011526369489729404,
-0.046332333236932755,
0.014279312454164028,
-0.010466576553881168,
0.03833964094519615,
-0.07445049285888672,
0.014335165731608868,
0.07067647576332092,
-0.013383534736931324,
-0.0826549232006073,
0.01976204663515091,
0.029139624908566475,
-0.00023765087826177478,
0.013021033257246017,
-0.03618442267179489,
0.03130185231566429,
-0.08071520179510117,
-0.029297640547156334,
-0.005075850989669561,
0.05804354324936867,
0.010514535009860992,
-0.0003280678065493703,
-0.0026190555654466152,
-0.07309608161449432,
-0.07252922654151917,
-0.0020438977517187595,
0.0061202035285532475,
0.06794408708810806,
0.024957511574029922,
-0.034475404769182205,
-0.03050689771771431,
-0.021718915551900864,
-0.01888834312558174,
-0.03481828421354294,
-0.025351420044898987,
0.007193403318524361,
0.0036752151791006327,
-0.039858266711235046,
-0.040243394672870636,
-0.0011765201343223453,
0.06194146350026131,
0.0012782140402123332,
0.022798923775553703,
-0.05441690608859062,
0.0038706008344888687,
0.023685043677687645,
-0.014575027860701084,
-0.06583037972450256,
-0.021470772102475166,
-0.05402819812297821,
-0.001182507025077939,
0.01824335940182209,
0.022629402577877045,
0.01605188101530075,
0.03548123314976692,
-0.04612703621387482,
-0.01277410238981247,
0.01717955991625786,
0.052718885242938995,
-0.007894339971244335,
-0.02410692721605301,
-0.026287918910384178,
-0.005657969508320093,
0.052252888679504395,
-0.01887769065797329,
-0.020218465477228165,
-0.0027109747752547264,
0.010100224986672401,
0.02551870048046112,
-0.026946507394313812,
-0.020395705476403236,
0.026445796713232994,
-0.0028929035179316998,
0.04607183113694191,
-0.018291547894477844,
-0.037912942469120026,
0.01199610996991396,
0.03309193626046181,
-0.011427163146436214,
0.026864826679229736,
-0.02458057552576065,
-0.03946520388126373,
0.053786639124155045,
0.007124744355678558,
-0.036840178072452545,
0.041953135281801224,
-0.005292787682265043,
0.004333487246185541,
-0.03390057012438774,
0.024007201194763184,
-0.06808027625083923,
-0.031887881457805634,
0.007168207783252001,
-0.01062733307480812,
0.03784624859690666,
-0.02430032193660736,
0.03960004076361656,
-0.029159121215343475,
0.01565476320683956,
0.07439760863780975,
0.04439053311944008,
0.009340156801044941,
0.028111906722187996,
-0.01996796205639839,
-0.007757893297821283,
0.016067882999777794,
-0.03803498297929764,
0.007685492280870676,
0.0016360105946660042,
0.021472791209816933,
0.04211212694644928,
0.011174974963068962,
-0.0072748796083033085,
0.0009264216059818864,
-0.05071473866701126,
-0.018084317445755005,
0.05450493097305298,
0.06281349062919617,
-0.054828621447086334,
-0.03350827470421791,
0.02601214125752449,
0.014577370136976242,
0.01367768831551075,
-0.02646019496023655,
0.004376598168164492,
0.004263137001544237,
0.01689755730330944,
-0.00042234844295307994,
-0.08597661554813385,
0.016948508098721504,
0.0416748933494091,
-0.04862683638930321,
-0.01835353672504425,
-0.012659845873713493,
0.024274922907352448,
-0.019452402368187904,
-0.05975056067109108,
0.029315335676074028,
-0.055283356457948685,
0.03752657771110535,
0.03356228396296501,
-0.004284321796149015,
-0.03513335436582565,
0.06426270306110382,
-0.04751163721084595,
0.006293037440627813,
-0.029705572873353958,
-0.0016184808919206262,
-0.008264048025012016,
-0.034616027027368546,
-0.038320694118738174,
-0.02613029256463051,
0.013338740915060043,
-0.026034852489829063,
0.0226285420358181,
-0.01824043318629265,
-0.05217672884464264,
-0.001458418439142406,
0.04755350947380066,
-0.07185330986976624,
0.034573204815387726,
-0.003027707803994417,
0.05251731351017952,
-0.013858244754374027,
-0.01998421549797058,
-0.00943822506815195,
-0.03827345371246338,
-0.05282643437385559,
0.021919190883636475,
0.013036055490374565,
-0.07317455857992172,
-0.0053777070716023445,
0.00011085489677498117,
-0.024439822882413864,
-0.001860191929154098,
0.009069579653441906,
0.04047713056206703,
0.017457863315939903,
0.04246269538998604,
-0.045462872833013535,
0.031092677265405655,
0.013748331926763058,
0.002102473983541131,
0.07531716674566269,
-0.030781907960772514,
-0.001998956548050046,
-0.03587624803185463,
-0.01206001453101635,
0.006683142390102148,
-0.024679653346538544,
-0.031111598014831543,
-0.018096385523676872,
-0.02685627155005932,
0.08735979348421097,
0.023699233308434486,
-0.006896447855979204,
-0.03380472585558891,
-0.041271451860666275,
0.021390661597251892,
0.02679779939353466,
0.026340821757912636,
0.030447212979197502,
0.0015942759346216917,
0.020864510908722878,
0.012153458781540394,
-0.0714646652340889,
0.0003245941479690373,
0.0036436826921999454,
0.12151992321014404,
0.006643419153988361,
-0.003416266990825534,
-0.03406022489070892,
-0.024758966639637947,
-0.01781483180820942,
0.012509188614785671,
0.03675444796681404,
0.018463565036654472,
-0.006744276266545057,
-0.07165099680423737,
0.0044523258693516254,
-0.06423249840736389,
-0.04405791312456131,
0.002205427037551999,
0.027999715879559517,
-0.02271329052746296,
-0.006538368295878172,
-0.02200344391167164,
0.057965539395809174,
-0.02415238507091999,
-0.01999511383473873,
0.0172348003834486,
0.0388336181640625,
0.041638411581516266,
0.0343141071498394,
0.015598258003592491,
-0.011719112284481525,
-0.013754039071500301,
0.014718967489898205,
0.001485347398556769,
0.00021450250642374158,
0.04467983916401863,
-0.0063407570123672485,
-0.04303325340151787,
0.01934771053493023,
0.02963099628686905,
0.022553611546754837,
-0.010017398744821548,
0.0197034552693367,
0.04563082382082939,
-0.011523650027811527,
-0.003411683486774564,
0.09067706018686295,
-0.04969557002186775,
0.029933994635939598,
0.05619969964027405,
0.05564495548605919,
-0.006292661651968956,
-0.007058898452669382,
-0.0015855986857786775,
0.024937404319643974,
-0.003137031802907586,
0.02127224951982498,
0.008862986229360104,
0.016103463247418404,
-0.010436632670462132
] |
<p>So here is an interesting question about inductors or coils in general. </p>
<p>Suppose you had a inductor which was 12 inch's in diameter and say 12 inch's in length and has 100 turns of wire. The total length of that wire would be 12(diam) x 3.14(pie) x 100(turns) = 3,768 inches/314 ft in length. </p>
<p>So if you apply a voltage across the coil, I assume the time needed for the current to start moving in the whole coil would about the time needed for the signal to traverse the length of the wire which would take about 314 nanoseconds at 1 ft per nanosecond. Otherwise if the electric field from the first wire just permeates out from wire to wire, then it would take a max of 1 nanosecond before the current in every wire was moving.</p>
<p>So which is it? Does the electric field need to move through all of the 314 ft of wire before the current is moving at the end of the coil or does electric field move through the length of the wire and ultimately cause the current in the end of the coil to start moving after 1 nanosecond?</p> | g1243 | [
0.04118199273943901,
0.04118875786662102,
0.010657664388418198,
-0.027577871456742287,
0.023823637515306473,
-0.0410831980407238,
0.05722448602318764,
0.03125833719968796,
-0.03214077651500702,
-0.002806226024404168,
-0.062362007796764374,
0.013822715729475021,
-0.06838855147361755,
0.015260194428265095,
0.014092609286308289,
-0.02938409522175789,
0.022303175181150436,
-0.006488276645541191,
0.016491664573550224,
0.03935452923178673,
0.04299386218190193,
0.003923016134649515,
-0.007085816934704781,
-0.02593008428812027,
-0.05634673684835434,
-0.0173956248909235,
0.023608898743987083,
0.00876061711460352,
0.012758700177073479,
-0.042729452252388,
0.017775574699044228,
0.004592891316860914,
-0.003846823936328292,
-0.039575524628162384,
-0.01051105186343193,
-0.024470200762152672,
-0.04730045795440674,
0.044430796056985855,
0.03934388607740402,
-0.03973562270402908,
0.027894269675016403,
0.012192527763545513,
0.06304857134819031,
-0.03168489411473274,
0.02157883159816265,
0.010166001506149769,
-0.01268834713846445,
0.030337072908878326,
-0.04970390349626541,
-0.018377669155597687,
-0.027811216190457344,
-0.032921429723501205,
-0.0521526113152504,
0.004840962588787079,
-0.010381066240370274,
0.012857808731496334,
0.03750167042016983,
-0.05642033740878105,
0.01672549732029438,
0.017508655786514282,
0.023413630202412605,
-0.002504979260265827,
-0.05197625979781151,
-0.01875755377113819,
0.0146252466365695,
0.002291148528456688,
0.024636710062623024,
-0.009812476113438606,
0.02976941131055355,
0.010895831510424614,
-0.032362036406993866,
-0.047228746116161346,
-0.0053889392875134945,
-0.04183076694607735,
-0.008338570594787598,
-0.004922178573906422,
0.039606619626283646,
-0.030146930366754532,
0.05540267005562782,
-0.020610230043530464,
-0.07369154691696167,
-0.034140970557928085,
-0.06170905753970146,
0.06046377867460251,
0.012147102504968643,
0.008815884590148926,
-0.025093333795666695,
0.000724895391613245,
0.02619207836687565,
0.028465718030929565,
-0.0301209744066,
0.03129260987043381,
-0.0019636487122625113,
0.03709755465388298,
-0.029663315042853355,
-0.05604984611272812,
0.016462309285998344,
0.022985737770795822,
-0.004158117808401585,
0.052044693380594254,
-0.051531706005334854,
-0.029341671615839005,
-0.031745195388793945,
-0.016916191205382347,
0.006909085437655449,
-0.006177206989377737,
0.07621622085571289,
-0.03375987336039543,
-0.007691221311688423,
0.02782563306391239,
-0.010016157291829586,
-0.06961575150489807,
-0.005746420472860336,
0.03408268839120865,
-0.016821403056383133,
0.02268374152481556,
-0.024890750646591187,
0.006993318907916546,
0.00906029436737299,
0.035238660871982574,
-0.005960335489362478,
0.008704328909516335,
0.023768262937664986,
0.005902711767703295,
-0.060168858617544174,
-0.0073915934190154076,
-0.02761940471827984,
0.08192020654678345,
0.02714892104268074,
0.013912288472056389,
-0.00900251418352127,
0.010380574502050877,
-0.04135758429765701,
0.009071879088878632,
0.0040583000518381596,
-0.03173847496509552,
0.021383000537753105,
0.013688851147890091,
-0.0574883297085762,
0.01238007191568613,
0.03656591475009918,
-0.09867005050182343,
0.04287911579012871,
-0.0662466287612915,
-0.047595154494047165,
0.03174608573317528,
0.027828743681311607,
-0.05027042329311371,
0.008343527093529701,
-0.02164416015148163,
0.038517363369464874,
0.0020623886957764626,
-0.01926366239786148,
-0.01987442933022976,
0.0037883964832872152,
0.04840264469385147,
0.03333926573395729,
0.02400817908346653,
0.03128344565629959,
-0.051318153738975525,
-0.00006316712824627757,
0.00792738888412714,
0.01975284516811371,
0.027797965332865715,
-0.06173126772046089,
0.038110047578811646,
0.04262595251202583,
-0.037440940737724304,
0.019861694425344467,
-0.02848273329436779,
-0.0817694142460823,
0.02299060858786106,
0.04097280651330948,
0.0803404450416565,
-0.004534496460109949,
-0.0013873495627194643,
0.07343678921461105,
-0.00531542906537652,
-0.034294161945581436,
0.0285552479326725,
-0.04432312771677971,
-0.04521767422556877,
0.016413334757089615,
-0.018794400617480278,
-0.008566614240407944,
0.00838650856167078,
-0.03519109636545181,
-0.053830910474061966,
-0.07600409537553787,
-0.012709961272776127,
-0.014058100059628487,
-0.03308965265750885,
0.029659196734428406,
0.04765574261546135,
-0.05497436970472336,
-0.016304945573210716,
0.006153956986963749,
-0.08388303965330124,
-0.032791998237371445,
-0.0734201967716217,
0.047856107354164124,
-0.02345503866672516,
0.05066113546490669,
0.06513354927301407,
0.04431169107556343,
-0.046431299299001694,
-0.021600468084216118,
0.025368476286530495,
0.04237525537610054,
0.010477876290678978,
0.007218075450509787,
0.05220279097557068,
-0.02833007276058197,
0.02980157546699047,
-0.053968291729688644,
-0.048662617802619934,
0.013374022208154202,
-0.008803394623100758,
-0.024185271933674812,
0.021190177649259567,
0.018863210454583168,
-0.024494443088769913,
0.08091866225004196,
-0.027767710387706757,
-0.08024445176124573,
-0.0352349653840065,
-0.02145881950855255,
-0.05888012796640396,
0.02062663435935974,
0.004346106201410294,
-0.03889845684170723,
-0.01123497448861599,
-0.02331354096531868,
-0.0400155633687973,
0.004726331681013107,
0.08161837607622147,
0.05274093151092529,
-0.017974941059947014,
-0.01900230348110199,
0.0014971564523875713,
0.03386839106678963,
0.01129772886633873,
0.04990028217434883,
0.03934786468744278,
-0.02864714339375496,
-0.0690261498093605,
0.06614755094051361,
-0.02391025982797146,
-0.024053020402789116,
0.049853935837745667,
-0.0050136009231209755,
-0.018428510054945946,
-0.016192933544516563,
0.01181044802069664,
-0.014381161890923977,
-0.05916610360145569,
0.025155222043395042,
0.0034369181375950575,
-0.00012001507275272161,
0.005944475531578064,
-0.015980513766407967,
-0.0299096517264843,
-0.016612205654382706,
0.01392978522926569,
-0.04578530043363571,
-0.012387322261929512,
-0.050475113093853,
0.022114994004368782,
0.014027497731149197,
0.010303572751581669,
-0.016965849325060844,
0.03572510555386543,
-0.015979459509253502,
-0.027057381346821785,
0.06269548088312149,
-0.019158203154802322,
0.03697230666875839,
-0.04774875193834305,
-0.014037573710083961,
0.05558369308710098,
-0.10615851730108261,
-0.003678065724670887,
-0.03085269220173359,
0.035890012979507446,
0.026974670588970184,
-0.03158929944038391,
0.004691494163125753,
-0.019925402477383614,
-0.040715258568525314,
0.015531198121607304,
-0.024969425052404404,
-0.031186150386929512,
0.061021048575639725,
-0.02071336656808853,
0.03583139181137085,
0.03380623087286949,
0.03685133904218674,
-0.019950557500123978,
0.012617260217666626,
-0.015605130232870579,
0.02847297117114067,
-0.02334856241941452,
-0.0387502983212471,
-0.02241634391248226,
0.03759884834289551,
0.0067084236070513725,
0.016334015876054764,
-0.06900116801261902,
-0.04010845720767975,
-0.05553293973207474,
-0.002339028986170888,
0.06079453229904175,
0.025084475055336952,
-0.05815719813108444,
-0.06213685870170593,
-0.058062806725502014,
-0.02697441540658474,
0.05930863693356514,
0.04562573879957199,
0.028609437867999077,
0.024619925767183304,
-0.05243019387125969,
0.010210015811026096,
0.007302232086658478,
0.03686879202723503,
0.013054752722382545,
0.01965949870646,
-0.018008651211857796,
-0.03414199501276016,
-0.08033668994903564,
-0.07206373661756516,
0.019245091825723648,
-0.08490380644798279,
-0.04417511075735092,
0.0046210759319365025,
-0.010063606314361095,
0.0197254940867424,
0.03780674189329147,
-0.0022149637807160616,
0.05513492226600647,
0.02200057916343212,
-0.012693125754594803,
-0.05511166527867317,
-0.005759036634117365,
0.0227552130818367,
0.021097280085086823,
0.028413284569978714,
0.001583158620633185,
-0.0006174623849801719,
0.018281741067767143,
0.07401824742555618,
0.025586888194084167,
-0.012492852285504341,
-0.03628052398562431,
-0.0030842330306768417,
0.06169235706329346,
0.0016374553088098764,
0.04385994374752045,
-0.03853423893451691,
-0.014316019602119923,
0.021551141515374184,
0.000565183931030333,
0.0521191731095314,
0.01733957976102829,
-0.02010801061987877,
0.006718108430504799,
0.009210319258272648,
0.020330026745796204,
0.009644703008234501,
-0.033733610063791275,
-0.007695780135691166,
0.03027750924229622,
-0.007733064237982035,
0.014411811716854572,
0.0021541547030210495,
-0.030289454385638237,
0.04419310763478279,
0.03226418048143387,
-0.04681861028075218,
0.006301316898316145,
-0.0025119443889707327,
0.022812625393271446,
-0.021364616230130196,
-0.0007900920463725924,
-0.01821291446685791,
0.015086823143064976,
-0.0047808438539505005,
0.0016050060512498021,
-0.01069755107164383,
0.0019499267218634486,
0.0004233701038174331,
0.001451237010769546,
0.038032595068216324,
0.011020543985068798,
-0.017948800697922707,
-0.03494580462574959,
0.009385778568685055,
0.054674092680215836,
0.016393929719924927,
-0.04720655083656311,
0.015045725740492344,
-0.001596642890945077,
-0.042190954089164734,
0.025594418868422508,
0.04448329657316208,
0.066696897149086,
-0.001272569876164198,
-0.002187304897233844,
0.024472352117300034,
-0.05184178054332733,
-0.03569210320711136,
0.02778836153447628,
-0.0682988166809082,
-0.0039642928168177605,
0.010051230899989605,
0.027268245816230774,
0.05134819075465202,
0.003793609794229269,
-0.020593002438545227,
-0.036495957523584366,
0.005018320400267839,
-0.025986595079302788,
0.07121814042329788,
0.00267096352763474,
-0.05203135311603546,
0.01335951965302229,
0.038627613335847855,
0.028535334393382072,
0.009563511237502098,
-0.03296973556280136,
-0.028697559610009193,
0.0633007362484932,
-0.004475263878703117,
-0.0009329402819275856,
-0.055774372071027756,
0.09706965833902359,
0.0041350917890667915,
0.03820781037211418,
0.058100610971450806,
0.06291881948709488,
0.0369059182703495,
-0.022382760420441628,
0.02171306312084198,
0.007400054484605789,
-0.02735619992017746,
0.0022550467401742935,
-0.06362393498420715,
-0.041546814143657684,
-0.026160093024373055,
-0.010872525162994862,
-0.001090585719794035,
0.06467681378126144,
-0.06579948216676712,
-0.020969850942492485,
-0.005031664855778217,
-0.030602959915995598,
0.040057938545942307,
-0.025350119918584824,
0.03306107223033905,
0.006362300831824541,
-0.056024350225925446,
0.018953924998641014,
-0.031079523265361786,
0.06480475515127182,
0.01688545197248459,
-0.0006429244531318545,
0.04940827563405037,
-0.0562065988779068,
-0.08784401416778564,
0.08786970376968384,
0.024361956864595413,
0.062134239822626114,
-0.005181154236197472,
0.012824848294258118,
0.07753785699605942,
0.03797603398561478,
0.038967277854681015,
0.045608360320329666,
-0.025426607578992844,
-0.025028755888342857,
-0.004711541812866926,
-0.03503169119358063,
-0.004282576963305473,
0.0037016968708485365,
0.06507670134305954,
-0.030321158468723297,
-0.03502412512898445,
0.032386645674705505,
0.021768074482679367,
-0.034984953701496124,
0.024563021957874298,
0.04839131981134415,
0.09036226570606232,
-0.003059783484786749,
-0.03966321796178818,
-0.013791852630674839,
0.009583384729921818,
0.00806350912898779,
-0.019955812022089958,
-0.0520179383456707,
-0.018177829682826996,
0.010914796032011509,
-0.04405239224433899,
0.01275210827589035,
-0.11665432900190353,
0.0223458893597126,
-0.01716836355626583,
0.005397023633122444,
-0.022844163700938225,
-0.03666162118315697,
-0.02105296589434147,
0.11697041988372803,
0.01774284802377224,
-0.05097787827253342,
0.01142795104533434,
0.014069969765841961,
-0.04783634468913078,
-0.004882096312940121,
0.007649867329746485,
0.022722231224179268,
0.01936362124979496,
-0.01237358059734106,
0.022250959649682045,
0.0328257754445076,
0.018561484292149544,
0.02320503629744053,
-0.06949722021818161,
0.004538318142294884,
0.06683430075645447,
0.015387334860861301,
0.05926433950662613,
0.018151698634028435,
-0.025078827515244484,
0.002548105316236615,
-0.04997185990214348,
0.009248009882867336,
0.021429041400551796,
-0.0802362784743309,
0.007819613441824913,
0.025964433327317238,
0.021811431273818016,
-0.0028221704997122288,
0.025595376268029213,
-0.0018050051294267178,
-0.04892740398645401,
-0.05133168771862984,
0.038523394614458084,
-0.06815315783023834,
0.015409884043037891,
-0.002414196263998747,
-0.0008891528123058379,
0.05833921581506729,
-0.006373873446136713,
-0.034458693116903305,
-0.004368468653410673,
0.07482387870550156,
0.0271376334130764,
-0.0029435602482408285,
0.020589085295796394,
-0.0369914248585701,
0.023312194272875786,
-0.004348401911556721,
-0.023750124499201775,
0.0005607028142549098,
0.03250489756464958,
0.015253176912665367,
0.00980684906244278,
0.01606382243335247,
0.07395144551992416,
0.08678404241800308,
0.0781090036034584,
-0.07493725419044495,
0.004796399734914303,
0.03700791299343109,
0.00691802566871047,
-0.0039939661510288715,
0.012513353489339352,
-0.033474717289209366,
-0.036675434559583664,
0.013038309291005135,
-0.04158087447285652,
-0.01992088556289673,
0.010341024957597256,
-0.05920469015836716,
-0.000526048825122416,
0.02176428586244583,
0.001478208927437663,
-0.009366354905068874,
0.039382025599479675,
0.03841402381658554,
-0.07270815968513489,
-0.020822975784540176,
0.04311588034033775,
-0.04932202026247978,
-0.018426790833473206,
-0.03287156671285629,
-0.011412891559302807,
0.010996176861226559,
0.010429860092699528,
0.08936777710914612,
-0.010112964548170567,
-0.042309630662202835,
0.019278228282928467,
-0.015108383260667324,
0.002246210118755698,
0.005562874488532543,
-0.009350667707622051,
0.030299672856926918,
0.03517580404877663,
-0.0016794356051832438,
0.0337899886071682,
-0.045791469514369965,
0.022608986124396324,
-0.03937124088406563,
-0.021766263991594315,
0.018821265548467636,
0.010199097916483879,
-0.05575213208794594,
0.05159484222531319,
0.06559225916862488,
0.017577314749360085,
0.0304255448281765,
-0.011722199618816376,
0.09217806160449982,
-0.038447968661785126,
0.01647808589041233,
-0.02395664155483246,
-0.019159462302923203,
0.034112099558115005,
-0.01312823686748743,
-0.010327447205781937,
0.020449021831154823,
-0.02184230089187622,
0.07216580212116241,
0.04333510622382164,
-0.04903135821223259,
0.00956733524799347,
0.01585446670651436,
0.035798948258161545,
-0.0021444829180836678,
0.030724626034498215,
-0.012329090386629105,
-0.03751976788043976,
0.05571639537811279,
-0.00909433327615261,
-0.029486406594514847,
-0.011313033290207386,
0.0724734291434288,
-0.0028618313372135162,
-0.006199243012815714,
0.01299450732767582,
0.012354235164821148,
-0.012888588011264801,
0.0030985830817371607,
0.019853295758366585,
-0.03277721628546715,
0.01147728506475687,
-0.022165190428495407,
-0.004528843332082033,
0.007018103264272213,
0.02422270178794861,
0.014775297604501247,
-0.048622895032167435,
-0.007810886949300766,
0.0431680753827095,
-0.024396013468503952,
-0.0008157015545293689,
-0.03544268012046814,
0.011068189516663551,
-0.03482269495725632,
0.04468774423003197,
-0.04038024693727493,
-0.002581629203632474,
-0.03153815492987633,
0.009654887951910496,
-0.014571688137948513,
-0.02859055995941162,
-0.040097106248140335,
0.0019190709572285414,
-0.00755613436922431,
-0.020278243348002434,
-0.0318276509642601,
-0.013664236292243004,
-0.03515514358878136,
-0.004858661442995071,
-0.004740358795970678,
-0.03226929530501366,
-0.01416720449924469,
-0.03469529002904892,
-0.02186429314315319,
0.04261288046836853,
-0.01579568162560463,
0.03003329411149025,
0.019087882712483406,
0.031142788007855415,
0.020875997841358185,
0.06156236678361893,
-0.03375905007123947,
0.026314062997698784,
-0.01632770337164402,
0.055965714156627655,
0.06495410203933716,
0.06281968206167221,
-0.006449462380260229,
0.04461125656962395,
0.03489489108324051,
-0.01668143831193447,
-0.011622448451817036,
-0.027691716328263283,
0.06597639620304108,
-0.001098293112590909,
0.008431460708379745,
-0.04019657522439957,
0.04472033306956291,
0.018476175144314766,
0.020639508962631226,
-0.06238294392824173,
-0.016840729862451553,
0.029274530708789825,
0.0021038674749433994,
-0.016757283359766006,
0.01039316039532423,
-0.024815138429403305,
-0.04471404850482941,
-0.02272416651248932,
-0.013561747968196869,
-0.0626625046133995,
0.015306219458580017,
0.004583716858178377,
-0.08548451215028763,
0.02217351831495762,
-0.05464114621281624,
-0.018305063247680664,
-0.07495323568582535,
-0.1020956039428711,
0.02983681485056877,
0.02426494099199772,
-0.017601069062948227,
0.01680786907672882,
-0.021732397377490997,
0.04268854483962059,
-0.019864408299326897,
-0.009621791541576385,
0.009203661233186722,
0.004169476684182882,
0.04241311177611351,
-0.024415137246251106,
0.017093047499656677,
0.03226255998015404,
0.008573736064136028,
0.007142722140997648,
0.021450400352478027,
-0.022322844713926315,
0.009404378943145275,
0.0161740742623806,
0.042444851249456406,
-0.05677025765180588,
0.02011759951710701,
-0.006138315889984369,
0.02548820897936821,
-0.0702797919511795,
0.02231852151453495,
0.012638372369110584,
0.008218199945986271,
0.06252961605787277,
-0.026748917996883392,
-0.036101534962654114,
0.0076507702469825745
] |
<p>For projector $p$, in finite dimension say, some unitaries $u, v$ does $upu^\dagger = vpv^\dagger$ implies $u = v$ ?
Intuitively, can we not say that a unitary is matrix permuting the basis and since $p$ is diagonal then obviously $u$ is $v$ ?
But for an exact proof ?</p>
<p>what if further, $p = upu^\dagger = vpv^\dagger$ ?</p> | g1244 | [
0.004523179959505796,
0.03726869449019432,
0.01856430433690548,
-0.010936297476291656,
0.01741955615580082,
-0.0333099365234375,
0.033521976321935654,
-0.016261616721749306,
0.02871761843562126,
0.018381254747509956,
-0.04117930307984352,
0.07005637884140015,
-0.034161947667598724,
0.015019180253148079,
0.010435288771986961,
-0.000779470952693373,
0.0414934977889061,
-0.03097083978354931,
-0.01467993762344122,
0.014601940289139748,
-0.07745041698217392,
0.02917221561074257,
0.010306619107723236,
0.024908216670155525,
0.06322355568408966,
-0.06607577204704285,
0.06576855480670929,
-0.019443513825535774,
-0.06823467463254929,
0.03860250115394592,
0.09040027111768723,
-0.025882041081786156,
0.029291421175003052,
-0.04871224984526634,
-0.01578396186232567,
-0.03814743831753731,
0.09250365942716599,
0.05692600831389427,
0.08233000338077545,
0.011488593183457851,
-0.03895322605967522,
0.030937081202864647,
-0.02170541323721409,
-0.014172976836562157,
-0.03970176726579666,
0.012372874654829502,
0.026281248778104782,
-0.015923289582133293,
-0.04732346534729004,
-0.029743338003754616,
-0.027524340897798538,
0.007130531128495932,
0.0728243961930275,
0.004296275787055492,
-0.06502338498830795,
0.058402661234140396,
-0.044152189046144485,
-0.04242919385433197,
0.013543919660151005,
0.06312643736600876,
0.02146383933722973,
-0.009782656095921993,
0.030591588467359543,
0.013174519874155521,
0.04137229919433594,
-0.013618570752441883,
-0.020819107070565224,
0.00004648658068617806,
0.008090637624263763,
0.02898053266108036,
-0.03178711235523224,
-0.01858239807188511,
0.04742886498570442,
-0.019996562972664833,
0.015621839091181755,
-0.04155537113547325,
-0.03524757921695709,
-0.0036574983969330788,
-0.0210998747497797,
0.0399712435901165,
-0.005593367386609316,
-0.036621492356061935,
0.04683242365717888,
-0.0023896105121821165,
0.02981514483690262,
0.020601529628038406,
0.035704463720321655,
0.06969484686851501,
-0.0018025615718215704,
0.08303985744714737,
0.04883969947695732,
0.0020457939244806767,
0.007259017322212458,
0.09610995650291443,
-0.02698448672890663,
-0.06380718946456909,
-0.028679465875029564,
0.023585215210914612,
0.01043921709060669,
-0.03418473154306412,
-0.054383330047130585,
0.0660489946603775,
0.016174783930182457,
-0.008009115234017372,
-0.034476138651371,
0.05049567669630051,
0.010291271843016148,
-0.01697920262813568,
-0.021352892741560936,
0.03355702757835388,
-0.11484481394290924,
0.007317370735108852,
-0.06553435325622559,
-0.003921788651496172,
-0.02189280092716217,
-0.008436073549091816,
0.06036459654569626,
-0.055673133581876755,
0.002011943608522415,
0.02294609136879444,
0.0024338385555893183,
0.008906710892915726,
-0.006666901987046003,
0.06775160133838654,
-0.000750538136344403,
0.0507274866104126,
-0.047994162887334824,
0.04593372344970703,
0.04721614345908165,
-0.003043601056560874,
0.026146097108721733,
-0.04084927588701248,
-0.037409085780382156,
0.043520133942365646,
0.10286789387464523,
-0.03785661607980728,
0.041220180690288544,
-0.019212331622838974,
0.06696292012929916,
0.04358971491456032,
-0.0535566471517086,
-0.010256306268274784,
-0.04547259584069252,
-0.05038951709866524,
-0.02412549778819084,
-0.007019911427050829,
0.0037159682251513004,
-0.02873944863677025,
-0.023963164538145065,
0.019306646659970284,
-0.017808249220252037,
0.08219300955533981,
0.014452327974140644,
-0.03809832036495209,
-0.02335604839026928,
-0.023550420999526978,
-0.028172887861728668,
-0.022108955308794975,
0.036266908049583435,
-0.09025973081588745,
0.015216591767966747,
0.03969182074069977,
0.030559957027435303,
-0.01025495957583189,
-0.023932939395308495,
-0.061690159142017365,
0.04824810102581978,
-0.041019659489393234,
-0.03251222148537636,
-0.0736943930387497,
0.01784413680434227,
0.0153233977034688,
0.04862973839044571,
0.018771493807435036,
0.03854517638683319,
0.01553602796047926,
-0.03829653188586235,
0.027857821434736252,
0.018435999751091003,
0.03234868124127388,
-0.06882668286561966,
0.005732977297157049,
-0.006661722902208567,
0.014859715476632118,
-0.014330947771668434,
-0.00784208718687296,
0.006988143548369408,
0.042939070612192154,
0.013719472102820873,
0.07994813472032547,
-0.05889769643545151,
0.027689000591635704,
0.022959236055612564,
0.0006903085159137845,
0.011584820225834846,
0.017670243978500366,
-0.0037815519608557224,
-0.029149947687983513,
-0.01038909051567316,
0.0027408807072788477,
-0.0495879128575325,
0.0397476851940155,
0.00919514149427414,
0.029520779848098755,
0.005236139986664057,
0.03601926192641258,
0.007653846405446529,
0.03097080998122692,
0.009740497916936874,
-0.054018016904592514,
0.046255480498075485,
-0.02393483556807041,
-0.012604759074747562,
0.02850831300020218,
-0.01297874003648758,
-0.03126119449734688,
0.05994025617837906,
-0.018393369391560555,
-0.0373539924621582,
-0.01099471002817154,
-0.02990269474685192,
-0.013103115372359753,
-0.01932467333972454,
0.04447218403220177,
-0.0062235211953520775,
0.03177431970834732,
-0.045327216386795044,
0.03224963694810867,
0.004848690703511238,
0.04666879400610924,
-0.009905422106385231,
-0.00170599773991853,
0.006116385571658611,
-0.030506182461977005,
-0.017145393416285515,
0.022627094760537148,
-0.0038203620351850986,
0.03313061594963074,
0.033899936825037,
-0.01805747114121914,
0.00130377896130085,
-0.06923983991146088,
-0.028447961434721947,
0.008579093031585217,
0.0004957100609317422,
-0.03622228279709816,
0.0023137335665524006,
-0.021976128220558167,
0.000018097813153872266,
0.020896436646580696,
-0.07011925429105759,
-0.03232370316982269,
0.017718294635415077,
0.023758139461278915,
-0.050845008343458176,
0.029716741293668747,
0.010527431033551693,
-0.007317236624658108,
-0.006952649913728237,
-0.0056417156010866165,
0.012986034154891968,
0.010844093747437,
-0.009836920537054539,
0.010410461574792862,
-0.02373935468494892,
0.008075704798102379,
-0.020241672173142433,
0.015646787360310555,
0.026605989784002304,
0.0532708503305912,
0.04680841416120529,
0.06992974877357483,
0.052144162356853485,
-0.03395094722509384,
-0.03879614546895027,
-0.0334734208881855,
0.017339317128062248,
-0.00309959938749671,
-0.04814625903964043,
0.019720373675227165,
-0.005117578897625208,
0.046042051166296005,
-0.08526665717363358,
0.03725861385464668,
0.016840333119034767,
-0.021705221384763718,
-0.06613869220018387,
0.021643444895744324,
-0.019003061577677727,
-0.0075153568759560585,
-0.043629519641399384,
0.031030528247356415,
0.055904634296894073,
-0.04279603436589241,
-0.05791287124156952,
0.00009863850573310629,
0.07758674025535583,
0.000779064663220197,
-0.042139265686273575,
0.01777743548154831,
0.0015633609145879745,
0.003597080009058118,
0.011945536360144615,
-0.026371553540229797,
0.04302193596959114,
-0.021178830415010452,
-0.02279059588909149,
-0.030345600098371506,
0.0007473384612239897,
-0.03271198272705078,
-0.03555258363485336,
0.09758177399635315,
-0.040599457919597626,
-0.04446249455213547,
-0.029628684744238853,
-0.06268952041864395,
0.012050328776240349,
0.004900719039142132,
-0.10187184810638428,
-0.01792857050895691,
-0.056084178388118744,
0.008484750054776669,
-0.0013252368662506342,
0.0034240400418639183,
-0.0013895515585318208,
-0.00897174421697855,
-0.07784943282604218,
0.05693253129720688,
0.005154962185770273,
-0.04529896378517151,
0.008880558423697948,
0.005182400345802307,
0.060680557042360306,
0.04102388024330139,
-0.028182530775666237,
-0.011928410269320011,
-0.011516655795276165,
0.020881403237581253,
0.012126821093261242,
0.03916450962424278,
0.03878681734204292,
-0.018064241856336594,
-0.00846443697810173,
-0.02435825765132904,
0.019579492509365082,
0.022161947563290596,
0.025504842400550842,
0.007880093529820442,
-0.024706939235329628,
0.014792685396969318,
-0.038380496203899384,
0.049748118966817856,
0.012492729350924492,
0.03908822685480118,
0.058795277029275894,
0.01528104767203331,
0.06000198796391487,
0.040248461067676544,
0.014070090837776661,
-0.017940020188689232,
-0.024352028965950012,
0.010200968943536282,
0.021617110818624496,
-0.03949994221329689,
-0.005182788707315922,
0.06337013840675354,
-0.0021311535965651274,
-0.02266135811805725,
0.019891418516635895,
0.043359410017728806,
-0.014992138370871544,
-0.02010159008204937,
-0.03112737461924553,
-0.00785986427217722,
-0.024130074307322502,
-0.05074606463313103,
0.016647683456540108,
-0.04085434228181839,
0.008235476911067963,
-0.005093985702842474,
0.07023607939481735,
0.035027191042900085,
0.09256112575531006,
0.021498920395970345,
0.0020208805799484253,
0.03956011310219765,
-0.005606129765510559,
-0.006239496637135744,
0.07474995404481888,
0.05278109014034271,
0.02973220683634281,
-0.056090742349624634,
0.00249580224044621,
0.0002593261015135795,
0.01375286653637886,
-0.011578370817005634,
-0.004937710240483284,
0.004290169570595026,
-0.01658623293042183,
-0.023549653589725494,
-0.01126455795019865,
-0.07037189602851868,
0.05170402675867081,
-0.049702029675245285,
-0.030927717685699463,
-0.0014351203572005033,
0.024434922263026237,
-0.007178735453635454,
0.013726967386901379,
-0.014677547849714756,
0.024848930537700653,
-0.018596366047859192,
0.004181877709925175,
-0.037918560206890106,
-0.002471927087754011,
0.08477232605218887,
-0.010157547891139984,
0.0426546111702919,
-0.011259722523391247,
0.021292349323630333,
0.025201966986060143,
0.046077661216259,
-0.001863414072431624,
0.024233799427747726,
-0.027084369212388992,
-0.018419364467263222,
0.02057221531867981,
0.01713053323328495,
0.016750311478972435,
0.0019696184899657965,
0.00594037352129817,
0.029490850865840912,
0.024599412456154823,
0.02193889208137989,
-0.03164716437458992,
-0.02019970491528511,
-0.01791694015264511,
0.016174377873539925,
0.010927700437605381,
0.040980856865644455,
0.03696461021900177,
-0.01720229908823967,
0.04302247613668442,
-0.054034531116485596,
-0.024650679901242256,
-0.008230392821133137,
-0.03122473880648613,
-0.015772216022014618,
-0.01134765800088644,
-0.028700489550828934,
-0.01337593887001276,
0.04682932049036026,
-0.006473164074122906,
-0.07152869552373886,
0.027177514508366585,
-0.0463658943772316,
-0.06007670611143112,
-0.018825063481926918,
0.059714049100875854,
-0.03877351060509682,
0.028894299641251564,
-0.055241040885448456,
-0.0031135794706642628,
0.003265048610046506,
0.039889346808195114,
-0.029850738123059273,
-0.09225784242153168,
0.03943511098623276,
-0.05477634072303772,
0.0012128946837037802,
0.057633861899375916,
0.06696289032697678,
-0.03024197556078434,
0.022304538637399673,
0.022214820608496666,
-0.06263160705566406,
0.020257366821169853,
0.007570916786789894,
-0.004024540074169636,
-0.051318127661943436,
0.0475577637553215,
-0.02677246183156967,
-0.04076051339507103,
-0.014622477814555168,
0.02588900551199913,
0.04672868922352791,
-0.04003068059682846,
-0.03611735999584198,
-0.022633912041783333,
-0.0384918637573719,
-0.03471037372946739,
-0.0361674427986145,
0.01650536246597767,
0.01874345727264881,
-0.01968970149755478,
-0.022648779675364494,
-0.018125128000974655,
-0.010431491769850254,
-0.012484684586524963,
-0.016173813492059708,
-0.022365735843777657,
-0.012026595883071423,
0.0433715283870697,
0.00278769270516932,
0.04399142414331436,
-0.019183648750185966,
0.10933906584978104,
0.004087928216904402,
0.00485762394964695,
0.05093703791499138,
0.04729136824607849,
-0.019530365243554115,
0.02021796815097332,
-0.07159581780433655,
-0.006206701509654522,
-0.0003321188560221344,
-0.011581418104469776,
0.029416542500257492,
-0.055825211107730865,
-0.02707400731742382,
0.014077875763177872,
0.026807324960827827,
0.02714627794921398,
-0.032599348574876785,
0.03542740270495415,
0.03248148784041405,
0.030638201162219048,
-0.060774948447942734,
-0.03394993394613266,
0.026652490720152855,
0.044550493359565735,
0.01498844102025032,
-0.024227619171142578,
-0.030098840594291687,
-0.008543022908270359,
-0.03629736974835396,
0.0012823562137782574,
0.008049136027693748,
0.0042317453771829605,
-0.0015197796747088432,
0.01596171222627163,
-0.05598337575793266,
0.0027959775179624557,
-0.0015137344598770142,
-0.03686286136507988,
0.014243977144360542,
-0.0037218621000647545,
0.006454175803810358,
0.026318032294511795,
-0.009995171800255775,
-0.03860820457339287,
0.0032948628067970276,
-0.06555110216140747,
-0.07365410774946213,
0.012135949917137623,
-0.018794391304254532,
0.03679338097572327,
-0.028654159978032112,
0.020984487608075142,
0.005628477782011032,
0.010057613253593445,
0.02563382312655449,
0.01785929873585701,
-0.04389651492238045,
0.011192215606570244,
-0.05772273615002632,
-0.00039118039421737194,
-0.001495777745731175,
0.012520333752036095,
0.018181297928094864,
-0.010898804292082787,
0.005730588920414448,
0.00840708240866661,
0.024632534012198448,
0.005787315778434277,
0.04758935794234276,
0.003388279350474477,
-0.05275016278028488,
-0.04775569587945938,
0.024768659844994545,
0.048563189804553986,
-0.04080405458807945,
0.025202834978699684,
0.04364435002207756,
-0.0063830791041255,
0.033224690705537796,
0.013503162190318108,
-0.03627537190914154,
0.02666029892861843,
0.009135986678302288,
-0.04354953020811081,
-0.02063760533928871,
-0.03200547397136688,
0.05016159266233444,
0.016095072031021118,
0.05673525482416153,
0.00307557824999094,
0.09081274271011353,
-0.0068727158941328526,
-0.020608650520443916,
0.0944410040974617,
0.017381755635142326,
0.030031688511371613,
-0.01204526238143444,
-0.03250466659665108,
0.025511717423796654,
-0.03848234564065933,
-0.007739825174212456,
-0.005119628272950649,
0.011420623399317265,
0.04817337915301323,
0.010903630405664444,
0.009979592636227608,
0.0451122485101223,
-0.042384516447782516,
-0.0713132843375206,
-0.032809603959321976,
-0.002342869993299246,
-0.024284129962325096,
0.05343732237815857,
0.04495210200548172,
-0.03240584582090378,
-0.0008096179808489978,
-0.03740011528134346,
0.0006661200313828886,
0.04877784848213196,
-0.02062048763036728,
-0.03285461664199829,
0.052634548395872116,
0.053220730274915695,
-0.027504373341798782,
-0.022821692749857903,
0.049185510724782944,
-0.0018627981189638376,
0.004258449655026197,
0.0536113902926445,
-0.07392343133687973,
0.0644746869802475,
-0.019039902836084366,
0.03620938956737518,
-0.03984864056110382,
-0.009713043458759785,
-0.016492465510964394,
-0.019715171307325363,
-0.021853942424058914,
0.013748652301728725,
0.03811608999967575,
-0.04441374912858009,
-0.019916869699954987,
-0.019149787724018097,
0.05224747955799103,
0.03263608738780022,
0.03962443023920059,
-0.00862415973097086,
-0.0525081530213356,
0.007235386408865452,
0.056551460176706314,
-0.010690899565815926,
-0.03930537402629852,
-0.024050910025835037,
0.016437826678156853,
0.006898126564919949,
-0.0157503392547369,
-0.027015620842576027,
0.016746938228607178,
0.0017507575685158372,
-0.016519254073500633,
0.0058244070969522,
0.009256649762392044,
-0.0219928827136755,
-0.03034571185708046,
-0.030658449977636337,
-0.02757265791296959,
-0.0060129049234092236,
0.00824384018778801,
0.016289182007312775,
-0.027685342356562614,
0.10282810032367706,
0.014438970014452934,
0.015009825117886066,
-0.003971168305724859,
0.022552456706762314,
-0.027176769450306892,
-0.012936259619891644,
-0.049144446849823,
-0.01978597603738308,
-0.02360679768025875,
-0.04755481332540512,
-0.010879991576075554,
-0.05288846418261528,
-0.032269369810819626,
0.011782151646912098,
0.09615831822156906,
0.004365792963653803,
-0.01464115921407938,
0.006627447437494993,
-0.009073945693671703,
0.014951451681554317,
0.01505561824887991,
-0.030910024419426918,
-0.03873150423169136,
-0.003942995332181454,
-0.029750308021903038,
0.02465471811592579,
-0.009666793048381805,
0.012444836087524891,
-0.022590946406126022,
0.043130017817020416,
-0.011184659786522388,
-0.05771000683307648,
0.04540378972887993,
-0.03971916809678078,
-0.04132575914263725,
-0.01448465883731842,
-0.012086126953363419,
-0.0569462776184082,
-0.08160710334777832,
0.03985374793410301,
-0.0237472765147686,
-0.03613019734621048,
0.03819219395518303,
-0.043804850429296494,
-0.002803739858791232,
-0.025275642052292824,
-0.022033285349607468,
-0.04295506328344345,
0.02182558737695217,
-0.020963814109563828,
-0.000582056469283998,
0.02178790234029293,
0.06566733866930008,
0.010765191167593002,
-0.058754242956638336,
0.03186982125043869,
0.004840063862502575,
-0.028626233339309692,
-0.04639970511198044,
-0.03647085279226303,
-0.01110950205475092,
-0.02140820398926735,
-0.003550684079527855,
-0.06564518064260483,
-0.010880478657782078,
0.01987862028181553,
-0.03237354755401611,
0.0027919288258999586,
-0.037815582007169724,
-0.06806782633066177,
-0.017736654728651047,
-0.0037000016309320927,
-0.08159061521291733,
0.019236983731389046,
-0.013600134290754795,
0.08793327957391739,
0.05461561679840088,
-0.0008452431065961719,
0.05104167014360428,
0.030602769926190376,
0.0024028641637414694,
0.03282741457223892,
0.016110064461827278,
-0.026361197233200073,
-0.012410229071974754,
-0.045871343463659286,
0.005519626196473837,
-0.043285220861434937,
-0.037913866341114044,
0.06941276788711548
] |
<p>I know the main problem with a quantum computer is that you can't read and write data from it until after it has run though all of its calculations. But would reading and writing quantum data to particles <i>without collapsing their probability fields</i> make this possible?</p> | g1245 | [
0.010050184093415737,
0.04136047512292862,
0.013904192484915257,
-0.07500029355287552,
-0.026950368657708168,
0.018408896401524544,
0.007518780883401632,
0.045381538569927216,
-0.05426071211695671,
-0.01707872748374939,
0.024198563769459724,
0.005003290716558695,
0.011320584453642368,
-0.02853216975927353,
-0.03537173196673393,
0.08533346652984619,
0.006777591537684202,
0.012832680717110634,
0.04821464419364929,
0.05431978031992912,
0.01654641516506672,
0.02430744655430317,
-0.01782657392323017,
-0.006667494308203459,
-0.0932905301451683,
-0.007918964140117168,
-0.06707624346017838,
-0.07707541435956955,
-0.005312209017574787,
-0.017540350556373596,
0.018657822161912918,
-0.021044043824076653,
-0.006462507881224155,
-0.053801339119672775,
0.031111828982830048,
-0.014831486158072948,
-0.05898568406701088,
-0.042762257158756256,
0.01198165025562048,
0.017235977575182915,
-0.009529497474431992,
-0.03426598384976387,
-0.013064238242805004,
-0.040074672549963,
-0.002626257250085473,
0.058007240295410156,
0.05056086182594299,
0.02054702118039131,
-0.02135549671947956,
-0.0513252355158329,
0.01321424636989832,
-0.02209225296974182,
-0.01136072538793087,
0.05931044742465019,
0.08001705259084702,
0.08408831804990768,
-0.005842416547238827,
-0.006406744476407766,
0.09192550182342529,
-0.04266086220741272,
0.008704845793545246,
-0.033984772861003876,
-0.004196538589894772,
0.013144653290510178,
-0.007611066568642855,
0.0012191110290586948,
-0.054942090064287186,
0.0013996094930917025,
-0.04015013203024864,
0.03577683866024017,
0.026186540722846985,
-0.018004007637500763,
-0.012849049642682076,
-0.05582921579480171,
0.05104513838887215,
0.013796432875096798,
0.0036372344475239515,
-0.025618303567171097,
0.030222482979297638,
0.049483079463243484,
-0.05803091451525688,
-0.05199902504682541,
-0.0007092914311215281,
-0.030464494600892067,
0.02690056338906288,
-0.0059377653524279594,
-0.03183414041996002,
-0.03146521747112274,
0.017587343230843544,
0.028433475643396378,
-0.04048933461308479,
-0.011134158819913864,
0.06375004351139069,
0.004276878200471401,
0.03164619579911232,
-0.003995114006102085,
-0.02751503698527813,
-0.00018948146316688508,
-0.06199416145682335,
-0.0022148811258375645,
0.0020099906250834465,
-0.0484972819685936,
0.06495232880115509,
0.0012664675014093518,
-0.04435885697603226,
-0.08886826038360596,
-0.0010387676302343607,
0.020619571208953857,
0.04858260601758957,
-0.01357431523501873,
-0.02810720168054104,
0.024400489404797554,
0.0037357897963374853,
0.02978011965751648,
-0.01700076274573803,
-0.002305836183950305,
0.047351717948913574,
-0.011493382975459099,
-0.05961071699857712,
0.03307019919157028,
-0.03773970901966095,
-0.0036843540146946907,
0.013377761468291283,
-0.027206024155020714,
-0.04186854138970375,
0.00241858814842999,
-0.013137605041265488,
0.05635553598403931,
0.017887553200125694,
0.006799541879445314,
0.027516337111592293,
0.06557665765285492,
-0.030977396294474602,
0.07610853761434555,
-0.05106242001056671,
0.04871285334229469,
-0.01281548012048006,
-0.011970020830631256,
0.030363399535417557,
-0.01238257810473442,
0.010080506093800068,
-0.022000279277563095,
-0.03749200701713562,
0.03189556673169136,
0.02963470295071602,
0.008535132743418217,
-0.0025579414796084166,
0.016836103051900864,
0.006994972005486488,
0.0645420253276825,
-0.0019415506394580007,
-0.03481040149927139,
0.024949023500084877,
-0.043964289128780365,
0.05027855560183525,
0.02220490761101246,
0.08007994294166565,
-0.0003537856391631067,
0.006841843947768211,
-0.0043644169345498085,
0.027566177770495415,
0.002090452006086707,
0.014016332104802132,
-0.03943260759115219,
-0.027181271463632584,
-0.0166934784501791,
-0.032841432839632034,
-0.0008590364013798535,
0.007945033721625805,
-0.046525660902261734,
-0.015985790640115738,
0.008136903867125511,
-0.031076880171895027,
0.022441888228058815,
-0.010885924100875854,
0.03326249495148659,
-0.036944739520549774,
0.013696172274649143,
0.01639993116259575,
-0.015463486313819885,
-0.025505753234028816,
0.01517840288579464,
-0.00044648200855590403,
0.009085217490792274,
-0.016748584806919098,
-0.04634454473853111,
0.0006615561433136463,
0.030598830431699753,
0.03134045749902725,
-0.035423438996076584,
-0.0540878102183342,
-0.010471791960299015,
0.03867477551102638,
0.009961578994989395,
0.03573974221944809,
-0.0244454238563776,
0.012122358195483685,
-0.05096130445599556,
0.007514674682170153,
0.030760010704398155,
0.03126482293009758,
0.07514206320047379,
-0.03886063024401665,
-0.007836849428713322,
0.06656834483146667,
-0.0018449254566803575,
-0.0025382523890584707,
-0.011534556746482849,
-0.03049275651574135,
-0.05379487946629524,
0.09799759089946747,
0.03694693371653557,
0.05372997745871544,
0.011813499964773655,
-0.005492610391229391,
-0.005521264858543873,
0.01653515361249447,
-0.03548303246498108,
0.007027843967080116,
-0.0041831620037555695,
-0.07127143442630768,
-0.03917478024959564,
0.07334983348846436,
-0.036365605890750885,
-0.004266825038939714,
0.07375112920999527,
-0.03637465089559555,
-0.025110546499490738,
-0.056502796709537506,
-0.015894481912255287,
-0.0873895213007927,
0.01016111858189106,
-0.045426659286022186,
0.011680619791150093,
0.04741339758038521,
0.06651448458433151,
-0.012558897957205772,
-0.005491691175848246,
0.04251433163881302,
0.015568284317851067,
-0.01849900186061859,
-0.03795403614640236,
0.02525528520345688,
-0.07186643034219742,
0.01916280947625637,
-0.05695699155330658,
-0.053171299397945404,
0.035069067031145096,
-0.008896393701434135,
-0.008500938303768635,
0.04513748735189438,
-0.06179066002368927,
-0.03983915224671364,
0.02794612944126129,
0.004377057775855064,
-0.006932761985808611,
0.006399169564247131,
-0.003794287797063589,
-0.017116375267505646,
-0.02098357118666172,
0.04212909936904907,
0.01316582877188921,
-0.03147175535559654,
0.03845648840069771,
0.03635600581765175,
0.018866175785660744,
0.027647556737065315,
0.025787582620978355,
-0.0013641148107126355,
0.02198929525911808,
0.00014030840247869492,
-0.006145236548036337,
0.0032409506384283304,
0.0034642331302165985,
0.017379270866513252,
-0.0012040570145472884,
-0.031092917546629906,
-0.04924419894814491,
0.014111177995800972,
-0.044712699949741364,
-0.06949808448553085,
0.0030501428991556168,
-0.028919989243149757,
0.02344954013824463,
0.010044730268418789,
-0.089121513068676,
-0.05379672348499298,
0.02659010700881481,
0.051988035440444946,
0.027628792449831963,
0.027985911816358566,
0.02872077003121376,
0.041728999465703964,
0.004839412868022919,
-0.0614682212471962,
0.04989350587129593,
0.017961084842681885,
0.02089472860097885,
0.0019129844149574637,
0.10769723355770111,
-0.05245574563741684,
0.019832707941532135,
0.004607788752764463,
0.04611562192440033,
-0.015430859290063381,
0.04149635508656502,
-0.07206276804208755,
0.06721381098031998,
-0.008060390129685402,
-0.07710098475217819,
0.0070670186541974545,
0.049355294555425644,
0.023213330656290054,
0.026012016460299492,
0.005678983870893717,
-0.04432553052902222,
-0.03119458630681038,
0.026050973683595657,
0.00668652169406414,
-0.028943339362740517,
-0.02873348630964756,
0.01195639930665493,
0.015520414337515831,
-0.024018369615077972,
0.08141028881072998,
0.05075618252158165,
-0.0112668601796031,
0.049713537096977234,
-0.02422874979674816,
-0.02817603200674057,
0.02854118123650551,
0.0022634908091276884,
0.022723205387592316,
0.02350897341966629,
-0.05254309996962547,
0.005300864577293396,
-0.02724372036755085,
-0.011850151233375072,
0.002418561838567257,
0.008681269362568855,
-0.01511980127543211,
0.019562039524316788,
-0.00041656752000562847,
0.02380436658859253,
0.026944849640130997,
0.020328758284449577,
0.026533737778663635,
-0.04117685183882713,
0.045026738196611404,
-0.02183985337615013,
0.0277822595089674,
0.0038044925313442945,
0.025313377380371094,
-0.002273354446515441,
0.017488669604063034,
0.016766294836997986,
-0.05614015832543373,
0.02583327144384384,
0.03085510805249214,
0.006641403306275606,
-0.018534423783421516,
-0.05142568424344063,
0.0977461040019989,
0.02984461560845375,
-0.01668347790837288,
-0.022290842607617378,
-0.0354820191860199,
-0.0022590376902371645,
0.05733819678425789,
0.05447707325220108,
-0.0028462198097258806,
-0.030624469742178917,
0.018242720514535904,
-0.02185315638780594,
0.011692558415234089,
-0.026136476546525955,
0.042397480458021164,
-0.04250263422727585,
0.007321376819163561,
0.030015235766768456,
0.013822725042700768,
-0.04740443825721741,
0.054400570690631866,
-0.011007536202669144,
0.010546695441007614,
0.016843609511852264,
-0.03290676325559616,
-0.013401909731328487,
-0.014560790732502937,
0.05942590534687042,
0.007617853116244078,
-0.05620431527495384,
-0.04172179847955704,
0.019813885912299156,
-0.020429158583283424,
0.013821685686707497,
-0.03483486920595169,
-0.053504154086112976,
-0.007479723077267408,
0.009049574844539165,
-0.03996799513697624,
0.04226011782884598,
0.033183105289936066,
0.06742458790540695,
0.011075335554778576,
-0.041926994919776917,
0.0036724114324897528,
0.04117162525653839,
-0.02999309077858925,
-0.04487572982907295,
-0.028284674510359764,
-0.06361352652311325,
0.04865236207842827,
0.05344066023826599,
-0.004128235392272472,
0.027692154049873352,
0.02598251774907112,
-0.023912616074085236,
0.009276089258491993,
-0.02428540214896202,
0.010264363139867783,
-0.02255268394947052,
0.06457439810037613,
0.022103693336248398,
-0.02601390704512596,
-0.001218185294419527,
0.015804557129740715,
-0.0025638772640377283,
-0.01896519958972931,
0.042576055973768234,
0.03622690215706825,
0.027013443410396576,
0.04499777778983116,
-0.020846201106905937,
-0.01204637810587883,
0.0024438840337097645,
-0.0032125215511769056,
-0.012449211440980434,
0.00452665239572525,
0.0036386887077242136,
0.0453258752822876,
-0.040024686604738235,
0.027401287108659744,
-0.01015783753246069,
0.012027942575514317,
0.04707919806241989,
-0.07757576555013657,
-0.0008185632759705186,
0.007862260565161705,
-0.00871563982218504,
0.006901261396706104,
-0.010438780300319195,
-0.03600016608834267,
-0.015500417910516262,
-0.023047886788845062,
-0.023060061037540436,
-0.03294377028942108,
0.021517163142561913,
0.029340500012040138,
0.08923152834177017,
-0.05339043214917183,
0.014524849131703377,
-0.0031393233221024275,
0.013825771398842335,
-0.06448661535978317,
0.017194267362356186,
-0.046966101974248886,
0.010705109685659409,
-0.04575267806649208,
-0.014969060197472572,
-0.023720886558294296,
-0.0028546631801873446,
0.026761887595057487,
0.00006871725054224953,
-0.005985660944133997,
-0.05624189227819443,
-0.057160548865795135,
-0.044136665761470795,
0.008002818562090397,
-0.010111324489116669,
0.031721219420433044,
0.024915620684623718,
0.00944516621530056,
0.037399329245090485,
-0.030054686591029167,
0.0016628348967060447,
-0.025934066623449326,
0.052614420652389526,
-0.05798054859042168,
-0.030931806191802025,
-0.014526409097015858,
-0.011382718570530415,
0.011320676654577255,
0.03032696433365345,
0.02777992933988571,
-0.06655728071928024,
0.034490689635276794,
0.014734383672475815,
-0.012368951924145222,
0.040079668164253235,
0.009173233062028885,
-0.032099250704050064,
-0.015106390230357647,
0.011749965138733387,
-0.01590956375002861,
0.0022399527952075005,
-0.005852479953318834,
0.015326361171901226,
0.00867550354450941,
0.028804371133446693,
-0.0052642677910625935,
-0.03109658882021904,
-0.041800156235694885,
0.007958700880408287,
0.015723558142781258,
0.02187623456120491,
-0.06010574474930763,
-0.007997947745025158,
-0.006879714317619801,
-0.010513076558709145,
-0.0027248109690845013,
0.043107323348522186,
0.011012528091669083,
0.029397400096058846,
-0.0447455458343029,
0.009740403853356838,
-0.056620579212903976,
-0.058090392500162125,
0.02972026728093624,
0.03503664582967758,
0.06279419362545013,
0.054030902683734894,
-0.023485666140913963,
0.00939259771257639,
-0.06234991177916527,
-0.03330940008163452,
-0.0039021787233650684,
0.01020024809986353,
0.0004164061101619154,
0.10243701934814453,
-0.014782403595745564,
0.00790015421807766,
0.013762199319899082,
0.06709819287061691,
0.03713351860642433,
-0.03427787870168686,
-0.0341200977563858,
0.0344921313226223,
0.006070910487323999,
-0.0592743344604969,
-0.051725175231695175,
0.019131863489747047,
-0.028858903795480728,
-0.015667950734496117,
0.00040734390495344996,
0.04863597825169563,
-0.007976874709129333,
-0.030315496027469635,
0.0339447520673275,
-0.019227029755711555,
0.022600460797548294,
-0.031433019787073135,
0.045515574514865875,
0.02114582620561123,
0.018722472712397575,
0.09796024858951569,
-0.04569818452000618,
0.011228889226913452,
0.04063962399959564,
0.0065004886128008366,
0.013456388376653194,
-0.01361418142914772,
-0.02519572339951992,
-0.011331573128700256,
-0.002898138016462326,
-0.02504454366862774,
0.07095585763454437,
-0.07738766074180603,
-0.032849252223968506,
-0.04995056241750717,
0.019748566672205925,
-0.0030679877381771803,
-0.03146129101514816,
-0.028341129422187805,
0.016069240868091583,
-0.011028258129954338,
-0.035275354981422424,
0.0704471617937088,
0.057639867067337036,
0.03718356415629387,
-0.028213152661919594,
-0.018600178882479668,
0.009107553400099277,
-0.06469199061393738,
-0.03510335460305214,
0.02034248597919941,
0.013849079608917236,
0.003877283539623022,
-0.032413240522146225,
-0.014512049034237862,
-0.01812567003071308,
-0.043059881776571274,
-0.05335855484008789,
-0.02512991428375244,
-0.05227776989340782,
0.04949824512004852,
-0.018068470060825348,
0.05233875662088394,
0.015289060771465302,
-0.03111199103295803,
-0.014901748858392239,
-0.01895367167890072,
0.0356445275247097,
0.012327082455158234,
0.016061674803495407,
-0.06960271298885345,
0.01422206126153469,
-0.014077574945986271,
-0.00017722789198160172,
-0.004160764627158642,
0.07226201146841049,
0.014217894524335861,
-0.04650059714913368,
-0.024320892989635468,
-0.025086482986807823,
0.04799564555287361,
-0.018725324422121048,
0.04366631060838699,
0.1217670887708664,
0.01473595667630434,
0.016145512461662292,
0.017942048609256744,
0.047573719173669815,
0.007525492925196886,
0.04234077036380768,
0.039037372916936874,
-0.052416134625673294,
-0.01309947855770588,
-0.027831925079226494,
0.009463058784604073,
0.011690257117152214,
-0.02138003334403038,
0.031819671392440796,
0.024459384381771088,
-0.03752252459526062,
0.031162532046437263,
0.03909601271152496,
0.01572440005838871,
-0.09730079770088196,
-0.010372981429100037,
0.0008031373145058751,
-0.014917046763002872,
-0.006819522939622402,
-0.001875696238130331,
0.01787492446601391,
0.03455667197704315,
-0.0015457550762221217,
0.00282417144626379,
-0.053331632167100906,
-0.06725318729877472,
0.03607095777988434,
-0.06214313209056854,
0.01810644380748272,
-0.08362150192260742,
0.05514536798000336,
0.0031695400830358267,
0.007238028571009636,
0.00026117576635442674,
-0.002201199298724532,
0.01564066670835018,
-0.02715114690363407,
-0.07582614570856094,
-0.09677059948444366,
-0.020467864349484444,
0.05318772420287132,
-0.029964013025164604,
-0.029949862509965897,
0.05438939109444618,
-0.024864906445145607,
0.010954270139336586,
-0.04018344730138779,
-0.01943870447576046,
-0.018511440604925156,
-0.012062453664839268,
0.03999966382980347,
0.05599512904882431,
0.02345041185617447,
0.009614863432943821,
0.011972897686064243,
0.0010658933315426111,
0.03287900984287262,
-0.026062585413455963,
0.04462645575404167,
-0.09115272760391235,
0.0026009788271039724,
0.02717248909175396,
0.026109324768185616,
-0.009206169284880161,
0.09762799739837646,
0.002278614556416869,
-0.004096583928912878,
0.021467184647917747,
0.03822347894310951,
-0.020409176126122475,
-0.004321153275668621,
0.014323429204523563,
-0.007076513022184372,
0.05002593249082565,
-0.06629740446805954,
-0.007314734626561403,
0.054621435701847076,
0.006515887565910816,
-0.039637241512537,
0.016441352665424347,
0.009809449315071106,
-0.02695947326719761,
-0.025024423375725746,
0.02253878116607666,
-0.0065872548148036,
-0.030013807117938995,
-0.023779721930623055,
-0.014005852863192558,
-0.023313814774155617,
0.02895861491560936,
0.029749322682619095,
-0.02309100329875946,
-0.060177527368068695,
0.035340238362550735,
-0.04495861381292343,
-0.006718904245644808,
0.043094586580991745,
0.005701275076717138,
-0.03634479269385338,
-0.024865025654435158,
0.011166519485414028,
0.0006831199862062931,
-0.10845881700515747,
0.00912468321621418,
-0.028726117685437202,
0.011709584854543209,
0.006316294427961111,
0.0495450422167778,
0.007286050356924534,
-0.016190815716981888,
-0.003247411921620369,
-0.07163748890161514,
-0.05138321965932846,
0.017048096284270287,
0.040266379714012146,
0.011014374904334545,
0.004072144627571106,
-0.07879588752985,
-0.010160030797123909,
0.056418273597955704,
0.02659401297569275,
-0.02244502305984497,
0.013148806989192963,
0.0678308755159378,
-0.009570690803229809,
-0.014462949708104134,
0.04460105672478676,
0.024441765621304512,
-0.009687472134828568,
-0.010286396369338036,
-0.05660025030374527,
-0.016312377527356148,
0.0013596294447779655,
0.07053390890359879
] |
<p>Interacting fermionic SPT phases in 1d and 3d with $\mathbb{Z}_2^T$ symmetry are classified by $\mathbb{Z}_8$ and $\mathbb{Z}_{16}$ respectively, as shown in the paper by Fidkowski and Kitaev <a href="http://arxiv.org/abs/1008.4138" rel="nofollow">http://arxiv.org/abs/1008.4138</a>, and Wang and Senthil <a href="http://arxiv.org/abs/1401.1142" rel="nofollow">http://arxiv.org/abs/1401.1142</a>. I'd like to know the classification for the 2d case. Can anyone suggest some reference on that?</p> | g1246 | [
0.008523408323526382,
-0.06445801258087158,
-0.01731509156525135,
-0.008383304812014103,
0.03096071258187294,
0.041419610381126404,
0.016939863562583923,
-0.004189098719507456,
0.004356174264103174,
-0.005198281724005938,
-0.002949310466647148,
0.03243974596261978,
0.03345764800906181,
-0.008258208632469177,
-0.023330440744757652,
0.03944879025220871,
0.028599614277482033,
0.050853461027145386,
-0.018099525943398476,
-0.020849071443080902,
0.007128809578716755,
0.004666301421821117,
-0.031140075996518135,
-0.03067632205784321,
0.039407625794410706,
0.012908602133393288,
-0.03041277453303337,
-0.05757395550608635,
-0.0023563290014863014,
-0.02091551385819912,
0.03400517255067825,
0.04512878507375717,
0.019590038806200027,
0.0034652426838874817,
-0.02012888714671135,
-0.06993039697408676,
0.11852966994047165,
-0.014418940991163254,
-0.0010793044930323958,
-0.015385627746582031,
-0.01378189492970705,
0.007464516442269087,
-0.0004260667774360627,
-0.06552614271640778,
-0.030129102990031242,
-0.011544094420969486,
-0.02181987278163433,
0.026003411039710045,
-0.06337285041809082,
0.06288059055805206,
0.0973481610417366,
0.01544881984591484,
0.05936383083462715,
0.00621986435726285,
-0.013605242595076561,
-0.08202748745679855,
-0.0323261134326458,
-0.017176350578665733,
0.015023785643279552,
0.0502762496471405,
-0.029853522777557373,
0.033700376749038696,
0.01420322060585022,
0.038596007972955704,
0.018336879089474678,
-0.006417145486921072,
-0.017919272184371948,
-0.03720386326313019,
0.02339843288064003,
-0.06879353523254395,
0.00800376757979393,
0.035952046513557434,
0.019826285541057587,
0.037644244730472565,
-0.025530818849802017,
-0.020855741575360298,
-0.03395099565386772,
-0.09673110395669937,
-0.0020011139567941427,
-0.007788645103573799,
-0.001795626012608409,
-0.013137667439877987,
0.007634392939507961,
-0.0264281053096056,
-0.01342074852436781,
-0.003996304702013731,
0.0002844890404958278,
-0.008328055031597614,
-0.06242303550243378,
0.007644781842827797,
-0.05688763037323952,
-0.050111036747694016,
-0.026747101917862892,
-0.0007823015912435949,
0.02303015999495983,
0.04324398189783096,
0.03380758315324783,
0.0012322112452238798,
0.009021070785820484,
-0.06396109610795975,
-0.00837759766727686,
0.012327637523412704,
0.0341707319021225,
0.04020731523633003,
-0.01937035098671913,
0.02127162739634514,
-0.021092023700475693,
-0.03254465386271477,
0.022254180163145065,
0.062185440212488174,
-0.012230255641043186,
0.05184667557477951,
-0.014139242470264435,
0.0056491419672966,
-0.0211945790797472,
0.04329986870288849,
0.030109142884612083,
-0.09366727620363235,
0.008155709132552147,
-0.0232156440615654,
0.0774383544921875,
-0.0001659499976085499,
0.04745851457118988,
0.060945991426706314,
0.013057348318397999,
0.03009667433798313,
-0.06272416561841965,
-0.05311186611652374,
0.012727402150630951,
-0.04183564707636833,
-0.02185642719268799,
-0.02852911502122879,
0.027765735983848572,
-0.0003271093883085996,
-0.006878283806145191,
0.07266397774219513,
0.025609690696001053,
-0.0074084154330194,
-0.025835026055574417,
-0.025880010798573494,
0.005806023254990578,
-0.03268657252192497,
-0.014891864731907845,
-0.012196668423712254,
0.022158818319439888,
-0.032939206808805466,
0.003066674806177616,
-0.042549438774585724,
-0.029999231919646263,
0.03752642124891281,
0.051631513983011246,
0.030103716999292374,
-0.009988179430365562,
0.0035531793255358934,
-0.10035259276628494,
-0.002918294630944729,
-0.008563404902815819,
-0.004020914901047945,
0.06103489175438881,
-0.011121398769319057,
-0.009563103318214417,
-0.02155645191669464,
-0.048760779201984406,
-0.042278602719306946,
-0.007651941850781441,
-0.035943128168582916,
0.03071240335702896,
-0.03157860040664673,
-0.029317805543541908,
0.02915044315159321,
0.004866163711994886,
0.0665958896279335,
-0.013149485923349857,
0.04751905798912048,
-0.01735870912671089,
-0.00016294098168145865,
-0.08458739519119263,
0.02487397938966751,
0.018154991790652275,
0.023692946881055832,
-0.010980871506035328,
-0.020708555355668068,
-0.04141540452837944,
0.03529706969857216,
-0.001184698543511331,
-0.015745503827929497,
0.005984408315271139,
0.014850285835564137,
0.00932644959539175,
0.028336968272924423,
0.023019511252641678,
-0.014196566306054592,
0.019886381924152374,
0.028380032628774643,
-0.02823229879140854,
-0.03413023054599762,
0.08475012332201004,
0.013465303927659988,
-0.09387107938528061,
-0.05413970351219177,
0.015118847601115704,
0.041778627783060074,
-0.01406112965196371,
0.0034529203549027443,
0.020925618708133698,
0.03327949345111847,
-0.003774390323087573,
0.037285733968019485,
-0.011475336737930775,
0.00007369635568466038,
-0.015216915868222713,
-0.01429749559611082,
0.005417775362730026,
-0.001206402201205492,
0.013036469928920269,
-0.029890883713960648,
-0.007249308284372091,
0.04409061372280121,
-0.04624049365520477,
-0.007747919298708439,
0.03310400992631912,
-0.024364009499549866,
-0.034899674355983734,
0.013264866545796394,
0.032284609973430634,
0.01572306454181671,
-0.013910767622292042,
0.07453810423612595,
0.027125630527734756,
0.011457990854978561,
-0.04109394550323486,
-0.002667729277163744,
-0.08904054015874863,
-0.020847711712121964,
-0.011848156340420246,
0.04273959994316101,
-0.04232146590948105,
0.020506152883172035,
0.008879697881639004,
-0.005260261707007885,
0.014007125981152058,
0.027525709941983223,
-0.02488076128065586,
0.003202622989192605,
0.032591186463832855,
-0.021781541407108307,
0.011832397431135178,
0.06736254692077637,
0.050985295325517654,
0.006859392859041691,
-0.01184421218931675,
-0.005975733045488596,
-0.016929268836975098,
0.02150147780776024,
0.00039750614087097347,
0.007182118017226458,
0.058560941368341446,
0.035028379410505295,
-0.04526790603995323,
-0.07431815564632416,
0.06821776926517487,
-0.0026130839250981808,
0.03095170482993126,
-0.017012201249599457,
0.06547662615776062,
-0.04417750611901283,
0.005670578684657812,
0.01752948760986328,
-0.015340015292167664,
-0.0004862158093601465,
0.003066237550228834,
0.06575017422437668,
-0.03532363474369049,
-0.061935052275657654,
-0.015564290806651115,
-0.03987738862633705,
0.021753164008259773,
-0.014602310955524445,
-0.030461575835943222,
-0.019239820539951324,
-0.014607287012040615,
-0.01734676957130432,
0.033138420432806015,
0.05937163159251213,
0.07099856436252594,
-0.019899096339941025,
-0.013638375326991081,
-0.013026867993175983,
-0.09826362878084183,
0.026214294135570526,
0.04855281114578247,
-0.05594508722424507,
-0.020998600870370865,
0.0057169729843735695,
0.009111855179071426,
-0.06809839606285095,
-0.03724605217576027,
-0.0016533012967556715,
-0.012683345004916191,
0.0668984055519104,
0.03518909588456154,
-0.04314609244465828,
0.031242234632372856,
-0.007199893239885569,
0.03887387737631798,
-0.06072530895471573,
-0.04023841768503189,
-0.04126528277993202,
-0.04773068055510521,
-0.050944674760103226,
-0.04356331005692482,
0.09434902667999268,
0.035717763006687164,
0.01728392206132412,
-0.014353812672197819,
0.012636669911444187,
-0.006120461039245129,
0.020731445401906967,
0.019213173538446426,
-0.03788868337869644,
-0.058069560676813126,
0.06328532844781876,
0.013372864574193954,
0.02136879414319992,
-0.014256510883569717,
0.041725896298885345,
-0.02497907169163227,
-0.0007990931626409292,
-0.01214083656668663,
-0.007361961994320154,
-0.010823410004377365,
-0.03513846546411514,
-0.027618946507573128,
-0.0799727588891983,
-0.03168636932969093,
-0.011302645318210125,
-0.02616799995303154,
0.030672257766127586,
-0.013201526366174221,
-0.04335607960820198,
0.009671059437096119,
0.017554886639118195,
0.05112846568226814,
0.006235615350306034,
0.06461978703737259,
-0.011604501865804195,
-0.03067144565284252,
-0.03994983807206154,
-0.033266473561525345,
0.015264288522303104,
0.0015419768169522285,
0.021123189479112625,
0.027071533724665642,
0.04889379441738129,
-0.0030024030711501837,
0.007480727043002844,
-0.0030735686887055635,
-0.03151706978678703,
-0.008822272531688213,
-0.007087545935064554,
0.022549107670783997,
0.012400330975651741,
-0.012043315917253494,
0.022654086351394653,
-0.045518387109041214,
-0.004738501273095608,
0.03181624785065651,
0.01617688313126564,
0.010826686397194862,
0.0087858522310853,
0.03556057810783386,
-0.056648120284080505,
0.016309654340147972,
-0.0041399067267775536,
0.03712867572903633,
-0.0068098618648946285,
-0.0003194645687472075,
-0.008846675045788288,
-0.027278169989585876,
-0.007122004870325327,
0.02943642996251583,
-0.07029470056295395,
0.052081771194934845,
0.02827482670545578,
0.05446527525782585,
0.021122721955180168,
0.02070808969438076,
0.025438515469431877,
-0.07235251367092133,
-0.011850066483020782,
0.05799819156527519,
0.02248961105942726,
-0.0013227959861978889,
-0.06291862577199936,
-0.014344406314194202,
0.021311748772859573,
-0.0037152660079300404,
0.05769720301032066,
0.022614430636167526,
-0.0026633504312485456,
-0.09550791233778,
-0.06548215448856354,
0.024037091061472893,
-0.10181295871734619,
-0.013989875093102455,
-0.008641879074275494,
-0.02297794818878174,
-0.010204900056123734,
-0.006022939924150705,
-0.0006045611225999892,
-0.0554269403219223,
0.07601892203092575,
0.0311112217605114,
0.00687198294326663,
0.05288229137659073,
-0.05180642381310463,
-0.04951910302042961,
-0.07806259393692017,
0.01920432597398758,
-0.02158120460808277,
0.02057858370244503,
0.008990159258246422,
0.018904024735093117,
-0.0489894263446331,
0.02781371958553791,
-0.005691962782293558,
0.059545647352933884,
-0.004986322019249201,
-0.12376030534505844,
0.02426358498632908,
-0.002778278896585107,
-0.019025461748242378,
-0.001185555593110621,
-0.011849208734929562,
-0.052360162138938904,
-0.07241179049015045,
-0.015029720030725002,
0.003639156697317958,
0.04093841463327408,
0.0019167595310136676,
0.04551760107278824,
-0.02783629298210144,
-0.041789211332798004,
0.017538128420710564,
0.03557664155960083,
-0.024912092834711075,
-0.04449586942791939,
-0.011907313950359821,
-0.007615576032549143,
0.06720949709415436,
-0.04353109374642372,
0.059850774705410004,
0.012377950362861156,
-0.0005961328279227018,
0.03202192485332489,
-0.021811842918395996,
0.029961280524730682,
-0.0003153950965497643,
-0.0187749695032835,
-0.010170952416956425,
-0.04170659929513931,
-0.029398124665021896,
0.036674220114946365,
-0.02922656014561653,
0.04978759586811066,
-0.00477015133947134,
-0.048875559121370316,
-0.01849152147769928,
-0.004720035940408707,
-0.0258499588817358,
-0.017312226817011833,
0.00027780557866208255,
0.015268196351826191,
-0.021214082837104797,
0.04163764789700508,
0.023981329053640366,
-0.06276623904705048,
-0.041818615049123764,
-0.015352269634604454,
-0.02516641840338707,
0.035979583859443665,
-0.028543885797262192,
0.06459391117095947,
0.0090685049071908,
-0.0042088148184120655,
0.016294360160827637,
-0.0006351256160996854,
0.015422411262989044,
0.007976964116096497,
-0.04157243296504021,
-0.009868352673947811,
-0.016570154577493668,
-0.0618860088288784,
-0.002104502636939287,
-0.02148657664656639,
0.024905143305659294,
0.06098499894142151,
0.004484016448259354,
0.006277694366872311,
0.07552362233400345,
-0.027857668697834015,
-0.009841885417699814,
0.05077666789293289,
0.03694048151373863,
0.013699880801141262,
0.05855384096503258,
0.12230978906154633,
-0.03824712708592415,
-0.05791215971112251,
-0.023642368614673615,
-0.003687598742544651,
0.012988466769456863,
-0.008587596006691456,
-0.03187546879053116,
-0.028161529451608658,
0.037505295127630234,
0.021990222856402397,
0.014298018999397755,
-0.012195674702525139,
-0.026211151853203773,
-0.005023893900215626,
-0.00011983155127381906,
-0.045840032398700714,
-0.08630586415529251,
0.005834272131323814,
-0.015674881637096405,
-0.04991011694073677,
-0.012215571478009224,
0.035850510001182556,
-0.0214438047260046,
0.027826692909002304,
0.011329281143844128,
-0.0056508854031562805,
-0.022199569270014763,
-0.01518109068274498,
-0.0357738621532917,
0.0019538116175681353,
0.012366235256195068,
0.041635431349277496,
0.045937031507492065,
0.014804114587605,
0.0004859876644331962,
-0.04444433003664017,
-0.027325578033924103,
0.041931942105293274,
0.004575501196086407,
0.05527744069695473,
0.019382398575544357,
-0.029819564893841743,
0.00891400221735239,
-0.009097103029489517,
0.02358546294271946,
-0.014628827571868896,
-0.04597476124763489,
0.00523559981957078,
0.008315317332744598,
0.006322512403130531,
0.024587133899331093,
0.0360342375934124,
-0.039036575704813004,
-0.03915984556078911,
0.04824787750840187,
-0.0323207713663578,
0.0021613703574985266,
-0.01600756123661995,
-0.035531606525182724,
-0.02294274978339672,
-0.007692508865147829,
-0.005392217077314854,
0.051329515874385834,
0.05830913037061691,
0.044871240854263306,
0.036720648407936096,
-0.008061797358095646,
0.040250394493341446,
0.005014721769839525,
0.010683299042284489,
0.014265335164964199,
0.038516219705343246,
-0.030797744169831276,
-0.02593272738158703,
0.04408625140786171,
0.03773604705929756,
0.0018324743723496795,
0.001783250248990953,
0.058580633252859116,
0.005309827160090208,
-0.026386262848973274,
-0.02425011247396469,
-0.029096631333231926,
0.016116812825202942,
-0.017515819519758224,
-0.04525802657008171,
0.016040900722146034,
0.04362545534968376,
-0.0006293648038990796,
0.0051409462466835976,
0.009359038434922695,
-0.018858367577195168,
0.08479441702365875,
0.008270173333585262,
-0.02123742364346981,
0.002156485104933381,
0.03889651596546173,
0.021195271983742714,
0.0672457367181778,
0.0023017076309770346,
0.10791471600532532,
0.044369444251060486,
0.06963461637496948,
-0.008325294591486454,
0.03177854046225548,
-0.06967128813266754,
0.014866555109620094,
0.016469715163111687,
-0.030399644747376442,
-0.0025001424364745617,
-0.017562193796038628,
-0.0005341521464288235,
-0.030813297256827354,
0.016874780878424644,
-0.02997857891023159,
-0.0609760582447052,
-0.04181960970163345,
0.0038104522973299026,
0.01188876386731863,
0.012653695419430733,
-0.028330007568001747,
0.07364881783723831,
-0.026715924963355064,
0.04860097914934158,
-0.058875225484371185,
0.0734611228108406,
0.03830879181623459,
0.010980064049363136,
0.0018548528896644711,
-0.06629189848899841,
-0.017195116728544235,
-0.02734890952706337,
0.04646340385079384,
-0.02912088856101036,
0.02974805422127247,
-0.0043863896280527115,
0.021821154281497,
-0.024291595444083214,
0.06192634254693985,
0.0037356119137257338,
0.019600993022322655,
-0.05492924153804779,
-0.01378726027905941,
0.014730161987245083,
0.002227535005658865,
-0.01935291476547718,
-0.04407019168138504,
-0.0715131163597107,
-0.06349857896566391,
0.02118486724793911,
0.01738089509308338,
0.028955765068531036,
0.01562533527612686,
-0.048553578555583954,
0.007221367210149765,
-0.047910671681165695,
-0.027425790205597878,
-0.012423114851117134,
0.050972163677215576,
0.02010725811123848,
0.03637920320034027,
-0.0023726618383079767,
-0.01635770872235298,
-0.08098019659519196,
0.0011985134333372116,
-0.03395281732082367,
-0.01999793015420437,
-0.030272584408521652,
-0.03717708960175514,
0.01744035631418228,
0.00990668497979641,
0.04382405802607536,
-0.020710885524749756,
0.06503789871931076,
0.021639831364154816,
0.012521292082965374,
-0.03639120236039162,
-0.006858901120722294,
0.017872653901576996,
0.05106275528669357,
-0.005412768572568893,
-0.013063742779195309,
0.023793255910277367,
-0.0032634257804602385,
0.0298667810857296,
-0.018701158463954926,
-0.02576528862118721,
-0.03506194055080414,
-0.024272410199046135,
0.019696088507771492,
0.03188519552350044,
-0.047417815774679184,
0.06300657242536545,
0.029412442818284035,
0.015288220718502998,
-0.04716059938073158,
0.040870361030101776,
-0.002139341551810503,
-0.014831628650426865,
0.005718911532312632,
-0.018556246533989906,
0.047248344868421555,
0.01797836273908615,
0.0098330182954669,
0.030912941321730614,
0.0501948818564415,
0.03833271935582161,
0.027869921177625656,
0.020679162815213203,
-0.06298866122961044,
-0.01238012034446001,
0.09306944161653519,
-0.0035803921055048704,
-0.01872892677783966,
0.011120928451418877,
0.0016987244598567486,
-0.035137347877025604,
-0.0724465548992157,
-0.060659509152173996,
0.060431234538555145,
0.025576507672667503,
0.07248720526695251,
0.04811622574925423,
-0.033121608197689056,
0.02358546108007431,
-0.037065599113702774,
0.051369596272706985,
-0.008586244657635689,
0.0660964772105217,
0.008740821853280067,
0.0016602504765614867,
0.01405888982117176,
0.0037227279972285032,
0.057916443794965744,
0.03226664289832115,
0.05449145287275314,
-0.0441439189016819,
-0.054568637162446976,
-0.020662205293774605,
-0.021062882617115974,
-0.00423832144588232,
0.03643535077571869,
0.004473000764846802,
-0.026613574475049973,
-0.0322551429271698,
0.034526389092206955,
0.004396545235067606,
0.008096345700323582,
-0.03918702155351639,
0.024139801040291786,
-0.015042080543935299,
0.009615694172680378,
-0.04471462965011597,
-0.02433961257338524,
0.02319863624870777,
-0.0032042115926742554,
0.05898324027657509,
-0.022130239754915237,
0.01869736611843109,
-0.048198677599430084,
0.051937319338321686
] |
<p>This is a problem that has been periodically bugging me, so I finally decided to work on it. I haven't done any physics since high school, so I'm a bit out of practice:</p>
<p>Consider a doorway with two hinged doors, one being the mirror of the other. Someone opens one of the doors (which open outward) and lets go, allowing the door to begin shutting. You want to walk though the doorway, but you need one of the doors to be fully open. When is it more optimal to open the closed door completely, as opposed to pulling the closing door back open? By optimal, I refer to the torque over time I would have to exert to open the door fully in time $t_{open}$</p>
<p><strong>Specifications</strong></p>
<ul>
<li>The doors use 2 manual door closers (a spring that is stretched when the door is open and pulls the door back) which are connected the top and bottom of the door (for simplicity) in such a way that they always pull perpendicular to the door frame</li>
<li>The doors have two sets of hinges equidistant from the center of the door (again, for simplicity)</li>
<li>The doors are fully open when they reach an angle $\theta_{open} < {\frac{\pi}{2}}$ from the frame.</li>
</ul>
<p><strong>Assumptions:</strong></p>
<ul>
<li>Ignoring friction/air resistance/gravity entirely</li>
<li>ignoring dampening mechanisms of door closer (I have no idea how they work)</li>
<li>Treating the door as though it had no width</li>
</ul>
<p><strong>Attempt</strong></p>
<p>So, we have a door of mass $m$ with length across $l_d$, and a handle offset some distance $l_h$ from the hinges of the door. There is are two springs connected to the inner side of the door some distance $l_{s}$ from the hinge edge.</p>
<p>Let the two springs each have a spring constant $\frac{k}{2}$. When offset some distance $x$, they pull on the door with force of magnitude $kx$, giving a torque on the door of $l_{s}kx\cos{\theta}$. The offset $x$ is related to $\theta$ by $l_{d}\sin{\theta} = x$, so torque is equal to $l_{d}l_{s}k\sin{\theta}\cos{\theta}$, and torque over time is equivalent. Since we can treat the door as a thin rod, moment of inertia $I$ of the door as $\frac{ml_{d}^{2}}{3}$, we know the angular acceleration $\alpha$ of the door: $$\alpha(t) = \frac{3l_{s}k\sin{\theta}\cos{\theta}}{ml_{d}}$$ Then, the angular velocity $\omega$ is : $$\omega(t) = \frac{3l_{s}k\sin{\theta}\cos{\theta}}{ml_{d}}t $$</p>
<p>and $\theta$ is: $$\theta(t) = \frac{3}{2}\frac{l_{s}k\sin{\theta}\cos{\theta}}{ml_{d}}t^2 $$</p>
<p>At this point, I pretty sure I've taken a wrong turn somewhere, probably involving conversion of angular acceleration to velocity, since theta is a function of time as well...</p>
<p>I feel like this is a problem I should be able to do relatively simply. Anyone want to help me along? Also, it seems like I'm probably over-complicating the situation...</p> | g1247 | [
0.050039906054735184,
0.032948076725006104,
0.02368558757007122,
0.004776827525347471,
0.0076591880060732365,
-0.028460578992962837,
0.11012212932109833,
0.03310081735253334,
-0.028263593092560768,
0.015278701670467854,
0.02950994297862053,
-0.01652231439948082,
-0.0528857447206974,
0.011681297793984413,
0.05801212415099144,
0.037288229912519455,
0.037282463163137436,
-0.016466738656163216,
0.06597074866294861,
0.03482361137866974,
-0.016815654933452606,
0.031028572469949722,
-0.01931610517203808,
-0.05423085018992424,
-0.01333603821694851,
0.0016767398919910192,
-0.05610382929444313,
0.043050941079854965,
-0.0238993838429451,
-0.020768607035279274,
0.017512548714876175,
0.006150390952825546,
0.0136421425268054,
-0.07354438304901123,
-0.09666807949542999,
-0.02685537375509739,
0.03876530006527901,
-0.0060354117304086685,
0.016545142978429794,
-0.012083428911864758,
0.021765124052762985,
-0.06304383277893066,
0.0112968934699893,
0.00405959552153945,
0.04357731342315674,
-0.0192104484885931,
0.024576470255851746,
0.007767297327518463,
-0.012424387037754059,
0.006752804387360811,
-0.02550162933766842,
0.023598691448569298,
-0.014583357609808445,
-0.010952126234769821,
-0.013578164391219616,
-0.0008943667053245008,
-0.00791200902312994,
-0.0425410158932209,
0.0381770096719265,
0.006616455037146807,
0.000634010590147227,
0.024529818445444107,
-0.04788851737976074,
-0.06366134434938431,
0.037824396044015884,
-0.008178706280887127,
0.030225440859794617,
0.004749342333525419,
0.08892945200204849,
-0.04236850142478943,
-0.013963080011308193,
-0.04600304365158081,
0.01564454846084118,
-0.06792357563972473,
0.0035679310094565153,
0.018584711477160454,
-0.01154342107474804,
-0.023445041850209236,
0.05328037962317467,
0.021353501826524734,
-0.09730169922113419,
-0.008361974731087685,
-0.01829197257757187,
0.02885013073682785,
0.042829979211091995,
0.0175592340528965,
0.003990937490016222,
0.021032460033893585,
0.017890000715851784,
-0.002975424751639366,
0.03334168717265129,
-0.04108226299285889,
0.026265501976013184,
-0.03412998095154762,
-0.03663462772965431,
0.0027720152866095304,
-0.013187825679779053,
0.05803891271352768,
0.0494699627161026,
0.05290753021836281,
0.00789644569158554,
-0.09530387818813324,
-0.009697728790342808,
-0.018230218440294266,
-0.02760620042681694,
-0.026577746495604515,
0.04210944101214409,
-0.009746295399963856,
-0.07934214919805527,
0.010155966505408287,
-0.05315512791275978,
0.021487658843398094,
0.024912791326642036,
-0.07566270977258682,
-0.0015688794665038586,
-0.014167251996695995,
0.040729083120822906,
0.044442273676395416,
0.022316357120871544,
0.05050280690193176,
-0.03303639590740204,
0.00951209757477045,
-0.039224326610565186,
0.0218804981559515,
-0.0041001541540026665,
-0.01694384217262268,
-0.04112393036484718,
-0.015247083269059658,
0.0018814373761415482,
-0.015544738620519638,
-0.03982327878475189,
0.02067641168832779,
0.041842859238386154,
0.04928913339972496,
-0.0030810688622295856,
0.07612942159175873,
-0.038973886519670486,
0.07697108387947083,
0.038870155811309814,
0.025137891992926598,
0.006810932885855436,
-0.04188475385308266,
-0.050865620374679565,
0.026199039071798325,
-0.0615893229842186,
0.07478520274162292,
-0.01879841834306717,
0.030030813068151474,
0.023330580443143845,
0.05503859743475914,
-0.026677802205085754,
0.050989408046007156,
-0.025656823068857193,
0.08822686225175858,
-0.020794454962015152,
-0.02549879066646099,
0.056594546884298325,
-0.05119458958506584,
0.017660563811659813,
-0.008563634939491749,
0.00940630678087473,
-0.0028484368231147528,
0.015592054463922977,
-0.03699162229895592,
-0.014149203896522522,
0.01615207828581333,
-0.044941049069166183,
-0.029439376667141914,
0.0008025937713682652,
-0.038207586854696274,
-0.09165263175964355,
0.004367777146399021,
0.061124078929424286,
0.010563808493316174,
-0.017264552414417267,
-0.017217960208654404,
0.07928425818681717,
-0.07534235715866089,
-0.013597431592643261,
0.020305627956986427,
0.022959541529417038,
-0.07956457138061523,
0.0641961619257927,
0.02120930887758732,
-0.0466105081140995,
-0.04919709265232086,
0.02864040993154049,
0.04205241799354553,
-0.0673704594373703,
-0.03485487028956413,
0.06203313171863556,
-0.0742451399564743,
0.0037692368496209383,
0.046544112265110016,
-0.06201993674039841,
0.007690394762903452,
0.013497456908226013,
-0.02048184536397457,
-0.013398543931543827,
0.0012492586392909288,
-0.029980771243572235,
0.0102570541203022,
0.030100660398602486,
0.03162515535950661,
-0.018758142367005348,
0.029044831171631813,
0.00765631627291441,
0.03455576300621033,
0.08960804343223572,
-0.013175219297409058,
0.011221029795706272,
0.02944694459438324,
-0.02498299442231655,
0.030190955847501755,
0.013658815063536167,
-0.043903231620788574,
-0.03448391333222389,
0.051740821450948715,
-0.003380361245945096,
-0.038920022547245026,
0.007506457157433033,
0.012742833234369755,
-0.0036944029852747917,
-0.050176117569208145,
-0.07041484862565994,
0.01918109692633152,
-0.020209848880767822,
-0.018989577889442444,
-0.017953554168343544,
0.006753194145858288,
0.0025813807733356953,
0.02633969485759735,
-0.0005300207994878292,
-0.02238503284752369,
0.051000311970710754,
-0.0038500307127833366,
-0.0030855818185955286,
0.07359780371189117,
0.010788215324282646,
-0.03181959688663483,
0.08858010172843933,
-0.03722396492958069,
-0.02649054490029812,
-0.022029805928468704,
-0.010700637474656105,
-0.059217702597379684,
-0.017421532422304153,
-0.03569011390209198,
0.011459414847195148,
-0.0017808479024097323,
-0.027971278876066208,
0.009667090140283108,
-0.05831785127520561,
-0.023609347641468048,
0.01057620532810688,
-0.01082976721227169,
0.0010506034595891833,
-0.01149020902812481,
-0.04435631260275841,
-0.04741540923714638,
0.009112739935517311,
-0.06527157127857208,
0.03750300034880638,
0.01244474295526743,
0.004731206689029932,
0.012123927474021912,
-0.00812237337231636,
-0.0023710643872618675,
-0.00026797130703926086,
0.01735575497150421,
0.026515956968069077,
0.05187986418604851,
-0.03493007645010948,
0.024766290560364723,
0.061180535703897476,
0.0018126916838809848,
-0.015958378091454506,
0.0017841876251623034,
0.01909514330327511,
0.014448828063905239,
-0.0492752306163311,
0.005586653016507626,
-0.026131348684430122,
0.043775420635938644,
0.041464123874902725,
-0.0515860915184021,
0.00041177382809109986,
0.012787078507244587,
-0.027802957221865654,
0.05231637880206108,
0.005412392783910036,
0.07758703082799911,
0.06473413109779358,
0.04948635771870613,
0.04722042381763458,
0.019531628116965294,
-0.042879436165094376,
-0.0030234663281589746,
-0.08341077715158463,
-0.012301485985517502,
-0.024976717308163643,
-0.046781495213508606,
-0.004064712207764387,
-0.01820405386388302,
0.024888653308153152,
-0.006973447743803263,
-0.003362223505973816,
-0.04844396561384201,
-0.017314786091446877,
0.057312414050102234,
-0.04848390445113182,
0.06576462090015411,
0.019194530323147774,
-0.0012412203941494226,
-0.03212304785847664,
-0.018783509731292725,
0.0025496934540569782,
0.01879866048693657,
-0.058702852576971054,
0.025297371670603752,
0.0026710904203355312,
-0.011082679033279419,
0.017989490181207657,
0.009649483487010002,
0.02449263446033001,
0.03502754494547844,
-0.04451294615864754,
0.010159417055547237,
-0.06077910214662552,
-0.03968559950590134,
0.03043132647871971,
0.07499188184738159,
0.007645175792276859,
-0.034106720238924026,
-0.05336861312389374,
0.035818371921777725,
-0.015166646800935268,
0.012057485058903694,
0.006497947499155998,
0.06318920850753784,
-0.026296058669686317,
-0.04105352237820625,
-0.07386468350887299,
-0.012662000954151154,
0.02613935060799122,
0.016214409843087196,
0.01112704910337925,
0.008053253404796124,
0.01500114519149065,
-0.0006114232237450778,
0.010827673599123955,
-0.0185360386967659,
-0.01196356862783432,
0.020514676347374916,
-0.017473379150032997,
0.03634973242878914,
-0.02630520612001419,
0.024359874427318573,
-0.022840945050120354,
0.016829445958137512,
0.0021104984916746616,
-0.003700998378917575,
-0.061770785599946976,
-0.034021683037281036,
-0.039343949407339096,
-0.03100357949733734,
0.03687494993209839,
0.05659133568406105,
0.00816420093178749,
-0.004998659249395132,
0.04109576344490051,
-0.031746819615364075,
0.009763124398887157,
-0.023145873099565506,
0.021587328985333443,
-0.052437420934438705,
0.04174501448869705,
0.011987579055130482,
0.045036040246486664,
0.03129911050200462,
-0.00932417530566454,
0.11184482276439667,
-0.046390365809202194,
0.0006521678296849132,
0.01059003733098507,
0.0462813638150692,
-0.03069552220404148,
-0.03442549332976341,
0.01604067161679268,
0.009175747632980347,
-0.005448242649435997,
0.00037629459984600544,
-0.01161598227918148,
0.0449087917804718,
0.041417915374040604,
0.011200900189578533,
0.01069206465035677,
0.005105695221573114,
-0.05417977645993233,
-0.011572807095944881,
-0.01971585489809513,
0.05976618826389313,
0.004792587365955114,
0.00697394460439682,
-0.056443389505147934,
0.047877829521894455,
0.016954300925135612,
0.052987873554229736,
-0.0317634716629982,
-0.010275314562022686,
0.016733234748244286,
-0.006936893332749605,
-0.0745694637298584,
0.02207763120532036,
-0.002800779649987817,
-0.015534463338553905,
0.004756176844239235,
-0.01261124573647976,
0.006756356917321682,
0.007171342149376869,
0.02033303678035736,
0.010457837954163551,
0.02816617116332054,
-0.021928373724222183,
0.01271101925522089,
0.06111490726470947,
0.06103881448507309,
0.04643136262893677,
0.004542932379990816,
-0.07325601577758789,
0.003315261797979474,
0.0027026794850826263,
0.014186025597155094,
-0.03211910277605057,
0.030302895233035088,
0.0019459546310827136,
0.0252812672406435,
0.0028407254721969366,
0.003335155313834548,
-0.010282712988555431,
-0.038742564618587494,
-0.01179442834109068,
0.017205098643898964,
0.027644477784633636,
-0.04401193931698799,
0.014049164019525051,
-0.039065565913915634,
-0.07453089952468872,
0.014210271649062634,
-0.07578016072511673,
-0.06749143451452255,
0.0250401571393013,
-0.033023443073034286,
-0.01215984858572483,
-0.0020139862317591906,
-0.016573360189795494,
-0.04360218718647957,
0.03393438458442688,
0.002607641275972128,
-0.012963901273906231,
-0.036526113748550415,
0.024500185623764992,
-0.05148061364889145,
0.011145038530230522,
0.03878121078014374,
-0.0005077469395473599,
-0.005360413808375597,
0.012818597257137299,
-0.03104555234313011,
-0.01548093557357788,
0.04147154837846756,
0.02688991092145443,
0.0416986308991909,
0.044821567833423615,
0.012235195375978947,
0.0013677607057616115,
-0.00023297798179555684,
0.05833183601498604,
0.04158952832221985,
-0.008351653814315796,
-0.01220715045928955,
-0.0669109970331192,
0.014793440699577332,
0.005676898639649153,
-0.008321434259414673,
-0.03696800768375397,
-0.04221484437584877,
-0.06860548257827759,
0.008156226016581059,
-0.006523586809635162,
0.03369762375950813,
0.08119852840900421,
-0.011411421932280064,
-0.03660045936703682,
0.005492036696523428,
0.01461060531437397,
0.03648676350712776,
0.027444755658507347,
-0.021637145429849625,
-0.030885623767971992,
-0.09847529977560043,
0.03029128909111023,
-0.023537589237093925,
-0.02110695280134678,
-0.04865746945142746,
0.002045743865892291,
-0.057068001478910446,
-0.018343720585107803,
-0.029507391154766083,
0.012318047694861889,
-0.02949805185198784,
0.04217660427093506,
-0.0016039367765188217,
-0.014959548600018024,
-0.02241501770913601,
0.0284721702337265,
0.0527055524289608,
-0.012808396480977535,
-0.04660549387335777,
-0.023374633863568306,
0.053865257650613785,
0.00349883153103292,
0.007617245428264141,
-0.047939132899045944,
-0.023259656503796577,
-0.00890978705137968,
-0.04978764429688454,
-0.013976424001157284,
-0.0814533531665802,
0.023770669475197792,
0.025317862629890442,
0.007227288093417883,
-0.006464529316872358,
-0.0019253259524703026,
-0.028093310073018074,
0.004016611725091934,
0.011221801862120628,
-0.024509692564606667,
-0.01961704157292843,
-0.009633556939661503,
-0.03160596638917923,
-0.026499774307012558,
0.035763587802648544,
0.016009032726287842,
-0.05917301028966904,
-0.02185942232608795,
0.004050589166581631,
-0.10731148719787598,
0.01324265543371439,
-0.009954022243618965,
-0.03547867387533188,
0.01784026250243187,
-0.05882920324802399,
-0.00712268752977252,
0.02571387030184269,
0.01338099129498005,
0.03373696655035019,
0.014213399030268192,
0.025852253660559654,
-0.0061394646763801575,
0.047440655529499054,
0.020552093163132668,
0.035794563591480255,
0.01237343531101942,
0.0140011515468359,
-0.04672476276755333,
-0.03286152333021164,
-0.033406052738428116,
-0.001766057568602264,
0.05054458975791931,
0.02142306976020336,
-0.027176808565855026,
0.020413393154740334,
0.04002232477068901,
0.009225334972143173,
0.06076803058385849,
-0.04582589119672775,
-0.06979385018348694,
-0.02306530252099037,
0.030834345147013664,
-0.015190847218036652,
-0.02216385304927826,
0.01907188817858696,
0.03068779595196247,
0.000724561105016619,
0.04141012951731682,
-0.036249689757823944,
-0.00821877084672451,
0.025255274027585983,
0.03403439000248909,
-0.03583440184593201,
0.011700351722538471,
-0.03643275052309036,
0.0177669208496809,
-0.009061867371201515,
0.018765563145279884,
0.05260483920574188,
-0.05558653920888901,
-0.05888894945383072,
0.07816152274608612,
0.04516787454485893,
0.014472686685621738,
0.02060060016810894,
0.0015598932513967156,
0.022002866491675377,
0.020374789834022522,
-0.01051079947501421,
0.03310859203338623,
0.02093842253088951,
-0.018170127645134926,
-0.01630762591958046,
0.010650401003658772,
0.026474960148334503,
0.04813455417752266,
-0.024277061223983765,
0.019831158220767975,
0.032431527972221375,
0.028760021552443504,
0.01039431244134903,
0.028346866369247437,
-0.004837447311729193,
-0.018693596124649048,
0.057032324373722076,
-0.028551751747727394,
-0.02210633084177971,
-0.002768795471638441,
-0.060111526399850845,
-0.01024658139795065,
0.013279286213219166,
0.006704576779156923,
0.048479799181222916,
-0.04079139977693558,
0.013187654316425323,
0.03492314741015434,
-0.03368501365184784,
0.034789957106113434,
-0.05859578028321266,
0.0706356018781662,
0.01159046683460474,
0.05672946944832802,
0.058525994420051575,
0.02875322476029396,
-0.03850720077753067,
0.07960858941078186,
0.025210082530975342,
-0.09461607038974762,
0.023373030126094818,
-0.03496713936328888,
-0.0592866912484169,
-0.027789121493697166,
-0.032434459775686264,
-0.04808006063103676,
-0.06194077059626579,
-0.0016792904352769256,
-0.06339577585458755,
0.018601149320602417,
-0.03746766224503517,
-0.016110703349113464,
0.027083439752459526,
-0.014616833999752998,
0.021309545263648033,
0.013745315372943878,
-0.0117958327755332,
0.031081562861800194,
-0.03364214673638344,
0.04510703310370445,
0.014462449587881565,
0.00296092894859612,
-0.00788892526179552,
-0.029831143096089363,
0.020440099760890007,
-0.0006990582915022969,
-0.004762256983667612,
0.04345150664448738,
0.01801552250981331,
0.034322597086429596,
0.016164399683475494,
-0.019844239577651024,
-0.01942254975438118,
-0.039740100502967834,
-0.024632751941680908,
-0.008857205510139465,
-0.014261581934988499,
-0.03705403953790665,
-0.0004671728238463402,
0.04571542516350746,
-0.008322667330503464,
0.008855529129505157,
0.008735917508602142,
-0.00037951074773445725,
-0.0246563907712698,
0.018005676567554474,
-0.008578292094171047,
0.03274179622530937,
-0.06418798118829727,
0.020823050290346146,
0.06218089908361435,
0.006736431270837784,
0.0020103389397263527,
0.02896157093346119,
0.003721648594364524,
0.039069149643182755,
0.035711340606212616,
0.03122163563966751,
0.018744034692645073,
0.04021298512816429,
-0.046599410474300385,
0.013072126545011997,
-0.00985303707420826,
0.012113237753510475,
0.040023867040872574,
0.019041582942008972,
0.07552552968263626,
0.044421885162591934,
0.045518264174461365,
-0.06782036274671555,
0.011780166067183018,
0.00928073562681675,
0.04318339750170708,
-0.006130313966423273,
0.028901316225528717,
0.003087336663156748,
-0.012233227491378784,
-0.062294572591781616,
-0.0428193174302578,
-0.03032340295612812,
-0.04322729632258415,
-0.08265415579080582,
-0.019242407754063606,
0.021879272535443306,
0.07923112064599991,
-0.08615731447935104,
0.02314653992652893,
0.009328752756118774,
-0.02713583968579769,
0.01671271212399006,
-0.01563507504761219,
-0.01795235462486744,
0.008824617601931095,
0.07262706756591797,
-0.06434036046266556,
-0.03188042715191841,
-0.016783345490694046,
-0.034089308232069016,
0.06768341362476349,
-0.020298469811677933,
0.024697624146938324,
0.048237040638923645,
0.05404817312955856,
0.009198641404509544,
0.013587787747383118,
-0.025326846167445183,
-0.0528758205473423,
0.006904839538037777,
0.011151820421218872,
0.019204843789339066,
-0.029636913910508156,
0.02559962123632431,
-0.03300512582063675,
0.008711752481758595,
-0.03953059762716293,
-0.0030369427986443043,
0.030416514724493027,
-0.09028144925832748,
-0.025363730266690254,
-0.008363853208720684,
-0.020507078617811203,
0.04860222712159157
] |
<p>I find the profound asymmetry in the sensitivity of left and right chiral particles to be one of the most remarkable analytical observations captured in the Standard Model. Yet for some, I've not found much in the way of discussions that worry about <em>why</em> of such as truly remarkable fact is true. I can't help but be reminded a wee bit of views on the motions of planets before Newton... you know, "it be Angels that do push them around, ask ye not why!"</p>
<p>Seriously, I know the Standard Model has a lot of givens in it... but surely <em>someone</em> has mulled over why the universe might exhibit such a non-intuitive and thus <em>interesting</em> asymmetry? And perhaps even developed some solid speculations or full theories on why such in-your-face chiral asymmetries exist in nature?</p>
<p>Do such theories exist, or is this asymmetry truly just a "given" and nothing more?</p> | g1248 | [
0.023249013349413872,
0.03462619706988335,
0.02212032489478588,
-0.0016126695554703474,
0.103804811835289,
0.016792623326182365,
0.026567239314317703,
-0.004464339464902878,
-0.010619409382343292,
-0.013928723521530628,
0.028103550896048546,
-0.023542221635580063,
0.019183337688446045,
0.040001001209020615,
0.0035240536089986563,
-0.007146988995373249,
-0.004221836104989052,
0.0032657221890985966,
0.04321321099996567,
0.031266339123249054,
-0.017109505832195282,
-0.003554046154022217,
0.033132437616586685,
0.018348408862948418,
-0.034363869577646255,
0.003306672675535083,
-0.008283776231110096,
-0.03819938749074936,
0.028359729796648026,
-0.03857157379388809,
0.03624146804213524,
-0.014324195683002472,
0.02195432223379612,
-0.008334051817655563,
-0.0063058012165129185,
-0.02713964320719242,
0.024462377652525902,
-0.026075812056660652,
0.01605440117418766,
0.02828851155936718,
0.05560573935508728,
-0.0714387446641922,
-0.038308605551719666,
0.006356217432767153,
0.022722620517015457,
0.019129613414406776,
-0.051248956471681595,
0.014977976679801941,
0.027058349922299385,
-0.0320722870528698,
0.025105802342295647,
-0.008932186290621758,
0.09543172270059586,
0.04782853648066521,
0.005154184065759182,
0.008724061772227287,
0.07556479424238205,
0.07701867818832397,
0.0558028481900692,
0.011826016008853912,
-0.031773339956998825,
0.014083800837397575,
0.0006623932858929038,
0.022463670000433922,
0.026694199070334435,
0.00949169136583805,
0.018928680568933487,
-0.008017042651772499,
0.03481980785727501,
-0.02094312570989132,
0.03692910820245743,
-0.030866168439388275,
-0.004801826551556587,
0.03041655197739601,
-0.03903708606958389,
0.04626334831118584,
-0.01619095541536808,
0.0026301175821572542,
-0.026028774678707123,
-0.018154898658394814,
0.02145981416106224,
-0.015507886186242104,
-0.0366646945476532,
-0.021963385865092278,
0.10211092978715897,
-0.00370539678260684,
0.01153800543397665,
-0.04161587730050087,
-0.006421227008104324,
-0.027562839910387993,
0.04804612323641777,
-0.023194044828414917,
0.006467444356530905,
-0.053286634385585785,
0.007627589162439108,
-0.014087448827922344,
-0.025617802515625954,
0.014830108731985092,
0.0065584322437644005,
0.060031767934560776,
-0.030564967542886734,
0.06678660213947296,
0.03155139088630676,
0.014080477878451347,
0.018486371263861656,
-0.022991692647337914,
0.06701647490262985,
0.03173689916729927,
-0.014118844643235207,
-0.05893193557858467,
0.005565532483160496,
0.0026081970427185297,
-0.009825917892158031,
0.07307900488376617,
-0.03589866682887077,
-0.05551084503531456,
0.08077114075422287,
-0.05190219357609749,
0.03715338557958603,
0.07016116380691528,
-0.029651682823896408,
0.026338811963796616,
-0.03581986948847771,
-0.010599694214761257,
0.0031055393628776073,
0.018602877855300903,
0.05612494423985481,
0.0013945645187050104,
0.012227958999574184,
-0.00578279560431838,
0.006791727617383003,
-0.002644520252943039,
-0.054589685052633286,
-0.01786341704428196,
0.017172932624816895,
0.02179364301264286,
-0.049028243869543076,
0.0286136232316494,
0.03290972113609314,
-0.011822901666164398,
-0.006395968608558178,
0.0029949068557471037,
0.005402915645390749,
0.031214550137519836,
-0.029080571606755257,
0.025754692032933235,
-0.05451663210988045,
-0.005598804447799921,
0.03905603662133217,
-0.016456443816423416,
0.014698905870318413,
0.0790943130850792,
0.043546926230192184,
-0.011996946297585964,
-0.017475062981247902,
0.0024381540715694427,
-0.024599844589829445,
0.009335629642009735,
-0.07837562263011932,
-0.03797375410795212,
0.04673654958605766,
0.0051720826886594296,
-0.047267764806747437,
-0.04698268696665764,
-0.009603035636246204,
0.0980549082159996,
-0.056407224386930466,
-0.09249603003263474,
-0.011628330685198307,
0.008505485020577908,
-0.09068834781646729,
0.019069449976086617,
0.01972237229347229,
0.025041168555617332,
0.03848861902952194,
0.03876492753624916,
-0.006473202258348465,
-0.07818104326725006,
-0.009233016520738602,
-0.02092071622610092,
-0.044174082577228546,
-0.0035739527083933353,
0.005103396717458963,
0.050313252955675125,
-0.06013193354010582,
-0.06405307352542877,
-0.013341112993657589,
-0.0009919586591422558,
-0.06586496531963348,
-0.018244147300720215,
0.04082779586315155,
-0.00803503766655922,
0.009211971424520016,
0.05988014116883278,
0.022459575906395912,
-0.00032637795084156096,
-0.05806813761591911,
0.03217103332281113,
-0.07426181435585022,
0.030546104535460472,
-0.03206014633178711,
0.004209638573229313,
0.03423117473721504,
-0.006498517468571663,
-0.022054441273212433,
0.017086708918213844,
-0.0022802732419222593,
0.05149717256426811,
0.07984159886837006,
-0.007032032590359449,
0.02809845842421055,
-0.03272442892193794,
0.025184165686368942,
0.011555616743862629,
0.01678626239299774,
0.006952290888875723,
-0.032390154898166656,
0.010090330615639687,
-0.015151270665228367,
-0.018288036808371544,
0.01988477259874344,
-0.0683620348572731,
0.020132115110754967,
0.03665679320693016,
0.010011877864599228,
0.008678431622684002,
-0.06386850774288177,
-0.013828692957758904,
-0.01464160718023777,
0.009415681473910809,
-0.06198565289378166,
0.07910194993019104,
0.046458806842565536,
0.007351450622081757,
0.012374390847980976,
-0.06908413022756577,
-0.03223440796136856,
-0.04020467773079872,
0.043870117515325546,
-0.02159705013036728,
-0.013809841126203537,
-0.0015749905724078417,
-0.0438319556415081,
0.03317117318511009,
0.05189991742372513,
0.008678956888616085,
0.01801256462931633,
-0.046846140176057816,
-0.03136457875370979,
0.010492273606359959,
0.011087908409535885,
0.0361899770796299,
-0.0867457389831543,
-0.0742042288184166,
0.014331565238535404,
-0.010693213902413845,
0.025330955162644386,
0.06478267163038254,
-0.04310581460595131,
-0.036105941981077194,
-0.02196091040968895,
-0.013139177113771439,
0.004589133895933628,
-0.020892200991511345,
0.05877050757408142,
0.009532882831990719,
-0.0026383567601442337,
0.06710352748632431,
-0.008491238579154015,
-0.013378169387578964,
0.011689841747283936,
0.06231359764933586,
0.047219716012477875,
0.08121698349714279,
-0.04851453751325607,
0.015792764723300934,
-0.03653222694993019,
0.003218845697119832,
0.0226528812199831,
-0.01854461245238781,
0.033663589507341385,
0.02750805951654911,
-0.025984102860093117,
-0.002625832101330161,
0.03015313856303692,
0.042854100465774536,
-0.059900738298892975,
0.0003077030705753714,
0.04377531260251999,
-0.019768310710787773,
-0.009195609949529171,
0.008070698007941246,
0.009698507376015186,
-0.0012032646918669343,
0.031329840421676636,
0.018526466563344002,
0.025094326585531235,
-0.002693027490749955,
-0.06586876511573792,
0.005368486978113651,
0.048890408128499985,
0.0300932414829731,
-0.01290102954953909,
0.0427316278219223,
0.007452304009348154,
0.02008933760225773,
0.0014115801313892007,
-0.002307248068973422,
-0.06132691353559494,
0.018414605408906937,
-0.010380665771663189,
0.04588962346315384,
0.009989424608647823,
0.05735241621732712,
-0.0007513726595789194,
-0.0018800433026626706,
-0.06965376436710358,
0.08314733952283859,
0.004571317229419947,
-0.016303708776831627,
-0.060543861240148544,
0.010502329096198082,
-0.021333793178200722,
0.012703090906143188,
0.04101957380771637,
-0.028317537158727646,
-0.035776667296886444,
-0.006183378864079714,
-0.02677621692419052,
-0.07288345694541931,
0.01058513019233942,
-0.01215418241918087,
0.052306752651929855,
0.024433664977550507,
-0.06794224679470062,
0.016999119892716408,
-0.06898436695337296,
0.006833500228822231,
0.04588576778769493,
-0.055504247546195984,
-0.04482573643326759,
-0.002794666448608041,
-0.03223023936152458,
0.011312004178762436,
-0.01158380601555109,
0.03508860617876053,
-0.02281159535050392,
0.0073287226259708405,
0.03616565465927124,
0.030494382604956627,
0.05023103207349777,
0.02694162167608738,
0.011280594393610954,
-0.00013258139370009303,
0.026692679151892662,
-0.0099504878744483,
-0.008121118880808353,
0.028123751282691956,
-0.01394890807569027,
0.013655895367264748,
-0.09123769402503967,
0.013678654097020626,
0.008168063126504421,
-0.0024487623013556004,
0.07554055750370026,
0.02497338503599167,
-0.044929083436727524,
-0.006762328557670116,
0.0008036203216761351,
0.0004846210067626089,
0.0022253552451729774,
0.0070013138465583324,
-0.011816167272627354,
0.029930545017123222,
0.027698026970028877,
-0.005368521902710199,
0.01933412067592144,
0.02607962116599083,
-0.03636772930622101,
0.00009573397983331233,
0.02691582404077053,
0.04090093821287155,
0.0055411322973668575,
0.04643931984901428,
0.02080332301557064,
0.00394671643152833,
-0.07378284633159637,
-0.03408248350024223,
-0.022827934473752975,
-0.03810174763202667,
0.05393436923623085,
-0.03629673644900322,
0.0036946558393538,
-0.014382431283593178,
0.04304502159357071,
-0.05837429314851761,
-0.016825582832098007,
-0.05199075862765312,
0.0173826701939106,
0.0075889998115599155,
-0.0012688413262367249,
-0.04812423139810562,
-0.022409413009881973,
-0.0049735261127352715,
-0.025563284754753113,
-0.029994435608386993,
0.00855856854468584,
-0.01962517760694027,
0.014592853374779224,
-0.0059877666644752026,
0.0582016296684742,
0.04686949402093887,
0.04389553517103195,
-0.01755162514746189,
-0.00003491025199764408,
0.02264368161559105,
-0.059155143797397614,
0.005409357603639364,
0.06881203502416611,
0.0025398589204996824,
0.00691014900803566,
0.028781602159142494,
0.008383523672819138,
0.003014641348272562,
0.09202100336551666,
0.059932105243206024,
0.049860529601573944,
-0.010305918753147125,
-0.033165544271469116,
0.002357503632083535,
0.07519637793302536,
0.02978273294866085,
0.015768198296427727,
0.002400095807388425,
0.09066124260425568,
0.008567729033529758,
-0.03180473670363426,
0.09022852778434753,
-0.01875971630215645,
0.02062014490365982,
0.04385152831673622,
0.007297714706510305,
0.013671950437128544,
0.0075288922525942326,
0.02889580838382244,
0.04375271499156952,
-0.03372521325945854,
0.0018663362134248018,
-0.02075687050819397,
-0.010409591719508171,
-0.0026282581966370344,
0.021288182586431503,
-0.03409189358353615,
-0.0358731746673584,
-0.06360854208469391,
-0.030645541846752167,
-0.00816770363599062,
0.0069305505603551865,
-0.011591772548854351,
0.002859386382624507,
-0.06852325052022934,
-0.06435494124889374,
0.052834395319223404,
0.0021044909954071045,
0.039830707013607025,
-0.005872324109077454,
-0.0004059033817611635,
0.02007811702787876,
-0.05908584967255592,
-0.04477555677294731,
-0.042217791080474854,
-0.021224433556199074,
-0.0018754758639261127,
0.006153514608740807,
-0.06735764443874359,
-0.03940849378705025,
0.017840785905718803,
-0.03522735461592674,
-0.01971612498164177,
0.009571865200996399,
-0.05169316381216049,
-0.0011073920177295804,
0.08237682282924652,
0.04148145020008087,
0.0007784802000969648,
0.006951446644961834,
-0.020383914932608604,
-0.014354445971548557,
-0.05312725901603699,
-0.019391633570194244,
0.03893335163593292,
-0.0591304674744606,
-0.036254819482564926,
-0.055124785751104355,
-0.034895770251750946,
-0.02418786846101284,
-0.017169702798128128,
-0.0011345992097631097,
-0.03326085954904556,
-0.03168065473437309,
-0.005352938547730446,
0.04741056263446808,
0.006693593226373196,
0.01722308248281479,
0.04413040727376938,
0.02684815414249897,
0.008699655532836914,
-0.012582178227603436,
-0.019399350509047508,
-0.06379441916942596,
0.022865496575832367,
-0.011282265186309814,
-0.0016126205446198583,
0.04194004833698273,
0.05487333610653877,
0.005461567081511021,
-0.013400488533079624,
-0.04088680446147919,
0.06447941809892654,
-0.06628957390785217,
-0.03948367014527321,
0.001687881420366466,
0.0017490274040028453,
-0.016856282949447632,
0.0404733344912529,
0.012094221077859402,
-0.059072162955999374,
0.02622666023671627,
-0.034816958010196686,
0.010173572227358818,
-0.025734923779964447,
-0.029675671830773354,
0.08872031420469284,
0.0010850423714146018,
0.02917029708623886,
-0.020792746916413307,
0.0557512603700161,
0.04961022362112999,
0.03548337146639824,
0.000046811168431304395,
-0.020055122673511505,
-0.01551488321274519,
0.004068615846335888,
0.021243777126073837,
-0.02892470173537731,
0.051492370665073395,
-0.008821448311209679,
-0.01721196621656418,
0.051664408296346664,
-0.04316610470414162,
-0.05483481287956238,
0.03597310557961464,
-0.04256169870495796,
-0.06035277247428894,
-0.024843191727995872,
0.03191903978586197,
-0.0560811311006546,
-0.033299922943115234,
0.030447540804743767,
-0.06696799397468567,
-0.020687153562903404,
-0.014389135874807835,
0.042847197502851486,
-0.0031687517184764147,
-0.058002788573503494,
-0.0000604745619057212,
0.0005942242569290102,
-0.03415605053305626,
0.01909971795976162,
0.04939919337630272,
-0.016191130504012108,
0.018942758440971375,
0.03966804966330528,
0.05671554431319237,
0.03870603069663048,
-0.023142825812101364,
-0.049287714064121246,
-0.03126756474375725,
-0.08392547070980072,
-0.048921678215265274,
0.05691257119178772,
-0.04661495238542557,
0.038564931601285934,
0.0021479458082467318,
0.00847826711833477,
0.03756028786301613,
-0.044358979910612106,
-0.010525020770728588,
0.06076454371213913,
-0.05578867718577385,
-0.05068805441260338,
0.004004158079624176,
-0.02206932194530964,
-0.007931140251457691,
-0.04109949246048927,
-0.012861786410212517,
0.019109155982732773,
-0.017635682597756386,
-0.029638633131980896,
-0.024839777499437332,
-0.0024019042029976845,
0.005714110564440489,
0.01442428957670927,
0.027065010741353035,
0.04669147729873657,
-0.04416494816541672,
0.00798166822642088,
0.001971612451598048,
0.029876988381147385,
0.04317520931363106,
-0.0023415437899529934,
0.016499945893883705,
-0.021597279235720634,
-0.005774511024355888,
-0.04346828535199165,
-0.08729580789804459,
0.03809422254562378,
-0.015522895380854607,
-0.06146325543522835,
-0.016801120713353157,
-0.0376514233648777,
0.032324500381946564,
-0.005633681081235409,
-0.01123580988496542,
0.033633045852184296,
0.004357857629656792,
-0.058686673641204834,
0.027454538270831108,
0.016968872398138046,
0.035112544894218445,
0.013014378026127815,
-0.009729628451168537,
0.013762205839157104,
0.04202568903565407,
-0.00600085686892271,
-0.051887452602386475,
-0.037648383527994156,
0.004037788603454828,
0.015455706976354122,
-0.01324456837028265,
-0.0029187900945544243,
0.03925856947898865,
-0.023011619225144386,
-0.026303838938474655,
-0.04133721813559532,
0.04503866285085678,
-0.000023571641577291302,
-0.0003174383018631488,
-0.03661947324872017,
-0.0174468494951725,
-0.012465720996260643,
-0.04599876329302788,
-0.01489383727312088,
-0.01882743276655674,
0.051689427345991135,
-0.034536655992269516,
-0.002307808492332697,
0.02798975072801113,
0.03419072926044464,
-0.08004696667194366,
-0.037929169833660126,
-0.04321477562189102,
0.01360538974404335,
-0.006716675125062466,
-0.0301202405244112,
0.0033032905776053667,
0.008962391875684261,
-0.003936505410820246,
-0.0030123568139970303,
-0.011144700460135937,
-0.014662637375295162,
0.014753798022866249,
-0.027325399219989777,
0.0028260010294616222,
-0.007009732536971569,
-0.05587419867515564,
0.03193026781082153,
-0.05188531428575516,
-0.03446938470005989,
0.011441037058830261,
0.012598584406077862,
0.026905080303549767,
-0.008847185410559177,
0.007838668301701546,
-0.021166468039155006,
-0.021476974710822105,
0.020886698737740517,
-0.04417983442544937,
-0.08640778809785843,
0.0014266028301790357,
0.0048858546651899815,
0.010512517765164375,
-0.053531091660261154,
-0.045804306864738464,
-0.03697284311056137,
0.02741585671901703,
0.015024217776954174,
0.06858506798744202,
0.017668692395091057,
0.003386245807632804,
-0.033198218792676926,
-0.013848009519279003,
0.01564762555062771,
-0.02054601162672043,
0.07416583597660065,
-0.05219466611742973,
0.03571172431111336,
-0.015348073095083237,
-0.045185890048742294,
0.0794392079114914,
-0.01919589750468731,
0.047669917345047,
0.008415766060352325,
0.02349795401096344,
0.06386188417673111,
-0.003277491545304656,
-0.003788027912378311,
0.008059700019657612,
0.07955297827720642,
-0.015575889497995377,
-0.006411008536815643,
-0.00008392312884097919,
-0.024226149544119835,
-0.04672950878739357,
-0.03596903383731842,
0.003549135522916913,
-0.028630055487155914,
-0.04356896132230759,
0.009383918717503548,
-0.012679925188422203,
0.07636361569166183,
0.029997635632753372,
0.022532779723405838,
0.046944618225097656,
-0.08885841071605682,
0.04420766234397888,
-0.02149827964603901,
-0.0012057132553309202,
-0.09784317016601562,
-0.004195043351501226,
0.022968892008066177,
-0.048842888325452805,
0.03178068995475769,
-0.017298240214586258,
-0.0477953776717186,
-0.046891000121831894,
0.008450143970549107,
0.03779759258031845,
-0.05837547034025192,
0.009897113777697086,
-0.01663137413561344,
0.0325281023979187,
-0.025372236967086792,
0.04122799262404442,
0.02939474768936634,
0.030542457476258278,
0.024962076917290688,
-0.00643371045589447,
-0.05953962728381157,
0.0008330197888426483,
0.01984807290136814,
0.025698639452457428,
0.04357829689979553,
0.020588692277669907,
0.006249073892831802,
0.015313506126403809,
-0.018454832956194878,
0.02579350955784321
] |
<p>Since the Higgs mechanism is so intimately tied to binding together massless chiral fermions, does it happen to have anything to say about the spin statistics issue?</p>
<p>I'm actually assuming the answer is no, but perhaps there is a deeper tie there that I'm missing completely. So, just curious...</p> | g1249 | [
0.009930136613547802,
0.030500292778015137,
0.023624101653695107,
0.0059821875765919685,
0.07039780169725418,
0.01639127917587757,
0.012649712152779102,
0.0975031778216362,
0.02128867618739605,
-0.04703793674707413,
-0.016675544902682304,
-0.05031974986195564,
-0.013235682621598244,
0.009985406883060932,
-0.0048970733769237995,
0.03172257915139198,
-0.0020792437717318535,
0.04377911612391472,
0.0029809812549501657,
0.05311208590865135,
-0.025256792083382607,
-0.03496655076742172,
0.0019557371269911528,
-0.003125793533399701,
-0.020739950239658356,
-0.0019290066557005048,
-0.027099156752228737,
-0.042093098163604736,
0.04029136151075363,
0.027628369629383087,
0.04277006909251213,
-0.009400768205523491,
0.03469862788915634,
-0.09230303019285202,
-0.02755029872059822,
-0.05283516272902489,
0.00971697922796011,
0.007563390303403139,
-0.001058970927260816,
0.03097962588071823,
0.07385029643774033,
0.011007163673639297,
-0.0025581656955182552,
-0.048218611627817154,
-0.010240292176604271,
0.05764660984277725,
-0.01084505207836628,
0.07662494480609894,
-0.054412536323070526,
0.043044909834861755,
-0.013543329201638699,
-0.03719935193657875,
0.05903097614645958,
0.09314737468957901,
0.0536549910902977,
0.00439861137419939,
0.07301757484674454,
0.042661286890506744,
0.04412040486931801,
0.05837523192167282,
-0.02057304047048092,
0.004910115618258715,
-0.03922566771507263,
0.027447698637843132,
0.034708172082901,
0.03699195757508278,
-0.031292784959077835,
-0.02291823923587799,
0.01936112716794014,
-0.011639073491096497,
-0.013859831728041172,
-0.025804610922932625,
0.019333697855472565,
-0.05079903453588486,
-0.021918969228863716,
0.002491156104952097,
0.0040931557305157185,
-0.030075017362833023,
-0.014904100447893143,
-0.011513814330101013,
-0.04676944017410278,
-0.06992720067501068,
0.016282441094517708,
0.004773421678692102,
0.04290706291794777,
-0.013339808210730553,
0.005296867806464434,
-0.002608046866953373,
-0.028876757249236107,
0.033994510769844055,
0.053767383098602295,
-0.03716595843434334,
-0.013950254768133163,
-0.004100041463971138,
-0.04286280274391174,
-0.015898631885647774,
0.007330829743295908,
0.007017409894615412,
-0.03772662207484245,
-0.016071297228336334,
-0.05116741359233856,
0.024350561201572418,
0.023791508749127388,
-0.004101719707250595,
0.0010650214971974492,
0.0034653188195079565,
0.029302408918738365,
0.0029540657997131348,
0.0034333844669163227,
0.00902506709098816,
-0.05698870122432709,
0.007628045976161957,
-0.026030080392956734,
0.03221103176474571,
-0.003767466638237238,
-0.030697209760546684,
0.10349990427494049,
-0.0565464049577713,
-0.01576470583677292,
0.0018377009546384215,
-0.006155783776193857,
0.014245894737541676,
-0.031103285029530525,
0.08429796248674393,
-0.031103039160370827,
-0.0030577743891626596,
0.011813057586550713,
0.028747424483299255,
0.024291619658470154,
0.038414761424064636,
-0.016712583601474762,
-0.03376477211713791,
0.042451635003089905,
0.011665924452245235,
-0.025458645075559616,
0.06803232431411743,
0.04087185114622116,
0.013979594223201275,
0.036291468888521194,
-0.0001527200365671888,
-0.03792744129896164,
-0.045053429901599884,
0.04049234464764595,
-0.020734557881951332,
0.023500291630625725,
0.0508539080619812,
0.04379666596651077,
-0.01185696478933096,
-0.01233703549951315,
-0.00455046072602272,
0.04161722585558891,
0.01608877070248127,
-0.002403266727924347,
-0.010089905932545662,
-0.01048735436052084,
0.005121521186083555,
0.03811360523104668,
0.006944568362087011,
0.008834483101963997,
-0.04841205105185509,
0.030943386256694794,
-0.0956088975071907,
-0.025979910045862198,
-0.059167973697185516,
-0.015533479861915112,
-0.0048570046201348305,
0.01993061974644661,
-0.017282143235206604,
-0.05439748242497444,
-0.00017510888574179262,
-0.053736936300992966,
0.01492531131953001,
-0.028622418642044067,
0.07159295678138733,
0.05032741650938988,
-0.002847717609256506,
-0.030552862212061882,
-0.025681527331471443,
0.024318816140294075,
0.05029411241412163,
0.020030435174703598,
0.03838064521551132,
0.020638085901737213,
-0.029010912403464317,
-0.032919447869062424,
-0.020763715729117393,
-0.010749826207756996,
0.013219425454735756,
0.0030084915924817324,
-0.007688167039304972,
-0.008394261822104454,
-0.02861952967941761,
-0.01677018404006958,
-0.00221062870696187,
0.04823549836874008,
-0.03499189391732216,
0.017983030527830124,
-0.007004134356975555,
-0.033062804490327835,
-0.0073375459760427475,
-0.009361139498651028,
0.048776380717754364,
-0.016660479828715324,
-0.013125596567988396,
0.02521863393485546,
-0.0638350248336792,
0.007552472874522209,
-0.021435271948575974,
0.1011156365275383,
0.0062050586566329,
0.02298188954591751,
0.03576292842626572,
-0.05216754972934723,
0.07051435858011246,
-0.0031699223909527063,
-0.0320129431784153,
0.025305021554231644,
0.045411352068185806,
0.019683148711919785,
-0.015963608399033546,
-0.0531412772834301,
-0.04057948291301727,
0.00450133066624403,
0.06539575010538101,
0.03963768482208252,
0.030552100390195847,
-0.008771132677793503,
-0.022095337510108948,
-0.04902089387178421,
0.07041651010513306,
-0.04245343431830406,
-0.02495863474905491,
0.06535502523183823,
-0.023154396563768387,
-0.040415022522211075,
0.011234249919652939,
-0.015491923317313194,
-0.01918504200875759,
-0.012328906916081905,
0.038689520210027695,
0.03677283227443695,
-0.01038237102329731,
-0.06890930980443954,
-0.003892509965226054,
0.0631275624036789,
0.04513903334736824,
0.030053799971938133,
0.01462397351861,
-0.012652912177145481,
0.02108747698366642,
0.05318975821137428,
-0.005724044516682625,
-0.04230579733848572,
-0.0217722337692976,
0.019499143585562706,
-0.028090493753552437,
0.0357220284640789,
-0.008454791270196438,
-0.08219341933727264,
-0.03633882850408554,
-0.008511507883667946,
-0.01601058430969715,
0.05059736222028732,
-0.02840665727853775,
-0.00916682556271553,
0.02785712480545044,
0.07658983021974564,
-0.01067163236439228,
-0.050396159291267395,
-0.010439428500831127,
-0.06775432825088501,
0.04284963756799698,
-0.005345144774764776,
0.07248326390981674,
-0.01636309176683426,
-0.022237228229641914,
-0.05906324461102486,
-0.010830532759428024,
-0.03262152895331383,
-0.05522212013602257,
-0.02118833176791668,
-0.0062812138348817825,
0.005816975142806768,
0.0008798076887615025,
0.04385939612984657,
-0.010557933710515499,
-0.034503545612096786,
-0.041680362075567245,
-0.011356975883245468,
0.04458807781338692,
0.014940014109015465,
-0.028682641685009003,
0.0697111263871193,
0.040793322026729584,
0.036601822823286057,
0.026333143934607506,
0.013809626922011375,
0.008697492070496082,
-0.01954788528382778,
0.04165796563029289,
0.04695577919483185,
0.01232238207012415,
-0.04433884844183922,
0.0037484948989003897,
0.03650166094303131,
0.008536547422409058,
-0.03689773753285408,
-0.016742825508117676,
-0.02639840543270111,
-0.08212941884994507,
-0.03153940290212631,
0.09178076684474945,
-0.012886397540569305,
0.041259005665779114,
-0.03111431375145912,
-0.03426124155521393,
-0.022299131378531456,
0.060915615409612656,
-0.010700852610170841,
-0.02995144948363304,
-0.04284089431166649,
0.002451579552143812,
0.016599806025624275,
-0.029727786779403687,
0.010000926442444324,
0.02006208524107933,
-0.05008650943636894,
0.02192491851747036,
-0.03338344767689705,
-0.006212078034877777,
0.04078543186187744,
-0.01859927736222744,
0.025785915553569794,
0.020605094730854034,
-0.08914767950773239,
0.05498339980840683,
-0.029506251215934753,
-0.00046250043669715524,
-0.01939396746456623,
0.028473762795329094,
-0.02321145310997963,
-0.017089135944843292,
-0.07445918023586273,
0.0033145048655569553,
-0.019678417593240738,
0.04297352209687233,
-0.03406977280974388,
-0.0016166813438758254,
0.05942096561193466,
0.0343264564871788,
0.001872396096587181,
0.04178484156727791,
-0.00208587059751153,
0.024050511419773102,
0.054735515266656876,
-0.032789140939712524,
-0.04554527625441551,
-0.02517370879650116,
0.0023606170434504747,
-0.028894513845443726,
0.027388375252485275,
0.008703167550265789,
0.020644262433052063,
-0.057537198066711426,
-0.029798191040754318,
0.025574233382940292,
-0.06611042469739914,
0.016817860305309296,
0.05987956002354622,
0.0008416144992224872,
-0.060632698237895966,
0.015565792098641396,
0.01619410142302513,
0.023256083950400352,
0.052050258964300156,
-0.010448040440678596,
0.06635339558124542,
0.010807567276060581,
-0.03770095109939575,
-0.011306703090667725,
0.009811918251216412,
0.07737549394369125,
-0.013908562250435352,
0.042517080903053284,
-0.04773012176156044,
-0.003926699515432119,
-0.06573707610368729,
0.013775295577943325,
-0.07329809665679932,
-0.006083731073886156,
-0.019403019919991493,
0.015484110452234745,
0.011226935312151909,
0.026432257145643234,
0.03613671287894249,
-0.05704181641340256,
-0.006402075756341219,
-0.032182011753320694,
0.05670556426048279,
0.01385323517024517,
-0.10759403556585312,
-0.019364479929208755,
-0.01675998605787754,
-0.020559418946504593,
0.033190663903951645,
0.021975921466946602,
0.008174195885658264,
0.03552941232919693,
-0.011568629182875156,
0.01412639208137989,
-0.031247900798916817,
0.002537154359742999,
-0.02690347284078598,
-0.007219660095870495,
0.02977597713470459,
-0.03159404546022415,
-0.04268619790673256,
-0.009888033382594585,
-0.07572159916162491,
-0.036466676741838455,
0.03252226114273071,
0.008978095836937428,
0.023048825562000275,
0.036891497671604156,
0.0422443151473999,
-0.005911804735660553,
0.039145711809396744,
0.046977195888757706,
-0.07985605299472809,
-0.05263368412852287,
0.031829994171857834,
0.0015794901410117745,
-0.006842266768217087,
-0.03461014851927757,
0.0071519953198730946,
0.015016135759651661,
-0.036385614424943924,
-0.03638128936290741,
-0.015981607139110565,
-0.007148548029363155,
-0.004323818255215883,
-0.02797267772257328,
0.0044845882803201675,
0.06067342683672905,
-0.017052065581083298,
0.04057430475950241,
-0.02497529424726963,
0.013566197827458382,
-0.0018219727789983153,
0.012078197672963142,
0.006043599918484688,
-0.04440080001950264,
-0.04817638173699379,
0.004269643221050501,
0.046380817890167236,
0.0026809752453118563,
0.006757846102118492,
0.006948300637304783,
0.024997252970933914,
-0.010975842364132404,
-0.09671493619680405,
-0.07706182450056076,
-0.014659624546766281,
0.015150931663811207,
-0.031216800212860107,
-0.05416836962103844,
0.009757155552506447,
-0.04254467785358429,
-0.055345386266708374,
0.002369759138673544,
0.01948016881942749,
-0.05129730701446533,
0.012762540020048618,
0.013867692090570927,
-0.010082936845719814,
0.019351648166775703,
-0.02529327943921089,
0.0012541369069367647,
-0.04228563979268074,
-0.05106993019580841,
-0.027630997821688652,
-0.040834974497556686,
-0.018155859783291817,
0.02214297279715538,
0.014071888290345669,
0.009597192518413067,
-0.013053856790065765,
-0.011807574890553951,
0.015901168808341026,
-0.06710301339626312,
0.02013215236365795,
-0.008725524879992008,
0.016178060322999954,
-0.008247396908700466,
0.022691497579216957,
-0.04909837245941162,
0.00992707721889019,
-0.026020139455795288,
-0.017358507961034775,
0.014495333656668663,
0.014590528793632984,
0.04586784541606903,
0.040802136063575745,
-0.01449107751250267,
-0.016708238050341606,
0.05809498205780983,
0.05695008859038353,
-0.018624810501933098,
0.015565839596092701,
-0.010482187382876873,
-0.029231149703264236,
0.0042557911947369576,
0.013553873635828495,
0.0003678294597193599,
-0.020213158801198006,
-0.02781885676085949,
-0.004197370260953903,
-0.0067233676090836525,
0.028361989185214043,
-0.012796458788216114,
-0.014177844859659672,
0.005785368848592043,
-0.03525247797369957,
-0.0005080554983578622,
-0.020166287198662758,
-0.05817733705043793,
-0.03409869596362114,
0.04055231064558029,
-0.017944859340786934,
0.020266041159629822,
0.011359421536326408,
-0.02405666373670101,
0.08343146741390228,
0.0597936175763607,
0.016186844557523727,
-0.0902872234582901,
0.01233759243041277,
0.018157394602894783,
0.01692940853536129,
0.06312409788370132,
-0.022862305864691734,
-0.02392374537885189,
0.02857351303100586,
-0.0029749858658760786,
-0.005639754235744476,
0.003875519847497344,
0.019554728642106056,
-0.03336029499769211,
0.016183657571673393,
-0.02800806239247322,
-0.064583919942379,
0.04078691452741623,
-0.01611710712313652,
-0.02024582214653492,
-0.05970865860581398,
0.030912229791283607,
-0.014177580364048481,
0.033373694866895676,
0.050926126539707184,
0.0045530167408287525,
-0.03902091830968857,
0.03540483117103577,
0.051536668092012405,
0.03648154065012932,
0.001604089979082346,
0.0355827733874321,
-0.013847945258021355,
-0.09430970251560211,
0.018081720918416977,
0.0023895783815532923,
-0.005560420453548431,
-0.031803686171770096,
-0.04212440177798271,
-0.01784539595246315,
-0.02615182101726532,
0.0004097127530258149,
-0.01191639807075262,
-0.008999538607895374,
-0.006607203744351864,
-0.06611592322587967,
0.013482787646353245,
-0.01187607180327177,
0.00019288304611109197,
-0.00480426661670208,
0.005944352131336927,
0.02020001970231533,
-0.01922457106411457,
0.03826439753174782,
-0.03610942140221596,
0.0030266856774687767,
-0.03605601564049721,
0.052408233284950256,
-0.03932413458824158,
0.034047145396471024,
-0.020181884989142418,
0.00916106067597866,
0.02050376683473587,
-0.02565724216401577,
-0.050932347774505615,
-0.06802543997764587,
0.09733846783638,
-0.001047325087711215,
0.050883665680885315,
0.01469009555876255,
-0.01218358799815178,
0.013367785140872002,
0.03648509457707405,
0.05874231085181236,
-0.029121629893779755,
0.06049811840057373,
-0.02210409939289093,
0.03631554916501045,
0.007535870186984539,
0.01058316882699728,
-0.02518802136182785,
-0.07795456051826477,
0.02010420896112919,
-0.00392393721267581,
-0.03580839931964874,
0.023297322914004326,
-0.027116192504763603,
0.018969742581248283,
-0.009260853752493858,
-0.09663720428943634,
0.028457866981625557,
-0.014866409823298454,
0.011229898780584335,
0.008232684805989265,
0.03924625739455223,
-0.03995303064584732,
0.07412951439619064,
0.00936828926205635,
0.014051868580281734,
0.06128402054309845,
0.022777745500206947,
0.013302458450198174,
-0.0830988734960556,
-0.05634673312306404,
0.04018336534500122,
0.0047437953762710094,
0.010131364688277245,
0.028326384723186493,
-0.02937800996005535,
0.012640828266739845,
-0.023895718157291412,
0.037210613489151,
0.03792382404208183,
-0.013969283550977707,
-0.04990234598517418,
-0.05047617107629776,
0.04147583246231079,
0.027579262852668762,
-0.0207672081887722,
-0.045537106692790985,
-0.01091687846928835,
-0.02653590589761734,
-0.021013401448726654,
0.04353483021259308,
0.0522787943482399,
-0.039169833064079285,
-0.028512217104434967,
0.008743628859519958,
-0.018464835360646248,
-0.03070612996816635,
0.0016023681964725256,
0.00673797307536006,
0.03649766370654106,
-0.006209402810782194,
0.04335601627826691,
0.035559944808483124,
-0.002902718260884285,
-0.008306967094540596,
-0.07212608307600021,
-0.015407849103212357,
-0.003088431665673852,
-0.05308391526341438,
0.03794265538454056,
-0.05679860711097717,
-0.034837815910577774,
0.018832361325621605,
0.022143779322504997,
-0.007857699878513813,
0.0025952106807380915,
0.0813746526837349,
-0.02667258121073246,
0.043321069329977036,
-0.038542065769433975,
-0.053762104362249374,
-0.00716120470315218,
0.03938678652048111,
0.045522548258304596,
-0.018091797828674316,
0.006546333897858858,
-0.030933542177081108,
-0.005574340000748634,
0.006052085198462009,
0.017022961750626564,
0.028783362358808517,
-0.033871427178382874,
0.03945305570960045,
0.020440509542822838,
-0.00013559388753492385,
-0.012975956313312054,
-0.006284303963184357,
0.1011829525232315,
0.0029554208740592003,
0.021967118605971336,
-0.02274833805859089,
-0.05430208519101143,
0.03365843743085861,
0.05933517590165138,
0.04055910184979439,
-0.005406221840530634,
0.029808562248945236,
0.01901828497648239,
-0.016101788729429245,
-0.0462212935090065,
-0.03151126950979233,
0.07700899243354797,
-0.0004445671511348337,
0.010140541940927505,
0.022572865709662437,
-0.0010778314899653196,
-0.00026643986348062754,
-0.04254678264260292,
-0.0363207682967186,
0.06708738952875137,
0.031493693590164185,
0.0010319751454517245,
0.05253279581665993,
0.05018487200140953,
0.020603077486157417,
-0.050188060849905014,
0.053411856293678284,
-0.024153200909495354,
0.026860255748033524,
0.006927330046892166,
0.02347337082028389,
0.022111942991614342,
-0.03163733705878258,
-0.020609373226761818,
0.026053788140416145,
0.0831616148352623,
-0.05017905682325363,
-0.028397133573889732,
0.0032753502018749714,
0.013893093913793564,
-0.04913921654224396,
-0.0009743771515786648,
0.06639283150434494,
-0.067779541015625,
0.0014670724049210548,
0.012158971279859543,
0.0783587321639061,
-0.002863643690943718,
-0.02019442990422249,
-0.008551757782697678,
-0.025434767827391624,
-0.027043092995882034,
0.04583292827010155,
0.05299214646220207,
-0.06903436034917831,
-0.0364156998693943,
-0.002753794426098466,
0.02117263898253441,
-0.06067192554473877,
-0.017439641058444977,
0.033084675669670105
] |
<p>According to equation (6) on the first page of <a href="http://www.nhn.ou.edu/~gut/notes/cm/lect_14.pdf" rel="nofollow">some lecture notes online</a>, the above equation is used to prove the virial theorem. For rectangular coordinates, the relation</p>
<p>$$
2T~=~\sum_i p_{i}\dot{q}^{i}
$$</p>
<p>is obvious. How would I show it holds for generalized coordinates $q^{i}$?</p> | g1250 | [
0.060038574039936066,
-0.010647117160260677,
0.006527412217110395,
0.037145886570215225,
0.019241590052843094,
0.015957720577716827,
0.007620920427143574,
-0.055226732045412064,
-0.004683367442339659,
0.040084365755319595,
-0.025119837373495102,
0.035445135086774826,
-0.03625767305493355,
-0.03176257386803627,
-0.03887662664055824,
-0.0435790978372097,
-0.002282603643834591,
-0.02186437137424946,
0.0477299690246582,
0.04961324855685234,
0.03613853454589844,
0.05406179279088974,
-0.05426286160945892,
-0.001756717567332089,
0.04737575352191925,
0.007009535096585751,
0.04465740546584129,
0.04300627484917641,
-0.026472335681319237,
-0.021389931440353394,
0.06598958373069763,
-0.01782815530896187,
0.03852216526865959,
-0.014041801914572716,
0.021482963114976883,
-0.023429274559020996,
-0.04689718782901764,
0.004817606881260872,
-0.013486075215041637,
-0.007474326062947512,
-0.018611084669828415,
-0.00678615178912878,
0.04101939871907234,
0.00991745013743639,
-0.02535746619105339,
-0.016093863174319267,
-0.00945991836488247,
-0.015024278312921524,
-0.026151061058044434,
-0.03251708671450615,
-0.0564686581492424,
0.0008026394061744213,
-0.005331284832209349,
-0.06358003616333008,
-0.05023841932415962,
0.05611004680395126,
0.023654749616980553,
0.04078015312552452,
0.018324464559555054,
0.06082529202103615,
-0.000974413298536092,
-0.000021212093997746706,
0.03299162909388542,
0.03338872641324997,
0.05796748772263527,
0.01304478757083416,
-0.07371827214956284,
0.010044443421065807,
-0.07367117702960968,
0.05443786084651947,
0.01918778382241726,
-0.0712561383843422,
0.027056248858571053,
-0.04639254882931709,
-0.08100147545337677,
0.005917594768106937,
-0.004077068995684385,
-0.0037954531144350767,
0.042242828756570816,
0.0009348011808469892,
-0.050721827894449234,
-0.0026279252488166094,
0.07896101474761963,
0.062422867864370346,
0.042199891060590744,
-0.004206582438200712,
0.07417331635951996,
0.014866831712424755,
-0.04132630676031113,
0.04386134073138237,
0.0372418574988842,
-0.006702248938381672,
0.042682383209466934,
0.051611173897981644,
-0.03012186288833618,
-0.024508701637387276,
0.06097904220223427,
0.06542932987213135,
-0.009111734107136726,
0.020603211596608162,
-0.05542607605457306,
-0.0008991607464849949,
0.02713872119784355,
0.008020146749913692,
0.006137843709439039,
-0.06217385455965996,
0.06856387108564377,
0.02301553077995777,
-0.02818996272981167,
0.007694037165492773,
-0.03233785182237625,
-0.04717698693275452,
-0.03801422193646431,
0.011657479219138622,
-0.004778034519404173,
0.002123788930475712,
0.01637239381670952,
-0.016587456688284874,
0.016157228499650955,
0.03550994023680687,
-0.029098112136125565,
0.06362661719322205,
-0.022564034909009933,
0.10113252699375153,
0.006552170030772686,
0.00542056979611516,
0.003580035176128149,
0.017864283174276352,
0.02538157068192959,
0.06900954991579056,
0.021067578345537186,
0.009306925348937511,
0.042112428694963455,
-0.02652508206665516,
-0.026893867179751396,
0.008056544698774815,
-0.026487428694963455,
0.014501882717013359,
-0.036215636879205704,
0.012288257479667664,
-0.06394451856613159,
-0.022684337571263313,
0.014822602272033691,
-0.03623133897781372,
-0.006137842312455177,
-0.007872171700000763,
0.016793206334114075,
-0.025332454591989517,
0.04003442823886871,
-0.02221747860312462,
-0.06889832764863968,
0.03846178203821182,
-0.0009874847019091249,
-0.007782784756273031,
0.006124533247202635,
-0.008535739034414291,
-0.03150365501642227,
0.006534706801176071,
-0.01708599179983139,
-0.030124176293611526,
0.05636094510555267,
0.012849745340645313,
-0.06329558044672012,
-0.027064230293035507,
0.020006630569696426,
-0.009649032726883888,
0.017004959285259247,
-0.033481959253549576,
-0.024515602737665176,
-0.00308542069979012,
-0.03556479886174202,
0.0447322316467762,
-0.042698659002780914,
-0.0032069720327854156,
0.04285438731312752,
0.0014448544243350625,
-0.0492107979953289,
0.02076679840683937,
-0.014973890967667103,
0.033882033079862595,
-0.06838568300008774,
-0.014651525765657425,
0.007314031478017569,
-0.04818565025925636,
-0.05847476050257683,
0.021190950646996498,
0.024831170216202736,
0.030378323048353195,
-0.06902190297842026,
0.045238446444272995,
0.013852831907570362,
0.0008459296659566462,
-0.038220975548028946,
0.03795110434293747,
-0.006029392592608929,
0.03558322414755821,
0.023923836648464203,
0.05462484434247017,
0.02820725552737713,
0.03893522545695305,
-0.0166275966912508,
0.01251800637692213,
0.04514843598008156,
-0.005441325716674328,
0.013866681605577469,
-0.009821165353059769,
-0.05156929790973663,
-0.06439220160245895,
0.031840402632951736,
0.04389957711100578,
-0.025237344205379486,
-0.013996502384543419,
0.009994715452194214,
0.02811574935913086,
0.0021893067751079798,
-0.013880401849746704,
-0.008657434023916721,
0.0032258382998406887,
-0.003952480386942625,
-0.029145177453756332,
-0.041862040758132935,
-0.015949854627251625,
-0.015912631526589394,
0.021069146692752838,
0.004846952389925718,
0.007040131837129593,
0.03227285295724869,
0.01581614464521408,
0.023246614262461662,
0.007915355265140533,
-0.005215187557041645,
-0.01851118542253971,
-0.0002986597828567028,
-0.019843703135848045,
-0.006906823720782995,
0.03906915709376335,
-0.09416660666465759,
0.019421176984906197,
0.032042160630226135,
0.08232194930315018,
0.044681716710329056,
-0.02979186549782753,
-0.009717358276247978,
-0.0054110209457576275,
0.008557286113500595,
0.010370848700404167,
0.07475356012582779,
-0.007254823576658964,
0.020367374643683434,
0.007447139360010624,
0.0312397088855505,
-0.014469354413449764,
0.04402128979563713,
0.016407819464802742,
0.009012441150844097,
-0.01758384145796299,
-0.033723022788763046,
-0.016816195100545883,
-0.027909578755497932,
-0.07380007952451706,
0.00943266972899437,
-0.06064021214842796,
0.012003377079963684,
0.07122723013162613,
-0.05626402050256729,
-0.009385057725012302,
-0.014191236346960068,
0.07282672077417374,
0.017171349376440048,
-0.01357704121619463,
-0.039207879453897476,
0.07130827754735947,
-0.017748255282640457,
0.0791700929403305,
-0.04938666149973869,
-0.027279378846287727,
-0.010747689753770828,
-0.04123304411768913,
0.004272084217518568,
0.053921330720186234,
-0.04993242025375366,
-0.00792542565613985,
-0.03479675203561783,
0.009891181252896786,
0.02793370559811592,
-0.022459646686911583,
0.005873506888747215,
0.0831579864025116,
0.005728038959205151,
-0.015774575993418694,
-0.03759561851620674,
0.016123048961162567,
-0.03934084624052048,
-0.015407371334731579,
0.021685628220438957,
0.024800779297947884,
-0.03994148224592209,
-0.0005531726055778563,
0.0804738700389862,
0.0067253331653773785,
0.04621373116970062,
-0.03651727735996246,
-0.021380754187703133,
0.02769702672958374,
0.009821715764701366,
0.041420307010412216,
0.024676982313394547,
-0.029712004587054253,
-0.0037134336307644844,
-0.04034662991762161,
-0.006302463822066784,
0.04815481975674629,
-0.03922932967543602,
-0.02158694714307785,
0.046863049268722534,
-0.0035140456166118383,
0.017151420935988426,
0.016143638640642166,
-0.014488352462649345,
0.031919125467538834,
-0.07202424108982086,
-0.017004918307065964,
0.02330390177667141,
-0.025946201756596565,
0.042568858712911606,
0.018255984410643578,
-0.017063241451978683,
-0.009000055491924286,
-0.011008497327566147,
0.03336067125201225,
-0.0290538240224123,
0.022022856399416924,
0.01049068570137024,
-0.034585412591695786,
0.0024566962383687496,
-0.036083757877349854,
-0.05874631181359291,
0.04221015051007271,
-0.0060526118613779545,
-0.019115235656499863,
0.0004729173961095512,
-0.016506265848875046,
-0.11031950265169144,
0.016648447141051292,
-0.02765941619873047,
-0.01920606940984726,
-0.03163878619670868,
0.06834767758846283,
0.01513428334146738,
0.02765694074332714,
-0.03727095574140549,
-0.04140838608145714,
0.05026756599545479,
0.019645020365715027,
0.030605772510170937,
0.03007420338690281,
-0.011734300293028355,
0.000027386657166061923,
-0.05447376146912575,
-0.02221345342695713,
-0.028125159442424774,
0.025144154205918312,
0.008295298554003239,
-0.006494399160146713,
0.041418373584747314,
-0.011883086524903774,
0.03206014633178711,
0.0032388169784098864,
-0.01388757023960352,
0.022924160584807396,
-0.012744627892971039,
-0.04885013401508331,
-0.01673908904194832,
-0.04142105206847191,
0.013207056559622288,
-0.02764306031167507,
-0.015419606119394302,
-0.0386912077665329,
-0.009664365090429783,
0.04343222454190254,
0.022071795538067818,
0.020856933668255806,
0.05424223095178604,
0.03414173796772957,
-0.02952025830745697,
-0.037545379251241684,
-0.02355044335126877,
0.04404399171471596,
0.030211668461561203,
-0.06992900371551514,
-0.02800743095576763,
0.0077230483293533325,
-0.013600312173366547,
-0.048440806567668915,
0.01971137337386608,
0.0000699843221809715,
0.004465028643608093,
0.02668069675564766,
-0.06035331264138222,
0.01618175022304058,
-0.001544336206279695,
-0.006832192651927471,
0.01985032483935356,
0.037345003336668015,
-0.0040341694839298725,
0.0027795296628028154,
-0.004100342746824026,
0.011263825930655003,
0.011959909461438656,
-0.030423926189541817,
-0.039342425763607025,
0.03109217807650566,
0.03325914964079857,
-0.057192545384168625,
0.02952573262155056,
0.09627576917409897,
-0.010070383548736572,
-0.04394682124257088,
-0.011552688665688038,
-0.030902942642569542,
-0.000773170730099082,
0.052623096853494644,
0.017666712403297424,
-0.012572028674185276,
0.05896538496017456,
-0.009158981963992119,
0.07122789323329926,
-0.029187100008130074,
0.00633673369884491,
-0.04096604883670807,
-0.027798660099506378,
-0.036711834371089935,
0.00194711540825665,
0.05026160180568695,
-0.017146412283182144,
-0.06510238349437714,
-0.07755954563617706,
0.06720585376024246,
-0.030809160321950912,
0.005304037127643824,
-0.0038031265139579773,
0.05244828388094902,
0.043273672461509705,
-0.01102281641215086,
-0.020254718139767647,
0.01680741459131241,
0.05904442444443703,
0.020367829129099846,
0.03916710987687111,
-0.07756057381629944,
0.04029268026351929,
-0.02955419197678566,
0.054176293313503265,
-0.02745298482477665,
0.01478694286197424,
0.029294949024915695,
0.019024178385734558,
-0.0044969418086111546,
-0.042655739933252335,
0.04924941807985306,
-0.016341904178261757,
0.0040325443260371685,
0.054031532257795334,
0.064089335501194,
0.06536535173654556,
-0.03078317455947399,
-0.06850288808345795,
-0.014694678597152233,
-0.015809429809451103,
-0.06856904923915863,
0.016383733600378036,
0.06649649143218994,
0.014488021843135357,
-0.03509996086359024,
0.013923528604209423,
-0.03830375522375107,
-0.05296595022082329,
0.005337163805961609,
-0.01536780595779419,
-0.07404445856809616,
-0.011678491719067097,
0.04485655575990677,
-0.020379221066832542,
0.027015529572963715,
0.0626002624630928,
-0.03981635719537735,
0.013919095508754253,
-0.013345492072403431,
0.0034297904931008816,
0.01321019884198904,
0.0019343836465850472,
-0.06850281357765198,
0.011343021877110004,
0.061314795166254044,
-0.035688742995262146,
-0.019868742674589157,
0.022989457473158836,
-0.07003845274448395,
0.0020263027399778366,
0.019910981878638268,
-0.048028990626335144,
0.005354794207960367,
-0.009688095189630985,
0.03687011078000069,
-0.015344539657235146,
-0.02443520724773407,
0.020278293639421463,
-0.021162178367376328,
0.007339778356254101,
0.04786831513047218,
0.05094151198863983,
-0.01440340094268322,
-0.046595919877290726,
0.0010753371752798557,
0.006963360123336315,
-0.0137177100405097,
-0.03086826577782631,
-0.008108971640467644,
-0.02985234186053276,
0.025572340935468674,
0.07783116400241852,
-0.030718909576535225,
0.04780616983771324,
-0.05524216964840889,
0.0022065413650125265,
-0.02249595709145069,
-0.02474866434931755,
-0.04746158793568611,
0.0038733233232051134,
0.017408957704901695,
-0.033710870891809464,
-0.011154979467391968,
0.04098997637629509,
0.03764987364411354,
-0.035622935742139816,
0.022875547409057617,
0.04589502513408661,
0.017343884333968163,
0.05037090182304382,
-0.010852821171283722,
-0.07671912014484406,
-0.08075246959924698,
-0.0010333856334909797,
-0.014301308430731297,
-0.026269372552633286,
0.001837854739278555,
-0.05250274017453194,
0.046605926007032394,
0.0338127538561821,
0.02046135440468788,
-0.06535491347312927,
-0.010209089145064354,
-0.015778744593262672,
0.015520566143095493,
-0.019184118136763573,
-0.008623514324426651,
0.034688010811805725,
-0.01912221871316433,
-0.019314471632242203,
0.01934903673827648,
-0.005026289727538824,
-0.027955003082752228,
-0.011514518409967422,
-0.01990916021168232,
0.007168801035732031,
-0.04033203795552254,
0.019058147445321083,
-0.008389255031943321,
0.0563417486846447,
0.03221161663532257,
0.0342126302421093,
0.004489068873226643,
0.016005149111151695,
-0.044276122003793716,
0.022381866350769997,
0.014584718272089958,
0.006759056355804205,
-0.030988315120339394,
-0.06343524903059006,
0.037135135382413864,
-0.0766206681728363,
-0.0008403901592828333,
-0.007235479075461626,
-0.017025703564286232,
-0.03469288721680641,
0.014959060586988926,
-0.004678475204855204,
0.014242175035178661,
0.03065778687596321,
-0.021642811596393585,
0.05518529191613197,
0.0058854022063314915,
-0.06329968571662903,
-0.017045294865965843,
-0.012682092376053333,
-0.024811798706650734,
0.023358136415481567,
0.05786081403493881,
-0.04245631769299507,
-0.026619702577590942,
0.058639444410800934,
-0.009342691861093044,
0.046355776488780975,
0.006568230222910643,
-0.0026385588571429253,
0.00011505427391966805,
-0.007366626523435116,
-0.021356727927923203,
-0.019903214648365974,
-0.022517021745443344,
-0.02612175978720188,
0.06816467642784119,
-0.013452472165226936,
0.03046274743974209,
0.05034486576914787,
-0.06844233721494675,
0.015308577567338943,
0.02344992384314537,
-0.004092042334377766,
-0.026064034551382065,
-0.0072881304658949375,
0.0084081357344985,
-0.01681751385331154,
0.023830940946936607,
0.04483859986066818,
-0.020929379388689995,
-0.03805641829967499,
-0.01178592536598444,
0.06744962930679321,
-0.060471296310424805,
0.009963196702301502,
-0.06495536118745804,
0.014970250427722931,
-0.0024336264468729496,
-0.006606841925531626,
-0.036913368850946426,
0.021248269826173782,
-0.03200722113251686,
0.09686824679374695,
0.06109483540058136,
-0.039407894015312195,
-0.0057271383702754974,
0.012245560064911842,
-0.004300175234675407,
-0.05066290870308876,
-0.028061583638191223,
-0.007352960295975208,
0.0014776326715946198,
-0.0687548965215683,
-0.008147818967700005,
0.07319170981645584,
-0.0319477804005146,
-0.05048246681690216,
0.03597819432616234,
-0.040492333471775055,
-0.004451366141438484,
0.044473402202129364,
-0.011691402643918991,
-0.009414708241820335,
-0.019926946610212326,
-0.06328027695417404,
0.02261471562087536,
0.021323256194591522,
0.0030546721536666155,
-0.04811134561896324,
0.020599929615855217,
-0.020368948578834534,
-0.07763661444187164,
0.0391424223780632,
0.01964755728840828,
0.0006524234777316451,
0.022825615480542183,
0.04178893193602562,
-0.05697188153862953,
-0.010934804566204548,
0.05205477774143219,
-0.017108533531427383,
-0.043362975120544434,
0.04480819031596184,
0.04390507936477661,
0.028245603665709496,
-0.018975306302309036,
0.029459550976753235,
-0.021946687251329422,
-0.04924958944320679,
0.07229550182819366,
0.02511570416390896,
-0.03302351385354996,
-0.007926342077553272,
0.004030126146972179,
0.007132518570870161,
-0.020432360470294952,
0.0005105140153318644,
-0.027599895372986794,
0.056222476065158844,
-0.010420417413115501,
0.009235253557562828,
0.06876027584075928,
-0.021888824179768562,
0.00808740220963955,
0.04665876552462578,
-0.0010881072375923395,
-0.020303839817643166,
0.04188575595617294,
0.0028952262364327908,
-0.010460712015628815,
0.018254125490784645,
-0.05238286033272743,
-0.06122881919145584,
-0.00887266080826521,
0.08921219408512115,
-0.022752465680241585,
-0.00030584653723053634,
0.0001829193060984835,
0.05087678134441376,
0.044518645852804184,
0.0020357780158519745,
0.04928003251552582,
0.008321396075189114,
-0.03588823229074478,
-0.030239000916481018,
-0.045643918216228485,
-0.040069255977869034,
-0.12788709998130798,
-0.03275797516107559,
0.020467286929488182,
0.03046351857483387,
-0.04901178926229477,
-0.016972104087471962,
0.004876433871686459,
-0.021793575957417488,
-0.02565494365990162,
0.01598246954381466,
0.07083785533905029,
0.0038404627703130245,
0.0019836241845041513,
-0.0024927547201514244,
-0.025343583896756172,
-0.004528807010501623,
0.015922676771879196,
0.002684015082195401,
-0.028481654822826385,
0.020736197009682655,
-0.04573680832982063,
-0.012591986916959286,
-0.008012481033802032,
-0.03022758662700653,
0.07409892231225967,
0.07783282548189163,
-0.03523266687989235,
0.024228982627391815,
0.013432665728032589,
-0.03147033229470253,
0.028092484921216965,
0.07794902473688126,
-0.06803713738918304,
-0.022505059838294983,
-0.0023127133026719093,
0.05364052206277847,
0.0050931959412992,
-0.018938088789582253,
0.04054137319326401,
-0.0064979903399944305,
-0.0007481230422854424,
0.005485168658196926,
-0.06250877678394318,
-0.05504932627081871,
-0.006625378970056772
] |
<p>My question is about <code>photo electric</code> but it could be applied to other daily routine phenomenon. As we know rest mass of photon is zero. When a photon strikes the metal surface it transfers its energy to the electrons. Whether electron will be emitted or not, it depends upon work function. But my question is about that photon which was hit on metal surface. Does that photon vanished? Does that photon turned into nothing? where does it go after scattering? When I study this I only find the story about the emitted electrons but not about photons after collision. Am i missing some basic concept?</p> | g1251 | [
0.016584813594818115,
0.01490847859531641,
0.009373475797474384,
0.019352629780769348,
0.03791127726435661,
0.058548830449581146,
0.0601864829659462,
0.013033139519393444,
-0.01334848627448082,
-0.02151205576956272,
0.0018179683247581124,
0.01125391200184822,
0.020128782838582993,
-0.05089769884943962,
-0.043960485607385635,
0.005511103197932243,
0.10117519646883011,
0.00620837090536952,
0.0285979975014925,
0.09347957372665405,
0.006069369614124298,
0.01719479262828827,
-0.009468062780797482,
-0.05089768022298813,
-0.06393718719482422,
0.03898677974939346,
0.02169572189450264,
-0.00588732585310936,
0.05404418334364891,
-0.11629832535982132,
-0.028601089492440224,
-0.029972052201628685,
0.034293174743652344,
-0.014722634106874466,
-0.05875028297305107,
-0.003725048154592514,
0.028413204476237297,
0.03282613679766655,
-0.01386897824704647,
0.040297336876392365,
0.05908802151679993,
-0.014962292276322842,
-0.007897482253611088,
-0.015430646948516369,
0.06834819167852402,
0.0427442267537117,
-0.04506504908204079,
-0.013200631365180016,
-0.00012763249105773866,
-0.005775595083832741,
0.012281354516744614,
-0.00830197986215353,
0.019541295245289803,
-0.012287965975701809,
0.05786626785993576,
-0.014405052177608013,
0.04928034916520119,
-0.017975620925426483,
0.05678830295801163,
0.011217430233955383,
0.0009289669105783105,
0.04262582212686539,
0.019141532480716705,
-0.02405554987490177,
0.038244541734457016,
-0.036937035620212555,
-0.0230452511459589,
-0.0014988705515861511,
0.03406526520848274,
0.0021009142510592937,
-0.02021799422800541,
0.02829650603234768,
-0.043334320187568665,
-0.004883948713541031,
0.04880892112851143,
-0.03321203589439392,
0.0023872479796409607,
-0.017217278480529785,
-0.004624406341463327,
0.034928224980831146,
-0.015208970755338669,
-0.04091599956154823,
0.0194048173725605,
-0.030076641589403152,
0.01291405875235796,
-0.007903092540800571,
-0.021277252584695816,
0.011583817191421986,
-0.022438619285821915,
-0.03151968494057655,
0.08572739362716675,
-0.0016532358713448048,
0.08253329992294312,
0.0018475523684173822,
-0.04395512118935585,
0.01563902571797371,
-0.01971651427447796,
0.06424489617347717,
-0.03428046032786369,
-0.03151162341237068,
-0.046503178775310516,
-0.07957655191421509,
0.01505234744399786,
0.012292636558413506,
0.033261194825172424,
-0.009398515336215496,
-0.01671716570854187,
-0.007029698695987463,
-0.011899827979505062,
0.01659318059682846,
0.002435971749946475,
-0.061518795788288116,
-0.06478536128997803,
-0.042436301708221436,
-0.026141172274947166,
0.0044073485769331455,
0.07015202194452286,
-0.038506507873535156,
-0.002718572271987796,
0.04077117517590523,
0.030389001592993736,
0.01690971478819847,
-0.01579945906996727,
-0.007004476618021727,
0.025208212435245514,
0.0245511531829834,
0.007576109375804663,
0.012411116622388363,
-0.009128428995609283,
0.022726871073246002,
0.016646886244416237,
0.06284245103597641,
-0.0556340329349041,
0.013375380076467991,
0.033286385238170624,
0.019856927916407585,
0.06612062454223633,
-0.005240084137767553,
0.028817148879170418,
-0.0197795107960701,
0.07158390432596207,
-0.024784186854958534,
-0.057796284556388855,
-0.029303524643182755,
-0.04854574054479599,
0.0037156967446208,
-0.032758306711912155,
-0.01635245978832245,
0.01938869245350361,
0.059306636452674866,
0.02879270352423191,
0.008169854991137981,
-0.0004501208895817399,
-0.09630925208330154,
0.04450917989015579,
-0.0844649076461792,
0.000008237422662205063,
-0.029554981738328934,
0.0035214019007980824,
0.020734412595629692,
0.037297606468200684,
-0.035889916121959686,
0.02091129682958126,
-0.029829032719135284,
-0.007329289801418781,
-0.03539071977138519,
-0.013665338978171349,
-0.07409041374921799,
-0.014463580213487148,
-0.07108712941408157,
0.005954581778496504,
0.0018082872265949845,
-0.019385503605008125,
-0.010841930285096169,
-0.0433143749833107,
0.000855334394145757,
-0.0041170609183609486,
-0.015200627036392689,
0.020150871947407722,
-0.02855384349822998,
-0.029232297092676163,
-0.045290105044841766,
0.05013079196214676,
-0.034300535917282104,
0.032724328339099884,
-0.016174055635929108,
-0.0129452645778656,
0.020538493990898132,
-0.027201898396015167,
-0.014279043301939964,
-0.06964792311191559,
0.015501853078603745,
0.054469913244247437,
-0.011840920895338058,
-0.039466243237257004,
-0.04250349849462509,
-0.007955428212881088,
-0.002876711543649435,
0.0005623019533231854,
-0.06777593493461609,
-0.02320253476500511,
0.09342271089553833,
-0.07271545380353928,
0.00177044328302145,
-0.005221671424806118,
0.01512591540813446,
0.002455043839290738,
-0.03856375813484192,
-0.006313906516879797,
-0.010456303134560585,
0.04443497583270073,
0.0035572736524045467,
0.030330829322338104,
0.044954653829336166,
-0.04584280401468277,
-0.00030813110060989857,
-0.04777039960026741,
0.0026748040691018105,
0.05685609579086304,
0.003591483226045966,
-0.0057044243440032005,
0.0055675203911960125,
0.01999589614570141,
-0.006657239515334368,
0.008188007399439812,
0.03260847181081772,
0.005156565457582474,
-0.02258479595184326,
0.0005987010081298649,
0.07693642377853394,
-0.041901491582393646,
0.05027341842651367,
-0.019518066197633743,
-0.005752019118517637,
0.055982790887355804,
0.03960726410150528,
-0.04442385956645012,
-0.034465353935956955,
0.012450935319066048,
-0.06670506298542023,
-0.0026354410219937563,
-0.03173163905739784,
-0.026307551190257072,
-0.0071485512889921665,
0.0010134088806807995,
-0.05276811867952347,
0.01709885336458683,
0.011149034835398197,
0.021908240392804146,
-0.02166212536394596,
0.07166971266269684,
-0.02217157743871212,
-0.0013567224377766252,
-0.004780516494065523,
-0.019715966656804085,
-0.07939020544290543,
-0.009379377588629723,
0.01933380216360092,
-0.03979143872857094,
-0.04579845815896988,
-0.006179613061249256,
-0.036255065351724625,
-0.06442346423864365,
0.012317267246544361,
-0.0593302957713604,
-0.016700850799679756,
-0.01127101294696331,
0.029384778812527657,
0.01716495119035244,
-0.00692356564104557,
-0.023274624720215797,
0.04266084358096123,
0.00728120282292366,
0.014350607991218567,
0.03093724511563778,
-0.019737806171178818,
-0.022177662700414658,
-0.023620814085006714,
0.02994273416697979,
-0.06343445926904678,
0.03886169567704201,
-0.004866381175816059,
-0.04501065984368324,
-0.08317535370588303,
-0.014738909900188446,
-0.09538855403661728,
0.00530382851138711,
0.0034827161580324173,
0.020953936502337456,
-0.033990051597356796,
-0.04513188451528549,
-0.06797754764556885,
0.031363796442747116,
0.014373392798006535,
-0.055596571415662766,
0.079558365046978,
0.0675845816731453,
0.030317604541778564,
-0.010289032012224197,
0.023092657327651978,
0.00558105343952775,
-0.014499987475574017,
-0.055643193423748016,
-0.03347744792699814,
0.011193498969078064,
0.05993476137518883,
-0.03219657391309738,
-0.011438701301813126,
-0.031051598489284515,
0.01740424335002899,
-0.004290510434657335,
0.06924289464950562,
0.046684276312589645,
0.015262133441865444,
-0.07314939796924591,
0.0034051218535751104,
-0.0178795475512743,
-0.01923033595085144,
-0.01716965064406395,
0.06131821498274803,
-0.03292344883084297,
0.02438613772392273,
0.055553387850522995,
-0.01639760471880436,
0.036368682980537415,
0.008256212808191776,
-0.01578146405518055,
0.03860897943377495,
-0.007524591870605946,
0.02558070793747902,
-0.05135537311434746,
0.03254648670554161,
-0.08864101767539978,
-0.031342290341854095,
0.030704336240887642,
0.020003754645586014,
0.0017988024046644568,
0.08006079494953156,
0.04358074441552162,
0.030231129378080368,
0.037586506456136703,
-0.00040832828381098807,
-0.03542653098702431,
-0.04056372493505478,
0.030961543321609497,
-0.01434888131916523,
-0.0050267246551811695,
-0.05065322667360306,
0.006704528350383043,
-0.03683577477931976,
0.08065218478441238,
0.028174903243780136,
0.006965247448533773,
0.026034463196992874,
-0.053253039717674255,
0.05387226119637489,
-0.01672493666410446,
0.03652700036764145,
0.056907135993242264,
-0.0017034609336405993,
-0.015755312517285347,
-0.021043626591563225,
0.07828237861394882,
-0.06211429461836815,
-0.0016787360655143857,
-0.005643592681735754,
-0.022629112005233765,
0.028240567073225975,
0.030749324709177017,
-0.04317363351583481,
-0.029585735872387886,
-0.019168198108673096,
-0.02278558537364006,
0.01853265054523945,
-0.06036222726106644,
0.00586486654356122,
-0.015714924782514572,
0.045550763607025146,
-0.06908592581748962,
0.04519036412239075,
-0.03378250077366829,
0.02689448930323124,
0.05795038118958473,
-0.001367412623949349,
0.019631436094641685,
0.004200241528451443,
-0.00845051184296608,
0.01141781359910965,
-0.03136930614709854,
0.004954139702022076,
0.017502285540103912,
-0.03928917273879051,
-0.04937652125954628,
0.026445463299751282,
0.026266688480973244,
-0.04618963599205017,
-0.0037693113554269075,
-0.060118600726127625,
0.04851147159934044,
-0.024948488920927048,
0.0028981126379221678,
0.023174317553639412,
-0.025992976501584053,
-0.0031483036000281572,
0.0320022888481617,
0.03393786400556564,
0.0462588295340538,
-0.032707542181015015,
0.006207594648003578,
-0.03628268092870712,
-0.0317329578101635,
-0.015113267116248608,
-0.05261363461613655,
-0.04085908085107803,
0.03471164032816887,
0.01722385734319687,
0.006004077848047018,
0.036687273532152176,
-0.025441518053412437,
-0.04209061339497566,
-0.020826375111937523,
0.018622945994138718,
0.09041636437177658,
-0.0046965135261416435,
-0.0009551522089168429,
0.039143506437540054,
0.004551522433757782,
-0.013023301027715206,
0.0021709217689931393,
-0.025920545682311058,
-0.0009517170838080347,
0.021528277546167374,
-0.030472291633486748,
0.04466522857546806,
-0.05277680233120918,
0.058642465621232986,
-0.007349175401031971,
0.043199535459280014,
0.015287410467863083,
0.07877343147993088,
0.14740921556949615,
0.01175326481461525,
0.009465447627007961,
0.03457634523510933,
-0.004004781600087881,
0.024865414947271347,
-0.05288169905543327,
-0.04111061245203018,
0.004532715771347284,
0.0009705004631541669,
-0.02509123459458351,
-0.041223492473363876,
-0.0390266478061676,
-0.02935105748474598,
-0.004347915295511484,
0.0006898323772475123,
-0.010295900516211987,
0.0022234669886529446,
-0.009725711308419704,
0.052993711084127426,
-0.06421858072280884,
0.0011803845409303904,
0.014040821231901646,
0.0020034199114888906,
0.019493235275149345,
-0.0681585893034935,
-0.01558491587638855,
0.014758742414414883,
-0.10066613554954529,
-0.02682938612997532,
-0.021138064563274384,
0.02255238965153694,
0.04662603139877319,
0.005912492983043194,
0.021172823384404182,
-0.017189137637615204,
-0.02722160331904888,
0.0005069483886472881,
0.016206318512558937,
-0.009936099871993065,
0.047342315316200256,
-0.02356862835586071,
-0.006114086601883173,
-0.041655879467725754,
-0.024666225537657738,
0.013168447650969028,
-0.04915899038314819,
0.0541781410574913,
-0.03613903000950813,
-0.07497754693031311,
0.02168045938014984,
-0.02160824090242386,
0.008207782171666622,
-0.05618508532643318,
-0.009001253172755241,
0.019748639315366745,
-0.03275778144598007,
0.05692226439714432,
0.023091474547982216,
-0.014020401984453201,
-0.0037707719020545483,
0.0028940376359969378,
-0.028284532949328423,
0.0113154212012887,
0.025639593601226807,
-0.006465616170316935,
0.0003717817598953843,
-0.06879441440105438,
0.023470140993595123,
0.017991334199905396,
-0.01410312857478857,
0.006179370451718569,
0.01390394289046526,
0.025607988238334656,
0.009019874036312103,
-0.024751102551817894,
-0.04638694226741791,
0.005421054549515247,
0.004639172460883856,
-0.0019202962284907699,
-0.017275460064411163,
0.0028626753482967615,
0.0020925123244524,
-0.0211256742477417,
0.046506308019161224,
-0.05439776927232742,
0.0034521075431257486,
0.0012717805802822113,
0.06121143698692322,
0.06745433807373047,
0.026654906570911407,
0.0035446351394057274,
0.037941206246614456,
0.024566812440752983,
-0.01692987233400345,
-0.04894491285085678,
0.002910749288275838,
0.05689304322004318,
0.0019122015219181776,
0.057378921657800674,
-0.01569942571222782,
-0.01926799677312374,
0.044887177646160126,
0.051997337490320206,
0.044778794050216675,
-0.000027856302040163428,
0.0296428631991148,
0.005197856109589338,
0.04660278186202049,
-0.001049995538778603,
0.058426786214113235,
0.03820918872952461,
0.06352122873067856,
0.003736457321792841,
-0.015668727457523346,
-0.004636777564883232,
0.0004348744114395231,
0.03403238207101822,
0.00007512916636187583,
-0.024394506588578224,
0.08389700949192047,
0.012986344285309315,
0.019114939495921135,
-0.01199421938508749,
0.06760025024414062,
-0.04804566502571106,
-0.04809829220175743,
-0.02142183482646942,
0.03643730655312538,
-0.015855152159929276,
0.0368134081363678,
0.02075018920004368,
0.046158816665410995,
0.006066076923161745,
-0.027124209329485893,
0.0408247746527195,
-0.03823670372366905,
-0.033554207533597946,
-0.08248881250619888,
-0.03827289119362831,
0.04749505594372749,
0.010868660174310207,
0.024238061159849167,
-0.05253336578607559,
0.0027198786847293377,
-0.017167335376143456,
-0.009338388219475746,
-0.012780032120645046,
0.06908949464559555,
-0.003452318487688899,
-0.024938616901636124,
0.039813876152038574,
0.034914374351501465,
-0.004789360798895359,
-0.03284266218543053,
-0.01709873229265213,
0.027408553287386894,
0.0033341138623654842,
0.02237090840935707,
0.05643701180815697,
-0.003531124209985137,
0.002807113341987133,
0.04277578368782997,
0.026953760534524918,
0.04660496860742569,
0.04708588495850563,
0.025872716680169106,
-0.03373897075653076,
0.00390699552372098,
-0.024682756513357162,
-0.05321957916021347,
-0.00271045439876616,
-0.05977567657828331,
-0.025363223627209663,
0.0007539528887718916,
-0.030062122270464897,
-0.04369339346885681,
-0.007094177883118391,
0.008660508319735527,
-0.01277308352291584,
-0.05243892967700958,
-0.09326815605163574,
0.047537971287965775,
-0.02824987843632698,
0.05082796886563301,
0.054853685200214386,
-0.009651840664446354,
0.03022717498242855,
0.06158009544014931,
0.014311360195279121,
-0.050326135009527206,
0.0032652185764163733,
0.0025715527590364218,
0.05497554689645767,
-0.019641177728772163,
0.05970710143446922,
0.02702302858233452,
-0.009887926280498505,
0.04339233785867691,
-0.009485914371907711,
-0.014385654591023922,
0.009886140003800392,
0.03403811901807785,
0.02103249914944172,
-0.05767831206321716,
0.04107685014605522,
-0.02398349530994892,
-0.015703998506069183,
-0.03202327713370323,
-0.0037655045744031668,
-0.0034062103368341923,
0.01699782907962799,
0.03962371498346329,
0.003341957228258252,
0.014014002867043018,
0.006357663311064243,
-0.04790892452001572,
0.02348129078745842,
-0.02188517153263092,
-0.04494128376245499,
-0.05969666317105293,
-0.047934651374816895,
-0.02106965333223343,
-0.021435407921671867,
-0.0031735673546791077,
0.03172396868467331,
0.03698526322841644,
-0.0805857852101326,
0.0006773842615075409,
0.02828686684370041,
-0.001709295785985887,
-0.04882485792040825,
-0.03703581541776657,
-0.028473123908042908,
0.031183434650301933,
0.036355938762426376,
0.005513842683285475,
0.06296038627624512,
-0.0460224375128746,
-0.018611393868923187,
-0.005047216080129147,
0.05979472026228905,
0.0027918340638279915,
0.002888206858187914,
0.014735628850758076,
-0.01750814914703369,
-0.04521770775318146,
0.057486165314912796,
-0.002680977573618293,
0.028519699349999428,
0.017767831683158875,
-0.015129041858017445,
0.04488210752606392,
-0.04235560819506645,
-0.01052212342619896,
-0.053267575800418854,
0.058436840772628784,
0.024302830919623375,
0.006464864127337933,
0.03137611225247383,
-0.015901973471045494,
-0.028172148391604424,
0.03977234289050102,
-0.02065081149339676,
-0.006466361694037914,
0.040082432329654694,
-0.01480562798678875,
-0.037605900317430496,
0.010456089861690998,
0.01227574236690998,
0.061709895730018616,
0.0080615459010005,
0.022636907175183296,
-0.006017179694026709,
-0.012064428068697453,
0.01017223671078682,
-0.0070402249693870544,
0.01861805096268654,
0.059998489916324615,
0.02018401399254799,
-0.011861111037433147,
0.01342112198472023,
-0.025592302903532982,
0.013570922426879406,
-0.008987117558717728,
0.019644705578684807,
0.00749369477853179,
-0.000715855450835079,
0.03506346419453621,
-0.019369151443243027,
-0.004090591799467802,
-0.014681335538625717,
-0.026777654886245728,
-0.0645458847284317,
0.005755701567977667,
0.009608888998627663,
0.05718816816806793,
0.006181496195495129,
0.018093310296535492,
-0.014731951989233494,
0.05040625482797623,
-0.09541705250740051,
-0.007853390648961067,
-0.0010417180601507425,
-0.014761615544557571,
-0.02256058156490326,
0.017239075154066086,
-0.003741110907867551,
0.01642126590013504,
-0.05301038175821304,
-0.0342303141951561,
0.04992072656750679,
-0.035806283354759216,
0.04302923381328583,
0.046903371810913086,
-0.07994221150875092,
0.024109195917844772,
-0.028133224695920944,
-0.02055356279015541,
0.022198567166924477,
0.005893366411328316,
-0.018485678359866142,
-0.03674731031060219,
-0.019212765619158745,
-0.017071204259991646,
-0.07617390900850296,
0.006347274873405695,
-0.032825861126184464
] |
<p>Suppose, in whatever dimension and theory, the action $S$ is invariant for a global symmetry with a continuous parameter $\epsilon$.</p>
<p>The trick to get the Noether current consists in making the variation local: the standard argument, which does't convince me and for which I'd like a more formal explanation, is that, since the global symmetry is in force, the <em>only</em> term appearing in the variation will be proportional to <em>derivatives</em> of $\epsilon,$ and thus the involved current $J^\mu$ will be conserved on shell:
$$ \delta S = \int \mathrm{d}^n x \ J^\mu \partial_\mu \epsilon $$</p>
<p>This is stated, e.g., in <em>Superstring Theory: Volume 1</em> by Green Schwarz Witten on page 69 and <em>The Quantum Theory of Fields, Volume 1</em> by Weinberg on page 307.</p>
<p>In other words, why a term $ \int \mathrm{d}^n x \ K(x) \epsilon(x)$ is forbidden?</p>
<hr>
<p>Taking from the answer below, I believe two nice references are</p>
<ol>
<li><a href="http://arxiv.org/abs/hep-th/0002245" rel="nofollow">theorem 4.1</a></li>
<li><a href="http://arxiv.org/abs/math/0108160" rel="nofollow">example 2.2.5</a></li>
</ol> | g1252 | [
0.04186282306909561,
-0.008170794695615768,
-0.009611980058252811,
-0.02107272297143936,
0.023129252716898918,
0.06381741911172867,
0.05986645445227623,
0.03768893703818321,
-0.022439410910010338,
0.015844782814383507,
-0.046568091958761215,
0.019259650260210037,
-0.030304115265607834,
0.002970120171085,
0.00006195878813741729,
-0.019607502967119217,
0.03701620548963547,
-0.049689602106809616,
0.007080149371176958,
-0.018605399876832962,
-0.05442971736192703,
-0.008612081408500671,
-0.016972772777080536,
-0.0009698657086119056,
0.046376317739486694,
0.048921748995780945,
0.04734053835272789,
-0.0874805673956871,
-0.031124811619520187,
-0.0792841836810112,
0.016346389427781105,
0.006824719253927469,
0.05879540741443634,
-0.007059459108859301,
-0.02371218055486679,
-0.021606024354696274,
0.0061297169886529446,
0.006665539927780628,
0.051359403878450394,
0.010766635648906231,
0.009529467672109604,
0.04823750630021095,
-0.0042451671324670315,
0.021238429471850395,
-0.04050323739647865,
-0.05979033187031746,
-0.021428514271974564,
-0.036838218569755554,
-0.034882090985774994,
-0.06213417276740074,
0.05055663734674454,
0.0118254404515028,
0.015121101401746273,
-0.04372463747859001,
0.01883101277053356,
-0.012927958741784096,
0.016662495210766792,
0.055581819266080856,
0.0019086154643446207,
-0.009011028334498405,
-0.011122146621346474,
0.0024806824512779713,
-0.018637629225850105,
0.003164294408634305,
0.057358913123607635,
-0.06197940558195114,
-0.06661828607320786,
0.014540698379278183,
0.01644846238195896,
0.03988129645586014,
-0.040006715804338455,
0.03117511235177517,
-0.03861508145928383,
-0.020354803651571274,
-0.018265705555677414,
0.05099902302026749,
-0.00915345549583435,
0.0163786131888628,
0.011276638135313988,
-0.002470881910994649,
-0.06808558851480484,
0.016396906226873398,
0.030189581215381622,
0.05270250886678696,
0.05339060723781586,
-0.03304453566670418,
-0.030173631384968758,
-0.013808421790599823,
-0.004372335970401764,
0.017892304807901382,
0.025610115379095078,
-0.046214137226343155,
-0.0253691915422678,
0.03201429545879364,
0.057996150106191635,
0.010850989259779453,
0.008955092169344425,
0.022608157247304916,
0.0284431092441082,
0.02163577266037464,
0.0018237608019262552,
-0.011246132664382458,
-0.007986389100551605,
0.0866539403796196,
0.012388557195663452,
0.04568870738148689,
0.034324631094932556,
0.018350832164287567,
0.03205359727144241,
-0.005497715901583433,
-0.016027556732296944,
-0.04389180988073349,
-0.018260732293128967,
0.0023273066617548466,
-0.051668547093868256,
0.007557931821793318,
0.0015060442965477705,
-0.025492476299405098,
0.015989983454346657,
0.016642626374959946,
-0.03057226724922657,
-0.0042817615903913975,
0.04365115985274315,
0.012464990839362144,
-0.01280545350164175,
0.07136233896017075,
0.01123258750885725,
0.024543628096580505,
0.08078180253505707,
-0.037738408893346786,
0.03147667646408081,
0.016614146530628204,
0.0029526103753596544,
0.031464409083127975,
0.022466732189059258,
-0.007010491099208593,
0.026670953258872032,
0.03678581118583679,
0.02374701201915741,
-0.021393965929746628,
-0.04876932129263878,
-0.024562066420912743,
-0.01984400674700737,
-0.022006843239068985,
-0.010963440872728825,
-0.0029981050174683332,
0.0014237010618671775,
-0.015237624756991863,
0.07231591641902924,
0.016296889632940292,
0.03397348150610924,
0.07125116884708405,
0.029617171734571457,
-0.009021801874041557,
0.02732633613049984,
-0.01704522594809532,
0.06691119074821472,
-0.007400981616228819,
-0.02009713090956211,
-0.016615379601716995,
0.004301068373024464,
-0.02096971683204174,
0.04084378108382225,
-0.011673042550683022,
-0.04669230058789253,
-0.02104431390762329,
0.03877561166882515,
0.0038663006853312254,
-0.05999896302819252,
-0.08628436923027039,
-0.027096489444375038,
0.033611878752708435,
0.04448937624692917,
0.043019767850637436,
0.013942214660346508,
0.04444762319326401,
0.009543204680085182,
-0.07055221498012543,
0.024397987872362137,
0.0059191640466451645,
-0.039084479212760925,
-0.023706043139100075,
0.025521568953990936,
-0.028802260756492615,
0.02432551048696041,
0.03907296806573868,
-0.0011381017975509167,
-0.009006324224174023,
-0.007164037320762873,
-0.024235347285866737,
-0.0412122942507267,
-0.011559048667550087,
-0.022224942222237587,
0.0723867267370224,
0.004812769591808319,
0.04228191077709198,
0.013821166940033436,
-0.045275844633579254,
-0.07470082491636276,
-0.005477412138134241,
0.0013659877004101872,
0.08472033590078354,
0.03364263102412224,
-0.0650831088423729,
0.022517846897244453,
0.016581572592258453,
-0.012857800349593163,
-0.010241854935884476,
0.06063774228096008,
-0.005833451636135578,
0.0784694254398346,
-0.05088300257921219,
-0.0410788431763649,
-0.06924628466367722,
0.013121171854436398,
-0.021397113800048828,
0.030110618099570274,
0.019133061170578003,
-0.060085196048021317,
0.014324103482067585,
-0.03688403218984604,
0.004468818195164204,
0.01544465683400631,
0.04980464279651642,
-0.07008721679449081,
0.0506347119808197,
-0.029712917283177376,
0.015283575281500816,
-0.01479168888181448,
0.031759120523929596,
-0.08591458946466446,
-0.012169762514531612,
-0.03690269961953163,
-0.0017675519920885563,
0.015776680782437325,
0.08111030608415604,
0.015390388667583466,
-0.03604166954755783,
0.01727285422384739,
0.020465152338147163,
0.05256079509854317,
-0.016485316678881645,
-0.04444721341133118,
0.03675943985581398,
0.026403389871120453,
0.01343388669192791,
0.0006972323171794415,
0.06067844107747078,
-0.045564357191324234,
0.0038051693700253963,
-0.030733084306120872,
-0.07609368860721588,
-0.014386645518243313,
-0.025477681308984756,
0.06955183297395706,
-0.031123075634241104,
0.015316207893192768,
0.022302983328700066,
0.06752046942710876,
0.034457121044397354,
-0.0009061629534699023,
-0.013558100908994675,
0.052057646214962006,
0.02005685679614544,
-0.016110612079501152,
-0.0031557243783026934,
0.004645010456442833,
0.020638803020119667,
0.01027387473732233,
0.004824595060199499,
-0.04520827531814575,
0.02077176235616207,
-0.03183039277791977,
0.041003160178661346,
-0.04020465165376663,
-0.04314102977514267,
-0.008411266840994358,
-0.032495856285095215,
0.0702265053987503,
0.0037261475808918476,
-0.04440445080399513,
0.012488710694015026,
-0.015476898290216923,
-0.03153322637081146,
0.05304373428225517,
-0.027553057298064232,
-0.03995711728930473,
-0.012244737707078457,
-0.0016141083324328065,
-0.01726515032351017,
0.001915143453516066,
0.05416535586118698,
0.03858613222837448,
0.006901586428284645,
-0.009678688831627369,
-0.027318987995386124,
-0.025448312982916832,
-0.08286608010530472,
-0.018778041005134583,
0.05224638059735298,
0.012615539133548737,
-0.05118792876601219,
-0.012899556197226048,
0.05963820219039917,
0.061733607202768326,
-0.012531206011772156,
-0.024721840396523476,
-0.05604510381817818,
0.022506780922412872,
0.018540387973189354,
0.03242209553718567,
0.034713055938482285,
0.01421448029577732,
-0.020003989338874817,
-0.06725107133388519,
0.035008665174245834,
-0.07755249738693237,
0.017509693279862404,
-0.01636776514351368,
-0.06028812751173973,
-0.023056307807564735,
-0.04607589915394783,
0.009661548770964146,
0.017562218010425568,
0.03285861015319824,
0.023065507411956787,
-0.06073881313204765,
0.0013111644657328725,
-0.04419073462486267,
-0.02537309192121029,
-0.008064075373113155,
-0.02633880078792572,
0.0053176311776041985,
-0.06992736458778381,
-0.038693372160196304,
-0.0819525197148323,
-0.02513778954744339,
-0.011312870308756828,
-0.000033771513699321076,
0.02008073776960373,
-0.060168083757162094,
-0.038485851138830185,
-0.043703850358724594,
0.00004794878259417601,
-0.036534614861011505,
0.023256314918398857,
-0.04209081456065178,
-0.05291878804564476,
-0.010744777508080006,
0.027286240831017494,
0.01350338850170374,
-0.03026016801595688,
0.022927850484848022,
-0.008180804550647736,
-0.006291839759796858,
-0.00008165370672941208,
0.0001174580684164539,
0.008220617659389973,
-0.026448136195540428,
0.03844096511602402,
0.027055520564317703,
-0.0006102831102907658,
-0.10288649797439575,
-0.008518554270267487,
0.028735825791954994,
0.023024732246994972,
-0.03296571224927902,
-0.033145662397146225,
-0.03760175406932831,
0.013710057362914085,
0.0233553908765316,
0.006134480703622103,
0.009656554087996483,
-0.0053356848657131195,
0.03881446644663811,
-0.03919987380504608,
0.000024964847398223355,
0.06840448081493378,
-0.06315723806619644,
-0.023837793618440628,
0.0007101764786057174,
-0.006173883564770222,
-0.03453119099140167,
-0.005004891660064459,
0.023703712970018387,
0.03099731169641018,
-0.04182974249124527,
0.02850729040801525,
-0.019934384152293205,
-0.0033585771452635527,
0.04799533262848854,
0.01006739865988493,
0.050834208726882935,
-0.04608975723385811,
-0.002831186866387725,
0.0462513193488121,
0.018351584672927856,
-0.010509300976991653,
0.00687901908531785,
0.006910077761858702,
0.0009573727729730308,
-0.015164008364081383,
0.01879286952316761,
-0.03156003728508949,
-0.025016548112034798,
-0.01960170269012451,
0.008614656515419483,
0.010059784166514874,
0.014809881336987019,
-0.052908796817064285,
-0.008317360654473305,
0.022928044199943542,
-0.031235063448548317,
-0.02428732067346573,
0.037771157920360565,
0.020398780703544617,
-0.006235779263079166,
-0.024586254730820656,
0.009808648377656937,
-0.049759671092033386,
0.043527234345674515,
-0.025931769981980324,
0.020038612186908722,
-0.01617312990128994,
0.04732128232717514,
0.039223186671733856,
0.04517859220504761,
-0.02234332449734211,
0.024639321491122246,
0.0031662059482187033,
0.015287496149539948,
0.033244457095861435,
-0.01684592105448246,
-0.03429695963859558,
-0.08169209212064743,
0.03899911791086197,
-0.04203198105096817,
0.08293923735618591,
-0.02088829129934311,
0.06194223836064339,
0.06815338134765625,
-0.001717194216325879,
0.05300087109208107,
0.0024479597341269255,
-0.03231664001941681,
0.05903352051973343,
-0.0590389259159565,
-0.006672724150121212,
0.0397263765335083,
0.02519385516643524,
-0.04771215096116066,
-0.01386235561221838,
0.003963562659919262,
-0.013467947021126747,
0.009872062131762505,
-0.03548986837267876,
0.01150174718350172,
-0.0142431715503335,
0.08615642786026001,
-0.010120089165866375,
-0.047126654535532,
-0.034961551427841187,
0.00977227184921503,
0.06924889981746674,
0.0926542803645134,
0.018978195264935493,
-0.027369365096092224,
0.039545461535453796,
-0.06658545136451721,
-0.04935215413570404,
0.05124549940228462,
0.009089664556086063,
0.004213334526866674,
-0.015939142554998398,
0.061662256717681885,
-0.007231755647808313,
0.03931243345141411,
-0.003215814707800746,
-0.015393506735563278,
-0.03021424449980259,
-0.015149189159274101,
-0.017730368301272392,
0.06206285208463669,
0.041992370039224625,
0.001883206539787352,
-0.02997579611837864,
-0.0022798036225140095,
0.011458342894911766,
-0.054608650505542755,
0.011457246728241444,
0.030573716387152672,
0.031131058931350708,
0.05925736948847771,
-0.022462546825408936,
-0.004323132336139679,
0.07369164377450943,
0.052944425493478775,
0.022480832412838936,
-0.02218458615243435,
-0.011102148331701756,
-0.014996360056102276,
0.00018015010573435575,
-0.012303276918828487,
0.015159226953983307,
-0.011241883039474487,
0.09932217001914978,
0.125809907913208,
0.012669069692492485,
0.0013695432571694255,
-0.016441935673356056,
0.014661136083304882,
0.0063777947798371315,
-0.004047885537147522,
-0.05639832094311714,
0.025048302486538887,
-0.014249413274228573,
-0.03966633602976799,
-0.04225463047623634,
-0.020906439051032066,
-0.034964121878147125,
0.015578560531139374,
0.07421602308750153,
0.011758565902709961,
-0.06401847302913666,
-0.009465504437685013,
-0.015380054712295532,
-0.013194769620895386,
-0.03807375952601433,
0.015656325966119766,
-0.03238869458436966,
0.028151659294962883,
0.027631649747490883,
0.030737996101379395,
0.016386106610298157,
0.06030181795358658,
-0.014913761988282204,
0.0018854998052120209,
-0.0030324195977300406,
-0.05250270664691925,
-0.0004776508139912039,
0.03097578138113022,
0.008958296850323677,
0.02263900265097618,
0.004703826736658812,
-0.060308486223220825,
0.04106888175010681,
-0.0015899086138233542,
-0.0021425161976367235,
-0.008599351160228252,
-0.0181735809892416,
-0.06741711497306824,
0.0004950431757606566,
-0.024438027292490005,
-0.019917888566851616,
-0.0002782861702144146,
0.027619611471891403,
0.019416023045778275,
-0.030531659722328186,
-0.036107055842876434,
-0.004938955418765545,
0.039117004722356796,
0.015061010606586933,
-0.0037026815116405487,
0.029319046065211296,
0.05375007539987564,
-0.014153254218399525,
-0.0025853097904473543,
0.020931461825966835,
0.07183606922626495,
0.07251650094985962,
-0.014615366235375404,
0.07216306030750275,
-0.0122532919049263,
0.0013124747201800346,
-0.022317158058285713,
-0.021240662783384323,
-0.04632369428873062,
-0.062340497970581055,
-0.04712033271789551,
0.001554156537167728,
-0.02971738763153553,
0.003983994480222464,
0.054347991943359375,
-0.06810494512319565,
-0.0036008525639772415,
0.0033436035737395287,
-0.023552488535642624,
-0.05532684922218323,
0.09835906326770782,
0.024135325103998184,
-0.018179412931203842,
-0.019203942269086838,
-0.011517597362399101,
0.09335682541131973,
-0.010365794412791729,
-0.003433169797062874,
-0.010646105743944645,
-0.018932588398456573,
-0.002475759945809841,
0.0031888969242572784,
0.022556880488991737,
-0.0015011199284344912,
0.04030764102935791,
0.026759073138237,
-0.013488334603607655,
0.033478349447250366,
-0.01648416370153427,
0.03886456787586212,
-0.0021230154670774937,
0.052916597574949265,
0.010089273564517498,
0.02036456950008869,
0.019607793539762497,
-0.021742437034845352,
-0.028334904462099075,
-0.05771231651306152,
0.009828353300690651,
0.013429775834083557,
-0.06093897297978401,
0.02166074886918068,
-0.0009270680602639914,
0.005346948746591806,
-0.03238275274634361,
0.01312474999576807,
0.01695863902568817,
0.04705824702978134,
-0.06741080433130264,
-0.043512582778930664,
0.01347211841493845,
0.020345404744148254,
-0.03331174701452255,
0.04540768265724182,
-0.04819788411259651,
0.06400757282972336,
-0.03900828957557678,
0.0342644527554512,
-0.035682789981365204,
-0.008155016228556633,
0.009740907698869705,
0.013271274976432323,
-0.031699612736701965,
0.03536641597747803,
0.020066779106855392,
-0.009395452216267586,
-0.051260851323604584,
0.03726397454738617,
0.012814990244805813,
0.07871805131435394,
-0.08013778179883957,
0.021229984238743782,
0.036781199276447296,
0.05561121553182602,
-0.0398334376513958,
-0.04761026054620743,
0.001636812463402748,
-0.0055801221169531345,
0.00930708833038807,
-0.031863536685705185,
-0.02370258793234825,
-0.01955190859735012,
-0.07184815406799316,
-0.04380336403846741,
0.003229050897061825,
-0.07694579660892487,
0.010537498630583286,
0.05884835496544838,
-0.029158389195799828,
-0.04821503907442093,
0.03419188782572746,
0.01696721278131008,
-0.03236798569560051,
-0.010625445283949375,
0.010175232775509357,
0.014320526272058487,
-0.007047017104923725,
-0.044439490884542465,
0.018351314589381218,
0.03354896977543831,
-0.033295392990112305,
-0.009499275125563145,
0.06430690735578537,
0.018094345927238464,
-0.040806714445352554,
-0.09064937382936478,
-0.07248540967702866,
-0.015970570966601372,
-0.0379599966108799,
-0.05211396515369415,
-0.005892908666282892,
-0.0035504931584000587,
0.02880721725523472,
-0.00013243217836134136,
0.019838973879814148,
-0.018815957009792328,
-0.0509648360311985,
0.03919340670108795,
0.046723220497369766,
0.003952885512262583,
-0.004378667101264,
0.03302593529224396,
0.04105281084775925,
-0.03367079049348831,
0.033232275396585464,
-0.008270405232906342,
0.039091624319553375,
-0.031079106032848358,
-0.03276945650577545,
-0.026650376617908478,
-0.030353587120771408,
0.03119789995253086,
-0.03925572708249092,
0.014399129897356033,
0.04064122587442398,
-0.024499760940670967,
0.07764676958322525,
0.038673605769872665,
0.03958246111869812,
-0.037768974900245667,
0.0026168283075094223,
0.02693716622889042,
0.0017063531558960676,
0.062181103974580765,
0.02044430933892727,
-0.03441381826996803,
-0.06145995855331421,
0.002937137149274349,
0.00653131864964962,
-0.029728762805461884,
-0.007557757664471865,
0.003853613045066595,
-0.10869589447975159,
0.016906224191188812,
-0.016104411333799362,
0.01599467173218727,
-0.02135581523180008,
-0.02539619617164135,
-0.024014009162783623,
-0.019026940688490868,
-0.03986445814371109,
-0.01195860467851162,
0.057186536490917206,
-0.020482147112488747,
-0.02011099085211754,
-0.020529255270957947,
-0.04908423498272896,
0.007654666434973478,
-0.006617950741201639,
0.008379941806197166,
0.009338430128991604,
-0.01785355992615223,
0.03784976899623871,
0.008444924838840961,
-0.02482706867158413,
0.006984157487750053,
-0.010753361508250237,
-0.005377789493650198,
0.012111383490264416,
-0.0026409642305225134,
0.008353399112820625,
0.04276847094297409,
-0.029557563364505768,
0.010233967565000057,
0.07003481686115265,
0.031470559537410736,
0.0002697580202948302,
-0.06482727080583572,
-0.0250252615660429,
0.009509867057204247
] |
<p>This is a theoretical problem. Suppose we have two ropes of the same material and diameter, but differing in length. We excert force on both ropes until they break. Let rope A be the longer one. What can be said about the stress in rope A compared to the stress in rope B at the moment of breaking, taking in account the deformation required to keep a constant volume?</p>
<p>You would expect them to be the same as the stress-strain diagram is derived for a specific material. But at the same strain of both ropes, the stress in rope A would be higher as it crosssection decreases more.</p>
<p><img src="http://i.stack.imgur.com/aj7XJ.jpg" alt="!"></p>
<p>Stress-strain diagram from <a href="http://cdn.transtutors.com/" rel="nofollow">http://cdn.transtutors.com/</a></p>
<p><a href="http://i.stack.imgur.com/aj7XJ.jpg" rel="nofollow">1</a></p> | g1253 | [
0.06628679484128952,
-0.007179525215178728,
0.007239270489662886,
-0.041779812425374985,
-0.0006465053302235901,
-0.02008618786931038,
0.010068994015455246,
-0.05219762399792671,
-0.07765227556228638,
0.05670025199651718,
-0.015357021242380142,
-0.03406151384115219,
-0.018688566982746124,
-0.06291232258081436,
0.09980800002813339,
0.011107098311185837,
0.07118511945009232,
-0.06978391110897064,
0.019319811835885048,
-0.0036257959436625242,
-0.08175056427717209,
0.024279221892356873,
0.036748625338077545,
0.007860153913497925,
0.0040289536118507385,
-0.01126171462237835,
0.028851564973592758,
0.009298271499574184,
-0.07238186150789261,
0.0055286940187215805,
0.05186568573117256,
-0.00838328804820776,
0.014064161106944084,
-0.03389086574316025,
0.0009092878317460418,
-0.011175411753356457,
0.0181729756295681,
-0.011870156042277813,
0.025833114981651306,
-0.00017187361663673073,
0.01702108047902584,
-0.04407760128378868,
-0.025183983147144318,
0.0231332890689373,
0.003346480429172516,
-0.10180302709341049,
-0.018682211637496948,
0.030051346868276596,
0.06658916920423508,
-0.05099053680896759,
0.010726566426455975,
0.07085853070020676,
-0.04749621823430061,
-0.03868855908513069,
0.05059763044118881,
0.030662687495350838,
0.03499317169189453,
-0.01393347792327404,
-0.02197408676147461,
0.000692273024469614,
-0.010639836080372334,
0.006219515111297369,
-0.008874695748090744,
0.024287119507789612,
0.040817227214574814,
-0.027900706976652145,
-0.0029737045988440514,
-0.02919847145676613,
0.025695528835058212,
0.050883084535598755,
-0.01604609563946724,
-0.03398115932941437,
0.04049166664481163,
-0.01886858232319355,
-0.026376154273748398,
-0.015058399178087711,
0.04230426996946335,
0.006030987948179245,
-0.000168685830431059,
-0.021964404731988907,
0.005290921311825514,
0.017284750938415527,
0.045297469943761826,
0.012586724944412708,
0.001614551991224289,
-0.004573976155370474,
0.02598372846841812,
0.037215329706668854,
-0.04988841712474823,
0.08304702490568161,
0.052329327911138535,
-0.02874915301799774,
0.057564567774534225,
0.041256118565797806,
0.015347066335380077,
-0.03507668897509575,
0.015863802284002304,
0.08294011652469635,
-0.01679987832903862,
0.03757990524172783,
0.02424008399248123,
-0.02741818316280842,
-0.010765042155981064,
0.03285767883062363,
-0.04071749746799469,
-0.02043607458472252,
0.0509178452193737,
-0.03575911372900009,
-0.09597819298505783,
-0.026919396594166756,
-0.025194477289915085,
0.023212481290102005,
-0.07185488939285278,
0.0004233517393004149,
0.02369384467601776,
-0.041841086000204086,
0.01821344718337059,
-0.0003147940442431718,
-0.021403014659881592,
0.012679564766585827,
0.010119017213582993,
-0.08961007744073868,
0.014912948943674564,
0.024312416091561317,
-0.023474711924791336,
-0.036841075867414474,
0.01636817492544651,
0.05752023309469223,
0.0424063503742218,
-0.0020841078367084265,
0.041574496775865555,
-0.014675222337245941,
0.04471185803413391,
0.024004381150007248,
0.022168954834342003,
0.015755891799926758,
-0.07410725951194763,
0.03470265865325928,
-0.008321150206029415,
0.003687177551910281,
-0.014543040655553341,
0.011662784032523632,
-0.06403397768735886,
0.014520891010761261,
-0.040437109768390656,
-0.016727710142731667,
-0.022952603176236153,
-0.009612711146473885,
0.02802368439733982,
-0.013280338607728481,
0.06347482651472092,
0.010929688811302185,
-0.02056834101676941,
-0.0013927493710070848,
-0.011011278256773949,
0.04322335496544838,
-0.0012524524936452508,
-0.010153930634260178,
0.019249042496085167,
-0.0025500382762402296,
0.00019895669538527727,
-0.032607078552246094,
-0.02105502411723137,
0.0034942878410220146,
-0.03550901263952255,
0.05753115192055702,
0.05521188676357269,
-0.01256340742111206,
0.016453132033348083,
-0.01870676875114441,
-0.019248683005571365,
0.027820372954010963,
0.014145714230835438,
0.022507427260279655,
-0.008920136839151382,
0.0460059680044651,
0.05957658588886261,
-0.0077677154913544655,
0.07421891391277313,
0.013918942771852016,
-0.006359456107020378,
0.032474614679813385,
0.0037132869474589825,
-0.025066865608096123,
0.02068154700100422,
0.01375989243388176,
0.03855830058455467,
-0.010523688048124313,
-0.07935026288032532,
0.0006282528629526496,
-0.03714536502957344,
0.00700936047360301,
-0.013056871481239796,
0.045484334230422974,
-0.043570149689912796,
-0.0455709770321846,
0.016732918098568916,
-0.013954210095107555,
-0.026416456326842308,
0.025284970179200172,
-0.0006722797406837344,
0.008781729266047478,
0.02145850658416748,
0.01873699203133583,
-0.04740507900714874,
0.019863830879330635,
-0.030005166307091713,
-0.043584149330854416,
0.08478495478630066,
-0.07019191235303879,
0.010234960354864597,
-0.0041671269573271275,
0.023940090090036392,
-0.00006491025123978034,
-0.043459292501211166,
-0.06040719151496887,
0.05463146045804024,
0.024420222267508507,
-0.058787014335393906,
-0.02142786979675293,
0.03279540687799454,
0.02889830805361271,
0.08802022784948349,
-0.06592568010091782,
-0.04973660036921501,
-0.055609382688999176,
0.015473312698304653,
-0.04219901189208031,
-0.003777653444558382,
-0.06467727571725845,
-0.07057181745767593,
0.010271859355270863,
-0.013545913621783257,
-0.004381820093840361,
-0.0499342605471611,
0.06088678166270256,
0.046999216079711914,
0.00660784961655736,
0.00941352266818285,
-0.004076297860592604,
0.04497301205992699,
-0.036538682878017426,
-0.023388631641864777,
-0.005783089902251959,
0.028371453285217285,
-0.03340264782309532,
0.03774664178490639,
-0.043416962027549744,
0.05804528295993805,
0.0756775364279747,
0.013248690403997898,
-0.01571361906826496,
-0.07575445622205734,
0.00025263437419198453,
0.009669636376202106,
-0.029008200392127037,
0.02145063504576683,
0.00013663055142387748,
-0.020171210169792175,
-0.02718721330165863,
0.010488053783774376,
0.06491952389478683,
0.049887459725141525,
0.043006666004657745,
-0.08849252760410309,
-0.0013921251520514488,
0.021993204951286316,
-0.02864496037364006,
0.018771139904856682,
0.0002490681945346296,
0.003265778301283717,
0.018740538507699966,
-0.019622977823019028,
0.006250798236578703,
0.0064790016040205956,
-0.01547492016106844,
0.0013085586251690984,
-0.008480198681354523,
-0.030550813302397728,
0.028753522783517838,
0.04287166893482208,
-0.006919023115187883,
-0.026794608682394028,
0.08334221690893173,
0.05250738188624382,
-0.038469523191452026,
0.004415220580995083,
-0.02677786536514759,
0.019172759726643562,
-0.006847434677183628,
-0.01368270069360733,
0.09688795357942581,
0.0017795354360714555,
-0.052344705909490585,
0.024933982640504837,
0.0725860670208931,
-0.01307656615972519,
-0.02844795025885105,
-0.049542125314474106,
-0.04513375833630562,
-0.10224539041519165,
-0.034339532256126404,
0.01067817211151123,
0.10480185598134995,
0.011830395087599754,
0.030270449817180634,
-0.020856937393546104,
-0.05580424144864082,
0.04978259652853012,
-0.02781081758439541,
-0.053891003131866455,
-0.00736015010625124,
0.032954972237348557,
-0.026849249377846718,
-0.0038568913005292416,
-0.03845829516649246,
0.03610769659280777,
-0.0012315368512645364,
-0.013712220825254917,
-0.021745653823018074,
-0.03477008268237114,
-0.00340996659360826,
0.018186379224061966,
-0.011819637380540371,
-0.08900348097085953,
0.010016768239438534,
-0.06188880279660225,
0.016197089105844498,
-0.040839992463588715,
0.0036828198935836554,
-0.03736020252108574,
-0.019067829474806786,
0.0008091586641967297,
-0.030456600710749626,
0.011357991024851799,
-0.018698571249842644,
0.021054459735751152,
-0.016340499743819237,
-0.007205219008028507,
0.03969435766339302,
-0.026975004002451897,
0.0027179582975804806,
-0.0008101544226519763,
-0.010545635595917702,
0.026275526732206345,
-0.010276826098561287,
0.03510682284832001,
0.018404819071292877,
0.031237460672855377,
0.021710902452468872,
0.03703831881284714,
0.0063172634690999985,
0.018400201573967934,
-0.04531046748161316,
-0.003612123429775238,
-0.043453965336084366,
0.07624361664056778,
0.002651023678481579,
-0.045808933675289154,
-0.004706067033112049,
0.04855947941541672,
0.010081461630761623,
0.02772597409784794,
-0.013774306513369083,
-0.04087267816066742,
-0.0024088993668556213,
0.02382751740515232,
0.028774788603186607,
0.018014976754784584,
-0.017450787127017975,
0.0011716693406924605,
-0.01960764452815056,
-0.04664691165089607,
-0.013226457871496677,
0.019726114347577095,
-0.03216463327407837,
0.06518248468637466,
-0.015260097570717335,
-0.020716335624456406,
0.04466426372528076,
0.09920472651720047,
0.01559050939977169,
-0.10833778232336044,
0.011916596442461014,
-0.032408397644758224,
-0.017780475318431854,
-0.025811051949858665,
-0.007835756987333298,
0.020864129066467285,
0.010596325621008873,
0.04554755240678787,
-0.026789387688040733,
-0.04271842539310455,
0.03376125171780586,
0.04916192218661308,
0.02486642450094223,
0.016935113817453384,
-0.026789680123329163,
-0.038791198283433914,
-0.007402599323540926,
0.0231599360704422,
-0.014493019320070744,
-0.05477866530418396,
0.020243389531970024,
-0.03132595121860504,
-0.026057912036776543,
0.08413159102201462,
0.0017562300199642777,
-0.02168065682053566,
0.03307325765490532,
0.043400492519140244,
-0.017582425847649574,
0.01663738489151001,
-0.04831539839506149,
0.018002640455961227,
-0.04405583441257477,
0.008597930893301964,
0.037116434425115585,
0.009545954875648022,
0.048256609588861465,
0.01430603303015232,
0.07963135838508606,
-0.030535263940691948,
0.013223380781710148,
0.0007594279595650733,
-0.0021970670204609632,
0.01867043599486351,
0.03031608834862709,
0.056283872574567795,
-0.04672623053193092,
-0.009714789688587189,
0.030057094991207123,
-0.05672408267855644,
-0.04949474707245827,
-0.017534729093313217,
0.0402616411447525,
-0.008232233114540577,
0.005901951342821121,
0.01583184115588665,
0.03222091868519783,
0.006461250130087137,
0.0627334713935852,
-0.010473712347447872,
0.0001452338183298707,
0.02583242952823639,
0.006363109219819307,
0.00008074427023530006,
-0.04562117159366608,
0.010699538514018059,
-0.02457791194319725,
-0.06101135537028313,
-0.02227994240820408,
0.04743899777531624,
-0.06935834139585495,
-0.013976657763123512,
-0.01708831451833248,
-0.002246377058327198,
-0.01688733883202076,
0.02327898144721985,
0.001300628180615604,
0.016870863735675812,
-0.007254236843436956,
-0.010166703723371029,
0.030029157176613808,
-0.020062820985913277,
0.00786316767334938,
-0.06796706467866898,
-0.0010335113620385528,
0.015306138433516026,
0.06002974882721901,
0.015329898335039616,
0.013798658736050129,
-0.03908386826515198,
0.00242607481777668,
-0.024432646110653877,
0.007912112399935722,
-0.05309503525495529,
0.006446408573538065,
-0.019222503527998924,
-0.05191845819354057,
0.004057208076119423,
-0.0011658372823148966,
0.0005546865868382156,
-0.08099934458732605,
0.10182703286409378,
0.0067310272715985775,
0.015445012599229813,
-0.000496464257594198,
0.050638891756534576,
0.006996053736656904,
0.06246809661388397,
-0.005911767948418856,
-0.023067770525813103,
0.008779652416706085,
-0.015235267579555511,
-0.04145749658346176,
0.06852073222398758,
-0.013034150004386902,
-0.009763317182660103,
-0.03614594414830208,
-0.006025942508131266,
0.006128726992756128,
0.012516149319708347,
-0.013364333659410477,
-0.05681708827614784,
0.06067012622952461,
0.005653344560414553,
0.03355807438492775,
0.054212335497140884,
0.04806388169527054,
-0.029835350811481476,
0.028798315674066544,
-0.0240099485963583,
-0.006565846037119627,
0.0053304568864405155,
0.032688286155462265,
0.026936227455735207,
-0.01928967610001564,
-0.01191624253988266,
0.005012541078031063,
0.0003453367098700255,
-0.017979925498366356,
0.0634937733411789,
-0.0073683965019881725,
0.04347006604075432,
-0.004925805609673262,
-0.028030503541231155,
0.030994616448879242,
-0.037886735051870346,
0.01038665696978569,
-0.014471805654466152,
-0.02404160611331463,
0.030702536925673485,
-0.03127404302358627,
-0.0026907739229500294,
-0.022951101884245872,
0.03418894484639168,
-0.006106206681579351,
0.022992441430687904,
-0.00980825163424015,
0.025544555857777596,
-0.04569360241293907,
0.04373379424214363,
0.04690507426857948,
-0.02535651996731758,
-0.07953590154647827,
-0.057820457965135574,
-0.03685564547777176,
0.031927917152643204,
0.004954286385327578,
-0.013447849079966545,
0.009605610743165016,
-0.04636251926422119,
0.008967697620391846,
0.02108202874660492,
0.03512737154960632,
0.023869918659329414,
-0.05491028353571892,
0.012735613621771336,
0.011829106137156487,
0.003842495381832123,
-0.024650834500789642,
-0.05177830904722214,
0.0034548472613096237,
0.015842335298657417,
-0.03028619848191738,
-0.03123394027352333,
-0.007434574421495199,
0.06563162803649902,
0.05823465436697006,
0.013577109202742577,
-0.010299433022737503,
0.04647909849882126,
-0.00737884733825922,
0.027413439005613327,
-0.007753758691251278,
-0.05604454129934311,
-0.0762813612818718,
0.028367487713694572,
-0.00954435020685196,
-0.042127348482608795,
0.010262217372655869,
-0.03584248200058937,
-0.005182773340493441,
-0.004059591796249151,
0.032694507390260696,
-0.007396698463708162,
-0.10040903836488724,
0.029470596462488174,
0.05109815672039986,
-0.04160410165786743,
0.011219046078622341,
-0.012060130946338177,
-0.00818451028317213,
0.037817515432834625,
-0.01014796830713749,
0.012829568237066269,
0.010163648054003716,
0.05850353091955185,
0.05737599730491638,
0.054403215646743774,
0.040520068258047104,
0.0883462205529213,
-0.027448555454611778,
-0.03070090338587761,
0.020226463675498962,
0.05485038831830025,
0.0018669272540137172,
-0.005071896594017744,
-0.025297770276665688,
-0.024792226031422615,
0.058950357139110565,
0.0014423215761780739,
0.025513073429465294,
0.017244815826416016,
0.0491444431245327,
-0.04225580766797066,
0.007152953185141087,
0.031565241515636444,
-0.037078939378261566,
-0.0012561017647385597,
-0.010741752572357655,
-0.008722498081624508,
-0.05391307920217514,
0.016089297831058502,
0.03379867970943451,
-0.06971896439790726,
0.009599260054528713,
0.010481315664947033,
-0.05589715763926506,
-0.012282073497772217,
0.023490391671657562,
0.017724186182022095,
0.0767560675740242,
-0.044061288237571716,
0.05275790020823479,
-0.019637692719697952,
-0.003961452282965183,
-0.02354973927140236,
0.04697263613343239,
-0.019964465871453285,
-0.027887972071766853,
0.0332237109541893,
-0.0022703870199620724,
0.018127070739865303,
-0.010676081292331219,
0.014207395724952221,
-0.030384670943021774,
-0.06096576526761055,
-0.003975227475166321,
0.005092851351946592,
-0.011179106310009956,
-0.059646379202604294,
0.03667527437210083,
-0.036841344088315964,
0.04037347063422203,
-0.016778267920017242,
-0.044186245650053024,
0.04390610009431839,
-0.0035272110253572464,
-0.010378197766840458,
0.009842443279922009,
0.009818227030336857,
-0.0014555577654391527,
0.01858627237379551,
-0.022677479311823845,
0.03291502967476845,
-0.08696626126766205,
-0.03847423940896988,
0.06660019606351852,
0.05741299316287041,
0.028172455728054047,
0.00722130574285984,
-0.013838700950145721,
0.04503326117992401,
0.0009808457689359784,
-0.017087668180465698,
-0.030936559662222862,
-0.03137503191828728,
0.016473781317472458,
-0.00455567566677928,
-0.021577078849077225,
0.014436736702919006,
-0.041729364544153214,
-0.01896493136882782,
0.03559349104762077,
-0.04797608405351639,
-0.010336916893720627,
0.015802554786205292,
-0.010425097309052944,
0.02734559401869774,
0.05662355199456215,
0.008489799685776234,
0.02938023768365383,
0.016405301168560982,
0.048673659563064575,
0.0036401296965777874,
0.001386318588629365,
0.050120361149311066,
-0.004849844146519899,
-0.030172152444720268,
0.0024091911036521196,
-0.03604466840624809,
-0.009903697296977043,
-0.022005176171660423,
-0.024261288344860077,
-0.0034832621458917856,
0.014120727777481079,
-0.02864348329603672,
-0.05125503987073898,
-0.02082039974629879,
0.05013122782111168,
-0.05294668301939964,
-0.03734440729022026,
-0.02689320594072342,
-0.01289424393326044,
-0.06343856453895569,
-0.03320819512009621,
0.048708874732255936,
0.006159207317978144,
-0.019180186092853546,
0.024443235248327255,
-0.008008765988051891,
-0.09834498912096024,
-0.03989240154623985,
-0.03616294637322426,
0.04400667920708656,
-0.02156401239335537,
-0.05486443638801575,
0.05795138329267502,
0.022956592962145805,
-0.013983813114464283,
0.016849437728524208,
-0.019135309383273125,
0.025263173505663872,
-0.01358149666339159,
0.04924933239817619,
0.05520981177687645,
-0.011859092861413956,
-0.03373848274350166,
-0.04399885982275009,
0.05055804178118706,
-0.08072477579116821,
0.003054786706343293,
0.022071942687034607,
0.02305573783814907,
-0.028243940323591232,
0.032551754266023636,
-0.004222801420837641,
-0.03931693732738495,
0.02579992637038231,
-0.05833902209997177,
0.024489054456353188,
0.008848680183291435,
-0.013147146441042423,
0.017483573406934738,
-0.07324275374412537,
-0.013156850822269917,
-0.011166119948029518,
-0.001978513551875949,
-0.012975559569895267,
0.05376186594367027,
-0.020729003474116325,
-0.06995357573032379,
0.024351172149181366,
-0.0023087162990123034,
0.027664905413985252,
0.02832592837512493
] |
<p>All particles exhibit wave-particle duality. And I have a strange question. </p>
<p>Why does a larger system, liken an atom that is just a set of smaller systems, itself exhibit wave-particle duality?</p>
<p>In principle all large systems can be defined as a set of smaller systems. An atom is a set of nucleus (a smaller set of up and down quarks held together by the strong interaction) and some electron(s) bound to the set of quarks by the electromagnetic force.</p>
<p>How is this set of smaller systems being able exhibit wave-particle duality as a whole as if it is a particle itself?</p>
<p>Does this imply that electron and all other elementary particles are indeed just another set of smaller sets and any sets can exhibit wave-particle duality?</p>
<p>And here comes the question: how do you define a set? We naturally define composition such as atom, molecule or "elementary particle" like electron as a set. Can the composition of electrons and up quarks be defined as a set (a system with wavefunction) and the down quarks that present in the atom be defined as a separated set (another system)?</p> | g1254 | [
0.024965384975075722,
0.0056313276290893555,
0.017666835337877274,
-0.07133910059928894,
0.058054450899362564,
0.025953199714422226,
0.0023124755825847387,
0.023999756202101707,
0.022374652326107025,
-0.05107813701033592,
-0.007279051002115011,
0.021999016404151917,
0.02321501262485981,
0.01740839146077633,
-0.049831125885248184,
-0.03220371529459953,
0.021111728623509407,
-0.026882782578468323,
0.04868284612894058,
0.06289707869291306,
0.049301374703645706,
0.05306178331375122,
-0.003769769100472331,
-0.021796509623527527,
-0.020006166771054268,
0.04462634027004242,
0.03705020248889923,
-0.042966753244400024,
0.02837258018553257,
0.011696643196046352,
0.0031566384714096785,
-0.04979826882481575,
0.038708318024873734,
0.022829335182905197,
0.004382319748401642,
-0.03394722566008568,
-0.00586898485198617,
0.01481020636856556,
-0.022699719294905663,
-0.010843831114470959,
-0.005267942789942026,
-0.020595554262399673,
-0.0016761873848736286,
-0.07041215151548386,
-0.0006455205148085952,
-0.00040014341357164085,
-0.011443833820521832,
0.0018089829245582223,
0.022084802389144897,
-0.06800033897161484,
0.012314075604081154,
-0.014607674442231655,
-0.04427673667669296,
0.03802073746919632,
0.045805204659700394,
0.012219913303852081,
0.015830794349312782,
0.03179037943482399,
0.07874596118927002,
0.01970798894762993,
0.007398854475468397,
0.06785208731889725,
0.02756207436323166,
0.006990350317209959,
0.04153268784284592,
-0.03162430226802826,
-0.020359694957733154,
0.02621610462665558,
0.029376529157161713,
-0.004928047768771648,
-0.04083734750747681,
-0.08797749131917953,
0.020153453573584557,
-0.059662554413080215,
0.03655529394745827,
-0.002882710425183177,
-0.046022459864616394,
0.01700136810541153,
-0.0015924591571092606,
-0.009391476400196552,
-0.005438140127807856,
-0.06448610872030258,
0.04110635071992874,
0.003094844054430723,
0.008619267493486404,
0.00894873682409525,
-0.00804200954735279,
-0.08436035364866257,
-0.04008501023054123,
-0.0016773816896602511,
0.03246276453137398,
-0.02279505506157875,
0.06648663431406021,
0.06691930443048477,
-0.0462290495634079,
-0.010646634735167027,
0.00897661130875349,
0.06743428856134415,
0.000020332590793259442,
0.04305097460746765,
0.007405587937682867,
0.0011090753832831979,
-0.005228297784924507,
-0.06720618903636932,
0.02592218481004238,
-0.0008084452711045742,
-0.02222096547484398,
0.02768515795469284,
0.02935776114463806,
0.002334637101739645,
-0.012787871062755585,
-0.04199574142694473,
-0.022998185828328133,
-0.028267666697502136,
-0.08730202168226242,
0.00519777974113822,
0.007391517050564289,
-0.022683797404170036,
-0.05426322668790817,
0.027128009125590324,
-0.017370764166116714,
-0.022008029744029045,
-0.041770726442337036,
-0.019457802176475525,
-0.01842571794986725,
-0.04674302041530609,
0.01873593218624592,
0.05212666094303131,
0.0339219905436039,
-0.010094699449837208,
0.05051107332110405,
-0.02218790352344513,
-0.007350131403654814,
-0.017367271706461906,
-0.00905365776270628,
-0.04256434738636017,
-0.029683683067560196,
-0.02093520574271679,
-0.0037263871636241674,
-0.057348016649484634,
-0.02816114015877247,
-0.014452786184847355,
-0.048752229660749435,
-0.03960456699132919,
-0.013526571914553642,
-0.0027296135667711496,
0.013375813141465187,
-0.046889111399650574,
0.013534690253436565,
0.06397280097007751,
0.055098969489336014,
0.046789735555648804,
0.002697589574381709,
-0.028186995536088943,
0.018002359196543694,
-0.006606793962419033,
0.015012029558420181,
0.020636191591620445,
-0.08016911149024963,
0.013985048979520798,
0.03740552440285683,
0.05782272294163704,
-0.02595888450741768,
0.016859915107488632,
-0.025746066123247147,
0.012534944340586662,
0.007986301556229591,
0.021414799615740776,
0.01931142620742321,
-0.0011576461838558316,
0.02251778356730938,
0.0013778486754745245,
-0.011245936155319214,
0.03270038962364197,
0.03909613564610481,
0.06664930284023285,
0.0639137253165245,
-0.016627129167318344,
0.016642127186059952,
0.014838502742350101,
-0.0353536456823349,
-0.003671729238703847,
-0.010741003789007664,
0.016223840415477753,
0.03134705498814583,
-0.0025124484673142433,
0.02768649533390999,
0.013699864968657494,
0.009729897603392601,
-0.007939903065562248,
-0.020212605595588684,
-0.027853528037667274,
0.0073150997050106525,
-0.03746941313147545,
0.0204186849296093,
-0.09376118332147598,
-0.03867774456739426,
0.026414578780531883,
0.0018892332445830107,
-0.013388758525252342,
-0.012659196741878986,
0.07671687006950378,
0.01692316122353077,
-0.03740377724170685,
0.10734491050243378,
0.04487480968236923,
-0.050740864127874374,
0.03281925246119499,
0.05552586168050766,
0.0051385643891990185,
0.030393533408641815,
-0.00905377697199583,
-0.012257200665771961,
-0.05298284813761711,
-0.019337249919772148,
-0.06209667772054672,
-0.024169789627194405,
0.02558869868516922,
-0.01055676769465208,
-0.00040776588139124215,
-0.04373515024781227,
-0.07553529739379883,
0.050450731068849564,
0.018077921122312546,
0.00205071154050529,
0.018869549036026,
-0.014565280638635159,
-0.0506218783557415,
-0.010480938479304314,
0.032233044505119324,
-0.06117909029126167,
0.048853080719709396,
-0.03248930722475052,
-0.05368659272789955,
0.03659052029252052,
0.04817766323685646,
-0.019783468917012215,
-0.03570567071437836,
0.043533146381378174,
-0.06234538182616234,
-0.025884926319122314,
-0.05449991673231125,
0.020298151299357414,
-0.03155035525560379,
0.06464821845293045,
-0.06101403757929802,
0.016753358766436577,
0.009384380653500557,
-0.0763109102845192,
-0.01792059652507305,
-0.008737276308238506,
-0.030542820692062378,
-0.07891101390123367,
-0.009886936284601688,
0.014510062523186207,
-0.09074968844652176,
-0.025638660416007042,
0.05213053897023201,
-0.018619554117321968,
-0.06974881142377853,
0.053387660533189774,
0.010257650166749954,
-0.04902181401848793,
0.062344569712877274,
-0.03716101124882698,
0.010249340906739235,
0.010532436892390251,
-0.017718961462378502,
0.0076513746753335,
0.004992812871932983,
0.028142957016825676,
0.05195697769522667,
0.04919545352458954,
-0.005047640763223171,
-0.04218719154596329,
-0.043448273092508316,
-0.026391731575131416,
-0.047195520251989365,
0.041502781212329865,
-0.0435454323887825,
0.00021853217913303524,
0.036791831254959106,
-0.02027822844684124,
-0.0021851102355867624,
0.03406575322151184,
-0.03298022598028183,
0.009852287359535694,
0.018858695402741432,
0.026809953153133392,
0.028621001169085503,
0.011340227909386158,
0.019853245466947556,
0.052625782787799835,
-0.007047321181744337,
-0.04531022533774376,
0.015067597851157188,
-0.004739886149764061,
-0.030568139627575874,
-0.0208576787263155,
0.035591188818216324,
-0.008426420390605927,
-0.06633606553077698,
-0.00511005287989974,
0.015069792047142982,
0.03388068825006485,
0.076420359313488,
-0.06522248685359955,
-0.023650016635656357,
-0.08906131982803345,
0.024055805057287216,
-0.015119665302336216,
0.10327737033367157,
-0.006751421373337507,
0.03935717046260834,
-0.040765199810266495,
0.015110156498849392,
-0.03193698823451996,
0.01434953324496746,
0.019605150446295738,
-0.07608922570943832,
-0.043042391538619995,
-0.027761932462453842,
0.06694258749485016,
-0.028873464092612267,
0.0020283632911741734,
0.0011268972884863615,
-0.010714676231145859,
0.003945616539567709,
0.0010562571696937084,
-0.008890241384506226,
-0.004293796140700579,
-0.03053922951221466,
0.003554689232259989,
0.05503997951745987,
-0.04563199728727341,
-0.024080146104097366,
-0.028398040682077408,
-0.057654913514852524,
0.019858861342072487,
-0.012188538908958435,
0.006877364125102758,
0.004670722410082817,
0.02772645279765129,
-0.02430826425552368,
-0.002031502313911915,
0.055386900901794434,
-0.0014044451527297497,
-0.012664595618844032,
0.031244179233908653,
-0.036848533898591995,
-0.012986410409212112,
0.050537340342998505,
0.0030830230098217726,
0.053133413195610046,
-0.05127609521150589,
-0.03538309410214424,
0.02467086911201477,
-0.014352484606206417,
0.08164092898368835,
-0.016340695321559906,
-0.032250214368104935,
-0.027764711529016495,
0.050889719277620316,
0.03319064527750015,
-0.013229533098638058,
-0.03919772058725357,
0.012865936383605003,
-0.0014620950678363442,
-0.0003464585170149803,
-0.022528035566210747,
-0.020390471443533897,
0.017768174409866333,
-0.037675634026527405,
-0.0033993422985076904,
-0.0034981276839971542,
-0.06902850419282913,
-0.022385451942682266,
0.006537743844091892,
-0.042153339833021164,
-0.032140471041202545,
0.012140434235334396,
0.07276486605405807,
0.04509876295924187,
0.04919798672199249,
0.03339703008532524,
0.02596190944314003,
-0.05963241308927536,
-0.011041123420000076,
-0.006653317715972662,
-0.006350265815854073,
0.008801246993243694,
-0.021935200318694115,
-0.08446533232927322,
0.007331230212002993,
0.018103448674082756,
0.003238764824345708,
-0.0013346406631171703,
-0.03851611912250519,
0.0584784671664238,
0.05899974703788757,
-0.055885881185531616,
-0.0007743171881884336,
-0.014625958167016506,
-0.1245373785495758,
0.04562604799866676,
0.0014088113093748689,
-0.0285689327865839,
-0.021444551646709442,
-0.04545827582478523,
-0.06020456179976463,
0.07466054707765579,
0.03940777853131294,
-0.004530367907136679,
-0.005628298036754131,
-0.04531112685799599,
0.03157802298665047,
-0.030505113303661346,
0.02127324603497982,
0.03210128843784332,
0.02198328822851181,
-0.043884728103876114,
0.06576292216777802,
-0.0010820860043168068,
-0.010848581790924072,
0.017657600343227386,
0.05211590975522995,
-0.005811181850731373,
0.033779773861169815,
-0.0367918461561203,
0.023916644975543022,
-0.017245784401893616,
0.034126002341508865,
0.037658970803022385,
0.025389380753040314,
-0.00846787728369236,
-0.029480701312422752,
0.004070728551596403,
0.008533840999007225,
0.05504946783185005,
0.029473718255758286,
0.05868828669190407,
-0.011719494126737118,
-0.020402148365974426,
0.0009586825035512447,
0.03240656480193138,
0.01650129444897175,
-0.03545081615447998,
0.0011757169850170612,
-0.04548899829387665,
-0.006058245897293091,
-0.0018774509662762284,
0.04818878695368767,
-0.08017022162675858,
-0.02643364854156971,
0.00008059628453338519,
-0.012643542140722275,
-0.03959186375141144,
0.006032601930201054,
-0.0371224619448185,
-0.03349769115447998,
-0.05872207134962082,
0.02312316745519638,
0.048231273889541626,
0.0869785025715828,
0.012551553547382355,
-0.015213587321341038,
-0.03886326402425766,
0.0003926999634131789,
-0.09834462404251099,
-0.014395367354154587,
0.03766374662518501,
-0.017421074211597443,
0.026211503893136978,
-0.006261382717639208,
0.036587271839380264,
-0.05169583112001419,
-0.01563572697341442,
-0.04881841316819191,
-0.02419774793088436,
-0.010067693889141083,
-0.004403403494507074,
-0.03725847601890564,
0.04228700324892998,
0.06005360931158066,
-0.04422016441822052,
0.01790504716336727,
0.03187210485339165,
0.0227357167750597,
-0.03514809533953667,
0.02697107382118702,
-0.005383236799389124,
-0.012355254963040352,
0.004111046902835369,
0.024106377735733986,
0.058137718588113785,
-0.049897611141204834,
-0.004581551533192396,
-0.0478384830057621,
0.0016971888253465295,
-0.036499734967947006,
0.019346697255969048,
0.0011864126427099109,
0.0032310294918715954,
0.025248268619179726,
-0.02389274537563324,
0.04120876267552376,
0.03996763750910759,
-0.036043960601091385,
0.0005011498578824103,
-0.030948076397180557,
0.08109263330698013,
0.01923953741788864,
0.002470713574439287,
-0.0034696131478995085,
0.0072408271953463554,
-0.009559061378240585,
-0.03892356902360916,
0.011991682462394238,
-0.007114870473742485,
-0.005218371283262968,
-0.03589402511715889,
-0.012134803459048271,
0.01413994375616312,
-0.05390232428908348,
-0.03555240109562874,
0.022523149847984314,
0.01566208526492119,
-0.015992963686585426,
0.03572646901011467,
0.11435766518115997,
0.0652371495962143,
0.023281104862689972,
-0.026161858811974525,
0.01769026555120945,
0.0029271231032907963,
-0.004558405838906765,
-0.05153229832649231,
0.0097282025963068,
0.03522396460175514,
0.02351500652730465,
0.0006497478461824358,
-0.01999506726861,
0.027129273861646652,
0.0508391410112381,
0.003188095986843109,
0.008302302099764347,
0.0072070518508553505,
-0.03437935560941696,
0.08010459691286087,
0.03559606894850731,
-0.01091448962688446,
0.0120254410430789,
-0.03568188101053238,
-0.046227775514125824,
0.01984199322760105,
0.06793298572301865,
-0.0003250058216508478,
-0.025034215301275253,
0.00263137836009264,
-0.018038950860500336,
0.015398351475596428,
0.0020160404965281487,
0.03273487091064453,
-0.0817732885479927,
0.050703905522823334,
0.008434062823653221,
-0.005078889429569244,
-0.0069302343763411045,
-0.02210107073187828,
0.060002703219652176,
-0.024575794115662575,
0.021560272201895714,
0.050600361078977585,
0.03618866577744484,
0.03413379564881325,
0.035272158682346344,
-0.04369544982910156,
-0.0028508410323411226,
-0.004232142120599747,
0.02715323492884636,
0.05933653935790062,
0.023662153631448746,
-0.03696373105049133,
-0.05152803286910057,
-0.012952026911079884,
-0.008561498485505581,
-0.014450021088123322,
-0.03749573230743408,
0.03712470084428787,
-0.006520820781588554,
0.0022023541387170553,
-0.008106059394776821,
-0.019715918228030205,
0.03327871859073639,
0.015216903761029243,
0.005575770512223244,
0.0193855632096529,
-0.00964992307126522,
-0.010420922189950943,
0.0351378433406353,
-0.01951073855161667,
0.01690160296857357,
0.01651242934167385,
-0.006487187463790178,
0.023469749838113785,
0.08858904242515564,
0.02340066246688366,
-0.019796766340732574,
-0.030078813433647156,
-0.0018450104398652911,
-0.023403186351060867,
-0.008108382113277912,
-0.05482238903641701,
-0.03396874666213989,
0.02260027825832367,
-0.09368318319320679,
0.01131350640207529,
-0.006001187022775412,
-0.04583374410867691,
0.024969900026917458,
0.0050247726030647755,
-0.018124403432011604,
-0.04667821526527405,
0.019082633778452873,
0.01701405830681324,
0.015285618603229523,
-0.011296127922832966,
0.0557357519865036,
0.043732259422540665,
0.010378459468483925,
-0.008326425217092037,
-0.03326253220438957,
0.0628337413072586,
0.05547500401735306,
-0.007849658839404583,
-0.026455391198396683,
-0.02238508127629757,
-0.014561556279659271,
0.02357611246407032,
-0.03286423534154892,
-0.009969611652195454,
0.07714841514825821,
0.010616950690746307,
0.011020001024007797,
-0.07230547070503235,
0.05273984745144844,
0.07131195068359375,
-0.04773922264575958,
-0.04093724861741066,
-0.059751011431217194,
-0.002556372433900833,
0.047052036970853806,
-0.02113291062414646,
0.033682506531476974,
0.015101633034646511,
-0.0009469508659094572,
-0.0004035114252474159,
-0.002403331222012639,
-0.01972200535237789,
-0.04811939597129822,
-0.02726450376212597,
-0.002411179943010211,
0.008003770373761654,
0.00964913796633482,
0.019389702007174492,
0.010279803536832333,
-0.02031541056931019,
-0.06216201186180115,
-0.053677305579185486,
-0.02136429399251938,
-0.052036166191101074,
-0.05973539501428604,
-0.022526133805513382,
-0.03477102145552635,
0.033646754920482635,
-0.06306349486112595,
0.0015742846298962831,
0.02643216773867607,
0.005307516548782587,
-0.041810110211372375,
0.030155843123793602,
0.05039934441447258,
0.04748031497001648,
0.0017183421878144145,
-0.0059888181276619434,
0.007733400445431471,
0.006069503724575043,
0.004190253093838692,
0.015378369018435478,
-0.03808306157588959,
0.024795887991786003,
-0.02262139692902565,
0.03807320073246956,
0.01275266706943512,
-0.002709592692553997,
-0.006721043959259987,
0.0716560035943985,
0.01506537850946188,
0.040006719529628754,
-0.006042537745088339,
-0.010756165720522404,
0.01041441410779953,
0.00029141304548829794,
0.016078751534223557,
0.04649829864501953,
0.04179965704679489,
0.03507975488901138,
-0.005306664388626814,
0.01345064677298069,
-0.023156508803367615,
-0.06834433227777481,
0.011334028095006943,
0.029287567362189293,
0.06355810165405273,
0.07426711916923523,
0.009749002754688263,
0.006016809958964586,
0.035322707146406174,
-0.011736410669982433,
-0.026402007788419724,
0.04791749641299248,
0.004285821691155434,
-0.007323977537453175,
-0.025768082588911057,
0.0200357623398304,
-0.027174776419997215,
0.05765233188867569,
-0.03583504259586334,
0.004409617744386196,
0.044799577444791794,
-0.042621783912181854,
0.004687711130827665,
-0.027820449322462082,
-0.0140186483040452,
-0.02723747119307518,
0.015936149284243584,
-0.025003444403409958,
0.00325365224853158,
-0.00924419891089201,
0.0052221729420125484,
-0.007957374677062035,
-0.03761615231633186,
-0.016564365476369858,
-0.03332795202732086,
-0.0398162305355072,
-0.02920425310730934,
-0.05128380283713341,
0.02171185426414013,
0.052182041108608246,
-0.03711279481649399,
-0.038685888051986694,
0.028661910444498062,
0.02394464984536171,
0.0734458789229393,
0.033309414982795715,
-0.006427215412259102,
0.07286339998245239,
0.055723004043102264,
-0.017902273684740067,
0.026647256687283516,
-0.0053292447701096535,
0.09356044232845306,
0.07209048420190811,
-0.03643088787794113,
-0.028666876256465912,
0.006078398786485195,
-0.029935378581285477,
0.007514387834817171
] |
<p>I saw a diagram of the photosensitivity (Current per Power) of a photodiode.
<img src="http://i.stack.imgur.com/44MQw.png" alt="Photodiode sensitivity"></p>
<p>So there is this diagonal stating the 100% quantum efficiency.
I wondered why the sensitivity for bluer light lower than that of redder light. </p>
<p>Is it because a blue photon has a higher energy? Thus fewer blue photons are needed to achieve the same power as with red photons?
The photocurrent is proportional to the number of converted photons. So a 1 watt beam in red has more photons, which generate more photo-electrons, thus more current per watt. </p>
<p>Is this reasoning correct and explains the curve in the diagram?</p> | g1255 | [
0.031639616936445236,
0.020214267075061798,
0.0096701355651021,
0.03399393707513809,
0.019885089248418808,
0.0006570102996192873,
0.036771636456251144,
0.0194806270301342,
0.00012451698421500623,
-0.0036084752064198256,
0.038665805011987686,
0.043418075889348984,
0.02791227400302887,
0.03395681828260422,
0.036863453686237335,
-0.011793271638453007,
0.02349139004945755,
-0.013740459457039833,
0.11514503508806229,
0.046868033707141876,
-0.06162538379430771,
0.015896758064627647,
-0.08512531220912933,
-0.027625538408756256,
0.001039279391989112,
0.017418039962649345,
-0.0014044941635802388,
-0.06240083649754524,
-0.09033644199371338,
-0.020436730235815048,
-0.026838893070816994,
-0.023973658680915833,
0.028084242716431618,
0.030055003240704536,
0.000924446911085397,
-0.038278061896562576,
0.06656578928232193,
-0.007391844876110554,
0.024174870923161507,
0.03202254697680473,
0.012603568844497204,
0.003021182492375374,
-0.03378039225935936,
-0.04035020247101784,
0.01838936284184456,
-0.08019328862428665,
0.02441949024796486,
0.032075244933366776,
-0.005560359917581081,
-0.056000951677560806,
-0.015167213045060635,
-0.006930815987288952,
0.0027844561263918877,
-0.011162712238729,
0.04501650854945183,
0.0015117472503334284,
-0.03451647609472275,
0.01704053208231926,
-0.04483874514698982,
-0.009380959905683994,
-0.011855801567435265,
-0.0024206486996263266,
0.01644071377813816,
-0.010487859137356281,
0.03310643509030342,
-0.0232301726937294,
0.01984238438308239,
-0.03479309007525444,
0.023449713364243507,
0.010897575877606869,
0.004843727219849825,
-0.0073029412887990475,
-0.0400514081120491,
0.02808666229248047,
0.10090417414903641,
-0.026818973943591118,
-0.05774066597223282,
-0.0480414517223835,
-0.02925318293273449,
0.030847471207380295,
-0.0191947054117918,
-0.04185754060745239,
0.018508430570364,
0.0075687142089009285,
0.05109067261219025,
0.015695247799158096,
0.01107905525714159,
0.0025088577531278133,
0.009746566414833069,
0.027535049244761467,
0.05859570950269699,
-0.06587440520524979,
0.10625968873500824,
0.01535146962851286,
0.016115881502628326,
-0.0018683632370084524,
0.02086229808628559,
0.04412861540913582,
-0.04103189706802368,
0.0485457181930542,
-0.04556567221879959,
-0.019957412034273148,
0.013908430002629757,
0.022210393100976944,
-0.01747029274702072,
-0.035300955176353455,
-0.0196897741407156,
-0.008942249231040478,
-0.06640463322401047,
0.007719840854406357,
-0.009393584914505482,
-0.010066905990242958,
-0.06392238289117813,
-0.020880844444036484,
-0.01912531815469265,
-0.032300204038619995,
0.047582801431417465,
-0.1011933907866478,
-0.009830736555159092,
0.06511884182691574,
0.01926976628601551,
-0.00045089158811606467,
-0.055045876652002335,
0.011912724003195763,
0.0035666364710778,
0.04247411713004112,
-0.010921820998191833,
-0.041148148477077484,
-0.012990178540349007,
0.010955438017845154,
0.0071877371519804,
0.0012348609743639827,
-0.027641793712973595,
0.03126433864235878,
0.08715467900037766,
0.013439521193504333,
0.06565647572278976,
0.026778027415275574,
0.02995658852159977,
0.03646000847220421,
0.008632742799818516,
-0.04037358611822128,
0.005566694773733616,
0.00972623098641634,
-0.026560667902231216,
0.008870505727827549,
-0.02985375188291073,
0.07894089072942734,
0.03541722893714905,
0.06087638810276985,
0.052774347364902496,
-0.0244905948638916,
0.0019022849155589938,
-0.06847930699586868,
0.003949621692299843,
-0.017454443499445915,
0.039468612521886826,
-0.04362491890788078,
-0.012585286982357502,
0.022258451208472252,
-0.020307376980781555,
0.055904775857925415,
0.023920530453324318,
-0.02091783657670021,
0.022524526342749596,
-0.040773410350084305,
0.060151003301143646,
-0.07399345934391022,
-0.026309415698051453,
-0.024698060005903244,
-0.03736041858792305,
0.017406586557626724,
-0.010610227473080158,
-0.018412338569760323,
0.012352590449154377,
0.08161855489015579,
0.05674009397625923,
0.036820393055677414,
-0.02315784990787506,
0.007943917997181416,
-0.07577943056821823,
0.0012936224229633808,
0.019649093970656395,
-0.022516904398798943,
-0.04231380671262741,
-0.037467632442712784,
-0.022305749356746674,
-0.05816063657402992,
-0.029479505494236946,
0.008058560080826283,
-0.0420638807117939,
0.018782541155815125,
-0.025098714977502823,
0.013209734112024307,
-0.04567043483257294,
-0.038318246603012085,
-0.027662763372063637,
-0.027802985161542892,
-0.033192429691553116,
-0.025544965639710426,
-0.03197455778717995,
0.061278294771909714,
0.013420728966593742,
-0.018902800977230072,
0.01654725894331932,
0.06597919017076492,
-0.038737185299396515,
0.0006526162615045905,
0.02829188108444214,
-0.02288632281124592,
0.007336313836276531,
-0.00368461268953979,
0.0701267346739769,
0.021193454042077065,
0.04856785759329796,
0.0029828634578734636,
-0.005234881769865751,
-0.022728824988007545,
-0.004721182398498058,
-0.03872254863381386,
0.000756113207899034,
0.053225256502628326,
0.06918884068727493,
0.02475741319358349,
-0.03502430021762848,
0.053490228950977325,
-0.004813755862414837,
0.01699560508131981,
0.049807123839855194,
-0.00217892462387681,
-0.022150320932269096,
0.004984338767826557,
-0.042557504028081894,
0.000662516220472753,
0.04428713396191597,
0.018111417070031166,
0.00880858302116394,
0.0043262820690870285,
-0.011117422953248024,
-0.0037411730736494064,
-0.03399428352713585,
-0.05849546566605568,
-0.030584298074245453,
0.054103951901197433,
-0.023289525881409645,
-0.012065271846950054,
-0.011590167880058289,
-0.026258686557412148,
-0.07515859603881836,
-0.0030642938800156116,
0.05031915754079819,
0.0004924839013256133,
0.04650270566344261,
0.05205722898244858,
0.0008887563017196953,
-0.005734642036259174,
-0.01565278135240078,
-0.012531287968158722,
-0.04740053042769432,
0.00008941631676862016,
-0.03661184012889862,
-0.06604082137346268,
-0.00903252698481083,
-0.018867511302232742,
-0.018183846026659012,
0.07001999020576477,
-0.047352924942970276,
-0.028731368482112885,
0.062152501195669174,
-0.029277412220835686,
-0.015455659478902817,
0.07123015820980072,
-0.03548829257488251,
-0.047433823347091675,
0.054151199758052826,
-0.03641587495803833,
0.012133532203733921,
0.03522609919309616,
0.03060328960418701,
-0.08479388058185577,
0.026661179959774017,
0.034774087369441986,
-0.09473085403442383,
0.04704315960407257,
0.05003781244158745,
-0.04539133608341217,
0.020196767523884773,
0.003671197686344385,
0.029005208984017372,
0.02844798006117344,
-0.0392332561314106,
0.0031423016916960478,
0.007887913845479488,
0.023074602708220482,
0.008658417500555515,
-0.03185680881142616,
0.02759813517332077,
-0.019365878775715828,
-0.04760098457336426,
0.006598565261811018,
-0.03034917451441288,
-0.03674880787730217,
-0.037829503417015076,
-0.01690128818154335,
-0.0029354176949709654,
0.020395375788211823,
-0.04941783472895622,
-0.04630551114678383,
-0.0768856629729271,
0.06370070576667786,
-0.055877286940813065,
0.0297086238861084,
-0.038321856409311295,
0.007878809235990047,
-0.017534323036670685,
-0.05121590569615364,
0.03486810624599457,
0.033662017434835434,
-0.00561140850186348,
0.0313405841588974,
-0.03184570372104645,
0.044341642409563065,
0.005821580532938242,
-0.011750674806535244,
-0.016116520389914513,
0.009673146530985832,
-0.049155864864587784,
0.019757691770792007,
0.021212425082921982,
0.026901409029960632,
0.04989342764019966,
0.010664411820471287,
-0.03665371611714363,
0.05695528909564018,
-0.022464239969849586,
-0.02793608419597149,
-0.054485101252794266,
0.001533943461254239,
-0.037071727216243744,
0.013396384194493294,
-0.0188516303896904,
0.011267801746726036,
-0.11001040041446686,
-0.026232091709971428,
0.0038289669901132584,
-0.01953100599348545,
0.007694900501519442,
0.011062677018344402,
0.002489929087460041,
-0.07565589994192123,
0.04437333345413208,
0.025628942996263504,
-0.0030828833114355803,
0.030420489609241486,
-0.023861339315772057,
-0.009411153383553028,
-0.049844272434711456,
0.04843898117542267,
-0.01578180119395256,
0.01549142599105835,
0.015584193170070648,
0.019895898178219795,
0.007933899760246277,
-0.00460920762270689,
-0.06369979679584503,
0.0036851288750767708,
-0.015822701156139374,
-0.003182907123118639,
0.00564059242606163,
-0.02592225931584835,
-0.05364895612001419,
-0.05043870210647583,
0.02629968523979187,
0.04897698387503624,
0.03759114444255829,
-0.012081908993422985,
-0.004034385085105896,
-0.06538010388612747,
0.01765623316168785,
0.029471293091773987,
-0.005471447948366404,
-0.015189746394753456,
0.050293609499931335,
0.0006510810926556587,
0.03115583024919033,
0.022350380197167397,
0.007873287424445152,
-0.04986831545829773,
-0.012999868020415306,
0.010208682157099247,
-0.06335177272558212,
-0.021686648949980736,
-0.0413748063147068,
0.010138479061424732,
0.024488110095262527,
-0.0022941152565181255,
-0.012747562490403652,
0.018601788207888603,
0.015397497452795506,
0.003268970875069499,
-0.0011854160111397505,
-0.014357903972268105,
-0.0019288210896775126,
0.00454559875652194,
-0.02563205547630787,
-0.02008163556456566,
-0.015300799161195755,
-0.0035056862980127335,
-0.00024351007596123964,
0.021518677473068237,
0.018584739416837692,
-0.01682296395301819,
0.011250628158450127,
-0.05299941077828407,
0.024512233212590218,
0.010371931828558445,
0.018426913768053055,
-0.031010296195745468,
0.042856693267822266,
0.052908528596162796,
0.04412373527884483,
-0.0006634342134930193,
0.007498270366340876,
-0.035522233694791794,
0.021806711331009865,
0.03780093416571617,
0.055811356753110886,
0.014678070321679115,
0.050913646817207336,
0.0012461327714845538,
0.1108001172542572,
0.060092199593782425,
-0.015724001452326775,
0.010272611863911152,
-0.02787850610911846,
0.04609745368361473,
-0.002583828754723072,
0.051287487149238586,
0.0681888535618782,
0.020993944257497787,
0.07696086168289185,
-0.0058138687163591385,
-0.014286315068602562,
-0.08492487668991089,
0.07616185396909714,
-0.021157434210181236,
-0.058541763573884964,
-0.011835113167762756,
-0.014465495944023132,
-0.0624479278922081,
-0.01168043166399002,
-0.02266867458820343,
-0.03589693456888199,
-0.03893602266907692,
0.014401710592210293,
-0.006117925979197025,
-0.0038407170213758945,
0.013260677456855774,
0.0473281629383564,
0.10580167174339294,
-0.05759108066558838,
0.01520765945315361,
0.030519932508468628,
0.01833624765276909,
0.024310950189828873,
-0.01889898255467415,
-0.07559706270694733,
0.0010117385536432266,
-0.07277096062898636,
-0.02021806314587593,
-0.013679791241884232,
-0.004499238450080156,
0.02951859124004841,
0.03560161218047142,
-0.03312641754746437,
-0.029340635985136032,
-0.009982949122786522,
-0.020644856616854668,
0.015105562284588814,
0.010139279998838902,
0.006971856113523245,
-0.03729677200317383,
0.010287834331393242,
0.010062475688755512,
-0.030815931037068367,
0.045288048684597015,
-0.054770439863204956,
0.07009190320968628,
-0.02784644067287445,
-0.05031108111143112,
0.03389236330986023,
0.023793548345565796,
-0.030514486134052277,
-0.0545530766248703,
-0.005699550732970238,
0.04571117088198662,
0.06634368747472763,
0.024681370705366135,
-0.026933981105685234,
0.05048659071326256,
-0.012056698091328144,
0.03529416024684906,
-0.0313446931540966,
-0.05793452635407448,
-0.04557575285434723,
0.009476322680711746,
0.037720516324043274,
-0.018428094685077667,
0.0074946945533156395,
0.03756701201200485,
-0.068220354616642,
-0.06718197464942932,
0.0623880960047245,
0.004922701045870781,
0.043919291347265244,
0.03183761611580849,
-0.08285656571388245,
-0.00006087131623644382,
0.04228411987423897,
-0.04153001308441162,
0.06749282777309418,
0.028372833505272865,
-0.03490153327584267,
-0.02474858984351158,
0.03797383978962898,
0.012051180005073547,
-0.039548441767692566,
0.014136545360088348,
0.07572421431541443,
-0.026862910017371178,
0.0547383613884449,
0.07175606489181519,
0.03346608579158783,
0.0081019913777709,
0.007564608473330736,
-0.028158143162727356,
0.09767776727676392,
0.0015893281670287251,
-0.005608274135738611,
0.03036385588347912,
0.021340928971767426,
0.01509092003107071,
0.012259354814887047,
-0.011340143159031868,
0.04046067222952843,
-0.0322163887321949,
-0.044383756816387177,
-0.08787472546100616,
-0.06470166146755219,
0.03125668689608574,
-0.0013844253262504935,
0.012047341093420982,
0.02894042246043682,
0.035629697144031525,
-0.013987276703119278,
0.015809305012226105,
0.009672209620475769,
-0.03067607805132866,
0.043450672179460526,
-0.036098506301641464,
0.01827266253530979,
0.02814025618135929,
-0.03143659979104996,
0.023266494274139404,
0.003783030901104212,
-0.08224382996559143,
-0.013099074363708496,
-0.029173223301768303,
-0.00044586267904378474,
0.04746772721409798,
0.04532274231314659,
-0.004631135147064924,
0.07949452102184296,
0.01947413757443428,
-0.0044289459474384785,
0.016418829560279846,
-0.01736712083220482,
-0.061073437333106995,
-0.06210397556424141,
-0.006346334703266621,
0.033003780990839005,
0.04960764944553375,
-0.002526280004531145,
-0.035812102258205414,
0.00744168134406209,
0.03774363547563553,
0.03280698135495186,
0.004139123018831015,
0.0644998624920845,
-0.024176999926567078,
-0.021379997953772545,
-0.001717455335892737,
0.008622759021818638,
-0.030519478023052216,
-0.005114078521728516,
-0.012432177551090717,
-0.006868453696370125,
0.03727611154317856,
-0.03921380639076233,
0.00877381395548582,
0.0060360063798725605,
-0.026389962062239647,
0.016731806099414825,
0.06792523711919785,
0.025093015283346176,
-0.010775556787848473,
0.009605632163584232,
-0.0052759964019060135,
0.014888832345604897,
0.021662579849362373,
0.015561086125671864,
-0.008451378904283047,
0.0024455413222312927,
-0.01360162254422903,
0.03579176217317581,
-0.04487910494208336,
0.01815592497587204,
0.03433748707175255,
-0.0004889121628366411,
0.026682469993829727,
0.013411943800747395,
-0.005304265301674604,
-0.0033684559166431427,
-0.04675406590104103,
0.07229350507259369,
0.04836958274245262,
-0.005953952204436064,
0.027164297178387642,
0.04929884523153305,
-0.03633539378643036,
-0.031096193939447403,
0.030188342556357384,
0.0096418596804142,
0.08271671086549759,
0.06944514065980911,
0.022627323865890503,
-0.046137116849422455,
-0.05863156542181969,
0.0021998684387654066,
0.004388636909425259,
-0.011037766002118587,
0.01780182495713234,
0.020885799080133438,
0.0036747907288372517,
-0.010963893495500088,
0.029374223202466965,
-0.014197799377143383,
0.007712787948548794,
-0.0010040196357294917,
-0.00045802126987837255,
0.012350079603493214,
0.017982587218284607,
0.0013009888352826238,
-0.07365579158067703,
0.004102599807083607,
0.023827146738767624,
-0.0529533214867115,
0.08473008871078491,
-0.009777790866792202,
-0.06900013983249664,
-0.0030043083243072033,
-0.0032743667252361774,
-0.04174215719103813,
0.015805315226316452,
0.040928035974502563,
-0.008929145522415638,
-0.008915423415601254,
0.002294713631272316,
-0.03387124836444855,
0.006650017108768225,
0.0009519338491372764,
-0.012370099313557148,
-0.004260366316884756,
-0.014119877479970455,
-0.014566058292984962,
0.026728538796305656,
-0.024247484281659126,
0.036830704659223557,
-0.02358180098235607,
-0.007475780788809061,
0.024608580395579338,
-0.01426470372825861,
0.024406662210822105,
-0.08559312671422958,
-0.01854751817882061,
-0.007415711414068937,
-0.05345795303583145,
-0.03438013419508934,
0.05415765568614006,
-0.03810998052358627,
-0.04715219885110855,
-0.0484594888985157,
-0.014106262475252151,
-0.03133056312799454,
-0.005147961899638176,
0.06624221056699753,
0.0012972474796697497,
0.017039068043231964,
0.0813136100769043,
-0.006482323165982962,
-0.0016301252180710435,
-0.06191202253103256,
0.021459797397255898,
0.01359693892300129,
0.03558046370744705,
0.009702174924314022,
-0.03203777223825455,
-0.0211930051445961,
-0.035643257200717926,
0.0025558825582265854,
0.009255914948880672,
-0.02027113176882267,
0.00650289561599493,
-0.010358704254031181,
-0.027225056663155556,
-0.00833884347230196,
-0.029378527775406837,
-0.013324961997568607,
-0.025554055348038673,
-0.007558586075901985,
0.0033978379797190428,
-0.02667049504816532,
-0.030734580010175705,
-0.06334793567657471,
-0.006755812093615532,
-0.023641211912035942,
0.0039281356148421764,
-0.032769039273262024,
-0.052468858659267426,
-0.032839562743902206,
-0.006157747469842434,
-0.010891527868807316,
0.008067885413765907,
0.015700755640864372,
-0.034344736486673355,
0.022319791838526726,
-0.02166139893233776,
0.023065023124217987,
0.005719957873225212,
0.027727726846933365,
0.03542681038379669,
-0.037389520555734634,
-0.02186269871890545,
0.040194861590862274,
0.010203437879681587,
0.01961476542055607,
0.008118918165564537,
0.017272355034947395,
0.08759292215108871,
-0.012086897157132626,
-0.004599414765834808,
-0.011652577668428421,
-0.022099273279309273,
0.005384976975619793,
0.024405186995863914,
-0.016966165974736214,
0.0666535347700119,
-0.01174145471304655,
0.0052009751088917255,
-0.0049580479972064495,
-0.023432694375514984,
0.024274490773677826,
-0.017601201310753822,
-0.00959056057035923,
-0.018861016258597374,
-0.024973273277282715,
-0.05691850930452347,
-0.05455050244927406
] |
<p>What is a practical way in an engineering or physics laboratory to create bubbles of a specified size in water within plastic tubing? The tubing is a few mm inner diameter. We'd like to make bubbles smaller in size than the diameter, for example 1/2 the diameter. We'd like to have control over the size, especially volume, and rate of bubble generation. </p>
<p>We have tried a metal hypodermic needle connected to a low-power air pump, but air accumulates over time to make one big bubble, which eventually breaks away. Maybe there is a way to knock the bubble off when it's the desired small size, instead of waiting for it to do as it pleases? </p>
<p>The water is at roughly 1 to 1.3 atm pressure, at room temperature. </p>
<p>We imagine possibilities of electrolysis, or acoustics, but haven't found any written experience through google searches.</p> | g1256 | [
0.004497644491493702,
0.013800100423395634,
0.018509414047002792,
-0.0029356086160987616,
-0.05006398260593414,
0.07361289858818054,
0.03719942271709442,
-0.009038656949996948,
-0.023432565852999687,
-0.02342439629137516,
0.05390652269124985,
0.024286849424242973,
-0.0014231452951207757,
-0.011732139624655247,
0.010532337240874767,
0.018536241725087166,
0.01627754420042038,
-0.03217032551765442,
-0.050831109285354614,
0.031092477962374687,
0.040440164506435394,
-0.030238987877964973,
-0.03213527053594589,
0.0018186019733548164,
-0.006852253340184689,
0.01793106086552143,
0.023763880133628845,
0.0005089567857794464,
0.006756994873285294,
0.002812167862430215,
-0.05426308512687683,
0.04032402113080025,
-0.02707809768617153,
-0.00863390602171421,
-0.012463301420211792,
-0.04789551720023155,
-0.05028211697936058,
-0.01145385205745697,
-0.054662320762872696,
0.011517016217112541,
0.03089960850775242,
-0.005679079797118902,
0.045465510338544846,
0.018264969810843468,
-0.009140117093920708,
0.05109688639640808,
0.05421871319413185,
-0.0009160381159745157,
-0.009470743127167225,
-0.032230183482170105,
0.07620920240879059,
0.008590816520154476,
-0.012585253454744816,
-0.01845391094684601,
0.004280240274965763,
-0.03010593168437481,
-0.001774156466126442,
-0.012758041732013226,
0.028569096699357033,
0.0073216757737100124,
-0.05698788911104202,
0.0004947806592099369,
-0.028444387018680573,
0.027842136099934578,
-0.002512038452550769,
0.06588691473007202,
-0.025677010416984558,
-0.02732708677649498,
0.049902256578207016,
0.06935717910528183,
-0.023963768035173416,
-0.06791318207979202,
0.012923222035169601,
-0.04176115244626999,
-0.05365834757685661,
-0.019751403480768204,
-0.08634566515684128,
-0.029104791581630707,
0.024814173579216003,
-0.003931197803467512,
0.01783675327897072,
0.007044956553727388,
-0.006343639921396971,
-0.01538168452680111,
0.038861170411109924,
0.010362467728555202,
-0.04893774539232254,
-0.06947745382785797,
-0.045974262058734894,
-0.024994326755404472,
-0.01353247370570898,
0.01786625199019909,
0.015482270158827305,
-0.004904476460069418,
0.03883335739374161,
-0.00390654755756259,
0.009050111286342144,
0.02827276475727558,
0.02423270046710968,
0.015384241938591003,
0.019455472007393837,
-0.023150021210312843,
0.05319451540708542,
0.008317948319017887,
-0.07321317493915558,
0.01070684939622879,
0.030657606199383736,
-0.03908352926373482,
0.007893461734056473,
-0.013874560594558716,
0.01626305654644966,
-0.03453363850712776,
-0.04902653023600578,
0.025853902101516724,
0.006534580606967211,
-0.002622430445626378,
-0.03951745107769966,
0.03470142185688019,
-0.040567439049482346,
0.0621161162853241,
0.01355136651545763,
0.016128946095705032,
0.025394733995199203,
-0.013498992659151554,
-0.023212512955069542,
0.016101431101560593,
-0.010964431799948215,
0.04352465271949768,
0.011723574250936508,
0.013402548618614674,
0.04217228665947914,
0.012561098672449589,
-0.0785614401102066,
-0.04204370453953743,
-0.011990123428404331,
0.09743967652320862,
-0.005882446654140949,
-0.03290790691971779,
0.02386639453470707,
-0.07599394023418427,
-0.02248273603618145,
-0.006375265307724476,
-0.013156766071915627,
0.019305668771266937,
-0.033246248960494995,
0.032439637929201126,
-0.050391923636198044,
0.012171914801001549,
-0.038188524544239044,
0.05545054003596306,
-0.013864750042557716,
0.0004801618924830109,
-0.016634149476885796,
-0.037717606872320175,
0.019038977101445198,
0.06894157081842422,
0.025838259607553482,
0.01784876547753811,
0.018024573102593422,
0.047315921634435654,
-0.01394808478653431,
-0.04419093206524849,
0.025020897388458252,
0.01821790635585785,
-0.035029083490371704,
0.09006231278181076,
0.02216525375843048,
0.000652490823995322,
-0.04056055471301079,
-0.08569692820310593,
-0.020232543349266052,
-0.08521321415901184,
-0.015406835824251175,
0.021697890013456345,
0.009147082455456257,
0.003395603969693184,
0.05134067311882973,
0.008414231240749359,
-0.016565047204494476,
0.03352067992091179,
-0.02321581356227398,
-0.06664801388978958,
-0.023557087406516075,
-0.019144883379340172,
-0.038709890097379684,
0.05415726080536842,
0.02696543000638485,
-0.016076188534498215,
-0.018725907430052757,
-0.0365232490003109,
-0.0034494942519813776,
0.01092719379812479,
-0.03437754511833191,
-0.015046872198581696,
-0.04081780090928078,
-0.0559174008667469,
0.07438302785158157,
-0.04301648959517479,
0.010809089988470078,
0.032133325934410095,
-0.03407300263643265,
0.03248700499534607,
0.003055219305679202,
-0.02516341209411621,
0.06954587250947952,
0.0200851671397686,
-0.031150145456194878,
-0.011562746949493885,
-0.0008647018694318831,
0.016533425077795982,
0.07821471989154816,
0.029914531856775284,
-0.033704083412885666,
-0.00637773284688592,
-0.024729279801249504,
0.0012643954250961542,
-0.0440790057182312,
-0.05858221650123596,
0.02613428235054016,
0.049971193075180054,
0.0339798629283905,
0.020215068012475967,
-0.02570248395204544,
0.0319114588201046,
0.007128030061721802,
-0.004892075899988413,
0.005690488498657942,
-0.028401879593729973,
0.012721238657832146,
-0.039294853806495667,
-0.004421411082148552,
-0.012126363813877106,
0.003041923278942704,
-0.017931468784809113,
-0.032940275967121124,
0.025812556967139244,
0.00797470472753048,
0.027972135692834854,
-0.04671676829457283,
-0.03570757433772087,
0.017075182870030403,
-0.0033175544813275337,
-0.04285077005624771,
-0.023540087044239044,
-0.025713937357068062,
-0.06367827206850052,
-0.0066855852492153645,
-0.0301061999052763,
0.006106394808739424,
0.022470993921160698,
-0.01389721967279911,
0.015500389970839024,
0.03518185392022133,
0.018011026084423065,
0.0008791170548647642,
-0.004589409101754427,
0.051567062735557556,
0.08328703790903091,
0.04101377725601196,
-0.025750083848834038,
0.012645990587770939,
0.009473255835473537,
0.030999111011624336,
0.05234939232468605,
-0.001261503086425364,
-0.019266825169324875,
-0.055657315999269485,
0.003185095265507698,
0.02861996740102768,
0.06453654170036316,
0.015926245599985123,
0.0061973994597792625,
-0.04702874645590782,
-0.027562223374843597,
0.015395594760775566,
-0.028043881058692932,
0.022641565650701523,
-0.009683272801339626,
0.056360211223363876,
-0.011431504972279072,
-0.015568031929433346,
-0.05545734241604805,
-0.0307364109903574,
0.011864985339343548,
0.01974756456911564,
-0.03724958002567291,
0.050149157643318176,
-0.004987511318176985,
0.041107967495918274,
0.0340147539973259,
0.02109736017882824,
-0.03856499120593071,
-0.02077031135559082,
-0.0707535669207573,
0.04034959897398949,
0.06742748618125916,
-0.03417155519127846,
0.0723903551697731,
0.008009539917111397,
-0.018876411020755768,
-0.004869365133345127,
-0.012066872790455818,
0.008847208693623543,
-0.0020020657684653997,
-0.0414031557738781,
0.009662425145506859,
-0.06637922674417496,
0.036065101623535156,
-0.025539187714457512,
0.023792145773768425,
0.0407586395740509,
-0.0025875684805214405,
0.00438140332698822,
0.04970298707485199,
-0.00953782070428133,
0.014450128190219402,
0.0042956857942044735,
-0.023039190098643303,
0.039283715188503265,
0.022544777020812035,
0.03035748191177845,
0.01735655404627323,
0.04631247743964195,
0.03261645883321762,
-0.0010599542874842882,
-0.022071659564971924,
0.04682572931051254,
-0.037663210183382034,
-0.059428323060274124,
-0.042928822338581085,
0.024331100285053253,
0.0003323232231196016,
-0.06265498697757721,
-0.005691928789019585,
0.014524326659739017,
-0.04673086106777191,
0.008731849491596222,
0.03944855183362961,
-0.007522502448409796,
-0.009127688594162464,
0.0006987090455368161,
-0.03887030854821205,
-0.03214096277952194,
-0.023990362882614136,
0.02457490935921669,
0.03457338362932205,
0.0059332214295864105,
0.035954758524894714,
0.010419928468763828,
-0.00003850597931887023,
0.10402867943048477,
-0.012988745234906673,
-0.0009204931557178497,
-0.06596837192773819,
0.026608088985085487,
0.00999663770198822,
0.05992008373141289,
0.043437935411930084,
0.014311515726149082,
-0.08672136813402176,
-0.033082544803619385,
-0.05137691646814346,
-0.025350645184516907,
0.023208171129226685,
-0.07658976316452026,
-0.04021503031253815,
0.05166344344615936,
0.011785313487052917,
-0.0590861476957798,
-0.04877308011054993,
0.004802808631211519,
0.06939571350812912,
-0.04885612428188324,
-0.003241849597543478,
-0.01942329853773117,
-0.008483429439365864,
0.047134868800640106,
0.019695846363902092,
0.010082404129207134,
-0.008724184706807137,
-0.01723557338118553,
0.011761035770177841,
0.01590697094798088,
-0.015028174966573715,
-0.031761061400175095,
-0.07661788165569305,
-0.010995057411491871,
0.024194495752453804,
0.02046799100935459,
-0.0691809430718422,
-0.04765281826257706,
0.017480069771409035,
-0.01814514771103859,
0.017392443493008614,
-0.015031770803034306,
0.050617873668670654,
0.0004881570639554411,
-0.01859760656952858,
-0.0338963158428669,
-0.03935353085398674,
-0.025724738836288452,
0.007346799597144127,
0.0019090608693659306,
0.051978424191474915,
0.00802066083997488,
-0.017581861466169357,
0.04936099797487259,
0.021712064743041992,
-0.04499921202659607,
-0.030955897644162178,
0.03693850338459015,
-0.028130047023296356,
0.019976304844021797,
-0.0036675420124083757,
-0.0076803117990493774,
-0.03941275179386139,
-0.05535833537578583,
0.018094705417752266,
0.07201752811670303,
0.03401155397295952,
-0.015453782863914967,
-0.016575364395976067,
0.0044416338205337524,
-0.00006117983139120042,
-0.02229158952832222,
0.04258286952972412,
-0.038038745522499084,
0.012038205750286579,
-0.025744356215000153,
-0.03982572630047798,
0.008954702876508236,
0.03542052581906319,
-0.03122243843972683,
-0.014049969613552094,
0.015764931216835976,
-0.01669936813414097,
-0.01808469183743,
-0.009863228537142277,
0.0255462396889925,
-0.009104517288506031,
0.021679891273379326,
0.00007122644456103444,
0.0026877662166953087,
0.038743916898965836,
0.015211421065032482,
0.07157646119594574,
0.04128822311758995,
-0.006605889182537794,
-0.001387911383062601,
0.07030883431434631,
0.01602485217154026,
0.006057559046894312,
0.0268743596971035,
-0.04844628646969795,
-0.008202249184250832,
0.03375653922557831,
0.01666705682873726,
0.014440078288316727,
-0.04752383381128311,
0.018711581826210022,
0.015986243262887,
0.05058981105685234,
-0.03890756517648697,
0.04866928234696388,
-0.01888349838554859,
-0.041437093168497086,
-0.0336582325398922,
-0.07922446727752686,
0.002638661302626133,
-0.02489357441663742,
-0.0029840716160833836,
0.060282811522483826,
0.030478209257125854,
0.06075403094291687,
-0.03433338925242424,
0.009151018224656582,
-0.07328376173973083,
-0.034726712852716446,
-0.007218072656542063,
-0.04269470274448395,
0.0009684700053185225,
0.04364093765616417,
-0.02074609138071537,
0.01197273563593626,
0.03984689339995384,
-0.005595654249191284,
-0.05651245266199112,
0.043046001344919205,
0.012577475979924202,
-0.03078046441078186,
0.022820716723799706,
0.029697375372052193,
0.07601765543222427,
-0.03696300834417343,
-0.046069707721471786,
-0.09066600352525711,
0.006707504391670227,
0.04951546713709831,
0.04411786049604416,
0.014529862441122532,
0.03413134068250656,
-0.051628321409225464,
-0.011742875911295414,
-0.023363692685961723,
0.02526768110692501,
-0.06422345340251923,
-0.06309358775615692,
0.026588071137666702,
0.03494904190301895,
0.02016560174524784,
0.011554313823580742,
0.07355865091085434,
-0.037420742213726044,
0.010745435953140259,
0.0461590550839901,
0.020032500848174095,
-0.05829063802957535,
0.0033534253016114235,
-0.020065532997250557,
0.0009699193178676069,
0.050175510346889496,
-0.05189068242907524,
-0.007427551783621311,
0.031971678137779236,
0.012948120944201946,
0.041862718760967255,
-0.014609802514314651,
-0.010456816293299198,
0.02412182092666626,
-0.026517992839217186,
-0.01961277425289154,
-0.06864102929830551,
0.01211315207183361,
-0.021147223189473152,
-0.033605076372623444,
0.003673227271065116,
0.02223704569041729,
0.007523598615080118,
0.06032119691371918,
0.018005013465881348,
0.012909908778965473,
0.0011864338302984834,
0.0217601228505373,
-0.0007845864747650921,
0.043741460889577866,
0.0257030688226223,
0.06876839697360992,
-0.004694059491157532,
-0.004974494222551584,
0.04452605918049812,
-0.02652563713490963,
0.003992096986621618,
0.011905399151146412,
-0.004113103728741407,
0.0036392107140272856,
0.030513621866703033,
-0.006087792105972767,
-0.023879706859588623,
0.015102933160960674,
-0.025377344340085983,
0.0260622538626194,
-0.0016935091698542237,
0.02761968784034252,
0.05454805865883827,
-0.04476451873779297,
-0.05232251435518265,
-0.01123358029872179,
0.007290523964911699,
0.004413514398038387,
0.08511286973953247,
-0.00897142942994833,
-0.016106463968753815,
-0.008422084152698517,
-0.03877917304635048,
0.015418298542499542,
-0.03138189762830734,
0.06190646439790726,
0.012234422378242016,
-0.011430353857576847,
0.04521220549941063,
-0.017103029415011406,
0.03980346396565437,
-0.020822104066610336,
-0.041775017976760864,
-0.015218342654407024,
-0.050984665751457214,
-0.03571923449635506,
-0.04611828923225403,
-0.02662455290555954,
-0.06682602316141129,
-0.018285084515810013,
-0.000481397524708882,
-0.08485492318868637,
-0.047556322067976,
0.02331152744591236,
-0.020095719024538994,
0.00023035999038256705,
-0.0034432513639330864,
-0.04214915260672569,
-0.00818428210914135,
-0.022612638771533966,
0.05686351656913757,
0.011396460235118866,
0.011409616097807884,
-0.029962783679366112,
0.005323594436049461,
-0.022290997207164764,
0.09486840665340424,
0.02868569828569889,
0.005678648129105568,
-0.04431378096342087,
-0.0024072935339063406,
-0.015084552578628063,
0.005210665054619312,
0.053918447345495224,
0.00630284333601594,
0.0850798711180687,
-0.02121810056269169,
0.044317957013845444,
-0.009964635595679283,
-0.01054325234144926,
0.006892617326229811,
0.042929988354444504,
-0.02690107934176922,
0.019538842141628265,
0.02404915541410446,
0.011496325023472309,
-0.01656157337129116,
-0.01115111168473959,
-0.036781299859285355,
0.01219295896589756,
-0.030432138592004776,
-0.05995958298444748,
0.06973377615213394,
-0.024362877011299133,
0.06309828162193298,
0.04523879289627075,
0.016763290390372276,
0.04440459609031677,
0.01716235652565956,
-0.012989122420549393,
0.025871844962239265,
0.05219641700387001,
0.09327153116464615,
-0.02814110927283764,
0.031523097306489944,
0.04616239666938782,
0.029764872044324875,
-0.05455984175205231,
-0.0037872730754315853,
0.004099939949810505,
-0.08379468321800232,
-0.041425593197345734,
-0.008635632693767548,
-0.04451417550444603,
0.04723517224192619,
-0.032950758934020996,
0.034183621406555176,
0.03786914795637131,
-0.05152251198887825,
-0.0479535311460495,
-0.0049582598730921745,
0.04237789288163185,
-0.012117339298129082,
0.055718619376420975,
0.05559249594807625,
-0.01980198360979557,
0.03366390988230705,
0.024220025166869164,
-0.03534100577235222,
0.03729815036058426,
0.058320552110672,
-0.002474205568432808,
-0.023344462737441063,
0.04337140917778015,
-0.027774102985858917,
0.07390743494033813,
0.062186021357774734,
-0.014342907816171646,
0.03040405735373497,
-0.011412497609853745,
-0.01800217665731907,
-0.029712459072470665,
-0.020901111885905266,
0.012840351089835167,
-0.055740952491760254,
-0.06033971160650253,
0.03354957699775696,
0.005419916473329067,
-0.03096841275691986,
-0.03181639686226845,
0.004241779912263155,
-0.021414898335933685,
-0.02680346369743347,
-0.016832424327731133,
0.02166198194026947,
0.08736378699541092,
-0.019811389967799187,
0.0002675112627912313,
-0.004409788642078638,
-0.03825508803129196,
-0.009338181465864182,
0.020585671067237854,
-0.023101549595594406,
0.03009030781686306,
0.01366693340241909,
-0.012963864021003246,
-0.02325042523443699,
-0.013545437715947628,
-0.007396996952593327,
-0.04601331800222397,
-0.0013003123458474874,
-0.011798089370131493,
-0.0479217991232872,
0.027259422466158867,
-0.05654800683259964,
-0.08120642602443695,
0.024616871029138565,
0.05771883577108383,
0.013380664400756359,
-0.013781829737126827,
0.01754479855298996,
0.03144093230366707,
0.027278060093522072,
-0.003973653074353933,
-0.07297680526971817,
0.03428173065185547,
0.06520036607980728,
-0.08357423543930054,
-0.022107884287834167,
-0.06790324300527573,
-0.041458286345005035,
0.010426584631204605,
0.017374441027641296,
-0.024399911984801292,
-0.03519197553396225,
0.0360499806702137,
0.01342699397355318,
-0.043497052043676376,
0.012056869454681873,
0.024209769442677498,
0.026735631749033928,
-0.03957390412688255,
-0.0438404344022274,
0.01907689869403839,
-0.008947057649493217,
-0.01718822680413723,
0.08012840151786804,
0.016759971156716347,
-0.0896773561835289,
-0.014619335532188416,
-0.015516886487603188,
0.04981546103954315,
0.0243387334048748,
0.039014123380184174,
-0.0829828530550003,
-0.01667260192334652,
0.04836622253060341,
-0.02790723741054535,
-0.05014140531420708,
0.03451071307063103,
0.10311309248209,
-0.01183940190821886,
0.05542720481753349,
-0.031233854591846466,
-0.005973050836473703,
0.07882189750671387,
-0.010819604620337486
] |
<p>Why is it that in stars undergoing gravitational collapse <a href="http://en.wikipedia.org/wiki/Electron_degeneracy_pressure" rel="nofollow">electron degeneracy</a> kicks in? Why couldn't the electrons form <a href="http://en.wikipedia.org/wiki/Energy_bands" rel="nofollow">energy bands</a> like in semiconductors? </p> | g1257 | [
-0.012749748304486275,
0.042297352105379105,
-0.016758859157562256,
-0.03582704812288284,
0.060250598937273026,
0.06950102746486664,
-0.03570740297436714,
0.04959859699010849,
-0.04031366482377052,
-0.019504904747009277,
0.024433229118585587,
0.0383518785238266,
0.06501266360282898,
0.006377051584422588,
0.036259789019823074,
-0.019306035712361336,
0.06416717171669006,
-0.017893385142087936,
0.020583689212799072,
0.03658049553632736,
-0.022279951721429825,
-0.037381235510110855,
-0.00382916908711195,
-0.01955142244696617,
0.0315319262444973,
0.014555695466697216,
0.02290637232363224,
-0.04619422182440758,
0.026088083162903786,
-0.02229529619216919,
0.024012815207242966,
0.05570625886321068,
0.061275482177734375,
-0.07011576741933823,
0.017563285306096077,
-0.020005760714411736,
0.008308712393045425,
-0.008767890743911266,
-0.00024043975281529129,
-0.03468741849064827,
-0.06940285116434097,
-0.05108052119612694,
-0.03447292745113373,
-0.006967321503907442,
-0.002073834650218487,
-0.01821480132639408,
-0.009867003187537193,
-0.030246278271079063,
0.01715864986181259,
-0.04762149974703789,
0.05895208567380905,
0.06599517911672592,
0.014773230999708176,
-0.036200374364852905,
0.051345743238925934,
-0.035946935415267944,
-0.038060810416936874,
0.00382895115762949,
0.10484125465154648,
-0.05452940613031387,
-0.05434473603963852,
0.02747524157166481,
0.011972792446613312,
0.007222854997962713,
0.01554003357887268,
-0.06475669890642166,
-0.001250041532330215,
0.012141820974647999,
0.031444959342479706,
0.027893396094441414,
0.03703634813427925,
-0.05932438373565674,
-0.062308646738529205,
-0.00948324054479599,
-0.010160406120121479,
-0.015478740446269512,
-0.04914231225848198,
0.024338632822036743,
-0.028885368257761,
0.017888152971863747,
-0.022620582953095436,
0.0018496341072022915,
0.027408646419644356,
0.020521238446235657,
0.024210575968027115,
-0.026928948238492012,
0.0025686922017484903,
-0.004257993306964636,
-0.0534924641251564,
0.028798580169677734,
-0.01350468024611473,
-0.0007084992248564959,
0.0428505577147007,
-0.02552410401403904,
-0.05857815966010094,
-0.025019634515047073,
-0.0027219851035624743,
0.036677077412605286,
-0.03129991143941879,
-0.02211228385567665,
0.01356213167309761,
-0.06182119995355606,
0.04668470472097397,
-0.006834357976913452,
0.005900549236685038,
-0.02920481376349926,
-0.071736179292202,
0.01048304233700037,
0.02504102885723114,
-0.04564826935529709,
-0.0024246189277619123,
0.037619251757860184,
0.04564310982823372,
0.019472220912575722,
-0.015410599298775196,
0.03707509860396385,
0.06610650569200516,
-0.04094730317592621,
-0.005496255122125149,
0.02653336338698864,
-0.0062036095187067986,
-0.013912398368120193,
-0.03504416346549988,
-0.0029733090195804834,
-0.042598873376846313,
0.042428676038980484,
0.03165857121348381,
-0.060614243149757385,
0.06952650099992752,
-0.01698124408721924,
-0.012752813287079334,
0.016614161431789398,
-0.07080093771219254,
-0.008994285948574543,
0.05608205869793892,
0.030387094244360924,
-0.010514768771827221,
-0.027085626497864723,
-0.03635730966925621,
0.006725490093231201,
0.008862260729074478,
0.0054153865203261375,
0.012438895180821419,
-0.045241642743349075,
-0.014852010644972324,
-0.012734770774841309,
-0.014570861123502254,
0.04642064869403839,
0.04259203374385834,
0.03171301260590553,
-0.060160014778375626,
0.0489853136241436,
0.047276925295591354,
-0.13181978464126587,
0.07062260806560516,
0.019982248544692993,
0.04955678433179855,
-0.03614028915762901,
0.008078528568148613,
0.04710854962468147,
0.08826018869876862,
-0.02919270284473896,
-0.02758338302373886,
0.004638878628611565,
-0.04834350571036339,
0.023627012968063354,
0.002158683491870761,
-0.04355376586318016,
0.03757969290018082,
-0.017469121143221855,
-0.020996544510126114,
-0.030058320611715317,
0.0354941226541996,
0.05473199859261513,
0.025019817054271698,
0.060699399560689926,
0.016983646899461746,
-0.03610292449593544,
0.024607906118035316,
-0.03702898323535919,
0.00243740133009851,
0.011076044291257858,
0.05903613939881325,
0.0047122822143137455,
0.056046269834041595,
0.004709136672317982,
0.034670379012823105,
0.026094136759638786,
-0.03109257109463215,
0.022250216454267502,
-0.006714623421430588,
0.002496706787496805,
-0.01282034907490015,
0.001956076128408313,
0.008479118347167969,
-0.0007316929986700416,
0.04006614536046982,
-0.04124588891863823,
-0.0944262444972992,
0.05326252803206444,
-0.0348593145608902,
0.006900605745613575,
-0.00852090772241354,
-0.026203501969575882,
0.003737300168722868,
0.024101082235574722,
-0.06409361213445663,
0.0323718823492527,
0.044633977115154266,
-0.0014613582752645016,
0.013470308855175972,
0.0006870604702271521,
-0.00009658392809797078,
-0.019922513514757156,
-0.012224648147821426,
-0.033750008791685104,
0.020481299608945847,
-0.03121909312903881,
-0.034266144037246704,
0.042459432035684586,
-0.08991533517837524,
-0.001644750707782805,
0.007410410791635513,
-0.030928509309887886,
-0.01601221412420273,
0.014853992499411106,
-0.034189291298389435,
-0.03364848345518112,
-0.018878450617194176,
-0.09642913937568665,
-0.044846177101135254,
0.04951733723282814,
-0.040209922939538956,
-0.022250769659876823,
0.013366315513849258,
-0.0039024585857987404,
0.0003662786621134728,
-0.04462617635726929,
-0.01818193309009075,
-0.019075285643339157,
0.023453619331121445,
-0.02664170041680336,
0.03338567540049553,
-0.04051688686013222,
0.04875008761882782,
-0.034096792340278625,
0.03418298810720444,
-0.002380451187491417,
-0.005959521513432264,
-0.014879152178764343,
0.05467769503593445,
-0.03202853724360466,
-0.05947795882821083,
0.009607496671378613,
-0.017989523708820343,
-0.017472779378294945,
-0.04840506613254547,
0.04757418856024742,
-0.025182610377669334,
-0.01024550013244152,
-0.005684273783117533,
0.03211286664009094,
-0.010917670093476772,
-0.053197454661130905,
-0.05089499428868294,
0.028768088668584824,
0.025137534365057945,
-0.07724650949239731,
0.026820454746484756,
-0.035594623535871506,
-0.053944606333971024,
0.0810498520731926,
-0.033412665128707886,
0.011189951561391354,
-0.013309570960700512,
0.002208500634878874,
-0.03478430584073067,
0.030691085383296013,
0.013990619219839573,
-0.032391682267189026,
-0.01391645334661007,
-0.02415197156369686,
-0.007668080274015665,
-0.055437494069337845,
0.016887344419956207,
-0.013071061111986637,
0.0020843183156102896,
-0.0017381981015205383,
-0.01893600821495056,
0.01869954913854599,
0.010275064036250114,
-0.052597030997276306,
0.01698627695441246,
0.019009839743375778,
-0.01886780373752117,
0.016162900254130363,
0.021486002951860428,
0.03558049723505974,
-0.09433932602405548,
0.066807821393013,
0.003913610242307186,
-0.020630860701203346,
-0.029661593958735466,
0.04463113099336624,
-0.01960093155503273,
0.03736845403909683,
-0.019399477168917656,
0.015741819515824318,
-0.08510256558656693,
-0.04751450568437576,
0.04673473536968231,
0.013271930627524853,
0.029472066089510918,
0.03204925358295441,
-0.02210872992873192,
0.006030102726072073,
-0.044025786221027374,
-0.0005966922035440803,
0.021590860560536385,
-0.03852246701717377,
-0.03361237421631813,
-0.003732423298060894,
0.0016642375849187374,
-0.04666220024228096,
-0.017336543649435043,
0.02811393514275551,
-0.0011214077239856124,
-0.02198641374707222,
-0.005512789357453585,
-0.020125163719058037,
-0.010041964240372181,
-0.05476395785808563,
0.022761311382055283,
0.007443652022629976,
-0.015505117364227772,
-0.02324078232049942,
-0.03025929071009159,
0.05556287243962288,
0.01469918992370367,
0.03812981769442558,
-0.05918849632143974,
0.049280282109975815,
-0.038122810423374176,
-0.008291469886898994,
0.0020174828823655844,
0.021763071417808533,
0.0015598126919940114,
-0.0011674001580104232,
-0.0031955649610608816,
-0.010589035227894783,
-0.004837524611502886,
-0.01207951083779335,
0.06336136162281036,
-0.014818168245255947,
-0.0574842169880867,
-0.04898236691951752,
-0.022227101027965546,
-0.002530017402023077,
-0.02436654269695282,
0.023314280435442924,
0.027643317356705666,
-0.00927424244582653,
0.008730566129088402,
0.02576923370361328,
-0.042347218841314316,
0.006030460819602013,
0.04061184450984001,
0.003559309057891369,
0.016128558665513992,
-0.025734180584549904,
0.008027083240449429,
0.016978243365883827,
-0.04796963930130005,
-0.019047383219003677,
0.05930482968688011,
-0.08515119552612305,
0.03726343810558319,
0.060427870601415634,
-0.0009440817520953715,
0.01263611949980259,
0.04852273315191269,
-0.03720907121896744,
0.028613096103072166,
0.01108158752322197,
0.0695328339934349,
-0.05417318269610405,
-0.016321377828717232,
0.017361756414175034,
-0.026086267083883286,
-0.009072895161807537,
0.007776304148137569,
-0.027289554476737976,
0.051647499203681946,
-0.002823407296091318,
-0.0449703112244606,
-0.0308978371322155,
0.07492725551128387,
-0.0267302505671978,
0.0647505596280098,
-0.003879019757732749,
0.01398515049368143,
0.001132040866650641,
-0.00016837919247336686,
-0.034421175718307495,
0.0514582060277462,
0.01648513413965702,
0.05014448240399361,
-0.04015827924013138,
-0.026645278558135033,
-0.0027278116904199123,
0.012176531367003918,
0.023987606167793274,
0.006167732644826174,
0.01836409606039524,
0.03127433732151985,
-0.011861632578074932,
0.0006266412674449384,
0.03563704714179039,
0.05153324455022812,
-0.012505201622843742,
0.039006128907203674,
0.04304036125540733,
0.0741453766822815,
-0.0076262690126895905,
-0.019727950915694237,
0.09048127382993698,
-0.008180724456906319,
-0.013936461880803108,
0.02423476241528988,
0.03483765199780464,
0.03563643991947174,
-0.00032096871291287243,
0.022367047145962715,
-0.008417008444666862,
-0.07151935994625092,
0.04342428222298622,
-0.032021455466747284,
0.027933748438954353,
0.0017259360756725073,
0.07770653069019318,
0.11746972054243088,
-0.04347074031829834,
0.026071488857269287,
0.017021548002958298,
0.02093295007944107,
0.06643607467412949,
0.03295359015464783,
-0.016021663323044777,
-0.036607302725315094,
-0.03914301469922066,
-0.00985573697835207,
-0.01269978005439043,
-0.01728936843574047,
0.035238396376371384,
0.00667820917442441,
-0.040556661784648895,
-0.04403793811798096,
0.039419978857040405,
0.025951359421014786,
0.09544520080089569,
0.006177903618663549,
-0.0048928530886769295,
0.030449409037828445,
0.03441144898533821,
0.023012002930045128,
0.012698777951300144,
-0.04777880385518074,
-0.0038862465880811214,
0.04556870833039284,
-0.026509517803788185,
-0.04048455134034157,
0.03190246596932411,
-0.019742658361792564,
0.05878043174743652,
0.06142008304595947,
-0.01945960335433483,
0.005234739277511835,
-0.06755607575178146,
0.005671750288456678,
-0.0607997328042984,
-0.00643825763836503,
-0.0006877314881421626,
0.03407188504934311,
0.024431809782981873,
-0.0181744284927845,
0.05775154009461403,
-0.0151915168389678,
0.009856953285634518,
-0.027157440781593323,
-0.058828894048929214,
-0.031997859477996826,
-0.02642340026795864,
-0.009823355823755264,
-0.014678660780191422,
-0.0015114981215447187,
-0.01584583893418312,
0.007781091146171093,
0.022701699286699295,
-0.008623345755040646,
-0.0008237334550358355,
-0.0398915633559227,
-0.03650553151965141,
-0.061809998005628586,
-0.0075570326298475266,
0.04531190171837807,
0.02857287973165512,
0.06722714006900787,
-0.01029165368527174,
0.019053563475608826,
-0.03226882964372635,
0.0024499681312590837,
0.005124613642692566,
0.08764693886041641,
0.031934842467308044,
0.01310664601624012,
-0.01077694445848465,
-0.047803230583667755,
-0.05194946005940437,
0.0024596983566880226,
-0.0708288922905922,
-0.0006781163974665105,
-0.04577791690826416,
0.010182845406234264,
0.00983226764947176,
0.05227629095315933,
0.024232735857367516,
-0.03199753910303116,
-0.03748375177383423,
-0.0029393446166068316,
0.02843140810728073,
0.04687971621751785,
-0.06733018904924393,
0.03520256280899048,
0.014345947653055191,
-0.00025327535695396364,
-0.007320745848119259,
0.014195375144481659,
0.03180718421936035,
0.0457429476082325,
0.023122159764170647,
-0.010555904358625412,
-0.00016596920613665134,
-0.014235569164156914,
0.04960799589753151,
0.030519267544150352,
-0.002490246668457985,
-0.017796216532588005,
0.03387107327580452,
-0.015160711482167244,
0.003384989220649004,
-0.009037342853844166,
0.028692549094557762,
-0.0067259822972118855,
-0.026272393763065338,
-0.074957475066185,
0.03439528867602348,
0.0438334196805954,
-0.024755602702498436,
-0.08789877593517303,
-0.03236152231693268,
0.0069809239357709885,
0.00890909880399704,
0.02966056391596794,
0.05262785777449608,
0.055133335292339325,
0.03376695141196251,
0.0023395020980387926,
-0.031123265624046326,
0.04099392890930176,
0.042208001017570496,
0.03882556036114693,
-0.019750049337744713,
0.011226198635995388,
-0.0010008952813223004,
-0.005974522326141596,
-0.015126642771065235,
0.0243222676217556,
-0.0020744148641824722,
-0.031155291944742203,
-0.06076270714402199,
0.03174110874533653,
-0.010165363550186157,
0.017899494618177414,
-0.02600589580833912,
0.007308273576200008,
-0.04164165258407593,
0.006793107371777296,
0.00861189141869545,
0.06197899952530861,
-0.02904394455254078,
-0.028358902782201767,
-0.011939148418605328,
0.06281906366348267,
0.03259586542844772,
-0.05313999205827713,
-0.018094098195433617,
-0.04274383559823036,
-0.012031580321490765,
-0.02374587208032608,
-0.012399238534271717,
0.016647053882479668,
0.029919179156422615,
0.07106558233499527,
0.05810631811618805,
0.03194144740700722,
-0.04575686529278755,
0.00673986179754138,
0.03403063490986824,
0.013178905472159386,
0.01423185970634222,
-0.06101815029978752,
0.009698999114334583,
-0.009921814315021038,
-0.04010285437107086,
-0.001837636111304164,
-0.032552193850278854,
-0.024191023781895638,
0.06158358231186867,
-0.005389017052948475,
0.04820067435503006,
-0.055155038833618164,
-0.026559507474303246,
0.01569017767906189,
-0.06288126856088638,
0.0328131839632988,
0.005175681319087744,
-0.028179418295621872,
0.037889644503593445,
0.05425499007105827,
0.0094844289124012,
-0.023181302472949028,
-0.0030607138760387897,
-0.06965979933738708,
0.03933614119887352,
0.021511834114789963,
0.01222428772598505,
0.02699897438287735,
-0.027702445164322853,
0.01585375890135765,
-0.025450754910707474,
-0.008200719952583313,
-0.014344795607030392,
0.08993645757436752,
0.04412178695201874,
0.0311066135764122,
0.0738421157002449,
0.010397052392363548,
-0.05818505585193634,
-0.012137544341385365,
-0.03945793956518173,
0.0252916868776083,
-0.06698771566152573,
0.024754434823989868,
0.012066671624779701,
-0.05064484477043152,
0.029734550043940544,
-0.0017064554849639535,
-0.03752628341317177,
-0.02816241793334484,
-0.0674048587679863,
0.005918002221733332,
-0.04273409768939018,
0.03767791762948036,
0.061726998537778854,
0.048735618591308594,
-0.017191290855407715,
0.0626731663942337,
-0.08875046670436859,
0.0204949788749218,
0.012761839665472507,
-0.028673700988292694,
-0.007379153277724981,
-0.005846789572387934,
-0.062486108392477036,
-0.050540633499622345,
-0.011817887425422668,
0.0048914323560893536,
-0.02929440140724182,
0.03159140795469284,
-0.0018411519704386592,
-0.013539787381887436,
0.02172981947660446,
0.036204420030117035,
-0.0677461251616478,
-0.048402294516563416,
-0.04605869576334953,
-0.015704941004514694,
0.013148937374353409,
0.017764685675501823,
0.055669814348220825,
0.013187043368816376,
0.04523168504238129,
0.04001162201166153,
0.0023082687985152006,
0.005278716329485178,
-0.013499189168214798,
-0.02743663266301155,
0.011715864762663841,
-0.008498788811266422,
-0.05501395836472511,
-0.010683240368962288,
0.005148258991539478,
-0.03252341225743294,
-0.0603935681283474,
0.025929013267159462,
0.03975994139909744,
0.0023772483691573143,
-0.015635274350643158,
-0.07693756371736526,
-0.03327637538313866,
0.04928265139460564,
-0.023408837616443634,
-0.00002285110895172693,
-0.026322821155190468,
-0.0029669313225895166,
0.005822338163852692,
-0.032667163759469986,
0.0027786733116954565,
-0.01429507415741682,
0.052467476576566696,
0.003132011741399765,
-0.044798143208026886,
0.030108101665973663,
-0.017838774248957634,
0.057593196630477905,
0.0013882833300158381,
0.027941731736063957,
-0.004180891904979944,
0.034003838896751404,
-0.03855649009346962,
-0.06378879398107529,
0.032909609377384186,
-0.005541855935007334,
-0.014932836405932903,
-0.010150764137506485,
-0.001447172719053924,
0.010820847935974598,
-0.05683884024620056,
-0.022167392075061798,
0.031984515488147736,
-0.06517581641674042,
-0.03560721129179001,
0.021842511370778084,
-0.021025266498327255,
0.018790001049637794,
-0.031242413446307182,
-0.013254528865218163,
0.024841906502842903,
0.07491523027420044,
-0.007262337952852249,
0.053335219621658325,
-0.0378098264336586,
0.018312230706214905,
0.0608912892639637,
0.0566737987101078,
0.0030542355962097645,
-0.013832063414156437,
0.027767524123191833,
0.017341794446110725,
0.0038734832778573036,
-0.01575908251106739,
0.016523027792572975,
-0.036319565027952194,
-0.007998118177056313,
0.017592696473002434,
-0.01714138686656952,
-0.012790117412805557,
0.016473395749926567
] |
<p>For my bachelor's thesis, I am investigating <a href="http://en.wikipedia.org/wiki/Divergent_series" rel="nofollow">Divergent Series</a>. Apart from the mathematical theory behind them (which I find fascinating), I am also interested in their applications in physics. </p>
<p>Currently, I am studying the divergent series that arise when considering the Riemann zeta function at negative arguments. The Riemann zeta function can be analytically continued. By doing this, finite constants can be assigned to the divergent series. For $n \geq 1$, we have the formula: </p>
<p>$$ \zeta(-n) = - \frac{B_{n+1}}{n+1} . $$</p>
<p>This formula can be used to find: </p>
<ul>
<li>$\zeta(-1) = \sum_{n=1}^{\infty} n = - \frac{1}{12} . $ This formula is used in Bosonic String Theory to find the so-called "critical dimension" $d = 26$. For more info, one can consult the relevant wikipedia <a href="http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%C2%B7_%C2%B7_%C2%B7" rel="nofollow">page</a>. </li>
<li>$\zeta(-3) = \sum_{n=1}^{\infty} n^3 = - \frac{1}{120} $ . This identity is used in the calculation of the energy per area between metallic plates that arises in the <a href="http://en.wikipedia.org/wiki/Casimir_effect" rel="nofollow">Casimir Effect</a>. </li>
</ul>
<p>My <strong>first question</strong> is: do more of these values of the Riemann zeta function at negative arguments arise in physics? If so: which ones, and in what context? </p>
<p>Furthermore, I consider summing powers of the Riemann zeta function at negative arguments. I try to do this by means of
<a href="http://mathworld.wolfram.com/FaulhabersFormula.html" rel="nofollow">Faulhaber's formula</a>. Let's say, for example, we want to compute the sum of $$p = \Big( \sum_{k=1}^{\infty} k \Big)^3 . $$
If we set $a = 1 + 2 + 3 + \dots + n = \frac{n(n+1)}{2} $, then from Faulhaber's formula we find that $$\frac{4a^3 - a^2}{3} = 1^5 + 2^5 + 3^5 + \dots + n^5 , $$ from which we can deduce that $$ p = a^3 = \frac{ 3 \cdot \sum_{k=1}^{\infty} k^5 + a^2 }{4} .$$
Since we can also sum the divergent series arising from the Riemann zeta function at negative arguments by means of <a href="http://en.wikipedia.org/wiki/Ramanujan_summation" rel="nofollow">Ramanujan Summation</a> (which produces that same results as analytic continuation) and the Ramanujan Summation method is linear, we find that the Ramanujan ($R$) or regularised sum of $p$ amounts to $$R(p) = R(a^3) = \frac{3}{4} R\Big(\sum_{k=1}^{\infty} k^5\Big) + \frac{1}{4} R(a^2) . $$
Again, we know from Faulhaber's Formula that $a^2 = \sum_{k=1}^{\infty} k^3 $ , so $R(a^2) = R(\zeta(-3)) = - \frac{1}{120} $, so $$R(p) = \frac{3}{4} \Big(- \frac{1}{252} \Big) + \frac{ ( \frac{1}{120} )} {4} = - \frac{1}{1120} . $$</p>
<p>My <strong>second</strong> (bunch of) <strong>question(s)</strong> is: Do powers of these zeta values at negative arguments arise in physics? If so, how? Are they summed in a manner similar to process I just described, or in a different manner? Of the latter is the case, which other summation method is used? Do powers of divergent series arise in physics in general? If so: which ones, and in what context?</p>
<p>My <strong>third and last</strong> (bunch of) <strong>question(s)</strong> is: which other divergent series arise in physics (not just considering (powers of) the Riemann zeta function at negative arguments) ?
I know there are whole books on renormalisation and/or regularisation in physics. However, for the sake of my bachelor's thesis I would like to know some concrete examples of divergent series that arise in physics which I can study. It would also be nice if you could mention some divergent series which have defied summation by any summation method that physicists (or mathematicians) currently employ. Please also indicate as to how these divergent series arise in physics. </p>
<p>I also posted a somewhat more general and improved version of this question on <a href="http://mathoverflow.net/questions/161872/what-are-some-geometric-physical-probabilistic-interpretations-of-the-rieman">MO</a>.</p> | g1258 | [
0.048128388822078705,
0.03860281780362129,
0.022160649299621582,
-0.04141969233751297,
0.03919350728392601,
-0.005708255805075169,
0.0317779965698719,
-0.018285250291228294,
-0.04027546942234039,
0.022596295922994614,
-0.07355160266160965,
0.012402945198118687,
-0.0021711664739996195,
0.03478003665804863,
0.036904048174619675,
-0.08863629400730133,
0.002313579898327589,
0.01111982949078083,
-0.055156491696834564,
0.01657775789499283,
-0.04301382973790169,
-0.005844959989190102,
0.01836235634982586,
-0.006470492109656334,
-0.0055337282828986645,
-0.032269641757011414,
0.04824351519346237,
0.0004060095234308392,
0.016116200014948845,
-0.03850213810801506,
0.026264069601893425,
-0.005023665726184845,
0.027817895635962486,
-0.03367649018764496,
0.03481622785329819,
0.015923038125038147,
0.04880378767848015,
-0.024314336478710175,
0.025680355727672577,
0.025993166491389275,
-0.037740226835012436,
-0.034716591238975525,
0.038343481719493866,
0.011356827802956104,
0.006501412950456142,
-0.012959472835063934,
-0.04932624101638794,
0.02078731171786785,
0.004769418388605118,
0.028481734916567802,
0.008136853575706482,
0.050582922995090485,
0.045709047466516495,
0.0024713885504752398,
0.013075296767055988,
0.012447495944797993,
-0.00338506861589849,
-0.014751937240362167,
0.07356327027082443,
0.049756985157728195,
0.01073220744729042,
0.044189319014549255,
0.003735438222065568,
-0.021191570907831192,
0.07185756415128708,
-0.05135565623641014,
-0.07377388328313828,
-0.03503316268324852,
0.036392875015735626,
0.0016441799234598875,
0.054320190101861954,
-0.036104511469602585,
-0.01282560732215643,
-0.04623383656144142,
-0.03377140313386917,
0.0003921035386156291,
0.0479993000626564,
-0.007983311079442501,
-0.025721020996570587,
0.00906412210315466,
-0.025784475728869438,
-0.05506793409585953,
-0.010885459370911121,
-0.040620941668748856,
0.08575350046157837,
-0.07501798868179321,
0.000723980600014329,
0.027891412377357483,
-0.0566200390458107,
-0.000679540797136724,
0.03912898898124695,
0.11081685870885849,
0.000022526226530317217,
-0.031008848920464516,
0.014156785793602467,
0.00738412095233798,
0.009521275758743286,
0.03785819560289383,
-0.03705061227083206,
0.006026138551533222,
0.05725087597966194,
0.053332481533288956,
0.03910334035754204,
0.01778678223490715,
-0.0034555760212242603,
-0.03432662412524223,
0.029400749132037163,
-0.010799674317240715,
0.014635603874921799,
-0.014661804772913456,
-0.0788082703948021,
0.0020324336364865303,
0.00330262235365808,
-0.031623151153326035,
-0.0270434208214283,
0.027874818071722984,
0.003847339656203985,
-0.0024402053095400333,
-0.04018773138523102,
0.05469764024019241,
0.01553386077284813,
0.0027299297507852316,
0.013269656337797642,
-0.05334736406803131,
-0.04230461269617081,
-0.033589087426662445,
0.03207824379205704,
-0.030077997595071793,
0.03306291997432709,
-0.049600835889577866,
0.06286507099866867,
-0.005852967035025358,
0.008459582924842834,
-0.011653861962258816,
-0.015298423357307911,
0.06390585750341415,
0.010855800472199917,
0.01807490363717079,
0.03864927217364311,
0.05370950326323509,
0.03889020159840584,
-0.040791429579257965,
-0.013030867092311382,
-0.026315471157431602,
0.010299471206963062,
0.004844955168664455,
-0.020922252908349037,
-0.021733218804001808,
-0.0018464605091139674,
-0.014159653335809708,
0.01964186690747738,
0.033968158066272736,
0.03629113361239433,
-0.026481863111257553,
0.011255545541644096,
0.05360633507370949,
0.02306361123919487,
-0.01723572611808777,
-0.0031375496182590723,
0.02116519957780838,
-0.020306698977947235,
-0.07607138156890869,
0.01842634566128254,
0.08730857074260712,
-0.03509262576699257,
0.010508241131901741,
-0.007528859656304121,
-0.0847836509346962,
0.012982315383851528,
-0.017978716641664505,
-0.09210658818483353,
0.017812855541706085,
-0.016478445380926132,
-0.04284760355949402,
0.05838941037654877,
0.01625683903694153,
-0.030198639258742332,
-0.060636140406131744,
-0.011483426205813885,
-0.005047440063208342,
-0.017208663746714592,
-0.06802503764629364,
0.003576755989342928,
-0.0012803379213437438,
0.010722864419221878,
-0.0025382384192198515,
-0.003686811774969101,
-0.02634839341044426,
-0.018959902226924896,
0.025639532133936882,
-0.05294203758239746,
-0.003569485154002905,
-0.01799781061708927,
-0.008462638594210148,
-0.023402318358421326,
0.005888217594474554,
0.04952210560441017,
0.0000460991905129049,
0.03919143229722977,
0.04115063324570656,
0.0029118461534380913,
0.05798151344060898,
0.026215728372335434,
0.002129939151927829,
0.05546633526682854,
-0.01254208479076624,
-0.03982978314161301,
-0.03984411060810089,
-0.01909189671278,
-0.017534473910927773,
0.024928439408540726,
-0.008306339383125305,
0.011533347889780998,
-0.02096095122396946,
-0.004593472462147474,
-0.053962599486112595,
-0.004757865332067013,
-0.027253229171037674,
0.019578909501433372,
0.08033665269613266,
0.006877595093101263,
-0.0044839102774858475,
0.014839009381830692,
0.04477706924080849,
-0.0706639438867569,
0.02906886115670204,
-0.02812839485704899,
-0.09160859882831573,
0.005915612448006868,
-0.051430366933345795,
-0.11606462299823761,
-0.04519116133451462,
0.08608424663543701,
-0.031037602573633194,
0.027835506945848465,
-0.005707200150936842,
0.0016132729360833764,
-0.010780083015561104,
0.05841049551963806,
-0.008010951802134514,
-0.038134973496198654,
-0.04498831182718277,
-0.022480711340904236,
0.019309714436531067,
-0.013989190571010113,
-0.024435505270957947,
-0.049249619245529175,
-0.030739905312657356,
0.008009870536625385,
-0.06258611381053925,
0.06874199956655502,
0.014301111921668053,
-0.023107066750526428,
0.08839006721973419,
-0.034574057906866074,
-0.0039221192710101604,
-0.011681590229272842,
0.06361488997936249,
0.049948595464229584,
-0.057863667607307434,
0.0063927979208528996,
0.01548095140606165,
0.05622701719403267,
0.005884816404432058,
-0.011569284833967686,
0.041482146829366684,
-0.011116484180092812,
-0.003789573209360242,
0.031741734594106674,
0.011725303716957569,
0.004472867585718632,
0.017556974664330482,
0.021060364320874214,
-0.009112567640841007,
-0.00784549955278635,
0.007007530890405178,
0.032920192927122116,
0.026247374713420868,
0.042764853686094284,
0.002372990595176816,
-0.06263638287782669,
0.074948750436306,
-0.011506162583827972,
0.05534009635448456,
-0.007293968927115202,
0.007243658881634474,
0.013374751433730125,
0.0035714053083211184,
-0.04789239168167114,
0.012741168029606342,
0.04116147384047508,
0.0022471328265964985,
0.024174682796001434,
-0.029625752940773964,
-0.027038615196943283,
0.036588989198207855,
-0.018556946888566017,
-0.09008119255304337,
-0.017340006306767464,
-0.014440599828958511,
0.05184606462717056,
-0.04523571953177452,
0.017504971474409103,
0.046123865991830826,
-0.01419973373413086,
0.03608831390738487,
-0.06808662414550781,
-0.020437100902199745,
0.02176501229405403,
-0.01741979829967022,
-0.08637271821498871,
0.01945137232542038,
0.11116629838943481,
0.07617080211639404,
-0.021239640191197395,
0.02202323079109192,
0.013419503346085548,
0.0073870886117219925,
0.0019859822932630777,
-0.022582415491342545,
-0.06456831097602844,
-0.0284334197640419,
0.010984302498400211,
-0.017561057582497597,
0.03876207023859024,
0.04770226031541824,
0.0007155589992180467,
-0.02309435047209263,
-0.013682594522833824,
0.022292442619800568,
-0.027718689292669296,
-0.01785835064947605,
-0.018730878829956055,
-0.010717065073549747,
-0.06890244781970978,
-0.04832056164741516,
-0.06998983025550842,
0.0005807599518448114,
0.0791090801358223,
0.020247137174010277,
-0.02811504155397415,
-0.018157392740249634,
0.05975305661559105,
-0.0048300898633897305,
-0.03258694335818291,
0.04683615639805794,
0.039999961853027344,
0.009443961083889008,
0.06356959044933319,
-0.014314998872578144,
0.01867240108549595,
0.00784600991755724,
0.07740431278944016,
0.02142002061009407,
0.009540935046970844,
-0.007000264246016741,
0.01359532680362463,
-0.022521808743476868,
-0.00436024833470583,
-0.012958639301359653,
-0.039587799459695816,
0.01602538488805294,
-0.020606063306331635,
-0.02549433708190918,
-0.012749064713716507,
-0.0214698426425457,
0.015939392149448395,
0.021507827565073967,
-0.01875441148877144,
-0.07601594179868698,
0.052981846034526825,
0.01795242540538311,
-0.03735457360744476,
-0.018062196671962738,
-0.005968085955828428,
-0.030585022643208504,
-0.03013351373374462,
0.07305866479873657,
-0.06552335619926453,
-0.035811424255371094,
0.03245783597230911,
0.02544279582798481,
0.012668249197304249,
0.057911138981580734,
-0.03455805778503418,
0.003626591293141246,
-0.01949586533010006,
-0.015583328902721405,
0.007665487937629223,
-0.024444714188575745,
0.00622666347771883,
0.02995086833834648,
-0.028714308515191078,
-0.04136432707309723,
-0.01170350331813097,
-0.05595925822854042,
-0.003750908188521862,
0.00984929222613573,
-0.0008823362295515835,
0.03471052646636963,
-0.018808040767908096,
-0.03493936359882355,
0.009702916257083416,
0.03556017950177193,
-0.03031272441148758,
-0.013640321791172028,
0.06965968757867813,
0.001259519369341433,
0.034199539572000504,
-0.02301078662276268,
0.022532695904374123,
-0.01053648255765438,
-0.032621853053569794,
-0.08852489292621613,
0.023944128304719925,
-0.025952331721782684,
0.0028095506131649017,
-0.0638849139213562,
0.027070285752415657,
0.0024436216335743666,
0.03075750730931759,
-0.005178187042474747,
-0.014749174937605858,
-0.003529563080519438,
-0.007302113343030214,
-0.02516109310090542,
0.009049057960510254,
0.032839249819517136,
-0.041325706988573074,
0.03155423328280449,
0.01501989271491766,
-0.008426113985478878,
0.046621084213256836,
0.017710775136947632,
-0.022943461313843727,
0.018896928057074547,
0.024760955944657326,
-0.03360757231712341,
0.02562800422310829,
0.07723163068294525,
0.026753822341561317,
-0.04137812554836273,
0.005501897539943457,
-0.007732529658824205,
0.014328316785395145,
0.01642615534365177,
-0.04191607981920242,
-0.01951288804411888,
0.01835509203374386,
0.024824539199471474,
-0.032524224370718,
0.053363826125860214,
0.0022383674513548613,
-0.00269491714425385,
-0.031148096546530724,
0.008846401236951351,
-0.03946420177817345,
-0.027422703802585602,
0.009825330227613449,
-0.06199627369642258,
-0.040894247591495514,
-0.003941824659705162,
-0.059008244425058365,
-0.041931699961423874,
0.023784132674336433,
0.0052752308547496796,
-0.03557666763663292,
0.02169816382229328,
0.006422675680369139,
0.02192400023341179,
-0.036131925880908966,
0.04505050182342529,
0.03743790090084076,
-0.00798360351473093,
-0.0560612827539444,
-0.045171115547418594,
0.03843566030263901,
0.0022524965461343527,
-0.05870458856225014,
0.028144435957074165,
0.013627409934997559,
-0.023051828145980835,
-0.016651984304189682,
0.024568207561969757,
-0.050234075635671616,
0.002070901682600379,
-0.0032073999755084515,
-0.010802743956446648,
-0.025513309985399246,
0.014025633223354816,
0.000305850466247648,
-0.04248425364494324,
0.0752079039812088,
-0.018800808116793633,
-0.05117487162351608,
0.004189466591924429,
-0.014268279075622559,
-0.04207880422472954,
-0.04083486646413803,
-0.006918010767549276,
-0.05775522440671921,
0.007595546077936888,
-0.03506217524409294,
-0.04231835901737213,
0.0005117792170494795,
0.018249783664941788,
0.07158524543046951,
-0.037377748638391495,
0.07847815006971359,
-0.0165435578674078,
0.02954360842704773,
0.049940187484025955,
0.033205363899469376,
-0.053173039108514786,
0.0020915709901601076,
0.022020097821950912,
-0.05351577699184418,
0.008336860686540604,
-0.017563417553901672,
-0.0562322661280632,
-0.01064298301935196,
0.028355253860354424,
0.0619894377887249,
0.022290993481874466,
0.05130458250641823,
0.02502373233437538,
-0.022426288574934006,
-0.008689368143677711,
-0.049759555608034134,
0.02282211370766163,
-0.016665715724229813,
0.0290067121386528,
-0.003208312438800931,
0.015170919708907604,
0.001984787406399846,
0.039041176438331604,
-0.07404972612857819,
0.05339133366942406,
-0.019391529262065887,
0.03991512209177017,
0.01952732913196087,
0.009852704592049122,
0.07971780747175217,
0.009213539771735668,
-0.03569100797176361,
0.012959606014192104,
0.027681397274136543,
0.020288165658712387,
0.0384054034948349,
-0.055381420999765396,
0.005041795317083597,
0.024272317066788673,
-0.06262210011482239,
-0.0665368065237999,
-0.03223958984017372,
0.011717477813363075,
-0.0007711502257734537,
-0.025866873562335968,
-0.02529323846101761,
-0.02197117917239666,
-0.039924588054418564,
-0.03475915268063545,
-0.009469416923820972,
0.0040939548052847385,
-0.047434985637664795,
-0.04347141459584236,
0.009981656447052956,
-0.0690137967467308,
0.03148968145251274,
0.03657662495970726,
0.025331342592835426,
0.01999899558722973,
-0.0010826915968209505,
0.01763303391635418,
0.046603407710790634,
-0.004492497071623802,
-0.03427429124712944,
-0.06640306115150452,
-0.015760084614157677,
-0.04408145323395729,
-0.02556905336678028,
0.03175943344831467,
0.03629651293158531,
-0.01142300758510828,
-0.03437676280736923,
0.044730473309755325,
0.013956503011286259,
-0.029124608263373375,
-0.07096348702907562,
-0.0077044544741511345,
-0.009708666242659092,
-0.017203575000166893,
0.012442214414477348,
-0.04282071813941002,
-0.0052551026456058025,
-0.0955912321805954,
0.05339249223470688,
0.00994108896702528,
-0.023977486416697502,
-0.029409321025013924,
0.006067276932299137,
0.013216676190495491,
0.0209439005702734,
-0.054267894476652145,
-0.04318254068493843,
-0.04484007880091667,
-0.00700253015384078,
-0.00627153692767024,
-0.004070283845067024,
-0.018514009192585945,
0.04024745151400566,
0.05173139274120331,
0.01135321706533432,
0.029083289206027985,
-0.028136739507317543,
0.040843665599823,
0.06802297383546829,
0.002133621834218502,
0.006002611946314573,
-0.0003517368750181049,
0.05281892418861389,
-0.002733142813667655,
0.055794622749090195,
-0.03657617047429085,
0.03246226906776428,
-0.0027527273632586002,
-0.0565938837826252,
0.07435539364814758,
-0.000947467633523047,
0.0390319749712944,
0.032447926700115204,
0.02910616807639599,
0.05255168303847313,
0.08592270314693451,
-0.004941040184348822,
0.06239072233438492,
-0.010584184899926186,
-0.004827446304261684,
0.008991842158138752,
0.005072368308901787,
-0.07818064093589783,
-0.007381626404821873,
0.03256051242351532,
-0.007033789996057749,
-0.03591366112232208,
0.04352215677499771,
-0.0028363196179270744,
-0.007990453392267227,
-0.0995960384607315,
0.03398868441581726,
0.05763537809252739,
-0.014116130769252777,
-0.03388546407222748,
0.01206242386251688,
-0.01855865865945816,
-0.00217604567296803,
-0.021848442032933235,
0.010980512946844101,
0.03230923041701317,
-0.02127377688884735,
-0.014877638779580593,
0.041928693652153015,
0.04732723906636238,
-0.0012336610816419125,
-0.014647182077169418,
0.09747219830751419,
0.04374832287430763,
-0.0104537233710289,
0.025538252666592598,
0.006141353864222765,
0.0579528734087944,
0.00838793721050024,
-0.03061741217970848,
0.03719983622431755,
-0.0002871854230761528,
-0.03605585917830467,
-0.0349404402077198,
0.03514803946018219,
-0.023135632276535034,
0.029300369322299957,
0.0020833464805036783,
-0.014563383534550667,
-0.029051220044493675,
-0.08189818263053894,
0.00823071226477623,
0.04571697860956192,
0.0057375202886760235,
-0.005929137114435434,
0.03727199509739876,
-0.01498663704842329,
-0.003464166074991226,
-0.02467583492398262,
0.02047816850244999,
-0.015893107280135155,
0.05039151385426521,
0.004649554379284382,
0.06629659235477448,
0.03582613542675972,
-0.0015162057243287563,
0.008913042955100536,
0.0342119075357914,
-0.02440176159143448,
-0.025202704593539238,
-0.010379895567893982,
-0.0166543647646904,
0.02269246056675911,
-0.009785080328583717,
-0.04665151983499527,
-0.01654415763914585,
0.019688084721565247,
0.007932106964290142,
-0.0006044122856110334,
-0.026753973215818405,
-0.04271716997027397,
0.0451691597700119,
-0.010745013132691383,
0.042966973036527634,
-0.047268737107515335,
-0.018935777246952057,
-0.008856644853949547,
-0.02043510042130947,
-0.005349061451852322,
-0.005332266911864281,
-0.004008490592241287,
-0.03424597904086113,
0.0028995154425501823,
-0.042009398341178894,
0.0008087294409051538,
-0.03470710292458534,
0.06458982825279236,
-0.033780910074710846,
0.04056628793478012,
0.01310146413743496,
0.018975386396050453,
-0.07386372983455658,
-0.003598054638132453,
0.04077932983636856,
0.01365768164396286,
0.052031010389328,
0.02578212507069111,
-0.03524326533079147,
-0.024335172027349472,
0.02866053394973278,
-0.04679419472813606,
-0.0250537246465683,
-0.013250731863081455,
-0.025234436616301537,
0.07639921456575394,
0.07283017039299011,
-0.003127902979031205,
-0.056101154536008835,
0.0410335473716259,
0.04855889081954956,
0.06915999948978424,
0.019601626321673393,
0.034650981426239014,
0.023993385955691338,
0.013456352055072784,
0.047804951667785645,
0.006410669069737196,
-0.020691489800810814,
-0.0026222921442240477,
-0.046488549560308456,
0.004345702938735485,
-0.01478106714785099,
-0.006707323249429464,
-0.037216443568468094,
-0.0030112997628748417
] |
<p>Let's say I am flowing a fluid through a pipe that has a constant surface temperature. Is it possible to determine the heat flux on the inner surface without knowing the pipe's length when the only two temperatures I know are the pipe surface temperature and the inlet flow temperature?</p>
<p>I am able to assume the flow is thermally and hydrodynamically developed. A fully developed pipe with constant surface temperature has a Nusselt number of 3.6568 which allows me to then determine the convection coefficient. I was going to calculate the heat flux using $$q''=\bar h\Delta T_{lm}$$</p>
<p>The log mean temperature difference would need to use the outlet temperature found by $$\frac{T_{s}-T(L)}{T_{s}-T_{in}}=exp(\frac{-\pi DL}{\dot m c_{p}}\bar h)$$</p>
<p>The problem lies in that I don't have the pipe's length so I can't calculate the outlet temperature or the LMTD. The only other method I could think of is using $$q''=h(T_{s}-T_{in})$$ but that will greatly underestimate the actual heat flux. </p> | g1259 | [
0.042661573737859726,
-0.037573471665382385,
0.008719652891159058,
-0.05460527911782265,
-0.031806476414203644,
-0.03208097070455551,
0.060641560703516006,
0.023373087868094444,
-0.09832577407360077,
-0.04381052777171135,
-0.09547073394060135,
0.0559508390724659,
0.041565053164958954,
-0.018763992935419083,
0.007541346363723278,
-0.002020006300881505,
0.043964046984910965,
-0.005768661852926016,
0.02766628935933113,
0.023792671039700508,
-0.04459762200713158,
0.007973401807248592,
0.07052060961723328,
0.00848771259188652,
-0.005091492086648941,
-0.08343158662319183,
-0.05312513932585716,
0.042863041162490845,
-0.013715841807425022,
-0.024660715833306313,
-0.025389134883880615,
0.023356657475233078,
0.04729952663183212,
-0.007940118201076984,
0.002436191076412797,
0.016316669061779976,
0.011631171219050884,
0.008463543839752674,
-0.0027634890284389257,
-0.054857637733221054,
0.01169513538479805,
0.0033890404738485813,
0.045186202973127365,
0.05877874046564102,
-0.002810023259371519,
0.005507501307874918,
-0.010233133099973202,
0.030164310708642006,
-0.01051931083202362,
-0.0036223186179995537,
0.04872865974903107,
0.023686787113547325,
0.002537883585318923,
-0.03482763096690178,
-0.061405956745147705,
-0.009124908596277237,
-0.004052366595715284,
-0.040942076593637466,
0.006512225139886141,
0.045246172696352005,
0.06283167004585266,
0.050414685159921646,
-0.04496520385146141,
-0.03267887607216835,
-0.03366782143712044,
0.04243225231766701,
-0.014341450296342373,
-0.049756791442632675,
-0.07080402970314026,
0.07825114578008652,
-0.029996875673532486,
-0.02290978841483593,
0.05327662453055382,
-0.0217902772128582,
-0.07280581444501877,
0.052910394966602325,
-0.0007911150460131466,
-0.03766646608710289,
-0.0064186337403953075,
0.023303290829062462,
0.02217533066868782,
-0.012638963758945465,
0.025071008130908012,
0.02544298581779003,
0.028569409623742104,
0.058071814477443695,
-0.022271765395998955,
0.011678273789584637,
0.023611582815647125,
0.024691514670848846,
-0.07742305099964142,
0.030966997146606445,
0.058228749781847,
0.03739175200462341,
0.06668645143508911,
-0.03570057079195976,
0.0068367961794137955,
0.02308797836303711,
-0.013740827329456806,
0.03389539197087288,
0.030128460377454758,
0.02815055102109909,
-0.01720527745783329,
0.036083098500967026,
0.020658761262893677,
-0.023366708308458328,
0.025811100378632545,
0.016795547679066658,
-0.026849322021007538,
-0.006503654178231955,
0.008878206834197044,
0.023162255063652992,
-0.06135851889848709,
-0.006015381310135126,
0.029379962012171745,
0.0018501668237149715,
0.01616610959172249,
0.022531041875481606,
-0.012952440418303013,
0.04920404776930809,
0.01101496908813715,
0.005164508242160082,
0.03657552972435951,
0.03102881833910942,
0.0563749223947525,
0.03613419085741043,
-0.020284825935959816,
0.012713484466075897,
0.02769842930138111,
0.022432366386055946,
-0.009653368964791298,
-0.001317345886491239,
0.006248230580240488,
0.06252533197402954,
0.015420136041939259,
0.011078760027885437,
-0.02736242115497589,
0.0508023202419281,
-0.02921181172132492,
0.06269978731870651,
0.01522869523614645,
-0.01901792176067829,
-0.019607745110988617,
-0.0548170730471611,
-0.008602133020758629,
0.10160467773675919,
-0.06316446512937546,
-0.030393820255994797,
0.030196398496627808,
-0.011368530802428722,
-0.012536422349512577,
0.06094645708799362,
0.03265627846121788,
0.019055474549531937,
-0.011310592293739319,
-0.0023942789994180202,
-0.019512522965669632,
-0.042565926909446716,
0.007518027909100056,
-0.03610944747924805,
-0.04404742270708084,
-0.021582147106528282,
0.0838766023516655,
-0.04257291927933693,
-0.021717408671975136,
0.005143760237842798,
-0.07090417295694351,
-0.019818754866719246,
-0.033699434250593185,
-0.0516321025788784,
-0.055252108722925186,
0.016068706288933754,
0.027222173288464546,
-0.04348841309547424,
0.0026977499946951866,
0.0036896653473377228,
0.015465211123228073,
0.04297361150383949,
-0.005037336610257626,
0.004901910666376352,
0.011152617633342743,
0.05102573707699776,
0.031564079225063324,
-0.038919415324926376,
-0.04157866910099983,
0.008965992368757725,
0.03198738023638725,
-0.02184494026005268,
0.013120951130986214,
-0.04842318966984749,
-0.07278037816286087,
0.01639890857040882,
0.004891377408057451,
0.024433698505163193,
-0.011574843898415565,
-0.008955844677984715,
0.0030435598455369473,
-0.07999788224697113,
-0.09448181092739105,
-0.03125934675335884,
-0.04117004573345184,
0.014422533102333546,
0.039258021861314774,
-0.03616180270910263,
0.0016578321810811758,
-0.015050975605845451,
-0.037533100694417953,
-0.01226489432156086,
0.005845095030963421,
-0.06951060891151428,
0.021013986319303513,
-0.01854296587407589,
-0.02395031414926052,
-0.004549254197627306,
0.02205059304833412,
-0.002120125573128462,
0.0267269816249609,
0.003194413147866726,
-0.007957498542964458,
-0.028073156252503395,
0.03345097228884697,
0.06390683352947235,
0.01670520007610321,
-0.004266876727342606,
-0.09886634349822998,
0.04885342717170715,
-0.025461820885539055,
0.017307084053754807,
-0.06511624902486801,
0.01619628630578518,
-0.020977716892957687,
-0.009080054238438606,
0.03890730440616608,
-0.011751532554626465,
0.02298184670507908,
-0.033175453543663025,
-0.012256010435521603,
-0.033011097460985184,
0.039120689034461975,
0.07097188383340836,
0.025600088760256767,
-0.038708776235580444,
-0.06361646950244904,
0.07231401652097702,
0.021390492096543312,
-0.015377156436443329,
-0.02297525480389595,
0.011985686607658863,
-0.028363436460494995,
0.007688785903155804,
-0.02046138234436512,
0.04984508827328682,
0.03942545875906944,
0.017281075939536095,
-0.025520386174321175,
-0.03273933753371239,
-0.022650204598903656,
-0.001548369531519711,
-0.04415782913565636,
-0.0400441475212574,
-0.028105176985263824,
-0.024348491802811623,
0.07566817849874496,
0.06330730020999908,
-0.0045134536921978,
-0.009267699904739857,
-0.040590550750494,
0.03825761750340462,
0.02268025279045105,
0.0050069293938577175,
0.000005615717327600578,
-0.029455531388521194,
0.0023942452389746904,
0.012940386310219765,
0.030076395720243454,
0.05807657912373543,
-0.038866154849529266,
0.012654734775424004,
0.034345146268606186,
-0.014670925214886665,
0.04353507235646248,
-0.048969972878694534,
-0.06364438682794571,
0.07695949822664261,
0.05430687963962555,
-0.09594281762838364,
0.0220219474285841,
0.04782987758517265,
0.011863209307193756,
-0.0019835953135043383,
0.05574632063508034,
0.00036425699363462627,
-0.05782797187566757,
-0.011456916108727455,
0.01721961237490177,
-0.0206870399415493,
0.025378214195370674,
-0.03332386165857315,
0.016770899295806885,
-0.05081102252006531,
-0.01385150570422411,
-0.024201886728405952,
-0.042313896119594574,
-0.0358634889125824,
-0.0395757220685482,
-0.011818569153547287,
-0.06298568099737167,
-0.06654015928506851,
0.08310138434171677,
-0.043779343366622925,
0.04235197976231575,
-0.019951993599534035,
0.02961774729192257,
0.015624740161001682,
0.033039774745702744,
0.0017397182527929544,
-0.03841844201087952,
0.019741445779800415,
0.05317326635122299,
0.06319893151521683,
-0.04274776950478554,
-0.05124177411198616,
0.010814351961016655,
0.0067812069319188595,
-0.01098124124109745,
-0.023941271007061005,
0.026959331706166267,
-0.058771006762981415,
-0.08289355039596558,
0.00741553632542491,
-0.006136834155768156,
0.04606877639889717,
-0.015261422842741013,
-0.027884289622306824,
0.04495406895875931,
0.0007372609688900411,
0.018559178337454796,
0.008086925372481346,
0.0476880744099617,
0.02670038305222988,
-0.021081749349832535,
-0.053497038781642914,
-0.0795804113149643,
-0.011917229741811752,
0.025637978687882423,
-0.03206843510270119,
-0.038962528109550476,
0.03790319710969925,
0.02318888157606125,
0.023315876722335815,
0.07118958234786987,
-0.03560931980609894,
0.012283487245440483,
0.011596768163144588,
0.0026930193416774273,
-0.0025676421355456114,
0.027462434023618698,
0.05236127972602844,
0.023505546152591705,
0.03149101883172989,
-0.005450854543596506,
-0.060504328459501266,
-0.0001630761835258454,
0.0223529115319252,
0.016594121232628822,
-0.01746303029358387,
0.05739462003111839,
-0.005230116657912731,
0.010851443745195866,
-0.04016021266579628,
-0.013984102755784988,
0.02765127830207348,
-0.022382788360118866,
-0.013277608901262283,
-0.01538611575961113,
-0.046885062009096146,
0.026784462854266167,
-0.0020258838776499033,
-0.028209714218974113,
0.05031459033489227,
-0.02911677211523056,
0.056917235255241394,
-0.04313227906823158,
0.0018167196540161967,
0.016061801463365555,
-0.03292518109083176,
-0.02252645045518875,
0.03199365362524986,
0.029091591015458107,
-0.02213072031736374,
0.0003041083400603384,
-0.01618262566626072,
0.013527806848287582,
-0.01113152876496315,
-0.009875747375190258,
-0.01335397083312273,
0.06018994748592377,
-0.013593216426670551,
-0.023838961496949196,
-0.0604938268661499,
-0.01778784766793251,
-0.015166583471000195,
0.05279233306646347,
-0.0020732495468109846,
-0.04287276417016983,
0.015190820209681988,
0.07602765411138535,
-0.010700929909944534,
-0.0013506042305380106,
-0.07118404656648636,
-0.001828231499530375,
0.0024653899017721415,
0.0191204771399498,
0.006795093417167664,
0.009692011401057243,
-0.04527170583605766,
0.008557702414691448,
-0.07205019891262054,
-0.004045973531901836,
0.0022927254904061556,
0.00878061167895794,
-0.04607642441987991,
-0.07280632853507996,
-0.0012607205426320434,
0.02303493022918701,
-0.01316058449447155,
0.014069739729166031,
0.048904575407505035,
0.006754076573997736,
-0.07683581858873367,
-0.030647065490484238,
0.00649937754496932,
-0.061366256326436996,
0.028015239164233208,
-0.01960696466267109,
0.06533178687095642,
-0.0167478509247303,
0.03210187330842018,
-0.021420886740088463,
-0.024905987083911896,
-0.01652948185801506,
0.023706672713160515,
-0.01933961547911167,
-0.013064100407063961,
-0.015961894765496254,
0.025687308982014656,
0.011270434595644474,
-0.0722353607416153,
-0.04421040043234825,
-0.006970166694372892,
-0.008404617197811604,
-0.009201706387102604,
-0.012706308625638485,
-0.011906621046364307,
-0.0718269795179367,
0.01550627313554287,
-0.024306196719408035,
0.00026450311997905374,
-0.03767284005880356,
-0.0005574626266025007,
-0.05916149914264679,
-0.03920217230916023,
-0.03762032464146614,
-0.012268882244825363,
0.01088982168585062,
-0.08008631318807602,
0.009585008956491947,
0.013278299011290073,
0.010157883167266846,
0.007935447618365288,
0.06368302553892136,
0.05063631758093834,
0.08139504492282867,
0.028963830322027206,
0.025580447167158127,
0.00409323675557971,
0.031138155609369278,
-0.003078227862715721,
0.004924302455037832,
-0.02753131091594696,
-0.01786447875201702,
0.016044974327087402,
0.03342865779995918,
0.06192437559366226,
0.008126482367515564,
-0.02677362598478794,
-0.07691463083028793,
-0.009930538013577461,
-0.028062870725989342,
0.024076534435153008,
-0.0030179268214851618,
-0.01030197273939848,
0.015822121873497963,
0.07208030670881271,
-0.07331197708845139,
-0.02579765021800995,
-0.009526119567453861,
-0.004529767204076052,
0.037100762128829956,
0.02612776681780815,
-0.03651002421975136,
0.049224939197301865,
-0.03264300897717476,
0.021649334579706192,
0.040384549647569656,
0.03507206216454506,
0.008524852804839611,
0.016825690865516663,
-0.013842200860381126,
0.03380614519119263,
0.07191303372383118,
0.005426440853625536,
-0.03502418473362923,
-0.060575056821107864,
0.051999300718307495,
0.003857547650113702,
0.04113660007715225,
0.001575977774336934,
0.08323856443166733,
-0.015141402371227741,
0.02417082153260708,
-0.010097081772983074,
-0.01630767621099949,
0.039799824357032776,
-0.019885344430804253,
0.0014087178278714418,
-0.050517674535512924,
-0.009000920690596104,
-0.017727985978126526,
-0.0162454042583704,
0.03377430513501167,
0.03916091099381447,
-0.011374280788004398,
-0.0026852539740502834,
-0.026747912168502808,
0.024063801392912865,
0.04424336552619934,
-0.005835321266204119,
-0.02741009183228016,
0.028081489726901054,
-0.04284583777189255,
-0.04682593420147896,
0.018422042950987816,
-0.02246806025505066,
0.04237108305096626,
-0.009450258687138557,
0.013404819183051586,
-0.030926590785384178,
-0.00602877140045166,
-0.03154222294688225,
-0.010945744812488556,
0.024178341031074524,
-0.0033433136995881796,
-0.014808191917836666,
0.013360725715756416,
0.010949308052659035,
0.026991412043571472,
-0.009125642478466034,
0.03530687838792801,
-0.0004788751539308578,
-0.022164706140756607,
-0.026313861832022667,
0.022885069251060486,
0.06801500916481018,
-0.04115191474556923,
0.010254273191094398,
-0.03524142876267433,
-0.006799544673413038,
0.049799442291259766,
0.027907131239771843,
0.014092518948018551,
-0.03537553921341896,
0.00999171007424593,
-0.0632476732134819,
0.06356394290924072,
0.03177564591169357,
-0.032855384051799774,
-0.0026634535752236843,
0.001166625996120274,
-0.01496683619916439,
-0.01220681145787239,
0.04552064463496208,
-0.019384341314435005,
-0.0029927382711321115,
0.03594733029603958,
0.060913391411304474,
-0.007260552141815424,
0.019400473684072495,
0.011404500342905521,
0.06580240279436111,
-0.011784963309764862,
-0.054213229566812515,
0.006726207211613655,
-0.011859194375574589,
0.015226354822516441,
-0.04141353443264961,
-0.020351916551589966,
-0.011704463511705399,
-0.021155746653676033,
0.026767347007989883,
-0.014906653203070164,
0.023730741813778877,
-0.0022700470872223377,
-0.041651710867881775,
-0.01654812879860401,
0.021157315000891685,
0.06099892035126686,
0.02165723592042923,
-0.023935416713356972,
-0.05046113207936287,
-0.002236392814666033,
0.020868215709924698,
0.009193789213895798,
0.014735808596014977,
-0.021694637835025787,
-0.014056476764380932,
-0.020419476553797722,
0.03731009364128113,
0.009418838657438755,
0.022144250571727753,
0.08864100277423859,
0.03061465360224247,
0.005986435804516077,
-0.04786054044961929,
0.07380569726228714,
0.07116023451089859,
-0.06615500897169113,
0.02559046633541584,
0.050324946641922,
-0.02449258603155613,
0.0033447113819420338,
-0.01871219091117382,
0.019820500165224075,
0.009357290342450142,
-0.0031065514776855707,
-0.005805023480206728,
0.01680050976574421,
0.02441474236547947,
0.013025028631091118,
0.0860464945435524,
-0.0379369892179966,
-0.040273070335388184,
0.022591833025217056,
0.024471426382660866,
-0.04127040132880211,
0.017264803871512413,
0.0013942953664809465,
0.020442135632038116,
-0.08889936655759811,
-0.010657068341970444,
-0.004583345260471106,
-0.005301621742546558,
-0.03915619105100632,
0.005038234405219555,
0.04494483023881912,
0.028741290792822838,
-0.01837586984038353,
0.059597041457891464,
-0.04598177224397659,
-0.02817237190902233,
0.052668262273073196,
-0.011747447773814201,
0.013566815294325352,
-0.011396828107535839,
0.061926547437906265,
0.0799214318394661,
-0.011139070615172386,
0.020762961357831955,
0.055611010640859604,
-0.012532640248537064,
0.005617556162178516,
-0.018434695899486542,
-0.003514900105074048,
0.08298245817422867,
-0.0045488919131457806,
-0.007688066456466913,
0.014447896741330624,
0.07216701656579971,
-0.04884776473045349,
0.019944602623581886,
-0.04973779246211052,
-0.027416110038757324,
0.014324434101581573,
-0.07425183057785034,
-0.020948030054569244,
-0.04271543771028519,
-0.017230642959475517,
-0.04305265098810196,
0.03777403384447098,
0.025167316198349,
-0.0587632991373539,
0.020193884149193764,
0.010104983113706112,
-0.04874619096517563,
-0.012862171046435833,
0.04336344078183174,
0.012593469582498074,
-0.030825713649392128,
0.06716093420982361,
0.015222991816699505,
0.10345302522182465,
-0.0044464305974543095,
-0.004356009885668755,
-0.010073674842715263,
0.004215097054839134,
0.052194830030202866,
-0.023751912638545036,
0.016280094161629677,
-0.05786241963505745,
-0.0059690470807254314,
0.0028700754046440125,
0.04796924814581871,
0.04937473312020302,
0.00311046140268445,
-0.025277797132730484,
-0.006018100772053003,
-0.03490445762872696,
-0.03265676647424698,
0.005332102533429861,
-0.024021955206990242,
-0.024483084678649902,
-0.057553645223379135,
0.021215492859482765,
-0.04079067334532738,
-0.024041367694735527,
-0.023898428305983543,
-0.06291291862726212,
0.007113506551831961,
-0.0487162247300148,
0.02348114177584648,
0.029845673590898514,
0.05377454310655594,
0.0008269498939625919,
-0.04436265304684639,
-0.05041249468922615,
0.011843710206449032,
0.021308533847332,
0.007404151372611523,
0.06386290490627289,
0.005550677422434092,
-0.027518287301063538,
0.016253380104899406,
0.03866231068968773,
-0.08323527872562408,
-0.02260984666645527,
-0.02721836231648922,
0.0033272565342485905,
0.02379349060356617,
-0.008818070404231548,
-0.027484320104122162,
0.03164079785346985,
-0.016799330711364746,
0.004206211306154728,
-0.013317870907485485,
0.04701251909136772,
-0.024566365405917168,
-0.06307196617126465,
0.02481943741440773,
-0.0354907400906086,
0.04317469149827957,
-0.048196472227573395,
-0.0177615899592638,
0.005668810103088617,
0.013928369618952274,
-0.01829315349459648,
-0.004335469100624323,
-0.018678708001971245,
-0.015383007004857063
] |
<p>The $\mathrm{U(1)}$ QED case has two physical degrees of freedom, which is easy to understand because the free electromagnetic field must be transverse to the direction of propagation. But what are the physical degrees of freedom the $\mathrm{SU(N)}$ Yang-Mills theory? </p>
<p>I believe that the $\mathrm{SU(N)}$ Y.M. theory has four degrees of freedom, and it is easy to see that by gauge fixing (such as the Lorentz condition or the Coulomb condition) that we can always remove one redundant degree of freedom. But then we still haven't completely fixed the redundant degrees of freedom. Thus my question is:</p>
<blockquote>
<p>How many physical degrees and how many are redundant degrees of freedom does the Y.M. theory have? </p>
</blockquote>
<p>I would be interested to understand how we can determine this mathematically, and also to understand what the physical intuition behind this is?</p> | g192 | [
0.0069872112944722176,
0.015787238255143166,
-0.012013792991638184,
0.041479263454675674,
0.05077409744262695,
-0.002423223340883851,
0.06195357069373131,
0.016110967844724655,
0.0002944486041087657,
0.015798261389136314,
-0.013919193297624588,
-0.0502462238073349,
0.003420343855395913,
-0.03877580165863037,
-0.036169178783893585,
-0.01148005947470665,
0.002243216848000884,
0.059484899044036865,
0.03990033641457558,
-0.06375223398208618,
-0.040645428001880646,
0.01709209755063057,
-0.022687572985887527,
-0.05889274924993515,
-0.03701167553663254,
0.003132500685751438,
0.02208339050412178,
0.017897147685289383,
0.0033044505398720503,
0.013752753846347332,
-0.03402262181043625,
0.026021184399724007,
0.0716678574681282,
-0.006076646503061056,
-0.031465157866477966,
0.005429217591881752,
0.0024166894145309925,
0.035909734666347504,
0.05153106153011322,
-0.000489288242533803,
-0.008824006654322147,
-0.0029072840698063374,
-0.011630442924797535,
-0.01990288682281971,
0.010189967229962349,
0.04282441735267639,
-0.0012751838658005,
-0.008122003637254238,
0.0208763238042593,
0.004457426723092794,
-0.017429769039154053,
0.00800613034516573,
0.0876670852303505,
0.0009823193540796638,
-0.019947251304984093,
-0.0021394812501966953,
0.03829921409487724,
0.03178763762116432,
0.018130632117390633,
0.041807904839515686,
0.008288444951176643,
0.03888535127043724,
-0.00943037960678339,
0.010969090275466442,
0.03326237574219704,
-0.020228702574968338,
-0.06756124645471573,
-0.05321844667196274,
-0.017617201432585716,
-0.006775291636586189,
-0.05478285253047943,
-0.07839352637529373,
-0.03813965991139412,
0.052718788385391235,
0.0045629520900547504,
0.038416001945734024,
0.027968142181634903,
-0.02232319861650467,
0.019670939072966576,
-0.04207621514797211,
-0.042775530368089676,
0.01194465160369873,
0.06817691028118134,
0.024932710453867912,
0.03153402730822563,
-0.04854416102170944,
-0.05121716484427452,
0.03736689314246178,
-0.061531562358140945,
-0.0006587966927327216,
0.038942985236644745,
0.029518654569983482,
0.003435452003031969,
0.009084930643439293,
0.025545066222548485,
-0.014113939367234707,
-0.006525325123220682,
0.04101501405239105,
0.049735743552446365,
-0.002903171582147479,
-0.02668875642120838,
-0.0038500160444527864,
0.005053096450865269,
-0.02194967120885849,
0.03719887137413025,
-0.006362255662679672,
0.08310219645500183,
-0.015071669593453407,
0.015881460160017014,
0.045014556497335434,
-0.07313987612724304,
0.00047866758541204035,
0.008601360954344273,
0.031642574816942215,
-0.05291884019970894,
-0.06855905801057816,
0.012114954181015491,
-0.02179546095430851,
0.046382833272218704,
-0.008632693439722061,
-0.04515589773654938,
0.005609194748103619,
-0.0251790601760149,
0.0015105641214177012,
-0.040624622255563736,
-0.028952183201909065,
-0.03562527894973755,
-0.01293154712766409,
-0.026715530082583427,
0.022413814440369606,
0.050455816090106964,
-0.01545886043459177,
-0.03308693692088127,
0.024922972545027733,
-0.0064146933145821095,
-0.010332710109651089,
0.06774971634149551,
0.006963420193642378,
-0.009445264004170895,
-0.02092510089278221,
0.022700536996126175,
-0.01231098361313343,
0.04103069752454758,
-0.0776653066277504,
0.015247014351189137,
-0.027945270761847496,
0.029823606833815575,
0.02055261842906475,
-0.010633643716573715,
0.024584464728832245,
0.03074844554066658,
0.030324697494506836,
0.04357622563838959,
-0.0542391799390316,
0.004080896731466055,
-0.0668778046965599,
-0.0022079404443502426,
-0.05175980553030968,
0.024092361330986023,
-0.03514772281050682,
-0.008447369560599327,
-0.021886199712753296,
0.07653667777776718,
0.02306458167731762,
0.0067014629021286964,
-0.030969670042395592,
-0.017356473952531815,
-0.03238564357161522,
-0.01881713792681694,
-0.06763160228729248,
-0.05642165616154671,
-0.04605644941329956,
0.014850831590592861,
0.05581653118133545,
-0.03456849977374077,
0.044120438396930695,
0.03291541710495949,
-0.005025268532335758,
-0.059315647929906845,
-0.011803068220615387,
-0.01743202842772007,
-0.018237702548503876,
0.024906137958168983,
0.016555150970816612,
-0.029214205220341682,
0.0010243718279525638,
0.026817185804247856,
0.04568122327327728,
-0.03212205320596695,
0.0018427118193358183,
0.028990475460886955,
0.002757081761956215,
-0.0895688459277153,
-0.01638706587255001,
-0.013053052127361298,
0.0020565565209835768,
-0.033948421478271484,
0.014319850131869316,
0.010906820185482502,
-0.0022725577000528574,
-0.024035878479480743,
0.018989576026797295,
0.07649227976799011,
-0.04540840908885002,
-0.0041074324399232864,
-0.018266843631863594,
0.010448542423546314,
-0.0008562938310205936,
0.009841165505349636,
0.026089012622833252,
0.021518684923648834,
0.006576756946742535,
0.009332923218607903,
0.04117516800761223,
0.0007784347981214523,
0.004632876720279455,
-0.01622587814927101,
-0.033242709934711456,
-0.03073279745876789,
0.010165791027247906,
0.003559558652341366,
0.044514015316963196,
0.09650802612304688,
-0.019925205036997795,
-0.023589137941598892,
0.024622660130262375,
-0.07469329237937927,
-0.029995031654834747,
-0.007398503832519054,
-0.0012843019794672728,
-0.05798549950122833,
0.0005312187131494284,
-0.0010260192211717367,
-0.04731041565537453,
-0.008952474221587181,
0.022978147491812706,
-0.05393321439623833,
-0.02367502450942993,
0.03297964483499527,
0.007760144304484129,
0.048689235001802444,
0.06910712271928787,
-0.040396496653556824,
0.004667292349040508,
0.02315428853034973,
0.023705273866653442,
0.04751398786902428,
-0.00528499623760581,
-0.012715351767838001,
0.06137003377079964,
0.048077285289764404,
-0.05838482454419136,
-0.028649810701608658,
0.05585233122110367,
-0.012657771818339825,
-0.013349741697311401,
-0.04635564982891083,
0.05101187527179718,
-0.10090678930282593,
-0.054556507617235184,
-0.009082651697099209,
-0.08680221438407898,
-0.026996878907084465,
0.02598763257265091,
-0.0588826984167099,
0.04603256285190582,
-0.03395077958703041,
0.014648722484707832,
0.020654480904340744,
0.016867931932210922,
-0.07158786058425903,
0.08756645023822784,
-0.01714705117046833,
-0.00818881019949913,
0.005217115394771099,
-0.034811832010746,
-0.0007607399020344019,
-0.0036070009227842093,
-0.029129598289728165,
-0.004147873725742102,
0.03487520292401314,
0.024555394425988197,
-0.035498518496751785,
0.055781275033950806,
0.041163258254528046,
-0.07977023720741272,
-0.04850627854466438,
-0.04023183882236481,
-0.04665686562657356,
0.04343847557902336,
-0.00838580820709467,
0.01595184952020645,
0.03669790178537369,
0.012291258201003075,
-0.05706178396940231,
0.03164295852184296,
0.022415602579712868,
-0.035836756229400635,
-0.035073257982730865,
-0.025446362793445587,
-0.025663819164037704,
0.06016557663679123,
-0.005476128775626421,
0.015083138830959797,
-0.02389609068632126,
0.027067560702562332,
-0.08778917044401169,
0.04374244436621666,
0.012327897362411022,
-0.061890702694654465,
0.007125507574528456,
0.06769339740276337,
-0.008498364128172398,
0.02091987617313862,
-0.06567291170358658,
0.017940184101462364,
0.028390705585479736,
-0.0015470803482457995,
-0.01123718824237585,
0.024935081601142883,
-0.05605195462703705,
-0.02911679819226265,
0.08455768972635269,
-0.04302903264760971,
0.0646713525056839,
0.037455420941114426,
-0.012103674933314323,
0.02723592333495617,
-0.013705037534236908,
-0.023975839838385582,
0.011022970080375671,
0.016077833250164986,
-0.02786410227417946,
-0.0025647608563303947,
-0.03055597096681595,
0.07217935472726822,
-0.058870915323495865,
-0.0065915994346141815,
0.09115425497293472,
-0.0014399774372577667,
0.02628897875547409,
-0.002833473728969693,
-0.07081690430641174,
-0.020291956141591072,
0.01651059463620186,
0.012809502892196178,
-0.07313492894172668,
0.009518777951598167,
0.025443408638238907,
0.0034475913271307945,
0.031011909246444702,
-0.02042797952890396,
-0.009835146367549896,
0.0008298689499497414,
0.03412620350718498,
0.027758771553635597,
0.004268266260623932,
0.0463268868625164,
-0.0074354736134409904,
-0.019367888569831848,
0.0020023712422698736,
-0.023460451513528824,
-0.006181517615914345,
-0.03747044503688812,
-0.041708141565322876,
0.029767276719212532,
0.009144919924438,
0.02739655412733555,
-0.030133455991744995,
-0.013689901679754257,
-0.03195193409919739,
-0.07936939597129822,
-0.05905742943286896,
-0.021923372521996498,
-0.023467445746064186,
0.00858108326792717,
-0.010217863135039806,
-0.052427906543016434,
-0.012607242912054062,
0.018498973920941353,
-0.0274495892226696,
0.08775480836629868,
0.038235459476709366,
0.042085397988557816,
-0.03602764382958412,
0.028405170887708664,
-0.06665275245904922,
0.031332939863204956,
-0.041457414627075195,
0.013765922747552395,
-0.002427245257422328,
-0.008447552099823952,
-0.040498632937669754,
0.04326232150197029,
0.0391090102493763,
-0.04860121011734009,
0.010922658257186413,
-0.015140668489038944,
-0.0027910799253731966,
-0.013453413732349873,
0.08025158196687698,
0.04728395864367485,
-0.00968772079795599,
-0.0038352152332663536,
0.009992705658078194,
0.0045042261481285095,
0.003529634326696396,
-0.007053398061543703,
0.05832107737660408,
0.001243526698090136,
-0.07634516805410385,
0.021632565185427666,
0.01921120285987854,
-0.051588963717222214,
0.0017716930015012622,
0.010524854063987732,
-0.04668205603957176,
-0.09613599628210068,
0.03599323332309723,
0.002776316599920392,
0.03944378346204758,
0.044282831251621246,
0.04890967532992363,
-0.03321801871061325,
0.0038005865644663572,
0.07670442014932632,
0.058378346264362335,
-0.006488783285021782,
-0.0008805490215308964,
-0.016127439215779305,
0.031238947063684464,
-0.018527809530496597,
-0.0017465109704062343,
0.028994103893637657,
-0.03435017541050911,
-0.007869105786085129,
0.028450245037674904,
0.04023610055446625,
-0.07465503364801407,
0.03145081549882889,
0.053356021642684937,
-0.015064746141433716,
0.028415005654096603,
-0.04608197137713432,
-0.04259198531508446,
-0.005790221504867077,
0.02978832647204399,
-0.04476337134838104,
-0.042116716504096985,
-0.04740625619888306,
0.046500954777002335,
0.015380513854324818,
-0.03302933648228645,
0.007582959719002247,
-0.04579796642065048,
-0.028797542676329613,
-0.05910484865307808,
0.004108993336558342,
0.023163042962551117,
0.028136609122157097,
-0.02987530641257763,
-0.04196061193943024,
0.02320505492389202,
-0.00757160410284996,
-0.02887112833559513,
-0.004467450547963381,
0.018384110182523727,
0.0031955745071172714,
-0.0742255449295044,
0.0016440442996099591,
0.03977307304739952,
0.008544078096747398,
0.03138444572687149,
0.016972772777080536,
-0.017905766144394875,
-0.0008461510296911001,
-0.0027368341106921434,
-0.03360144793987274,
0.0005707707023248076,
-0.04722314327955246,
0.052757054567337036,
-0.013395603746175766,
0.041782040148973465,
0.021824903786182404,
-0.01752546615898609,
-0.028675053268671036,
0.01163498591631651,
-0.007511460687965155,
-0.07670190930366516,
-0.049185287207365036,
-0.013160176575183868,
-0.03684898093342781,
0.030332425609230995,
-0.02373792603611946,
-0.06906663626432419,
0.0011820648796856403,
-0.0393182598054409,
0.02790188044309616,
-0.03748048469424248,
0.0037087062373757362,
0.009144902229309082,
0.03708117455244064,
0.03330697864294052,
-0.0008388789719901979,
0.007211032789200544,
0.006122783292084932,
0.008552602492272854,
-0.04896055534482002,
-0.04063085466623306,
-0.05402880162000656,
0.026715831831097603,
-0.05624008551239967,
-0.046046361327171326,
0.03596961498260498,
0.07498753815889359,
0.0074765062890946865,
-0.0041869585402309895,
-0.012071015313267708,
0.01593426614999771,
-0.01570100151002407,
0.06015973538160324,
-0.010170082561671734,
0.03607834875583649,
-0.06526370346546173,
-0.06739702820777893,
0.05221031606197357,
-0.07007696479558945,
0.005518423393368721,
0.0013295450480654836,
0.09528865665197372,
-0.028277087956666946,
-0.053125493228435516,
-0.03155280277132988,
0.012402763590216637,
-0.021416081115603447,
0.0032581400591880083,
0.023837173357605934,
-0.08043563365936279,
0.04923468455672264,
0.04495041444897652,
0.014085051603615284,
-0.014287630096077919,
0.04077573120594025,
0.016484305262565613,
-0.024417269974946976,
-0.022988194599747658,
0.03127477318048477,
-0.020784545689821243,
0.007352160755544901,
0.005272644106298685,
-0.03171741962432861,
-0.00354746263474226,
-0.022880179807543755,
-0.03351426497101784,
-0.035130809992551804,
0.039331916719675064,
0.021584348753094673,
-0.006962726358324289,
-0.04467142000794411,
-0.0031951116397976875,
-0.0127698490396142,
-0.00003784122600336559,
0.03487350419163704,
0.022092195227742195,
-0.04327353462576866,
0.012772061862051487,
-0.023806335404515266,
-0.007166475523263216,
0.042356494814157486,
0.05054400488734245,
-0.01228123065084219,
0.028932467103004456,
-0.01652543433010578,
-0.008595755323767662,
0.030099891126155853,
0.049099892377853394,
-0.03328276798129082,
0.0074983080849051476,
-0.06823553889989853,
-0.021350739523768425,
0.02933385781943798,
0.061668578535318375,
0.018773749470710754,
-0.04009329527616501,
0.0067763258703053,
0.06428815424442291,
-0.04349520057439804,
0.012973831035196781,
0.06192486733198166,
0.0216868594288826,
0.02066926471889019,
0.022825969383120537,
-0.03718181326985359,
0.013438243418931961,
-0.03534070774912834,
0.04714079201221466,
0.035371046513319016,
0.001848962507210672,
-0.03365742787718773,
0.023493897169828415,
0.11066035181283951,
-0.00033460446866229177,
0.014084525406360626,
0.021342232823371887,
0.020175538957118988,
0.08932596445083618,
-0.03960175812244415,
-0.007619294337928295,
-0.008273006416857243,
-0.013862760737538338,
0.012281515635550022,
0.02654975838959217,
-0.0007712099468335509,
-0.01154613122344017,
0.002179414499551058,
-0.00008388439164264128,
0.009697195142507553,
0.03800670802593231,
-0.04531417414546013,
0.0067972890101373196,
0.05179613083600998,
-0.015186919830739498,
0.004989945329725742,
-0.025614537298679352,
-0.05993097648024559,
0.028950529173016548,
0.04182695969939232,
-0.008266540244221687,
0.08659805357456207,
-0.05349106714129448,
0.028132116422057152,
-0.04359912499785423,
0.03350858390331268,
0.019409291446208954,
-0.0003504535707179457,
0.011291990987956524,
-0.0380847193300724,
0.034162603318691254,
0.04083504527807236,
0.04450881481170654,
-0.0259513258934021,
-0.023594602942466736,
0.08112382888793945,
0.015867898240685463,
0.007011583540588617,
-0.008124936372041702,
0.062317561358213425,
-0.0005873801419511437,
-0.05568105727434158,
0.005256681703031063,
-0.011842601001262665,
-0.015456954017281532,
-0.043392740190029144,
0.020034383982419968,
-0.05940021201968193,
0.011993110179901123,
-0.059706877917051315,
0.01526231225579977,
-0.003472039010375738,
-0.024782007560133934,
-0.04953061789274216,
-0.003010296728461981,
0.02127692848443985,
0.015152517706155777,
-0.014059258624911308,
-0.022533521056175232,
0.032957207411527634,
-0.060929782688617706,
0.02776888757944107,
-0.00894232653081417,
-0.04031926766037941,
0.061726201325654984,
0.010474651120603085,
0.001611351384781301,
-0.05224697291851044,
-0.01733315922319889,
-0.003229462541639805,
-0.02522062323987484,
0.0014408095739781857,
0.015606950037181377,
-0.03249339386820793,
0.040370311588048935,
0.03351086005568504,
-0.03761698678135872,
-0.026000531390309334,
0.025502623990178108,
0.03498348966240883,
-0.007353984750807285,
0.04545265808701515,
-0.013394299894571304,
0.005143569316715002,
-0.055307164788246155,
0.014215528033673763,
0.01676173508167267,
0.02778855711221695,
0.015449471771717072,
0.06939122080802917,
-0.003893338842317462,
0.07527429610490799,
0.028621280565857887,
0.03763343021273613,
-0.0652308464050293,
-0.020431406795978546,
0.010532510466873646,
0.04516787827014923,
0.03537304326891899,
-0.026524625718593597,
-0.03552154079079628,
-0.021994834765791893,
-0.011227120645344257,
-0.014570938423275948,
0.008210984990000725,
0.035358741879463196,
0.0681869387626648,
0.03920207917690277,
-0.006497360300272703,
-0.03254701569676399,
0.042645640671253204,
0.01425960659980774,
0.011402158066630363,
-0.027746999636292458,
0.03350367397069931,
0.026296444237232208,
-0.008608449250459671,
-0.04381074756383896,
0.019755229353904724,
0.03788599371910095,
-0.018080804497003555,
-0.003112243954092264,
-0.011182878166437149,
0.0053236158564686775,
0.011489810422062874,
0.01492349337786436,
0.044367704540491104,
-0.03904964029788971,
0.032493095844984055,
-0.03408936411142349,
0.009049379266798496,
0.015179253183305264,
-0.012174010276794434,
-0.013257790356874466,
0.01180079486221075,
0.008087070658802986,
-0.03662049025297165,
-0.07315991073846817,
0.00037011929089203477,
-0.03304186463356018,
0.0665607899427414,
0.07060059159994125,
0.00592272263020277,
-0.008949924260377884,
-0.014393918216228485,
-0.019725758582353592,
0.07104460150003433,
0.038447123020887375,
-0.04263777285814285,
0.005303113255649805,
-0.026092763990163803,
0.031394168734550476,
0.04333162307739258,
0.07536786794662476,
0.006178042385727167,
0.05415858328342438,
0.0034261068794876337,
-0.04782681539654732,
-0.007844527252018452,
-0.02236276865005493,
-0.0215056911110878
] |
<p>I'm currently studying at the spectra of some supersymmetric models, and would like to know whether the parameter points I'm looking at are ruled out due to excessive CP violation.</p>
<p>I am using <a href="http://www.physik.uni-wuerzburg.de/~porod/SPheno.html" rel="nofollow">SPheno</a>, which allows me to test my spectra against various other experimental bounds. It provides a <code>Block SPhenoLowEnergy</code> in its SLHA output that has, for example, the predicted branching ratio $B_s \rightarrow \mu\mu$, or the anomalous muon $g-2$.</p>
<p>What's the variable to look for when one colloquially says "ruled out because of CP violation"? How to get it in SPheno (or with any other spectrum generator / event generator, I can switch)? I feel like the answer is obvious but I'm missing the forest for the trees.</p> | g1260 | [
0.0315885953605175,
-0.008885272778570652,
0.004447178449481726,
-0.04471832141280174,
0.006020107306540012,
0.002905974630266428,
0.026586441323161125,
0.05463196337223053,
-0.052392907440662384,
0.004060263745486736,
-0.014185795560479164,
0.028813209384679794,
-0.012777736410498619,
0.03333824872970581,
0.04492328315973282,
-0.06275857239961624,
0.028625620529055595,
-0.024140790104866028,
-0.05579354986548424,
-0.0011097504757344723,
0.0005039445823058486,
-0.002967376494780183,
-0.0003797686076723039,
-0.04444432631134987,
0.04868803173303604,
-0.015693170949816704,
0.009322076104581356,
-0.023242611438035965,
-0.020619947463274002,
-0.005267003085464239,
-0.018650304526090622,
0.03781306743621826,
0.05096767097711563,
-0.03942146152257919,
-0.0578768216073513,
-0.03759023919701576,
0.09121153503656387,
0.02141604758799076,
0.04691866412758827,
0.010052895173430443,
0.03332122787833214,
-0.009304828010499477,
-0.022268489003181458,
-0.012727135792374611,
-0.062319669872522354,
-0.04765177518129349,
0.02532535418868065,
-0.015568702481687069,
0.028052832931280136,
-0.05468123033642769,
0.010335804894566536,
-0.018827073276042938,
0.06779678165912628,
-0.04730965197086334,
-0.012078443542122841,
-0.0018096185522153974,
-0.012746940366923809,
-0.002505013020709157,
0.018268296495079994,
0.05056438222527504,
-0.006771564483642578,
0.0050340937450528145,
0.06409997493028641,
0.008208910003304482,
0.027572788298130035,
0.037788026034832,
-0.056743323802948,
-0.06079167500138283,
-0.06536973267793655,
-0.003549716202542186,
0.0006821335409767926,
-0.03594968467950821,
0.011925983242690563,
-0.03641588240861893,
-0.017045000568032265,
-0.02334476076066494,
-0.07706161588430405,
0.010275375097990036,
-0.01881096325814724,
0.02690485492348671,
-0.04557293653488159,
0.03972100839018822,
-0.036665525287389755,
0.034165430814027786,
-0.004671724978834391,
0.013211521320044994,
0.0026615983806550503,
0.042459432035684586,
-0.030274754390120506,
-0.018397053703665733,
-0.009276719763875008,
-0.04050350561738014,
-0.030675673857331276,
-0.090346559882164,
0.03788301348686218,
0.029811300337314606,
0.02762441337108612,
0.03528376668691635,
-0.007024342194199562,
0.007145333103835583,
-0.038071587681770325,
0.07231699675321579,
-0.016034668311476707,
0.028039295226335526,
-0.0548730194568634,
-0.035274673253297806,
0.023477813228964806,
-0.08753117173910141,
-0.02397138439118862,
-0.09696269780397415,
-0.01666204445064068,
0.014962022192776203,
-0.019678501412272453,
0.04953920096158981,
-0.10430210828781128,
-0.07228130847215652,
0.06318900734186172,
0.0016401909524574876,
0.024232370778918266,
-0.002580918837338686,
-0.028643449768424034,
-0.03366661071777344,
0.018523061648011208,
0.04915222153067589,
-0.03191034123301506,
0.015034573152661324,
-0.04193206876516342,
0.041363298892974854,
0.0360102578997612,
-0.037747956812381744,
-0.007109809201210737,
-0.0023106809239834547,
0.012259664945304394,
0.029439810663461685,
0.01812179572880268,
0.02555893547832966,
0.06575094163417816,
0.018760614097118378,
0.05532818287611008,
-0.08510620892047882,
0.014368067495524883,
0.002086864784359932,
0.02176998369395733,
-0.030235789716243744,
0.005196733865886927,
-0.016134528443217278,
0.03260771930217743,
-0.020643867552280426,
0.01755024865269661,
0.04993570223450661,
-0.009120696224272251,
0.05667700245976448,
-0.0047697946429252625,
-0.020135629922151566,
-0.025823384523391724,
-0.016887014731764793,
0.032205890864133835,
-0.032943934202194214,
-0.02903820015490055,
0.011513021774590015,
0.026877176016569138,
-0.004717607982456684,
-0.01005385722965002,
-0.05506868287920952,
-0.047103818506002426,
-0.04886098578572273,
-0.019142810255289078,
-0.013058562763035297,
-0.03165198117494583,
-0.049086395651102066,
0.02148270048201084,
0.04318246617913246,
0.07509570568799973,
0.02949126437306404,
0.008403823710978031,
0.060242775827646255,
0.05393726006150246,
-0.029968291521072388,
0.08093956112861633,
0.04446518048644066,
-0.0014844003599137068,
-0.008965594694018364,
0.006367525085806847,
-0.013166431337594986,
-0.03768721967935562,
-0.021503621712327003,
-0.040023013949394226,
-0.0003781209816224873,
0.00022596259077545255,
0.009654927998781204,
0.037005987018346786,
-0.002384544350206852,
0.0011534439399838448,
0.006797493435442448,
-0.008045921102166176,
-0.05631959065794945,
-0.06112923100590706,
-0.035068362951278687,
-0.002033489989116788,
-0.05951238051056862,
-0.016916466876864433,
0.06254351884126663,
-0.022577838972210884,
0.026560645550489426,
0.020248105749487877,
0.014699133113026619,
-0.006777531933039427,
0.03323083370923996,
0.0007183522102423012,
-0.006996574345976114,
0.010082017630338669,
0.013275756500661373,
-0.017535772174596786,
0.012899437919259071,
-0.07056775689125061,
-0.04598333686590195,
-0.005263893399387598,
0.0347430594265461,
-0.017931822687387466,
-0.03027985244989395,
-0.01363209169358015,
-0.05572545900940895,
0.01647092215716839,
0.07523909956216812,
-0.00960639026015997,
0.04432833194732666,
-0.02525155246257782,
0.013785538263618946,
0.047263942658901215,
-0.05196458101272583,
-0.020856505259871483,
-0.005164494272321463,
-0.030242731794714928,
-0.05536350607872009,
0.009447830729186535,
0.023366307839751244,
-0.029120124876499176,
-0.024560073390603065,
0.03182646632194519,
-0.046706683933734894,
0.06429573148488998,
-0.006356476806104183,
-0.00033263437217101455,
0.05632910504937172,
0.04084666445851326,
-0.011312980204820633,
0.03212268650531769,
-0.022839505225419998,
-0.021968990564346313,
0.06729801744222641,
-0.055227652192115784,
0.07218405604362488,
0.006829751655459404,
0.058681048452854156,
0.011866199783980846,
0.003069361438974738,
-0.013175389729440212,
0.049934886395931244,
-0.06027320399880409,
0.02862418070435524,
-0.007622054778039455,
-0.01455522421747446,
-0.0044598267413675785,
-0.046061791479587555,
0.0063216290436685085,
-0.01807296648621559,
-0.021304627880454063,
-0.10280584543943405,
-0.05269002914428711,
-0.017031898722052574,
-0.033778876066207886,
0.02617814764380455,
0.041071243584156036,
0.007081608287990093,
0.03330705314874649,
0.06793809682130814,
-0.05156317353248596,
0.018461622297763824,
0.062297265976667404,
-0.032910510897636414,
-0.029881805181503296,
-0.037838414311409,
0.06722007691860199,
0.04380308836698532,
0.03610239550471306,
0.004017091356217861,
-0.028691543266177177,
-0.006985573098063469,
-0.0511462576687336,
-0.02878502942621708,
-0.013133944943547249,
0.006317316088825464,
0.01852964051067829,
0.0009782399283722043,
-0.03280805051326752,
-0.012293165549635887,
0.019578926265239716,
0.005235214717686176,
0.009888513945043087,
0.06476901471614838,
0.014514654874801636,
0.04259612783789635,
-0.01631620153784752,
0.02484486810863018,
0.0381258986890316,
-0.002590959193184972,
-0.0450747013092041,
0.04288630560040474,
0.11249659210443497,
-0.0051307063549757,
0.013966009952127934,
0.0464608371257782,
-0.015423527918756008,
-0.006324050948023796,
0.02384544163942337,
-0.005366183817386627,
-0.06738439947366714,
0.05358594283461571,
-0.03429364040493965,
-0.06337886303663254,
-0.009366114623844624,
0.007966197095811367,
0.03358392417430878,
0.041073027998209,
0.0023813717998564243,
-0.040698785334825516,
-0.02100769802927971,
0.015373959206044674,
-0.04933566972613335,
-0.0595611110329628,
0.005759961903095245,
-0.0324738547205925,
0.02180083468556404,
0.024815643206238747,
-0.0458926260471344,
-0.013633640483021736,
-0.009387155994772911,
0.009250583127140999,
-0.023626428097486496,
-0.01870185323059559,
0.014439091086387634,
-0.006814158987253904,
0.003364714328199625,
-0.0054005468264222145,
-0.0021573957055807114,
-0.006817852146923542,
0.0022398270666599274,
0.019004404544830322,
-0.0068768225610256195,
-0.01517824362963438,
-0.0010295292595401406,
0.0014297479065135121,
0.002461287658661604,
0.004497942049056292,
0.030678611248731613,
-0.008284453302621841,
0.019741633906960487,
0.019137388095259666,
-0.030949203297495842,
0.030521992594003677,
0.06827174127101898,
-0.005928712897002697,
-0.02118908427655697,
-0.05365752801299095,
-0.01536491233855486,
0.008204306475818157,
0.0019518508343026042,
0.057639140635728836,
0.053207408636808395,
-0.03409890830516815,
0.061873987317085266,
0.0060013397596776485,
0.03572222962975502,
0.0022226651199162006,
0.05369504913687706,
-0.022814128547906876,
0.062013451009988785,
0.05061881244182587,
0.027701739221811295,
0.07866819202899933,
-0.02297721616923809,
-0.023632530122995377,
0.02203459106385708,
0.016954699531197548,
0.029905518516898155,
-0.044292379170656204,
-0.02160128951072693,
0.060210056602954865,
-0.014915131032466888,
-0.07938053458929062,
0.0634690672159195,
-0.01581534370779991,
-0.07578923553228378,
-0.036179933696985245,
0.012475037947297096,
0.005234527867287397,
0.014813416637480259,
-0.03356919437646866,
0.051283612847328186,
0.0558551549911499,
0.010807118378579617,
0.015325597487390041,
-0.007576719392091036,
-0.04470939189195633,
0.03881871700286865,
-0.05580199509859085,
0.003075313288718462,
0.07305789738893509,
0.005638535600155592,
0.05689878761768341,
-0.013235500082373619,
-0.01775924116373062,
-0.01978161558508873,
-0.08725088089704514,
0.023886021226644516,
-0.0461815670132637,
-0.008642046712338924,
-0.05826977267861366,
0.059190768748521805,
-0.007385311648249626,
0.015371006913483143,
-0.008100508712232113,
-0.00036011100746691227,
-0.03909965977072716,
0.023746546357870102,
0.02971581742167473,
0.017499050125479698,
-0.042323313653469086,
-0.015570427291095257,
-0.007996486499905586,
0.0029710810631513596,
-0.013810760341584682,
-0.026574913412332535,
0.00002801481787173543,
0.014807510189712048,
0.0019310314673930407,
-0.04976034536957741,
-0.03847647085785866,
-0.012353286147117615,
0.04014243185520172,
0.02628982439637184,
-0.005821078550070524,
0.09602674841880798,
0.011356383562088013,
-0.01459455955773592,
-0.007036405149847269,
0.0009438346023671329,
-0.00871842447668314,
-0.02326587401330471,
0.05630068480968475,
-0.04397815465927124,
-0.02070668525993824,
-0.03473590686917305,
-0.01010650210082531,
0.0372842438519001,
-0.030839502811431885,
0.02503080852329731,
0.06978073716163635,
-0.0029964977875351906,
0.023117726668715477,
-0.002904318505898118,
-0.10076054185628891,
-0.039787422865629196,
-0.02050819806754589,
0.04246726632118225,
0.043557703495025635,
-0.09583994001150131,
-0.03693937882781029,
0.021257862448692322,
-0.017508521676063538,
0.010800130665302277,
-0.027367331087589264,
0.06601113080978394,
0.0027537811547517776,
0.004492172505706549,
-0.03425684943795204,
-0.07313793152570724,
0.03264269232749939,
-0.01960812881588936,
-0.02986990101635456,
-0.04068242385983467,
0.017430908977985382,
0.0018835767405107617,
0.004948955029249191,
-0.008132669143378735,
0.019744012504816055,
0.020402325317263603,
-0.030908554792404175,
0.03030632622539997,
0.016254262998700142,
0.006970933172851801,
0.06951366364955902,
0.028721947222948074,
-0.011659079231321812,
0.048873621970415115,
-0.005505197215825319,
0.04032326489686966,
-0.003746336093172431,
-0.03733484074473381,
-0.050905611366033554,
-0.06915628910064697,
0.01143626682460308,
0.08882849663496017,
0.029782166704535484,
-0.009963298216462135,
0.03711627423763275,
0.08846229314804077,
0.02924848534166813,
0.009770866483449936,
-0.0627598837018013,
0.008639789186418056,
0.021734166890382767,
0.004650217946618795,
0.02116275578737259,
-0.021880164742469788,
-0.0029599699191749096,
-0.002808190882205963,
0.048302847892045975,
-0.017466282472014427,
-0.09809928387403488,
0.013236604630947113,
-0.009688863530755043,
0.01335311308503151,
-0.051320936530828476,
0.009810775518417358,
0.016612693667411804,
-0.012918293476104736,
-0.019575808197259903,
0.07947805523872375,
-0.02565498650074005,
0.04650406166911125,
-0.006807378027588129,
-0.04797790199518204,
-0.003679530695080757,
0.09748057276010513,
-0.06217841058969498,
-0.0010202501434832811,
-0.05259443819522858,
-0.05700581148266792,
-0.03292237967252731,
-0.05025255307555199,
-0.031645774841308594,
-0.013637864962220192,
-0.05361993983387947,
-0.00561485905200243,
0.01375724095851183,
0.0007741004810668528,
0.07303285598754883,
-0.06864183396100998,
-0.021740831434726715,
-0.015338068827986717,
0.05378073453903198,
0.0678214281797409,
-0.021172579377889633,
0.009337740950286388,
0.010839073918759823,
0.053456470370292664,
0.029729213565587997,
-0.014658070169389248,
0.03741857409477234,
-0.04972311109304428,
-0.017784245312213898,
0.05361098423600197,
0.02247220277786255,
0.023041123524308205,
-0.03261265903711319,
-0.05711659416556358,
-0.03633309155702591,
-0.0105006517842412,
0.04155599698424339,
-0.019130440428853035,
0.03684321045875549,
-0.0058463215827941895,
0.05941649526357651,
-0.04317799583077431,
-0.0378863550722599,
0.004655326716601849,
0.0366474948823452,
0.021783174946904182,
0.03608976677060127,
-0.021306054666638374,
0.011328388936817646,
0.05138813704252243,
-0.018164999783039093,
0.031420525163412094,
0.00014071531768422574,
-0.01823420450091362,
0.0856386125087738,
-0.021764453500509262,
0.011436236090958118,
0.008609526790678501,
-0.005534989759325981,
-0.01568077690899372,
0.06874997913837433,
0.019553901627659798,
-0.029735667631030083,
-0.020783625543117523,
0.007245753426104784,
-0.03210665285587311,
-0.01995888724923134,
0.04027993977069855,
0.025630496442317963,
0.0350554957985878,
-0.020887941122055054,
0.04127434268593788,
0.02286268025636673,
-0.04533975571393967,
0.04398547112941742,
-0.022108126431703568,
0.012504485435783863,
-0.017536655068397522,
-0.038205958902835846,
-0.005677390843629837,
-0.0038872009608894587,
0.019283141940832138,
-0.011791066266596317,
-0.0073189325630664825,
-0.004487332887947559,
-0.05579272285103798,
0.05626431852579117,
0.04280528798699379,
-0.02802620828151703,
0.008018497377634048,
-0.03722795844078064,
0.012791644781827927,
0.038337353616952896,
0.02983412705361843,
-0.01290146354585886,
0.02722930908203125,
0.0009194833692163229,
0.001999186584725976,
0.021450640633702278,
0.02333715185523033,
-0.006437254603952169,
-0.030451400205492973,
0.04481678828597069,
-0.08212676644325256,
0.046995922923088074,
0.060597263276576996,
0.03951267525553703,
0.03884091600775719,
0.03447282686829567,
-0.00016406684881076217,
-0.03881491348147392,
0.018814213573932648,
-0.026150686666369438,
0.02463996410369873,
0.03433274105191231,
0.007282322272658348,
-0.05239551514387131,
0.003530876012519002,
-0.023247772827744484,
-0.0011870675953105092,
-0.0008599998545832932,
-0.028536437079310417,
0.04257243126630783,
0.00010080940410261974,
0.00014746647502761334,
0.006173445377498865,
0.0009619725169613957,
-0.02867821604013443,
-0.04422520101070404,
-0.011152761057019234,
-0.015835974365472794,
0.002080537611618638,
0.05009829252958298,
-0.024812474846839905,
-0.0435878224670887,
0.06180860474705696,
-0.03217344358563423,
-0.03911016508936882,
-0.029670948162674904,
-0.04850329831242561,
0.016520513221621513,
0.004780369810760021,
-0.04204865172505379,
0.009685782715678215,
-0.02543151006102562,
0.007462157867848873,
-0.048673950135707855,
0.048029907047748566,
-0.028376208618283272,
-0.03142201155424118,
0.01574566774070263,
-0.023497793823480606,
-0.022905196994543076,
-0.04488898813724518,
-0.024900980293750763,
0.015781905502080917,
0.02145414985716343,
-0.0186370350420475,
0.0032608024775981903,
-0.0016371082747355103,
-0.06498456746339798,
-0.018338419497013092,
-0.0008185582119040191,
-0.04088497906923294,
0.07395157217979431,
0.025616483762860298,
0.023544082418084145,
0.012944384478032589,
0.023238271474838257,
-0.018199529498815536,
-0.010027729906141758,
0.04480108246207237,
0.01659993827342987,
-0.011264385655522346,
-0.03132854029536247,
-0.036448389291763306,
-0.004384099505841732,
-0.005442642141133547,
0.07766860723495483,
-0.0162920244038105,
0.006796468049287796,
0.052743300795555115,
0.009704654105007648,
0.005215702578425407,
0.031039778143167496,
0.057933706790208817,
0.008944090455770493,
-0.06387671083211899,
0.03611795976758003,
-0.017085112631320953,
-0.0008770280401222408,
0.004833759739995003,
-0.034011632204055786,
-0.006306648254394531,
0.028523080050945282,
0.016760800033807755,
0.03812273219227791,
-0.030902579426765442,
0.006018957123160362,
-0.019425008445978165,
-0.01803511194884777,
-0.052407924085855484,
-0.014699507504701614,
-0.019205717369914055,
-0.021082045510411263,
-0.043709512799978256,
0.04048030450940132,
-0.039126090705394745,
0.02347925491631031,
-0.019988873973488808,
-0.019551023840904236,
-0.017435943707823753,
0.0066583710722625256,
-0.024071181192994118,
-0.00027782272081822157,
0.04776843637228012,
0.012519119307398796,
0.04849006608128548,
0.016881173476576805,
-0.033369436860084534,
0.07116616517305374,
0.035258110612630844,
-0.02183954417705536,
0.029162416234612465,
-0.032545141875743866,
-0.010158821940422058,
0.01134661864489317,
0.01578683778643608,
-0.018151871860027313,
0.025282809510827065,
0.03668349236249924,
-0.059860602021217346,
-0.04761262983083725,
0.011629991233348846,
0.03554767370223999
] |
<p>Is it true:From equation $C=Q/V$</p>
<p>1)If Potential difference is kept
<strong>constant</strong>
$C \propto Q$</p>
<p>2)If charge is kept <strong>constant</strong>
$C \propto 1/V$
Then if 2nd is true I do have a question:
Don't we say that capacitance is the ability of a body to store charge,so my question goes this way,if the charge is kept constant and potential difference is decrease,then by the above assumption the capacitance should increase(and which is true).But we have said that charge is kept constant,then how would the capacitance increase?
I need an answer</p> | g1261 | [
0.07526668906211853,
-0.0005426090792752802,
0.01544291339814663,
0.02990964986383915,
0.07045377045869827,
0.023872675374150276,
0.008093765936791897,
-0.0074613094329833984,
-0.020211176946759224,
0.013829853385686874,
-0.09235279262065887,
0.021188046783208847,
0.0039047820027917624,
-0.0094913886860013,
0.008902335539460182,
-0.010474896058440208,
0.030865147709846497,
-0.03714021295309067,
-0.007726545911282301,
-0.012447279877960682,
-0.03942101076245308,
-0.03169642761349678,
0.02403470128774643,
-0.01694728620350361,
-0.016268014907836914,
-0.028628462925553322,
-0.0013085919199511409,
0.031480688601732254,
-0.02708834409713745,
-0.04994213208556175,
0.025298381224274635,
-0.017935575917363167,
0.061308689415454865,
0.0016629224410280585,
-0.03298933058977127,
-0.030866926535964012,
0.08203631639480591,
0.018162187188863754,
0.01548072136938572,
-0.0465763583779335,
0.044428952038288116,
0.002640494843944907,
0.03952636942267418,
-0.01223534531891346,
-0.022585248574614525,
-0.0730065107345581,
0.007780719082802534,
-0.01609903760254383,
-0.021725913509726524,
-0.018239887431263924,
-0.013709576800465584,
-0.001733125071041286,
-0.007329212035983801,
0.010192475281655788,
0.0373326912522316,
-0.011367551982402802,
0.02811465971171856,
0.00043395598186179996,
-0.010983435437083244,
0.02532951347529888,
0.03707828372716904,
0.0014637442072853446,
0.030252987518906593,
0.019258758053183556,
0.027049925178289413,
-0.06341221928596497,
-0.026772325858473778,
0.023860694840550423,
-0.03012106753885746,
0.018705949187278748,
-0.023494336754083633,
-0.06249940022826195,
-0.0351528525352478,
-0.04117881506681442,
0.05842934921383858,
0.0066408212296664715,
0.0535723902285099,
-0.047393132001161575,
0.012534854002296925,
-0.03407234698534012,
-0.0411050021648407,
-0.03799291327595711,
0.08053171634674072,
0.04409031569957733,
-0.002172354608774185,
-0.02260366640985012,
0.019393371418118477,
0.025484688580036163,
-0.018850792199373245,
0.05333426967263222,
0.0399087518453598,
-0.05993310734629631,
0.056285545229911804,
0.033534735441207886,
0.02333582006394863,
-0.02349131740629673,
-0.0031699188984930515,
0.041532229632139206,
0.000021505098629859276,
-0.015341159887611866,
-0.029937252402305603,
-0.026533201336860657,
0.06205559894442558,
0.028159664943814278,
-0.026564771309494972,
0.034952059388160706,
0.031398311257362366,
0.01976635865867138,
-0.03913209214806557,
-0.01090386975556612,
0.043399471789598465,
-0.05001270771026611,
0.0036647841334342957,
-0.009354065172374249,
-0.0796939805150032,
-0.004749471787363291,
0.05170707404613495,
-0.0780961811542511,
0.023963332176208496,
-0.016722507774829865,
-0.09280198812484741,
0.04843556508421898,
-0.008792806416749954,
0.0223833117634058,
0.030107775703072548,
0.02458779886364937,
0.03457028418779373,
0.007120738737285137,
-0.007900895550847054,
0.010516399517655373,
0.022032199427485466,
0.0011521045817062259,
-0.02866188809275627,
0.00040035234997048974,
-0.011561267077922821,
0.03225615248084068,
0.04234412685036659,
-0.025387948378920555,
0.0255377646535635,
-0.0068126339465379715,
0.049007970839738846,
-0.020711755380034447,
0.0016203423729166389,
0.013581935316324234,
-0.05613322928547859,
-0.02713741734623909,
0.014147884212434292,
0.010829039849340916,
0.009659168310463428,
0.022330639883875847,
0.0649566575884819,
0.037638988345861435,
-0.014848272316157818,
-0.034185588359832764,
0.004901394248008728,
-0.01360213104635477,
0.06791265308856964,
0.035334762185811996,
0.039616361260414124,
0.043091289699077606,
0.020533332601189613,
0.021737873554229736,
0.030693907290697098,
-0.01456540822982788,
-0.035052184015512466,
-0.014196749776601791,
0.011997489258646965,
-0.017200369387865067,
-0.01086474023759365,
-0.003016977570950985,
-0.0020233679097145796,
-0.0009257423225790262,
-0.010657770559191704,
0.08975512534379959,
0.015161189250648022,
-0.017575204372406006,
0.024614891037344933,
0.031423069536685944,
0.00515234237536788,
-0.01642473042011261,
-0.06608846783638,
0.07472546398639679,
-0.01100140530616045,
-0.0528268925845623,
-0.030318601056933403,
0.05998362973332405,
0.004583907313644886,
0.017135225236415863,
-0.060133934020996094,
-0.0027793061453849077,
-0.09751472622156143,
0.008549707010388374,
-0.04944036155939102,
0.0657818466424942,
0.01252419501543045,
0.021858999505639076,
0.02246740832924843,
-0.025087127462029457,
-0.0226825512945652,
-0.01929701492190361,
-0.04232930392026901,
0.0312179047614336,
0.06558103859424591,
0.015615412034094334,
0.04227602854371071,
0.011015620082616806,
0.005872475448995829,
-0.08415234833955765,
0.07765661180019379,
0.0062204510904848576,
0.02181987091898918,
0.06103053316473961,
-0.019519103690981865,
0.06472490727901459,
0.013186017982661724,
-0.015460733324289322,
-0.0032864497043192387,
0.02210807427763939,
-0.024732161313295364,
-0.040214069187641144,
-0.02286660484969616,
-0.023971837013959885,
0.007291925139725208,
0.026813723146915436,
-0.06584031134843826,
-0.018288196995854378,
-0.020409008488059044,
0.0001948458084370941,
-0.03340208902955055,
0.021345404908061028,
-0.019398046657443047,
0.03834782913327217,
-0.023221975192427635,
-0.011827207170426846,
-0.01147746667265892,
0.08769658207893372,
-0.055018384009599686,
0.004724002908915281,
0.0069373915903270245,
-0.007063235156238079,
-0.027286089956760406,
-0.04405657947063446,
-0.01917652040719986,
0.03456055745482445,
0.004636276513338089,
-0.023881511762738228,
-0.045229677110910416,
-0.004799248185008764,
0.018877049908041954,
-0.006768850609660149,
0.023150241002440453,
-0.03189268708229065,
-0.003040279960259795,
-0.00843483954668045,
0.011337272822856903,
-0.017024097964167595,
0.011082913726568222,
0.017238670960068703,
-0.034874625504016876,
-0.037128712981939316,
-0.025905922055244446,
-0.006742111407220364,
-0.01210453175008297,
0.022889547049999237,
-0.0026371534913778305,
0.0336577445268631,
-0.04040000960230827,
0.035576462745666504,
0.04814259335398674,
-0.011629528366029263,
-0.002114300848916173,
0.07850149273872375,
0.0034751531202346087,
0.04604099690914154,
0.010198879055678844,
-0.016934899613261223,
0.010566708631813526,
-0.06388390064239502,
0.039664898067712784,
-0.024746572598814964,
-0.005843429826200008,
-0.04126029834151268,
-0.09069593250751495,
0.029435405507683754,
0.008893915452063084,
0.008120177313685417,
0.03279430419206619,
-0.07924387603998184,
0.00031821324955672026,
-0.013485905714333057,
-0.047678589820861816,
0.05623062327504158,
0.02547752484679222,
-0.03259091451764107,
-0.003357282839715481,
0.03768195956945419,
0.01878516376018524,
-0.04618426039814949,
-0.0500820055603981,
0.015818629413843155,
-0.027096744626760483,
0.010270976461470127,
-0.006663788575679064,
0.030415577813982964,
0.08975446969270706,
0.08683948218822479,
-0.03737713769078255,
-0.021801654249429703,
0.05045458674430847,
0.01323244534432888,
-0.0552232563495636,
0.031786561012268066,
-0.040919091552495956,
0.016294576227664948,
-0.017638318240642548,
-0.005980247166007757,
-0.002473945263773203,
0.010702384635806084,
-0.00755533529445529,
-0.05401661992073059,
-0.0063854120671749115,
-0.0395347960293293,
0.005204787943512201,
0.016866179183125496,
0.025955859571695328,
0.021185722202062607,
-0.07270146161317825,
0.015828458592295647,
-0.015990950167179108,
-0.008267066441476345,
-0.003600780852138996,
0.06451909989118576,
-0.0024811283219605684,
-0.037377551198005676,
0.028044968843460083,
-0.008454198949038982,
0.015676487237215042,
-0.007460079621523619,
0.019831128418445587,
0.016809355467557907,
0.03236079588532448,
-0.004293359816074371,
-0.06318141520023346,
-0.023971619084477425,
-0.03606276586651802,
0.055066563189029694,
0.011695241555571556,
-0.006799815688282251,
-0.015291540883481503,
-0.02491690218448639,
0.06428159773349762,
0.002399183576926589,
0.029574032872915268,
0.024846458807587624,
-0.06516943871974945,
-0.06040645018219948,
-0.022968359291553497,
0.028375092893838882,
-0.05878889560699463,
0.05283690243959427,
0.05280096456408501,
-0.054380327463150024,
0.07036565244197845,
0.027544742450118065,
0.015021105296909809,
-0.0069364826194942,
-0.015062196180224419,
0.04962917044758797,
-0.029527561739087105,
-0.03350168839097023,
-0.03225429728627205,
0.0192138459533453,
-0.026969879865646362,
0.07204730063676834,
0.06400478631258011,
-0.01875067502260208,
-0.0431176982820034,
0.0032416596077382565,
-0.012968301773071289,
0.0028770328499376774,
0.029777567833662033,
-0.01121497806161642,
-0.0069753616116940975,
0.028243212029337883,
-0.05261124670505524,
-0.01721642166376114,
0.03910234570503235,
0.034466516226530075,
-0.005210772156715393,
-0.02960463985800743,
0.012779779732227325,
-0.02548992820084095,
-0.04824426397681236,
-0.02010415866971016,
-0.010508176870644093,
-0.03369363397359848,
-0.06079522892832756,
-0.07131357491016388,
0.04595363512635231,
0.008951650932431221,
-0.03816893696784973,
-0.033739373087882996,
-0.016295457258820534,
-0.03442936763167381,
0.015536963939666748,
-0.03219105303287506,
0.06670021265745163,
-0.013372459448873997,
-0.05212312564253807,
-0.023638995364308357,
-0.013723892159759998,
-0.03254086151719093,
-0.018353058025240898,
-0.05308595672249794,
-0.01167804840952158,
-0.02237306535243988,
-0.004079234786331654,
0.01432982087135315,
0.051862992346286774,
0.009867657907307148,
0.020282773301005363,
0.043274980038404465,
-0.03556087985634804,
0.02365976572036743,
0.03783724457025528,
0.010074486024677753,
0.0004027727118227631,
-0.0012708435533568263,
0.005476676858961582,
-0.009620808996260166,
-0.03114917501807213,
0.04703083634376526,
0.025958262383937836,
0.034710727632045746,
-0.034058261662721634,
0.07019028812646866,
-0.06084255874156952,
0.0292060486972332,
-0.03719956800341606,
0.0054556941613554955,
0.07285593450069427,
0.04333702474832535,
0.07135685533285141,
-0.03282361850142479,
-0.030552957206964493,
0.04673554748296738,
-0.03200673684477806,
0.06474892795085907,
0.05124092474579811,
-0.08042671531438828,
-0.054606761783361435,
0.04032335430383682,
-0.001432860386557877,
-0.023327650502324104,
-0.017255274578928947,
-0.04979761317372322,
0.022153422236442566,
-0.05651945620775223,
-0.0021157211158424616,
0.030679630115628242,
-0.0804889127612114,
0.007360776420682669,
0.035507529973983765,
0.01296253688633442,
0.01720377802848816,
-0.017691507935523987,
-0.04146658629179001,
-0.0591927096247673,
-0.022758202627301216,
-0.0017401051009073853,
0.049427639693021774,
0.04006524756550789,
0.012725181877613068,
0.012331769801676273,
-0.010479227639734745,
-0.04433215409517288,
-0.011167418211698532,
0.04965813830494881,
-0.06948306411504745,
-0.038146890699863434,
0.017803987488150597,
0.003977116663008928,
0.0013753542443737388,
0.02549019269645214,
-0.015276409685611725,
-0.006783503573387861,
-0.007013760972768068,
-0.011289381422102451,
-0.010324263013899326,
-0.029455816373229027,
0.05870938301086426,
0.031672943383455276,
0.03792578727006912,
0.05953436717391014,
-0.014132059179246426,
-0.024378811940550804,
0.01689849980175495,
-0.007480632048100233,
-0.03777720034122467,
0.053779300302267075,
0.013089482672512531,
0.03329675644636154,
0.004732818808406591,
0.0006744834827259183,
-0.029097525402903557,
0.05559355020523071,
0.03259213641285896,
0.00497093191370368,
-0.008553008548915386,
0.02198869362473488,
-0.010725107975304127,
0.03153826668858528,
0.05591562017798424,
0.048527978360652924,
0.01993279531598091,
0.059493258595466614,
-0.024967053905129433,
-0.024962229654192924,
-0.034043993800878525,
-0.012928448617458344,
0.045556217432022095,
0.024816684424877167,
0.03212757036089897,
-0.008972445502877235,
0.0055650705471634865,
0.017514631152153015,
0.005289068445563316,
-0.03276212885975838,
0.01760764978826046,
0.03592047467827797,
0.029723795130848885,
0.06309877336025238,
-0.0007860898040235043,
0.003818860510364175,
-0.03046928159892559,
0.016324903815984726,
-0.04819108173251152,
-0.004553675651550293,
0.023022977635264397,
0.043387703597545624,
-0.023777296766638756,
-0.044307608157396317,
0.02311430498957634,
0.09821802377700806,
-0.008335675112903118,
-0.06769336760044098,
-0.10856955498456955,
-0.009159974753856659,
0.04531224071979523,
-0.03303222730755806,
-0.04079703241586685,
-0.030894897878170013,
-0.04270206019282341,
0.006156536750495434,
0.0769171267747879,
-0.02048085257411003,
0.03496691957116127,
-0.025525640696287155,
0.009418636560440063,
-0.023417124524712563,
0.03635656461119652,
-0.017507800832390785,
-0.01237204484641552,
-0.03959096968173981,
0.029296208173036575,
-0.049181222915649414,
0.04397618770599365,
-0.007500094827264547,
0.0967789962887764,
0.026133056730031967,
0.01348754670470953,
0.01084212027490139,
0.009795429185032845,
-0.045343413949012756,
-0.011895159259438515,
-0.020317381247878075,
-0.04476270452141762,
-0.022096311673521996,
-0.03445041924715042,
0.02357577718794346,
-0.017995193600654602,
-0.033254172652959824,
-0.02550244890153408,
-0.04370664060115814,
0.0074831582605838776,
0.06714990735054016,
0.0439608208835125,
-0.014873887412250042,
0.08870984613895416,
-0.009591486304998398,
0.024678179994225502,
0.016276152804493904,
0.019611189141869545,
-0.03632865846157074,
0.03041660599410534,
-0.025503262877464294,
0.021306173875927925,
-0.01813935674726963,
0.026649288833141327,
0.035737570375204086,
0.054937634617090225,
-0.005199521780014038,
-0.010338916443288326,
-0.017980072647333145,
0.047767676413059235,
0.0336528904736042,
0.01763700321316719,
0.046342357993125916,
-0.03330448269844055,
-0.0204011257737875,
-0.024251766502857208,
-0.02806420996785164,
-0.008048772811889648,
-0.03828606382012367,
0.021332435309886932,
-0.025821728631854057,
0.02865460142493248,
0.05298544093966484,
-0.025815090164542198,
0.04238172993063927,
-0.009923688136041164,
0.03536701202392578,
0.008337683044373989,
0.042686138302087784,
0.07257211208343506,
0.07175525277853012,
-0.015484076924622059,
-0.005730523727834225,
0.05160970985889435,
-0.031223734840750694,
-0.03865363076329231,
0.023671304807066917,
0.038625869899988174,
0.01740902103483677,
0.0017683734185993671,
0.010946282185614109,
-0.03147755563259125,
-0.04116296395659447,
-0.023582084104418755,
-0.021786749362945557,
-0.01061408594250679,
0.032864589244127274,
0.08425083011388779,
0.0011009989539161325,
-0.016983991488814354,
0.02868722565472126,
0.08369606733322144,
0.0003444774483796209,
-0.04627937078475952,
-0.017314450815320015,
0.05324738100171089,
-0.006284297909587622,
-0.03503844887018204,
0.020442944020032883,
-0.0083722909912467,
-0.016206877306103706,
-0.029122622683644295,
-0.03254157677292824,
0.0243840254843235,
-0.042997971177101135,
-0.01287867221981287,
-0.034132231026887894,
-0.005092666018754244,
0.006715184077620506,
0.05014284700155258,
-0.0009123592753894627,
-0.017896898090839386,
-0.0730469599366188,
-0.002453080378472805,
-0.03340007737278938,
-0.002388900611549616,
-0.02996916137635708,
0.0019663346465677023,
-0.011507933959364891,
0.008498935028910637,
-0.004202445037662983,
-0.028541361913084984,
0.009253736585378647,
0.0034579141065478325,
0.014883299358189106,
0.0016079472843557596,
-0.03389608860015869,
0.0021275090985000134,
-0.012323201633989811,
-0.046585533767938614,
0.05609066039323807,
-0.09434781223535538,
-0.06900365650653839,
0.03851339593529701,
0.01750832237303257,
-0.022157927975058556,
-0.04678558185696602,
-0.007278156001120806,
0.046789009124040604,
-0.02993139438331127,
0.020580116659402847,
0.006254551000893116,
0.052730511873960495,
0.02768760733306408,
0.006577837280929089,
0.02703891694545746,
-0.0735524445772171,
-0.025986323133111,
0.02307782880961895,
-0.008538400754332542,
0.017259180545806885,
-0.07803643494844437,
-0.05881856009364128,
-0.05678544566035271,
0.03658990189433098,
0.026985902339220047,
-0.014574040658771992,
0.03180473670363426,
-0.041605930775403976,
0.0325261689722538,
-0.008009685203433037,
-0.013080273754894733,
0.002664829371497035,
0.019079146906733513,
0.0027954434044659138,
-0.05269087478518486,
-0.054659631103277206,
-0.0030499796848744154,
-0.06033655256032944,
-0.029934082180261612,
-0.018816927447915077,
-0.009697666391730309,
-0.016186119988560677,
-0.02448221854865551,
0.0032135574147105217,
0.02436811290681362,
-0.022533366456627846,
-0.00886906310915947,
-0.049600519239902496,
0.024422433227300644,
-0.025203656405210495,
0.04594114422798157,
0.08141611516475677,
0.030183497816324234,
0.007801720406860113,
-0.08879665285348892,
-0.017970358952879906,
0.0064265187829732895,
-0.013252491131424904,
-0.03357807174324989,
0.01403927430510521,
-0.025918828323483467,
0.01302095502614975,
0.08013495802879333,
-0.027928944677114487,
-0.011500240303575993,
-0.06571792811155319,
-0.09448250383138657,
0.044211894273757935,
0.05115349590778351,
-0.06418656557798386,
0.007242338266223669,
0.014379996806383133,
0.02160610444843769,
-0.011892185546457767,
-0.05630793049931526,
-0.0022730291821062565,
0.01044628769159317,
-0.047807835042476654,
0.018436633050441742,
-0.0280368123203516,
-0.0312457587569952,
-0.01434267032891512
] |
<p>I know QFT at graduate level but I'll like to master the skill of working with Feynman diagrams. I'm looking for a book of solved exercises on this topic. </p>
<p>Specifically, I'm looking for the kind of repetitive exercises, just like in elementary school you have to do e.g. 10 multiplications, 10 divisions, etc. I haven't found anything like that.</p>
<p>The topics I'm interested in are, for example, calculating invariant amplitudes, cross sections, etc. from Feynman diagrams, computing the Feynman rules from some Lagrangian theory and calculating the lower order tree expansion, etc.</p> | g12 | [
0.039924148470163345,
0.0045522479340434074,
0.0006862565060146153,
-0.08004900813102722,
-0.006747199688106775,
-0.0618102066218853,
0.021775497123599052,
0.03564953804016113,
0.012662738561630249,
0.03616146370768547,
-0.028375977650284767,
-0.008455588482320309,
-0.014463240280747414,
0.004996285308152437,
-0.02841140329837799,
0.03853537514805794,
-0.031559813767671585,
0.03107943758368492,
-0.015904132276773453,
-0.00974662322551012,
0.005127971991896629,
0.08852262794971466,
-0.0021448119077831507,
0.002952423645183444,
-0.047176189720630646,
-0.015254339203238487,
-0.009602667763829231,
-0.00934560876339674,
-0.05576013773679733,
-0.05061385780572891,
-0.06013699620962143,
-0.03229740634560585,
0.023663613945245743,
-0.06862024962902069,
-0.013869371265172958,
0.02545192465186119,
0.020342670381069183,
-0.06400143355131149,
0.05063513293862343,
0.031054243445396423,
0.04927719384431839,
-0.05490085482597351,
-0.025179848074913025,
0.024247396737337112,
-0.05102759599685669,
0.0053834253922104836,
-0.012285660021007061,
0.03642416000366211,
-0.045887090265750885,
-0.002014655852690339,
0.008236965164542198,
-0.0021549868397414684,
0.10974384099245071,
-0.01745348982512951,
0.0019951844587922096,
0.03504904732108116,
-0.03638783097267151,
-0.00215076538734138,
0.0554821603000164,
0.007264712825417519,
0.039661917835474014,
0.016259871423244476,
-0.0027346292044967413,
-0.04086761921644211,
0.06809686124324799,
-0.013844865374267101,
-0.0004648984468076378,
-0.045149218291044235,
0.01759159192442894,
0.024572117254137993,
0.02172156423330307,
-0.06102655455470085,
0.0036061499267816544,
0.030366037040948868,
0.02696702443063259,
0.014795142225921154,
-0.005619202274829149,
-0.017044801265001297,
0.05577089637517929,
0.0180464219301939,
-0.11841270327568054,
-0.02920154482126236,
-0.0035290534142404795,
0.013997623696923256,
0.047583721578121185,
-0.016305137425661087,
-0.0033910705242305994,
0.010824940167367458,
-0.0019749579951167107,
-0.0026348086539655924,
0.012924711219966412,
0.051787033677101135,
0.040160730481147766,
-0.005666650831699371,
-0.010530530475080013,
-0.039987772703170776,
0.010994620621204376,
0.022994963452219963,
-0.05240251496434212,
-0.02501380443572998,
-0.07619504630565643,
0.00768729904666543,
0.03350088372826576,
-0.00015156654990278184,
-0.06618835031986237,
-0.017456714063882828,
0.018174385651946068,
-0.03443269431591034,
0.020761271938681602,
0.04552704095840454,
-0.038529880344867706,
0.023797662928700447,
-0.02887279912829399,
0.011632335372269154,
-0.026930006220936775,
0.031272586435079575,
0.02368546463549137,
-0.06255672872066498,
-0.002333220560103655,
0.05324278399348259,
0.020997829735279083,
-0.008579118177294731,
0.047675780951976776,
-0.020236225798726082,
0.03559555113315582,
-0.0033814285416156054,
-0.05957244709134102,
0.029519015923142433,
-0.03831028938293457,
-0.02509119175374508,
0.07052450627088547,
0.015011554583907127,
-0.0345022976398468,
0.03432372957468033,
-0.02697010338306427,
0.07411505281925201,
0.008072600699961185,
0.015358245931565762,
0.048396021127700806,
-0.038918595761060715,
-0.008092301897704601,
-0.03441346809267998,
-0.04381458833813667,
-0.024500101804733276,
0.033289626240730286,
0.014916077256202698,
0.027934124693274498,
-0.02478725276887417,
-0.03821934759616852,
0.0400179959833622,
-0.00861714780330658,
0.006526593118906021,
0.021121039986610413,
-0.00023524643620476127,
0.03784593939781189,
0.010281496681272984,
0.06514842808246613,
0.017938630655407906,
0.006584460381418467,
-0.03463408350944519,
-0.003943773452192545,
0.0076552401296794415,
-0.013764305971562862,
0.0043830061331391335,
0.0036478147376328707,
0.06626170873641968,
-0.01830938830971718,
-0.04727606102824211,
0.0260957982391119,
-0.020642897114157677,
-0.035676319152116776,
-0.041146811097860336,
0.077569380402565,
0.08844786137342453,
-0.04719305410981178,
0.07124075293540955,
-0.005300484132021666,
-0.03375103697180748,
-0.02384944260120392,
0.015638718381524086,
-0.0018515957053750753,
-0.01446874812245369,
0.04217447340488434,
0.0030710690189152956,
-0.0693272203207016,
0.024617621675133705,
-0.04429589956998825,
0.04705765098333359,
-0.05353087559342384,
-0.03685829043388367,
-0.0008454482886008918,
0.047348879277706146,
-0.012423718348145485,
0.02818010188639164,
-0.00414231838658452,
-0.045457348227500916,
-0.02583400532603264,
-0.020518051460385323,
-0.013059478253126144,
-0.022309741005301476,
0.034409310668706894,
0.000732303480617702,
0.067515529692173,
0.03945016488432884,
0.04836126044392586,
0.05219019576907158,
-0.06425000727176666,
-0.03636102005839348,
0.08106714487075806,
-0.006475002970546484,
0.01518996898084879,
0.00880676880478859,
0.07255833595991135,
0.04459337890148163,
0.02613339014351368,
-0.005323362071067095,
-0.019931921735405922,
-0.008172908797860146,
0.012665766291320324,
0.004329593852162361,
0.0723847895860672,
-0.03676058351993561,
-0.0343504473567009,
0.008839504793286324,
0.021497435867786407,
0.02918259985744953,
0.00008159435674315318,
0.02237200364470482,
-0.0063734701834619045,
-0.0030158122535794973,
-0.10510846227407455,
0.040875744074583054,
-0.04363693296909332,
-0.032294273376464844,
0.03272470086812973,
-0.02494252845644951,
-0.023236673325300217,
-0.020838813856244087,
0.034317247569561005,
0.0731518492102623,
0.008608904667198658,
0.05786355584859848,
0.037565529346466064,
-0.02883448451757431,
0.00436434056609869,
-0.04884765297174454,
0.030178450047969818,
0.020532764494419098,
0.003264149185270071,
0.04287327080965042,
0.03262549266219139,
-0.0057661100290715694,
-0.02487420290708542,
0.0015395936788991094,
-0.04011708125472069,
0.045305464416742325,
0.01761499047279358,
0.01018280815333128,
0.043456923216581345,
0.0038753969129174948,
0.005351757165044546,
0.009441239759325981,
-0.02103968895971775,
0.03160973638296127,
-0.06191414222121239,
-0.06895560026168823,
0.0021871905773878098,
-0.05143798142671585,
-0.03211621940135956,
-0.052559446543455124,
-0.03918004781007767,
0.01763749308884144,
0.01582326926290989,
-0.029110614210367203,
0.020182646811008453,
-0.02486400678753853,
0.05369710922241211,
0.028939440846443176,
-0.0035185583401471376,
0.004883636254817247,
0.021850142627954483,
-0.06636020541191101,
-0.0165124349296093,
0.06510309875011444,
0.035929277539253235,
-0.019025489687919617,
-0.004833298269659281,
-0.0057387398555874825,
0.0014206251362338662,
0.022594526410102844,
-0.0003834674134850502,
-0.03831310197710991,
0.0265528354793787,
-0.020662708207964897,
-0.11418160051107407,
-0.00492719653993845,
0.01868932694196701,
-0.0038428641855716705,
-0.04889716953039169,
0.0020760989282280207,
-0.04324852302670479,
0.0498441606760025,
0.08662083745002747,
-0.022244712337851524,
0.040978074073791504,
-0.017463792115449905,
-0.03935074061155319,
-0.03062886744737625,
0.0008481535478495061,
0.016305003315210342,
-0.030228734016418457,
-0.044035132974386215,
-0.018444964662194252,
0.030602190643548965,
-0.003134191734716296,
-0.002031125361099839,
-0.020628441125154495,
0.046484243124723434,
0.08659398555755615,
-0.060142576694488525,
-0.04661121219396591,
-0.0298179741948843,
0.08794048428535461,
-0.06158655509352684,
0.038641173392534256,
0.0011972442734986544,
0.007880407385528088,
-0.051774762570858,
-0.0425555557012558,
-0.041523270308971405,
0.006307889241725206,
-0.03867756202816963,
0.042384933680295944,
0.008889757096767426,
-0.017437731847167015,
-0.07513626664876938,
-0.04860560595989227,
-0.058989014476537704,
0.00046014905092306435,
-0.027974283322691917,
0.031175026670098305,
-0.046295374631881714,
-0.045950356870889664,
-0.02236074022948742,
-0.00002380671321589034,
-0.025717221200466156,
-0.008307242766022682,
0.021741855889558792,
0.046140801161527634,
-0.031207794323563576,
0.020251324400305748,
0.013417134061455727,
0.03044160269200802,
0.014835321344435215,
0.013612119480967522,
0.006544402800500393,
-0.013521073386073112,
-0.029350319877266884,
0.03347193822264671,
-0.020486950874328613,
-0.022617343813180923,
0.019501112401485443,
-0.07620197534561157,
0.065731942653656,
-0.03185587376356125,
-0.0036301722284406424,
-0.0061088381335139275,
0.0703107938170433,
0.006171179935336113,
0.0059220013208687305,
-0.003043076256290078,
0.058713000267744064,
0.027113575488328934,
0.025290001183748245,
-0.07629171013832092,
0.00915379635989666,
0.0027917071711272,
0.015336601994931698,
-0.004416280891746283,
-0.02692963182926178,
-0.04925503954291344,
0.0035751957911998034,
-0.011071345768868923,
0.0034736832603812218,
0.019137533381581306,
0.02773885615170002,
-0.026970719918608665,
0.011076847091317177,
-0.041633620858192444,
0.02299286611378193,
0.0681990459561348,
-0.060466472059488297,
-0.03323785215616226,
0.026260579004883766,
0.01509315799921751,
-0.07112984359264374,
0.053487107157707214,
0.008738736622035503,
-0.0015626477543264627,
0.03962410241365433,
0.030277367681264877,
-0.01209917850792408,
0.012610943987965584,
0.011408149264752865,
-0.013074032962322235,
-0.015246497467160225,
0.019465046003460884,
0.021407462656497955,
0.039973076432943344,
-0.028677476570010185,
-0.004383798222988844,
0.013336903415620327,
0.023013370111584663,
-0.029830697923898697,
0.022713903337717056,
0.0021418710239231586,
0.022409847006201744,
-0.07804570347070694,
0.010389531031250954,
-0.031133517622947693,
0.0017576997634023428,
0.029176633805036545,
-0.00042681998456828296,
-0.014861324802041054,
0.028176359832286835,
0.031894002109766006,
0.006595858838409185,
-0.010912460274994373,
0.018783675506711006,
-0.03845126926898956,
-0.003761457046493888,
-0.06478630006313324,
-0.02247915044426918,
-0.02876306138932705,
-0.006679608020931482,
-0.03947407007217407,
-0.014108024537563324,
0.06862425804138184,
-0.0034150953870266676,
0.040295492857694626,
0.03099226951599121,
-0.00948091596364975,
0.020672887563705444,
-0.020045747980475426,
-0.03954147920012474,
0.067050501704216,
-0.03969203308224678,
-0.03961321711540222,
0.013282394036650658,
0.017852718010544777,
0.03829047828912735,
0.01174511481076479,
0.032766327261924744,
0.004445374943315983,
-0.04681460186839104,
-0.10461563616991043,
-0.028327874839305878,
-0.021406210958957672,
0.10021225363016129,
0.006074721459299326,
-0.04695314168930054,
0.0020735638681799173,
-0.0027896296232938766,
0.024552999064326286,
-0.0047049918211996555,
0.01808282732963562,
-0.03589045628905296,
0.048565637320280075,
-0.02498791366815567,
0.002501591807231307,
0.024529453366994858,
-0.001530245877802372,
0.06992502510547638,
-0.02550344727933407,
0.04979516938328743,
0.013547590002417564,
-0.036117494106292725,
-0.024708189070224762,
0.0347110889852047,
-0.008996550925076008,
-0.010840857401490211,
-0.008758114650845528,
0.0007243171567097306,
0.03734327480196953,
0.006142132915556431,
-0.044695742428302765,
0.02963661216199398,
-0.012592984363436699,
-0.003459946485236287,
-0.07586925476789474,
0.0017261949833482504,
-0.04351130500435829,
0.06845502555370331,
0.02105133980512619,
-0.018902435898780823,
-0.040585145354270935,
0.05490545928478241,
0.004180870484560728,
-0.0019489875994622707,
-0.0034084925428032875,
0.007482455112040043,
0.0017657862044870853,
-0.03837703913450241,
-0.0489482581615448,
0.029069337993860245,
0.03941401466727257,
-0.020235832780599594,
-0.01106314454227686,
-0.02056998573243618,
0.01809260994195938,
-0.010601130314171314,
-0.005183670669794083,
0.022985853254795074,
0.05428733304142952,
0.03467154502868652,
0.017452780157327652,
-0.04338925704360008,
0.001561008975841105,
-0.018122602254152298,
-0.023776041343808174,
0.06592980772256851,
-0.027041759341955185,
-0.02380354143679142,
-0.00970680546015501,
0.056599292904138565,
-0.025158263742923737,
-0.05047839134931564,
-0.039053596556186676,
-0.022006653249263763,
0.05073807016015053,
0.05325595661997795,
0.01926770620048046,
-0.056929346174001694,
0.004533560946583748,
-0.045089300721883774,
0.026373863220214844,
0.004284122493118048,
-0.043700527399778366,
0.004728746134787798,
0.08173782378435135,
0.050568342208862305,
0.026043595746159554,
0.02641701139509678,
0.002413789741694927,
0.014236688613891602,
-0.029583796858787537,
0.0047050886787474155,
-0.009047318249940872,
0.04250532388687134,
-0.014241511933505535,
-0.0394384004175663,
-0.04602822661399841,
0.002474511042237282,
-0.07749485969543457,
-0.017185555770993233,
0.05789661407470703,
-0.03649180382490158,
-0.03013920970261097,
0.017134517431259155,
0.04194921627640724,
0.04463908076286316,
-0.05188274011015892,
0.01068129763007164,
-0.010911804623901844,
-0.024738872423768044,
-0.0016300624702125788,
-0.017196793109178543,
0.02121277153491974,
0.05493323877453804,
0.055671513080596924,
0.0057136924006044865,
-0.02355578914284706,
-0.016148226335644722,
0.030059047043323517,
0.022654838860034943,
0.032226644456386566,
0.02732873149216175,
-0.07225199043750763,
0.024146344512701035,
-0.02252175286412239,
0.0026604444719851017,
0.1048412173986435,
0.04067125543951988,
-0.05796714872121811,
0.0014608963392674923,
0.07299856096506119,
-0.021834013983607292,
0.023640528321266174,
0.007874694652855396,
0.03157127648591995,
-0.03907756507396698,
0.049283467233181,
-0.05653506517410278,
-0.03585371747612953,
0.06151891127228737,
0.002687641652300954,
0.0887441486120224,
0.021114367991685867,
0.021585237234830856,
0.027620138600468636,
0.0343930721282959,
0.03014433942735195,
0.009457518346607685,
-0.02592470496892929,
0.024432340636849403,
0.059358786791563034,
-0.03556470200419426,
0.03161078318953514,
0.0025638022925704718,
-0.029088344424962997,
0.017717871814966202,
-0.01358603872358799,
-0.018860407173633575,
0.001254873932339251,
-0.007915779948234558,
-0.04541663080453873,
0.0048570046201348305,
0.06034109368920326,
-0.02505330555140972,
0.0023427086416631937,
0.006815315689891577,
-0.027048280462622643,
-0.02587021328508854,
-0.04051048681139946,
-0.036167390644550323,
0.06062143296003342,
0.04649635776877403,
0.015111331827938557,
0.021731600165367126,
-0.0520845390856266,
-0.04700617864727974,
0.029138080775737762,
0.05023520439863205,
0.01060582511126995,
-0.0388699471950531,
0.03823431581258774,
-0.052807167172431946,
-0.006572760175913572,
0.003943784162402153,
0.04013102129101753,
-0.08857370167970657,
-0.0014858744107186794,
0.07993665337562561,
-0.027917560189962387,
0.05479668825864792,
-0.06864138692617416,
-0.002354381140321493,
-0.00426910538226366,
-0.08233427256345749,
-0.003383631817996502,
0.0692393109202385,
-0.022638961672782898,
-0.01636195369064808,
-0.018933484330773354,
-0.02638806402683258,
0.0012660347856581211,
0.018516672775149345,
-0.019826602190732956,
0.018338819965720177,
-0.023025326430797577,
0.0009876618860289454,
0.013149736449122429,
0.04057079553604126,
0.020618392154574394,
-0.028719328343868256,
0.02300252392888069,
0.0035215853713452816,
-0.007218335289508104,
0.008104804903268814,
-0.010886860080063343,
-0.030977675691246986,
0.008186772465705872,
-0.06580065935850143,
0.04270615056157112,
0.025034504011273384,
-0.006500680465251207,
-0.0329584963619709,
0.02797681652009487,
-0.01325302105396986,
-0.030043402686715126,
-0.04928357154130936,
-0.009126228280365467,
-0.030194072052836418,
-0.016561485826969147,
-0.023330073803663254,
-0.025186758488416672,
-0.041346557438373566,
0.02871176041662693,
0.014616861939430237,
0.038304753601551056,
-0.005968563258647919,
0.02813001722097397,
-0.038353439420461655,
-0.02204052545130253,
-0.011352353729307652,
-0.021199334412813187,
0.04125591740012169,
-0.05816098675131798,
0.025146637111902237,
0.013265298679471016,
0.026206612586975098,
-0.03084266185760498,
-0.02537279576063156,
-0.02210789918899536,
0.036089204251766205,
-0.013346433639526367,
0.011746481992304325,
-0.051699284464120865,
-0.002976766088977456,
-0.029280219227075577,
0.035374440252780914,
0.04272865504026413,
0.009275111369788647,
0.007013124413788319,
0.01610475778579712,
0.02306682989001274,
-0.05457072705030441,
0.017824703827500343,
0.012458051554858685,
-0.01941225491464138,
0.01622512936592102,
0.008114928379654884,
0.012571146711707115,
-0.025714820250868797,
0.025275306776165962,
-0.06709308922290802,
-0.0053786770440638065,
0.032464124262332916,
-0.010752633213996887,
0.01013670302927494,
0.04853228107094765,
-0.04215903952717781,
-0.0027413044590502977,
0.050073396414518356,
0.034701935946941376,
-0.030040550976991653,
-0.011459043249487877,
-0.06247444078326225,
0.01929611898958683,
0.028979936614632607,
0.049997612833976746,
-0.01737954095005989,
-0.011449378915131092,
-0.013920314610004425,
0.00759420869871974,
-0.09032636135816574,
-0.0480889193713665,
-0.03343523293733597,
0.045786745846271515,
-0.00876349862664938,
-0.05856823921203613,
0.011482489295303822,
0.05472288280725479,
0.015376820228993893,
-0.00038952441536821425,
-0.001249263877980411,
-0.01623871922492981,
0.024688897654414177,
0.06814108788967133,
0.0017408800777047873,
-0.06345783919095993,
-0.00006476639828179032,
0.051358386874198914,
-0.008023439906537533,
-0.03263392299413681,
-0.03993065282702446,
-0.003059913869947195,
-0.014949296601116657
] |
<p>These are some further important queries regarding the question here <a href="http://physics.stackexchange.com/questions/102910/why-would-spacetime-curvature-cause-gravity">Why would spacetime curvature cause gravity?</a></p>
<p>Q1. Explain the statement “Everything in spacetime moves at the speed of light”. Is this statement even true or false? My naïve understanding is as follows: If an object is stationary in space (relative to an observer?) then it will be moving in time, so, it will, say, move from (x=0,t=0) to (x=0,t=10). The velocity is the space interval / time interval, which from above coordinates is still zero. So it is moving through spacetime, but at zero velocity. So velocity will just determine the angle of its path to the time axis. If this angle is zero, ie it is moving parallel to the time axis, then velocity = zero, and it can really move in time from one time point to the other at zero velocity. Where am I wrong, and what is the real explanation?</p>
<p>Q2. Suppose there are two objects (see fig), an apple A above the earth at x=0, and the earth E at x=10 as shown in the fig. If there is no earth and just the apple in open space, then the spacetime is not curved due to the gravity of the earth, and the apple stays at x=0 but moves in time from A to B (fig a). Now the earth is at x=10 and presumably the spacetime curves and the axes tilt as in fig b. Then the apple moves from A to C, just following the geodesic. But if we assume this, then the apple has not moved at all, because, due to the tilt of the axis, point C is also at x=0. So fig b cannot be the correct situation, otherwise the apple will arrive at point C which is still on the x=0 axis.
So I assume that in fact the apple has not moved from A to C in fig b, but has moved from A to D in fig. a, where D is really at x=10. But if I assume this, then it is not spacetime itself that has curved. The spacetime is still straight, but the apple has moved from (x=0,t=0) to (x=10,t=10). Again, where am I wrong, and what is the correct explanation? How exactly has the spacetime curved or tilted for the apple at A due to the presence of the Earth at E, and how does the apple move to the earth by following the geodesic in free fall? (assume only one spatial dimention)</p>
<p><img src="http://i.stack.imgur.com/9QQXe.png" alt="spacetime curved by gravity?"></p>
<p>Q3: We say that gravity is not just a “force of attraction” between two pieces of mass, and it does not “pull” the two pieces of mass towards each other. Instead, acceleration is manifested because the two pieces of mass are simply following their now curved geodesics. But it can be shown that there really is an attractive force due to gravity. E.g. Take the apple in the earth’s gravity and suspend it on a spring balance. The spring will extend. Yes, you can say that since it is suspended motionless, so it is no longer in free fall, and since the spring balance exerts an external force upwards on the apple, so it no longer follows its free fall geodesic. But it is not only the spring balance which is exerting an upward force on the apple. The apple is also exerting a downward force on the spring, which causes the spring to extend. Surely it is too naïve to say that the downward force which the earth exerts on the apple and in turn the apple exerts on the spring suddenly vanishes if the apple is released into free fall. </p>
<p>If two masses were remotely attracting each other with a force, why would they cease to attract each other with a force when in free fall? It is logically a much more satisfying explanation that the gravitational attraction force which was there at rest remains in free fall too and it is this gravitational attraction force which causes the freefall acceleration by F=ma, just like any force on any object would cause an acceleration. Also, it is the net force on the object which causes the acceleration. When the object was suspended, the net force was zero, so acceleration was zero. When in free fall, the net force IS THE GRAVITATIONAL ATTRACTION FORCE, so acceleration is accordingly. This seems totally opposite to the statement that there is no gravitational force in free fall. </p>
<p>The reason why the spring of the spring balance does not extend when in free fall is that there IS a gravitational force downwards, but there is no force exerted by the spring upwards, so the net force on the object is downwards due to gravity, which causes the acceleration F=ma. Where am I wrong? What is the correct explanation?</p> | g1262 | [
0.08861338347196579,
0.042651694267988205,
-0.0029287850484251976,
0.010618207976222038,
0.03212736174464226,
0.061444900929927826,
0.10661469399929047,
0.0032616225071251392,
-0.10040071606636047,
0.0007483405061066151,
0.0016158868093043566,
-0.01231571938842535,
0.07257460057735443,
0.04673872888088226,
-0.052478525787591934,
-0.0014118690742179751,
0.033065129071474075,
0.014147068373858929,
0.0013389785308390856,
-0.004396113567054272,
0.020765341818332672,
0.0013175599742680788,
0.021628065034747124,
-0.03937515243887901,
-0.05337011441588402,
0.0011895332718268037,
0.018566878512501717,
-0.0023169671185314655,
-0.053758181631565094,
-0.0359775684773922,
0.006124419625848532,
0.06318322569131851,
-0.012546255253255367,
-0.054573122411966324,
-0.011894973926246166,
-0.07646843045949936,
0.02007795311510563,
0.0014186914777383208,
0.005588747560977936,
0.03572063520550728,
-0.03752189129590988,
-0.01722668670117855,
-0.014170119538903236,
0.03686473146080971,
0.04155465215444565,
0.04805847257375717,
0.015579775907099247,
0.02864769473671913,
0.05291549116373062,
-0.02946213074028492,
-0.00039724030648358166,
0.04729905351996422,
0.009835527278482914,
-0.043869003653526306,
-0.06937780976295471,
0.030296504497528076,
0.05053623393177986,
0.015794094651937485,
0.02488473802804947,
0.0609426312148571,
-0.053309373557567596,
-0.007701545022428036,
0.06323191523551941,
-0.0014834654284641147,
0.009394597262144089,
0.03016703575849533,
-0.01546110026538372,
-0.06345765292644501,
0.02317027375102043,
-0.016414016485214233,
0.016187895089387894,
-0.06973277777433395,
-0.030190665274858475,
-0.04105795919895172,
-0.04122580587863922,
0.03571302071213722,
0.028191322460770607,
0.004639297258108854,
-0.005425609648227692,
-0.03955520689487457,
0.0025729851331561804,
0.05633971095085144,
-0.000728839950170368,
0.01726873219013214,
0.04108353331685066,
-0.04277836158871651,
-0.050004489719867706,
0.008761415258049965,
-0.018221082165837288,
-0.010599721223115921,
0.03539956361055374,
-0.020236128941178322,
0.041900016367435455,
0.018414903432130814,
-0.04612255468964577,
-0.059220634400844574,
-0.02117995359003544,
0.054342109709978104,
0.007467738352715969,
0.04120619595050812,
-0.04524161294102669,
-0.04008520022034645,
0.026223761960864067,
0.05382026731967926,
0.04883115738630295,
-0.010997002944350243,
-0.00179040536750108,
0.035039711743593216,
-0.0032892567105591297,
-0.04501781612634659,
-0.0039050213526934385,
0.014016539789736271,
0.004897580947726965,
-0.025420116260647774,
-0.05476723611354828,
-0.03551197424530983,
0.0569818913936615,
0.02193501777946949,
-0.0021066786721348763,
0.05582182854413986,
-0.05595070496201515,
0.09739650785923004,
0.03325803205370903,
0.05360814556479454,
-0.037414878606796265,
-0.0495939627289772,
-0.008356628939509392,
-0.032927706837654114,
-0.030304552987217903,
0.001210101880133152,
-0.04790325090289116,
0.004900997970253229,
-0.04551004245877266,
0.011567137204110622,
-0.005454270169138908,
0.006220411974936724,
-0.030627798289060593,
-0.019070107489824295,
-0.010129591450095177,
0.013887098990380764,
0.011645209975540638,
-0.013733546249568462,
0.03845379501581192,
-0.02765600197017193,
-0.06473670899868011,
0.013644922524690628,
0.010906694456934929,
0.038326095789670944,
0.09514927119016647,
0.004948983900249004,
-0.02984672039747238,
0.086864173412323,
-0.03751734644174576,
-0.03429887816309929,
0.04375889524817467,
-0.029337426647543907,
-0.036079417914152145,
-0.03968704119324684,
0.0356360487639904,
-0.007022941950708628,
0.08314451575279236,
0.022998761385679245,
0.014026806689798832,
-0.00824262946844101,
-0.02075088955461979,
0.055984336882829666,
-0.038197699934244156,
-0.04953500255942345,
-0.00813013594597578,
-0.06259351223707199,
-0.09573651105165482,
-0.045095305889844894,
0.017307952046394348,
0.06941378116607666,
-0.00980132445693016,
-0.02611207403242588,
0.04778001084923744,
-0.03210672363638878,
-0.027172043919563293,
0.007655170280486345,
0.01901639625430107,
-0.04457045719027519,
0.0005672827828675508,
-0.020322391763329506,
-0.03733082860708237,
-0.02639441378414631,
-0.034027256071567535,
0.015069509856402874,
-0.06737883388996124,
0.018345586955547333,
-0.008278685621917248,
-0.07775057107210159,
-0.022744884714484215,
0.024846311658620834,
0.013202676549553871,
0.003090004902333021,
0.039251793175935745,
0.012630410492420197,
-0.023079104721546173,
0.061505578458309174,
-0.03551105037331581,
-0.02117622084915638,
0.011690850369632244,
0.006961521692574024,
0.011904643848538399,
0.031048240140080452,
0.003301783697679639,
-0.00557858869433403,
0.005633009597659111,
0.003639509668573737,
0.04104043170809746,
-0.021345486864447594,
0.07350850850343704,
-0.015483220107853413,
0.0067259687930345535,
0.05430063232779503,
-0.01715574972331524,
-0.05891728028655052,
0.0013182592811062932,
0.017453614622354507,
0.05030662938952446,
0.000757544650696218,
-0.006664622575044632,
-0.0007104959222488105,
-0.02753729559481144,
-0.034421034157276154,
-0.0710773915052414,
-0.07981386035680771,
-0.03493098169565201,
0.0045539033599197865,
-0.04525192454457283,
-0.027935585007071495,
-0.030267436057329178,
0.01708180457353592,
0.050203949213027954,
0.02920978143811226,
0.021621864289045334,
0.024563858285546303,
0.014269018545746803,
0.008553762920200825,
0.0075491080060601234,
-0.005970294121652842,
-0.021045608446002007,
-0.07454008609056473,
0.03359880670905113,
-0.05717748403549194,
0.030715782195329666,
-0.04038045182824135,
0.008772517554461956,
0.03372080251574516,
-0.013305578380823135,
-0.012591204605996609,
-0.01815398596227169,
0.027656426653265953,
0.044797107577323914,
-0.05660911276936531,
-0.004859762266278267,
0.08310189843177795,
-0.07405582070350647,
-0.00030780411907471716,
-0.017193181440234184,
-0.036698270589113235,
-0.008760247379541397,
0.000018933964383904822,
-0.10310617834329605,
0.0019715516828000546,
-0.028656495735049248,
-0.028491267934441566,
0.008153394795954227,
0.019165126606822014,
-0.061974212527275085,
0.023163355886936188,
-0.025987206026911736,
0.039158355444669724,
0.0350060872733593,
0.00120509450789541,
0.00363914854824543,
0.03903982788324356,
-0.003848473308607936,
0.0067786951549351215,
0.061801690608263016,
-0.004112573806196451,
-0.06588264554738998,
-0.020177654922008514,
0.012937013059854507,
0.004672084003686905,
-0.04745132476091385,
-0.00840104091912508,
0.017275508493185043,
0.033857375383377075,
0.011613127775490284,
0.07575619965791702,
-0.0010396318975836039,
-0.014271085150539875,
-0.018622281029820442,
0.04119053855538368,
-0.06034880876541138,
-0.01556561328470707,
-0.05059517174959183,
-0.019966380670666695,
-0.01925763487815857,
0.05361529067158699,
0.04661150276660919,
0.01769140735268593,
0.002212024759501219,
0.009887457825243473,
-0.01812429167330265,
-0.1220594123005867,
-0.02345227263867855,
-0.003287496278062463,
-0.01533353142440319,
0.018173974007368088,
-0.022440433502197266,
0.04188663884997368,
0.01477579865604639,
0.01561750192195177,
-0.051562294363975525,
0.017032288014888763,
-0.0039458065293729305,
0.012188914231956005,
-0.053665563464164734,
0.020769834518432617,
-0.02940460667014122,
-0.0020174398086965084,
0.0053943125531077385,
0.022400055080652237,
0.03128578141331673,
-0.03130733221769333,
-0.029877837747335434,
-0.004325978457927704,
0.06646440178155899,
0.005799505859613419,
0.0183852631598711,
0.014364064671099186,
-0.01621066778898239,
-0.018454866483807564,
0.022676853463053703,
0.01759113371372223,
0.012309124693274498,
0.05616523325443268,
0.002918672515079379,
0.037899453192949295,
-0.08861999958753586,
0.00719881197437644,
0.010977455414831638,
0.051658257842063904,
-0.02280665747821331,
0.004938127938657999,
-0.028450243175029755,
0.04127506911754608,
0.049702733755111694,
-0.027935830876231194,
-0.037003468722105026,
0.0011082403361797333,
-0.014562787488102913,
0.010122288949787617,
-0.027992364019155502,
-0.00699953455477953,
-0.025275863707065582,
-0.016517557203769684,
0.022702403366565704,
-0.002032538875937462,
-0.00036322398227639496,
0.07568991929292679,
0.012038841843605042,
0.0033814581111073494,
0.012154274620115757,
-0.020502353087067604,
-0.025195522233843803,
-0.03979916870594025,
0.045608341693878174,
0.021570835262537003,
-0.05715278163552284,
-0.023674922063946724,
0.02711554989218712,
-0.00966290757060051,
0.03550709784030914,
0.019063275307416916,
-0.06846258044242859,
0.012729842215776443,
0.07234256714582443,
0.027996553108096123,
0.027091821655631065,
0.03267912194132805,
0.06037626415491104,
0.01849399320781231,
-0.07573314011096954,
-0.04102364927530289,
0.0039274850860238075,
-0.05904299393296242,
0.01830197684466839,
-0.03100692480802536,
-0.0026111912447959185,
-0.02171432599425316,
-0.012999720871448517,
-0.022759316489100456,
0.022964706644415855,
0.0653931275010109,
0.005725419614464045,
0.010957280173897743,
-0.004630969371646643,
0.053925637155771255,
-0.028230391442775726,
-0.00567594263702631,
-0.005643057636916637,
0.04016320779919624,
0.015674354508519173,
-0.04337821528315544,
0.011939438991248608,
0.048131152987480164,
0.0361965112388134,
0.05737186595797539,
-0.010996083728969097,
-0.059662386775016785,
0.020811686292290688,
0.011669814586639404,
0.003092988394200802,
-0.011853255331516266,
0.02132275141775608,
-0.05784234404563904,
0.016786133870482445,
0.009154499508440495,
-0.002740101423114538,
-0.03571424260735512,
0.037853747606277466,
0.1200651228427887,
0.00731131574138999,
-0.02383815124630928,
-0.056780677288770676,
-0.021169280633330345,
-0.008571762591600418,
0.000164231940289028,
0.006070663686841726,
0.024909446015954018,
-0.00613574031740427,
0.09859815984964371,
0.022511309012770653,
0.11332441121339798,
-0.006319780368357897,
-0.02898622490465641,
0.05558628961443901,
0.028198936954140663,
0.01311217900365591,
-0.021680697798728943,
0.013786920346319675,
0.003668044460937381,
-0.04663160815834999,
-0.045613955706357956,
0.004892307333648205,
-0.011787276715040207,
-0.011392589658498764,
0.06028423458337784,
-0.0005726703675463796,
-0.012153812684118748,
-0.013899700716137886,
0.0012756215874105692,
-0.019591638818383217,
0.00842584390193224,
0.0027752071619033813,
0.03945683687925339,
-0.062487367540597916,
0.005933041218668222,
0.030063914135098457,
-0.0054924748837947845,
0.02353019081056118,
-0.025854414328932762,
-0.011075608432292938,
-0.06158195436000824,
-0.0303544569760561,
-0.010757030919194221,
-0.04302855581045151,
0.0033248597756028175,
-0.039292532950639725,
0.03349820524454117,
0.016968850046396255,
0.08295221626758575,
-0.016572030261158943,
0.006798082496970892,
-0.023196522146463394,
-0.05685720965266228,
-0.0377177819609642,
-0.01727256551384926,
0.035614125430583954,
-0.048357997089624405,
-0.006752490531653166,
-0.03279384598135948,
-0.005509787704795599,
0.013198157772421837,
0.034415148198604584,
-0.041573647409677505,
0.042140569537878036,
-0.051645126193761826,
-0.013829323463141918,
-0.027966322377324104,
-0.02389872632920742,
-0.004804397001862526,
-0.03168889507651329,
0.05185392498970032,
-0.01565956510603428,
-0.0321655198931694,
-0.0533297173678875,
0.02631971798837185,
0.010503475554287434,
0.014591447077691555,
0.022761235013604164,
0.008498115465044975,
0.017817359417676926,
0.025031959637999535,
-0.05341440066695213,
0.09196172654628754,
0.023245621472597122,
0.0526767298579216,
-0.01610887609422207,
0.010081545449793339,
0.09799585491418839,
-0.020772716030478477,
0.015111676417291164,
0.004909649956971407,
0.013245007954537868,
0.009375880472362041,
-0.002945316256955266,
-0.01899770274758339,
-0.012178906239569187,
-0.021261919289827347,
0.06223476678133011,
0.023526152595877647,
-0.018128756433725357,
0.026291584596037865,
0.03191603347659111,
-0.024700233712792397,
0.028966916725039482,
-0.015808025375008583,
0.06498865783214569,
-0.004665844142436981,
-0.016390955075621605,
-0.017789244651794434,
0.0627603530883789,
-0.021385828033089638,
0.08787908405065536,
-0.008704169653356075,
-0.06432761996984482,
-0.03404175490140915,
-0.0017788654658943415,
0.052119120955467224,
-0.013108369894325733,
0.027183521538972855,
0.02858125977218151,
-0.02171454206109047,
0.02863227017223835,
-0.058398403227329254,
-0.05634020268917084,
0.036450181156396866,
0.026511603966355324,
-0.0037584283854812384,
-0.017727866768836975,
0.026591043919324875,
-0.006776310037821531,
-0.033561091870069504,
0.0051253847777843475,
-0.07427077740430832,
0.05494294315576553,
-0.008447331376373768,
0.008201953023672104,
-0.01983240805566311,
-0.017617279663681984,
0.019871551543474197,
0.014650857076048851,
-0.03682471811771393,
0.05425170063972473,
-0.003267685417085886,
-0.00412113219499588,
0.009630203247070312,
-0.025264635682106018,
0.03818344697356224,
0.009186854586005211,
0.018532633781433105,
-0.02125430665910244,
-0.045769546180963516,
-0.10556062310934067,
0.004021018277853727,
0.035831015557050705,
-0.02665494754910469,
0.009886283427476883,
-0.08123510330915451,
-0.017428232356905937,
0.04034338518977165,
-0.027162885293364525,
-0.010495174676179886,
0.01653197593986988,
-0.03231678903102875,
-0.019642969593405724,
-0.003054832573980093,
-0.00696595897898078,
-0.040091946721076965,
-0.0762886181473732,
-0.007896819151937962,
0.045191921293735504,
0.009279657155275345,
-0.019358079880475998,
0.0077500357292592525,
-0.005603381898254156,
0.025265075266361237,
0.06773275136947632,
-0.0003538415185175836,
0.006509675178676844,
-0.007227903697639704,
-0.02123032510280609,
-0.016577379778027534,
0.044909343123435974,
-0.004963360261172056,
0.0008782621007412672,
0.012560411356389523,
0.02083061821758747,
0.005202428437769413,
-0.0020471420139074326,
-0.018042340874671936,
-0.006358215119689703,
-0.020267577841877937,
-0.035154540091753006,
-0.025355834513902664,
0.036432866007089615,
-0.006657003425061703,
0.02281010150909424,
-0.002388281747698784,
0.019541800022125244,
0.014319181442260742,
-0.001376316067762673,
0.019030751660466194,
0.0012713191099464893,
0.0002659963211044669,
-0.051533933728933334,
0.013822207227349281,
-0.03587459772825241,
0.042032934725284576,
0.03413982689380646,
0.05792543664574623,
0.04163575544953346,
0.029937975108623505,
0.018746448680758476,
0.015153090469539165,
0.05856812745332718,
-0.006932241376489401,
-0.025227375328540802,
0.025088435038924217,
-0.04762003943324089,
-0.03756042569875717,
0.01858539693057537,
-0.03946767747402191,
-0.06254778802394867,
-0.00943622924387455,
0.0007309369975700974,
-0.022020133212208748,
-0.01587427593767643,
0.013657300733029842,
-0.04026052728295326,
-0.029741965234279633,
-0.09192315489053726,
0.005768288858234882,
0.0059411535039544106,
-0.0941944345831871,
-0.03613515943288803,
0.003411364508792758,
-0.00047569736489094794,
0.013531179167330265,
-0.009528026916086674,
0.06480655819177628,
-0.000650377944111824,
0.01055698748677969,
0.011024599894881248,
0.021977271884679794,
0.0010562021052464843,
0.03506859019398689,
0.040837932378053665,
0.004848623648285866,
0.024456439539790154,
0.030950825661420822,
-0.034219659864902496,
0.0114142382517457,
0.014491011388599873,
0.027874357998371124,
0.039451148360967636,
0.043401915580034256,
-0.0024053798988461494,
-0.010771017521619797,
-0.052089810371398926,
-0.012148947454988956,
0.045942120254039764,
0.024275178089737892,
-0.034648243337869644,
-0.0002881234686356038,
0.0009188679978251457,
0.06697160750627518,
-0.07351706176996231,
-0.030380800366401672,
-0.010473580099642277,
0.03179102763533592,
0.004481206182390451,
0.01503224391490221,
-0.0027402739506214857,
0.01643090695142746,
-0.017576515674591064,
-0.03386658430099487,
-0.04811491817235947,
0.018009474501013756,
0.07166070491075516,
0.03413425385951996,
-0.02089669369161129,
-0.014082827605307102,
0.005453038960695267,
0.02282279171049595,
0.06087766960263252,
-0.008642521686851978,
0.0021010227501392365,
-0.05168436840176582,
0.04003441333770752,
-0.022056635469198227,
-0.004893757868558168,
0.026093121618032455,
-0.03533298522233963,
-0.03709651902318001,
-0.05624067410826683,
-0.028555547818541527,
-0.016396304592490196,
-0.08080632239580154,
-0.049552708864212036,
0.04158368706703186,
-0.002728463150560856,
-0.05982764810323715,
-0.03955652937293053,
-0.023834185674786568,
-0.0051345801912248135,
0.005067519377917051,
-0.002424199366942048,
0.03749789670109749,
0.0005184983019717038,
0.03276781365275383,
-0.006044117268174887,
-0.04625852406024933,
-0.01412421278655529,
0.02512170560657978,
-0.04582260549068451,
0.025371896103024483,
-0.04619946703314781,
0.003938102629035711,
0.016034046187996864,
-0.02549724467098713,
0.037755370140075684,
0.07354409247636795,
0.0280618853867054,
-0.0073464410379529,
0.015406633727252483,
0.03293544426560402,
-0.07717007398605347,
0.02889246493577957,
0.027679072692990303,
-0.04613253474235535,
0.02556491643190384,
-0.0002207367797382176,
0.03706178441643715,
-0.013317466713488102,
-0.039042942225933075,
0.009724578820168972,
0.03393770381808281,
-0.001569442800246179,
-0.02489488385617733,
-0.007140894420444965,
-0.025601094588637352,
0.017926083877682686
] |
<p>This is just a quick question. I would figure this out myself if I wouldn't have an exam about this tomorrow.</p>
<p>I am working on the non-relativistic approximation of the Dirac equation for an electron in an EM field. On one point, I need the following relation:</p>
<p>$$
\epsilon^{klm} \sigma^{m} = \sigma^m \epsilon^{mkl}
$$
where $\sigma^m$ denotes the $m$th Pauli matrix and $\epsilon^{klm}$ denotes the Levi-Civita symbol and the Einstein summation convention is used.</p>
<p>The question is: does this relation hold in general for the Levi-Civita symbol or is this specific for the Pauli matrices?</p>
<p>TIA, Eric.</p> | g1263 | [
0.0002598007267806679,
0.005243383813649416,
0.005449837073683739,
-0.0540018267929554,
0.04460439831018448,
-0.023652082309126854,
0.013283084146678448,
0.023542756214737892,
-0.05684845894575119,
0.050583213567733765,
-0.02338680997490883,
0.014342027716338634,
0.0028505821246653795,
0.057929396629333496,
0.0041696070693433285,
-0.04085608199238777,
0.12144725769758224,
0.07306257635354996,
0.004574464168399572,
-0.0469127781689167,
-0.03197174891829491,
0.020054234191775322,
0.0007802110048942268,
0.0013951548608019948,
0.046141743659973145,
-0.06544294208288193,
0.041191477328538895,
-0.020673388615250587,
-0.01663053408265114,
-0.04979897662997246,
0.043819695711135864,
0.012157648801803589,
0.033366747200489044,
-0.07156256586313248,
-0.037362877279520035,
-0.03674445301294327,
0.04105018079280853,
0.05136749520897865,
-0.012379354797303677,
0.03819984197616577,
-0.006166993640363216,
0.007262093015015125,
0.01447266060858965,
0.010279309935867786,
0.032706305384635925,
-0.025555286556482315,
-0.03805679455399513,
0.026346253231167793,
-0.010997306555509567,
-0.030781317502260208,
-0.03456367924809456,
-0.032545194029808044,
0.02302534505724907,
0.05014543980360031,
0.005307583138346672,
-0.0006076934514567256,
0.059528250247240067,
-0.0016883093630895019,
0.0660955011844635,
0.0697130560874939,
0.014468889683485031,
-0.03298963978886604,
0.02200956642627716,
-0.0222846157848835,
0.023798419162631035,
0.030396750196814537,
-0.0004386715590953827,
-0.002506779972463846,
-0.05403571203351021,
-0.009780230931937695,
-0.017513679340481758,
-0.019635332748293877,
0.02146085910499096,
-0.058042529970407486,
0.007968447171151638,
0.0015279006911441684,
-0.005625337362289429,
-0.020055918022990227,
0.10141049325466156,
-0.038037531077861786,
0.004570899996906519,
0.013709965161979198,
0.09546233713626862,
0.010229481384158134,
0.027771346271038055,
0.010435600765049458,
-0.002016468672081828,
0.044216956943273544,
-0.0191416684538126,
0.0327666811645031,
0.0051229046657681465,
-0.017605047672986984,
-0.011312566697597504,
-0.002527934266254306,
-0.0022826476488262415,
-0.040200550109148026,
-0.019332755357027054,
0.03505250811576843,
-0.0092070447281003,
-0.02178330533206463,
0.02625402808189392,
0.010740344412624836,
0.02022387832403183,
-0.0001543460675748065,
0.01888282783329487,
-0.011966777965426445,
-0.04165883734822273,
-0.011808790266513824,
-0.014588763006031513,
-0.012152218259871006,
-0.08921004831790924,
-0.02462654374539852,
-0.019994737580418587,
-0.027873001992702484,
-0.021043434739112854,
-0.0056768120266497135,
0.014648288488388062,
-0.04354456812143326,
-0.007265378721058369,
0.04099540412425995,
-0.0050169192254543304,
-0.007434675935655832,
0.09457121044397354,
-0.0014802550431340933,
-0.0046361093409359455,
0.046635277569293976,
0.008224325254559517,
0.01635097712278366,
0.07065623998641968,
-0.041223764419555664,
0.02502366341650486,
-0.012356623075902462,
0.04081782326102257,
0.012063100002706051,
-0.010015716776251793,
0.012219434604048729,
-0.021426193416118622,
-0.015374000184237957,
0.03038182482123375,
-0.03213837742805481,
-0.03534000366926193,
-0.04921853914856911,
-0.0022166224662214518,
-0.04543754830956459,
-0.06324754655361176,
-0.008765799924731255,
-0.03558668494224548,
-0.02305046282708645,
0.0904247835278511,
0.03505154326558113,
0.012185297906398773,
0.005253833252936602,
-0.03523699566721916,
0.01466191466897726,
0.03487467020750046,
0.029225025326013565,
-0.025406578555703163,
-0.017250211909413338,
-0.031406842172145844,
-0.016728853806853294,
-0.016450561583042145,
0.004424608778208494,
0.03478684648871422,
-0.04609385505318642,
-0.007507015485316515,
-0.023346273228526115,
0.010887254029512405,
-0.028291702270507812,
0.028163306415081024,
-0.05550433322787285,
0.01668815314769745,
-0.00933355838060379,
-0.012819799594581127,
0.0003918735310435295,
-0.01111399382352829,
0.0790410190820694,
-0.0031381123699247837,
-0.00910252146422863,
0.016015589237213135,
0.009696966968476772,
-0.011505704373121262,
-0.021536488085985184,
0.030439486727118492,
-0.033190563321113586,
0.027025219053030014,
-0.003888132981956005,
0.061976924538612366,
0.08044655621051788,
-0.06192604824900627,
-0.04569942504167557,
0.03380376473069191,
-0.024427875876426697,
-0.01332950685173273,
0.03750479593873024,
0.005273351911455393,
0.052055031061172485,
0.006577132735401392,
-0.016240611672401428,
-0.011887874454259872,
0.025100965052843094,
0.019023051485419273,
0.0794106274843216,
-0.050805673003196716,
0.03859659284353256,
0.013669301755726337,
-0.00897158496081829,
-0.038027867674827576,
-0.03544515371322632,
0.07092604041099548,
-0.03132256120443344,
0.012521015480160713,
-0.023813404142856598,
0.012432048097252846,
0.013493184000253677,
-0.03767167404294014,
-0.03304954245686531,
0.0012169990222901106,
-0.009405646473169327,
-0.010955925099551678,
0.07917061448097229,
-0.03623541444540024,
-0.07238341122865677,
0.027676274999976158,
0.006246099714189768,
-0.0061697992496192455,
-0.013981344178318977,
0.046599164605140686,
-0.0005545957828871906,
-0.016331909224390984,
-0.0235936027020216,
-0.07213976234197617,
0.032202694565057755,
-0.0488547682762146,
0.013553906232118607,
0.003838829230517149,
0.016564710065722466,
-0.003927300218492746,
0.020534573122859,
0.03484644368290901,
0.06780748069286346,
0.011207228526473045,
-0.0032973589841276407,
-0.021458134055137634,
0.04343048855662346,
-0.0075760213658213615,
0.03154963254928589,
0.0699913427233696,
-0.020993830636143684,
-0.0554613396525383,
-0.004359839484095573,
-0.06729772686958313,
-0.005540697369724512,
-0.08863262832164764,
0.03131505101919174,
0.055911049246788025,
-0.026635892689228058,
-0.005973799619823694,
-0.012358988635241985,
-0.013004988431930542,
0.03337600454688072,
0.013100458309054375,
-0.02743571251630783,
-0.01426040567457676,
0.03469349443912506,
-0.05429905652999878,
0.04401804506778717,
-0.004385187290608883,
0.02117079496383667,
0.06003681942820549,
-0.004798854701220989,
-0.06674597412347794,
0.05031023919582367,
0.015205500647425652,
-0.00029052430181764066,
0.014705379493534565,
-0.057953011244535446,
-0.03345022723078728,
-0.02806565910577774,
-0.04388653486967087,
-0.04793580621480942,
-0.03100673481822014,
-0.03870747610926628,
0.04755914583802223,
0.01372852735221386,
0.028647014871239662,
-0.06222029775381088,
0.008146676234900951,
-0.008841250091791153,
-0.032491691410541534,
0.02139967307448387,
0.019730137661099434,
0.07897688448429108,
0.0044766683131456375,
0.04531543329358101,
-0.015584125183522701,
-0.02828855812549591,
0.05001252517104149,
0.003413556842133403,
-0.014102999120950699,
0.08028389513492584,
0.02052527852356434,
-0.021447524428367615,
-0.041124410927295685,
-0.051267292350530624,
0.056692663580179214,
0.05563933029770851,
-0.08708235621452332,
-0.04571734368801117,
0.027268821373581886,
0.00030201245681382716,
-0.017419500276446342,
-0.02421199344098568,
0.06541401892900467,
0.0017604776658117771,
-0.02133643440902233,
0.024952838197350502,
0.03245937079191208,
-0.0376504510641098,
-0.011249863542616367,
-0.002312256721779704,
-0.03581034392118454,
-0.06357742100954056,
0.015246285125613213,
0.02451297827064991,
0.0320262536406517,
0.025914939120411873,
-0.0490141361951828,
0.04529241845011711,
-0.035614944994449615,
-0.0016951692523434758,
-0.019184011965990067,
-0.048781175166368484,
0.08742216229438782,
-0.0014111986383795738,
-0.06628710776567459,
0.015316315926611423,
-0.04829099774360657,
0.018382327631115913,
-0.05236544460058212,
-0.03153103217482567,
-0.020898547023534775,
0.0028237532824277878,
0.02954918146133423,
0.027213096618652344,
-0.004608431365340948,
0.0063168685883283615,
0.008587674237787724,
0.038011472672224045,
-0.011550071649253368,
-0.013995976187288761,
-0.007939404807984829,
-0.025500988587737083,
0.016847562044858932,
0.023461956530809402,
-0.011949648149311543,
-0.021946672350168228,
0.0186938289552927,
0.014585691504180431,
-0.018663091585040092,
0.014921911992132664,
0.017039841040968895,
-0.012651961296796799,
0.009715473279356956,
0.024444442242383957,
-0.0006012595258653164,
-0.04212073236703873,
0.045171964913606644,
0.01279967650771141,
0.018121842294931412,
0.014284675009548664,
-0.012516368180513382,
0.027215996757149696,
0.04053671658039093,
0.06343458592891693,
-0.055089209228754044,
-0.02694193460047245,
0.033149655908346176,
-0.036517184227705,
-0.03393862023949623,
0.03883274272084236,
-0.029322288930416107,
0.01411875244230032,
-0.02168526127934456,
0.015847185626626015,
0.0552370585501194,
-0.01646985299885273,
-0.016166582703590393,
0.06477902829647064,
0.07593780755996704,
-0.011103221215307713,
-0.0022812846582382917,
-0.06504317373037338,
-0.055814556777477264,
0.02070770040154457,
0.017326900735497475,
-0.05611608922481537,
0.08967237919569016,
-0.024907832965254784,
0.010551654733717442,
0.025773214176297188,
0.0032302977051585913,
0.0360201895236969,
0.08759194612503052,
0.0276947021484375,
0.008266603574156761,
0.02140836790204048,
0.00845294538885355,
-0.0008630402153357863,
0.004282468929886818,
-0.02515043318271637,
0.009335199370980263,
-0.03041023574769497,
-0.0012283797841519117,
-0.04461223632097244,
-0.0037184758111834526,
0.009979572147130966,
0.002532619284465909,
-0.0031449031084775925,
0.008174316957592964,
0.011767754331231117,
-0.03447403758764267,
-0.03402160480618477,
0.028839003294706345,
0.013188048265874386,
0.010672664269804955,
0.0162805262953043,
0.03620221093297005,
0.04114200547337532,
0.013754808343946934,
-0.012441140599548817,
-0.021728796884417534,
-0.013916641473770142,
-0.003826127853244543,
-0.014295638538897038,
-0.06751896440982819,
-0.007414011750370264,
-0.027952145785093307,
0.024980776011943817,
-0.012040372006595135,
-0.033933546394109726,
0.046055927872657776,
0.014797828160226345,
0.08677781373262405,
-0.04089267924427986,
-0.047808386385440826,
0.032508037984371185,
-0.03105577826499939,
0.03335275128483772,
-0.04412352293729782,
-0.00855086836963892,
-0.02596909925341606,
0.0010855967411771417,
0.01671813428401947,
-0.014223583973944187,
0.013218417763710022,
-0.030633991584181786,
0.007575342431664467,
-0.0027778076473623514,
0.027336571365594864,
0.02142982929944992,
0.01535846572369337,
0.017161136493086815,
0.04400402680039406,
0.029889417812228203,
0.05414601415395737,
-0.0321037694811821,
-0.04197980836033821,
-0.042876675724983215,
-0.06031567603349686,
0.000009187624527839944,
0.04330077022314072,
0.0209483839571476,
0.03721999749541283,
-0.03129712492227554,
-0.024921592324972153,
-0.028683291748166084,
-0.026300465688109398,
0.020957596600055695,
-0.09924427419900894,
-0.05651525780558586,
-0.025192800909280777,
0.0020181876607239246,
-0.008708455599844456,
0.022301433607935905,
0.03146135061979294,
0.030311672016978264,
0.020381085574626923,
-0.0008276578155346215,
0.011151195503771305,
-0.030018843710422516,
0.04078654944896698,
-0.009573528543114662,
-0.05602504685521126,
-0.018074961379170418,
0.016953181475400925,
0.030968355014920235,
-0.007159270346164703,
-0.014038228429853916,
0.04030010476708412,
0.011509710922837257,
-0.008739977143704891,
0.06875860691070557,
-0.010128223337233067,
0.02179962769150734,
-0.04417070001363754,
-0.016194447875022888,
0.047237347811460495,
0.005399203859269619,
0.023421861231327057,
0.002324555302038789,
0.002413020236417651,
-0.020204398781061172,
-0.006440432276576757,
-0.05059868097305298,
-0.039639730006456375,
0.021118231117725372,
-0.011770205572247505,
-0.023295462131500244,
-0.01159740798175335,
-0.05531078204512596,
0.028596552088856697,
-0.041782792657613754,
0.02323049306869507,
-0.003956901375204325,
-0.02485634759068489,
-0.04795145243406296,
0.02842307835817337,
-0.036773305386304855,
0.04658935219049454,
0.02438332699239254,
-0.016141073778271675,
0.011599360965192318,
0.01062128134071827,
0.01346080657094717,
0.003997111693024635,
-0.033082135021686554,
0.028635071590542793,
0.04162152484059334,
0.02067323960363865,
-0.012598426081240177,
0.05526090785861015,
-0.007943517528474331,
0.0009225811227224767,
0.0708526223897934,
0.01347881369292736,
0.04000836983323097,
-0.009560427628457546,
0.026439763605594635,
-0.053080759942531586,
-0.023803146556019783,
-0.01488083228468895,
-0.062256887555122375,
0.011338693089783192,
0.022477414458990097,
0.03656454011797905,
-0.03161098062992096,
0.018601035699248314,
-0.01519643422216177,
-0.03254672512412071,
0.07265094667673111,
0.02137664705514908,
-0.03829987347126007,
0.06388216465711594,
0.029324522241950035,
-0.07227487862110138,
0.017201973125338554,
0.012641657143831253,
-0.06333200633525848,
0.02605520561337471,
0.024931203573942184,
0.017176836729049683,
-0.013313651084899902,
0.0008361215004697442,
-0.024814654141664505,
-0.015471970662474632,
0.02776235342025757,
-0.02098095789551735,
-0.08654000610113144,
-0.07169618457555771,
0.03465095907449722,
0.05486774444580078,
0.030862387269735336,
-0.016696469858288765,
-0.05190037190914154,
-0.07992750406265259,
-0.019355472177267075,
0.004824905656278133,
0.016142865642905235,
0.056293386965990067,
0.04277500882744789,
-0.040091224014759064,
-0.018637336790561676,
-0.029652182012796402,
0.02072756364941597,
-0.05236717313528061,
0.031389057636260986,
-0.03749343752861023,
-0.016405737027525902,
0.00612882524728775,
0.07968045026063919,
0.024559997022151947,
0.04804582893848419,
-0.0009898203425109386,
0.05171990767121315,
0.04828380420804024,
0.05904283747076988,
-0.056154437363147736,
0.06859096139669418,
-0.03027624636888504,
-0.010050574317574501,
0.0016220269026234746,
0.021192241460084915,
0.013288192451000214,
0.06039130315184593,
-0.012763729318976402,
-0.043483614921569824,
-0.019894210621714592,
0.029086250811815262,
-0.10586337745189667,
0.011139603331685066,
-0.04092172905802727,
-0.06495130807161331,
-0.01954897865653038,
0.042179372161626816,
-0.03364640101790428,
0.06880562752485275,
-0.04182904213666916,
0.0005160286673344672,
0.002611593808978796,
-0.05193271115422249,
-0.03591100499033928,
-0.060933083295822144,
-0.012788712978363037,
-0.017484936863183975,
0.04128317907452583,
0.022666845470666885,
-0.027405476197600365,
-0.038590312004089355,
0.013867435045540333,
0.020695272833108902,
-0.06586021184921265,
0.011262004263699055,
0.02923499047756195,
-0.03462589159607887,
-0.027573252096772194,
0.0019845571368932724,
0.020585956051945686,
-0.005508538335561752,
-0.13431762158870697,
-0.00054580980213359,
0.09088063985109329,
0.01522822305560112,
-0.042982980608940125,
0.0475708544254303,
-0.02324029430747032,
-0.04167408496141434,
0.010775993578135967,
-0.007000685203820467,
0.03141027316451073,
-0.04916214570403099,
-0.02124854363501072,
-0.023449134081602097,
0.012908082455396652,
-0.02663319557905197,
-0.02110174298286438,
0.0236847884953022,
-0.02693713828921318,
-0.040944088250398636,
0.019252430647611618,
0.0562128871679306,
-0.02364388480782509,
-0.04732499644160271,
0.007037801202386618,
0.01863722689449787,
-0.030606510117650032,
0.014076026156544685,
-0.005578238517045975,
-0.004480106756091118,
-0.08635357767343521,
0.02065877616405487,
0.0016394214471802115,
0.007269213907420635,
0.0002308969123987481,
-0.008983955718576908,
-0.07716935873031616,
0.020978447049856186,
0.03148789331316948,
-0.026102062314748764,
0.004515442531555891,
0.06343327462673187,
0.00985304731875658,
-0.003081404371187091,
0.02285941131412983,
-0.033835723996162415,
0.02555491402745247,
0.04101737216114998,
-0.015941420570015907,
-0.005803626962006092,
0.027181778103113174,
0.0437936894595623,
-0.029327986761927605,
0.006276440341025591,
-0.05938660725951195,
0.044030800461769104,
-0.01288306899368763,
-0.002858236199244857,
-0.014203561469912529,
0.008775759488344193,
-0.08561427146196365,
0.025124212726950645,
0.025559470057487488,
-0.026684975251555443,
-0.020291533321142197,
0.04435531422495842,
0.03136364370584488,
0.003548884065821767,
-0.003212012117728591,
0.07514435052871704,
-0.027712834998965263,
-0.04432697966694832,
0.014304997399449348,
0.04783400520682335,
-0.01066623069345951,
-0.039364106953144073,
-0.05450678989291191,
-0.05078573897480965,
-0.02618119679391384,
0.0007296917028725147,
0.027849292382597923,
-0.018629467114806175,
-0.02378893457353115,
0.0354570597410202,
-0.025965873152017593,
0.0540277361869812,
-0.0020751068368554115,
0.0493372306227684,
0.007265398278832436,
-0.009554044343531132,
0.04202320799231529,
0.032027121633291245,
-0.07070529460906982,
-0.04366089776158333,
0.002822283422574401,
0.03792593628168106,
0.04625677317380905,
-0.01775887981057167,
0.0004728469648398459,
-0.02838621847331524,
-0.007209042552858591,
0.011019619181752205,
-0.048768550157547,
0.05227931961417198,
-0.009110025130212307,
0.07889699935913086,
0.08791285753250122,
-0.002987547777593136,
0.014454899355769157,
-0.0050810850225389,
0.007034470327198505,
0.006125470157712698,
-0.05192172899842262,
-0.024706102907657623,
-0.019929302856326103,
0.011288044042885303,
0.03779175132513046,
-0.047882843762636185,
-0.06531338393688202,
0.02796313911676407
] |
<p>I'm slightly befuddled by is what it means when I'm asked to </p>
<blockquote>
<p>Draw the Feynman diagram in momentum space for the two point function of $\frac{\lambda}{3!}\phi^3$ theory for order $O(\lambda^2).$</p>
</blockquote>
<p>I can draw Feynman diagrams, and I thought two-point function meant</p>
<p>$$\langle0\|\phi(x)\phi(y)\|0\rangle$$</p>
<p>and what I know about $ O(\lambda^2)$ is that it will have more diagrams than $ O(\lambda).$</p>
<p>Other than that, I'm a bit lost. I mean, I'm not even sure if this is a really simple calculation or quite a long one. </p>
<p>Apologies to myself if anything I've written above is embarrassing. </p> | g1264 | [
0.019378220662474632,
0.0312713123857975,
0.006654858123511076,
-0.03324093669652939,
0.07238907366991043,
0.019318755716085434,
0.0015155923319980502,
0.005772008560597897,
-0.039268992841243744,
-0.012302717193961143,
-0.008344395086169243,
0.02018767222762108,
-0.009568390436470509,
-0.012873643077909946,
0.009138910099864006,
-0.01708882488310337,
0.02197960577905178,
0.009872108697891235,
0.01915346458554268,
-0.008862805552780628,
-0.017579982057213783,
0.014509227126836777,
-0.01746649108827114,
-0.016450027003884315,
0.021110249683260918,
-0.01881520077586174,
-0.019305691123008728,
0.015215114690363407,
-0.06799537688493729,
0.021256517618894577,
0.03281167894601822,
0.07270262390375137,
0.016657810658216476,
-0.0670490562915802,
-0.03622813895344734,
-0.001927474164403975,
0.0723535493016243,
0.03097597137093544,
0.016312940046191216,
-0.021437784656882286,
-0.005301533732563257,
-0.027194632217288017,
-0.024419238790869713,
-0.007626816164702177,
-0.0497412383556366,
-0.029598841443657875,
-0.06456471979618073,
0.012977597303688526,
-0.006627009715884924,
0.014562894590198994,
0.005818142089992762,
0.05721354857087135,
0.08150734007358551,
0.026522215455770493,
0.014205917716026306,
0.0571819506585598,
0.013054247945547104,
-0.07359123975038528,
0.07944896072149277,
-0.000003013168225152185,
-0.018517522141337395,
0.042584098875522614,
-0.00786115787923336,
-0.027347419410943985,
0.02789955586194992,
-0.004759292583912611,
-0.009860684163868427,
-0.05940583348274231,
-0.006245444528758526,
0.011482405476272106,
0.0050153727643191814,
-0.07849537581205368,
0.04759008809924126,
-0.03719137981534004,
-0.010760250501334667,
0.044715192168951035,
-0.03334030881524086,
-0.04074423015117645,
0.029346467927098274,
0.017453840002417564,
-0.040266770869493484,
-0.04288679361343384,
-0.0031582308001816273,
0.009610358625650406,
0.04839808866381645,
0.031730588525533676,
-0.019662030041217804,
-0.016332438215613365,
-0.04553830623626709,
0.033079423010349274,
-0.04371773451566696,
0.014392871409654617,
-0.042691707611083984,
-0.021754717454314232,
-0.010431941598653793,
-0.0005411970196291804,
0.002624864224344492,
0.014175900258123875,
-0.00796857476234436,
0.01980295218527317,
-0.07321381568908691,
-0.008827676065266132,
0.0044016288593411446,
0.019626514986157417,
0.018404385074973106,
-0.0025814715772867203,
0.04874101281166077,
0.02016517147421837,
0.05296282097697258,
-0.02488880418241024,
-0.08766169100999832,
0.00888914056122303,
-0.026911143213510513,
-0.0045796711929142475,
-0.03991949185729027,
-0.04935337230563164,
0.05595669522881508,
-0.06782795488834381,
-0.0006465377518907189,
0.03969930112361908,
0.01998550444841385,
-0.049505334347486496,
0.12116540223360062,
0.0343388207256794,
0.029878579080104828,
-0.012849434278905392,
-0.04351124167442322,
0.007376223802566528,
-0.02452324517071247,
-0.004478035494685173,
0.01713920757174492,
-0.003629673272371292,
0.015961308032274246,
0.041108615696430206,
-0.0028855260461568832,
0.056770000606775284,
-0.03793146088719368,
0.02616802044212818,
0.05102970451116562,
0.022023962810635567,
0.04903202876448631,
-0.029873039573431015,
-0.027618208900094032,
-0.04812220111489296,
-0.047386348247528076,
-0.04062061756849289,
0.05956881120800972,
-0.0034040461760014296,
0.01086376328021288,
-0.002552543766796589,
-0.01595541089773178,
0.05323229357600212,
-0.009629089385271072,
0.0644877701997757,
0.05601707100868225,
0.044787224382162094,
0.07255399972200394,
0.030682148411870003,
0.023299625143408775,
0.00974127184599638,
0.03248973935842514,
0.0370108000934124,
0.06888211518526077,
-0.0209660604596138,
-0.06270474195480347,
-0.025698186829686165,
0.01342139020562172,
-0.08810795843601227,
-0.05676458403468132,
-0.05250959470868111,
-0.009631291963160038,
0.01230198796838522,
0.05454288423061371,
0.038572560995817184,
-0.015034929849207401,
0.00786577258259058,
-0.029436929151415825,
0.04168558493256569,
0.021013451740145683,
0.05337611213326454,
0.005770500283688307,
-0.02301177568733692,
-0.009225403890013695,
0.007101182825863361,
-0.07121838629245758,
0.043189506977796555,
-0.024680504575371742,
0.0905957818031311,
-0.017048154026269913,
-0.029113613069057465,
-0.001686628209426999,
0.005179489031434059,
-0.03387848660349846,
0.06350857019424438,
0.006796593777835369,
0.040404487401247025,
-0.017335880547761917,
-0.07579571008682251,
-0.027043720707297325,
-0.03822197765111923,
-0.011921115219593048,
-0.02355458401143551,
0.05867106467485428,
0.014817684888839722,
0.03028467856347561,
0.018992163240909576,
-0.045020733028650284,
0.024010861292481422,
0.05481167882680893,
0.03286512568593025,
0.03104255348443985,
-0.03546604886651039,
0.04269750043749809,
0.028366513550281525,
-0.016119666397571564,
-0.06269766390323639,
-0.03402545675635338,
0.019976193085312843,
-0.04231541231274605,
0.000045396838686428964,
0.002395892282947898,
-0.00014415847545024008,
0.03098125383257866,
-0.0015924754552543163,
0.027866924181580544,
0.023349199444055557,
0.031234242022037506,
-0.0035304022021591663,
-0.008994558826088905,
-0.020247723907232285,
-0.04285348206758499,
0.0036552369128912687,
-0.026999900117516518,
-0.04563328996300697,
-0.013024683110415936,
-0.04397822916507721,
-0.07002396881580353,
0.010981554165482521,
0.0033909480553120375,
0.06942097842693329,
0.012181326746940613,
0.031342461705207825,
0.042086973786354065,
-0.045477043837308884,
0.027393702417612076,
-0.03564466908574104,
0.0415232889354229,
0.018177734687924385,
-0.033945925533771515,
0.051603469997644424,
0.03177089989185333,
0.03053372912108898,
0.014832749031484127,
0.04293104633688927,
-0.023433752357959747,
0.030459342524409294,
-0.011608587577939034,
0.025385785847902298,
-0.03068862482905388,
-0.02682325430214405,
-0.010929216630756855,
-0.03266919031739235,
0.0018491602968424559,
-0.007927385158836842,
-0.061718761920928955,
0.0069573381915688515,
-0.03939949348568916,
0.02328292466700077,
0.05611222982406616,
-0.06202636659145355,
-0.039400119334459305,
-0.0024350944440811872,
0.025023695081472397,
0.02517213672399521,
0.0017676879651844501,
-0.06704061478376389,
0.030621828511357307,
-0.02556193247437477,
0.040501587092876434,
-0.03440538048744202,
-0.02402384765446186,
0.013994701206684113,
-0.06428622454404831,
0.12919844686985016,
0.014984563924372196,
-0.021720029413700104,
-0.05858907476067543,
0.06079747527837753,
-0.023062925785779953,
0.005109510850161314,
-0.018811488524079323,
0.019298825412988663,
0.01373992394655943,
-0.020238617435097694,
-0.0013774270191788673,
-0.004816378932446241,
0.01983361318707466,
-0.027064595371484756,
-0.04035152867436409,
0.015510228462517262,
0.03151717409491539,
-0.003184898756444454,
0.02150655724108219,
-0.000636747048702091,
0.06843971461057663,
0.013365297578275204,
-0.041355714201927185,
-0.022663647308945656,
0.002172383712604642,
0.03485601022839546,
0.020916219800710678,
0.0333896242082119,
-0.028574764728546143,
0.002640078542754054,
-0.001481534680351615,
0.0040987348183989525,
0.023270176723599434,
0.03616204112768173,
-0.005956570617854595,
-0.0156029611825943,
-0.030475910753011703,
-0.02395660988986492,
0.011100780218839645,
-0.021837718784809113,
0.06554251909255981,
-0.007027218118309975,
-0.01128184050321579,
-0.025562407448887825,
-0.039184845983982086,
-0.0314236655831337,
0.018394341692328453,
-0.04369106516242027,
-0.007081959396600723,
-0.01860569603741169,
-0.0523732528090477,
-0.04580172523856163,
-0.03861386701464653,
0.012280582450330257,
0.020923610776662827,
-0.054758552461862564,
0.014488989487290382,
0.0029711530078202486,
-0.009430083446204662,
-0.043528709560632706,
0.011789803393185139,
-0.07867053896188736,
-0.014836154878139496,
0.0637899711728096,
0.06445931643247604,
0.005096503533422947,
0.01875416748225689,
0.0031277360394597054,
0.008008722215890884,
0.03574530407786369,
0.04241585358977318,
-0.031701523810625076,
-0.01520639006048441,
-0.002825956093147397,
0.002615473000332713,
-0.035058021545410156,
0.016016047447919846,
0.01138005405664444,
-0.023155706003308296,
-0.031350430101156235,
0.00803996529430151,
-0.024515947327017784,
-0.0471089705824852,
0.054701387882232666,
0.010108375921845436,
0.02268417552113533,
0.018320512026548386,
-0.04395226016640663,
0.01029293704777956,
0.06254956871271133,
0.05145455524325371,
-0.06289347261190414,
0.008511791005730629,
-0.03762748837471008,
-0.02731426991522312,
0.06317291408777237,
-0.031175337731838226,
0.009596682153642178,
-0.03321415185928345,
-0.010770183987915516,
0.005738098174333572,
0.051628705114126205,
-0.06003608554601669,
0.010202079080045223,
0.010480226948857307,
-0.02268294431269169,
0.035112034529447556,
-0.007481601554900408,
-0.04072018340229988,
-0.0008100130944512784,
-0.0022517044562846422,
-0.06626108288764954,
0.041725799441337585,
0.044224150478839874,
-0.0539364293217659,
0.06305345892906189,
-0.041487786918878555,
-0.0022371720988303423,
-0.02562006004154682,
-0.037074100226163864,
-0.0173378624022007,
-0.037388160824775696,
0.047924190759658813,
-0.019546326249837875,
0.03499726578593254,
-0.057311225682497025,
0.03816165030002594,
-0.01406185980886221,
0.037770871073007584,
-0.02952815592288971,
-0.019270209595561028,
-0.06750567257404327,
-0.06464698910713196,
-0.08254744112491608,
-0.022730721160769463,
0.04948176443576813,
0.03399127349257469,
0.025958964601159096,
0.027595441788434982,
-0.0235490370541811,
-0.050624653697013855,
0.01670130342245102,
0.016081571578979492,
0.019936295226216316,
0.0004787644720636308,
-0.03439413756132126,
0.033246785402297974,
0.04928291216492653,
-0.03755013272166252,
0.033891282975673676,
-0.009379900991916656,
0.05176205188035965,
-0.03144622594118118,
0.06405851989984512,
-0.07329149544239044,
0.03873072564601898,
0.008346260525286198,
-0.08856913447380066,
0.013228431344032288,
-0.025660473853349686,
-0.01575748808681965,
-0.0422690324485302,
-0.04119914770126343,
-0.032158948481082916,
0.007747053634375334,
0.02181044965982437,
-0.02698216587305069,
0.008440850302577019,
0.06335528194904327,
0.003231377573683858,
0.01856277510523796,
0.013829618692398071,
-0.017759088426828384,
-0.03059559315443039,
0.04504474624991417,
0.01124835480004549,
-0.09185314923524857,
0.008220795542001724,
0.0275379940867424,
-0.02137055993080139,
0.07011550664901733,
0.03389883041381836,
-0.0461362861096859,
-0.009081938304007053,
-0.009451312012970448,
-0.0861450806260109,
0.04851386696100235,
-0.06851251423358917,
0.032430458813905716,
-0.024289533495903015,
0.013703393749892712,
-0.010286830365657806,
0.0025922893546521664,
0.0320403166115284,
-0.003384919138625264,
-0.033622145652770996,
0.017659666016697884,
0.03920423239469528,
0.03741709142923355,
0.017616471275687218,
0.01681607961654663,
-0.00996934249997139,
-0.001266380539163947,
0.01774291880428791,
-0.018731947988271713,
0.029476143419742584,
0.012261242605745792,
0.03040185384452343,
0.024353336542844772,
0.028692593798041344,
-0.017901886254549026,
-0.003790869377553463,
0.04775134101510048,
-0.019733170047402382,
0.003259289311245084,
0.003431149525567889,
0.03179086372256279,
-0.03145109489560127,
-0.008962239138782024,
-0.05440079793334007,
-0.012243333272635937,
0.029706355184316635,
0.032573383301496506,
-0.024514079093933105,
0.016957471147179604,
0.02045425958931446,
-0.0066101267002522945,
-0.033734388649463654,
0.010910307057201862,
-0.02908436581492424,
-0.0464678592979908,
0.05236559733748436,
0.002916788449510932,
-0.033275652676820755,
-0.022353170439600945,
-0.03497416526079178,
0.08100125193595886,
0.014144845306873322,
0.025620203465223312,
-0.045714352279901505,
0.030482959002256393,
0.005301990546286106,
-0.04280146583914757,
-0.02972830832004547,
0.005077753681689501,
0.07840410619974136,
-0.014773473143577576,
-0.010213589295744896,
0.007942686788737774,
-0.005898572038859129,
-0.003045629011467099,
-0.0489845834672451,
0.030569491907954216,
0.001353556988760829,
0.036190081387758255,
0.02449825033545494,
-0.001913909218274057,
-0.00890753511339426,
-0.02911798469722271,
0.050938498228788376,
0.01168647687882185,
0.045307260006666183,
-0.010060389526188374,
-0.035399895161390305,
0.0567861907184124,
-0.031185289844870567,
-0.020944757387042046,
-0.05118531361222267,
-0.04084077849984169,
-0.034244783222675323,
0.015131616033613682,
0.03589086979627609,
0.009402497671544552,
0.0031577027402818203,
0.013580387458205223,
0.03003474324941635,
0.003232510993257165,
-0.011792431585490704,
-0.017497820779681206,
-0.0251543577760458,
0.024825481697916985,
-0.023111466318368912,
-0.03566678985953331,
0.013120499439537525,
0.006567729637026787,
0.032217033207416534,
-0.0007570730522274971,
0.040910422801971436,
-0.08195724338293076,
0.053276050835847855,
0.05782861262559891,
0.05349588766694069,
0.0011033816263079643,
-0.02317211776971817,
-0.012183468788862228,
-0.023405656218528748,
-0.044934868812561035,
0.08459651470184326,
0.05748073011636734,
-0.06828232109546661,
-0.035256072878837585,
0.08139751106500626,
0.00360610312782228,
-0.03180840611457825,
0.06020690128207207,
0.04104629531502724,
-0.05520513653755188,
0.08173791319131851,
-0.055247701704502106,
-0.0117566529661417,
0.01498614251613617,
0.007236482109874487,
0.03010093979537487,
-0.034364569932222366,
-0.005011393688619137,
0.05338313430547714,
0.006030406802892685,
0.025748692452907562,
-0.03855975717306137,
-0.02947217971086502,
0.005774227902293205,
0.058991625905036926,
-0.005870451219379902,
0.03923330456018448,
0.014606371521949768,
-0.041148774325847626,
-0.0399310439825058,
0.05881141498684883,
-0.03236398473381996,
0.03683366999030113,
0.04555704444646835,
0.007685562130063772,
-0.00939537025988102,
0.015902364626526833,
-0.04302065074443817,
0.034593552350997925,
0.0690864622592926,
-0.039128538221120834,
-0.016250252723693848,
-0.035856202244758606,
0.0404982715845108,
0.0695400983095169,
-0.0012931841192767024,
0.01360994391143322,
0.0052574812434613705,
0.006248170509934425,
-0.017160169780254364,
-0.04814967140555382,
-0.001210617832839489,
0.04781093820929527,
0.0003781184204854071,
-0.019175060093402863,
-0.007716704625636339,
-0.01626291498541832,
-0.0013381122844293714,
0.022954154759645462,
-0.05394495278596878,
0.03086245246231556,
0.01464591734111309,
-0.0476207435131073,
-0.024685248732566833,
-0.03717804327607155,
-0.004270262084901333,
0.028946617618203163,
-0.08607921004295349,
-0.021003376692533493,
-0.008824336342513561,
0.0015660121571272612,
0.011556876823306084,
-0.03280090540647507,
0.004519565496593714,
0.010211024433374405,
-0.010762017220258713,
0.054312121123075485,
0.001309130690060556,
-0.011152776889503002,
-0.02811865694820881,
0.03832894563674927,
0.007028739433735609,
-0.0013963155215606093,
-0.01807149313390255,
0.01635625772178173,
-0.013026531785726547,
-0.026271026581525803,
-0.003408376593142748,
-0.027659785002470016,
-0.044401656836271286,
0.011912303976714611,
-0.05833395570516586,
0.050256527960300446,
0.018104057759046555,
-0.024071097373962402,
0.01919330097734928,
0.004928399343043566,
-0.02584131807088852,
-0.025011926889419556,
-0.032734159380197525,
0.019981635734438896,
-0.05182264372706413,
-0.07204651832580566,
-0.03256455808877945,
0.0018796295626088977,
-0.051923174411058426,
-0.022140854969620705,
-0.04141955450177193,
0.0017139211995527148,
0.08357959240674973,
0.01409653015434742,
0.0008133479859679937,
-0.0843861848115921,
0.040663354098796844,
0.05503258854150772,
0.04198988154530525,
-0.010313495993614197,
0.017969101667404175,
0.03241068124771118,
0.052820149809122086,
-0.09581320732831955,
-0.032331883907318115,
-0.0031592913437634706,
0.04987882822751999,
0.0047271535731852055,
0.03311527147889137,
-0.03148522600531578,
-0.038332171738147736,
-0.059161752462387085,
-0.004333094228059053,
0.01602715253829956,
0.02097262814640999,
0.004020434804260731,
0.008010501973330975,
0.0323166660964489,
0.0005145722534507513,
0.013804870657622814,
0.021545132622122765,
-0.05464772880077362,
-0.003213807474821806,
0.014589894562959671,
-0.03796005621552467,
-0.03788554295897484,
-0.03257777914404869,
0.0020737117156386375,
-0.010070230811834335,
0.025295590981841087,
0.009425139985978603,
0.07402115315198898,
-0.010286346077919006,
-0.00503614591434598,
-0.016752682626247406,
0.05555837228894234,
-0.025213468819856644,
-0.045038703829050064,
0.0021570860408246517,
-0.020032299682497978,
0.0485570915043354,
-0.03623269125819206,
0.02657625637948513,
0.01619875803589821,
-0.006418331526219845,
-0.0030958240386098623,
0.04133132845163345,
-0.08264937251806259,
-0.07199948281049728,
0.003937961533665657,
0.10530626028776169,
0.03209635242819786,
-0.0014788932166993618,
0.03631846234202385,
0.026743777096271515,
0.021044686436653137,
0.04616875201463699,
-0.005023136269301176,
0.00257420283742249,
0.005913286469876766,
0.003847347106784582,
-0.007564141880720854,
-0.0348973385989666,
0.006373440846800804,
0.018061459064483643,
0.006979202851653099,
-0.01722445711493492,
-0.049836836755275726,
-0.02351638674736023,
0.03574547916650772
] |
<p>I try to understand why Algodoo software (freeware) give an efficiency greater than unity. I tested several scenes and at each time I can look the software give energy, I don't say it's all the time the case, a lot of scene have energy constant or decrease but with particular forces Algodoo give energy. </p>
<p>The energy is not very high compare to sum of energy, I only have 50 J each second (the system give 50 W) with a total energy of 10000 J, it's small only 0.5 % of the total energy. But I can test until 12000 Hz for some scenes and the energy don't decrease. The system can be a 2 objects or better 3 objects in a free rotation, there is no axis. I compute with a large scale of frequencies from 100 Hz to 12000 Hz. I can't increase more frequency because forces become unstable: forces are unstable. </p>
<p>It seems 1200 Hz give good results in a lot of scene and for a lot of scenes results don't change from 800 Hz to 1200 Hz. I compute datas with a spreadsheet for test the result of energy, when Algodoo give energy (efficiency >1) datas give energy. I looked at center of gravity and with good frequency it don't move, sometimes like 0.1 mm for an object of 4 m * 4 m for the main object and 0.3 m for the second object (for example). No friction and no gravity in this study. Friction and restitution is at 0.5 for all material. I changed only density for have best result.</p>
<p><strong>Example of a scene: (not the best error but easy)</strong></p>
<p><img src="http://i.stack.imgur.com/6MjbY.png" alt="enter image description here"></p>
<p><strong>Forces:</strong></p>
<p><img src="http://i.stack.imgur.com/zOnz2.png" alt="enter image description here"></p>
<p><strong>Energy and informations:</strong></p>
<p><img src="http://i.stack.imgur.com/KeCbC.png" alt="enter image description here"></p>
<p><strong>Position of center of gravity:</strong></p>
<p><img src="http://i.stack.imgur.com/pMt5N.png" alt="enter image description here"></p>
<p>I'm not sure, but with some tests (not all), I find a phase angle between 2 objects (or 3 with 3 free objects in rotation). Like sum of force from one object is the same (value) than other, if there is a phase angle between two center of gravity, there is a torque from these center of gravity. Or at least one center works in positive and other in negative. Like centers of gravity don't move in the same distance, the work is not the same. </p>
<p><strong>Angle: 6°</strong></p>
<p><img src="http://i.stack.imgur.com/9y1BB.png" alt="enter image description here"></p>
<p><strong>A link for download an example:</strong></p>
<p><a href="https://drive.google.com/file/d/0B63Jbse1IMAkUUo2Sm0tcnI5ak0/edit?usp=sharing" rel="nofollow">https://drive.google.com/file/d/0B63Jbse1IMAkUUo2Sm0tcnI5ak0/edit?usp=sharing</a></p>
<p><strong>I have several questions:</strong></p>
<p>1/ For you, the error come from this phase angle ? If not, where the error come from ? </p>
<p>2/ If there is a phase angle, there a torque ? </p>
<p>3/ Is it possible in reality that centers of gravity are in phase angle ? I think it's not possible but I asked the question to be sure. </p>
<p>4/ Why Algodoo find a phase angle ? Is there a physical explanation ?</p>
<p>Maybe the error don't come from the phase angle but when I compute sum of energy, center of gravity of red object give energy but in the same time green object don't consume this energy. I made a lot of tests and at each time it's the energy come from the small object. If you have an idea for find the error ? Or a test I can do for find the error ? If necessary I can give another scenes with more power with 3 objects.</p>
<p><strong>For example, this 3 objects:</strong></p>
<p><img src="http://i.stack.imgur.com/t7v7X.png" alt="enter image description here"></p>
<p><strong>The energy increase like:</strong></p>
<p><img src="http://i.stack.imgur.com/u68hf.png" alt="enter image description here"></p>
<p><strong>I thought 4800 Hz is a good frequency, but some seconds after the sum is:</strong></p>
<p><img src="http://i.stack.imgur.com/GPfWF.png" alt="enter image description here"></p>
<p><strong>I study the system and find something: the energy increase only when forces are like :</strong></p>
<p><img src="http://i.stack.imgur.com/GYihS.png" alt="enter image description here"></p>
<p><strong>Details of forces:</strong></p>
<p><img src="http://i.stack.imgur.com/UCtRp.png" alt="enter image description here"></p>
<p><strong>The energy increase more if red and orange objects have forces like before (but in opposite direction):</strong></p>
<p><img src="http://i.stack.imgur.com/cw6ZH.png" alt="enter image description here"></p>
<p><strong>When I compute energy I have more than Algodoo:</strong></p>
<p><img src="http://i.stack.imgur.com/bb0g6.png" alt="enter image description here"></p>
<p><strong>A link for download the scene:</strong></p>
<p><a href="https://drive.google.com/file/d/0B63Jbse1IMAkTUUzTzNlc1VORXM/edit?usp=sharing" rel="nofollow">https://drive.google.com/file/d/0B63Jbse1IMAkTUUzTzNlc1VORXM/edit?usp=sharing</a></p>
<p>In this scene, I don't find always a phase angle or small. But each time forces are like image shows, the energy increase and if I compute datas with a spreadsheet, it's red and orange objects (small objects) that give energy. In the contrary, green object don't consume energy, the sum is near zero.</p>
<hr>
<p>It's not possible it's the moment of inertia the problem ? If one part of object give a torque from friction it receive a torque in the same time, but the work from a torque is torque by angle of rotation. If inertia is not the same, angle of rotation is not the same too even the torque is equal in value, no ? I don't find the error from Algodoo and it's the only idea I have found. At least, if someone can say if it's a possibility or not.</p> | g1265 | [
0.06180877611041069,
0.04222841188311577,
0.030711982399225235,
0.015226095914840698,
0.01154482550919056,
-0.00014431258023250848,
0.06950114667415619,
0.0006200125790201128,
-0.11621414124965668,
0.005963129457086325,
0.01503708679229021,
-0.02597367763519287,
0.00166414980776608,
-0.0328308530151844,
0.025933802127838135,
0.009975074790418148,
0.01955566368997097,
-0.005965161602944136,
0.0017774321604520082,
0.09105077385902405,
-0.019114840775728226,
-0.005098054185509682,
0.018778810277581215,
-0.03251582011580467,
0.019522804766893387,
0.01055850088596344,
-0.026281248778104782,
-0.04077637568116188,
-0.04875045642256737,
-0.014774877578020096,
0.00820606853812933,
-0.01661217026412487,
-0.002348541282117367,
-0.01985091343522072,
0.009820039384067059,
-0.01259127538651228,
0.01303913164883852,
-0.036765702068805695,
0.0036720496136695147,
0.01312741357833147,
-0.01089834701269865,
0.008011490106582642,
0.028187930583953857,
0.02049338072538376,
0.00011735312727978453,
-0.0259761493653059,
0.022722814232110977,
-0.03102097474038601,
0.017067324370145798,
-0.06530269980430603,
-0.029149774461984634,
0.035570792853832245,
0.0188044011592865,
-0.0037321080453693867,
0.030559316277503967,
0.0870879590511322,
-0.0015114895068109035,
-0.008706023916602135,
0.02941504493355751,
-0.0368480309844017,
0.0003745260473806411,
0.03991721570491791,
0.025113636627793312,
-0.008184876292943954,
-0.01460359152406454,
-0.004958360455930233,
0.028926659375429153,
-0.0264297965914011,
0.02424728311598301,
-0.00590131850913167,
-0.040314797312021255,
0.02435721457004547,
-0.014318063855171204,
-0.04172499477863312,
-0.016596268862485886,
-0.008187361992895603,
0.004849845543503761,
0.008138982579112053,
-0.03100479394197464,
-0.0038518968503922224,
-0.008112565614283085,
0.00893397256731987,
-0.016641734167933464,
0.02935171313583851,
-0.025058526545763016,
-0.0420139841735363,
0.02596914954483509,
0.00742136687040329,
0.010752160102128983,
0.04419952258467674,
0.057040419429540634,
0.006261967122554779,
0.0657896026968956,
-0.01554593350738287,
-0.002212274121120572,
0.009244321845471859,
-0.02594226412475109,
0.08658936619758606,
0.01807865872979164,
0.023459216579794884,
-0.06528804451227188,
-0.004200393334031105,
-0.01160004548728466,
-0.0354655385017395,
0.02832566760480404,
-0.04999620467424393,
-0.015950702130794525,
0.047207850962877274,
-0.08964736759662628,
-0.00902479887008667,
0.06411262601613998,
-0.0031520016491413116,
-0.018144020810723305,
-0.04835456982254982,
0.00862673670053482,
-0.03557652607560158,
0.10313412547111511,
-0.02951679565012455,
0.007586962543427944,
-0.05229479447007179,
-0.04212481528520584,
-0.01639195717871189,
0.026843588799238205,
-0.006170326378196478,
-0.029778961092233658,
-0.015368093736469746,
0.03727090358734131,
-0.04981641098856926,
-0.01935221441090107,
-0.010503650642931461,
0.01628050208091736,
0.014709717594087124,
-0.03754938766360283,
-0.01956942491233349,
0.03811627998948097,
0.04864354059100151,
-0.05613720417022705,
-0.011559884995222092,
0.005124828778207302,
0.03540218621492386,
0.012577934190630913,
-0.008896596729755402,
0.022165274247527122,
-0.03909951448440552,
0.0090580889955163,
0.017515134066343307,
-0.03822106122970581,
0.000420239579398185,
0.04801113158464432,
0.05318127200007439,
0.002980332588776946,
0.04321426525712013,
-0.021355628967285156,
-0.030538327991962433,
0.02012455277144909,
0.014650361612439156,
-0.03024282306432724,
-0.02816195972263813,
0.008640049956738949,
0.037819549441337585,
0.058532558381557465,
-0.019895581528544426,
0.09913602471351624,
0.0010905361268669367,
-0.018593043088912964,
-0.034409381449222565,
0.0803598165512085,
-0.03762803226709366,
0.017273159697651863,
0.013733215630054474,
-0.06053479388356209,
-0.020581115037202835,
0.014415535144507885,
0.002637269673869014,
-0.0076921856962144375,
0.09209668636322021,
0.013162191025912762,
-0.033191658556461334,
0.075034961104393,
0.045499566942453384,
0.014583374373614788,
-0.012485324405133724,
0.01937023550271988,
-0.05234513431787491,
0.0363277941942215,
-0.01752225123345852,
0.03239300847053528,
0.03236493095755577,
-0.04712877795100212,
0.010031402111053467,
-0.06058435142040253,
0.030293462797999382,
-0.022649554535746574,
0.012995953671634197,
0.029432518407702446,
0.052350856363773346,
-0.013423263095319271,
-0.08841285109519958,
-0.08608924597501755,
0.012114245444536209,
-0.02103600651025772,
-0.027051428332924843,
-0.014461765065789223,
0.0015719073126092553,
-0.02582257054746151,
0.04488321766257286,
0.022767361253499985,
0.018817154690623283,
-0.032831814140081406,
-0.0467161163687706,
0.022675279527902603,
0.020204542204737663,
-0.0013690629275515676,
0.04789453744888306,
0.0018392311176285148,
0.023256737738847733,
-0.011595573276281357,
-0.08081766963005066,
0.014251848682761192,
0.027465492486953735,
0.002530606696382165,
0.012929406948387623,
0.024477213621139526,
0.060462016612291336,
-0.02768714912235737,
-0.043451182544231415,
-0.037100788205862045,
-0.0010488145053386688,
-0.033753588795661926,
-0.028845343738794327,
-0.05025125667452812,
0.020363187417387962,
0.03961785137653351,
0.0025738084223121405,
0.09841923415660858,
-0.017421986907720566,
0.011064383201301098,
-0.019338736310601234,
-0.0023179790005087852,
0.03699007257819176,
0.0072332583367824554,
-0.05477260798215866,
-0.0392613410949707,
-0.09035170823335648,
0.03264908492565155,
0.011933599598705769,
0.02877955138683319,
-0.03702473267912865,
0.027672521770000458,
0.06759849935770035,
0.007364243268966675,
-0.0027940727304667234,
-0.03297710791230202,
0.0220573041588068,
-0.018304569646716118,
0.005090410355478525,
-0.014454097487032413,
0.015453340485692024,
-0.009642490185797215,
-0.018691005185246468,
-0.05131090432405472,
0.00574750080704689,
0.019356686621904373,
0.06221916899085045,
0.02968648076057434,
0.05339333787560463,
0.006958151236176491,
-0.019331084564328194,
-0.033706746995449066,
0.014609958045184612,
-0.07667601108551025,
0.08005998283624649,
-0.03944625332951546,
0.002789129735901952,
0.018182653933763504,
0.04078714922070503,
0.06439737975597382,
-0.00441777566447854,
0.018959321081638336,
0.017972657456994057,
-0.012169643305242062,
-0.04674482345581055,
-0.023518197238445282,
0.060287024825811386,
0.03249085694551468,
-0.024781284853816032,
0.004306031856685877,
0.0031673680059611797,
-0.03237840533256531,
-0.017334772273898125,
0.03626898676156998,
0.02988450601696968,
0.01444404199719429,
-0.00556916231289506,
-0.047987960278987885,
-0.009268022142350674,
0.017121432349085808,
-0.005827520042657852,
-0.03749318793416023,
0.05935043469071388,
-0.0035316026769578457,
-0.0012361770495772362,
0.01566944643855095,
0.07107039541006088,
0.012650256045162678,
-0.006011310964822769,
-0.0010302102891728282,
-0.03367854282259941,
-0.039099156856536865,
-0.03234660252928734,
-0.010032937861979008,
0.01778375543653965,
-0.05318933725357056,
-0.007292827591300011,
-0.05602642148733139,
0.007128802593797445,
0.017681412398815155,
0.005310709122568369,
-0.07776724547147751,
-0.06685931980609894,
0.018923349678516388,
-0.04752544313669205,
-0.054892707616090775,
-0.042484384030103683,
-0.08158495277166367,
0.05380820110440254,
-0.02155587263405323,
0.02824019081890583,
-0.025608746334910393,
0.04814545065164566,
0.054849304258823395,
0.027518318966031075,
-0.022897083312273026,
0.018017800524830818,
-0.01346338540315628,
-0.012116099707782269,
-0.0004774649569299072,
0.04751289635896683,
0.020867766812443733,
0.03679351508617401,
-0.1046997532248497,
0.020545000210404396,
-0.04539594426751137,
-0.0158902108669281,
-0.03573312982916832,
0.02617686428129673,
-0.012634709477424622,
-0.011856375262141228,
-0.04977372661232948,
0.02373763732612133,
0.029049577191472054,
-0.018219156190752983,
-0.005467824172228575,
-0.023003913462162018,
0.013999640941619873,
-0.04195854067802429,
0.004264910239726305,
0.019428947940468788,
-0.026665112003684044,
0.01283043809235096,
0.011892947368323803,
0.011827511712908745,
0.0054093883372843266,
-0.01462891511619091,
0.0001550830784253776,
0.011326382867991924,
0.01176638063043356,
0.0784517303109169,
0.009877460077404976,
-0.07085848599672318,
-0.003848401131108403,
0.006347686983644962,
-0.007256347686052322,
-0.026515956968069077,
0.0157772284001112,
-0.04986255243420601,
0.010808398947119713,
-0.014748229645192623,
-0.021987613290548325,
0.03571700304746628,
0.069111168384552,
-0.022757304832339287,
-0.0304004717618227,
0.024846266955137253,
0.006589682772755623,
-0.016989465802907944,
0.00005435115599539131,
0.006106552202254534,
0.04291873052716255,
-0.029409578070044518,
-0.059400249272584915,
-0.01848333142697811,
-0.022097419947385788,
0.04358704760670662,
0.003558595199137926,
-0.06281042844057083,
0.0030119051225483418,
-0.03149259462952614,
-0.0003977362939622253,
0.03384271636605263,
-0.0015743945259600878,
-0.04020347073674202,
-0.04214504733681679,
0.009159493260085583,
-0.015347418375313282,
-0.01515998039394617,
0.03019229881465435,
0.0019815824925899506,
-0.025078559294342995,
-0.00868112314492464,
0.025833919644355774,
-0.03198312595486641,
0.02659165859222412,
-0.061320044100284576,
-0.032507043331861496,
-0.04074845090508461,
0.0053652445785701275,
0.011263817548751831,
0.02478765696287155,
-0.007524864748120308,
0.03746156394481659,
0.09513843059539795,
-0.009315535426139832,
-0.029107436537742615,
-0.01831858418881893,
0.04029659926891327,
-0.04954357445240021,
0.06073973327875137,
-0.004169839899986982,
-0.002872199984267354,
0.02239576354622841,
-0.0014341656351462007,
0.048408299684524536,
-0.01924924924969673,
-0.10348818451166153,
0.0644339993596077,
-0.00011908626765944064,
0.11188730597496033,
0.0328243114054203,
0.05069109424948692,
0.011538207530975342,
0.06279852986335754,
0.030961956828832626,
-0.051436085253953934,
-0.00013405167555902153,
0.027885213494300842,
0.027095753699541092,
-0.037994615733623505,
0.04090438038110733,
-0.017513202503323555,
-0.03377328813076019,
-0.00023362977663055062,
-0.01861170306801796,
0.014354168437421322,
0.04225550591945648,
0.02466072328388691,
-0.02537042647600174,
0.0377710796892643,
-0.05128518491983414,
0.038571737706661224,
-0.036104172468185425,
0.002784053096547723,
-0.05026598647236824,
-0.0030649991240352392,
0.003577850991860032,
0.023254748433828354,
-0.020114218816161156,
-0.04572799801826477,
-0.045153118669986725,
0.003149534808471799,
0.020730677992105484,
-0.010745800100266933,
0.06866685301065445,
0.00733828404918313,
-0.01728806085884571,
-0.018477605655789375,
0.008945238776504993,
0.0023335260339081287,
0.06406363844871521,
-0.01762925647199154,
-0.018420467153191566,
-0.006165018305182457,
0.03671819344162941,
0.020818430930376053,
0.001989475218579173,
0.03428022935986519,
-0.09056160598993301,
0.033587247133255005,
0.007505085319280624,
-0.007754398975521326,
0.00679544685408473,
-0.0045565469190478325,
-0.037089794874191284,
-0.1302628070116043,
0.010507731698453426,
0.05332577973604202,
0.007796880789101124,
-0.0022816509008407593,
-0.02597520500421524,
0.01833816058933735,
-0.041584741324186325,
0.014512134715914726,
0.034003376960754395,
-0.017540358006954193,
0.005334632471203804,
-0.01577119715511799,
0.1230025663971901,
-0.002629275666549802,
0.003970183432102203,
0.026565520092844963,
-0.03439716622233391,
0.011468488723039627,
0.0720290094614029,
0.028592942282557487,
0.005049575120210648,
-0.0448540598154068,
0.025121765211224556,
-0.0010259952396154404,
-0.05080515891313553,
-0.001733682001940906,
0.06037016585469246,
-0.004150464199483395,
0.041234783828258514,
-0.008291595615446568,
-0.005467911716550589,
0.0731537938117981,
-0.01067849900573492,
0.027831843122839928,
0.09060919284820557,
0.057296205312013626,
-0.020616568624973297,
0.0343046560883522,
-0.02190573886036873,
0.002913094824180007,
-0.01730990782380104,
0.007059431169182062,
0.023787403479218483,
-0.0453343540430069,
0.013552620075643063,
-0.009855781681835651,
0.03889128193259239,
-0.05343877524137497,
0.012318458408117294,
0.02183007448911667,
0.01855858974158764,
-0.012063156813383102,
-0.026390301063656807,
-0.015851102769374847,
0.01219375804066658,
-0.06571554392576218,
0.010698986239731312,
0.06445197761058807,
-0.024799883365631104,
-0.003814819036051631,
-0.016151608899235725,
0.002648906083777547,
-0.04099320247769356,
-0.03981030359864235,
0.05340578034520149,
-0.007347246631979942,
0.03090510703623295,
0.024914052337408066,
0.04918605834245682,
0.009708825498819351,
0.042229533195495605,
-0.10644163936376572,
-0.004936614539474249,
-0.0004045710957143456,
-0.00416357209905982,
0.04970014467835426,
0.0014952864730730653,
0.032465144991874695,
-0.008267867378890514,
0.04816434159874916,
0.08410704880952835,
-0.006216703448444605,
-0.005492397118359804,
-0.029723811894655228,
-0.03283058851957321,
-0.020482126623392105,
-0.03841060400009155,
-0.053663600236177444,
-0.007774819619953632,
0.0012954046251252294,
0.030650483444333076,
0.01864810101687908,
-0.023050034418702126,
0.04992836341261864,
0.026708735153079033,
-0.027994129806756973,
-0.015084768645465374,
0.002930796006694436,
0.030431348830461502,
-0.043173614889383316,
-0.050960127264261246,
-0.060915302485227585,
-0.0011139876442030072,
-0.03499830886721611,
-0.00017020758241415024,
0.003146370640024543,
-0.017527863383293152,
-0.037964481860399246,
-0.010393652133643627,
-0.0021928828209638596,
-0.043616633862257004,
0.0062096151523292065,
-0.009231215342879295,
-0.0004904538509435952,
-0.0253228098154068,
-0.008890381082892418,
-0.05443686619400978,
0.016864873468875885,
0.0027956501580774784,
0.04883026331663132,
-0.044251419603824615,
0.018506847321987152,
0.00682601286098361,
-0.030188405886292458,
0.06429526954889297,
-0.033062297850847244,
0.020435187965631485,
-0.04628115892410278,
0.04143908619880676,
-0.018749449402093887,
0.010950332507491112,
0.04717925190925598,
-0.08915269374847412,
0.03278471902012825,
0.0659237802028656,
0.0111756706610322,
0.03265000879764557,
0.05690912902355194,
-0.06800813972949982,
0.03858400508761406,
-0.03530959412455559,
0.007648952305316925,
-0.1054878756403923,
-0.03083718568086624,
0.04778224602341652,
0.08332248032093048,
-0.005029734224081039,
0.02820553071796894,
0.017088264226913452,
-0.00019817546126432717,
0.002192945219576359,
-0.015689468011260033,
0.026384325698018074,
0.04313477501273155,
-0.01691376231610775,
0.009685546159744263,
0.01250550989061594,
-0.014992899261415005,
0.03462141379714012,
-0.021384166553616524,
-0.05941678211092949,
0.04759472981095314,
-0.018758274614810944,
-0.023460837081074715,
0.015333922579884529,
-0.06031600013375282,
-0.06394317001104355,
0.011985396035015583,
-0.011481468565762043,
0.032665252685546875,
-0.06677031517028809,
0.028716042637825012,
0.01022131834179163,
0.009124531410634518,
0.00818744208663702,
0.002506299875676632,
0.004913080483675003,
0.048783883452415466,
-0.06923307478427887,
-0.02561689168214798,
-0.03135695680975914,
-0.03405607119202614,
-0.01977084018290043,
-0.02417852357029915,
-0.03184555843472481,
0.01637716218829155,
0.012817810289561749,
0.03454586863517761,
0.0019389827502891421,
0.017627833411097527,
0.022844335064291954,
0.000688407861161977,
-0.05024479702115059,
0.029773680493235588,
-0.07634101063013077,
-0.0011195580009371042,
-0.04648110270500183,
0.07003506273031235,
0.024992141872644424,
0.027709033340215683,
-0.07388267666101456,
0.023021584376692772,
0.020017633214592934,
0.0440254881978035,
0.030134959146380424,
0.0032020944636315107,
-0.03479934483766556,
-0.04466475173830986,
-0.04338524863123894,
0.031103234738111496,
-0.04001916944980621,
0.02543041855096817,
0.011664465069770813,
0.009893975220620632,
0.004822441842406988,
0.0076444572769105434,
-0.020315904170274734,
-0.025329140946269035,
0.0015279097715392709,
-0.017273085191845894,
-0.0076620508916676044,
0.03604818508028984,
-0.016560638323426247,
0.024381941184401512,
0.015305056236684322,
0.05837148055434227,
0.006292771082371473,
-0.0588870644569397,
-0.010321252048015594,
-0.0148798618465662,
-0.02117231674492359,
0.009128963574767113,
0.044203393161296844,
-0.029127812013030052,
0.03727239370346069,
-0.027455216273665428,
-0.018810896202921867,
-0.012550514191389084,
-0.01563544198870659,
0.008264117874205112,
0.010409926995635033,
0.021750114858150482,
-0.022751372307538986,
-0.02227086015045643,
-0.002368479734286666,
0.037207819521427155,
0.055013205856084824,
-0.012933820486068726,
-0.022057732567191124,
-0.07061979919672012,
0.05498660355806351,
0.02210325002670288,
0.005565895698964596,
0.08259609341621399,
0.002319108694791794,
-0.04561809450387955,
-0.019198942929506302,
0.008601800538599491,
-0.041865378618240356,
-0.023769119754433632,
-0.03965132683515549,
-0.01675226353108883,
0.05697588995099068,
-0.04747767001390457,
0.008913983590900898,
-0.05325239151716232,
-0.056341540068387985,
0.014493840746581554,
-0.013983807526528835,
-0.043478574603796005,
0.01899023726582527,
-0.05068172514438629,
0.01530306227505207,
0.03349995240569115
] |
<p>I'm fine with $U(1)$ symmetry and <a href="http://en.wikipedia.org/wiki/Noether%27s_theorem" rel="nofollow">Noether's Theorem</a>, but struggling with the translations of the field; namely</p>
<p>$$\phi'(x^{\mu})=\phi(x^{\mu}-a^{\mu}),$$ where $a^{\mu}$ constant four-vector</p>
<p>$$x^{\mu}=x^{\mu}+a^{\mu},$$</p>
<p>and the Lagrangian density</p>
<p>$${\cal L}=\frac{1}{2}\partial_{\mu}\phi^*\partial^{\mu}\phi-V(\phi^*\phi).$$</p>
<p>So a few questions:</p>
<ol>
<li><p>I can't show the Lagrangian is invariant under this transformation. Is it just a case that as $a^{\mu}$ is constant then the first term in the Lagrangian will obviously stay the same? But what about $V$? How I can show that's invariant?</p></li>
<li><p>Infinitesimally, is the transformation $\phi'(x^{\mu})=\phi(x^{\mu})-a^{\mu}\partial_{\mu}\phi(x^{\mu})?$ </p></li>
<li><p>If I'm right in point 2., how can I apply Noether's Theorem to this?</p></li>
</ol> | g1266 | [
0.05315869301557541,
0.009507480077445507,
-0.021731562912464142,
-0.08611438423395157,
0.006169632542878389,
0.01128416508436203,
0.012343927286565304,
0.0798388421535492,
-0.039860546588897705,
0.04230988025665283,
-0.04107621684670448,
0.00741526810452342,
-0.05544072017073631,
-0.02321832813322544,
0.025231607258319855,
0.012113625183701515,
0.023506149649620056,
0.0007669294136576355,
0.058594513684511185,
-0.04996475949883461,
-0.03470689058303833,
0.01891261152923107,
-0.011941664852201939,
-0.02268580161035061,
0.07199619710445404,
-0.039581913501024246,
0.02317092940211296,
-0.022222569212317467,
-0.057102277874946594,
-0.09868510812520981,
0.04851206764578819,
0.02361769787967205,
0.040921300649642944,
-0.02503134123980999,
0.03606060519814491,
0.02736065536737442,
0.020536191761493683,
0.006440194323658943,
0.038533683866262436,
0.0157108586281538,
0.005875245667994022,
0.03999249264597893,
0.053916867822408676,
0.030098188668489456,
-0.06763867288827896,
0.03562255576252937,
-0.060554139316082,
-0.04766581207513809,
-0.055567946285009384,
-0.00011562211875570938,
0.07104099541902542,
0.023161927238106728,
0.025592973455786705,
-0.022127943113446236,
-0.05361606180667877,
0.018826454877853394,
0.00755780003964901,
-0.011223782785236835,
-0.007869820110499859,
-0.009292413480579853,
0.018039755523204803,
-0.0688718855381012,
-0.034620869904756546,
-0.022907612845301628,
0.03266628831624985,
-0.02288118377327919,
0.006374652497470379,
0.014829888939857483,
-0.030846957117319107,
0.008905411697924137,
-0.05193470045924187,
-0.025003235787153244,
0.04243575781583786,
-0.024012785404920578,
-0.0030126837082207203,
-0.02389645203948021,
-0.007952098734676838,
0.015329252928495407,
0.008066867478191853,
-0.08334290236234665,
-0.04995223507285118,
0.0030667800456285477,
-0.007399224676191807,
0.015058531425893307,
0.06009086221456528,
-0.02890341728925705,
-0.026482678949832916,
-0.0402873158454895,
0.010463565587997437,
-0.0074689872562885284,
0.01693125255405903,
0.01035425253212452,
-0.013555270619690418,
-0.00877134595066309,
-0.0014035571366548538,
-0.01588553935289383,
-0.00701181823387742,
0.068503238260746,
-0.0335707850754261,
-0.048306290060281754,
-0.041627783328294754,
0.058681897819042206,
0.022060751914978027,
0.0029158741235733032,
0.059734344482421875,
0.03937414288520813,
0.07347740232944489,
-0.0034303017891943455,
0.004948698915541172,
0.02879464067518711,
-0.05236579477787018,
-0.04302964732050896,
0.054317835718393326,
0.016422804445028305,
-0.03577259182929993,
-0.013774746097624302,
0.014342361129820347,
-0.007391439750790596,
0.017303114756941795,
0.040588539093732834,
0.01193727646023035,
0.015434514731168747,
0.045294079929590225,
0.020809780806303024,
0.0056481012143194675,
0.03874881938099861,
-0.010424554347991943,
0.02802344597876072,
0.029182830825448036,
-0.03320755437016487,
0.02656828984618187,
0.0017808761913329363,
0.003929276950657368,
0.06212837994098663,
0.01754099875688553,
0.012333620339632034,
0.0024090688675642014,
0.09465790539979935,
0.03033381886780262,
0.009990639984607697,
0.006553357001394033,
-0.0504172183573246,
-0.013027964159846306,
-0.045606814324855804,
-0.032342538237571716,
0.031125137582421303,
-0.02600339986383915,
-0.04358066990971565,
0.04045983776450157,
0.0011228998191654682,
-0.02292049676179886,
0.07923369109630585,
0.026717256754636765,
0.03292637690901756,
-0.023128202185034752,
0.0009110314422287047,
0.026286525651812553,
0.007763836532831192,
-0.025448299944400787,
-0.0248259324580431,
0.022994263097643852,
-0.018779143691062927,
0.06769712269306183,
0.014433307573199272,
-0.007026400417089462,
0.03828725218772888,
0.005130361299961805,
-0.04829995706677437,
-0.007816617377102375,
-0.06518026441335678,
-0.019668947905302048,
0.03208937495946884,
-0.0038107361178845167,
0.0387461893260479,
-0.03173598274588585,
0.005456844810396433,
-0.051210276782512665,
0.034789033234119415,
-0.0019096919568255544,
0.00245734048075974,
-0.047043509781360626,
-0.0657619908452034,
0.04088382050395012,
-0.026438413187861443,
-0.0237030778080225,
-0.01409335620701313,
0.05084915831685066,
-0.015640435740351677,
-0.0016083433292806149,
0.05810125917196274,
-0.03210178017616272,
0.006663928739726543,
-0.016773657873272896,
0.055193282663822174,
0.05093603581190109,
0.013670003972947598,
0.025313178077340126,
-0.09493207186460495,
-0.07447397708892822,
-0.1213468685746193,
0.04420117288827896,
-0.003810877213254571,
0.040912482887506485,
-0.024961035698652267,
0.01899794489145279,
0.01291570533066988,
-0.044957585632801056,
-0.05389074981212616,
0.019420228898525238,
-0.0057490128092467785,
0.028776677325367928,
-0.10892236977815628,
-0.01437393855303526,
0.003457349259406328,
0.018318071961402893,
0.01885812357068062,
-0.009720109403133392,
0.00855683721601963,
-0.042271025478839874,
0.04291694611310959,
-0.02468833141028881,
0.017714345827698708,
0.018526379019021988,
0.05599679797887802,
-0.03473427891731262,
0.07224973291158676,
0.0036722030490636826,
0.0010790866799652576,
0.038063980638980865,
-0.0020617228001356125,
-0.026023730635643005,
0.010807153768837452,
0.022507501766085625,
0.0049637798219919205,
0.004994616378098726,
0.04531731456518173,
-0.03646670654416084,
0.03555168956518173,
0.026512855663895607,
0.08305007219314575,
0.004659248981624842,
-0.02976575493812561,
-0.05076698213815689,
0.0007855279836803675,
0.08424607664346695,
0.00826335046440363,
0.04746481776237488,
-0.022030048072338104,
0.016801374033093452,
-0.005818112287670374,
-0.0603378489613533,
-0.028249839320778847,
0.02058424986898899,
-0.019173137843608856,
0.00397962611168623,
-0.02984542027115822,
0.028236694633960724,
-0.015654196962714195,
0.036147721111774445,
0.012300821021199226,
0.044158849865198135,
-0.03499070927500725,
-0.021493729203939438,
0.010984067805111408,
-0.07991289347410202,
-0.011769063770771027,
-0.018460629507899284,
0.016282107681035995,
-0.020255031064152718,
0.014080394059419632,
0.027570724487304688,
0.0645628497004509,
0.033625245094299316,
0.0488402284681797,
-0.03412637859582901,
-0.014464388601481915,
-0.05790673568844795,
-0.03489988297224045,
0.025233907625079155,
-0.06214214861392975,
0.01589571125805378,
-0.01939329504966736,
0.00998537614941597,
-0.0010233669308945537,
0.03383967652916908,
-0.048827629536390305,
-0.07803954184055328,
-0.0014422658132389188,
-0.04145707190036774,
0.04396616667509079,
0.04538567736744881,
0.033629611134529114,
0.048323653638362885,
-0.036414045840501785,
-0.049911923706531525,
0.018464265391230583,
-0.006528932601213455,
-0.027866020798683167,
0.016726193949580193,
0.015224863775074482,
-0.05903696268796921,
-0.03083331510424614,
0.01192257460206747,
-0.012462308630347252,
0.01809483952820301,
-0.001492034294642508,
-0.012187544256448746,
-0.021790362894535065,
0.02378794550895691,
0.007838225923478603,
-0.0036495502572506666,
-0.06233466416597366,
-0.0013121796073392034,
0.003053719876334071,
-0.0537416972219944,
0.009906555525958538,
-0.02842957340180874,
0.003369856160134077,
0.06319542974233627,
-0.05497485026717186,
-0.049334581941366196,
-0.06588950008153915,
0.0072431559674441814,
-0.01344896387308836,
0.06559893488883972,
-0.03348903730511665,
-0.052934255450963974,
-0.011101596988737583,
-0.03680897876620293,
-0.05072919651865959,
-0.01806478202342987,
-0.028930403292179108,
0.021407099440693855,
-0.08961082249879837,
-0.0207150187343359,
0.023122595623135567,
-0.050038762390613556,
-0.005290857516229153,
0.0077408985234797,
-0.011919483542442322,
-0.06177620589733124,
-0.016438862308859825,
-0.07481824606657028,
0.0810416117310524,
0.002635435201227665,
-0.048548709601163864,
0.0031216873321682215,
-0.008605576120316982,
0.013659373857080936,
0.018645336851477623,
0.02607037127017975,
0.011425641365349293,
0.03795115277171135,
0.02621006965637207,
0.04579344019293785,
-0.038875408470630646,
0.016393912956118584,
0.004044969566166401,
-0.06041897088289261,
0.019850559532642365,
0.0185856893658638,
-0.018205968663096428,
-0.05226942151784897,
0.02397915907204151,
-0.013290325179696083,
0.0381864532828331,
-0.07570073008537292,
-0.020924583077430725,
0.014004661701619625,
0.04331265762448311,
0.017712824046611786,
-0.05894552543759346,
0.011451099067926407,
0.027996109798550606,
-0.029493337497115135,
-0.05602075904607773,
0.007945258170366287,
0.01343421172350645,
-0.0008329417323693633,
0.010121974162757397,
0.0375959649682045,
0.001649395446293056,
-0.003383546369150281,
0.00569482147693634,
0.019417569041252136,
0.02292795665562153,
-0.0015231457073241472,
-0.02217102237045765,
0.012736886739730835,
-0.04608490690588951,
0.05639722943305969,
0.027990981936454773,
-0.009450242854654789,
0.009513250552117825,
0.041330985724925995,
-0.0012796979863196611,
-0.04796212539076805,
0.003793584881350398,
-0.06759394705295563,
0.012657956220209599,
-0.0025610551238059998,
-0.02695496194064617,
0.0021695236209779978,
-0.08040094375610352,
0.005651293322443962,
-0.04495540261268616,
0.09439615905284882,
0.03166951984167099,
0.004265096038579941,
-0.012462999671697617,
-0.024491535499691963,
-0.03915342688560486,
0.04626080021262169,
-0.04674075171351433,
-0.015715207904577255,
0.05452108383178711,
-0.03358902037143707,
-0.09362643957138062,
-0.04476798698306084,
-0.01353047601878643,
0.002884344896301627,
0.0042102644219994545,
0.033538512885570526,
-0.05911208689212799,
-0.004959051962941885,
0.0355236679315567,
0.04829644411802292,
0.002111957408487797,
0.020545726642012596,
0.023364685475826263,
-0.007584424689412117,
0.03161855414509773,
0.0666596069931984,
-0.016295896843075752,
-0.03687912970781326,
0.023177998140454292,
-0.05496821179986,
0.027418097481131554,
-0.014775194227695465,
0.006720721255987883,
0.06498710811138153,
-0.005045733880251646,
-0.003153779311105609,
-0.000039725240640109405,
-0.02833574078977108,
0.004972816910594702,
0.007180824875831604,
-0.027373019605875015,
0.06610863655805588,
0.03522698953747749,
-0.0026424715761095285,
-0.01881711371243,
-0.00044182047713547945,
-0.027521979063749313,
0.05203414708375931,
-0.01622629538178444,
0.011263257823884487,
0.05558423697948456,
0.0005306163220666349,
-0.0003083398914895952,
-0.032304663211107254,
0.009642000310122967,
0.004925258457660675,
0.010051853954792023,
0.06466713547706604,
-0.01736748404800892,
-0.036882348358631134,
0.042702339589595795,
-0.015738222748041153,
-0.06349245458841324,
-0.0012615763116627932,
-0.01714755967259407,
-0.01158459484577179,
-0.03277907520532608,
0.011186467483639717,
0.02034713700413704,
-0.007480893284082413,
0.00820516049861908,
-0.034282904118299484,
-0.05470455065369606,
0.02349407970905304,
-0.0000798022301751189,
0.06154249608516693,
0.014287013560533524,
-0.008436126634478569,
-0.013195467181503773,
-0.020384596660733223,
0.02027524635195732,
-0.02760813944041729,
-0.031162718310952187,
-0.0027128485962748528,
0.022986946627497673,
0.06874969601631165,
0.03220386803150177,
-0.028490401804447174,
0.01884078048169613,
-0.00878842268139124,
-0.030283618718385696,
0.004256590269505978,
-0.00005833096292917617,
-0.025583066046237946,
0.04211851954460144,
0.015980521216988564,
0.009382462128996849,
-0.022304533049464226,
0.07823245972394943,
0.08969570696353912,
0.04386929050087929,
-0.020400553941726685,
0.055817555636167526,
0.031306467950344086,
-0.013055232353508472,
-0.01502925343811512,
-0.030816998332738876,
-0.028593964874744415,
0.004311972297728062,
-0.04488110914826393,
-0.002678331220522523,
-0.023473113775253296,
0.010020711459219456,
0.01186944730579853,
0.04191950708627701,
0.024289989843964577,
-0.039490606635808945,
0.018903251737356186,
0.01273870375007391,
0.000284000881947577,
-0.09568428248167038,
-0.023571498692035675,
0.012601291760802269,
0.03106471337378025,
0.002880703890696168,
0.0222184881567955,
-0.04299316927790642,
0.04785454273223877,
-0.007120352704077959,
-0.02051636204123497,
-0.03755981847643852,
0.04932957887649536,
0.00586674502119422,
0.028707167133688927,
-0.05849837511777878,
-0.03147589787840843,
-0.03700900822877884,
-0.09069035202264786,
0.04755917936563492,
-0.00139972276519984,
0.008629430085420609,
0.018906932324171066,
-0.02068023942410946,
-0.009589056484401226,
-0.05361054837703705,
0.0011938144452869892,
-0.008248111233115196,
-0.0263548381626606,
0.0679863765835762,
0.021850967779755592,
0.01695946417748928,
0.009025889448821545,
-0.023606136441230774,
0.05023336037993431,
0.0292471032589674,
0.020968163385987282,
-0.0416029654443264,
0.029753558337688446,
0.016445426270365715,
-0.017560334876179695,
-0.016750365495681763,
0.057283900678157806,
0.04975464195013046,
-0.0014610064681619406,
0.04078998044133186,
0.01596347987651825,
0.009381545707583427,
0.03215654939413071,
0.01828344538807869,
-0.03956463187932968,
-0.041461650282144547,
-0.058327995240688324,
0.023318752646446228,
0.0065617342479527,
-0.007187067996710539,
0.009092545136809349,
-0.028684135526418686,
-0.05861533805727959,
-0.014998707920312881,
-0.03985491767525673,
-0.043580759316682816,
0.03835371509194374,
0.011450226418673992,
-0.025320451706647873,
-0.0006104860221967101,
-0.012721932493150234,
0.06376631557941437,
-0.00573281804099679,
0.027999047189950943,
0.002421230310574174,
-0.0048568518832325935,
-0.007254240568727255,
0.03723336011171341,
0.052990518510341644,
0.020707009360194206,
0.03766504302620888,
-0.014856211841106415,
0.00015662144869565964,
0.0402633398771286,
-0.0529353991150856,
0.03344491496682167,
0.010372274555265903,
-0.04865121841430664,
0.03139590844511986,
0.014303253032267094,
-0.03591831773519516,
0.022945336997509003,
0.010625522583723068,
0.011930217035114765,
-0.02550259418785572,
0.013295358046889305,
-0.028155144304037094,
0.014353497885167599,
0.032464995980262756,
-0.021657688543200493,
-0.0968373715877533,
0.03910541161894798,
-0.0036510927602648735,
0.0474984236061573,
-0.03271501511335373,
-0.011941558681428432,
0.05735427513718605,
-0.032380688935518265,
0.02397758699953556,
-0.012464259751141071,
0.0198511965572834,
0.06378369778394699,
0.023131851106882095,
0.016305092722177505,
-0.054876282811164856,
0.03262236714363098,
0.08895266056060791,
0.055856939405202866,
-0.013686127960681915,
0.03658812865614891,
0.030157670378684998,
-0.01199969183653593,
-0.05328701063990593,
0.03238527849316597,
-0.057148244231939316,
0.017854886129498482,
-0.10094128549098969,
0.0032367787789553404,
0.009881827980279922,
-0.004290487617254257,
-0.010263164527714252,
-0.0774683952331543,
-0.0070854672230780125,
0.014123572036623955,
0.007783175446093082,
0.0011641746386885643,
-0.007108064368367195,
-0.007788830902427435,
-0.03506867215037346,
0.009040147997438908,
0.05503079295158386,
-0.00022115725732874125,
-0.03240266442298889,
0.009956036694347858,
-0.011075503192842007,
-0.01148137915879488,
0.0692567229270935,
-0.0060373032465577126,
0.0007645981968380511,
-0.012595984153449535,
-0.02081281505525112,
0.01660870388150215,
0.02801838144659996,
-0.019096985459327698,
0.04812302067875862,
0.10214274376630783,
-0.01141136884689331,
0.006580276880413294,
-0.05370812490582466,
-0.016219275072216988,
-0.014631622470915318,
-0.018271885812282562,
-0.08697200566530228,
-0.04967756196856499,
-0.029825545847415924,
0.03499572351574898,
-0.033021725714206696,
0.04372626170516014,
-0.015559057705104351,
-0.050196077674627304,
-0.00003172306969645433,
0.040486082434654236,
-0.011831460520625114,
-0.01563873142004013,
0.06487736105918884,
0.006334120873361826,
0.0029850187711417675,
-0.0018707052804529667,
0.010647010989487171,
-0.049109917134046555,
-0.006456855218857527,
0.017257267609238625,
-0.01975061558187008,
-0.04789264127612114,
-0.0026198269333690405,
-0.026344366371631622,
0.013582509011030197,
0.06144922971725464,
-0.048415157943964005,
0.040957093238830566,
-0.0006409709458239377,
-0.006762413308024406,
0.11525550484657288,
0.028820568695664406,
-0.009023929014801979,
0.023898757994174957,
-0.035473983734846115,
0.031064366921782494,
-0.027687054127454758,
0.03458976373076439,
0.00047127262223511934,
-0.017095888033509254,
-0.014011017978191376,
-0.0047489432618021965,
0.03269524872303009,
0.012032989412546158,
-0.006023204419761896,
-0.01699686236679554,
-0.05017336085438728,
0.00492203701287508,
-0.00733538344502449,
0.029687916859984398,
-0.03093915432691574,
-0.02277538552880287,
0.03636165335774422,
-0.025987934321165085,
0.04265616089105606,
-0.006278962828218937,
0.026172064244747162,
-0.010496414266526699,
0.02814796194434166,
0.024060890078544617,
-0.05089510232210159,
-0.02439303696155548,
-0.011777125298976898,
0.07794328778982162,
0.021298741921782494,
-0.06283987313508987,
0.012381738051772118,
0.03584854304790497,
0.03798984736204147,
0.021826641634106636,
-0.007163118105381727,
-0.029587652534246445,
0.05706002563238144,
0.01788889430463314,
0.04387461394071579,
0.03180728107690811,
0.009698932059109211,
-0.03396332263946533,
0.026347925886511803,
0.00767501862719655,
-0.07182471454143524,
-0.03194700554013252,
-0.01741412654519081,
-0.03398372232913971
] |
<p>As I understand it, <a href="http://en.wikipedia.org/wiki/Paramagnetism" rel="nofollow">paramagnetism</a> is similar in its short-term effect to <a href="http://en.wikipedia.org/wiki/Ferromagnetism" rel="nofollow">ferromagnetism</a> (spins of the electrons line up with the magnetic field, etc.), though apparently the effect is weaker. What is it exactly that determines whether an atom or molecule is ferromagnetic versus paramagnetic, and why is the paramagnetic effect weaker?</p> | g1267 | [
-0.00038717404822818935,
-0.019853606820106506,
-0.042476799339056015,
-0.03618929162621498,
0.08237910270690918,
0.0023090553004294634,
0.029522022232413292,
0.06153203547000885,
-0.010132001712918282,
-0.01487269252538681,
-0.01911432296037674,
-0.00029881190857850015,
0.01390844862908125,
0.0021015750244259834,
0.014216839335858822,
0.014057130552828312,
-0.004711811430752277,
0.022887898609042168,
0.06782437860965729,
0.042636044323444366,
0.008755977265536785,
0.025118380784988403,
-0.012310901656746864,
-0.008569628931581974,
-0.033370114862918854,
0.03216831758618355,
-0.06592722237110138,
-0.06893809884786606,
0.017299635335803032,
0.04123940318822861,
-0.008139177225530148,
0.01721782796084881,
0.0549338199198246,
-0.0015046321786940098,
-0.0036338004283607006,
-0.08102694898843765,
0.05613851174712181,
0.02669719234108925,
0.00004537131462711841,
0.00922014843672514,
-0.016201889142394066,
0.0016327137127518654,
-0.003089893376454711,
-0.021922729909420013,
0.019517291337251663,
-0.05928174778819084,
-0.02684437297284603,
0.026132145896553993,
-0.023471426218748093,
-0.0017713275738060474,
-0.024439621716737747,
0.013097970746457577,
0.01532441470772028,
0.03273340314626694,
0.08831901103258133,
-0.07370179146528244,
0.006048326380550861,
0.05235208943486214,
0.02853653021156788,
-0.0014103392604738474,
0.008144430816173553,
0.03787696734070778,
-0.01586981676518917,
0.04090874269604683,
0.029478242620825768,
-0.054019514471292496,
-0.03362129628658295,
-0.008629531599581242,
0.0026656403206288815,
0.014048819430172443,
-0.010716537944972515,
-0.03957150876522064,
-0.0584537573158741,
-0.03144704923033714,
-0.028982946649193764,
0.018718065693974495,
0.010332996025681496,
-0.03891318291425705,
0.0737636536359787,
0.021325405687093735,
0.06576978415250778,
0.00019952721777372062,
-0.0251685231924057,
0.052833378314971924,
-0.010749473236501217,
0.015622843988239765,
-0.012188240885734558,
-0.04132409021258354,
0.02063344232738018,
0.043612606823444366,
0.03450992330908775,
0.032468393445014954,
0.022581757977604866,
0.02297343872487545,
-0.07851199060678482,
0.0021406961604952812,
0.041520532220602036,
0.0006252128514461219,
-0.005917266942560673,
0.04008328914642334,
-0.03895169124007225,
-0.008810027502477169,
0.026868417859077454,
-0.0027598331216722727,
0.029737111181020737,
-0.023015480488538742,
-0.025836143642663956,
0.06892026960849762,
-0.030095050111413002,
-0.010085633024573326,
-0.06816529482603073,
0.009215470403432846,
-0.06036826968193054,
0.016849951818585396,
-0.06704869121313095,
-0.003377720946446061,
0.035374339669942856,
-0.0078059835359454155,
0.001028053811751306,
0.025400863960385323,
0.006759050767868757,
0.06651899963617325,
-0.022176245227456093,
0.08390431106090546,
-0.0835735946893692,
0.01671159639954567,
-0.03422696888446808,
0.006939711049199104,
0.035871345549821854,
-0.00717915128916502,
0.036760274320840836,
-0.0061867679469287395,
-0.001329449936747551,
0.018575696274638176,
-0.014713055454194546,
-0.0009680478251539171,
0.005984493065625429,
0.0006399492849595845,
-0.004504472948610783,
-0.014442476443946362,
-0.004872247576713562,
-0.004650430288165808,
0.009462314657866955,
-0.05746523663401604,
-0.05929442495107651,
0.014323151670396328,
0.0009107262012548745,
0.004985989537090063,
0.06155100464820862,
0.06275301426649094,
0.09314683079719543,
0.010236736387014389,
0.03579888120293617,
-0.01355613674968481,
-0.0183113943785429,
-0.03380493074655533,
0.006949210073798895,
-0.0028795613907277584,
0.01736193150281906,
0.02507997490465641,
0.02828441560268402,
-0.04231720045208931,
-0.007726090028882027,
-0.004663585219532251,
-0.08022018522024155,
0.02391762100160122,
0.014533733949065208,
0.008442037738859653,
-0.0361420214176178,
-0.053120192140340805,
0.007765047252178192,
0.0371871292591095,
-0.003779798047617078,
0.044406816363334656,
0.05007394775748253,
0.05670168995857239,
0.013028718531131744,
-0.03111635521054268,
0.03296975418925285,
0.001685263472609222,
-0.024776866659522057,
-0.011918465606868267,
0.021831447258591652,
-0.024019397795200348,
0.00995555054396391,
-0.00393338967114687,
-0.007362005766481161,
0.00717250257730484,
-0.11909691244363785,
-0.047048766165971756,
0.022267041727900505,
-0.04600829631090164,
-0.00837618112564087,
0.012837201356887817,
-0.004624654073268175,
-0.04201888293027878,
-0.0591462105512619,
0.046781133860349655,
-0.004278088919818401,
-0.02559707500040531,
-0.03694619610905647,
-0.023115184158086777,
0.027275871485471725,
0.04368394613265991,
0.008363612927496433,
-0.0068369158543646336,
0.008925255388021469,
0.0028343102894723415,
0.06338802725076675,
0.0373423807322979,
0.010145814158022404,
0.08352479338645935,
0.003971992991864681,
-0.034301143139600754,
-0.0016971842851489782,
0.05792945623397827,
0.03621987625956535,
0.030783724039793015,
-0.056755561381578445,
-0.002520462963730097,
0.00042707048123702407,
-0.020864026620984077,
0.04981882870197296,
-0.002941012615337968,
-0.027339961379766464,
0.013531294651329517,
-0.020102137699723244,
0.015748044475913048,
-0.040128983557224274,
0.016619320958852768,
0.013200837187469006,
-0.03956334665417671,
-0.03161168843507767,
0.0173475481569767,
0.0292489193379879,
0.0384799987077713,
0.059917349368333817,
-0.021027326583862305,
-0.005321581847965717,
-0.03461814671754837,
-0.06903354823589325,
0.005377557594329119,
-0.021530525758862495,
0.03330475091934204,
0.0009154731524176896,
-0.08098267763853073,
0.03960317000746727,
-0.06712670624256134,
-0.01777629554271698,
-0.02323889173567295,
0.0502014234662056,
0.003992714919149876,
-0.03235652297735214,
0.019453328102827072,
0.005247109569609165,
0.023977288976311684,
-0.010744402185082436,
0.0422930046916008,
-0.05616818368434906,
0.007063537370413542,
-0.02440986968576908,
-0.023910336196422577,
0.03697342425584793,
0.03599308058619499,
-0.009461275301873684,
-0.01894565112888813,
-0.04732108861207962,
0.020275965332984924,
0.039875101298093796,
-0.04421420395374298,
-0.056538015604019165,
0.06393394619226456,
-0.028491739183664322,
-0.022344471886754036,
-0.03359701856970787,
-0.013770746067166328,
-0.0014797524781897664,
0.009250925853848457,
0.010419299826025963,
0.010827681049704552,
-0.022074036300182343,
-0.02924993634223938,
-0.03769996017217636,
-0.005696537904441357,
0.004140866454690695,
0.012015366926789284,
-0.023307576775550842,
-0.02995842695236206,
-0.019950201734900475,
0.014307898469269276,
0.0087716244161129,
0.08113091439008713,
0.03471388295292854,
0.013779477216303349,
-0.004897634964436293,
-0.04776303097605705,
0.0182026457041502,
0.021973436698317528,
-0.022884739562869072,
0.0767844095826149,
0.011806557886302471,
0.061738066375255585,
0.003297594143077731,
0.010157652199268341,
0.05226593837141991,
0.058944571763277054,
-0.0607021301984787,
-0.06055707111954689,
-0.06957384198904037,
-0.0016579912044107914,
-0.05052919685840607,
0.023099135607481003,
-0.026867933571338654,
0.017029782757163048,
-0.0236704982817173,
-0.023483389988541603,
-0.04618469998240471,
0.08918094635009766,
0.044000111520290375,
0.010399897582828999,
-0.0297695342451334,
-0.05625545233488083,
-0.009644869714975357,
-0.03622567281126976,
0.03278352692723274,
0.014028643257915974,
-0.011657015420496464,
-0.03603705018758774,
0.008161474950611591,
-0.0007053579902276397,
0.026323147118091583,
0.048910461366176605,
0.013222668319940567,
-0.0049363356083631516,
-0.07217487692832947,
0.003214736934751272,
-0.005077051930129528,
0.025800805538892746,
-0.046692054718732834,
-0.03018980100750923,
0.05989520624279976,
0.005135057959705591,
-0.008832653984427452,
0.02308296039700508,
0.02136341854929924,
0.04323037713766098,
-0.05152087286114693,
-0.008318635635077953,
-0.0024002711288630962,
-0.024621114134788513,
0.025008326396346092,
0.02127271704375744,
0.025890110060572624,
-0.031032336875796318,
0.003702063811942935,
-0.0442093089222908,
0.00710191298276186,
0.0018219520570710301,
-0.037379346787929535,
0.034557510167360306,
-0.01637890189886093,
-0.01788683608174324,
0.045996975153684616,
0.008763926103711128,
-0.06027398630976677,
0.03274478390812874,
0.03039604052901268,
0.04592343047261238,
0.017866648733615875,
-0.0452483668923378,
0.006918324623256922,
-0.003759064245969057,
0.04523886367678642,
-0.0008695574942976236,
-0.008957644924521446,
-0.007862220518290997,
0.03152656555175781,
-0.00893460214138031,
-0.027858614921569824,
-0.03843563422560692,
0.007102503441274166,
0.04207674413919449,
0.010023585520684719,
0.0819929763674736,
0.026397688314318657,
-0.058663301169872284,
-0.042235493659973145,
0.006022414658218622,
-0.008704903535544872,
-0.047842543572187424,
-0.06852199137210846,
0.030065491795539856,
-0.036418367177248,
0.043493837118148804,
0.029881594702601433,
0.04684266075491905,
0.032308727502822876,
-0.02669197879731655,
0.030660148710012436,
0.023326558992266655,
-0.03889211267232895,
-0.004043731838464737,
-0.04251078516244888,
0.008795666508376598,
0.034908272325992584,
-0.015148472972214222,
0.015323705039918423,
0.02702692337334156,
-0.03425310179591179,
-0.040240608155727386,
-0.021441210061311722,
0.05948066711425781,
-0.04425177350640297,
-0.04705529659986496,
-0.03914413973689079,
0.025076674297451973,
-0.0011589151108637452,
0.009507683105766773,
0.011215537786483765,
-0.0357048399746418,
0.02425045147538185,
0.03359505906701088,
-0.006004266906529665,
-0.028730379417538643,
-0.03957943618297577,
0.07146279513835907,
0.05087687075138092,
0.03956669569015503,
0.021006198599934578,
-0.0050667207688093185,
0.019423412159085274,
0.026503808796405792,
0.0016979484353214502,
-0.01284355204552412,
-0.01675214059650898,
-0.009160218760371208,
-0.05766814202070236,
0.018842903897166252,
0.0737929567694664,
-0.03646772354841232,
0.07633992284536362,
0.05362403020262718,
0.023991771042346954,
0.050290562212467194,
-0.04335140809416771,
0.01759815774857998,
-0.03512192144989967,
0.0233464278280735,
-0.058567263185977936,
-0.04628227651119232,
-0.07250405848026276,
0.025240160524845123,
-0.028782125562429428,
-0.0018947399221360683,
-0.008091975934803486,
-0.0016391148092225194,
-0.03029884770512581,
0.01703745685517788,
0.04154587537050247,
0.06379874050617218,
-0.07486388087272644,
-0.01943083480000496,
-0.001577534363605082,
0.014083140529692173,
0.016730979084968567,
0.037925735116004944,
-0.026398159563541412,
-0.03987908363342285,
-0.10320790112018585,
0.022799275815486908,
-0.03459213301539421,
-0.01207819115370512,
0.060049887746572495,
0.016394104808568954,
0.13220669329166412,
0.028927767649292946,
0.06124274060130119,
-0.07186374068260193,
-0.010085515677928925,
-0.07868075370788574,
-0.06858689337968826,
-0.039476729929447174,
0.04009813815355301,
0.006045039277523756,
-0.01800708658993244,
0.014674806036055088,
-0.013892259448766708,
0.051146917045116425,
-0.035008903592824936,
-0.07125925272703171,
0.031211819499731064,
0.02281106635928154,
-0.05091479793190956,
-0.0637737438082695,
-0.0016440701438114047,
-0.04497840255498886,
-0.016310537233948708,
0.03729796037077904,
-0.014072855934500694,
-0.052465666085481644,
-0.038699205964803696,
0.06206367909908295,
0.034338001161813736,
-0.03906739130616188,
-0.027411706745624542,
0.03190623223781586,
0.054071322083473206,
-0.01924779824912548,
0.025513967499136925,
0.007519119884818792,
-0.07637762278318405,
-0.044354382902383804,
0.00003738476152648218,
0.03357898071408272,
0.041553083807229996,
0.06371381878852844,
-0.032279402017593384,
0.04266161471605301,
-0.013848246075212955,
0.02142668142914772,
-0.008022580295801163,
-0.008937622420489788,
0.06081797182559967,
-0.07694726437330246,
0.02126535400748253,
-0.030703630298376083,
-0.038477182388305664,
0.0005382520030252635,
0.012069962918758392,
0.07941856980323792,
0.01900872029364109,
0.011770403012633324,
0.05391279608011246,
0.013968003913760185,
0.05173772946000099,
-0.050597235560417175,
-0.02073843590915203,
-0.006718938238918781,
0.01545789372175932,
0.07832128554582596,
-0.021044103428721428,
-0.008634280413389206,
-0.00002057810706901364,
0.007019552402198315,
0.02664034441113472,
-0.025503352284431458,
0.012385318987071514,
-0.004939523991197348,
0.03128570318222046,
-0.01782746985554695,
-0.052344661206007004,
0.0024172388948500156,
-0.018462125211954117,
-0.01294360589236021,
0.036266520619392395,
0.06357431411743164,
-0.002926390152424574,
-0.04676714539527893,
0.008872765116393566,
0.012150010094046593,
0.04482598230242729,
-0.012420449405908585,
0.02281002886593342,
-0.009731222875416279,
0.028144877403974533,
0.03021128475666046,
-0.06712249666452408,
0.016393335536122322,
-0.0010556129273027182,
0.020945703610777855,
-0.02924198843538761,
-0.053462039679288864,
-0.02488064393401146,
0.01611783728003502,
-0.015586081892251968,
0.044249799102544785,
-0.0320361964404583,
-0.041357025504112244,
-0.011369598098099232,
0.01775287464261055,
0.04405943304300308,
0.001919788308441639,
0.00566421914845705,
-0.024937890470027924,
0.03985389322042465,
0.012829052284359932,
-0.03817711025476456,
0.0055159637704491615,
0.09408874064683914,
0.03478977456688881,
0.0005674315034411848,
0.011624050326645374,
-0.0022491568233817816,
-0.025807006284594536,
0.014616555534303188,
-0.029616212472319603,
-0.04622630402445793,
-0.010449064895510674,
-0.0390036404132843,
0.00026019313372671604,
0.053042177110910416,
-0.03730517625808716,
0.03782007843255997,
0.012597959488630295,
0.05893944948911667,
0.06246165931224823,
-0.012186392210423946,
0.02338763140141964,
-0.008532492443919182,
0.014895541593432426,
-0.042116567492485046,
0.0426652766764164,
-0.014276809059083462,
0.03129013627767563,
-0.011648496612906456,
-0.042590972036123276,
-0.034368667751550674,
0.04089413210749626,
-0.039513178169727325,
0.01794544793665409,
-0.060915056616067886,
-0.04291624203324318,
0.006701706908643246,
-0.012352272868156433,
0.03928820416331291,
0.01573793590068817,
0.000772109895478934,
0.027297265827655792,
-0.026830192655324936,
-0.02295428141951561,
-0.025339029729366302,
0.006679914426058531,
0.00618694256991148,
0.09755531698465347,
0.00565531849861145,
-0.05792665481567383,
0.016927102580666542,
-0.055000994354486465,
0.027823004871606827,
0.06512811034917831,
-0.03813663125038147,
-0.0367826409637928,
0.025000162422657013,
0.025115029886364937,
-0.029574887827038765,
0.0006949009257368743,
-0.034040872007608414,
-0.030759552493691444,
-0.06478998810052872,
-0.021017974242568016,
-0.004623886197805405,
0.004742584191262722,
0.006807137746363878,
0.0077462950721383095,
-0.00906960479915142,
0.05769653990864754,
-0.0129929818212986,
0.01685956120491028,
0.009823768399655819,
-0.042747195810079575,
-0.058820195496082306,
-0.010453236289322376,
-0.03487785905599594,
0.0022430915851145983,
0.027069011703133583,
0.02771940268576145,
-0.03246789053082466,
-0.028817521408200264,
0.025504376739263535,
-0.004417569376528263,
-0.02126500755548477,
-0.01999484933912754,
-0.0031898694578558207,
0.007877935655415058,
0.06311516463756561,
0.00025974950403906405,
-0.020989108830690384,
-0.019980857148766518,
0.019121652469038963,
-0.032564785331487656,
-0.05760177597403526,
0.021151047199964523,
0.04129514843225479,
-0.054723694920539856,
-0.006366390734910965,
-0.001775547512806952,
-0.07245614379644394,
0.03737103193998337,
-0.020639101043343544,
-0.04079228639602661,
0.014875583350658417,
-0.06446920335292816,
0.025082329288125038,
0.01833251677453518,
-0.0502723790705204,
0.014621741138398647,
0.013142339885234833,
-0.016348782926797867,
-0.0011580060236155987,
-0.03542240709066391,
0.02752103842794895,
-0.06359551846981049,
0.03599231317639351,
-0.02028966136276722,
0.08404769003391266,
-0.011556589975953102,
0.0027640475891530514,
0.04700328782200813,
-0.03990427032113075,
-0.030994389206171036,
0.007910418324172497,
-0.00046914213453419507,
0.04834006726741791,
0.06240981072187424,
-0.011201282031834126,
-0.006979584228247404,
-0.03057321533560753,
-0.006880468223243952,
-0.02628747932612896,
-0.020910708233714104,
-0.021086780354380608,
0.02064519189298153,
0.03740156069397926,
-0.05869143456220627,
-0.04786655679345131,
-0.008379511535167694,
0.02861359342932701,
0.03771686181426048,
0.050520047545433044,
-0.018463000655174255,
0.0014909899327903986,
0.025653230026364326,
0.015613633207976818,
-0.02540362998843193,
-0.056308723986148834,
0.04776609688997269,
0.02064608223736286,
-0.01009798888117075,
-0.0005628815852105618,
-0.039131369441747665,
0.01229044795036316,
0.023233942687511444,
-0.0222786795347929,
0.0030924093443900347,
-0.014119676314294338,
-0.026344140991568565,
-0.014837500639259815,
0.09694722294807434,
0.017965048551559448,
0.004891590215265751,
-0.061562757939100266,
-0.050174228847026825,
-0.021962618455290794,
-0.0029278805013746023,
0.03231356292963028,
0.01653248257935047,
-0.004952812101691961,
0.04774011671543121,
0.0456274040043354,
0.02247825264930725,
0.016832806169986725,
0.019856825470924377,
-0.0005612178356386721,
-0.012780862860381603,
-0.04138518124818802,
0.010913736186921597,
-0.07335082441568375,
-0.02933342568576336
] |
<p>I can conceive of a particle existing in empty spacetime, but not a wave. A wave appears to me at least, to insist upon a medium for its very definition. </p>
<p>I understand that the 19C physicists postulated the lumineferous aether for this very reason, but abandoned it in favour of the electromagnetic field.</p>
<p>In the textbooks I've looked at, its always said that the physicists eventually understood that a wave does not necessarily require a medium. But it seems to me tht they abandoned the idea of a medium mechanically conceived (I assume because of the high prestige of newtonian mechanics, its status as a defining, fundamental paradigm which privileges our naive & intuitive understanding of mechanical phenonema) for a medium conceived in a a more general manner.</p>
<p>Afterall, this field permeates spacetime, and its state evolves through time. This is how I would naively conceive of a medium in a general sense.</p>
<p>I should add this is maybe more of a history of physics question, and I've added a tag as such to stop people getting upset.</p> | g1268 | [
0.0313425213098526,
0.001681035035289824,
0.0024989955127239227,
-0.07691866159439087,
0.02358442172408104,
0.053058430552482605,
0.00818557944148779,
0.007608682848513126,
-0.0012360205873847008,
-0.08910686522722244,
0.04314553737640381,
-0.011235816404223442,
0.04069344699382782,
0.032254304736852646,
-0.014060924760997295,
-0.03997380658984184,
0.04734046384692192,
-0.015750953927636147,
0.07134250551462173,
0.0031032722909003496,
0.012922408059239388,
-0.03713417053222656,
0.019082702696323395,
-0.024720573797822,
-0.06388776749372482,
-0.03471391275525093,
0.039208292961120605,
-0.05529877915978432,
0.06755028665065765,
-0.05634437873959541,
0.0336952768266201,
-0.044126544147729874,
0.02581733651459217,
0.0028464740607887506,
-0.0037495072465389967,
-0.07306769490242004,
-0.0383206345140934,
0.06846662610769272,
-0.009442673996090889,
0.02070820890367031,
-0.029862208291888237,
-0.01749197207391262,
-0.048604097217321396,
0.02359902858734131,
0.0077722459100186825,
0.028498748317360878,
-0.04165886342525482,
-0.013680721633136272,
-0.007953895255923271,
-0.035976260900497437,
0.00597256189212203,
0.0033119029831141233,
0.030898161232471466,
0.020006783306598663,
0.011288364417850971,
0.009595435112714767,
0.018230706453323364,
0.041058868169784546,
0.09044638276100159,
0.022535745054483414,
-0.013069408014416695,
0.017606079578399658,
0.00879145972430706,
0.0245574489235878,
0.05009645223617554,
-0.0329362191259861,
-0.01940932683646679,
-0.005864466540515423,
0.028589025139808655,
-0.02097969315946102,
-0.005122514441609383,
-0.09281358122825623,
-0.05299592390656471,
-0.03748098760843277,
0.0023268277291208506,
0.06300763040781021,
-0.033636704087257385,
0.048724137246608734,
0.04041649028658867,
-0.052482955157756805,
-0.00550756836310029,
-0.019158009439706802,
0.027069028466939926,
-0.006020341068506241,
0.04439264163374901,
-0.05534449219703674,
0.003689016681164503,
-0.05234212800860405,
0.02585858851671219,
-0.014029103331267834,
-0.027256961911916733,
-0.027083614841103554,
0.07232214510440826,
0.01664884202182293,
-0.003323363373056054,
-0.04642786830663681,
0.019100328907370567,
0.044768113642930984,
0.0013788850046694279,
0.03107951581478119,
-0.01347308699041605,
-0.041753996163606644,
0.012931743636727333,
-0.00652529438957572,
0.02155870757997036,
0.0004311003431212157,
-0.024174273014068604,
-0.02883617766201496,
0.006171419285237789,
-0.00474938889965415,
-0.04313240572810173,
0.03205505758523941,
-0.05834980309009552,
-0.03969328850507736,
-0.037538859993219376,
-0.02199978195130825,
0.03150222823023796,
0.02786867506802082,
0.020442858338356018,
0.06741809844970703,
-0.0431787446141243,
0.06934180855751038,
0.023324118927121162,
0.012721705250442028,
0.016014130786061287,
0.018051104620099068,
-0.010306895710527897,
-0.03415343537926674,
-0.023780914023518562,
-0.036689210683107376,
-0.0007965718978084624,
0.03366505727171898,
-0.0038921148516237736,
0.005185393150895834,
-0.01926819421350956,
0.00893303845077753,
-0.017464812844991684,
-0.06587009876966476,
-0.022888274863362312,
0.022098559886217117,
0.03231789916753769,
-0.053580351173877716,
0.025486985221505165,
-0.038039132952690125,
-0.0015824370784685016,
-0.0016990510048344731,
0.0042005241848528385,
-0.0308308657258749,
0.047906529158353806,
0.015866611152887344,
0.011410759761929512,
0.09385265409946442,
0.001728763454593718,
0.0022826946806162596,
-0.012880279682576656,
-0.013122976757586002,
0.08956354111433029,
0.02052825503051281,
0.011097012087702751,
-0.004555738531053066,
0.05503338202834129,
0.03362024948000908,
-0.021790551021695137,
0.019229112192988396,
-0.04436846077442169,
0.008602343499660492,
-0.009018291719257832,
-0.07563701272010803,
-0.005937960930168629,
-0.009147534146904945,
-0.04486026242375374,
-0.00582600012421608,
-0.03238334134221077,
0.06805258989334106,
-0.059275127947330475,
0.04157508537173271,
0.08914707601070404,
-0.03431015461683273,
-0.01548867579549551,
-0.0016335981199517846,
0.0013898833421990275,
-0.03303825110197067,
-0.04584887996315956,
-0.08811751753091812,
-0.003655219916254282,
0.0017626398475840688,
-0.018834751099348068,
0.03625445440411568,
-0.04893047735095024,
-0.00958738848567009,
-0.01793406903743744,
-0.04905429109930992,
0.008206697180867195,
0.05066535621881485,
-0.01428031176328659,
0.012752681039273739,
0.005501606967300177,
-0.0012071988312527537,
0.005887510720640421,
-0.02249898761510849,
0.015776585787534714,
0.06012752279639244,
0.041942574083805084,
0.010135614313185215,
-0.005113908555358648,
-0.021469734609127045,
-0.04265318810939789,
0.03329368308186531,
0.026598285883665085,
-0.021651413291692734,
0.04758216068148613,
-0.003601302159950137,
-0.012768634594976902,
-0.02575569413602352,
-0.008403437212109566,
-0.04576597362756729,
-0.05704493820667267,
0.03200440853834152,
-0.0027510214131325483,
0.024380508810281754,
-0.016493849456310272,
0.011254842393100262,
0.043434228748083115,
-0.01453394629061222,
-0.03208601102232933,
0.007884879596531391,
-0.05546741560101509,
-0.003062079893425107,
0.002600689884275198,
-0.0010017924942076206,
-0.056013982743024826,
-0.023357264697551727,
-0.012962295673787594,
0.010900095105171204,
0.06388351321220398,
0.015081541612744331,
-0.045914556831121445,
0.005106620490550995,
0.03710189461708069,
0.010839028283953667,
0.0005438420921564102,
-0.010718844830989838,
-0.010153115727007389,
-0.026748280972242355,
0.016124997287988663,
-0.08369516581296921,
-0.018674060702323914,
-0.06494514644145966,
-0.03793033957481384,
-0.0029535056091845036,
0.046819690614938736,
-0.053645309060811996,
-0.021273311227560043,
-0.009220268577337265,
0.007617557886987925,
-0.011458102613687515,
0.015330723486840725,
0.028134459629654884,
-0.12300681322813034,
0.02431303821504116,
0.0125631894916296,
-0.048042602837085724,
-0.007781879976391792,
0.008928319439291954,
-0.0390513651072979,
0.003558462020009756,
-0.03949078544974327,
0.060305312275886536,
0.011832923628389835,
-0.03214763477444649,
0.05715763941407204,
0.017759395763278008,
0.005176771432161331,
-0.05342492461204529,
-0.019112462177872658,
-0.007153108716011047,
-0.02343233861029148,
-0.007193905767053366,
0.0434473417699337,
-0.04200069233775139,
0.009932557120919228,
0.010449777357280254,
-0.030078662559390068,
0.019026869907975197,
-0.0019848861265927553,
-0.09283944964408875,
0.010813969187438488,
0.03923327848315239,
-0.015500005334615707,
-0.008522974327206612,
-0.002003860892727971,
0.04594709351658821,
-0.08364550024271011,
0.0013917818432673812,
-0.06050499901175499,
0.03486107662320137,
0.029611757025122643,
-0.006010565906763077,
-0.01692616380751133,
-0.01754491962492466,
-0.037400808185338974,
-0.02291388250887394,
0.05549858883023262,
-0.026939895004034042,
0.0184637438505888,
0.007340616546571255,
-0.023735634982585907,
-0.045238494873046875,
-0.020001038908958435,
-0.019462458789348602,
0.0011841050582006574,
0.08195219933986664,
-0.008200782351195812,
0.027794577181339264,
-0.07890103757381439,
0.03869735077023506,
0.03487378731369972,
-0.014589909464120865,
0.03238241374492645,
0.0031591239385306835,
-0.005565862637013197,
0.02134752832353115,
0.07472651451826096,
-0.019762467592954636,
0.055452823638916016,
0.006924331188201904,
0.027549229562282562,
-0.011211685836315155,
-0.07204540073871613,
-0.010392438620328903,
-0.044511277228593826,
-0.019920984283089638,
0.004056710284203291,
-0.018638864159584045,
-0.023429298773407936,
-0.07060703635215759,
-0.016226382926106453,
0.00038294357364065945,
0.0163074042648077,
-0.012335768900811672,
0.04416905716061592,
-0.039416152983903885,
0.008765063248574734,
0.05433039739727974,
0.02102561481297016,
0.04135093837976456,
-0.008962633088231087,
-0.02276911586523056,
-0.0005638328148052096,
-0.007761066313832998,
0.03918160870671272,
0.031218821182847023,
0.015329831279814243,
0.02540353499352932,
-0.026009129360318184,
0.013418366201221943,
0.08918453007936478,
0.02661977708339691,
0.05436599999666214,
-0.042761072516441345,
-0.0059264423325657845,
-0.04059996083378792,
0.05257502943277359,
-0.034644946455955505,
0.01031955424696207,
0.021941227838397026,
-0.019959615543484688,
-0.006863783113658428,
-0.0071296994574368,
-0.02366485632956028,
0.03532487899065018,
-0.013569023460149765,
-0.05289767310023308,
0.05365344136953354,
-0.0037629057187587023,
-0.019873367622494698,
0.03125864639878273,
0.011712403036653996,
-0.05268505960702896,
-0.012998067773878574,
0.013184770941734314,
-0.01048824843019247,
0.0306941457092762,
-0.011840908788144588,
-0.013439938426017761,
0.05675039812922478,
-0.054917074739933014,
0.02779858000576496,
-0.049721624702215195,
-0.007003445643931627,
0.04695729911327362,
0.0522596500813961,
-0.004284391645342112,
-0.03856639936566353,
-0.011530047282576561,
0.030109478160738945,
-0.0038437186740338802,
-0.06106271222233772,
0.04926066845655441,
-0.019245455041527748,
0.035579223185777664,
0.004558498039841652,
0.041724227368831635,
-0.01375512033700943,
0.029514897614717484,
0.055004894733428955,
0.05587620660662651,
-0.05416363477706909,
0.02967510186135769,
-0.03776294365525246,
0.01852111704647541,
0.033843811601400375,
-0.016407540068030357,
-0.08318118005990982,
-0.008839503861963749,
-0.05422482639551163,
-0.017140623182058334,
-0.04936935007572174,
0.041980694979429245,
0.08094381541013718,
-0.027200140058994293,
0.028562162071466446,
-0.0015293060569092631,
-0.012260602787137032,
0.027234839275479317,
0.07805106788873672,
-0.0053400155156850815,
0.008445069193840027,
-0.048749860376119614,
-0.03583851456642151,
-0.0099739795550704,
0.023009900003671646,
-0.006012227386236191,
0.027038486674427986,
0.015372594818472862,
-0.004476368892937899,
-0.03906092047691345,
0.04111726954579353,
0.08371855318546295,
0.0014226454077288508,
0.07678215950727463,
-0.01662958599627018,
0.015218852087855339,
-0.030276643112301826,
-0.010855361819267273,
0.029454641044139862,
0.0021305319387465715,
-0.009313729591667652,
-0.023483317345380783,
0.002837994135916233,
0.008317840285599232,
0.04122139886021614,
-0.039211075752973557,
-0.032888613641262054,
-0.033207520842552185,
-0.003725973656401038,
-0.06559281796216965,
0.006496366113424301,
0.001495579956099391,
0.01227402314543724,
-0.058905258774757385,
0.034297097474336624,
0.01807677373290062,
0.0639917254447937,
0.012943250127136707,
0.012136789970099926,
0.016256902366876602,
-0.005951198749244213,
-0.08964181691408157,
-0.023279309272766113,
-0.017460525035858154,
0.0038100332021713257,
0.04377507418394089,
-0.03147924691438675,
-0.02258850820362568,
-0.011463940143585205,
-0.019575709477066994,
-0.04152423515915871,
-0.039289381355047226,
0.02966460958123207,
-0.0024573008995503187,
0.006732936017215252,
0.04509709030389786,
0.06399799883365631,
-0.03626693785190582,
0.07537668943405151,
-0.03862234577536583,
0.08412480354309082,
-0.04365751892328262,
-0.02954074740409851,
0.02620549127459526,
-0.0593661367893219,
0.008425609208643436,
0.010460155084729195,
-0.0017762104980647564,
-0.02700042724609375,
-0.022726750001311302,
0.00710378447547555,
-0.018392618745565414,
-0.005153521429747343,
-0.05221211910247803,
-0.031198827549815178,
0.013243436813354492,
-0.016228139400482178,
-0.028368821367621422,
-0.030611315742135048,
0.022722693160176277,
0.023874014616012573,
-0.018318725749850273,
0.09162645041942596,
0.027233218774199486,
-0.02060312032699585,
-0.037774380296468735,
0.04639376699924469,
0.09420839697122574,
0.00857852678745985,
-0.03569916635751724,
0.0225240346044302,
-0.022692160680890083,
0.0031644366681575775,
-0.06606649607419968,
-0.007158995606005192,
0.06141900643706322,
-0.024765141308307648,
-0.00012303378025535494,
0.04606525972485542,
-0.06923160701990128,
-0.01494179479777813,
0.004614317324012518,
0.01339412946254015,
0.03361102566123009,
0.0268308874219656,
0.06279518455266953,
-0.013806945644319057,
-0.000035474440664984286,
-0.034829165786504745,
-0.01508322637528181,
0.0600140206515789,
0.0030689085833728313,
0.012819802388548851,
-0.06378939002752304,
-0.030701516196131706,
-0.02432730793952942,
0.02244388870894909,
0.03929523751139641,
0.0759260356426239,
0.050207074731588364,
0.039442092180252075,
0.07151197642087936,
-0.04868479073047638,
-0.04865449666976929,
-0.007078204303979874,
0.022640708833932877,
-0.007898512296378613,
-0.0037841899320483208,
0.04135504737496376,
-0.034574586898088455,
-0.017123466357588768,
0.00953851267695427,
-0.02023475617170334,
0.0051317219622433186,
0.048386696726083755,
0.004944908898323774,
-0.023976698517799377,
-0.025924982503056526,
0.0011626860359683633,
0.03825925663113594,
-0.03442522883415222,
0.06406616419553757,
0.04113566875457764,
-0.02220364660024643,
0.038149334490299225,
-0.028599034994840622,
-0.05071184039115906,
0.019977107644081116,
0.04297365993261337,
0.025648340582847595,
0.0016851590480655432,
-0.008658938109874725,
0.03909052908420563,
0.04597204923629761,
0.01696832850575447,
0.0058943419717252254,
-0.06270900368690491,
-0.02688544988632202,
0.015883807092905045,
-0.02376493811607361,
0.009409486316144466,
0.05278888717293739,
0.05185747146606445,
0.005308654624968767,
0.01133820042014122,
-0.021434204652905464,
-0.03856026753783226,
0.008685928769409657,
0.051557958126068115,
-0.0012532685650512576,
-0.03386760130524635,
-0.0676284059882164,
0.012536874040961266,
0.034863051027059555,
0.0014494797214865685,
-0.04190884530544281,
0.005516848061233759,
0.05175730213522911,
0.05635222792625427,
0.004816058091819286,
-0.02559703029692173,
0.0031906391959637403,
-0.024852054193615913,
-0.024793703109025955,
-0.010508952662348747,
-0.021234242245554924,
-0.028456928208470345,
0.008011434227228165,
-0.020717492327094078,
-0.0277246180921793,
0.07309973984956741,
-0.011543414555490017,
-0.011098730377852917,
0.04645765945315361,
0.002006599446758628,
0.042325351387262344,
0.014150045812129974,
-0.009040405042469501,
-0.03399152308702469,
-0.0284623671323061,
0.03667265921831131,
0.06456774473190308,
-0.03758187219500542,
-0.011005007661879063,
-0.029330283403396606,
0.0075367107056081295,
0.029247745871543884,
-0.006221785210072994,
-0.0015180613845586777,
-0.009765910916030407,
-0.0442727766931057,
0.05187638849020004,
-0.09240903705358505,
-0.0037899103481322527,
0.01313711702823639,
0.06293875724077225,
0.04276794195175171,
-0.04667193070054054,
0.009138574823737144,
0.05032147094607353,
-0.007338843774050474,
-0.030927203595638275,
0.024250425398349762,
-0.01673867553472519,
-0.020687265321612358,
-0.03315969929099083,
0.01886722631752491,
-0.013553661294281483,
0.07948841899633408,
-0.04733528941869736,
0.005956042092293501,
0.033094026148319244,
-0.09056272357702255,
-0.01191625650972128,
-0.06736944615840912,
-0.0004934010794386268,
-0.02807706966996193,
-0.02960679680109024,
0.05877133086323738,
-0.0059684463776648045,
-0.017687706276774406,
0.018604369834065437,
-0.017167305573821068,
0.01204703375697136,
0.029347741976380348,
0.016657741740345955,
-0.047599490731954575,
-0.0201121736317873,
-0.0362638421356678,
-0.05438302084803581,
0.057964909821748734,
0.012868478894233704,
0.013243574649095535,
-0.030905896797776222,
0.02805235981941223,
-0.004133080597966909,
0.030336808413267136,
0.00976268295198679,
0.024829421192407608,
-0.03819848224520683,
0.001779034617356956,
-0.04091581329703331,
-0.003263188758864999,
-0.02269841730594635,
0.03033537045121193,
0.030727887526154518,
0.004443199839442968,
0.05844506621360779,
-0.027914300560951233,
0.12276066094636917,
0.023660877719521523,
0.060839347541332245,
-0.03272491693496704,
-0.09146976470947266,
-0.004271185025572777,
-0.016867468133568764,
0.00262983120046556,
0.013900897465646267,
-0.013154002837836742,
0.015526548959314823,
0.014727996662259102,
-0.04947706311941147,
0.018673067912459373,
-0.037524279206991196,
0.038543444126844406,
0.026250330731272697,
0.0012395764933899045,
0.0357944630086422,
0.028434768319129944,
-0.015114380978047848,
0.0391988530755043,
0.013902876526117325,
-0.011619264259934425,
0.004927505739033222,
0.018620124086737633,
-0.023345833644270897,
-0.03259405493736267,
-0.02442844957113266,
0.050562020391225815,
0.03160029649734497,
-0.020438335835933685,
-0.00012868396879639477,
-0.06961041688919067,
-0.025277186185121536,
0.01708187535405159,
-0.014578902162611485,
0.004858043044805527,
-0.05570511147379875,
0.0006540077738463879,
-0.026678353548049927,
0.028085676953196526,
0.01487978920340538,
-0.0039040828123688698,
-0.008066368289291859,
0.0007215215009637177,
-0.006835029926151037,
-0.0012673153541982174,
-0.014736620709300041,
0.038610782474279404,
-0.017250627279281616,
0.017786746844649315,
0.00289147044532001,
-0.01955294981598854,
-0.014372523874044418,
0.0852106511592865,
-0.009839912876486778,
0.05674142390489578,
0.07102152705192566,
-0.08671661466360092,
0.039686765521764755,
-0.014018521644175053,
0.03145449236035347,
-0.06167256832122803,
0.01573159545660019,
-0.01688304729759693,
0.029064465314149857,
-0.015226918272674084,
-0.030774695798754692,
0.03201381117105484,
0.030238570645451546,
0.008661092258989811
] |
<p>As a fun project, I would like to roughly simulate the suspension operation of a full-suspension mountain bike. This is <em>not</em> another one of those "How does a bicycle stay upright?" questions.</p>
<p>Follow some metrics of interest.</p>
<ul>
<li>Pedal bob - the amount of movement in the rear triangle upon pedaling up an incline. An estimate of the lost energy due to this.</li>
<li>Sharp obstacle transient response - for example how does the bike move, when hitting a curb at high speed.</li>
<li>Large obstacle transient response - for example, how does the bike move when it falls (along with the rider) 1 meter.</li>
</ul>
<p>I am somewhat familiar with python, Mathematica, <a href="http://www.scilab.org/" rel="nofollow">ScyLab</a>, Matlab, Ansys. I guess an analytical solution would be too difficult.</p>
<p><em>Which approach will give quickly a parameterizable model and analyze it for the abovementioned information?</em></p>
<p><a href="http://www.bikeradar.com/gear/article/buyers-guide-to-mountain-bike-suspension-part-2-28438/" rel="nofollow">Here</a> several common frame variations are mentioned.</p>
<p>EDIT:</p>
<p>More concretely:</p>
<ul>
<li>What model to use? Is there a widespread "bicycle" model for dynamic analysis?</li>
<li>What software to utilize, in order to help me solve the problem?</li>
</ul> | g1269 | [
0.025514423847198486,
0.031837720423936844,
0.005000732373446226,
0.024104731157422066,
-0.019823918119072914,
-0.03956472873687744,
0.05899117514491081,
-0.0040940940380096436,
-0.061468206346035004,
0.008160575293004513,
-0.002289713127538562,
-0.039060454815626144,
-0.0048665511421859264,
0.012776022776961327,
-0.0107621680945158,
-0.0177784264087677,
0.013095560483634472,
-0.026448357850313187,
-0.007052641361951828,
-0.00413914117962122,
0.006642240099608898,
0.08904557675123215,
-0.003185887821018696,
-0.012293747626245022,
-0.008095361292362213,
0.00969548337161541,
-0.040451910346746445,
0.02494419366121292,
-0.014899819158017635,
0.035067420452833176,
-0.03659893572330475,
-0.006879362743347883,
0.02044779434800148,
-0.04127264395356178,
-0.03141007572412491,
0.04740757867693901,
0.02549785189330578,
-0.03568192198872566,
-0.04859241098165512,
0.007456881459802389,
0.02688680589199066,
-0.04679834097623825,
-0.03478333353996277,
0.058247800916433334,
0.018012048676609993,
-0.025787999853491783,
0.016063090413808823,
-0.01600959151983261,
-0.01250498928129673,
-0.01146347913891077,
-0.03207322582602501,
0.06749209016561508,
-0.014845185913145542,
0.012416355311870575,
0.03098309226334095,
0.011682848446071148,
0.05898027494549751,
0.03543458133935928,
0.0429718941450119,
-0.018987048417329788,
-0.059773195534944534,
-0.06977684050798416,
-0.025787003338336945,
-0.04766825959086418,
-0.03253629803657532,
-0.03147675842046738,
-0.01783849485218525,
-0.05370927229523659,
0.09330795705318451,
-0.025091489776968956,
0.02885538898408413,
-0.033205196261405945,
-0.0004087022680323571,
-0.038050614297389984,
-0.014785101637244225,
0.012941469438374043,
-0.0460214726626873,
-0.0420653335750103,
0.019353214651346207,
-0.008184811100363731,
-0.04301639646291733,
0.10304656624794006,
-0.015361192636191845,
-0.02008647844195366,
0.009061308577656746,
-0.008835374377667904,
0.01487826369702816,
0.03800586611032486,
-0.05603327974677086,
-0.04292730242013931,
-0.014598356559872627,
-0.02250109612941742,
0.06967700272798538,
0.0009862743318080902,
-0.007827620953321457,
-0.046946391463279724,
-0.1071198582649231,
0.09764602035284042,
0.025653868913650513,
0.029656212776899338,
0.004347189795225859,
-0.03188348934054375,
-0.030224725604057312,
-0.018065452575683594,
0.012714791111648083,
-0.058814454823732376,
0.005800728686153889,
-0.0033068067859858274,
0.020341187715530396,
-0.03955098241567612,
-0.031020058318972588,
-0.015191799961030483,
-0.014439866878092289,
-0.07337256520986557,
-0.09040071070194244,
-0.001931260689161718,
0.12408336251974106,
-0.0007089626742526889,
-0.0032828347757458687,
-0.01655973494052887,
-0.01875176467001438,
-0.02397835999727249,
-0.07296324521303177,
0.03473154082894325,
-0.026143863797187805,
-0.0038100702222436666,
-0.0363423116505146,
0.011454187333583832,
0.013099445961415768,
0.052464310079813004,
0.026950037106871605,
-0.008300618268549442,
-0.0110628642141819,
-0.009324951097369194,
0.028733504936099052,
0.04242506995797157,
-0.01500139944255352,
0.043134815990924835,
0.013911936432123184,
0.040969520807266235,
0.047008536756038666,
-0.06481200456619263,
-0.07085425406694412,
0.022258147597312927,
-0.01730797253549099,
0.07145833969116211,
-0.04732502996921539,
0.0709628313779831,
0.05017827823758125,
-0.004746356047689915,
0.0062043312937021255,
0.08654820919036865,
-0.03455081954598427,
0.0004929265123791993,
0.02944329008460045,
0.00791358295828104,
0.0023488060105592012,
-0.0053124455735087395,
-0.017582399770617485,
0.03952454775571823,
0.012985646724700928,
-0.062092557549476624,
0.031243184581398964,
-0.011359496042132378,
-0.04415528103709221,
0.058595817536115646,
-0.0392281673848629,
-0.028950285166502,
-0.028658738359808922,
0.01336611621081829,
-0.006664056796580553,
-0.04465726017951965,
0.002983570797368884,
0.025606481358408928,
0.017155686393380165,
0.010331666097044945,
0.03445006534457207,
-0.0016689910553395748,
0.024871159344911575,
0.035322155803442,
0.0026617920957505703,
-0.01402897760272026,
0.016839899122714996,
0.007828951813280582,
-0.01042106281965971,
-0.0035928499419242144,
0.05321910232305527,
0.027675559744238853,
-0.03290198743343353,
-0.04495900869369507,
0.027398332953453064,
-0.008957848884165287,
-0.027577538043260574,
-0.02428055740892887,
-0.029931537806987762,
-0.03778243064880371,
0.03976459801197052,
-0.02661951258778572,
-0.022067837417125702,
0.01688978634774685,
0.055029209703207016,
-0.02636227011680603,
-0.009068969637155533,
0.042211905121803284,
-0.01406184397637844,
-0.04251984879374504,
0.015996336936950684,
-0.02503437176346779,
-0.011896935291588306,
-0.024221111088991165,
0.012006490491330624,
-0.02789146639406681,
0.009565338492393494,
0.05319036915898323,
0.013374237343668938,
-0.04294813796877861,
-0.0189075730741024,
-0.022489603608846664,
0.03570428490638733,
0.03473730757832527,
0.0014775012386962771,
-0.03999459743499756,
-0.04782763868570328,
-0.008862907998263836,
-0.05053827539086342,
-0.022586390376091003,
-0.024701053276658058,
0.016102196648716927,
-0.0257568396627903,
0.05539112538099289,
0.0688750147819519,
0.10179467499256134,
-0.010435695759952068,
-0.042903147637844086,
0.059853024780750275,
0.034466203302145004,
0.009279778227210045,
0.010656328871846199,
0.003825460560619831,
-0.037575311958789825,
0.03994115814566612,
0.00414773216471076,
0.03339570388197899,
-0.036665137857198715,
-0.004489043727517128,
-0.020330525934696198,
0.03793173283338547,
0.06585598737001419,
-0.016195904463529587,
-0.004765172954648733,
0.01426471583545208,
-0.017425719648599625,
0.010106658563017845,
-0.005939456634223461,
-0.002223306568339467,
-0.019931567832827568,
0.014026673510670662,
-0.08633270114660263,
-0.0534076914191246,
0.033569782972335815,
-0.0073350295424461365,
-0.03952294588088989,
0.004585277289152145,
0.057533908635377884,
-0.02006216160953045,
-0.028305942192673683,
0.049904122948646545,
-0.059422530233860016,
-0.06785789877176285,
0.011437197215855122,
-0.007757633924484253,
-0.04569385573267937,
-0.028036797419190407,
0.023703886196017265,
-0.024225035682320595,
-0.06740796566009521,
-0.004905057605355978,
0.02268565632402897,
-0.010581749491393566,
-0.0070588113740086555,
0.017455168068408966,
-0.08611311763525009,
-0.006814196705818176,
0.03191190958023071,
0.022215846925973892,
0.016917286440730095,
0.004865783732384443,
-0.028036169707775116,
0.003553230781108141,
0.0015637619653716683,
0.007055630441755056,
-0.0041479854844510555,
0.0024069391656666994,
0.0507284551858902,
-0.044596116989851,
0.05314856022596359,
-0.08303742110729218,
-0.028075428679585457,
-0.06091516092419624,
-0.012376947328448296,
-0.006365585140883923,
0.018799377605319023,
0.04699750989675522,
0.006832065060734749,
-0.02968898043036461,
0.015822671353816986,
-0.04628509655594826,
-0.008810347877442837,
-0.014792858622968197,
0.004657231271266937,
-0.03264860063791275,
-0.0027819739188998938,
-0.04245941340923309,
0.00394668523222208,
-0.024771425873041153,
0.06845004856586456,
0.007748155854642391,
0.009031029418110847,
-0.007364129647612572,
-0.019169477745890617,
-0.04955523461103439,
-0.05008983612060547,
-0.006801628973335028,
0.048388175666332245,
0.006001921370625496,
0.043200619518756866,
-0.052371278405189514,
0.09788824617862701,
-0.03649226948618889,
-0.055672537535429,
0.046239882707595825,
-0.00784586276859045,
0.0605187863111496,
-0.02522421069443226,
-0.007205271627753973,
-0.06297965347766876,
0.09010297060012817,
-0.03410506248474121,
0.032034505158662796,
-0.0226580910384655,
0.030872700735926628,
-0.014182907529175282,
-0.012978415936231613,
-0.03857816383242607,
0.007707496639341116,
-0.008618693798780441,
-0.0078005604445934296,
-0.03044041246175766,
-0.004831365775316954,
-0.02871367521584034,
0.02620050124824047,
0.03537382557988167,
-0.0017372736474499106,
-0.04646230861544609,
0.008986403234302998,
-0.01858827844262123,
0.01599264144897461,
-0.03498721867799759,
-0.03150973469018936,
0.0660056471824646,
0.05619153380393982,
-0.0020721557084470987,
0.025348637253046036,
0.05908246710896492,
0.013400179333984852,
-0.02036520093679428,
-0.03413192927837372,
0.022267375141382217,
-0.03031386062502861,
0.006456347182393074,
0.0589175820350647,
0.03738550469279289,
0.010354313999414444,
-0.04315970838069916,
-0.0005007248255424201,
-0.041690245270729065,
0.007624605670571327,
0.02191777713596821,
0.05827351287007332,
0.029021430760622025,
0.02713039331138134,
-0.010927435010671616,
0.022601192817091942,
-0.07533913850784302,
0.030184905976057053,
-0.004726912826299667,
-0.034150585532188416,
0.02970830164849758,
0.019871776923537254,
-0.0035920697264373302,
0.09982776641845703,
-0.05970732122659683,
-0.0597652867436409,
0.0037606859114021063,
0.0425758957862854,
0.004420374520123005,
-0.03460907191038132,
-0.02259729988873005,
0.0022481041960418224,
0.04006044194102287,
-0.0026385136879980564,
0.013718048110604286,
-0.023326195776462555,
0.027539806440472603,
-0.019741903990507126,
0.02533884532749653,
0.031308863312006,
-0.04635586217045784,
-0.03085547499358654,
0.01616962067782879,
0.058922600001096725,
0.03461350128054619,
0.01667892374098301,
-0.07726966589689255,
-0.000028575414035003632,
-0.02613423950970173,
0.03303540498018265,
0.029575157910585403,
0.021220482885837555,
0.054934579879045486,
-0.012031786143779755,
0.031184539198875427,
-0.024114616215229034,
-0.0019190054154023528,
0.004468788392841816,
0.048840925097465515,
-0.03220876306295395,
0.02888033352792263,
-0.08631092309951782,
0.045183002948760986,
-0.005017411895096302,
0.04357677698135376,
0.02787485532462597,
0.03438903018832207,
-0.015282860025763512,
0.03873664513230324,
0.029702510684728622,
0.015210938639938831,
0.00970748346298933,
-0.039311256259679794,
-0.011026117950677872,
0.06063578277826309,
-0.010240618139505386,
-0.012581072747707367,
-0.025710251182317734,
-0.004289247561246157,
0.04363881051540375,
-0.030040903016924858,
-0.01351705938577652,
-0.050346046686172485,
-0.04453214630484581,
-0.004991188179701567,
0.009039421565830708,
0.00888567790389061,
-0.0076331766322255135,
-0.005946843884885311,
0.0659797340631485,
-0.007585413288325071,
-0.000753918313421309,
0.002583644352853298,
-0.015327021479606628,
-0.017485400661826134,
-0.030675586313009262,
-0.03755466639995575,
-0.049150414764881134,
0.021189415827393532,
-0.011290134862065315,
-0.030915673822164536,
0.0021935715340077877,
-0.014883466064929962,
-0.0035925586707890034,
-0.04013579711318016,
0.014772363007068634,
0.017361247912049294,
0.093874990940094,
-0.006385494489222765,
-0.055090807378292084,
-0.007981419563293457,
0.03720298409461975,
-0.00386931374669075,
0.004993523936718702,
-0.044179778546094894,
0.0098244808614254,
-0.02516363002359867,
-0.02334182895720005,
-0.04178624227643013,
0.018008891493082047,
-0.009370725601911545,
-0.01781994290649891,
0.011585486121475697,
0.007834302261471748,
0.06868511438369751,
-0.04459761083126068,
-0.031112106516957283,
0.05239036679267883,
-0.011254516430199146,
-0.005103643052279949,
0.04410974308848381,
-0.010264920070767403,
0.021825077012181282,
-0.028833501040935516,
0.007423345930874348,
0.047413893043994904,
-0.03780920431017876,
-0.013013350777328014,
0.008697353303432465,
0.07026556879281998,
0.005058446899056435,
-0.026689020916819572,
0.055352833122015,
-0.0375768207013607,
0.07605556398630142,
-0.0033470073249191046,
0.04346771538257599,
-0.046999137848615646,
-0.0322178415954113,
0.05913078412413597,
0.03383483737707138,
-0.0011405390687286854,
-0.0016571084270253778,
0.054015543311834335,
-0.013523201458156109,
0.07703736424446106,
-0.006749620195478201,
-0.001825859653763473,
0.03736872598528862,
0.014267103746533394,
-0.05634896457195282,
-0.005249788518995047,
-0.04809562489390373,
-0.028407908976078033,
-0.019484061747789383,
-0.03238343447446823,
0.02487836219370365,
-0.07208391278982162,
0.0025642146356403828,
0.03825313225388527,
0.02114712819457054,
-0.040030546486377716,
-0.037342485040426254,
-0.03417840600013733,
0.04797951877117157,
0.019552895799279213,
0.0707191452383995,
0.02013019286096096,
-0.016770044341683388,
0.018293872475624084,
-0.0018262728117406368,
0.021531106904149055,
-0.08862485736608505,
0.022886984050273895,
0.016912102699279785,
-0.022431805729866028,
0.011594393290579319,
0.010457421652972698,
0.026973513886332512,
0.011570481583476067,
-0.08307952433824539,
-0.02045081928372383,
0.0003086550859734416,
0.005768961273133755,
0.03190822899341583,
0.05762682482600212,
0.017581529915332794,
0.035782817751169205,
0.03288247808814049,
-0.017593098804354668,
-0.006692445371299982,
0.0612994022667408,
-0.042573556303977966,
0.019212180748581886,
-0.027002178132534027,
-0.0037308470346033573,
0.0031280035618692636,
-0.0002688668027985841,
0.0028533160220831633,
-0.010940199717879295,
-0.013263771310448647,
-0.03226563334465027,
0.016482990235090256,
0.01717490702867508,
0.004759082105010748,
-0.0007936523761600256,
0.016107451170682907,
-0.03150204196572304,
-0.0026378626935184,
-0.09037771821022034,
0.0013830347452312708,
-0.012448262423276901,
0.04407115280628204,
0.01289334986358881,
0.040849167853593826,
-0.0332980677485466,
-0.059372540563344955,
0.028057733550667763,
0.010822860524058342,
0.02667444571852684,
0.010660500265657902,
-0.015163007192313671,
0.03970732167363167,
0.027696240693330765,
0.012741610407829285,
0.02463235892355442,
-0.0764952301979065,
0.02123548462986946,
0.02947758510708809,
0.004057392943650484,
0.031619857996702194,
-0.02172056771814823,
-0.03578072786331177,
-0.026927199214696884,
0.03268762677907944,
0.05979420617222786,
0.012057381682097912,
-0.07930778712034225,
0.02983269840478897,
-0.004544819705188274,
0.0144709637388587,
-0.01779627427458763,
-0.021452387794852257,
-0.09238150715827942,
0.014185340143740177,
0.015963999554514885,
-0.03292624652385712,
0.029040003195405006,
-0.020942796021699905,
-0.04856039211153984,
-0.014711695723235607,
0.020981401205062866,
-0.006777247879654169,
0.05327307805418968,
0.037469882518053055,
-0.004147012252360582,
0.03350161761045456,
-0.02348204329609871,
0.09835775941610336,
-0.03779226168990135,
0.03590874746441841,
0.04588783159852028,
0.04122794046998024,
0.04611553996801376,
0.032278843224048615,
-0.04653046280145645,
0.003936382010579109,
-0.0016205088468268514,
-0.04086147993803024,
0.005617741495370865,
0.05237147584557533,
0.008935692720115185,
-0.0029304104391485453,
0.0650249570608139,
0.00783560425043106,
0.025678927078843117,
0.005834334064275026,
-0.059755221009254456,
0.005221449304372072,
-0.0413188673555851,
0.04573630541563034,
0.04806290939450264,
-0.037818774580955505,
0.01419107336550951,
-0.04504845663905144,
0.0328986756503582,
-0.04288735240697861,
0.022753208875656128,
0.006949012633413076,
-0.010394943878054619,
0.011705662123858929,
0.0547393299639225,
0.04119535908102989,
0.01141507737338543,
-0.027397820726037025,
-0.06375265121459961,
0.030771272256970406,
0.037265367805957794,
-0.04787247255444527,
-0.04272116720676422,
-0.01746399514377117,
-0.025403043255209923,
-0.010425317101180553,
-0.005485570058226585,
0.06903008371591568,
0.004606134258210659,
-0.004080199636518955,
0.027507025748491287,
0.022514227777719498,
0.020022373646497726,
0.04539933800697327,
-0.041521087288856506,
-0.03732931241393089,
-0.013469529338181019,
0.10924921929836273,
-0.005477914121001959,
-0.039984315633773804,
-0.037915054708719254,
0.023250693455338478,
-0.035759199410676956,
-0.02767106331884861,
0.05035306140780449,
0.008907054550945759,
0.03512094169855118,
0.012591378763318062,
-0.013682874850928783,
0.04830891266465187,
0.004194242414087057,
-0.04728778824210167,
-0.02860182337462902,
-0.029476223513484,
0.021821800619363785,
0.011456555686891079,
0.04384351894259453,
0.054805856198072433,
-0.016738012433052063,
0.014331347309052944,
-0.0417756624519825,
-0.007261640392243862,
0.022496765479445457,
-0.015489463694393635,
-0.030851365998387337,
-0.019163165241479874,
0.02823253534734249,
-0.0026176138781011105,
0.010106104426085949,
0.04944396764039993,
0.07214780151844025,
-0.10796026140451431,
-0.03177648410201073,
0.07696402072906494,
0.013504412956535816,
-0.022212114185094833,
-0.028623094782233238,
-0.04424074664711952,
-0.04992980509996414,
-0.0025879342574626207,
-0.006319444160908461,
0.014179452322423458,
0.021033335477113724,
-0.07203306257724762,
0.004159411881119013,
-0.025872427970170975,
-0.033628616482019424,
0.050306711345911026,
-0.02532772533595562,
-0.006732296664267778,
0.06711164861917496,
-0.026229988783597946,
-0.006576623767614365,
-0.030318913981318474,
0.05461091175675392,
-0.03716691583395004,
0.011920657940208912,
-0.013949904590845108,
0.05109195411205292,
0.0007427894743159413,
-0.019446173682808876,
-0.009236173704266548,
-0.016148891299962997,
-0.03193362057209015,
0.019475003704428673,
-0.010535185225307941,
0.01032052282243967,
0.028654666617512703,
-0.026018274948000908,
-0.013757511042058468,
0.011023573577404022,
-0.025180695578455925,
-0.012113337405025959,
-0.016782814636826515
] |
<p>In order to determine the relative motion between the Earth and the ether (the medium through which light supposedly propagated. It has zero density and complete transparency), scientists used the concept of the <a href="http://en.wikipedia.org/wiki/Aberration_of_light" rel="nofollow">aberration of starlight</a>. If the Earth frame of reference was not <a href="http://en.wikipedia.org/wiki/Aether_drag_hypothesis" rel="nofollow">dragging the ether frame of reference</a>, then the direction of starlight as seen from both frames of reference separately would be different. Whereas if the Earth frame of reference was indeed dragging the ether frame of reference, then the starlight observed from both frames of reference separately would appear to come from the same direction. This is all intuitive. But how do we prove whether either is the case, when we are unable to identify the ether frame of reference itself, and conduct experiments within this frame of reference to determine the observed direction of starlight from within this frame of reference?</p> | g1270 | [
0.01322221476584673,
0.013474511913955212,
0.009365784004330635,
-0.066053606569767,
0.022540342062711716,
0.03149676322937012,
0.07210085541009903,
0.004124296363443136,
-0.0289140734821558,
-0.0036379615776240826,
0.0739508718252182,
-0.0022844464983791113,
0.10358194261789322,
0.027417268604040146,
0.002538819797337055,
-0.019447892904281616,
0.07562301307916641,
-0.030473746359348297,
0.02432573027908802,
0.015140612609684467,
0.021292388439178467,
0.026852600276470184,
0.00389279518276453,
-0.018147237598896027,
0.0019194157794117928,
-0.056290823966264725,
0.016786755993962288,
-0.06566599011421204,
-0.05571886897087097,
-0.022258834913372993,
0.07084675133228302,
-0.049716223031282425,
0.055668506771326065,
-0.03138752654194832,
0.03587164729833603,
-0.034765906631946564,
-0.047526538372039795,
0.07152040302753448,
-0.005460710730403662,
-0.011132434010505676,
0.039730533957481384,
0.026985444128513336,
-0.010229204781353474,
0.009878510609269142,
0.019636336714029312,
0.01747913472354412,
0.02238618955016136,
-0.0029834068845957518,
0.004481242038309574,
-0.01680152863264084,
-0.011174021288752556,
0.10642899572849274,
-0.02484782412648201,
0.021378517150878906,
-0.05076826736330986,
-0.016177838668227196,
0.0026220304425805807,
-0.00781846884638071,
0.058043330907821655,
0.025200458243489265,
0.0068568033166229725,
-0.015329648740589619,
0.016615215688943863,
-0.02254277653992176,
0.022932445630431175,
-0.010226699523627758,
-0.0036792284809052944,
-0.017743466421961784,
0.05368184670805931,
-0.07627543061971664,
0.02843940071761608,
-0.01838349737226963,
-0.040149934589862823,
0.008622356690466404,
-0.06523498892784119,
-0.018257856369018555,
0.03419151529669762,
-0.009249675087630749,
-0.01922941394150257,
0.04535447433590889,
0.005967271514236927,
-0.03803699463605881,
0.001273249159567058,
0.03558756411075592,
0.044054821133613586,
0.021832378581166267,
-0.02438964694738388,
0.020915092900395393,
0.00005666667493642308,
-0.018008237704634666,
0.028103433549404144,
-0.022131239995360374,
0.07208062708377838,
0.006860995665192604,
-0.03475836291909218,
-0.049789607524871826,
-0.0049105859361588955,
0.03649752959609032,
0.02608116902410984,
0.03257190063595772,
-0.08462867140769958,
-0.004732068162411451,
-0.021647984161973,
0.042649805545806885,
0.03177916631102562,
-0.01641859859228134,
-0.004857848864048719,
0.004388425499200821,
-0.01393882930278778,
-0.07078083604574203,
-0.07594779878854752,
-0.03311392292380333,
-0.003335295245051384,
0.004803630523383617,
-0.0019580840598791838,
-0.06420864909887314,
0.05811168625950813,
-0.0030301676597446203,
0.014965799637138844,
0.03800105303525925,
-0.014599892310798168,
0.03296448662877083,
0.03133712336421013,
0.06363116949796677,
-0.05858573690056801,
0.04292263463139534,
0.016942912712693214,
-0.045002225786447525,
-0.007180652115494013,
-0.0033455369994044304,
-0.03913956508040428,
-0.007242441643029451,
0.049067676067352295,
-0.023340042680501938,
-0.00981498695909977,
-0.051257386803627014,
-0.010996892116963863,
-0.005694379098713398,
0.0040982267819345,
0.050385065376758575,
-0.01071527972817421,
-0.010989446192979813,
0.019502976909279823,
-0.034033533185720444,
-0.017409343272447586,
0.018500711768865585,
0.009661078453063965,
0.01057895366102457,
0.052227478474378586,
0.0387752540409565,
0.03981693461537361,
0.06256988644599915,
-0.0000070305572990037035,
-0.010360512882471085,
0.045935094356536865,
-0.06328005343675613,
0.05808446556329727,
-0.005557590164244175,
-0.03311720862984657,
-0.000037971076380927116,
0.04045533016324043,
-0.0046814316883683205,
0.007660957518965006,
-0.036589834839105606,
0.004731824621558189,
0.024809466674923897,
0.03496198728680611,
-0.05421201139688492,
-0.007906980812549591,
-0.07449004054069519,
-0.08068883419036865,
-0.006491874810308218,
0.0406842976808548,
-0.00696246512234211,
0.03969406336545944,
0.04746592044830322,
0.11205878853797913,
-0.020126232877373695,
-0.028499498963356018,
0.039298608899116516,
0.013719810172915459,
-0.008611470460891724,
-0.018486114218831062,
-0.029356084764003754,
0.0059690107591450214,
-0.034191206097602844,
0.028343478217720985,
-0.048961251974105835,
-0.040813032537698746,
-0.024468133226037025,
0.046869441866874695,
-0.02081344649195671,
-0.027070261538028717,
0.03309568017721176,
-0.028999293223023415,
-0.027736319229006767,
-0.030719133093953133,
-0.0327179878950119,
0.0029094815254211426,
0.012051800265908241,
-0.06363627314567566,
0.04671136289834976,
-0.005927753169089556,
-0.008660830557346344,
0.007197747007012367,
-0.011375275440514088,
-0.014787026681005955,
-0.01122360210865736,
0.06083815172314644,
-0.02744341269135475,
0.013843930326402187,
0.025966055691242218,
0.009855442680418491,
0.03591194376349449,
-0.043235745280981064,
-0.02841091901063919,
0.032019294798374176,
0.04214636608958244,
-0.08394380658864975,
0.0010670906631276011,
-0.010372461751103401,
-0.004353699740022421,
0.040253326296806335,
-0.01940147951245308,
0.011339555494487286,
-0.04604756087064743,
-0.06547573208808899,
0.009852196089923382,
-0.012702452018857002,
0.05245833098888397,
-0.08636993169784546,
-0.02976863645017147,
0.04688822850584984,
-0.006659680977463722,
0.04479290172457695,
0.014629264362156391,
-0.0015793776838108897,
0.00131496402900666,
0.0040740398690104485,
0.056034136563539505,
-0.0023651199880987406,
0.03158067166805267,
-0.06132950633764267,
-0.02089439518749714,
0.03917889669537544,
0.0059724547900259495,
0.09942834824323654,
0.027288910001516342,
-0.014352626167237759,
0.022992538288235664,
0.017421716824173927,
0.06855767220258713,
0.016078300774097443,
0.0233517624437809,
0.004705940838903189,
0.00508936308324337,
-0.03977850824594498,
0.031590525060892105,
-0.0314631350338459,
0.01682138629257679,
-0.04208976402878761,
-0.06403671950101852,
0.003047026228159666,
-0.019242295995354652,
-0.046607617288827896,
-0.03981226310133934,
-0.05253003165125847,
0.020226215943694115,
-0.02830640785396099,
-0.03831297159194946,
-0.015575094148516655,
-0.021247221156954765,
0.03295068070292473,
0.01582980901002884,
0.0015483523020520806,
0.07116788625717163,
0.0075310454703867435,
-0.02902323193848133,
0.021913964301347733,
0.0005566764157265425,
-0.0005756079335696995,
0.04394646733999252,
-0.028019573539495468,
-0.026591913774609566,
0.0576423741877079,
-0.01465355884283781,
-0.041583869606256485,
0.03768773376941681,
-0.011556202545762062,
0.015598619356751442,
-0.05708305537700653,
0.024106714874505997,
-0.004003868903964758,
0.02856752648949623,
0.0008602907182648778,
0.035878971219062805,
0.04997638240456581,
0.026425467804074287,
-0.05977874621748924,
-0.004627605900168419,
-0.04424823448061943,
0.00993591733276844,
0.029194382950663567,
0.0415901355445385,
0.06920842081308365,
-0.01611819677054882,
-0.06434739381074905,
-0.08615431934595108,
-0.008001923561096191,
0.0009487812640145421,
-0.023326469585299492,
0.021615508943796158,
-0.018234360963106155,
0.009812735952436924,
-0.007464273367077112,
-0.023880332708358765,
-0.005710236728191376,
0.02748839184641838,
0.027521291747689247,
0.05391206964850426,
0.026648269966244698,
0.06896456331014633,
-0.013509297743439674,
-0.0010475735180079937,
0.032108332961797714,
-0.039197903126478195,
-0.01052713394165039,
-0.013957858085632324,
-0.06576243788003922,
-0.025727760046720505,
-0.022801537066698074,
0.007503532338887453,
-0.020138541236519814,
-0.020453382283449173,
-0.06025965139269829,
0.030148660764098167,
-0.04720192030072212,
-0.015620688907802105,
0.011885212734341621,
0.06083962693810463,
-0.03829214349389076,
0.010237852111458778,
-0.023016227409243584,
-0.01467211078852415,
0.0037722953129559755,
0.022581087425351143,
-0.03489208221435547,
0.03505179286003113,
-0.002467652317136526,
0.01730959117412567,
0.06371746957302094,
-0.03105260618031025,
0.01857723481953144,
-0.03768736496567726,
0.013296397402882576,
0.035153359174728394,
0.03370848670601845,
0.021212764084339142,
0.020226461812853813,
-0.041035689413547516,
0.013860219158232212,
-0.00912537332624197,
0.003945916425436735,
-0.05135294049978256,
0.023214973509311676,
-0.03481981158256531,
0.0007638796232640743,
0.01590059883892536,
0.000040934824937721714,
0.004008221440017223,
0.01012804452329874,
-0.048521462827920914,
-0.03087550215423107,
-0.005348653066903353,
0.01344766654074192,
-0.059934958815574646,
0.07106061279773712,
-0.008454302325844765,
-0.02664710208773613,
0.07229067385196686,
0.02738560549914837,
0.037311799824237823,
-0.014705856330692768,
-0.01680033653974533,
0.03694697842001915,
-0.016575075685977936,
-0.006031809374690056,
-0.030888862907886505,
0.023910705000162125,
0.017240231856703758,
0.04612281173467636,
-0.0218350850045681,
-0.007135529071092606,
-0.019812097772955894,
0.03292864188551903,
0.01083003543317318,
0.03837932273745537,
0.05128507316112518,
-0.042757634073495865,
-0.027288958430290222,
0.021102385595440865,
-0.03073239140212536,
-0.0010739420540630817,
0.015414359048008919,
-0.048945773392915726,
0.0115565937012434,
0.009028651751577854,
-0.025796569883823395,
-0.0023144276347011328,
0.04345085844397545,
0.02339247241616249,
0.03816347196698189,
-0.04299825057387352,
-0.06668055802583694,
0.034848153591156006,
0.004315052647143602,
0.035135164856910706,
0.008079707622528076,
0.046950820833444595,
0.016820665448904037,
0.024847576394677162,
0.0713251382112503,
-0.011805403977632523,
-0.04022888466715813,
-0.012517262250185013,
0.1451944261789322,
0.07253013551235199,
-0.008382881991565228,
0.007530186325311661,
0.0027226388920098543,
0.0019759852439165115,
-0.003084834897890687,
-0.022778764367103577,
0.09580644220113754,
-0.027608690783381462,
0.04949245601892471,
-0.0082998750731349,
0.06625555455684662,
0.07648814469575882,
0.06574549525976181,
0.03653779625892639,
0.005530734546482563,
0.036454156041145325,
-0.012526798993349075,
0.009565809741616249,
0.11413270980119705,
-0.011076586320996284,
-0.029824912548065186,
-0.030571185052394867,
-0.0192237738519907,
-0.009605535306036472,
-0.005920414347201586,
-0.04352768883109093,
0.0622597374022007,
-0.0561261810362339,
0.0002771436993498355,
-0.05359121784567833,
0.021014781668782234,
-0.05920413136482239,
-0.026737362146377563,
-0.014989394694566727,
-0.006533352192491293,
0.026071930304169655,
0.01430382952094078,
0.050001323223114014,
-0.009422277100384235,
-0.03209767863154411,
-0.007678482215851545,
-0.021797899156808853,
-0.010547701269388199,
-0.010824705474078655,
0.0016709266928955913,
-0.012686596252024174,
0.007445790339261293,
0.01152439322322607,
0.0003692928876262158,
-0.024646984413266182,
0.013285649940371513,
-0.010245089419186115,
-0.03584447130560875,
-0.03710576519370079,
-0.04255996271967888,
0.016978688538074493,
-0.025845952332019806,
-0.0142934275791049,
0.020622102543711662,
-0.07849546521902084,
0.014190703630447388,
-0.019901730120182037,
-0.051250629127025604,
-0.08261781185865402,
-0.03830677270889282,
-0.024064265191555023,
-0.029888173565268517,
-0.003734866390004754,
0.014606726355850697,
-0.024053208529949188,
0.032592277973890305,
-0.015561510808765888,
-0.006632645148783922,
-0.029009787365794182,
0.06499102711677551,
0.033081941306591034,
-0.019949642941355705,
0.02738841436803341,
-0.025888698175549507,
0.03910452872514725,
0.02369949035346508,
-0.06631875783205032,
0.007872176356613636,
-0.03688719496130943,
0.011423145420849323,
-0.023392358794808388,
0.026760123670101166,
0.05036682263016701,
-0.011587966233491898,
-0.0018394639482721686,
0.02657479979097843,
0.03482908383011818,
-0.0669221505522728,
-0.035497743636369705,
0.033299896866083145,
-0.005800748709589243,
-0.015565028414130211,
0.0012364601716399193,
-0.017787737771868706,
0.004217352718114853,
0.01687159202992916,
-0.012963763438165188,
-0.005553530063480139,
0.0056863753125071526,
-0.0032112784683704376,
0.06070977449417114,
-0.017376886680722237,
0.06806261092424393,
-0.05163491889834404,
0.029168391600251198,
-0.012734548188745975,
-0.01501096598803997,
0.007012658752501011,
-0.05799667164683342,
-0.010129996575415134,
0.032271210104227066,
0.009507892653346062,
-0.0352005772292614,
0.009890688583254814,
-0.013480976223945618,
0.01884310506284237,
0.05553755536675453,
-0.03219839930534363,
-0.05077661946415901,
0.062468525022268295,
-0.06299632787704468,
0.013716313056647778,
-0.04631364718079567,
0.007665440905839205,
-0.015613771043717861,
-0.0518626868724823,
-0.02377823367714882,
0.023903626948595047,
0.035758860409259796,
0.014141359366476536,
0.06046169996261597,
0.0007679734844714403,
-0.02132989466190338,
-0.038051143288612366,
0.02255343087017536,
-0.030479010194540024,
-0.009627636522054672,
0.04909622296690941,
-0.031969305127859116,
-0.023742901161313057,
-0.02323688194155693,
-0.007499909959733486,
0.03686940297484398,
-0.019765781238675117,
-0.051884155720472336,
0.0008709924877621233,
-0.04310987517237663,
0.0005931647610850632,
0.030219919979572296,
0.006830515339970589,
0.0500803217291832,
-0.03230792284011841,
0.020945526659488678,
-0.02049172855913639,
-0.001000037882477045,
-0.006528834346681833,
0.021626127883791924,
-0.03637070208787918,
-0.024153022095561028,
-0.01703990250825882,
-0.02603762224316597,
-0.015761734917759895,
-0.05462945997714996,
-0.03507748246192932,
-0.001785405445843935,
0.026613749563694,
-0.04601113870739937,
0.04791358858346939,
0.002822499256581068,
-0.010002503171563148,
0.11429111659526825,
-0.03331209346652031,
0.03790639340877533,
0.0033937834668904543,
-0.03160013630986214,
0.020813727751374245,
0.06735177338123322,
-0.02608039416372776,
0.02040945366024971,
0.025871893391013145,
0.004891538992524147,
-0.001838392112404108,
-0.016543414443731308,
-0.010073700919747353,
-0.00809667631983757,
0.01264076866209507,
0.004543158691376448,
0.037924669682979584,
0.02971407026052475,
-0.02850889414548874,
-0.017383921891450882,
-0.040627896785736084,
0.009824677370488644,
0.03999483957886696,
-0.10243602097034454,
-0.028690876439213753,
-0.026909297332167625,
0.013439166359603405,
0.014026478864252567,
0.005073773209005594,
0.014543800614774227,
-0.002248154254630208,
0.06266354769468307,
-0.006194826681166887,
-0.006179418880492449,
0.08159991353750229,
0.023571515455842018,
0.007534352596849203,
-0.015970924869179726,
-0.023316819220781326,
-0.029110828414559364,
0.01314524095505476,
-0.028162667527794838,
0.00971947144716978,
-0.007502723019570112,
-0.03848717361688614,
-0.03619210422039032,
-0.014102204702794552,
-0.006763311102986336,
-0.030854709446430206,
0.021055569872260094,
0.011298718862235546,
0.019611293449997902,
0.08982182294130325,
-0.03230157122015953,
0.048913370817899704,
-0.021730802953243256,
-0.06904242932796478,
-0.05712135508656502,
-0.035660888999700546,
-0.05357520654797554,
0.005715389735996723,
-0.09336075186729431,
-0.01518485601991415,
-0.012318729422986507,
-0.08308728039264679,
-0.020762909203767776,
0.035550590604543686,
0.06306972354650497,
0.032019514590501785,
-0.0041573974303901196,
0.020967213436961174,
-0.04572952538728714,
-0.009232030250132084,
-0.023616589605808258,
0.005101186688989401,
-0.015511849895119667,
-0.02584882639348507,
-0.032248605042696,
0.05628487467765808,
0.05439601093530655,
0.019741831347346306,
-0.09334053099155426,
-0.0354342982172966,
0.011624039150774479,
-0.0570894256234169,
-0.025030070915818214,
-0.06265383213758469,
-0.041381824761629105,
0.05343374237418175,
-0.030967190861701965,
-0.012943688780069351,
-0.03991302475333214,
0.015860307961702347,
0.07759569585323334,
-0.024688521400094032,
-0.0053743901662528515,
0.01570715196430683,
-0.03525121510028839,
0.0006135451840236783,
0.01146416924893856,
-0.02165575884282589,
0.040890052914619446,
-0.005019056610763073,
0.007748164236545563,
0.045734114944934845,
0.0036394144408404827,
-0.003810990834608674,
0.0638548731803894,
0.02682431973516941,
0.008998231031000614,
0.016422757878899574,
0.005167713854461908,
0.021324513480067253,
-0.012188725173473358,
0.04917176067829132,
-0.015103797428309917,
-0.0037780581042170525,
-0.007902434095740318,
0.04048879072070122,
0.002197385998442769,
-0.03182367607951164,
-0.023765580728650093,
0.03389548510313034,
0.022901425138115883,
0.0016688499599695206,
0.0462166890501976,
-0.07107404619455338,
0.009990548714995384,
0.04485635831952095,
-0.013865332119166851,
-0.019117960706353188,
-0.050149936228990555,
0.04227977246046066,
-0.022804930806159973,
-0.04197452962398529,
-0.003703717840835452,
-0.02945304475724697,
-0.03692477196455002,
-0.02035455033183098,
-0.004054108168929815,
-0.037404123693704605,
0.04958280548453331,
-0.04279039427638054,
0.034536950290203094,
0.029125018045306206,
-0.014634693041443825,
-0.02515372820198536,
0.02143176458775997,
0.06293731927871704,
0.034002337604761124,
0.0009417268447577953,
0.02254263311624527,
0.027934052050113678,
-0.05614674091339111,
-0.03607158362865448,
-0.03195471316576004,
0.024912534281611443,
-0.036163780838251114,
-0.056640803813934326,
0.03520268574357033,
0.027006326243281364,
-0.03860079497098923,
-0.02372048608958721,
-0.02811977081000805,
0.07547131925821304
] |
<p>Context: My room is being painted, and i sit and study in a corner of the room, surrounded by walls on 2 sides, such that i am facing the wall. A tube light is at my 4-5 o'clock, and a door(transparent) at my 7 o'clock. These are the only two sources of light. There is a TV mounted just in front of my desk. </p>
<p>Problem: I want to paint only one wall with a dark color and the rest with a light yellowish green color. Now, which wall should be painted with the dark color so as to maximize light in the corner?? IE, the one facing me, on which the TV is mounted, or any other?</p> | g1271 | [
0.04943465813994408,
0.02247055247426033,
0.019417807459831238,
-0.008902088738977909,
0.018170811235904694,
0.00998249277472496,
0.002445074962452054,
0.037339065223932266,
-0.02753213420510292,
-0.02128678932785988,
0.03226027265191078,
0.04275395721197128,
-0.009046507999300957,
0.032643869519233704,
-0.02491907961666584,
0.024782080203294754,
0.0726974681019783,
0.01026140246540308,
-0.011378183029592037,
0.00942336954176426,
-0.01254253275692463,
-0.01127677969634533,
0.011381766758859158,
-0.03669301047921181,
-0.02419831044971943,
-0.015353318303823471,
-0.03045286051928997,
0.01806148700416088,
-0.002385535277426243,
-0.010556237772107124,
0.022065380588173866,
0.003482701489701867,
0.004588101990520954,
-0.0010274122469127178,
-0.045863550156354904,
-0.005702044349163771,
0.003556487848982215,
0.002257376443594694,
-0.010559181682765484,
-0.0017454270273447037,
0.05792668089270592,
0.033281564712524414,
0.07019352167844772,
-0.023869125172495842,
0.01370871439576149,
-0.032051876187324524,
-0.009041288867592812,
-0.0065161860547959805,
0.010198686271905899,
0.005478329490870237,
-0.012777802534401417,
0.03402886167168617,
-0.0377616249024868,
-0.07527201622724533,
-0.041678644716739655,
-0.017885830253362656,
-0.042450323700904846,
-0.07667838037014008,
0.0055543421767652035,
0.061496634036302567,
0.05725414678454399,
0.038466159254312515,
-0.056203193962574005,
-0.008417605422437191,
-0.021799884736537933,
0.04831797629594803,
0.02212740108370781,
0.010903952643275261,
0.04092257469892502,
-0.022201789543032646,
-0.07226702570915222,
-0.029741112142801285,
0.0692303329706192,
-0.005408537108451128,
0.014106161892414093,
-0.005832884926348925,
0.04447906091809273,
-0.006522363983094692,
0.0593717135488987,
0.06515637040138245,
-0.028844064101576805,
0.013633796945214272,
0.014363415539264679,
0.015132795087993145,
0.030589094385504723,
0.06254252791404724,
-0.0024201341439038515,
-0.047221068292856216,
-0.008381281979382038,
-0.037710040807724,
-0.0071695283986628056,
0.014772545546293259,
0.03498510271310806,
-0.015879658982157707,
-0.03835685923695564,
0.033016785979270935,
0.037949856370687485,
0.06519497185945511,
0.030494192615151405,
0.0620977059006691,
-0.03911248594522476,
-0.08499347418546677,
-0.02133558876812458,
-0.004216317553073168,
0.00763871893286705,
-0.002976194489747286,
0.024070344865322113,
0.029541950672864914,
-0.11398851126432419,
0.01072624046355486,
-0.09361841529607773,
-0.038459911942481995,
-0.0030102762393653393,
-0.044534727931022644,
0.012765212915837765,
-0.05029240623116493,
0.06911997497081757,
-0.016682161018252373,
0.07485738396644592,
0.07441572099924088,
0.04103967547416687,
0.027842089533805847,
0.03199954330921173,
-0.0340140275657177,
-0.017414825037121773,
0.007931358180940151,
-0.04573969915509224,
-0.04030422121286392,
0.036461129784584045,
0.006798506714403629,
0.03382355347275734,
0.010072809644043446,
0.05927635356783867,
0.0475347563624382,
0.01828594133257866,
0.019217347726225853,
0.026088133454322815,
0.022138550877571106,
0.015134412795305252,
0.019950469955801964,
0.019844671711325645,
-0.009008700959384441,
-0.029733842238783836,
-0.004879266023635864,
-0.057880841195583344,
0.05007043480873108,
-0.00795959122478962,
0.0010573409963399172,
0.06364314258098602,
-0.028831837698817253,
0.007405430544167757,
-0.040866583585739136,
-0.018931163474917412,
0.000918711069971323,
0.007835319265723228,
-0.04615866392850876,
-0.004032476339489222,
-0.057991426438093185,
-0.014523790217936039,
-0.07177583128213882,
-0.01344124786555767,
0.012586524710059166,
-0.019706200808286667,
-0.04257582873106003,
-0.03863881528377533,
-0.04614540562033653,
-0.010343740694224834,
-0.00250241719186306,
-0.001837597112171352,
-0.0840897336602211,
-0.02977527119219303,
-0.0011728487443178892,
0.006747303064912558,
-0.006409537512809038,
0.07458852231502533,
0.009512213058769703,
0.1200554370880127,
-0.018444053828716278,
0.0347495935857296,
0.039249733090400696,
0.026816463097929955,
-0.05156157910823822,
-0.005665667820721865,
-0.040777433663606644,
-0.03367368131875992,
-0.07200367748737335,
0.021059853956103325,
0.0008267720695585012,
-0.09980703145265579,
0.052506741136312485,
0.021869327872991562,
0.006606964394450188,
-0.009072539396584034,
0.0204787515103817,
-0.03378807380795479,
-0.027307942509651184,
0.06412826478481293,
-0.00968866515904665,
-0.01756877824664116,
-0.031313035637140274,
-0.022539203986525536,
-0.012840218842029572,
0.014926995150744915,
0.05805596336722374,
-0.016524245962500572,
0.013882041908800602,
-0.06944626569747925,
0.016801651567220688,
0.06168104335665703,
-0.057912539690732956,
-0.03237440809607506,
0.0006283333641476929,
-0.013848476111888885,
0.050019051879644394,
-0.01788744516670704,
-0.06702259927988052,
-0.05910779908299446,
0.0700518786907196,
-0.028398429974913597,
-0.03276672959327698,
-0.020959947258234024,
0.0753864049911499,
-0.010304461233317852,
-0.03976163640618324,
-0.006191066931933165,
0.026996387168765068,
0.0000775566732045263,
-0.01926092617213726,
-0.006769275758415461,
0.009482459165155888,
-0.055313896387815475,
-0.03978046774864197,
0.035919833928346634,
-0.012739070691168308,
0.010195027105510235,
-0.02041040174663067,
-0.014823650941252708,
-0.01417101826518774,
0.021749578416347504,
-0.0038805052172392607,
-0.016377290710806847,
-0.014983595348894596,
0.026049332693219185,
-0.09255539625883102,
-0.014294479973614216,
0.05285727605223656,
0.0032745529897511005,
-0.04647831991314888,
0.05613495409488678,
0.06255649775266647,
-0.026185784488916397,
-0.0005910494364798069,
-0.030267586931586266,
-0.021654145792126656,
-0.0025443031918257475,
-0.018878068774938583,
-0.013723704032599926,
0.004344420973211527,
-0.015478876419365406,
-0.02298704721033573,
0.02645791508257389,
-0.09425529837608337,
0.0234476700425148,
0.021772723644971848,
0.011575753800570965,
0.064822718501091,
-0.028317810967564583,
0.02882268652319908,
0.03775736317038536,
-0.03435569256544113,
-0.011796229518949986,
0.05658470094203949,
-0.03813467547297478,
-0.014859745278954506,
-0.00040965829975903034,
-0.01003623940050602,
0.019088199362158775,
-0.018866512924432755,
0.01767774298787117,
0.08598130196332932,
0.04019425809383392,
0.007370025850832462,
0.010236190631985664,
-0.0003949867677874863,
0.03945426270365715,
-0.022184094414114952,
0.030888698995113373,
0.01143271941691637,
0.012435775250196457,
0.09688062965869904,
-0.07182279229164124,
0.0332951657474041,
-0.009378530085086823,
-0.014042398892343044,
-0.008488928899168968,
-0.013606495223939419,
-0.012054076418280602,
0.04361006245017052,
-0.01753724366426468,
0.02416125498712063,
-0.030931605026125908,
-0.02733449637889862,
-0.003136547515168786,
0.03089894913136959,
0.06899343430995941,
-0.029998669400811195,
-0.03896697238087654,
-0.0838809460401535,
0.0006445077015087008,
0.029886582866311073,
-0.016726713627576828,
-0.017499279230833054,
0.005018975120037794,
0.04464201256632805,
0.04279894009232521,
0.02476939745247364,
-0.011266793124377728,
-0.009822704829275608,
-0.0496395006775856,
0.03909529745578766,
0.0006174938171170652,
0.09707989543676376,
-0.003562245052307844,
0.009735443629324436,
-0.046493273228406906,
-0.005052248947322369,
0.01105955708771944,
0.017624668776988983,
-0.0596909262239933,
0.018020257353782654,
0.0316462516784668,
0.02046625129878521,
-0.010479897260665894,
0.014162309467792511,
0.004597903229296207,
-0.009792648255825043,
0.02514481544494629,
-0.003639113623648882,
-0.03507200628519058,
0.01960495114326477,
0.003172365017235279,
0.0019031092524528503,
0.029012098908424377,
-0.03134617581963539,
0.05315849930047989,
-0.06892693787813187,
-0.015903081744909286,
-0.023163530975580215,
-0.006243705749511719,
0.03498036041855812,
0.01680048182606697,
-0.0005688764504157007,
0.008188922889530659,
-0.016708742827177048,
0.0019017676822841167,
0.003375497879460454,
-0.007446144707500935,
0.060112934559583664,
-0.004878629930317402,
-0.01624433510005474,
0.007229149807244539,
-0.037069082260131836,
-0.032205335795879364,
-0.10281025618314743,
-0.017162254080176353,
-0.04280071705579758,
0.08411315083503723,
0.019070932641625404,
-0.025602471083402634,
0.02339709922671318,
0.024445446208119392,
0.036491766571998596,
0.014661122113466263,
0.03189101815223694,
0.02393202669918537,
-0.0354779027402401,
-0.037081025540828705,
0.010632970370352268,
-0.025943631306290627,
0.04868830367922783,
-0.017405405640602112,
0.02924623340368271,
-0.026152633130550385,
-0.02524733543395996,
0.030417155474424362,
0.03252415359020233,
0.014226957224309444,
0.0017869577277451754,
0.036870308220386505,
-0.035510700196027756,
-0.005942138843238354,
0.014273880049586296,
-0.031171616166830063,
0.047201067209243774,
-0.04830893129110336,
0.0214851014316082,
0.08954419195652008,
0.08141068369150162,
-0.06025265157222748,
-0.019044317305088043,
-0.012776033952832222,
-0.014174109324812889,
0.05050352215766907,
-0.009172982536256313,
-0.006404589395970106,
-0.012965254485607147,
0.03345249220728874,
0.010523735545575619,
0.047236599028110504,
0.02984420396387577,
-0.0008124175947159529,
-0.019354280084371567,
-0.014791810885071754,
0.06035102903842926,
0.054266609251499176,
0.0004979049554094672,
-0.0075587136670947075,
0.018229035660624504,
0.0009700045338831842,
0.07926695793867111,
0.05246979743242264,
-0.00927166361361742,
-0.050272706896066666,
-0.09642192721366882,
0.05332505330443382,
0.015095960348844528,
0.018489275127649307,
0.059729307889938354,
-0.03146219998598099,
0.03365001827478409,
0.043161023408174515,
-0.006121049635112286,
-0.030494585633277893,
-0.06271786987781525,
0.009946650825440884,
-0.010827401652932167,
-0.02884923294186592,
0.004363956395536661,
0.05520324781537056,
0.011915875598788261,
0.01042774599045515,
0.01918700896203518,
-0.0043645938858389854,
-0.013304179534316063,
0.012211332097649574,
0.018088210374116898,
-0.04049171879887581,
-0.025891395285725594,
0.02797529473900795,
-0.010339702479541302,
0.003933573141694069,
0.001955174608156085,
-0.06253215670585632,
-0.04942280799150467,
-0.012218120507895947,
0.0016668062889948487,
-0.01864635944366455,
0.028444034978747368,
0.07420298457145691,
0.038404181599617004,
0.01567886210978031,
0.04833858832716942,
0.016957495361566544,
-0.036531712859869,
0.08429395407438278,
-0.037247300148010254,
-0.04057202860713005,
0.037461236119270325,
-0.05218575894832611,
-0.01845846138894558,
-0.0294870026409626,
0.009514182806015015,
0.00799949374049902,
0.03908968344330788,
0.0011148108169436455,
-0.02436639368534088,
-0.05322754755616188,
0.03227507323026657,
-0.01717560738325119,
-0.009500149637460709,
-0.03892840817570686,
-0.04855389520525932,
0.02408508211374283,
0.02452976070344448,
0.003765667323023081,
0.03207714855670929,
-0.01566952094435692,
0.021919546648859978,
0.0012240562355145812,
-0.00900987721979618,
0.019286584109067917,
0.008523780852556229,
-0.022240979596972466,
0.01390594057738781,
0.025851745158433914,
-0.038090042769908905,
-0.0058463034220039845,
0.03795582428574562,
0.012327753938734531,
0.05137038603425026,
0.00189768907148391,
0.00992497242987156,
0.03048046864569187,
-0.024003786966204643,
-0.015130436979234219,
-0.013266721740365028,
-0.03829710930585861,
-0.058736685663461685,
0.010594633407890797,
0.040653493255376816,
-0.042472124099731445,
-0.026561545208096504,
0.030599411576986313,
-0.027959225699305534,
-0.024579739198088646,
-0.07698825001716614,
-0.030294744297862053,
0.015581240877509117,
0.013690459541976452,
0.008302045054733753,
0.043558068573474884,
-0.0007426540832966566,
-0.062286220490932465,
-0.029229484498500824,
0.04147525876760483,
0.05251072347164154,
0.011508817784488201,
-0.02576005458831787,
0.04782190918922424,
0.006129355635493994,
0.013190656900405884,
0.014121602289378643,
0.0004954010946676135,
-0.03646072372794151,
-0.05042025074362755,
-0.010044877417385578,
0.013420119881629944,
0.01419400330632925,
-0.006970040965825319,
0.014721700921654701,
-0.0024375454522669315,
-0.007410326041281223,
0.05058981478214264,
0.028130022808909416,
0.02465762011706829,
-0.046774331480264664,
-0.005358702037483454,
-0.023402800783514977,
-0.08987853676080704,
0.042092349380254745,
-0.002244562841951847,
0.02458788827061653,
-0.01652875728905201,
0.04215741902589798,
0.06407900899648666,
-0.011023778468370438,
0.028758766129612923,
-0.013363449834287167,
0.05012522637844086,
-0.020318400114774704,
0.06871592998504639,
-0.017233755439519882,
-0.03263907507061958,
0.01840038038790226,
-0.006764739751815796,
-0.000655431707855314,
-0.03663931414484978,
-0.02678956650197506,
-0.006114395800977945,
0.03867848590016365,
0.02714584954082966,
-0.023174315690994263,
-0.023509053513407707,
-0.0008641350432299078,
-0.010840056464076042,
0.009996303357183933,
-0.02526789717376232,
-0.053860828280448914,
-0.06443574279546738,
0.054221928119659424,
0.00414612190797925,
0.004002455621957779,
-0.03993386775255203,
-0.023187270388007164,
-0.04217901453375816,
0.08390442281961441,
0.03234722465276718,
-0.033190399408340454,
-0.04128534346818924,
-0.01442450750619173,
-0.02000906690955162,
-0.005154154729098082,
-0.011718563735485077,
0.030900076031684875,
0.01030944474041462,
-0.02637437917292118,
-0.06165360286831856,
-0.026389792561531067,
-0.04548940807580948,
0.047529276460409164,
0.014061413705348969,
-0.018686825409531593,
0.03130941465497017,
0.03439629450440407,
0.03649265691637993,
0.07219766080379486,
-0.018684078007936478,
0.014600399881601334,
0.005111086647957563,
-0.031217060983181,
-0.032970696687698364,
0.07969041913747787,
-0.017448989674448967,
-0.005990003701299429,
0.0063530802726745605,
-0.0056340256705880165,
-0.01505288016051054,
0.004360673483461142,
-0.0014832107117399573,
-0.02083173207938671,
0.07238460332155228,
-0.006408517248928547,
-0.002255610190331936,
-0.012886812910437584,
0.00356066576205194,
0.025586269795894623,
-0.10086695104837418,
-0.0032251428347080946,
0.06011596694588661,
0.03323647752404213,
-0.019533643499016762,
-0.1140054240822792,
-0.053908467292785645,
-0.005236453842371702,
-0.026956062763929367,
-0.017390087246894836,
-0.02587272599339485,
0.015877200290560722,
-0.006286424584686756,
0.026484334841370583,
-0.037744250148534775,
0.03514331951737404,
-0.0002457500377204269,
0.0395018570125103,
0.023573100566864014,
0.001846196362748742,
0.07011828571557999,
-0.018269594758749008,
-0.021181488409638405,
-0.002280786167830229,
0.023174230009317398,
-0.01321271900087595,
-0.03320833295583725,
-0.024282444268465042,
-0.08433021605014801,
-0.006949991453438997,
-0.00665467232465744,
-0.04328368231654167,
0.06635504215955734,
-0.008606269024312496,
-0.0013437020825222135,
-0.06499725580215454,
-0.08806700259447098,
0.04826280102133751,
-0.0033656770829111338,
-0.0008851881138980389,
0.02349913865327835,
0.022562189027667046,
-0.05251237377524376,
-0.03222796693444252,
0.047067392617464066,
-0.010988226160407066,
-0.048269122838974,
0.008445821702480316,
0.029573936015367508,
0.0186770036816597,
-0.005894881207495928,
0.03898203372955322,
0.02514427714049816,
-0.03971961885690689,
0.0341457724571228,
-0.06022638455033302,
-0.021579580381512642,
-0.05403359606862068,
0.0024907172191888094,
-0.045217663049697876,
0.020480990409851074,
-0.00000932151306187734,
0.009420165792107582,
-0.04169044271111488,
0.005105827935039997,
-0.001173866679891944,
0.007280716672539711,
-0.05026485398411751,
-0.02396055869758129,
0.06676675379276276,
-0.038102567195892334,
-0.014202754944562912,
0.07968910783529282,
-0.0074659003876149654,
-0.027529001235961914,
-0.005133306607604027,
-0.02626313455402851,
0.03400399535894394,
-0.02111363410949707,
-0.02144770510494709,
-0.045310743153095245,
0.023397574201226234,
-0.019612673670053482,
-0.04828937351703644,
0.01701454259455204,
0.018610931932926178,
0.07271119952201843,
0.02132130227982998,
-0.020755775272846222,
0.013800999149680138,
-0.03136091306805611,
0.05263970047235489,
0.05914357304573059,
0.036548223346471786,
0.008798695169389248,
-0.02505365014076233,
-0.052545927464962006,
-0.014071839861571789,
-0.006653002928942442,
0.005589987151324749,
-0.011370164342224598,
-0.02445095032453537,
0.03046993538737297,
0.022101446986198425,
-0.0005931837949901819,
0.0013466659002006054,
0.03234773501753807,
0.051612645387649536,
-0.009475094266235828,
-0.003984397277235985,
-0.008442522026598454,
0.001317937159910798,
0.09585476666688919,
0.013054276816546917,
0.0025366945192217827,
-0.010531325824558735,
-0.03951893001794815,
-0.043564990162849426,
0.01891038380563259,
0.015521724708378315,
0.006438929587602615,
-0.005512269679456949,
0.05320281907916069,
0.029813146218657494,
-0.03953288495540619,
0.00887432973831892,
-0.03300091624259949,
0.01253698579967022,
-0.0012630803976207972,
-0.0876295417547226,
0.009870183654129505,
-0.007213488686829805,
-0.03901154175400734,
0.047674283385276794,
-0.005595065653324127,
-0.0037791079375892878,
0.020436283200979233,
-0.031202659010887146,
-0.024035882204771042,
-0.0006916241254657507,
0.002608708804473281,
-0.07864134013652802
] |
<p>When writing a method for an experiment, does it always have to be set out in orderly numbered steps? Can it not also be a paragraph of text that outlines the method?</p>
<p><strong>A mundane example</strong>:</p>
<ol>
<li>Place a tripod on a table, and the wire gause mesh ontop </li>
<li>Following that, place a busen burner underneath it, and hook it up to the gas</li>
<li>Fill a beaker with 100ml of water</li>
<li>Place the beaker on the wire gause, turn on the gas and lit the Busen burner</li>
<li><p>Heat the water until it boils</p>
<p><strong>...</strong></p></li>
</ol>
<p><strong>VERSUS</strong> </p>
<p>Firstly, place a tripod, ensuring that you place a wire gause on on top. Following that step, ...</p>
<p>Thanks.</p> | g1272 | [
0.008817747235298157,
0.015232994221150875,
0.0070940786972641945,
-0.034507233649492264,
0.046027932316064835,
-0.035290081053972244,
0.043718334287405014,
0.04558940604329109,
-0.04179640859365463,
-0.04695300757884979,
0.0007843932253308594,
-0.018988903611898422,
0.023082848638296127,
0.06484588980674744,
-0.007051279302686453,
-0.06489702314138412,
0.08869535475969315,
-0.031693726778030396,
0.058466676622629166,
0.04852994531393051,
-0.010114689357578754,
0.07905454933643341,
0.020907992497086525,
-0.022258710116147995,
-0.06395787000656128,
-0.03028426691889763,
-0.027452463284134865,
-0.032035451382398605,
-0.0005628978833556175,
-0.03205614164471626,
-0.003719786647707224,
-0.00014683982590213418,
0.041817642748355865,
0.0008961855201050639,
-0.04278978705406189,
-0.07778241485357285,
-0.02443423680961132,
0.04510713741183281,
-0.02421761304140091,
-0.056730758398771286,
0.010073402896523476,
0.01444705855101347,
0.029769686982035637,
-0.010481542907655239,
-0.047291770577430725,
0.0257729422301054,
0.009438766166567802,
-0.006543726194649935,
0.0033483030274510384,
0.018937576562166214,
0.00031941483030095696,
-0.015644708648324013,
-0.025504186749458313,
-0.0338398702442646,
0.03269724175333977,
0.05510665848851204,
-0.04598114639520645,
0.0049855150282382965,
0.015758946537971497,
0.009124279022216797,
0.042766790837049484,
0.022476423531770706,
0.0026264870539307594,
-0.05104241520166397,
0.009468453004956245,
0.05347530171275139,
-0.07184597849845886,
-0.03518492728471756,
-0.008719732984900475,
-0.021007686853408813,
0.021968336775898933,
-0.052417635917663574,
0.049255162477493286,
-0.07391784340143204,
0.03038109838962555,
0.029755210503935814,
-0.020571965724229813,
0.0005523319123312831,
0.023386050015687943,
0.06488274782896042,
-0.0201343335211277,
-0.008104493841528893,
0.047873444855213165,
0.03588288277387619,
0.010096321813762188,
-0.018219713121652603,
-0.020975040271878242,
-0.04458708316087723,
0.00398677634075284,
0.04738997668027878,
-0.034284889698028564,
-0.00656375614926219,
0.03010474517941475,
0.05862865597009659,
-0.05702190846204758,
-0.02309660241007805,
-0.02377193421125412,
0.017690252512693405,
0.029938021674752235,
0.00484084989875555,
-0.06207597628235817,
-0.013114739209413528,
-0.04097169265151024,
-0.030635682865977287,
-0.08205737173557281,
-0.02315547503530979,
0.027811624109745026,
0.009550809860229492,
-0.0551789253950119,
-0.07777319103479385,
-0.029196985065937042,
-0.041048258543014526,
-0.06478865444660187,
0.00900639034807682,
-0.00039562073652632535,
0.06595384329557419,
0.0793507918715477,
0.020554719492793083,
0.024021420627832413,
-0.007085341494530439,
-0.005040280520915985,
-0.0013468419201672077,
0.015859145671129227,
-0.013575944118201733,
-0.03090183436870575,
-0.03115542232990265,
0.024695951491594315,
0.030109308660030365,
0.028616512194275856,
-0.009826818481087685,
0.005079526919871569,
0.02526106871664524,
-0.06290829181671143,
0.03349606320261955,
0.0073268478736281395,
-0.004177430644631386,
0.001837745774537325,
0.038267165422439575,
0.024987291544675827,
-0.07640356570482254,
-0.03157655522227287,
0.005659675225615501,
-0.002456157235428691,
-0.03874053806066513,
0.050877440720796585,
0.061578989028930664,
0.02005518041551113,
0.014337528496980667,
0.0545438677072525,
0.02167125791311264,
-0.043398745357990265,
0.007445773109793663,
-0.014223534613847733,
-0.011006333865225315,
0.005123425275087357,
0.006217328831553459,
0.030333220958709717,
-0.04639295116066933,
0.07081890851259232,
-0.004882849287241697,
0.0138566754758358,
-0.018819797784090042,
-0.005483316723257303,
-0.015774928033351898,
-0.05281979218125343,
0.009016862139105797,
-0.02095774933695793,
-0.0227125845849514,
-0.010743864811956882,
-0.03710583224892616,
-0.03536176308989525,
0.002944617299363017,
0.027211207896471024,
0.0039009919855743647,
-0.014915015548467636,
0.06524574011564255,
0.0455174446105957,
0.031791336834430695,
0.05049767345190048,
-0.01714564673602581,
0.008218593895435333,
0.013828784227371216,
-0.00618212204426527,
-0.0032416488975286484,
-0.03377143666148186,
-0.010167875327169895,
-0.025974156334996223,
-0.027097469195723534,
-0.016510682180523872,
-0.015596853569149971,
-0.04093588888645172,
0.012355108745396137,
-0.02712002582848072,
0.07968906313180923,
-0.029023872688412666,
-0.03688924014568329,
-0.00960503052920103,
-0.06679137051105499,
-0.022128967568278313,
0.012792414985597134,
0.011941730976104736,
0.04587145149707794,
-0.03354572132229805,
0.03050149977207184,
-0.04010719805955887,
0.019334891811013222,
-0.015694811940193176,
0.0041595264337956905,
-0.02393798530101776,
0.018428703770041466,
0.09203698486089706,
0.10762679576873779,
-0.004527655430138111,
0.036727700382471085,
-0.03468695282936096,
-0.040811244398355484,
-0.0007847619708627462,
-0.046596091240644455,
-0.03018060326576233,
0.0022178469225764275,
-0.011079777032136917,
-0.048053108155727386,
-0.033551428467035294,
-0.056094300001859665,
0.04145251214504242,
0.003449132200330496,
-0.0017762957140803337,
-0.04340853542089462,
-0.010820605792105198,
-0.02327672764658928,
-0.07879316061735153,
-0.011913574300706387,
-0.040335267782211304,
-0.08518288284540176,
0.04276749864220619,
-0.021439293399453163,
-0.00485672103241086,
-0.030528832226991653,
0.028420304879546165,
0.053816553205251694,
-0.004287641029804945,
-0.06603273749351501,
0.02578873001039028,
0.004757963586598635,
-0.04009120166301727,
-0.014057380147278309,
0.041248664259910583,
0.011174234561622143,
-0.02713632397353649,
0.04218669608235359,
0.00614922447130084,
-0.01620163954794407,
-0.017419660463929176,
0.05384070798754692,
-0.03389795497059822,
0.03323711082339287,
-0.01421439554542303,
-0.010424475185573101,
0.007972313091158867,
0.011471397243440151,
0.06509062647819519,
0.026236291974782944,
0.035899825394153595,
0.014577598311007023,
-0.06326167285442352,
-0.018825683742761612,
-0.05571113899350166,
-0.03158091381192207,
0.03351185470819473,
-0.01846652291715145,
-0.033187661319971085,
-0.022778905928134918,
0.025558821856975555,
-0.014603798277676105,
-0.021786555647850037,
0.03970445320010185,
-0.002210750011727214,
-0.012128523550927639,
0.049877770245075226,
0.051845431327819824,
-0.038732290267944336,
-0.03258071839809418,
-0.05903521552681923,
0.01180625706911087,
0.04799375310540199,
-0.011019340716302395,
0.043029848486185074,
0.026472438126802444,
-0.03073679283261299,
-0.04391000419855118,
0.0025168198626488447,
-0.010606236755847931,
0.034474488347768784,
0.021533707156777382,
0.006295695900917053,
0.05057751387357712,
0.022270159795880318,
-0.058602526783943176,
0.055345095694065094,
-0.07541653513908386,
-0.022640928626060486,
-0.0025747562758624554,
-0.04871339350938797,
0.030800536274909973,
0.022656133398413658,
0.06374156475067139,
-0.05560695752501488,
-0.04094478487968445,
-0.006876690313220024,
-0.015365174040198326,
0.07258685678243637,
0.028727570548653603,
-0.03736374154686928,
-0.014912026934325695,
-0.013717178255319595,
-0.005846335552632809,
-0.016090936958789825,
-0.026494106277823448,
0.02134730853140354,
-0.008721151389181614,
-0.05450531467795372,
0.010122766718268394,
0.00015859211271163076,
-0.027624012902379036,
0.025363188236951828,
0.025041408836841583,
0.032608263194561005,
-0.003149992786347866,
-0.04816708341240883,
-0.0014366025570780039,
0.012938665226101875,
0.07422484457492828,
-0.01466824859380722,
-0.03240441530942917,
0.052583981305360794,
-0.03506755456328392,
-0.0296477023512125,
-0.0484602227807045,
0.0032470417208969593,
0.010277374647557735,
0.03120158053934574,
-0.03789690136909485,
0.023910915479063988,
0.0014101475244387984,
0.03263223171234131,
-0.040657732635736465,
0.04001418501138687,
0.02794785611331463,
0.02661903202533722,
-0.018960701301693916,
0.0839686319231987,
0.053479403257369995,
-0.07563851028680801,
-0.05992177873849869,
-0.023816585540771484,
-0.003508305177092552,
0.051272351294755936,
0.056527502834796906,
0.008957860060036182,
-0.03137023374438286,
-0.026777740567922592,
-0.0046204859390854836,
-0.016368476673960686,
0.01529474463313818,
-0.031098859384655952,
0.008633715100586414,
0.05363088473677635,
0.07789760082960129,
0.034946508705616,
0.008637298829853535,
-0.03538650646805763,
-0.01766383834183216,
-0.03947104513645172,
-0.06259454786777496,
0.018417758867144585,
0.03911000117659569,
0.07196994870901108,
0.032741010189056396,
-0.023009203374385834,
0.04157354310154915,
-0.02688463218510151,
-0.023348404094576836,
0.016151757910847664,
-0.017221491783857346,
-0.01924077235162258,
0.015681026503443718,
-0.027280811220407486,
0.04565911367535591,
0.015826774761080742,
0.012592063285410404,
-0.003354959422722459,
-0.03435530140995979,
-0.0021121720783412457,
0.014746982604265213,
-0.024827903136610985,
0.0037678037770092487,
0.04826745390892029,
0.09550778567790985,
-0.05672996863722801,
0.04816920682787895,
-0.028334081172943115,
-0.02742510847747326,
0.00016767901252023876,
0.03529592230916023,
-0.01882540062069893,
0.03251519799232483,
-0.005883919075131416,
-0.012023601680994034,
-0.054064441472291946,
-0.006763305515050888,
0.014670648612082005,
-0.05593947693705559,
-0.045375190675258636,
0.015761250630021095,
0.03132709488272667,
-0.0823473185300827,
0.0037505219224840403,
-0.021581856533885002,
-0.055046018213033676,
0.006517526227980852,
0.007769051939249039,
0.043986763805150986,
0.0043068137019872665,
-0.05374268814921379,
-0.031232992187142372,
0.01349346712231636,
-0.006960356142371893,
0.008430005982518196,
0.04451984539628029,
-0.004348237533122301,
-0.029714226722717285,
0.017027489840984344,
-0.008520054630935192,
-0.014231151901185513,
-0.0114011000841856,
0.02014009654521942,
0.004037922248244286,
0.044952910393476486,
0.012367216870188713,
0.10034966468811035,
0.017043674364686012,
-0.002541886642575264,
-0.0013745632022619247,
0.004452667664736509,
-0.0016001908807083964,
-0.006387173663824797,
-0.040036890655756,
-0.0043000527657568455,
-0.0027162961196154356,
-0.0019258189713582397,
-0.03276130184531212,
0.04374478757381439,
0.013799101114273071,
0.005911247339099646,
-0.022704768925905228,
0.020957043394446373,
-0.011014450341463089,
0.003857625648379326,
-0.04083096981048584,
0.006691843271255493,
-0.03907682001590729,
-0.01578458398580551,
0.007848011329770088,
0.04103084281086922,
-0.056546129286289215,
-0.011674963869154453,
-0.05349539592862129,
-0.04934246093034744,
-0.06758202612400055,
0.021949661895632744,
0.0028548380360007286,
0.005679247435182333,
0.07308884710073471,
0.02918492816388607,
0.026047121733427048,
0.02126087062060833,
-0.024874504655599594,
0.04538438096642494,
-0.020233042538166046,
-0.004414884373545647,
-0.03866741433739662,
-0.025614771991968155,
0.01537777017802,
0.029318993911147118,
0.04506668448448181,
-0.011011756956577301,
-0.03631526231765747,
-0.04291178658604622,
0.03890565410256386,
0.0011599326971918344,
-0.027085328474640846,
0.040822289884090424,
0.0506732240319252,
0.00767960911616683,
-0.016877302899956703,
-0.022385962307453156,
0.059906452894210815,
-0.026514660567045212,
0.007593510206788778,
-0.004042860120534897,
0.025795990601181984,
0.014720415696501732,
-0.010370866395533085,
0.026085684075951576,
0.005292779300361872,
-0.014982771128416061,
-0.0237091276794672,
-0.0030923900194466114,
-0.04571596533060074,
-0.04204701632261276,
0.035377636551856995,
0.0529031828045845,
-0.046432338654994965,
0.054496392607688904,
0.007984623312950134,
-0.000645739957690239,
0.00449841795489192,
0.0181991346180439,
-0.08131837099790573,
-0.008128663524985313,
0.059344373643398285,
0.015155910514295101,
-0.02036380022764206,
-0.016804492101073265,
-0.031115274876356125,
-0.05383223295211792,
-0.12434212863445282,
-0.02525467984378338,
0.07782351970672607,
0.04158429801464081,
-0.041636593639850616,
0.053343698382377625,
0.018137739971280098,
0.06651738286018372,
-0.037453122437000275,
-0.06183093413710594,
-0.012844236567616463,
0.02877672202885151,
0.01044305507093668,
-0.009326491504907608,
-0.024675916880369186,
0.036667678505182266,
0.03467033803462982,
0.016362426802515984,
0.05007636919617653,
-0.05003498122096062,
0.06588238477706909,
-0.02752205915749073,
0.039790187031030655,
-0.032967183738946915,
-0.03751504793763161,
0.0008835470653139055,
-0.002518503461033106,
0.02981526218354702,
-0.0010285809403285384,
-0.004900808446109295,
-0.01029854267835617,
-0.06413835287094116,
0.032707177102565765,
0.008379528298974037,
-0.012289528734982014,
-0.011270305141806602,
0.020749341696500778,
0.014381734654307365,
0.03530087694525719,
-0.03474430367350578,
-0.0817032977938652,
-0.033782947808504105,
-0.034591928124427795,
0.08920079469680786,
0.01992889866232872,
-0.07549981772899628,
-0.0656847208738327,
-0.03059268184006214,
-0.040485281497240067,
0.016870589926838875,
-0.03240936994552612,
0.06528465449810028,
0.022984929382801056,
-0.002177364658564329,
-0.0016515651950612664,
0.03789509832859039,
-0.012218713760375977,
-0.005228410474956036,
-0.031259626150131226,
-0.006526478566229343,
-0.010673320852220058,
0.07280325889587402,
0.015790456905961037,
-0.001663166913203895,
-0.034014444798231125,
0.010403941385447979,
-0.06209414079785347,
0.042520921677351,
-0.010545126162469387,
0.018089819699525833,
0.02080313116312027,
0.06920598447322845,
-0.0068148402497172356,
0.04503892362117767,
-0.02813136763870716,
0.023465821519494057,
0.016274182125926018,
-0.04561116173863411,
0.004367608577013016,
0.05703725293278694,
0.01883694902062416,
0.05403260886669159,
0.054748713970184326,
0.005841437261551619,
0.03128629922866821,
0.03558572754263878,
0.024982886388897896,
-0.01134847104549408,
-0.024636711925268173,
-0.05033430457115173,
-0.007292290683835745,
-0.026759181171655655,
0.05836254730820656,
0.025246398523449898,
0.049983467906713486,
-0.003018922870978713,
0.04980425909161568,
-0.013298437930643559,
0.04339058697223663,
0.03582382947206497,
-0.05555891990661621,
0.020427031442523003,
-0.003194655990228057,
-0.034714724868535995,
-0.03861774876713753,
0.02060818113386631,
-0.0659705102443695,
0.016295500099658966,
-0.0007343180477619171,
0.016726111993193626,
-0.07868725061416626,
0.002369890222325921,
0.0033227521926164627,
0.033574044704437256,
-0.018028348684310913,
0.010934241116046906,
0.04190099611878395,
0.016914980486035347,
-0.0024325179401785135,
0.02888314425945282,
-0.00833636149764061,
-0.012158780358731747,
-0.031154930591583252,
-0.02991660311818123,
0.029526066035032272,
-0.024170828983187675,
-0.028526704758405685,
0.0018162056803703308,
0.03561505675315857,
0.056722551584243774,
-0.0232084933668375,
0.03939187526702881,
-0.034741323441267014,
-0.005884155165404081,
0.0026040992233902216,
0.02482965961098671,
-0.01305494923144579,
-0.019757142290472984,
0.004452808760106564,
0.032046642154455185,
-0.02000124752521515,
-0.011823156848549843,
0.009092245250940323,
0.007885263301432133,
0.008982119150459766,
-0.016530174762010574,
-0.01899828389286995,
0.01090508047491312,
0.0220514927059412,
-0.004746587481349707,
0.06929744780063629,
0.019979041069746017,
0.005265046376734972,
-0.026774728670716286,
0.00943047646433115,
0.005356962326914072,
0.004539815708994865,
-0.02085544727742672,
-0.006819271948188543,
-0.026729295030236244,
-0.017370589077472687,
0.03119422309100628,
-0.05965569242835045,
-0.060760337859392166,
-0.00890826154500246,
0.03178419917821884,
0.013944554142653942,
-0.042535342276096344,
0.019334636628627777,
0.050244130194187164,
0.06487859785556793,
-0.042622629553079605,
0.017969483509659767,
0.03657066822052002,
0.07772527635097504,
0.008176770061254501,
0.016953973099589348,
0.033966999500989914,
0.01343264989554882,
0.04019397124648094,
-0.031298115849494934,
0.05007031187415123,
-0.007046169135719538,
-0.08367311954498291,
-0.010871488600969315,
0.06291285157203674,
0.0008117726538330317,
0.027575835585594177,
0.023760056123137474,
-0.009432142600417137,
-0.05993790552020073,
-0.02721494808793068,
0.014843317680060863,
0.008062907494604588,
-0.05355675518512726,
0.0361170656979084,
-0.0075673735700547695,
0.029136212542653084,
0.05618143081665039,
0.02764812670648098,
0.02257186733186245,
0.058297425508499146,
-0.06616904586553574,
0.04850296676158905,
0.04037399962544441,
-0.020280536264181137,
-0.010152822360396385,
0.07207294553518295,
0.036789003759622574,
-0.008080193772912025,
0.028566541150212288,
-0.04826685041189194,
0.014059011824429035,
-0.014738054014742374,
0.08430690318346024,
0.06137000396847725,
-0.021693022921681404,
0.013246637769043446,
-0.0047498359344899654,
-0.05383424460887909,
-0.04390622302889824,
-0.01598540134727955,
0.05064605176448822,
-0.04634347930550575,
0.0021497472189366817,
0.0497443787753582,
0.02948790043592453,
-0.02393202856183052,
-0.03313720226287842,
0.030561523512005806,
-0.04844004660844803,
-0.006056469399482012,
0.038404371589422226,
0.034356966614723206,
-0.06303128600120544,
0.025151913985610008,
-0.028108470141887665,
-0.020160967484116554,
-0.02361842803657055,
-0.03735532611608505,
-0.021246375516057014,
-0.031707871705293655
] |
<p>Does the curvature of space-time cause objects to look smaller than they really are? What is the relationship between the optical distortion and the mass of the objects?</p> | g1273 | [
0.016345227137207985,
0.04690118134021759,
-0.014493409544229507,
-0.015999874100089073,
0.02084512449800968,
0.08503209054470062,
0.004063157830387354,
-0.004780542105436325,
-0.03654656186699867,
0.011298086494207382,
0.018361711874604225,
-0.03873949870467186,
0.07421303540468216,
0.011057781986892223,
0.004286318086087704,
0.030106380581855774,
0.005014189053326845,
-0.014834292232990265,
0.0035572072956711054,
0.006564172450453043,
0.009663433767855167,
-0.016564035788178444,
0.010425716638565063,
-0.036723993718624115,
-0.00519828125834465,
0.05954815074801445,
0.03745383769273758,
-0.03377886116504669,
-0.01059943437576294,
-0.012443599291145802,
0.069000743329525,
0.033312734216451645,
0.008784163743257523,
-0.046507108956575394,
0.01503182202577591,
-0.06121034920215607,
0.016582733020186424,
0.027958063408732414,
0.06561996042728424,
0.038751270622015,
0.029353616759181023,
0.021486015990376472,
-0.012134779244661331,
-0.0031047856900840998,
-0.015034607611596584,
-0.01286797970533371,
-0.007236459758132696,
0.033377885818481445,
0.030757328495383263,
-0.020361073315143585,
-0.0020468852017074823,
0.05728576332330704,
0.004086032044142485,
-0.003259719116613269,
0.04431513696908951,
-0.02007438801229,
0.00875143613666296,
0.008087696507573128,
0.09326352924108505,
0.02460560016334057,
-0.013187006115913391,
-0.007430468685925007,
0.039897385984659195,
0.032710909843444824,
0.03877418115735054,
0.007030550390481949,
-0.01962166652083397,
-0.057907138019800186,
0.07293634116649628,
-0.01241208054125309,
0.009070264175534248,
0.004735610447824001,
-0.038972679525613785,
-0.0554460808634758,
-0.023479033261537552,
0.017529653385281563,
0.0044920435175299644,
-0.006116997450590134,
-0.054656460881233215,
-0.006117908284068108,
0.03544027358293533,
0.01441974751651287,
-0.03433690220117569,
0.005783610511571169,
0.048385635018348694,
-0.03171045705676079,
-0.04245176911354065,
0.016641035676002502,
-0.03958284482359886,
0.02629435993731022,
0.013040857389569283,
-0.04113125056028366,
0.003763173706829548,
0.048835717141628265,
-0.03533650189638138,
0.012522689066827297,
-0.024144891649484634,
0.06855640560388565,
-0.02042694389820099,
0.006940300576388836,
-0.02556004747748375,
0.034007564187049866,
0.003164013149216771,
-0.004248414188623428,
-0.054403726011514664,
0.0717608854174614,
-0.02737855166196823,
-0.011195686645805836,
0.0183657705783844,
-0.030357472598552704,
-0.03920302167534828,
-0.0739201083779335,
-0.039832379668951035,
-0.008458653464913368,
-0.06968008726835251,
-0.07813872396945953,
0.041750118136405945,
-0.07014608383178711,
0.004621732048690319,
0.04695086553692818,
-0.002594930352643132,
-0.0021169553510844707,
0.006792308297008276,
0.0297954473644495,
-0.010753627866506577,
-0.022905442863702774,
-0.018066799268126488,
0.021212223917245865,
0.04559120908379555,
-0.02367028407752514,
0.04388472065329552,
0.020863858982920647,
-0.028841642662882805,
-0.003893903223797679,
-0.03424302861094475,
0.055803898721933365,
-0.044891078025102615,
-0.020346175879240036,
-0.025394083932042122,
0.05778929963707924,
0.03781338036060333,
-0.001735612633638084,
0.08199827373027802,
-0.05367391183972359,
-0.04985693842172623,
-0.003543108468875289,
-0.004333026707172394,
-0.017903175204992294,
-0.008847461082041264,
0.017627205699682236,
-0.0263529010117054,
0.009938736446201801,
0.0005511054187081754,
-0.05712653324007988,
-0.0038604920264333487,
-0.015177485533058643,
-0.004421483259648085,
0.020800897851586342,
0.023402780294418335,
-0.016268184408545494,
0.02204209566116333,
-0.0251773688942194,
0.04417113959789276,
0.02136986516416073,
-0.0325828492641449,
-0.025032183155417442,
-0.017205841839313507,
-0.06516775488853455,
-0.016740169376134872,
-0.05927306041121483,
-0.03864990174770355,
-0.018535614013671875,
0.000884427223354578,
0.06050311401486397,
-0.04780329763889313,
0.022157028317451477,
-0.014548777602612972,
-0.06968152523040771,
0.030401593074202538,
0.05629931390285492,
0.011779324151575565,
-0.02753809466958046,
-0.016416586935520172,
-0.04018833860754967,
0.04708906635642052,
-0.014435765333473682,
0.015363233163952827,
0.00728985108435154,
-0.027616221457719803,
0.04555759206414223,
-0.017986342310905457,
-0.06141551956534386,
-0.00007843809726182371,
0.04118983820080757,
0.030105244368314743,
-0.039167437702417374,
0.0306930560618639,
-0.00960967130959034,
-0.08343064785003662,
0.04303170368075371,
-0.06950577348470688,
0.012895410880446434,
0.036635421216487885,
0.0023717207368463278,
0.02485104836523533,
0.00122075155377388,
-0.05544271692633629,
0.015710018575191498,
-0.0025670595932751894,
-0.060867488384246826,
0.05182672664523125,
-0.03041803278028965,
0.06343771517276764,
-0.0726918950676918,
-0.08031771332025528,
0.045805901288986206,
-0.023260585963726044,
-0.016826778650283813,
0.035115793347358704,
0.052498407661914825,
-0.0001953297178260982,
0.008389139547944069,
0.0653335228562355,
-0.026329027488827705,
0.04823187738656998,
-0.020681897178292274,
-0.01338240783661604,
-0.016305645927786827,
-0.003664245828986168,
-0.03574860095977783,
-0.040060579776763916,
-0.004943834617733955,
0.014682349748909473,
0.05183964967727661,
0.03550172597169876,
0.03077450953423977,
-0.004595526028424501,
-0.015748171135783195,
-0.005236409604549408,
-0.007429143413901329,
0.004633826203644276,
-0.02577383816242218,
-0.0007252253126353025,
-0.03655495122075081,
0.03163519874215126,
-0.024535944685339928,
0.01691085658967495,
-0.04584513604640961,
-0.007236040662974119,
-0.027706459164619446,
0.0009765545255504549,
0.04589272662997246,
-0.024972880259156227,
0.017582513391971588,
0.029331672936677933,
0.007522406056523323,
-0.022861095145344734,
0.06572968512773514,
-0.08128316700458527,
0.019980253651738167,
-0.04260590299963951,
0.028962941840291023,
-0.01636528968811035,
-0.012627977877855301,
-0.024647468701004982,
-0.03353900834918022,
0.010121786966919899,
-0.00989747978746891,
0.0611044242978096,
0.03629621863365173,
-0.00041626181337051094,
0.09733692556619644,
-0.013104088604450226,
0.04736867547035217,
0.01048092171549797,
0.02205214463174343,
-0.01351884938776493,
0.019835269078612328,
-0.044566381722688675,
-0.04514714702963829,
0.04373849183320999,
0.007045156788080931,
-0.09432614594697952,
0.01674450933933258,
0.05778013914823532,
-0.015679527074098587,
-0.04170159623026848,
0.038929183036088943,
0.03603430092334747,
0.03313489630818367,
-0.024110980331897736,
0.09108666330575943,
0.009655135683715343,
-0.04104790464043617,
-0.016699209809303284,
0.009091762825846672,
-0.002084743930026889,
0.01759927347302437,
-0.024416310712695122,
0.03694474324584007,
0.0024257167242467403,
0.0035264366306364536,
0.04291100800037384,
0.029642000794410706,
0.012763123027980328,
0.040457408875226974,
0.014981803484261036,
-0.03939059004187584,
-0.042885955423116684,
-0.03796324506402016,
-0.05729585513472557,
0.033206354826688766,
-0.0014159638667479157,
0.06420816481113434,
0.005775946192443371,
-0.058985959738492966,
-0.012494909577071667,
-0.020211221650242805,
-0.03614160045981407,
0.0028219271916896105,
-0.016957558691501617,
0.016830015927553177,
-0.05379486829042435,
-0.04663057252764702,
-0.016180064529180527,
-0.05030354857444763,
0.007169720251113176,
-0.06075672060251236,
0.04509127885103226,
0.01432682853192091,
0.012647115625441074,
-0.08094397932291031,
-0.016204172745347023,
0.022196009755134583,
-0.03422515466809273,
0.027196064591407776,
-0.034324340522289276,
-0.02848869562149048,
0.01163993775844574,
-0.03629684075713158,
0.0000014183242456056178,
0.07841500639915466,
-0.06859595328569412,
-0.009095885790884495,
0.035057198256254196,
0.053580790758132935,
-0.033341772854328156,
-0.018057459965348244,
0.003606052603572607,
-0.024984538555145264,
0.020141014829277992,
-0.004797416739165783,
0.022220099344849586,
-0.023606304079294205,
0.03789636120200157,
0.03872254490852356,
0.0043618022464215755,
-0.00033124181209132075,
0.026327461004257202,
-0.064496710896492,
-0.008724146522581577,
-0.021298950538039207,
0.01375194638967514,
0.004640114493668079,
-0.01379584800451994,
-0.004887302406132221,
0.019530409947037697,
0.024758677929639816,
0.0008950416813604534,
0.008947525173425674,
0.007132214959710836,
0.034915827214717865,
-0.03823982551693916,
0.05975360795855522,
0.011282860301434994,
0.0045004598796367645,
0.007757014129310846,
0.04201510548591614,
-0.04218567907810211,
-0.054685261100530624,
0.05545651540160179,
0.0582968145608902,
-0.007975109852850437,
-0.015030724927783012,
0.0009027677006088197,
-0.03450231999158859,
-0.028408097103238106,
-0.10094885528087616,
0.038905706256628036,
-0.05089721456170082,
0.01750064454972744,
-0.04892904683947563,
-0.011691459454596043,
-0.02670891210436821,
0.01578550413250923,
-0.029143935069441795,
0.015262750908732414,
-0.04697934538125992,
-0.0032770016696304083,
0.011821395717561245,
-0.013032213784754276,
0.07477705180644989,
0.016392411664128304,
-0.0411577932536602,
-0.0323202982544899,
-0.0064909933134913445,
0.01968972757458687,
-0.018954124301671982,
-0.07945389300584793,
-0.02475815825164318,
-0.008090992458164692,
0.018251698464155197,
0.008755666203796864,
-0.10618966072797775,
0.012820836156606674,
0.018319793045520782,
0.017752746120095253,
-0.00750103360041976,
0.056423865258693695,
0.044932689517736435,
-0.022234966978430748,
0.04470903426408768,
-0.03766176849603653,
0.01444459892809391,
-0.08377400040626526,
0.07275735586881638,
-0.02216058410704136,
-0.05321071669459343,
-0.04357733950018883,
0.012622579000890255,
0.02122458629310131,
0.00044665488530881703,
0.04523279890418053,
0.032243940979242325,
-0.009083152748644352,
0.05176039785146713,
0.033812016248703,
0.05792386457324028,
-0.005319191608577967,
-0.011869600974023342,
0.053807277232408524,
-0.005405259318649769,
0.03454749658703804,
-0.009356952272355556,
0.01758466847240925,
0.05304279923439026,
-0.040500517934560776,
-0.017520930618047714,
0.009309178218245506,
0.02110138162970543,
-0.018558919429779053,
0.015327627770602703,
0.0342397503554821,
-0.02472979761660099,
0.012203700840473175,
0.0016097078332677484,
-0.025877565145492554,
0.032139088958501816,
-0.01838715374469757,
-0.026697086170315742,
-0.02171212062239647,
0.03555494546890259,
-0.0076138731092214584,
0.0054551661014556885,
0.03682916611433029,
-0.02664983831346035,
-0.046753980219364166,
-0.028141764923930168,
-0.023013107478618622,
0.014272748492658138,
-0.05558175593614578,
0.02020917274057865,
-0.028698235750198364,
0.028633950278162956,
0.06419619172811508,
0.02303062379360199,
-0.05406470224261284,
-0.03160344064235687,
-0.0016844228375703096,
-0.023907024413347244,
-0.013176243752241135,
-0.00143044360447675,
0.03544260561466217,
-0.020192958414554596,
-0.002964732004329562,
0.05446048453450203,
0.0388241745531559,
0.057588908821344376,
0.0207032710313797,
0.0070197549648582935,
0.039005979895591736,
-0.03467763960361481,
-0.0386866070330143,
0.013121160678565502,
-0.01570313051342964,
0.055077385157346725,
0.010429794900119305,
0.02518073096871376,
0.056123197078704834,
0.01513903308659792,
-0.05778512731194496,
-0.022180218249559402,
0.01601436547935009,
0.010757378302514553,
-0.004148942418396473,
0.021238921210169792,
0.03775103762745857,
-0.062192827463150024,
0.0017740337643772364,
0.07457753270864487,
0.01623252034187317,
0.061578169465065,
0.02554226480424404,
0.008534029126167297,
0.03592013567686081,
-0.05121907964348793,
-0.045285385102033615,
0.04499495029449463,
0.03492036834359169,
-0.025137662887573242,
0.0029946076683700085,
-0.013774080201983452,
0.018553193658590317,
0.027136418968439102,
0.00513827707618475,
0.05498172715306282,
0.043454088270664215,
0.029149625450372696,
0.08184315264225006,
0.017042839899659157,
0.019991036504507065,
0.02440427616238594,
0.07787956297397614,
-0.015881020575761795,
0.030471406877040863,
-0.04056595638394356,
0.0640064999461174,
0.05118244141340256,
0.06298099458217621,
0.008458182215690613,
-0.03425010293722153,
-0.04335812106728554,
-0.015284799970686436,
0.0632082000374794,
0.0667547807097435,
-0.0004929692368023098,
0.05395932495594025,
-0.000012807951861759648,
0.06531334668397903,
-0.008059150539338589,
-0.0066689383238554,
0.019997665658593178,
-0.017473651096224785,
-0.030894359573721886,
-0.016754113137722015,
0.01791040599346161,
0.0358843132853508,
-0.022302286699414253,
-0.029242713004350662,
-0.045882098376750946,
0.07702817767858505,
0.010665399953722954,
0.010303162038326263,
-0.05232224985957146,
-0.043055109679698944,
-0.06045019254088402,
0.03519139811396599,
0.0011875865748152137,
0.020959872752428055,
-0.05355500429868698,
-0.0424177311360836,
-0.04888855665922165,
0.044240035116672516,
0.004817106295377016,
-0.006556591019034386,
0.0068229809403419495,
-0.025238635018467903,
-0.075216144323349,
-0.07896314561367035,
-0.021625684574246407,
0.03958165645599365,
-0.017910344526171684,
-0.01724354363977909,
-0.041696470230817795,
0.019532911479473114,
0.007790228817611933,
-0.020536771044135094,
-0.00683023314923048,
0.0032985955476760864,
-0.040617987513542175,
-0.03494831547141075,
0.0015541985630989075,
-0.006392202340066433,
-0.04722486436367035,
-0.01741952635347843,
0.007111135870218277,
-0.06373957544565201,
0.0382954403758049,
-0.0929490476846695,
-0.011389441788196564,
-0.019200773909687996,
0.025510285049676895,
0.05038467422127724,
0.024682646617293358,
0.014028659090399742,
-0.03743256628513336,
-0.04813724383711815,
0.032161250710487366,
0.028821473941206932,
-0.00504080206155777,
-0.030992258340120316,
0.02819492295384407,
0.0021916034165769815,
0.003389775287359953,
-0.0046119121834635735,
0.006153104826807976,
-0.01764654740691185,
-0.022156160324811935,
-0.06174265220761299,
-0.06983305513858795,
0.04598865658044815,
0.003287576837465167,
0.006120219361037016,
-0.03449573367834091,
0.030930818989872932,
0.035651419311761856,
-0.012231455184519291,
-0.05152294039726257,
-0.008016836829483509,
0.007541704457253218,
-0.06258635222911835,
-0.04431686922907829,
0.05144815891981125,
0.04730186611413956,
0.043624889105558395,
0.07598617672920227,
-0.02133909985423088,
0.06451039016246796,
0.06222120672464371,
0.04013493284583092,
0.05788959935307503,
-0.014533146284520626,
-0.013614759780466557,
0.008190631866455078,
-0.07915721088647842,
-0.01228315383195877,
0.03136048838496208,
0.034131865948438644,
-0.012239578180015087,
-0.058726876974105835,
0.018469421193003654,
0.02289312332868576,
0.027496982365846634,
-0.011756997555494308,
-0.06602001935243607,
0.010348033159971237,
-0.0931302011013031,
0.055958475917577744,
0.013770082965493202,
-0.09560311585664749,
-0.08745968341827393,
-0.03255993500351906,
-0.027444472536444664,
-0.020206693559885025,
0.015838833525776863,
0.05575765296816826,
0.03700678423047066,
-0.0015571743715554476,
-0.057381127029657364,
0.032524194568395615,
0.024868568405508995,
0.01546610426157713,
0.00470130005851388,
0.022356517612934113,
0.05925231799483299,
-0.0152990547940135,
-0.0833708792924881,
0.019893579185009003,
0.005223345011472702,
0.04189253970980644,
-0.00045405744458548725,
0.058488450944423676,
0.03542046621441841,
0.008785104379057884,
-0.028395576402544975,
-0.0018263435922563076,
-0.023319784551858902,
-0.004902324173599482,
0.010183040052652359,
-0.020204218104481697,
-0.0465162992477417,
0.021382996812462807,
-0.03167681396007538,
-0.007227238733321428,
0.001392628182657063,
-0.027847029268741608,
0.020981425419449806,
0.0242801234126091,
-0.0034956124145537615,
0.0051949517801404,
-0.045538946986198425,
-0.019454600289463997,
-0.021271372213959694,
-0.028447797521948814,
0.04310539737343788,
-0.0021273023448884487,
-0.015583346597850323,
0.03807739540934563,
0.033289238810539246,
0.03491416946053505,
0.05975552648305893,
-0.018034236505627632,
-0.016099490225315094,
-0.03993276506662369,
0.010666555725038052,
-0.048291511833667755,
-0.039633046835660934,
-0.017229655757546425,
-0.052599694579839706,
-0.025973474606871605,
-0.0046838861890137196,
0.005866486579179764,
0.018049903213977814,
-0.08507988601922989,
0.050184909254312515,
-0.008499463088810444,
0.03536694124341011,
-0.05174676701426506,
-0.025195186957716942,
-0.024726971983909607,
-0.01800205558538437,
0.05882341414690018,
-0.040268320590257645,
0.010894197970628738,
-0.008861157111823559,
0.018139565363526344,
-0.03998653218150139,
0.01072834711521864,
0.021563204005360603,
-0.045967791229486465,
0.04283257946372032,
-0.0278545543551445,
0.007971060462296009,
0.019451286643743515,
0.03144169971346855,
-0.009811392053961754,
0.01157336588948965,
0.00801976677030325,
0.006233874708414078,
0.008848552592098713,
0.0009211486321873963,
0.02863699197769165,
-0.007885930128395557,
0.008235957473516464,
0.05432632565498352,
-0.0032390952110290527,
-0.02669684588909149,
-0.030845127999782562,
-0.0022396657150238752,
0.03488607704639435,
-0.007585167419165373,
-0.007218792103230953,
-0.013087152503430843,
0.00425511272624135,
-0.011804223991930485,
-0.025695713236927986,
-0.030805978924036026,
0.010847593657672405
] |
<p>Are virtual particles only popping in and out of existence where the local energy density is below a certain point? What I wonder is, does any kind of matter prevent the pairs from appearing? Is there a shell surrounding an atom or maybe I should call it a boundary beyond which particle pair production occurs, and within the boundary it does not, I have wondered if the different orbitals around an atom are affected (set)by the influence of the virtual particles.</p> | g1274 | [
0.040288932621479034,
0.05658487230539322,
0.00663222698494792,
-0.008294525556266308,
0.016941433772444725,
0.06109902262687683,
-0.024004701524972916,
0.03898448497056961,
-0.011996000073850155,
-0.007782806176692247,
0.03098592348396778,
0.01550896093249321,
0.018990641459822655,
-0.01661751978099346,
-0.041272614151239395,
-0.009275203570723534,
-0.00806551892310381,
-0.06679213047027588,
0.009504660032689571,
0.023521356284618378,
-0.039180073887109756,
-0.030784670263528824,
0.002807551994919777,
-0.014728707261383533,
-0.025308819487690926,
0.027318449690937996,
0.003139448817819357,
-0.03900827094912529,
-0.009142249822616577,
-0.004007263574749231,
0.043955933302640915,
-0.00239416747353971,
0.049987971782684326,
-0.056935425847768784,
0.01598462648689747,
-0.04756404086947441,
0.018270663917064667,
-0.012788874097168446,
-0.03732433170080185,
-0.03225094825029373,
-0.01015791017562151,
-0.026402710005640984,
0.011556529439985752,
-0.027892326936125755,
-0.04121919721364975,
0.034907035529613495,
-0.019810857251286507,
0.009775877930223942,
-0.014199531637132168,
-0.027940820902585983,
0.00182027043774724,
0.003334231674671173,
-0.057236894965171814,
0.011207622475922108,
0.030004745349287987,
-0.002540658228099346,
0.03768232837319374,
-0.012971177697181702,
0.094706691801548,
-0.01585170067846775,
0.023351656273007393,
0.02489154040813446,
0.024371294304728508,
0.035310693085193634,
0.0553191602230072,
-0.03684208169579506,
-0.06537832319736481,
0.03294917568564415,
0.042238716036081314,
-0.0023101535625755787,
0.00787557102739811,
0.012520779855549335,
-0.03176277503371239,
-0.023312944918870926,
0.003980221226811409,
0.03706672042608261,
-0.0260304007679224,
0.05126268044114113,
0.010935361497104168,
0.00414078775793314,
-0.032000698149204254,
0.003980923909693956,
-0.01569671370089054,
-0.05690685659646988,
0.0708218663930893,
-0.02427823096513748,
-0.008345930837094784,
-0.06140622869133949,
-0.014847202226519585,
0.011620932258665562,
0.0010888127144426107,
-0.0021016986574977636,
-0.010447838343679905,
-0.04867458716034889,
-0.04470200091600418,
-0.04302560165524483,
0.028454575687646866,
0.05006267875432968,
-0.019168324768543243,
0.007981373928487301,
0.01860261708498001,
0.038260992616415024,
0.020419467240571976,
-0.05877920985221863,
-0.0016250454355031252,
-0.0334271639585495,
0.020030653104186058,
0.026949143037199974,
0.03862282261252403,
0.0016801434103399515,
-0.055038366466760635,
-0.048696763813495636,
-0.00869528204202652,
-0.008548324927687645,
-0.049648966640233994,
0.00330737023614347,
0.0001524269173387438,
0.011712978594005108,
-0.010992862284183502,
0.11068746447563171,
-0.0017300685867667198,
0.05837775766849518,
-0.01250761654227972,
-0.024805188179016113,
-0.0022089043632149696,
-0.021689994260668755,
0.013810109347105026,
-0.022477570921182632,
-0.028233418241143227,
-0.03623312711715698,
0.07513121515512466,
0.022936057299375534,
-0.0009800130501389503,
-0.0007037382456474006,
0.00009880946163320914,
-0.05400136113166809,
0.031429994851350784,
0.02679257281124592,
0.042074549943208694,
-0.009478144347667694,
-0.005117577966302633,
0.02593664824962616,
-0.004229458048939705,
-0.04706420376896858,
-0.03436633571982384,
-0.04031599313020706,
-0.0018668774282559752,
0.013228858821094036,
-0.09208901226520538,
0.023515744134783745,
0.01769215241074562,
0.01403630618005991,
0.018725264817476273,
-0.02380717732012272,
-0.03570114076137543,
-0.0076004513539373875,
0.030086802318692207,
0.05386830121278763,
0.03647562116384506,
0.03509781137108803,
0.061926085501909256,
-0.019200166687369347,
0.013586455024778843,
-0.004370455630123615,
-0.04287305474281311,
0.03483739495277405,
-0.016801072284579277,
-0.0297267884016037,
-0.028213268145918846,
-0.0037740329280495644,
-0.013213892467319965,
-0.052637211978435516,
-0.043557677417993546,
0.06255242228507996,
0.0011158554116263986,
0.01063835620880127,
0.010272124782204628,
-0.05373983085155487,
0.05293731018900871,
0.019879242405295372,
0.015064396895468235,
-0.06723866611719131,
0.0032683813478797674,
0.015611954964697361,
0.04253699257969856,
-0.02444080449640751,
-0.027153147384524345,
0.013092207722365856,
-0.06926847249269485,
0.013304726220667362,
0.02062397263944149,
-0.03310628980398178,
0.043620575219392776,
-0.027205780148506165,
0.010521242395043373,
-0.0728258416056633,
0.07054346799850464,
-0.04109122231602669,
0.02870548516511917,
-0.03449410945177078,
-0.04146125540137291,
0.04076739028096199,
-0.012131942436099052,
0.017224401235580444,
0.04507619887590408,
0.007575666066259146,
0.000021287261915858835,
-0.003404633142054081,
0.009211000055074692,
-0.006814935710281134,
0.031135501340031624,
-0.028926286846399307,
0.019962241873145103,
-0.008738032542169094,
0.005958720110356808,
0.008905732072889805,
-0.008265289478003979,
-0.01093857642263174,
-0.012066579423844814,
-0.0170975923538208,
-0.021510958671569824,
-0.007310379762202501,
-0.0038878435734659433,
-0.026955479755997658,
0.011822128668427467,
0.002812515012919903,
-0.0019130149157717824,
-0.03764995560050011,
-0.01237074937671423,
0.05095551908016205,
-0.07617165893316269,
0.02659633383154869,
0.004314412362873554,
-0.04289618507027626,
-0.0026549038011580706,
0.00929656159132719,
-0.029534121975302696,
0.002748776227235794,
0.009291253052651882,
-0.03190675750374794,
0.02247481979429722,
-0.0780550092458725,
-0.040911607444286346,
0.03263033553957939,
0.05739150196313858,
-0.06911598145961761,
0.0038787180092185736,
-0.010901860892772675,
0.007988661527633667,
-0.04812491312623024,
0.050320129841566086,
-0.019412998110055923,
-0.04552532359957695,
0.017838502302765846,
0.014541185460984707,
-0.00032213874510489404,
-0.07246673852205276,
0.04848702624440193,
-0.02938540279865265,
-0.060545310378074646,
-0.03385115787386894,
0.029847415164113045,
0.038470786064863205,
0.01768673211336136,
-0.017233271151781082,
0.01591941900551319,
0.004830472636967897,
-0.013012402690947056,
0.002491666004061699,
0.046731796115636826,
-0.03212801367044449,
0.07437479496002197,
0.006742379162460566,
0.011349468491971493,
0.0043004658073186874,
-0.012848458252847195,
-0.01050450000911951,
-0.022106949239969254,
0.025482188910245895,
-0.027662545442581177,
-0.025049205869436264,
0.021165816113352776,
-0.020840371027588844,
0.00431375065818429,
0.043275412172079086,
-0.03369060903787613,
-0.04138313978910446,
-0.031282730400562286,
0.0288784708827734,
-0.05200032889842987,
-0.00043485098285600543,
-0.005889021325856447,
0.031980033963918686,
0.016475573182106018,
-0.027393680065870285,
0.018164070323109627,
0.020984826609492302,
0.005023734178394079,
-0.06138963624835014,
0.06319732218980789,
-0.008832109160721302,
-0.032196953892707825,
-0.01252902951091528,
-0.010290106758475304,
0.05888577178120613,
0.03100103884935379,
-0.048542045056819916,
0.03896922245621681,
-0.0550207793712616,
-0.042333826422691345,
-0.0033506324980407953,
0.05100073292851448,
0.02102815918624401,
0.005534762982279062,
0.0005064284196123481,
0.029699908569455147,
-0.008052056655287743,
0.06815019249916077,
-0.05159322917461395,
-0.05137008801102638,
-0.049734797328710556,
0.05792415142059326,
-0.0014088315656408668,
-0.024377640336751938,
0.05450919270515442,
0.03990846127271652,
-0.057588279247283936,
-0.04435291141271591,
0.052150093019008636,
0.022272633388638496,
0.011846206150949001,
-0.05800732970237732,
-0.008869159035384655,
-0.020401207730174065,
-0.069611094892025,
-0.006343207322061062,
-0.06615880876779556,
-0.026700785383582115,
0.016669031232595444,
0.027218949049711227,
0.04712050035595894,
0.04555530846118927,
0.03237239643931389,
0.02087773010134697,
0.018584834411740303,
0.062491610646247864,
-0.06827284395694733,
0.01768602803349495,
-0.010636151768267155,
-0.03452024608850479,
0.038689758628606796,
0.035085730254650116,
0.050918299704790115,
-0.002440623240545392,
-0.008254053071141243,
0.011325285769999027,
0.02973511815071106,
-0.022519022226333618,
0.02738220989704132,
-0.029416633769869804,
-0.011919521726667881,
-0.04476059600710869,
0.030138486996293068,
-0.02083900198340416,
-0.024272708222270012,
-0.05011618137359619,
-0.044406991451978683,
-0.026664020493626595,
0.05304061993956566,
-0.007543439976871014,
-0.03131720423698425,
-0.007658216170966625,
0.015590609051287174,
0.056455522775650024,
0.04135941341519356,
0.020444616675376892,
0.00037720915861427784,
0.05593525245785713,
0.009306368418037891,
-0.011749207973480225,
0.007477934472262859,
0.026809576898813248,
0.0030991840176284313,
0.04125957563519478,
0.03999382257461548,
0.013172479346394539,
-0.04701676592230797,
-0.034304387867450714,
0.04848651960492134,
-0.02260899543762207,
-0.0005029055755585432,
-0.019724607467651367,
-0.05132007226347923,
0.024422509595751762,
0.028285786509513855,
0.01549292542040348,
0.025401633232831955,
-0.02087601274251938,
0.05238658934831619,
0.030540280044078827,
-0.02143992856144905,
0.017547113820910454,
-0.0893315002322197,
-0.08380492031574249,
0.06528295576572418,
-0.027023397386074066,
-0.037004098296165466,
0.05043855682015419,
-0.05096983537077904,
-0.06288059800863266,
0.024016404524445534,
-0.005149081815034151,
-0.01819288544356823,
-0.0173636581748724,
-0.040170084685087204,
-0.0022980349604040384,
0.010783503763377666,
0.07917095720767975,
0.008684778586030006,
0.04868534952402115,
-0.06177806109189987,
0.07222167402505875,
-0.011926593258976936,
0.02107682079076767,
0.012579894624650478,
0.10007812827825546,
0.005990815348923206,
-0.039574459195137024,
-0.042461927980184555,
0.02764289081096649,
0.0233022291213274,
-0.0023507121950387955,
0.003337122732773423,
-0.027045877650380135,
0.030159594491124153,
-0.01681240275502205,
-0.05513405799865723,
-0.04624379053711891,
0.03152938187122345,
0.023329265415668488,
0.06794141232967377,
-0.021683579310774803,
0.032188791781663895,
0.056833066046237946,
-0.025408156216144562,
0.03785126283764839,
-0.06993188709020615,
0.00954869482666254,
0.010169567540287971,
0.005959645379334688,
-0.029484286904335022,
0.009531003423035145,
-0.04817197471857071,
-0.07034344226121902,
-0.04607442393898964,
-0.014321260154247284,
-0.018189573660492897,
0.00331356399692595,
-0.04201323911547661,
-0.021213065832853317,
-0.08118871599435806,
0.01236489973962307,
0.010519461706280708,
0.10087493062019348,
-0.009396493434906006,
-0.01218730490654707,
-0.01846742257475853,
-0.015181033872067928,
-0.05183902382850647,
-0.004692849703133106,
-0.022660676389932632,
0.054347533732652664,
0.03839344158768654,
-0.022563301026821136,
0.06149481236934662,
-0.054389480501413345,
-0.010079553350806236,
-0.0030308179557323456,
0.03738570213317871,
-0.04189246520400047,
0.04278659448027611,
0.041375353932380676,
0.02977871522307396,
0.08189595490694046,
-0.05384227633476257,
0.03694941848516464,
-0.00467140506953001,
0.06265945732593536,
0.010349607095122337,
0.01701919361948967,
0.05892549082636833,
-0.03318728134036064,
-0.007272579241544008,
0.028890594840049744,
0.0333501473069191,
-0.054201673716306686,
0.007221876177936792,
0.012331686913967133,
-0.055982887744903564,
0.04277268052101135,
-0.02280963584780693,
-0.0529736690223217,
0.02961069345474243,
-0.0231559369713068,
-0.01798955164849758,
0.08495593816041946,
0.07583726197481155,
-0.04458222910761833,
0.04531954601407051,
-0.01921575702726841,
-0.06899240612983704,
-0.03024185821413994,
-0.0069654700346291065,
0.004948631394654512,
-0.018055178225040436,
0.0030964110046625137,
-0.0365225151181221,
0.05382421985268593,
-0.06369631737470627,
-0.05195627361536026,
-0.005878765136003494,
-0.01657872460782528,
0.012215354479849339,
0.04199966415762901,
0.027336327359080315,
-0.02649477869272232,
-0.032215818762779236,
0.036396127194166183,
0.037455346435308456,
0.0935758575797081,
-0.004999938886612654,
-0.013919600285589695,
-0.013143718242645264,
0.012377539649605751,
-0.006875031627714634,
-0.0012130587128922343,
-0.02299436926841736,
0.004174119792878628,
0.03625749424099922,
0.06262649595737457,
0.01976531185209751,
-0.03336910158395767,
-0.01760871335864067,
0.07816916704177856,
0.012499984353780746,
0.009549177251756191,
-0.03739826753735542,
0.07822469621896744,
0.08939891308546066,
0.03272838890552521,
-0.020085254684090614,
0.0366792306303978,
-0.06609822809696198,
0.024602560326457024,
-0.031465865671634674,
0.026556316763162613,
0.01046670600771904,
0.0193554125726223,
0.006057560443878174,
-0.007430941332131624,
0.009859313257038593,
0.024464771151542664,
0.017160039395093918,
0.024991074576973915,
0.00014911664766259491,
0.03060414455831051,
-0.021501362323760986,
-0.019988449290394783,
-0.03076275624334812,
0.0005542685394175351,
0.016154427081346512,
-0.0012365815928205848,
0.03269020840525627,
0.0077821193262934685,
0.05550496280193329,
-0.005492395721375942,
-0.0186819639056921,
-0.02707865834236145,
-0.06085466593503952,
0.019916798919439316,
0.0464325025677681,
0.0317879281938076,
-0.009472480043768883,
-0.03207165002822876,
0.0558287613093853,
-0.01169842854142189,
0.03648732602596283,
-0.03728107362985611,
0.025560608133673668,
-0.015589744783937931,
-0.00967310182750225,
-0.02433294802904129,
-0.031131774187088013,
0.009966832585632801,
0.0032350639812648296,
-0.015806755051016808,
-0.00044654871453531086,
-0.033412523567676544,
-0.053820010274648666,
0.014943065121769905,
0.03590235859155655,
0.0016042373608797789,
-0.011792424134910107,
0.05369170755147934,
-0.010552633553743362,
-0.005116796586662531,
-0.019749917089939117,
0.04932777211070061,
-0.09581528604030609,
0.025192677974700928,
-0.021500246599316597,
-0.013791047036647797,
0.039310943335294724,
0.03998931124806404,
0.007900731638073921,
-0.05864046886563301,
0.054356593638658524,
0.02169860154390335,
-0.01742708310484886,
0.021072881296277046,
-0.04119069129228592,
-0.06641841679811478,
0.006705882493406534,
-0.04712644964456558,
0.02627999149262905,
0.013344763778150082,
0.001990018179640174,
0.04857877641916275,
0.08829342573881149,
0.024241022765636444,
0.013007126748561859,
-0.02267504297196865,
-0.02918161451816559,
0.03377104550600052,
-0.0555281862616539,
0.057154420763254166,
-0.0034798344131559134,
0.016434073448181152,
0.030377749353647232,
-0.0022501603234559298,
0.023203441873192787,
-0.058141786605119705,
0.05473993346095085,
0.004956965800374746,
-0.04804801940917969,
0.0013982609380036592,
0.0471944585442543,
-0.0658167377114296,
-0.01228465884923935,
-0.028549110516905785,
0.005864838603883982,
-0.018543366342782974,
0.017341740429401398,
-0.004285393748432398,
0.014857906848192215,
0.04712354391813278,
-0.054801393300294876,
-0.023000238463282585,
-0.014113440178334713,
-0.043344225734472275,
-0.05090878903865814,
0.005405060481280088,
0.008271897211670876,
-0.0023472090251743793,
0.043213922530412674,
0.013831887394189835,
0.024978984147310257,
-0.0722823217511177,
-0.02856886386871338,
-0.05236157402396202,
0.01287625078111887,
-0.08592727035284042,
-0.07545872032642365,
0.008035825565457344,
0.06348434835672379,
-0.031218111515045166,
-0.040417276322841644,
0.06287303566932678,
0.006421433761715889,
-0.057109229266643524,
0.04426687955856323,
0.06101522967219353,
0.015314057469367981,
0.0014540610136464238,
0.012639565393328667,
0.039714984595775604,
0.040649984031915665,
-0.02378658577799797,
-0.03669610247015953,
0.018257662653923035,
0.013654972426593304,
0.004763707518577576,
-0.005498870741575956,
-0.04255497828125954,
-0.04199190437793732,
-0.012892006896436214,
0.0616091787815094,
0.03788844123482704,
0.0020217951387166977,
-0.011761877685785294,
0.006108553148806095,
0.00265936809591949,
0.023354224860668182,
-0.015083678998053074,
0.0252228993922472,
-0.022180551663041115,
0.06883774697780609,
0.06738704442977905,
-0.04274618253111839,
0.014487029053270817,
0.0055460818111896515,
-0.04069184884428978,
0.08709964901208878,
-0.010728411376476288,
0.0036379911471158266,
-0.03901059925556183,
-0.021679669618606567,
0.07455672323703766,
0.02167481556534767,
0.030343830585479736,
0.0035576887894421816,
-0.03093384951353073,
0.003510080510750413,
-0.0054005710408091545,
0.007922629825770855,
-0.002615135395899415,
0.034882958978414536,
0.016368983313441277,
0.020562540739774704,
-0.009841752238571644,
-0.0426873080432415,
-0.011264549568295479,
-0.019923238083720207,
0.022053714841604233,
-0.09549345821142197,
0.0003802498977165669,
0.013789854012429714,
-0.004912678152322769,
-0.0012823219876736403,
0.02272404544055462,
-0.038248319178819656,
-0.10305707156658173,
0.03645022585988045,
0.0041320230811834335,
-0.004076076205819845,
-0.06824478507041931,
0.013742542825639248,
0.025081267580389977,
0.017678216099739075,
0.055643677711486816,
-0.007191338576376438,
-0.01582566648721695,
-0.043773215264081955,
0.0504702664911747,
0.03801729902625084,
-0.05044985190033913,
-0.010386212728917599,
0.02018352411687374,
-0.0004995776107534766,
-0.008640625514090061,
-0.03632895648479462,
-0.00633144611492753,
0.04564381763339043,
-0.035844046622514725,
0.010592982172966003,
-0.0023767328821122646,
0.012080934830009937,
-0.02048872597515583
] |
<p>In a wave guide, graphics of propagation of Transversal Magnetic modes show closed field lines for the electric field. </p>
<p>For example, for a rectangular guide:</p>
<p>$E_x (x,y,z) = \frac {-j\beta m \pi}{a k^2_c} B_{mn}\cos\frac{m\pi x}{a}\sin\frac{n\pi y}{b}e^{-j(\beta z + \omega t)}$</p>
<p>$E_y (x,y,z) = \frac {-j\beta n \pi}{b k^2_c} B_{mn}\sin\frac{m\pi x}{a}\cos\frac{n\pi y}{b}e^{-j(\beta z + \omega t)}$</p>
<p>$E_z (x,y,z) = B_{mn}\sin \frac{m\pi x}{a}\sin\frac{n\pi y}{b}e^{-j(\beta z + \omega t)}$</p>
<p>Is it possible to have closed lines for the electric field?</p> | g1275 | [
0.0008889802265912294,
0.022159848362207413,
0.008553055115044117,
-0.061745528131723404,
0.044301874935626984,
0.0062706652097404,
0.0434647798538208,
0.015118718147277832,
-0.029048403725028038,
-0.003892553737387061,
-0.0127634322270751,
0.008731287904083729,
-0.040227942168712616,
0.05115459859371185,
0.020762572064995766,
-0.03006291575729847,
0.054308295249938965,
0.013607420958578587,
0.05398387461900711,
-0.05378042161464691,
0.03558873385190964,
0.02491876669228077,
0.010708133690059185,
-0.003102500457316637,
-0.025635631754994392,
0.019163673743605614,
0.0019045474473387003,
-0.03672565892338753,
0.01339483167976141,
-0.04314487427473068,
-0.016418930143117905,
-0.028070462867617607,
0.08608894795179367,
-0.009264297783374786,
-0.008728722110390663,
0.05037277564406395,
-0.03345285728573799,
0.055844321846961975,
0.030901139602065086,
0.0410325713455677,
0.027413271367549896,
-0.026740556582808495,
0.021896814927458763,
-0.03468553349375725,
0.030355429276823997,
-0.039650559425354004,
-0.013181036338210106,
0.01876991055905819,
-0.06674418598413467,
-0.00926282536238432,
-0.0403776541352272,
-0.012426418252289295,
0.10554137080907822,
-0.005340965930372477,
-0.0004715416580438614,
0.012006456963717937,
-0.06581318378448486,
0.011296503245830536,
0.0370059609413147,
0.02334742434322834,
0.06076117977499962,
0.024271970614790916,
0.04130078852176666,
-0.017900705337524414,
0.006434418261051178,
-0.0015452447114512324,
-0.07680004835128784,
-0.03540755435824394,
0.000689780805259943,
0.018608879297971725,
0.019323760643601418,
-0.008486662991344929,
-0.00888113770633936,
-0.018086368218064308,
-0.01806901954114437,
0.014820325188338757,
0.030579710379242897,
0.002761641051620245,
-0.031481701880693436,
0.011950644664466381,
-0.03300711512565613,
0.013147021643817425,
-0.055730853229761124,
0.004551263526082039,
0.014530505053699017,
0.024900028482079506,
0.02775423973798752,
0.011694823391735554,
-0.04032247141003609,
-0.051343925297260284,
-0.03209950774908066,
0.028446519747376442,
0.003104768693447113,
-0.037058498710393906,
0.07696198672056198,
0.01591751165688038,
-0.007874914444983006,
-0.020593445748090744,
-0.01822383888065815,
-0.009995990432798862,
0.005102920811623335,
0.009338553063571453,
-0.011392610147595406,
0.0054053920321166515,
-0.028089411556720734,
0.0025927568785846233,
0.040021806955337524,
-0.04468624293804169,
0.04190914332866669,
0.027192572131752968,
0.012997053563594818,
0.013654513284564018,
-0.07229045778512955,
0.05296781659126282,
-0.08770405501127243,
-0.025672081857919693,
0.0032772033009678125,
-0.004864791873842478,
-0.002685214625671506,
0.048303086310625076,
-0.0239336509257555,
-0.06894385069608688,
-0.051069486886262894,
0.052326083183288574,
0.027188938111066818,
0.08086226880550385,
-0.030666397884488106,
-0.01602417603135109,
0.05236100032925606,
0.01134913694113493,
-0.07321787625551224,
-0.004341750871390104,
-0.0363459475338459,
0.018211713060736656,
0.017599821090698242,
0.010002071969211102,
0.029374616220593452,
0.02910713665187359,
-0.019656920805573463,
0.010930857621133327,
-0.028775464743375778,
-0.056216541677713394,
0.00419616000726819,
-0.048476092517375946,
-0.01204371266067028,
-0.008010865189135075,
0.02368958294391632,
-0.020260946825146675,
0.059675272554159164,
0.009428994730114937,
0.016528939828276634,
0.05748136341571808,
0.0035390746779739857,
0.06548585742712021,
-0.036783844232559204,
-0.03554517775774002,
0.03121335059404373,
-0.03257524222135544,
0.0013321017613634467,
-0.019351497292518616,
0.03876224160194397,
0.0010645096190273762,
-0.013646325096487999,
0.037266917526721954,
0.060271527618169785,
-0.04639961197972298,
0.08727292716503143,
-0.027302496135234833,
0.02724032662808895,
-0.030728669837117195,
-0.06791259348392487,
0.04992098733782768,
0.018877316266298294,
0.03731895610690117,
0.061695780605077744,
0.025219712406396866,
-0.003094303421676159,
-0.019955318421125412,
0.06868529319763184,
0.04494287073612213,
-0.03108176402747631,
0.043070223182439804,
0.012838940136134624,
0.023951098322868347,
0.014194639399647713,
-0.0010402501793578267,
-0.059563443064689636,
-0.0064906529150903225,
-0.048830900341272354,
-0.03559954836964607,
0.02625991776585579,
0.019016381353139877,
-0.01325123943388462,
0.05045784264802933,
0.04080400615930557,
0.005170609336346388,
-0.01050481852144003,
0.017108388245105743,
-0.02799397148191929,
0.0341191366314888,
-0.013448131270706654,
0.09287191927433014,
0.076747365295887,
0.005215333309024572,
-0.020114894956350327,
0.006592823192477226,
-0.00019023720233235508,
-0.019874604418873787,
0.04989076778292656,
0.008674572221934795,
-0.005938866641372442,
0.032184746116399765,
-0.03744106739759445,
0.05809026584029198,
-0.027792558073997498,
-0.034624289721250534,
0.05670883506536484,
0.008953476324677467,
-0.06857679039239883,
0.01749628223478794,
-0.02741243876516819,
-0.007927902974188328,
0.05106060206890106,
0.005675534252077341,
-0.030736863613128662,
0.02245861478149891,
-0.02101435326039791,
0.011235327459871769,
0.006495284382253885,
-0.04496201127767563,
-0.024410458281636238,
0.010810555890202522,
0.04363694787025452,
-0.055458225309848785,
-0.034321434795856476,
-0.04700968787074089,
-0.0714987963438034,
0.00004320780135458335,
0.01842455379664898,
-0.03329014033079147,
0.06486383080482483,
-0.009920350275933743,
0.06277655065059662,
-0.02473762445151806,
0.030656322836875916,
-0.02244189940392971,
0.012261143885552883,
0.033457592129707336,
0.030019918456673622,
0.08673378825187683,
0.06094155088067055,
0.0463327094912529,
-0.0538770817220211,
0.07668337970972061,
-0.037560708820819855,
-0.01886935718357563,
0.00058737926883623,
0.008244844153523445,
-0.020625831559300423,
-0.0266614630818367,
-0.035661712288856506,
-0.021239815279841423,
0.014298363588750362,
0.009686390869319439,
0.0036361832171678543,
-0.0019531685393303633,
-0.022930854931473732,
-0.004080695565789938,
0.01980157382786274,
-0.005883564706891775,
-0.050871193408966064,
0.06438985466957092,
0.016816504299640656,
0.0629667416214943,
-0.004877249710261822,
-0.0212404765188694,
0.03941631689667702,
-0.004338087514042854,
0.00469052093103528,
-0.006425355561077595,
0.0149923674762249,
-0.021060602739453316,
-0.004961834754794836,
0.02964438498020172,
-0.0178450345993042,
-0.06733854115009308,
-0.021069902926683426,
-0.008264928124845028,
-0.04088466987013817,
0.0630171149969101,
-0.09617887437343597,
0.02986437827348709,
0.027317358180880547,
-0.035047609359025955,
-0.041173093020915985,
0.00483039952814579,
-0.015101900324225426,
-0.06476596742868423,
-0.0029776094015687704,
-0.02475486882030964,
-0.030848398804664612,
0.0023358215112239122,
-0.06283970177173615,
-0.009690175764262676,
-0.023053321987390518,
-0.008047220297157764,
-0.034510139375925064,
-0.04371087998151779,
0.027105171233415604,
0.004306889604777098,
0.039968617260456085,
-0.04236127436161041,
0.02830437384545803,
0.0191511157900095,
0.006122540682554245,
0.043921396136283875,
0.0048459917306900024,
-0.041720226407051086,
0.012966780923306942,
0.04336296394467354,
-0.07552313804626465,
-0.005406185984611511,
0.03452347218990326,
-0.006000873167067766,
0.020314093679189682,
0.028134414926171303,
-0.008670770563185215,
0.006378781050443649,
-0.015183252282440662,
0.031174995005130768,
-0.05076807364821434,
0.0020585909951478243,
-0.00595614779740572,
0.04142150655388832,
-0.023518908768892288,
0.024102741852402687,
0.015320290811359882,
0.04883569851517677,
-0.008011071011424065,
-0.011412937194108963,
0.001140893087722361,
-0.04860011115670204,
-0.10059893876314163,
-0.00047816039295867085,
0.046321503818035126,
0.036610476672649384,
-0.042514264583587646,
0.012824964709579945,
-0.02850385755300522,
-0.06148067116737366,
-0.034304775297641754,
0.047579340636730194,
0.014440742321312428,
0.0342198945581913,
-0.06505027413368225,
0.002165289595723152,
0.05297891050577164,
0.01818297989666462,
0.02578747645020485,
0.05846906080842018,
-0.0057566361501812935,
0.051949020475149155,
-0.021332331001758575,
-0.03551925718784332,
0.008378256112337112,
0.045649003237485886,
0.04077666625380516,
0.04388051852583885,
0.015429455786943436,
-0.03534626588225365,
0.0278968196362257,
-0.028346622362732887,
0.04487857595086098,
0.023408494889736176,
-0.02934619039297104,
0.000572659308090806,
-0.028891270980238914,
-0.00017098344687838107,
-0.03288557007908821,
0.08941427618265152,
-0.052586644887924194,
-0.014753973111510277,
0.04819880798459053,
0.038244057446718216,
0.00312795233912766,
-0.050219256430864334,
0.0414745919406414,
-0.020391110330820084,
-0.0003274075861554593,
0.02243395708501339,
-0.0467928946018219,
-0.023690542206168175,
0.052249010652303696,
0.04152204841375351,
0.007812786847352982,
-0.08360902220010757,
-0.04215092211961746,
0.021132508292794228,
-0.023353487253189087,
-0.011424011550843716,
0.022263024002313614,
0.024105669930577278,
-0.04049597680568695,
0.01628902368247509,
-0.0385662317276001,
-0.025040550157427788,
-0.014954089187085629,
0.018454506993293762,
0.04369361698627472,
-0.019122542813420296,
0.008750754408538342,
-0.024860357865691185,
0.0018889887724071741,
-0.023127229884266853,
0.038364071398973465,
0.012028085999190807,
0.05450998619198799,
0.015133317559957504,
0.015501675195991993,
-0.01710541546344757,
0.04260857775807381,
0.05753159523010254,
0.007201982196420431,
-0.013375451788306236,
-0.006971350405365229,
0.056862566620111465,
0.018783485516905785,
-0.02679727040231228,
0.024651411920785904,
-0.006056723650544882,
-0.00828829687088728,
-0.032969214022159576,
-0.03739622235298157,
-0.034039903432130814,
-0.04634031653404236,
0.001036343746818602,
-0.08123768866062164,
-0.01262775156646967,
0.024993976578116417,
-0.027775771915912628,
-0.005992966704070568,
-0.02713462896645069,
0.037547267973423004,
-0.02737428806722164,
-0.06122232973575592,
0.012420754879713058,
0.014567018486559391,
-0.004812199156731367,
0.03975735977292061,
-0.038186341524124146,
-0.056166037917137146,
-0.00619124760851264,
-0.01170021016150713,
-0.004699427634477615,
-0.0016804957995191216,
-0.09653660655021667,
0.006565461866557598,
0.02954103797674179,
0.05847177654504776,
-0.021780870854854584,
-0.042436353862285614,
0.0021127150394022465,
-0.03504354879260063,
0.028076481074094772,
0.06608635187149048,
-0.018065139651298523,
-0.009135848842561245,
0.006650193128734827,
0.009326743893325329,
-0.024817075580358505,
0.06340531259775162,
0.06813013553619385,
0.031913384795188904,
-0.004613735247403383,
-0.022482676431536674,
-0.018523307517170906,
-0.03218802809715271,
0.023483915254473686,
-0.08155445009469986,
-0.11925952881574631,
-0.004586252849549055,
-0.017203938215970993,
0.023220771923661232,
0.031011322513222694,
-0.021304793655872345,
-0.03676559776067734,
-0.04611703008413315,
0.02361668273806572,
-0.031317371875047684,
-0.026199117302894592,
0.05532633140683174,
-0.03853102773427963,
-0.006452146451920271,
0.0061661601066589355,
-0.03206147626042366,
-0.024560773745179176,
0.01955471746623516,
-0.07438790053129196,
-0.03683820366859436,
-0.04946444556117058,
0.007664833217859268,
-0.008091103285551071,
-0.08036129176616669,
-0.021144941449165344,
0.017432594671845436,
0.0537644624710083,
-0.022350285202264786,
-0.04504132270812988,
-0.00695612421259284,
-0.009632737375795841,
-0.04149748384952545,
-0.026144981384277344,
-0.03973759338259697,
0.01308094710111618,
0.026003221049904823,
-0.008999798446893692,
-0.055065203458070755,
-0.016313355416059494,
-0.061044931411743164,
-0.026340626180171967,
0.038703322410583496,
-0.0077344635501503944,
0.029208127409219742,
-0.045288510620594025,
-0.06697098165750504,
0.026280637830495834,
-0.03589252009987831,
-0.008943741209805012,
0.03306828439235687,
-0.040750518441200256,
0.04028277099132538,
-0.004435674753040075,
-0.003838108154013753,
0.002190393628552556,
-0.06372866779565811,
-0.021849701181054115,
0.05820401385426521,
-0.04864411801099777,
-0.08159547299146652,
0.05251755565404892,
0.016475118696689606,
-0.03984648361802101,
0.028991831466555595,
0.02393331006169319,
0.016713524237275124,
0.011736604385077953,
0.045883599668741226,
0.02837951108813286,
-0.03419957309961319,
-0.028876768425107002,
-0.0429735966026783,
-0.03045312501490116,
-0.016117800027132034,
-0.030222326517105103,
-0.01967914029955864,
0.01657787896692753,
-0.031075945124030113,
-0.012675781734287739,
0.017372671514749527,
-0.0005838547367602587,
0.06298904865980148,
-0.008597512729465961,
-0.035031404346227646,
-0.00503532076254487,
-0.03389592468738556,
0.030183400958776474,
0.05277445912361145,
0.03440343588590622,
0.0587838850915432,
0.013873789459466934,
-0.03758912906050682,
-0.04003538191318512,
0.05429895967245102,
0.04713860899209976,
0.02572314813733101,
-0.004701125435531139,
0.06798136234283447,
-0.04213641583919525,
0.027954906225204468,
-0.008949950337409973,
0.030268194153904915,
0.04479029029607773,
0.009130200371146202,
0.042920589447021484,
0.024038519710302353,
0.005531542468816042,
-0.09687136858701706,
-0.018308570608496666,
0.03133508190512657,
-0.030230030417442322,
-0.011182479560375214,
-0.010008420795202255,
0.043328024446964264,
0.0645143985748291,
0.0008519036346115172,
0.01159917563199997,
0.059896938502788544,
0.0568513497710228,
0.04203332960605621,
0.008923288434743881,
0.018301116302609444,
0.03447467461228371,
-0.024514034390449524,
0.014508522115647793,
0.0478486604988575,
-0.017283162102103233,
-0.0073814671486616135,
0.030837593600153923,
-0.0454963743686676,
0.0008205134654417634,
0.0643891990184784,
0.015844479203224182,
0.026025984436273575,
0.021011056378483772,
0.0016110738506540656,
-0.004553020931780338,
0.010852673090994358,
0.01688089594244957,
-0.03507987782359123,
0.03272126242518425,
0.015478568151593208,
-0.004285067785531282,
-0.02607860416173935,
-0.03362229838967323,
-0.051115959882736206,
-0.02511737309396267,
0.028003323823213577,
-0.048010386526584625,
0.031327877193689346,
-0.05098109692335129,
0.017798561602830887,
-0.010823002085089684,
-0.016848476603627205,
-0.047563813626766205,
-0.015188410878181458,
0.0337858647108078,
0.009917311370372772,
0.0038861148059368134,
0.08420591056346893,
-0.0002852108154911548,
-0.0004311986267566681,
0.027704477310180664,
0.059776339679956436,
0.04987698048353195,
-0.043745577335357666,
0.04530926048755646,
-0.04193617403507233,
-0.006475989241153002,
-0.11722860485315323,
0.022703392431139946,
0.039107438176870346,
0.03992731496691704,
-0.07276307046413422,
0.005081819370388985,
0.0044839512556791306,
0.018372919410467148,
-0.028500543907284737,
-0.016070835292339325,
-0.01674501970410347,
0.009026836603879929,
0.022362979128956795,
-0.02797611989080906,
-0.002392234979197383,
-0.04134208336472511,
0.022682981565594673,
-0.03518999367952347,
-0.028010644018650055,
-0.04080386087298393,
-0.04237322509288788,
0.005495383404195309,
0.010532489977777004,
-0.015710437670350075,
-0.022944657132029533,
0.046461474150419235,
-0.031037522479891777,
-0.016014553606510162,
-0.07579062134027481,
0.001947094569914043,
0.010674354620277882,
-0.019564131274819374,
0.021495580673217773,
0.008895416744053364,
0.03401998057961464,
-0.025304164737462997,
0.04355445131659508,
-0.010665589943528175,
0.014331835322082043,
-0.02496657706797123,
0.00880041066557169,
0.01176587212830782,
0.0058645098470151424,
0.007367754355072975,
0.05195300653576851,
-0.012539636343717575,
0.008973409421741962,
-0.003318418050184846,
-0.009483905509114265,
0.04491814225912094,
0.0201759971678257,
0.03958592191338539,
0.049626532942056656,
0.024990856647491455,
-0.000352533592376858,
0.0315350741147995,
0.044963110238313675,
-0.007591418456286192,
-0.025273658335208893,
-0.07167169451713562,
0.00727832829579711,
0.009593168273568153,
-0.02347886748611927,
0.04488276317715645,
-0.0016494907904416323,
0.05909893289208412,
-0.015726909041404724,
0.05702532082796097,
-0.04028457775712013,
0.01437102910131216,
-0.023929907009005547,
0.0009532147087156773,
-0.0670272633433342,
0.02901742421090603,
0.018328679725527763,
-0.043462082743644714,
0.00963948667049408,
0.050025686621665955,
-0.033929623663425446,
0.05058405548334122,
-0.005417904816567898,
0.016259748488664627,
-0.0237893033772707,
-0.04328412935137749,
-0.0037443835753947496,
0.01913040690124035,
-0.06065196916460991,
-0.04938734695315361,
-0.04042186588048935,
-0.049031082540750504,
0.02700817584991455,
0.0009818340186029673,
0.027817169204354286,
-0.02844257839024067,
-0.03535710275173187,
0.019741687923669815,
0.03000413253903389,
0.07738280296325684,
-0.07384152710437775,
-0.0026538174133747816,
0.00902476254850626,
0.018437104299664497,
0.030738182365894318,
-0.006361929699778557,
-0.04603930935263634,
-0.009880493395030499,
0.01618177630007267,
-0.02789660543203354,
-0.021489808335900307,
-0.020897725597023964,
0.06179943308234215,
0.04294517636299133,
-0.040240027010440826,
0.018365679308772087,
-0.01755690947175026,
0.03225608170032501,
-0.06773754209280014,
-0.02845258265733719,
-0.013107863254845142,
0.02281387522816658
] |
<p>Recently I have started to study the classical theory of gravity. In Landau, Classical Theory of Field, paragraph 84 ("Distances and time intervals") , it is written</p>
<p>We also state that the determinanats $g$ and $\gamma$, formed respectively from the quantities $g_{ik}$ and $\gamma_{\alpha\beta}$ are related to one another by $$-g=g_{00}\gamma $$
I don't understand how this relation between the determinants of the metric tensors can be obtained. Could someone explain, or make some hint, or give a direction? </p>
<p>In this formulas $g_{ik}$ is the metric tensor of the four-dimensional space-time and $\gamma_{\alpha\beta}$ is the corresponding three-dimensional metric tensor of the space. These tensors are related to one another by the following formulas $$\gamma_{\alpha\beta}=(-g_{\alpha\beta}+\frac{g_{0\alpha}g_{0\beta}}{g_{00}})$$ $$\gamma^{\alpha\beta}=-g^{\alpha\beta}$$</p>
<p>Thanks a lot.</p> | g1276 | [
0.018671715632081032,
0.020804544910788536,
-0.012730910442769527,
-0.007144688628613949,
0.0512072928249836,
0.06882458925247192,
0.08983977884054184,
-0.008498790673911572,
-0.09806462377309799,
-0.04234980046749115,
-0.049715641885995865,
0.004762331489473581,
0.04455044865608215,
0.011830272153019905,
0.0025906020309776068,
-0.04809090495109558,
0.060773905366659164,
-0.019772794097661972,
-0.0184929296374321,
-0.009606027975678444,
0.038609858602285385,
-0.010261928662657738,
0.036853186786174774,
-0.06004585698246956,
0.07468023151159286,
-0.0055320849642157555,
0.09398836642503738,
0.0354338139295578,
-0.010986502282321453,
-0.02001236006617546,
0.014178711920976639,
0.07986731827259064,
0.027002470567822456,
-0.039221394807100296,
0.019829126074910164,
-0.0406830757856369,
0.017780505120754242,
0.04147891327738762,
0.006513678468763828,
-0.037108488380908966,
0.01431626919656992,
-0.013804031535983086,
-0.008407564833760262,
0.013447465375065804,
0.04110848158597946,
0.03739010542631149,
-0.07793473452329636,
-0.02111399546265602,
0.026587195694446564,
0.04081015661358833,
-0.01749870367348194,
0.07751061022281647,
-0.018051136285066605,
-0.025519350543618202,
-0.0020637274719774723,
0.006733207497745752,
0.07559937238693237,
-0.04729912430047989,
0.03470100462436676,
0.018907612189650536,
-0.035888541489839554,
-0.027069425210356712,
0.039799366146326065,
-0.0046968054957687855,
0.032999299466609955,
-0.06589066982269287,
-0.03470375016331673,
-0.03708634153008461,
0.0012899982975795865,
0.013413382694125175,
-0.001575411413796246,
-0.023766668513417244,
0.006182459648698568,
0.014867703430354595,
0.0359310656785965,
0.0738425999879837,
0.034736450761556625,
0.09172825515270233,
0.02494911290705204,
-0.022560833021998405,
0.04504028707742691,
-0.03796415776014328,
0.03627053275704384,
0.003375003580003977,
0.02600337564945221,
-0.015374640002846718,
-0.017643362283706665,
0.012230528518557549,
-0.0172500591725111,
0.02143978886306286,
-0.05458761379122734,
-0.05008871853351593,
0.06149900332093239,
0.05022170767188072,
0.0012231975561007857,
0.008322375826537609,
0.020290140062570572,
0.058897849172353745,
-0.0020241164602339268,
-0.046615034341812134,
-0.0067966696806252,
0.02619093470275402,
-0.004018694628030062,
-0.06068866699934006,
-0.027125779539346695,
0.00241881818510592,
0.004677484277635813,
0.01182975247502327,
0.013567951507866383,
-0.019809989258646965,
-0.08343330770730972,
0.035865191370248795,
-0.03533492237329483,
-0.039821919053792953,
-0.00920006912201643,
-0.021532537415623665,
0.0023653830867260695,
-0.08442512899637222,
0.0315912626683712,
0.003563913516700268,
-0.0557425394654274,
0.01725674420595169,
-0.010766648687422276,
-0.015202896669507027,
-0.03306351602077484,
-0.012411171570420265,
-0.027127176523208618,
0.024593552574515343,
-0.007577376905828714,
-0.0007143691182136536,
0.05312813073396683,
0.002169317565858364,
0.04788440093398094,
0.004505123011767864,
-0.010444741696119308,
0.04896596074104309,
-0.017480047419667244,
0.0543455109000206,
-0.021368401125073433,
0.016216503456234932,
-0.03907904028892517,
-0.0313645638525486,
0.02932119369506836,
-0.0887363851070404,
-0.032985180616378784,
0.04847990348935127,
0.004762304946780205,
-0.05901721492409706,
0.06956274807453156,
0.005257722456008196,
0.03170476108789444,
0.07192471623420715,
0.001421174849383533,
-0.008018052205443382,
0.056121617555618286,
0.02687595598399639,
-0.053888775408267975,
-0.036450017243623734,
-0.037367772310972214,
-0.007938775233924389,
0.06448883563280106,
-0.07900737971067429,
0.023042377084493637,
0.002483874326571822,
0.015366621315479279,
0.03145022317767143,
0.04730071872472763,
-0.06025632843375206,
0.029637973755598068,
-0.02114451490342617,
-0.04971587657928467,
-0.004146341234445572,
0.002204027259722352,
0.06658636033535004,
-0.025469109416007996,
0.0518999882042408,
-0.05366542562842369,
-0.05413830280303955,
0.011404221877455711,
-0.01040351577103138,
0.0092033501714468,
-0.013013285584747791,
0.03522828221321106,
-0.05508585646748543,
-0.002416015835478902,
0.042346928268671036,
-0.0075951991602778435,
-0.025181017816066742,
-0.02132910117506981,
0.0257941372692585,
0.021773342043161392,
-0.05197657272219658,
0.01033711340278387,
0.054220885038375854,
0.02700509876012802,
0.0166119746863842,
0.0516020841896534,
-0.029942672699689865,
-0.04647984355688095,
0.027893604710698128,
-0.05735192075371742,
-0.022025786340236664,
0.052675217390060425,
-0.02533464878797531,
0.016187958419322968,
0.008649323135614395,
-0.025118760764598846,
-0.013973469845950603,
0.05793214216828346,
0.00844272505491972,
0.0038273294921964407,
-0.03906602784991264,
0.06076548621058464,
-0.01199258677661419,
-0.007223892956972122,
-0.05036373808979988,
-0.008025486022233963,
-0.013971679843962193,
0.03880215808749199,
0.05041629821062088,
-0.027500389143824577,
0.021774258464574814,
0.04104083776473999,
-0.01771601103246212,
-0.02851930819451809,
-0.03488260507583618,
0.014054249040782452,
0.007895272225141525,
-0.010092800483107567,
-0.0009433839004486799,
-0.05323067680001259,
-0.022204933688044548,
0.0007465282687917352,
0.03618524223566055,
0.023040737956762314,
0.028973480686545372,
-0.002839406719431281,
-0.04894110932946205,
0.02093748189508915,
0.07620615512132645,
0.0027437175158411264,
-0.037321463227272034,
0.023082317784428596,
0.017923105508089066,
-0.02021867409348488,
-0.004264567978680134,
0.08114452660083771,
-0.020948845893144608,
-0.008387582376599312,
0.030957521870732307,
0.00030534376855939627,
0.013298685662448406,
-0.02708486095070839,
0.04366215318441391,
0.021442972123622894,
-0.0030278735794126987,
0.00294139189645648,
0.04794856905937195,
-0.06846205145120621,
-0.006081463769078255,
-0.013808883726596832,
-0.08170964568853378,
0.020351091399788857,
0.015852391719818115,
-0.05305296927690506,
-0.055893491953611374,
0.03740210831165314,
0.00797959603369236,
-0.023239513859152794,
0.012985007837414742,
-0.013493496924638748,
0.028111150488257408,
0.08402639627456665,
0.05435522645711899,
-0.06972689926624298,
0.01033196784555912,
0.009168270044028759,
-0.028270401060581207,
-0.005970664322376251,
-0.024733882397413254,
-0.0274528618901968,
0.029224930331110954,
-0.038384340703487396,
-0.01336285937577486,
0.008094532415270805,
-0.06435354799032211,
0.05006184056401253,
0.0810721218585968,
0.008243082091212273,
0.06281203776597977,
0.017919516190886497,
0.014677025377750397,
-0.00562374759465456,
0.00685871159657836,
-0.021545954048633575,
-0.01569100096821785,
0.00425510061904788,
0.024793274700641632,
-0.03050674870610237,
0.020683838054537773,
0.05460653826594353,
-0.019093969836831093,
0.015504572540521622,
-0.009919919073581696,
0.018838228657841682,
0.0011446286225691438,
-0.08753964304924011,
-0.03646986559033394,
-0.007835137657821178,
0.007110079750418663,
-0.01290472038090229,
0.005414060782641172,
0.026708899065852165,
0.017291244119405746,
-0.01496143452823162,
-0.015189542435109615,
-0.012419485487043858,
-0.008924071677029133,
-0.05025314539670944,
-0.002852206351235509,
-0.018851861357688904,
-0.03831850737333298,
-0.04078639671206474,
-0.02258448116481304,
0.010501389391720295,
-0.008864169009029865,
-0.05445567145943642,
0.010230733081698418,
-0.036634448915719986,
0.014952520839869976,
-0.029783355072140694,
-0.07938018441200256,
-0.021973051130771637,
0.0059022437781095505,
-0.05765654146671295,
0.022098716348409653,
-0.008472145535051823,
0.008473949506878853,
0.0028148884885013103,
-0.03363500535488129,
0.009938814677298069,
0.01790481247007847,
-0.08152439445257187,
0.023421261459589005,
-0.02337394468486309,
0.003099834080785513,
0.016774704679846764,
0.013351730071008205,
-0.007139830384403467,
0.009154032915830612,
-0.054131656885147095,
-0.03535338118672371,
0.06500864773988724,
0.022285349667072296,
-0.005308249033987522,
-0.03464405611157417,
0.023282401263713837,
0.07072218507528305,
0.05041006579995155,
-0.02394051104784012,
0.0007804554188624024,
0.023655224591493607,
-0.037755630910396576,
-0.002146895043551922,
-0.02558986470103264,
-0.042446643114089966,
0.03772546350955963,
0.011644858866930008,
0.017553048208355904,
-0.02903769351541996,
0.032746464014053345,
0.016161978244781494,
0.009723085910081863,
0.031002234667539597,
0.0067781065590679646,
-0.03724614158272743,
-0.008784747682511806,
-0.011939208023250103,
-0.06283286213874817,
0.02524203062057495,
0.04027673974633217,
0.04623955115675926,
0.037171993404626846,
0.006507314275950193,
0.01639905385673046,
-0.03965965658426285,
-0.021830683574080467,
-0.03599831089377403,
0.005034204106777906,
-0.04829619452357292,
-0.014249722473323345,
0.04656358063220978,
-0.028637127950787544,
-0.02456827647984028,
0.011539253406226635,
0.04813908785581589,
0.03840642049908638,
0.1300130933523178,
-0.0011714319698512554,
0.05812367796897888,
0.010046963579952717,
0.014047371223568916,
-0.03308182582259178,
0.015281029045581818,
-0.04108421877026558,
-0.013346181251108646,
0.0011891270987689495,
-0.02477947436273098,
0.06951580196619034,
-0.03473031520843506,
-0.030690975487232208,
-0.019360674545168877,
0.00818543415516615,
-0.09756949543952942,
0.07372499257326126,
0.025788381695747375,
-0.02500275894999504,
-0.05343290790915489,
0.0319654606282711,
-0.012593105435371399,
0.00726265087723732,
0.027209540829062462,
0.02594880759716034,
-0.032093971967697144,
0.03956185281276703,
0.03048747032880783,
0.04320871829986572,
-0.0048729474656283855,
-0.07233862578868866,
-0.002989831380546093,
0.004296652041375637,
-0.01405434962362051,
-0.014252102002501488,
0.06377751380205154,
-0.03598228469491005,
0.029112309217453003,
-0.018141303211450577,
0.022276245057582855,
0.04547041654586792,
-0.017928890883922577,
0.0514240525662899,
-0.0024828510358929634,
0.02157489024102688,
-0.08169396966695786,
0.01845269463956356,
0.09441711753606796,
-0.02301219291985035,
-0.01737762615084648,
0.014833133667707443,
0.025040313601493835,
-0.0019560959190130234,
0.004609133582562208,
0.03348195180296898,
-0.05555906519293785,
0.0020629719365388155,
-0.00838188361376524,
0.027147924527525902,
0.053137581795454025,
0.003283168887719512,
-0.010740776546299458,
-0.03501296788454056,
-0.003088943427428603,
0.03174297511577606,
-0.01804262585937977,
0.03715870901942253,
0.018292170017957687,
-0.02206963673233986,
0.04070335626602173,
-0.062273792922496796,
-0.02744971588253975,
0.006111957132816315,
-0.007005771156400442,
-0.0682392343878746,
-0.02528875693678856,
-0.005448970943689346,
0.030747635290026665,
-0.04370354115962982,
0.0065265828743577,
-0.015309310518205166,
-0.07083950936794281,
-0.04678703099489212,
-0.04243561625480652,
0.011529426090419292,
-0.01785879395902157,
0.022400857880711555,
0.03906915336847305,
0.013374323025345802,
-0.04176659509539604,
0.011936020106077194,
-0.00693831592798233,
-0.01975632831454277,
-0.037874605506658554,
0.07165234535932541,
0.036053795367479324,
-0.04436848312616348,
-0.032813798636198044,
0.010765784420073032,
0.026318557560443878,
0.03302204981446266,
0.03903496265411377,
0.0003996287996415049,
0.048369329422712326,
-0.0003728248120751232,
-0.0062061152420938015,
-0.0028496216982603073,
0.07861549407243729,
0.03193056583404541,
-0.04341844469308853,
-0.021761244162917137,
0.08798790723085403,
0.013665063306689262,
0.003551248461008072,
-0.01043848879635334,
0.0402008593082428,
-0.007351268082857132,
-0.007008204702287912,
0.04004606232047081,
-0.005856198258697987,
0.005751755554229021,
-0.060020167380571365,
0.0359741635620594,
0.009111038409173489,
0.02545243315398693,
-0.0336606465280056,
0.05348803848028183,
-0.009333724156022072,
-0.04210502281785011,
-0.0160721093416214,
0.08669787645339966,
-0.0043974583968520164,
0.03370025381445885,
-0.013122834265232086,
-0.05902770906686783,
-0.021398372948169708,
0.03466363996267319,
-0.047773655503988266,
0.02496849186718464,
0.01361534371972084,
0.03912932798266411,
-0.010469604283571243,
-0.024584533646702766,
0.024928370490670204,
-0.05564361438155174,
0.004204744007438421,
0.030024977400898933,
-0.01991814374923706,
-0.007925636135041714,
-0.015360617078840733,
0.009161259979009628,
-0.04364759102463722,
-0.04728315398097038,
-0.043060991913080215,
0.016544194892048836,
0.011857938021421432,
-0.006078335456550121,
-0.026620451360940933,
-0.003500050399452448,
0.026349510997533798,
-0.08097398281097412,
0.013194567523896694,
0.04240991175174713,
0.07113132625818253,
-0.019403992220759392,
0.07007359713315964,
0.017797650769352913,
-0.029119109734892845,
0.022108161821961403,
-0.03782224282622337,
0.03179732337594032,
-0.04575550556182861,
0.022165188565850258,
-0.011549302376806736,
0.008319413289427757,
0.031816549599170685,
-0.023343496024608612,
0.0381140299141407,
-0.004047652240842581,
-0.0953715518116951,
-0.009622191078960896,
0.006163747049868107,
-0.005046403035521507,
-0.03244961053133011,
-0.0015448095509782434,
-0.08795215934515,
-0.06673655658960342,
0.06853490322828293,
-0.01960679516196251,
-0.03614591062068939,
-0.008321860805153847,
0.022592812776565552,
-0.020825695246458054,
-0.03324947878718376,
-0.010845553129911423,
-0.03388811647891998,
-0.05524582043290138,
-0.032772406935691833,
-0.0024018005933612585,
0.01318143866956234,
-0.015537520870566368,
-0.025522254407405853,
-0.010615065693855286,
0.053887128829956055,
0.042162276804447174,
-0.004017692059278488,
0.03055090829730034,
0.07091066241264343,
-0.0323103591799736,
-0.024325288832187653,
0.006021266803145409,
-0.022430144250392914,
0.03815075010061264,
0.04313709959387779,
-0.044248927384614944,
0.055396225303411484,
-0.01283930242061615,
0.010672880336642265,
-0.015387353487312794,
0.03139190748333931,
-0.03796781599521637,
-0.004032814875245094,
0.06527572870254517,
0.005890900734812021,
-0.0014434162294492126,
-0.030507875606417656,
0.028113512322306633,
0.03545381501317024,
0.027644364163279533,
-0.00520794652402401,
-0.03846576809883118,
0.01929359883069992,
-0.017015717923641205,
-0.030149409547448158,
-0.01813589781522751,
0.018458982929587364,
0.007377437315881252,
0.03357905521988869,
-0.040315549820661545,
0.048553843051195145,
-0.012512837536633015,
0.0533793568611145,
-0.03289560601115227,
-0.010907241143286228,
-0.021198121830821037,
-0.0029636367689818144,
-0.02256787195801735,
-0.01598641835153103,
0.035285353660583496,
0.036587055772542953,
-0.049128539860248566,
-0.02079542726278305,
0.006579395849257708,
-0.03349905088543892,
-0.013462575152516365,
0.0259951613843441,
-0.07391705363988876,
-0.04389958456158638,
-0.008203186094760895,
0.011316888965666294,
0.013213963247835636,
-0.03194880858063698,
-0.01182177010923624,
-0.02036590501666069,
-0.04184187576174736,
0.03949536755681038,
-0.01306852139532566,
0.027427243068814278,
0.002460536314174533,
0.010830778628587723,
0.010502954013645649,
0.005427469499409199,
0.01747000403702259,
0.009627973660826683,
-0.007177166175097227,
-0.025260131806135178,
-0.03477458655834198,
0.03022204339504242,
-0.017563674598932266,
0.0007632649503648281,
0.004482727963477373,
-0.013146812096238136,
-0.035387225449085236,
0.024126281961798668,
-0.034724969416856766,
-0.042748112231492996,
-0.02569415792822838,
0.04991806298494339,
0.024472566321492195,
-0.036852721124887466,
0.042267970740795135,
0.020090414211153984,
0.005192138720303774,
0.008177753537893295,
-0.017095452174544334,
-0.025084996595978737,
0.05383540317416191,
-0.07331227511167526,
-0.0012788667809218168,
0.04660431295633316,
-0.03427118435502052,
-0.010352403856813908,
0.02152283303439617,
0.004174439236521721,
-0.04841258004307747,
0.010149550624191761,
-0.003935243934392929,
0.017858149483799934,
-0.023478511720895767,
-0.02767341397702694,
-0.04957549646496773,
-0.025192856788635254,
0.030793560668826103,
-0.03364533931016922,
-0.03393244370818138,
0.014695318415760994,
0.019328463822603226,
0.0556388795375824,
-0.03020695596933365,
0.007883750833570957,
-0.006140266545116901,
-0.03340699151158333,
0.00043921516044065356,
-0.013817842118442059,
-0.02249244973063469,
-0.047804348170757294,
-0.11453258991241455,
0.03117164969444275,
-0.00307915429584682,
-0.02604486048221588,
0.015779858455061913,
0.042866408824920654,
-0.035317812114953995,
-0.04143349453806877,
-0.0879681408405304,
0.04831450805068016,
-0.028825197368860245,
0.004031202290207148,
0.06777273863554001,
-0.04350389540195465,
0.07198426872491837,
0.020703120157122612,
0.002965641673654318,
-0.03355242684483528,
-0.011937986128032207,
0.0010396871948614717,
0.04773978888988495,
-0.05238752067089081,
0.01806512288749218,
-0.01354623306542635,
-0.01842208206653595,
0.015621320344507694,
-0.0409708172082901,
0.03509094566106796,
0.08850636333227158,
0.03086826391518116,
0.026851527392864227,
-0.05328332260251045,
0.02063743956387043,
0.026722516864538193,
0.009959565475583076,
0.03259313479065895,
0.002164392499253154,
0.011601405218243599,
0.0014810607535764575,
0.02504570595920086,
-0.046485934406518936,
0.05374165251851082,
0.00017954831128008664,
0.02394791878759861
] |
<p>Suppose I am trying to determine the value of the acceleration due to gravity by simply dropping objects from a ledge. If I did not account for air resistance, would the acceleration due to gravity measured be less than if I did account for air resistance?</p>
<p>This is what a thought: Suppose I had an object of mass $m$ that was being dropped and let $F_{drag}$ be the force due to air resistance. Then </p>
<p>$mg - F_{drag} = ma$. Then with some algebra I get $a = g - \frac{F_{drag}}{m}$. If I do not account for air resistance, I get $a = g$. But if I do account for air resistance $a < g$. So I get that the value of $g$ is greater if I do not account for air resistance. </p> | g1277 | [
0.052742477506399155,
0.042104024440050125,
-0.000599894265178591,
0.01999559998512268,
0.020077116787433624,
0.07028602063655853,
0.08818216621875763,
0.011090485379099846,
-0.08224452286958694,
0.007174819707870483,
-0.006252558436244726,
-0.022167515009641647,
0.012131939642131329,
0.05408566817641258,
0.03205103427171707,
0.029974842444062233,
0.037873074412345886,
-0.04084251448512077,
0.0011150940554216504,
0.0007357723079621792,
0.03906768187880516,
-0.0343170091509819,
-0.041673872619867325,
-0.0326656773686409,
0.05648275464773178,
-0.04370428994297981,
0.06201217323541641,
-0.005944019183516502,
-0.12531867623329163,
0.04723230376839638,
-0.00726018100976944,
-0.025406116619706154,
0.054191187024116516,
-0.03035641647875309,
-0.05072278901934624,
-0.055022433400154114,
0.04392572492361069,
0.0830182433128357,
0.06975074112415314,
-0.02372319996356964,
-0.010769453831017017,
-0.06884634494781494,
-0.028412653133273125,
0.05652794614434242,
0.023663567379117012,
0.004067057743668556,
0.014830387197434902,
0.04087455943226814,
-0.0030320859514176846,
-0.014789063483476639,
-0.016449755057692528,
0.03204958140850067,
-0.02639400027692318,
-0.05628744512796402,
-0.0739615187048912,
0.05607496201992035,
0.018673602491617203,
-0.012148811481893063,
-0.0326177179813385,
0.047186411917209625,
-0.03413030877709389,
-0.016383668407797813,
0.01618272252380848,
-0.03920626640319824,
0.05637378245592117,
0.030749712139368057,
0.015761079266667366,
-0.013432282954454422,
-0.014873294159770012,
0.026643618941307068,
0.03607560321688652,
0.0010891087586060166,
-0.01780816912651062,
-0.025625426322221756,
-0.03292965888977051,
0.019960027188062668,
-0.024923229590058327,
0.03333882614970207,
0.006036720704287291,
-0.0006379931000992656,
-0.015037433244287968,
0.04711373150348663,
0.04445245862007141,
0.028991730883717537,
0.05381473898887634,
-0.0020038937218487263,
0.026792673394083977,
0.03959331288933754,
-0.020334359258413315,
-0.0022234513889998198,
0.03413359075784683,
-0.029158063232898712,
0.11081881821155548,
0.01026909053325653,
-0.007936282083392143,
-0.023131821304559708,
-0.008618051186203957,
0.05138680338859558,
-0.04763681814074516,
-0.0029733991250395775,
-0.002963236765936017,
0.012089939787983894,
-0.023400479927659035,
-0.0005752047873102129,
0.0425899513065815,
-0.04112941771745682,
0.06600544601678848,
0.022146539762616158,
-0.009567132219672203,
-0.05500243231654167,
0.0353708416223526,
0.030358517542481422,
-0.11769837886095047,
-0.06755959242582321,
-0.03876238316297531,
-0.06034887582063675,
0.06498921662569046,
-0.009745328687131405,
-0.04085841774940491,
-0.011620077304542065,
-0.04345815256237984,
0.033841490745544434,
0.016131732612848282,
0.06676497310400009,
-0.012230105698108673,
-0.003749116091057658,
0.03312002122402191,
0.031782180070877075,
0.0023829289712011814,
0.00034198618959635496,
0.037705231457948685,
-0.04376213252544403,
0.04645107686519623,
-0.0024483678862452507,
-0.043639279901981354,
-0.020209483802318573,
-0.036507073789834976,
0.05714047700166702,
-0.027763493359088898,
0.023819901049137115,
-0.07725388556718826,
-0.013735524378716946,
-0.004040474537760019,
-0.06117305904626846,
-0.024497583508491516,
0.037102874368429184,
-0.028765777125954628,
0.060736238956451416,
0.030910488218069077,
0.03390759974718094,
0.01883707568049431,
0.05681660398840904,
0.007395587395876646,
-0.056518688797950745,
0.045256562530994415,
-0.0311477892100811,
-0.025816679000854492,
-0.02969217300415039,
-0.015530521981418133,
0.012689162977039814,
0.057340845465660095,
-0.018434513360261917,
0.06482217460870743,
0.01431355532258749,
-0.04543911665678024,
0.05425037071108818,
-0.05794266238808632,
-0.009468870237469673,
0.020837770774960518,
-0.046090349555015564,
-0.029085710644721985,
-0.0139821982011199,
0.02894955687224865,
0.03848595544695854,
0.0023621900472790003,
0.02725590206682682,
0.060509808361530304,
-0.04244687035679817,
0.024257369339466095,
0.0013756603002548218,
0.061020758002996445,
-0.014306807890534401,
0.04374547675251961,
-0.028036657720804214,
-0.025927279144525528,
-0.048040397465229034,
0.0421573631465435,
0.0015104147605597973,
-0.06997016817331314,
-0.009270844981074333,
-0.016713786870241165,
0.021799681708216667,
-0.025808926671743393,
0.044129062443971634,
-0.06629053503274918,
0.0075067817233502865,
-0.0043678004294633865,
0.012896343134343624,
-0.016759904101490974,
0.03238186240196228,
0.006531557533890009,
0.028987538069486618,
0.0009698855574242771,
-0.032882992178201675,
0.044116195291280746,
0.02513735368847847,
-0.015404289588332176,
-0.03151567652821541,
0.041180700063705444,
-0.03239639848470688,
0.03192878141999245,
0.03674408420920372,
0.07539231330156326,
0.011145362630486488,
0.005671234801411629,
-0.007232097443193197,
0.0222974494099617,
0.012171352282166481,
0.0005185121553950012,
0.006502103991806507,
0.01960185170173645,
-0.0450662262737751,
0.010928049683570862,
-0.0071893008425831795,
-0.036931198090314865,
-0.022404661402106285,
0.005213012918829918,
-0.0063329702243208885,
-0.03197729215025902,
-0.026589300483465195,
-0.021185753867030144,
0.018026476725935936,
-0.015562391839921474,
-0.0024898876436054707,
0.03446485847234726,
0.01152899768203497,
-0.0030131626408547163,
0.012432156130671501,
0.04151654615998268,
-0.034220725297927856,
-0.006547737400978804,
-0.03400363028049469,
-0.024504542350769043,
-0.009572053328156471,
0.03572564944624901,
0.005133350845426321,
-0.0007955035544000566,
0.030559657141566277,
0.013089971616864204,
0.02800346352159977,
-0.06495729088783264,
0.02111690491437912,
-0.027342339977622032,
-0.009904890321195126,
0.017608655616641045,
0.05344177410006523,
-0.03635462000966072,
-0.03179440647363663,
0.00575394369661808,
0.052935391664505005,
0.0038908200804144144,
-0.053904980421066284,
-0.007851284928619862,
0.015390550717711449,
-0.08878931403160095,
0.028872765600681305,
-0.0058054206892848015,
-0.017933497205376625,
0.005818093195557594,
0.004577517509460449,
-0.01093823742121458,
0.01590009219944477,
-0.03670388087630272,
0.046272482722997665,
-0.040211934596300125,
-0.03148172050714493,
0.015602855011820793,
-0.01998375914990902,
0.0197413582354784,
0.020590130239725113,
-0.0062816692516207695,
-0.016631068661808968,
-0.09413695335388184,
0.032821137458086014,
0.024474356323480606,
-0.010433773510158062,
0.0056528658606112,
0.03607719764113426,
-0.028906768187880516,
0.01792147569358349,
-0.04775525629520416,
0.02592393569648266,
0.00204772362485528,
0.00842883437871933,
0.0031403321772813797,
0.0657377764582634,
-0.001227694214321673,
0.009400391019880772,
0.006175536196678877,
0.04997890070080757,
-0.01520485244691372,
-0.011678952723741531,
-0.005180452950298786,
-0.02536686696112156,
0.014416702091693878,
0.026761604472994804,
-0.032623082399368286,
-0.11025688052177429,
0.00746097881346941,
0.006592991761863232,
-0.029101379215717316,
0.04194672778248787,
-0.01764097437262535,
-0.03702765330672264,
-0.03446439653635025,
-0.04916822910308838,
0.006482863798737526,
-0.007496115751564503,
-0.028332343325018883,
-0.02482266165316105,
-0.037742115557193756,
-0.06410937011241913,
0.004909260664135218,
0.022554364055395126,
-0.013190630823373795,
-0.0034258393570780754,
-0.036945588886737823,
0.08374069631099701,
0.005217697471380234,
-0.0504075288772583,
0.06604401022195816,
0.027635464444756508,
-0.0025470289401710033,
0.045660268515348434,
-0.030679797753691673,
-0.05278816446661949,
0.016881421208381653,
-0.03243701159954071,
-0.017299551516771317,
-0.03512030094861984,
-0.05468325316905975,
-0.03445624187588692,
-0.033088263124227524,
-0.014737570658326149,
-0.0391789972782135,
0.0359795019030571,
-0.03904213011264801,
0.05187331885099411,
0.012336942367255688,
-0.04048646241426468,
0.044410090893507004,
-0.06308014690876007,
-0.00405498081818223,
-0.024224312976002693,
-0.0036920844577252865,
-0.0017337554600089788,
0.05004502460360527,
0.03168491646647453,
-0.040746111422777176,
0.02919471077620983,
0.02796952612698078,
-0.015259278006851673,
-0.045473240315914154,
0.03976381942629814,
0.036113440990448,
-0.051788344979286194,
-0.011166824959218502,
0.04822423309087753,
-0.029333410784602165,
0.00429438566789031,
0.007939649745821953,
-0.03821399435400963,
0.018182728439569473,
0.02086629904806614,
0.05633077770471573,
-0.08125095069408417,
0.05877237021923065,
-0.0231256615370512,
-0.0000684875703882426,
-0.01625158078968525,
0.030598856508731842,
0.016320208087563515,
0.00564735010266304,
-0.04857507348060608,
0.023307818919420242,
-0.024328060448169708,
0.008379724808037281,
0.012022344395518303,
0.02104588970541954,
-0.017763864248991013,
-0.05026603490114212,
-0.037186913192272186,
-0.06867950409650803,
0.04825340956449509,
0.030376741662621498,
-0.0021290036384016275,
-0.0264555886387825,
0.008521816693246365,
-0.007525658700615168,
0.05687432363629341,
-0.0003635526227299124,
0.035992857068777084,
0.019345834851264954,
0.0648157000541687,
-0.024174820631742477,
0.00012315885396674275,
0.0650542601943016,
-0.007322667166590691,
-0.012850656174123287,
0.04205404222011566,
-0.0009842566214501858,
-0.059969596564769745,
-0.04930324852466583,
-0.0707327276468277,
-0.03831888362765312,
-0.049770861864089966,
0.009953849948942661,
-0.002231057733297348,
0.06533746421337128,
-0.00147333147469908,
0.09139258414506912,
0.0508832223713398,
0.001626357319764793,
-0.05791248008608818,
0.0014124029548838735,
0.05175555497407913,
0.024694614112377167,
0.015493475832045078,
0.024918368086218834,
-0.0015776869840919971,
-0.023701973259449005,
0.01138401310890913,
-0.0217654537409544,
0.03322604298591614,
-0.01811971887946129,
0.06742718815803528,
-0.017761874943971634,
0.06062578409910202,
0.040707800537347794,
-0.004474966786801815,
0.015942620113492012,
0.06554408371448517,
-0.02206459455192089,
0.004696860909461975,
0.028502602130174637,
0.045498091727495193,
-0.005236880388110876,
-0.020315291360020638,
0.014961331151425838,
0.03348822146654129,
-0.0517674945294857,
-0.016107259318232536,
0.029059814289212227,
-0.019566619768738747,
-0.029684005305171013,
0.003580748802050948,
0.021172361448407173,
-0.019197598099708557,
0.00019562691159080714,
0.0267568901181221,
0.0033919205889105797,
0.01983761601150036,
0.005674357060343027,
-0.013065792620182037,
-0.0217126552015543,
-0.03401443734765053,
-0.047424644231796265,
0.039777971804142,
-0.034595705568790436,
-0.01913631707429886,
0.03797348961234093,
-0.06356455385684967,
0.002487942110747099,
0.028170151636004448,
0.03253701329231262,
0.012172614224255085,
0.0023892016615718603,
0.048959020525217056,
0.006510190200060606,
-0.024599391967058182,
-0.01385065820068121,
-0.01059003546833992,
-0.006779817398637533,
-0.021697591990232468,
0.0002570807409938425,
0.0533776730298996,
-0.03404228761792183,
-0.02057904563844204,
0.07379329204559326,
-0.07412964105606079,
0.042211081832647324,
0.02774089202284813,
-0.0639076754450798,
0.00971751008182764,
-0.045622196048498154,
0.03944272920489311,
-0.004187584389001131,
0.005819323007017374,
0.02082544006407261,
-0.034271515905857086,
-0.04247574135661125,
0.04642036184668541,
0.032735373824834824,
0.01439065020531416,
-0.0001487668341724202,
0.015453774482011795,
0.05385635420680046,
-0.02365332841873169,
-0.03280210122466087,
0.07369805127382278,
-0.023545563220977783,
0.033659111708402634,
0.038011327385902405,
0.007954641245305538,
-0.005645127967000008,
0.0012815315276384354,
0.018651358783245087,
0.00975053757429123,
-0.024924715980887413,
-0.018418122082948685,
0.05845068767666817,
-0.01673019863665104,
0.012218124233186245,
-0.025772834196686745,
-0.0014847293496131897,
0.02293097786605358,
-0.017588088288903236,
-0.04334339499473572,
-0.031009919941425323,
0.0017065020510926843,
0.035099953413009644,
-0.02150157280266285,
0.001377532142214477,
-0.02703288197517395,
-0.00212882156483829,
-0.015591641888022423,
0.021301621571183205,
0.00194073049351573,
0.05282435566186905,
-0.05121004208922386,
-0.05979308485984802,
0.014971842058002949,
0.03401494398713112,
0.043206002563238144,
-0.015850244089961052,
0.031347669661045074,
-0.06501879543066025,
0.0004962029634043574,
0.012955940328538418,
-0.052795782685279846,
-0.06222416087985039,
0.03772452846169472,
-0.012083856388926506,
0.008442902006208897,
-0.022619228810071945,
0.07532566040754318,
-0.015326687134802341,
0.01607850380241871,
-0.03572768345475197,
0.020314287394285202,
0.031202277168631554,
0.01704326644539833,
0.029858451336622238,
-0.019052375108003616,
0.04020564630627632,
-0.04494078829884529,
0.02075078897178173,
-0.03282838687300682,
0.0025393750984221697,
0.018635425716638565,
-0.041583288460969925,
0.002054593525826931,
-0.00997667945921421,
0.012477900832891464,
0.003743539797142148,
0.028077298775315285,
-0.06790817528963089,
-0.10922463238239288,
0.0002088993351208046,
0.012638279236853123,
0.0014263606863096356,
0.0006539967143908143,
0.029157523065805435,
-0.07120011746883392,
-0.015336836688220501,
-0.03934554383158684,
-0.06033529341220856,
-0.011524059809744358,
0.05677473545074463,
-0.037444278597831726,
-0.05346124246716499,
0.010899524204432964,
0.0017887215362861753,
0.04072157293558121,
-0.08928864449262619,
-0.03838271647691727,
0.057268839329481125,
-0.04196549579501152,
0.014991083182394505,
-0.00018775546050164849,
0.07866190373897552,
0.02725064940750599,
0.06159253790974617,
-0.03745418041944504,
0.03457323834300041,
-0.008046313188970089,
-0.03871213644742966,
-0.01570083387196064,
0.032052528113126755,
-0.08378565311431885,
0.019298970699310303,
0.0585629865527153,
0.03528071567416191,
0.029164867475628853,
0.0364871546626091,
-0.021808581426739693,
0.03401145339012146,
-0.06357987225055695,
-0.017911406233906746,
-0.0017097339732572436,
-0.02883443795144558,
0.016269423067569733,
0.019273385405540466,
-0.05656825006008148,
0.029359063133597374,
-0.009364568628370762,
-0.029830440878868103,
0.022795334458351135,
-0.001126802060753107,
0.0005731368437409401,
-0.00785120576620102,
0.04341486096382141,
-0.003371262224391103,
0.019434936344623566,
0.06958801299333572,
0.08888350427150726,
0.024543624371290207,
0.0650264248251915,
0.0011609933571889997,
0.05105319619178772,
-0.026525309309363365,
0.04929620772600174,
-0.02949312888085842,
0.03247443214058876,
-0.06713118404150009,
-0.0333133339881897,
0.004966827109456062,
0.025189930573105812,
-0.02227742224931717,
-0.038832008838653564,
0.010449390858411789,
0.017074326053261757,
-0.007930044084787369,
0.032245200127363205,
-0.04123904928565025,
-0.022942980751395226,
-0.0015028259949758649,
0.04681571200489998,
0.010836802423000336,
-0.024744518101215363,
-0.05264729633927345,
-0.03977622464299202,
0.034170422703027725,
0.04252151399850845,
-0.0188558679074049,
-0.019571032375097275,
-0.022145884111523628,
0.00329236569814384,
0.006896653678268194,
-0.00908853579312563,
-0.012352044694125652,
-0.06796514987945557,
0.006238294765353203,
-0.011902447789907455,
-0.005710544064640999,
0.023341987282037735,
-0.039696820080280304,
-0.04155689850449562,
-0.035895511507987976,
0.008536966517567635,
-0.02744634822010994,
0.02974860556423664,
-0.006489065010100603,
0.0011216697748750448,
-0.03650655224919319,
-0.015558481216430664,
-0.0030605928041040897,
-0.0016926246462389827,
0.023545609787106514,
-0.05653928592801094,
-0.06179298460483551,
0.005426379851996899,
0.09026416391134262,
0.028345178812742233,
-0.02815050259232521,
-0.020946817472577095,
-0.028257017955183983,
0.03817927464842796,
0.016515791416168213,
-0.033417534083127975,
0.05392863228917122,
-0.05311475321650505,
0.01417213398963213,
-0.010075035504996777,
0.005678261164575815,
0.017140967771410942,
0.00010498415940674022,
-0.006975067779421806,
-0.03023824468255043,
0.006628416012972593,
-0.007599934004247189,
0.027169985696673393,
0.026856236159801483,
0.010669921524822712,
-0.006963691208511591,
-0.0058718654327094555,
-0.042966779321432114,
-0.00645584799349308,
-0.012985710985958576,
-0.056018128991127014,
0.04139280691742897,
-0.05649591237306595,
-0.005578237120062113,
-0.0960911363363266,
-0.01514799427241087,
0.00931029673665762,
-0.07733147591352463,
0.024269992485642433,
-0.021252643316984177,
0.04178304970264435,
0.0071935951709747314,
-0.015576009638607502,
0.034361135214567184,
0.04947463050484657,
-0.005718792788684368,
0.012071257457137108,
0.049554310739040375,
-0.0007011842099018395,
-0.04139081761240959,
0.02181524783372879,
-0.040278658270835876,
0.0023435931652784348,
-0.043562304228544235,
0.05526965484023094,
0.03517536446452141,
-0.0691179558634758,
0.020623493939638138,
0.04754878953099251,
0.02508276328444481,
-0.03249141573905945,
0.02600303664803505,
0.028579620644450188,
-0.04181012883782387,
0.011208390817046165,
0.009033952839672565,
-0.0005468276212923229,
-0.012862038798630238,
0.004591239150613546,
0.007239567115902901,
-0.04296714439988136,
-0.011481717228889465,
0.018697675317525864,
-0.0066901929676532745,
0.008243994787335396,
-0.020503878593444824,
-0.05611681565642357,
-0.010875888168811798,
0.02136457897722721
] |
<p>The question goes along the lines:</p>
<blockquote>
<p>Uranium-$236$ fissions when it absorbs a slow-moving neutron. The two fission fragments can be almost any two nuclei whose charges $Q_1$ and $Q_2$ add up to $92e$ ($e$ is the charge of a proton, $1.6 \times 10^{-19}C$), and whose nucleons add up to $236$ protons and neutrons. One of the possible fission modes involves nearly equal fragments of the two palladium nuclei with $Q_1 = Q_2 = 46e$. The rest masses of the two palladium nuclei add up to less than the rest of the mass of the original nucleus. Make the assumption that there are no free neutrons, jus the palladium nuclei. The rest mass of the U-$236$ is 235.996 u (unified atomic mass units), and the rest mass of each $Pd-118$ nucleus is 117.894 u, where $1$ $u = 1.7 \times 10^{-27} kg$.</p>
<p>(a) Calculate the final speed $v$, when the Pd nuclei have moved far apart (due to the mutual electric repulsion). Is this speed small enough that $\frac{p^2}{2m}$ is an adequate ($p$ is momentum) approximation for the kinetic energy of one of the palladium nuclei? (make the non relativistic assumption first, then compare $v$ is indeed small enough to $c$)</p>
<p>(b) Using energy considerations, calculate the distance between centers of the palladium nuclei just after fission, when they are starting from rest.</p>
</blockquote>
<p>So the beginning step is to chose the system, for which I include both the Pd nuclei. So the energy principle is now: $$\Delta E_{sys} = W_{ext}$$ We know that $W_{ext} = 0$ since my system is defined not including any external work done on the system. So now instead the system is $\Delta E_{sys} = 0 = \Delta K_{m_1} + \Delta K_{m_2} + \Delta U_{elec_1} + \Delta U_{elec_2}$ We can ignore the earth and the gravitational potential energy sine the masses are very small. If we expand the equation, we get:
$$K_{f_1} - K_{i_1} + K_{f_2} + K_{i_2} + U_{f_1} - U_{i_1} + U_{f_2} - U_{i_2} = 0$$
getting rid of terms that are $0$, we get:
$$K_{f_1} + K_{f_2} - U_{i_1} - U_{i_2} = 0$$
furthermore:
$$K_{f_1} + K_{f_2} = U_{i_1} + U_{i_2}$$
We know that $K = \frac{1}{2}mv^2$ and that $K_{f_1} = K_{f_2}$ are equal since the masses are the same. So we can simplify that to $2K_f = mv^2$. Same for $U = \frac{1}{2 \pi \epsilon_0} \frac{Q_1 Q_2}{r}$. So $U_{i_1} = U_{i_2} = 2U_i = \frac{2}{2 \pi \epsilon_0} \frac{Q_1 Q_2}{r}$. So we can essentially write:
$$mv^2 = 2 \frac{1}{4 \pi \epsilon_0} \frac{Q_1 Q_2}{r}$$
$$v = \sqrt{\frac{2}{m} \frac{1}{4 \pi \epsilon_0} \frac{Q_1 Q_2}{r}}$$
I then get lost n finding $r$ since it is not given, furthermore, (b) asks us to find the distance before they move apart. So I am approaching the problem incorrectly. I would need to figure out the error here and how to commence part b. </p> | g1278 | [
0.044547975063323975,
0.04582194983959198,
0.022055000066757202,
-0.004145200829952955,
0.03886155039072037,
-0.035001181066036224,
-0.01426674984395504,
0.00868731178343296,
-0.030693525448441505,
-0.018497290089726448,
0.011262665502727032,
0.027207331731915474,
-0.007098127156496048,
-0.07889064401388168,
0.004978701006621122,
0.01692318171262741,
0.08963116258382797,
-0.052531201392412186,
0.0160609669983387,
0.06502331793308258,
-0.025516092777252197,
0.08516707271337509,
-0.03896685689687729,
-0.02612076699733734,
-0.004845233168452978,
0.005333829205483198,
-0.01481509767472744,
-0.011431069113314152,
-0.04847436770796776,
-0.016688022762537003,
0.025771692395210266,
-0.016933266073465347,
-0.008080617524683475,
-0.054439131170511246,
-0.02842695452272892,
-0.019437948241829872,
-0.004777145106345415,
-0.05551765859127045,
0.0009932953398674726,
0.04058147221803665,
-0.0023942862171679735,
-0.0313880629837513,
-0.03060884028673172,
-0.026487449184060097,
0.058101799339056015,
-0.015365604311227798,
0.018260013312101364,
-0.07520557940006256,
0.007495126221328974,
0.016735898330807686,
-0.01274703536182642,
0.10262300074100494,
0.013734692707657814,
-0.008442830294370651,
-0.03030950203537941,
0.0602370947599411,
0.03684335574507713,
-0.03579302877187729,
0.01671716198325157,
-0.0013900903286412358,
0.012861261144280434,
0.005809343419969082,
0.04463382065296173,
-0.08924971520900726,
0.016126662492752075,
0.011374090798199177,
-0.03633199259638786,
-0.009559362195432186,
0.06900517642498016,
-0.004473235458135605,
-0.020200517028570175,
-0.013257092796266079,
-0.10507316887378693,
-0.026892831549048424,
0.024493267759680748,
-0.015183561481535435,
0.046192582696676254,
-0.04381391406059265,
0.03349617123603821,
-0.021676061674952507,
-0.07129465788602829,
-0.010795853100717068,
0.018189826980233192,
0.05764734372496605,
-0.010339176282286644,
0.06274799257516861,
-0.02297203242778778,
0.06689436733722687,
-0.005777339916676283,
0.03150058165192604,
0.0070552099496126175,
-0.019557001069188118,
0.03468853607773781,
-0.03660829737782478,
0.02435670793056488,
-0.006023807916790247,
-0.05801284685730934,
0.0415860079228878,
-0.03619793429970741,
0.028232378885149956,
0.008230987936258316,
0.018323402851819992,
0.014852181077003479,
-0.01678098551928997,
-0.025184260681271553,
-0.03778461366891861,
-0.037613555788993835,
-0.013269265182316303,
0.025147859007120132,
0.020602433010935783,
0.009858527220785618,
-0.07602138072252274,
0.01200019009411335,
-0.04062189906835556,
0.009365192614495754,
-0.026766926050186157,
0.00041020652861334383,
-0.03098909743130207,
-0.027836015447974205,
0.04813752695918083,
0.027170082554221153,
0.02103385329246521,
-0.01983560249209404,
-0.01212453842163086,
0.008103977888822556,
-0.060181450098752975,
-0.030244287103414536,
0.018254393711686134,
0.012969489209353924,
0.03766220808029175,
-0.04484447091817856,
-0.015482746064662933,
0.04949893429875374,
0.02019491046667099,
-0.027929222211241722,
0.0675843209028244,
0.03603651002049446,
0.031215663999319077,
-0.021058741956949234,
-0.025212643668055534,
-0.010478399693965912,
-0.006886635906994343,
-0.009501936845481396,
-0.031836334615945816,
-0.06661158800125122,
0.047122515738010406,
-0.03027188777923584,
0.01163425762206316,
-0.038103628903627396,
0.006002912763506174,
0.007339542731642723,
0.0025440086610615253,
-0.0025702144484966993,
0.01559488195925951,
0.04751569777727127,
-0.006648647598922253,
0.02929823286831379,
-0.03749382495880127,
0.055115606635808945,
-0.00411835266277194,
0.05576120689511299,
0.009678381495177746,
-0.00041407474782317877,
0.013724998570978642,
0.0013315333053469658,
0.008330377750098705,
0.12956275045871735,
-0.027646107599139214,
-0.012090431526303291,
-0.04824235290288925,
-0.04756299406290054,
-0.0970851480960846,
0.003412348683923483,
0.043521590530872345,
-0.029886405915021896,
0.021257370710372925,
0.01312587596476078,
0.016959676519036293,
-0.062043461948633194,
0.005253966432064772,
-0.026533491909503937,
-0.015586636029183865,
0.055519573390483856,
0.038608402013778687,
-0.017764123156666756,
-0.02892555110156536,
0.007815668359398842,
0.026855364441871643,
-0.022234737873077393,
0.022500889375805855,
0.0369316004216671,
0.02271190844476223,
0.03454478085041046,
-0.006155714858323336,
-0.015397794544696808,
0.01978304423391819,
-0.00498992158100009,
-0.04261499643325806,
0.022159188985824585,
0.024569444358348846,
-0.009244784712791443,
0.008022000081837177,
-0.0011490574106574059,
-0.03475285321474075,
0.1346767246723175,
-0.032998427748680115,
-0.03664355352520943,
0.0024061198346316814,
0.02901340462267399,
-0.01724596880376339,
-0.013950116001069546,
0.008417867124080658,
-0.07641353458166122,
0.05024116858839989,
-0.036610379815101624,
-0.024428201839327812,
-0.047369152307510376,
0.030397584661841393,
-0.005151923280209303,
-0.03918345272541046,
-0.06466706842184067,
0.02721809409558773,
-0.013291643932461739,
-0.027113059535622597,
-0.03423691913485527,
-0.018498046323657036,
-0.02228771150112152,
0.02770346589386463,
-0.0708298459649086,
0.046164028346538544,
-0.04703493416309357,
0.06867630034685135,
-0.014645812101662159,
-0.02611721120774746,
0.04073156416416168,
0.01614685170352459,
-0.00622303131967783,
-0.0019093413138762116,
0.015286305919289589,
-0.08194197714328766,
-0.011804143898189068,
-0.03216972202062607,
-0.011831431649625301,
0.07019248604774475,
-0.00023658177815377712,
-0.038757145404815674,
0.03935285285115242,
-0.013784424401819706,
0.0033544283360242844,
0.006143520120531321,
-0.013083781115710735,
0.005897657945752144,
-0.007241703569889069,
-0.013895366340875626,
-0.007477617356926203,
-0.020827341824769974,
-0.018792441114783287,
0.016812510788440704,
-0.03707146644592285,
-0.02888702042400837,
0.015777770429849625,
-0.01851017400622368,
-0.020693430677056313,
0.02768341451883316,
-0.033594243228435516,
0.02270660176873207,
-0.05562102422118187,
0.01442194264382124,
-0.008693921379745007,
0.006303316913545132,
-0.032776329666376114,
0.016174638643860817,
0.05265315994620323,
0.001305631478317082,
0.03330996632575989,
-0.08915738016366959,
0.07719682902097702,
-0.027013391256332397,
-0.018547091633081436,
0.049500614404678345,
-0.006865873001515865,
0.003979337867349386,
-0.02013550139963627,
-0.009230945259332657,
0.004183697514235973,
-0.04162193462252617,
-0.006178112234920263,
0.05442946031689644,
0.07347292453050613,
0.0225314199924469,
-0.024664266034960747,
0.024383092299103737,
0.05794472619891167,
0.018600715324282646,
0.06160365417599678,
0.07760470360517502,
0.06742837280035019,
-0.054502926766872406,
-0.02845475636422634,
-0.06738269329071045,
0.06034713238477707,
-0.028404485434293747,
0.007991577498614788,
0.03704175353050232,
-0.014417467638850212,
-0.0023433116730302572,
-0.0381675586104393,
-0.02034940756857395,
-0.004420037381350994,
-0.029487434774637222,
0.02857148088514805,
0.05002852901816368,
-0.020154252648353577,
0.026461657136678696,
-0.017658067867159843,
-0.02626859024167061,
0.0009208130068145692,
0.012373780831694603,
0.013784205541014671,
-0.006448603700846434,
0.0024412316270172596,
-0.025917598977684975,
0.05917740240693092,
0.013051209039986134,
-0.02817489020526409,
0.049745913594961166,
-0.06995446234941483,
0.03590196371078491,
-0.031067324802279472,
-0.019776612520217896,
-0.007783371489495039,
0.021557172760367393,
-0.032217953354120255,
-0.01906442455947399,
-0.038062792271375656,
-0.05789239704608917,
0.0825149342417717,
0.09841635078191757,
0.021364573389291763,
0.04322534799575806,
0.011634529568254948,
0.014753593131899834,
-0.01281762309372425,
0.01244072150439024,
-0.03797173127532005,
-0.01505152229219675,
-0.0011020120000466704,
-0.042781658470630646,
-0.01690024696290493,
-0.0037795864045619965,
0.024608192965388298,
-0.006307609844952822,
-0.039317697286605835,
0.05522657558321953,
0.01781301572918892,
0.02831346169114113,
-0.03320979326963425,
-0.04086596146225929,
0.018147548660635948,
0.03654799237847328,
0.025629477575421333,
0.018812639638781548,
0.03591711446642876,
0.004759219009429216,
-0.019726045429706573,
-0.025834787636995316,
-0.054575372487306595,
0.015442675910890102,
-0.015455913729965687,
0.002622529398649931,
-0.022797783836722374,
-0.01527139451354742,
0.03113413043320179,
-0.007007958833128214,
-0.015306634828448296,
0.004782155621796846,
0.031522367149591446,
0.03783125430345535,
-0.08204995840787888,
0.03261684998869896,
-0.027819134294986725,
-0.02402801439166069,
-0.004686411470174789,
-0.013040287420153618,
-0.0017316824523732066,
-0.03428246080875397,
0.0018809044267982244,
-0.033518921583890915,
0.047168537974357605,
-0.007712358608841896,
0.01632555015385151,
-0.07706379890441895,
-0.04593340680003166,
-0.008032101206481457,
-0.024971850216388702,
-0.048531245440244675,
0.027815310284495354,
0.03378378972411156,
-0.012167666107416153,
0.030506610870361328,
-0.0751650407910347,
0.004390353336930275,
-0.04566821828484535,
-0.023179123178124428,
-0.039137378334999084,
-0.00819280557334423,
-0.04301279038190842,
-0.022399434819817543,
0.008990872651338577,
-0.00034309865441173315,
-0.03815477713942528,
-0.009033073671162128,
0.0299152173101902,
-0.0016206565778702497,
-0.036367710679769516,
-0.009584772400557995,
-0.02234746515750885,
-0.024528775364160538,
-0.02669530175626278,
0.06343685835599899,
0.014497509226202965,
-0.029565870761871338,
-0.03855546936392784,
-0.03450876101851463,
-0.03175686299800873,
0.02574843354523182,
0.03694479912519455,
-0.006666208151727915,
-0.0025847535580396652,
-0.019302725791931152,
-0.020686110481619835,
0.027103383094072342,
-0.010959340259432793,
0.02861175686120987,
-0.025558533146977425,
-0.03637009486556053,
0.009133724495768547,
0.052370909601449966,
-0.01084166206419468,
0.05900527909398079,
0.0592496395111084,
0.03352826461195946,
0.009326272644102573,
0.07741792500019073,
0.0336095355451107,
0.02309141866862774,
0.014666806906461716,
-0.03270222246646881,
0.029175588861107826,
-0.04830562323331833,
0.01125600840896368,
0.021266700699925423,
0.003681017318740487,
-0.017276057973504066,
-0.008588363416492939,
0.005837265867739916,
-0.06360665708780289,
0.03352823480963707,
0.0026217743288725615,
0.05857422947883606,
0.032471153885126114,
0.06787002831697464,
0.0778830349445343,
-0.03270525857806206,
-0.022612497210502625,
-0.012073222547769547,
0.029812375083565712,
-0.014088813215494156,
-0.047565121203660965,
-0.02698909305036068,
0.03338708356022835,
0.0032274650875478983,
-0.03187791258096695,
-0.002485687145963311,
-0.010871047154068947,
-0.003832555841654539,
-0.030928384512662888,
-0.010411537252366543,
0.10348840802907944,
-0.014142726548016071,
-0.03546290099620819,
-0.013363945297896862,
-0.020247824490070343,
0.01574823074042797,
0.01959797367453575,
0.02196354791522026,
0.013162141665816307,
0.05058568716049194,
0.03655426576733589,
-0.017196988686919212,
0.040783610194921494,
0.001194672891870141,
0.022960234433412552,
-0.014467344619333744,
0.030044259503483772,
0.0054042162373661995,
0.03750843554735184,
-0.00132657028734684,
0.013923556543886662,
0.018404031172394753,
0.004205714445561171,
0.024207087233662605,
0.010057416744530201,
-0.03141641616821289,
0.042541347444057465,
0.08060576766729355,
0.0417199432849884,
0.038669176399707794,
-0.01879372075200081,
0.005438885185867548,
-0.00011204941984033212,
0.025270553305745125,
0.021779509261250496,
-0.033261947333812714,
-0.004485838580876589,
0.010112093761563301,
0.02858758717775345,
0.008447292260825634,
0.0016131217125803232,
-0.04690367728471756,
0.062196504324674606,
0.019649723544716835,
0.049132268875837326,
-0.014444769360125065,
-0.025215042755007744,
-0.031575363129377365,
-0.04641667380928993,
-0.0267630647867918,
-0.01612795889377594,
0.026264887303113937,
0.0818604826927185,
-0.08458036184310913,
-0.02354385331273079,
-0.025546390563249588,
0.003934909123927355,
0.008486773818731308,
-0.06295474618673325,
-0.04591759666800499,
-0.003499950747936964,
-0.004791281186044216,
0.04721801355481148,
-0.022355178371071815,
0.018416594713926315,
0.05827561020851135,
-0.05516491085290909,
-0.014805657789111137,
0.003109951736405492,
-0.019865335896611214,
-0.02433265931904316,
-0.04024285823106766,
0.05062161386013031,
-0.020757237449288368,
-0.006889397278428078,
-0.06887971609830856,
0.023395352065563202,
-0.021209439262747765,
0.026422716677188873,
-0.02848568558692932,
-0.02681821957230568,
-0.05018121004104614,
0.015895484015345573,
-0.00239715282805264,
0.016148392111063004,
0.06039484590291977,
0.07326111197471619,
-0.1109127476811409,
-0.009271635673940182,
-0.02032630704343319,
0.020335987210273743,
0.00030054981471039355,
0.04439888894557953,
-0.019895248115062714,
-0.03312363848090172,
0.008294341154396534,
0.04640534520149231,
-0.02009056694805622,
0.014019116759300232,
-0.0029870253056287766,
0.03946950286626816,
-0.05403025820851326,
-0.018440287560224533,
0.030505595728754997,
0.00520695373415947,
0.03413144871592522,
0.010331922210752964,
0.03982175141572952,
0.009861503727734089,
-0.02936265803873539,
-0.014778642915189266,
-0.021172817796468735,
0.004993529058992863,
0.023164698854088783,
-0.031002474948763847,
-0.06627709418535233,
0.008294221013784409,
0.001701931469142437,
-0.027205049991607666,
-0.05973602831363678,
-0.06452728807926178,
0.03989788517355919,
0.027000727131962776,
0.026680901646614075,
0.05625910311937332,
0.020479366183280945,
0.035053323954343796,
0.001085517113097012,
-0.020702477544546127,
-0.011472994461655617,
-0.0016183903208002448,
-0.0010279768612235785,
0.00012815854279324412,
0.05921437591314316,
0.014184718020260334,
-0.012467805296182632,
-0.07404286414384842,
-0.03940694034099579,
0.015606432221829891,
0.04247744753956795,
-0.013156533241271973,
0.023003285750746727,
0.07520629465579987,
-0.052123043686151505,
0.017031824216246605,
-0.028713246807456017,
0.016427988186478615,
0.03146742284297943,
-0.09467381983995438,
-0.01757201924920082,
0.046038173139095306,
0.005881209392100573,
0.01627039909362793,
-0.058158859610557556,
0.01854788139462471,
0.0448167659342289,
0.034647487103939056,
0.05441229045391083,
-0.002587131457403302,
0.017175206914544106,
0.013069532811641693,
0.0066292001865804195,
0.034174006432294846,
-0.039677366614341736,
0.014733442105352879,
0.01653420925140381,
-0.018763704225420952,
-0.0006094682030379772,
0.04456157609820366,
0.018547840416431427,
-0.020170915871858597,
-0.009132315404713154,
-0.026865879073739052,
-0.039043210446834564,
-0.0048019071109592915,
0.048256684094667435,
-0.03777622804045677,
0.013530612923204899,
-0.018067022785544395,
0.008312920108437538,
-0.0031605183612555265,
-0.004494013264775276,
0.04935053363442421,
-0.007277636788785458,
0.011593685485422611,
-0.04536040872335434,
0.00016849557869136333,
-0.013523445464670658,
0.0063309739343822,
0.005137531086802483,
-0.009619741700589657,
-0.05256706103682518,
0.02197837270796299,
0.015696074813604355,
-0.03226274996995926,
-0.023512188345193863,
0.02156369760632515,
-0.028589440509676933,
0.03538727015256882,
-0.015408161096274853,
0.021792946383357048,
-0.019679991528391838,
-0.02805335633456707,
-0.015535714104771614,
-0.051427651196718216,
0.03596891090273857,
-0.030901573598384857,
0.1087147668004036,
0.018661975860595703,
-0.001992087345570326,
-0.003389576682820916,
0.08836861699819565,
-0.029275402426719666,
0.06334513425827026,
0.05206828564405441,
-0.007340567652136087,
-0.05419604107737541,
-0.011918696574866772,
-0.022238563746213913,
0.005035593640059233,
0.021537167951464653,
-0.027968745678663254,
-0.04051379859447479,
0.020550651475787163,
0.06622717529535294,
-0.008501609787344933,
0.02101910300552845,
-0.016449516639113426,
-0.01933818869292736,
-0.026959603652358055,
0.05374513193964958,
-0.04529108479619026,
0.05375185236334801,
0.030624359846115112,
-0.014586545526981354,
-0.059993285685777664,
0.036828044801950455,
-0.0785217136144638,
-0.02977551706135273,
-0.03434125706553459,
0.01622609794139862,
0.006289598066359758,
-0.013911382295191288,
-0.03632976859807968,
-0.04171106219291687,
-0.03718484565615654,
0.03181726485490799,
-0.05125052481889725,
-0.03703103959560394,
-0.023521939292550087,
0.016530418768525124,
-0.009482267312705517,
-0.0011684364872053266,
0.015595084987580776,
-0.03812447935342789,
-0.008266853168606758,
0.02380884252488613,
-0.02212640643119812,
0.0004095971817150712,
-0.022717662155628204,
-0.032606154680252075,
0.059594325721263885,
0.015191557817161083,
-0.04924425482749939,
0.02860623225569725,
0.020412471145391464,
-0.03011949546635151,
-0.05063055083155632,
0.005322680342942476,
0.0612008236348629,
0.0809003934264183,
-0.01000300794839859,
0.0016304643359035254,
0.014356089755892754,
-0.07019467651844025,
0.06680499017238617,
0.11446373909711838,
0.012902711518108845,
0.05884392932057381,
0.023385249078273773,
-0.08024075627326965,
0.025678861886262894,
-0.04252982884645462,
0.02302626520395279,
-0.028576528653502464,
-0.0009440347785130143,
0.04369945824146271,
-0.021586397662758827,
-0.017713097855448723,
-0.0029750370886176825
] |
<p>I realize I'm trying to get a simple answer on a complicated subject, but here goes anyway. I've done some research and I understand (well, mostly) about how Vc is the amount of energy required to get two nucleons past the electric repulsive force so the strong force can take over. I know about the Maxwell-Boltzmann distribution, quantum tunneling, and the Gamow peak.</p>
<p>But all that is about how the Coulomb barrier is overcome by ambient temperatures in stars. The texts always go from how Vc is calculated, to how hot a star would have to be to overcome it, and how they aren't actually that hot, and why quantum tunneling comes to the rescue, yada yada, yada.</p>
<p>I want a more concrete understanding of what Vc really represents. If I had two protons and was using my patented Nucleon Energizer 3000, does Vc represent the amount of energy I'd have to set the MeV dial to so that I could force the two protons together past the Coulomb barrier and get them to fuse? And how much would my electric bill be afterwards?</p> | g1279 | [
0.020134354010224342,
0.056207168847322464,
0.004247147589921951,
0.025203542783856392,
0.03476117551326752,
0.022644856944680214,
-0.005590192507952452,
0.07723887264728546,
-0.008379815146327019,
0.01105586253106594,
-0.041440192610025406,
0.02263774909079075,
-0.05513413995504379,
-0.028165753930807114,
0.06438063830137253,
0.009886686690151691,
-0.014723937027156353,
-0.04643947631120682,
0.04046380892395973,
0.0019070100970566273,
-0.04364160820841789,
0.022306928411126137,
-0.04427516087889671,
-0.05000382289290428,
0.004750764928758144,
-0.045372266322374344,
0.023133371025323868,
-0.012625012546777725,
-0.05934811756014824,
-0.02385282702744007,
0.030492596328258514,
0.004701528698205948,
0.07077252119779587,
-0.0518534854054451,
-0.07379048317670822,
0.01013584341853857,
0.004169601947069168,
-0.04774009808897972,
0.01625422202050686,
-0.04303187504410744,
0.057261038571596146,
0.0383598618209362,
0.07164224237203598,
-0.06009885296225548,
-0.038058724254369736,
0.03776170313358307,
-0.014560731127858162,
-0.06800086051225662,
-0.022595958784222603,
0.007002422586083412,
0.007747600320726633,
0.015003921464085579,
0.04192175716161728,
0.06940752267837524,
0.003767960937693715,
-0.015523874200880527,
0.023593073710799217,
-0.03130704164505005,
0.07769117504358292,
0.04099493846297264,
0.0693792924284935,
0.020257743075489998,
0.015158005058765411,
-0.025684397667646408,
0.11618757992982864,
-0.010830347426235676,
-0.017659006640315056,
0.0399569496512413,
0.034304603934288025,
0.01035655103623867,
-0.06155756488442421,
-0.04802499711513519,
-0.01671595871448517,
-0.014351450838148594,
0.023533977568149567,
-0.012457575649023056,
-0.005208889022469521,
-0.026532551273703575,
0.03842359036207199,
0.013290253467857838,
-0.033700037747621536,
-0.00650949077680707,
0.004269500728696585,
0.016126930713653564,
0.1152787134051323,
-0.03710928186774254,
-0.048718780279159546,
0.024549098685383797,
-0.06533737480640411,
-0.00663888081908226,
-0.0416235476732254,
0.03435378894209862,
0.06282225251197815,
-0.05910433083772659,
0.033719077706336975,
-0.03830796480178833,
0.0024893234949558973,
0.029454652220010757,
0.008546655997633934,
0.07485306262969971,
-0.05347801744937897,
-0.05700104311108589,
0.06524787843227386,
-0.02357264794409275,
-0.03589312732219696,
-0.011297370307147503,
0.005723425652831793,
-0.001363907242193818,
0.034812599420547485,
0.031459078192710876,
-0.07817040383815765,
-0.03583256155252457,
0.02301173284649849,
0.01797712966799736,
-0.007340574637055397,
0.0235571451485157,
0.04222358018159866,
-0.032942384481430054,
0.004792046267539263,
0.019291521981358528,
-0.00008329291449626908,
0.07696504145860672,
-0.05362492427229881,
0.008441509678959846,
-0.026656487956643105,
0.017182113602757454,
-0.01933685503900051,
-0.020913369953632355,
0.005384765565395355,
0.008874253369867802,
0.061024922877550125,
-0.013812548480927944,
-0.0084761967882514,
-0.007640082389116287,
-0.003309758845716715,
-0.007990725338459015,
-0.010265035554766655,
-0.021346108987927437,
-0.0010297491680830717,
0.025101354345679283,
0.03364703059196472,
-0.029760433360934258,
-0.000814869359601289,
-0.029760297387838364,
-0.05410708114504814,
-0.0044470299035310745,
-0.061019375920295715,
-0.012357203289866447,
-0.028861261904239655,
-0.050269391387701035,
0.03248944133520126,
0.05319700762629509,
0.03996306285262108,
-0.06937859952449799,
0.010482467710971832,
-0.03170907497406006,
0.046066321432590485,
-0.005711656529456377,
-0.00709114596247673,
0.033457908779382706,
0.07003965973854065,
0.0002853639889508486,
0.021988147869706154,
-0.01569492556154728,
-0.04194726049900055,
-0.006953462492674589,
0.029390545561909676,
-0.06260741502046585,
0.004340900108218193,
0.013545792549848557,
-0.015647079795598984,
-0.010792204178869724,
0.023820891976356506,
0.04921199753880501,
-0.023320922628045082,
0.01190008781850338,
0.03049890324473381,
-0.0329543761909008,
-0.00277262763120234,
0.0668240338563919,
0.005980437155812979,
0.005714989732950926,
0.0357283353805542,
-0.001044486416503787,
-0.041146520525217056,
-0.03847764804959297,
-0.029607513919472694,
-0.020024504512548447,
0.013583741150796413,
0.07366330176591873,
0.007615700364112854,
-0.022967444732785225,
0.04115821421146393,
-0.014296075329184532,
-0.025890083983540535,
-0.00938277505338192,
0.014625119976699352,
-0.032947853207588196,
-0.036990199238061905,
-0.008304638788104057,
-0.06663795560598373,
0.04333660006523132,
0.024436170235276222,
0.019768545404076576,
0.08351730555295944,
0.09716933965682983,
0.010249939747154713,
0.015386666171252728,
0.012859835289418697,
0.005173463840037584,
-0.0029110321775078773,
0.044947072863578796,
0.002980677643790841,
0.021900726482272148,
-0.03620303049683571,
-0.009329823777079582,
-0.0014878412475809455,
0.00476189935579896,
-0.06621827930212021,
-0.01441935170441866,
-0.04825340956449509,
-0.03813951089978218,
0.09193790704011917,
-0.021821336820721626,
-0.048732560127973557,
0.0376131571829319,
-0.040774695575237274,
-0.026100430637598038,
0.01567794941365719,
-0.0024440952111035585,
-0.0727141797542572,
0.027427515015006065,
-0.0515979640185833,
-0.02441147156059742,
-0.006353297270834446,
0.06741305440664291,
0.02090209349989891,
0.047729503363370895,
0.004080386832356453,
-0.007632325869053602,
0.04517699033021927,
-0.08603917062282562,
-0.03864121437072754,
0.032591238617897034,
-0.00030344666447490454,
0.005103849805891514,
-0.000802181544713676,
-0.03448842838406563,
-0.04150103032588959,
-0.024046286940574646,
0.0298797395080328,
-0.028949463739991188,
-0.09626051038503647,
0.005587191320955753,
-0.05203646048903465,
0.009631453081965446,
-0.04287778213620186,
-0.004313117358833551,
-0.08703116327524185,
0.00793537963181734,
0.04675981029868126,
-0.048107028007507324,
-0.029207762330770493,
0.04430468752980232,
-0.017124570906162262,
0.011401628144085407,
-0.021274620667099953,
0.031096162274479866,
0.027775166556239128,
-0.026163509115576744,
0.015150446444749832,
0.07599838823080063,
-0.0015951485838741064,
-0.06255794316530228,
-0.0003107232041656971,
-0.04545595124363899,
0.020092865452170372,
-0.05257859826087952,
0.05394147336483002,
-0.0554010234773159,
-0.029684890061616898,
-0.01333174854516983,
-0.049424123018980026,
-0.008597106672823429,
-0.03275779262185097,
-0.06307743489742279,
-0.018380099907517433,
0.0008543091244064271,
0.04463627189397812,
-0.008632771670818329,
0.015624267980456352,
0.004564756061881781,
-0.0035445934627205133,
0.006135588511824608,
0.007687442936003208,
-0.010406426154077053,
0.05977068096399307,
0.01923506148159504,
-0.019773520529270172,
0.024391889572143555,
0.01179339736700058,
-0.03274248540401459,
0.024382062256336212,
-0.031215470284223557,
-0.008951760828495026,
-0.015559579245746136,
-0.03136373311281204,
0.010904117487370968,
0.011984666809439659,
-0.07312102615833282,
-0.006730580236762762,
0.02723020128905773,
0.039274975657463074,
0.05858983099460602,
-0.041854627430438995,
-0.02019386924803257,
0.014865554869174957,
0.008054899051785469,
0.013644402846693993,
0.05286896973848343,
-0.032711125910282135,
0.009978458285331726,
0.06050613522529602,
-0.0013542555971071124,
0.049168530851602554,
-0.0031200586818158627,
0.009240059182047844,
-0.012629372999072075,
0.06759552657604218,
-0.018222132697701454,
0.0228019580245018,
0.015507862903177738,
-0.012789110653102398,
-0.009129148907959461,
-0.048444025218486786,
-0.012957848608493805,
-0.026865456253290176,
0.024685127660632133,
0.023487890139222145,
0.027972089126706123,
-0.00013474782463163137,
-0.023605430498719215,
-0.06701929867267609,
0.0231422558426857,
0.03044840320944786,
0.025102393701672554,
-0.005011525470763445,
0.03434999659657478,
0.01356067880988121,
-0.06877506524324417,
0.050476375967264175,
-0.0012806125450879335,
-0.025888318195939064,
0.018860377371311188,
-0.0441463366150856,
-0.016583263874053955,
-0.03306695446372032,
0.02992469258606434,
-0.04223015159368515,
0.0425068736076355,
0.042645517736673355,
0.018208185210824013,
0.01248694397509098,
0.010444707237184048,
-0.04542693868279457,
-0.04031100869178772,
-0.007772005628794432,
0.02306053228676319,
-0.04687041416764259,
0.0152205815538764,
-0.03620705381035805,
0.008800356648862362,
-0.08342527598142624,
0.023464597761631012,
0.038835518062114716,
-0.011658350005745888,
0.0016686038579791784,
0.006256038788706064,
-0.039553578943014145,
0.05241420120000839,
-0.015438447706401348,
0.010356336832046509,
0.0511685274541378,
0.04542417451739311,
0.04666472598910332,
-0.029498282819986343,
-0.07791446149349213,
0.005907286889851093,
0.0028499464970082045,
-0.026914387941360474,
-0.032038599252700806,
0.01515838410705328,
-0.022722607478499413,
0.03934954106807709,
0.014053305611014366,
-0.07065669447183609,
0.03337465971708298,
-0.015366718173027039,
0.023764032870531082,
0.012438622303307056,
0.00809746328741312,
-0.0003275762719567865,
-0.004293730482459068,
-0.04322066158056259,
-0.0058782342821359634,
0.003356503089889884,
0.033327098935842514,
-0.05268137902021408,
-0.04797316715121269,
0.019285421818494797,
-0.0026744080241769552,
0.013358747586607933,
0.0008492050692439079,
-0.05813686177134514,
-0.009419671259820461,
-0.019810330122709274,
-0.0027812044136226177,
-0.010449378751218319,
0.02245025709271431,
0.001812021597288549,
0.009348348714411259,
0.0075286696664988995,
0.044578470289707184,
-0.02566078118979931,
0.03592618927359581,
0.07619249820709229,
0.03771552816033363,
0.006750470958650112,
-0.0023087547160685062,
-0.038438986986875534,
0.05934087559580803,
0.00767474714666605,
-0.020229937508702278,
0.0037125188391655684,
-0.008666044101119041,
0.10283878445625305,
-0.05069615691900253,
0.0022970689460635185,
-0.0329185426235199,
0.08668414503335953,
0.11499428004026413,
-0.003446773858740926,
-0.015412911772727966,
0.03309379518032074,
-0.00011098282266175374,
-0.004121941048651934,
0.005619066767394543,
-0.048697106540203094,
0.009072594344615936,
-0.06688158959150314,
-0.03822670876979828,
0.03024682216346264,
-0.045148275792598724,
0.0031295602675527334,
0.008742956444621086,
-0.0035120840184390545,
-0.015361526980996132,
-0.014914543367922306,
-0.002320785541087389,
0.0023171722423285246,
-0.06959329545497894,
0.03794850409030914,
0.025539111346006393,
-0.01169318426400423,
0.06233234703540802,
-0.012805961072444916,
-0.01628297008574009,
-0.008015737868845463,
-0.020589960739016533,
0.04021017625927925,
-0.011203484609723091,
-0.035198431462049484,
-0.009614315815269947,
0.015086118131875992,
0.07351316511631012,
-0.001184219028800726,
0.043099820613861084,
0.011355821043252945,
0.04381897673010826,
-0.06048183888196945,
0.02084222249686718,
0.069435253739357,
-0.021610965952277184,
0.053196825087070465,
-0.03649266064167023,
0.01785912737250328,
-0.00048438276280649006,
0.052035585045814514,
0.022669898346066475,
0.012813153676688671,
0.0043752845376729965,
0.0664464682340622,
0.04730690270662308,
0.011498740874230862,
0.009980220347642899,
0.0103202685713768,
0.02836480736732483,
0.0176899041980505,
0.017381517216563225,
0.05350420996546745,
0.0028065505903214216,
-0.00814423430711031,
-0.0013773615937680006,
0.0014639250002801418,
0.02749951370060444,
-0.029208017513155937,
0.010668295435607433,
-0.017179962247610092,
0.014671633020043373,
-0.0033826574217528105,
-0.004525052383542061,
-0.030351363122463226,
0.002330128801986575,
0.05735395476222038,
-0.0026317150332033634,
0.011220965534448624,
-0.02972455509006977,
-0.020048368722200394,
0.002546468749642372,
-0.016206270083785057,
0.0028414581902325153,
-0.009816480800509453,
-0.01046093087643385,
0.012402714230120182,
-0.07252803444862366,
0.01883169822394848,
-0.05043518915772438,
0.006483335979282856,
0.017647478729486465,
0.028879983350634575,
0.013350853696465492,
-0.02336214669048786,
-0.00220032618381083,
0.02689938433468342,
-0.059216007590293884,
0.048478949815034866,
0.021747037768363953,
-0.008303319104015827,
0.02678772248327732,
-0.006619848310947418,
0.016547448933124542,
0.006889373064041138,
0.019645804539322853,
0.09233000874519348,
0.012883545830845833,
0.006640156265348196,
-0.0035290515515953302,
0.02019510045647621,
0.059566572308540344,
-0.02819686383008957,
-0.01877512037754059,
-0.07146504521369934,
-0.007971721701323986,
-0.014776348136365414,
0.018795398995280266,
0.02068345434963703,
0.027039533481001854,
-0.04685711860656738,
-0.004648146685212851,
-0.00018361055117566139,
-0.0676136165857315,
-0.025774624198675156,
0.025447411462664604,
0.05401523411273956,
0.057364046573638916,
-0.055077869445085526,
0.010415744967758656,
-0.0009739401866681874,
0.04119154065847397,
0.011831958778202534,
0.029544545337557793,
0.004600699990987778,
0.02742117829620838,
-0.03765743225812912,
0.029493771493434906,
0.0014652216341346502,
-0.05110914632678032,
-0.014702684246003628,
-0.046108752489089966,
0.001405823160894215,
0.025065477937459946,
0.010445422492921352,
0.010376046411693096,
-0.008409062400460243,
0.03994650021195412,
0.024732556194067,
-0.006646415218710899,
-0.03643512725830078,
0.008307784795761108,
-0.01456405222415924,
0.041798487305641174,
-0.008906344883143902,
-0.03341466933488846,
-0.030656596645712852,
-0.054816681891679764,
0.011932730674743652,
0.0039911395870149136,
-0.032342579215765,
-0.021577177569270134,
0.035686664283275604,
0.03865297883749008,
0.01863490603864193,
-0.02297806926071644,
-0.009272558614611626,
0.07061964273452759,
-0.001886438112705946,
-0.043924130499362946,
0.008076505735516548,
0.01283850334584713,
-0.004921560641378164,
-0.03327547386288643,
-0.07129425555467606,
0.021684568375349045,
-0.08275425434112549,
0.011246542446315289,
0.02498917281627655,
-0.016359368339180946,
0.013214459642767906,
0.05301513522863388,
0.04104801267385483,
-0.02085115760564804,
-0.03106331080198288,
0.0811280757188797,
0.004382308106869459,
0.06617441773414612,
0.02083195000886917,
0.013536776416003704,
0.03307804837822914,
0.07597929239273071,
0.0009882744634523988,
-0.01747450977563858,
-0.018451301380991936,
0.012609112076461315,
0.019015386700630188,
-0.0009386745514348149,
0.0068060182966291904,
0.014938689768314362,
-0.006015614606440067,
0.010067502968013287,
0.041715316474437714,
-0.019730612635612488,
-0.0016777128912508488,
0.027843989431858063,
0.010940219275653362,
-0.024350810796022415,
-0.026393091306090355,
0.006256969645619392,
-0.0284632109105587,
-0.03801844269037247,
-0.003178412327542901,
-0.019319869577884674,
-0.03884328529238701,
0.015964865684509277,
0.02287747897207737,
-0.0658579021692276,
0.015013109892606735,
-0.0344754122197628,
-0.0013788585783913732,
-0.04336098954081535,
0.003962877206504345,
0.007779746316373348,
-0.022243458777666092,
-0.046986158937215805,
0.044244322925806046,
0.06078464165329933,
0.04617810621857643,
-0.011225973255932331,
-0.0351918488740921,
0.03328491374850273,
-0.09302814304828644,
-0.004562728106975555,
-0.053360190242528915,
-0.09042274206876755,
-0.04048227146267891,
0.0012480763252824545,
-0.07896944880485535,
-0.03553592041134834,
0.03286091610789299,
-0.02459104359149933,
-0.06516450643539429,
0.0004057488404214382,
0.01499820314347744,
0.022921988740563393,
-0.0071065351366996765,
0.0026208434719592333,
-0.0199776291847229,
-0.03816133365035057,
-0.010144615545868874,
0.0023594277445226908,
0.026110218837857246,
-0.01175256073474884,
-0.05716836452484131,
0.022041145712137222,
0.02643892727792263,
-0.012790670618414879,
0.04240129515528679,
0.05186113715171814,
0.0462581142783165,
0.0683383047580719,
-0.007474874146282673,
0.05772251635789871,
0.00686561968177557,
0.029797151684761047,
-0.006651849951595068,
0.02739918977022171,
0.04530121758580208,
0.007450544275343418,
0.022708768025040627,
-0.026361435651779175,
-0.0018606114899739623,
0.010289400815963745,
0.019942060112953186,
0.04208676144480705,
-0.017072319984436035,
0.032692860811948776,
0.004083168692886829,
-0.0695078894495964,
0.012576693668961525,
0.010405829176306725,
0.060584913939237595,
-0.03714851662516594,
-0.015090098604559898,
0.01622181013226509,
-0.03265947848558426,
0.04390447586774826,
-0.03831149637699127,
-0.010554430074989796,
-0.03423028811812401,
-0.013582626357674599,
0.010095752775669098,
0.03761839121580124,
-0.03381285071372986,
0.012157576158642769,
-0.03379266709089279,
-0.026245513930916786,
-0.027811557054519653,
0.028724495321512222,
0.021001683548092842,
-0.04162581264972687,
-0.005204151850193739,
-0.041175831109285355,
-0.005955559201538563,
-0.002188881626352668,
-0.02483515627682209,
-0.08750960230827332,
-0.04927684739232063,
-0.052483659237623215,
0.024354463443160057,
0.08990459889173508,
0.013243062421679497,
0.038137298077344894,
-0.006182704586535692,
-0.05956597626209259,
0.007941877469420433,
0.07211638242006302,
-0.06429115682840347,
-0.0802125483751297,
0.01040846947580576,
-0.028973335400223732,
0.019135378301143646,
-0.0330735482275486,
0.00942246988415718,
-0.003194265766069293,
-0.02886117249727249,
0.013743899762630463,
-0.0296742282807827,
-0.033646803349256516,
-0.05528649687767029
] |
<p>There is a very fundamental flaw in the common explanation given of the space-time curvature due to massive objects. It is said that a massive object curves space time just like a bowling ball on a rubber sheet, and another object near the massive object simply rolls down-hill on the rubber sheet, that is the reason why we observe that the other object is experiencing gravitational attraction to the massive object which curved the space-time. </p>
<p>The flaw is this:</p>
<p>Even if the massive object did bend the spacetime downwards, and there was a second object in the vicinity, this second object just would not roll down-hill automatically, unless there was a SECOND EXTERNAL source gravity, other than these two objects pulling everything downwards. In other words, even if the space time is curved, there is no particular reason for the second object to move closer to or be attracted by the first, because there is no other external force that would force it to move down-hill.</p>
<p>As a visualization, consider the bowling ball on a rubber sheet and another object on the same rubber sheet in outer space where there is no other source of gravity. Now, neither will the bowling ball curve the rubber sheet downwards (because it is not being pulled downwards), nor will the other object move down-hill on the rubber sheet even if the rubber sheet was depressed downwards, because there is no downward gravitational force from earth or another external source which would cause either of these two effects. So, there would be no reason for the other object to be attracted towards the first object. This is inconsistent with observation because objects do really experience gravitational attraction towards each other. But it certainly can't be explained by the bowlig ball and rubber sheet example.
What is the explanation for all this?</p>
<p>Flaw 2:
If there are 2 massive objects on the rubber sheet, they will both bend spacetime around themselves, and they will both remain trapped in their own depressions, and would never move towards or be attracted to each other. This is again contrary to observation. Since both masses are in reality attracted to each other, so they can't possibly bend spacetime and can't be trapped in their own depressions. Why?</p>
<p>Flaw 3: All pictures of bent spacetime on the web show spacetime being bent downwards. Why? In open space, with no other object nearby, all directions are equivalent to all other directions, and "downward" is undefined. So if spacetime is really bent, in which direction is it really bent?</p> | g13 | [
0.031001979485154152,
0.03816928341984749,
0.015152733772993088,
-0.005422474816441536,
0.02580857090651989,
0.08188959956169128,
0.044604863971471786,
0.006620059721171856,
-0.035089947283267975,
-0.010769038461148739,
0.04124290868639946,
0.002692852634936571,
0.05102187395095825,
-0.0030405395664274693,
-0.006235284730792046,
0.003361340379342437,
0.025619979947805405,
-0.048120856285095215,
-0.024299083277583122,
0.006261200178414583,
-0.005938849411904812,
0.0010219928808510303,
0.01736144907772541,
-0.04459648206830025,
-0.06378819048404694,
0.028961844742298126,
0.03177279978990555,
-0.02573154680430889,
-0.028773780912160873,
-0.011863059364259243,
0.09193684160709381,
-0.01772449165582657,
0.001105253817513585,
-0.022332709282636642,
-0.0018342549446970224,
-0.02264220453798771,
-0.048465389758348465,
-0.04544619098305702,
-0.015729665756225586,
0.04174705967307091,
-0.0025517959147691727,
0.00311911478638649,
0.003257409669458866,
0.002189566846936941,
0.0011222042376175523,
-0.038824569433927536,
-0.017687683925032616,
0.04846283420920372,
0.05456387996673584,
-0.05216078832745552,
0.027196209877729416,
0.030840661376714706,
0.02431071549654007,
-0.04209248721599579,
-0.04511471092700958,
-0.012081483379006386,
0.005050580482929945,
0.04889127239584923,
0.0759560614824295,
0.0350271500647068,
-0.004460528492927551,
0.01084742322564125,
0.008323917165398598,
0.027414198964834213,
0.04510395973920822,
0.023190099745988846,
-0.05094118043780327,
-0.06574109941720963,
0.05691823363304138,
0.011806231923401356,
0.030118467286229134,
0.012579592876136303,
0.005864471662789583,
-0.021907774731516838,
-0.07430773973464966,
0.05274198576807976,
-0.021006973460316658,
-0.0030349097214639187,
0.004108469467610121,
0.007816927507519722,
0.01860910840332508,
0.02885250747203827,
-0.011694828048348427,
0.03891804814338684,
0.05984639376401901,
-0.05725190415978432,
-0.0457649864256382,
-0.020146673545241356,
-0.06401994824409485,
0.013891353271901608,
0.020027849823236465,
-0.017383333295583725,
0.022634560242295265,
0.03582362085580826,
-0.0514812096953392,
-0.04300690069794655,
-0.04652197286486626,
0.10916795581579208,
-0.02499224990606308,
0.04839355871081352,
-0.00707526970654726,
-0.007176707498729229,
-0.005729959346354008,
0.04785095527768135,
0.01817644014954567,
0.03708299249410629,
0.012500707060098648,
0.05853089317679405,
-0.030089231207966805,
-0.07284288108348846,
-0.006922966334968805,
-0.026721447706222534,
-0.0054346597753465176,
-0.07571853697299957,
0.011946635320782661,
-0.023169664666056633,
0.05773366242647171,
-0.01845967024564743,
0.014576698653399944,
0.0657772570848465,
-0.027796832844614983,
-0.0041205701418221,
-0.021884746849536896,
0.06465192139148712,
0.01640056073665619,
-0.032566241919994354,
0.029215596616268158,
0.01019709650427103,
0.009405347518622875,
-0.049068085849285126,
-0.03746737167239189,
0.018903836607933044,
0.009555633179843426,
-0.01431874930858612,
-0.054981112480163574,
0.017800262197852135,
-0.012023496441543102,
-0.002727783052250743,
-0.031949203461408615,
-0.012062336318194866,
0.023727329447865486,
0.004851904232054949,
0.004211151506751776,
-0.04091361165046692,
-0.03015138767659664,
0.04597075656056404,
-0.0186516884714365,
0.032435305416584015,
0.05851306393742561,
0.010549153201282024,
-0.012670929543673992,
0.07446352392435074,
-0.04299848899245262,
-0.04569731280207634,
-0.011255436576902866,
0.00019079152843914926,
0.004381246864795685,
-0.01558166928589344,
0.016821758821606636,
0.029420142993330956,
0.035903338342905045,
-0.014102610759437084,
-0.04515906795859337,
-0.002437868621200323,
0.009210350923240185,
0.05395061522722244,
-0.010208061896264553,
-0.027363736182451248,
-0.06216459348797798,
-0.051143620163202286,
-0.11687779426574707,
-0.031635843217372894,
0.040444307029247284,
0.0032254040706902742,
-0.0027421102859079838,
0.02621723711490631,
0.02450951188802719,
-0.0473143607378006,
-0.025438692420721054,
0.025531351566314697,
0.007848929613828659,
-0.03123815730214119,
-0.03484300523996353,
0.020412292331457138,
0.03910908102989197,
-0.051634062081575394,
-0.04768688604235649,
0.00879818294197321,
-0.03854913264513016,
0.018939798697829247,
0.005004896316677332,
-0.02383524738252163,
-0.021816544234752655,
0.02174104005098343,
-0.012679873034358025,
-0.024762380868196487,
0.04207751527428627,
0.009445944800972939,
0.006814870517700911,
0.04060431942343712,
-0.03149989992380142,
-0.05005599185824394,
0.04296255111694336,
-0.018495166674256325,
-0.010754446499049664,
0.012652994133532047,
0.004493002314120531,
0.0419916994869709,
-0.004237957298755646,
-0.056804388761520386,
0.07621676474809647,
-0.026336194947361946,
0.0424882173538208,
-0.04506559297442436,
-0.04884720221161842,
0.023905491456389427,
-0.021253664046525955,
-0.0113248685374856,
-0.020567120984196663,
0.04192391037940979,
0.07336337864398956,
0.011940340511500835,
0.06735822558403015,
-0.034645676612854004,
0.04421151801943779,
0.0034092182759195566,
-0.06729254126548767,
-0.07220787554979324,
-0.012315976433455944,
-0.035567380487918854,
-0.04296347498893738,
0.023143839091062546,
0.002771024825051427,
0.05187932401895523,
0.036616165190935135,
-0.009561719372868538,
0.02599613182246685,
0.0452275276184082,
-0.00323657039552927,
0.011477639898657799,
0.025532688945531845,
-0.04388865455985069,
-0.029201176017522812,
-0.03586224094033241,
0.022215668112039566,
-0.028927017003297806,
-0.002936961827799678,
-0.0038095288909971714,
0.06090936064720154,
0.09009659290313721,
0.01689811609685421,
0.001868263352662325,
-0.05006284639239311,
0.01791810430586338,
0.05679481104016304,
-0.03795496001839638,
-0.008692333474755287,
0.016159866005182266,
-0.06369391083717346,
-0.054050933569669724,
0.010429724119603634,
-0.03274385258555412,
0.06601763516664505,
0.019240235909819603,
-0.10217102617025375,
-0.03899640217423439,
-0.0014904241543263197,
-0.0082861902192235,
0.0010961525840684772,
-0.023594504222273827,
-0.07055506110191345,
0.0686594769358635,
-0.02143065631389618,
0.030777374282479286,
-0.0053346422500908375,
0.06480827927589417,
-0.07607894390821457,
0.029281271621584892,
0.01009291410446167,
-0.004161900375038385,
0.008177317678928375,
0.03351470082998276,
-0.057962287217378616,
-0.011732474900782108,
0.04056323319673538,
-0.015412538312375546,
-0.09630442410707474,
-0.003094174200668931,
0.02225804328918457,
0.027598394080996513,
-0.01894507370889187,
0.08465796709060669,
0.026036055758595467,
-0.05158626660704613,
0.005144568160176277,
0.05705560743808746,
-0.028310323134064674,
0.052835091948509216,
-0.026464669033885002,
-0.04842076078057289,
-0.01907576620578766,
0.02815856784582138,
0.047273073345422745,
0.005003662779927254,
-0.012001654133200645,
0.01295766606926918,
0.008489998057484627,
-0.04479065537452698,
-0.014009823091328144,
-0.04046958312392235,
0.029366686940193176,
0.020508183166384697,
-0.03502475470304489,
0.01666230335831642,
0.029970336705446243,
0.0106888422742486,
-0.021977117285132408,
0.0404387004673481,
0.0019228418823331594,
0.07496640831232071,
-0.016286572441458702,
0.027760013937950134,
-0.010592475533485413,
-0.01596085913479328,
-0.010462449863553047,
0.00322145689278841,
-0.0640045553445816,
-0.04771032556891441,
0.012000981718301773,
0.010439099743962288,
-0.023596899583935738,
-0.056219860911369324,
0.019763506948947906,
-0.017004666849970818,
-0.026650765910744667,
-0.0062351287342607975,
0.013068584725260735,
-0.03421911597251892,
0.03001919947564602,
-0.0034127861727029085,
-0.03953063488006592,
0.0011382169323042035,
-0.07346794009208679,
-0.013884038664400578,
0.0277157761156559,
0.05908466875553131,
-0.022009948268532753,
-0.0014935021754354239,
0.016129782423377037,
0.017974011600017548,
0.03632458671927452,
-0.04020729288458824,
0.029069548472762108,
-0.03120715171098709,
-0.018397323787212372,
-0.029912058264017105,
-0.03141207993030548,
-0.03504834324121475,
-0.009364329278469086,
-0.03804536536335945,
-0.028492961078882217,
0.04882015287876129,
-0.027948632836341858,
-0.005828135646879673,
0.046129148453474045,
0.011777092702686787,
-0.021848348900675774,
-0.02691265195608139,
0.006070639472454786,
-0.0005212625837884843,
0.026886826381087303,
0.030234262347221375,
-0.028037678450345993,
-0.022644655779004097,
0.14327946305274963,
-0.01514634769409895,
0.046667005866765976,
0.021028582006692886,
-0.02201433666050434,
0.021295655518770218,
0.10056520998477936,
0.04554755240678787,
0.016858762130141258,
0.07116787135601044,
0.010698928497731686,
0.031395625323057175,
-0.07011250406503677,
-0.034359224140644073,
0.005884453654289246,
-0.007846809923648834,
0.01757262460887432,
-0.013245206326246262,
0.014411838725209236,
-0.024704720824956894,
-0.011581387370824814,
-0.01979266107082367,
0.034606605768203735,
0.020538555458188057,
0.04165060445666313,
-0.0394580103456974,
-0.04530645161867142,
0.051887258887290955,
-0.027558378875255585,
-0.013977349735796452,
-0.012678287923336029,
-0.007408148143440485,
0.02886248752474785,
0.007785262539982796,
-0.05150638893246651,
-0.021167965605854988,
0.019731929525732994,
0.0446331724524498,
-0.02326321415603161,
-0.028410958126187325,
0.01969909481704235,
-0.013564277440309525,
-0.010198930278420448,
0.06228499114513397,
0.05003160238265991,
-0.03315437585115433,
0.009928754530847073,
0.060744933784008026,
-0.056802187114953995,
-0.053142841905355453,
0.015782935544848442,
0.10531933605670929,
-0.023673105984926224,
0.014362944290041924,
-0.02600843831896782,
-0.00872061774134636,
0.03219005465507507,
0.027545113116502762,
0.007379878778010607,
0.0319041907787323,
-0.014249383471906185,
0.04137282073497772,
0.03573555871844292,
0.09079282730817795,
-0.0013399891322478652,
-0.010316251777112484,
0.0796586349606514,
-0.026359891518950462,
0.0007983054383657873,
0.03356877341866493,
0.021771235391497612,
0.056815288960933685,
-0.06755280494689941,
-0.031136194244027138,
-0.029236184433102608,
-0.0017669866792857647,
0.001993975369259715,
-0.04176131635904312,
-0.020027805119752884,
0.08460423350334167,
-0.030861804261803627,
-0.00973351951688528,
0.044789038598537445,
0.03952668607234955,
-0.04027567803859711,
-0.0019910805858671665,
-0.04160989448428154,
-0.010245129466056824,
-0.02527572028338909,
0.057760242372751236,
-0.04881466180086136,
-0.018223144114017487,
-0.022898932918906212,
-0.029804062098264694,
-0.01065542921423912,
0.02336750365793705,
-0.0596751905977726,
0.06134291738271713,
0.00877375341951847,
0.04870634898543358,
0.028971193358302116,
0.02780737727880478,
-0.04353398084640503,
0.005828384310007095,
-0.0025971580762416124,
-0.09279756247997284,
-0.0559394545853138,
-0.008991618640720844,
0.05827518180012703,
-0.04360313341021538,
-0.019299346953630447,
0.013778925873339176,
-0.0010706281755119562,
0.03364837169647217,
0.017636144533753395,
0.01667151413857937,
0.05640041083097458,
-0.03232407197356224,
-0.019300643354654312,
-0.0032456619665026665,
-0.00677976431325078,
0.026309983804821968,
0.0027516670525074005,
0.03206859529018402,
0.02079802192747593,
-0.02690599299967289,
-0.042174920439720154,
0.06143368408083916,
0.008295617066323757,
0.003135930048301816,
-0.0035391307901591063,
0.021906835958361626,
0.015759669244289398,
-0.033979035913944244,
-0.04574437811970711,
0.04476684331893921,
-0.01563793607056141,
0.013933427631855011,
-0.012354117818176746,
-0.00685327360406518,
0.005790193099528551,
0.018395666033029556,
0.053419776260852814,
-0.015406797640025616,
0.00363998138345778,
-0.03328004479408264,
-0.007631464395672083,
0.0029486326966434717,
0.013328964821994305,
-0.028644639998674393,
0.011027016676962376,
0.05775910243391991,
-0.010903894901275635,
0.002039220416918397,
0.011464600451290607,
0.008964733220636845,
0.011204078793525696,
-0.04267754405736923,
0.04660124331712723,
-0.014977071434259415,
-0.016405928879976273,
0.00016492449503857642,
0.0456177219748497,
-0.020985940471291542,
0.04371416196227074,
-0.03159203752875328,
0.016502171754837036,
-0.033934641629457474,
0.03302447870373726,
-0.022035688161849976,
-0.023644063621759415,
-0.0011082475539296865,
-0.013234054669737816,
-0.018244361504912376,
0.06444467604160309,
-0.025134483352303505,
-0.014900662936270237,
0.06636402010917664,
-0.0010430776746943593,
0.04485125467181206,
-0.02252999134361744,
0.0026271119713783264,
0.014372002333402634,
-0.06620224565267563,
-0.03602788224816322,
-0.020801657810807228,
-0.005497596226632595,
-0.035219062119722366,
-0.019345108419656754,
-0.005657201632857323,
0.009171920828521252,
0.026126109063625336,
-0.006801477167755365,
0.014709850773215294,
0.05333152040839195,
-0.014213302172720432,
-0.04408375918865204,
0.01045951060950756,
0.07500047981739044,
0.030338823795318604,
-0.02589770406484604,
0.0009281776146963239,
-0.012459036894142628,
-0.03262920305132866,
-0.02741496078670025,
-0.000879905535839498,
0.021000217646360397,
-0.06101619452238083,
0.03488258272409439,
-0.046286050230264664,
-0.03415392339229584,
-0.0013657236704602838,
-0.07543138414621353,
-0.027790747582912445,
0.05715532973408699,
-0.043009646236896515,
-0.038991063833236694,
-0.0021567721851170063,
0.031110620126128197,
-0.05112958699464798,
-0.06173074617981911,
-0.03260815143585205,
-0.0033573810942471027,
0.030054550617933273,
-0.11857607960700989,
-0.005276849493384361,
-0.05340348556637764,
0.005086863879114389,
0.04446651041507721,
0.00010660133557394147,
0.020388081669807434,
-0.01654595136642456,
-0.01582927629351616,
-0.01491382997483015,
0.0192551352083683,
-0.014116447418928146,
-0.03816116228699684,
0.05356379970908165,
0.006993734743446112,
0.012855349108576775,
0.015682129189372063,
-0.025765756145119667,
0.017738763242959976,
0.01666172780096531,
-0.0004950646543875337,
-0.09100500494241714,
0.047190383076667786,
0.006992738228291273,
0.02133823186159134,
0.01202812884002924,
-0.0021823139395564795,
-0.06123776361346245,
-0.059013742953538895,
0.011394641362130642,
0.017476938664913177,
0.0009593559079803526,
-0.06042978912591934,
-0.00227687181904912,
-0.008789494633674622,
0.005355805158615112,
0.017242690548300743,
0.024702340364456177,
0.006406345404684544,
0.05856890231370926,
0.029783323407173157,
0.008302942849695683,
0.011679554358124733,
0.0051798513159155846,
0.009843147359788418,
0.03318097069859505,
-0.0507674477994442,
0.01637645810842514,
0.0251003485172987,
-0.015453428030014038,
-0.01961599849164486,
-0.03451137617230415,
-0.003354827407747507,
-0.008164571598172188,
-0.00864685233682394,
0.03798527270555496,
-0.051635682582855225,
-0.0048165046609938145,
-0.02168269082903862,
-0.0297388918697834,
0.049295905977487564,
-0.044971954077482224,
-0.04645397886633873,
-0.003326411359012127,
0.006516339257359505,
0.021054774522781372,
-0.05557079613208771,
0.03710821270942688,
0.03639184683561325,
-0.02435952052474022,
-0.04366901144385338,
0.011268049478530884,
0.03686228021979332,
-0.03645354509353638,
0.005414380691945553,
0.0001316371199209243,
-0.0071381693705916405,
-0.025078795850276947,
0.017619451507925987,
-0.02989661693572998,
0.011351024731993675,
0.008680553175508976,
0.014816978015005589,
0.004201049450784922,
0.04905097931623459,
0.038866691291332245,
-0.051990557461977005,
-0.002679037395864725,
-0.00577196478843689,
0.009595160372555256,
-0.046908486634492874,
0.05863400921225548,
-0.024117611348628998,
0.050593893975019455,
-0.033768244087696075,
-0.01900256797671318,
0.00824606791138649,
0.009350518696010113,
-0.015095775946974754,
0.02674591913819313,
0.007670676801353693,
0.0065717631950974464,
-0.014039089903235435,
-0.016454188153147697,
0.004171227570623159,
-0.04223280027508736,
0.04876942187547684,
0.053730521351099014,
-0.037096306681632996,
-0.010815816931426525,
-0.01737765036523342,
0.018122496083378792,
0.031523142009973526,
0.04753895476460457,
-0.03832226246595383,
-0.031097067520022392,
0.02754703164100647,
0.005851242691278458,
-0.0571834072470665,
0.013366230763494968,
-0.00625800434499979,
-0.03573361039161682,
-0.025630617514252663,
-0.003418954322114587,
0.010762130841612816,
-0.11610076576471329,
0.02505793608725071,
0.009219648316502571,
0.06472697108983994,
-0.05482713133096695,
-0.031217196956276894,
-0.028632869943976402,
-0.007270372938364744,
0.0053449226543307304,
0.009817181155085564,
0.037244684994220734,
-0.025830257683992386,
0.03273208066821098,
-0.027172043919563293,
0.005587895400822163,
-0.037074338644742966,
-0.04983369633555412,
0.017763344570994377,
-0.003046266734600067,
-0.018670832738280296,
0.005398365203291178,
-0.023679645732045174,
0.015274644829332829,
0.013587038964033127,
0.029998674988746643,
0.01579313725233078,
0.010748413391411304,
0.08654859662055969,
-0.012383555062115192,
-0.04492394998669624,
0.03304353356361389,
0.1018640547990799,
-0.014128985814750195,
-0.03703294321894646,
0.015386567451059818,
0.007172857411205769,
-0.010754236951470375,
-0.0047721583396196365,
0.03318401798605919,
0.010432901792228222,
-0.013566557317972183,
0.00034989049891009927,
-0.028176646679639816,
-0.04823242872953415,
0.10982366651296616
] |
<p>When I was young I read one book in which is written that you get more tan on the morning than on evening even light angle from Sun to Earth is the same. Don't remember exact reason, I think because ultraviolet is more absorbed on the evening because air is more humid or something like this. Is it true?</p> | g1280 | [
0.03024202585220337,
-0.03392645716667175,
-0.00019976527255494148,
0.02078300341963768,
0.027383429929614067,
0.10321947932243347,
0.015648990869522095,
-0.018315238878130913,
0.030016416683793068,
-0.017806079238653183,
0.04144057631492615,
-0.04222160950303078,
0.04292771965265274,
0.06094572693109512,
0.02689358778297901,
-0.0007958863861858845,
0.03690548986196518,
-0.02222767286002636,
0.027464810758829117,
-0.02610531821846962,
-0.02656194195151329,
-0.03635160252451897,
0.01238946057856083,
-0.04436865448951721,
-0.05865531787276268,
-0.009264439344406128,
-0.06126956269145012,
0.005701916757971048,
-0.029305385425686836,
-0.025073131546378136,
0.049645714461803436,
-0.015418385155498981,
-0.00652598962187767,
0.015036453492939472,
-0.002974811242893338,
-0.0569087415933609,
0.008633582852780819,
-0.02041582576930523,
0.014075282029807568,
-0.010676375590264797,
0.052726950496435165,
0.03821827843785286,
0.007094876375049353,
0.06829261779785156,
-0.02751500904560089,
-0.027461322024464607,
-0.046097587794065475,
0.01958061195909977,
-0.024613622575998306,
-0.038413990288972855,
-0.050110865384340286,
-0.036481741815805435,
-0.011662067845463753,
-0.003489632159471512,
0.029016083106398582,
0.0013702334836125374,
0.02230738289654255,
-0.055642060935497284,
0.006043503526598215,
0.12031319737434387,
0.042634278535842896,
-0.03498542681336403,
-0.007860777899622917,
-0.0033302796073257923,
0.037051424384117126,
0.0006930508534424007,
0.07624927163124084,
0.02256796322762966,
0.006976035889238119,
0.02600238472223282,
-0.020628318190574646,
0.002986335661262274,
-0.08715521544218063,
-0.0683874785900116,
0.04575050622224808,
-0.009821371175348759,
0.026671241968870163,
-0.034594934433698654,
0.01062126737087965,
0.09590171277523041,
-0.007879520766437054,
0.01870381087064743,
0.015396947972476482,
0.035542700439691544,
-0.0017800875939428806,
-0.08739282935857773,
0.04350094869732857,
-0.002417680574581027,
0.020759746432304382,
0.0201935525983572,
0.09628530591726303,
0.011907591484487057,
0.08730057626962662,
0.02176639437675476,
-0.054359305649995804,
-0.016520410776138306,
0.03882579505443573,
0.05847501754760742,
-0.02671520970761776,
-0.038834474980831146,
-0.06425107270479202,
-0.01801157370209694,
0.06119287759065628,
0.034966014325618744,
0.033516380935907364,
-0.003204894019290805,
0.003939888905733824,
-0.024577395990490913,
-0.09630201011896133,
0.035876087844371796,
-0.018746117129921913,
-0.04533865302801132,
-0.10379296541213989,
-0.022767607122659683,
-0.004993729759007692,
0.017800239846110344,
0.0241086483001709,
-0.028264079242944717,
0.04838695377111435,
-0.02176571451127529,
0.03211206942796707,
0.0627533495426178,
-0.052030131220817566,
0.0069352309219539165,
0.056057628244161606,
0.0026750201359391212,
-0.02447717823088169,
-0.025217097252607346,
-0.017654363065958023,
-0.0019152241293340921,
0.04686160385608673,
0.026011796668171883,
-0.030866002663969994,
0.008363811299204826,
-0.03828933835029602,
0.0019325533648952842,
0.01204646285623312,
0.007382748648524284,
-0.0008824678952805698,
0.021081332117319107,
0.04655016213655472,
0.02957748994231224,
0.00992963183671236,
-0.06074237450957298,
-0.07622421532869339,
0.0427781380712986,
-0.007134591694921255,
-0.059633493423461914,
0.040515441447496414,
0.04224097728729248,
-0.003078853478655219,
0.0012839279370382428,
-0.004684950225055218,
-0.022353334352374077,
-0.03697408363223076,
-0.07134295254945755,
-0.028305524960160255,
-0.004408337641507387,
0.041893936693668365,
-0.013628348708152771,
0.008543008007109165,
-0.014022725634276867,
0.03357119858264923,
-0.021422535181045532,
-0.055132102221250534,
-0.04284479841589928,
-0.06255301833152771,
-0.055812858045101166,
-0.09045946598052979,
0.005469688214361668,
-0.035172268748283386,
0.07858945429325104,
-0.021766260266304016,
-0.023731211200356483,
0.014772556722164154,
0.0410296805202961,
0.06768935918807983,
-0.03845462203025818,
0.026867138221859932,
0.055531758815050125,
0.009073379449546337,
0.016544805839657784,
-0.042876262217760086,
-0.09943387657403946,
0.03098350577056408,
-0.0294023584574461,
-0.018842032179236412,
-0.0727171078324318,
-0.05935356765985489,
-0.00890168733894825,
0.017122287303209305,
-0.03277142718434334,
0.04693341255187988,
0.020747840404510498,
-0.009508996270596981,
0.008564289659261703,
-0.040264640003442764,
0.03689876198768616,
-0.050879500806331635,
0.0932627022266388,
-0.013282074593007565,
0.06772784143686295,
0.026704346761107445,
0.020622091367840767,
0.012000047601759434,
0.06538519263267517,
-0.018063029274344444,
0.012643854133784771,
0.08413513004779816,
-0.05758243054151535,
-0.016323385760188103,
0.030890433117747307,
0.032871127128601074,
0.03320955112576485,
-0.010088086128234863,
0.04222629964351654,
-0.015272688120603561,
0.06584393233060837,
0.03605381026864052,
-0.0440143458545208,
0.026721540838479996,
-0.019173482432961464,
0.032961856573820114,
0.033751364797353745,
-0.012548483908176422,
0.02202354557812214,
-0.009559870697557926,
-0.02899950183928013,
0.07471327483654022,
0.02959095500409603,
-0.040298838168382645,
-0.028777923434972763,
0.008905062451958656,
0.010669839568436146,
0.013956563547253609,
-0.005753024481236935,
0.03783641755580902,
0.0005986932083033025,
0.007400615606456995,
-0.04862937703728676,
0.04408919811248779,
-0.008332635276019573,
-0.0300906989723444,
0.02084973454475403,
0.015047072432935238,
-0.0037205214612185955,
-0.05464125797152519,
-0.014756434597074986,
0.013894718140363693,
0.013666316866874695,
0.00903825368732214,
0.03328361734747887,
0.0045755174942314625,
-0.05702701210975647,
0.007788336835801601,
-0.016032997518777847,
-0.042788904160261154,
-0.01530993077903986,
-0.025774741545319557,
-0.0746665820479393,
-0.05107215791940689,
-0.036377739161252975,
0.011682124808430672,
-0.023307060822844505,
0.020340150222182274,
0.057443052530288696,
-0.033645063638687134,
0.01881824992597103,
0.016673244535923004,
-0.03973843902349472,
0.05004596337676048,
0.07740402221679688,
0.012822266668081284,
0.01451827585697174,
-0.00875118374824524,
0.017082054167985916,
-0.05003710463643074,
-0.0061452132649719715,
-0.0002992158697452396,
-0.04227203503251076,
0.008172836154699326,
0.015579817816615105,
-0.007944147102534771,
0.013911168090999126,
0.07484219968318939,
-0.004361686762422323,
0.004586373455822468,
0.02528219483792782,
-0.018104111775755882,
-0.03846956416964531,
0.0024785269051790237,
0.025531355291604996,
0.056201137602329254,
0.028070541098713875,
-0.011599700897932053,
-0.019473686814308167,
0.08138835430145264,
-0.03948677331209183,
-0.045739784836769104,
-0.01491594035178423,
-0.004130146466195583,
-0.012175099924206734,
0.01961657777428627,
0.02004583366215229,
0.038627319037914276,
0.019633891060948372,
-0.04796163737773895,
-0.06118258461356163,
0.0376523993909359,
-0.03869163617491722,
-0.04593648761510849,
-0.005273055750876665,
-0.03235942870378494,
0.08160069584846497,
-0.027831299230456352,
0.02283148281276226,
0.011259464547038078,
-0.024758920073509216,
0.036500509828329086,
0.0011995150707662106,
-0.0759531557559967,
0.0006052203825674951,
0.013292870484292507,
-0.003947891760617495,
0.007878894917666912,
-0.04274579510092735,
-0.007013277616351843,
0.06510646641254425,
0.03383266553282738,
-0.01178363710641861,
0.008217314258217812,
0.039603158831596375,
-0.06975454092025757,
-0.002839831169694662,
-0.0708790197968483,
0.04125552251935005,
-0.04840918257832527,
0.04373323172330856,
-0.03364849090576172,
-0.01489456370472908,
-0.044951342046260834,
-0.023572169244289398,
-0.06305133551359177,
-0.0503675676882267,
-0.019957158714532852,
0.014333178289234638,
-0.00822546985000372,
-0.008331026881933212,
-0.02288484014570713,
0.04328208416700363,
0.08497978001832962,
0.021689489483833313,
-0.0012347946176305413,
0.007989551872015,
-0.02838323824107647,
-0.016209565103054047,
-0.02790858782827854,
0.0778270959854126,
-0.009827620349824429,
-0.031040146946907043,
0.017899930477142334,
0.010277379304170609,
0.023575251922011375,
-0.04028204828500748,
-0.0001577528746565804,
-0.007487336173653603,
0.007678634487092495,
0.07069090753793716,
0.019279196858406067,
0.04709634929895401,
-0.0032007417175918818,
0.04378601163625717,
-0.0041202460415661335,
0.04999595135450363,
0.01808059588074684,
-0.0067696645855903625,
0.04313128814101219,
0.02702665701508522,
0.02768642269074917,
0.062297310680150986,
0.03235511854290962,
0.018248559907078743,
-0.023148002102971077,
0.018311413004994392,
0.009397619403898716,
-0.0021384793799370527,
-0.04871954023838043,
-0.040117841213941574,
-0.020324384793639183,
-0.07322443276643753,
0.018080582842230797,
0.012964478693902493,
-0.02119230292737484,
0.0027598384767770767,
0.045648474246263504,
-0.049658577889204025,
0.010888229124248028,
0.029921427369117737,
-0.019536003470420837,
0.009659580886363983,
0.07747785747051239,
0.024314608424901962,
0.019247883930802345,
0.023914804682135582,
-0.06572123616933823,
0.03182142972946167,
0.009401364251971245,
0.007846993394196033,
0.009341846220195293,
-0.025801388546824455,
0.01563410274684429,
-0.02420293539762497,
0.0016904771327972412,
-0.04223252832889557,
0.012207482010126114,
0.08773986995220184,
-0.005432081874459982,
-0.02321779914200306,
-0.011104288510978222,
0.016421258449554443,
-0.04856331646442413,
0.04050371050834656,
-0.027490908280014992,
0.0006548181991092861,
0.02604520134627819,
0.03385017067193985,
0.04012231156229973,
-0.043788518756628036,
-0.022346781566739082,
-0.05682465434074402,
0.0016317383851855993,
-0.011568651534616947,
0.0026919441297650337,
0.025394299998879433,
-0.03128104284405708,
0.015198072418570518,
0.05810645967721939,
-0.003888386767357588,
0.05418151244521141,
-0.011440316215157509,
0.019445355981588364,
0.013066860847175121,
-0.014466406777501106,
-0.012330695055425167,
0.02019393816590309,
0.04167478159070015,
-0.009243429638445377,
0.010847038589417934,
-0.003938054200261831,
0.016593091189861298,
-0.05259712412953377,
0.04643166810274124,
0.002029693452641368,
-0.024538109079003334,
-0.02808043546974659,
-0.010582211427390575,
-0.061046041548252106,
-0.014169864356517792,
-0.02673284150660038,
0.006061844527721405,
-0.026529813185334206,
-0.008079222403466702,
0.053526971489191055,
0.0013473413418978453,
0.010319937020540237,
-0.07975878566503525,
-0.03194276988506317,
0.06957212090492249,
-0.024724885821342468,
0.02782302349805832,
-0.0331118106842041,
-0.012002356350421906,
0.02086016535758972,
0.03471692278981209,
0.05747728794813156,
0.027266569435596466,
0.01030473131686449,
-0.01428559236228466,
0.04505590349435806,
-0.05931735783815384,
-0.013566109351813793,
0.058153193444013596,
0.01996232569217682,
0.07588664442300797,
-0.06594296544790268,
0.029895110055804253,
-0.019148588180541992,
0.004693051800131798,
0.02085302211344242,
-0.011738760396838188,
0.028041591867804527,
-0.03091883845627308,
0.03065764345228672,
-0.03234226629137993,
-0.044783640652894974,
-0.013436097651720047,
0.015607470646500587,
-0.027192160487174988,
-0.0024350627791136503,
0.011125622317194939,
-0.02960623800754547,
0.07003026455640793,
-0.011398152448236942,
-0.09234488010406494,
0.06568906456232071,
-0.03769858181476593,
-0.0030967211350798607,
-0.028130806982517242,
0.020662488415837288,
0.0729023814201355,
0.007430342957377434,
-0.04725705459713936,
-0.012873947620391846,
0.013232518918812275,
0.04626178368926048,
-0.022583194077014923,
-0.01851787604391575,
0.0350283719599247,
0.051799073815345764,
-0.021106289699673653,
0.04362514987587929,
-0.008696656674146652,
-0.002840290777385235,
0.033982593566179276,
0.02727028913795948,
0.010645588859915733,
-0.011751750484108925,
0.0198069978505373,
-0.02115972526371479,
-0.05461668595671654,
0.007928603328764439,
0.0733821839094162,
0.013183495961129665,
-0.010320181027054787,
0.06543726474046707,
-0.0020754374563694,
-0.023056698963046074,
0.06839917600154877,
-0.020385541021823883,
0.013271010480821133,
-0.042178183794021606,
-0.04592765122652054,
0.011347148567438126,
0.03462035581469536,
0.05572795867919922,
0.010730640962719917,
-0.028410226106643677,
0.005485265050083399,
0.03959016129374504,
0.04276561364531517,
0.06775722652673721,
0.02998998947441578,
-0.02835068665444851,
-0.025877855718135834,
-0.04651174321770668,
0.0027382755652070045,
0.001045326585881412,
0.03391510993242264,
0.05511516332626343,
-0.02586066722869873,
0.039208002388477325,
0.01758803054690361,
0.01635332778096199,
-0.01970209926366806,
-0.010256458073854446,
-0.03438759595155716,
-0.0043372721411287785,
-0.016263477504253387,
-0.010194217786192894,
0.04676034674048424,
0.045708540827035904,
-0.03819835186004639,
0.03257707878947258,
-0.011608900502324104,
-0.03172498196363449,
-0.04160911962389946,
-0.0004139467782806605,
-0.04797496274113655,
-0.028469465672969818,
-0.03033358044922352,
0.03058016300201416,
-0.05717315524816513,
-0.03853243589401245,
-0.02124413661658764,
-0.03613212704658508,
-0.01487347949296236,
-0.020585115998983383,
0.035828106105327606,
0.016577409580349922,
0.026424529030919075,
-0.011020532809197903,
0.02939971350133419,
-0.03521495312452316,
0.036749813705682755,
-0.028234561905264854,
-0.015089305117726326,
-0.010232344269752502,
0.04923875257372856,
0.002162450458854437,
-0.07457362115383148,
-0.007259466219693422,
-0.01922585815191269,
0.07222991436719894,
-0.0470794141292572,
0.05348356440663338,
0.032294340431690216,
-0.013808002695441246,
-0.014510600827634335,
0.055755309760570526,
-0.00743997422978282,
-0.040256693959236145,
-0.007522808387875557,
-0.030524801462888718,
-0.006169862113893032,
-0.014503886923193932,
-0.022098705172538757,
-0.04657494276762009,
0.010494545102119446,
0.029310820624232292,
-0.02872634492814541,
0.056763600558042526,
0.006873759441077709,
0.04500996321439743,
-0.005895063281059265,
0.008449261076748371,
0.061889514327049255,
-0.04662028327584267,
-0.03326984867453575,
0.004664150066673756,
0.002958892146125436,
-0.002616529818624258,
-0.03455943986773491,
-0.009699526242911816,
0.06934287399053574,
0.029962759464979172,
-0.0029753728304058313,
0.011694845743477345,
0.005382793489843607,
-0.02730819582939148,
0.034572847187519073,
-0.04407072812318802,
-0.01042283046990633,
-0.014639927074313164,
-0.0052996608428657055,
0.033203352242708206,
-0.021266307681798935,
-0.011979715898633003,
-0.0972764790058136,
-0.0037920610047876835,
0.0037864057812839746,
0.06113607436418533,
0.0018855712842196226,
0.012614818289875984,
-0.013454325497150421,
0.04444009065628052,
-0.01348060555756092,
-0.043539632111787796,
0.003491293406113982,
0.027820555493235588,
-0.041407570242881775,
-0.017432022839784622,
-0.021289559081196785,
-0.019174849614501,
0.07045984268188477,
-0.002180858049541712,
0.019893603399395943,
0.0071747866459190845,
-0.03469207137823105,
-0.03526243939995766,
-0.020476114004850388,
-0.019725682213902473,
0.0056147025898098946,
0.00555356964468956,
-0.010098741389811039,
-0.018745984882116318,
-0.008786804974079132,
-0.03705257177352905,
-0.026427077129483223,
0.001734175137244165,
0.04038263484835625,
0.024984372779726982,
0.009643062949180603,
0.019080830737948418,
0.025494879111647606,
0.0014728803653270006,
-0.060141418129205704,
-0.06991597265005112,
0.01937754824757576,
0.023481547832489014,
-0.046204905956983566,
-0.03799156844615936,
-0.009583362378180027,
-0.0381462499499321,
-0.00012225382670294493,
0.0016206583241000772,
-0.025116967037320137,
0.010112806223332882,
0.0013492442667484283,
-0.03540902957320213,
-0.06317733973264694,
0.007117904257029295,
-0.03876108303666115,
0.041468165814876556,
-0.055470872670412064,
0.027608228847384453,
-0.01074995193630457,
-0.011678687296807766,
0.048377957195043564,
0.0029841880314052105,
0.030966535210609436,
0.05253206193447113,
-0.019434038549661636,
0.03931074216961861,
0.02977941557765007,
0.025485055521130562,
0.0004071106668561697,
-0.0574607327580452,
-0.011929023079574108,
-0.04699484631419182,
0.015297927893698215,
-0.03481312841176987,
-0.058440983295440674,
0.010482817888259888,
-0.022613251581788063,
-0.0369865857064724,
-0.0348956473171711,
0.01866573467850685,
-0.013639599084854126,
0.07989471405744553,
-0.008188599720597267,
0.02119515836238861,
-0.016857590526342392,
-0.004144743084907532,
-0.07102391123771667,
0.03756995126605034,
0.025618981570005417,
-0.025559529662132263,
0.027463331818580627,
-0.02188192494213581,
-0.03004227951169014,
-0.007921271957457066,
-0.00810990296304226,
-0.015565561130642891,
-0.012494266964495182,
-0.029809946194291115,
-0.007942496798932552,
-0.008014105260372162,
0.043853890150785446,
-0.0046136765740811825,
-0.034039322286844254,
-0.01824340410530567,
0.00737391971051693,
-0.0010598174994811416,
0.002829787088558078,
-0.01651935651898384,
0.016596471890807152,
0.01792874187231064,
-0.03315227851271629,
0.014321474358439445,
-0.05389099195599556,
-0.039280906319618225,
-0.02491604909300804,
0.013464589603245258,
-0.03942568227648735,
0.022609423846006393,
-0.022170821204781532,
-0.013354578986763954,
-0.026145722717046738
] |
<p>Condensed matter physicists have shown using quantum information that in many condensed matter systems, entanglement entropy only scales as the area of the boundary, and not the volume. This is the basis for the density matrix renormalization group and Projected Entangled Pair States (PEPS). Does this also explain the holographic principle in quantum gravity?</p> | g1281 | [
0.009725147858262062,
0.06574232876300812,
-0.004195299930870533,
-0.027467451989650726,
-0.02839621715247631,
0.0431440994143486,
-0.03288450464606285,
0.02641078270971775,
-0.03450771048665047,
-0.013514958322048187,
0.0635724887251854,
-0.07132276892662048,
-0.027101658284664154,
-0.03871294483542442,
-0.008657120168209076,
0.0669339969754219,
0.05877569690346718,
0.0069641051813960075,
0.007189666852355003,
-0.00039196625584736466,
-0.06048629432916641,
-0.052340731024742126,
0.0193497147411108,
-0.07507286220788956,
-0.008781294338405132,
0.018926886841654778,
0.03467857837677002,
-0.06168294697999954,
-0.023518092930316925,
0.02027834579348564,
0.0007926564430817962,
-0.002065771259367466,
-0.020415885373950005,
-0.0916842371225357,
-0.04749472439289093,
-0.045350998640060425,
0.02283155731856823,
0.008670519106090069,
0.027873041108250618,
-0.03171448037028313,
-0.04332420602440834,
-0.040910571813583374,
-0.022480836138129234,
-0.0409708172082901,
-0.03862054646015167,
0.019020766019821167,
0.03308109566569328,
-0.0002715286682359874,
0.015901900827884674,
0.0030333069153130054,
0.019855232909321785,
0.10997318476438522,
0.02777218632400036,
0.030639471486210823,
0.02728099562227726,
0.1348755657672882,
0.016197187826037407,
0.029321996495127678,
0.08356595784425735,
-0.03659811243414879,
0.022361746057868004,
0.034618835896253586,
-0.00426380755379796,
0.03821929171681404,
0.0915491133928299,
-0.03788810223340988,
-0.052474457770586014,
-0.028143618255853653,
0.0023363640066236258,
0.06295263022184372,
-0.009263725019991398,
-0.01954435184597969,
-0.005363821983337402,
-0.0016904841177165508,
-0.004670570604503155,
0.033056486397981644,
-0.01342125702649355,
0.030670570209622383,
0.019111916422843933,
-0.06258649379014969,
-0.030222108587622643,
-0.06754951179027557,
0.04624975472688675,
-0.08415008336305618,
0.06753694266080856,
-0.021235888823866844,
0.015521416440606117,
-0.0185827799141407,
-0.04263690114021301,
0.05746195837855339,
-0.04093996435403824,
-0.028541726991534233,
0.05768395587801933,
0.02100224420428276,
-0.004227565135806799,
-0.01672670990228653,
0.03424416854977608,
-0.017474234104156494,
0.0017390133580192924,
0.023661671206355095,
-0.04815887287259102,
0.029160967096686363,
0.03779112920165062,
0.04537331685423851,
-0.0361812561750412,
0.029301384463906288,
-0.0344049446284771,
-0.045642632991075516,
0.015002136118710041,
0.017699632793664932,
-0.0343986414372921,
-0.024299785494804382,
-0.0405564159154892,
0.02629966102540493,
0.002406804356724024,
-0.006905815564095974,
0.08247292786836624,
-0.037278417497873306,
-0.08148084580898285,
0.03491836413741112,
-0.05033290013670921,
0.020966311916708946,
0.0642666295170784,
0.027131808921694756,
0.015677915886044502,
0.09603320062160492,
0.0596717931330204,
-0.048634789884090424,
0.009559720754623413,
-0.04750742018222809,
0.08831886947154999,
-0.016466425731778145,
-0.08122825622558594,
-0.019530080258846283,
0.012168520130217075,
0.010610322467982769,
0.012919184751808643,
-0.027549661695957184,
0.06397874653339386,
0.009602738544344902,
-0.06933680921792984,
-0.026036450639367104,
-0.01983417198061943,
-0.056657034903764725,
0.037874091416597366,
-0.04694854095578194,
-0.019986582919955254,
-0.01741325482726097,
0.012962927110493183,
-0.027962684631347656,
0.026448532938957214,
0.040039051324129105,
0.018312888219952583,
-0.027665553614497185,
-0.018414393067359924,
0.04137406498193741,
0.06733676791191101,
0.03267580270767212,
0.03531394526362419,
-0.027338379994034767,
0.009928014129400253,
0.048958539962768555,
-0.0006665386608801782,
0.0006464651087298989,
-0.0005531485076062381,
-0.024527112022042274,
0.05277436226606369,
-0.06475470960140228,
0.01743793487548828,
-0.054957762360572815,
-0.06718706339597702,
0.005770265124738216,
-0.048471663147211075,
0.03907650336623192,
0.013165886513888836,
0.03906306251883507,
-0.013196039013564587,
0.011416755616664886,
0.028699535876512527,
0.010843170806765556,
0.02356695756316185,
0.025110440328717232,
0.024493809789419174,
0.010810771957039833,
-0.02445516362786293,
0.0348893441259861,
0.032247599214315414,
0.028744174167513847,
-0.0371701642870903,
-0.0007174533093348145,
-0.03717850148677826,
0.05260084196925163,
-0.06525194644927979,
-0.003855954622849822,
0.05463108792901039,
0.009847025386989117,
0.056361690163612366,
-0.0459919273853302,
-0.006263288203626871,
-0.026046808809041977,
-0.0651007890701294,
0.029643481597304344,
0.0016777730779722333,
-0.022325661033391953,
0.0018218177137896419,
0.042542219161987305,
-0.045768752694129944,
0.03633273392915726,
0.005037340801209211,
-0.013241669163107872,
-0.030890686437487602,
-0.02786470763385296,
0.009919446893036366,
0.021042870357632637,
0.021746020764112473,
0.008054063655436039,
-0.010830524377524853,
-0.02630668878555298,
-0.015014026314020157,
0.0676296278834343,
-0.0020177867263555527,
0.04445170983672142,
-0.00631022360175848,
0.04515395313501358,
-0.017980659380555153,
-0.0027829636819660664,
-0.04968249052762985,
-0.02054089494049549,
-0.0458042174577713,
0.00420650839805603,
-0.10018803924322128,
0.06715039908885956,
-0.007852990180253983,
0.015742408111691475,
-0.007369378115981817,
0.047903385013341904,
-0.001494957716204226,
0.04779698699712753,
0.011471187695860863,
0.021168986335396767,
0.024669073522090912,
-0.022742819041013718,
-0.03094015084207058,
0.04255087673664093,
0.03674938157200813,
0.010006059892475605,
0.025682950392365456,
-0.04433252289891243,
0.039174750447273254,
0.021196646615862846,
0.0465853288769722,
0.0034797731786966324,
-0.023389825597405434,
-0.02106252871453762,
0.006790162064135075,
0.013449854217469692,
0.0023171149659901857,
-0.028504393994808197,
-0.0018202244536951184,
-0.03804655745625496,
-0.02230175770819187,
0.030706405639648438,
0.004036580212414265,
-0.016871292144060135,
-0.040595151484012604,
0.017176127061247826,
0.005918996874243021,
0.03647975996136665,
0.016803763806819916,
0.07078557461500168,
0.07519220560789108,
0.07777631282806396,
0.012689650058746338,
0.006840487942099571,
-0.003328978316858411,
0.010037979111075401,
0.007497693412005901,
-0.017565855756402016,
-0.001344093238003552,
-0.011104179546236992,
-0.03250556439161301,
-0.046692319214344025,
-0.040324658155441284,
0.03296031057834625,
-0.017189713194966316,
-0.10267510265111923,
-0.006143517792224884,
-0.02521698735654354,
0.0562199130654335,
-0.0008610907825641334,
0.055795494467020035,
0.022942880168557167,
-0.023606514558196068,
0.030238639563322067,
-0.03286328166723251,
0.008451230823993683,
0.06818022578954697,
-0.04488007724285126,
-0.04091661795973778,
0.03553592413663864,
-0.02542596496641636,
-0.0641770139336586,
0.04725205898284912,
0.025856686756014824,
0.012791995890438557,
0.044028617441654205,
-0.03479309380054474,
0.0011209440417587757,
-0.014974363148212433,
-0.02281387522816658,
-0.03539220616221428,
0.0317574217915535,
-0.015155373141169548,
0.018939247354865074,
-0.018122736364603043,
-0.021907886490225792,
0.03677826374769211,
-0.025828255340456963,
-0.0012964120833203197,
-0.06290936470031738,
-0.0003004216414410621,
0.026615971699357033,
0.007484033703804016,
0.011856740340590477,
0.04182474687695503,
-0.02250475436449051,
-0.07269923388957977,
0.007977649569511414,
-0.017809128388762474,
0.0016063426155596972,
0.0006777371745556593,
-0.08910801261663437,
0.02557794563472271,
0.01758962869644165,
-0.06440110504627228,
-0.06133392080664635,
-0.042975615710020065,
-0.004083736799657345,
0.05128995701670647,
-0.004074490629136562,
0.011126128025352955,
-0.015819624066352844,
-0.004802672658115625,
0.03642405942082405,
0.007886807434260845,
0.05225903168320656,
-0.05372926592826843,
-0.0037062137853354216,
0.06196023151278496,
-0.018656639382243156,
0.0023318827152252197,
0.03881186246871948,
0.039222944527864456,
-0.02262805588543415,
0.008638194762170315,
0.02806619182229042,
0.021262219175696373,
-0.033861562609672546,
-0.0003263502148911357,
-0.028585901483893394,
-0.001817188924178481,
-0.02171798050403595,
-0.006023603491485119,
-0.024292660877108574,
-0.006381899584084749,
-0.03186364844441414,
-0.028506796807050705,
-0.011492514051496983,
-0.013548663817346096,
-0.004215981811285019,
0.016951128840446472,
-0.07056030631065369,
-0.0001320314040640369,
0.07267452776432037,
0.04269712418317795,
-0.007586184423416853,
-0.0009036799892783165,
-0.03036382794380188,
0.017898375168442726,
-0.058090388774871826,
0.0020969794131815434,
-0.017288167029619217,
0.031716495752334595,
-0.017549768090248108,
-0.012198301963508129,
-0.021838854998350143,
-0.05511912703514099,
-0.02731717936694622,
0.010739317163825035,
-0.013063671067357063,
-0.04360666498541832,
-0.025130806490778923,
-0.020119262859225273,
0.020698094740509987,
0.013434386812150478,
0.025617796927690506,
0.01377338171005249,
0.03952303156256676,
0.0022019711323082447,
0.007196338381618261,
-0.022402338683605194,
0.0024538461584597826,
-0.047083530575037,
0.03396173194050789,
0.01636068895459175,
-0.040185973048210144,
-0.002970326691865921,
0.009222284890711308,
-0.0727667436003685,
0.012604258954524994,
0.050241030752658844,
0.040701501071453094,
0.020668312907218933,
-0.006481560878455639,
0.011852460913360119,
-0.004016261547803879,
0.0003463196044322103,
-0.04059943929314613,
0.03335525840520859,
-0.008561250753700733,
-0.0005772141157649457,
0.08675407618284225,
-0.017398415133357048,
0.06085091829299927,
-0.0530719980597496,
0.06289876997470856,
0.011556832119822502,
0.01915285363793373,
-0.030327031388878822,
-0.07200295478105545,
0.04122961685061455,
-0.01670486479997635,
-0.044989265501499176,
0.04765855893492699,
-0.05458071827888489,
0.0317671038210392,
-0.03423858433961868,
-0.02690180018544197,
-0.020946364849805832,
-0.003911089617758989,
0.020562969148159027,
-0.00946194026619196,
-0.036153364926576614,
0.022851301357150078,
0.021557515487074852,
0.05034133791923523,
0.020203368738293648,
0.016840742900967598,
-0.034660328179597855,
0.0016482993960380554,
0.019048281013965607,
-0.017945220693945885,
-0.014838973060250282,
-0.040256317704916,
0.026685215532779694,
0.03254387155175209,
-0.032699521631002426,
0.04506906494498253,
0.024112747982144356,
0.014843500219285488,
-0.06763052195310593,
0.03715093061327934,
-0.019681205973029137,
0.043475814163684845,
-0.048598043620586395,
-0.05638398230075836,
-0.036985721439123154,
0.02058294229209423,
0.017099209129810333,
-0.012053542770445347,
0.01285757776349783,
0.0028516098391264677,
-0.01580769568681717,
0.029464002698659897,
0.04506097361445427,
0.00020763406064361334,
0.04453102871775627,
-0.006249530706554651,
0.01328895054757595,
-0.06922942399978638,
-0.0063237822614610195,
0.03370006009936333,
0.016781006008386612,
0.030557913705706596,
0.03120431676506996,
0.04327757656574249,
0.009528844617307186,
0.02759820595383644,
-0.04484349489212036,
0.004231440369039774,
0.016854820773005486,
-0.016481643542647362,
-0.0037030710373073816,
0.021366799250245094,
-0.04594093933701515,
-0.023833656683564186,
-0.024259839206933975,
0.004848410841077566,
-0.005289142020046711,
0.0021652360446751118,
0.021612485870718956,
0.023239413276314735,
0.01456035953015089,
-0.020824672654271126,
-0.011878715828061104,
-0.012397113256156445,
-0.00716210063546896,
-0.02350960113108158,
0.000876277219504118,
0.03992381691932678,
-0.0334169864654541,
-0.006495889741927385,
0.02654922567307949,
0.03236136958003044,
0.037510380148887634,
-0.08510389178991318,
-0.01559895183891058,
-0.003969570156186819,
-0.035716716200113297,
-0.0004161374527029693,
0.02068929560482502,
-0.020306864753365517,
-0.014770940877497196,
0.02811107411980629,
0.04819547384977341,
0.04597393423318863,
-0.024372920393943787,
0.002032459946349263,
0.023909060284495354,
0.058606330305337906,
0.014488205313682556,
0.015209007076919079,
0.02647564373910427,
0.0302154328674078,
0.01513636950403452,
-0.037786275148391724,
-0.011231731623411179,
0.04811403155326843,
0.031705647706985474,
-0.022443460300564766,
-0.00507325166836381,
-0.0007955991313792765,
-0.07081432640552521,
0.06499464064836502,
-0.007833417505025864,
0.024899771437048912,
-0.05885179713368416,
-0.05316394194960594,
0.01392489392310381,
-0.04668520390987396,
0.0064325351268053055,
-0.022350497543811798,
-0.033973418176174164,
0.009197128936648369,
-0.01479384582489729,
-0.017851706594228745,
-0.025864696130156517,
0.006612348835915327,
-0.006719238590449095,
0.08123410493135452,
0.06766919046640396,
0.042820315808057785,
0.01534013170748949,
-0.024737033993005753,
-0.015993338078260422,
-0.04453985393047333,
0.0051465327851474285,
0.009166669100522995,
-0.03973390907049179,
-0.009270579554140568,
-0.06393414735794067,
0.0320759043097496,
0.03757200390100479,
-0.000587817863561213,
-0.012854006141424179,
0.0022434769198298454,
-0.053478434681892395,
-0.052419111132621765,
-0.02989054098725319,
-0.040086571127176285,
-0.053384535014629364,
0.032621826976537704,
0.00840521976351738,
-0.03679683059453964,
-0.02894962951540947,
0.03216318413615227,
-0.02831452339887619,
-0.03910408914089203,
0.03527619317173958,
0.046591538935899734,
-0.015349830500781536,
0.01666869781911373,
-0.03288653865456581,
0.0211770199239254,
-0.05444522202014923,
-0.004343412816524506,
-0.01081835012882948,
0.03355703502893448,
-0.010693859308958054,
-0.017465639859437943,
0.03062925674021244,
0.0581701435148716,
-0.009352407418191433,
-0.028240444138646126,
-0.005071862135082483,
0.020038317888975143,
-0.029563218355178833,
-0.030987847596406937,
-0.016360346227884293,
0.014664863236248493,
0.019119227305054665,
-0.0015976028516888618,
0.023722589015960693,
0.032025113701820374,
0.0505758635699749,
-0.002896279562264681,
0.007861963473260403,
0.04447014629840851,
-0.02528749592602253,
0.034939952194690704,
0.055617738515138626,
0.03436325490474701,
0.02339138649404049,
-0.04754897207021713,
0.01678011752665043,
0.07292142510414124,
-0.002403647406026721,
0.005696240346878767,
0.011980541981756687,
0.04431890696287155,
0.028520766645669937,
0.012689548544585705,
0.054541151970624924,
0.05425654351711273,
-0.0634400025010109,
-0.02820727601647377,
-0.03903723135590553,
0.0006144324433989823,
0.04475802183151245,
-0.04244682937860489,
0.010258397087454796,
-0.02054600790143013,
0.07013783603906631,
0.014030154794454575,
-0.06915859133005142,
0.019488919526338577,
-0.021926455199718475,
-0.010348910465836525,
-0.05678967386484146,
0.012774777598679066,
0.03493007645010948,
-0.01060637179762125,
-0.008058344013988972,
0.04447798430919647,
-0.07561146467924118,
0.018446573987603188,
-0.020073670893907547,
-0.028276070952415466,
0.03194792568683624,
-0.07241218537092209,
-0.016704794019460678,
0.003936720080673695,
0.06850811094045639,
0.020515277981758118,
-0.0018317012581974268,
0.002524122130125761,
0.049538128077983856,
0.0365729033946991,
-0.00008643221372039989,
-0.03860963135957718,
0.021241897717118263,
-0.1157383993268013,
-0.0013822397449985147,
0.07971751689910889,
-0.027465762570500374,
-0.01155171450227499,
-0.022589778527617455,
0.016201915219426155,
-0.006528528872877359,
0.014286946505308151,
0.012619669549167156,
0.013725940138101578,
-0.009007575921714306,
0.03178851306438446,
0.014752198942005634,
0.038127899169921875,
0.017275769263505936,
0.011096077971160412,
-0.00874244887381792,
0.03690022975206375,
0.04335171356797218,
-0.05102655291557312,
0.016271211206912994,
-0.008617479354143143,
-0.006848610937595367,
0.031152542680501938,
0.05452750623226166,
0.04632412642240524,
-0.012022295035421848,
-0.02998582273721695,
0.009183190762996674,
-0.016952872276306152,
-0.03166114538908005,
-0.02108771912753582,
0.03962572664022446,
-0.05824916064739227,
0.052466168999671936,
-0.01826157420873642,
-0.030468231067061424,
-0.039237890392541885,
0.034300658851861954,
-0.0360385961830616,
0.03324993699789047,
-0.04098140075802803,
0.02198357693850994,
-0.038319047540426254,
-0.0587272010743618,
-0.06526052206754684,
0.01866922527551651,
-0.01610264554619789,
0.030658887699246407,
-0.005474080331623554,
-0.06732361018657684,
-0.020867254585027695,
-0.02069694921374321,
-0.00887059886008501,
0.016836196184158325,
-0.005217965226620436,
0.012670965865254402,
0.016445351764559746,
-0.05166735127568245,
-0.005281457677483559,
-0.011861964128911495,
-0.02674735151231289,
-0.048422671854496,
0.061678752303123474,
0.025685377418994904,
0.008266857825219631,
0.05101480334997177,
0.0033776811324059963,
-0.025126775726675987,
-0.0451340451836586,
0.0758669376373291,
-0.016101976856589317,
0.04327252134680748,
-0.08521810173988342,
-0.08340049535036087,
-0.0004174255591351539,
0.022264916449785233,
-0.023395687341690063,
0.0049367425963282585,
-0.05792686715722084,
-0.013182650320231915,
0.013481257483363152,
0.005138450302183628,
0.009359217248857021,
0.06093255802989006,
0.0022914339788258076,
0.026084892451763153,
-0.038611214607954025,
0.015198012813925743,
-0.04148044437170029,
0.01802520453929901,
-0.033668890595436096,
-0.028622031211853027,
0.006951755844056606,
-0.036664243787527084,
0.0242235716432333
] |
<p>I just thought of an interesting question.Is the sun actually moving?
I have learnt that the way the lunar landers and the space ships of the Mercury and Apallo missions moved and controlled their positions through the use of thrusters.NoW apply that same concept to the sun are the constant explosions on the surface of the sun enough to move it?</p> | g1282 | [
0.037759386003017426,
0.038243554532527924,
0.016529297456145287,
0.04788407310843468,
0.01626949943602085,
0.024751683697104454,
0.00921151414513588,
0.010804980993270874,
0.01041257195174694,
-0.035231854766607285,
0.0468888059258461,
-0.00878866109997034,
0.017152588814496994,
-0.024350615218281746,
0.024061208590865135,
-0.023147419095039368,
0.06681162118911743,
-0.01458966638892889,
0.003957962617278099,
0.06249980628490448,
0.04818052053451538,
-0.00773492781445384,
0.029773470014333725,
-0.012381413020193577,
-0.008642837405204773,
0.01727861911058426,
-0.0067525506019592285,
-0.04962005838751793,
0.008016603998839855,
-0.03620893880724907,
0.05086241662502289,
-0.010871222242712975,
0.01407844852656126,
-0.045773833990097046,
-0.02743401750922203,
-0.03748554736375809,
-0.015355542302131653,
-0.00521550327539444,
0.040162861347198486,
-0.00848725438117981,
-0.008711758069694042,
0.03601924329996109,
-0.007365124765783548,
0.0784267708659172,
0.051482051610946655,
0.016356922686100006,
0.004930430557578802,
-0.019642014056444168,
-0.005784978158771992,
-0.021888861432671547,
-0.011881176382303238,
-0.017816582694649696,
-0.04895881935954094,
0.0029033750761300325,
0.01753854937851429,
-0.009310796856880188,
0.0867573544383049,
-0.017535487189888954,
0.0015117586590349674,
0.0015630542766302824,
0.04604782909154892,
-0.002319176448509097,
0.05462897568941116,
-0.05377422273159027,
0.0010986145352944732,
-0.0378706268966198,
-0.04100160673260689,
0.00021336233476176858,
0.028203679248690605,
-0.01208439003676176,
0.057097427546978,
0.026363054290413857,
-0.02813958376646042,
-0.04158060997724533,
-0.024572016671299934,
-0.006547620519995689,
0.03795834630727768,
-0.07278230786323547,
-0.00537031888961792,
0.0008332541328854859,
0.022491760551929474,
-0.0589962899684906,
0.09052829444408417,
-0.0662473663687706,
0.022531989961862564,
-0.05382172390818596,
-0.012904380448162556,
0.03027612529695034,
-0.022446228191256523,
-0.04706192389130592,
0.035934459418058395,
-0.012112599797546864,
0.0699128732085228,
0.05311301723122597,
-0.04446498677134514,
-0.004301311448216438,
-0.013693391345441341,
0.048616454005241394,
-0.009699336253106594,
-0.011227171868085861,
-0.08145087957382202,
-0.011713423766195774,
0.005735758692026138,
0.055145878344774246,
0.06700510531663895,
-0.04120572656393051,
0.03726218640804291,
-0.03785457834601402,
0.025685500353574753,
-0.03162819892168045,
0.02773720771074295,
-0.03654325008392334,
0.05287697911262512,
-0.04737141355872154,
-0.05112392455339432,
-0.008187001571059227,
0.015348835848271847,
-0.016794942319393158,
0.06696871668100357,
-0.0003578061005100608,
0.018419284373521805,
0.05989677086472511,
-0.04990526661276817,
0.01876848004758358,
0.05186331272125244,
-0.037766341120004654,
0.003672307822853327,
-0.03077314794063568,
-0.04297753795981407,
0.024463336914777756,
-0.031211528927087784,
0.03661501407623291,
-0.040800921618938446,
0.025434639304876328,
0.042005542665719986,
-0.04013005644083023,
0.04312901198863983,
0.03122219629585743,
0.027886565774679184,
0.013637778349220753,
0.030777152627706528,
0.03906474635004997,
0.013626580126583576,
-0.0280461423099041,
-0.04660020023584366,
0.06559966504573822,
0.043258186429739,
0.01012791134417057,
-0.01608055830001831,
0.001664225710555911,
-0.0004575258062686771,
0.024077460169792175,
0.03348452225327492,
-0.03792257979512215,
-0.0032698686700314283,
-0.026564912870526314,
0.01454286091029644,
-0.02435920387506485,
-0.03226567432284355,
0.02934582717716694,
0.05772017315030098,
-0.034926801919937134,
0.03371509909629822,
-0.04867059737443924,
-0.049650680273771286,
0.007546798326075077,
-0.07682541757822037,
-0.01356012374162674,
-0.0443287193775177,
0.015103456564247608,
-0.043232861906290054,
-0.048808157444000244,
-0.024786418303847313,
0.033550720661878586,
0.022690199315547943,
-0.037185654044151306,
0.0790393128991127,
0.06404097378253937,
-0.028323646634817123,
-0.05056597664952278,
-0.0505971796810627,
-0.00043265160638839006,
-0.047662582248449326,
0.005200013052672148,
0.013289621099829674,
-0.008787928149104118,
-0.03773759678006172,
-0.08580099791288376,
-0.03248396888375282,
0.005648626945912838,
0.015464073978364468,
0.02656778134405613,
0.04395562782883644,
-0.0033764890395104885,
0.014802881516516209,
-0.01967918872833252,
-0.05478239059448242,
0.00997191946953535,
-0.009445205330848694,
0.013582417741417885,
0.026691772043704987,
0.02477569878101349,
-0.01906043291091919,
-0.034128472208976746,
-0.0016219845274463296,
0.010994412936270237,
-0.018272755667567253,
-0.008751962333917618,
-0.001984861446544528,
0.018083015456795692,
0.08861161023378372,
0.01690926030278206,
0.009131098166108131,
0.032010309398174286,
-0.02944662608206272,
-0.015606693923473358,
-0.06536604464054108,
0.018010783940553665,
0.03646676987409592,
-0.09060470759868622,
-0.032507386058568954,
0.07972433418035507,
0.03405197709798813,
0.03889352083206177,
0.01738237403333187,
0.05562691390514374,
-0.017661621794104576,
0.04162093251943588,
0.03214320167899132,
0.0524427592754364,
-0.030503742396831512,
-0.036872439086437225,
0.008137285709381104,
0.01775815151631832,
-0.00808809045702219,
0.013536741957068443,
-0.029156863689422607,
0.0222103800624609,
0.0018168763490393758,
0.06651052087545395,
0.018206896260380745,
-0.02816707454621792,
-0.03393182158470154,
-0.02927778661251068,
0.0808318555355072,
-0.05936574563384056,
-0.001000765128992498,
0.06468654423952103,
-0.012790719978511333,
0.0000933977571548894,
0.08106280863285065,
-0.0428672656416893,
-0.057927533984184265,
-0.04087439924478531,
0.041507914662361145,
-0.0010564413387328386,
-0.045423999428749084,
-0.010002327151596546,
-0.014312847517430782,
-0.00911130290478468,
-0.015582568012177944,
0.009617657400667667,
0.0621432326734066,
0.014401106163859367,
-0.01582409255206585,
-0.003445050911977887,
-0.0008127927430905402,
-0.005282929167151451,
0.008177543058991432,
0.011370808817446232,
-0.02159849740564823,
-0.008032629266381264,
0.04920187219977379,
0.06731586158275604,
-0.01892312616109848,
0.022146075963974,
-0.02230091765522957,
-0.0038347842637449503,
-0.02626083232462406,
-0.016085799783468246,
0.012392211705446243,
0.01153009943664074,
-0.05671597272157669,
-0.039648231118917465,
-0.014201839454472065,
-0.05026588961482048,
-0.0256432443857193,
-0.016570936888456345,
0.028005411848425865,
-0.013654700480401516,
0.0019420187454670668,
-0.04013097658753395,
0.0813109278678894,
-0.023254428058862686,
-0.07172080874443054,
0.01678200252354145,
-0.0061202519573271275,
-0.03320768103003502,
-0.021718235686421394,
-0.01686747558414936,
0.027553429827094078,
-0.0070874965749681,
-0.059825263917446136,
0.04224355146288872,
0.02563357912003994,
0.0652708038687706,
-0.03780800849199295,
-0.060719456523656845,
0.012553775683045387,
-0.01773558370769024,
0.015373547561466694,
0.07943779975175858,
-0.022164693102240562,
0.09164148569107056,
-0.022404490038752556,
0.005869550630450249,
-0.02787739410996437,
0.01294003613293171,
0.033856045454740524,
0.03445238620042801,
0.008645068854093552,
-0.034970130771398544,
-0.04234485700726509,
0.033323023468256,
0.05181615427136421,
0.0459020733833313,
-0.006093039643019438,
-0.024664951488375664,
-0.017608346417546272,
-0.06268929690122604,
0.001733318786136806,
0.0586404874920845,
-0.0528859943151474,
-0.04966648668050766,
0.010009706020355225,
0.045922040939331055,
-0.008099843747913837,
0.06478456407785416,
0.0252798181027174,
0.007719745393842459,
0.008467327803373337,
0.004323503468185663,
-0.04751620069146156,
0.02555926889181137,
-0.0010769538348540664,
0.023765085265040398,
-0.012746340595185757,
-0.0744892805814743,
-0.030435016378760338,
0.023560505360364914,
0.05907884240150452,
-0.014208992011845112,
-0.013460231944918633,
-0.0041763801127672195,
-0.03077862039208412,
-0.004478097893297672,
0.03141828626394272,
-0.001297184731811285,
-0.04439480975270271,
-0.021774910390377045,
0.012834825552999973,
0.03933607414364815,
-0.00906530860811472,
0.04080263897776604,
0.017770785838365555,
-0.02122548036277294,
-0.04143036901950836,
0.040835268795490265,
0.008259454742074013,
-0.03381672129034996,
0.022224433720111847,
0.029162835329771042,
0.0010367062641307712,
0.025542091578245163,
0.023649344220757484,
-0.025046303868293762,
0.04132114350795746,
-0.02953988127410412,
0.001231594942510128,
0.026475626975297928,
0.026642540469765663,
0.013493724167346954,
0.034737903624773026,
-0.007238882128149271,
0.009522448293864727,
0.02627757377922535,
-0.02230972796678543,
0.012363838031888008,
0.008793254382908344,
-0.061653830111026764,
0.01929604634642601,
-0.05973336473107338,
-0.007887760177254677,
-0.029046667739748955,
0.03300148993730545,
-0.0146542489528656,
0.014994257129728794,
0.03871547058224678,
0.013056134805083275,
-0.043099477887153625,
0.04379663243889809,
0.01828697696328163,
-0.0028994365129619837,
-0.041084568947553635,
-0.04051775857806206,
0.029515022411942482,
0.019832579419016838,
-0.016252972185611725,
-0.009338239207863808,
0.03418353199958801,
0.002696861047297716,
0.051779404282569885,
-0.052562590688467026,
-0.04078541696071625,
0.04169999808073044,
0.021714478731155396,
-0.06348446011543274,
0.05483498051762581,
-0.0045806607231497765,
0.006053128279745579,
-0.016247373074293137,
0.08426585048437119,
0.014635494910180569,
0.03064846806228161,
-0.014850382693111897,
0.05240543186664581,
0.028922105208039284,
-0.05828093737363815,
0.04148613661527634,
-0.05673208087682724,
-0.003585629165172577,
-0.02272864431142807,
0.032071612775325775,
0.053072795271873474,
0.0070396303199231625,
0.07263438403606415,
0.0021840326953679323,
0.030733179301023483,
0.00574576947838068,
-0.008598187938332558,
0.035393066704273224,
0.02036662958562374,
0.01877657137811184,
0.06607472896575928,
-0.04338129237294197,
0.04896309971809387,
0.01878172531723976,
-0.045521605759859085,
-0.011442339047789574,
-0.06286679208278656,
-0.035287126898765564,
-0.021561898291110992,
-0.0062923673540353775,
0.058842532336711884,
-0.02106136456131935,
0.03832276538014412,
-0.05136393383145332,
-0.012952979654073715,
-0.022822929546236992,
0.054919127374887466,
0.012414759956300259,
-0.046469442546367645,
0.06853612512350082,
0.07343956083059311,
0.06090223044157028,
-0.018264062702655792,
-0.060439109802246094,
-0.011494829319417477,
-0.038560714572668076,
-0.004466535523533821,
-0.008054163306951523,
0.02628318779170513,
0.032966867089271545,
0.00762065639719367,
-0.0956338420510292,
-0.0419284924864769,
0.04830961301922798,
-0.007205464877188206,
-0.007681984454393387,
-0.024886805564165115,
0.013706415891647339,
0.003525778651237488,
-0.01797236129641533,
-0.029101066291332245,
-0.010834848508238792,
0.010752338916063309,
0.0028301398269832134,
-0.00891181267797947,
0.00918887834995985,
-0.005326352547854185,
-0.002457325579598546,
-0.0442972406744957,
-0.020132331177592278,
-0.051095809787511826,
-0.038398515433073044,
-0.014716632664203644,
-0.03663772717118263,
0.010562888346612453,
0.03790678828954697,
-0.0042444923892617226,
0.013047613203525543,
0.013882816769182682,
0.014605900272727013,
-0.04080573841929436,
-0.004196524154394865,
-0.05519234761595726,
-0.019144805148243904,
0.00817030668258667,
-0.027523938566446304,
-0.0010548561112955213,
0.046156495809555054,
0.049108702689409256,
-0.040438294410705566,
0.030433939769864082,
0.009387586265802383,
-0.07929829508066177,
-0.0015346459113061428,
0.0068070837296545506,
0.00015369321045000106,
-0.03563009202480316,
-0.020227447152137756,
0.021857192739844322,
0.014638838358223438,
0.03440190851688385,
0.04642680287361145,
-0.030514782294631004,
-0.06505092233419418,
-0.010844658128917217,
-0.01052579190582037,
0.023253900930285454,
0.011931657791137695,
0.00007499007188016549,
0.02985607646405697,
-0.05362771451473236,
-0.06610548496246338,
-0.044341377913951874,
0.04399244114756584,
0.03613144904375076,
0.06045208126306534,
-0.03320367634296417,
-0.003438642481341958,
-0.030770834535360336,
0.011395522393286228,
0.05372736603021622,
0.06412462145090103,
0.06539708375930786,
-0.05728733539581299,
0.012441578321158886,
0.043408073484897614,
-0.01280487421900034,
-0.05943690612912178,
0.0496780090034008,
-0.021212883293628693,
0.018527919426560402,
0.004544692113995552,
0.00620532501488924,
-0.08174868673086166,
-0.05830034613609314,
0.022023694589734077,
-0.0700775533914566,
-0.014427833259105682,
-0.000699886935763061,
0.045074645429849625,
-0.047702740877866745,
-0.01594538986682892,
-0.017974140122532845,
0.06681199371814728,
-0.042153265327215195,
0.016137588769197464,
0.05206431448459625,
-0.021516477689146996,
-0.035461802035570145,
0.02527822181582451,
0.01453335676342249,
0.015267068520188332,
-0.067454032599926,
0.011921015568077564,
0.007723079528659582,
-0.12381087988615036,
0.018454715609550476,
0.03167321905493736,
0.030316710472106934,
-0.019411887973546982,
-0.05737825855612755,
0.002204360906034708,
-0.027570774778723717,
-0.025729680433869362,
0.03806988149881363,
-0.038765981793403625,
-0.03352181613445282,
0.0016113788587972522,
0.0482453778386116,
-0.02084328979253769,
0.022525429725646973,
-0.053324319422245026,
0.01791546680033207,
0.01629471592605114,
0.03132758289575577,
0.019607312977313995,
-0.021164903417229652,
0.019058125093579292,
0.050546422600746155,
0.05207940563559532,
-0.011009392328560352,
0.010051249526441097,
-0.03391033783555031,
0.03931917995214462,
0.09387759119272232,
0.03188507631421089,
-0.01789526641368866,
-0.010132338851690292,
0.03436010703444481,
-0.029683783650398254,
-0.00885811448097229,
-0.01617402955889702,
-0.0055448394268751144,
-0.016116131097078323,
-0.010544984601438046,
0.036806393414735794,
-0.0390072725713253,
0.0030892237555235624,
0.01809743046760559,
-0.012072168290615082,
0.004380560480058193,
-0.046576548367738724,
-0.0050695245154201984,
-0.05035017803311348,
0.00563611788675189,
-0.01574859581887722,
0.005501879379153252,
0.003383413888514042,
0.0102295633405447,
0.020231202244758606,
0.02669486403465271,
0.11467351764440536,
-0.024688759818673134,
0.01468544639647007,
0.028811197727918625,
-0.06736598908901215,
-0.017520852386951447,
-0.04510807245969772,
-0.03715481609106064,
-0.027781520038843155,
0.026795489713549614,
-0.054342228919267654,
-0.004247142467647791,
-0.05827360972762108,
-0.04771828651428223,
0.004193336237221956,
0.008542483672499657,
-0.014206863939762115,
-0.11349114030599594,
-0.041966456919908524,
0.02581176720559597,
-0.02615121752023697,
0.09764078259468079,
-0.04759538546204567,
-0.002315093297511339,
-0.027106745168566704,
-0.055402301251888275,
0.006601864937692881,
-0.005427156109362841,
0.021630780771374702,
-0.03136858344078064,
-0.0009412016370333731,
-0.024014050140976906,
0.03912106156349182,
0.033931490033864975,
-0.0053086779080331326,
0.007168769370764494,
0.04634326696395874,
0.07064829766750336,
0.011056018993258476,
-0.003929168451577425,
-0.01721467636525631,
0.025577785447239876,
0.039593495428562164,
-0.01597023196518421,
0.02404121868312359,
-0.018622610718011856,
0.002747528487816453,
-0.016909262165427208,
0.00019913552387151867,
0.05413830280303955,
0.04976729676127434,
-0.032169949263334274,
-0.02382214553654194,
-0.02324645407497883,
-0.024763740599155426,
-0.02503400854766369,
0.03861573338508606,
0.000574082660023123,
-0.046329014003276825,
-0.009408114477992058,
0.04095920920372009,
-0.041231147944927216,
-0.02863524667918682,
0.025757184252142906,
0.011094271205365658,
-0.01565951108932495,
-0.051634032279253006,
-0.009791187942028046,
0.010088863782584667,
-0.0070564583875238895,
0.014633402228355408,
0.04299614951014519,
0.011303435079753399,
0.04394055902957916,
-0.036589428782463074,
-0.01685846596956253,
0.048861268907785416,
0.00790403876453638,
-0.03458911180496216,
-0.027322128415107727,
-0.003570077009499073,
-0.011423623189330101,
-0.012210287153720856,
0.003103073686361313,
0.016923213377594948,
-0.0022065883968025446,
0.036092374473810196,
-0.010990461334586143,
0.03291323781013489,
-0.014089282602071762,
0.01827571727335453,
-0.0025977331679314375,
-0.0009316475479863584,
-0.05380331724882126,
0.026407390832901,
-0.037332408130168915,
0.05039219185709953,
0.026230568066239357,
-0.009288685396313667,
-0.07973375916481018,
-0.03314419463276863,
-0.02152150683104992,
0.03174246847629547,
-0.082919642329216,
0.01743162050843239,
-0.0057896897196769714,
-0.02068157307803631,
-0.013854753226041794,
0.02890278398990631,
-0.006211074534803629,
0.021267199888825417,
-0.01173971127718687,
0.0028754607774317265,
0.010988796129822731,
-0.021830681711435318,
-0.022048136219382286,
0.04742860794067383,
0.0826355516910553,
-0.010032630525529385,
-0.0680437684059143,
-0.0020205825567245483,
0.04012973979115486,
-0.057338107377290726,
-0.058310430496931076,
0.004763195291161537,
0.02018054574728012,
0.0037408419884741306,
-0.016221284866333008,
0.023484962061047554,
-0.023304037749767303,
-0.0316447950899601,
-0.041063643991947174,
-0.017191840335726738,
-0.010157541371881962
] |
<p>Our calculus book, Stewart, has a problem where they claim that for a metal cable (inner radius $r$) encased in insulation (outer radius $R$), the speed of an electrical impulse is given by</p>
<p>$$v = - k \left(\frac{r}{R}\right)^2 \ln \left(\frac{r}{R}\right)$$</p>
<p>where $k$ is a positive constant.</p>
<p><strong>My question</strong>
What I would like to know is the physical justification for their claim.</p>
<p><strong>My thoughts</strong>
There claim is somewhat surprising, since for sufficiently high insulation R, with r fixed, the speed of the impulse <em>decreases</em> (by L'Hospital) with <em>more</em> insulation.</p>
<hr>
<p><em>EDIT</em>: I received this email after contacting Brooks/Cole, the publisher of the textbook. The response didn't really help unfortunately.</p>
<blockquote>
<p>Hi Professor ...,</p>
<p>I just heard back from the author regarding your query: “I can understand why Professor
... thinks this equation is counterintuitive, but it is in fact correct. I have been >trying to track down the source that I used in devising this problem, but unfortunately I >can’t seem to find it right now.” I will certainly let you know if he is able to track >down the source information. I’m sorry I can’t give you a more concrete answer at this >time. Best, ...</p>
<p>[JIRA] (KYTS-1199) Content Feedback from Instructor for ISBN: 0495014281 Essential >Calculus: Early Transcendentals 1st edition.</p>
</blockquote> | g1283 | [
0.07104390114545822,
0.03403565660119057,
0.012094036675989628,
0.0016367281787097454,
0.02400573156774044,
-0.004805807489901781,
0.05183614045381546,
-0.0029554839711636305,
-0.09514722973108292,
0.04837432876229286,
-0.0059617361985147,
0.02491062879562378,
-0.053236428648233414,
0.006113030482083559,
0.056690264493227005,
-0.019011517986655235,
0.07493694871664047,
-0.03770698234438896,
0.016654180362820625,
-0.006099393125623465,
-0.03491450473666191,
-0.0225201565772295,
-0.002770696533843875,
-0.01666674017906189,
0.007556434255093336,
0.013887804001569748,
0.03297215700149536,
-0.03979690372943878,
-0.02170969918370247,
-0.053804002702236176,
-0.040386732667684555,
-0.0242050401866436,
-0.001050464459694922,
-0.05918607488274574,
-0.10527219623327255,
0.010953468270599842,
0.01192097831517458,
-0.01078809704631567,
0.009239294566214085,
0.0055218045599758625,
0.042139772325754166,
-0.011658286675810814,
0.057743530720472336,
-0.040002793073654175,
0.025396915152668953,
0.01372434850782156,
-0.0009320946992374957,
0.01024398859590292,
-0.0034939919132739305,
-0.023937009274959564,
-0.04933725297451019,
-0.0062457239255309105,
0.05586599186062813,
-0.024943221360445023,
-0.03613991662859917,
0.009352960623800755,
0.01952393352985382,
-0.010065012611448765,
-0.025749100372195244,
0.040381111204624176,
0.0017766689416021109,
-0.021936530247330666,
0.002418067306280136,
-0.07705073803663254,
0.07816021144390106,
-0.004312141798436642,
-0.009967250749468803,
-0.02698015794157982,
0.08394472301006317,
0.03245417773723602,
-0.013843719847500324,
-0.046705324202775955,
-0.007382962387055159,
-0.04214974120259285,
-0.03369756042957306,
0.02109377458691597,
0.03444661200046539,
-0.00860096700489521,
0.017813652753829956,
0.03914279863238335,
-0.022477127611637115,
0.0460539311170578,
-0.022053007036447525,
-0.022749237716197968,
0.004688407760113478,
0.0035779683385044336,
0.013352713547647,
0.02108113281428814,
-0.020361213013529778,
0.047563016414642334,
-0.012366537936031818,
0.006830425001680851,
0.049991752952337265,
-0.020746935158967972,
0.006981986574828625,
-0.03197767212986946,
-0.04051246494054794,
0.023134250193834305,
0.013429468497633934,
0.06081746518611908,
-0.0310604739934206,
-0.05814848095178604,
0.060189008712768555,
-0.01248672790825367,
-0.07242891192436218,
0.03273683413863182,
0.02230246365070343,
-0.04329840838909149,
-0.07578283548355103,
0.0063978396356105804,
0.07300359010696411,
-0.033664897084236145,
-0.05631568282842636,
-0.02970731444656849,
-0.014395617879927158,
0.0072130779735744,
0.029268641024827957,
-0.0217658169567585,
-0.03894234821200371,
0.06018418073654175,
-0.044924382120370865,
0.0003435069229453802,
-0.04815850779414177,
0.0036551731172949076,
0.021909959614276886,
0.01859641820192337,
-0.009733002632856369,
0.010285009630024433,
0.005247610155493021,
0.02061859890818596,
-0.01990393176674843,
0.02676350250840187,
-0.0185789056122303,
-0.020187223330140114,
0.0016293993685394526,
0.045371681451797485,
0.030618207529187202,
-0.010800875723361969,
-0.009249592199921608,
0.019857898354530334,
0.007226856891065836,
-0.013926954008638859,
0.009987822733819485,
0.006311230827122927,
-0.01722598448395729,
0.05792833864688873,
-0.04192616418004036,
-0.016687951982021332,
0.02944527566432953,
-0.019585020840168,
-0.02119339257478714,
0.05455673485994339,
0.0008666723151691258,
-0.010682142339646816,
-0.023768316954374313,
0.025784218683838844,
0.030041692778468132,
0.024576831609010696,
0.020552637055516243,
0.034975770860910416,
0.05011243745684624,
0.014858163893222809,
-0.031376130878925323,
0.03988240286707878,
0.004239835776388645,
0.013641169294714928,
0.044835638254880905,
0.003849170869216323,
0.004084645304828882,
-0.05567874014377594,
-0.01697879657149315,
-0.009756546467542648,
0.09547494351863861,
0.06549462676048279,
-0.030978716909885406,
0.002015535719692707,
0.08786847442388535,
-0.06580915302038193,
0.007612056564539671,
0.010622684843838215,
-0.06678558886051178,
-0.007573308888822794,
0.04425462707877159,
-0.07320096343755722,
-0.004042224958539009,
-0.024515720084309578,
0.021895261481404305,
0.05582379177212715,
-0.06742077320814133,
-0.041040077805519104,
-0.03759843111038208,
-0.028125019744038582,
-0.03388006240129471,
0.021340161561965942,
-0.02034991793334484,
0.008364612236618996,
0.06726992875337601,
0.018052658066153526,
0.0009209866402670741,
0.03497939184308052,
0.013734788633883,
0.0676027461886406,
0.041604239493608475,
-0.0221184641122818,
-0.02322225645184517,
0.016933077946305275,
-0.02937391772866249,
-0.029528165236115456,
0.029974613338708878,
-0.0213728379458189,
0.04492473602294922,
0.027293872088193893,
-0.04346634820103645,
0.07849324494600296,
0.010276969522237778,
-0.05581730976700783,
-0.0030411991756409407,
0.03556038811802864,
-0.04953622817993164,
-0.020964015275239944,
0.027947885915637016,
-0.054299209266901016,
0.05563313141465187,
-0.0661943182349205,
-0.05963953211903572,
-0.05810081213712692,
-0.059897005558013916,
-0.0593523308634758,
-0.062410663813352585,
-0.014502166770398617,
-0.051670387387275696,
0.006117726676166058,
-0.021201075986027718,
0.006103935185819864,
0.0066853719763457775,
0.0423009991645813,
0.0306443702429533,
0.005268927197903395,
0.027716638520359993,
0.004863017238676548,
0.05264449492096901,
-0.0388227216899395,
-0.01386167947202921,
-0.004859432578086853,
-0.051738180220127106,
-0.020925747230648994,
-0.017707930877804756,
-0.05587643012404442,
0.025434840470552444,
0.04845356196165085,
0.039095085114240646,
0.038516800850629807,
-0.022794391959905624,
-0.0369020476937294,
-0.013818684034049511,
-0.03984556719660759,
-0.00567946070805192,
0.027886001393198967,
-0.03265702351927757,
-0.059632688760757446,
-0.00675080856308341,
-0.008106254041194916,
0.06914562731981277,
0.030795440077781677,
-0.10721362382173538,
0.020262809470295906,
-0.04985521733760834,
-0.00022167543647810817,
0.02689296193420887,
0.027451222762465477,
-0.012045247480273247,
0.04720673710107803,
-0.010459494777023792,
0.03426281735301018,
0.009157727472484112,
-0.08449877798557281,
0.031895168125629425,
-0.06053971126675606,
0.01803678274154663,
-0.0294741652905941,
0.039322540163993835,
-0.046649008989334106,
-0.05286207050085068,
0.061281606554985046,
-0.02543964982032776,
-0.10776440054178238,
-0.006026317365467548,
0.04772910475730896,
0.008533638902008533,
-0.014493903145194054,
-0.030691787600517273,
0.033613141626119614,
-0.00524522177875042,
-0.00579373724758625,
0.022336162626743317,
0.07174298912286758,
0.024363286793231964,
-0.07102978229522705,
0.0028138835914433002,
-0.0718635618686676,
-0.0022225265856832266,
0.012583969160914421,
-0.04892200976610184,
0.030425889417529106,
0.023686299100518227,
-0.030181288719177246,
-0.05551711842417717,
-0.011091610416769981,
0.044094692915678024,
-0.02884938381612301,
0.043241195380687714,
0.027040714398026466,
0.045736391097307205,
-0.0020234331022948027,
-0.03183359280228615,
-0.005541595630347729,
0.006392816547304392,
0.046899184584617615,
0.059679850935935974,
0.06374431401491165,
-0.03369464352726936,
-0.045755621045827866,
0.013250368647277355,
0.012886312790215015,
0.024504302069544792,
-0.048486147075891495,
0.01285326573997736,
0.05224178358912468,
-0.06464224308729172,
-0.003456928301602602,
-0.014333575963973999,
0.011788787320256233,
0.057737573981285095,
-0.012876712717115879,
-0.019935933873057365,
-0.06335212290287018,
-0.009983476251363754,
0.06605515629053116,
0.013982190750539303,
0.0013109797146171331,
-0.008041354827582836,
-0.035031840205192566,
-0.06686641275882721,
0.015511433593928814,
0.04021936655044556,
0.01271251030266285,
-0.04738428443670273,
0.041218675673007965,
0.04245113953948021,
0.017701195552945137,
0.017950389534235,
0.009611476212739944,
0.007791288662701845,
-0.030148304998874664,
-0.02114657498896122,
0.03214653208851814,
0.02723529189825058,
0.04555332660675049,
-0.033451102674007416,
0.0046035656705498695,
0.011237905360758305,
-0.017673704773187637,
0.035345014184713364,
0.002051734598353505,
-0.004128227476030588,
0.019141633063554764,
0.01590605638921261,
0.07776747643947601,
-0.056994494050741196,
0.004266848787665367,
-0.011377479881048203,
0.05068071186542511,
-0.04178883507847786,
0.021118171513080597,
0.00928852241486311,
-0.025300372391939163,
-0.014365054666996002,
0.03251876309514046,
-0.010495484806597233,
0.04192306473851204,
0.04035932943224907,
0.008883058093488216,
0.008559300564229488,
0.00017043664411175996,
0.011591041460633278,
0.02938608080148697,
-0.0017002880340442061,
-0.0027482027653604746,
-0.0027149098459631205,
-0.0665365532040596,
0.027146097272634506,
0.005144990514963865,
-0.04338909313082695,
0.025133676826953888,
-0.01464018039405346,
-0.04872046038508415,
-0.018043814226984978,
-0.022875353693962097,
-0.050589870661497116,
-0.013296583667397499,
0.022263135761022568,
-0.0855446457862854,
0.03028145246207714,
0.0637296512722969,
-0.06966487318277359,
0.004157482646405697,
0.0718182921409607,
0.007362989243119955,
0.03143561631441116,
-0.04434666410088539,
-0.02774522453546524,
-0.009919987991452217,
-0.021133238449692726,
-0.08876410871744156,
0.02664671279489994,
0.04435977339744568,
0.06435354799032211,
-0.012988101691007614,
0.03202148899435997,
-0.017488595098257065,
0.018386146053671837,
-0.022045224905014038,
0.03516227379441261,
-0.02366025373339653,
0.02866223081946373,
0.017805099487304688,
0.0974767729640007,
0.007864277809858322,
0.0012107985094189644,
-0.025950808078050613,
-0.027972204610705376,
-0.006045059766620398,
-0.06426221132278442,
0.04271511733531952,
0.005184910260140896,
0.05463756248354912,
-0.03289388492703438,
0.08634001761674881,
-0.02771487459540367,
0.05639517307281494,
0.01998329535126686,
-0.03765791282057762,
0.04745930805802345,
-0.006975797936320305,
0.0348099023103714,
0.053191233426332474,
-0.024279724806547165,
-0.011438877321779728,
0.014447124674916267,
0.001069979858584702,
0.0629480630159378,
0.04249906539916992,
0.014190882444381714,
-0.007023048587143421,
-0.00742445420473814,
-0.02546793594956398,
-0.017694124951958656,
-0.0011348642874509096,
0.0645061656832695,
0.0005177550483494997,
0.00038713551475666463,
0.05621086061000824,
-0.04041609913110733,
0.015043812803924084,
0.04197569563984871,
0.00980317872017622,
0.03303471952676773,
-0.0193770844489336,
-0.08145827054977417,
0.03861367329955101,
0.039463162422180176,
0.07922676205635071,
-0.010067477822303772,
-0.012047956697642803,
0.02074735052883625,
-0.006471702363342047,
-0.006578993983566761,
0.055780645459890366,
-0.09180185943841934,
-0.028163287788629532,
-0.026863977313041687,
0.0004676532407756895,
-0.03326667100191116,
-0.02568763867020607,
0.018134985119104385,
-0.014839687384665012,
-0.04581574350595474,
0.002132006222382188,
-0.056640852242708206,
-0.028420621529221535,
0.07557801902294159,
-0.003853191388770938,
0.015636298805475235,
0.05129449814558029,
-0.051840975880622864,
0.003955983556807041,
0.09252729266881943,
0.026726868003606796,
-0.03894740715622902,
0.008361784741282463,
-0.017833422869443893,
-0.029374856501817703,
-0.016179878264665604,
0.01360275037586689,
-0.011493726633489132,
0.030470004305243492,
-0.012890259735286236,
0.024812551215291023,
-0.01854860968887806,
0.00959884375333786,
0.04812302067875862,
0.02504046820104122,
0.03343382105231285,
-0.026645919308066368,
0.04101021960377693,
-0.03834575042128563,
-0.06980098783969879,
-0.0059887985698878765,
-0.0021772223990410566,
-0.04339823126792908,
0.08352671563625336,
-0.0025946819223463535,
0.00891292653977871,
-0.015557583421468735,
-0.03349805995821953,
0.03450887277722359,
-0.04679670184850693,
-0.06180671229958534,
-0.025345971807837486,
0.018484866246581078,
0.021190335974097252,
-0.003887983039021492,
0.01150012668222189,
-0.03325410187244415,
-0.027780044823884964,
0.02828744240105152,
0.020361533388495445,
-0.010544931516051292,
-0.05271965265274048,
0.005942654795944691,
-0.015986373648047447,
-0.00288276351056993,
0.02473508194088936,
-0.0010469130938872695,
0.00020351445709820837,
0.030759532004594803,
-0.023492416366934776,
-0.05836746096611023,
0.01897740736603737,
-0.019237015396356583,
0.0049686431884765625,
-0.031021231785416603,
0.0022879713214933872,
-0.03164134919643402,
0.03620309382677078,
0.0011839639628306031,
0.0033672198187559843,
0.019394466653466225,
-0.0065167550928890705,
-0.009727712720632553,
0.009177475236356258,
-0.051839809864759445,
0.016149036586284637,
0.05242133140563965,
-0.0008303509675897658,
-0.07802455127239227,
0.06693512201309204,
0.023589231073856354,
0.032153502106666565,
0.046120040118694305,
0.0319218672811985,
0.010563604533672333,
0.024381350725889206,
-0.017862729728221893,
0.024846715852618217,
-0.01923271454870701,
0.008696972392499447,
-0.05945691093802452,
0.009412380866706371,
-0.011609361506998539,
-0.032669488340616226,
0.012347519397735596,
0.026691952720284462,
-0.06022358685731888,
0.008674224838614464,
-0.05561141297221184,
0.00004451143104233779,
0.017059341073036194,
0.009787245653569698,
-0.08601376414299011,
-0.036371227353811264,
0.045161109417676926,
-0.024597732350230217,
-0.04628659784793854,
-0.026013825088739395,
-0.02025161311030388,
0.020366298034787178,
0.03281285986304283,
-0.02860799804329872,
0.008292625658214092,
0.018519658595323563,
-0.03452308475971222,
0.019947346299886703,
-0.0520205982029438,
0.035400211811065674,
-0.01485794223845005,
0.04029905050992966,
0.024619661271572113,
-0.045437220484018326,
0.011077270843088627,
-0.010770886205136776,
0.0392267145216465,
0.02404153160750866,
0.021472886204719543,
-0.0018092571990564466,
0.003424079390242696,
-0.006820052862167358,
0.0075147440657019615,
0.01980144903063774,
-0.008362814784049988,
0.05803493410348892,
0.05241293087601662,
0.014573225751519203,
-0.026216572150588036,
0.013305287808179855,
0.02433244325220585,
0.013513264246284962,
0.05901451036334038,
-0.01433318667113781,
0.0014358448097482324,
-0.0027910543140023947,
-0.012727961875498295,
-0.03329021483659744,
0.019646894186735153,
-0.001348245656117797,
0.0063036526553332806,
0.021498775109648705,
0.025793006643652916,
0.027724556624889374,
0.03124796412885189,
0.03984934836626053,
-0.04815327748656273,
0.00277627632021904,
-0.002055513206869364,
-0.08036182075738907,
-0.039216767996549606,
0.020260609686374664,
-0.01190901268273592,
-0.05720585584640503,
-0.013266420923173428,
0.01480310969054699,
0.045446671545505524,
-0.037324804812669754,
0.00444449856877327,
-0.005058777052909136,
-0.06590690463781357,
-0.005181928630918264,
0.01247184444218874,
0.06731319427490234,
0.020022094249725342,
-0.030276693403720856,
-0.03263275325298309,
-0.0014146437169983983,
-0.01515820249915123,
0.02726222388446331,
0.021874427795410156,
-0.019566096365451813,
-0.046904802322387695,
-0.011276576668024063,
-0.04581884294748306,
-0.015318110585212708,
0.014296848326921463,
0.030139489099383354,
-0.025956306606531143,
0.034985482692718506,
0.029047397896647453,
-0.01788783073425293,
0.01106307189911604,
-0.016520071774721146,
-0.0062090326100587845,
0.030030058696866035,
0.021050188690423965,
-0.004425729159265757,
-0.015111950226128101,
-0.006728774402290583,
0.06404760479927063,
-0.07373058795928955,
-0.04723348096013069,
0.03027716465294361,
0.010548899881541729,
-0.013789677061140537,
0.04528771713376045,
0.06017328426241875,
-0.006451620254665613,
0.04419662803411484,
0.029945606365799904,
-0.030263494700193405,
0.06712871789932251,
-0.008286613039672375,
-0.0075192018412053585,
-0.027251427993178368,
-0.0052877250127494335,
0.04621018469333649,
0.032369788736104965,
-0.00945183914154768,
0.02930251508951187,
-0.028531624004244804,
-0.03243362531065941,
-0.04544832929968834,
0.020516613498330116,
0.022484511137008667,
-0.01227368414402008,
0.01079036295413971,
-0.008329835720360279,
0.05518915876746178,
0.010351517237722874,
-0.037815071642398834,
-0.010784721001982689,
-0.0012152920244261622,
-0.014230637811124325,
0.02949777990579605,
-0.005894066765904427,
-0.006793020758777857,
-0.016512582078576088,
-0.03487049415707588,
-0.0061348071321845055,
-0.019663020968437195,
0.018801992759108543,
-0.08271102607250214,
0.006202459800988436,
0.06706253439188004,
-0.03376489505171776,
0.01721310243010521,
0.03898429498076439,
-0.05706589296460152,
-0.0439954474568367,
0.01385959330946207,
0.06491096317768097,
0.0012917864369228482,
0.02342953160405159,
0.007726801093667746,
-0.014621121808886528,
-0.04715842753648758,
0.02120289020240307,
0.0038661444559693336,
-0.0061481185257434845,
-0.04581588879227638,
0.059522129595279694,
0.0325838178396225,
-0.05171620100736618,
0.014351793564856052,
-0.04291008412837982,
-0.10394789278507233,
-0.027563385665416718,
0.013287696056067944,
-0.023935483768582344,
-0.02417110465466976,
0.003952414728701115,
0.0001498795609222725,
0.014808956533670425,
-0.028624635189771652,
-0.04262121021747589,
0.030946768820285797,
-0.006295476574450731,
-0.010963688604533672,
-0.050182487815618515,
0.014540107920765877,
0.00004387569788377732
] |
<p>I'm a maths undergrad taking a course on electromagnetism, I've drawn a diagram to represent this following question, but I'm having a bit of trouble approaching it:</p>
<p>"Two tiny balls of mass m = 0:1 g and charge q are suspended on silk threads of
length l = 30 cm (see picture below). Their centers are separated by D = 6 cm.
Find the charge q." </p> | g14 | [
0.06305523961782455,
0.027062753215432167,
0.0072364299558103085,
-0.07564469426870346,
0.04213126376271248,
0.004316277336329222,
0.012951442040503025,
-0.02126261405646801,
-0.006053609307855368,
0.0329076312482357,
-0.06937657296657562,
0.005305049475282431,
0.029571231454610825,
-0.0338408499956131,
-0.015904860571026802,
0.04023856297135353,
0.048079121857881546,
-0.005072818137705326,
-0.02279934659600258,
0.0005434076301753521,
0.014470003545284271,
-0.005545587744563818,
0.036844708025455475,
-0.030266664922237396,
0.013410067185759544,
-0.025563919916749,
0.028734421357512474,
0.0614231638610363,
-0.08069713413715363,
0.022281989455223083,
-0.05463218688964844,
0.016628678888082504,
0.04931611940264702,
-0.04277034103870392,
-0.05146177113056183,
-0.011741713620722294,
0.003829364664852619,
0.0170237198472023,
-0.019133247435092926,
0.03627319633960724,
0.030870284885168076,
-0.042089786380529404,
0.015040932223200798,
-0.026991011574864388,
0.017200693488121033,
0.0002571739605627954,
0.028117651119828224,
0.022939318791031837,
-0.023519814014434814,
-0.02097463607788086,
-0.021509535610675812,
0.07848500460386276,
0.016916261985898018,
-0.026321962475776672,
0.005408842116594315,
0.014466911554336548,
0.015345810912549496,
-0.0248143058270216,
0.07137967646121979,
0.07714951783418655,
0.01280314102768898,
0.07402518391609192,
-0.009223912842571735,
0.027087023481726646,
0.007817191071808338,
-0.01708730310201645,
-0.0462445504963398,
-0.04756314307451248,
-0.02477130852639675,
0.02866348996758461,
-0.05464475601911545,
-0.059269096702337265,
0.020108221098780632,
0.009663690812885761,
-0.06279497593641281,
0.004812704864889383,
-0.017643602564930916,
0.0042283255606889725,
0.030662691220641136,
-0.02702651359140873,
-0.05491192266345024,
0.020658086985349655,
0.014050532132387161,
0.006448389962315559,
0.09362299740314484,
0.0001547831780044362,
-0.029750555753707886,
-0.027858510613441467,
-0.05030975490808487,
0.017267365008592606,
0.03460632264614105,
0.06563772261142731,
0.0479629822075367,
-0.01807204633951187,
0.036424748599529266,
-0.050002653151750565,
-0.0024741606321185827,
0.011670484207570553,
0.014199838973581791,
-0.004710691515356302,
-0.0256687980145216,
-0.043907806277275085,
-0.03186783567070961,
0.007537219673395157,
-0.037794120609760284,
0.01139153353869915,
0.019464105367660522,
0.007353638298809528,
0.010232876054942608,
0.011818152852356434,
-0.047741085290908813,
-0.04904851317405701,
-0.08163036406040192,
-0.014849558472633362,
-0.030943285673856735,
-0.006285728886723518,
0.05597032606601715,
-0.03100728802382946,
-0.052917324006557465,
0.019549250602722168,
-0.03020062856376171,
-0.01839977130293846,
0.04387042298913002,
0.05077769234776497,
0.005730651319026947,
0.0010848473757505417,
0.00029045643168501556,
0.030970152467489243,
0.004358399193733931,
0.006953141186386347,
0.03372974693775177,
-0.05851060897111893,
0.006170463748276234,
-0.04354828968644142,
-0.03314783051609993,
0.04894670471549034,
-0.030189374461770058,
0.0319003090262413,
-0.003863907651975751,
0.02251819334924221,
0.052757423371076584,
-0.05869721248745918,
-0.02892388217151165,
-0.01208017859607935,
-0.02156190201640129,
0.005025433376431465,
0.000313093070872128,
-0.010757356882095337,
0.026438044384121895,
0.009912165813148022,
-0.0014588767662644386,
0.07762914150953293,
-0.02759292535483837,
-0.036495715379714966,
0.024899719282984734,
0.0026056531351059675,
0.1090325191617012,
-0.007742274086922407,
-0.021029919385910034,
-0.03733344003558159,
0.02474411204457283,
-0.022346286103129387,
0.06559508293867111,
0.028835386037826538,
-0.031398143619298935,
-0.004383356310427189,
0.06765682995319366,
-0.0011515780352056026,
0.005170132033526897,
-0.07401948422193527,
0.01497694943100214,
-0.05303141474723816,
0.06435899436473846,
0.03468082472681999,
0.007707193028181791,
0.05212292820215225,
-0.0036800249945372343,
-0.04896846413612366,
0.07766073942184448,
0.005968061741441488,
0.00010117402416653931,
0.011958361603319645,
0.06141086667776108,
-0.005129697732627392,
-0.04166330024600029,
-0.0032066302374005318,
-0.0007481382344849408,
0.062072377651929855,
-0.027203401550650597,
-0.044535014778375626,
-0.05171095207333565,
0.013609268702566624,
-0.0538063682615757,
0.02126150019466877,
-0.016819145530462265,
-0.0419527105987072,
0.04309018328785896,
-0.022410530596971512,
-0.009866026230156422,
-0.05993819236755371,
0.03157651051878929,
0.0069944788701832294,
0.014091379940509796,
0.04017549380660057,
0.03629882261157036,
0.014839054085314274,
-0.045857835561037064,
-0.050254177302122116,
0.04257303848862648,
0.009561222046613693,
0.024431856349110603,
0.017078258097171783,
-0.020061684772372246,
0.04918725788593292,
-0.07293423265218735,
-0.008123799227178097,
0.05383467674255371,
-0.009140663780272007,
-0.028703348711133003,
0.05343335121870041,
-0.03320034220814705,
-0.019368549808859825,
0.03340274095535278,
-0.030268577858805656,
0.02143331989645958,
-0.0263870507478714,
0.015055903233587742,
-0.051293518394231796,
-0.09221579134464264,
-0.012363502755761147,
-0.053000565618276596,
0.006549545098096132,
0.006731376983225346,
-0.025305815041065216,
0.050604403018951416,
-0.0015725762350484729,
-0.06137770414352417,
-0.008844414725899696,
-0.00455215061083436,
-0.0381377674639225,
-0.0015461842995136976,
0.002552306279540062,
0.05801111459732056,
0.014133409596979618,
0.00702766003087163,
0.005619312170892954,
0.08462163060903549,
0.022555526345968246,
-0.019815543666481972,
0.07787488400936127,
0.056651771068573,
-0.010340564884245396,
-0.0032654614187777042,
0.012799669988453388,
0.0006857147673144937,
-0.04387390613555908,
0.019014665856957436,
0.009684518910944462,
0.006213281769305468,
-0.07204196602106094,
-0.01975104585289955,
-0.06192943826317787,
0.008777407929301262,
0.032683491706848145,
-0.0652957484126091,
-0.06747902929782867,
-0.014253814704716206,
-0.012419761158525944,
0.02530747279524803,
-0.047303635627031326,
-0.02919752150774002,
0.01852552406489849,
-0.007078652270138264,
-0.022898351773619652,
-0.010135573334991932,
-0.051492586731910706,
0.04155527800321579,
0.02836746908724308,
0.02978214994072914,
0.02672083117067814,
0.04793737456202507,
-0.036314621567726135,
-0.020236540585756302,
0.018873175606131554,
0.01495142187923193,
-0.06490722298622131,
0.0016385169001296163,
0.029133588075637817,
0.01799868978559971,
0.0056751444935798645,
-0.06384778767824173,
0.04131641983985901,
0.04604952037334442,
-0.052081622183322906,
-0.015930669382214546,
0.05144554749131203,
0.04664045572280884,
0.0027492681983858347,
-0.04031394049525261,
0.019725138321518898,
-0.004529972095042467,
0.036604512482881546,
0.022908085957169533,
0.00903300940990448,
0.026023460552096367,
0.048176009207963943,
-0.017444495111703873,
-0.005869980435818434,
0.0544004812836647,
0.02317742444574833,
-0.0030160637106746435,
0.012414573691785336,
0.08529387414455414,
-0.03358123451471329,
-0.057012446224689484,
0.013261819258332253,
0.0013279217528179288,
0.026094995439052582,
0.041848406195640564,
0.013056526891887188,
0.0058989557437598705,
0.029738672077655792,
0.0624028742313385,
0.013328473083674908,
-0.02536838874220848,
0.018073903396725655,
-0.0200748723000288,
-0.023616578429937363,
0.012934457510709763,
-0.02606097050011158,
-0.017303111031651497,
-0.014636782929301262,
0.0045540290884673595,
0.007256987504661083,
0.029921075329184532,
-0.08431149274110794,
-0.008201922290027142,
-0.01848790794610977,
-0.034219980239868164,
-0.032849617302417755,
-0.062420669943094254,
-0.017670296132564545,
-0.0564468577504158,
-0.087374247610569,
0.029305972158908844,
-0.0014501640107482672,
-0.015639837831258774,
0.015532121993601322,
0.027860820293426514,
-0.060497161000967026,
0.004366246983408928,
-0.0007134307525120676,
0.009288382716476917,
0.012792974710464478,
0.010281761176884174,
-0.040084872394800186,
0.023355234414339066,
0.013817430473864079,
-0.033185504376888275,
0.0027944794856011868,
0.035622160881757736,
0.018171409144997597,
-0.06033412739634514,
-0.04171210527420044,
0.03046932816505432,
-0.014865702018141747,
-0.029715141281485558,
0.05909893289208412,
-0.011214863508939743,
-0.0022933711297810078,
-0.01905197836458683,
0.02881055511534214,
-0.02204059809446335,
-0.017377512529492378,
0.0016255240188911557,
-0.05756562575697899,
-0.009265681728720665,
0.005333984736353159,
-0.012102111242711544,
0.02221023663878441,
-0.023663120344281197,
0.02420632913708687,
-0.021998755633831024,
-0.032296400517225266,
0.02426687255501747,
0.02771461196243763,
0.0029430044814944267,
0.0036941347643733025,
-0.04500947147607803,
-0.02945517748594284,
0.01768370345234871,
-0.026289384812116623,
0.00014062767149880528,
0.003297158982604742,
-0.04183077812194824,
-0.005072354804724455,
0.027312174439430237,
-0.017249001190066338,
-0.009412160143256187,
-0.009504363872110844,
0.047407619655132294,
0.013978261500597,
0.008067584596574306,
-0.03518042713403702,
0.022539541125297546,
-0.020764775574207306,
0.011273391544818878,
-0.042995866388082504,
0.0542403943836689,
-0.026757314801216125,
0.025822259485721588,
-0.021152149885892868,
0.006556279491633177,
-0.02786710113286972,
-0.02189105749130249,
-0.00762505829334259,
-0.010893270373344421,
0.022047316655516624,
-0.05377289280295372,
-0.01609012484550476,
0.0380580760538578,
0.05376836284995079,
-0.0196879543364048,
-0.07755020260810852,
-0.044144149869680405,
0.02611132152378559,
0.042748503386974335,
0.03324619680643082,
0.044034432619810104,
-0.0316929891705513,
-0.04839243367314339,
0.05391205474734306,
-0.058100733906030655,
0.043970707803964615,
-0.056486789137125015,
0.003888120176270604,
-0.04151264950633049,
0.015361019410192966,
-0.00967319868505001,
0.0400889553129673,
0.04596719518303871,
0.012315254658460617,
0.015347696840763092,
-0.04163613170385361,
-0.038863010704517365,
0.00524245947599411,
-0.012600624933838844,
0.002864048583433032,
-0.04950021207332611,
-0.028077850118279457,
0.016460241749882698,
0.008837281726300716,
-0.03869536519050598,
-0.03289121389389038,
0.0005022596451453865,
0.01962730847299099,
0.013396702706813812,
-0.0095379538834095,
0.01818646863102913,
0.050599049776792526,
-0.0059874337166547775,
0.017226535826921463,
-0.022226329892873764,
-0.03839864209294319,
0.028940482065081596,
-0.05134321749210358,
0.002593095414340496,
-0.025808436796069145,
0.015655098482966423,
-0.0500069223344326,
0.016509151086211205,
0.033670973032712936,
0.03343583270907402,
-0.009703820571303368,
0.04290687292814255,
0.010153847746551037,
0.010328041389584541,
0.017970673739910126,
-0.023521801456809044,
0.009621824137866497,
-0.03992137312889099,
0.017367109656333923,
-0.031706303358078,
0.023115405812859535,
0.04549536108970642,
0.005449481774121523,
0.02041148766875267,
0.04267517477273941,
0.014690100215375423,
0.01523760985583067,
0.03297218307852745,
-0.04965727776288986,
-0.012029211968183517,
0.00856856070458889,
-0.0001758634898578748,
-0.05178207904100418,
0.060321465134620667,
0.04071827977895737,
-0.008315956220030785,
0.03696476295590401,
0.005852128844708204,
0.01794450357556343,
-0.015518905594944954,
0.06492631137371063,
-0.05146041885018349,
-0.0012280653463676572,
-0.021771850064396858,
0.00547976978123188,
0.009552232921123505,
0.04581271857023239,
-0.08545037358999252,
0.0007575908093713224,
0.06877660006284714,
-0.022226253524422646,
-0.010153302922844887,
0.06852395087480545,
-0.02890436351299286,
-0.03037644922733307,
-0.00015867891488596797,
0.022529713809490204,
0.037920992821455,
-0.005418111570179462,
0.037245139479637146,
-0.054253801703453064,
0.052189331501722336,
0.022290032356977463,
-0.031061474233865738,
-0.019117627292871475,
0.03870005905628204,
0.00180337717756629,
-0.0006879593129269779,
0.01822998747229576,
-0.03124832734465599,
-0.01848568022251129,
0.036523446440696716,
-0.010993566364049911,
0.06133614107966423,
-0.04090077057480812,
0.01680763065814972,
0.022726960480213165,
-0.033275436609983444,
-0.05760670825839043,
0.0446399450302124,
-0.018242396414279938,
0.0071013374254107475,
-0.029416000470519066,
0.03147859498858452,
-0.017169199883937836,
0.043982867151498795,
0.0185810849070549,
-0.007722401060163975,
-0.010461214929819107,
-0.03156885877251625,
0.02176957204937935,
-0.003044754033908248,
0.06341409683227539,
-0.002387240994721651,
-0.0381808876991272,
-0.04430849105119705,
0.027123700827360153,
0.06903886049985886,
-0.03671896457672119,
-0.007412284146994352,
0.041223809123039246,
-0.021280739456415176,
-0.030126430094242096,
-0.034963253885507584,
0.023118481040000916,
0.0719514712691307,
0.015108411200344563,
0.03769828751683235,
-0.024087825790047646,
-0.0029791027773171663,
0.02685007080435753,
0.058835674077272415,
-0.003767171874642372,
0.008028783835470676,
-0.025266364216804504,
-0.045835722237825394,
0.020661022514104843,
0.0076506775803864,
0.05461044982075691,
-0.011572699062526226,
-0.04289507120847702,
0.029474221169948578,
0.05171845853328705,
-0.03347412124276161,
-0.0784684345126152,
0.036813247948884964,
-0.0173034630715847,
0.007690721191465855,
0.04724229499697685,
-0.0033480371348559856,
-0.024035818874835968,
-0.02116224355995655,
-0.02302224561572075,
0.016234369948506355,
-0.02620590478181839,
-0.007735077757388353,
0.05678034573793411,
0.02421475574374199,
-0.019663522019982338,
-0.0013895444571971893,
0.02745588682591915,
0.06871131807565689,
0.06389176100492477,
-0.006195066496729851,
0.016957826912403107,
-0.055538568645715714,
-0.023677930235862732,
-0.028788510710000992,
0.010961523279547691,
-0.04462650418281555,
0.0436723567545414,
0.030251266434788704,
-0.012406600639224052,
-0.0003530176472850144,
0.07157019525766373,
-0.015030544251203537,
-0.006887214258313179,
-0.008038346655666828,
0.021926548331975937,
-0.027580030262470245,
-0.02466047927737236,
0.06495644152164459,
0.029532458633184433,
0.009883335791528225,
0.026590462774038315,
0.01952023059129715,
-0.0014808395644649863,
-0.043357618153095245,
0.018161842599511147,
-0.0023845117539167404,
0.008574315346777439,
0.017180874943733215,
0.049499936401844025,
-0.0181774590164423,
0.01678345538675785,
0.025969676673412323,
0.0837879478931427,
-0.048506323248147964,
0.05435889959335327,
0.008638417348265648,
0.033867254853248596,
-0.026042090728878975,
-0.06682360917329788,
0.07974818348884583,
0.020400304347276688,
-0.006444040685892105,
0.03309224173426628,
0.03196442872285843,
0.018903100863099098,
-0.03743836656212807,
-0.05307912826538086,
-0.009600337594747543,
-0.04571562260389328,
0.004309105686843395,
0.005440813023597002,
0.05411859601736069,
-0.01760757900774479,
-0.061113111674785614,
0.03184089437127113,
-0.026714224368333817,
-0.07191071659326553,
-0.015864524990320206,
0.05529056116938591,
0.01002348680049181,
-0.01563199982047081,
-0.03193686529994011,
-0.06087267026305199,
-0.04757881909608841,
-0.0382189005613327,
-0.031223773956298828,
-0.021050672978162766,
0.024122510105371475,
-0.03789481148123741,
-0.009734642691910267,
0.049474719911813736,
-0.016576621681451797,
-0.023562533780932426,
0.009267866611480713,
-0.034333448857069016,
-0.032174061983823776,
-0.009379612281918526,
-0.02791770175099373,
0.032091282308101654,
-0.02989700809121132,
0.026474006474018097,
0.08585475385189056,
0.05728660151362419,
0.06133837625384331,
0.044563837349414825,
0.00043133311555720866,
-0.015104097314178944,
0.011075745336711407,
-0.0032496023923158646,
0.018354300409555435,
0.017226524651050568,
0.05038733407855034,
-0.024085115641355515,
0.03508628159761429,
-0.02190844900906086,
0.0034266735892742872,
-0.007241995073854923,
-0.002199579030275345,
0.009881369769573212,
-0.054512131959199905,
-0.025714559480547905,
-0.10423417389392853,
-0.020242473110556602,
0.0026919390074908733,
-0.006957004312425852,
0.0016391024691984057,
0.017960038036108017,
0.0527203306555748,
0.0635949894785881,
-0.04381820559501648,
0.015275321900844574,
-0.0022540325298905373,
0.030923131853342056,
-0.04254618287086487,
0.04658718779683113,
-0.031828075647354126,
-0.04207445681095123,
-0.022857286036014557,
-0.08390629291534424,
-0.01811543107032776,
0.06759095191955566,
0.014923053793609142,
-0.032939888536930084,
0.0359385684132576,
-0.0444466695189476,
0.012472433969378471,
0.038052357733249664,
-0.01953679323196411,
-0.0340103879570961,
-0.023385919630527496,
-0.041986070573329926,
0.04599391669034958,
-0.005846109241247177,
-0.0209751445800066,
-0.07956340909004211,
-0.040276724845170975,
-0.057594191282987595,
-0.012073151767253876,
0.00783936120569706,
-0.05926240608096123,
0.05572548136115074,
0.10627789050340652,
0.03815756365656853,
0.02694922313094139,
-0.07690461724996567,
-0.06728364527225494,
0.041351594030857086,
0.05310594663023949,
-0.03854166716337204,
0.04199475795030594,
0.0524124801158905,
-0.012380879372358322,
-0.045837223529815674,
-0.03882525488734245,
-0.06917311996221542,
-0.040368352085351944,
0.07870016247034073,
0.014591557905077934,
-0.04826363921165466,
0.0042986683547496796,
0.009695073589682579
] |
<p>If an astronomer moves at relativistic speed, the stars and constellations are distorted. He sees the stars towards which he is moving blue shifted, while the ones he's moving away from are red shifted. In addition, the apparent direction of distant stars is modified. I think that the coolest way of representing this is the "relativistic ellipse".</p>
<p>Think of a spherical shell with the inner surface reflective. Imagine a flashbulb going off at the center. The light is reflected and returns to the source.</p>
<p>Now think of the same situation observed from a moving frame of reference. The light is still emitted and returns to the center at the same time, but that point has now moved. Since the speed of light is the same in all frames of reference, the distance traveled by each light ray has to be the same. So the paths of the light rays (and the boundary of the spherical shell) describes an ellipse, the <a href="http://www.relativitybook.com/resources/relativistic_ellipse.html" rel="nofollow">"relativistic ellipse"</a>: </p>
<p><img src="http://i.stack.imgur.com/9PoOJ.png" alt="RelativisticEllipse"></p>
<p>The above drawing is from the book "Relativity in Curved Spacetime" which I highly recommend and can be purchased <a href="http://rads.stackoverflow.com/amzn/click/0955706807" rel="nofollow">here</a> or <a href="http://www.relativitybook.com/book_cover.html" rel="nofollow">here</a>.</p>
<p>Perhaps when my copy arrives it will have the equation. Should be possible to work it out using Lorentz invariance or contraction or something similar.</p>
<hr>
<p>Per the answer by <a href="http://physics.stackexchange.com/users/1257/helder-velez">Helder Velez</a>, <a href="http://physics-quest.org/Book_Chapter_Non_Simultaneity.pdf" rel="nofollow">Chapter 4 of Hans de Vries's book</a> has the following useful diagram:<br>
<img src="http://i.stack.imgur.com/gC4Gu.jpg" alt="HansEllipse"></p> | g1284 | [
0.011028357781469822,
0.019559897482395172,
0.0070927864871919155,
-0.0027007623575627804,
0.05287537723779678,
-0.017034394666552544,
0.01908634789288044,
0.01709626242518425,
-0.009258894249796867,
0.0007976543856784701,
0.04337571933865547,
0.05755012482404709,
0.06125272810459137,
-0.0026208392810076475,
0.028736639767885208,
-0.008815525099635124,
0.06401906907558441,
-0.05301592871546745,
0.04490906745195389,
0.040151990950107574,
0.07597923278808594,
0.01620950549840927,
-0.0034302701242268085,
-0.04920784756541252,
-0.011135243810713291,
0.01097024418413639,
0.07744774967432022,
-0.050523851066827774,
-0.06920448690652847,
-0.01935270056128502,
0.02105848863720894,
-0.004356013610959053,
-0.019708335399627686,
-0.03017870895564556,
0.027579162269830704,
-0.032640669494867325,
-0.029627148061990738,
0.06035272032022476,
0.02372080646455288,
0.04823319613933563,
-0.02858523093163967,
0.040322769433259964,
0.001795856631360948,
-0.008398712612688541,
0.07330463826656342,
-0.04844462871551514,
0.010210221633315086,
0.008639010600745678,
-0.015201972797513008,
-0.004969587083905935,
-0.025246866047382355,
0.01773201860487461,
0.003141068620607257,
-0.033633384853601456,
0.025049634277820587,
-0.009233105927705765,
0.022949211299419403,
-0.0072797308675944805,
0.052155353128910065,
-0.012933772057294846,
-0.0375741645693779,
0.0140445027500391,
-0.0039755734615027905,
-0.026641301810741425,
0.02949262224137783,
0.009288878180086613,
-0.015886317938566208,
0.031413327902555466,
0.0069864895194768906,
-0.05643148720264435,
0.013689201325178146,
-0.00641744676977396,
-0.030530311167240143,
-0.02032671496272087,
-0.03364311903715134,
0.010568264871835709,
0.023493435233831406,
-0.010333464480936527,
0.008565481752157211,
0.023452885448932648,
-0.030019685626029968,
-0.04955177754163742,
0.011289600282907486,
0.0361860990524292,
0.09221871197223663,
-0.019789403304457664,
0.03547503799200058,
0.04055573791265488,
-0.04237936809659004,
-0.0649513453245163,
-0.012819105759263039,
-0.052238449454307556,
0.05393661558628082,
0.026470448821783066,
-0.0004280424618627876,
-0.06586027890443802,
-0.034276332706213,
0.008919190615415573,
-0.03855698183178902,
0.013561725616455078,
-0.039212144911289215,
-0.047203708440065384,
-0.027324441820383072,
0.018344121053814888,
-0.015204723924398422,
-0.021014854311943054,
0.010303273797035217,
0.0006010663928464055,
-0.05754934251308441,
-0.02935795485973358,
0.010328502394258976,
-0.14013263583183289,
0.06407570093870163,
-0.0366690494120121,
-0.039859842509031296,
-0.05422750115394592,
0.050499673932790756,
-0.03134066238999367,
-0.001893555629067123,
0.10101490467786789,
0.06147202104330063,
0.036516811698675156,
-0.015607576817274094,
0.05209614336490631,
-0.013593455776572227,
-0.031230708584189415,
-0.03653192147612572,
-0.04919328913092613,
0.040764372795820236,
-0.040134742856025696,
-0.018689438700675964,
0.03012320213019848,
0.029329633340239525,
0.0724816620349884,
-0.016898950561881065,
0.02180139720439911,
0.041207801550626755,
-0.02950715646147728,
-0.04860273376107216,
-0.004864050075411797,
0.09038659930229187,
-0.017914654687047005,
0.056302640587091446,
-0.02749629318714142,
-0.023608217015862465,
0.0012321495451033115,
-0.008057189173996449,
0.009241735562682152,
0.10197842866182327,
-0.05656260997056961,
0.011875773780047894,
0.06227559968829155,
-0.027129603549838066,
0.0036107406485825777,
0.01086402777582407,
-0.019222097471356392,
0.022503238171339035,
0.020668724551796913,
-0.04330073669552803,
0.05305320769548416,
0.10674037039279938,
0.013859344646334648,
-0.05350838601589203,
0.006505698896944523,
-0.006928158923983574,
0.04737360402941704,
-0.006854953244328499,
-0.02408488281071186,
-0.0028292073402553797,
-0.05341021344065666,
-0.04575740545988083,
-0.058756474405527115,
-0.0002258955646539107,
0.02668941020965576,
-0.0016523436643183231,
0.0016174425836652517,
0.023983756080269814,
-0.010458131320774555,
-0.07636874914169312,
0.025670250877738,
-0.03603192791342735,
-0.04633352905511856,
0.031344909220933914,
0.016311774030327797,
0.02916295826435089,
-0.04279775172472,
-0.016603007912635803,
0.00016931058780755848,
-0.05369213595986366,
-0.0030867953319102526,
0.0650552287697792,
0.002584983129054308,
-0.0172060988843441,
0.012888025492429733,
0.022786302492022514,
-0.01019709650427103,
0.047548808157444,
-0.01992032490670681,
-0.024983229115605354,
0.07401255518198013,
0.03974434360861778,
0.024378005415201187,
0.04313727840781212,
-0.005482934415340424,
0.03311259672045708,
-0.004946365486830473,
-0.014875104650855064,
-0.01815369352698326,
-0.02822558395564556,
0.05673728138208389,
0.0758538767695427,
0.014146181754767895,
-0.01810542680323124,
-0.031647395342588425,
0.005385587457567453,
0.05392320081591606,
-0.02000473625957966,
0.0020960508845746517,
-0.03478073328733444,
0.05562000349164009,
-0.024707527831196785,
0.002081839134916663,
-0.003943833522498608,
-0.060763198882341385,
0.02327137067914009,
-0.044392138719558716,
-0.04011347517371178,
0.006600657943636179,
0.05492570251226425,
0.0004676415410358459,
-0.009115136228501797,
0.048969972878694534,
-0.017616763710975647,
0.037298258394002914,
0.04070354625582695,
-0.027926785871386528,
0.01150408387184143,
0.04101651534438133,
0.010565879754722118,
-0.0005361634539440274,
0.027667786926031113,
0.005977953784167767,
-0.03536588326096535,
-0.05072314292192459,
0.020080028101801872,
-0.00029191060457378626,
0.09316712617874146,
-0.008092157542705536,
-0.008565401658415794,
0.046295154839754105,
0.0721440240740776,
-0.011956360191106796,
-0.00885565485805273,
-0.0191670972853899,
0.06245678663253784,
0.024147827178239822,
-0.0251358300447464,
0.0807248130440712,
-0.03626192733645439,
0.02636265754699707,
-0.05292230471968651,
0.01062636636197567,
-0.003650941187515855,
-0.009234383702278137,
0.002416787203401327,
0.003705748124048114,
0.015354025177657604,
0.02370183728635311,
0.029970023781061172,
-0.008051613345742226,
-0.033520620316267014,
0.03918921574950218,
0.004516079556196928,
-0.00220153434202075,
-0.017967689782381058,
-0.017851106822490692,
-0.024667944759130478,
-0.03472701832652092,
-0.019996238872408867,
0.022801710292696953,
0.0236181803047657,
0.020326774567365646,
-0.07380782812833786,
-0.017293598502874374,
0.009603265672922134,
-0.049921732395887375,
0.013105425052344799,
0.04395388439297676,
-0.014089079573750496,
0.010256660170853138,
0.00451681250706315,
0.04209887236356735,
0.004359823185950518,
-0.028908006846904755,
-0.0014878740767017007,
0.03579501807689667,
0.04627593606710434,
0.0027184300124645233,
-0.00012149733811384067,
0.0028696879744529724,
0.0068612671457231045,
0.030410919338464737,
0.03673076257109642,
0.07842151820659637,
-0.010985503904521465,
-0.011997438035905361,
-0.06066952645778656,
-0.035394929349422455,
0.05840950086712837,
-0.006157029420137405,
0.030442463234066963,
-0.004499723669141531,
0.008446348831057549,
0.06553247570991516,
-0.025576438754796982,
0.006028034724295139,
-0.039065565913915634,
0.011957773938775063,
0.049246884882450104,
0.023326091468334198,
0.03579968586564064,
0.012189052999019623,
0.005631753709167242,
-0.01028483361005783,
0.055106449872255325,
0.002264217007905245,
-0.008176702074706554,
-0.009495502337813377,
-0.039436135441064835,
-0.02750966139137745,
0.004758949391543865,
0.015309328213334084,
0.03604738414287567,
0.005623307544738054,
-0.014964746311306953,
-0.00903458520770073,
-0.029826801270246506,
0.0023080711252987385,
0.05322348698973656,
-0.003616892732679844,
0.02654757909476757,
-0.03344383090734482,
-0.003565720282495022,
0.018562842160463333,
0.02400599606335163,
-0.00156997365411371,
0.03131161630153656,
-0.04319635033607483,
0.004980495665222406,
-0.010938752442598343,
0.023419201374053955,
-0.07759789377450943,
0.039959657937288284,
-0.0344180203974247,
0.005630697123706341,
-0.05036107823252678,
0.010921462439000607,
-0.0070555624552071095,
0.07584366947412491,
-0.034742750227451324,
0.010867821052670479,
-0.020648933947086334,
-0.06638453155755997,
0.04910111054778099,
-0.008892941288650036,
-0.010548708960413933,
0.02435014396905899,
0.03127641975879669,
-0.03327677398920059,
0.004005043767392635,
-0.009660327807068825,
0.008963258005678654,
-0.019286086782813072,
-0.02177261747419834,
0.04204665124416351,
-0.04417005926370621,
0.035072728991508484,
-0.0030570258386433125,
-0.005160144064575434,
0.041236281394958496,
0.03205392509698868,
0.04668189957737923,
-0.02396569401025772,
0.011280843988060951,
0.003325975500047207,
0.026353031396865845,
-0.025271806865930557,
-0.029696470126509666,
0.028434278443455696,
-0.008122173137962818,
0.00948474183678627,
-0.020502272993326187,
0.007591573055833578,
-0.056286897510290146,
-0.0019731668289750814,
-0.014195905067026615,
0.06949342787265778,
0.007143678143620491,
-0.039091695100069046,
-0.016762400045990944,
-0.032683536410331726,
0.017738668248057365,
-0.01044838223606348,
0.018176643177866936,
-0.07921445369720459,
-0.08816330879926682,
0.006654685363173485,
-0.06399695575237274,
0.01035840343683958,
-0.028452536091208458,
-0.01819007657468319,
-0.02290898747742176,
-0.0016510928981006145,
-0.03632344678044319,
0.05219594016671181,
0.05617852509021759,
-0.002933790907263756,
0.009534449316561222,
0.002692730398848653,
0.023900626227259636,
-0.02124682627618313,
0.06476560980081558,
0.06342585384845734,
-0.010125607252120972,
0.05451835319399834,
0.06492124497890472,
0.04966326057910919,
0.003921056166291237,
0.01741560362279415,
-0.0005049651954323053,
0.026051172986626625,
0.019623082131147385,
-0.012959584593772888,
0.02663589082658291,
-0.052223920822143555,
0.028870193287730217,
-0.014487415552139282,
0.07616846263408661,
0.047422487288713455,
-0.0059147183783352375,
0.019055327400565147,
-0.006608455441892147,
0.016601132228970528,
-0.05001292750239372,
-0.04355374723672867,
0.08788815885782242,
-0.05782736837863922,
-0.021377334371209145,
-0.03348670154809952,
-0.05161914974451065,
-0.008084315806627274,
0.008963305503129959,
0.0071111456491053104,
0.07359733432531357,
-0.025090022012591362,
0.005367298144847155,
-0.053373225033283234,
0.026209691539406776,
0.0433381088078022,
-0.0036586986389011145,
0.0014750141417607665,
0.053629081696271896,
0.07040233910083771,
-0.00583144836127758,
0.02418244630098343,
0.002389016794040799,
-0.0434858575463295,
-0.032623663544654846,
-0.011141854338347912,
0.008764619939029217,
-0.017206644639372826,
0.02586139179766178,
-0.020330963656306267,
-0.02137427031993866,
-0.012085018679499626,
0.03116784058511257,
-0.005334679037332535,
-0.012823936529457569,
-0.04468804597854614,
-0.011079806834459305,
-0.09654942899942398,
-0.021197304129600525,
0.06920940428972244,
-0.01491890661418438,
0.004428722895681858,
0.04585249722003937,
-0.00965259037911892,
0.042364008724689484,
0.005871856585144997,
-0.004926682449877262,
0.01922443136572838,
-0.041962865740060806,
0.004818981979042292,
-0.02196715958416462,
0.03426505997776985,
-0.004047048278152943,
0.027361787855625153,
-0.018745368346571922,
0.029324613511562347,
0.006679194048047066,
-0.07989436388015747,
0.05543825402855873,
0.0435151681303978,
-0.005861636716872454,
-0.02814939059317112,
0.041972871869802475,
0.023445669561624527,
0.03892454877495766,
-0.021590624004602432,
0.039761021733284,
0.03258868306875229,
-0.006586540024727583,
0.026896078139543533,
0.003203533822670579,
0.02396637760102749,
-0.03161679208278656,
-0.053259242326021194,
0.03998774662613869,
0.01635090447962284,
-0.034246739000082016,
-0.027847079560160637,
-0.007443858310580254,
-0.007510792929679155,
-0.05217258632183075,
0.02699846401810646,
0.025973742827773094,
-0.02139819972217083,
0.0016337892739102244,
0.02898488938808441,
0.013118574395775795,
0.0022757849656045437,
-0.017452610656619072,
0.06570715457201004,
-0.047546759247779846,
-0.008119978941977024,
0.00043984674266539514,
0.008454089984297752,
0.00858516525477171,
0.028803391382098198,
-0.00717161362990737,
-0.04998800903558731,
0.028518198058009148,
0.03145326301455498,
0.0880754142999649,
-0.011051267385482788,
-0.01570853218436241,
-0.03793186694383621,
0.0071950131095945835,
0.017626222223043442,
-0.023806273937225342,
-0.020686795935034752,
0.032432179898023605,
-0.011846338398754597,
0.003432694124057889,
-0.012458931654691696,
0.017955511808395386,
-0.01744319312274456,
-0.07770407199859619,
-0.052465714514255524,
-0.06640104204416275,
-0.023570187389850616,
-0.012787122279405594,
0.04237455502152443,
0.03131662309169769,
-0.022201817482709885,
-0.04474799707531929,
0.016926618292927742,
-0.031142612919211388,
0.10441607236862183,
0.021076766774058342,
-0.023329976946115494,
-0.019813263788819313,
-0.017715144902467728,
-0.008335312828421593,
-0.006559508386999369,
-0.033070050179958344,
0.0346539206802845,
-0.030445776879787445,
-0.014064038172364235,
-0.006970614660531282,
0.007482460699975491,
0.03261158987879753,
0.005676813889294863,
-0.04807586222887039,
-0.041836753487586975,
0.012630559504032135,
-0.004784685559570789,
0.035863615572452545,
0.0011730121914297342,
-0.041544459760189056,
0.018987931311130524,
-0.03547941893339157,
-0.03230317309498787,
-0.050742313265800476,
-0.08302152901887894,
0.04154173657298088,
-0.005736986640840769,
0.02009710669517517,
-0.04431687295436859,
0.03225068375468254,
-0.07392556220293045,
0.0014582620933651924,
0.0430278405547142,
-0.0024464197922497988,
0.03629531338810921,
-0.015807928517460823,
-0.0894935131072998,
0.013126891106367111,
-0.005083397030830383,
-0.038727592676877975,
0.009588473476469517,
0.038912542164325714,
-0.018103523179888725,
0.001818095101043582,
-0.0362468920648098,
0.021813955157995224,
-0.02527550980448723,
0.003826022846624255,
0.02461664006114006,
0.006174044217914343,
0.023962827399373055,
-0.0014120226260274649,
0.010852317325770855,
-0.038054291158914566,
-0.025037363171577454,
0.015619260258972645,
-0.07315246760845184,
0.016495488584041595,
-0.0071215215139091015,
-0.030824581161141396,
0.005935212597250938,
-0.06996847689151764,
-0.019254054874181747,
0.07172910869121552,
0.07642457634210587,
0.00040675202035345137,
-0.006727262400090694,
0.03956393525004387,
0.02271345630288124,
0.04315554350614548,
0.022462135180830956,
-0.026747481897473335,
-0.011072886176407337,
-0.014075066894292831,
-0.05440673604607582,
-0.016368331387639046,
0.017444532364606857,
-0.01346425712108612,
-0.09550615400075912,
-0.018174849450588226,
0.016922717913985252,
-0.02336844429373741,
-0.01886083371937275,
0.013574344106018543,
-0.046601034700870514,
0.007832802832126617,
-0.031163915991783142,
0.046590641140937805,
0.008072758093476295,
-0.08431392163038254,
-0.06794363260269165,
-0.05437648668885231,
-0.023709401488304138,
-0.05162091553211212,
-0.00043062755139544606,
0.012244736775755882,
-0.0012547692749649286,
0.008672571741044521,
-0.0519905686378479,
0.03184584528207779,
-0.024452591314911842,
0.006206190213561058,
-0.01515315193682909,
0.020196497440338135,
-0.027264226227998734,
-0.030023204162716866,
-0.024563631042838097,
-0.013339651748538017,
-0.029440656304359436,
-0.03347986564040184,
0.010721007362008095,
0.10338978469371796,
0.020178072154521942,
0.016764363273978233,
-0.05866656079888344,
-0.0029028989374637604,
-0.05354073643684387,
-0.005090678110718727,
-0.00539875915274024,
-0.016041403636336327,
-0.013913992792367935,
0.08789989352226257,
-0.05371394753456116,
0.0184879582375288,
-0.0033878523390740156,
0.019113129004836082,
0.046374935656785965,
0.021233748644590378,
-0.004126930609345436,
-0.0413559228181839,
-0.05087020993232727,
0.03687990829348564,
0.020035095512866974,
0.041682176291942596,
0.03430301696062088,
-0.013135557062923908,
-0.04722302034497261,
-0.025839421898126602,
-0.0059145595878362656,
0.03293998911976814,
0.020968370139598846,
0.03352614492177963,
0.032037727534770966,
-0.07098856568336487,
-0.06116596609354019,
0.0027786283753812313,
0.008707207627594471,
0.03840487822890282,
-0.040888719260692596,
-0.0014531293418258429,
-0.04189254343509674,
0.020534325391054153,
0.008981761522591114,
-0.023773636668920517,
0.03899088874459267,
-0.06126802787184715,
0.0015427963808178902,
-0.02653481811285019,
0.0012838855618610978,
-0.08472835272550583,
0.027131948620080948,
0.05558512359857559,
-0.055300597101449966,
0.046591706573963165,
-0.02978559397161007,
0.040585801005363464,
-0.07310908287763596,
-0.02953164279460907,
-0.04446398466825485,
-0.006621671374887228,
-0.04420115426182747,
-0.07379285991191864,
-0.018675057217478752,
-0.03165079653263092,
0.014001753181219101,
-0.03960445523262024,
-0.0069544618017971516,
-0.018143657594919205,
0.05277666077017784,
0.046860795468091965,
0.048676252365112305,
0.016280191019177437,
-0.02088341861963272,
0.013679479248821735,
0.003835466457530856,
0.0029501826502382755,
0.028881939128041267,
-0.030190905556082726,
-0.045444685965776443,
-0.021939340978860855,
-0.04425862431526184,
-0.03543754667043686,
0.014114981517195702,
0.038022708147764206,
-0.04216860234737396,
-0.01500353217124939,
-0.023754332214593887,
0.04327836632728577
] |
<p>It would be nice to have a cute method that uses Lorentz transformations of basis vectors by exponential transformation using gamma matrices. To avoid confusion, let's assume -+++ signature. Given $\gamma_\mu$ as gamma matrices that satisfy ${\rm tr}(\gamma_\mu\gamma_\nu) = 4\eta_{\mu\nu}$, then we have ${\rm tr}(\gamma'_\mu\gamma'_\nu) = 4\eta_{\mu\nu}$ if we put:<br>
$\gamma'_\mu = \exp(-A)\gamma_\mu\exp(+A)$<br>
where $A$ is any matrix.</p>
<p>Boosts and rotations use $A$ as a bivector. For example, with $\alpha$ a real number, $A=\alpha\gamma_0\gamma_3$ boosts in the z direction while $A=\alpha\gamma_1\gamma_2$ gives a rotation around the z axis.</p>
<p>Solving for the value of $\alpha$ that gives a boost with velocity $\beta = v/c$ appears to be straightforward. But how to do the rotations?</p>
<p>And by the way, what happens when you generalize $A$ to be something other than bivectors?</p> | g1285 | [
-0.0471917986869812,
-0.010422799736261368,
0.0029681127052754164,
-0.06332078576087952,
0.041074566543102264,
-0.04928744584321976,
0.06340228021144867,
-0.02743455208837986,
0.010962558910250664,
0.011576557531952858,
-0.009581776335835457,
0.034709393978118896,
0.05550932139158249,
0.02643551304936409,
-0.01548756007105112,
-0.024828270077705383,
0.024406511336565018,
0.016415707767009735,
-0.005420115776360035,
-0.02762262523174286,
-0.016126753762364388,
-0.0010735859395936131,
0.044317252933979034,
-0.02915612794458866,
0.05674733221530914,
-0.017037885263562202,
-0.015362394042313099,
0.01006633322685957,
-0.02626919001340866,
0.0171954408288002,
-0.01905231364071369,
-0.006953171920031309,
0.030074775218963623,
0.021956056356430054,
0.025191154330968857,
0.01829116977751255,
0.020170200616121292,
0.0118088498711586,
0.02954651229083538,
-0.010973559692502022,
-0.013921071775257587,
-0.011723928153514862,
0.0022528497502207756,
0.07501312345266342,
0.014375370927155018,
0.004696929361671209,
0.017092783004045486,
-0.008683126419782639,
-0.01434510201215744,
0.07012429088354111,
-0.014578108675777912,
-0.005407539661973715,
0.011780966073274612,
-0.041275326162576675,
-0.03872927650809288,
0.08222596347332001,
0.06336289644241333,
-0.018986182287335396,
-0.006136967334896326,
0.07857542484998703,
-0.03956819325685501,
-0.0784626305103302,
0.038878846913576126,
-0.03732890263199806,
-0.0057884082198143005,
-0.02281404845416546,
-0.016723554581403732,
0.027371279895305634,
-0.02440103143453598,
0.016373546794056892,
-0.016618484631180763,
0.03876546025276184,
0.05136816203594208,
-0.0009697313653305173,
-0.027923880144953728,
0.023442640900611877,
0.003539350116625428,
0.01454657968133688,
0.03031507320702076,
0.002951831789687276,
-0.002866301452741027,
-0.012855671346187592,
0.006794235669076443,
-0.02436206303536892,
0.019190911203622818,
0.01801835373044014,
0.010134976357221603,
0.07434836030006409,
0.025873437523841858,
-0.040114011615514755,
0.015728728845715523,
-0.02255767397582531,
0.02826840989291668,
0.013325771316885948,
-0.01374737173318863,
-0.03039071522653103,
0.0021213919389992952,
-0.019026268273591995,
0.03329462185502052,
-0.0708998367190361,
0.036961205303668976,
0.057768210768699646,
-0.04085772857069969,
0.027726750820875168,
-0.07565941661596298,
-0.002995067508891225,
0.03370847925543785,
0.00877788383513689,
-0.026994580402970314,
0.02830313891172409,
-0.0810864195227623,
-0.02671944908797741,
0.03019242361187935,
-0.021709632128477097,
-0.08032674342393875,
-0.025654075667262077,
0.000458539929240942,
0.005899303592741489,
-0.020561594516038895,
0.05518985167145729,
0.014074302278459072,
0.02078176848590374,
-0.026897776871919632,
0.008312673307955265,
0.0203718189150095,
0.020157363265752792,
-0.04186796396970749,
0.007149950601160526,
0.029801078140735626,
-0.0879381075501442,
0.04907047376036644,
-0.028804508969187737,
0.024843063205480576,
0.025660837069153786,
-0.005490305367857218,
-0.002376544987782836,
-0.022295471280813217,
0.05525832995772362,
0.037523675709962845,
0.015231932513415813,
-0.022239290177822113,
-0.05371705815196037,
0.006570187397301197,
-0.005488187540322542,
0.005955416243523359,
0.021970154717564583,
-0.018741227686405182,
-0.028154179453849792,
0.058699775487184525,
0.019551152363419533,
-0.05302668362855911,
0.06313216686248779,
-0.02038559876382351,
0.03046277165412903,
0.07171350717544556,
0.0066388193517923355,
0.008720949292182922,
-0.020565567538142204,
-0.02140076830983162,
0.025653818622231483,
0.05260463431477547,
-0.02948429435491562,
0.017131397500634193,
-0.0332675464451313,
-0.006800441071391106,
0.03161640837788582,
-0.02537064254283905,
-0.023003751412034035,
-0.06024628505110741,
0.02949998900294304,
-0.07329574972391129,
-0.05916399136185646,
0.04942105710506439,
-0.0386434830725193,
-0.02179151214659214,
0.050365157425403595,
-0.09510745853185654,
-0.06403594464063644,
-0.008227972313761711,
-0.02434896118938923,
-0.002566572045907378,
-0.03668443113565445,
0.031040165573358536,
0.012631649151444435,
0.02580724097788334,
-0.01137044932693243,
-0.014055421575903893,
0.04964069649577141,
-0.05876842513680458,
0.002865544520318508,
0.07072237133979797,
0.011409933678805828,
0.011578569188714027,
-0.012329782359302044,
0.0027341966051608324,
0.00021788325102534145,
0.030466990545392036,
-0.06240665912628174,
-0.08755181729793549,
0.09838972985744476,
-0.012947854585945606,
0.040615521371364594,
0.05584096536040306,
-0.007063054479658604,
-0.03146429732441902,
-0.0032446503173559904,
0.004027404822409153,
0.0030628610402345657,
0.030604738742113113,
-0.018247390165925026,
0.05798794701695442,
-0.007427171338349581,
0.001787698594853282,
-0.030848832800984383,
-0.05832991376519203,
-0.05210932344198227,
-0.01669144630432129,
-0.03476110100746155,
-0.05734872445464134,
0.022796327248215675,
0.0016263625584542751,
-0.015685953199863434,
-0.017123332247138023,
0.01514288317412138,
-0.0435364656150341,
-0.01453095767647028,
0.019686682149767876,
-0.03329256549477577,
0.05046459659934044,
0.012774351984262466,
-0.06018934026360512,
0.0804671198129654,
-0.028855517506599426,
-0.00795453879982233,
0.03162965551018715,
-0.02290082722902298,
-0.01852547749876976,
0.05702858790755272,
-0.02185169979929924,
0.015909094363451004,
0.0724901482462883,
-0.008885429240763187,
-0.00033916643587872386,
-0.021267183125019073,
0.023631155490875244,
-0.019172070547938347,
0.03860278055071831,
0.04473205655813217,
-0.0011769543634727597,
-0.030615676194429398,
0.00954018160700798,
-0.014429519884288311,
-0.019560130313038826,
-0.006598828360438347,
-0.022393126040697098,
0.0022656472865492105,
-0.022958701476454735,
0.022712811827659607,
-0.008707055822014809,
0.027526775375008583,
-0.036167047917842865,
-0.00960738118737936,
-0.03564394637942314,
0.01091468520462513,
0.018447861075401306,
0.026061322540044785,
-0.02854989282786846,
0.021758219227194786,
-0.05035169795155525,
0.024492859840393066,
-0.01446673832833767,
0.0343620739877224,
0.05973578616976738,
-0.019718443974852562,
-0.026178941130638123,
-0.02186478115618229,
0.016877567395567894,
-0.008332250639796257,
-0.043192058801651,
0.013618875294923782,
-0.01894771121442318,
-0.0326508954167366,
-0.01672537624835968,
0.013863657601177692,
-0.019736947491765022,
-0.004245838616043329,
0.02294960804283619,
0.07863584905862808,
-0.030110575258731842,
0.009005207568407059,
-0.027558583766222,
0.012187317945063114,
0.006560852751135826,
-0.10262802243232727,
0.034734487533569336,
0.026888761669397354,
0.10641597956418991,
-0.02682757005095482,
0.003323857905343175,
0.07181590050458908,
0.00040757740498520434,
-0.010965054854750633,
0.04460098594427109,
-0.016746843233704567,
0.03180154040455818,
-0.01455756463110447,
-0.08722302317619324,
-0.011777415871620178,
-0.023286597803235054,
0.032354630529880524,
0.00474677886813879,
-0.039172835648059845,
-0.0307622030377388,
0.023409342393279076,
-0.012298156507313251,
-0.020938724279403687,
-0.044362910091876984,
-0.04698898270726204,
0.035772934556007385,
-0.005287451669573784,
-0.08534642308950424,
-0.07262992858886719,
0.015538700856268406,
0.05931498855352402,
0.04507365822792053,
0.014189250767230988,
-0.020076340064406395,
0.025890370830893517,
-0.03039519675076008,
-0.008635083213448524,
0.03209635242819786,
0.014813264831900597,
0.04574917256832123,
0.02647853083908558,
-0.00582513865083456,
0.03239167481660843,
-0.025567980483174324,
0.00444635609164834,
-0.05949932709336281,
-0.02654854953289032,
-0.04730667918920517,
-0.04426657035946846,
0.0174612607806921,
-0.017299769446253777,
0.04006536304950714,
-0.023058483377099037,
0.026269974187016487,
-0.028115855529904366,
-0.0014050716999918222,
0.027746526524424553,
-0.03987718001008034,
-0.0006737772491760552,
0.020186366513371468,
0.00359664810821414,
0.0241305660456419,
-0.018496301025152206,
0.013628793880343437,
0.054274871945381165,
0.03158502280712128,
-0.020346740260720253,
-0.013239155523478985,
-0.007507010828703642,
-0.020692184567451477,
-0.006260189227759838,
-0.03192073106765747,
0.022503525018692017,
-0.013483436778187752,
0.03272267058491707,
-0.04865903779864311,
0.022343501448631287,
0.041113175451755524,
-0.02842680737376213,
0.04041125625371933,
0.003153769765049219,
-0.08765329420566559,
-0.040306590497493744,
0.0046520838513970375,
-0.0018520393641665578,
-0.010344292968511581,
0.0573531873524189,
-0.001987545983865857,
-0.034258633852005005,
0.09075380861759186,
0.018957234919071198,
-0.014511889778077602,
0.02402137964963913,
-0.0040018875151872635,
0.07073474675416946,
0.011163456365466118,
-0.011068380437791348,
0.03121686354279518,
0.05712202563881874,
0.05195160210132599,
0.026688653975725174,
-0.007990526035428047,
-0.10874480754137039,
0.015108120627701283,
-0.04200511798262596,
-0.054527442902326584,
0.06841010600328445,
-0.04534851759672165,
0.032288242131471634,
0.04213010147213936,
-0.054338082671165466,
-0.0480472631752491,
0.013380159623920918,
0.020753484219312668,
0.05543193966150284,
0.06823329627513885,
-0.026025934144854546,
-0.0009595860028639436,
0.006062016356736422,
0.11908698827028275,
-0.07623061537742615,
0.08754526078701019,
0.0197024904191494,
-0.019850900396704674,
-0.01539281290024519,
-0.01810942031443119,
0.005390985868871212,
-0.03691304475069046,
0.04537878558039665,
0.04729873314499855,
0.014790661633014679,
-0.001318110735155642,
0.0018768622539937496,
0.1090342327952385,
0.03386664763092995,
0.022400982677936554,
-0.03677031770348549,
0.03569573536515236,
0.05993247777223587,
-0.011198718100786209,
0.0328960046172142,
-0.038513779640197754,
-0.011162848211824894,
0.0026038875803351402,
0.01482344325631857,
0.051717594265937805,
-0.03429830074310303,
0.05127713829278946,
-0.014539653435349464,
0.02509116940200329,
-0.019522972404956818,
-0.06734649091959,
0.04894780367612839,
0.018864281475543976,
-0.04014941304922104,
0.00688100466504693,
0.06797250360250473,
-0.03132132813334465,
0.03041061758995056,
0.0073778978548944,
0.010817602276802063,
0.015102769248187542,
0.010081651620566845,
-0.03328107297420502,
0.028354879468679428,
0.028479965403676033,
0.06793516129255295,
-0.04463544115424156,
-0.012286032550036907,
-0.02534785121679306,
-0.0034541452769190073,
0.015605342574417591,
0.0029402615036815405,
-0.008059308864176273,
0.033972520381212234,
-0.00162130210082978,
0.01570799946784973,
0.01665894128382206,
0.00437556579709053,
-0.015159247443079948,
0.02069917507469654,
-0.019506758078932762,
0.06767498701810837,
-0.04236908629536629,
0.00357411103323102,
-0.0578206405043602,
-0.030764257535338402,
-0.004525844007730484,
-0.03546425327658653,
0.007057014387100935,
-0.039486609399318695,
0.004367318470031023,
-0.0013161274837329984,
0.0020478072110563517,
-0.04278774932026863,
0.04769406467676163,
-0.002454368630424142,
0.01268388144671917,
0.06258583068847656,
0.005538418889045715,
-0.01849883794784546,
-0.03477692976593971,
-0.03066822700202465,
-0.01325294654816389,
-0.037217795848846436,
-0.00039140519220381975,
-0.008047978393733501,
-0.02401992492377758,
0.03276165574789047,
-0.0080180112272501,
0.018208179622888565,
0.009615345858037472,
-0.04052135348320007,
0.046071942895650864,
0.06591861695051193,
-0.019001277163624763,
0.01333552598953247,
-0.05515453591942787,
0.016262760385870934,
0.038786739110946655,
-0.01867893524467945,
-0.03838636726140976,
-0.015436765737831593,
-0.015159226953983307,
-0.032107144594192505,
0.026037124916911125,
-0.05506407842040062,
-0.00342578929848969,
-0.03307225927710533,
-0.03079252503812313,
-0.03867116570472717,
0.028337683528661728,
0.06299012154340744,
-0.07421000301837921,
-0.04249794781208038,
-0.0060083018615841866,
0.0015102265169844031,
-0.04025665670633316,
-0.09000025689601898,
0.004084897693246603,
0.015931274741888046,
0.018508749082684517,
-0.03269852697849274,
0.02159927971661091,
-0.04958268627524376,
-0.00906115211546421,
-0.005950247403234243,
-0.02011430449783802,
-0.012969634495675564,
0.033021144568920135,
0.05979963764548302,
0.00521718617528677,
0.00013824373309034854,
0.012851892039179802,
0.007371219340711832,
0.0023175596725195646,
0.013026214204728603,
-0.06225813552737236,
-0.02858065254986286,
0.01834065280854702,
-0.0009559640311636031,
-0.02332981675863266,
-0.01210393663495779,
-0.034558411687612534,
-0.053195249289274216,
-0.04926459118723869,
0.06506269425153732,
0.0129207419231534,
-0.004549731500446796,
0.055408988147974014,
0.028221148997545242,
0.01162021141499281,
0.008556589484214783,
-0.014089034870266914,
0.0017323076026514173,
0.033517297357320786,
0.0012548235245049,
-0.026193765923380852,
-0.013453265652060509,
-0.000049536432925378904,
0.0876193717122078,
-0.012205425649881363,
0.03720363229513168,
0.025878658518195152,
-0.004918831400573254,
-0.08008146286010742,
0.02529962733387947,
-0.012939391657710075,
0.0544947050511837,
-0.026744091883301735,
0.025844454765319824,
-0.0362381711602211,
-0.036341991275548935,
-0.07766874134540558,
-0.00859122071415186,
-0.030479691922664642,
0.001443746848963201,
-0.050980135798454285,
0.00789028313010931,
-0.06803115457296371,
-0.036388080567121506,
-0.07636494934558868,
-0.01312029268592596,
0.003318272763863206,
-0.011424185708165169,
0.036935847252607346,
0.00291273626498878,
0.023657364770770073,
-0.004406520631164312,
-0.00901674572378397,
0.01711670123040676,
-0.046820368617773056,
-0.013552773743867874,
-0.027046404778957367,
0.03016090765595436,
0.03956673666834831,
-0.04828408360481262,
-0.029062563553452492,
0.022637438029050827,
-0.054508186876773834,
0.03999435901641846,
0.03952757641673088,
-0.026900727301836014,
-0.006592913530766964,
0.03211566060781479,
-0.006093424279242754,
0.01906806044280529,
-0.008987068198621273,
-0.005265500862151384,
0.011612246744334698,
0.03334570303559303,
0.0835895761847496,
0.04441792890429497,
0.010588672943413258,
0.03539030998945236,
-0.0025771507062017918,
-0.03692350536584854,
0.04431859776377678,
-0.00898007769137621,
-0.0056568318977952,
0.04030568152666092,
0.02330530807375908,
0.033169690519571304,
-0.026695676147937775,
0.07863028347492218,
0.004001557361334562,
0.0768081322312355,
-0.007852623239159584,
0.06843716651201248,
-0.017498614266514778,
-0.04429677873849869,
0.017243333160877228,
-0.004256479442119598,
0.022127628326416016,
-0.003512619761750102,
-0.0798141211271286,
0.03840180113911629,
0.06476245820522308,
-0.012406457215547562,
0.006666762754321098,
0.030682232230901718,
-0.08188685774803162,
-0.004487764090299606,
0.02365783229470253,
-0.0018900588620454073,
0.053836118429899216,
-0.0142099279910326,
0.02680382877588272,
-0.040135227143764496,
0.06382416188716888,
-0.018273575231432915,
0.005680676084011793,
0.00851520523428917,
-0.03894759714603424,
-0.022175665944814682,
0.042546093463897705,
0.0025596432387828827,
-0.0255571436136961,
0.004097894765436649,
-0.007980810478329659,
0.023677952587604523,
0.03613811358809471,
-0.005379160866141319,
-0.008934423327445984,
0.014990932308137417,
-0.05667087435722351,
-0.012154458090662956,
-0.02423981949687004,
0.02274104207754135,
-0.07353169471025467,
0.03415163233876228,
0.006253154017031193,
0.02099812589585781,
-0.026297930628061295,
-0.0052050198428332806,
-0.0009925850899890065,
0.01571340672671795,
-0.02951415628194809,
0.0273901354521513,
-0.03694406896829605,
0.011673483066260815,
-0.0327933244407177,
0.03541148453950882,
-0.021689126268029213,
0.01483696699142456,
-0.051544930785894394,
0.036163248121738434,
-0.029041573405265808,
-0.009113028645515442,
0.03006059303879738,
-0.015792209655046463,
-0.009771822020411491,
-0.04109648987650871,
-0.01870129443705082,
-0.03411487862467766,
-0.012319603003561497,
-0.06673918664455414,
-0.04026157781481743,
-0.024010691791772842,
-0.06971056759357452,
0.06213897094130516,
0.001623189658857882,
0.05756096914410591,
0.03386850282549858,
0.06210868060588837,
0.029987448826432228,
0.026388395577669144,
-0.025253048166632652,
-0.014305312186479568,
0.007371584884822369,
-0.02320214919745922,
-0.008890346623957157,
-0.0552038811147213,
-0.01596503145992756,
0.003958446439355612,
-0.006747571285814047,
-0.006958361715078354,
-0.01256552617996931,
-0.04978316277265549,
-0.07090307027101517,
0.06940049678087234,
-0.011498202569782734,
-0.017227258533239365,
-0.03764945641160011,
-0.058010488748550415,
0.04072611406445503,
0.006223875097930431,
-0.026216313242912292,
-0.04443702846765518,
-0.018446674570441246,
0.017932996153831482,
0.011566350236535072,
0.010195786133408546,
-0.016966169700026512,
0.014162842184305191,
-0.050061747431755066,
-0.018559154123067856,
0.012793231755495071,
0.015474838204681873,
0.022547760978341103,
0.030264724045991898,
-0.029974717646837234,
0.059817783534526825,
0.016935361549258232,
-0.02979951538145542,
0.0723685696721077,
-0.012594538740813732,
0.022464202716946602,
0.026000821962952614,
-0.0016507543623447418,
-0.012793237343430519,
0.001004891819320619,
-0.09090550243854523,
-0.05090229958295822,
0.06636638939380646
] |
<p>You may have noticed over the last few years that Moore's law is no longer applying to the real world.
This observation states that over the history of computing hardware, the number of transistors on integrated circuits doubles approximately every two years.</p>
<p>However, as microprocessors in computers have continued to become smaller, the architecture size has become incredibly small:- the new Skylake architecture to be released by Intel will use 14nm semiconductors.</p>
<p>We are beginning to reach the limit in size where the information being passed is still completely reliable.</p>
<p>Would it be reasonable to ask how much quantum tunneling would occur in a semiconductor 5nm in length? We can assume that in this CPU</p>
<p>Voltage = 1.2V
Amperage = 63A</p>
<p>I enjoy physics, but I'm not that great at it; I'd love to hear the results! Even if massive approximations!</p> | g1286 | [
-0.02484036423265934,
0.11074627935886383,
-0.002252276986837387,
0.005289653781801462,
-0.07312172651290894,
-0.06304063647985458,
0.05596569925546646,
-0.012296122498810291,
0.007099963258951902,
0.048389773815870285,
-0.029076045379042625,
0.03414196893572807,
-0.05692145228385925,
0.02089737355709076,
0.0482911691069603,
0.018041839823126793,
-0.014175228774547577,
-0.01794152893126011,
0.0386042483150959,
-0.007360673509538174,
-0.04125412181019783,
-0.02072671428322792,
-0.04436933621764183,
-0.06977095454931259,
-0.03866245225071907,
-0.019199661910533905,
-0.01752987504005432,
0.0012570950202643871,
-0.05172131583094597,
0.04391639307141304,
0.06842314451932907,
-0.06418697535991669,
0.019421372562646866,
-0.07605458050966263,
-0.08258125931024551,
-0.004952719900757074,
0.034611184149980545,
-0.03467902913689613,
0.07472992688417435,
0.012985523790121078,
0.07730453461408615,
-0.03984946757555008,
-0.012901462614536285,
0.0024271029978990555,
-0.0010146183194592595,
-0.04797891527414322,
0.0361199676990509,
-0.017823858186602592,
0.019544385373592377,
-0.040174759924411774,
-0.035716649144887924,
0.05955062061548233,
0.023728763684630394,
0.049498483538627625,
0.023572959005832672,
-0.0019195512868463993,
-0.05693943426012993,
0.005188388284295797,
-0.009690133854746819,
0.04135596379637718,
0.04028068110346794,
-0.01947871595621109,
-0.054903920739889145,
0.011170268058776855,
0.06455094367265701,
0.037434566766023636,
-0.050333842635154724,
0.0034565539099276066,
-0.026766056194901466,
0.05598670244216919,
0.028637859970331192,
-0.0807114988565445,
-0.06536132842302322,
-0.026794692501425743,
0.046245504170656204,
0.046890854835510254,
-0.02818700484931469,
0.02306422032415867,
-0.021973060443997383,
0.05281540006399155,
-0.04482444003224373,
-0.04180432856082916,
0.003595509799197316,
-0.00006533558189403266,
0.019535768777132034,
0.002523792674764991,
-0.028881993144750595,
0.014370112679898739,
-0.0430721677839756,
0.06771612167358398,
-0.03212446719408035,
0.07191670686006546,
0.051531292498111725,
-0.05059434846043587,
0.04034794867038727,
-0.0668291449546814,
0.021625757217407227,
-0.025696346536278725,
-0.05382993444800377,
0.058812111616134644,
0.012546489015221596,
-0.02471785806119442,
0.00028644694248214364,
-0.04926976561546326,
-0.0071007306687533855,
0.004851817153394222,
-0.06800742447376251,
0.010461422614753246,
0.012608046643435955,
0.08905835449695587,
-0.024184783920645714,
-0.0005395612097345293,
0.015087945386767387,
0.03731228783726692,
-0.019861916080117226,
0.018940942361950874,
-0.0209044162184,
-0.027579234912991524,
0.009846295230090618,
0.009282005950808525,
-0.04103550687432289,
0.01712372526526451,
-0.0031743934378027916,
0.029674852266907692,
0.037168364971876144,
0.07183369249105453,
-0.04085749015212059,
0.05326008424162865,
0.02054142951965332,
-0.0020112870261073112,
0.0008850161102600396,
-0.0023190800566226244,
-0.03515268862247467,
0.06183268874883652,
0.03301987051963806,
0.035469915717840195,
0.006239603273570538,
-0.026880605146288872,
-0.026644757017493248,
-0.010562974959611893,
-0.011984343640506268,
-0.03943754732608795,
0.005733328405767679,
-0.024147091433405876,
0.021080516278743744,
-0.0001992152101593092,
-0.012794220820069313,
0.07737891376018524,
-0.04480037838220596,
-0.02037661336362362,
-0.02125469036400318,
0.02937312237918377,
0.026444211602211,
-0.008251898922026157,
-0.032588232308626175,
0.03419213369488716,
0.00840429775416851,
-0.018562069162726402,
0.01858590357005596,
-0.026767319068312645,
-0.0341152623295784,
0.00900255423039198,
0.03968510031700134,
0.03368230164051056,
-0.08083638548851013,
-0.020139288157224655,
0.021594282239675522,
-0.004454356152564287,
0.04216215759515762,
-0.056494250893592834,
-0.02535797283053398,
-0.018980011343955994,
0.00695068808272481,
0.052287399768829346,
-0.06918510794639587,
0.044135745614767075,
0.03810790553689003,
-0.023784073069691658,
-0.00018450283096171916,
0.01098622102290392,
0.03031853958964348,
0.01701097935438156,
0.010450351983308792,
-0.019980400800704956,
-0.0813969299197197,
-0.007867706939578056,
0.053288307040929794,
-0.04539131745696068,
-0.034896884113550186,
-0.02740827575325966,
-0.028767239302396774,
-0.048330821096897125,
0.028533631935715675,
0.00014441007806453854,
-0.034534770995378494,
0.022997688502073288,
0.022895077243447304,
-0.028796361759305,
0.016659602522850037,
-0.0551123172044754,
-0.04309011995792389,
0.03273223713040352,
-0.043737005442380905,
-0.013883691281080246,
0.08768618851900101,
0.01933351159095764,
-0.056590571999549866,
0.014859474264085293,
-0.007378163281828165,
0.012865379452705383,
0.03045528568327427,
0.059730879962444305,
-0.018699711188673973,
0.014456058852374554,
0.03729763627052307,
0.002539107808843255,
0.05213764309883118,
-0.007536760531365871,
0.020797913894057274,
0.03985931724309921,
0.013146675191819668,
-0.019943295046687126,
0.08229909092187881,
0.023250924423336983,
0.021522333845496178,
0.0036125986371189356,
-0.042859554290771484,
0.007714184932410717,
0.020764650776982307,
-0.010596448555588722,
-0.06948307156562805,
0.02369556576013565,
-0.021871760487556458,
-0.0042925127781927586,
0.0010264819720759988,
0.0363730750977993,
-0.006008778233081102,
-0.019261114299297333,
0.03640040382742882,
-0.0016546371625736356,
0.01880328357219696,
0.05113225430250168,
-0.09066685289144516,
-0.008239557035267353,
-0.004659524653106928,
-0.043405868113040924,
-0.062154289335012436,
-0.0027859832625836134,
0.0049004931934177876,
-0.024479690939188004,
0.05229611322283745,
-0.044035401195287704,
0.006244699936360121,
0.03808687999844551,
-0.03437371551990509,
0.0016483127838000655,
0.0210171677172184,
-0.022836856544017792,
0.005811021663248539,
-0.03224584460258484,
-0.0399131141602993,
-0.01426594890654087,
0.0036395471543073654,
-0.01645796000957489,
0.024274973198771477,
-0.01163236889988184,
0.035702452063560486,
0.016574401408433914,
0.026084916666150093,
0.02902279980480671,
-0.01819784753024578,
0.022861752659082413,
-0.00409743282943964,
0.004982386250048876,
0.06778926402330399,
-0.04603040590882301,
-0.011267763562500477,
0.004648055415600538,
0.03677744045853615,
-0.026058383285999298,
-0.10852786153554916,
-0.0007127800490707159,
-0.06566902995109558,
0.018846385180950165,
0.053812574595212936,
-0.06107266992330551,
-0.009721397422254086,
-0.04328858107328415,
0.04175528138875961,
0.07605458796024323,
-0.01583012565970421,
-0.022653551772236824,
0.03267117217183113,
0.05776157230138779,
-0.018005063757300377,
0.03926009684801102,
0.013442362658679485,
-0.017601754516363144,
-0.013497577980160713,
0.059393350034952164,
-0.008945939131081104,
0.009276933036744595,
-0.006728496868163347,
0.006259610876441002,
-0.019408153370022774,
0.011023876257240772,
-0.008747588843107224,
-0.03744722157716751,
0.011953254230320454,
-0.07632320374250412,
-0.02396787703037262,
0.0011473225895315409,
0.05071002617478371,
0.00847552064806223,
0.003320585237815976,
-0.02688244916498661,
0.009971188381314278,
0.0545005202293396,
0.05851125344634056,
-0.031487174332141876,
-0.05307943373918533,
-0.06140729784965515,
0.001131362048909068,
0.022471394389867783,
0.04017933830618858,
0.005700140260159969,
0.00030073392554186285,
0.03312007337808609,
0.023272164165973663,
0.030468417331576347,
-0.0004958069766871631,
-0.06223275139927864,
-0.01743432506918907,
-0.008670978248119354,
-0.06344645470380783,
-0.06004391983151436,
0.010235999710857868,
0.045375000685453415,
0.036269087344408035,
0.020633859559893608,
-0.05004506930708885,
-0.0023810372222214937,
-0.07567733526229858,
-0.033134590834379196,
0.022663379088044167,
0.045529015362262726,
-0.04935787245631218,
0.007047164253890514,
0.013435900211334229,
0.0007178999949246645,
0.06202516332268715,
-0.07132026553153992,
-0.02988465502858162,
-0.00209264038130641,
-0.019610853865742683,
0.031886763870716095,
-0.05210450291633606,
0.0688701942563057,
0.0575077161192894,
-0.027603190392255783,
-0.006865564733743668,
-0.04987301304936409,
0.10040323436260223,
-0.036349859088659286,
-0.027828320860862732,
-0.01702045276761055,
-0.02152767777442932,
0.05045684427022934,
0.023045074194669724,
-0.04284659028053284,
-0.048328615725040436,
0.03181203082203865,
0.011911478824913502,
-0.0456574521958828,
-0.032078344374895096,
0.009306061081588268,
0.004825181793421507,
-0.0011016931384801865,
-0.01026195753365755,
0.014023599214851856,
-0.00048572052037343383,
0.04598049074411392,
-0.027209654450416565,
-0.020521065220236778,
0.004065471701323986,
-0.05554400011897087,
-0.0322696715593338,
-0.039108410477638245,
-0.030781975015997887,
-0.006514606066048145,
-0.05478561297059059,
-0.024459335952997208,
-0.024769553914666176,
0.034181613475084305,
-0.05873655900359154,
-0.040243376046419144,
0.012259862385690212,
-0.008157611824572086,
0.01793384738266468,
0.025753861293196678,
0.0279709342867136,
0.006755635142326355,
0.032613229006528854,
0.061599619686603546,
0.03675314411520958,
-0.021649420261383057,
0.06787919253110886,
0.009859777987003326,
-0.005521264858543873,
-0.013096369802951813,
-0.046899739652872086,
0.07531886547803879,
-0.02873496152460575,
-0.012946541421115398,
-0.01575317606329918,
0.0047762137837708,
-0.02052328735589981,
-0.06851218640804291,
0.015197363682091236,
0.007974503561854362,
0.006908109411597252,
0.03488203510642052,
0.033201150596141815,
0.018529320135712624,
-0.010595262981951237,
-0.04775303602218628,
-0.04139566794037819,
-0.05174308642745018,
0.037475135177373886,
-0.026508230715990067,
-0.0031765582971274853,
0.02769259363412857,
-0.028934547677636147,
0.029519828036427498,
-0.06791091710329056,
0.014196512289345264,
0.021948739886283875,
-0.008114914409816265,
-0.02581317350268364,
0.002425677143037319,
0.03242454677820206,
-0.03362828865647316,
0.023802557960152626,
0.07599899172782898,
0.014050409197807312,
0.00661493232473731,
-0.03585847094655037,
-0.027751952409744263,
-0.029937151819467545,
-0.013366014696657658,
0.003964894451200962,
0.03439494967460632,
-0.00012772403715644032,
-0.011709689162671566,
-0.03585720807313919,
-0.05022864416241646,
-0.06172500178217888,
0.025855593383312225,
0.062470898032188416,
0.0629672035574913,
-0.08811549097299576,
0.031480588018894196,
-0.04150576889514923,
0.006265632808208466,
-0.023919489234685898,
-0.023593690246343613,
0.004661915358155966,
0.042396947741508484,
-0.04342177137732506,
-0.040717076510190964,
0.032827023416757584,
-0.06095029413700104,
-0.015161672607064247,
0.060573697090148926,
0.00534258084371686,
-0.03825012966990471,
-0.013324780389666557,
0.040536753833293915,
0.05238649994134903,
-0.007397518493235111,
-0.011568884365260601,
-0.0008123530424199998,
0.03267423436045647,
0.06351954489946365,
0.02438019961118698,
0.07255194336175919,
-0.010708717629313469,
0.021397750824689865,
-0.027161099016666412,
-0.03474113717675209,
-0.0037228057626634836,
-0.033492136746644974,
-0.0125217130407691,
0.02915787696838379,
-0.021054988726973534,
-0.04590746387839317,
0.01508247945457697,
0.029139237478375435,
-0.013841455802321434,
0.0455985851585865,
0.024299362674355507,
0.008618085645139217,
0.010557805188000202,
-0.037456028163433075,
0.012219826690852642,
-0.02181016094982624,
0.011013939045369625,
-0.05066338926553726,
-0.0030672454740852118,
-0.016666533425450325,
0.03270565718412399,
0.027566971257328987,
0.009875044226646423,
-0.07071205228567123,
-0.004196967463940382,
-0.013884403742849827,
-0.04336896538734436,
-0.001038992777466774,
-0.011243210174143314,
0.03212042525410652,
0.05742679908871651,
-0.0518350787460804,
0.023271463811397552,
-0.012447800487279892,
-0.03364696726202965,
0.012601238675415516,
-0.02370968833565712,
-0.008157906122505665,
-0.01100404653698206,
-0.005270435009151697,
0.06836877763271332,
-0.02833675406873226,
-0.05487189069390297,
-0.03846878558397293,
-0.01259687077254057,
0.030173378065228462,
0.021446386352181435,
-0.027070242911577225,
0.028919776901602745,
0.042494889348745346,
-0.027444062754511833,
-0.0008222854230552912,
0.01165393553674221,
0.07796943187713623,
0.04947035014629364,
-0.01576586626470089,
0.013407602906227112,
-0.022492198273539543,
0.02358715794980526,
-0.0465046763420105,
0.007259315345436335,
0.02070963755249977,
-0.061065662652254105,
0.013666803948581219,
0.036213673651218414,
0.01804635114967823,
-0.017886323854327202,
-0.006391430739313364,
-0.004282990470528603,
0.02896926924586296,
0.03574839234352112,
-0.009701879695057869,
0.020166072994470596,
-0.03636196255683899,
-0.010961169376969337,
0.0018219691701233387,
-0.015977615490555763,
0.001484414329752326,
0.002009744755923748,
0.09925124794244766,
0.011524706147611141,
-0.0341300442814827,
-0.005157101433724165,
0.042538274079561234,
0.07274486869573593,
0.05191095545887947,
0.019792305305600166,
-0.0011253210250288248,
-0.03241969272494316,
-0.016802512109279633,
-0.03140678256750107,
0.03994337096810341,
0.04554509371519089,
-0.000051900795369874686,
0.027523566037416458,
0.04398520663380623,
-0.028867574408650398,
0.06735122948884964,
0.022771375253796577,
0.0063174134120345116,
-0.044321559369564056,
0.02646457962691784,
-0.00392896356061101,
-0.03207805007696152,
-0.031043609604239464,
-0.02840440347790718,
0.04170060530304909,
-0.05335976928472519,
0.0053430586121976376,
0.04539097473025322,
0.04508017376065254,
0.02194918692111969,
-0.024909812957048416,
-0.02327391691505909,
-0.005801238585263491,
0.01578463800251484,
-0.045109134167432785,
0.023392105475068092,
-0.024234982207417488,
-0.007212884724140167,
0.017577804625034332,
-0.06489840894937515,
0.035574086010456085,
0.00523764593526721,
-0.016220487654209137,
0.008166586048901081,
0.05350567400455475,
0.0020447534043341875,
-0.032283347100019455,
0.05015569552779198,
-0.02381313219666481,
0.010116418823599815,
-0.04806869849562645,
-0.0045251003466546535,
0.0033497163094580173,
0.03373707830905914,
0.032655760645866394,
0.019950371235609055,
0.056529633700847626,
0.030362002551555634,
0.014064128510653973,
-0.0336487740278244,
0.0555419847369194,
0.033810362219810486,
0.022855637595057487,
0.03812374547123909,
0.012478782795369625,
-0.06735820323228836,
0.001942985923960805,
-0.0018884292803704739,
0.017243294045329094,
-0.03062085062265396,
-0.036258798092603683,
0.019546180963516235,
0.025742890313267708,
-0.02505878545343876,
0.03494170680642128,
0.06454391032457352,
-0.013163191266357899,
-0.011527340859174728,
0.02448973059654236,
-0.004650136921554804,
-0.02009144052863121,
0.03707774728536606,
-0.000004247119250067044,
-0.007136777509003878,
-0.02442384697496891,
0.02076239511370659,
-0.00044597123633138835,
-0.06248614937067032,
0.019273502752184868,
-0.00925474800169468,
0.06016111373901367,
-0.038860805332660675,
0.026335440576076508,
0.0522880032658577,
0.02052481658756733,
0.012192266061902046,
0.03089367225766182,
-0.050355859100818634,
-0.010013886727392673,
-0.03719118982553482,
0.005382875446230173,
0.013423777185380459,
0.00039393347105942667,
-0.03518655523657799,
-0.03906307369470596,
-0.004803910385817289,
-0.05017149820923805,
-0.010262815281748772,
0.0767703503370285,
-0.020777810364961624,
0.021700704470276833,
-0.032469335943460464,
0.03268997743725777,
0.01529526524245739,
-0.053113315254449844,
-0.01565963216125965,
-0.03153648599982262,
0.03261938691139221,
0.007542750798165798,
-0.08417743444442749,
-0.0195884071290493,
-0.03570862486958504,
0.020279185846447945,
0.08566544204950333,
0.012883683666586876,
0.04520365223288536,
0.035943739116191864,
-0.02044796012341976,
0.013498732820153236,
0.016040639951825142,
0.029580945149064064,
-0.0005183321190997958,
0.006503887474536896,
0.010704255662858486,
-0.01065270509570837,
-0.04682457447052002,
0.00402483344078064,
-0.04037168622016907,
-0.009791149757802486,
0.015649795532226562,
0.052151553332805634,
-0.001996275270357728,
0.08419746160507202,
-0.00010228650353383273,
0.0029346770606935024,
-0.05221075564622879,
0.01455165445804596,
0.011693891137838364,
0.029086964204907417,
-0.02962307073175907,
0.03299383074045181,
0.0880490094423294,
-0.008446228690445423,
-0.057933054864406586,
-0.02031635493040085,
0.050165820866823196,
0.017186790704727173,
-0.014845798723399639,
0.013259137980639935,
0.0027673146687448025,
-0.024616101756691933,
-0.037254735827445984,
-0.04331665113568306,
-0.011809094808995724,
0.03166697546839714,
0.038556016981601715,
-0.02660701610147953,
0.017027372494339943,
-0.02501947060227394,
-0.07219229638576508,
-0.00009576521551935002,
-0.04931941255927086,
0.002713412046432495,
-0.006693016737699509,
-0.04037100076675415,
-0.04106692969799042,
-0.0038275106344372034,
-0.05525132641196251,
-0.0010648741154000163,
-0.02767617627978325,
-0.0077013433910906315,
0.06029452010989189,
0.04058361053466797,
-0.007693595718592405,
-0.00503043457865715,
0.03281556814908981,
-0.03382602334022522,
0.0469779409468174,
-0.024259621277451515,
-0.0013013493735343218,
-0.01154953334480524,
0.026577850803732872,
-0.02930930070579052,
-0.044282928109169006,
-0.023959852755069733,
-0.04096489027142525
] |
<ol>
<li><p>Where the gravitational pull of Earth exist up to? </p></li>
<li><p>What distance from Earth it will be zero?</p></li>
<li><p>How do the skydivers fly at a same altitude? </p></li>
<li><p>Won't they feel gravitational pull? </p></li>
<li><p>What is the Earth's gravitational pull?</p></li>
</ol> | g1287 | [
-0.013740264810621738,
0.06572800129652023,
-0.025433558970689774,
0.009627807885408401,
0.0003482444735709578,
0.09208517521619797,
-0.025706937536597252,
-0.008072548545897007,
-0.07938271015882492,
-0.05269914120435715,
-0.02195434458553791,
-0.006913318298757076,
0.020224979147315025,
-0.011357134208083153,
0.047368019819259644,
0.024328526109457016,
0.031860630959272385,
-0.052640803158283234,
0.07744630426168442,
-0.003140584798529744,
-0.01183154247701168,
-0.01707589440047741,
0.020768947899341583,
-0.06102178618311882,
-0.018842030316591263,
-0.028567016124725342,
-0.012055693194270134,
0.009476291947066784,
-0.13409548997879028,
0.00014859884686302394,
0.0012373084900900722,
-0.02157188393175602,
0.06894532591104507,
-0.09928461164236069,
-0.00938127376139164,
0.003021219978109002,
0.011545282788574696,
-0.016444476321339607,
-0.012362913228571415,
-0.009483332745730877,
-0.014381197281181812,
-0.0405995175242424,
-0.010145523585379124,
-0.021715067327022552,
0.02914019674062729,
-0.027416778728365898,
0.00012107309885323048,
0.0044970023445785046,
0.05530811473727226,
-0.007985616102814674,
-0.06724154204130173,
0.038940440863370895,
0.0303123090416193,
-0.002499418333172798,
-0.028164787217974663,
-0.019980162382125854,
-0.0015969779342412949,
-0.025958435609936714,
0.03053418919444084,
0.007312544155865908,
-0.002335448982194066,
-0.009181947447359562,
0.011770730838179588,
-0.017826586961746216,
0.03160950168967247,
-0.04686802998185158,
-0.02907595783472061,
-0.013764002360403538,
0.027849026024341583,
-0.017730334773659706,
0.03136801719665527,
-0.09561462700366974,
-0.016330085694789886,
0.04976574331521988,
-0.11247467249631882,
0.004739929921925068,
-0.00008933171920944005,
0.05436219647526741,
0.038945041596889496,
0.003057427704334259,
0.014780418016016483,
0.011950218118727207,
-0.0427551306784153,
-0.056914765387773514,
0.021789681166410446,
0.015555297024548054,
0.009035359136760235,
0.016093764454126358,
-0.0027836898807436228,
0.06934723258018494,
-0.01829914189875126,
0.04007719084620476,
0.03630495443940163,
0.037492331117391586,
-0.027154576033353806,
-0.024125531315803528,
0.013743560761213303,
0.062139954417943954,
-0.017432527616620064,
-0.051380548626184464,
-0.03104703687131405,
0.007027357816696167,
-0.0174261461943388,
0.032307807356119156,
0.0356639139354229,
0.027422383427619934,
0.05722328647971153,
0.0011415102053433657,
0.02721506915986538,
-0.04722531884908676,
0.005100602749735117,
-0.01735643297433853,
0.00026793271536007524,
-0.029896263033151627,
-0.012789650820195675,
-0.01814289204776287,
0.023314354941248894,
-0.00246627489104867,
0.02796313725411892,
0.03119756281375885,
0.015886979177594185,
0.016757531091570854,
0.024953067302703857,
-0.05052724853157997,
-0.016593294218182564,
-0.062335141003131866,
0.004107690881937742,
-0.035495825111866,
-0.00813502911478281,
-0.01502195093780756,
-0.015493807382881641,
-0.016581188887357712,
-0.07319557666778564,
-0.007882820442318916,
-0.03195596858859062,
-0.0029816662427037954,
-0.04377278313040733,
-0.0015173134161159396,
-0.024012520909309387,
0.017380720004439354,
-0.02510756440460682,
-0.0436372272670269,
0.0333683080971241,
-0.020650504156947136,
0.013786491937935352,
-0.01923113316297531,
-0.0014997177058830857,
0.05861911177635193,
0.0669737234711647,
-0.019505778327584267,
0.035140182822942734,
0.05870829522609711,
0.014603814110159874,
-0.06551145017147064,
0.040104784071445465,
-0.025170497596263885,
0.010643835179507732,
0.03623781353235245,
-0.007075064349919558,
0.022981742396950722,
0.027097709476947784,
-0.008719014003872871,
0.08217110484838486,
0.028473850339651108,
0.013163767755031586,
0.0633760616183281,
0.010798394680023193,
-0.040116794407367706,
0.056703098118305206,
0.025111360475420952,
-0.06532245129346848,
-0.033696018159389496,
0.05280502885580063,
0.04028148949146271,
-0.029823975637555122,
0.04356833174824715,
0.021773111075162888,
-0.03845322132110596,
0.0045981984585523605,
-0.03084397502243519,
0.05884752795100212,
0.003909256309270859,
0.06865707039833069,
0.004568517208099365,
0.009396687150001526,
-0.05036162957549095,
-0.035658396780490875,
-0.006685194093734026,
0.05037948489189148,
-0.034394681453704834,
0.015247538685798645,
0.006579801440238953,
0.021178841590881348,
-0.01452178880572319,
-0.04138156399130821,
-0.042133647948503494,
0.05631689354777336,
-0.06256859749555588,
0.0033480513375252485,
0.002059998456388712,
-0.0024728626012802124,
0.03146148473024368,
0.01421163696795702,
-0.022373611107468605,
-0.025509284809231758,
-0.012014079838991165,
0.0072447629645466805,
0.00979578960686922,
0.02289910614490509,
-0.021686498075723648,
0.015325642190873623,
-0.06993898749351501,
0.057671599090099335,
0.010430539026856422,
-0.00020302327175159007,
0.07025217264890671,
-0.05294699966907501,
0.019769247621297836,
-0.008346856571733952,
0.027616309002041817,
-0.0039541455917060375,
0.02214709296822548,
0.028519175946712494,
-0.00246775452978909,
0.025835683569312096,
-0.02827507257461548,
-0.08561095595359802,
-0.028710613027215004,
0.05912260338664055,
-0.031070634722709656,
-0.025123966857790947,
-0.006316339131444693,
-0.005543878767639399,
-0.008726204745471478,
0.023398956283926964,
0.04388078302145004,
0.023999478667974472,
0.026927312836050987,
0.005316831171512604,
0.029973097145557404,
0.012537617236375809,
-0.0035240105353295803,
0.006332381162792444,
-0.0017055076314136386,
0.04743325337767601,
-0.07958763837814331,
0.019627487286925316,
0.028602855280041695,
-0.03295104578137398,
0.010074418969452381,
0.026109615340828896,
0.0044141230173408985,
-0.027527835220098495,
0.060530755668878555,
-0.01911882497370243,
0.0015805740840733051,
0.00720226252451539,
0.06120816618204117,
-0.055148396641016006,
-0.016887104138731956,
-0.008975336328148842,
-0.020146310329437256,
0.05322132632136345,
0.012025104835629463,
-0.054900720715522766,
-0.012824295088648796,
-0.05387312173843384,
0.020754244178533554,
0.009305181913077831,
-0.057472363114356995,
-0.022233575582504272,
0.03023928962647915,
-0.006566718686372042,
0.0650632306933403,
-0.04503297433257103,
-0.03390969708561897,
0.02033371292054653,
0.017111705616116524,
0.0051739108748734,
-0.006900141015648842,
0.02349115163087845,
0.007503170054405928,
-0.030093610286712646,
0.012099051848053932,
0.04453092813491821,
-0.06120879948139191,
-0.0453018844127655,
-0.00013892725110054016,
-0.04757552966475487,
-0.02846229448914528,
0.004478069953620434,
-0.006869758944958448,
0.06358234584331512,
0.006457637529820204,
-0.030745064839720726,
0.022240575402975082,
-0.005487867631018162,
0.02068488858640194,
-0.038514427840709686,
0.013443985022604465,
-0.04385647922754288,
-0.04482073709368706,
0.006241463590413332,
0.0006744478014297783,
-0.030842415988445282,
0.020045973360538483,
0.013838466256856918,
-0.07626206427812576,
-0.03851095587015152,
-0.004296529106795788,
-0.00704630883410573,
0.07113076746463776,
0.037159521132707596,
-0.024214046075940132,
0.01030108705163002,
0.011107993312180042,
0.019914722070097923,
-0.02557516284286976,
0.009034655056893826,
0.022953448817133904,
0.033716727048158646,
-0.08495265990495682,
-0.0006424753810279071,
-0.027469180524349213,
-0.010860709473490715,
0.053186558187007904,
-0.018242018297314644,
0.03303367272019386,
-0.020647574216127396,
-0.01097542978823185,
0.002708595246076584,
0.0005201841122470796,
0.027003398165106773,
0.015313093550503254,
-0.005974587053060532,
0.020789839327335358,
-0.020144633948802948,
0.008991838432848454,
0.042694028466939926,
0.045383624732494354,
-0.05120190605521202,
0.05763503536581993,
-0.06060761958360672,
-0.0009468589560128748,
0.025946522131562233,
0.044603921473026276,
-0.005402366630733013,
0.03349359706044197,
-0.0178388599306345,
0.0027948501519858837,
0.04611735790967941,
-0.05101228505373001,
-0.011210335418581963,
-0.06092880666255951,
-0.010742539539933205,
0.031887251883745193,
-0.04059819504618645,
-0.0015742435352876782,
0.03148064389824867,
-0.01602206751704216,
0.02962421253323555,
0.06829717010259628,
0.03213004022836685,
-0.02738582342863083,
-0.0015410867054015398,
-0.06946428120136261,
-0.040298670530319214,
-0.003502658335492015,
-0.036566250026226044,
-0.0022257333621382713,
0.05350130796432495,
0.03333134204149246,
-0.024002091959118843,
-0.008686389774084091,
0.0376368910074234,
-0.06372234970331192,
0.03464462235569954,
-0.04670283570885658,
-0.02784603461623192,
0.02894759736955166,
0.012591449543833733,
0.04338150471448898,
-0.014330602250993252,
-0.03685828298330307,
0.01590869575738907,
-0.008545001968741417,
-0.03930922597646713,
0.00031756001408211887,
0.036362823098897934,
-0.007899998687207699,
0.027493959292769432,
-0.11644773185253143,
0.059102412313222885,
0.015177211724221706,
0.044887229800224304,
-0.00622041430324316,
0.02727429009974003,
0.015571662224829197,
0.008686883375048637,
0.016172334551811218,
-0.004577157087624073,
0.04919198155403137,
0.03546527773141861,
0.009605549275875092,
-0.03229304030537605,
0.05230279639363289,
0.042989108711481094,
0.027848074212670326,
0.061968378722667694,
0.045211080461740494,
0.06966902315616608,
0.013736709021031857,
-0.0017621364677324891,
-0.06898456066846848,
0.05828588828444481,
-0.011433961801230907,
0.00046185750397853553,
0.008103734813630581,
0.06113097444176674,
0.00936413649469614,
0.016648152843117714,
0.0012919307919219136,
0.009642430581152439,
-0.08203435689210892,
0.014445880427956581,
0.0587712898850441,
0.03267085924744606,
-0.02794867753982544,
-0.007637660484761,
0.02885090932250023,
-0.02675480581820011,
0.004737142473459244,
0.029723571613430977,
0.04042872041463852,
-0.03140826150774956,
0.0715876966714859,
0.05388011038303375,
0.062258608639240265,
0.0019381208112463355,
0.016589034348726273,
0.029290348291397095,
0.014403864741325378,
0.019246812909841537,
0.028543343767523766,
-0.02160879783332348,
0.06852392852306366,
-0.02560613304376602,
-0.07492900639772415,
-0.0017991818021982908,
0.004528368823230267,
-0.006697468459606171,
-0.015023394487798214,
-0.06080465391278267,
0.027142098173499107,
-0.04220297187566757,
0.0175595972687006,
-0.000620652106590569,
0.001661663525737822,
0.01275753602385521,
-0.04247962310910225,
-0.014804431237280369,
-0.045410796999931335,
-0.0068472763523459435,
0.012526452541351318,
-0.04158540070056915,
-0.04857320711016655,
-0.008625092916190624,
-0.03506001457571983,
-0.022941293194890022,
-0.05363134667277336,
0.016659284010529518,
0.013641885481774807,
0.04744860157370567,
0.08947820961475372,
-0.033936817198991776,
-0.03232225775718689,
-0.010175659321248531,
-0.007386010140180588,
0.041852835565805435,
-0.028743116185069084,
-0.008226264268159866,
0.07506150752305984,
-0.04664909094572067,
-0.03837989270687103,
-0.027370968833565712,
-0.027718152850866318,
0.02369721233844757,
-0.03736460581421852,
-0.00738002173602581,
-0.07388122379779816,
-0.052276257425546646,
-0.06562600284814835,
-0.04213368892669678,
-0.05745819956064224,
-0.05196555331349373,
-0.01594850793480873,
-0.052987124770879745,
0.018953703343868256,
0.003279943484812975,
-0.007020025979727507,
-0.01060783676803112,
-0.015209242701530457,
-0.00894499197602272,
0.0010585831478238106,
-0.012082838453352451,
0.01711314730346203,
0.06500475853681564,
-0.006227582227438688,
0.004664087202399969,
0.036255765706300735,
-0.08466283977031708,
0.018313227221369743,
-0.014785118401050568,
0.0236273854970932,
0.037349097430706024,
-0.019340859726071358,
0.035286031663417816,
0.05379161238670349,
-0.033587746322155,
0.030732668936252594,
0.010275143198668957,
-0.05606791749596596,
0.06647337973117828,
0.007286189589649439,
-0.00009592842980055138,
0.008342957124114037,
-0.0011992063373327255,
0.025016697123646736,
0.02705351822078228,
0.05147535726428032,
0.010058355517685413,
0.03566081076860428,
-0.03861825540661812,
-0.05087530240416527,
0.03971496969461441,
-0.035629451274871826,
0.05075877904891968,
0.01823263429105282,
0.018261749297380447,
-0.054930590093135834,
0.01985478214919567,
0.021062497049570084,
-0.007522048428654671,
0.028152834624052048,
-0.04008326679468155,
0.027311138808727264,
-0.0428069569170475,
0.06894801557064056,
0.010835887864232063,
-0.0399787463247776,
-0.002524423645809293,
0.006535287015140057,
0.04137111082673073,
0.04924953728914261,
-0.027931801974773407,
-0.004938689526170492,
0.01545665692538023,
0.013048073276877403,
-0.047611549496650696,
-0.023630453273653984,
0.039349265396595,
0.052697066217660904,
-0.04799569025635719,
-0.0054919240064918995,
-0.0004587655421346426,
-0.0012787606101483107,
0.0030239264015108347,
-0.03607528656721115,
0.08607446402311325,
0.02002739906311035,
-0.030301256105303764,
-0.009462220594286919,
0.01652659848332405,
-0.03605933487415314,
0.03836236521601677,
-0.013027658686041832,
0.005028864368796349,
-0.03628574684262276,
-0.02071174420416355,
-0.005462608765810728,
0.027652934193611145,
0.01998681202530861,
0.006865650415420532,
-0.0956570953130722,
-0.060840051621198654,
0.05056123808026314,
-0.024136235937476158,
-0.025251030921936035,
0.027378778904676437,
-0.011702653020620346,
-0.008993115276098251,
0.003705109702423215,
0.018185406923294067,
-0.03963625058531761,
-0.0409347265958786,
-0.06890314072370529,
0.07032041251659393,
-0.004218345042318106,
-0.009749473072588444,
0.026230130344629288,
-0.006108190398663282,
0.040975168347358704,
0.04290628433227539,
0.0428173653781414,
0.09093087911605835,
0.004327505361288786,
-0.013808207586407661,
-0.03828717768192291,
0.0002570359210949391,
-0.0415545329451561,
-0.020753545686602592,
0.042302802205085754,
-0.009906002320349216,
-0.005328167229890823,
0.01246024388819933,
-0.03950876742601395,
0.051453448832035065,
0.060371194034814835,
-0.038991156965494156,
0.02439305931329727,
0.00477846572175622,
-0.05719573423266411,
-0.0007696395623497665,
-0.02645244263112545,
-0.0019337263656780124,
-0.000912912713829428,
-0.013781556859612465,
0.020030882209539413,
-0.004935199860483408,
-0.00901228841394186,
-0.05337146669626236,
0.01226353645324707,
-0.009430034086108208,
0.04095491021871567,
-0.007743879221379757,
0.06215725839138031,
-0.016760148108005524,
0.012998233549296856,
0.011180966161191463,
0.027317561209201813,
0.03082524985074997,
-0.011723005212843418,
0.024130290374159813,
-0.01227811723947525,
-0.030564285814762115,
0.012950839474797249,
-0.04897003620862961,
-0.006922171916812658,
-0.00803210586309433,
-0.05688470974564552,
0.012795044109225273,
-0.05595746636390686,
-0.015577804297208786,
0.03714683651924133,
-0.014285849407315254,
0.03860994800925255,
-0.05045340955257416,
-0.03942020982503891,
-0.0223267562687397,
-0.0959562212228775,
0.029586970806121826,
-0.038937121629714966,
-0.02608531154692173,
0.07280702143907547,
-0.04214475303888321,
0.015581244602799416,
0.01237726304680109,
-0.045151494443416595,
-0.00898769125342369,
0.02444392442703247,
0.017645027488470078,
0.013914761133491993,
0.000593840260989964,
-0.03167314827442169,
-0.006126773077994585,
0.022802000865340233,
-0.06539783626794815,
-0.010278510861098766,
0.008201964199543,
-0.012043178081512451,
-0.026926670223474503,
0.06579519808292389,
-0.03423253074288368,
0.009771042503416538,
-0.020091010257601738,
0.05788438022136688,
0.005564009305089712,
-0.017972305417060852,
-0.00004345323031884618,
-0.029641350731253624,
-0.03914082050323486,
0.07409046590328217,
-0.022547541186213493,
-0.07771912962198257,
0.029198696836829185,
-0.009004983119666576,
0.025786951184272766,
-0.023570232093334198,
-0.013007995672523975,
-0.03292403742671013,
0.025567390024662018,
-0.02803077921271324,
0.003045575926080346,
0.04782684147357941,
-0.013688026927411556,
0.018001608550548553,
-0.01257920078933239,
0.06331388652324677,
-0.0598781444132328,
0.04640120640397072,
0.03936257213354111,
0.020762495696544647,
0.025172211229801178,
0.006495526991784573,
-0.02041035331785679,
0.07998292148113251,
0.005746068898588419,
0.05405431240797043,
-0.026601547375321388,
-0.016574086621403694,
0.08292795717716217,
-0.037422556430101395,
0.03711347654461861,
-0.1008518785238266,
-0.053180474787950516,
0.057563416659832,
-0.026514818891882896,
0.023724768310785294,
0.04226739704608917,
-0.07503746449947357,
0.010503801517188549,
0.018856346607208252,
-0.011439372785389423,
-0.01439143717288971,
0.00889025442302227,
0.016118185594677925,
-0.014219800010323524,
-0.02736121229827404,
-0.024174990132451057,
0.021673815324902534,
-0.013398786075413227,
-0.019176065921783447,
-0.03340686857700348,
0.0027515122201293707,
0.009489042684435844,
-0.03616392984986305,
-0.045202162116765976,
0.007920666597783566,
0.03182051330804825,
-0.002052807016298175,
0.042082786560058594,
0.02342173643410206,
0.007302904035896063,
0.05129365622997284,
0.021740064024925232,
-0.02578972838819027,
-0.007066241931170225,
0.004983148537576199,
0.02485840395092964,
-0.05652027577161789,
-0.013407276943325996,
-0.04013058915734291,
0.023703455924987793,
0.012706470675766468,
-0.07016370445489883,
0.009875082410871983,
-0.019467761740088463,
0.06563445180654526
] |
<p>What are the units of the damping constant from the following equation by dimensional analysis?</p>
<p>$$\zeta = \frac{c}{2\sqrt{mk}}$$</p>
<p>I'm assuming the units have to be s^-1, as the damping constant is present in the exponential equation which plots damping of y=Ae^kt (which plots amplitude vs time). Is that a correct assumption?</p>
<p>If somebody could do a quick dimensional analysis to confirm it would be great.</p> | g1288 | [
0.038801729679107666,
-0.05785256251692772,
0.008991850540041924,
-0.05843237042427063,
0.06485863775014877,
0.029531309381127357,
0.13238994777202606,
0.028750503435730934,
-0.05208749696612358,
0.0372488908469677,
0.0018688006093725562,
0.02641717903316021,
0.0064337048679590225,
0.015816835686564445,
0.013553576543927193,
-0.01897791586816311,
0.022590992972254753,
0.013056552037596703,
-0.055016350001096725,
0.00220498233102262,
0.011310738511383533,
-0.03017006255686283,
-0.07315598428249359,
-0.04942985251545906,
0.07320586591959,
-0.04296458140015602,
0.005682108458131552,
0.010033361613750458,
0.010405445471405983,
-0.04123026505112648,
0.034989483654499054,
-0.029316870495676994,
0.08912509679794312,
-0.02191121131181717,
-0.06719478219747543,
-0.012318072840571404,
0.040519971400499344,
0.04228406026959419,
0.06980689615011215,
-0.03533758595585823,
0.003247120650485158,
0.0035556007642298937,
-0.018620004877448082,
0.05407299846410751,
0.0023389444686472416,
0.014010448008775711,
-0.049515463411808014,
-0.015879254788160324,
-0.05396891385316849,
0.022195832803845406,
-0.00672266585752368,
0.008695092983543873,
0.04416798800230026,
0.022288478910923004,
-0.08346755802631378,
0.03460347652435303,
0.026667144149541855,
-0.00995257031172514,
0.023598048835992813,
0.10480711609125137,
0.03916742652654648,
0.023988675326108932,
-0.03933393582701683,
-0.037673477083444595,
0.08064375072717667,
-0.012837864458560944,
-0.014260509982705116,
-0.05572308599948883,
0.009958974085748196,
0.00048006049473769963,
0.0059074098244309425,
-0.06435174494981766,
-0.013841993175446987,
-0.007313779555261135,
0.000986065249890089,
0.022502286359667778,
0.025201408192515373,
0.0072499047964811325,
-0.020304610952734947,
-0.0397273488342762,
-0.003531739115715027,
0.008545937947928905,
0.02144218608736992,
0.030797885730862617,
0.04341718554496765,
-0.01593773066997528,
0.005656675901263952,
0.009514551609754562,
-0.058950118720531464,
-0.03880710154771805,
-0.002502588788047433,
0.03793785721063614,
-0.03008434735238552,
0.022289006039500237,
0.027301685884594917,
-0.062484703958034515,
-0.018803924322128296,
-0.003126926487311721,
-0.001479493104852736,
0.03645806759595871,
0.0002794363535940647,
0.03143203258514404,
0.05095696449279785,
-0.01133788377046585,
0.009981540963053703,
-0.037249207496643066,
-0.009918007999658585,
-0.0661580041050911,
0.04628762602806091,
-0.017396006733179092,
-0.052910346537828445,
0.028969012200832367,
-0.028867878019809723,
-0.004433699417859316,
-0.06958405673503876,
-0.02437540516257286,
0.046906813979148865,
-0.04345368966460228,
-0.043257936835289,
-0.01564975641667843,
0.02688569575548172,
0.012475722469389439,
0.025359991937875748,
0.020469117909669876,
-0.03146648779511452,
0.05103220418095589,
0.025104770436882973,
0.06615511327981949,
0.02294343337416649,
0.021903708577156067,
0.02959890477359295,
-0.013298369012773037,
-0.04994570091366768,
-0.0094260573387146,
-0.00039430049946531653,
0.05606212094426155,
-0.02743055857717991,
-0.028404563665390015,
0.004890426993370056,
0.04743443801999092,
-0.0018140418687835336,
-0.05397866293787956,
0.0679328441619873,
-0.06057954952120781,
-0.07796349376440048,
0.045796576887369156,
0.029803184792399406,
-0.0654013529419899,
0.007931200787425041,
-0.021672016009688377,
0.0017047972651198506,
0.03765493631362915,
0.0420985221862793,
-0.02037952095270157,
-0.013314452953636646,
0.014268338680267334,
0.04190277308225632,
0.024688350036740303,
0.003448797855526209,
0.03462912514805794,
0.015617955476045609,
0.013628227636218071,
0.05295833572745323,
0.023443877696990967,
-0.012068386189639568,
-0.01508827693760395,
-0.003867178224027157,
-0.041325729340314865,
0.03098069131374359,
0.025065964087843895,
-0.049759749323129654,
0.011683695018291473,
-0.0018968175863847136,
0.03742716833949089,
-0.03781282901763916,
0.012378633953630924,
0.06717879325151443,
-0.028988884761929512,
0.03298112377524376,
0.0030887608882039785,
0.022708280012011528,
0.0330476276576519,
0.025306586176156998,
-0.021739786490797997,
-0.02239544317126274,
0.035602886229753494,
0.019867051392793655,
0.0281065646559,
0.02205032669007778,
0.018755735829472542,
-0.017336754128336906,
-0.05212118849158287,
-0.01321354229003191,
0.02792426012456417,
0.005160413682460785,
0.02244757115840912,
-0.010996478609740734,
-0.013156736269593239,
0.00006630682764807716,
-0.0017006841953843832,
0.029193734750151634,
-0.0007379809976555407,
0.10637404024600983,
-0.041952360421419144,
0.06044149398803711,
-0.0025008388329297304,
-0.02264132723212242,
0.005193501245230436,
-0.041103336960077286,
-0.05256820097565651,
-0.018355797976255417,
-0.04506490007042885,
0.012055374681949615,
-0.0013059994671493769,
0.08247920870780945,
-0.0528179332613945,
0.00825677439570427,
0.021604668349027634,
-0.016774553805589676,
0.04889816790819168,
-0.04055105149745941,
0.019930509850382805,
0.0307600274682045,
-0.021461356431245804,
-0.043571069836616516,
-0.027476809918880463,
-0.018183454871177673,
-0.01911083608865738,
0.007365916855633259,
-0.013613889925181866,
-0.08017927408218384,
-0.00677981274202466,
0.006102424580603838,
-0.0019844896160066128,
-0.008185022510588169,
0.010334936901926994,
-0.06388389319181442,
0.005423018708825111,
0.023604650050401688,
-0.044193726032972336,
0.055919867008924484,
0.011731721460819244,
0.0205577053129673,
-0.03629498928785324,
0.029771938920021057,
-0.0381469801068306,
-0.03773385286331177,
-0.004897112026810646,
-0.018868714570999146,
-0.05886007100343704,
-0.014051027595996857,
0.01630478724837303,
0.030050475150346756,
0.03846029192209244,
-0.013718475587666035,
-0.09485666453838348,
0.050847649574279785,
-0.04066349193453789,
0.02364034578204155,
-0.00028985904646106064,
0.03071371465921402,
0.028470216318964958,
0.04892422631382942,
0.03132593259215355,
-0.0036285051610320807,
-0.05536963790655136,
-0.025209149345755577,
0.051030147820711136,
0.002522142371162772,
0.01897379755973816,
0.051862932741642,
0.048341430723667145,
-0.005865533370524645,
0.015658318996429443,
0.04792117327451706,
-0.05813474953174591,
0.055004626512527466,
-0.02783227153122425,
-0.028853964060544968,
-0.02311670035123825,
0.008790631778538227,
0.01752408593893051,
-0.010813464410603046,
0.06818851083517075,
0.05478392168879509,
0.011886806227266788,
0.04583999887108803,
0.06083314120769501,
-0.01669752039015293,
-0.007276600226759911,
0.012677055783569813,
0.020671959966421127,
-0.03844299912452698,
-0.03074761852622032,
-0.005002593155950308,
0.04203920438885689,
0.0185716412961483,
-0.08633186668157578,
-0.012594657018780708,
0.062080129981040955,
-0.01437597069889307,
-0.00820145569741726,
0.02099512703716755,
-0.0237986221909523,
-0.03743721917271614,
0.005247239489108324,
0.009062884375452995,
-0.04476109519600868,
-0.04996835067868233,
-0.0018047610064968467,
-0.01266204472631216,
0.039150819182395935,
0.05353522673249245,
0.0013338933931663632,
-0.011525760404765606,
0.0032178296241909266,
-0.011535041965544224,
-0.030816424638032913,
-0.032971225678920746,
0.0328289195895195,
-0.03876296430826187,
-0.08346349000930786,
0.038046419620513916,
0.02938498556613922,
0.0010885968804359436,
0.03852510824799538,
-0.00683706346899271,
0.018139874562621117,
-0.06795541197061539,
-0.029414750635623932,
-0.007407041732221842,
-0.052363328635692596,
0.0421854630112648,
0.009186677634716034,
-0.04196067526936531,
-0.05310976132750511,
-0.07994937151670456,
-0.023446515202522278,
-0.00872618705034256,
0.004089173395186663,
-0.049568984657526016,
-0.03829053416848183,
0.006048598326742649,
-0.07568959146738052,
-0.03807801008224487,
-0.027219578623771667,
0.010066676884889603,
0.013287979178130627,
-0.04661082103848457,
0.011853048577904701,
-0.015467261895537376,
0.014463263563811779,
0.014763489365577698,
-0.05505617335438728,
0.022247040644288063,
0.04395057633519173,
0.02390318550169468,
0.04177498817443848,
-0.02984299324452877,
0.0081794960424304,
0.0799160972237587,
-0.10815045237541199,
0.02950863353908062,
0.005411182530224323,
0.010126020759344101,
-0.02817614935338497,
0.0005375216715037823,
0.0680004209280014,
-0.013532960787415504,
0.03320901468396187,
0.0031452353578060865,
0.0355827771127224,
0.0073139481246471405,
0.02059013582766056,
-0.003714566584676504,
0.004714318551123142,
-0.018523674458265305,
0.03921564668416977,
-0.029276710003614426,
0.009849722497165203,
0.013968652114272118,
0.03426316753029823,
0.015528077259659767,
-0.0031252691987901926,
0.007024145685136318,
0.014349348843097687,
0.01210898905992508,
0.0193951316177845,
-0.024724487215280533,
-0.05730067193508148,
0.047101445496082306,
-0.04155503213405609,
-0.004917776212096214,
-0.0336899533867836,
0.005791023373603821,
-0.07484831660985947,
0.010689027607440948,
0.003768723225221038,
-0.06360691785812378,
0.0212104469537735,
0.03421339392662048,
-0.040526144206523895,
0.0377495177090168,
0.00395535072311759,
0.026765186339616776,
-0.023367810994386673,
0.03296925500035286,
-0.021726293489336967,
0.009358156472444534,
-0.008470051921904087,
-0.024082740768790245,
-0.00450704013928771,
0.015885962173342705,
-0.0557263046503067,
-0.021584652364253998,
0.03449578955769539,
-0.03161301091313362,
0.03056509979069233,
0.06915616989135742,
0.023262321949005127,
0.034396715462207794,
-0.0005551940412260592,
-0.044613927602767944,
0.04917411506175995,
-0.01691092923283577,
-0.051242291927337646,
0.008567911572754383,
-0.016843678429722786,
-0.10670320689678192,
-0.013999653980135918,
0.005850723013281822,
-0.05063902586698532,
-0.0005023106350563467,
-0.005135337822139263,
-0.06236351653933525,
0.022531941533088684,
0.011137344874441624,
-0.013614201918244362,
-0.030239896848797798,
0.005910608451813459,
-0.006500037387013435,
-0.001171655603684485,
0.0038843248039484024,
0.04750298708677292,
0.02213992178440094,
0.018952997401356697,
0.012068744748830795,
-0.03934260085225105,
0.022251781076192856,
0.02755161188542843,
-0.03196771815419197,
0.06378286331892014,
-0.0064871590584516525,
-0.06417873501777649,
0.028289794921875,
0.05041138082742691,
-0.013173412531614304,
-0.021934200078248978,
0.036185771226882935,
-0.008598310872912407,
-0.00020397042680997401,
0.02856043539941311,
-0.04657486081123352,
-0.016348542645573616,
0.0524250864982605,
-0.048033636063337326,
-0.027530601248145103,
0.020359152927994728,
-0.023524507880210876,
0.05874825641512871,
0.0012346734292805195,
-0.018354326486587524,
-0.011326653882861137,
-0.01109901163727045,
0.02082820050418377,
-0.017328865826129913,
-0.022418227046728134,
0.0004089108551852405,
-0.0621698722243309,
-0.00786571204662323,
0.028875814750790596,
-0.054441943764686584,
0.005049128085374832,
0.007895641960203648,
-0.03328314796090126,
0.03422004356980324,
0.021053500473499298,
0.04047344624996185,
-0.051803216338157654,
0.05104214325547218,
-0.04300307482481003,
-0.028188196942210197,
-0.02114228345453739,
0.029070328921079636,
-0.00557810440659523,
-0.029788753017783165,
0.03166894614696503,
-0.06716115027666092,
-0.021868105977773666,
-0.05601934343576431,
-0.025593126192688942,
-0.024617018178105354,
-0.04610336199402809,
0.038692887872457504,
-0.05493905395269394,
0.004799886140972376,
0.053449101746082306,
-0.05863885208964348,
-0.015527334064245224,
0.07894916832447052,
0.0030935555696487427,
-0.00044271297520026565,
0.12028826773166656,
0.03890562430024147,
0.020358243957161903,
-0.041455939412117004,
0.006865763571113348,
0.05847155302762985,
0.03997257351875305,
-0.03097391687333584,
0.027741078287363052,
0.036864832043647766,
0.0011799795320257545,
-0.07838084548711777,
0.029917534440755844,
0.02837277762591839,
0.023611033335328102,
0.007508028298616409,
0.028453199192881584,
-0.03475845605134964,
0.029732132330536842,
0.015099254436790943,
-0.053252264857292175,
-0.04775271937251091,
0.0074606542475521564,
-0.06652753055095673,
0.00396794592961669,
-0.07101385295391083,
-0.0361047238111496,
-0.02141093835234642,
-0.014914260245859623,
-0.00821867398917675,
0.022152401506900787,
0.010804691351950169,
-0.059435002505779266,
0.014878308400511742,
0.03326552361249924,
0.02481055073440075,
-0.008781805634498596,
-0.013280751183629036,
-0.0058921463787555695,
0.025026744231581688,
-0.06403162330389023,
0.03217119723558426,
-0.02617875672876835,
0.03969297185540199,
-0.002845271024852991,
0.021656299009919167,
-0.02463361620903015,
-0.037187132984399796,
-0.05037007853388786,
0.062328703701496124,
-0.012943667359650135,
-0.006873627658933401,
0.015736643224954605,
-0.05318900942802429,
0.03712218254804611,
0.016651371493935585,
0.07198230177164078,
0.007553713861852884,
-0.0032269160728901625,
0.026323840022087097,
-0.011376732029020786,
0.08630070090293884,
0.02401062101125717,
0.021801384165883064,
0.005491824820637703,
-0.006938364822417498,
0.00499521940946579,
0.04554019495844841,
-0.03519243374466896,
0.06233464926481247,
0.05725099518895149,
0.005764118395745754,
0.012055298313498497,
0.014842611737549305,
-0.005060785915702581,
0.00507067795842886,
-0.04209832102060318,
0.010387275367975235,
-0.0666489526629448,
0.021430326625704765,
-0.0665300115942955,
0.020398445427417755,
0.007539182901382446,
-0.030113281682133675,
0.014517504721879959,
0.016666507348418236,
0.00764310359954834,
-0.026582131162285805,
0.031061168760061264,
0.010146022774279118,
-0.024681653827428818,
-0.038230642676353455,
-0.028677305206656456,
-0.014760748483240604,
0.002624416956678033,
-0.007715718355029821,
0.0006116555887274444,
0.010722490958869457,
0.04978112131357193,
-0.014686151407659054,
0.021972430869936943,
0.03749920800328255,
0.005059993825852871,
-0.06236189603805542,
0.06114066392183304,
-0.02147071622312069,
-0.06656909734010696,
0.017954139038920403,
0.027273444458842278,
0.021613195538520813,
0.013467621058225632,
0.01470167562365532,
-0.024257000535726547,
0.02290588617324829,
-0.015143335796892643,
0.012638842687010765,
-0.0006424166494980454,
0.0031393440440297127,
0.019357940182089806,
0.0046783932484686375,
0.0418480709195137,
0.019957279786467552,
-0.02067040093243122,
0.030932381749153137,
-0.08467298746109009,
0.06562048941850662,
0.018830735236406326,
0.014972981065511703,
0.021432550624012947,
0.003335333429276943,
0.024092750623822212,
-0.013887216337025166,
-0.05753939226269722,
0.002583341207355261,
0.058265138417482376,
0.027883080765604973,
-0.019751662388443947,
-0.0026487954892218113,
0.04974392056465149,
0.03711352124810219,
0.02955387346446514,
0.0005025921855121851,
0.012061755172908306,
-0.00851657148450613,
0.03236012905836105,
0.0005539005505852401,
-0.02104215882718563,
0.0027437740936875343,
-0.014717060141265392,
-0.05607159063220024,
0.03525467589497566,
-0.0001569465093780309,
-0.053465887904167175,
0.09174215793609619,
0.04770044982433319,
-0.026723094284534454,
0.03840949386358261,
-0.037328265607357025,
-0.0326235294342041,
-0.030911622568964958,
0.009087732993066311,
-0.029045158997178078,
0.008964031003415585,
0.05893560126423836,
-0.005876976530998945,
-0.03393227607011795,
0.04203232377767563,
0.014925503171980381,
0.04016963019967079,
-0.06333789229393005,
-0.030719313770532608,
-0.10039082169532776,
-0.046510543674230576,
0.03313949331641197,
0.009364047087728977,
-0.01939322054386139,
0.057522330433130264,
0.014873710460960865,
-0.060069359838962555,
0.02505161054432392,
0.0024711608421057463,
-0.025283310562372208,
-0.027916228398680687,
-0.008478989824652672,
-0.01601232960820198,
0.0017596757970750332,
-0.03746037185192108,
0.027410423383116722,
0.0283217690885067,
-0.014425499364733696,
0.019306451082229614,
0.008587044663727283,
0.01905227079987526,
-0.046581853181123734,
-0.0035918266512453556,
-0.1029207855463028,
0.0082282405346632,
0.010042482055723667,
0.03271697834134102,
0.01883665658533573,
-0.03643663600087166,
0.014447630383074284,
0.03581633046269417,
0.033375125378370285,
-0.00393096124753356,
-0.033620353788137436,
0.012580085545778275,
-0.04392406344413757,
-0.04268280044198036,
-0.010124285705387592,
-0.02023969031870365,
-0.06169113889336586,
0.05536114051938057,
-0.022796964272856712,
-0.012343120761215687,
0.015114222653210163,
-0.01910068653523922,
0.05100289732217789,
-0.005615745205432177,
0.0547669343650341,
-0.023580266162753105,
0.04456683248281479,
-0.029243698343634605,
-0.0371382050216198,
0.04886398836970329,
0.04971826821565628,
-0.000371131842257455,
-0.003689108183607459,
-0.01923527382314205,
-0.04577293619513512,
0.01670844480395317,
-0.031306058168411255,
-0.028050491586327553,
0.00040209986036643386,
-0.03045867383480072,
0.029727870598435402,
0.08382690697908401,
-0.04411506652832031,
0.020055895671248436,
0.008713683113455772,
-0.007378199137747288,
-0.042519085109233856,
-0.002393563510850072,
-0.035796117037534714,
-0.012767779640853405,
-0.0075784530490636826,
-0.03972313180565834,
-0.03912435844540596,
0.000612823641858995,
0.020972013473510742,
0.030970832332968712,
0.01434887945652008,
0.01096410397440195,
-0.03560608997941017,
-0.025993026793003082,
0.04873760789632797
] |
<p>Let us say a block of mass is placed on the surface of earth. Then while drawing the forces on that body, we say:</p>
<ol>
<li>Force $F = mg$ acting towards the center of Earth.</li>
<li>Normal reaction $N$ offered by the surface of Earth.</li>
</ol>
<p>If no other forces are acting, we say $F=N$. But what about the centrifugal force $m\omega^2R$ . Why don't we ever bring that into picture? What am I missing?</p> | g18 | [
0.05578690022230148,
0.06250461935997009,
-0.00035924179246649146,
0.0206186231225729,
0.035289064049720764,
0.03654564917087555,
0.05423159897327423,
0.03521871566772461,
-0.07095667719841003,
-0.09395194053649902,
0.046402812004089355,
-0.01703691855072975,
-0.006528135854750872,
0.041066285222768784,
0.03907778486609459,
0.01963546872138977,
0.0646292120218277,
-0.04978325217962265,
0.05594298243522644,
0.06970912963151932,
-0.0060808612033724785,
0.018316341564059258,
-0.0034264707937836647,
0.004485524725168943,
0.0038112541660666466,
0.013231468386948109,
0.021446434780955315,
-0.039997320622205734,
-0.016508236527442932,
-0.0056784194894135,
-0.00893313903361559,
0.03298768401145935,
0.021731305867433548,
-0.07410986721515656,
-0.026047993451356888,
-0.025671130046248436,
0.00006544737698277459,
0.04605446010828018,
0.015414241701364517,
-0.043241746723651886,
-0.005561335012316704,
0.04020289331674576,
-0.008530470542609692,
-0.004530786070972681,
-0.002938072429969907,
-0.013114994391798973,
-0.04589017853140831,
-0.025610357522964478,
0.011051760986447334,
0.007848258130252361,
-0.07934476435184479,
-0.002998591400682926,
0.05531851574778557,
0.0006637103506363928,
0.018986335024237633,
0.02425323612987995,
0.054899342358112335,
0.025089122354984283,
-0.005857263691723347,
0.01379845105111599,
-0.01485756691545248,
-0.020691903308033943,
0.015039504505693913,
-0.019222980365157127,
0.030541367828845978,
-0.015185977332293987,
-0.044745784252882004,
0.042050283402204514,
0.04577399045228958,
0.053550612181425095,
-0.04486855864524841,
-0.041830066591501236,
0.0005046591395512223,
0.011194612830877304,
-0.01556756254285574,
0.022566433995962143,
0.016617057844996452,
0.02419334463775158,
0.04650532826781273,
-0.029362641274929047,
0.02083328180015087,
0.01782796159386635,
0.028378352522850037,
0.019733231514692307,
0.10055793821811676,
-0.013150488957762718,
-0.030939413234591484,
-0.006329670082777739,
0.0004922127700410783,
0.017926793545484543,
0.0387621745467186,
0.020944420248270035,
0.06664875149726868,
0.042430002242326736,
-0.05330425500869751,
-0.09574174135923386,
-0.0018784477142617106,
0.038588862866163254,
-0.05190138891339302,
0.01550634577870369,
-0.046226490288972855,
0.019347723573446274,
-0.00917100440710783,
-0.0009395304368808866,
0.04573541507124901,
-0.0009503023466095328,
0.0504685640335083,
0.035223860293626785,
-0.0070382277481257915,
-0.06420139223337173,
0.018175940960645676,
-0.006847886368632317,
-0.02250613644719124,
-0.03747586905956268,
0.008009007200598717,
-0.05273855850100517,
0.07888119667768478,
-0.00287151918746531,
-0.011914742179214954,
0.04017208516597748,
-0.056209746748209,
0.04718968644738197,
0.011702041141688824,
0.0015781382098793983,
-0.05396401882171631,
-0.06190263852477074,
0.06545480340719223,
0.013634645380079746,
0.05349350720643997,
-0.04337446019053459,
0.015622450970113277,
0.00018413053476251662,
-0.019620995968580246,
-0.03210741654038429,
0.05152152478694916,
0.014074972830712795,
-0.10735621303319931,
-0.028867315500974655,
-0.026466650888323784,
-0.0062349108047783375,
-0.03402121737599373,
0.0025470831897109747,
0.013683034107089043,
0.007383390795439482,
-0.015184293501079082,
0.03920898959040642,
-0.016876356676220894,
0.013660553842782974,
0.06457007676362991,
-0.0024306983686983585,
-0.026362081989645958,
0.06444347649812698,
0.046357713639736176,
-0.023384088650345802,
0.06209195777773857,
-0.007870765402913094,
0.07247218489646912,
-0.026381241157650948,
-0.029633183032274246,
-0.013663865625858307,
0.09804926812648773,
-0.02002090774476528,
-0.030026761814951897,
-0.005599347408860922,
-0.04197874665260315,
-0.009064272046089172,
-0.02028479613363743,
-0.0383886992931366,
0.012706998735666275,
-0.01991487853229046,
-0.07030458003282547,
0.00534606771543622,
0.013104503974318504,
0.07414266467094421,
-0.012883476912975311,
0.04770367592573166,
0.0049096206203103065,
-0.04666811227798462,
-0.021163631230592728,
0.042354170233011246,
-0.0022904626093804836,
-0.010717203840613365,
0.04439586400985718,
0.019866852089762688,
-0.01860305294394493,
-0.01349019818007946,
0.009157687425613403,
0.06372788548469543,
-0.015888189896941185,
0.028189219534397125,
-0.06502966582775116,
0.02143554575741291,
0.01585407927632332,
0.024959715083241463,
0.002106791827827692,
0.0393122062087059,
-0.02758525125682354,
-0.053217675536870956,
-0.04158153384923935,
0.016785243526101112,
-0.02857222966849804,
0.026692701503634453,
0.0017718907911330462,
-0.021373357623815536,
-0.04769550636410713,
-0.018846457824110985,
0.03341572731733322,
0.037518516182899475,
0.051772572100162506,
-0.043648719787597656,
0.012315874919295311,
-0.018552757799625397,
-0.020842894911766052,
-0.006174531299620867,
-0.057425424456596375,
0.00685223238542676,
-0.0039476011879742146,
0.016721976920962334,
-0.033716414123773575,
0.010535644367337227,
-0.01239123847335577,
-0.007308177649974823,
0.010202066972851753,
0.013455759733915329,
-0.016710758209228516,
0.019433168694376945,
-0.036090899258852005,
-0.011233859695494175,
-0.006467153318226337,
0.022418158128857613,
-0.08783993870019913,
0.03671722114086151,
0.012517254799604416,
0.015086733736097813,
-0.014791945926845074,
0.04239434003829956,
-0.010003290139138699,
-0.013273289427161217,
0.02126794308423996,
0.016162382438778877,
0.008504179306328297,
-0.04744838923215866,
-0.017707841470837593,
-0.00980206299573183,
0.01645425520837307,
-0.06619801372289658,
0.007860167883336544,
0.007151372730731964,
0.014715993776917458,
0.035876695066690445,
-0.019501404836773872,
-0.0112455440685153,
-0.028940141201019287,
-0.00863389577716589,
0.04850870743393898,
-0.018872881308197975,
-0.08239501714706421,
0.024027448147535324,
-0.029557202011346817,
-0.02900891937315464,
-0.06683817505836487,
0.02857929840683937,
0.06458967179059982,
0.060257650911808014,
-0.09785445034503937,
-0.030526889488101006,
-0.06632985919713974,
0.023639917373657227,
0.0172866377979517,
0.002558052772656083,
-0.030879000201821327,
0.029419295489788055,
0.022245079278945923,
0.038059383630752563,
-0.06566698849201202,
-0.030557777732610703,
-0.00939299538731575,
-0.05906905606389046,
0.012194077484309673,
0.023659657686948776,
0.004011207260191441,
0.04381556063890457,
-0.000913674826733768,
0.017889216542243958,
0.04439442232251167,
-0.01140510942786932,
-0.02034149318933487,
0.012747826986014843,
-0.015617357566952705,
-0.05686502531170845,
-0.05532482638955116,
0.01642506569623947,
0.05350614711642265,
-0.037838924676179886,
-0.014421536587178707,
0.04825214669108391,
0.04510124400258064,
-0.043243151158094406,
-0.012468093074858189,
0.0850452333688736,
0.024785371497273445,
-0.06263513118028641,
-0.006785145029425621,
0.03201499208807945,
-0.04815729707479477,
0.015552693977952003,
0.06715134531259537,
-0.08167173713445663,
-0.040015846490859985,
0.040674153715372086,
-0.011713151820003986,
0.10014230012893677,
-0.007411728147417307,
-0.024070950224995613,
-0.09416418522596359,
-0.03329283744096756,
0.022190844640135765,
-0.001259632408618927,
0.05407961085438728,
-0.04027629643678665,
-0.05998912826180458,
-0.0618564747273922,
0.007193472236394882,
-0.027310725301504135,
0.0023785242810845375,
0.06962762027978897,
-0.10865063220262527,
0.028891215100884438,
-0.017622459679841995,
-0.05357052758336067,
0.03670834004878998,
0.07152201235294342,
-0.048348963260650635,
-0.007681511342525482,
-0.04647909477353096,
-0.001560250879265368,
-0.002760903676971793,
-0.0035940154921263456,
0.016801493242383003,
0.02953406609594822,
-0.027095869183540344,
-0.02857135608792305,
-0.07294762134552002,
-0.0006998283788561821,
0.0022047380916774273,
0.009877561591565609,
-0.039714377373456955,
0.03969920799136162,
-0.010084051638841629,
-0.025340303778648376,
0.01421079970896244,
-0.04327552020549774,
0.006290679797530174,
-0.0005362798692658544,
0.0351601280272007,
0.015890231356024742,
0.027886027470231056,
-0.03505382314324379,
-0.013267283327877522,
0.04363066330552101,
0.025030389428138733,
-0.0021802347619086504,
-0.01205929834395647,
0.06313074380159378,
0.04603223875164986,
0.008033277466893196,
-0.031156964600086212,
0.03893309086561203,
-0.032306041568517685,
-0.08123169094324112,
0.07371973246335983,
-0.01022669393569231,
-0.013290183618664742,
0.014768330380320549,
0.0685005933046341,
-0.09389034658670425,
0.017198748886585236,
0.029092935845255852,
0.030026448890566826,
-0.026804547756910324,
0.042710136622190475,
0.007995286956429482,
-0.029427099972963333,
-0.017875386402010918,
-0.004839097149670124,
-0.018695829436182976,
-0.07170406728982925,
0.022963786497712135,
0.018231814727187157,
-0.01839347556233406,
-0.001098183449357748,
-0.03103507310152054,
0.010333308950066566,
0.06147997826337814,
0.006983691826462746,
0.010538398288190365,
0.04272912070155144,
-0.03544266149401665,
0.008647057227790356,
-0.01783791184425354,
-0.009815556928515434,
0.002583261812105775,
-0.038575924932956696,
-0.004104414954781532,
0.011833780445158482,
0.0189539585262537,
0.02033199742436409,
-0.049645353108644485,
0.031033001840114594,
-0.020297758281230927,
0.04063839092850685,
-0.010932086035609245,
-0.014619461260735989,
-0.006116336211562157,
0.05852915346622467,
-0.05405445024371147,
-0.007648669648915529,
0.029507048428058624,
0.01452616136521101,
-0.05912547931075096,
0.009704853408038616,
0.04171161353588104,
-0.013317268341779709,
-0.011435297317802906,
-0.020581087097525597,
0.051528073847293854,
0.03136936575174332,
-0.0009484252077527344,
0.02234748564660549,
-0.050621747970581055,
-0.024164164438843727,
0.06552863121032715,
-0.026868436485528946,
0.04071338474750519,
-0.05081804469227791,
0.019050084054470062,
-0.047998059540987015,
0.057699110358953476,
0.020108865574002266,
0.05326240137219429,
0.03998033329844475,
0.06099911034107208,
0.02240917459130287,
0.027423446998000145,
0.002228768775239587,
0.08698806911706924,
-0.018865955993533134,
-0.003837205935269594,
0.018552912399172783,
-0.026162710040807724,
-0.03595741465687752,
-0.02794566936790943,
-0.025258073583245277,
0.005325499922037125,
-0.016826050356030464,
0.009973582811653614,
0.008855709806084633,
0.03729808330535889,
-0.01964103989303112,
0.05915599316358566,
-0.03878051042556763,
-0.04517906904220581,
-0.018459446728229523,
-0.004585868678987026,
-0.01458303164690733,
0.01941104419529438,
0.007694665342569351,
-0.01302135270088911,
-0.03454146534204483,
0.0021611670963466167,
0.08815664798021317,
0.012016640044748783,
0.0430544912815094,
-0.010455195792019367,
-0.004015986807644367,
0.04181251674890518,
0.0406326949596405,
0.006004022434353828,
0.04472244530916214,
-0.04152534529566765,
-0.0020931889303028584,
0.003310787258669734,
-0.003919132519513369,
-0.010116632096469402,
0.013320565223693848,
-0.03518696501851082,
-0.013710793107748032,
-0.0498616024851799,
-0.0562727265059948,
-0.013656473718583584,
0.013739844784140587,
-0.020988741889595985,
-0.034280404448509216,
-0.05549919977784157,
0.021009694784879684,
0.015030973590910435,
-0.022540004923939705,
-0.02594262734055519,
-0.012769426219165325,
-0.01429657731205225,
-0.0697827935218811,
0.03793054819107056,
-0.04516938328742981,
0.011307650245726109,
-0.0012175386073067784,
0.04201240837574005,
-0.005146920680999756,
-0.021781709045171738,
0.00040672800969332457,
0.07941310107707977,
0.026470869779586792,
-0.006631513126194477,
0.0014333977596834302,
0.004595048725605011,
0.0016572729218751192,
-0.01558543462306261,
-0.009276436641812325,
-0.052782513201236725,
0.018050290644168854,
-0.003979085478931665,
0.03367870673537254,
-0.018844274803996086,
0.02809840254485607,
-0.07929820567369461,
0.0024010282941162586,
-0.0017409297870472074,
-0.008023519068956375,
-0.009559382684528828,
-0.013933718204498291,
0.06384436786174774,
-0.0011234127450734377,
-0.0043404605239629745,
0.03888016194105148,
0.025873331353068352,
0.002547644777223468,
-0.053139470517635345,
0.04585493355989456,
0.038435980677604675,
0.06961766630411148,
-0.04752432927489281,
-0.02371744066476822,
-0.027259105816483498,
0.04244952276349068,
0.031177295371890068,
0.011433077976107597,
0.07938433438539505,
0.011946441605687141,
-0.016255853697657585,
0.022549699991941452,
0.009073186665773392,
-0.04648826643824577,
0.040122341364622116,
-0.012659342028200626,
0.026574503630399704,
-0.02485000528395176,
0.006941068451851606,
0.008451813831925392,
-0.0013910295674577355,
-0.059074148535728455,
-0.010193211026489735,
0.03315233066678047,
0.004241427406668663,
0.004290454089641571,
-0.0014828004641458392,
0.0021632444113492966,
-0.04241544008255005,
0.02269350178539753,
0.03240625932812691,
-0.009392555803060532,
0.024092160165309906,
0.036158472299575806,
0.013376777060329914,
0.012066035531461239,
0.018631096929311752,
0.08470793068408966,
0.04296915605664253,
-0.03855490684509277,
0.02150946483016014,
-0.044653117656707764,
0.011188157834112644,
0.0067712776362895966,
-0.04981927201151848,
0.03628584370017052,
-0.05405692756175995,
0.009905833750963211,
0.008990324102342129,
-0.007010409142822027,
-0.03244773671030998,
0.0473523810505867,
-0.06717037409543991,
0.019690409302711487,
-0.024704109877347946,
0.0068650334142148495,
0.011641845107078552,
-0.02976960688829422,
-0.029862424358725548,
-0.006302067078649998,
0.05417686700820923,
0.035120364278554916,
-0.01587737165391445,
0.021734537556767464,
0.028193604201078415,
0.05091862753033638,
-0.022504329681396484,
0.053188882768154144,
0.0011088864412158728,
-0.021079879254102707,
-0.06038995459675789,
0.04909520596265793,
0.018235474824905396,
-0.027604345232248306,
-0.00696388678625226,
-0.028105704113841057,
-0.01588781364262104,
0.024847952648997307,
-0.07461432367563248,
0.0004271403013262898,
0.025863630697131157,
-0.05165952816605568,
0.023494582623243332,
-0.01159049291163683,
-0.015466522425413132,
0.06542395800352097,
-0.008890882134437561,
0.023375893011689186,
-0.001785671105608344,
-0.09134121239185333,
0.02777760475873947,
0.047761913388967514,
-0.014167528599500656,
0.039201147854328156,
0.027511190623044968,
-0.007037732750177383,
0.029149778187274933,
-0.0010617837542667985,
0.05465065315365791,
-0.037262529134750366,
0.003446768969297409,
0.03377782553434372,
-0.011150447651743889,
-0.05514528602361679,
0.04204564169049263,
0.051996294409036636,
-0.015698665753006935,
-0.09038969874382019,
0.02971821278333664,
0.06504040956497192,
0.013429496437311172,
-0.05370181053876877,
-0.025422383099794388,
0.037316128611564636,
-0.03915245085954666,
-0.004864453338086605,
0.004348768386989832,
-0.022786851972341537,
0.013135144487023354,
0.003590458771213889,
-0.009690310806035995,
0.002359714126214385,
-0.040483586490154266,
-0.03144393861293793,
-0.0211386289447546,
0.0034581879153847694,
0.004701470024883747,
-0.02391059882938862,
0.04286374896764755,
-0.013523086905479431,
0.019775092601776123,
0.04453492909669876,
0.01546318456530571,
-0.03693468123674393,
-0.06595093756914139,
-0.003146839328110218,
0.03843541443347931,
-0.045051511377096176,
0.03514865040779114,
0.01801714114844799,
-0.01981840841472149,
0.03695032745599747,
-0.00002185312769142911,
0.024583512917160988,
0.004490368999540806,
-0.017292233183979988,
0.021820181980729103,
-0.06325049698352814,
-0.013370306231081486,
0.008775241672992706,
0.01075976062566042,
-0.04767042025923729,
-0.03464527055621147,
0.04729006811976433,
0.03136696666479111,
0.005525032989680767,
-0.004525261931121349,
-0.018178068101406097,
0.007118893787264824,
0.01899198815226555,
0.02710212953388691,
0.0014963315334171057,
-0.009586954489350319,
0.008989269845187664,
-0.08454470336437225,
-0.0768900141119957,
-0.03287168964743614,
0.06668679416179657,
-0.010442664846777916,
-0.024199137464165688,
-0.004989415407180786,
-0.034687694162130356,
-0.0010100542567670345,
0.00032085596467368305,
0.04215851426124573,
0.011793605051934719,
-0.01301419734954834,
0.03591807186603546,
0.06936939060688019,
-0.031289905309677124,
0.03290374204516411,
0.0656113550066948,
-0.0372786819934845,
0.004286825656890869,
0.003578050294891,
-0.02109445258975029,
-0.08671431243419647,
-0.05136895924806595,
0.009912684559822083,
-0.01279456913471222,
-0.038850437849760056,
0.0037226618733257055,
0.02785399556159973,
-0.038831837475299835,
-0.029895447194576263,
0.013644170947372913,
-0.012393761426210403,
-0.0124648567289114,
-0.011166890151798725,
0.0028243111446499825,
-0.05740335211157799,
-0.052509576082229614,
-0.018616363406181335,
0.002208210062235594,
-0.011639520525932312,
-0.018690435215830803,
0.010919654741883278,
0.010891389101743698,
-0.031184453517198563,
-0.056545358151197433,
0.02903716266155243,
0.011577818542718887,
0.047251079231500626,
-0.02518083155155182,
0.018612312152981758,
-0.034405417740345,
-0.002750149229541421,
0.004443750251084566,
-0.042403727769851685,
-0.02356974221765995,
0.01519083697348833,
0.0607440285384655,
-0.01599055528640747,
-0.0048776366747915745,
0.024529391899704933,
-0.017455341294407845,
-0.04914581775665283,
0.012260906398296356,
-0.030396021902561188,
-0.05260403826832771,
0.01189761608839035
] |
<p>I am working on a variational problem involving elastic stability of a beam.</p>
<p>The deformation of the beam is given by six functions of the material coordinate along the beams longitudinal axis. The governing functional looks like
$$
\int_{s_1}^{s_2} F \left(
u(s),v(s),w(s),\phi(s),\chi(s),\psi(s) \right) ds.
$$
(It represents the beam's strain energy.)</p>
<p>Now I want to impose the condition that transverse shear deformation and elongation are zero. The consequence is that the 6 degrees of freedom of the beam are reduced to essentially 3. It can be shown that the three relations
$$
\frac{du}{ds} = \sin(\chi), \quad
\frac{dv}{ds} = -\sin(\phi)\cos(\chi), \quad
\frac{dw}{ds} = \cos(\phi)\cos(\chi) -1
\qquad (*)
$$
between the coordinates are valid in case transverse shear deformation and elongation are neglected.</p>
<p>My understanding is that there are now two ways to incorporate this constraint condition:</p>
<ol>
<li>eliminate variables in the original functional by substitution </li>
<li>include equations (*) by means of Lagrange multipliers</li>
</ol>
<p>I would like to use the latter method. The book <em>The variational principles of mechanics</em> by Lanczos explains this for both holonomic and non-holonomic constraints (and isoperimetric ones as well). Though I can see that equations (*) are clearly not some algebraic relation
$$
f_i(u,v,w,\phi,\chi,\psi)=0, \quad i=1\dots3
$$
between the coordinates, does this means the constraint qualifies as non-holonomic? I am confused because it seems integrable. Or does it then become an isoperimetric constraint?</p>
<h2>Edit</h2>
<p>I am getting more confused; can we only call constraints non-holonomic if derivatives with respect to <em>time</em> are involved? (Meaning that all equations (*) above just represent holonomic constraints, since it is all static?)</p>
<p>In <em>The enigma of nonholonomic constraints</em> by Flannery (2005), it is explained that for the typical action
$$
S = \int_{t_1}^{t_2} L({q},\dot{q},t) dt
$$
the Lagrange multiplier rule can only be used for holonomic and semi-holonomic (exact linear) conditions. Here, the independent variable clearly is time, but in my case it is some spatial coordinate.</p>
<p>If we assume that the independent variables space and time are interchangeable, my (*) equations appear non-holonomic (so, not to be incorporated with Lagrange multipliers), as they cannot be expressed as exact differential.. But, is this correct reasoning?</p> | g1289 | [
0.08370020985603333,
-0.024926941841840744,
0.01518060453236103,
-0.014699889346957207,
0.011831829324364662,
-0.028292518109083176,
-0.010534165427088737,
-0.005638947244733572,
-0.0027397817466408014,
0.013402819633483887,
-0.04464702680706978,
-0.012137803249061108,
-0.025261301547288895,
-0.01159391738474369,
0.01756810024380684,
0.026220038533210754,
0.03067837469279766,
0.03209812566637993,
-0.01403866708278656,
0.03925689682364464,
0.044113583862781525,
0.0731164738535881,
0.015015633776783943,
-0.028577743098139763,
0.04864511266350746,
-0.0020189837086945772,
0.01815434731543064,
-0.018047528341412544,
-0.08363445848226547,
0.02944328263401985,
0.0639423206448555,
-0.018892304971814156,
0.03321889787912369,
-0.02156698890030384,
0.01739184744656086,
-0.025523008778691292,
0.0403897650539875,
0.00731645617634058,
0.057606711983680725,
-0.005162814166396856,
-0.03147690370678902,
-0.0045499736443161964,
-0.018564730882644653,
0.016282200813293457,
-0.06769777089357376,
-0.040182288736104965,
-0.006691471673548222,
0.001252918504178524,
0.0030147244688123465,
-0.038663219660520554,
0.006053498946130276,
-0.0015592591371387243,
-0.0009096473804675043,
-0.05519099533557892,
-0.04678212106227875,
0.026159005239605904,
0.025660555809736252,
0.012754871509969234,
-0.0365065261721611,
0.05028664693236351,
-0.014112177304923534,
-0.08490228652954102,
0.00028053397545590997,
0.0200255885720253,
0.022301023826003075,
-0.0652318000793457,
-0.03876766934990883,
0.002520487178117037,
-0.015125297009944916,
-0.009401652030646801,
-0.027703700587153435,
-0.023738812655210495,
0.028806693851947784,
-0.021618572995066643,
-0.01799630932509899,
-0.03540290892124176,
0.026862481608986855,
-0.022496085613965988,
0.0032761041074991226,
-0.01617426797747612,
-0.038696564733982086,
0.027104608714580536,
0.06038178876042366,
0.04279397428035736,
-0.015411116182804108,
-0.01603126898407936,
0.01853710412979126,
-0.035707488656044006,
0.007800957188010216,
0.030352797359228134,
0.01592707261443138,
-0.015619993209838867,
0.01808684691786766,
0.02594226785004139,
-0.010557258501648903,
-0.01777615211904049,
0.001469468348659575,
0.02911428175866604,
0.07976499199867249,
-0.014723502099514008,
-0.03625361993908882,
0.002621057676151395,
0.024686045944690704,
0.00045822979882359505,
0.001470597693696618,
-0.03520972281694412,
0.0709390789270401,
0.009570886380970478,
-0.007959596812725067,
-0.05499746650457382,
0.029522765427827835,
0.06328753381967545,
-0.025644702836871147,
-0.0656326562166214,
-0.09286267310380936,
-0.06059865280985832,
0.035885896533727646,
-0.014764062128961086,
0.037879567593336105,
-0.00856493879109621,
-0.029328705742955208,
-0.009154798462986946,
0.0977533832192421,
0.08132088929414749,
-0.032877057790756226,
0.014839413575828075,
-0.025688692927360535,
0.04354781657457352,
0.05593867599964142,
-0.06842376291751862,
-0.02780192717909813,
0.04567266255617142,
0.04133184254169464,
0.032179348170757294,
-0.0025610572192817926,
0.04009699076414108,
-0.05947406589984894,
-0.02518344111740589,
0.021314091980457306,
0.06364338845014572,
-0.014504407532513142,
-0.01047116331756115,
-0.006671051029115915,
-0.06436716765165329,
-0.050293825566768646,
0.009210105985403061,
-0.024433007463812828,
-0.009412472136318684,
0.029695214703679085,
0.009224940091371536,
-0.032637543976306915,
0.06820345669984818,
-0.02161473222076893,
-0.0186824481934309,
-0.0008882191614247859,
0.0088574830442667,
0.01775943674147129,
-0.037783071398735046,
0.0048385364934802055,
-0.0018063575262203813,
0.04523426666855812,
0.02992057241499424,
0.037718430161476135,
0.018546154722571373,
-0.015798714011907578,
0.043290674686431885,
-0.03936038166284561,
-0.007502349559217691,
0.025141485035419464,
-0.0556238517165184,
-0.057468611747026443,
0.012094151228666306,
0.03928167000412941,
-0.013483049347996712,
0.06654016673564911,
0.10592636466026306,
-0.02668001689016819,
-0.007978126406669617,
0.005611680913716555,
0.02738153003156185,
-0.027024362236261368,
-0.005609496496617794,
-0.015200786292552948,
0.012322363443672657,
-0.049180518835783005,
0.03498619422316551,
0.019703691825270653,
0.004498684778809547,
-0.07528755813837051,
0.04469703882932663,
0.016071496531367302,
-0.029134361073374748,
-0.05947766453027725,
-0.03379981964826584,
-0.046068981289863586,
0.040877386927604675,
0.054427795112133026,
-0.019277814775705338,
0.012281319126486778,
0.050837140530347824,
0.0003679329820442945,
0.039059218019247055,
0.03924374282360077,
0.024166634306311607,
0.06991713494062424,
-0.025318937376141548,
-0.0784936249256134,
0.01316758245229721,
-0.017140431329607964,
0.0077800205908715725,
-0.011106105521321297,
-0.052421025931835175,
-0.009625725448131561,
0.034442394971847534,
0.025851836428046227,
-0.04700465127825737,
0.019149255007505417,
0.0586465559899807,
-0.03791569173336029,
0.02857734076678753,
-0.042869683355093,
0.011634375900030136,
0.018182281404733658,
0.024620885029435158,
0.012048347853124142,
-0.08635232597589493,
0.02926245518028736,
-0.036860331892967224,
-0.016779500991106033,
-0.03302811086177826,
-0.06237585097551346,
0.022129865363240242,
0.015104995109140873,
-0.026995325461030006,
0.014689154922962189,
-0.03224761039018631,
-0.020077235996723175,
0.012529396452009678,
0.035872865468263626,
0.07557078450918198,
0.0005456545623019338,
0.00920436717569828,
-0.026113441213965416,
0.035138677805662155,
0.06831061840057373,
-0.03895223140716553,
0.04457927867770195,
-0.013253770768642426,
-0.02919146418571472,
0.002399613382294774,
-0.007839166559278965,
-0.02799413353204727,
-0.0551452673971653,
-0.005344942212104797,
0.003556111129000783,
-0.0517098531126976,
-0.02212313562631607,
0.04180217161774635,
-0.05117642879486084,
0.01382494904100895,
0.027713356539607048,
0.025364119559526443,
0.010721873492002487,
0.053311001509428024,
-0.014533024281263351,
0.020243234932422638,
0.018611717969179153,
-0.03854964300990105,
0.043632399290800095,
0.010313635692000389,
-0.005110817030072212,
0.09397652745246887,
-0.015523668378591537,
0.035133928060531616,
-0.019689159467816353,
-0.029599281027913094,
-0.06758010387420654,
-0.004869504831731319,
0.009164152666926384,
-0.004928072448819876,
0.014200694859027863,
0.023390669375658035,
-0.015989627689123154,
0.02735879458487034,
-0.011973277665674686,
0.05758470669388771,
-0.010846076533198357,
-0.017024559900164604,
-0.02547854371368885,
-0.0010645579313859344,
-0.0776280090212822,
0.08443368971347809,
0.017406878992915154,
-0.047511085867881775,
-0.021708926185965538,
-0.07237572968006134,
-0.05329715833067894,
-0.02656267210841179,
-0.0627247616648674,
0.08184085786342621,
-0.045339684933423996,
-0.010997218079864979,
-0.03730672970414162,
0.08663154393434525,
0.011705168522894382,
0.01430777832865715,
-0.021710576489567757,
-0.04184216260910034,
0.01986892893910408,
-0.01467303466051817,
0.023853909224271774,
-0.00882641039788723,
-0.00809638574719429,
0.00040354151860810816,
-0.04533940553665161,
0.03995220735669136,
0.010540192015469074,
-0.04322023689746857,
-0.013050097972154617,
0.027166401967406273,
-0.08612130582332611,
-0.037778522819280624,
-0.043418314307928085,
-0.03143562749028206,
0.03397577628493309,
0.038869429379701614,
0.027116628363728523,
-0.01914716511964798,
-0.03208747133612633,
-0.0011962997959926724,
-0.04734048247337341,
-0.026541493833065033,
0.03926147148013115,
-0.0455656535923481,
0.03320802375674248,
-0.030985256657004356,
-0.08343181759119034,
-0.04082706570625305,
0.08191774785518646,
-0.0016962228110060096,
0.007177043240517378,
0.02007496915757656,
-0.05004911497235298,
0.02683008648455143,
0.004925070330500603,
-0.05947154760360718,
-0.07067108154296875,
0.057533539831638336,
-0.03302757069468498,
-0.012388387694954872,
0.0019317122641950846,
-0.033350881189107895,
-0.014421308413147926,
-0.016598980873823166,
0.03204056993126869,
0.018566226586699486,
-0.009793524630367756,
0.03342953696846962,
-0.0147325424477458,
-0.00809797178953886,
0.038713887333869934,
-0.040912143886089325,
-0.014737989753484726,
-0.013328487053513527,
0.05356748029589653,
-0.016833683475852013,
0.07119545340538025,
0.04956307262182236,
-0.03501877933740616,
-0.03591327741742134,
0.04715269058942795,
-0.017453374341130257,
0.0004557825159281492,
-0.01997913420200348,
0.028507554903626442,
-0.02711286023259163,
0.01630721427500248,
-0.0006519384332932532,
-0.006176672875881195,
0.01392320729792118,
-0.02696126326918602,
-0.01603720709681511,
0.03710160404443741,
0.013915431685745716,
0.019661691039800644,
0.011334896087646484,
0.02522999420762062,
0.012320246547460556,
-0.020007062703371048,
0.04622415825724602,
-0.03635657951235771,
-0.05586264282464981,
0.045396946370601654,
-0.07730245590209961,
0.05715732276439667,
-0.009602938778698444,
0.03485162556171417,
-0.00024657242465764284,
-0.046570390462875366,
0.02516450732946396,
0.01897173747420311,
0.013869253918528557,
-0.018757086247205734,
-0.04310392215847969,
0.00856787245720625,
0.0018012512009590864,
-0.011324276216328144,
0.008743580430746078,
0.01111779548227787,
-0.05311686545610428,
0.024632805958390236,
-0.08702853322029114,
0.02986270934343338,
-0.016261272132396698,
0.03958616033196449,
-0.053401827812194824,
0.03109864331781864,
-0.03848860785365105,
-0.05213069170713425,
0.022210311144590378,
0.022427469491958618,
0.0885927677154541,
-0.015032880939543247,
-0.0020112053025513887,
0.07487596571445465,
0.0681484192609787,
0.03468827158212662,
-0.035140033811330795,
0.026837492361664772,
-0.015622666105628014,
-0.025557320564985275,
0.0345333069562912,
0.05730132758617401,
-0.02433190494775772,
-0.02310223877429962,
-0.0041974312625825405,
-0.004554860293865204,
0.01255621574819088,
-0.0041215550154447556,
0.04090375453233719,
-0.05484281852841377,
0.020845837891101837,
0.01872250810265541,
-0.011569802649319172,
-0.042975813150405884,
0.057442519813776016,
-0.07708804309368134,
-0.05397340655326843,
-0.011102723889052868,
0.003961531445384026,
-0.0013834501150995493,
-0.001711021875962615,
0.03670794516801834,
-0.004490354564040899,
-0.01820560172200203,
-0.010558556765317917,
-0.025803042575716972,
-0.03553598374128342,
0.010523645207285881,
-0.005411203950643539,
-0.056190069764852524,
-0.03709244728088379,
-0.01718173362314701,
-0.007769790943711996,
0.044071100652217865,
0.026663027703762054,
-0.03227187693119049,
0.0007586650899611413,
-0.046760715544223785,
-0.004950400907546282,
0.036646462976932526,
0.029286794364452362,
0.01935589127242565,
0.07623612880706787,
0.051150791347026825,
-0.010676424019038677,
0.009302930906414986,
0.017195211723446846,
0.025252895429730415,
-0.04008200392127037,
-0.015398277901113033,
0.005151411984115839,
-0.01622825302183628,
0.017993610352277756,
0.005193296354264021,
-0.04728946089744568,
0.012797477655112743,
-0.03955059126019478,
0.038146305829286575,
0.011498537845909595,
0.022876614704728127,
-0.007651718333363533,
0.0013518370687961578,
0.012496698647737503,
0.004403913859277964,
0.02585676871240139,
-0.013974511995911598,
-0.04254046455025673,
0.01655653864145279,
-0.00681089935824275,
-0.03557754307985306,
0.03669966384768486,
0.021321354433894157,
0.005698715336620808,
-0.010349394753575325,
-0.019442502409219742,
0.059391606599092484,
-0.03135941922664642,
-0.014093050733208656,
0.02941608987748623,
0.002066514454782009,
0.05675215274095535,
-0.02282279171049595,
-0.020433953031897545,
-0.015153411775827408,
-0.03713555634021759,
0.001068276702426374,
0.016542872413992882,
-0.06234147399663925,
-0.00939259771257639,
0.00790806021541357,
-0.021841218695044518,
0.0277488362044096,
-0.02967843972146511,
0.0008476903894916177,
0.02696465514600277,
0.02691102772951126,
0.0062701706774532795,
-0.026422202587127686,
0.07305669039487839,
-0.018929671496152878,
0.031094782054424286,
0.009559186175465584,
0.026159396395087242,
-0.0007161270477809012,
0.022177301347255707,
-0.022059014067053795,
-0.0009257645579054952,
0.002220327267423272,
-0.05451440066099167,
0.0018985567148774862,
-0.01254467386752367,
0.003997166641056538,
0.02516879327595234,
-0.05202328413724899,
-0.003857421688735485,
-0.020740192383527756,
-0.020626462996006012,
-0.01126885786652565,
-0.05364149808883667,
-0.0655033141374588,
0.005738449282944202,
0.008212059736251831,
-0.03404756262898445,
-0.043605007231235504,
0.017104828730225563,
-0.03892410546541214,
-0.009971458464860916,
-0.025151671841740608,
-0.029884302988648415,
0.054840147495269775,
-0.010595673695206642,
-0.015261328779160976,
0.0014869810547679663,
-0.009936894290149212,
-0.016951613128185272,
0.0005227316287346184,
-0.007488469127565622,
0.0053270780481398106,
0.009151352569460869,
-0.022003503516316414,
0.012699573300778866,
0.034857820719480515,
0.042895905673503876,
0.010282514616847038,
-0.0033581748139113188,
-0.0550256110727787,
-0.028045576065778732,
-0.06976329535245895,
0.0016504921950399876,
-0.07553107291460037,
0.019423672929406166,
0.005892509128898382,
-0.06453002244234085,
-0.0008712228154763579,
0.0024663745425641537,
-0.05257490277290344,
-0.03094012290239334,
-0.014288096688687801,
0.017768671736121178,
0.03014991618692875,
0.010220392607152462,
0.007284244522452354,
0.06777137517929077,
0.039059873670339584,
0.03171228989958763,
0.00926473829895258,
0.0884580984711647,
0.005472287070006132,
0.04541614279150963,
0.046205006539821625,
0.0473739318549633,
0.09564854204654694,
0.03326040878891945,
0.010879529640078545,
0.029005711898207664,
-0.02645590901374817,
0.011649339459836483,
0.014603175222873688,
-0.049620967358350754,
-0.03876245394349098,
0.022550253197550774,
0.048393722623586655,
0.02417822554707527,
0.046891823410987854,
0.015914801508188248,
-0.039013106375932693,
-0.004468210972845554,
-0.041530266404151917,
0.014827875420451164,
0.01921462081372738,
0.00149242184124887,
-0.031924210488796234,
0.06685326248407364,
-0.059426501393318176,
0.01372020784765482,
-0.06604437530040741,
-0.04645735025405884,
-0.005078339949250221,
-0.04972745105624199,
-0.03633151575922966,
-0.011056262068450451,
-0.022965099662542343,
0.042512401938438416,
-0.028671421110630035,
0.029091449454426765,
-0.05667436867952347,
0.08840250968933105,
0.04208354279398918,
0.0007776950369589031,
0.019138747826218605,
0.004370746668428183,
0.03342520818114281,
0.025792503729462624,
-0.03682365268468857,
-0.025014879181981087,
-0.01852327212691307,
-0.04449614882469177,
-0.09506819397211075,
0.01487184688448906,
-0.009714944288134575,
-0.01194431260228157,
-0.04086186736822128,
0.06274345517158508,
-0.020375143736600876,
-0.033585578203201294,
-0.03010747954249382,
-0.018229153007268906,
-0.05090531334280968,
0.008486323989927769,
-0.0034257969819009304,
0.019268367439508438,
0.006732886657118797,
0.021716667339205742,
0.007728158961981535,
0.051763344556093216,
0.010893940925598145,
0.02321118488907814,
-0.010486861690878868,
0.013457736000418663,
0.04377548769116402,
0.02589309774339199,
-0.010705478489398956,
0.07228519022464752,
-0.04419374838471413,
0.053527217358350754,
-0.009807576425373554,
0.05153697729110718,
-0.007345640566200018,
0.0393606573343277,
-0.010649247094988823,
0.0767214223742485,
0.024093203246593475,
-0.0005541119608096778,
-0.04249941185116768,
-0.06158941239118576,
0.01746586710214615,
-0.06736759096384048,
-0.0013331113150343299,
0.02219187468290329,
-0.09822569042444229,
0.05095963552594185,
0.03709985315799713,
0.01834484189748764,
-0.024202551692724228,
-0.005531943868845701,
0.06973117589950562,
-0.020361416041851044,
0.028867201879620552,
0.010664669796824455,
-0.026150140911340714,
0.00224516773596406,
0.019031239673495293,
0.04520023614168167,
-0.02972055785357952,
-0.019358545541763306,
-0.021289654076099396,
-0.009389881044626236,
-0.02103274129331112,
0.044851358979940414,
-0.007133484818041325,
0.018182752653956413,
-0.0422317311167717,
-0.025569338351488113,
0.032868642359972,
-0.03377120569348335,
0.0020485457498580217,
0.010596906766295433,
-0.028639864176511765,
-0.053667712956666946,
-0.0016353027895092964,
0.00669201510027051,
0.01608809269964695,
-0.10601344704627991,
0.022977281361818314,
-0.006884022615849972,
-0.030479906126856804,
-0.04985138773918152,
0.03338688984513283,
0.011006314307451248,
-0.004605995956808329,
-0.012864687480032444,
-0.012400414794683456,
-0.009365175850689411,
0.03822685033082962,
0.045672059059143066,
0.02707073837518692,
-0.032854557037353516,
-0.008215174078941345,
0.07781046628952026,
0.0019500944763422012,
0.006703568156808615,
-0.06394752115011215,
0.0009513307013548911,
-0.0149914575740695,
-0.0010910440469160676,
0.03403161093592644,
0.021191176027059555,
0.07118222862482071,
0.022865217179059982,
-0.02436787821352482,
-0.01581420749425888,
0.04026593267917633,
0.028156006708741188,
0.034984055906534195,
-0.06205834075808525,
-0.03723720461130142,
0.056582655757665634,
0.0740869864821434,
0.060407593846321106,
0.005816546268761158,
0.038009051233530045,
-0.0018860864220187068,
0.0011441736714914441,
0.013090104795992374,
-0.014677682891488075,
-0.005011675413697958,
0.05272601917386055
] |
<p>Consider a thick wire that narrows for some part of its length, connected to the terminals of a battery, hence carrying some current.</p>
<p>Presumably the electrons have to speed up as the wire gets thinner - if the current is constant everywhere, then if the wire cross-section is less, they have to go through faster in order for the same number of electrons to pass any point in a given time.</p>
<p>What accelerates them as the wire narrows?</p>
<p>And what decelerates them again as the wire widens out again after the narrow bit?</p> | g1290 | [
0.07036509364843369,
0.05338919535279274,
0.00960509292781353,
0.017511829733848572,
0.048773057758808136,
0.012976127676665783,
0.04781043902039528,
0.03037518635392189,
-0.07800038903951645,
0.004988261964172125,
-0.009998861700296402,
0.05228063464164734,
-0.034816592931747437,
0.012701376341283321,
0.05965261906385422,
-0.002739605726674199,
0.007631305605173111,
-0.008838566951453686,
0.06105462834239006,
0.03150501474738121,
0.041416898369789124,
0.02234911173582077,
-0.004674928262829781,
-0.049262527376413345,
-0.014707225374877453,
0.029935747385025024,
-0.01846812665462494,
0.0023484015837311745,
0.007423339411616325,
-0.025129804387688637,
0.011693278327584267,
-0.03514956682920456,
0.025718841701745987,
-0.021738620474934578,
-0.006480447016656399,
0.014518588781356812,
0.019386908039450645,
-0.009117764420807362,
0.027321217581629753,
0.016232240945100784,
0.015135927125811577,
-0.0312843956053257,
0.005982935894280672,
0.019942671060562134,
0.009551598690450191,
-0.05851590633392334,
-0.044703949242830276,
0.008434615097939968,
-0.007417595945298672,
-0.059544287621974945,
-0.05610796809196472,
0.01935976929962635,
0.008456802926957607,
-0.008599597029387951,
0.05769117921590805,
-0.02604183927178383,
-0.005881082732230425,
-0.010757350362837315,
0.0325196199119091,
0.0778612568974495,
-0.0075135184451937675,
-0.025745175778865814,
0.06036105751991272,
0.0010457569733262062,
0.07529991120100021,
-0.034095898270606995,
0.051948267966508865,
-0.012256918475031853,
0.06072897091507912,
-0.001577346702106297,
0.007724642287939787,
-0.08581964671611786,
-0.06843846291303635,
-0.06716977804899216,
0.0002626189379952848,
-0.02237149327993393,
-0.007410977501422167,
-0.03295179083943367,
0.0005582589656114578,
-0.008889800868928432,
-0.12660759687423706,
0.04129581153392792,
-0.0339190736413002,
0.050324853509664536,
-0.02001381106674671,
0.033601824194192886,
0.02040656842291355,
-0.04274647682905197,
0.0009287871653214097,
-0.005071436520665884,
0.04450144246220589,
-0.006700321100652218,
0.04109949991106987,
-0.03347590193152428,
-0.10335022956132889,
-0.028763379901647568,
-0.0009830882772803307,
0.055831871926784515,
0.02604714035987854,
0.017580736428499222,
-0.016206171363592148,
-0.0635177418589592,
0.01692330650985241,
0.0003507358196657151,
-0.03337891772389412,
0.014440176077187061,
-0.004464596509933472,
-0.06403053551912308,
-0.003606033744290471,
0.033174898475408554,
-0.01992172561585903,
-0.10932976752519608,
-0.025729574263095856,
-0.021507596597075462,
-0.02625245414674282,
0.05673640966415405,
-0.013134122826159,
0.04354401305317879,
-0.029239743947982788,
0.03792958706617355,
0.01385597512125969,
0.005271600093692541,
-0.00471588084474206,
-0.0019156357739120722,
-0.027927136048674583,
0.046094220131635666,
0.011417822912335396,
0.04746932536363602,
0.004942212253808975,
0.00027453331858851016,
0.030206719413399696,
0.05877687782049179,
0.02148171328008175,
0.033465269953012466,
0.013760406523942947,
-0.0565558522939682,
-0.06163269281387329,
0.0019008803647011518,
-0.007076622918248177,
0.017081111669540405,
-0.003030839143320918,
-0.06330303102731705,
0.044144921004772186,
-0.02347487583756447,
-0.006064348388463259,
-0.01031748577952385,
-0.045088011771440506,
-0.0003940404858440161,
0.04742143675684929,
0.03216400370001793,
-0.008232178166508675,
0.053217336535453796,
-0.0013019995531067252,
-0.08333852142095566,
0.04285189509391785,
0.0224445890635252,
0.0750269740819931,
0.000911108625587076,
0.0332355760037899,
0.03079153038561344,
0.014719916507601738,
-0.03315884247422218,
-0.01588977500796318,
0.014972824603319168,
-0.08885736018419266,
0.003227798966690898,
0.04078599810600281,
-0.05461239069700241,
0.03560404106974602,
0.02429335005581379,
-0.005892397835850716,
0.00613789726048708,
0.005200009327381849,
0.0277907345443964,
0.00045162008609622717,
0.05139557272195816,
0.06507540494203568,
-0.027147335931658745,
-0.016902033239603043,
-0.0274436566978693,
-0.05249201878905296,
-0.02429976686835289,
0.03573598712682724,
0.02885027602314949,
0.05405225604772568,
-0.008955910801887512,
-0.030587218701839447,
-0.007919084280729294,
-0.08795413374900818,
-0.010772556066513062,
0.012636994943022728,
-0.08529945462942123,
-0.030506866052746773,
-0.0020598345436155796,
-0.03616013750433922,
-0.0508810430765152,
-0.007886209525167942,
-0.016536816954612732,
-0.00398551719263196,
-0.0736069530248642,
0.0024412120692431927,
0.03687223419547081,
0.06724918633699417,
0.04825887084007263,
0.06693332642316818,
0.012411298230290413,
-0.03593192622065544,
-0.04783523082733154,
0.04900817945599556,
0.017310960218310356,
0.05520327389240265,
0.029416484758257866,
-0.002622179454192519,
0.0120759978890419,
-0.016472743824124336,
-0.015542736276984215,
-0.045474741607904434,
0.005645616911351681,
0.03248526528477669,
-0.003439015941694379,
0.019319327548146248,
-0.07292445003986359,
-0.010689844377338886,
-0.00341437547467649,
-0.03480551019310951,
-0.04096657782793045,
0.024991488084197044,
-0.07023819535970688,
0.017274975776672363,
0.01027707476168871,
-0.05487584322690964,
0.015271799638867378,
-0.09634758532047272,
-0.06643681228160858,
0.015058805234730244,
0.010529659688472748,
-0.000476571440231055,
0.022896090522408485,
-0.022658556699752808,
-0.08132103830575943,
0.008383148349821568,
0.03259586542844772,
0.033992376178503036,
-0.03876664116978645,
-0.011804372072219849,
-0.09291572123765945,
0.0796564370393753,
-0.034420136362314224,
0.012996145524084568,
0.027767915278673172,
0.028005139902234077,
-0.026215728372335434,
-0.024287201464176178,
0.07359639555215836,
-0.012986937537789345,
-0.030818315222859383,
0.0005588824860751629,
0.03372683748602867,
-0.017130492255091667,
-0.04901126027107239,
-0.006297842133790255,
0.07441844791173935,
-0.01144152320921421,
-0.004544432740658522,
-0.050564274191856384,
-0.03971017152070999,
-0.01220865547657013,
-0.05957033112645149,
0.008997814729809761,
-0.022702593356370926,
-0.03785916045308113,
0.054440222680568695,
-0.055644407868385315,
-0.0313141755759716,
0.04233342409133911,
-0.035980790853500366,
0.026006145402789116,
-0.023246753960847855,
0.0260996762663126,
0.008312462829053402,
0.004521658644080162,
0.015991900116205215,
-0.019247913733124733,
0.010363458655774593,
0.0019105495885014534,
-0.037777822464704514,
0.014087650924921036,
0.01821664348244667,
0.018647190183401108,
0.0017661453457549214,
-0.027515528723597527,
0.002113813068717718,
0.1250116378068924,
-0.03758334368467331,
0.053889427334070206,
0.06587417423725128,
0.06037406623363495,
-0.03337372466921806,
-0.020067857578396797,
-0.009633682668209076,
-0.0244756992906332,
-0.02640925534069538,
-0.02458588406443596,
0.02518949657678604,
0.03862859308719635,
0.05149922892451286,
-0.01793028600513935,
-0.03848213329911232,
-0.027152348309755325,
-0.017257442697882652,
-0.001458026934415102,
-0.05376244708895683,
0.06100044026970863,
-0.026729626581072807,
-0.023793218657374382,
-0.06907908618450165,
-0.015671029686927795,
0.04891861230134964,
0.06239995360374451,
-0.018934588879346848,
-0.010209336876869202,
-0.04751502722501755,
-0.025978729128837585,
0.018645014613866806,
0.01600777544081211,
0.014213480055332184,
0.018582550808787346,
-0.0006572419661097229,
-0.014534597285091877,
0.022256286814808846,
-0.012819032184779644,
-0.020661910995841026,
-0.03433465585112572,
-0.009666750207543373,
-0.0315309576690197,
-0.046893250197172165,
0.05028877407312393,
0.0880657508969307,
0.028083695098757744,
0.023264622315764427,
-0.002855744445696473,
0.05818543955683708,
-0.0708368644118309,
-0.0015038849087432027,
-0.014429940842092037,
-0.012681528925895691,
0.026337608695030212,
-0.0018055896507576108,
-0.004200931638479233,
-0.03451981022953987,
0.059790872037410736,
0.026192225515842438,
0.020053040236234665,
-0.012581135146319866,
-0.03641863912343979,
-0.0008991507929749787,
-0.06318449974060059,
-0.057859763503074646,
-0.01835467480123043,
-0.0326247364282608,
-0.013592809438705444,
-0.015606156550347805,
0.03800256550312042,
0.05559099093079567,
-0.062427226454019547,
-0.017276180908083916,
0.03335897624492645,
0.04850180819630623,
0.00637777941301465,
-0.051830701529979706,
0.006088825408369303,
0.008187107741832733,
-0.019451377913355827,
0.02645544707775116,
-0.03831592574715614,
-0.013983823359012604,
0.016137052327394485,
0.02296663261950016,
-0.021115975454449654,
-0.011237495578825474,
0.021397866308689117,
-0.020813986659049988,
-0.016685770824551582,
-0.005376518238335848,
-0.014861867763102055,
-0.04245980456471443,
-0.01570725068449974,
-0.03108918108046055,
-0.014780369587242603,
-0.026698706671595573,
0.04979260638356209,
0.029363788664340973,
-0.007564753759652376,
0.016825716942548752,
0.013354264199733734,
-0.018359558656811714,
0.03310807794332504,
-0.02046818844974041,
0.006103789899498224,
0.004249628633260727,
0.029111817479133606,
0.062446631491184235,
-0.03836529701948166,
0.04744454473257065,
0.025261778384447098,
0.039491742849349976,
0.024213893339037895,
-0.003783844644203782,
-0.009369894862174988,
0.02193267270922661,
-0.009414675645530224,
0.010373969562351704,
-0.03665517643094063,
-0.029045751318335533,
0.002404190134257078,
0.03679117560386658,
0.09534739702939987,
-0.00002687677988433279,
-0.05124830827116966,
0.013146325014531612,
-0.0340314619243145,
0.000946269603446126,
0.0364704504609108,
-0.014084949158132076,
-0.05827920511364937,
0.006100179627537727,
0.014406776987016201,
0.02460063248872757,
0.015284176915884018,
-0.00808141753077507,
-0.02628716453909874,
0.05335333198308945,
-0.004363819025456905,
0.00790223479270935,
-0.010959493927657604,
0.03754559904336929,
0.009544114582240582,
0.03177832439541817,
-0.00041036587208509445,
0.048615869134664536,
0.07007353752851486,
-0.026871124282479286,
0.0025909666437655687,
0.010796151123940945,
-0.043463267385959625,
0.03138969838619232,
-0.0519915372133255,
0.0038940829690545797,
0.00010084463428938761,
-0.010238598100841045,
-0.02602437324821949,
0.025546174496412277,
0.00987992249429226,
-0.03989240527153015,
-0.0013424400240182877,
-0.020580071955919266,
-0.05026908963918686,
-0.011658580042421818,
0.04968496412038803,
0.061460353434085846,
-0.041158080101013184,
0.055890657007694244,
-0.02220575511455536,
0.016606168821454048,
-0.027139432728290558,
-0.008410511538386345,
0.03275962918996811,
0.0009523715707473457,
-0.06173388659954071,
-0.0007134467596188188,
-0.04801701381802559,
0.028742389753460884,
0.011014401912689209,
0.032184675335884094,
0.05168627202510834,
0.002139319898560643,
0.01045924797654152,
0.03549954667687416,
-0.06072189658880234,
0.013261836022138596,
-0.041307900100946426,
-0.04302529990673065,
0.014693881385028362,
-0.024895265698432922,
-0.03271281719207764,
0.018311966210603714,
-0.007757710292935371,
0.05836695060133934,
0.00275499583221972,
-0.041503019630908966,
0.02133697085082531,
0.036532383412122726,
0.01821402832865715,
0.0004922759835608304,
-0.05085430666804314,
0.00949778500944376,
0.06464026868343353,
0.07733768969774246,
-0.03014937788248062,
-0.01891840063035488,
-0.00622164411470294,
-0.015666889026761055,
-0.04896381124854088,
0.008410799317061901,
0.0041645667515695095,
0.06310199201107025,
-0.007444698363542557,
-0.07223771512508392,
0.023827048018574715,
-0.01459200493991375,
-0.08717495948076248,
0.08985894173383713,
0.015148214995861053,
-0.008090410381555557,
0.028912479057908058,
-0.010691908188164234,
-0.06648723781108856,
-0.031735554337501526,
-0.0037699518725275993,
-0.04396188259124756,
0.07322239875793457,
0.020816177129745483,
-0.012128083035349846,
0.01398586668074131,
0.02689494378864765,
-0.019299523904919624,
-0.07319330424070358,
0.01781502552330494,
0.04063190892338753,
0.012471719644963741,
0.08351873606443405,
-0.021618787199258804,
-0.005200343672186136,
-0.013079395517706871,
-0.005191172007471323,
0.04733975604176521,
0.05997593328356743,
-0.046291202306747437,
-0.02900366112589836,
0.003771405201405287,
-0.020224321633577347,
0.005841368809342384,
0.010306193493306637,
0.09956379234790802,
-0.0059641283005476,
-0.06472471356391907,
0.00818127766251564,
-0.00960712879896164,
0.034790750592947006,
-0.03231559321284294,
-0.04157673567533493,
-0.027807187288999557,
-0.012378793209791183,
0.029196983203291893,
-0.016865946352481842,
0.059371985495090485,
0.040133263915777206,
0.03773907572031021,
0.014887670986354351,
-0.04624444618821144,
0.05960625410079956,
0.02579665742814541,
0.023630432784557343,
0.0006057914579287171,
0.04140999913215637,
-0.08761409670114517,
-0.058259204030036926,
0.05060971528291702,
0.07127023488283157,
0.04525785520672798,
0.014875124208629131,
-0.01062830351293087,
-0.00006801859854022041,
-0.006347622722387314,
0.023822806775569916,
0.03890589252114296,
-0.03736816346645355,
-0.012377939186990261,
-0.032463811337947845,
-0.0012280020164325833,
-0.0023124050348997116,
0.031017260625958443,
0.009943476878106594,
-0.0025993434246629477,
0.005191904492676258,
0.022544261068105698,
-0.03566911444067955,
0.018441686406731606,
0.06581491976976395,
0.03871018439531326,
-0.051141440868377686,
0.05154849588871002,
0.012497992254793644,
0.017315976321697235,
-0.0410035103559494,
-0.018617719411849976,
-0.04201063513755798,
0.020507188513875008,
-0.013336244970560074,
0.03286774456501007,
-0.02040136232972145,
0.027362778782844543,
0.05610031262040138,
0.03862559422850609,
0.01156458631157875,
0.0024086071643978357,
0.03233266621828079,
0.004279003012925386,
-0.0025532618165016174,
-0.002367683220654726,
0.045199643820524216,
0.01105517242103815,
0.03932234272360802,
-0.0008040631655603647,
0.0011422710958868265,
0.022420046851038933,
-0.027667799964547157,
-0.04028503969311714,
0.00941975973546505,
0.0015949272783473134,
0.0018945400370284915,
-0.06104995310306549,
-0.04003872349858284,
0.046825066208839417,
0.02192862518131733,
0.0035128092858940363,
-0.01210140809416771,
-0.02003924734890461,
0.01044710073620081,
-0.06650648266077042,
0.013347296044230461,
0.027322279289364815,
-0.005433779209852219,
0.010708914138376713,
0.037862200289964676,
-0.02242787554860115,
0.020953765138983727,
0.0026168348267674446,
-0.02604133076965809,
0.033087678253650665,
0.05987478792667389,
0.006524200085550547,
-0.06659765541553497,
0.04095625504851341,
-0.02091410383582115,
-0.06393327564001083,
-0.0033825356513261795,
0.010358571074903011,
0.0060550374910235405,
-0.01443660631775856,
0.0004031108692288399,
-0.04307032376527786,
-0.02806963212788105,
0.026926469057798386,
0.029309630393981934,
-0.026308901607990265,
0.016337459906935692,
-0.006787674967199564,
0.03248219192028046,
0.04016905277967453,
-0.029926879331469536,
-0.03680117800831795,
0.010116503573954105,
0.02301369421184063,
0.024890722706913948,
0.0210733562707901,
-0.011423563584685326,
-0.03468547761440277,
-0.03585844486951828,
-0.011393366381525993,
-0.005125891882926226,
-0.03690808638930321,
0.055340029299259186,
-0.010106047615408897,
0.072794109582901,
-0.00807257555425167,
-0.05783779174089432,
0.012084918096661568,
0.020488522946834564,
-0.02121155522763729,
0.036080215126276016,
0.02602769248187542,
-0.016545172780752182,
-0.024956613779067993,
-0.014921123161911964,
0.010945865884423256,
-0.03924710676074028,
0.03248570114374161,
-0.023906489834189415,
-0.03240255266427994,
0.018066486343741417,
-0.01947307400405407,
0.00935337319970131,
0.03616419434547424,
0.013081280514597893,
0.0545908622443676,
0.02019774168729782,
-0.009107581339776516,
-0.026120614260435104,
0.01750491000711918,
-0.023785768076777458,
0.03601791709661484,
-0.011508412659168243,
0.07881928235292435,
-0.005378550849854946,
-0.007970863953232765,
-0.025454459711909294,
-0.05460469052195549,
-0.028292236849665642,
0.000447168480604887,
-0.019591309130191803,
0.001263583661057055,
-0.022025227546691895,
0.024867381900548935,
0.03646950423717499,
-0.028217006474733353,
-0.022109942510724068,
-0.0017614340176805854,
-0.0039415801875293255,
-0.003406834788620472,
-0.022821346297860146,
0.0027863015420734882,
0.0014846534468233585,
0.035299934446811676,
0.02247687615454197,
-0.030129093676805496,
0.005769857671111822,
-0.006556513719260693,
-0.009589068591594696,
0.04257194325327873,
-0.04323406517505646,
-0.020725425332784653,
0.032304562628269196,
-0.020748373121023178,
-0.041366420686244965,
-0.01584659330546856,
0.012895477935671806,
-0.036415889859199524,
-0.005159431602805853,
0.020937860012054443,
0.02462470531463623,
-0.010600320063531399,
-0.060903895646333694,
0.026134978979825974,
-0.029240835458040237,
0.018507638946175575,
0.011844087392091751,
0.02660422958433628,
0.08436024934053421,
-0.05688817799091339,
0.04606153070926666,
-0.06856854259967804,
-0.07784264534711838,
-0.0052723209373652935,
0.00965940486639738,
0.039418190717697144,
-0.0183330699801445,
0.028863240033388138,
-0.05735950917005539,
-0.004052727948874235,
-0.05278325080871582,
-0.009364086203277111,
-0.003992876037955284,
-0.03688887506723404,
0.003425144823268056,
-0.06844346225261688,
-0.050689276307821274,
-0.0009062480530701578
] |
<p>I tried to calculate earth's orbital period using <a href="https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion#Third_law" rel="nofollow">Kepler's third law</a>, but I found 365.2075 days for the orbital period instead of 365.256363004 which is the correct value. I checked everything, and I couldn't find what's the problem.
I used these values for my calculation:</p>
<ul>
<li>Semi-major axis, a: 149,598,261 km</li>
<li>Gravitational constant, G: 6.67*10<sup>-11</sup> N·(m/kg)<sup>2</sup></li>
<li>Solar mass, M: 1.9891*10<sup>30</sup> kg</li>
</ul> | g1291 | [
0.014693659730255604,
0.07671560347080231,
0.023560496047139168,
-0.0077977851033210754,
-0.0015345608117058873,
0.0634806752204895,
0.015296123921871185,
-0.003877107286825776,
-0.0068130106665194035,
0.03712394833564758,
0.042247019708156586,
-0.020744280889630318,
0.022070059552788734,
-0.011610021814703941,
0.05576546490192413,
0.01618572138249874,
0.098714679479599,
-0.01693672500550747,
0.014854153618216515,
0.05321890860795975,
0.037864867597818375,
0.04061046987771988,
-0.035138651728630066,
-0.04111345112323761,
0.05691414326429367,
-0.029664168134331703,
0.04414420574903488,
0.017901530489325523,
-0.01816149242222309,
0.028594698756933212,
0.028013944625854492,
0.007508224807679653,
0.04350589960813522,
-0.05062547326087952,
0.0088981157168746,
-0.02811303734779358,
0.01886620931327343,
0.03568523749709129,
0.013584664091467857,
0.0050505646504461765,
-0.007657638750970364,
-0.03244716674089432,
-0.02139248512685299,
0.028307121247053146,
-0.0010923423105850816,
-0.03996848315000534,
-0.0680803433060646,
-0.016323819756507874,
0.018668970093131065,
-0.01650772988796234,
-0.012341216206550598,
0.08458968251943588,
0.008337241597473621,
-0.04715993255376816,
0.022110918536782265,
0.0022026190999895334,
-0.012651259079575539,
-0.026684533804655075,
-0.005061904899775982,
0.007203756831586361,
0.0414067879319191,
-0.015125446021556854,
0.04725714400410652,
0.023486971855163574,
-0.0066741229966282845,
-0.013322841376066208,
0.0031000918243080378,
0.034768205136060715,
0.014366963878273964,
-0.0007274220697581768,
0.032387807965278625,
-0.027820665389299393,
-0.01891278848052025,
-0.05341964587569237,
-0.02339167706668377,
-0.018458038568496704,
0.009098018519580364,
0.04069928824901581,
0.03730151802301407,
0.045947957783937454,
-0.03353092074394226,
0.05466005578637123,
-0.027119973674416542,
0.025766797363758087,
0.004422613885253668,
0.004653974901884794,
0.011090612970292568,
0.014434616081416607,
-0.013820379972457886,
0.018150456249713898,
-0.06151347607374191,
0.002441280521452427,
0.05627711862325668,
-0.007933230139315128,
-0.028967654332518578,
-0.06420904397964478,
0.006919342093169689,
0.08843827992677689,
-0.04155036807060242,
0.04150315001606941,
-0.0007090523140504956,
0.029612816870212555,
0.024987205862998962,
-0.008080863393843174,
0.035762012004852295,
-0.008843619376420975,
0.028654474765062332,
-0.026604417711496353,
-0.05444754660129547,
-0.050519928336143494,
-0.041451346129179,
-0.05653231963515282,
0.056234125047922134,
-0.013951104134321213,
0.05141095444560051,
0.020643016323447227,
0.02813020534813404,
-0.05452166497707367,
0.09442780911922455,
0.01178333442658186,
0.024045314639806747,
-0.03211428225040436,
0.004125571344047785,
0.06502553075551987,
-0.023197198286652565,
-0.05499705299735069,
0.0374351404607296,
-0.047600530087947845,
0.031133217737078667,
-0.03323332965373993,
-0.04611125960946083,
0.0037091027479618788,
-0.04555701091885567,
0.0024391666520386934,
0.006632684264332056,
0.030626613646745682,
-0.0063489144667983055,
0.015403248369693756,
-0.06552132219076157,
0.012141893617808819,
0.006823230534791946,
-0.03586031496524811,
0.08220691978931427,
-0.03975069895386696,
-0.007888256572186947,
0.06893599778413773,
-0.07585995644330978,
0.0031081256456673145,
0.06918645650148392,
0.03383640572428703,
-0.0030012670904397964,
0.05759063735604286,
0.0452217198908329,
-0.004602092318236828,
-0.018252769485116005,
-0.04689677059650421,
-0.03727615624666214,
0.030963286757469177,
-0.010916553437709808,
0.023494020104408264,
0.036222878843545914,
-0.009323057718575,
0.022051602602005005,
0.02379048801958561,
-0.013634014874696732,
0.08234255015850067,
0.013826885260641575,
-0.03047134168446064,
-0.02531765215098858,
0.0018244775710627437,
-0.009105082601308823,
0.0005262402701191604,
0.005264857318252325,
-0.022713584825396538,
-0.05163589492440224,
0.06119260564446449,
0.04027729108929634,
-0.0027724280953407288,
-0.01860610395669937,
-0.02623591013252735,
0.04038042202591896,
-0.052636079490184784,
-0.005360300187021494,
-0.012303884141147137,
-0.05154344066977501,
-0.005651944316923618,
0.060194868594408035,
-0.04123833775520325,
-0.07719570398330688,
0.030861619859933853,
-0.024976912885904312,
-0.03604748845100403,
0.05265083536505699,
0.009994026273488998,
-0.03956986591219902,
-0.009863581508398056,
-0.0021585882641375065,
-0.03535740450024605,
-0.10050827264785767,
-0.000047536577767459676,
-0.012515678070485592,
-0.033085521310567856,
-0.026553776115179062,
-0.010365936905145645,
0.021717509254813194,
-0.03353303670883179,
0.02080407738685608,
0.0084754703566432,
0.034155964851379395,
0.030131887644529343,
0.017691098153591156,
0.04239395260810852,
-0.004901534412056208,
0.06532290577888489,
0.006302214693278074,
0.07818508893251419,
-0.021697551012039185,
0.0009284712723456323,
0.003059788141399622,
0.017071440815925598,
-0.01959529146552086,
0.04055106267333031,
-0.0020977850072085857,
-0.020733695477247238,
0.020308159291744232,
-0.019878027960658073,
-0.03874943032860756,
0.009305479004979134,
0.004443258047103882,
-0.013169807381927967,
0.007201476022601128,
-0.0007405171636492014,
-0.05720297247171402,
0.02934475988149643,
0.06829535961151123,
0.0442134328186512,
0.030367450788617134,
-0.0636974647641182,
0.018179774284362793,
0.04111693054437637,
-0.005039421375840902,
0.016860369592905045,
0.005183957051485777,
-0.02506694383919239,
0.07569199800491333,
-0.08436749875545502,
-0.030090030282735825,
0.0033895138185471296,
-0.023030880838632584,
0.08795878291130066,
0.01976758986711502,
0.05522548779845238,
-0.00725047942250967,
0.02495887130498886,
0.04645131528377533,
0.04084712266921997,
-0.06703884899616241,
0.008246689103543758,
-0.04872409254312515,
0.010517220012843609,
0.02849978767335415,
-0.04953417927026749,
0.08829595148563385,
0.012560278177261353,
-0.006324095651507378,
-0.05707322433590889,
-0.06898073852062225,
0.03680351376533508,
-0.03461982682347298,
-0.02813880704343319,
0.017563937231898308,
0.01806766726076603,
0.018556341528892517,
0.06857617199420929,
-0.032082270830869675,
-0.033677663654088974,
0.017011389136314392,
-0.024353746324777603,
-0.008627805858850479,
0.011579995043575764,
0.0041071567684412,
-0.014205103740096092,
-0.005606710445135832,
0.03294273093342781,
0.05650770664215088,
0.008181795477867126,
-0.04776449501514435,
0.03756600618362427,
0.01393885724246502,
-0.01324564591050148,
0.01794508844614029,
0.032801251858472824,
-0.02243274264037609,
0.02666003257036209,
0.02895592711865902,
0.04667321965098381,
0.048324450850486755,
0.0010670085903257132,
0.04090983048081398,
0.03806920349597931,
0.036803245544433594,
-0.009741540066897869,
-0.034166742116212845,
0.011651279404759407,
-0.022794004529714584,
0.026658736169338226,
0.016024114564061165,
-0.013090412132441998,
-0.008336582221090794,
0.006568800192326307,
0.016852200031280518,
-0.014074575155973434,
0.014417163096368313,
-0.018755003809928894,
-0.02532796747982502,
0.05114771053195,
-0.03870493546128273,
0.02903117425739765,
-0.014777456410229206,
-0.022830180823802948,
-0.06673728674650192,
-0.05010701343417168,
-0.01817321591079235,
-0.013037779368460178,
-0.046882882714271545,
0.10597635060548782,
-0.044537659734487534,
-0.04336714744567871,
-0.002846895018592477,
-0.01561884954571724,
-0.06853035092353821,
0.0004215590306557715,
-0.027421358972787857,
0.03493938595056534,
-0.030421245843172073,
0.009746884927153587,
0.025795161724090576,
0.009578369557857513,
0.0029167456086724997,
0.026205429807305336,
-0.037930794060230255,
0.03466104343533516,
-0.024509822949767113,
-0.03991374373435974,
0.023335697129368782,
-0.03317253291606903,
-0.0021994311828166246,
-0.020219286903738976,
-0.0418580062687397,
0.041463639587163925,
0.07867279648780823,
0.00988062284886837,
-0.06923364847898483,
0.010695678181946278,
-0.03296622261404991,
0.04752383381128311,
-0.022988995537161827,
0.035939205437898636,
-0.004023323301225901,
0.00368647207506001,
0.003746307222172618,
-0.042027298361063004,
-0.0211636945605278,
0.03737562894821167,
0.030526088550686836,
0.05600739270448685,
0.023734446614980698,
0.058974042534828186,
0.06321375072002411,
-0.005923606920987368,
-0.013399518094956875,
-0.019392741844058037,
0.10194182395935059,
-0.069085031747818,
0.04917255789041519,
-0.08896451443433762,
0.009079734794795513,
-0.01577780209481716,
-0.04615911468863487,
0.06721950322389603,
0.006853526923805475,
0.006860528606921434,
-0.0038609905168414116,
0.005535210948437452,
0.035995688289403915,
-0.03182235732674599,
0.005920210387557745,
0.0006737986695952713,
0.03305385634303093,
-0.04201235994696617,
0.012737180106341839,
-0.012999647296965122,
0.0014138065744191408,
0.020718256011605263,
0.023723579943180084,
-0.05103975161910057,
0.026815060526132584,
0.05876508355140686,
-0.005042484495788813,
-0.008840257301926613,
0.009947092272341251,
-0.03341493755578995,
0.005904759746044874,
0.03704361617565155,
-0.022492503747344017,
0.07205112278461456,
0.03161519765853882,
-0.00601152703166008,
0.020757535472512245,
0.0252800602465868,
-0.050378601998090744,
-0.00005350448554963805,
-0.02596314251422882,
-0.015476815402507782,
0.02597784623503685,
0.0067468429915606976,
-0.017464693635702133,
-0.007973136380314827,
0.009601091966032982,
0.025759655982255936,
-0.017761580646038055,
0.05183209106326103,
-0.033343151211738586,
-0.08381005376577377,
0.003821010235697031,
0.05893188342452049,
0.018546026200056076,
-0.030727986246347427,
0.03723718598484993,
-0.004432320594787598,
0.02052753046154976,
0.02872130647301674,
-0.036448679864406586,
0.024553919211030006,
-0.028347942978143692,
0.03757750615477562,
-0.018450740724802017,
0.08466699719429016,
0.0086721396073699,
-0.022047918289899826,
0.010255168192088604,
0.018676428124308586,
-0.010174238122999668,
0.03686526417732239,
-0.02570721134543419,
-0.0003558577736839652,
-0.04080142080783844,
-0.03527476266026497,
0.012044291011989117,
-0.014797340147197247,
0.0036988824140280485,
-0.04277665168046951,
0.019993212074041367,
0.046716295182704926,
-0.04420412704348564,
-0.01948365941643715,
-0.04993930086493492,
0.04242691770195961,
-0.040490396320819855,
0.07471118122339249,
-0.05373850837349892,
0.002198501955717802,
0.004682527855038643,
0.014246754348278046,
-0.011233734898269176,
-0.01891512982547283,
0.030327195301651955,
-0.007140067405998707,
0.052765700966119766,
-0.03332556039094925,
0.02970610372722149,
-0.01450758334249258,
-0.03931082412600517,
0.05041512846946716,
0.001017399481497705,
-0.06962227076292038,
0.008301186375319958,
-0.009615355171263218,
-0.0239399503916502,
-0.027658769860863686,
-0.019547631964087486,
-0.04235850274562836,
0.009691368788480759,
0.09472836554050446,
-0.017868272960186005,
0.01242081169039011,
-0.011058351956307888,
-0.048682525753974915,
0.021925870329141617,
0.004782942123711109,
-0.01635720208287239,
-0.012681086547672749,
0.02585381641983986,
-0.04280809313058853,
0.01696181111037731,
0.022862287238240242,
-0.013301585800945759,
-0.0016072584548965096,
0.008044620044529438,
-0.007214417215436697,
-0.042628102004528046,
0.03186790272593498,
-0.037386320531368256,
-0.004822208546102047,
0.040508855134248734,
0.0170601699501276,
-0.0034331991337239742,
-0.011364977806806564,
0.025606747716665268,
-0.04045156389474869,
0.03865848109126091,
-0.011767000891268253,
-0.0035823783837258816,
-0.04797112196683884,
-0.026472683995962143,
0.020408323034644127,
0.05953962728381157,
0.036624450236558914,
-0.017766911536455154,
-0.001907771686092019,
-0.0229275431483984,
0.027316594496369362,
0.07333999127149582,
-0.038349345326423645,
0.03002936579287052,
-0.019921530038118362,
-0.02573711983859539,
-0.05822337418794632,
0.0002693698916118592,
0.01434449665248394,
-0.06174958124756813,
0.007487151771783829,
0.05020866543054581,
-0.05243566259741783,
0.013133987784385681,
-0.005911397747695446,
-0.017633827403187752,
0.017477288842201233,
0.09124787896871567,
-0.08704664558172226,
-0.024642322212457657,
0.0065629673190414906,
0.005296042189002037,
-0.024541253224015236,
-0.022118063643574715,
-0.0011250983225181699,
-0.03423027694225311,
0.004433047957718372,
0.04589034616947174,
-0.036018699407577515,
0.0004158001102041453,
-0.012634570710361004,
-0.05618347227573395,
-0.06513006240129471,
-0.012757397256791592,
0.054629236459732056,
0.033956389874219894,
0.05182076245546341,
-0.05823122709989548,
0.01985749788582325,
0.0006518518202938139,
-0.008149392902851105,
-0.010291560553014278,
0.039445824921131134,
-0.008032873272895813,
-0.03700903803110123,
-0.025169601663947105,
-0.0030522053129971027,
-0.004626127891242504,
-0.014233392663300037,
0.015112966299057007,
0.01000223495066166,
-0.09066233783960342,
0.02179676480591297,
0.03383776172995567,
0.040528688579797745,
0.014429793693125248,
-0.06481103599071503,
-0.03491766005754471,
-0.05266815796494484,
-0.02758847363293171,
-0.012500644661486149,
-0.0008787251426838338,
-0.033068496733903885,
-0.013955686241388321,
-0.016247661784291267,
0.0012805452570319176,
-0.0445585697889328,
-0.026831286028027534,
-0.08646028488874435,
0.018672078847885132,
0.021436523646116257,
-0.03105982393026352,
-0.011167999356985092,
0.01485682837665081,
-0.024111732840538025,
-0.046896085143089294,
-0.005876332521438599,
0.003955279476940632,
0.01874457485973835,
0.05629432573914528,
0.0416947603225708,
0.029654929414391518,
0.0062303924933075905,
0.060963984578847885,
-0.03689759969711304,
-0.033981963992118835,
0.01379637885838747,
0.026523781940340996,
0.001049807877279818,
0.019990714266896248,
0.04556357115507126,
-0.010227772407233715,
0.03798097372055054,
-0.015390037558972836,
-0.04527267441153526,
0.009868965484201908,
0.0426851324737072,
-0.03039219044148922,
0.01597958616912365,
0.0015837036771699786,
0.012426414526998997,
-0.010143700055778027,
-0.021824641153216362,
-0.010165928862988949,
0.02730688452720642,
-0.08678016811609268,
-0.01127198152244091,
0.017943134531378746,
-0.03440716862678528,
0.012503201141953468,
-0.09522570669651031,
-0.04637330770492554,
0.044191766530275345,
0.043034616857767105,
-0.012915926054120064,
-0.07408297806978226,
-0.004728854168206453,
-0.013778791762888432,
-0.00843246839940548,
-0.05090322345495224,
-0.05603789538145065,
0.020379099994897842,
-0.001502101426012814,
-0.05423455685377121,
-0.009951154701411724,
0.004747866652905941,
-0.043850287795066833,
-0.037358395755290985,
0.004237215034663677,
0.053367480635643005,
-0.01918271742761135,
-0.038224540650844574,
0.04265524819493294,
0.06049153953790665,
0.004765991121530533,
-0.025379294529557228,
-0.005478432402014732,
0.04235844686627388,
-0.02747306227684021,
-0.009290709160268307,
-0.035437293350696564,
0.03063821792602539,
0.05047839879989624,
0.047401685267686844,
-0.02277650497853756,
0.004457640927284956,
-0.02995443530380726,
0.0026603310834616423,
-0.021669700741767883,
-0.006272692698985338,
-0.000047116576752159745,
-0.00006942493928363547,
-0.011334231123328209,
-0.008087455295026302,
0.0636686459183693,
-0.004478843417018652,
-0.04610006883740425,
0.0017835604958236217,
0.016299491748213768,
-0.0576796680688858,
0.03311460465192795,
-0.06148755922913551,
-0.012963039800524712,
-0.05689755454659462,
-0.004358303267508745,
-0.015421637333929539,
-0.007166122552007437,
0.04655977338552475,
0.04693084582686424,
0.05657458305358887,
0.11002995073795319,
0.01755397766828537,
-0.019790735095739365,
-0.024198563769459724,
-0.04938184842467308,
0.041210342198610306,
-0.02348605915904045,
0.07009527087211609,
-0.028980959206819534,
0.014679007232189178,
-0.03463352471590042,
-0.027687154710292816,
-0.017170440405607224,
0.00316629302687943,
0.040089089423418045,
-0.052740659564733505,
-0.025144249200820923,
-0.04615851119160652,
0.02191849984228611,
0.022581348195672035,
-0.02046005241572857,
0.006653144955635071,
-0.00838026124984026,
0.023714542388916016,
-0.004019270185381174,
0.058947812765836716,
-0.013013994321227074,
-0.07242631912231445,
-0.03366168215870857,
-0.027727017179131508,
-0.07469316571950912,
0.006651534698903561,
-0.0869433581829071,
-0.024480029940605164,
0.0038296678103506565,
-0.021233921870589256,
-0.008457380346953869,
0.045197103172540665,
-0.03901684284210205,
0.05046648904681206,
0.028074998408555984,
-0.008724728599190712,
-0.01119733415544033,
-0.0057718632742762566,
0.011979124508798122,
-0.02421373501420021,
-0.06946837157011032,
0.009082268923521042,
0.013185696676373482,
-0.011878201737999916,
-0.03229733183979988,
-0.021471528336405754,
-0.041207004338502884,
0.026291418820619583,
-0.017625197768211365,
-0.09509377181529999,
-0.0021356544457376003,
0.055860958993434906,
0.0035846089012920856,
-0.039699986577034,
0.02355453185737133,
-0.031962595880031586,
-0.016351500526070595,
0.021428825333714485,
0.012802976183593273,
-0.00585898756980896,
-0.06051564961671829,
0.010944741778075695,
-0.015306283719837666,
0.00403868081048131,
-0.016402600333094597,
0.05108324810862541,
0.019952768459916115,
0.03496866673231125,
-0.04401879385113716,
-0.034835923463106155,
0.03970770910382271
] |
<p>for any real and positive 's' and in the sense of semiclassical approximation </p>
<p>is this valid ??</p>
<p>$ \sum_{n}exp(-sE_{n})\sim \iint_{C}dxdpe^{-s(p^{2}+V(x))}$ valid for every 's'</p>
<p>here simply both the sum and integral are convergent, so in this case the approximation can be seen as the replacement of a sum by an integral.</p> | g1292 | [
0.00007027813990134746,
-0.01895061694085598,
-0.010909580625593662,
-0.026820451021194458,
-0.04756027087569237,
-0.014448300935328007,
-0.012981352396309376,
0.023586604744195938,
0.01377884205430746,
0.015880698338150978,
-0.029813328757882118,
0.004973674193024635,
0.009465728886425495,
0.058754533529281616,
-0.002454170258715749,
0.02892022579908371,
0.03202316537499428,
-0.003239751560613513,
-0.02598290704190731,
-0.021082041785120964,
-0.0282998476177454,
-0.0449589341878891,
0.0013738359557464719,
-0.044294118881225586,
0.012624246999621391,
-0.009356897324323654,
-0.0017497333465144038,
0.014550776220858097,
0.009010317735373974,
-0.0559309683740139,
0.014532812871038914,
0.010014809668064117,
0.05986332520842552,
0.030014149844646454,
0.016968555748462677,
0.029964102432131767,
0.013788790442049503,
0.02134261466562748,
0.05752278491854668,
-0.02648807503283024,
0.01458565704524517,
0.008798743598163128,
0.050605446100234985,
0.040980011224746704,
-0.018514765426516533,
-0.029434531927108765,
-0.03760582581162453,
0.07633252441883087,
0.029033025726675987,
-0.033774618059396744,
-0.03562358394265175,
-0.004402304999530315,
-0.010314199142158031,
0.032703012228012085,
-0.04219070449471474,
0.032906047999858856,
-0.03065696731209755,
0.013394255191087723,
-0.012403247877955437,
0.023797396570444107,
0.03339758142828941,
0.028417177498340607,
-0.0010003418428823352,
0.0051031033508479595,
0.010909953154623508,
0.022098878398537636,
-0.01574433036148548,
0.029726667329669,
0.01608813926577568,
-0.0021405071020126343,
-0.008501789532601833,
-0.027658861130475998,
0.026735421270132065,
-0.029529986903071404,
-0.028122423216700554,
-0.025559736415743828,
0.02419077232480049,
-0.016570478677749634,
-0.010286695323884487,
0.017196234315633774,
-0.05894523859024048,
-0.08286280184984207,
-0.007005051709711552,
0.013898312114179134,
-0.03917914628982544,
-0.05030122771859169,
0.017526820302009583,
-0.04076434299349785,
-0.031873904168605804,
0.007084392476826906,
-0.011023454368114471,
-0.02834542840719223,
-0.05347529426217079,
0.02226126752793789,
-0.005714100319892168,
-0.03798011690378189,
-0.0018564555794000626,
0.02452532760798931,
0.03610897436738014,
-0.0607721172273159,
0.010660162195563316,
-0.04676850140094757,
0.04636799171566963,
-0.005981635767966509,
-0.05899227410554886,
0.00586271146312356,
-0.019913924857974052,
-0.022685769945383072,
0.05153929069638252,
-0.03497990965843201,
-0.024092569947242737,
-0.05013526976108551,
-0.014459808357059956,
-0.05993761867284775,
-0.04979272186756134,
0.048815999180078506,
-0.003947187215089798,
-0.0815577283501625,
0.005113281775265932,
0.02108664996922016,
0.062427304685115814,
0.05102537199854851,
0.047474876046180725,
0.10039353370666504,
0.040299952030181885,
0.006510652601718903,
-0.016998201608657837,
-0.015735842287540436,
0.031765591353178024,
-0.03550222888588905,
-0.02147623896598816,
0.012265444733202457,
-0.024841703474521637,
0.006366019602864981,
0.029508251696825027,
-0.003006140934303403,
0.007134579587727785,
-0.049986060708761215,
-0.016268882900476456,
0.016436761245131493,
-0.043143920600414276,
0.01153241191059351,
0.034726276993751526,
-0.03736363723874092,
-0.04877233877778053,
0.008424436673521996,
0.008714664727449417,
-0.0673857182264328,
-0.06004497408866882,
-0.010172335430979729,
0.018337925896048546,
0.03358710929751396,
0.03341502696275711,
-0.004799244459718466,
0.001098082633689046,
0.03867227956652641,
0.005395994056016207,
0.0046820552088320255,
0.048829641193151474,
0.0012927117059007287,
-0.0455750897526741,
0.016356904059648514,
-0.0779048502445221,
-0.0037337259855121374,
0.08098507672548294,
0.024068191647529602,
0.001512060989625752,
-0.02535627782344818,
-0.017464876174926758,
-0.06476236879825592,
0.013912362977862358,
0.034570612013339996,
0.018997978419065475,
0.025683099403977394,
0.025506453588604927,
-0.05251017212867737,
-0.019508836790919304,
-0.009607893414795399,
0.0013864027569070458,
0.052972566336393356,
-0.040315140038728714,
0.0015231597935780883,
-0.0029878311324864626,
-0.03448507562279701,
0.06362340599298477,
0.02216499112546444,
0.05163189023733139,
0.01386393141001463,
-0.02743598259985447,
0.021997002884745598,
-0.003245213069021702,
-0.004193664062768221,
0.0400627963244915,
0.054651226848363876,
-0.04049106687307358,
-0.01683090254664421,
0.021000860258936882,
-0.08769801259040833,
0.003608076134696603,
-0.013604006730020046,
-0.0028728533070534468,
0.08598155528306961,
0.05711011961102486,
-0.03125644847750664,
0.05860288441181183,
-0.03600723668932915,
-0.026295190677046776,
-0.04805416241288185,
0.012275654822587967,
0.015671517699956894,
0.06656550616025925,
-0.026349982246756554,
-0.013139506801962852,
0.05246073380112648,
0.014312422834336758,
-0.055043287575244904,
-0.005454487632960081,
-0.02489178068935871,
0.03639724478125572,
0.02350301668047905,
-0.07904534786939621,
-0.0867435559630394,
0.033284302800893784,
0.05406985804438591,
-0.04331735149025917,
0.009549980983138084,
-0.03526505082845688,
0.017870048061013222,
0.018839772790670395,
0.03402808681130409,
-0.051189128309488297,
-0.08171770721673965,
0.016102327033877373,
-0.0064838966354727745,
0.002635751850903034,
-0.00963215995579958,
-0.02262790873646736,
-0.04241978004574776,
0.022775733843445778,
0.003500173334032297,
0.05407256260514259,
-0.03643489256501198,
-0.010877572000026703,
0.07703709602355957,
0.00832656305283308,
-0.010571666061878204,
-0.03041885979473591,
-0.0016870020190253854,
-0.01036485843360424,
-0.0007918531773611903,
-0.012049063108861446,
0.01889028027653694,
-0.005747504997998476,
0.029144925996661186,
0.02342512458562851,
-0.017617376521229744,
0.021381758153438568,
-0.04736773297190666,
0.019220761954784393,
0.0561259426176548,
-0.009837795980274677,
0.03208203986287117,
-0.08045558631420135,
-0.01689516194164753,
0.046884894371032715,
0.06221248582005501,
-0.005818922538310289,
-0.023162877187132835,
0.03228580579161644,
-0.0033705048263072968,
-0.012683704495429993,
0.021076548844575882,
0.030671576038002968,
0.07700768113136292,
0.022116731852293015,
-0.009238958358764648,
-0.03159815073013306,
0.03979095444083214,
-0.0010702506406232715,
-0.01435905136168003,
0.010264573618769646,
-0.004761291667819023,
0.05731302872300148,
-0.010486794635653496,
-0.004777248483151197,
-0.07926791906356812,
0.09852297604084015,
0.010117863304913044,
-0.01263530645519495,
0.01582741178572178,
0.00005634454282699153,
0.005050731357187033,
-0.02372412569820881,
0.011471067555248737,
-0.04627224802970886,
0.04381263628602028,
0.023639271035790443,
-0.08711971342563629,
-0.046783022582530975,
0.0176374614238739,
0.006592554971575737,
-0.0010875500738620758,
-0.012225850485265255,
0.045891016721725464,
0.0749024748802185,
0.028438489884138107,
0.00009044670150615275,
-0.02714277058839798,
0.040269624441862106,
-0.07151653617620468,
-0.0009421842405572534,
0.05169990658760071,
-0.014477658085525036,
-0.07830490916967392,
-0.009404927492141724,
0.050927042961120605,
0.047579772770404816,
-0.004866473842412233,
0.03135238215327263,
-0.012485967017710209,
0.0033250043634325266,
-0.023835426196455956,
0.048549551516771317,
0.02211032062768936,
0.013671232387423515,
-0.010757745243608952,
0.07447110861539841,
-0.0377977080643177,
-0.06211546063423157,
0.013476820662617683,
0.03924638032913208,
-0.039468009024858475,
0.05700533464550972,
0.004740376956760883,
0.005185537040233612,
0.008302089758217335,
0.04344825819134712,
0.030009867623448372,
0.03977508842945099,
0.042217858135700226,
-0.05242670327425003,
-0.02217392437160015,
-0.00995482038706541,
0.02366277202963829,
-0.0051708826795220375,
-0.011854397132992744,
0.049211736768484116,
0.01804264634847641,
-0.02730586566030979,
0.0240306556224823,
0.002353288698941469,
0.02488836832344532,
-0.02824028767645359,
0.04996400699019432,
-0.027304871007800102,
0.0678742378950119,
0.042510632425546646,
0.029469937086105347,
-0.01940189301967621,
0.004117695149034262,
0.01192986685782671,
-0.014615005813539028,
-0.0008990289061330259,
0.019973784685134888,
-0.03683585673570633,
-0.011448093689978123,
0.015091479755938053,
0.07133247703313828,
-0.048349469900131226,
0.04484787583351135,
0.006323117762804031,
0.06592969596385956,
0.037422988563776016,
0.007198411505669355,
0.007240589242428541,
-0.05548346787691116,
-0.019438503310084343,
0.017011770978569984,
0.014845361933112144,
-0.012213890440762043,
0.031090186908841133,
0.02770743891596794,
0.0012874481035396457,
0.018359657377004623,
-0.0037701083347201347,
-0.002179930219426751,
-0.004773756489157677,
-0.005043033044785261,
0.011601199395954609,
0.003479773411527276,
0.05499820411205292,
-0.006418907083570957,
-0.01312689483165741,
0.04998241364955902,
0.0577123761177063,
-0.04482856020331383,
0.022796127945184708,
-0.07427063584327698,
-0.034929659217596054,
-0.0012597161112353206,
0.01412179321050644,
-0.038028717041015625,
0.004998479969799519,
-0.03266354650259018,
-0.04815046116709709,
-0.005595142021775246,
0.009572329930961132,
0.03508944809436798,
0.028011512011289597,
-0.06615768373012543,
-0.01842326670885086,
-0.004498206544667482,
0.030285675078630447,
-0.01586371287703514,
0.002018822357058525,
0.044827792793512344,
0.017809400334954262,
-0.05928674340248108,
-0.040444985032081604,
0.040266308933496475,
-0.021978000178933144,
-0.04711306840181351,
-0.03736913949251175,
0.0014476110227406025,
0.016174383461475372,
0.04241560772061348,
0.038755517452955246,
-0.032782550901174545,
0.04502023383975029,
-0.0003002611338160932,
-0.08040226250886917,
0.03684668987989426,
0.03876962140202522,
0.03576759994029999,
-0.041258394718170166,
0.03258981183171272,
0.044354166835546494,
0.0066713811829686165,
-0.058801501989364624,
0.008591239340603352,
0.018385786563158035,
0.0009008882334455848,
0.009944411925971508,
-0.006016199477016926,
0.05771365761756897,
0.024703720584511757,
-0.025154005736112595,
-0.08936145901679993,
0.05149645358324051,
-0.02278931811451912,
-0.01407033670693636,
0.03884962946176529,
0.02700217068195343,
0.010942386463284492,
0.012503615580499172,
0.011961311101913452,
-0.032072827219963074,
-0.025304382666945457,
-0.033013999462127686,
0.025057466700673103,
0.048468343913555145,
-0.040102265775203705,
-0.011269526556134224,
-0.026811841875314713,
0.08005890250205994,
0.055432967841625214,
-0.06425739824771881,
-0.016261957585811615,
0.004193270578980446,
0.0120584387332201,
0.0257082711905241,
0.008562898263335228,
0.008760126307606697,
-0.04508507251739502,
0.004150808788836002,
-0.09802017360925674,
-0.029862869530916214,
0.013662596233189106,
-0.01176493987441063,
0.0253458172082901,
-0.049691617488861084,
-0.05593105033040047,
0.0003789355105254799,
0.044029317796230316,
-0.00005924429569859058,
0.014716004021465778,
0.09150790423154831,
-0.04383188858628273,
-0.019334621727466583,
-0.017092449590563774,
0.0852595865726471,
-0.05025000497698784,
0.025496937334537506,
-0.028025031089782715,
-0.007376828230917454,
0.04600793123245239,
0.0003369547484908253,
0.0037183952517807484,
-0.02104523591697216,
0.04578781500458717,
-0.06561165302991867,
-0.010419840924441814,
-0.027030309662222862,
-0.021220896393060684,
-0.008320550434291363,
0.0374285951256752,
0.06157080456614494,
0.014544015750288963,
-0.005671888589859009,
-0.0014590173959732056,
0.054466407746076584,
-0.012639045715332031,
0.008541349321603775,
0.020847950130701065,
-0.0075525883585214615,
0.008322910405695438,
-0.029342269524931908,
-0.02773527428507805,
-0.014883685857057571,
-0.06182757019996643,
0.08975198119878769,
-0.030554931610822678,
-0.040996577590703964,
0.02474399469792843,
-0.00034795631654560566,
-0.0449867844581604,
0.023318594321608543,
-0.044994160532951355,
0.029254361987113953,
0.026904722675681114,
0.02915302664041519,
-0.008306494913995266,
-0.019336551427841187,
-0.05685235932469368,
-0.005374461878091097,
-0.05962831899523735,
-0.09037227183580399,
0.03308548778295517,
0.0035069729201495647,
0.016949309036135674,
-0.022526709362864494,
-0.05515015870332718,
-0.020247187465429306,
0.01952630653977394,
-0.0194521714001894,
0.047688696533441544,
-0.003629902843385935,
0.010392138734459877,
0.032733283936977386,
-0.052792638540267944,
0.017657136544585228,
0.009728871285915375,
-0.0680241733789444,
-0.0499010905623436,
0.04384548217058182,
0.009586744010448456,
-0.05246572196483612,
-0.0002492053899914026,
0.08387141674757004,
-0.03561294078826904,
-0.034445635974407196,
-0.09677360951900482,
-0.05418132245540619,
-0.04158882796764374,
-0.04123634845018387,
-0.0421573743224144,
0.047120966017246246,
0.015547651797533035,
-0.048008378595113754,
-0.04053850099444389,
-0.012011359445750713,
-0.03604419156908989,
0.029551928862929344,
-0.02767101302742958,
0.021018091589212418,
-0.01543258037418127,
0.05017064884305,
-0.04667079821228981,
0.03792710602283478,
-0.047014690935611725,
-0.029939064756035805,
0.048762768507003784,
0.01247627567499876,
0.05123322084546089,
0.01162368431687355,
-0.03567487746477127,
-0.03963010758161545,
-0.01707340218126774,
0.013195057399570942,
-0.005532143171876669,
0.014371286146342754,
0.0066394321620464325,
0.001570571563206613,
0.05132424086332321,
0.03406382352113724,
-0.011131396517157555,
-0.014311764389276505,
0.027869094163179398,
0.0437634140253067,
0.017462613061070442,
0.06402576714754105,
0.006473195739090443,
0.019032126292586327,
-0.04632745310664177,
-0.04039204865694046,
0.005706043913960457,
0.00801569502800703,
0.018730876967310905,
-0.057828132063150406,
0.018987931311130524,
-0.040848508477211,
0.0031633772887289524,
-0.006523106712847948,
0.046379443258047104,
0.019744139164686203,
-0.06906652450561523,
-0.03745410963892937,
-0.015694212168455124,
0.01084123644977808,
-0.025604331865906715,
-0.013967975974082947,
-0.0005553567316383123,
-0.01882491447031498,
0.006570240017026663,
-0.019910546019673347,
0.07208609580993652,
0.010083433240652084,
0.018233763054013252,
0.029228324070572853,
-0.007355994079262018,
0.005051599349826574,
0.023312343284487724,
-0.01168527826666832,
-0.0613689050078392,
-0.005363295320421457,
0.0736931785941124,
-0.0008957151439972222,
-0.01721045933663845,
-0.006435120943933725,
0.0473262220621109,
-0.08598297834396362,
0.026854626834392548,
-0.025851057842373848,
-0.01716320589184761,
-0.036164410412311554,
-0.044312771409749985,
0.06271163374185562,
0.0468183271586895,
0.0017936091171577573,
-0.02393597923219204,
0.08926403522491455,
0.05188015475869179,
-0.023137154057621956,
0.027958707883954048,
-0.05959706753492355,
-0.04724672809243202,
0.029497718438506126,
0.0070491391234099865,
0.01615833304822445,
-0.04083695635199547,
0.01700585149228573,
-0.015622992999851704,
-0.05419328436255455,
-0.02872622013092041,
0.014057007618248463,
0.033874381333589554,
0.01680782623589039,
-0.04315175861120224,
-0.060941632837057114,
-0.021688932552933693,
0.028833413496613503,
0.01351530384272337,
-0.013334907591342926,
0.039565861225128174,
0.03031058982014656,
0.007432912942022085,
-0.029709380120038986,
0.003470309777185321,
-0.04736723750829697,
0.0012386864982545376,
0.038269560784101486,
-0.04804845154285431,
-0.010746918618679047,
0.03191635385155678,
0.008737429045140743,
0.012784570455551147,
0.039691321551799774,
-0.001803977764211595,
-0.016181176528334618,
0.05273043364286423,
-0.010451611131429672,
0.023164177313447,
0.027715343981981277,
0.006723044905811548,
0.053251709789037704,
0.05059370771050453,
0.007288212887942791,
0.02056833729147911,
-0.015987053513526917,
0.01207041833549738,
-0.02449369989335537,
0.02438378520309925,
0.010849634185433388,
-0.005642405711114407,
-0.0062424661591649055,
-0.02519623376429081,
-0.04506439343094826,
-0.03234891593456268,
0.011805820278823376,
-0.029228435829281807,
0.04805091768503189,
-0.022297391667962074,
-0.029816707596182823,
0.04303762689232826,
0.04247312247753143,
-0.044044945389032364,
-0.0260775089263916,
-0.019309718161821365,
0.032215215265750885,
-0.006591755896806717,
-0.00496656633913517,
0.034430962055921555,
-0.028432974591851234,
-0.005180911161005497,
-0.018981482833623886,
-0.030167846009135246,
-0.031149912625551224,
-0.0388663150370121,
0.01435219869017601,
0.02388560026884079,
-0.031470343470573425,
0.005977924447506666,
-0.02068541944026947,
0.046681880950927734,
-0.02598273754119873,
-0.025641784071922302,
0.05710683390498161,
-0.012986652553081512,
0.00673691788688302,
0.029872652143239975,
-0.048058755695819855,
-0.06755481660366058,
0.07857046276330948,
0.01447757612913847,
0.023577652871608734,
-0.002697511576116085,
0.024714699015021324,
-0.11978559195995331,
0.07619261741638184,
-0.023763343691825867,
-0.041487712413072586,
0.017102094367146492,
-0.028154734522104263,
0.028316844254732132,
0.07726690173149109,
0.009481132961809635,
0.03510017693042755,
0.010815792717039585,
0.03084319643676281,
0.01481012161821127,
-0.050768088549375534,
-0.027784332633018494,
-0.009973933920264244,
-0.00234827003441751,
-0.002562775742262602,
-0.09429740160703659,
0.013326644897460938,
0.028783127665519714
] |
<p>Can someone answer and explain it please.
Here are the options:</p>
<ul>
<li>Moving downwards and decelerating.</li>
<li>Moving downwards with a constant velocity.</li>
<li>Moving upwards and decelerating.</li>
<li>Moving upwards with a constant velocity.</li>
</ul> | g1293 | [
0.06737634539604187,
0.0281252209097147,
0.0003166949318256229,
0.047561824321746826,
0.08458398282527924,
0.04178842529654503,
0.06201767176389694,
0.014012226834893227,
-0.04442005231976509,
-0.06328278034925461,
-0.05636380985379219,
0.016523201018571854,
0.03848186507821083,
0.01893278770148754,
0.03159252181649208,
-0.048072174191474915,
0.06041967496275902,
-0.026873862370848656,
0.01165055949240923,
-0.007674610707908869,
-0.0076582226902246475,
0.034472350031137466,
-0.01587894931435585,
-0.019626446068286896,
0.010816385969519615,
-0.024984361603856087,
-0.03712823614478111,
-0.004303993657231331,
-0.06824043393135071,
0.003249312285333872,
0.07424233853816986,
-0.055948976427316666,
0.02372153475880623,
-0.06054457649588585,
0.024267040193080902,
-0.0024563244078308344,
0.06699750572443008,
-0.01780104450881481,
-0.02036978118121624,
-0.013153335079550743,
0.054281290620565414,
-0.018552517518401146,
0.06073806807398796,
0.017381340265274048,
-0.0004675466625485569,
-0.00814113486558199,
0.013198958709836006,
-0.05758343264460564,
-0.010206776671111584,
0.02343299798667431,
-0.01535495650023222,
-0.008017354644834995,
-0.014050666242837906,
-0.004627948626875877,
0.00906752236187458,
0.030277816578745842,
-0.005831100977957249,
-0.018521416932344437,
-0.014999326318502426,
0.007178242318332195,
-0.011458687484264374,
-0.07135803997516632,
0.04851415753364563,
-0.07758157700300217,
0.03837590664625168,
-0.05004260316491127,
-0.049914710223674774,
-0.04063493013381958,
0.0038340522442013025,
-0.05718376114964485,
0.03833100199699402,
-0.04740295186638832,
-0.03270848095417023,
-0.05936531722545624,
-0.07760895043611526,
-0.01238364726305008,
0.030681133270263672,
-0.03748602420091629,
0.04597093537449837,
0.00032537832157686353,
-0.10545630007982254,
0.01960660330951214,
0.03860880061984062,
0.01473117247223854,
0.055670738220214844,
0.020376957952976227,
0.018451819196343422,
0.06767632812261581,
-0.04544775187969208,
-0.04520955681800842,
-0.01558461133390665,
0.0003788618778344244,
0.039153091609478,
0.062210410833358765,
-0.049736205488443375,
-0.04559604078531265,
-0.050634682178497314,
0.09890766441822052,
0.0737513080239296,
-0.014988395385444164,
-0.008590634912252426,
0.027424393221735954,
-0.0012480182340368629,
0.021984320133924484,
0.027351340278983116,
-0.010622292757034302,
0.033205337822437286,
-0.04977580904960632,
-0.01284340862184763,
-0.0680760070681572,
-0.011498454958200455,
-0.037574540823698044,
0.00007383825141005218,
-0.03477894887328148,
0.03283357247710228,
-0.015241317451000214,
0.05620816722512245,
0.028416788205504417,
0.022168606519699097,
0.01999489590525627,
-0.011587921530008316,
0.0031821783632040024,
-0.04065942391753197,
0.06676068902015686,
0.019958797842264175,
-0.009625948965549469,
-0.0034275029320269823,
-0.016791751608252525,
0.011128000915050507,
0.02957313321530819,
0.053756486624479294,
0.00954254437237978,
-0.021930137649178505,
0.011928414925932884,
0.057045772671699524,
0.005466121714562178,
-0.013469632714986801,
0.014690491370856762,
-0.05501028150320053,
0.04317592829465866,
0.010279158130288124,
-0.05712084099650383,
-0.024344608187675476,
0.017063314095139503,
-0.039247915148735046,
0.004131562076508999,
-0.02576427534222603,
0.033000800758600235,
0.01756846345961094,
-0.002762608462944627,
0.019144395366311073,
0.034643057733774185,
0.02536149136722088,
0.014257614500820637,
-0.005408183205872774,
-0.02069784514605999,
0.053488440811634064,
0.036357566714286804,
0.021860405802726746,
0.016001250594854355,
0.04363107308745384,
-0.04516594484448433,
0.05130324885249138,
-0.012645109556615353,
-0.09789014607667923,
0.05291258171200752,
-0.010901368223130703,
0.05004772171378136,
0.012023995630443096,
0.06609336286783218,
-0.03921695426106453,
0.006298579275608063,
0.015896042808890343,
0.05673438310623169,
0.08618276566267014,
0.05337489768862724,
0.028602777048945427,
-0.018567711114883423,
-0.016715221107006073,
-0.02557193860411644,
-0.0150160426273942,
-0.005718871485441923,
0.006697271950542927,
-0.01079615205526352,
0.04774823039770126,
-0.0030707435216754675,
-0.010418164543807507,
0.03911639750003815,
-0.05187855288386345,
0.00447423942387104,
0.06268912553787231,
-0.0861670970916748,
-0.01723756454885006,
-0.039443306624889374,
-0.020284853875637054,
-0.02018202468752861,
0.025027846917510033,
0.007200195454061031,
-0.07945256680250168,
0.005007435102015734,
0.01288757473230362,
0.0019340551225468516,
0.044789496809244156,
-0.0536070242524147,
-0.06416168063879013,
-0.05488962307572365,
-0.018794938921928406,
0.06606288999319077,
0.0025627301074564457,
0.012264937162399292,
0.0724775493144989,
0.00300210970453918,
-0.001957306871190667,
0.027138372883200645,
0.04290058836340904,
-0.021493876352906227,
0.010743224993348122,
-0.0012407508911564946,
-0.011789530515670776,
-0.004118727054446936,
-0.0025875051505863667,
0.0056953164748847485,
-0.0046325018629431725,
0.007560511585325003,
-0.04161522537469864,
-0.025615401566028595,
0.011801752261817455,
0.004955603741109371,
0.04830033704638481,
-0.012669969350099564,
-0.02821226790547371,
-0.041066739708185196,
0.042220551520586014,
-0.07859757542610168,
0.018410034477710724,
0.03524858504533768,
-0.005255694501101971,
0.0841657817363739,
-0.041052885353565216,
0.010579830035567284,
-0.005051010753959417,
-0.019839318469166756,
0.040760528296232224,
-0.01659102365374565,
0.021945275366306305,
-0.027196405455470085,
0.03348557651042938,
-0.002026952337473631,
-0.02479291521012783,
0.029783526435494423,
-0.013591960072517395,
-0.04627532884478569,
-0.11157888174057007,
0.014285203069448471,
-0.04938690364360809,
-0.030915645882487297,
-0.05053582414984703,
0.007328883744776249,
-0.029227858409285545,
-0.004622763488441706,
0.029650701209902763,
0.018661189824342728,
0.03291996568441391,
-0.007551427930593491,
-0.05653654783964157,
-0.018695583567023277,
-0.018665259703993797,
0.014233090914785862,
0.03341753035783768,
0.010988296009600163,
0.03314113989472389,
0.00030229371623136103,
0.05612168833613396,
0.025742536410689354,
-0.00744642922654748,
0.00802352000027895,
0.029875384643673897,
0.0012126017827540636,
-0.021264303475618362,
0.04197564348578453,
0.0007880076882429421,
-0.050460707396268845,
-0.0018955280538648367,
0.0040375180542469025,
0.04014604911208153,
0.005782261025160551,
-0.016824543476104736,
0.02787463180720806,
-0.03435162827372551,
0.003491481300443411,
-0.0057120188139379025,
0.033894386142492294,
0.08713257312774658,
-0.0077737062238156796,
0.008229763247072697,
0.0681345984339714,
0.0596541129052639,
-0.038091156631708145,
-0.0538698211312294,
-0.03451528400182724,
0.008411966264247894,
-0.01642010360956192,
0.04894297569990158,
0.0017027478897944093,
-0.035411443561315536,
0.025698423385620117,
0.026437444612383842,
0.02190244197845459,
-0.04071430489420891,
-0.01755627989768982,
-0.03127660974860191,
0.053064752370119095,
-0.024707667529582977,
0.0314503014087677,
0.012135924771428108,
-0.012347747571766376,
-0.0056277369149029255,
0.000022162032109918073,
0.004536543972790241,
0.018266994506120682,
-0.02577481046319008,
-0.07549593597650528,
0.011710116639733315,
0.0348794162273407,
0.00013874427531845868,
0.0232587568461895,
-0.01060398668050766,
-0.008819831535220146,
-0.055240873247385025,
-0.03216731548309326,
0.00873563252389431,
0.07918622344732285,
0.02019021287560463,
-0.01079507265239954,
0.02785485051572323,
0.023351455107331276,
-0.035566989332437515,
-0.014483344741165638,
0.048305612057447433,
0.008734878152608871,
0.0026767742820084095,
-0.005762705113738775,
-0.02566460147500038,
0.0322459377348423,
0.008027814328670502,
0.0064351498149335384,
0.004825313109904528,
-0.011665646918118,
-0.03288247808814049,
0.012853658758103848,
0.01725633814930916,
0.018089773133397102,
-0.030400780960917473,
-0.08697996288537979,
0.00262730591930449,
-0.03082852065563202,
-0.018323026597499847,
0.050065889954566956,
-0.034103501588106155,
0.05813707038760185,
-0.0526859313249588,
-0.026892846450209618,
-0.036150913685560226,
0.06406677514314651,
0.0333404503762722,
0.049292758107185364,
-0.028882542625069618,
0.06772443652153015,
-0.04534202441573143,
0.04030982777476311,
0.019924556836485863,
0.008466195315122604,
-0.01291851606220007,
-0.04423443600535393,
-0.004415145143866539,
0.006847741547971964,
0.07317914813756943,
0.010048814117908478,
-0.02131875418126583,
0.04938322305679321,
0.07318298518657684,
0.023295553401112556,
0.019832169637084007,
0.02141636796295643,
-0.02307361178100109,
0.06126086786389351,
-0.058765918016433716,
-0.014825535006821156,
0.03115740604698658,
-0.013259956613183022,
0.07401292771100998,
0.009989248588681221,
0.02073001116514206,
0.004896370228379965,
0.011938712559640408,
-0.008989394642412663,
-0.012456906028091908,
0.031410206109285355,
-0.055092085152864456,
-0.00941870454698801,
0.014051053673028946,
-0.006571446545422077,
-0.05111447349190712,
0.0019751028157770634,
-0.015573220327496529,
0.021806661039590836,
0.011598709970712662,
-0.007783857639878988,
0.021887460723519325,
-0.00934804230928421,
0.019281955435872078,
-0.01802367903292179,
0.011982963420450687,
0.02296331897377968,
-0.025052228942513466,
-0.006807131227105856,
-0.018151190131902695,
0.07542689889669418,
-0.04499155282974243,
0.0491248182952404,
0.024791225790977478,
0.09116148948669434,
-0.007961303927004337,
-0.01527971588075161,
-0.059416744858026505,
0.012316877022385597,
0.02308596670627594,
0.046298328787088394,
-0.0024017596151679754,
-0.016836246475577354,
-0.0069894976913928986,
0.02598736621439457,
0.03346243128180504,
-0.008456544950604439,
-0.0761314257979393,
0.04238453507423401,
0.030207889154553413,
0.02861757203936577,
0.0037517365999519825,
0.018446408212184906,
-0.020748024806380272,
-0.002604038454592228,
-0.012980347499251366,
0.023286739364266396,
-0.05835884436964989,
0.050542376935482025,
0.006479541305452585,
-0.0366424135863781,
0.023126430809497833,
-0.05293165147304535,
-0.04548871889710426,
0.03958193585276604,
-0.05755654722452164,
0.002447453560307622,
-0.026035994291305542,
-0.03270692378282547,
0.00048549255006946623,
0.00849946215748787,
-0.016741089522838593,
-0.02415044605731964,
-0.012513513676822186,
0.04358697682619095,
-0.0006662193918600678,
-0.026168201118707657,
-0.01006880309432745,
-0.04571160301566124,
-0.03146856650710106,
-0.0555899553000927,
-0.02874891832470894,
-0.005864644423127174,
0.0459667332470417,
-0.007126485463231802,
-0.0031299979891628027,
0.10566307604312897,
0.015958957374095917,
-0.0009921955643221736,
0.028961464762687683,
0.03988286852836609,
-0.00738445483148098,
-0.01236762385815382,
-0.03601353242993355,
-0.017449496313929558,
0.020460043102502823,
-0.04273820295929909,
-0.0043186005204916,
-0.010098862461745739,
-0.020196495577692986,
-0.052278097718954086,
0.032046977430582047,
-0.015810314565896988,
0.0017260947497561574,
0.01104716770350933,
0.012228744104504585,
-0.0026059874799102545,
-0.04007231071591377,
-0.02977907843887806,
-0.04853473976254463,
0.007201352622359991,
-0.03821685165166855,
-0.03651782125234604,
-0.1027432233095169,
-0.03367055207490921,
0.027371864765882492,
0.0018989760428667068,
-0.013336742296814919,
-0.012072309851646423,
0.09192328155040741,
0.054799579083919525,
0.016790928319096565,
-0.015542358160018921,
-0.02158360183238983,
-0.002312474651262164,
0.05517255887389183,
-0.04963120073080063,
-0.04269916191697121,
-0.028999149799346924,
0.027683716267347336,
0.01924789883196354,
0.003180841915309429,
0.013785243034362793,
0.020258016884326935,
-0.026507746428251266,
0.010842381045222282,
-0.0023612570948898792,
0.013798062689602375,
0.032427407801151276,
-0.03722521290183067,
-0.028083322569727898,
0.03549640253186226,
0.013239567168056965,
0.011893105693161488,
-0.018699146807193756,
0.04597035422921181,
-0.034693196415901184,
-0.025869112461805344,
-0.020350247621536255,
0.03896084800362587,
-0.024011682718992233,
-0.018270984292030334,
0.007519907783716917,
-0.026105869561433792,
-0.023690776899456978,
-0.011326131410896778,
0.09354102611541748,
-0.01683901622891426,
-0.017911724746227264,
0.0028113413136452436,
0.03217640519142151,
0.0002216360007878393,
-0.13811852037906647,
-0.021570317447185516,
0.002816657302901149,
0.005969264544546604,
0.018351681530475616,
-0.05751844123005867,
-0.008797000162303448,
0.03111858479678631,
0.009392273612320423,
0.010595970787107944,
-0.02403903193771839,
0.04416672885417938,
-0.07200174033641815,
0.046982329338788986,
0.005254977382719517,
0.06244261935353279,
-0.081001415848732,
0.012442798353731632,
0.0010292859515175223,
0.028352845460176468,
0.028743213042616844,
-0.019596025347709656,
0.010056876577436924,
-0.047334231436252594,
0.029757246375083923,
0.0027399808168411255,
-0.009136976674199104,
-0.028564369305968285,
-0.006270652171224356,
-0.0388149619102478,
0.03300594165921211,
-0.017735114321112633,
-0.008670086041092873,
-0.032761599868535995,
0.003210693132132292,
-0.09077668935060501,
0.013295016251504421,
-0.03585539758205414,
-0.025996584445238113,
-0.013703923672437668,
-0.028358880430459976,
-0.052427615970373154,
0.01646982878446579,
-0.06253404915332794,
-0.030512815341353416,
-0.01804427243769169,
0.012889357283711433,
-0.057949937880039215,
-0.01707175001502037,
0.010460537858307362,
-0.005400402937084436,
0.007494605146348476,
0.02850962243974209,
-0.014163708314299583,
0.000469117978354916,
-0.029996760189533234,
0.013049240224063396,
0.0016961375949904323,
0.05584833770990372,
0.06711045652627945,
0.021608976647257805,
-0.06398066133260727,
0.04808169975876808,
0.04222913086414337,
0.014323599636554718,
0.014268958941102028,
0.019238127395510674,
-0.060654446482658386,
-0.0002521466522011906,
0.06804937869310379,
-0.02144201099872589,
-0.013734730891883373,
-0.029435472562909126,
-0.009247999638319016,
-0.04780205711722374,
0.013373940251767635,
-0.0252350065857172,
-0.08039890229701996,
-0.014719715341925621,
-0.02085679955780506,
0.02430790662765503,
0.010155762545764446,
0.015279612503945827,
0.018178505823016167,
0.009613714180886745,
-0.010913219302892685,
0.06658364832401276,
-0.03637959063053131,
0.03836330398917198,
0.06067335605621338,
0.03468931093811989,
0.08128010481595993,
0.061987247318029404,
-0.018305473029613495,
0.004345454275608063,
0.005732971243560314,
0.02498338185250759,
0.019949357956647873,
-0.06078622117638588,
-0.019741417840123177,
-0.0016839605523273349,
-0.009318317286670208,
-0.015596194192767143,
-0.020149454474449158,
0.02115888148546219,
-0.009333637543022633,
0.05168256163597107,
-0.0015775850042700768,
-0.002153112320229411,
0.0051951054483652115,
-0.033515915274620056,
-0.014515643008053303,
-0.03884361311793327,
0.01584329456090927,
0.016470827162265778,
-0.024471387267112732,
-0.014781061559915543,
-0.037983596324920654,
-0.013159320689737797,
0.009189925156533718,
-0.00894229020923376,
-0.0013602941762655973,
-0.0017152864020317793,
-0.03665871545672417,
0.010847911238670349,
-0.02347593754529953,
0.015019489452242851,
-0.05011293664574623,
0.009519301354885101,
0.010945780202746391,
-0.02338159829378128,
0.04176560416817665,
0.027195017784833908,
-0.029965629801154137,
-0.07002478092908859,
-0.07554446160793304,
-0.018832525238394737,
0.004095296375453472,
-0.0246437881141901,
0.050006989389657974,
-0.04273001104593277,
0.004294176120311022,
0.09306932240724564,
0.04447619989514351,
0.005035822279751301,
-0.03769352287054062,
0.032403286546468735,
-0.05528266727924347,
-0.0034377812407910824,
0.019689753651618958,
-0.013214637525379658,
-0.0220919419080019,
0.03408777713775635,
0.007789131253957748,
0.08078528195619583,
-0.06126986816525459,
0.012085401453077793,
-0.002975650830194354,
0.017086496576666832,
-0.04876972362399101,
-0.041233159601688385,
-0.03390313312411308,
0.010818698443472385,
0.02783147804439068,
-0.006642072461545467,
0.0020904650446027517,
0.04952043294906616,
0.04018671065568924,
0.01600712351500988,
-0.05546962842345238,
0.02751169353723526,
0.05177314206957817,
-0.00250539043918252,
0.03275807946920395,
-0.036983832716941833,
-0.005370786413550377,
-0.06619971990585327,
-0.006832819432020187,
-0.02002129890024662,
-0.04606715962290764,
0.012730129994452,
-0.029508251696825027,
0.04168594256043434,
-0.05030658468604088,
0.0009065626654773951,
-0.033781155943870544,
0.008563214913010597,
-0.0331333726644516,
0.00242923223413527,
0.009014258161187172,
0.003052614163607359,
-0.015468189492821693,
-0.019918762147426605,
-0.008096511475741863,
0.02703617513179779,
0.034647222608327866,
-0.005639980547130108,
0.021823452785611153,
0.07836959511041641,
0.039396949112415314,
-0.03699851408600807,
0.09040894359350204,
0.021509336307644844,
-0.06843791902065277,
0.025788694620132446,
0.03853033855557442,
0.041068319231271744,
0.004867846611887217,
0.023426180705428123,
-0.02850865200161934,
-0.007630949839949608,
-0.012533243745565414,
-0.01988164149224758,
0.007551903370767832,
-0.03468045964837074,
0.010033191181719303,
-0.024209098890423775,
-0.05283648520708084,
0.033586353063583374
] |
<p>I suggest the following thought experiment that describes a machine which makes everybody happy.</p>
<p>Suppose a lottery is conducted. The winner is awarded a billion dollars plus the title of eternal Earth dictator.</p>
<p>The winner is determined in the following way.</p>
<ul>
<li><p>There is a thorough isolated black box inside which a pretender is placed.</p></li>
<li><p>Inside the box a quantum experiment is conducted with equal probability of the two outcomes: 0 or 1 (it may be based on an atom decay)</p></li>
<li><p>The pretender measures the result with an apparatus. </p></li>
<li><p>The black box is connected by a quantum link (in form of an optical fiber) to an external quantum computer</p></li>
<li><p>After the measurement by the pretender is done the result is automatically transmitted by the optical link to the quantum computer</p></li>
<li><p>The transmitted qubit is used by quantum computer as an initial state of the quantum register instead of usual Hadamard transform before performing a Shor factorization algorithm.</p></li>
<li><p>After the algorithm is performed, the result is checked whether it is correct.</p></li>
<li><p>If it is correct the pretender is declared the looser. If the factorization returned a wrong result, the pretender is declared the winner.</p></li>
</ul>
<p>What happens.</p>
<p>Any average person placed in the black box will measure the result of the atom decay and similarly to a Schroedinger cat will enter the superposition of two states: the one which saw 0 and the one which saw 1.</p>
<p>Similarly the measuring apparatus will enter the superposition. So the qubit sent via the optical fiber will be a superposition of two states:</p>
<p>$$\frac{1}{\sqrt{2}}|0\rangle+\frac{1}{\sqrt{2}}|1\rangle$$</p>
<p>As this value is exactly the same what Hadamard gate returns after being applied to an empty qubit, this will allow the quantum computer to perform the factorization as usual and return the correct result, dispite that the initial step of applying the Hadamard gate has been replaced by loading the qubit obtained from the black box.</p>
<p>Now suppose the observer himself is placed in the black box. After the atom decay he will perform measurement which will collapse the wave function. The observer will be in either state where he saw 0 or where he saw 1. So either basis state 0 or basis state 1 is sent via the cable to the quantum computer.</p>
<p>Since this is different from the usual value which should be loaded in the register before performing the factorization, the factorization will return a wrong result. So the pretender will be declared the winner.</p>
<hr>
<p>It follows that any person, when he or she is observing the lottery from outside will see all other pretenders to loose.</p>
<p>At the same time any participant that tries the lottery himself will find himself a winner.</p>
<p>This is a fascinating lottery which will make all the participation pretenders the winners in their own eyes. Each person who goes through this machine will see other people to congratulate them, to proclaim them the eternal emperor and so on.</p>
<p>I would like to see whether there any mistake in the reasoning.</p> | g1294 | [
0.031184032559394836,
0.060787785798311234,
0.016382887959480286,
-0.03586600348353386,
0.018829284235835075,
0.012610572390258312,
0.009876265190541744,
0.05765433982014656,
0.01942429319024086,
-0.037347059696912766,
0.027973012998700142,
0.03374548256397247,
-0.012731512077152729,
0.027515994384884834,
0.013200146146118641,
0.06611623615026474,
0.04615366831421852,
-0.021094275638461113,
0.028467509895563126,
0.03130991756916046,
-0.0181797593832016,
0.051260240375995636,
-0.03868015855550766,
-0.04683014377951622,
-0.018510466441512108,
-0.04324395954608917,
-0.04794721677899361,
-0.03169924393296242,
-0.03354339301586151,
0.029856551438570023,
-0.05297117680311203,
-0.006788581609725952,
-0.012410556897521019,
-0.026974963024258614,
-0.0034238710068166256,
-0.008944596163928509,
0.017057182267308235,
0.014828355051577091,
0.014193478040397167,
0.046772800385951996,
-0.01747233420610428,
0.020389612764120102,
-0.04174615070223808,
-0.040304504334926605,
0.0024729077704250813,
0.019579220563173294,
0.08096039295196533,
-0.016064027324318886,
0.05578552931547165,
-0.037143774330616,
-0.01905045472085476,
-0.018324486911296844,
0.06046785041689873,
0.03739511966705322,
0.030863318592309952,
0.04425981640815735,
-0.026846492663025856,
0.010880020447075367,
0.00023887069255579263,
0.016192777082324028,
0.010891290381550789,
-0.034793078899383545,
0.08506927639245987,
-0.017686204984784126,
0.061148542910814285,
0.01054810918867588,
-0.017616748809814453,
0.06228521093726158,
0.04100269079208374,
0.03288767859339714,
-0.020381417125463486,
-0.029024554416537285,
0.024404188618063927,
0.036922208964824677,
0.09594233334064484,
0.025090081617236137,
-0.012402450665831566,
0.02242863178253174,
0.033557016402482986,
0.05955284461379051,
-0.008523931726813316,
-0.07763288915157318,
-0.015320895239710808,
0.03933977335691452,
0.004150728229433298,
-0.04851944372057915,
-0.021734699606895447,
-0.058047786355018616,
-0.010987434536218643,
-0.011925006285309792,
0.0012714978074654937,
-0.015609518624842167,
0.07186084985733032,
0.05113809183239937,
-0.00762059586122632,
-0.004050318151712418,
0.01204567402601242,
0.0012529744999483228,
-0.0073455399833619595,
-0.00656152656301856,
-0.028941331431269646,
-0.021826349198818207,
0.009711786173284054,
-0.04674292728304863,
-0.024344494566321373,
-0.03535517677664757,
-0.030304327607154846,
0.05614742264151573,
-0.02984643541276455,
0.023727862164378166,
0.0000969077882473357,
-0.05168195068836212,
-0.03310855105519295,
-0.07586755603551865,
0.019280970096588135,
0.0010037386091426015,
0.03858697786927223,
-0.026779904961586,
0.006904282607138157,
0.005558033008128405,
-0.008992728777229786,
0.044070374220609665,
0.020774751901626587,
-0.011948607861995697,
0.02663642354309559,
0.0039574443362653255,
-0.054908864200115204,
0.023923775181174278,
-0.0286713857203722,
-0.04329521581530571,
0.023965399712324142,
0.021547280251979828,
-0.007939359173178673,
0.06126037985086441,
-0.05204465240240097,
0.029525404796004295,
0.03615136444568634,
-0.027426576241850853,
0.0531015619635582,
-0.04684324935078621,
-0.016540832817554474,
-0.007633515167981386,
-0.05387270823121071,
0.062198247760534286,
-0.023327117785811424,
-0.0033852034248411655,
0.05013636499643326,
0.0014958445681259036,
0.013532041572034359,
0.011988842859864235,
-0.03923606127500534,
-0.007898612879216671,
-0.049522798508405685,
0.02817397192120552,
0.011183541268110275,
-0.008458138443529606,
0.03408103436231613,
0.04662938416004181,
0.017354946583509445,
0.028582917526364326,
0.00008752538269618526,
-0.01295936107635498,
-0.014787189662456512,
0.031470734626054764,
-0.021359680220484734,
0.018444908782839775,
0.06184043735265732,
-0.009185642004013062,
0.014985294081270695,
-0.006186760030686855,
-0.027880579233169556,
-0.05577206239104271,
-0.0694146379828453,
0.02684304118156433,
0.007072592619806528,
0.019579004496335983,
-0.02207714132964611,
0.002316573401913047,
0.04712577164173126,
-0.017372293397784233,
-0.002606449881568551,
-0.03393390774726868,
0.028430107980966568,
-0.047342151403427124,
-0.02066372148692608,
-0.03149611875414848,
0.016204753890633583,
0.06885446608066559,
-0.01972622238099575,
0.02703738771378994,
0.06419476866722107,
-0.032314740121364594,
-0.020477844402194023,
-0.0028760875575244427,
-0.046720195561647415,
-0.0059996098279953,
0.092335045337677,
-0.022800546139478683,
0.02613707259297371,
-0.03263435140252113,
0.04866344481706619,
0.009368927218019962,
-0.0038364913780242205,
-0.010572560131549835,
0.007702252361923456,
-0.02432466670870781,
0.03171160817146301,
0.0029762987978756428,
-0.019495785236358643,
0.016502147540450096,
0.0715969130396843,
0.042663149535655975,
-0.0015771739417687058,
0.00499895540997386,
-0.014248140156269073,
0.046533457934856415,
-0.01659085974097252,
-0.030737653374671936,
0.008353766053915024,
0.004689431749284267,
0.00695683853700757,
-0.00031269239843823016,
0.029839100316166878,
-0.021703381091356277,
0.03190076723694801,
0.034914083778858185,
-0.07098551839590073,
-0.07967034727334976,
-0.07427537441253662,
0.04659449681639671,
0.005255993455648422,
-0.04837016388773918,
-0.013965407386422157,
-0.035983890295028687,
0.012836074456572533,
0.053225766867399216,
-0.0023304536007344723,
0.012975448742508888,
0.028310781344771385,
0.06356760114431381,
0.022538406774401665,
0.06003386154770851,
-0.09700558334589005,
-0.011368575505912304,
-0.06702493131160736,
-0.012565845623612404,
-0.0739845260977745,
-0.011836599558591843,
0.018256956711411476,
0.019325273111462593,
-0.024379264563322067,
-0.010872479528188705,
0.016768718138337135,
-0.0878351479768753,
0.02324300818145275,
-0.03991721570491791,
-0.014910113997757435,
0.03100571408867836,
0.0397566519677639,
0.02429523505270481,
0.013431615196168423,
-0.008613960817456245,
0.04833699390292168,
0.006705202162265778,
0.02747792750597,
-0.02193153090775013,
-0.0075296335853636265,
-0.033086955547332764,
0.02080439403653145,
0.020319471135735512,
-0.005824352148920298,
0.06912815570831299,
0.013994167558848858,
0.010405880399048328,
0.0020136756356805563,
0.0022421753965318203,
-0.05047586187720299,
0.014714736491441727,
0.042643822729587555,
-0.02063923515379429,
-0.001123621012084186,
0.01139282900840044,
-0.05961338430643082,
-0.01290795486420393,
0.015490546822547913,
-0.08662541955709457,
-0.029228899627923965,
0.024914870038628578,
-0.003814944066107273,
-0.017888039350509644,
0.006755337584763765,
0.05616183578968048,
0.0001537251373520121,
0.012388770468533039,
0.0005358922062441707,
0.08871369063854218,
0.03827548027038574,
-0.022505735978484154,
-0.02851705811917782,
0.06922221928834915,
-0.0088136475533247,
-0.022000225260853767,
0.030262544751167297,
0.054216958582401276,
0.022770563140511513,
-0.027717074379324913,
-0.01854378543794155,
0.01149787474423647,
-0.04042552039027214,
-0.05912058800458908,
-0.044076643884181976,
-0.008358567021787167,
0.008117868565022945,
-0.0255327969789505,
-0.00841102097183466,
-0.03000061586499214,
-0.006633223500102758,
0.026123469695448875,
0.026051705703139305,
-0.046477001160383224,
0.004623084794729948,
-0.024645302444696426,
-0.002800913294777274,
-0.011878572404384613,
0.033556580543518066,
0.05639484524726868,
-0.006539449095726013,
0.009407355450093746,
-0.04402187094092369,
-0.06580835580825806,
-0.014355411753058434,
0.05030841752886772,
0.033291079103946686,
-0.02959465980529785,
-0.035465992987155914,
-0.06539829820394516,
-0.05005956441164017,
0.036710355430841446,
-0.06335895508527756,
0.04224834218621254,
0.0438099205493927,
-0.01973375864326954,
0.026519998908042908,
-0.023197658360004425,
0.061721473932266235,
-0.022608313709497452,
0.0010611432371661067,
-0.006404912564903498,
0.053787197917699814,
0.006612121593207121,
0.00578195508569479,
-0.037278566509485245,
-0.0007060407078824937,
-0.012145654298365116,
0.00120207155123353,
0.018146520480513573,
-0.04044653847813606,
-0.00948147289454937,
0.029703276231884956,
-0.012299523688852787,
0.012630720622837543,
0.022865362465381622,
0.010135985910892487,
0.0019204920390620828,
-0.0299738347530365,
0.04419582709670067,
0.006428038235753775,
0.04766876995563507,
0.00789246242493391,
0.01996983028948307,
-0.025325970724225044,
0.012125439010560513,
-0.003423724789172411,
-0.03212753310799599,
-0.018316300585865974,
0.005476170685142279,
0.03912515938282013,
-0.03701129928231239,
-0.022839903831481934,
0.013976103626191616,
-0.00890895165503025,
0.04104204848408699,
-0.03607235848903656,
-0.003173582488670945,
0.038940101861953735,
0.0017204012256115675,
-0.013930870220065117,
-0.06185520812869072,
0.03906223922967911,
0.03552636131644249,
0.03132200986146927,
0.004361605737358332,
-0.04893411695957184,
0.04923000931739807,
0.009370139800012112,
0.06192268058657646,
-0.0015427730977535248,
-0.06545749306678772,
0.02132446877658367,
-0.02037430927157402,
0.018921319395303726,
0.00809165183454752,
0.011138849891722202,
0.02512856014072895,
-0.020130280405282974,
-0.04572194442152977,
-0.03913704305887222,
-0.022546030580997467,
0.049726467579603195,
-0.0323721244931221,
-0.02309059165418148,
0.026744946837425232,
0.016296975314617157,
-0.021077431738376617,
0.012171785347163677,
0.0060716853477060795,
0.06657762825489044,
-0.005960565991699696,
-0.02354816161096096,
-0.025728050619363785,
0.0025879675522446632,
-0.0036830096505582333,
-0.039691291749477386,
0.02406231313943863,
-0.0476003997027874,
-0.057721033692359924,
0.00856001116335392,
0.013786283321678638,
0.009229214861989021,
-0.014544879086315632,
0.04472797363996506,
0.004861751105636358,
-0.017215359956026077,
0.00799740944057703,
-0.006470339372754097,
0.020758727565407753,
-0.021136634051799774,
-0.041406143456697464,
-0.025981828570365906,
0.03266562893986702,
0.09243901073932648,
0.0024475622922182083,
-0.008588382974267006,
-0.0005309060798026621,
0.04272400215268135,
0.08052729815244675,
-0.04548574984073639,
-0.04445984587073326,
-0.027709374204277992,
-0.028105556964874268,
-0.002250709803774953,
0.048155106604099274,
0.0028270974289625883,
0.015824513509869576,
0.018024522811174393,
-0.04794720932841301,
-0.0657719224691391,
0.025540344417095184,
0.03901394084095955,
0.020232973620295525,
-0.03312450647354126,
-0.002599319675937295,
-0.05014535412192345,
0.06011268496513367,
-0.00808167178183794,
0.03954273834824562,
-0.021776633337140083,
-0.007392209954559803,
-0.0396759957075119,
-0.020298432558774948,
0.006562637165188789,
0.008472238667309284,
0.035205479711294174,
-0.0014834406320005655,
-0.04684446007013321,
-0.029884662479162216,
-0.06150631606578827,
0.009911325760185719,
0.032089073210954666,
0.038924507796764374,
-0.05082598328590393,
0.025313755497336388,
0.07732325792312622,
-0.010877974331378937,
0.031176496297121048,
0.0005849485751241446,
0.01028970442712307,
0.013404603116214275,
-0.062264587730169296,
-0.08116669952869415,
0.013164074160158634,
-0.012382450513541698,
-0.0006394078955054283,
-0.08311323821544647,
0.02757900208234787,
-0.038982730358839035,
-0.04742100462317467,
-0.01930994540452957,
0.08091911673545837,
0.0513993576169014,
-0.06824462115764618,
0.0754539966583252,
-0.045640990138053894,
-0.033198803663253784,
-0.05631554126739502,
-0.04104993864893913,
-0.022270679473876953,
0.015307414345443249,
0.005488285329192877,
0.023488618433475494,
-0.05167369171977043,
0.0016183468978852034,
-0.021839143708348274,
0.015810653567314148,
-0.020262915641069412,
-0.005681520327925682,
0.005237283650785685,
-0.00020338408648967743,
0.011056534014642239,
-0.004219216760247946,
0.04628157615661621,
-0.008400624617934227,
-0.008164453320205212,
-0.05019021034240723,
0.007072495762258768,
0.027927009388804436,
-0.02179407700896263,
-0.011285816319286823,
0.08773455768823624,
-0.017752906307578087,
0.04625173285603523,
0.06802399456501007,
0.06217414513230324,
-0.02303961291909218,
-0.012468439526855946,
-0.0028245088178664446,
-0.004502117168158293,
0.01565396785736084,
0.04504216089844704,
0.01900925114750862,
0.08212675154209137,
-0.017541972920298576,
0.06387396901845932,
-0.020295798778533936,
0.030293287709355354,
-0.008840641938149929,
-0.08697278797626495,
0.020441513508558273,
-0.00786934420466423,
-0.06368415802717209,
-0.03401142358779907,
-0.023226723074913025,
-0.0024353519547730684,
0.04992761090397835,
0.022663602605462074,
0.002727366052567959,
-0.017566988244652748,
-0.04236265644431114,
0.012333319522440434,
0.05003361031413078,
-0.006482331082224846,
0.060151487588882446,
0.050777725875377655,
0.013174056075513363,
0.03182584047317505,
-0.0006293452461250126,
0.028609590604901314,
-0.023543830960989,
-0.01872229389846325,
0.03978158161044121,
0.006042137276381254,
0.04039660096168518,
-0.07060264050960541,
-0.018155811354517937,
-0.00891033373773098,
-0.027324579656124115,
0.03554636240005493,
-0.05970963463187218,
-0.03895140439271927,
-0.069183349609375,
0.02010899968445301,
-0.040293797850608826,
0.012027258053421974,
-0.04990849643945694,
-0.006486374419182539,
0.01784064806997776,
-0.030824830755591393,
0.018877971917390823,
-0.00568788219243288,
0.00576834985986352,
-0.07763156294822693,
-0.012883777730166912,
-0.026597846299409866,
-0.06656729429960251,
-0.01242852583527565,
0.033349767327308655,
-0.014365344308316708,
-0.06735660135746002,
-0.02915825881063938,
-0.004882361274212599,
-0.08055245131254196,
0.011268622241914272,
0.004129969980567694,
-0.013767855241894722,
-0.015758417546749115,
0.05095018073916435,
-0.035302989184856415,
-0.01053883507847786,
0.054028790444135666,
0.03598015755414963,
-0.028982210904359818,
-0.0015705691184848547,
0.002629954135045409,
-0.018140124157071114,
0.013223514892160892,
0.006389360874891281,
0.053802020847797394,
-0.0059291948564350605,
0.0430375300347805,
0.019831812009215355,
0.033684417605400085,
-0.012507564388215542,
0.04946384206414223,
-0.0339374877512455,
0.04721799120306969,
0.038018807768821716,
-0.0386340357363224,
-0.004529832396656275,
0.07829461991786957,
0.005172649398446083,
-0.07105012983083725,
-0.019979950040578842,
0.04831410199403763,
0.04223378747701645,
-0.024851948022842407,
0.03177797794342041,
-0.03605993837118149,
0.0018956457497552037,
0.043351415544748306,
0.034668147563934326,
-0.007856382988393307,
0.03150061517953873,
0.015401123091578484,
-0.0043342215940356255,
0.013073809444904327,
0.04003574326634407,
0.07904210686683655,
-0.017096998170018196,
-0.04094415158033371,
-0.03817888721823692,
-0.03524437174201012,
-0.012038887478411198,
-0.023661503568291664,
0.007200778461992741,
-0.04284939542412758,
0.015806516632437706,
0.031524017453193665,
0.05075375363230705,
0.05082499235868454,
-0.09066317230463028,
0.03229057788848877,
-0.03735591471195221,
-0.06693923473358154,
0.021555064246058464,
-0.003077095141634345,
-0.0036680526100099087,
-0.04214337468147278,
-0.014671772718429565,
-0.03675943985581398,
0.003937217406928539,
0.05146106705069542,
0.0023244728799909353,
-0.0653381273150444,
-0.06279608607292175,
-0.00881881732493639,
-0.057995863258838654,
-0.03044520504772663,
0.058655351400375366,
-0.028226656839251518,
-0.026197105646133423,
0.003830468514934182,
0.017875876277685165,
-0.0500243604183197,
-0.012731716968119144,
0.00476877624168992,
0.012404801324009895,
-0.008338470943272114,
0.025295337662100792,
-0.024509146809577942,
0.008314735256135464,
-0.012958175502717495,
-0.01630047895014286,
-0.028241069987416267,
-0.05050577223300934,
0.004705337807536125,
0.042641013860702515,
-0.004569831769913435,
0.0250704288482666,
0.04812430962920189,
0.01466241106390953,
-0.029555613175034523,
0.029755448922514915,
0.030835341662168503,
0.01760091446340084,
-0.0033606861252337694,
-0.0751306414604187,
-0.03313102945685387,
0.014445981942117214,
-0.04359586536884308,
-0.008903950452804565,
0.014576997607946396,
0.026908090338110924,
-0.03408534824848175,
-0.0010028642136603594,
0.013255986385047436,
0.007295629475265741,
-0.02960716187953949,
0.04487551003694534,
0.01700194925069809,
0.015846362337470055,
0.07551036030054092,
0.048315927386283875,
-0.03784438967704773,
-0.0139679666608572,
-0.041111964732408524,
-0.051945582032203674,
-0.0184090044349432,
-0.05645136907696724,
-0.007124485448002815,
-0.0024421652778983116,
0.0774807408452034,
0.020161360502243042,
-0.02839624136686325,
-0.010010521858930588,
0.03269411250948906,
0.012521463446319103,
-0.05910273268818855,
-0.045137107372283936,
-0.042532242834568024,
-0.005585663486272097,
-0.02269308641552925,
-0.07017508149147034,
0.009211272932589054,
0.0007465686067007482,
0.04428882896900177,
-0.036846842616796494,
-0.053286440670490265,
-0.013918362557888031,
-0.0011711717816069722,
-0.02954559400677681,
-0.02147022821009159,
-0.09092273563146591,
-0.05929750204086304,
0.039893992245197296,
0.07493655383586884,
0.013177071698009968,
0.04182540997862816,
0.029809916391968727,
0.0402081124484539,
-0.03065541759133339,
-0.03857855498790741,
-0.022936632856726646,
-0.018793892115354538,
0.00838455744087696,
-0.05985526740550995,
0.04116004332900047,
0.09792866557836533,
0.05534205585718155
] |
<p>I have the following reaction: $^{10}_5\mathrm{Be} +\space ^2_1\mathrm{H} \rightarrow \space^{11}_5\mathrm{B} + \space ^1_1\mathrm{H}$ </p>
<p>And I know that I have to use the formula: $E = \Delta m\cdot c^2 = \Delta m \cdot \frac{931,5MeV}{u}$.</p>
<p>So I just need $\Delta m$ which is equal to:
$\Delta m = m_b - m_a$ where $m_b$ represents the mass "before the reaction" and $m_a$ the mass "after the reaction" so we have:<br>
$m_b = m(^{10}_5\mathrm{Be}) + m(^2_1\mathrm{H})$<br>
$m_a = m(^{11}_5\mathrm{B}) + m(^1_1\mathrm{H})$ </p>
<p>The book which contains this problem contains the following table:
<a href="http://i.imgur.com/esoGDVf.png" rel="nofollow">http://i.imgur.com/esoGDVf.png</a> but from this table, I only know $ m(^1_1\mathrm{H})$ and $m(^2_1\mathrm{H})$ i.e.<br>
$m_b = m(^{10}_5\mathrm{Be}) + 2.01410u$<br>
$m_a = m(^{11}_5\mathrm{B}) + 1.00783u$ </p>
<p>How do I calculate $m(^{10}_5\mathrm{Be})$ and $m(^{11}_5\mathrm{B})$ ?</p>
<p>P.S. I don't know if the tag is correct. The chapter in the book where I found this exercise is called "Basics of nuclear physics".</p> | g1295 | [
0.003063538344576955,
0.008009876124560833,
-0.0069069694727659225,
0.008652725256979465,
0.056398820132017136,
-0.012733466923236847,
0.061187587678432465,
0.04624762758612633,
-0.04272404685616493,
-0.04458014294505119,
-0.048360675573349,
0.041348449885845184,
0.04212912172079086,
0.02713351510465145,
0.018650615587830544,
-0.058367274701595306,
0.010620213113725185,
0.01975000463426113,
-0.019832782447338104,
0.03534074127674103,
-0.04194807633757591,
0.027348674833774567,
-0.03677579015493393,
-0.026080599054694176,
-0.0224077720195055,
-0.013630895875394344,
-0.015413549728691578,
0.05725829303264618,
-0.029065877199172974,
0.004867515992373228,
-0.05234350636601448,
0.04769941419363022,
0.04376502335071564,
0.011922091245651245,
-0.0543031319975853,
-0.03246629238128662,
-0.016712315380573273,
0.013434119522571564,
0.021294282749295235,
-0.012067500501871109,
0.014706841669976711,
-0.07256636768579483,
0.06015128269791603,
0.04201661795377731,
0.012302995659410954,
-0.0036991217639297247,
-0.008234634064137936,
-0.006431901827454567,
-0.051859162747859955,
0.03801979497075081,
-0.031138556078076363,
0.05675610527396202,
0.04452754557132721,
-0.020195044577121735,
-0.06272360682487488,
0.02380964905023575,
0.02921174094080925,
-0.07102081924676895,
0.03384057804942131,
0.03930310159921646,
0.021079443395137787,
-0.0571332611143589,
-0.0016079529887065291,
-0.03446634113788605,
0.08717804402112961,
0.013050412759184837,
-0.05048993229866028,
0.008289208635687828,
-0.04378540813922882,
0.019837211817502975,
0.027426378801465034,
-0.022258171811699867,
0.08859435468912125,
0.0296213086694479,
-0.00535973347723484,
-0.06795690208673477,
0.006797486916184425,
-0.00261232303455472,
0.025017833337187767,
-0.01046776957809925,
0.0065042972564697266,
0.012905663810670376,
0.05553031340241432,
-0.008270409889519215,
-0.006955799181014299,
-0.005876488517969847,
-0.022062895819544792,
0.042439088225364685,
-0.03430116921663284,
-0.030699029564857483,
0.02910027839243412,
-0.033597156405448914,
-0.002230673097074032,
0.008450018242001534,
0.04338124021887779,
-0.000782764342147857,
0.007525142282247543,
-0.005215717479586601,
-0.03425247594714165,
-0.042099300771951675,
0.05478331074118614,
0.008586712181568146,
-0.0033481481950730085,
0.017061352729797363,
0.0070598796010017395,
-0.01602408103644848,
0.05731680616736412,
0.0052703567780554295,
-0.021752094849944115,
-0.01960635371506214,
-0.029208995401859283,
-0.03499690443277359,
-0.0630272701382637,
-0.08312339335680008,
-0.003585195867344737,
-0.006909423507750034,
0.019332680851221085,
-0.015458386391401291,
-0.022004591301083565,
-0.0065927281975746155,
0.054056089371442795,
0.005702250637114048,
0.009908249601721764,
0.0005847805878147483,
-0.010362312197685242,
-0.04349217936396599,
-0.03151939809322357,
0.046022891998291016,
0.08633789420127869,
0.01595272496342659,
0.014590815640985966,
-0.020158367231488228,
0.05340491980314255,
0.025024354457855225,
0.01473730243742466,
0.03231420740485191,
-0.006717390846461058,
0.06620047241449356,
-0.013464466668665409,
-0.049301452934741974,
-0.002618473954498768,
0.02268861047923565,
-0.061540815979242325,
0.027938518673181534,
-0.05150628462433815,
0.07077406346797943,
-0.02601212076842785,
-0.0010334985563531518,
0.02986271306872368,
0.03519235923886299,
-0.02694113738834858,
0.0220662709325552,
-0.01264388207346201,
0.025640564039349556,
0.06188135966658592,
-0.03171037137508392,
0.028100689873099327,
-0.014647947624325752,
-0.0065603177063167095,
-0.016278967261314392,
0.02473461627960205,
0.00033026302116923034,
-0.06908825784921646,
-0.008177179843187332,
-0.02400990203022957,
-0.020045246928930283,
0.023166239261627197,
-0.051264725625514984,
-0.016384577378630638,
-0.05990290641784668,
-0.04101661220192909,
-0.021118266507983208,
0.053093381226062775,
0.020835166797041893,
-0.011922753416001797,
0.047995828092098236,
-0.03629415109753609,
0.013577441684901714,
0.02147541008889675,
0.049879904836416245,
0.02545285038650036,
-0.03612588346004486,
0.04547145962715149,
-0.00807931087911129,
-0.00860039796680212,
-0.04053010046482086,
0.00980047881603241,
0.07912028580904007,
-0.05467960238456726,
-0.0037719302345067263,
0.02096429467201233,
0.03534013777971268,
0.06029348447918892,
-0.0022098878398537636,
-0.004418357741087675,
0.08462440222501755,
0.0024121433962136507,
0.0066478196531534195,
0.011208138428628445,
0.020716499537229538,
-0.04644331336021423,
0.03768650442361832,
0.02322467602789402,
-0.010481891222298145,
0.054884303361177444,
0.010927336290478706,
-0.0007701936992816627,
-0.0007294027600437403,
-0.0074897888116538525,
-0.01694716140627861,
-0.033540692180395126,
-0.035112760961055756,
-0.029326913878321648,
-0.030729111284017563,
-0.023489324375987053,
0.011473327875137329,
-0.040153082460165024,
-0.027797184884548187,
0.001461153500713408,
0.044218361377716064,
-0.03212917596101761,
-0.03306856006383896,
-0.00896178837865591,
0.037683919072151184,
-0.006711337715387344,
0.04285436123609543,
0.03729533404111862,
-0.003249158849939704,
-0.004651838447898626,
-0.013452103361487389,
-0.020944880321621895,
0.07770655304193497,
0.0000012002587936876807,
-0.013277043588459492,
-0.011296074837446213,
0.028459623456001282,
-0.007723328657448292,
0.04726993665099144,
0.017274925485253334,
0.050938960164785385,
-0.03518432751297951,
-0.01436812523752451,
-0.017427915707230568,
0.010349062271416187,
0.006186026614159346,
-0.05654019117355347,
0.04782646521925926,
0.04507764056324959,
-0.02860027365386486,
-0.0019418848678469658,
-0.05750253051519394,
-0.008853727951645851,
-0.0035011747386306524,
0.016232721507549286,
-0.03997365012764931,
-0.008177267387509346,
-0.04155030846595764,
-0.02237790636718273,
-0.011572835966944695,
0.013654671609401703,
0.016799254342913628,
-0.07134073227643967,
0.01802160032093525,
0.06099781394004822,
-0.07522179186344147,
-0.07631981372833252,
-0.0828203409910202,
-0.03671678155660629,
0.028808342292904854,
0.0035599989350885153,
-0.03244975954294205,
0.00842288974672556,
0.004813105799257755,
0.014475153759121895,
-0.059525467455387115,
-0.04675446078181267,
0.08747877180576324,
-0.007328420877456665,
0.06425192952156067,
-0.028968321159482002,
0.04621896892786026,
0.013404137454926968,
0.010886832140386105,
0.046298038214445114,
0.03237996995449066,
-0.04207096993923187,
-0.03254712373018265,
0.04439905658364296,
0.022079985588788986,
-0.005916306283324957,
-0.009981321170926094,
-0.04767325893044472,
0.012577149085700512,
-0.0031197424978017807,
0.01267959550023079,
0.01547900028526783,
0.06745082139968872,
-0.017721716314554214,
-0.012573533691465855,
0.03441227227449417,
0.03514501452445984,
-0.027768170461058617,
-0.005732150748372078,
-0.012809565290808678,
0.014148714020848274,
-0.0026735311839729548,
0.023939963430166245,
-0.052739035338163376,
-0.02020055241882801,
0.023090926930308342,
0.005039258860051632,
-0.006644906010478735,
-0.0008953610667958856,
-0.03762609884142876,
-0.03154826909303665,
0.0037022095639258623,
0.0340133011341095,
-0.02719435840845108,
0.03288745880126953,
-0.023538103327155113,
-0.0568118691444397,
-0.09061278402805328,
0.061588842421770096,
0.00034045896609313786,
-0.00741067249327898,
0.0426354706287384,
-0.04556657746434212,
-0.02026628889143467,
-0.04095363989472389,
-0.04220588132739067,
0.01782950945198536,
0.04426199570298195,
0.008974148891866207,
0.01594206690788269,
-0.06805437803268433,
-0.04480910301208496,
0.018970157951116562,
0.011580262333154678,
-0.028133012354373932,
-0.02446123957633972,
-0.0035293002147227526,
-0.01603594794869423,
-0.012557501904666424,
-0.008292477577924728,
0.05354311689734459,
-0.02206428349018097,
0.015539449639618397,
0.03951210528612137,
-0.0006122812628746033,
-0.039682988077402115,
-0.004673896357417107,
0.01384134404361248,
-0.013501309789717197,
-0.01853056438267231,
0.021257467567920685,
0.03247126564383507,
0.014382611028850079,
0.002134334295988083,
0.024150677025318146,
0.0032072984613478184,
-0.04638351500034332,
-0.010480796918272972,
-0.005676393397152424,
0.0784837156534195,
0.013942012563347816,
0.014306065626442432,
-0.00036444069701246917,
0.04515758529305458,
-0.01196437980979681,
-0.020211827009916306,
0.006750480737537146,
-0.014830082654953003,
0.04172927886247635,
-0.03615262359380722,
-0.02724955789744854,
-0.04314609244465828,
-0.01956835202872753,
0.019376397132873535,
-0.019699715077877045,
0.01107263844460249,
-0.0017762058414518833,
-0.011326871812343597,
-0.005145746748894453,
0.007926332764327526,
0.030211344361305237,
-0.03440253436565399,
-0.03767983615398407,
-0.00566696934401989,
0.06911339610815048,
0.009576823562383652,
0.07042501121759415,
-0.023308420553803444,
-0.06154709309339523,
0.01657986454665661,
-0.00989442877471447,
-0.0318244993686676,
0.03912440314888954,
0.05919862911105156,
-0.04382752254605293,
0.011112255044281483,
-0.024109506979584694,
-0.0008085223962552845,
0.023006614297628403,
0.0019789286889135838,
-0.033803071826696396,
-0.001174674485810101,
-0.02353452704846859,
0.011487304233014584,
0.06682268530130386,
-0.017493033781647682,
0.01667182333767414,
-0.03994735702872276,
-0.009884322993457317,
0.029413094744086266,
-0.06046605110168457,
-0.005403187591582537,
-0.004758034832775593,
-0.007145488169044256,
-0.03239641711115837,
-0.009314187802374363,
-0.05312341824173927,
0.022402597591280937,
-0.025645161047577858,
-0.026654861867427826,
-0.04295984283089638,
0.03924395516514778,
0.0581856407225132,
0.0016131509328261018,
0.08070312440395355,
-0.004415806848555803,
-0.0020260438323020935,
0.0587693452835083,
-0.032714903354644775,
0.01908765733242035,
-0.06365116685628891,
0.08233478665351868,
-0.07219259440898895,
0.004528062418103218,
-0.0015242549125105143,
-0.031555965542793274,
0.040576834231615067,
0.03656481206417084,
-0.01805879920721054,
0.04810944199562073,
0.038734909147024155,
0.04103172942996025,
-0.05650186911225319,
-0.07697759568691254,
-0.012731810100376606,
-0.07379231601953506,
-0.004613272380083799,
0.02326367422938347,
0.04226364940404892,
-0.029156358912587166,
-0.018994057551026344,
0.014040273614227772,
0.002514823339879513,
0.052604954689741135,
0.007835871540009975,
0.06448541581630707,
-0.021485252305865288,
-0.008344984613358974,
0.10876883566379547,
0.033101294189691544,
-0.020137522369623184,
-0.003963839262723923,
-0.0007720291032455862,
0.02518371492624283,
-0.015066894702613354,
0.013639476150274277,
0.03527892753481865,
0.03328875079751015,
0.025237416848540306,
-0.08006203174591064,
0.009451943449676037,
0.08133207261562347,
-0.0049271187745034695,
-0.023881686851382256,
0.010089265182614326,
0.04130611941218376,
-0.022236892953515053,
-0.0010531269945204258,
-0.04277724400162697,
0.06592913717031479,
0.015927612781524658,
0.03277025371789932,
0.04645220935344696,
-0.009869013912975788,
0.040062494575977325,
-0.031255967915058136,
-0.01149740070104599,
-0.02229863405227661,
0.013660833239555359,
-0.05352647975087166,
0.058332666754722595,
-0.03343227505683899,
-0.02442874200642109,
-0.010519665665924549,
0.02397269196808338,
0.04450061172246933,
-0.03454214334487915,
-0.022769084200263023,
-0.015247407369315624,
-0.011308479122817516,
0.01165693998336792,
0.029534218832850456,
0.021776486188173294,
0.04768089950084686,
-0.017276274040341377,
-0.033089105039834976,
0.03390183672308922,
-0.01191605906933546,
0.04968077316880226,
0.033336371183395386,
0.043510906398296356,
0.008187989704310894,
0.012064734473824501,
-0.003993418533354998,
0.05067344009876251,
-0.05641241371631622,
0.09151537716388702,
-0.013035924173891544,
0.03476225212216377,
-0.024358535185456276,
0.05062809959053993,
-0.037471428513526917,
-0.026628481224179268,
-0.027117036283016205,
-0.013163940981030464,
0.07344461232423782,
-0.029561826959252357,
-0.057313937693834305,
-0.03480486571788788,
0.011725883930921555,
-0.02239379845559597,
-0.0025004418566823006,
-0.01489177905023098,
0.02330346219241619,
0.023080365732312202,
0.002388692693784833,
-0.02118743397295475,
0.0011380665237084031,
0.012297063134610653,
0.027735453099012375,
0.025190679356455803,
0.00608837278559804,
0.006445249076932669,
-0.02026689425110817,
-0.010072789154946804,
0.03987607732415199,
-0.045297592878341675,
0.020846059545874596,
0.003562233177945018,
-0.08847466856241226,
0.02496442198753357,
0.030142826959490776,
0.030604517087340355,
0.008434843271970749,
0.006570941768586636,
-0.008021949790418148,
0.0005725697265006602,
-0.011621251702308655,
-0.056597743183374405,
0.029774466529488564,
-0.04782937467098236,
-0.05593494325876236,
0.008144397288560867,
0.024964449927210808,
-0.007172072306275368,
-0.0573623962700367,
-0.0436704084277153,
0.01945328526198864,
-0.07510991394519806,
-0.013743748888373375,
0.04331077262759209,
0.05758783593773842,
0.025610581040382385,
-0.06498737633228302,
-0.03662257641553879,
0.029276538640260696,
-0.00194629468023777,
0.025325339287519455,
0.029322324320673943,
-0.03533141314983368,
-0.05181949958205223,
0.03469268977642059,
0.013352121226489544,
0.0021349559538066387,
0.0034156565088778734,
0.027757709845900536,
-0.04064600542187691,
0.02003149688243866,
-0.015252235345542431,
-0.015534845180809498,
-0.008902482688426971,
-0.03156895190477371,
-0.01853921078145504,
0.03544982895255089,
0.011899253353476524,
0.08927600085735321,
0.02196548879146576,
-0.012484587728977203,
0.01997552067041397,
-0.01931140385568142,
-0.026604823768138885,
0.05244728550314903,
-0.03312302380800247,
0.0029589978512376547,
-0.02249080128967762,
-0.009212463162839413,
-0.032832469791173935,
-0.009579440578818321,
0.05622418224811554,
0.01556211244314909,
0.014482280239462852,
-0.021000294014811516,
0.04052688553929329,
0.08494831621646881,
0.008902495726943016,
0.005166058428585529,
0.06019268184900284,
-0.03520989418029785,
-0.003324662335216999,
-0.03387327492237091,
0.032172638922929764,
-0.00930667296051979,
-0.011076784692704678,
-0.022767022252082825,
0.02583235315978527,
-0.02544875629246235,
-0.00020140832930337638,
-0.013632620684802532,
-0.010789766907691956,
0.0003548708336893469,
-0.03308788686990738,
0.04964035376906395,
-0.002331709023565054,
0.056689802557229996,
-0.02677103504538536,
0.06540154665708542,
-0.049999672919511795,
-0.004974311217665672,
0.03819398581981659,
0.00824376568198204,
-0.07491348683834076,
-0.030069738626480103,
0.06888385862112045,
-0.029617920517921448,
-0.07382757216691971,
-0.02529086358845234,
0.06696900725364685,
0.0043383026495575905,
-0.019698308780789375,
0.05565924569964409,
-0.057800233364105225,
-0.0069449166767299175,
0.048825789242982864,
0.019717570394277573,
0.03897427022457123,
-0.004534829407930374,
0.007519216742366552,
-0.036288026720285416,
0.020844582468271255,
0.011144907213747501,
0.05468575656414032,
0.015851512551307678,
-0.019309027120471,
0.03370024263858795,
0.06547199189662933,
-0.10605884343385696,
-0.020675083622336388,
-0.021477730944752693,
-0.02978207729756832,
0.08583016693592072,
-0.0390491783618927,
0.051423490047454834,
0.04051218181848526,
0.019254907965660095,
-0.013725410215556622,
-0.0234322939068079,
-0.03102024458348751,
-0.021635478362441063,
-0.06741445511579514,
-0.006224377080798149,
-0.006689511239528656,
0.06459309160709381,
-0.026097571477293968,
0.021284885704517365,
0.028287291526794434,
0.07816583663225174,
-0.09323949366807938,
0.007418726570904255,
0.002361150225624442,
-0.04710445553064346,
-0.04067419096827507,
0.0077449241653084755,
-0.005567688494920731,
-0.0021018418483436108,
0.02305072359740734,
-0.06756140291690826,
0.029070096090435982,
0.013408823870122433,
-0.007256876677274704,
-0.03277512267231941,
-0.02095826342701912,
-0.011100583709776402,
-0.013364186510443687,
-0.027113493531942368,
0.021750900894403458,
-0.02369883842766285,
0.03899316489696503,
-0.008923668414354324,
-0.04454662278294563,
-0.03538820892572403,
0.0414092130959034,
-0.054144054651260376,
-0.05773264914751053,
0.019660646095871925,
0.04879852756857872,
-0.051152754575014114,
-0.023393062874674797,
-0.009630748070776463,
-0.017026744782924652,
-0.05305192247033119,
-0.004274794366210699,
-0.029041403904557228,
-0.035213470458984375,
-0.02845463529229164,
0.02697848528623581,
0.02164425328373909,
-0.02342616580426693,
-0.044365044683218,
-0.007387155666947365,
0.01136092096567154,
0.013572575524449348,
-0.03410661965608597,
-0.005312952678650618,
-0.08558523654937744,
0.021324675530195236,
0.010447570122778416,
-0.002006169408559799,
-0.058268800377845764,
-0.005561179015785456,
-0.017212430015206337,
-0.007078239694237709,
-0.047525554895401,
-0.0474313423037529,
0.05122290179133415,
0.09778421372175217,
-0.018128350377082825,
0.03034459799528122,
0.016655322164297104,
-0.07118027657270432,
0.040657851845026016,
0.08504173904657364,
-0.019344819709658623,
0.023783694952726364,
0.03869355469942093,
0.030695710331201553,
0.03628300875425339,
-0.016122644767165184,
0.009879445657134056,
-0.06013229116797447,
0.0102347731590271,
0.012594230473041534,
-0.027601629495620728,
0.01928558759391308,
-0.060981303453445435
] |
<p>Consider a $\varphi^3$ theory:
$$
Z_1(J) \propto \exp\left[\frac{i}{6} Z_g g\int \mathrm{d}^4 x \left(\frac{1}{i}\frac{\delta}{\delta J}\right)^3\right] Z_0(J),
$$
where
$$
Z_0(J) = \exp\left[\frac{i}{2} \int \mathrm{d}^4 x \mathrm{d}^4 x' J(x)\Delta(x-x')J(x')\right].
$$
That is
$$
Z_1(J) \propto \sum_{V=0}^\infty \frac{1}{V!}\left[\frac{i}{6} Z_g g \int \mathrm{d}^4 x \, \left(\frac{1}{i}\frac{\delta}{\delta J}\right)^3\right]^V \times \sum_{P=0}^\infty \frac{1}{P!}\left[\frac{i}{2} \int \mathrm{d}^4 y \, \,\mathrm{d}^4 z\, J(y)\Delta(y-z)J(z)\right]^P.
$$
In particular, we can consider the term when $V=2, P=3$. Calculation shows that
\begin{equation}
- i \frac{1}{2!}\frac{1}{3!} \frac{(Z_g g)^2}{6^2*2^3} \left[\int \mathrm{d}^4\, x_1 \, \mathrm{d}^4 x_2 \, \left(\frac{\delta}{\delta J(x_1)}\right)^3 \left(\frac{\delta}{\delta J(x_2)}\right)^3\right] \left[\int \mathrm{d}^4 y \, \mathrm{d}^4 z \, J(y)\Delta(y-z)J(z)\right]^3\\=
- i \frac{1}{2!}\frac{1}{3!} \frac{(Z_g g)^2}{6^2*2^3} \int \mathrm{d}^4 x_1 \, \mathrm{d}^4 x_2 \, \left[3^3*2^4 \Delta(x_1-x_1)\Delta(x_1-x_2)\Delta(x_2-x_2) + \\ 3^2\times 2^5\Delta(x_1-x_2)\Delta(x_1-x_2)\Delta(x_1-x_2)\right]\\=
-i(Z_g g)^2 \int \mathrm{d}^4 x_1 \, \mathrm{d}^4 x_2\, \times \left[\frac{1}{2^3} \Delta(x_1-x_1)\Delta(x_1-x_2)\Delta(x_2-x_2) + \\ \frac{1}{2\times 3!}\Delta(x_1-x_2)\Delta(x_1-x_2)\Delta(x_1-x_2)\right],
\end{equation}
where $\Delta(x_1-x_1)\Delta(x_1-x_2)\Delta(x_2-x_2)$ and $\Delta(x_1-x_2)\Delta(x_1-x_2)\Delta(x_1-x_2)$ correspond to their Feynman diagram. Then the question is why $\frac{1}{2^3}$ and $\frac{1}{2\times 3!}$ are just the reciprocal of symmetry factors of the corresponding Feynman diagram respectively? </p>
<p>In the general case of $V, P$, why the coefficients of the terms in the result of calculation are just the reciprocal of symmetry factors of the corresponding Feynman diagram respectively? </p> | g1296 | [
0.03159857541322708,
0.00044428021647036076,
0.008387367241084576,
-0.013809401541948318,
0.04553599655628204,
-0.0015482357703149319,
0.0635041818022728,
-0.007239398080855608,
0.011835995130240917,
0.027135634794831276,
-0.027558263391256332,
0.08666802942752838,
-0.08411359786987305,
-0.011007671244442463,
0.01757238619029522,
0.042331527918577194,
0.01948164775967598,
0.034484729170799255,
0.02471522055566311,
-0.0015682140365242958,
-0.08483860641717911,
-0.0032989857718348503,
-0.022988703101873398,
0.0003990153199993074,
0.0431317538022995,
-0.01908489689230919,
0.0007367541547864676,
0.019855013117194176,
0.01819923147559166,
-0.013403529301285744,
0.02522376738488674,
0.07530239969491959,
-0.02257392928004265,
-0.05470547452569008,
0.003962049726396799,
0.030393287539482117,
0.059245821088552475,
0.07067261636257172,
0.029805820435285568,
-0.020137639716267586,
0.005329897627234459,
-0.01737852580845356,
0.03486037999391556,
0.045712340623140335,
-0.034329239279031754,
0.017979856580495834,
-0.0765405222773552,
0.026411952450871468,
-0.021359577775001526,
0.01143564097583294,
-0.008111732080578804,
0.06084996834397316,
0.05573328956961632,
-0.05741240456700325,
0.02704428881406784,
0.02265286073088646,
0.030077878385782242,
-0.07641153037548065,
0.006886382587254047,
0.05895903706550598,
0.003422175068408251,
0.004240815062075853,
-0.006862343288958073,
-0.014003622345626354,
0.05550261586904526,
-0.014061362482607365,
-0.05450974777340889,
-0.0047905282117426395,
0.0003349848266225308,
-0.04184770956635475,
0.006645656190812588,
-0.019948432222008705,
0.03502332419157028,
-0.03732964023947716,
-0.04956915229558945,
0.013510971330106258,
0.02058078721165657,
-0.04308658093214035,
-0.015412973240017891,
0.0070198350585997105,
-0.018802661448717117,
-0.04014463350176811,
-0.04327014088630676,
0.044193465262651443,
-0.011027339845895767,
-0.04801362007856369,
0.013968197628855705,
0.024752993136644363,
-0.04752792418003082,
0.002973450580611825,
-0.04386863484978676,
-0.01951397769153118,
-0.07128335535526276,
0.028775054961442947,
-0.026920001953840256,
0.015826575458049774,
0.039056066423654556,
0.022230073809623718,
-0.018637849017977715,
-0.020840277895331383,
-0.042124804109334946,
-0.0053596775978803635,
0.07224853336811066,
0.027487140148878098,
-0.012675038538873196,
-0.01555931381881237,
0.09836230427026749,
-0.028357861563563347,
-0.004622604697942734,
-0.0075722066685557365,
-0.0879465639591217,
0.04731707274913788,
0.014280867762863636,
0.003004211001098156,
-0.011009897105395794,
0.024692105129361153,
-0.0423966608941555,
-0.047614868730306625,
-0.0039967866614460945,
0.0034496495500206947,
-0.012176182121038437,
0.0038308340590447187,
0.05849291384220123,
0.02788146398961544,
-0.018892742693424225,
0.024030476808547974,
-0.010668160393834114,
0.01645561493933201,
0.036150310188531876,
0.010156599804759026,
0.014881729148328304,
0.0015344794373959303,
0.01195366121828556,
0.04965568706393242,
0.020986666902899742,
0.0018381024710834026,
-0.05811307579278946,
0.008796174079179764,
-0.02765263244509697,
0.06343057751655579,
0.004275514744222164,
-0.042719095945358276,
-0.0014994075754657388,
-0.051200348883867264,
-0.03575321286916733,
-0.019477875903248787,
0.010661705397069454,
-0.04772264137864113,
-0.04304632544517517,
-0.05867492035031319,
0.037589579820632935,
0.04458069056272507,
-0.006294555962085724,
0.002494828775525093,
-0.02819308638572693,
0.003552595619112253,
0.050614792853593826,
0.009301337413489819,
-0.03433483839035034,
0.01629440113902092,
0.01330809760838747,
-0.022884439677000046,
-0.008289529010653496,
0.030591323971748352,
0.010275318287312984,
-0.0004957524943165481,
0.01986715756356716,
-0.0698172003030777,
-0.053666796535253525,
-0.015036867000162601,
-0.05719185620546341,
0.07149706035852432,
0.03202803060412407,
-0.0039056153036653996,
0.031309824436903,
-0.005243436433374882,
-0.06851314753293991,
0.011825310066342354,
0.017869504168629646,
0.027838673442602158,
-0.013902684673666954,
-0.027636168524622917,
-0.01063525676727295,
-0.035705309361219406,
-0.05036334693431854,
0.009644768200814724,
0.016077373176813126,
0.012648249045014381,
-0.010791555978357792,
0.01911936327815056,
-0.03207585588097572,
0.09313307702541351,
0.04924234375357628,
0.0630488395690918,
-0.013121981173753738,
0.011471652425825596,
0.018415585160255432,
-0.07306388020515442,
-0.03129572793841362,
-0.011457908898591995,
-0.012380082160234451,
0.028989171609282494,
0.06589081883430481,
-0.006389269605278969,
0.0619647242128849,
-0.0011379329953342676,
-0.03175946697592735,
-0.007886607199907303,
0.01937233656644821,
0.030580347403883934,
-0.012281057424843311,
-0.040436532348394394,
-0.00005318681360222399,
0.018765214830636978,
-0.008095613680779934,
-0.07160095870494843,
0.013543733395636082,
0.005387693643569946,
-0.019307507202029228,
0.029277684167027473,
0.03750859573483467,
-0.002130276057869196,
0.06065421178936958,
-0.0008940488914959133,
-0.07112434506416321,
0.03897278383374214,
-0.02644241601228714,
0.01110015343874693,
-0.03497769311070442,
-0.020124215632677078,
-0.021591488271951675,
-0.03825344890356064,
-0.024557705968618393,
-0.028218181803822517,
-0.027476303279399872,
-0.02237982675433159,
-0.014939666725695133,
-0.05505935102701187,
0.0630088672041893,
0.026699846610426903,
-0.005580426659435034,
-0.03307761996984482,
0.0400162935256958,
0.02134345844388008,
0.014521007426083088,
0.006859069690108299,
0.005508542526513338,
0.052688032388687134,
0.005319314543157816,
0.025240253657102585,
-0.0127670057117939,
0.027229011058807373,
0.01476531382650137,
0.0251120887696743,
0.022964222356677055,
-0.025856761261820793,
0.019074950367212296,
0.01687186397612095,
0.054520994424819946,
-0.004091896582394838,
0.02177853137254715,
-0.021654393523931503,
-0.0038216973189264536,
0.007805596571415663,
-0.01971643604338169,
0.022707294672727585,
-0.00005364571916288696,
-0.02716752141714096,
-0.02648644521832466,
0.007539031561464071,
-0.04840203374624252,
-0.007460812572389841,
0.01326158456504345,
0.025528641417622566,
-0.05983163043856621,
-0.009061942808330059,
-0.019927339628338814,
0.011173714883625507,
0.05167902633547783,
-0.013441714458167553,
-0.05796946957707405,
-0.001363488961942494,
-0.027445800602436066,
0.0743754580616951,
0.03536023199558258,
-0.05029159411787987,
-0.017791688442230225,
0.035266876220703125,
-0.02161051146686077,
0.025927582755684853,
0.03819433972239494,
0.0465557724237442,
-0.012133283540606499,
-0.008181145414710045,
-0.034631337970495224,
-0.02538745105266571,
0.02247253619134426,
-0.050825584679841995,
0.0300593301653862,
0.0390271320939064,
0.01478052232414484,
0.025197401642799377,
0.01611863262951374,
0.017964964732527733,
0.07002685964107513,
0.030613958835601807,
-0.014016288332641125,
-0.0301868487149477,
0.015349099412560463,
-0.022868795320391655,
0.003085146192461252,
-0.01872652769088745,
0.0010376493446528912,
-0.026660099625587463,
-0.02864382416009903,
0.06982401013374329,
0.021604718640446663,
-0.021458419039845467,
-0.014246265403926373,
-0.02643507532775402,
-0.05323588848114014,
0.0011947504244744778,
-0.024813316762447357,
-0.01625983417034149,
0.041151732206344604,
0.003619885304942727,
-0.055197667330503464,
0.007002875674515963,
0.00010117516649188474,
0.04427899792790413,
-0.03486951068043709,
0.02263440564274788,
-0.016389844939112663,
-0.06909368932247162,
-0.02407839708030224,
-0.0013103531673550606,
0.008283448405563831,
0.05015832930803299,
0.040152858942747116,
-0.04830869659781456,
-0.0357748344540596,
-0.009227542206645012,
-0.008522392250597477,
-0.03679817169904709,
-0.005670527927577496,
0.003739831503480673,
-0.010827189311385155,
0.05060579627752304,
0.02296474575996399,
0.04526229202747345,
0.020931558683514595,
0.01419630367308855,
0.009886222891509533,
0.01261917781084776,
0.011144346557557583,
0.0067752329632639885,
-0.002111322246491909,
0.07806053012609482,
-0.004065425135195255,
-0.02808315120637417,
0.026577115058898926,
-0.010447029955685139,
-0.056760452687740326,
-0.017741797491908073,
-0.008594675920903683,
-0.002499541500583291,
0.0018932002130895853,
0.0009903612080961466,
-0.007048871833831072,
0.01713295467197895,
0.023162249475717545,
-0.02347894199192524,
0.043770261108875275,
0.03436633571982384,
0.011642911471426487,
-0.09736175090074539,
-0.03684144467115402,
-0.005470337811857462,
-0.048188216984272,
0.02408648654818535,
0.04513288289308548,
-0.0013042113278061152,
0.006656925193965435,
0.030199147760868073,
0.010903198271989822,
0.015818145126104355,
-0.014391300268471241,
0.0042104865424335,
-0.047199226915836334,
0.029533851891756058,
0.017804523929953575,
0.011045567691326141,
0.016431624069809914,
0.022033274173736572,
0.011527402326464653,
-0.02039368450641632,
-0.001542163547128439,
0.041754163801670074,
-0.00015063956379890442,
-0.00185644521843642,
-0.07120094448328018,
0.004245121497660875,
0.025104548782110214,
-0.015040778554975986,
-0.08885804563760757,
-0.026874562725424767,
0.03623659163713455,
-0.04196469485759735,
-0.0033865636214613914,
-0.03608888387680054,
-0.04959788918495178,
-0.008763757534325123,
0.03202734515070915,
-0.045849379152059555,
-0.039744265377521515,
-0.03789078816771507,
0.017102636396884918,
-0.04814205691218376,
0.02125982567667961,
0.0013216612860560417,
0.04896491765975952,
-0.003705092705786228,
0.03516630828380585,
-0.04665553942322731,
0.005751046817749739,
0.029117172583937645,
0.04550662636756897,
0.007078615948557854,
-0.028951384127140045,
-0.04461074247956276,
-0.011300632730126381,
0.05876429006457329,
-0.05540798231959343,
-0.01843082159757614,
-0.05447923019528389,
0.038357820361852646,
-0.03180641308426857,
0.07214508950710297,
-0.038845039904117584,
0.02745218575000763,
0.09221109747886658,
0.017348993569612503,
-0.0074896239675581455,
0.008490461856126785,
0.018479853868484497,
-0.02620174176990986,
-0.025148632004857063,
-0.0586019903421402,
0.08360610157251358,
0.013435004279017448,
-0.08698512613773346,
0.036057110875844955,
0.01833569072186947,
-0.021616997197270393,
0.05399825796484947,
0.008349302224814892,
-0.06525468081235886,
-0.011018742807209492,
0.016768349334597588,
-0.02169220522046089,
-0.055850859731435776,
0.038545746356248856,
-0.04211055114865303,
-0.014111288823187351,
0.058050528168678284,
-0.017241088673472404,
-0.028015367686748505,
-0.015160730108618736,
0.00600076001137495,
-0.01445439737290144,
0.022712109610438347,
-0.018120037391781807,
-0.008130062371492386,
0.0008405452244915068,
-0.020747771486639977,
-0.00854460522532463,
0.021769260987639427,
0.025195760652422905,
-0.06803131103515625,
-0.03639143705368042,
0.03306850418448448,
-0.03155945613980293,
-0.0229487344622612,
0.013623271137475967,
0.015383408404886723,
-0.038075968623161316,
-0.00003817494507529773,
-0.04588313028216362,
-0.07017569988965988,
-0.0401894673705101,
0.04206635802984238,
-0.02121802605688572,
0.05127166584134102,
0.012476756237447262,
-0.05140167847275734,
0.020807629451155663,
0.032257843762636185,
-0.018546875566244125,
0.00559907965362072,
0.019857678562402725,
0.02634665183722973,
-0.05642295628786087,
-0.06622505187988281,
-0.05275911092758179,
-0.02603210136294365,
-0.0022024703212082386,
0.04191519320011139,
-0.04723883792757988,
0.04311257600784302,
0.03582744300365448,
0.05832189694046974,
-0.015380275435745716,
0.0298294760286808,
0.039297785609960556,
-0.0034442634787410498,
0.026176968589425087,
0.018321355804800987,
-0.015013470314443111,
-0.014100923202931881,
-0.031105730682611465,
0.06434973329305649,
-0.00024432301870547235,
-0.0134230125695467,
-0.040582261979579926,
0.08020181953907013,
0.022530023008584976,
-0.051045939326286316,
-0.0608198419213295,
0.002527340315282345,
-0.05931469053030014,
-0.03774295374751091,
-0.057730820029973984,
0.022045986726880074,
-0.004897439852356911,
0.033918365836143494,
0.006443167570978403,
0.004876713268458843,
-0.023869069293141365,
0.030255189165472984,
0.00628658477216959,
-0.012680325657129288,
-0.027364330366253853,
-0.004779646173119545,
0.016383612528443336,
-0.05654953792691231,
0.038009800016880035,
0.00552608584985137,
0.022307977080345154,
0.04631803557276726,
-0.008156156167387962,
0.006639676168560982,
-0.07589390128850937,
-0.06544984877109528,
-0.007180678658187389,
-0.011103752069175243,
0.026184307411313057,
-0.00339553807862103,
0.0027068746276199818,
-0.04174426198005676,
-0.019841551780700684,
-0.02336456999182701,
-0.0064633977599442005,
-0.011099507100880146,
0.009242823347449303,
-0.041582394391298294,
-0.07395517826080322,
0.02374076098203659,
0.011316063813865185,
0.02032308280467987,
0.03993269056081772,
-0.012624241411685944,
-0.0030385972931981087,
-0.009210276417434216,
0.013304540887475014,
0.06292591989040375,
0.06408381462097168,
0.04026857018470764,
-0.13387981057167053,
-0.03515779599547386,
-0.009169898927211761,
0.01509934663772583,
0.02285795845091343,
0.0434933640062809,
-0.04143751412630081,
-0.015479028224945068,
0.06487104296684265,
-0.026751548051834106,
-0.0442434698343277,
0.0032949456945061684,
-0.021304450929164886,
-0.043412286788225174,
0.01751328445971012,
-0.05543949455022812,
0.000896082550752908,
-0.009587535634636879,
0.012428720481693745,
0.10420683771371841,
0.045567866414785385,
0.021309247240424156,
-0.015887543559074402,
0.03415172919631004,
0.004745587706565857,
0.04843057319521904,
-0.007346174214035273,
-0.00451342249289155,
-0.006210098508745432,
-0.002941407263278961,
-0.011748922057449818,
0.00381553266197443,
0.016509775072336197,
0.04597818851470947,
0.04190053045749664,
0.019662803038954735,
0.0609106607735157,
0.04034219682216644,
0.032236069440841675,
0.022988690063357353,
-0.003356409724801779,
0.03640560805797577,
0.009199176914989948,
0.025686442852020264,
-0.002664693398401141,
0.02370874211192131,
-0.04463326558470726,
0.05601222440600395,
0.042832259088754654,
0.020389346405863762,
-0.03439194709062576,
0.021067501977086067,
0.05334286764264107,
0.04139644280076027,
-0.06078667938709259,
-0.004199645482003689,
0.04859671741724014,
0.008547035977244377,
-0.020983628928661346,
-0.039154186844825745,
0.002157248556613922,
-0.003072184743359685,
0.03404442220926285,
-0.07450517266988754,
0.06093357130885124,
-0.008446875028312206,
-0.03933336213231087,
-0.05243857949972153,
0.003954939544200897,
0.05710984766483307,
0.04921025410294533,
-0.0969771221280098,
-0.049293775111436844,
0.0385100431740284,
-0.021829703822731972,
-0.009209420531988144,
0.0116533562541008,
0.0026794441509991884,
-0.07330457866191864,
0.020448997616767883,
-0.009875541552901268,
0.021041274070739746,
-0.002056181663647294,
-0.04756392911076546,
0.02423795685172081,
0.03924178704619408,
0.03719160705804825,
-0.011400418356060982,
0.06372920423746109,
-0.017930183559656143,
-0.033983588218688965,
0.022015893831849098,
-0.0019114038441330194,
-0.027911711484193802,
-0.03298850730061531,
-0.004370508715510368,
-0.0034912144765257835,
0.003597761271521449,
-0.00881177093833685,
0.03823425993323326,
-0.0030373050831258297,
-0.0028083836659789085,
0.013578160665929317,
0.0028884094208478928,
-0.016691919416189194,
-0.032560136169195175,
0.00800799485296011,
-0.04442697763442993,
0.02163396030664444,
0.018155435100197792,
-0.02475658245384693,
-0.08528761565685272,
0.0724257230758667,
0.024733569473028183,
-0.032821886241436005,
0.035820093005895615,
-0.006270645651966333,
0.009304123930633068,
0.09099946171045303,
0.035739194601774216,
0.005061003379523754,
0.013889102265238762,
0.03785067796707153,
0.04661846533417702,
-0.06671569496393204,
-0.0019612153992056847,
-0.017762256786227226,
0.07459703087806702,
-0.012535055167973042,
-0.02220364846289158,
0.0051201810128986835,
-0.01689765229821205,
0.009705294854938984,
0.004077513236552477,
-0.005342265125364065,
0.02894410863518715,
-0.01678752899169922,
0.05591079965233803,
0.005727149546146393,
-0.0677400678396225,
-0.02372623048722744,
0.004521344322711229,
-0.02471970207989216,
0.014931764453649521,
0.002314720768481493,
-0.04280497878789902,
-0.042602140456438065,
-0.049193378537893295,
-0.014777752570807934,
0.004084340762346983,
-0.08302882313728333,
0.07008381932973862,
0.05654652789235115,
-0.03182900696992874,
0.02768278680741787,
-0.031948234885931015,
0.09086514264345169,
-0.04443009942770004,
0.038259655237197876,
0.010472387075424194,
-0.042879410088062286,
0.03731125593185425,
0.0057358467020094395,
0.011764253489673138,
0.03777119889855385,
0.02804679051041603,
-0.08427627384662628,
0.03152662515640259,
0.011249886825680733,
-0.052176583558321,
0.011174382641911507,
0.09790825843811035,
-0.0124775730073452,
-0.052683211863040924,
-0.008600889705121517,
-0.04232872277498245,
0.036853987723588943,
0.06831233203411102,
0.06337535381317139,
-0.03730286285281181,
-0.014965853653848171,
0.0028040644247084856,
-0.04397210106253624,
-0.06201978400349617,
-0.07757218927145004,
-0.006164163816720247,
0.03807596117258072,
0.01869242452085018,
-0.054244332015514374,
-0.010610154829919338,
0.04238150641322136
] |
<p>I have the following equation:</p>
<p>$$\frac{\partial U}{\partial t}=k\frac{\partial^2 U}{\partial x^2}-v_{0}\frac{\partial U}{\partial x}, x>0$$</p>
<p>with initial conditions:</p>
<p>$$U(0,t)=0$$</p>
<p>$$U(x,0)=f(x)$$</p>
<p>In the problem is requested to give an interpretation of each of the terms in the above equation, and noting that such systems can model, besides solving by Fourier Transform.
The Fourier Transform solution is quite simple to do; however, I can not give a physical interpretation of the terms of the equation not to mention a system that can model it. So I wanted to ask your help to answer this question. Thank you very much for your help and attention.</p> | g1297 | [
-0.007509658578783274,
0.02662557177245617,
-0.014115906320512295,
-0.038009051233530045,
0.0728316605091095,
-0.04344135895371437,
-0.020322196185588837,
0.023373490199446678,
-0.011214148253202438,
0.00478264270350337,
-0.02779521979391575,
0.00896932277828455,
0.002387427259236574,
0.020269466564059258,
-0.020530352368950844,
0.0039030471816658974,
0.03539743274450302,
0.04246622696518898,
-0.08159133791923523,
-0.004758912604302168,
-0.041591577231884,
0.046965911984443665,
0.04046369716525078,
-0.02101818099617958,
0.004274452570825815,
0.004800121299922466,
-0.024073688313364983,
0.06504751741886139,
-0.04999065399169922,
-0.028537670150399208,
-0.034179531037807465,
-0.0001748283684719354,
0.008792456239461899,
-0.02184373326599598,
-0.06564358621835709,
-0.030155643820762634,
0.05781365931034088,
-0.008834298700094223,
0.005598541349172592,
-0.05145859345793724,
0.018447639420628548,
0.018466854467988014,
-0.012521777302026749,
0.00394823495298624,
-0.02681049332022667,
-0.03764054551720619,
-0.023545382544398308,
0.020631246268749237,
-0.038603730499744415,
0.05574394389986992,
0.03864113986492157,
0.01947382651269436,
0.026537971571087837,
-0.04027438908815384,
-0.0333111546933651,
-0.003710131160914898,
0.014421052299439907,
-0.034528572112321854,
0.07339553534984589,
0.052214667201042175,
-0.003271675668656826,
-0.005833814386278391,
-0.01953659951686859,
-0.052786026149988174,
0.02207055501639843,
-0.056051477789878845,
0.025697898119688034,
-0.04894318804144859,
0.01668102666735649,
-0.046285636723041534,
-0.00033937435364350677,
0.018621370196342468,
-0.015690119937062263,
-0.047691863030195236,
0.00020616852270904928,
-0.025065651163458824,
-0.041304875165224075,
-0.021920572966337204,
-0.0044440352357923985,
-0.01326487585902214,
0.004078825935721397,
0.0218857042491436,
0.024573931470513344,
0.03244283050298691,
-0.008032712154090405,
-0.039998844265937805,
-0.0011304038343951106,
0.03155240789055824,
-0.013307093642652035,
0.05934135243296623,
-0.02272314764559269,
0.04990919306874275,
-0.015156861394643784,
-0.022932548075914383,
0.009993062354624271,
0.007337313611060381,
-0.09499238431453705,
0.0435592457652092,
0.02462085708975792,
-0.018294744193553925,
-0.015287199057638645,
-0.006078788079321384,
-0.03467143699526787,
-0.04222223535180092,
0.004509719088673592,
-0.0008994218660518527,
0.024106167256832123,
0.05699026212096214,
0.009434056468307972,
-0.03686940670013428,
-0.043123509734869,
0.008100762963294983,
-0.030552785843610764,
-0.034385912120342255,
0.010721473023295403,
-0.04762750491499901,
-0.011875636875629425,
0.05857015773653984,
-0.02796321175992489,
0.03408072143793106,
0.01472930796444416,
0.014758175238966942,
0.024050546810030937,
0.05763127654790878,
0.014900811947882175,
0.007310725748538971,
-0.004132614936679602,
0.00046407434274442494,
0.08351130783557892,
0.02549475058913231,
0.03376525640487671,
-0.0286086518317461,
0.0032062700483947992,
0.03469393402338028,
0.06179710477590561,
0.04979606345295906,
-0.05311761051416397,
-0.009298184886574745,
0.013713962398469448,
0.02386690489947796,
-0.006893944926559925,
-0.09123233705759048,
-0.053283192217350006,
-0.003707368392497301,
-0.017573373392224312,
-0.0052932738326489925,
0.0027439205441623926,
-0.0932755097746849,
0.038276124745607376,
-0.04793066903948784,
-0.049959585070610046,
0.0927467942237854,
-0.001270429347641766,
-0.012905068695545197,
-0.01713559217751026,
-0.028234217315912247,
0.01836087554693222,
0.04416090250015259,
-0.0318007692694664,
-0.07742597162723541,
0.039488159120082855,
0.027491439133882523,
0.040398988872766495,
-0.004552042111754417,
-0.05647043511271477,
0.02034217305481434,
-0.020484143868088722,
-0.060147833079099655,
0.017420386895537376,
0.007449498400092125,
-0.04949592053890228,
0.043417882174253464,
0.03021763637661934,
0.08276267349720001,
0.037187691777944565,
0.06110760569572449,
0.053901348263025284,
-0.017260966822504997,
-0.002670120447874069,
0.04833750054240227,
-0.027382241562008858,
-0.04130160063505173,
0.009163277223706245,
-0.04969934746623039,
-0.015793576836586,
-0.0352494940161705,
-0.0015769987367093563,
0.10551971942186356,
-0.08015014231204987,
0.032209839671850204,
-0.0155279990285635,
0.012473044916987419,
0.014319591224193573,
-0.006572439335286617,
0.008164575323462486,
0.053950849920511246,
0.01559012196958065,
-0.016114892438054085,
-0.0026984773576259613,
0.010285880416631699,
0.05674930661916733,
0.03976581245660782,
0.07350414246320724,
0.029748963192105293,
0.03965195268392563,
-0.017098238691687584,
-0.05033149570226669,
-0.02813381515443325,
-0.0019914465956389904,
0.01943044178187847,
-0.04279789328575134,
-0.063963383436203,
-0.0298191886395216,
0.05519580841064453,
-0.10519500821828842,
-0.032901450991630554,
0.04272981733083725,
-0.012169918976724148,
-0.029074031859636307,
0.035546232014894485,
0.012721196748316288,
0.010520490817725658,
-0.033015456050634384,
0.01922306977212429,
-0.05098967254161835,
-0.02445891499519348,
-0.034302350133657455,
-0.04425574466586113,
-0.033943869173526764,
0.015507874079048634,
0.022687654942274094,
-0.06049681454896927,
0.04434386268258095,
-0.02064848132431507,
0.07427378743886948,
0.03666030243039131,
-0.03300277888774872,
-0.004169176798313856,
-0.016258131712675095,
0.03844126686453819,
-0.000770546670537442,
-0.003501228056848049,
-0.0018811271293088794,
-0.03269518166780472,
0.02293231151998043,
0.02564357779920101,
0.01834484562277794,
-0.0381559319794178,
0.031779319047927856,
0.026647493243217468,
-0.02899360843002796,
0.0026263687759637833,
0.007479062769562006,
-0.05854048952460289,
-0.042957600206136703,
-0.10767287760972977,
0.026221802458167076,
0.07106059044599533,
-0.017972858622670174,
-0.034120429307222366,
-0.04993213713169098,
-0.009302469901740551,
-0.04633675515651703,
0.05460724979639053,
-0.04893667623400688,
-0.04716280847787857,
-0.0008812375017441809,
0.0032898264471441507,
0.015031984075903893,
0.01874595135450363,
0.03296901658177376,
0.016951758414506912,
-0.0012591398553922772,
0.04162650927901268,
-0.0019567350391298532,
-0.039083369076251984,
0.02167621999979019,
0.006450021639466286,
-0.025707287713885307,
0.025287630036473274,
-0.012643021531403065,
-0.06044696271419525,
0.015172164887189865,
0.07507674396038055,
0.04866960644721985,
-0.04870273917913437,
0.014458216726779938,
0.048891905695199966,
0.017845092341303825,
0.01902167685329914,
-0.03160221129655838,
0.0357649140059948,
0.010160963982343674,
-0.034239109605550766,
-0.12328412383794785,
0.057474978268146515,
0.015255900099873543,
-0.07031483203172684,
0.050223421305418015,
0.03678327053785324,
0.027448521926999092,
-0.008178690448403358,
0.0042345658876001835,
0.020475255325436592,
-0.031046969816088676,
-0.011152365244925022,
-0.003973504528403282,
-0.024103805422782898,
0.03048776090145111,
-0.002296911319717765,
-0.04488718882203102,
0.02644529938697815,
0.006902447901666164,
-0.012779264710843563,
-0.006303197704255581,
0.028049174696207047,
-0.03223727270960808,
-0.003943084739148617,
0.0032341598998755217,
0.016633521765470505,
-0.03294361010193825,
-0.046406835317611694,
0.005039056297391653,
0.0021882823202759027,
-0.03263869509100914,
0.03263278678059578,
-0.04851624742150307,
-0.033275358378887177,
-0.08981902152299881,
-0.01423661783337593,
0.015428898856043816,
0.008452503941953182,
0.023355633020401,
-0.045540399849414825,
-0.025873620063066483,
-0.030415931716561317,
-0.07541803270578384,
0.041804779320955276,
0.015193980187177658,
-0.052450913935899734,
0.0025687196757644415,
-0.026690011844038963,
-0.03437865898013115,
-0.001970547717064619,
-0.020719410851597786,
-0.016874032095074654,
-0.05414750799536705,
0.04797156900167465,
0.045957788825035095,
-0.07792747765779495,
-0.030020037665963173,
0.06679023057222366,
0.04734797403216362,
-0.017995914444327354,
0.0028168654534965754,
0.01499662920832634,
0.09244514256715775,
0.06892232596874237,
0.01181565411388874,
0.008724181912839413,
0.04587150365114212,
-0.07191165536642075,
-0.0010620886459946632,
0.05928841605782509,
0.009909357875585556,
0.02066248655319214,
0.0522146113216877,
0.053080879151821136,
-0.04646269232034683,
-0.001840007957071066,
0.027629220858216286,
0.018902020528912544,
0.035800863057374954,
0.010252270847558975,
-0.010531474836170673,
-0.025226563215255737,
0.030344581231474876,
-0.029650047421455383,
-0.05642811581492424,
0.06982564926147461,
0.07267528772354126,
-0.01187252625823021,
-0.0034830200020223856,
0.06082075089216232,
0.07318837195634842,
-0.05342448502779007,
-0.007316300179809332,
0.008561442606151104,
0.003373561892658472,
0.04124879091978073,
0.10371261835098267,
-0.019202053546905518,
-0.062343500554561615,
0.058126553893089294,
-0.02198955975472927,
-0.021446052938699722,
0.02040860243141651,
-0.025692425668239594,
-0.04770578444004059,
-0.020686348900198936,
-0.024804309010505676,
-0.033464785665273666,
0.0008027555304579437,
-0.00400514854118228,
0.0005510707851499319,
0.005640924908220768,
0.0035523693077266216,
-0.0832575187087059,
-0.04820501059293747,
-0.029622560366988182,
-0.057513609528541565,
-0.027430318295955658,
0.027785351499915123,
-0.05695047229528427,
-0.027383118867874146,
0.014373024925589561,
0.033314138650894165,
-0.004958895966410637,
0.06836019456386566,
0.01096735056489706,
0.0006633785669691861,
-0.029003458097577095,
-0.03677469119429588,
0.0018008315237239003,
-0.006438854616135359,
-0.0009974577696993947,
0.07424722611904144,
0.0013201195979490876,
-0.013679384253919125,
0.010800370946526527,
-0.06527570635080338,
-0.0010883323848247528,
0.0006235195905901492,
0.007912862114608288,
-0.018329976126551628,
0.025160640478134155,
-0.04711489751935005,
-0.01913355477154255,
-0.008774691261351109,
0.030168108642101288,
0.05087381601333618,
-0.003839650424197316,
-0.04446074739098549,
-0.015144296921789646,
0.012765620835125446,
0.009327574633061886,
0.02314508520066738,
-0.07521927356719971,
0.006306523457169533,
-0.0188787579536438,
-0.04650456830859184,
0.06696424633264542,
-0.02152685821056366,
-0.034252408891916275,
0.005798326339572668,
-0.043807681649923325,
-0.022865481674671173,
-0.03711565211415291,
0.015636751428246498,
-0.014497525058686733,
0.04930853843688965,
0.03159528970718384,
-0.01091464702039957,
-0.012851421721279621,
0.03373045101761818,
-0.06115071102976799,
-0.024617500603199005,
0.04373473301529884,
-0.021771781146526337,
-0.021314194425940514,
0.006999134551733732,
-0.027915848419070244,
0.04597938433289528,
0.06415050476789474,
0.029443277046084404,
0.018244462087750435,
-0.04605407267808914,
0.004439156968146563,
0.008707219734787941,
0.019902875646948814,
0.05657206103205681,
0.005278292112052441,
0.04567569121718407,
0.030081484466791153,
0.018219776451587677,
0.024081554263830185,
0.028743254020810127,
0.0405232198536396,
-0.0028176698833703995,
-0.0017410825239494443,
0.03055701218545437,
0.07645470649003983,
-0.004914120305329561,
0.02228379435837269,
0.0103248730301857,
-0.030307890847325325,
-0.005710975266993046,
-0.013664147816598415,
0.03485529124736786,
0.04292706027626991,
-0.023298416286706924,
0.01595699042081833,
-0.0006811268394812942,
0.042522214353084564,
0.02003183402121067,
0.055925533175468445,
0.0340520478785038,
-0.006051500793546438,
0.0337638258934021,
0.07058975845575333,
-0.011318099685013294,
-0.00663932878524065,
0.0308955330401659,
-0.014657544903457165,
-0.01153577957302332,
-0.04091932624578476,
-0.05369731783866882,
0.0009100961615331471,
0.019437875598669052,
-0.04983721300959587,
0.04304521530866623,
-0.04152432829141617,
0.029060767963528633,
-0.027113938704133034,
0.043741095811128616,
0.012450149282813072,
-0.000727292092051357,
-0.07037501037120819,
0.011698608286678791,
-0.0016303682932630181,
-0.0005337765323929489,
0.0006200019270181656,
-0.02073589526116848,
0.026542896404862404,
0.003116828855127096,
-0.010026284493505955,
-0.0077683343552052975,
-0.007822118699550629,
0.024823768064379692,
-0.007279349956661463,
0.003936267923563719,
0.012209435924887657,
0.005644629243761301,
-0.005143271759152412,
-0.04097365587949753,
0.019893601536750793,
0.07108623534440994,
0.037147361785173416,
0.056666046380996704,
0.04731133580207825,
0.01046289224177599,
-0.022574536502361298,
-0.006923063658177853,
-0.05550174415111542,
0.07839246094226837,
-0.0005769794806838036,
0.013425923883914948,
0.019921651110053062,
-0.01843017153441906,
-0.06071147695183754,
0.017716221511363983,
0.002909859409555793,
-0.02886590175330639,
-0.0037673735059797764,
0.005065869074314833,
-0.017125293612480164,
0.03276862949132919,
0.027154965326189995,
0.008373137563467026,
0.014646793715655804,
0.03819041699171066,
-0.00565680954605341,
-0.006177601870149374,
0.011150365695357323,
-0.016337590292096138,
0.013218145817518234,
-0.009292260743677616,
-0.026716984808444977,
0.0097489133477211,
-0.02204691246151924,
-0.04014864191412926,
0.019689001142978668,
-0.008795471861958504,
0.03507964313030243,
-0.04763394594192505,
-0.006470856722444296,
-0.011234263889491558,
-0.018250077962875366,
0.027783699333667755,
0.013327401131391525,
-0.016821062192320824,
0.010920336470007896,
-0.025547439232468605,
-0.0077894991263747215,
0.04879848659038544,
0.026390139013528824,
0.007693585939705372,
0.023657044395804405,
-0.007113672327250242,
0.03129599615931511,
0.017802836373448372,
0.03029012680053711,
-0.028654076159000397,
-0.00043006171472370625,
-0.008997710421681404,
-0.05555185303092003,
0.0019416279392316937,
0.03419775888323784,
0.007345082703977823,
0.031852055341005325,
0.00506905373185873,
0.05422787740826607,
0.010492188856005669,
0.029576532542705536,
-0.0029199288692325354,
-0.01882329024374485,
0.013282207772135735,
0.045269254595041275,
0.03449122607707977,
-0.03378615900874138,
0.07833203673362732,
-0.04017842188477516,
0.004479108843952417,
-0.04589872434735298,
0.05936400964856148,
0.008951736614108086,
-0.030315322801470757,
0.05139418691396713,
0.06962568312883377,
-0.0072680567391216755,
0.040861379355192184,
-0.02750333771109581,
0.01747375726699829,
-0.0011913783382624388,
-0.019056173041462898,
0.050179701298475266,
-0.03111523576080799,
0.016219362616539,
0.029423607513308525,
0.021754926070570946,
0.011899241246283054,
0.017601318657398224,
0.033128537237644196,
-0.013835628516972065,
-0.042658716440200806,
0.029107021167874336,
0.07593407481908798,
-0.10357722640037537,
-0.09144063293933868,
0.019002867862582207,
0.013933326117694378,
0.022266458719968796,
0.005298085976392031,
-0.008972054347395897,
-0.011144637130200863,
-0.030218323692679405,
-0.04199772700667381,
0.05719316750764847,
0.01837320253252983,
0.0257361251860857,
-0.022873643785715103,
-0.00048386500566266477,
-0.06159985437989235,
0.025279927998781204,
-0.002518640598282218,
0.07883881032466888,
0.0218263678252697,
-0.02283002994954586,
-0.03466996178030968,
-0.017588386312127113,
0.022596141323447227,
-0.004024602472782135,
0.028262218460440636,
0.020698130130767822,
0.0002569572243373841,
-0.003148231189697981,
-0.016319425776600838,
0.03413369879126549,
-0.014839808456599712,
0.008089806884527206,
0.0044330693781375885,
0.0012472260277718306,
0.0289420485496521,
-0.022308260202407837,
0.00872898567467928,
0.02261023037135601,
0.030916085466742516,
-0.0012533263070508838,
-0.04055461660027504,
0.06151139736175537,
-0.0436394028365612,
0.08338935673236847,
0.061120931059122086,
0.002017692429944873,
-0.006762844044715166,
-0.03814547508955002,
-0.07118149846792221,
0.04752231761813164,
0.00833864975720644,
-0.006013227626681328,
0.024118997156620026,
0.01381878461688757,
-0.01710584945976734,
-0.0329744815826416,
-0.038627710193395615,
-0.07417181879281998,
-0.010520094074308872,
-0.0715232565999031,
0.0009266096749342978,
-0.054396986961364746,
0.02075415663421154,
-0.023228008300065994,
-0.03349355608224869,
0.02885592356324196,
-0.014074365608394146,
-0.048485975712537766,
-0.05535973981022835,
0.0356459841132164,
-0.041110679507255554,
-0.02504901774227619,
-0.03361109644174576,
-0.008116192184388638,
-0.011295473203063011,
-0.09537841379642487,
-0.03421689197421074,
0.02574351243674755,
-0.046399034559726715,
-0.010841471143066883,
-0.031335070729255676,
0.010975873097777367,
-0.005173070821911097,
0.003929327707737684,
-0.04108746722340584,
0.016888311132788658,
0.003126655239611864,
0.02483386918902397,
-0.03448484465479851,
-0.01986176148056984,
-0.009964807890355587,
0.012461747042834759,
-0.05592068284749985,
-0.04571438953280449,
-0.01824544370174408,
0.019712574779987335,
0.013971037231385708,
0.043314576148986816,
-0.04460690915584564,
-0.003809733781963587,
0.029889676719903946,
0.013553529977798462,
0.03982998803257942,
0.027294784784317017,
0.005120725370943546,
0.01596534438431263,
-0.011901301331818104,
-0.02588420733809471,
-0.004992817994207144,
0.0744796022772789,
-0.005129177123308182,
-0.0011261444306001067,
-0.04174879938364029,
-0.0070669627748429775,
-0.06018935516476631,
0.038206059485673904,
0.028965512290596962,
-0.03836889937520027,
-0.02805989980697632,
0.018983878195285797
] |
<p>$$y(x,t)=2A\sin(Kx)\cos(\omega t)$$
$A$ and $x$ are in metre, $\omega$ is angular frequency.
Then find dimensions of $A$ and $K$.</p>
<p>In this equation how can I find the dimension of $K$?</p> | g1298 | [
0.030014215037226677,
-0.01152602955698967,
0.008427223190665245,
-0.10104560852050781,
-0.004292293451726437,
-0.02199884131550789,
0.04246221482753754,
-0.05435245856642723,
-0.0009751861216500401,
0.041507966816425323,
0.014951071701943874,
0.028673196211457253,
0.026530522853136063,
-0.013905966654419899,
0.0361320786178112,
-0.005273662507534027,
0.005340156611055136,
0.0319359228014946,
-0.002138791372999549,
0.03973863646388054,
0.04864680767059326,
-0.03618684038519859,
0.008396025747060776,
-0.04672306030988693,
0.08079253137111664,
0.02640366367995739,
0.0181112140417099,
-0.019424008205533028,
-0.02419634722173214,
0.014842974953353405,
0.02824513055384159,
0.01428903453052044,
0.03702717274427414,
-0.0035391459241509438,
-0.00102378916926682,
-0.009057407267391682,
0.006734453607350588,
0.04116561636328697,
0.02944762445986271,
-0.0096043162047863,
-0.027508705854415894,
-0.02750569023191929,
-0.011352458968758583,
0.07593551278114319,
0.015448354184627533,
0.020838433876633644,
-0.01104231458157301,
0.012081267312169075,
-0.020631464198231697,
-0.04754253476858139,
-0.017177168279886246,
0.033448923379182816,
0.03630080819129944,
-0.016359904780983925,
-0.03322239965200424,
0.03318776935338974,
0.02145930379629135,
-0.04567578807473183,
0.048403266817331314,
0.034451987594366074,
0.03385218232870102,
-0.0188007615506649,
0.001453959383070469,
0.041319530457258224,
0.050060782581567764,
-0.023142606019973755,
-0.012935612350702286,
0.019367093220353127,
-0.004889027681201696,
-0.03681770712137222,
0.02341432124376297,
-0.015424338169395924,
0.04236888512969017,
0.02615409344434738,
-0.08317913115024567,
0.03010515123605728,
0.08445253223180771,
0.035791512578725815,
-0.06457103043794632,
0.04613574221730232,
-0.05263185128569603,
0.012660304084420204,
0.07987841218709946,
-0.0482669472694397,
0.04162439703941345,
-0.007725127972662449,
0.01512101199477911,
0.034366536885499954,
0.01478531677275896,
0.03043445199728012,
0.01952943578362465,
0.0035204922314733267,
0.04547141119837761,
0.009726885706186295,
0.039960917085409164,
-0.04216211661696434,
-0.007272043731063604,
0.04452620446681976,
0.01972038671374321,
0.036670539528131485,
-0.002780131995677948,
0.028740622103214264,
0.03699447959661484,
0.01877022720873356,
0.05947987735271454,
0.07665859162807465,
0.0010633340571075678,
-0.010192803107202053,
0.02714565210044384,
-0.01306061539798975,
-0.042509712278842926,
-0.023009303957223892,
-0.018015163019299507,
-0.016840878874063492,
-0.010279794223606586,
0.01080038957297802,
0.019237244501709938,
-0.008573160506784916,
0.03240976110100746,
0.045091189444065094,
0.017873767763376236,
-0.0608704499900341,
-0.0022432527039200068,
0.0679650753736496,
0.017927834764122963,
0.06335709989070892,
0.03553668409585953,
0.022313041612505913,
0.07504374533891678,
0.017023185268044472,
-0.031183073297142982,
0.0360356941819191,
0.021983005106449127,
-0.023435629904270172,
0.033287737518548965,
0.06897707283496857,
-0.019512152299284935,
-0.033396318554878235,
-0.03635804355144501,
0.05978749319911003,
-0.04374362528324127,
-0.05091983824968338,
0.035203855484724045,
0.011564063839614391,
-0.0801781564950943,
-0.017336789518594742,
0.015587381087243557,
-0.07416874170303345,
0.020308678969740868,
-0.001141429878771305,
0.0022807761561125517,
0.06604047119617462,
0.02574143186211586,
-0.007087999489158392,
-0.04449921101331711,
-0.05286433547735214,
-0.027512190863490105,
-0.02021346054971218,
-0.015332869254052639,
-0.028115302324295044,
-0.027628079056739807,
0.0013641122495755553,
0.02224641479551792,
0.00011681581963784993,
-0.04210264980792999,
-0.0610506534576416,
-0.04003038629889488,
-0.006824679672718048,
-0.03434320539236069,
-0.03838861733675003,
-0.037607498466968536,
0.008093073032796383,
0.01446565892547369,
-0.027142604812979698,
-0.0022165277041494846,
0.07643391937017441,
-0.025479596108198166,
-0.05595485866069794,
0.01806275174021721,
0.014761584810912609,
0.02228948287665844,
0.006007933057844639,
0.012088526971638203,
-0.015254542231559753,
0.0020450467709451914,
-0.0674750953912735,
0.025273244827985764,
-0.009165526367723942,
-0.06318368762731552,
0.029929138720035553,
0.029688715934753418,
-0.015364866703748703,
-0.014577462337911129,
-0.025482574477791786,
0.031693100929260254,
0.05070780962705612,
0.04197787493467331,
0.014609729871153831,
-0.002963349688798189,
0.050657786428928375,
0.012590435333549976,
0.019604414701461792,
0.05874206870794296,
0.028645794838666916,
0.02627582475543022,
0.010157538577914238,
0.00009339398820884526,
0.01163574866950512,
0.0010478131007403135,
-0.00402970053255558,
-0.05111369490623474,
-0.006900458596646786,
-0.06264925003051758,
-0.004571557976305485,
-0.02342773601412773,
0.04949814826250076,
0.04857182130217552,
0.028057916089892387,
-0.03622376546263695,
0.02854222059249878,
-0.038989972323179245,
-0.019533470273017883,
0.031023068353533745,
-0.005644310265779495,
0.018994277343153954,
-0.022821849212050438,
-0.03512296453118324,
0.0071207936853170395,
0.006658746860921383,
0.009450982324779034,
-0.01582985185086727,
-0.010262353345751762,
-0.0005782424123026431,
0.007227908819913864,
-0.013418897055089474,
0.029315605759620667,
-0.03818536549806595,
-0.014983759261667728,
0.014033044688403606,
0.060306645929813385,
0.04611947014927864,
0.029871873557567596,
0.05322088301181793,
-0.011982731521129608,
0.009440568275749683,
0.017069872468709946,
0.03719894960522652,
0.011257554404437542,
-0.014040384441614151,
0.01991201564669609,
-0.009808797389268875,
-0.03204131871461868,
-0.022289305925369263,
-0.011374804191291332,
-0.03644896298646927,
-0.004455242771655321,
-0.0025531542487442493,
0.03693537041544914,
-0.10395433008670807,
-0.017064986750483513,
-0.011565511114895344,
-0.00926399789750576,
0.01490780059248209,
0.026726745069026947,
0.001326135010458529,
-0.056871943175792694,
-0.039443716406822205,
0.06640596687793732,
0.021030407398939133,
-0.023596884682774544,
-0.04856336489319801,
0.05797771364450455,
0.003975645639002323,
-0.03877507895231247,
-0.031982991844415665,
-0.01969854161143303,
-0.01864389143884182,
-0.0831327885389328,
0.003604750381782651,
-0.013170196674764156,
-0.008002808317542076,
0.05049258843064308,
-0.02712436020374298,
0.07972384989261627,
-0.0287442859262228,
0.013269741088151932,
0.006772234104573727,
0.0805516391992569,
0.001957129454240203,
0.011675386689603329,
-0.03810170665383339,
0.021122092381119728,
0.02314106374979019,
0.020017417147755623,
0.017701271921396255,
0.05386687070131302,
0.030894294381141663,
-0.060125697404146194,
0.02399873360991478,
0.020567134022712708,
0.04101734235882759,
0.058104392141103745,
-0.012321106158196926,
-0.06722311675548553,
-0.031266696751117706,
-0.018906014040112495,
0.02309291809797287,
-0.04036090523004532,
-0.0023976655211299658,
-0.027672408148646355,
0.007663364056497812,
-0.01764049381017685,
0.07479377835988998,
-0.01279477123171091,
-0.04129142314195633,
0.012026551179587841,
0.05491287633776665,
0.002000793581828475,
0.0003312058688607067,
0.0663767009973526,
0.0192375760525465,
-0.0819113478064537,
0.022212069481611252,
0.06562329828739166,
-0.012857488356530666,
0.01855883188545704,
0.01523999311029911,
0.00045115186367183924,
-0.024526067078113556,
0.011497212573885918,
-0.051215074956417084,
0.007994475774466991,
0.03129816800355911,
-0.009243111126124859,
-0.027303365990519524,
-0.02013925090432167,
-0.05544792115688324,
-0.015160379000008106,
0.01572454907000065,
0.010605260729789734,
-0.02007068693637848,
0.0046844035387039185,
-0.04176228865981102,
-0.05027991905808449,
0.000013399946510617156,
-0.006915917154401541,
-0.11415868252515793,
0.019378328695893288,
0.0118965283036232,
-0.07221714407205582,
-0.037652306258678436,
-0.04977865889668465,
0.023198433220386505,
-0.016853362321853638,
0.03197631984949112,
0.03171536698937416,
0.052793145179748535,
0.030385557562112808,
-0.04477255791425705,
-0.0415693074464798,
0.0017625951441004872,
-0.04499147832393646,
-0.0036791402380913496,
0.00906517542898655,
-0.01057294849306345,
-0.0045710401609539986,
0.0687151625752449,
0.06727978587150574,
-0.034023262560367584,
0.009311209432780743,
0.025479089468717575,
-0.023655422031879425,
0.0036984316539019346,
-0.03777497634291649,
0.0018446975154802203,
-0.06072286143898964,
-0.07744034379720688,
-0.04606880620121956,
0.019830135628581047,
0.03995763882994652,
-0.02242925763130188,
0.03268364444375038,
0.055105023086071014,
-0.025935426354408264,
0.03870224207639694,
-0.021730631589889526,
-0.052995715290308,
0.041153792291879654,
-0.025737887248396873,
-0.053077418357133865,
0.0325862392783165,
-0.04122989624738693,
-0.064357690513134,
-0.009075816720724106,
-0.03126099333167076,
-0.09210710227489471,
0.03984406590461731,
0.021925555542111397,
-0.057098954916000366,
-0.028055928647518158,
0.005808863323181868,
-0.007308423984795809,
0.037641700357198715,
-0.009570951573550701,
0.0020934154745191336,
0.032918013632297516,
0.0631067305803299,
0.00801431480795145,
0.018254544585943222,
-0.009062087163329124,
-0.0499102920293808,
-0.025750737637281418,
0.03399167209863663,
-0.07565901428461075,
0.004863175097852945,
0.02574925683438778,
-0.00731543218716979,
0.014623940922319889,
0.017186138778924942,
-0.03644268214702606,
-0.0389707051217556,
0.042274076491594315,
-0.027585947886109352,
-0.011943667195737362,
0.05750435218214989,
0.026001960039138794,
0.05209937319159508,
-0.005205377470701933,
-0.05452907085418701,
0.021685723215341568,
-0.0186335276812315,
-0.09076698124408722,
-0.01996067352592945,
-0.00676970137283206,
-0.07029130309820175,
-0.0035653843078762293,
-0.04662046954035759,
-0.008629563264548779,
-0.023686230182647705,
0.015040873549878597,
0.017759419977664948,
0.04358016699552536,
-0.005090870428830385,
0.0012672552838921547,
-0.01703694835305214,
-0.01406693272292614,
-0.012540977448225021,
-0.04728611558675766,
-0.009621522389352322,
-0.000052216171752661467,
-0.00215336075052619,
0.012464761734008789,
-0.04285699129104614,
-0.03262338414788246,
-0.006615541409701109,
-0.01984347216784954,
-0.0634552612900734,
0.006260021589696407,
0.000389053369872272,
0.021082617342472076,
-0.02210794761776924,
-0.02897849678993225,
-0.05713101476430893,
-0.0342157781124115,
0.011388874612748623,
-0.03263997286558151,
-0.025735897943377495,
-0.007631655316799879,
-0.07414393126964569,
0.02496561035513878,
0.01719403639435768,
-0.03176802769303322,
-0.012616798281669617,
-0.016668740659952164,
-0.01752239465713501,
0.045108627527952194,
-0.034478720277547836,
-0.037699781358242035,
-0.03033100813627243,
0.007481401786208153,
0.009714681655168533,
-0.034401848912239075,
0.039206694811582565,
0.07159406691789627,
-0.007473850157111883,
0.018086859956383705,
-0.018908092752099037,
-0.018925420939922333,
0.024553081020712852,
0.02809826098382473,
-0.029002772644162178,
0.044910214841365814,
-0.045670993626117706,
-0.013516138307750225,
-0.036941755563020706,
0.048509631305933,
0.0007623315905220807,
-0.04840952157974243,
0.02646861970424652,
0.018409745767712593,
0.05022449046373367,
-0.010831162333488464,
0.015083148144185543,
0.00434071896597743,
-0.007815342396497726,
0.032673146575689316,
0.05528711900115013,
-0.010923050343990326,
-0.00629655085504055,
0.07496403902769089,
0.05251756310462952,
-0.04401565343141556,
0.016963794827461243,
0.08149081468582153,
0.04875662177801132,
-0.04512983560562134,
-0.024628164246678352,
0.08439777046442032,
0.020732106640934944,
-0.0040993052534759045,
0.03601057454943657,
0.005033754277974367,
0.01968398690223694,
-0.077152319252491,
-0.0004371944523882121,
0.002507395576685667,
-0.008786317892372608,
-0.029487738385796547,
0.011295638978481293,
-0.03830662742257118,
-0.01995774544775486,
-0.036341097205877304,
-0.048150867223739624,
-0.038186971098184586,
0.01057626772671938,
-0.029212364926934242,
0.025021176785230637,
0.001543940743431449,
-0.03831711411476135,
0.0011955257505178452,
-0.04475700110197067,
-0.014661627821624279,
0.007087583653628826,
-0.04658086597919464,
-0.007392204366624355,
0.02134321816265583,
0.05513611435890198,
-0.010304749943315983,
0.06487390398979187,
0.06608277559280396,
-0.03715461492538452,
-0.007315346505492926,
0.01168881356716156,
-0.023758361116051674,
-0.03959330543875694,
-0.01473892480134964,
0.015213020145893097,
0.022089049220085144,
-0.049611009657382965,
-0.043695297092199326,
0.012700551189482212,
0.006547028198838234,
0.048183735460042953,
-0.026364510878920555,
-0.009327183477580547,
-0.046814389526844025,
0.007313002832233906,
0.020539218559861183,
0.14032255113124847,
0.03571660444140434,
-0.055546753108501434,
0.024685299023985863,
-0.04760530963540077,
0.025055939331650734,
0.06350543349981308,
0.008981652557849884,
-0.004476091358810663,
-0.014653773978352547,
0.015847153961658478,
0.01709495298564434,
0.011898820288479328,
0.06875178962945938,
0.006088599096983671,
0.011852666735649109,
-0.00804857723414898,
-0.006595560349524021,
0.04321948438882828,
-0.045705415308475494,
0.04054462909698486,
-0.04716743528842926,
0.019547507166862488,
0.006748485844582319,
0.003189555136486888,
-0.002006608759984374,
-0.011908096261322498,
-0.044540975242853165,
0.016200069338083267,
0.07379055768251419,
-0.0017410032451152802,
-0.021161828190088272,
0.07240201532840729,
0.015041723847389221,
0.03449059650301933,
0.04222873970866203,
-0.032219503074884415,
0.0016627706354483962,
-0.03066612221300602,
-0.033034417778253555,
-0.037110500037670135,
0.034053828567266464,
-0.025963956490159035,
0.02253269962966442,
-0.009245401248335838,
0.037512555718421936,
-0.01841728575527668,
-0.02538859285414219,
0.09219750761985779,
0.026882462203502655,
0.0030679027549922466,
0.023242827504873276,
0.1158595159649849,
0.0240879375487566,
0.00743924081325531,
-0.00005680668618879281,
0.006719591096043587,
0.022338390350341797,
0.025777604430913925,
-0.013518334366381168,
-0.0015400266274809837,
-0.02706228941679001,
0.01664920523762703,
-0.019718119874596596,
-0.03204881399869919,
-0.008900381624698639,
-0.02586646005511284,
0.03895440697669983,
-0.04478783160448074,
0.03799579665064812,
0.004852484446018934,
0.04507927596569061,
0.0031464649364352226,
-0.010932249948382378,
-0.0038412243593484163,
0.006075217388570309,
-0.026099616661667824,
-0.05899026617407799,
-0.015314383432269096,
0.006319989450275898,
-0.07005968689918518,
0.00357608194462955,
0.04840867221355438,
-0.026403384283185005,
0.010184730403125286,
-0.011118870228528976,
-0.050769317895174026,
-0.009988376870751381,
0.036103181540966034,
-0.02163204737007618,
0.0040692659094929695,
0.01583665795624256,
-0.07969333231449127,
-0.05187506228685379,
-0.002810718258842826,
-0.04595506191253662,
-0.03418733924627304,
0.07680074870586395,
0.022039569914340973,
-0.0012690923176705837,
0.017142005264759064,
-0.023319866508245468,
-0.0592452734708786,
0.02478349208831787,
-0.026820076629519463,
-0.011030719615519047,
-0.028358062729239464,
0.039805274456739426,
-0.017109153792262077,
0.017506321892142296,
-0.002703038277104497,
-0.029880477115511894,
0.0011765758972615004,
-0.03360123187303543,
-0.013931943103671074,
-0.012305445037782192,
0.009789854288101196,
0.01604967564344406,
-0.002190736820921302,
-0.037052642554044724,
-0.00025669444585219026,
0.03385092690587044,
-0.03572005406022072,
0.037624865770339966,
-0.0059784166514873505,
-0.032379262149333954,
0.03157096728682518,
-0.057254187762737274,
-0.011094149202108383,
0.027621669694781303,
-0.01023334264755249,
0.02358001098036766,
0.06751008331775665,
-0.013071785680949688,
0.00011309424007777125,
0.02983783558011055,
-0.030814988538622856,
0.0001466803951188922,
0.012834551744163036,
-0.03385162726044655,
-0.02583443932235241,
-0.036706600338220596,
-0.015251612290740013,
-0.007637491449713707,
-0.0029250499792397022,
0.023348884657025337,
0.09758396446704865,
0.024210209026932716,
-0.03969995677471161,
0.012606806121766567,
0.048672955483198166,
-0.05481959879398346,
-0.08971991389989853,
-0.04629533737897873,
0.0684070959687233,
-0.08937249332666397,
-0.0011659536976367235,
-0.05344828590750694,
-0.0028329475317150354,
0.04397464916110039,
0.013573762029409409,
0.02155039831995964,
0.030193565413355827,
0.053767118602991104,
-0.010283338837325573,
0.04020177200436592,
0.017983179539442062,
-0.006822339259088039,
-0.014750373549759388,
-0.021286429837346077,
-0.011824500747025013,
0.01912854239344597,
-0.009499259293079376,
-0.027348127216100693,
-0.003969655372202396,
0.005441292654722929,
-0.03623638674616814,
0.0244633499532938,
-0.029878320172429085,
0.012300125323235989,
0.06441045552492142,
-0.012535502202808857,
0.00015075264673214406,
0.017038138583302498,
-0.04871475324034691,
0.06914412975311279,
-0.03406888246536255,
-0.0446559302508831,
0.05110745131969452,
-0.0036567009519785643,
-0.07589056342840195,
-0.05004755035042763,
0.0041099051013588905,
0.054163601249456406,
-0.011350291781127453,
0.0659654438495636,
0.04928944259881973,
-0.07445447891950607,
-0.037992943078279495,
-0.011733146384358406
] |
<p>I have been taught that space-time should be viewed as a fabric and that objects with a large gravitational influence indent that fabric. My question is, if the singularity of a black-hole punctures space-time, how is this accomplished if the universe is 3D? Can an object move completely around the black-hole in all directions? Would you be able to travel "below" a black-hole?</p> | g13 | [
-0.009059424512088299,
0.020916670560836792,
0.022323457524180412,
-0.03274615854024887,
-0.003507348010316491,
0.06766218692064285,
-0.00887913629412651,
0.019321201369166374,
-0.022183559834957123,
-0.005736147053539753,
0.006101799663156271,
-0.06411470472812653,
0.0709739476442337,
-0.041595567017793655,
-0.04093342274427414,
-0.034084420651197433,
-0.01676621288061142,
-0.007769694086164236,
-0.029286030679941177,
-0.022975021973252296,
0.04059965908527374,
-0.0014432889875024557,
0.045909058302640915,
-0.013393804430961609,
-0.019581500440835953,
-0.028066877275705338,
0.019160855561494827,
-0.015268961898982525,
-0.026448838412761688,
0.03699135035276413,
0.07398685812950134,
-0.0042363558895885944,
-0.004916398320347071,
-0.009433341212570667,
0.02095506526529789,
-0.014261562377214432,
-0.021890541538596153,
-0.024988722056150436,
0.004268688149750233,
0.03325498476624489,
-0.01526233647018671,
-0.0243711918592453,
-0.02732025645673275,
-0.03787994012236595,
0.0013596322387456894,
-0.0484151616692543,
-0.008720414713025093,
-0.001861737109720707,
0.07025516033172607,
-0.023427920415997505,
-0.019832387566566467,
0.019405879080295563,
0.011271393857896328,
-0.021393029019236565,
0.00763559527695179,
-0.002127815270796418,
0.04521721228957176,
-0.026593290269374847,
0.09688586741685867,
0.02530551701784134,
-0.07344535738229752,
0.008870409801602364,
0.0717335194349289,
0.022096827626228333,
0.023492831736803055,
-0.043035563081502914,
-0.08620736002922058,
-0.026652056723833084,
-0.015366524457931519,
0.004573186859488487,
0.054404616355895996,
-0.0006786574958823621,
0.025390731170773506,
0.003336644731462002,
-0.035036761313676834,
0.06321780383586884,
0.005035520531237125,
-0.027816910296678543,
-0.016261817887425423,
-0.04708041250705719,
-0.007027874700725079,
-0.01842680387198925,
-0.0036502068396657705,
-0.018432028591632843,
0.05965790897607803,
-0.022226795554161072,
-0.004150439985096455,
-0.06994491070508957,
-0.054825738072395325,
0.004754994530230761,
-0.0029838948976248503,
0.028685826808214188,
0.05318919196724892,
0.05174468457698822,
0.006734443362802267,
0.0038411482237279415,
0.00017903326079249382,
0.0811157301068306,
-0.002388246590271592,
0.021121952682733536,
-0.058263447135686874,
0.00974197220057249,
0.011670018546283245,
-0.04436077922582626,
-0.027330337092280388,
0.006675425451248884,
0.04222594201564789,
0.02647850476205349,
0.04063526540994644,
-0.015260550193488598,
-0.010060078464448452,
-0.06486217677593231,
-0.025777995586395264,
0.011087360791862011,
-0.04719337821006775,
0.014975530095398426,
0.022359615191817284,
-0.017188232392072678,
0.00003892894528689794,
0.08369173854589462,
-0.02966686338186264,
0.044507332146167755,
-0.01662888564169407,
0.045504357665777206,
-0.015622851438820362,
-0.0401155985891819,
-0.06478698551654816,
0.008434114046394825,
0.00872825924307108,
0.026095326989889145,
0.01818236894905567,
0.029356161132454872,
0.026523934677243233,
0.0057844119146466255,
-0.007821342907845974,
0.025592511519789696,
0.0002465606667101383,
0.0011151577346026897,
-0.024370083585381508,
0.013245913200080395,
-0.01890481635928154,
-0.04970916360616684,
-0.032783444970846176,
0.028848953545093536,
0.020761458203196526,
-0.009017453528940678,
0.015468653291463852,
0.007492705248296261,
-0.01640245132148266,
-0.03314844146370888,
0.014900684356689453,
0.13916923105716705,
-0.008957713842391968,
-0.050460487604141235,
-0.027078231796622276,
0.04444355145096779,
0.005028553772717714,
-0.00454375147819519,
0.003634141990914941,
-0.02253325656056404,
0.08155987411737442,
-0.020957445725798607,
-0.027967331930994987,
0.023862823843955994,
-0.04040232673287392,
0.059534329921007156,
-0.0104227839037776,
-0.046614356338977814,
0.030950767919421196,
-0.0157148577272892,
-0.03045337088406086,
0.045401088893413544,
-0.022561190649867058,
0.016061970964074135,
0.011870070360600948,
-0.04982637241482735,
-0.00993916392326355,
-0.017280351370573044,
-0.0014335692394524813,
-0.039689451456069946,
0.023375799879431725,
-0.02691311202943325,
-0.03084268793463707,
-0.02469673380255699,
0.02075301483273506,
0.00023195661196950823,
0.030158374458551407,
-0.037675704807043076,
0.011632183566689491,
0.05916181206703186,
0.016096753999590874,
0.0030635748989880085,
0.03290444612503052,
0.050991255789995193,
-0.04502200335264206,
-0.03946777060627937,
0.06677268445491791,
0.0450640507042408,
-0.017302194610238075,
0.013716771267354488,
-0.024862324818968773,
-0.008823692798614502,
0.05903899297118187,
0.002243327209725976,
0.044283460825681686,
0.00917312316596508,
-0.04575864598155022,
0.014866704121232033,
0.012397783808410168,
0.030561937019228935,
0.051922816783189774,
-0.022992374375462532,
0.05768509581685066,
-0.014640433713793755,
-0.07967891544103622,
0.008150403387844563,
-0.09263977408409119,
0.016241244971752167,
0.0049122972413897514,
0.021460913121700287,
-0.00977702159434557,
-0.03950483724474907,
-0.0018244972452521324,
-0.029863914474844933,
-0.0008768421248532832,
0.00567112909629941,
-0.0536377876996994,
-0.06972207129001617,
0.01033660490065813,
-0.0476958267390728,
-0.07120286673307419,
-0.012590625323355198,
-0.02829400636255741,
0.018618915230035782,
0.0746799036860466,
0.022316711023449898,
0.03574155643582344,
-0.015371768735349178,
-0.03149888291954994,
-0.026140738278627396,
0.004133561160415411,
0.023751450702548027,
0.02650010585784912,
-0.020261097699403763,
0.10938186198472977,
-0.012503942474722862,
0.015937604010105133,
-0.04643670842051506,
-0.0018266867846250534,
0.012495619244873524,
0.01914704591035843,
-0.05519795045256615,
-0.024437133222818375,
0.043826255947351456,
0.0011318116448819637,
-0.03953360766172409,
0.0005208231741562486,
0.06541356444358826,
-0.09122488647699356,
-0.07531335204839706,
0.0655716061592102,
-0.032472722232341766,
0.024987468495965004,
0.03467865660786629,
-0.04817377030849457,
-0.004430125933140516,
-0.04531005397439003,
-0.017746834084391594,
-0.032604753971099854,
0.04904408007860184,
-0.021508105099201202,
-0.005273072049021721,
0.04132324457168579,
-0.02644629031419754,
-0.030900757759809494,
0.00681545352563262,
-0.03968368470668793,
0.010042625479400158,
-0.0074621569365262985,
-0.0036580138839781284,
-0.013783863745629787,
0.04301685467362404,
-0.04491167515516281,
-0.005321689415723085,
-0.019407428801059723,
-0.021201355382800102,
-0.01653810404241085,
0.020329279825091362,
-0.01025775633752346,
0.006562072783708572,
-0.030299324542284012,
0.010187752544879913,
-0.05528483912348747,
0.023989707231521606,
0.026165593415498734,
0.02816939912736416,
-0.0019101741490885615,
0.06616248935461044,
-0.03623957931995392,
-0.01630222238600254,
0.006968501955270767,
0.009934058412909508,
-0.00828565377742052,
0.014938869513571262,
-0.005163748282939196,
-0.008995057083666325,
0.022380398586392403,
-0.03806686773896217,
-0.010054434649646282,
-0.04938613623380661,
-0.03753408044576645,
0.0334123820066452,
0.013277867808938026,
0.05532006919384003,
0.027569418773055077,
-0.03604407235980034,
-0.009318438358604908,
0.03265321999788284,
-0.035999465733766556,
0.027075134217739105,
0.03685975447297096,
0.0473429374396801,
-0.02944040298461914,
0.00028242167900316417,
0.02195410057902336,
0.017505839467048645,
0.04182889312505722,
-0.061645325273275375,
-0.03063914366066456,
0.003730609780177474,
-0.028587650507688522,
-0.007574539631605148,
-0.03425111994147301,
-0.021128389984369278,
-0.01383003406226635,
0.030990708619356155,
0.014153103344142437,
-0.018328357487916946,
0.05403716489672661,
-0.06449100375175476,
-0.004757549613714218,
-0.06472322344779968,
0.022838644683361053,
0.027636047452688217,
0.07404465228319168,
0.06453868746757507,
-0.018902888521552086,
0.02088465355336666,
-0.012562488205730915,
0.006061643827706575,
0.019794847816228867,
-0.021608570590615273,
0.05718117579817772,
-0.04898438975214958,
0.0542718842625618,
0.03581453859806061,
-0.00170783675275743,
0.015382528305053711,
0.03228311613202095,
-0.025835134088993073,
0.024625200778245926,
-0.002381267724558711,
0.018814869225025177,
-0.020242707803845406,
0.03200219199061394,
-0.04349839314818382,
0.0715513750910759,
-0.022254688665270805,
0.01650797575712204,
0.05547235906124115,
0.039846859872341156,
0.023641232401132584,
0.01180332899093628,
-0.01409766636788845,
0.052747033536434174,
-0.0473334938287735,
-0.005703124683350325,
0.033878616988658905,
0.031600773334503174,
-0.002931529190391302,
0.020227329805493355,
0.013127891346812248,
0.046534646302461624,
0.04921083524823189,
-0.029889730736613274,
0.05064200982451439,
-0.062053974717855453,
-0.05998888239264488,
-0.002027401700615883,
-0.02684452198445797,
0.05238933116197586,
-0.03616099804639816,
0.014286214485764503,
-0.10565486550331116,
0.009857770055532455,
-0.020711414515972137,
-0.023963427171111107,
-0.003679312067106366,
0.003028199775144458,
-0.0472981259226799,
0.05710316821932793,
0.06606301665306091,
0.008098699152469635,
0.02073335088789463,
0.013047097250819206,
-0.015343651175498962,
0.013615773990750313,
-0.03786681964993477,
-0.00798689853399992,
-0.01995236799120903,
0.0225524865090847,
0.017260398715734482,
-0.013169649057090282,
-0.0734972432255745,
-0.0155396843329072,
-0.0680088996887207,
0.003396316897124052,
0.004067948553711176,
-0.011347256600856781,
-0.005784308072179556,
0.06781887263059616,
-0.005708926357328892,
0.029081135988235474,
0.028791191056370735,
-0.010164451785385609,
0.028766954317688942,
0.022287994623184204,
0.014566421508789062,
-0.0168283823877573,
0.056439802050590515,
-0.006653707940131426,
-0.02283441461622715,
-0.011714387685060501,
0.05170030891895294,
-0.04963117465376854,
0.009136314503848553,
0.030967053025960922,
-0.00030013962532393634,
0.05035945773124695,
0.009151667356491089,
0.02685585804283619,
-0.005942561198025942,
-0.0012008730554953218,
0.0179763063788414,
-0.023278571665287018,
0.015765372663736343,
0.015084551647305489,
-0.01904142275452614,
-0.014861228875815868,
-0.008876829408109188,
-0.0069261048920452595,
0.023751480504870415,
-0.01878763921558857,
-0.027522942051291466,
-0.06494961678981781,
0.05579166114330292,
-0.019195398315787315,
0.02909262664616108,
-0.008771239779889584,
-0.01797390915453434,
-0.03125564381480217,
-0.005103243049234152,
-0.025881148874759674,
0.06480351835489273,
-0.02268732339143753,
-0.013811557553708553,
-0.005261650774627924,
0.0002958108962047845,
-0.07101138681173325,
0.046233877539634705,
-0.0403447188436985,
0.028386954218149185,
-0.02453221194446087,
0.038084883242845535,
-0.011830288916826248,
0.026571987196803093,
-0.03657623380422592,
-0.052963629364967346,
-0.01435317937284708,
-0.018381182104349136,
-0.016961896792054176,
-0.07066550105810165,
0.05206862837076187,
-0.0036682665813714266,
-0.0030206700321286917,
-0.013039989396929741,
0.01157018356025219,
0.029006870463490486,
0.0028386476915329695,
0.05966222658753395,
-0.00104165927041322,
-0.04787689074873924,
0.0130359111353755,
0.042476803064346313,
-0.04198062792420387,
0.014663629233837128,
0.04971960559487343,
-0.0005900117103010416,
-0.01201616507023573,
0.03129548951983452,
-0.015965262427926064,
0.009064252488315105,
0.05913444235920906,
-0.008185332641005516,
-0.04986610263586044,
0.04868105798959732,
0.04772832989692688,
-0.044643521308898926,
-0.008324561640620232,
0.043986428529024124,
-0.0033410813193768263,
0.049219220876693726,
-0.04329453408718109,
0.04488229751586914,
0.0501427985727787,
-0.045331019908189774,
0.040766485035419464,
-0.002886754460632801,
0.014676099643111229,
0.009596220217645168,
-0.023130245506763458,
0.04179823398590088,
0.002100047655403614,
0.03824334964156151,
0.0812598243355751,
0.005681370850652456,
-0.015923039987683296,
0.03859933838248253,
0.06957252323627472,
-0.008328334428369999,
0.07594183087348938,
0.018110956996679306,
-0.007795893121510744,
-0.0234382301568985,
-0.03483617305755615,
0.004272548947483301,
0.04633929207921028,
0.011949190869927406,
0.08828163892030716,
-0.014138279482722282,
-0.01888003572821617,
-0.024798158556222916,
-0.0045251562260091305,
0.034594517201185226,
-0.002654670737683773,
-0.01646171323955059,
-0.018503708764910698,
0.004179957788437605,
0.03362657129764557,
-0.04227082431316376,
-0.07745113968849182,
0.0039827837608754635,
-0.07229655236005783,
0.051515113562345505,
-0.012148636393249035,
0.048740144819021225,
0.03512159362435341,
-0.07303093373775482,
0.015785424038767815,
-0.08146189898252487,
0.019925549626350403,
-0.026437750086188316,
-0.0007185365539044142,
-0.08709855377674103,
-0.010362934321165085,
-0.01500629261136055,
-0.0234784297645092,
-0.033646613359451294,
0.035734083503484726,
0.01901175267994404,
-0.07786085456609726,
-0.03471080958843231,
0.027376174926757812,
-0.008374933153390884,
-0.03429418057203293,
-0.019836753606796265,
0.022464953362941742,
-0.02319473586976528,
-0.04159087315201759,
0.0060900188982486725,
-0.009052121080458164,
0.017003320157527924,
0.11421944946050644,
-0.057315897196531296,
0.021124226972460747,
0.012651827186346054,
-0.018317116424441338,
0.042445600032806396,
-0.0020500083919614553,
0.018099842593073845,
-0.03222164511680603,
0.05971331149339676,
0.022781051695346832,
-0.02850557677447796,
-0.030213644728064537,
-0.01782023347914219,
-0.011267167516052723,
0.022202402353286743,
-0.0744648426771164,
-0.03309031203389168,
-0.02088974229991436,
0.027455326169729233,
-0.008748692460358143,
-0.011265628971159458,
-0.011967025697231293,
0.03295915946364403,
-0.049717117100954056,
-0.00393645279109478,
0.055263739079236984,
0.047019943594932556,
0.06663185358047485,
0.03248872607946396,
-0.07040724158287048,
0.04838298633694649,
0.0308636873960495,
0.019293978810310364,
0.013627368025481701,
-0.0625472217798233,
0.09393677115440369,
-0.03661639615893364,
0.04509078338742256,
0.011226347647607327,
0.003766551148146391,
-0.012801108881831169,
0.020096179097890854,
-0.035129811614751816,
-0.06544193625450134,
0.05755358934402466,
0.027398735284805298,
0.033251628279685974,
-0.02502484619617462,
-0.013890950009226799,
-0.012349685654044151,
0.036758311092853546,
0.01879432052373886,
0.020487140864133835,
-0.04546167328953743,
0.032396841794252396,
0.013621535152196884,
0.028320781886577606,
0.023557497188448906,
-0.02351551316678524,
0.013307752087712288,
0.011398804374039173,
-0.014784791506826878,
0.025749700143933296,
0.005899903364479542,
0.04167662560939789,
-0.05551378056406975,
0.023436039686203003,
0.02658630907535553,
0.00668846582993865,
-0.06428483128547668,
0.022553982213139534,
-0.05535617843270302,
-0.08254644274711609,
-0.07640496641397476,
-0.004008826799690723,
0.008102898485958576,
-0.07585275918245316,
-0.03879828751087189,
-0.019230082631111145,
-0.05372573807835579,
0.00652454886585474,
0.03590681776404381,
0.03276146948337555,
0.053533636033535004,
-0.0003542249614838511,
-0.003013420384377241,
-0.03930913284420967,
-0.0024604867212474346,
-0.012618149630725384,
-0.046268630772829056,
0.0014643588801845908,
-0.029813552275300026,
-0.09027247130870819,
-0.04020724818110466,
0.05419168248772621,
-0.02635703608393669,
0.023482974618673325,
0.035893332213163376,
0.0005847251159138978,
0.04832382872700691,
-0.0029122275300323963,
-0.02235334925353527,
-0.012929204851388931,
0.012739643454551697,
0.06695858389139175,
-0.03030397556722164,
-0.02929071895778179,
0.0229477658867836,
0.012985778041183949,
-0.057549651712179184,
-0.0038266454357653856,
0.035122957080602646,
-0.042377013713121414,
0.07117719203233719,
0.0031243558041751385,
-0.029642680659890175,
-0.03550228103995323,
-0.04754297062754631,
0.02276795729994774,
0.013107843697071075,
-0.05586039647459984,
0.02118667960166931,
0.017370548099279404,
-0.020600346848368645,
-0.05997946858406067,
-0.04487437382340431,
0.01734240911900997,
0.04181577265262604,
0.01748013310134411,
-0.05114748701453209,
0.005597148090600967,
0.04187898710370064,
-0.04233596846461296,
0.01963607594370842,
0.0035937963984906673,
-0.013650612905621529,
-0.028751883655786514,
-0.022016676142811775,
0.05170120298862457,
-0.0016670313198119402,
-0.06443613022565842,
-0.04873404651880264,
0.0675700455904007,
-0.008587464690208435,
-0.029587743803858757,
0.010004064999520779,
-0.041250187903642654,
-0.004122554790228605,
-0.03198264166712761,
-0.028323255479335785,
0.016284232959151268,
-0.04078042134642601,
-0.0014888198347762227,
0.004037570208311081,
-0.020619399845600128,
0.032595377415418625,
-0.0034040366299450397,
-0.009684287011623383,
-0.05356897413730621,
-0.003197030397132039,
-0.013161392882466316,
0.020508449524641037,
-0.014417777769267559,
0.02457871474325657,
0.03542376682162285,
0.04285949096083641,
0.021774884313344955,
0.030173620209097862,
0.014204234816133976,
0.03337140753865242,
-0.010522927157580853,
0.021365851163864136,
0.009009326808154583,
-0.05268208310008049,
-0.032803650945425034,
-0.062113288789987564,
0.020412536337971687,
-0.015443435870110989,
0.07026530057191849,
0.016204647719860077,
-0.009508799761533737,
-0.011844098567962646,
-0.021174350753426552,
0.0625268742442131,
0.042498160153627396
] |
<p>We know that the CMB is isotropic when viewed outside of the spinning and revolving earth.</p>
<p>Is it homogeneous?</p>
<p>Can we relate the CMB to an inertial frame in the Newtonian sense (in which space and time are homogeneous and isotropic)? Or can it just provide an idea to build upon a new theory in which global (privileged) inertial frames exist?</p>
<p>Einstein's General Theory of Relativity could be useful in an answer, but some outside-the-box thinking would be appreciated; feel free to question GR.</p> | g1299 | [
0.0075514959171414375,
0.022917097434401512,
0.0005005730781704187,
0.024982063099741936,
0.015417800284922123,
0.05442937836050987,
0.1025993674993515,
0.015063327737152576,
0.04069254919886589,
-0.013265883550047874,
0.019560517743229866,
-0.009860534220933914,
-0.013898196630179882,
0.004851129371672869,
0.05305616185069084,
-0.06635735929012299,
-0.01166642177850008,
0.0002151113876607269,
0.04886246845126152,
0.014155722223222256,
0.017358975484967232,
0.016245989128947258,
0.03328488767147064,
-0.006130055990070105,
0.007772911339998245,
0.010315579362213612,
0.036852601915597916,
-0.05563385784626007,
0.028795715421438217,
-0.005625537130981684,
-0.006790267303586006,
0.0034522830974310637,
-0.030997728928923607,
0.006332520395517349,
0.03116152249276638,
0.0060577597469091415,
-0.00469496613368392,
0.03808565437793732,
0.02449963241815567,
0.06919264048337936,
0.041091419756412506,
-0.014309264719486237,
-0.05624111741781235,
-0.0241360105574131,
0.005045168101787567,
0.06554578989744186,
-0.0382845513522625,
-0.0015581818297505379,
-0.009996362030506134,
-0.03917976841330528,
-0.05784693360328674,
0.05453448370099068,
0.08724619448184967,
0.01558629423379898,
0.016203945502638817,
-0.02134910225868225,
0.03950795903801918,
-0.015647226944565773,
0.06591115891933441,
0.023856472223997116,
-0.03672125190496445,
-0.053616780787706375,
0.007834473624825478,
-0.018241021782159805,
0.016530627384781837,
-0.006997688673436642,
-0.053261980414390564,
-0.003354121698066592,
-0.0009942090837284923,
-0.010925769805908203,
0.05550643056631088,
-0.07438928633928299,
0.015001336112618446,
0.02048501931130886,
-0.061149466782808304,
0.039454590529203415,
-0.011913495138287544,
0.00452986778691411,
0.06180699169635773,
-0.014271555468440056,
-0.012534805573523045,
0.0746612623333931,
0.007389042526483536,
-0.056267984211444855,
0.060825951397418976,
-0.04006950184702873,
0.026848694309592247,
0.03491906449198723,
-0.027787085622549057,
0.03780173137784004,
0.035847101360559464,
-0.04478807374835014,
0.029633745551109314,
0.020743394270539284,
-0.009659686125814915,
-0.008663640357553959,
-0.04713251069188118,
0.027575204148888588,
0.0005959034897387028,
0.05364961549639702,
-0.03839148208498955,
-0.0032790489494800568,
-0.0016409065574407578,
0.004678907338529825,
0.03754777833819389,
-0.027830207720398903,
0.029784763231873512,
0.018420856446027756,
-0.04729128256440163,
-0.022181237116456032,
-0.027982626110315323,
-0.02255142107605934,
0.004082013852894306,
0.047976505011320114,
-0.08502614498138428,
-0.01676695980131626,
0.07920185476541519,
-0.04129761829972267,
0.01793215051293373,
0.04349592328071594,
0.01845618523657322,
0.05340440571308136,
-0.021987203508615494,
0.05600760877132416,
-0.053864818066358566,
0.0035866680555045605,
0.016881072893738747,
-0.03366246446967125,
0.021289469674229622,
-0.03098803386092186,
0.016237013041973114,
0.04515279456973076,
0.013636835850775242,
-0.03287918493151665,
-0.024547697976231575,
-0.02536807395517826,
0.009247085079550743,
0.04149769991636276,
-0.033619288355112076,
0.037441153079271317,
-0.04192700237035751,
-0.024922005832195282,
0.003992840182036161,
0.03477617725729942,
0.013259521685540676,
0.04017774760723114,
-0.035738471895456314,
0.04609213396906853,
0.04370507970452309,
0.03032011166214943,
-0.026305919513106346,
0.09180904179811478,
0.017247162759304047,
-0.05045505613088608,
0.07146090269088745,
-0.02220548503100872,
-0.0019540030043572187,
-0.02089061588048935,
0.002635631710290909,
0.0038622128777205944,
0.051605552434921265,
-0.03375653550028801,
0.013367461040616035,
-0.026922335848212242,
-0.04996300861239433,
0.026235109195113182,
-0.036096569150686264,
0.0009763420093804598,
0.10861445963382721,
-0.10437243431806564,
-0.04303587228059769,
-0.002175065455958247,
-0.03175801411271095,
0.05312635749578476,
-0.011983661912381649,
-0.012199030257761478,
0.0035354052670300007,
-0.03558594360947609,
0.005711177829653025,
-0.050044603645801544,
-0.018928004428744316,
-0.01619425229728222,
-0.005819374695420265,
-0.029032262042164803,
-0.03675534948706627,
0.0024201488122344017,
0.029747948050498962,
-0.0009794984944164753,
-0.010253789834678173,
0.013291660696268082,
0.002303612418472767,
-0.04774468019604683,
-0.017792269587516785,
0.05091777443885803,
0.008933920413255692,
-0.011065834201872349,
-0.013917394913733006,
0.01113809272646904,
0.0035658336710184813,
0.03126350790262222,
-0.03209368884563446,
0.05514921620488167,
0.031166400760412216,
0.045928049832582474,
0.012127624824643135,
-0.022763624787330627,
0.0008753086440265179,
0.03929466754198074,
0.047602567821741104,
0.01859738864004612,
0.026769883930683136,
-0.056556396186351776,
-0.006111961789429188,
0.03023000992834568,
-0.051134224981069565,
-0.03642498329281807,
0.032503023743629456,
0.028551878407597542,
-0.019521519541740417,
0.016588207334280014,
-0.0019022253109142184,
0.01918816938996315,
-0.016840489581227303,
0.032177913933992386,
0.0012518663424998522,
-0.040056511759757996,
-0.10353990644216537,
0.04053713008761406,
0.03490273654460907,
0.04232511669397354,
-0.04838840290904045,
0.020214585587382317,
0.016416000202298164,
0.02312648296356201,
0.04648957774043083,
-0.006415000185370445,
-0.00589588051661849,
-0.024191509932279587,
0.012060354463756084,
0.025757839903235435,
-0.01832214742898941,
-0.029874296858906746,
0.006001715082675219,
-0.010887936688959599,
-0.006038330495357513,
-0.029903437942266464,
0.04136105254292488,
-0.006766080856323242,
0.017168710008263588,
0.001204719883389771,
0.027505600824952126,
-0.025391720235347748,
-0.05879896134138107,
-0.03520367294549942,
0.017733778804540634,
0.0003188474802300334,
-0.014345439150929451,
0.020557181909680367,
-0.11230560392141342,
-0.005090783350169659,
0.02749386988580227,
-0.078860804438591,
-0.030022963881492615,
0.03847692906856537,
-0.07070227712392807,
0.01882925257086754,
-0.008442679420113564,
0.026632023975253105,
-0.038479581475257874,
-0.03208421915769577,
-0.014995262958109379,
0.01604265347123146,
0.021957429125905037,
0.06936319917440414,
-0.047635938972234726,
-0.005914344452321529,
-0.01910100132226944,
-0.04094197228550911,
-0.05084264278411865,
-0.03678898140788078,
-0.027456197887659073,
0.0550113320350647,
-0.041531555354595184,
-0.056590039283037186,
0.03469018638134003,
-0.023837074637413025,
-0.018742093816399574,
0.012909731827676296,
0.058950040489435196,
-0.008016573265194893,
0.01348597276955843,
0.06196841970086098,
0.04152023419737816,
0.03321260213851929,
0.002837003208696842,
0.04331535845994949,
0.016773434355854988,
-0.038193512707948685,
-0.047644130885601044,
0.04157237708568573,
0.0098899956792593,
-0.03880499303340912,
0.07025781273841858,
0.03158910199999809,
-0.029445702210068703,
0.011874796822667122,
-0.03109276480972767,
-0.025999754667282104,
-0.06435725092887878,
-0.0447913333773613,
-0.0640818402171135,
0.060087189078330994,
-0.01191532239317894,
0.04173751547932625,
-0.03329768031835556,
-0.006312835030257702,
-0.002238236367702484,
-0.009075062349438667,
0.02037622034549713,
-0.006823614705353975,
-0.04325457662343979,
-0.017308127135038376,
-0.05507326126098633,
-0.03468557447195053,
0.049218010157346725,
0.020256657153367996,
-0.027227578684687614,
-0.04164295271039009,
-0.06555651128292084,
-0.03194457292556763,
-0.026695001870393753,
0.010720178484916687,
-0.021025821566581726,
0.0668187364935875,
-0.07179634273052216,
0.0200912207365036,
0.00007304955943254754,
-0.02008233033120632,
0.11321477591991425,
-0.005134441424161196,
0.03602856025099754,
-0.0004558772488962859,
-0.019387822598218918,
-0.0000496456450491678,
-0.020869197323918343,
0.040459685027599335,
0.004207622725516558,
-0.04337932914495468,
-0.007712345104664564,
0.039301056414842606,
0.03658098727464676,
-0.053417351096868515,
-0.003915299195796251,
-0.07403943687677383,
0.026939632371068,
0.06340888142585754,
0.01647287979722023,
0.047688115388154984,
-0.03251643478870392,
-0.010928051546216011,
0.008391229435801506,
-0.04787514731287956,
0.023898497223854065,
0.019101763144135475,
0.019996510818600655,
-0.01653893105685711,
-0.005932716652750969,
-0.024321259930729866,
-0.014014037325978279,
-0.022350922226905823,
-0.0136952493339777,
-0.008062505163252354,
-0.0066573768854141235,
-0.002759120427072048,
0.06240929663181305,
-0.06455740332603455,
0.0717426985502243,
0.026407865807414055,
-0.014804094098508358,
-0.03237149864435196,
-0.007126008626073599,
-0.009752626530826092,
-0.0380374938249588,
0.038768548518419266,
0.06808458268642426,
0.01593533158302307,
-0.02082831598818302,
-0.03319559991359711,
-0.010998658835887909,
-0.0165259949862957,
0.005942193325608969,
-0.0414966456592083,
-0.013179692439734936,
-0.032684311270713806,
0.042977120727300644,
0.0020917074289172888,
-0.024317704141139984,
-0.00721729313954711,
0.057903748005628586,
0.0034093521535396576,
0.044480565935373306,
-0.003940647002309561,
-0.006476706359535456,
-0.0027606268413364887,
-0.03404523804783821,
0.018756989389657974,
0.016892757266759872,
-0.0722087025642395,
0.019414449110627174,
0.0056310417130589485,
0.04302702844142914,
-0.01090947724878788,
0.014518513344228268,
-0.06663311272859573,
0.08386088162660599,
0.010109626688063145,
0.053932975977659225,
-0.044496089220047,
0.01626003533601761,
0.011274912394583225,
0.016684914007782936,
0.027217525988817215,
-0.012152749113738537,
-0.03660281375050545,
0.027349984273314476,
0.0989714041352272,
0.051646385341882706,
0.03806203231215477,
-0.030900079756975174,
0.0783926472067833,
0.022245638072490692,
-0.0005301653291098773,
0.04086606949567795,
-0.01320676039904356,
-0.006006833165884018,
0.0278814397752285,
-0.03349122032523155,
-0.0280649084597826,
0.029970873147249222,
-0.03626212105154991,
0.018005866557359695,
-0.02168411761522293,
-0.004327412229031324,
-0.03469473496079445,
0.003935914486646652,
0.09498339146375656,
0.039435625076293945,
-0.0015541745815426111,
-0.057911790907382965,
-0.03775259852409363,
-0.00006663991371169686,
-0.018480682745575905,
-0.0440046489238739,
0.070489302277565,
-0.020133400335907936,
-0.012252132408320904,
-0.03137530758976936,
0.0068939910270273685,
-0.027485042810440063,
0.049588143825531006,
-0.057213183492422104,
-0.03760344535112381,
-0.015581723302602768,
0.007753871846944094,
0.02215498499572277,
0.0035038250498473644,
-0.063245989382267,
0.0511566624045372,
-0.13102538883686066,
-0.003629351034760475,
0.005340445786714554,
0.019883234053850174,
-0.021637292578816414,
-0.040833573788404465,
0.002354628639295697,
0.0463506244122982,
0.016966629773378372,
-0.04275140166282654,
0.040769100189208984,
-0.03938781097531319,
-0.012060360051691532,
-0.03513360023498535,
-0.007691558450460434,
-0.000005456087819766253,
0.01056523248553276,
0.026474619284272194,
-0.06400014460086823,
-0.005012312438338995,
-0.04922141507267952,
-0.030728917568922043,
0.009412369690835476,
0.008537748828530312,
0.00846127700060606,
-0.03867175802588463,
0.02065233327448368,
0.03854125738143921,
-0.018967274576425552,
-0.053203970193862915,
-0.01222805492579937,
-0.011560493148863316,
-0.014492007903754711,
0.010964570567011833,
0.0020751473493874073,
0.053922317922115326,
-0.008643831126391888,
0.01650431379675865,
0.004224031697958708,
-0.011129288002848625,
-0.060971133410930634,
0.0622854009270668,
-0.009842175990343094,
-0.03993324190378189,
-0.05704726278781891,
0.03823553025722504,
0.013979188166558743,
-0.04853760451078415,
0.0018803076818585396,
-0.035774342715740204,
0.011089234612882137,
-0.06572511792182922,
-0.007501761429011822,
0.043802693486213684,
0.037666626274585724,
0.02385013736784458,
-0.030039871111512184,
0.08186694234609604,
-0.017327073961496353,
-0.00898352637887001,
0.00047312251990661025,
0.05548412725329399,
-0.023633984848856926,
-0.03601270541548729,
0.05899052321910858,
-0.030872108414769173,
0.06665012985467911,
-0.024659814313054085,
0.0059320516884326935,
0.06101023033261299,
0.04546498879790306,
0.022883664816617966,
-0.07921086251735687,
-0.011041874065995216,
-0.02023439295589924,
0.02022583782672882,
-0.028482915833592415,
0.03239715099334717,
0.0185710322111845,
0.034373171627521515,
0.05224228277802467,
-0.06209887936711311,
-0.08836028724908829,
-0.0051459078676998615,
-0.005779138300567865,
-0.030244050547480583,
-0.029124829918146133,
0.03227633610367775,
0.013542510569095612,
-0.006328045390546322,
0.013855095952749252,
0.006372794974595308,
-0.01222790963947773,
0.008904843591153622,
0.03797254338860512,
-0.005191801115870476,
-0.04157232120633125,
-0.017535828053951263,
0.042678844183683395,
-0.024882707744836807,
0.06773953139781952,
-0.049362871795892715,
-0.03197541832923889,
-0.04838300868868828,
-0.02587384358048439,
-0.00627284636721015,
-0.015895158052444458,
-0.05915389209985733,
-0.05471881479024887,
-0.021248558536171913,
-0.05524532496929169,
0.03624752163887024,
0.040101028978824615,
-0.015894407406449318,
0.03398331627249718,
-0.0002881882537622005,
-0.06741631776094437,
0.011882438324391842,
-0.03923514485359192,
-0.006298517342656851,
-0.036815889179706573,
-0.004882632289081812,
-0.04217550531029701,
0.005635065957903862,
-0.014847546815872192,
0.006309496704488993,
-0.0344233401119709,
0.03263863921165466,
-0.00479690358042717,
0.0019962915685027838,
-0.030067024752497673,
-0.03170512244105339,
0.03810448944568634,
-0.008311990648508072,
0.0664975494146347,
-0.003706485964357853,
0.09036210924386978,
-0.0065847765654325485,
-0.053642284125089645,
-0.026949841529130936,
0.033745039254426956,
0.016847414895892143,
-0.004812480416148901,
-0.013050624169409275,
0.0456824004650116,
0.025538943707942963,
0.017282752320170403,
-0.03845132142305374,
0.0007916667382232845,
-0.01450400147587061,
0.0033499635756015778,
0.0005078323883935809,
0.020067187026143074,
0.012361581437289715,
0.027185920625925064,
-0.009272661060094833,
0.001731524127535522,
0.04801790788769722,
-0.02543405257165432,
0.0242288950830698,
-0.006743519566953182,
-0.013510159216821194,
-0.012624749913811684,
0.04629971459507942,
0.01816415600478649,
0.012500378303229809,
0.011379835195839405,
0.008016403764486313,
-0.01742921583354473,
0.0034373821690678596,
0.03739423304796219,
-0.03350038081407547,
-0.004857655614614487,
0.00550673296675086,
-0.004834432620555162,
0.017985934391617775,
-0.04982371628284454,
-0.008123808540403843,
0.0886092260479927,
-0.06024327501654625,
-0.0012719770893454552,
0.01164897158741951,
-0.012632270343601704,
-0.03585601598024368,
-0.033317871391773224,
0.024853253737092018,
-0.026352213695645332,
-0.002778738271445036,
0.02927272394299507,
0.0074124084785580635,
0.06524273753166199,
-0.038786813616752625,
0.010025526396930218,
0.02234816551208496,
-0.032789573073387146,
-0.015265528112649918,
-0.037123508751392365,
0.03254571929574013,
-0.019872579723596573,
-0.03958854079246521,
0.02085207775235176,
0.03074714168906212,
0.026232071220874786,
-0.020990338176488876,
0.00347691192291677,
0.01319056749343872,
-0.01103501208126545,
-0.003195732831954956,
-0.05128810554742813,
0.00223048054613173,
0.01015769224613905,
-0.017071908339858055,
0.025298751890659332,
0.09803114831447601,
-0.0043844920583069324,
0.03315664455294609,
-0.023044129833579063,
0.03481396287679672,
0.013932663016021252,
-0.05377153679728508,
-0.008279163390398026,
-0.047832686454057693,
-0.025508761405944824,
0.015178061090409756,
-0.0026642472948879004,
-0.04222964495420456,
-0.017601843923330307,
0.04378162696957588,
0.0036349433939903975,
0.04570936784148216,
-0.0028393776156008244,
-0.01889592595398426,
-0.028907399624586105,
-0.01701790653169155,
-0.013624008744955063,
-0.002575699472799897,
0.06111863628029823,
-0.03644024580717087,
-0.05925830081105232,
-0.03746509552001953,
-0.06350408494472504,
0.06608147919178009,
0.021883651614189148,
0.07759564369916916,
0.03995433822274208,
-0.04581589624285698,
-0.03198961541056633,
0.013303148560225964,
-0.07704927772283554,
-0.020759057253599167,
0.016712963581085205,
-0.021557336673140526,
-0.00026256166165694594,
0.05125374346971512,
-0.014086250215768814,
-0.04004760459065437,
0.003342963755130768,
-0.017731541767716408,
0.024727175012230873,
-0.07588325440883636,
0.04351743683218956,
-0.046368587762117386,
-0.014170193113386631,
0.02278314158320427,
-0.002038203412666917,
0.030797073617577553,
0.030292538926005363,
0.01541078556329012,
0.005912077147513628,
-0.07068153470754623,
-0.019436107948422432,
0.014041796326637268,
0.0015424200100824237,
-0.03133656084537506,
-0.014677857048809528,
-0.00884405430406332,
0.021772610023617744,
0.012458079494535923,
-0.005718596745282412,
0.011384181678295135,
-0.013513363897800446,
0.02271348051726818,
0.006432457827031612,
0.07233984023332596,
0.016258934512734413,
-0.010670904070138931,
0.0629698783159256,
-0.049695711582899094,
0.01912260241806507,
0.023527756333351135,
0.0027026725001633167,
-0.003564460901543498,
-0.01911190152168274,
0.008886019699275494,
-0.01185460202395916,
-0.024274174124002457,
0.0015790582401677966,
0.007099783048033714,
-0.0300446804612875,
0.09074941277503967
] |
<blockquote>
<p>Bodies $A$ and $B$ are moving in the same direction in a straight line with a constant velocities on a frictionless surface. The mass and the velocity of $A$ are $2 \text{kg}$ and $10 \text{m/s}$. The mass and the velocity of $B$ are $6 \text{kg}$ and $4 \text{m/s}$. A spring is connected to the back of the body $B$ and its rate is $800 \text{N/m}$.</p>
<ul>
<li><p>What is the velocity of $A$ relatively to $B$ before the collision and after the collision?</p>
<p>(Answer: $6 \text{m/s}$ and $-6 \text{m/s}$)</p></li>
<li><p>What is the relative velocity between the objects when the spring achieves its maximum contraction? </p>
<p>(Answer: $0$)</p></li>
</ul>
</blockquote>
<p><img src="http://i.stack.imgur.com/lB3mI.png" alt="Illustration"></p>
<p>I had no problem with the first question. We know that in elastic collision the coefficient of restitution is $1$, therefore the relative velocities before and after the collision are equal but are opposite in sign. The relatve velocity before the collision is $10-4=6\text{m/s}$ .</p>
<p>My trouble is with the second question. I though a lot about it and came to a contradiction in my thoughts (of course it is because I'm missing something):</p>
<p>On the one hand, it seems to me that when the contraction of the spring is maximal, all the kinetic energy of $A$ was transformed to a potential elastic energy and to some portion of kinetic energy of $B$ (it will move faster). So it means that $A$ has no velocity at that moment, but $B$ has, so it's impossible that their relative velocity is zero. Intuitively, it means that $A$ has some kinetic energy. So it means that $A$ will be slowed down by the spring, until its velocity is zero, and the spring can finally return to its normal state. So it seems that the spring will be contracted maximally for some relatively short period of time until the kinetic energy of $A$ becomes zero. But something tells me that I'm wrong. Anyway, I've tried to play with the law of conservation of energy and to wrap it around my thoughts, but it didn't quite work well. So what am I missing? I will appreciate any help.</p>
<hr>
<p>Proposed solution:</p>
<p><strong>Relative speed during the maximal contraction</strong></p>
<p>The moment $A$ reaches the spring, the spring will push both of the bodies as a reaction to the $A$'s push. Therefore, the $A$ will start to decelerate while $B$ will start to gain more speed. Although $A$ is losing its kinetic energy, its velocity won't be zero at the moment of the maximal contraction. This is because $A$ will continue to contract the spring as long as its speed is higher than the speed of $B$ (and therefore the speed of the spring itself). The moment their velocities are the same, $A$ will no longer be "overtaking" the spring, therefore its contraction will be maximal at that point. Therefore, the relative speed is zero.</p>
<p><strong>Finding the maximal contraction:</strong></p>
<p>The net momentum is conserved at any point in the time, so:</p>
<p>$m_A v_A + m_B v_B = (m_A + m_B) V$</p>
<p>In this particular question, $V$ would be: $5.5 \text{m/s}$</p>
<p>We also know that the total mechanical energy is conserved (the collision is perfectly elastic), therefore, the mechanical energy before the collision (which only consists of kinetic energies) will be equal to the total mechanical energy during the max contract. Therefore:</p>
<p>$\frac{1}{2} m_A v_A^2 + \frac{1}{2} m_B v_B^2 = \frac{1}{2} (m_A + m_B) V^2 + \frac{1}{2} k (\Delta x_{max})^2$</p>
<p>The energy when the contraction is maximal consists of kinetic energies of $A$ and $B$ (which are moving with the same velocity) and of elastic potential energy due to the fact that the spring is contracted.</p>
<p>In this particular question $\Delta x_{max}$ would be:</p>
<p>$\Delta x_{max} = \sqrt{\frac{27}{400}} \approx 26 \text{cm}$</p> | g1300 | [
0.10013410449028015,
-0.032066479325294495,
0.017995093017816544,
0.07972459495067596,
0.09040100872516632,
-0.00918714702129364,
0.024812964722514153,
0.02341414801776409,
-0.026532193645834923,
-0.008298604749143124,
-0.05668910965323448,
-0.00913089420646429,
0.027844266965985298,
-0.018942585214972496,
-0.01979818195104599,
-0.0551566481590271,
0.07083918899297714,
-0.06310097873210907,
-0.0027316452469676733,
0.07823050767183304,
-0.04882421717047691,
0.027764350175857544,
-0.016133276745676994,
-0.036408431828022,
0.03760124742984772,
-0.011779073625802994,
-0.015128794126212597,
-0.00010711528011597693,
-0.06667420268058777,
-0.040782008320093155,
0.015936337411403656,
-0.004986622836440802,
-0.00955580547451973,
-0.04186972230672836,
-0.043224647641181946,
0.04907095804810524,
0.03469841927289963,
-0.01970425620675087,
-0.021587543189525604,
0.019209541380405426,
0.08356492966413498,
-0.054119132459163666,
0.01708267442882061,
-0.003472255077213049,
0.058559924364089966,
-0.001388676231727004,
0.01811765320599079,
-0.03932327404618263,
-0.02555316500365734,
0.044994793832302094,
-0.015835478901863098,
0.07277780771255493,
-0.0006316921790130436,
-0.03707321733236313,
-0.04589761421084404,
0.023410901427268982,
0.05647772550582886,
-0.013312086462974548,
-0.01232798770070076,
0.010421710088849068,
-0.017656873911619186,
0.00009041357407113537,
0.011889668181538582,
-0.05065763369202614,
0.03888331353664398,
-0.018384259194135666,
-0.0011352308792993426,
0.015669694170355797,
0.05393526703119278,
-0.009396588429808617,
0.00145524216350168,
0.008631828241050243,
-0.001648194040171802,
-0.027332205325365067,
-0.06102066487073898,
-0.01716957800090313,
0.025767214596271515,
-0.042329538613557816,
0.031211568042635918,
-0.027846451848745346,
-0.026878153905272484,
0.05579768493771553,
0.0028337696567177773,
0.010475530289113522,
0.022296473383903503,
0.02060595154762268,
0.009760057553648949,
0.019650408998131752,
-0.05144231393933296,
0.049612607806921005,
-0.0027508207131177187,
-0.07259146869182587,
0.05483793094754219,
0.0034484590869396925,
-0.054431792348623276,
0.020221130922436714,
-0.03553153574466705,
0.06004280596971512,
0.032558806240558624,
-0.003894813358783722,
-0.017400674521923065,
0.0001967824500752613,
-0.005349036306142807,
0.024010563269257545,
-0.010228668339550495,
-0.03438354656100273,
0.07369034737348557,
0.02250535786151886,
-0.07607227563858032,
-0.026343783363699913,
0.01063663512468338,
-0.10735836625099182,
0.015284791588783264,
-0.04278090223670006,
-0.00962041225284338,
-0.05319163203239441,
-0.020535793155431747,
-0.010129276663064957,
-0.010086534544825554,
0.054893650114536285,
-0.03220697119832039,
0.03425756096839905,
-0.022883547469973564,
-0.022443363443017006,
0.028031326830387115,
0.00482783280313015,
0.019854139536619186,
0.009314307011663914,
0.011409172788262367,
0.008399495854973793,
-0.017042068764567375,
-0.0018548755906522274,
0.046608950942754745,
0.017205988988280296,
-0.06965775787830353,
0.02898646891117096,
-0.014212017878890038,
0.03480152413249016,
-0.037106867879629135,
0.015873782336711884,
0.017796438187360764,
0.014698936603963375,
-0.03150936961174011,
-0.0016745502362027764,
-0.027982190251350403,
0.0694260373711586,
-0.03185494616627693,
0.014296009205281734,
0.02146231383085251,
0.0543237067759037,
-0.0030302058439701796,
0.05283835902810097,
-0.047712404280900955,
-0.005475054960697889,
0.015698449686169624,
0.00673460029065609,
0.05390020087361336,
-0.008634401485323906,
-0.0191813874989748,
0.011117087677121162,
0.03699453920125961,
-0.003093195613473654,
0.012252393178641796,
-0.013276025652885437,
0.00028712183120660484,
0.02337547205388546,
-0.045029960572719574,
-0.005694353021681309,
0.046532902866601944,
-0.012481888756155968,
-0.07851524651050568,
-0.059831757098436356,
0.010017029009759426,
0.043802931904792786,
-0.008626256138086319,
-0.006525376811623573,
0.002485678531229496,
-0.04837028309702873,
-0.014321806840598583,
-0.02548012137413025,
-0.026688789948821068,
-0.01203123852610588,
0.037104155868291855,
0.018791893497109413,
0.0008618738502264023,
0.0023488407023251057,
0.00001989983138628304,
0.07897596061229706,
-0.06711195409297943,
0.0031855753622949123,
-0.010754917748272419,
-0.009154997766017914,
-0.015242597088217735,
0.006937721278518438,
-0.029771236702799797,
0.028025709092617035,
0.01929478719830513,
-0.01259869895875454,
-0.0334906205534935,
-0.001582857919856906,
0.008899016305804253,
0.04079585522413254,
0.005545518361032009,
-0.014475786127150059,
-0.010726471431553364,
-0.014481514692306519,
-0.029918545857071877,
-0.010204169899225235,
0.024639582261443138,
0.04871668294072151,
0.029738150537014008,
0.017802614718675613,
-0.013162403367459774,
0.03774963691830635,
-0.019026700407266617,
-0.049742694944143295,
-0.028391407802700996,
-0.012498357333242893,
-0.013607046566903591,
-0.0031368655618280172,
-0.00255948631092906,
-0.003608111059293151,
0.04397386685013771,
-0.052391186356544495,
-0.05509098991751671,
-0.027808045968413353,
-0.016400232911109924,
-0.0016091259894892573,
-0.02990851178765297,
0.0236279908567667,
-0.029072215780615807,
0.03376041352748871,
0.04148796573281288,
-0.02122708037495613,
0.003991284873336554,
0.01244919840246439,
-0.008574329316616058,
0.07621325552463531,
-0.0035591868218034506,
-0.011095637455582619,
0.0977071151137352,
-0.03749154135584831,
-0.037426501512527466,
0.014770197682082653,
0.034826211631298065,
0.006508735474199057,
0.017796380445361137,
0.021990636363625526,
0.04051191732287407,
0.059123385697603226,
0.0026352214626967907,
0.016230128705501556,
-0.008032058365643024,
-0.002583540976047516,
0.057676903903484344,
-0.012569769285619259,
-0.02007494680583477,
0.024574697017669678,
-0.03294757753610611,
-0.039590347558259964,
-0.011998798698186874,
-0.012394232675433159,
-0.0004909160197712481,
0.02573343925178051,
-0.1057915985584259,
0.04955402389168739,
-0.04556741565465927,
-0.03036973439157009,
0.013593931682407856,
-0.011455199681222439,
-0.039643388241529465,
-0.00940850842744112,
-0.026435738429427147,
0.08487100899219513,
0.030168702825903893,
-0.015840720385313034,
0.005296648014336824,
-0.02689887024462223,
-0.013182942755520344,
0.0035269379150122404,
0.004317091312259436,
0.0019951111171394587,
-0.030527958646416664,
-0.051724765449762344,
0.005868101958185434,
-0.04075154289603233,
-0.031004583463072777,
0.05178486555814743,
-0.013901491649448872,
0.01875378005206585,
0.006616635248064995,
0.04678530991077423,
0.04085240140557289,
0.04339129105210304,
0.00011434125917730853,
0.08257020264863968,
0.04427552968263626,
-0.015616425313055515,
-0.0566180944442749,
-0.004071649629622698,
0.013561485335230827,
-0.050952937453985214,
0.011580311693251133,
0.04624821990728378,
0.0568535290658474,
0.02877224050462246,
-0.06750015914440155,
-0.046695828437805176,
0.03429689630866051,
0.06415243446826935,
-0.01059105433523655,
-0.011493337340652943,
0.0055288830772042274,
-0.026191288605332375,
-0.07111047953367233,
0.01667245849967003,
-0.0009054373949766159,
-0.04240122810006142,
0.0026424042880535126,
0.022162172943353653,
-0.007246450986713171,
-0.020169967785477638,
0.061018943786621094,
-0.018376819789409637,
-0.022125795483589172,
-0.0002404332481091842,
-0.07893447577953339,
0.007752357982099056,
-0.029482008889317513,
-0.006785161327570677,
-0.04266231134533882,
0.07814328372478485,
0.01296900399029255,
-0.03110865317285061,
-0.009867176413536072,
-0.04117196425795555,
-0.027966076508164406,
0.032157596200704575,
0.038106996566057205,
0.08804486691951752,
0.04313772916793823,
0.03683900460600853,
0.0017437952337786555,
-0.007124800235033035,
0.023432845249772072,
0.035447388887405396,
0.024707576259970665,
0.005646044854074717,
-0.004869799129664898,
-0.03956646844744682,
0.08438906073570251,
-0.03336075693368912,
-0.04122662544250488,
0.003987384494394064,
-0.012134196236729622,
0.01354016549885273,
0.004558135289698839,
0.042906809598207474,
-0.06913023442029953,
0.00385538418777287,
0.03400947526097298,
0.020424148067831993,
-0.02916749007999897,
-0.00418948894366622,
-0.0365203395485878,
-0.022750388830900192,
-0.04257846623659134,
-0.019141802564263344,
-0.041062019765377045,
-0.001202490646392107,
-0.002750988584011793,
-0.05567449331283569,
-0.02504611574113369,
0.004883114248514175,
0.026876777410507202,
-0.06308121979236603,
0.017841650173068047,
0.05496821179986,
-0.020632749423384666,
0.01800883747637272,
0.04892467334866524,
0.012211203575134277,
-0.04178760573267937,
0.027621634304523468,
-0.030185630545020103,
0.03128108009696007,
-0.027303868904709816,
-0.019951231777668,
0.0351555161178112,
-0.03533769026398659,
0.016717832535505295,
-0.024663666263222694,
-0.06742411851882935,
0.013522941619157791,
0.033549629151821136,
-0.01240871474146843,
0.01759372092783451,
0.018694894388318062,
-0.010580701753497124,
0.016665443778038025,
-0.06472312659025192,
0.061557479202747345,
-0.06427951157093048,
0.009431197308003902,
-0.022207697853446007,
0.022489575669169426,
-0.0007142762769944966,
0.009005606174468994,
0.02306555025279522,
-0.022580647841095924,
-0.005763733759522438,
-0.005414577666670084,
-0.04849934205412865,
-0.01486205868422985,
-0.01826033927500248,
0.04600291699171066,
-0.029469450935721397,
-0.011687694117426872,
0.026643522083759308,
-0.018912553787231445,
0.02419823408126831,
0.0034690815955400467,
0.018717993050813675,
-0.041279107332229614,
0.0513102263212204,
0.0701582133769989,
0.06474437564611435,
-0.010298755019903183,
-0.003236382035538554,
-0.008442393504083157,
-0.0029656714759767056,
0.024815939366817474,
0.0057362779043614864,
0.05606904625892639,
-0.03666684404015541,
0.10906654596328735,
0.004304233007133007,
0.05157613009214401,
0.03127682954072952,
-0.006887583527714014,
0.013843941502273083,
0.016776172444224358,
0.013882028870284557,
0.002802565461024642,
-0.021123524755239487,
0.013803176581859589,
-0.06267532706260681,
-0.058934833854436874,
-0.026428619399666786,
-0.07276971638202667,
-0.011833170428872108,
0.03262533247470856,
0.002645339583978057,
-0.015303514897823334,
-0.046367447823286057,
-0.0007863544742576778,
-0.023688919842243195,
0.07481982558965683,
-0.005071805790066719,
0.0028098186012357473,
-0.006944010499864817,
0.022288678213953972,
0.032448943704366684,
0.004812445025891066,
-0.003357825567945838,
-0.01735362596809864,
0.023754311725497246,
0.013513092882931232,
-0.061153579503297806,
0.00725638959556818,
-0.001908972393721342,
0.03572123497724533,
0.020972810685634613,
0.05185801163315773,
-0.02982458285987377,
0.02172403782606125,
0.03307798132300377,
0.046732477843761444,
0.0353095605969429,
0.012128205969929695,
-0.015498975291848183,
-0.030730649828910828,
-0.0474126972258091,
-0.024767901748418808,
-0.006725901737809181,
-0.013775631785392761,
-0.05698366090655327,
-0.005235092248767614,
0.06398629397153854,
0.023455346003174782,
0.028174573555588722,
0.0347675122320652,
-0.0507727712392807,
0.02145783044397831,
0.023171616718173027,
0.0487634651362896,
-0.014483955688774586,
0.013518128544092178,
-0.032289985567331314,
0.04233546927571297,
-0.0682918056845665,
0.011450382880866528,
-0.001525756437331438,
0.030257152393460274,
-0.026708688586950302,
0.03931991755962372,
0.02131696604192257,
0.04058963432908058,
-0.022153470665216446,
-0.0006981770857237279,
-0.048716090619564056,
0.028743743896484375,
0.011419098824262619,
-0.021653197705745697,
-0.04227985069155693,
0.00021432105859275907,
0.06477189809083939,
-0.038063351064920425,
-0.04710172861814499,
-0.02697797678411007,
0.03406413272023201,
-0.003155558602884412,
0.03693322464823723,
0.04590604081749916,
0.002754861256107688,
0.006472591310739517,
-0.011325241066515446,
0.00027394178323447704,
-0.023001370951533318,
0.061122968792915344,
-0.011947991326451302,
-0.00826180912554264,
0.02188088372349739,
0.001665449352003634,
-0.0840538889169693,
-0.0019858782179653645,
-0.02088690921664238,
-0.045503925532102585,
-0.04483916983008385,
-0.009269626811146736,
-0.06439805030822754,
-0.0043727317824959755,
0.028386449441313744,
0.04696528613567352,
-0.045981742441654205,
0.016991958022117615,
-0.04343569278717041,
-0.07559267431497574,
-0.05547618493437767,
-0.016671329736709595,
-0.00910657923668623,
0.03187766298651695,
-0.02633238025009632,
-0.06148827075958252,
0.017918264493346214,
0.00227931491099298,
0.040435824543237686,
-0.052088066935539246,
-0.03222931548953056,
-0.013154777698218822,
0.0776255652308464,
0.0062864418141543865,
0.0131106898188591,
0.012660221196711063,
0.03454584628343582,
-0.0682017058134079,
-0.022657768800854683,
-0.04153796657919884,
0.05298745632171631,
-0.015856197103857994,
-0.023134848102927208,
-0.004009205382317305,
0.05442199110984802,
-0.006523825228214264,
0.05662604793906212,
0.023932162672281265,
-0.05813805013895035,
-0.03868816792964935,
-0.09258898347616196,
-0.003147152252495289,
0.011608225293457508,
-0.064154714345932,
0.014091741293668747,
0.009098042733967304,
-0.03755682334303856,
0.001614849898032844,
-0.0022891622502356768,
-0.011974635533988476,
0.030260823667049408,
-0.02942446991801262,
0.011858208104968071,
0.002226493554189801,
0.012413378804922104,
-0.03309551998972893,
-0.022709382697939873,
-0.017532361671328545,
-0.005467480514198542,
-0.0022293643560260534,
-0.06159607321023941,
0.03382217884063721,
0.002648837398737669,
0.010525689460337162,
0.02176813781261444,
-0.0060057127848267555,
0.02006843313574791,
0.010660603642463684,
-0.02190595678985119,
0.03519171476364136,
-0.033111583441495895,
-0.024574948474764824,
-0.04850419610738754,
0.07135038822889328,
-0.005664323456585407,
0.038423940539360046,
-0.009132424369454384,
0.029822150245308876,
-0.01657203771173954,
0.020094191655516624,
-0.004666617140173912,
-0.023025278002023697,
0.053183212876319885,
-0.006195546127855778,
0.05347543582320213,
-0.050380345433950424,
0.037752583622932434,
-0.007681705057621002,
-0.09318672865629196,
0.04187720641493797,
0.038201235234737396,
-0.008701809681952,
0.07038236409425735,
-0.0028192109894007444,
-0.02087932825088501,
0.02486247755587101,
0.08468855172395706,
0.055841948837041855,
-0.01430418249219656,
0.03862062096595764,
0.027165260165929794,
0.035998355597257614,
-0.003581937402486801,
-0.022043537348508835,
0.00325346109457314,
0.036528609693050385,
-0.021089913323521614,
0.004552294034510851,
0.06316734105348587,
-0.04936152324080467,
-0.04468909651041031,
-0.008991599082946777,
-0.08312102407217026,
-0.01710445247590542,
-0.039559684693813324,
0.017278341576457024,
-0.015666496008634567,
0.025352299213409424,
-0.03215111419558525,
-0.013172117993235588,
0.044692087918519974,
-0.01646747998893261,
-0.00017086611478589475,
-0.03534349799156189,
0.03471061587333679,
-0.06561998277902603,
0.0011410736478865147,
0.0665341392159462,
-0.012594965286552906,
-0.01494433544576168,
0.015146690420806408,
-0.02539132349193096,
0.058938853442668915,
-0.0003683744871523231,
-0.009167666547000408,
0.00484537472948432,
-0.004035320598632097,
-0.003805368673056364,
0.024301880970597267,
0.027572449296712875,
0.05019986256957054,
0.017345720902085304,
-0.0028893654234707355,
0.015464804135262966,
-0.042655833065509796,
0.02345350757241249,
-0.024480855092406273,
0.03308898210525513,
-0.012361866421997547,
0.03421428054571152,
0.0011851268354803324,
-0.013463392853736877,
-0.057127587497234344,
0.028773711994290352,
0.018028300255537033,
0.046956878155469894,
0.05016886815428734,
0.0008497197995893657,
0.020120281726121902,
0.08876214921474457,
0.028621448203921318,
-0.035449009388685226,
0.019834527745842934,
0.029310137033462524,
-0.0064119817689061165,
0.08621328324079514,
0.03328226879239082,
0.06248440966010094,
-0.049316443502902985,
-0.05522119253873825,
-0.014170648530125618,
-0.003861964214593172,
0.02056519128382206,
0.026177501305937767,
0.03334902226924896,
-0.014693808741867542,
-0.02967769466340542,
-0.004474117886275053,
-0.031552620232105255,
0.04642089456319809,
0.015138078480958939,
-0.017732566222548485,
0.013486625626683235,
-0.01869397610425949,
0.0030271520372480154,
-0.10065773129463196,
-0.047821030020713806,
-0.051635053008794785,
-0.014032061211764812,
-0.0039045808371156454,
-0.007231460884213448,
-0.015888435766100883,
-0.026798179373145103,
-0.027008360251784325,
-0.009843749925494194,
0.008896000683307648,
-0.04971906542778015,
0.029766887426376343,
-0.04788198694586754,
-0.02308984100818634,
-0.02313116565346718,
0.02825932204723358,
-0.04904954135417938,
-0.05415990576148033,
-0.02220993861556053,
-0.006492634303867817,
-0.006931262090802193,
-0.05613057315349579,
0.04340984299778938,
0.08591357618570328,
0.02151864767074585,
-0.04089738428592682,
0.10230232775211334,
0.02651030756533146,
-0.035626672208309174,
0.10056386888027191,
0.0015563680790364742,
-0.02005830407142639,
0.06771955639123917,
0.003074576146900654,
-0.06091263145208359,
0.008885437622666359,
-0.08042056113481522,
-0.022044209763407707,
-0.02439454011619091,
-0.048981618136167526,
-0.010754883289337158,
-0.012631690129637718,
-0.02582513727247715,
0.011886498890817165
] |
<p>This question is trying to see if anyone has some simple notation (or tricks) for dealing with operators acting on coherent states in a Fock space. I use bosons for concreteness; what I'm interested in might not be applicable to fermions.</p>
<p>If I have a multiparticle state defined by</p>
<p>$$|\phi\rangle=|n_1 n_2 ...n_k\rangle=\frac{(a_1^\dagger)^{n_1}}{\sqrt{n_1 !}}\frac{(a_2^\dagger)^{n_2}}{\sqrt{n_2 !}}...\frac{(a_k^\dagger)^{n_k}}{\sqrt{n_k !}}|0\rangle$$</p>
<p>I can write this compactly as</p>
<p>$$|\phi\rangle=\prod_{i=1}^{k}\frac{(a_i^\dagger)^{n_i}}{\sqrt{n_i !}}|0\rangle.$$</p>
<p>Now, I would like to act on this state with some operator consisting of creation and annihilation operators; this could be quite complicated, like</p>
<p>$$a_ja_ka^\dagger_l.$$</p>
<p>Now, IF the above product was a sum, I could find the answer very easily using commutation relations and delta functions:</p>
<p>\begin{align}
a_ja_ka^\dagger_l|\phi\rangle&=a^\dagger_la_j\sum_i\frac{(\delta_{ki}+a^\dagger_{i}a_k)}{\sqrt{n_i!}}|0\rangle\\
&=a^\dagger_la_j\left(\frac{1}{\sqrt{n_k!}}|0\rangle \right)
\end{align}</p>
<p>...continue until you get it to normal form, and you are done. Of course, this is a different problem but I am just illustrating how neat this notation is.</p>
<p>You can't just throw around delta functions in the product above, since they would make the entire product vanish. What I want is a clean way to denote "I have passed $a_k$ through all $i\neq k$, used the commutation relations to get $1+a^\dagger_ia_k$, and am now ready to hit this with another creation opertaor $a_l$."</p>
<p>I think it's fairly clear what I am looking for; anyone have any notation or tricks to make calculations using arbitrary operators like the one I have above easier?</p> | g1301 | [
-0.004777021240442991,
-0.013470858335494995,
0.023970749229192734,
-0.012143717147409916,
0.004358626902103424,
-0.056615084409713745,
0.04946526512503624,
0.052682287991046906,
0.03689267858862877,
-0.031046679243445396,
-0.02489473856985569,
-0.0298033207654953,
0.06654033064842224,
0.03577498719096184,
-0.004800973925739527,
0.019007273018360138,
0.008091224357485771,
0.038925331085920334,
0.017592310905456543,
0.016130002215504646,
-0.015016075223684311,
0.02003752626478672,
0.03432198241353035,
-0.017052477225661278,
0.029241375625133514,
-0.04789715260267258,
0.02296566404402256,
-0.0067323013208806515,
-0.036251649260520935,
-0.02629256434738636,
0.06210080161690712,
0.04685718193650246,
-0.04546990990638733,
0.042782533913850784,
-0.0019554621540009975,
-0.08733781427145004,
0.04393751546740532,
-0.0018023792654275894,
0.048329293727874756,
-0.007067717146128416,
-0.03782040253281593,
0.006749674677848816,
0.005461577326059341,
0.0015482171438634396,
-0.00796735379844904,
0.006631297990679741,
0.03986204415559769,
-0.037850502878427505,
-0.08965618908405304,
0.005294324364513159,
-0.02888217382133007,
-0.012901917099952698,
0.030552413314580917,
0.02023451402783394,
0.02665173076093197,
0.04641091451048851,
-0.0497894249856472,
-0.043927062302827835,
0.04654807969927788,
0.02393851988017559,
-0.025493931025266647,
-0.04238506406545639,
0.005213912110775709,
-0.02192901447415352,
0.040338184684515,
-0.008094163611531258,
-0.009628988802433014,
0.04904261231422424,
0.013585406355559826,
-0.02265196666121483,
0.020930659025907516,
-0.024081489071249962,
0.020641809329390526,
-0.011160905472934246,
0.0173773355782032,
0.01841489039361477,
-0.07594509422779083,
-0.030149009078741074,
0.04226423799991608,
-0.009860030375421047,
-0.05073137953877449,
-0.08099646121263504,
0.04550504684448242,
-0.016818951815366745,
-0.029815122485160828,
-0.021361760795116425,
0.0015711637679487467,
0.009557558223605156,
0.05687490850687027,
0.012702162377536297,
0.015143506228923798,
0.0033079979475587606,
-0.003348696045577526,
0.022035950794816017,
0.0013630330795422196,
-0.053532924503088,
0.022548897191882133,
0.016437798738479614,
-0.039926253259181976,
-0.026180701330304146,
-0.04900270700454712,
0.06127612665295601,
0.0012609754921868443,
-0.06323642283678055,
0.009952417574822903,
-0.01568712666630745,
0.0021741408854722977,
-0.03031124547123909,
-0.06076300889253616,
-0.006678249221295118,
0.006278337445110083,
-0.008956240490078926,
0.009692021645605564,
0.00009449087519897148,
0.017763685435056686,
-0.00009517533908365294,
-0.0018372931517660618,
-0.002480207709595561,
-0.005345790181308985,
0.03903850540518761,
-0.0058037713170051575,
-0.0071749915368855,
0.03196170926094055,
0.00397798977792263,
0.028184929862618446,
0.0001583570847287774,
-0.0036643061321228743,
-0.007544839289039373,
0.09425216913223267,
0.011523431167006493,
0.041759390383958817,
0.03140313923358917,
0.015015658922493458,
0.030652383342385292,
-0.05453022941946983,
0.024427443742752075,
0.004001721739768982,
-0.003233344294130802,
0.07296774536371231,
-0.0908413678407669,
0.004554009530693293,
-0.002641119295731187,
-0.01425662636756897,
0.024921108037233353,
0.015586038120090961,
-0.02057625912129879,
0.014014681801199913,
-0.10417545586824417,
0.007319480646401644,
0.038728103041648865,
0.028309335932135582,
0.005020969547331333,
0.004689179360866547,
0.02253955975174904,
0.06694961339235306,
0.060969967395067215,
0.04066533222794533,
-0.010490900836884975,
-0.028875937685370445,
-0.0012753719929605722,
0.010617993772029877,
-0.001658018329180777,
-0.0049935574643313885,
-0.0008981988648883998,
-0.016017844900488853,
-0.08135148137807846,
0.015337090007960796,
-0.03977995365858078,
-0.05526978150010109,
0.017308581620454788,
0.0019301786087453365,
0.025689780712127686,
0.016433672979474068,
0.018900105729699135,
0.06371381878852844,
0.025224316865205765,
-0.06322072446346283,
0.04674264416098595,
0.023100022226572037,
-0.021076176315546036,
-0.020913612097501755,
0.05268797278404236,
0.047065913677215576,
0.06558028608560562,
0.03149983659386635,
0.01989700272679329,
-0.056787531822919846,
-0.04491216316819191,
-0.008992779068648815,
0.059826720505952835,
0.0039018094539642334,
0.011371847242116928,
0.0472799651324749,
0.08656619489192963,
-0.0472835935652256,
0.0038586289156228304,
-0.01989315263926983,
-0.07199300080537796,
0.013010666705667973,
-0.00229702889919281,
-0.04759809747338295,
0.03270301967859268,
0.03326042741537094,
0.04942338913679123,
0.03812435641884804,
-0.011719412170350552,
-0.004499402828514576,
0.022603733465075493,
-0.04286288470029831,
0.03674565255641937,
-0.028897978365421295,
-0.027359867468476295,
-0.015873994678258896,
-0.012344672344624996,
0.002502812771126628,
0.005895665846765041,
-0.017837880179286003,
-0.03723464906215668,
-0.01935015246272087,
-0.019182028248906136,
-0.06185546889901161,
-0.03221839293837547,
0.03675832971930504,
0.02574082277715206,
-0.05146431177854538,
0.0636075884103775,
-0.0028481001500040293,
0.056887734681367874,
0.012439997866749763,
0.0008295302395708859,
-0.038013946264982224,
0.07235628366470337,
-0.016229476779699326,
-0.08487973362207413,
-0.018672682344913483,
0.0011170903453603387,
0.0000026442648959346116,
0.026531437411904335,
0.020291360095143318,
0.0757792741060257,
-0.040776319801807404,
-0.03621209040284157,
-0.06749366968870163,
-0.00026946101570501924,
-0.03741404041647911,
0.024947745725512505,
0.04299195483326912,
0.04327383637428284,
-0.02966366335749626,
-0.01838792860507965,
-0.05584841966629028,
-0.05133260041475296,
0.027000291272997856,
-0.0383007749915123,
0.025089100003242493,
0.0030333693139255047,
-0.017477424815297127,
0.026411890983581543,
-0.01059729140251875,
-0.0017991556087508798,
0.009286375716328621,
-0.020551852881908417,
-0.03836338222026825,
0.04688449203968048,
0.024700382724404335,
-0.02383223921060562,
-0.011479256674647331,
0.0021274888422340155,
-0.024859992787241936,
0.0421331487596035,
-0.06475905328989029,
-0.019848134368658066,
0.012592509388923645,
-0.03745315968990326,
-0.03671339526772499,
-0.047087229788303375,
-0.02155623398721218,
-0.015463096089661121,
0.015458167530596256,
0.0287750456482172,
-0.039633117616176605,
0.03996198996901512,
-0.0076843369752168655,
0.017511162906885147,
0.027210790663957596,
-0.0719224289059639,
0.0119966184720397,
0.07360968738794327,
-0.02421511523425579,
0.021324729546904564,
0.03463183343410492,
0.023122495040297508,
-0.027179036289453506,
0.007362401578575373,
-0.04228679835796356,
0.03723670169711113,
-0.019433630630373955,
-0.008584961295127869,
0.02434680424630642,
0.0705299824476242,
0.07909798622131348,
-0.03158900514245033,
0.03392389044165611,
0.015074570663273335,
0.017805539071559906,
0.030588438734412193,
-0.04658541828393936,
-0.023375285789370537,
-0.00507209450006485,
-0.026872120797634125,
-0.008492754772305489,
0.04951455816626549,
-0.04757343977689743,
-0.04418874531984329,
-0.00725721288472414,
-0.046184241771698,
-0.023228568956255913,
0.0232123751193285,
-0.02395954728126526,
0.00539042754098773,
-0.013551671989262104,
-0.03324209898710251,
0.04933343082666397,
-0.036937907338142395,
0.02639363706111908,
0.04506726935505867,
-0.02127300202846527,
-0.01593933068215847,
-0.013081984594464302,
-0.0077806799672544,
0.008167427033185959,
-0.025136468932032585,
0.0028247793670743704,
-0.027477877214550972,
-0.09112124145030975,
-0.06996306031942368,
-0.007121254224330187,
-0.06462355703115463,
-0.00035777883022092283,
-0.026540236547589302,
0.020621148869395256,
-0.0495181679725647,
0.022058382630348206,
-0.020501652732491493,
-0.026553956791758537,
-0.015112919732928276,
0.049152765423059464,
0.047916311770677567,
0.0021477651316672564,
-0.027116427198052406,
-0.04212768375873566,
0.002764985430985689,
0.08575382828712463,
-0.015632057562470436,
-0.000002578184194135247,
0.010749484412372112,
0.058911506086587906,
0.025530708953738213,
0.013015908189117908,
0.020729096606373787,
0.015515223145484924,
0.0119190514087677,
-0.022864170372486115,
0.043582506477832794,
-0.03256005048751831,
0.03448045998811722,
0.05456605181097984,
-0.010166497901082039,
0.036749500781297684,
0.0571107380092144,
0.022475723177194595,
0.05249413102865219,
-0.024314891546964645,
0.005914994049817324,
-0.06440043449401855,
-0.09921909123659134,
-0.008001473732292652,
-0.023954473435878754,
-0.009387673810124397,
-0.017652733251452446,
0.003022741060703993,
0.03738298639655113,
0.04693789780139923,
-0.016109975054860115,
-0.00803427305072546,
0.020584911108016968,
-0.009525668807327747,
0.000637461373116821,
0.025114834308624268,
0.036440394818782806,
0.035373467952013016,
-0.04021594300866127,
0.008629496209323406,
0.00444013113155961,
0.020104577764868736,
0.011280812323093414,
0.046102773398160934,
-0.04731413349509239,
-0.0611785426735878,
0.06208740919828415,
-0.03202586621046066,
-0.05796664580702782,
0.03713076189160347,
0.00038486302946694195,
-0.018446987494826317,
-0.03743838891386986,
0.009302601218223572,
0.028663270175457,
-0.0016412236727774143,
-0.06654845178127289,
-0.034555740654468536,
0.008523097261786461,
0.0028816249687224627,
0.035546690225601196,
-0.07063739001750946,
-0.03549736365675926,
-0.006163293495774269,
0.0132238008081913,
-0.01541448850184679,
0.00031119887717068195,
-0.0036711720749735832,
0.01643332652747631,
0.02315092273056507,
-0.0434107668697834,
0.04389113932847977,
0.0018335584318265319,
0.021391354501247406,
0.0054940516129136086,
0.05741066485643387,
0.04477314278483391,
0.0007851365953683853,
-0.0016845779027789831,
-0.010141776874661446,
0.08067665994167328,
-0.0711788535118103,
0.0048796688206493855,
-0.10230675339698792,
-0.019705139100551605,
0.08723235875368118,
0.040253736078739166,
0.009343842975795269,
-0.008551406674087048,
-0.04850560799241066,
0.025904864072799683,
-0.008525647222995758,
0.04600983113050461,
-0.041115276515483856,
-0.0459783673286438,
-0.011137212626636028,
-0.044854383915662766,
-0.04405057802796364,
0.026921309530735016,
-0.02931196056306362,
-0.054483380168676376,
-0.0025644891429692507,
0.03320271521806717,
0.0013163124676793814,
-0.015876339748501778,
0.053328730165958405,
-0.007529638707637787,
0.03748450055718422,
0.009199090301990509,
-0.03003118373453617,
-0.08434459567070007,
-0.05793766304850578,
0.0713423565030098,
-0.061687223613262177,
0.03071022219955921,
-0.015694160014390945,
-0.013745542615652084,
0.05143676698207855,
0.020605597645044327,
0.040507372468709946,
-0.051624394953250885,
0.0446523055434227,
0.015468086116015911,
0.029536250978708267,
0.045310065150260925,
-0.04749636724591255,
0.05119996890425682,
-0.006440259516239166,
-0.030025266110897064,
0.00963057391345501,
-0.009411115199327469,
0.027496585622429848,
0.015994960442185402,
0.04152506962418556,
0.0007594246417284012,
0.001086850999854505,
-0.030133020132780075,
0.006256542634218931,
-0.0010161129757761955,
-0.04505771026015282,
0.009360572323203087,
-0.002707474632188678,
0.0070708435960114,
-0.0031623432878404856,
-0.018832843750715256,
-0.0028400178998708725,
0.042891986668109894,
-0.04122190549969673,
-0.015568927861750126,
0.06322620064020157,
0.0553114227950573,
0.017819233238697052,
-0.0031367535702884197,
0.07177338004112244,
-0.0037494718562811613,
0.048243116587400436,
0.0467141829431057,
0.038983721286058426,
0.03619450330734253,
0.0403730608522892,
-0.009669508785009384,
-0.04251057282090187,
0.02669205516576767,
-0.0626390129327774,
0.01792236603796482,
-0.06446859240531921,
-0.06493059545755386,
0.04313221201300621,
0.038527682423591614,
-0.07083320617675781,
0.004704041872173548,
0.01959407888352871,
0.02809651382267475,
-0.09051955491304398,
-0.018192045390605927,
-0.028308626264333725,
0.04329369217157364,
0.01538031455129385,
-0.0015092864632606506,
0.02103308215737343,
-0.011931930668652058,
0.020334366708993912,
-0.0860585942864418,
-0.023314040154218674,
-0.0020157883409410715,
0.03246237337589264,
0.047007519751787186,
0.007314309943467379,
0.013930543325841427,
-0.013905130326747894,
0.01401706412434578,
-0.008679495193064213,
-0.039400383830070496,
0.019700095057487488,
-0.002547899493947625,
-0.013830365613102913,
-0.010758919641375542,
-0.04423161596059799,
-0.017887039110064507,
-0.04139651358127594,
-0.06716086715459824,
0.03506971150636673,
0.015098419040441513,
0.023969992995262146,
-0.013119840994477272,
-0.04838744178414345,
0.0036573437973856926,
-0.010562006384134293,
0.06319348514080048,
0.02864179201424122,
0.0556260421872139,
0.017538174986839294,
0.010736752301454544,
-0.0026199312414973974,
0.0030771500896662474,
0.009421243332326412,
0.10539030283689499,
-0.012420757673680782,
0.02811034396290779,
-0.04121420904994011,
-0.03414269909262657,
-0.028792236000299454,
0.02437819354236126,
-0.005396127700805664,
-0.04819364473223686,
-0.050383396446704865,
0.06883372366428375,
0.001395330997183919,
0.04453136771917343,
0.03184041380882263,
-0.06244584545493126,
-0.045082032680511475,
0.040388789027929306,
-0.0047048176638782024,
-0.002893045311793685,
0.01206154003739357,
0.05511971190571785,
-0.0489768460392952,
0.0020635384134948254,
-0.01041756197810173,
0.01590568944811821,
0.002883264562115073,
0.03963616117835045,
0.0016016741283237934,
0.039002276957035065,
-0.0020250945817679167,
-0.014369487762451172,
-0.006345088128000498,
-0.010166705586016178,
-0.0012706738198176026,
-0.010472665540874004,
-0.051410406827926636,
0.07752614468336105,
-0.08342251181602478,
-0.014978257939219475,
-0.05148390680551529,
-0.051062263548374176,
-0.015142458491027355,
-0.021354693919420242,
0.023646052926778793,
0.05743929743766785,
0.007049106992781162,
-0.033246904611587524,
0.02229456603527069,
0.015616713091731071,
0.028934616595506668,
0.048177193850278854,
0.03142452985048294,
-0.022521208971738815,
0.013546636328101158,
-0.055973540991544724,
0.04674370214343071,
0.06968673318624496,
0.01592266373336315,
-0.03768238425254822,
0.00214011431671679,
-0.014825032092630863,
0.0005802314844913781,
0.025727959349751472,
0.06648347526788712,
0.008621200919151306,
0.002862800844013691,
0.011366499587893486,
-0.03281223773956299,
0.04126683622598648,
-0.019926104694604874,
0.03824369236826897,
-0.03973639756441116,
0.003235124982893467,
0.06315319240093231,
-0.03884449228644371,
-0.08198241889476776,
0.014413258992135525,
0.05272059887647629,
-0.0008240308379754424,
-0.059757597744464874,
0.007400039583444595,
0.031907737255096436,
-0.021627625450491905,
0.02746795490384102,
0.018526582047343254,
-0.023403607308864594,
-0.0059754676185548306,
0.07320298999547958,
0.021636685356497765,
-0.0066132619976997375,
-0.021620089188218117,
-0.012802020646631718,
0.012653592973947525,
-0.03407435491681099,
-0.014660879038274288,
-0.00035821273922920227,
0.012328739278018475,
0.043947216123342514,
0.013908685185015202,
0.07282216846942902,
-0.043096620589494705,
-0.0017348065739497542,
-0.00031396624399349093,
-0.0003736645739991218,
0.032911840826272964,
0.0007290098583325744,
-0.016438696533441544,
-0.012518482282757759,
0.04327334463596344,
-0.018029559403657913,
-0.010768791660666466,
-0.01715267077088356,
-0.0171820055693388,
-0.039260391145944595,
-0.0030152853578329086,
-0.021120905876159668,
0.043609265238046646,
0.031192168593406677,
0.06140616908669472,
-0.012426731176674366,
-0.0016912971623241901,
0.011876074597239494,
-0.009643349796533585,
0.003825081279501319,
-0.08845783025026321,
-0.037784822285175323,
-0.008859614841639996,
0.03936218097805977,
0.02734438329935074,
0.050220999866724014,
0.019855018705129623,
0.00119861401617527,
-0.02907085046172142,
-0.030577687546610832,
-0.08000902831554413,
0.009752653539180756,
0.004667958244681358,
-0.03556187078356743,
-0.04996556043624878,
-0.012319670058786869,
0.032427866011857986,
-0.0009269926813431084,
-0.0034068734385073185,
-0.04104180634021759,
-0.01695845276117325,
-0.03185074031352997,
-0.0434538833796978,
0.015628255903720856,
0.019335879012942314,
-0.006585828959941864,
0.05153147131204605,
-0.05600760877132416,
-0.03110594116151333,
-0.0466461107134819,
0.027578772976994514,
0.0395684614777565,
-0.036444924771785736,
-0.03904511034488678,
0.049812201410532,
-0.027976827695965767,
0.04474085941910744,
0.01930065080523491,
-0.06141374632716179,
-0.06298910826444626,
0.047931332141160965,
-0.010450897738337517,
-0.007355062291026115,
-0.02958948165178299,
-0.04087666794657707,
-0.0009767484152689576,
0.007340394891798496,
-0.003261648351326585,
-0.07104777544736862,
-0.027752475813031197,
-0.04263580963015556,
0.03781929239630699,
-0.04716061055660248,
0.020533401519060135,
0.009642357937991619,
0.03605607524514198,
-0.04359535127878189,
0.031244713813066483,
0.04232190549373627,
-0.022150589153170586,
0.015432897955179214,
0.05531385540962219,
0.007081968709826469,
0.03788609802722931,
0.01936919242143631,
0.04452335834503174,
-0.03228963911533356,
-0.013650084845721722,
0.0020014378242194653,
-0.04799114167690277,
-0.00615781731903553,
-0.0450722798705101,
-0.041760873049497604,
0.018040694296360016,
0.01453813724219799
] |
<p>See Griffiths Quantum Mechanics, eq. 11.21. Evidently,
$$\psi(r,\theta,\phi)=Ae^{ikz}+A\sum\limits_{l,m}^{\infty}C_{l,m}h_{l}(kr)Y_{l}^{m}(\theta,\phi).$$
But I don't see why the $l$th Hankel function necessarily needs to multiply the $l$th spherical harmonic. Seeing as we arrived at this equation through separation of variables, my feeling is that the equation should look something like:
$$\psi(r,\theta,\phi)=Ae^{ikz}+A\sum\limits_{l,m,n}^{\infty}C_{l,m,n}h_{n}(kr)Y_{l}^{m}(\theta,\phi).$$</p> | g1302 | [
-0.007836478762328625,
-0.0047269645147025585,
-0.013769557699561119,
-0.04105312377214432,
-0.002007295610383153,
-0.05889754742383957,
0.0018740749219432473,
-0.005365015938878059,
-0.013370014727115631,
0.00909577589482069,
-0.03200802206993103,
-0.056571222841739655,
0.042567238211631775,
0.00341550400480628,
0.056656837463378906,
-0.04456279054284096,
0.019339196383953094,
0.04022888466715813,
-0.030811240896582603,
-0.0001668027398409322,
-0.03657323494553566,
-0.0012706281850114465,
-0.007902933284640312,
-0.050628162920475006,
0.06872130930423737,
-0.00866943970322609,
0.007047479506582022,
0.012212339788675308,
-0.011939292773604393,
0.02949979342520237,
0.043905045837163925,
0.04098045080900192,
0.03195631131529808,
-0.07923230528831482,
-0.046089135110378265,
0.04217561334371567,
0.07752357423305511,
0.03853107988834381,
0.02017548680305481,
-0.017948422580957413,
-0.00359150767326355,
-0.03613067790865898,
0.06812489777803421,
0.02807038091123104,
0.011930000968277454,
0.057544268667697906,
0.0185627993196249,
0.05420905724167824,
-0.029325498268008232,
-0.018969684839248657,
0.03001163713634014,
-0.006458871532231569,
0.03557054325938225,
0.011533414013683796,
0.012503414414823055,
-0.0013969114515930414,
0.08315158635377884,
-0.0525771826505661,
0.016247984021902084,
0.06948237866163254,
-0.0013296332908794284,
-0.011231708340346813,
-0.04836105555295944,
0.011606840416789055,
0.025245608761906624,
-0.05465489998459816,
-0.026952892541885376,
-0.041678234934806824,
-0.008945581503212452,
-0.00004431654087966308,
-0.00640108110383153,
-0.0440380796790123,
0.025633852928876877,
-0.011493884027004242,
-0.02082623913884163,
0.03160359337925911,
0.01852918602526188,
-0.010174989700317383,
0.06901228427886963,
0.002077532932162285,
0.004405831918120384,
0.006423694081604481,
0.05050709471106529,
-0.007644167169928551,
-0.026323534548282623,
-0.015738606452941895,
-0.01763097755610943,
-0.06522663682699203,
-0.020082442089915276,
0.01882212609052658,
0.06783564388751984,
-0.01592358388006687,
0.007038537412881851,
0.011676519177854061,
-0.06522523611783981,
-0.045758165419101715,
0.014129452407360077,
0.003695826278999448,
-0.03027675487101078,
-0.01488650031387806,
-0.02182919532060623,
0.01734291762113571,
0.054319482296705246,
-0.04507233947515488,
0.031010866165161133,
0.01617315784096718,
-0.017900686711072922,
0.02680978924036026,
0.016204731538891792,
-0.00240166368894279,
-0.01642574742436409,
0.04737868160009384,
0.023723222315311432,
-0.004426511470228434,
-0.05116915702819824,
-0.02347586303949356,
0.046984780579805374,
-0.027711285278201103,
0.0024703145027160645,
0.051544442772865295,
0.025807233527302742,
0.01821482926607132,
0.055337436497211456,
0.0033523296006023884,
-0.040276847779750824,
0.0014083250425755978,
0.035885024815797806,
-0.00889632012695074,
0.060857608914375305,
-0.05320447310805321,
0.032957375049591064,
0.015865007415413857,
0.002432780573144555,
0.011777601204812527,
-0.002182058524340391,
-0.020245444029569626,
-0.004026716575026512,
-0.010290919803082943,
-0.017547843977808952,
0.027840448543429375,
-0.016630660742521286,
-0.06376590579748154,
0.05066344514489174,
0.004134249873459339,
-0.008170035667717457,
0.03350824490189552,
0.004312497563660145,
-0.03824426606297493,
-0.0039055217057466507,
-0.030214941129088402,
-0.026814701035618782,
0.0406486913561821,
0.028710024431347847,
0.03741912916302681,
0.01883537322282791,
0.01754605770111084,
0.0546940453350544,
-0.0332767553627491,
0.003789179492741823,
-0.01568569988012314,
-0.009922878816723824,
-0.007479644380509853,
0.03378545492887497,
-0.00018963118782266974,
-0.043334681540727615,
0.08884722739458084,
-0.033750083297491074,
0.011870095506310463,
-0.0494060143828392,
-0.05209790915250778,
-0.002426228718832135,
-0.011138414032757282,
0.04180114343762398,
0.014057698659598827,
-0.00048407563008368015,
0.037154071033000946,
-0.014407284557819366,
0.004863137844949961,
-0.04266070947051048,
0.031573228538036346,
0.01060385163873434,
-0.004337175749242306,
0.03323158249258995,
-0.05703798308968544,
0.023965615779161453,
-0.01550610363483429,
-0.007572630885988474,
-0.014608637429773808,
-0.028548071160912514,
0.0413999930024147,
0.029713060706853867,
0.068829745054245,
-0.013033806346356869,
0.045413583517074585,
0.02275730110704899,
0.08228914439678192,
0.01343848928809166,
-0.07513920962810516,
-0.07168897241353989,
0.06964456290006638,
0.0013733857776969671,
0.0421258807182312,
0.043562036007642746,
-0.0009911339730024338,
0.010555473156273365,
0.04774629697203636,
-0.0189413633197546,
0.0024805949069559574,
-0.0040258136577904224,
-0.008043362759053707,
0.026559505611658096,
-0.060123320668935776,
0.023519979789853096,
0.02258935756981373,
0.015227265655994415,
-0.03570307046175003,
0.029506497085094452,
0.005705359857529402,
0.009926063939929008,
0.010071001946926117,
-0.03688512369990349,
0.003606945974752307,
0.021741490811109543,
-0.03971264883875847,
-0.04403187707066536,
0.007526479661464691,
-0.022605866193771362,
-0.02981560118496418,
-0.023894215002655983,
0.0045546963810920715,
0.0011748954420909286,
-0.0144923971965909,
-0.01631109043955803,
0.002882070140913129,
-0.04225816950201988,
0.011631162837147713,
-0.035919494926929474,
0.0038646894972771406,
-0.007568299304693937,
0.04944291710853577,
0.00010320518049411476,
-0.014123720116913319,
0.020260173827409744,
0.04005200415849686,
0.011664855293929577,
0.056489065289497375,
0.0296018123626709,
-0.03303368762135506,
-0.039385996758937836,
-0.001074633444659412,
0.024028077721595764,
-0.040865831077098846,
-0.028501519933342934,
0.049676090478897095,
-0.011459686793386936,
-0.029368605464696884,
-0.03535110503435135,
0.029735231772065163,
-0.029025308787822723,
-0.0099583575502038,
-0.02107936702668667,
0.002770861843600869,
0.014751384034752846,
0.024677248671650887,
-0.0542372465133667,
0.03981435298919678,
0.007105275522917509,
0.06428257375955582,
0.006066333968192339,
-0.05169901251792908,
-0.04253939166665077,
0.11421258747577667,
0.02765067294239998,
0.04303585737943649,
-0.02599470689892769,
-0.04989026114344597,
-0.0519513301551342,
0.025905674323439598,
0.06860026717185974,
0.0018504014005884528,
-0.04039204493165016,
-0.014156264252960682,
0.0053457822650671005,
0.03901683911681175,
0.008114004507660866,
-0.08156435191631317,
0.03008861094713211,
0.06332828849554062,
0.04311232641339302,
-0.003842009464278817,
-0.076030433177948,
0.016772843897342682,
0.004403394181281328,
-0.005368417128920555,
0.003992459271103144,
0.008157528005540371,
0.03976329788565636,
-0.04461986571550369,
0.0031211620662361383,
0.07348812371492386,
0.03712863102555275,
-0.03300876542925835,
-0.03153225779533386,
0.04302895441651344,
0.01813546195626259,
0.0153906075283885,
-0.037283819168806076,
-0.062363456934690475,
-0.02045498974621296,
0.0516706258058548,
0.06006985530257225,
-0.003673885017633438,
0.004590596072375774,
-0.037206754088401794,
-0.04596439749002457,
0.024003827944397926,
-0.05550370737910271,
-0.057140324264764786,
-0.008062802255153656,
0.03242984041571617,
-0.025928344577550888,
-0.07017779350280762,
-0.021171044558286667,
0.005907475017011166,
0.006550065241754055,
0.008408508263528347,
-0.07365766167640686,
-0.0745558813214302,
-0.03375925496220589,
-0.051469508558511734,
-0.04012584313750267,
-0.006386150605976582,
0.030282627791166306,
0.009318455122411251,
-0.027302877977490425,
-0.014262204989790916,
-0.021679257974028587,
0.004564572125673294,
0.0025628015864640474,
0.004193578846752644,
-0.006226981524378061,
-0.029310908168554306,
-0.0012874930398538709,
0.028712615370750427,
-0.009539265185594559,
-0.009385522454977036,
-0.08416636288166046,
0.05926388502120972,
0.04153712838888168,
0.0008921836270019412,
0.000158235096023418,
0.0038562414702028036,
0.0246640183031559,
-0.0067911711521446705,
0.02513190731406212,
-0.017472542822360992,
0.045913781970739365,
0.045719921588897705,
0.00342037295922637,
-0.02338796854019165,
0.06223965436220169,
0.010736772790551186,
-0.00004867877214564942,
-0.011566872708499432,
-0.004271929617971182,
-0.032149966806173325,
0.06274943053722382,
0.05761975049972534,
-0.014987013302743435,
-0.06677881628274918,
-0.029216375201940536,
0.02106364816427231,
-0.0376347117125988,
0.010617326013743877,
0.04962603747844696,
-0.06711161136627197,
0.04469677433371544,
-0.009432599879801273,
-0.0010739851277321577,
0.01066623441874981,
0.0003978686290793121,
-0.024354318156838417,
-0.047579146921634674,
0.021631354466080666,
0.04341553896665573,
-0.009652853012084961,
-0.032582130283117294,
0.014626306481659412,
-0.0016928912373259664,
-0.01741296611726284,
0.015012675896286964,
-0.06789687275886536,
-0.018005449324846268,
-0.01579248532652855,
-0.032994505017995834,
-0.00875296350568533,
0.04629241302609444,
-0.0009294350165873766,
-0.040273260325193405,
0.04815421253442764,
-0.046005334705114365,
-0.019569629803299904,
0.001491472707130015,
-0.010898711159825325,
0.0008672525291331112,
-0.00521307485178113,
0.06408927589654922,
-0.011068015359342098,
0.020978808403015137,
-0.007675405591726303,
0.00835530087351799,
-0.0548672154545784,
0.023709628731012344,
-0.06215581297874451,
0.041318219155073166,
-0.045867543667554855,
0.01357709988951683,
-0.02399217151105404,
-0.023172803223133087,
0.014545134268701077,
-0.06469160318374634,
-0.015277677215635777,
0.020444991067051888,
0.010909593664109707,
0.055763088166713715,
0.007322657387703657,
0.057328756898641586,
0.05560838431119919,
-0.052182938903570175,
-0.13803459703922272,
-0.016110777854919434,
0.013196034356951714,
0.0032042241655290127,
-0.0012876057298853993,
-0.04342293366789818,
0.027728186920285225,
-0.03891410678625107,
0.0186326801776886,
-0.03895019739866257,
-0.02420976012945175,
0.019994065165519714,
0.027262326329946518,
0.027225999161601067,
0.008625947870314121,
0.022558825090527534,
-0.017848750576376915,
-0.04433564469218254,
-0.10448886454105377,
-0.0065304869785904884,
-0.022243451327085495,
-0.00764673063531518,
-0.049968551844358444,
0.0048411027528345585,
0.010933834128081799,
0.013555124402046204,
-0.04490235075354576,
-0.026473555713891983,
0.027218254283070564,
0.0031202055979520082,
0.01751374453306198,
-0.04495055228471756,
-0.008032433688640594,
-0.04345841333270073,
-0.0225836131721735,
0.050284791737794876,
0.003962620627135038,
-0.0699140876531601,
0.0034538330510258675,
-0.017791012302041054,
-0.0016498835757374763,
-0.014688551425933838,
0.020225072279572487,
0.06441660970449448,
-0.01601451449096203,
-0.02239745669066906,
-0.021511096507310867,
-0.01661784201860428,
0.022856218740344048,
-0.041878774762153625,
-0.03926386311650276,
-0.013653518632054329,
-0.028630724176764488,
0.018634816631674767,
0.056263718754053116,
-0.03310905769467354,
0.03817984089255333,
0.02003561332821846,
-0.052308518439531326,
-0.02744074910879135,
0.007223851978778839,
0.007898015901446342,
0.014820761978626251,
0.0012386483140289783,
0.03776866942644119,
0.005710248835384846,
-0.019878404214978218,
0.02383940853178501,
-0.054872721433639526,
-0.016076264902949333,
0.06863285601139069,
-0.02798365242779255,
0.019232874736189842,
-0.04739144444465637,
0.010034245438873768,
0.00492443609982729,
0.024761291220784187,
0.05064374580979347,
0.030717717483639717,
0.008668790571391582,
0.010599380359053612,
0.021074211224913597,
-0.04316806420683861,
0.028889643028378487,
-0.001004309393465519,
-0.004542097449302673,
-0.007025419734418392,
-0.02240649238228798,
0.023061759769916534,
-0.011898927390575409,
0.007494811899960041,
0.07035773247480392,
0.0005720095941796899,
-0.06945160776376724,
-0.03732873871922493,
0.0039842440746724606,
0.059014007449150085,
-0.0194307342171669,
-0.047329917550086975,
-0.027147527784109116,
0.011702774092555046,
-0.008301455527544022,
-0.05961945280432701,
-0.0240183062851429,
0.004850153811275959,
0.07319609820842743,
0.00004564780101645738,
0.002595366910099983,
0.0016233969945460558,
0.04469172656536102,
0.008374329656362534,
-0.03848087042570114,
-0.06025843322277069,
0.0333021804690361,
0.02791891060769558,
-0.0302234198898077,
-0.02435496263206005,
0.03741440922021866,
0.009542078711092472,
-0.003866120707243681,
0.040329281240701675,
-0.09481611102819443,
-0.03487634286284447,
0.006235240958631039,
0.035104066133499146,
-0.007334606721997261,
-0.005296962335705757,
0.04732286185026169,
-0.03475961089134216,
-0.04483972489833832,
0.015608735382556915,
0.03294345363974571,
-0.009760853834450245,
0.007580080069601536,
0.029892506077885628,
0.04074690863490105,
-0.027962082996964455,
-0.018545813858509064,
-0.01152479462325573,
0.08640997111797333,
0.019693532958626747,
-0.08857443928718567,
0.025760592892766,
0.02721838280558586,
0.02236209250986576,
0.06258049607276917,
0.03091215342283249,
-0.03116409108042717,
-0.02810828387737274,
0.01980953849852085,
-0.008151134476065636,
-0.01565377227962017,
-0.005688266362994909,
0.03292778506875038,
-0.06858009099960327,
-0.012573027983307838,
0.05106233060359955,
-0.024301841855049133,
-0.023890389129519463,
0.07734501361846924,
0.02970714308321476,
-0.009622359648346901,
0.00151800864841789,
-0.016976919025182724,
0.012070123106241226,
0.006777354050427675,
0.006950946059077978,
0.031398069113492966,
0.0010280192364007235,
-0.012948856689035892,
-0.0423278734087944,
0.06410481780767441,
-0.0058474051766097546,
0.048019200563430786,
-0.014474141411483288,
0.048194561153650284,
0.006311980541795492,
-0.035094570368528366,
-0.025576816871762276,
-0.02277757227420807,
0.04628830775618553,
0.034239742904901505,
0.016931254416704178,
0.058186888694763184,
-0.007530723698437214,
0.01518341340124607,
-0.04510829970240593,
0.012425407767295837,
0.06479872763156891,
-0.020532557740807533,
-0.012869026511907578,
0.07256755977869034,
0.012875237502157688,
0.001462948159314692,
0.01120931189507246,
0.08754724264144897,
-0.004119073040783405,
-0.018725844100117683,
0.005127732176333666,
-0.01314946636557579,
0.00023470095766242594,
0.037906501442193985,
0.0344330333173275,
-0.020861973986029625,
0.02048901654779911,
-0.029489008709788322,
-0.023482564836740494,
-0.05420910194516182,
-0.016249854117631912,
-0.023398157209157944,
0.062142834067344666,
-0.036184802651405334,
0.03740842640399933,
0.06537836790084839,
-0.0019299972336739302,
-0.09527873992919922,
0.026313303038477898,
0.09785996377468109,
-0.019821256399154663,
-0.17489725351333618,
0.0007426787633448839,
0.009483699686825275,
0.005565929692238569,
-0.04815158620476723,
0.027223721146583557,
-0.011010954156517982,
-0.02945396676659584,
-0.006039401516318321,
-0.0036346737761050463,
0.06493790447711945,
-0.021025685593485832,
0.00011492390331113711,
0.02553584799170494,
0.03021583892405033,
-0.012231593951582909,
0.0081716887652874,
0.07967060059309006,
0.022566134110093117,
-0.053754016757011414,
0.042853862047195435,
-0.02713826671242714,
0.03799964487552643,
0.04259364679455757,
-0.04181867837905884,
-0.05592062696814537,
-0.00327598350122571,
-0.004124696832150221,
0.012948364950716496,
-0.030140554532408714,
-0.006197001319378614,
0.012609966099262238,
-0.03748747706413269,
0.00032365642255172133,
-0.0044256336987018585,
-0.0032720412127673626,
-0.015944428741931915,
-0.01736786589026451,
-0.008467761799693108,
-0.0315745584666729,
0.05800121650099754,
0.05855099856853485,
-0.03348470479249954,
0.018429027870297432,
-0.015308516100049019,
0.024317076429724693,
-0.0028733150102198124,
0.043203625828027725,
0.04964101314544678,
0.014541501179337502,
0.027118181809782982,
0.05309305340051651,
0.013432684354484081,
-0.03977375105023384,
0.020625777542591095,
-0.009221481159329414,
0.005793434102088213,
0.014074994251132011,
-0.031331662088632584,
-0.03155280649662018,
-0.0015802239067852497,
0.043936531990766525,
-0.001822464051656425,
-0.003123786300420761,
-0.03700481727719307,
0.07454375922679901,
0.05100538209080696,
-0.011800904758274555,
-0.04258773848414421,
0.04374216869473457,
0.0071215033531188965,
-0.10517764091491699,
-0.026033056899905205,
-0.0007386297802440822,
0.00012865805183537304,
-0.047319233417510986,
0.01991107314825058,
-0.03187616541981697,
0.023977141827344894,
-0.025562988594174385,
0.0010320410365238786,
-0.013894932344555855,
-0.07427310198545456,
-0.029194850474596024,
-0.017008645460009575,
-0.002326095709577203,
-0.044070255011320114,
-0.0048768175765872,
-0.009174513630568981,
-0.0198080912232399,
0.05156583711504936,
-0.004537463188171387,
-0.014701946638524532,
-0.03965609893202782,
0.03998879715800285,
-0.001613563159480691,
-0.046174511313438416,
-0.024182802066206932,
-0.06049080565571785,
0.004678812343627214,
0.09398531168699265,
0.01837925985455513,
0.024101806804537773,
0.03192558512091637,
-0.02595810778439045,
0.05523776262998581,
0.019038556143641472,
-0.07513655722141266,
0.04656216502189636,
0.050680991262197495,
-0.020717043429613113,
-0.018180381506681442,
-0.012700931169092655,
-0.057716552168130875,
0.0221327543258667,
0.061325956135988235,
0.03612082079052925,
-0.06328524649143219,
-0.014375939033925533,
0.006296477746218443
] |
<ul>
<li><p>How does unitarity require that every scalar operator in a $2+1$ SCFT will have to have a scaling dimension $\geq \frac{1}{2}$ ? </p></li>
<li><p>Why is an operator with scaling dimension exactly equal to $\frac{1}{2}$ said to be "free (i.e decoupled from the rest of the theory)" ? </p></li>
<li><p>Let us say that we know in some such theory the R-charge is monotonically decreasing with increasing coupling constant (say $\lambda$). Then define $\lambda _n ^f$ to be that value of the coupling constant at which the R-charge of the operator $Tr[\phi ^n]$ becomes $= \frac{1}{2n}$. Let $\lambda _n ^m$ be that that value of the coupling at which the R-charge of the same operator becomes $= \frac{2}{n}$ (..marginal ?..) Then clearly $\lambda _n ^m < \lambda_n ^f$. </p></li>
</ul>
<p>How does this imply that there has to exist a $\lambda _c \leq \lambda_2^f$ where the theory might undergo a phase transition? </p> | g1303 | [
0.015784308314323425,
0.02577885240316391,
-0.0038518444634974003,
0.009433528408408165,
0.022594884037971497,
0.010117126628756523,
0.021315358579158783,
0.06285563856363297,
-0.01171428058296442,
0.017514897510409355,
-0.04527369886636734,
-0.0022182392422109842,
-0.004693074617534876,
0.04634984955191612,
-0.019356800243258476,
-0.008761681616306305,
0.02167254313826561,
0.0076365103013813496,
0.002761803800240159,
-0.009971252642571926,
-0.05435917153954506,
0.038868505507707596,
0.01844860054552555,
-0.051420845091342926,
0.032299965620040894,
-0.029313573613762856,
0.05017849802970886,
0.025596927851438522,
-0.04174519702792168,
-0.0735214576125145,
0.06667444109916687,
0.013199485838413239,
0.020722048357129097,
-0.033938292413949966,
-0.02454525977373123,
-0.024429619312286377,
0.07385127991437912,
0.04553058370947838,
0.02557741105556488,
0.028399789705872536,
0.005242092069238424,
-0.005722798407077789,
-0.001661305082961917,
-0.018746819347143173,
-0.060274120420217514,
-0.015807420015335083,
-0.024873467162251472,
0.010616965591907501,
-0.011181025765836239,
0.0263667032122612,
0.020375261083245277,
0.03158175200223923,
0.006022071931511164,
-0.00139894662424922,
-0.06517866253852844,
0.01058052759617567,
-0.016517193987965584,
0.008272458799183369,
0.03101084753870964,
0.04237851873040199,
0.001053197425790131,
0.026650091633200645,
0.010912751778960228,
0.010420423932373524,
0.0579775832593441,
0.015360753983259201,
0.02007474936544895,
-0.03630201518535614,
0.006754075177013874,
-0.052658624947071075,
-0.005667287390679121,
-0.07224156707525253,
-0.011139016598463058,
0.05294693633913994,
0.00997389666736126,
-0.04681360721588135,
0.006460107397288084,
0.005369172431528568,
-0.00037650420563295484,
-0.03234785422682762,
-0.06892003118991852,
-0.053781650960445404,
0.02894613891839981,
0.044965676963329315,
0.03450578451156616,
0.01613115519285202,
0.04203834757208824,
0.015533261001110077,
-0.0007942164083942771,
0.09027493000030518,
0.016991330310702324,
-0.04158656299114227,
0.008224588818848133,
0.0028266985900700092,
0.012044856324791908,
-0.050733983516693115,
0.00870261900126934,
-0.0017063554842025042,
0.006997105199843645,
-0.06505093723535538,
-0.011507495306432247,
0.06454147398471832,
0.06673119217157364,
0.009369846433401108,
-0.019864343106746674,
0.06598124653100967,
-0.008530760183930397,
0.01027370523661375,
0.038886990398168564,
-0.003053569933399558,
-0.057457685470581055,
0.025335311889648438,
-0.02139795571565628,
-0.0015117318835109472,
0.020013734698295593,
0.0390930250287056,
0.07149997353553772,
-0.09495667368173599,
0.010753986425697803,
-0.03685210645198822,
-0.013620112091302872,
0.014007801190018654,
0.04417380690574646,
0.011649200692772865,
-0.03880582004785538,
0.05059466138482094,
0.042236387729644775,
-0.0019133217865601182,
0.00242143077775836,
0.007968968711793423,
0.04223194718360901,
-0.02018638141453266,
-0.05600355938076973,
0.016199609264731407,
0.05932571366429329,
0.013624532148241997,
-0.018715323880314827,
0.008619769476354122,
0.024065988138318062,
-0.015283285640180111,
-0.0549514964222908,
-0.03238973766565323,
0.0006676349439658225,
0.005553971044719219,
0.001256925635971129,
-0.039537545293569565,
-0.015364578925073147,
-0.022209303453564644,
-0.006439617834985256,
0.01667323149740696,
-0.009131869301199913,
0.08248230069875717,
0.0016686036251485348,
-0.056010857224464417,
-0.0030608498491346836,
-0.005810177884995937,
0.06584006547927856,
0.0003905559715349227,
0.007281160447746515,
-0.09282397478818893,
0.02072838507592678,
0.022607212886214256,
-0.0035257108975201845,
0.016560539603233337,
-0.035457342863082886,
-0.020779570564627647,
-0.00558929517865181,
-0.03859651833772659,
0.023626836016774178,
-0.02960626780986786,
0.012898906134068966,
0.05189644172787666,
0.045324407517910004,
0.07202179729938507,
0.02777562290430069,
0.08135122060775757,
-0.018614940345287323,
0.03167007490992546,
-0.030238253995776176,
0.03529094159603119,
-0.050467487424612045,
-0.014744284562766552,
0.0390469953417778,
-0.05242643505334854,
0.04943002387881279,
-0.019272487610578537,
0.010891985148191452,
0.034226980060338974,
0.030317725613713264,
-0.008763979189097881,
-0.032377690076828,
-0.004414443392306566,
0.007553699892014265,
0.028463756665587425,
0.007515202276408672,
-0.007058179005980492,
0.01460621040314436,
-0.026027558371424675,
-0.010388236492872238,
-0.04868043214082718,
0.005744764115661383,
-0.00015626738604623824,
-0.0403473936021328,
-0.011796964332461357,
0.019942227751016617,
-0.004974964074790478,
-0.070362389087677,
0.050008635967969894,
0.01741732284426689,
0.0031600031070411205,
-0.01928522251546383,
-0.062422510236501694,
0.0060769012197852135,
0.02017315849661827,
-0.01019605528563261,
-0.010829201899468899,
0.033926013857126236,
-0.04561027139425278,
-0.07464274019002914,
0.03497447445988655,
0.04301212355494499,
0.015378178097307682,
0.06870242953300476,
0.027518177404999733,
0.03276108577847481,
0.0064960867166519165,
-0.024754030629992485,
0.025190843269228935,
-0.003417019499465823,
-0.0029432298615574837,
-0.043151017278432846,
0.0645596981048584,
-0.016338763758540154,
-0.0352296382188797,
-0.016928767785429955,
0.0305262953042984,
0.0018466990441083908,
-0.015265552327036858,
-0.0033503971062600613,
0.018438920378684998,
0.04807664453983307,
0.02983521856367588,
0.00041036782204173505,
-0.012412292882800102,
0.00936606153845787,
-0.026611635461449623,
0.03978705406188965,
0.039740342646837234,
-0.09760144352912903,
0.002356343436986208,
-0.04500986635684967,
-0.0038691465742886066,
-0.01873224414885044,
0.01934056542813778,
-0.055195532739162445,
0.02683352679014206,
0.0825701430439949,
0.013485495932400227,
-0.029316721484065056,
-0.04816040024161339,
0.052912637591362,
0.042456693947315216,
0.002994765294715762,
0.019185403361916542,
-0.06008831039071083,
0.013747302815318108,
-0.016984205693006516,
0.06925603747367859,
-0.015459948219358921,
-0.02662798948585987,
0.03626815229654312,
0.0704893246293068,
-0.005965508986264467,
0.03459863364696503,
0.00454871729016304,
0.007196767721325159,
0.010183666832745075,
-0.012814987450838089,
0.056854404509067535,
-0.01722005568444729,
-0.01083975937217474,
-0.007731347810477018,
-0.03454902395606041,
0.030057888478040695,
0.021305933594703674,
-0.027982128784060478,
-0.019579371437430382,
0.03303101658821106,
-0.009860098361968994,
0.010192523710429668,
0.03554338961839676,
0.027779752388596535,
-0.006229826249182224,
-0.028086727485060692,
0.05345657840371132,
-0.018262892961502075,
0.016420066356658936,
-0.05305005982518196,
-0.056000716984272,
0.010109076276421547,
0.005070922896265984,
-0.03890252858400345,
0.0546480268239975,
-0.020302290096879005,
0.0007207933813333511,
0.030804431065917015,
-0.03174963220953941,
-0.02933727391064167,
-0.06540845334529877,
0.011564848013222218,
-0.03159894794225693,
0.10290918499231339,
0.009666712023317814,
-0.0389292947947979,
-0.008296268992125988,
-0.04419330880045891,
0.04345983639359474,
0.05925614386796951,
-0.0061470018699765205,
-0.04688185825943947,
0.005656253080815077,
-0.012728923000395298,
-0.002375183627009392,
-0.014150171540677547,
-0.05050831288099289,
0.014807711355388165,
-0.070345439016819,
0.0021673827432096004,
-0.04565946012735367,
-0.005487583111971617,
0.03613600879907608,
0.012986946851015091,
0.06978856772184372,
0.0038561264518648386,
-0.0603267177939415,
0.008482846431434155,
-0.0362614169716835,
-0.05144410952925682,
0.04664335027337074,
0.007375782821327448,
-0.018240911886096,
-0.022059451788663864,
-0.06012320518493652,
-0.016397526487708092,
-0.037311118096113205,
0.002085468266159296,
-0.003342896932736039,
-0.02545480616390705,
0.024175724014639854,
-0.028512338176369667,
-0.03262454271316528,
-0.0013434094144031405,
0.04113529250025749,
-0.028557315468788147,
0.017047910019755363,
0.02804878167808056,
0.07353624701499939,
0.07438068836927414,
-0.044273070991039276,
0.005234865006059408,
-0.001542608137242496,
-0.05602244660258293,
0.02363947220146656,
0.024881597608327866,
-0.011860695667564869,
0.017464328557252884,
0.009609727188944817,
0.034277964383363724,
0.0034521191846579313,
0.0028988285921514034,
0.000490149890538305,
0.045752257108688354,
-0.02620064839720726,
0.04240453988313675,
-0.030259910970926285,
-0.039487820118665695,
0.03252049908041954,
0.001768617075867951,
0.038089703768491745,
0.024010132998228073,
0.030407056212425232,
0.07517919689416885,
-0.03154274448752403,
-0.0522073395550251,
0.032455164939165115,
-0.0055283717811107635,
-0.03346611186861992,
-0.011144207790493965,
-0.009806266985833645,
-0.04403665289282799,
-0.020675895735621452,
-0.042336154729127884,
-0.004600533749908209,
-0.02034809999167919,
0.020727613940835,
-0.001472671632654965,
0.037253111600875854,
0.008170773275196552,
0.01641896553337574,
0.03175319731235504,
0.05868542194366455,
-0.06175478175282478,
0.027495427057147026,
-0.03463423252105713,
-0.014728643000125885,
-0.01884394697844982,
0.018980644643306732,
-0.02215309627354145,
0.01278154831379652,
-0.009346880950033665,
-0.003486670320853591,
0.0030007970053702593,
0.015858599916100502,
-0.012849909253418446,
-0.006699412129819393,
-0.08377022296190262,
0.007627608720213175,
0.023731719702482224,
0.025307223200798035,
0.021276753395795822,
0.008101064711809158,
-0.015254299156367779,
0.038170699030160904,
-0.02464459091424942,
-0.00936618447303772,
-0.005801260005682707,
-0.007706769742071629,
0.0020385158713907003,
0.010465376079082489,
0.01712438277900219,
0.017123209312558174,
0.05429254472255707,
-0.026858555153012276,
0.02855858765542507,
-0.11906366050243378,
-0.0027483312878757715,
-0.03856419026851654,
0.07007123529911041,
-0.11243557929992676,
0.05979979783296585,
0.014287996105849743,
0.0015126264188438654,
0.01065985020250082,
0.014851107262074947,
0.014902734197676182,
-0.030137185007333755,
0.02879353240132332,
-0.01754871942102909,
-0.017361756414175034,
-0.022462913766503334,
-0.03288576751947403,
0.04880228638648987,
-0.0142805315554142,
-0.0411832369863987,
0.06711236387491226,
-0.06989282369613647,
-0.01637733355164528,
0.02413026988506317,
0.03736656904220581,
-0.029106833040714264,
-0.0653119683265686,
-0.039797794073820114,
0.04078484699130058,
-0.037782955914735794,
0.028287453576922417,
-0.044893763959407806,
-0.05755862221121788,
0.00010167185246245936,
-0.08283749967813492,
0.027992380782961845,
0.022850673645734787,
0.009972152300179005,
0.025793198496103287,
0.0009128713281825185,
0.013047962449491024,
-0.024791134521365166,
0.07529100030660629,
0.02397623285651207,
-0.032956380397081375,
-0.02445092424750328,
0.07634811103343964,
0.006611644756048918,
-0.022806202992796898,
0.006049605552107096,
-0.00685465894639492,
0.053881242871284485,
-0.006399765610694885,
-0.00032133341301232576,
-0.030384181067347527,
-0.03293171152472496,
-0.010943081229925156,
0.029569566249847412,
0.05883483216166496,
0.056809376925230026,
-0.019983485341072083,
0.06114501133561134,
-0.013842918910086155,
0.005997106432914734,
-0.030829984694719315,
-0.028864877298474312,
-0.03408995643258095,
0.016379542648792267,
-0.012597780674695969,
0.03355960175395012,
-0.0526542067527771,
-0.005376236047595739,
0.043214406818151474,
-0.020589401945471764,
0.006800797302275896,
0.03347207233309746,
0.052762676030397415,
0.04041380062699318,
0.03079524077475071,
-0.05680301785469055,
0.025306139141321182,
-0.026943620294332504,
0.005896801128983498,
-0.005744262598454952,
-0.02716354839503765,
-0.061542898416519165,
0.031720757484436035,
0.03168237954378128,
0.051530975848436356,
-0.03276991844177246,
0.0030590256210416555,
0.078094482421875,
-0.009541601873934269,
-0.04627513512969017,
0.002774870954453945,
0.07489684969186783,
0.042410243302583694,
0.023072252050042152,
0.012184864841401577,
0.000786353659350425,
0.03617076948285103,
-0.0367964506149292,
0.0327901765704155,
0.00293850083835423,
-0.03439079225063324,
0.028572237119078636,
-0.004291086457669735,
-0.017301229760050774,
-0.05226099491119385,
0.04178900644183159,
-0.032535817474126816,
-0.02978728897869587,
0.02201332151889801,
-0.016499802470207214,
0.004154538735747337,
-0.038300253450870514,
-0.04494215175509453,
-0.00516292080283165,
-0.05454075708985329,
0.0021797316148877144,
-0.0034440141171216965,
-0.046989936381578445,
0.018075840547680855,
-0.04905843362212181,
-0.03918660059571266,
0.019907481968402863,
0.010756516829133034,
0.007964563556015491,
0.027258511632680893,
0.014529639855027199,
0.05765126645565033,
-0.10536913573741913,
0.0506863035261631,
-0.0073568494990468025,
0.050028711557388306,
0.03693239390850067,
-0.054241061210632324,
0.044490087777376175,
0.015368965454399586,
-0.03879912570118904,
0.0035681487061083317,
-0.019597359001636505,
-0.00142556126229465,
0.00596665870398283,
-0.04940791800618172,
-0.038474250584840775,
0.007873443886637688,
0.007850718684494495,
0.014471675269305706,
-0.08749176561832428,
-0.10719944536685944,
0.010571685619652271,
0.002680086297914386,
-0.04774042218923569,
0.03897010162472725,
0.01865207776427269,
-0.048551060259342194,
-0.012892975471913815,
-0.020419912412762642,
0.01572870835661888,
-0.01179791335016489,
-0.009251084178686142,
-0.018605433404445648,
-0.03611380234360695,
-0.03576265275478363,
0.036960434168577194,
0.022445445880293846,
-0.00033715617610141635,
0.016818027943372726,
-0.033625733107328415,
-0.03343156352639198,
0.061997201293706894,
-0.020517533645033836,
-0.020128391683101654,
0.03600111976265907,
0.049012623727321625,
-0.040119465440511703,
0.012330153025686741,
0.00443227868527174,
0.04433006793260574,
-0.01823292300105095,
-0.04278668388724327,
0.019963612779974937,
0.03708162158727646,
-0.04419149085879326,
0.02511696144938469,
0.051415834575891495,
0.037549011409282684,
0.02912219427525997,
0.02480785921216011,
0.016779610887169838,
0.024749496951699257,
0.06388138979673386,
-0.023875828832387924,
0.037347570061683655,
-0.014146561734378338,
-0.024301961064338684,
0.041739653795957565,
0.0379364937543869,
0.050699442625045776,
-0.00018028507474809885,
0.020911570638418198,
-0.057209957391023636,
-0.026139700785279274,
0.03415340185165405,
0.0001512764283688739,
0.005804826505482197,
0.0016277387039735913,
0.02813251130282879,
-0.0135801387950778,
-0.05029753968119621,
0.023684516549110413,
0.04250681400299072,
-0.021379387006163597,
-0.05735660716891289,
0.036108557134866714,
0.04692729935050011,
0.0326249822974205,
-0.019323082640767097,
-0.06013768911361694,
-0.12234065681695938,
-0.012600675225257874,
0.021913442760705948,
0.026356084272265434,
-0.026380138471722603,
-0.028913700953125954,
0.000710007268935442,
0.017218079417943954,
0.018463341519236565,
0.009866461157798767,
-0.004908898379653692,
0.0706259086728096,
0.020157795399427414,
-0.06369072943925858,
0.026108773425221443,
-0.10732291638851166,
-0.026007410138845444,
0.02482432872056961,
-0.016839155927300453,
0.01997583918273449,
0.024795161560177803,
-0.04438092187047005,
-0.027737058699131012,
0.06402041763067245,
-0.007803414948284626,
0.040954530239105225,
0.05641965940594673,
0.031176384538412094,
0.034645549952983856,
-0.0753592923283577,
-0.06250884383916855,
0.01267831027507782,
0.03718583285808563,
-0.023966742679476738,
0.004119766876101494,
0.0005869671585969627,
0.006897501647472382,
-0.0023794304579496384,
0.05459824204444885,
0.014395425096154213,
-0.026986967772245407,
0.0004531691374722868,
-0.05833625793457031,
0.01538937445729971,
0.01721976511180401,
0.041052404791116714,
-0.015087299980223179,
-0.042782966047525406,
-0.038643479347229004,
-0.07441478967666626,
0.04061420261859894,
-0.010998752899467945,
-0.024328669533133507,
-0.030622070655226707,
-0.06558853387832642,
-0.03907202184200287,
-0.04374832287430763,
-0.008688976988196373,
0.00798888225108385,
-0.016016412526369095,
0.046645764261484146,
-0.05796278640627861,
0.003159342333674431,
-0.007830718532204628,
0.04342765733599663,
-0.04715452343225479,
0.04656963050365448,
-0.011729425750672817,
0.007430837955325842,
-0.04394366964697838,
0.03098844736814499,
-0.007865062914788723,
-0.01083929929882288,
-0.04345779865980148,
-0.0526135116815567,
0.0016564953839406371,
-0.04360046982765198,
-0.014912215061485767,
-0.01811215840280056,
0.035280559211969376,
-0.0417829267680645,
0.058777909725904465,
-0.010511238127946854,
0.03797319531440735,
0.011713048443198204,
-0.08807072788476944,
-0.003287591738626361,
-0.008648737333714962,
0.054225560277700424,
0.003301902674138546,
-0.038503825664520264,
0.018276169896125793,
-0.042238082736730576,
-0.002910616109147668,
-0.009685509838163853,
-0.01053426694124937,
-0.020137999206781387,
0.018173040822148323,
-0.03808826953172684,
0.023970847949385643,
0.09717195481061935,
-0.017508044838905334,
-0.04314659163355827,
0.01638643816113472,
-0.02482164092361927,
-0.01150660589337349,
0.0016079018823802471,
-0.02083534002304077,
-0.01538834348320961,
0.005608756095170975,
0.021386152133345604,
-0.054116006940603256,
-0.03291872888803482,
0.007607706822454929
] |
<p>I have read an answer on this site regarding the change of laws over time . However a physisct told me that the laws did evolve at planck era and then stopped evolving after it , is that true even in case of a TOE ( namingly as the best candidate string theory )</p> | g1304 | [
0.029370149597525597,
0.0036186273209750652,
0.02799871563911438,
0.039829276502132416,
0.04001728817820549,
0.0374143011868,
0.009944617748260498,
0.020240511745214462,
0.015093234367668629,
-0.015432890504598618,
-0.031837012618780136,
-0.004135382827371359,
0.006227867212146521,
0.009855089709162712,
0.016944758594036102,
-0.04040826857089996,
0.0318564809858799,
-0.03173070028424263,
0.03832757845520973,
-0.03814076632261276,
-0.022693099454045296,
0.005831704009324312,
-0.010834377259016037,
-0.06876019388437271,
-0.012199071235954762,
-0.04296175763010979,
-0.0001601680414751172,
0.059392672032117844,
0.011228097602725029,
-0.016517357900738716,
0.08146844804286957,
-0.027502333745360374,
0.0726843923330307,
-0.03169981390237808,
0.01433579158037901,
-0.06985348463058472,
0.03375673294067383,
-0.004416500683873892,
0.0624106265604496,
-0.014973386190831661,
0.06359529495239258,
0.021209407597780228,
-0.010074439458549023,
-0.0007395311840809882,
0.05431284382939339,
-0.09451845288276672,
-0.03546483814716339,
-0.011756675317883492,
-0.01895037479698658,
-0.004219343885779381,
-0.009043351747095585,
0.025898100808262825,
0.035247430205345154,
0.026497500017285347,
0.014489292167127132,
-0.0033070959616452456,
0.0010114567121490836,
-0.01858457922935486,
0.08387033641338348,
0.0080507667735219,
-0.05782943218946457,
-0.02207818254828453,
0.013030392117798328,
0.01032941322773695,
0.05460847541689873,
0.02340097352862358,
0.009427743963897228,
-0.03745343163609505,
0.030664531514048576,
-0.006411296781152487,
0.006536237429827452,
-0.041277479380369186,
-0.045160651206970215,
-0.02201651781797409,
-0.00994587130844593,
0.04880367964506149,
-0.046685103327035904,
-0.023586319759488106,
-0.04276392236351967,
0.0131935840472579,
-0.03496364876627922,
0.02818567492067814,
-0.027762513607740402,
0.03768054023385048,
0.0565672293305397,
-0.08880665153265,
0.02093026041984558,
0.04522209241986275,
-0.046101488173007965,
0.07803975045681,
0.0046898615546524525,
-0.006001539994031191,
0.010126792825758457,
0.0061709582805633545,
-0.02081042155623436,
-0.07090400159358978,
-0.01124853827059269,
0.06155970320105553,
-0.015142496675252914,
-0.004882441367954016,
-0.07645273953676224,
-0.008817717432975769,
0.059215791523456573,
-0.013172969222068787,
-0.035656146705150604,
0.04393399506807327,
-0.03332559019327164,
-0.03656551614403725,
-0.046168502420186996,
-0.017773590981960297,
-0.030450791120529175,
0.011838716454803944,
-0.02205907367169857,
0.04397084563970566,
-0.03374284878373146,
0.0016743326559662819,
-0.03134515881538391,
0.01650051958858967,
0.005426160059869289,
0.03465075045824051,
-0.0089689576998353,
-0.07053813338279724,
0.016018254682421684,
0.04794888570904732,
-0.03984203189611435,
0.0034197571221739054,
-0.02283032238483429,
-0.03881923481822014,
0.027033338323235512,
0.01683933287858963,
-0.021941998973488808,
0.06551102548837662,
-0.061845988035202026,
0.012800090946257114,
-0.0016021289629861712,
0.061814166605472565,
-0.009047710336744785,
0.0059680757112801075,
-0.01979515329003334,
-0.06305641680955887,
0.023089371621608734,
-0.07903754711151123,
0.03661405295133591,
-0.04713149741292,
-0.0004761488817166537,
-0.01171962358057499,
0.03930661082267761,
0.004055702593177557,
-0.0036045692395418882,
0.04477711766958237,
-0.018841784447431564,
0.03860015794634819,
0.023184403777122498,
-0.02375892736017704,
-0.02905024215579033,
0.036860909312963486,
0.01938020996749401,
0.05117087811231613,
-0.02231385000050068,
-0.027531327679753304,
-0.051054611802101135,
-0.029929691925644875,
-0.017624320462346077,
-0.02132011391222477,
-0.06651077419519424,
0.023201115429401398,
-0.013743139803409576,
-0.036971163004636765,
-0.00005533114745048806,
-0.013750845566391945,
-0.07453690469264984,
0.024150170385837555,
0.017299652099609375,
0.07451643794775009,
-0.014398613013327122,
0.03810641169548035,
-0.017743365839123726,
-0.030874190852046013,
-0.014220134355127811,
0.012894776649773121,
-0.01936132274568081,
-0.02427496947348118,
-0.045312922447919846,
0.008991317823529243,
0.050453007221221924,
0.07287713885307312,
-0.031539443880319595,
-0.04217173531651497,
-0.03569865599274635,
-0.034756388515233994,
-0.06623055785894394,
-0.05458422750234604,
-0.0400911346077919,
0.03176634758710861,
0.04699678719043732,
-0.019673941656947136,
-0.017281368374824524,
-0.04433179646730423,
-0.014094446785748005,
0.04870254546403885,
0.03179887309670448,
0.042919449508190155,
0.011931377463042736,
-0.0053511327132582664,
-0.02785390242934227,
0.002806664677336812,
0.0187136959284544,
-0.024664901196956635,
0.05546388402581215,
-0.009523754008114338,
0.02713513933122158,
0.023769378662109375,
-0.06232927739620209,
0.026238827034831047,
-0.09957347065210342,
-0.003777283476665616,
-0.01669309474527836,
0.04005248099565506,
0.030306443572044373,
0.04431169480085373,
0.019240133464336395,
0.0369645394384861,
0.040808770805597305,
0.06926330924034119,
0.03560923412442207,
-0.016513554379343987,
-0.033864591270685196,
-0.03423173725605011,
0.02105080522596836,
0.052300240844488144,
-0.07993532717227936,
-0.02792743407189846,
-0.03744661435484886,
-0.024627020582556725,
-0.003099895780906081,
0.08497704565525055,
0.026326153427362442,
-0.0866146981716156,
0.07431802153587341,
-0.024653587490320206,
0.007657470181584358,
0.01275295577943325,
-0.014070226810872555,
-0.018069982528686523,
0.018147151917219162,
-0.04114219918847084,
-0.015821775421500206,
0.0056245350278913975,
-0.014612368308007717,
0.020806536078453064,
0.05464525148272514,
-0.017223645001649857,
0.008997156284749508,
0.08931692689657211,
-0.020669789984822273,
0.024406254291534424,
0.03950769454240799,
-0.0006207015831023455,
-0.0638791099190712,
-0.016227323561906815,
0.05896460637450218,
0.010865971446037292,
-0.004097542259842157,
0.006701989099383354,
-0.035844139754772186,
-0.03978651762008667,
0.011804859153926373,
-0.04647750407457352,
-0.027103491127490997,
0.03944670781493187,
-0.031227026134729385,
0.04151735454797745,
-0.011486182920634747,
0.036563750356435776,
0.010660620406270027,
0.011232294142246246,
0.0025637922808527946,
-0.00518406368792057,
-0.0352456271648407,
-0.011106479912996292,
-0.03905414044857025,
-0.033292338252067566,
-0.03414561599493027,
-0.01771070994436741,
0.03324224054813385,
-0.09255077689886093,
0.0037379253190010786,
-0.023421427235007286,
-0.016121217980980873,
0.04833415150642395,
0.016356196254491806,
0.04594267159700394,
0.06894844770431519,
0.03676628693938255,
-0.012286197394132614,
0.05541196092963219,
-0.047482989728450775,
-0.056667059659957886,
-0.0629892498254776,
0.05241922289133072,
0.011259622871875763,
-0.011795206926763058,
0.01388320792466402,
-0.0037399479188024998,
0.072251096367836,
0.005612523760646582,
-0.06273938715457916,
-0.05697571858763695,
0.04199858009815216,
-0.038765374571084976,
0.004449264612048864,
0.05955703184008598,
0.010061047039926052,
-0.05457368120551109,
-0.02600877732038498,
0.00006882648449391127,
-0.004584440961480141,
0.06821830570697784,
-0.01758313551545143,
-0.0570392832159996,
-0.016901714727282524,
-0.03997109830379486,
-0.00793332327157259,
-0.08981328457593918,
0.008900310844182968,
-0.0056583029218018055,
-0.04834446310997009,
-0.03819815441966057,
-0.028269734233617783,
0.0304152499884367,
0.003253886941820383,
-0.020802151411771774,
0.02724563144147396,
-0.008765678852796555,
-0.0582236610352993,
0.020961100235581398,
-0.011980026960372925,
-0.020025061443448067,
0.032183937728405,
0.05007832124829292,
-0.012659321539103985,
-0.04569236561655998,
-0.04170229658484459,
0.008235925808548927,
-0.000539113418199122,
0.09485986828804016,
0.05776793137192726,
-0.04679560661315918,
0.0061334967613220215,
0.03253686800599098,
0.0698232650756836,
-0.00048623583279550076,
0.011440333910286427,
0.04335345700383186,
-0.018814830109477043,
0.013140144757926464,
0.003390613943338394,
0.02585718035697937,
0.006351470481604338,
-0.03420243039727211,
-0.021190619096159935,
-0.05920180678367615,
0.008528136648237705,
0.010344858281314373,
-0.013652610592544079,
0.02520698681473732,
0.014701569452881813,
0.05511654540896416,
0.023305704817175865,
0.07645975798368454,
-0.002503151074051857,
0.03552776202559471,
0.014647066593170166,
0.0575924851000309,
-0.012508551590144634,
0.004938154015690088,
0.039663974195718765,
0.05977459251880646,
-0.005471076816320419,
0.046957142651081085,
0.047418903559446335,
0.025300409644842148,
-0.0240018367767334,
-0.011458396911621094,
0.016189496964216232,
0.020717917010188103,
-0.015215322375297546,
-0.05036020278930664,
0.03166411072015762,
0.00018857377290260047,
0.0016662339912727475,
0.013362432830035686,
0.043475229293107986,
-0.06227158382534981,
0.03856167569756508,
-0.015751615166664124,
-0.026979288086295128,
-0.008397502824664116,
0.0027203899808228016,
-0.022800521925091743,
0.015364782884716988,
0.03696749359369278,
-0.03696401044726372,
0.0054557123221457005,
0.03339437395334244,
0.035435039550065994,
-0.010111343115568161,
-0.024652255699038506,
0.03535076603293419,
-0.052274204790592194,
-0.004771680571138859,
0.05727474018931389,
-0.036409515887498856,
-0.030147461220622063,
0.0033261836506426334,
0.017041515558958054,
0.010561678558588028,
-0.06081506982445717,
0.014097842387855053,
0.04475158452987671,
0.00452533969655633,
-0.0026769181713461876,
-0.020963352173566818,
-0.03603716939687729,
-0.034299321472644806,
-0.000041223771404474974,
-0.016695192083716393,
0.018924959003925323,
-0.0118233198300004,
0.03498153015971184,
-0.026898078620433807,
-0.02415676973760128,
-0.03362347185611725,
-0.005285057704895735,
-0.09297717362642288,
0.035700924694538116,
0.01651463843882084,
-0.0327339842915535,
-0.065569207072258,
-0.01436037290841341,
0.047105155885219574,
-0.020984061062335968,
0.0325661301612854,
0.024253394454717636,
-0.0358707457780838,
0.06348668783903122,
0.0266075748950243,
-0.014835146255791187,
0.08630386739969254,
-0.016139432787895203,
-0.040090348571538925,
0.040900517255067825,
0.011232207529246807,
0.019570734351873398,
-0.022283557802438736,
-0.022153247147798538,
-0.036212556064128876,
0.016388269141316414,
-0.021350985392928123,
0.07140287011861801,
-0.06485718488693237,
0.027987608686089516,
-0.010071606375277042,
0.02745991386473179,
-0.03868212550878525,
-0.030277248471975327,
-0.06294524669647217,
0.02316892147064209,
0.04189535975456238,
0.04378560930490494,
0.013960612937808037,
-0.008887565694749355,
0.0014684345806017518,
-0.023959314450621605,
-0.000006591742021555547,
-0.04283680021762848,
0.003259682096540928,
-0.033815424889326096,
0.004193657543510199,
-0.06687561422586441,
-0.0034351912327110767,
-0.0026416159234941006,
0.024657679721713066,
-0.008484374731779099,
0.02489648200571537,
0.07499553263187408,
-0.035953812301158905,
0.02504120022058487,
0.01027792226523161,
-0.056317683309316635,
-0.026439910754561424,
0.015086604282259941,
0.06919828802347183,
0.015006882138550282,
-0.04043538495898247,
-0.022221209481358528,
-0.0248935017734766,
-0.021024098619818687,
-0.015820765867829323,
0.03158365935087204,
-0.033420879393815994,
0.021056853234767914,
0.04637753590941429,
-0.01970716565847397,
-0.024226682260632515,
0.021444199606776237,
0.003226493950933218,
-0.01738913729786873,
-0.03715101256966591,
-0.001528291730210185,
0.03685129061341286,
0.062316205352544785,
0.008118039928376675,
0.027146367356181145,
0.025414427742362022,
-0.030266402289271355,
-0.05375983566045761,
-0.014841740019619465,
-0.007378517184406519,
-0.049536217004060745,
0.028835637494921684,
-0.010840914212167263,
0.055628180503845215,
0.029498226940631866,
0.04037719964981079,
0.07815124839544296,
-0.048583462834358215,
-0.0050018769688904285,
-0.008345099166035652,
-0.008312243968248367,
-0.017235981300473213,
-0.058436665683984756,
0.013606362976133823,
0.005919184535741806,
0.0494454987347126,
0.027217166498303413,
0.04336991161108017,
0.01686755008995533,
-0.0023278039880096912,
-0.020240355283021927,
-0.018722278997302055,
-0.007031911984086037,
0.00829707458615303,
0.03104708530008793,
0.022689078003168106,
0.028730016201734543,
-0.05597062408924103,
0.04738708212971687,
0.04942399263381958,
-0.05986367538571358,
-0.05990040674805641,
0.05973413959145546,
-0.023416593670845032,
0.00045699765905737877,
-0.041574399918317795,
0.060834433883428574,
0.028538696467876434,
-0.030149681493639946,
0.01790660060942173,
0.05697130039334297,
0.07946515828371048,
0.06808222830295563,
0.012629639357328415,
-0.00007506929978262633,
-0.024757705628871918,
-0.032127223908901215,
0.00026350526604801416,
-0.06588508188724518,
0.09026267379522324,
0.05388519540429115,
0.06096256524324417,
0.06026715412735939,
-0.04177425429224968,
0.039305392652750015,
-0.0151637252420187,
0.0092332037165761,
-0.05091125890612602,
-0.04231632128357887,
-0.005570462439209223,
-0.01209230162203312,
-0.03346977010369301,
-0.029975103214383125,
-0.04184005782008171,
0.019021140411496162,
-0.06747453659772873,
0.028519144281744957,
0.010944278910756111,
0.013737025670707226,
0.0692422091960907,
0.00627020513638854,
-0.007332097738981247,
0.01606110855937004,
-0.04677236080169678,
0.012335389852523804,
-0.005472397897392511,
0.02915961667895317,
0.006639533676207066,
-0.012008518911898136,
0.04277622327208519,
0.02015521377325058,
0.049112770706415176,
-0.012408899143338203,
0.02697027660906315,
-0.05035235732793808,
-0.004771165084093809,
0.03771911561489105,
0.00484731188043952,
0.04680829122662544,
0.053324732929468155,
0.0321660041809082,
0.01613168977200985,
-0.014375614002346992,
-0.009429890662431717,
0.02839418686926365,
0.009287135675549507,
0.03798730671405792,
-0.012104460038244724,
0.0637718215584755,
-0.08134868741035461,
0.02725973352789879,
0.0005433015176095068,
0.020720280706882477,
0.0015760939568281174,
0.030486730858683586,
-0.005335142370313406,
0.05846751853823662,
-0.0036555060651153326,
0.022531192749738693,
0.017857477068901062,
0.008886029943823814,
0.02371087297797203,
0.007836989127099514,
-0.009756924584507942,
0.015146655030548573,
-0.06315843760967255,
-0.007010360714048147,
0.02026374638080597,
-0.008746779523789883,
-0.056508563458919525,
0.06903503835201263,
0.031324028968811035,
-0.021428197622299194,
0.024944979697465897,
-0.0028963973745703697,
0.0018701929366216063,
0.04192720353603363,
0.07096830010414124,
-0.0030537156853824854,
-0.07625527679920197,
-0.01680098846554756,
0.016851676627993584,
-0.02687119133770466,
-0.03534935787320137,
-0.007929387502372265,
0.004564874805510044,
-0.0032824999652802944,
-0.01485590822994709,
-0.03268783912062645,
0.007968303747475147,
-0.061152879148721695,
-0.07693691551685333,
-0.023309798911213875,
0.0399790033698082,
-0.004741708282381296,
0.010770849883556366,
0.004133617039769888,
0.042458392679691315,
-0.08779625594615936,
0.03593914210796356,
-0.012322568334639072,
0.009991333819925785,
-0.00009040205623023212,
0.01827758178114891,
-0.02687898650765419,
0.020698009058833122,
-0.02793996036052704,
-0.040399376302957535,
0.01757199317216873,
0.010733607225120068,
0.07766425609588623,
0.03167719766497612,
0.019360307604074478,
0.021506136283278465,
-0.027691669762134552,
-0.018056979402899742,
0.04460036754608154,
-0.05472227558493614,
-0.03115430846810341,
-0.0053658392280340195,
0.020622270181775093,
0.0001439659099560231,
0.008649088442325592,
0.001253084046766162,
-0.03252081945538521,
-0.0030373730696737766,
0.003531005932018161,
0.03983578085899353,
-0.005628911312669516,
0.014354980550706387,
-0.029392272233963013,
-0.00978523213416338,
-0.011494924314320087,
-0.06205030530691147,
-0.04597809910774231,
0.006520448252558708,
-0.014149855822324753,
-0.05706986412405968,
-0.01963617652654648,
-0.05449359863996506,
-0.012876673601567745,
-0.0366780050098896,
-0.01449653971940279,
0.011278875172138214,
0.06385881453752518,
0.04099540412425995,
-0.005718050990253687,
0.011438581161201,
-0.04713418334722519,
-0.010792559944093227,
0.034265197813510895,
0.01340966671705246,
0.004055495373904705,
0.012622241862118244,
-0.04889411851763725,
-0.06619637459516525,
0.010350995697081089,
0.01787123642861843,
-0.0015953379916027188,
-0.031722042709589005,
-0.02295428141951561,
-0.025459246709942818,
-0.027769871056079865,
-0.03358961641788483,
-0.03192867711186409,
-0.0205013919621706,
0.0700259730219841,
0.010442121885716915,
-0.00013142405077815056,
-0.04547766223549843,
-0.06190314143896103,
-0.01610345020890236,
-0.0273929201066494,
0.019776832312345505,
0.003155567217618227,
-0.002775647910311818,
-0.017372895032167435,
-0.007394313812255859,
-0.023054638877511024,
-0.008687895722687244,
-0.05184807628393173,
-0.011393260210752487,
0.01944642700254917,
-0.011792859993875027,
0.06933451443910599,
-0.03680672124028206,
-0.010441519320011139,
0.016321908682584763,
-0.00466863764449954,
-0.020175034180283546,
-0.00941765308380127,
0.02879699505865574,
0.008939933031797409,
0.03182542324066162,
-0.01812724582850933,
-0.017493335530161858,
-0.03485703468322754,
0.02366558089852333,
0.011371891014277935
] |
<p>A clock near the surface of the earth will run slower than one on the top of the mountain. If the equivalence principal tells us that being at rest in a gravitational field is equivalent to being in an accelerated frame of reference in free space, shouldn't the clock near the earth run <em>increasingly</em> slower than the other clock over time? If those two clocks are considered to be in two different frames of acceleration, the one near the earth will have a greater acceleration than the one on the mountain, and thus over time, their relative velocity will increase over time which will increase the time dilation. Or is this not a proper use of the equivalence principle?</p> | g1305 | [
0.08392846584320068,
0.04854190722107887,
0.011895230039954185,
-0.05142071098089218,
0.018849298357963562,
0.06565947830677032,
0.07605553418397903,
0.0026580169796943665,
-0.05214156210422516,
0.0036966234911233187,
0.010361725464463234,
0.013889011926949024,
-0.020989762619137764,
0.0003037226852029562,
-0.003809048095718026,
0.041028641164302826,
0.13266226649284363,
-0.01701938547194004,
0.03166067227721214,
0.010428670793771744,
0.05238243564963341,
0.01133536547422409,
-0.003800713922828436,
-0.03230302035808563,
-0.0010737029369920492,
0.03086504153907299,
0.033302851021289825,
-0.05149650573730469,
-0.07428695261478424,
0.002991950837895274,
0.04294418916106224,
-0.01271675806492567,
0.018565205857157707,
-0.00451484601944685,
0.021177517250180244,
-0.02675332874059677,
0.042473506182432175,
0.057814761996269226,
0.01116967387497425,
0.01173841767013073,
0.03598163276910782,
-0.03967805951833725,
0.014666207134723663,
0.014318736270070076,
0.01828373596072197,
-0.03690958023071289,
-0.024469561874866486,
0.014878595247864723,
0.028378160670399666,
-0.03715645149350166,
-0.036715250462293625,
0.014651195146143436,
0.0013331901282072067,
-0.03376173600554466,
-0.014381332322955132,
0.0698903426527977,
0.03454171121120453,
0.0033289778511971235,
0.006282065063714981,
0.06031224504113197,
-0.026788901537656784,
-0.035752132534980774,
0.038792647421360016,
-0.0119766341522336,
0.07578983902931213,
0.03399306535720825,
0.018232177942991257,
-0.003349978942424059,
0.07300906628370285,
-0.00021705796825699508,
-0.021753817796707153,
-0.007822057232260704,
-0.08277685195207596,
-0.0027156316209584475,
-0.01336264330893755,
0.00019856690778397024,
0.00043770502088591456,
-0.041401926428079605,
0.007423358503729105,
0.02504144050180912,
-0.032433584332466125,
0.026581741869449615,
0.047224048525094986,
0.024816805496811867,
0.08830397576093674,
-0.0372568815946579,
0.04940445348620415,
0.06885647773742676,
0.014253606088459492,
0.055853575468063354,
0.007186390925198793,
-0.07039645314216614,
0.07812155038118362,
0.026242004707455635,
-0.05833318457007408,
0.006828533951193094,
0.00017147698963526636,
0.06925533711910248,
-0.004209553357213736,
0.04356171190738678,
-0.07659292221069336,
0.006857742089778185,
0.021018655970692635,
0.050814636051654816,
0.020479345694184303,
-0.02529415301978588,
0.02256649173796177,
-0.00045631881221197546,
-0.0769423320889473,
-0.059053193777799606,
0.037581395357847214,
-0.030077658593654633,
-0.0005974570522084832,
-0.04092434048652649,
-0.027292516082525253,
-0.06006923317909241,
0.0319087989628315,
0.0054457224905490875,
0.02184678427875042,
0.02332313545048237,
0.013942423276603222,
0.0075484528206288815,
-0.06167490780353546,
0.014616455882787704,
-0.02727571502327919,
-0.0003388503391761333,
0.017552008852362633,
-0.014704826287925243,
0.01815304346382618,
0.03325894474983215,
0.0005980929126963019,
0.012029137462377548,
0.004793697968125343,
-0.012254459783434868,
-0.03850754722952843,
-0.02753700502216816,
0.008880303241312504,
-0.031831029802560806,
-0.022801009938120842,
0.03469346836209297,
-0.025152182206511497,
-0.0741434395313263,
0.0030870307236909866,
-0.053559187799692154,
0.00906220730394125,
0.0650256797671318,
-0.022056961432099342,
-0.027758607640862465,
0.03970060124993324,
0.050009485334157944,
-0.016592856496572495,
0.1148398369550705,
-0.0007693236111663282,
-0.009187192656099796,
0.0595642551779747,
0.02274579554796219,
-0.03506222739815712,
0.023602105677127838,
-0.015521257184445858,
0.004057134967297316,
0.02732914127409458,
-0.020910490304231644,
0.03360145166516304,
-0.021847577765583992,
-0.031016087159514427,
0.04158153757452965,
0.019065432250499725,
-0.05084855481982231,
-0.008883042261004448,
-0.014296431094408035,
-0.044883813709020615,
0.01503873709589243,
-0.010124213062226772,
0.03942744433879852,
-0.03168412297964096,
0.040883228182792664,
-0.00002445543941576034,
-0.04030166193842888,
-0.05801597610116005,
-0.004003192763775587,
-0.01341027207672596,
-0.06340654194355011,
-0.04207173362374306,
-0.021357864141464233,
-0.03229660168290138,
-0.025447767227888107,
0.021053116768598557,
-0.00032620737329125404,
-0.11827104538679123,
0.0010039667831733823,
-0.007636369206011295,
-0.013569685630500317,
-0.027915526181459427,
0.06853637844324112,
-0.033856380730867386,
0.044935110956430435,
-0.034570757299661636,
-0.0015818305546417832,
-0.009950235486030579,
0.04670051112771034,
-0.030884794890880585,
0.020905189216136932,
0.0018093419494107366,
0.013847551308572292,
0.00763305788859725,
0.030733622610569,
-0.056741319596767426,
-0.018426356837153435,
0.038489989936351776,
-0.010499237105250359,
0.04294310137629509,
0.059203967452049255,
0.02829485759139061,
0.007643055636435747,
-0.008220241405069828,
0.04956001043319702,
-0.012455757707357407,
0.017510859295725822,
-0.03750361502170563,
0.04323005676269531,
-0.037631306797266006,
-0.006532896775752306,
0.077416330575943,
-0.07603465020656586,
-0.008611150085926056,
-0.09657768905162811,
-0.06333748996257782,
-0.005162777379155159,
0.0037092373240739107,
0.009661375544965267,
-0.05409330129623413,
0.041016705334186554,
-0.0269574336707592,
0.03968574479222298,
0.05408734455704689,
0.02391977049410343,
0.006349725183099508,
0.025116268545389175,
0.042903970927000046,
0.015008102171123028,
0.0280925165861845,
0.013300510123372078,
-0.03206650912761688,
0.0062265400774776936,
0.04487592726945877,
-0.047428034245967865,
0.06591808050870895,
-0.013225972652435303,
0.0019332491792738438,
0.03581159934401512,
-0.005916070193052292,
-0.019731689244508743,
-0.0017983143916353583,
-0.02907346561551094,
0.0005736023304052651,
-0.020536361262202263,
0.0003013605601154268,
-0.008390599861741066,
-0.07057735323905945,
-0.02527673728764057,
0.05666165426373482,
-0.044111091643571854,
-0.010279896669089794,
0.05638100951910019,
0.0023977160453796387,
0.014851965010166168,
0.02641054429113865,
0.045076292008161545,
-0.02329176850616932,
-0.008645306341350079,
-0.006962621118873358,
0.023856768384575844,
0.04384969174861908,
0.0895257368683815,
-0.05214858800172806,
0.017004024237394333,
-0.006209843792021275,
-0.02932850830256939,
-0.002072312403470278,
0.004707294050604105,
-0.009367147460579872,
-0.03444953262805939,
-0.059368208050727844,
-0.004033846780657768,
0.05205261707305908,
-0.08240888267755508,
0.006242369767278433,
0.045815084129571915,
-0.030513938516378403,
-0.0009269718430005014,
-0.01291199866682291,
0.06548904627561569,
0.02090572938323021,
0.0656762346625328,
0.01021041814237833,
0.04862404242157936,
-0.009994800202548504,
-0.055562328547239304,
-0.019377773627638817,
0.012489202432334423,
0.03255827724933624,
-0.07733070850372314,
-0.01209272351115942,
0.02349235676229,
-0.003875700756907463,
0.035588137805461884,
-0.05236950144171715,
-0.06730474531650543,
-0.045696064829826355,
-0.012686856091022491,
-0.03592803329229355,
0.029678167775273323,
-0.04061353951692581,
-0.0239728931337595,
-0.01036078017205,
-0.0003014584362972528,
0.008159657940268517,
-0.02708376571536064,
0.04690577834844589,
0.01092793419957161,
-0.01869174838066101,
-0.023476693779230118,
-0.041518449783325195,
-0.03240577504038811,
-0.006659892853349447,
-0.021581050008535385,
0.01635713316500187,
0.002587836468592286,
-0.06193400174379349,
-0.02061597816646099,
-0.0011623648460954428,
0.012376942671835423,
-0.04625682160258293,
0.01637209765613079,
-0.01889456994831562,
-0.004721253644675016,
0.001166964997537434,
0.019731370732188225,
0.04171367362141609,
0.003778895828872919,
-0.004501708783209324,
0.05546614155173302,
-0.07420973479747772,
0.05276208370923996,
0.017786286771297455,
0.012307797558605671,
0.016579238697886467,
-0.033037133514881134,
-0.04376799240708351,
-0.030985524877905846,
0.01775512471795082,
-0.04046366736292839,
0.017266754060983658,
0.02259359322488308,
-0.012109048664569855,
0.05095165967941284,
0.0509546734392643,
-0.0021343764383345842,
-0.012941867113113403,
-0.0008396272314712405,
0.04024144634604454,
0.056352823972702026,
-0.004201834090054035,
0.04425976797938347,
-0.03956488519906998,
0.00146918382961303,
-0.039953045547008514,
0.049418941140174866,
-0.0027349628508090973,
-0.04401075094938278,
0.033723581582307816,
0.013167046941816807,
0.031338416039943695,
0.0016072675352916121,
0.07510007917881012,
-0.07721389830112457,
0.05237578973174095,
-0.004740369040518999,
-0.0014093697536736727,
0.01438952051103115,
0.016977205872535706,
-0.01798783801496029,
-0.0651407390832901,
-0.04203113541007042,
0.0332372672855854,
-0.012604597955942154,
-0.02545783668756485,
-0.01567239873111248,
-0.01149052008986473,
-0.018140776082873344,
0.01901746168732643,
-0.03146795928478241,
-0.03527435287833214,
0.057922448962926865,
0.01627458818256855,
0.02372705191373825,
-0.01231418177485466,
0.0036310891155153513,
0.05108146369457245,
0.013830573298037052,
0.03789171203970909,
0.05725795403122902,
-0.034322403371334076,
0.06094439700245857,
-0.0749274268746376,
0.01958072930574417,
0.013866115361452103,
-0.015530151315033436,
-0.04209849610924721,
0.043533142656087875,
-0.026059934869408607,
-0.002684444421902299,
-0.03493876755237579,
-0.05258956551551819,
0.04709077626466751,
0.02665545977652073,
-0.0010320828296244144,
-0.024093465879559517,
0.07055949419736862,
-0.0020346844103187323,
-0.015982814133167267,
0.037321239709854126,
0.04299219325184822,
-0.07232838124036789,
0.009123205207288265,
0.10814245790243149,
0.048327378928661346,
0.02390618994832039,
-0.016433998942375183,
-0.06269095093011856,
-0.000276837294222787,
0.042254962027072906,
-0.02098909206688404,
0.016187818720936775,
-0.030529607087373734,
0.013454293832182884,
-0.02396460250020027,
0.03729541227221489,
0.016694379970431328,
0.03427796810865402,
0.012084146030247211,
0.0048477440141141415,
0.015798265114426613,
-0.013925466686487198,
-0.008626336231827736,
0.07477478682994843,
-0.014762304723262787,
-0.05852118134498596,
-0.016690753400325775,
-0.06299246102571487,
-0.04723658785223961,
0.03658032417297363,
-0.006276548840105534,
0.030118392780423164,
0.0059267510659992695,
-0.017105117440223694,
-0.006337293423712254,
0.0036924255546182394,
-0.0033301478251814842,
0.015238258987665176,
-0.05475172400474548,
-0.013881204649806023,
-0.0019316397374495864,
-0.007004828192293644,
-0.016219541430473328,
0.0015022136503830552,
-0.06721939891576767,
-0.06313452124595642,
-0.0424184612929821,
-0.002836151747033,
0.02482788637280464,
-0.06576688587665558,
-0.03753745183348656,
-0.01858651079237461,
0.0028734118677675724,
0.013498270884156227,
0.008621616289019585,
-0.024225955829024315,
0.07033831626176834,
-0.05230569839477539,
-0.05415036529302597,
0.0009313247865065932,
0.026221923530101776,
0.010311814025044441,
-0.029273496940732002,
0.011349988169968128,
-0.006406480446457863,
-0.007790538482367992,
0.014554738998413086,
-0.04973142594099045,
-0.0004582708643283695,
-0.05547601357102394,
0.0004449919506441802,
-0.0028675307985395193,
0.02671247161924839,
0.04471246153116226,
0.04334468021988869,
0.03515438735485077,
0.02856331504881382,
-0.04199148714542389,
-0.03488057851791382,
0.04553839936852455,
-0.010789958760142326,
-0.006950653623789549,
0.033073801547288895,
0.055482182651758194,
0.01080050878226757,
0.023790137842297554,
-0.03149723261594772,
0.020583761855959892,
0.012538024224340916,
0.013026019558310509,
-0.05091291666030884,
0.04308633133769035,
0.054804179817438126,
-0.03004639782011509,
0.007720929570496082,
-0.0459742546081543,
0.003961961250752211,
-0.07884880900382996,
0.04618643596768379,
-0.004864543676376343,
0.009041134268045425,
0.033907171338796616,
0.04657084122300148,
0.006631579250097275,
0.004302581772208214,
-0.0021495274268090725,
-0.011256310157477856,
-0.0035222184378653765,
0.038818057626485825,
-0.04739297181367874,
-0.021890362724661827,
0.004469512030482292,
0.020418662577867508,
-0.0019510986749082804,
0.008901739493012428,
-0.008772698231041431,
0.013280862011015415,
0.0059135593473911285,
-0.05712845176458359,
-0.08568138629198074,
0.07529105991125107,
0.01847187429666519,
-0.04046299308538437,
0.018023528158664703,
-0.06443402916193008,
0.0008647037902846932,
0.020680345594882965,
-0.035393502563238144,
-0.07605205476284027,
-0.010767262428998947,
0.021586205810308456,
0.042548272758722305,
-0.03909976780414581,
0.07430294156074524,
-0.0002630672533996403,
0.010310940444469452,
-0.021382151171565056,
-0.008467626757919788,
0.04155993461608887,
0.055829063057899475,
-0.000115429655124899,
-0.010857992805540562,
-0.019505338743329048,
-0.078374944627285,
0.011109307408332825,
-0.042498230934143066,
0.04383014887571335,
-0.06458314508199692,
-0.005662594921886921,
-0.011401687748730183,
-0.007700028829276562,
0.003594457171857357,
-0.005104575771838427,
0.03333105891942978,
-0.0332079753279686,
-0.027057647705078125,
-0.037072762846946716,
-0.004578901454806328,
-0.02124812640249729,
-0.031283341348171234,
0.007701741997152567,
-0.05283823236823082,
-0.03680825233459473,
0.009079107083380222,
-0.03690479323267937,
-0.0440807044506073,
0.04844360798597336,
0.003198998048901558,
-0.005386823322623968,
-0.0395096018910408,
0.008875031024217606,
0.011377708986401558,
-0.021967045962810516,
0.03282229229807854,
-0.012938684783875942,
0.007143013179302216,
-0.06759472191333771,
0.01099550910294056,
0.05343670770525932,
-0.023435043171048164,
0.10088040679693222,
-0.04171442985534668,
0.018600814044475555,
0.03801991418004036,
-0.03610490262508392,
-0.04650457575917244,
0.036986272782087326,
-0.03931264206767082,
0.0003212234878446907,
-0.005433906801044941,
0.026785792782902718,
0.05866008251905441,
-0.013406672514975071,
0.02513943985104561,
-0.007940623909235,
-0.007468977943062782,
-0.04161926731467247,
0.02049727365374565,
0.09198875725269318,
0.013085038401186466,
-0.017385151237249374,
-0.023609263822436333,
0.0033851657062768936,
0.03558416664600372,
-0.027721812948584557,
0.026056185364723206,
0.023940559476614,
0.016618015244603157,
-0.0008546327007934451,
-0.03156626597046852,
-0.029688561335206032,
-0.008828945457935333,
0.034010764211416245,
-0.008148860186338425,
-0.009479174390435219,
0.03473315387964249,
-0.06480523943901062,
0.013461942784488201,
-0.02241116389632225,
0.019880706444382668,
-0.028641721233725548,
0.0045389742590487,
-0.05754483491182327,
-0.0025517477188259363,
0.04037518799304962,
0.013365168124437332,
-0.009054641239345074,
0.017694933339953423,
-0.018521467223763466,
-0.03321997448801994,
-0.07183565199375153,
0.036864183843135834,
-0.007410234771668911,
-0.02212107926607132,
-0.00047626771265640855,
-0.021689675748348236,
0.022445542737841606,
-0.029950693249702454,
0.003980754408985376,
-0.0028742861468344927,
-0.016607172787189484,
0.028396354988217354,
-0.019058004021644592,
-0.0023771042469888926,
-0.0035353240091353655,
-0.01993529684841633,
0.014926398172974586,
0.017018496990203857,
0.0009479025029577315,
-0.008769260719418526,
0.01522798091173172,
-0.007827846333384514,
0.02362799644470215,
0.05566267669200897,
-0.050714001059532166,
-0.04609823599457741,
-0.011363736353814602,
0.03072800301015377,
-0.012312079779803753,
-0.012510287575423717,
-0.027473583817481995,
0.011971918866038322,
0.04113610461354256,
0.06853984296321869,
0.014974373392760754,
-0.015675390139222145,
-0.019242415204644203,
-0.0338895320892334,
-0.009470261633396149,
0.03894664719700813,
0.015510857105255127,
-0.017270565032958984,
0.039824314415454865,
0.051731567829847336,
0.013550170697271824,
-0.0003562913916539401,
-0.028701983392238617,
-0.029196348041296005,
-0.023577801883220673,
0.004451907705515623,
0.023969165980815887,
-0.0027522966265678406,
0.03389326110482216,
0.012543866410851479,
-0.02743196114897728,
0.030600454658269882,
-0.07800684124231339,
-0.0038080764934420586,
0.037190183997154236,
0.05726448446512222,
0.03702081739902496,
-0.017401596531271935,
0.011666436679661274,
-0.03054412268102169,
-0.01545017585158348,
-0.04090743884444237,
-0.023032043129205704,
-0.045105986297130585,
0.023910192772746086,
0.005807786714285612,
-0.016551509499549866,
-0.08850114792585373,
0.023889966309070587,
0.00402784813195467,
0.04618167504668236,
-0.05130765587091446,
0.03991870954632759,
-0.07224944233894348,
-0.0075145382434129715,
-0.035527899861335754,
0.01526779867708683,
0.04124771058559418,
-0.007888886146247387,
0.049275998026132584,
0.018590813502669334,
-0.03209603950381279,
-0.053044434636831284,
0.001493647345341742,
-0.02178787998855114,
-0.026379892602562904,
-0.0182894729077816,
0.030732082203030586,
-0.04160234332084656,
-0.014069986529648304,
0.054106853902339935,
0.02146037295460701,
0.014618576504290104,
-0.05982318893074989,
0.037486299872398376,
0.026349522173404694,
-0.0834803506731987,
0.03510434553027153,
0.051607176661491394,
-0.018298689275979996,
0.04959360510110855,
0.00002273415884701535,
-0.00312921404838562,
-0.011673707515001297,
-0.04940754175186157,
-0.005906581413000822,
0.0036630521062761545,
-0.05073225870728493,
-0.041862159967422485,
-0.037691470235586166,
-0.007448491640388966,
0.04199977591633797
] |
<p>I have heard that area is a vector quantity in 3 dimensions, e.g. <a href="http://physics.stackexchange.com/q/14165/">this</a> Phys.SE post, what about the length/distance? Since area is the product of two lengths, does this mean that length is also a vector quantity, and why?</p> | g1306 | [
0.07981614768505096,
0.007818234153091908,
-0.004655655473470688,
-0.004586223978549242,
-0.03167470917105675,
0.06864429265260696,
0.002237520879134536,
0.02004236727952957,
-0.02793593518435955,
-0.01465950720012188,
0.026101313531398773,
-0.012364882975816727,
0.030906641855835915,
-0.03548066318035126,
0.011351547203958035,
-0.04463411867618561,
-0.009402450174093246,
-0.02045578695833683,
0.024081597104668617,
0.0004911614232696593,
-0.01725597493350506,
0.000030422204872593284,
0.0444771908223629,
-0.043978214263916016,
0.03162220120429993,
-0.10936243832111359,
0.0642307698726654,
-0.026547472923994064,
-0.01770723983645439,
-0.05024487525224686,
0.02081269770860672,
0.02476002275943756,
0.059519801288843155,
0.015688717365264893,
-0.06399839371442795,
-0.050763268023729324,
-0.017291396856307983,
-0.006867131218314171,
0.014723255299031734,
-0.04668714478611946,
0.0033989648800343275,
-0.00490746321156621,
0.055684950202703476,
-0.025667384266853333,
-0.0014175309333950281,
0.015357576310634613,
-0.05392877757549286,
0.03587453067302704,
-0.0007801633328199387,
-0.030130892992019653,
-0.022410541772842407,
0.016746750101447105,
-0.01556033082306385,
0.06130795180797577,
0.06250029057264328,
0.011408294551074505,
0.02656419575214386,
-0.009557683020830154,
0.09043801575899124,
0.013056776486337185,
0.005232726223766804,
0.06123944744467735,
-0.005512736272066832,
0.02388644590973854,
0.03347323462367058,
-0.020642651244997978,
-0.03304427117109299,
-0.0013979048235341907,
-0.0243573896586895,
0.007843837141990662,
0.03988435119390488,
-0.033933497965335846,
0.06169307976961136,
-0.024462813511490822,
0.03038712963461876,
-0.027408786118030548,
0.048135824501514435,
0.05841928720474243,
0.02324792556464672,
0.014937028288841248,
-0.06898190826177597,
0.004697875585407019,
0.0023009164724498987,
0.0013255008962005377,
0.04551425948739052,
0.006456892937421799,
-0.0011873312760144472,
-0.02486203983426094,
-0.012226568534970284,
0.0025269973557442427,
-0.04270177707076073,
0.041347187012434006,
0.02153133414685726,
0.02980482205748558,
-0.08390464633703232,
-0.07264512032270432,
0.005984232295304537,
-0.0048533412627875805,
-0.06670770794153214,
0.04692698270082474,
-0.045003678649663925,
0.07493021339178085,
0.09323812276124954,
0.03644551336765289,
0.002745469566434622,
0.020688414573669434,
-0.005899687297642231,
-0.00705223111435771,
-0.019911989569664,
-0.024480022490024567,
-0.058442141860723495,
-0.03421023488044739,
-0.03350305184721947,
0.021487802267074585,
0.0016840466996654868,
0.042633056640625,
0.08826146274805069,
-0.03889035806059837,
0.023337405174970627,
0.07173632830381393,
0.04892246425151825,
0.001791485701687634,
0.07986385375261307,
0.02277609147131443,
-0.003398382803425193,
-0.01520306896418333,
0.016637451946735382,
0.03910018876194954,
-0.0013826795620843768,
-0.006648963317275047,
0.027300629764795303,
0.0013507693074643612,
-0.030796688050031662,
0.002386401640251279,
0.016978811472654343,
0.007664152886718512,
0.008572740480303764,
0.035095181316137314,
0.06002688780426979,
0.058604173362255096,
-0.02968505397439003,
-0.010217432864010334,
-0.007669943850487471,
0.0033690035343170166,
-0.004958024714142084,
0.002859954023733735,
-0.010288079269230366,
-0.04939911887049675,
-0.03366117179393768,
-0.04526850953698158,
0.018155844882130623,
0.0249855387955904,
-0.010031221434473991,
-0.05953731760382652,
0.010141991078853607,
0.014161136001348495,
-0.010336057282984257,
0.02335219644010067,
0.047697871923446655,
-0.040268152952194214,
0.006569176446646452,
0.00966486893594265,
0.02875797264277935,
0.0028911347035318613,
-0.020575392991304398,
-0.03577382490038872,
0.0065293824300169945,
-0.08226031810045242,
-0.048671361058950424,
-0.05888039246201515,
-0.05334573984146118,
0.006161155179142952,
0.008303585462272167,
0.03191686421632767,
-0.026254601776599884,
-0.003400648245587945,
-0.010658824816346169,
0.0433029942214489,
-0.00960416067391634,
-0.0002683397615328431,
-0.01572151482105255,
0.010527481324970722,
0.021003542467951775,
0.012884835712611675,
-0.02661161869764328,
0.024519287049770355,
0.04721576347947121,
0.014234357513487339,
-0.028730379417538643,
0.026662344112992287,
-0.05785990133881569,
-0.001792050781659782,
-0.04911941662430763,
0.004503769334405661,
0.03891017660498619,
0.015975376591086388,
0.023495078086853027,
-0.057543814182281494,
-0.04468892514705658,
0.012457836419343948,
-0.004883674904704094,
-0.00930909626185894,
0.013379105366766453,
0.034781377762556076,
0.007820124737918377,
0.027895301580429077,
-0.02936231531202793,
0.034973494708538055,
0.02398819662630558,
0.029646240174770355,
0.04450878128409386,
-0.02835645154118538,
0.052530426532030106,
0.06170659512281418,
-0.002536159474402666,
-0.0304294154047966,
-0.036342814564704895,
-0.007991956546902657,
-0.00785231776535511,
-0.023815706372261047,
0.01048461813479662,
-0.03584108129143715,
0.01911391317844391,
-0.026709001511335373,
-0.01843731477856636,
0.04993727058172226,
-0.01123983133584261,
-0.028249775990843773,
-0.04146230220794678,
-0.0018792843911796808,
-0.046078503131866455,
-0.018258346244692802,
0.025711948052048683,
0.008740023709833622,
-0.0319632962346077,
0.05188643932342529,
0.00913374125957489,
-0.014861480332911015,
0.0017060015816241503,
0.021989062428474426,
0.059837356209754944,
-0.01483110710978508,
0.018357206135988235,
0.04723967984318733,
0.05107651650905609,
0.031849488615989685,
0.023923156782984734,
-0.044528938829898834,
-0.02329237200319767,
-0.017136350274086,
-0.050915516912937164,
0.002607897622510791,
0.03364532068371773,
0.03351426124572754,
0.0007107928395271301,
-0.01745455525815487,
0.005505878943949938,
0.02715315856039524,
-0.015005701221525669,
-0.009772136807441711,
-0.018361635506153107,
-0.01742999069392681,
-0.005786783993244171,
0.03695689141750336,
-0.006806842517107725,
0.015684349462389946,
-0.08469580858945847,
0.05055331438779831,
0.04763505980372429,
0.0013328567147254944,
0.00958056841045618,
-0.019505761563777924,
0.010802467353641987,
-0.007028046529740095,
0.0018583594355732203,
-0.036692697554826736,
0.018094420433044434,
-0.03703102469444275,
0.03956180810928345,
-0.06290633231401443,
0.04428572207689285,
0.022474514320492744,
-0.031392600387334824,
0.026287904009222984,
0.02805284969508648,
0.03292781487107277,
0.0006621750653721392,
-0.011261784471571445,
-0.007417785469442606,
-0.046372249722480774,
-0.025730162858963013,
-0.02065758779644966,
0.013261253014206886,
-0.07694685459136963,
-0.008188704028725624,
0.01059113722294569,
0.010823072865605354,
-0.0121713662520051,
-0.026056906208395958,
-0.00901550892740488,
-0.029956938698887825,
-0.01150189433246851,
-0.007561093661934137,
-0.05474448204040527,
0.06564973294734955,
0.04755423590540886,
-0.03906542807817459,
-0.0820738673210144,
-0.06303638219833374,
-0.052932221442461014,
-0.008632333017885685,
0.033790867775678635,
-0.002534344792366028,
-0.019825348630547523,
-0.0530523918569088,
0.04097393527626991,
-0.05519166588783264,
0.02707587741315365,
-0.040813006460666656,
-0.004407184664160013,
0.018346654251217842,
-0.04470035061240196,
0.02537391521036625,
-0.0032699157018214464,
0.016251880675554276,
-0.00980913732200861,
0.031419698148965836,
0.00906942505389452,
0.030313149094581604,
-0.007721686270087957,
-0.060396112501621246,
-0.07939334213733673,
0.029410675168037415,
-0.058742791414260864,
-0.021170277148485184,
-0.02662583626806736,
-0.013927248306572437,
0.05235385522246361,
0.026636604219675064,
-0.049622442573308945,
0.058130327612161636,
-0.0034742585849016905,
-0.013937976211309433,
-0.015226460993289948,
-0.016586529091000557,
0.02668055333197117,
-0.022680038586258888,
0.00404334207996726,
0.07907981425523758,
-0.0075638373382389545,
0.003883443307131529,
0.023017436265945435,
0.006307532079517841,
-0.033291444182395935,
0.0010567855788394809,
0.029401402920484543,
0.0013928868575021625,
-0.03340920805931091,
-0.06189708039164543,
-0.0472109355032444,
-0.015233378857374191,
-0.04494823142886162,
0.004136604256927967,
-0.04263867065310478,
-0.024530604481697083,
-0.0023709903471171856,
0.0273522287607193,
0.03674619644880295,
-0.004791943356394768,
-0.025643954053521156,
0.028323814272880554,
-0.03570728749036789,
-0.06466678529977798,
0.03969619423151016,
0.03693951293826103,
-0.05147712677717209,
-0.024835124611854553,
-0.0020630161743611097,
-0.06658246368169785,
-0.03718739375472069,
0.023113243281841278,
0.0682506337761879,
0.035490646958351135,
-0.003904018085449934,
-0.03359142690896988,
-0.037667255848646164,
-0.062073715031147,
0.0034736187662929296,
-0.026276733726263046,
-0.04387044161558151,
-0.015393340960144997,
-0.023038892075419426,
-0.0483633391559124,
-0.05022852495312691,
-0.006767368409782648,
0.00010944705718429759,
0.018893251195549965,
0.03320014476776123,
0.00693765701726079,
0.04216834530234337,
-0.04606639966368675,
0.038290563970804214,
0.004053869284689426,
0.02985204942524433,
0.05847594887018204,
-0.007033827248960733,
0.07581377774477005,
-0.006807384081184864,
0.03187630698084831,
0.023160815238952637,
-0.014474838972091675,
-0.009364095516502857,
0.048987098038196564,
-0.04001610353589058,
-0.002329661510884762,
0.01896536909043789,
-0.06649913638830185,
-0.018135961145162582,
0.02450726553797722,
0.013204560615122318,
0.04393170401453972,
-0.009723692201077938,
0.030410300940275192,
-0.01208627037703991,
-0.06459854543209076,
0.07238341122865677,
0.03179773688316345,
-0.0174470916390419,
-0.009303724393248558,
0.0352129302918911,
0.01704873889684677,
0.032784994691610336,
-0.0002188573416788131,
0.014118722639977932,
-0.05277535319328308,
0.020942894741892815,
-0.05380336567759514,
0.04141524061560631,
0.04032743722200394,
-0.014082765206694603,
0.03592526912689209,
0.03398774936795235,
0.02649730257689953,
0.03233769163489342,
-0.0345618762075901,
-0.017583712935447693,
-0.04482926428318024,
-0.04655298590660095,
-0.06083660200238228,
-0.016555815935134888,
-0.009997003711760044,
0.029725180938839912,
-0.05948280170559883,
-0.0731017217040062,
-0.010064839385449886,
0.046292565762996674,
-0.03613005578517914,
0.0402180440723896,
0.0333867147564888,
0.03522937372326851,
0.013812233693897724,
-0.0010174477938562632,
-0.07896790653467178,
0.04170570522546768,
0.01236503291875124,
-0.015356723219156265,
-0.0494513139128685,
-0.024298684671521187,
0.01354791410267353,
0.014248778112232685,
0.049316707998514175,
0.01045959908515215,
-0.07924102991819382,
-0.031114088371396065,
0.05054989084601402,
-0.04545750096440315,
-0.026216784492135048,
0.05501003563404083,
-0.04874970763921738,
-0.049911390990018845,
-0.017311107367277145,
-0.04056864604353905,
0.03444741666316986,
0.017603674903512,
0.02750565856695175,
0.014203228987753391,
0.005126886535435915,
-0.02475375309586525,
0.014872267842292786,
-0.007420660462230444,
0.016403930261731148,
0.05851118639111519,
0.07140778750181198,
-0.0118026128038764,
-0.06694094836711884,
-0.024897616356611252,
-0.024241363629698753,
-0.04719296097755432,
0.008309679105877876,
0.007083008997142315,
0.0066721513867378235,
-0.02964911237359047,
0.036770932376384735,
-0.015319081023335457,
-0.05162737891077995,
-0.015753865242004395,
0.05036534368991852,
-0.02632017619907856,
0.011308038607239723,
-0.00999398808926344,
0.046052541583776474,
-0.005771234631538391,
0.01307673193514347,
0.04539833590388298,
0.02448882907629013,
-0.04295506700873375,
0.037235695868730545,
0.08509393036365509,
0.018622461706399918,
0.08154147863388062,
0.04302728548645973,
-0.00004740236545330845,
0.0031614969484508038,
-0.012915014289319515,
-0.008307703770697117,
0.0036054456140846014,
-0.0636347308754921,
-0.010085316374897957,
0.00993432942777872,
0.09681379795074463,
0.020418681204319,
0.06862767785787582,
-0.04105539992451668,
-0.026101795956492424,
-0.06968610733747482,
-0.06806015968322754,
0.010875788517296314,
-0.026083961129188538,
0.12133105844259262,
-0.010192557238042355,
-0.030695272609591484,
-0.06591557711362839,
-0.06100253388285637,
0.07407519221305847,
0.0021569954697042704,
-0.044399335980415344,
0.011549755930900574,
-0.06141148507595062,
0.028835853561758995,
-0.018195858225226402,
0.0124193811789155,
-0.030130084604024887,
-0.018519695848226547,
-0.07685389369726181,
-0.0018858009716495872,
-0.0037603594828397036,
-0.04121264070272446,
0.06085502728819847,
-0.0020111650228500366,
0.008481322787702084,
0.03229004517197609,
0.011372745968401432,
-0.05771174281835556,
-0.02147800289094448,
-0.03366737812757492,
-0.023338567465543747,
-0.0020974623039364815,
0.009872905910015106,
-0.004891663324087858,
0.017082413658499718,
-0.00614147400483489,
-0.023890430107712746,
-0.027337653562426567,
0.012171161361038685,
0.028326937928795815,
0.011661466211080551,
0.00824397150427103,
-0.07565969228744507,
-0.06254864484071732,
0.017024273052811623,
0.015256714075803757,
0.006522777024656534,
0.0036370325833559036,
-0.04141276329755783,
-0.005516722798347473,
0.013158377259969711,
0.008772476576268673,
-0.05381203442811966,
0.04164275899529457,
-0.013909942470490932,
-0.053263336420059204,
0.014263241551816463,
-0.010170494206249714,
-0.030341552570462227,
-0.03083558939397335,
-0.02960589900612831,
0.012220215983688831,
0.05251156538724899,
0.048218127340078354,
0.002494942396879196,
0.005821872036904097,
0.045125991106033325,
0.06588168442249298,
0.00813993439078331,
0.04547087103128433,
0.0805477648973465,
-0.01460245531052351,
-0.051610495895147324,
0.00030246598180383444,
0.0018929688958451152,
0.008992244489490986,
0.003752461401745677,
-0.024224581196904182,
0.05662959814071655,
0.004914283752441406,
-0.042419202625751495,
-0.005704506300389767,
-0.039228737354278564,
0.027716754004359245,
0.008837947621941566,
-0.014024011790752411,
-0.031239349395036697,
-0.027620289474725723,
-0.025062575936317444,
0.017283469438552856,
0.06464830040931702,
0.014179331250488758,
0.08712112158536911,
0.04208650067448616,
0.024168619886040688,
0.011222581379115582,
0.017655296251177788,
0.030180830508470535,
0.04384632408618927,
-0.029467415064573288,
0.02745676226913929,
-0.07041867822408676,
-0.015949299558997154,
0.023280421271920204,
0.006441902834922075,
-0.04188881069421768,
-0.059575486928224564,
0.046921923756599426,
-0.01592310331761837,
-0.03521477058529854,
-0.10889748483896255,
-0.009205155074596405,
0.01828506402671337,
-0.030037958174943924,
0.023601947352290154,
0.005268685054033995,
0.03958933427929878,
-0.029952190816402435,
-0.00255577452480793,
0.002676059491932392,
-0.008963420987129211,
-0.019055115059018135,
-0.03535046428442001,
0.01912692002952099,
-0.059357013553380966,
-0.01805984415113926,
-0.023915840312838554,
-0.012650983408093452,
0.04327003285288811,
0.014041553251445293,
0.049446363002061844,
0.02327767014503479,
-0.003396972781047225,
0.015340968035161495,
-0.028439242392778397,
0.030290285125374794,
-0.00594524247571826,
0.00046572659630328417,
0.06572616100311279,
-0.03252521902322769,
0.04289869964122772,
0.021318234503269196,
-0.029225746169686317,
0.00757549749687314,
0.01172329019755125,
0.047966521233320236,
0.05470794439315796,
-0.027602428570389748,
0.007214520126581192,
-0.08171834796667099,
-0.0008378196507692337,
-0.00044023574446327984,
-0.02029619924724102,
0.0066399602219462395,
0.01707889698445797,
0.0511210672557354,
-0.026302823796868324,
0.013191317208111286,
-0.009903044439852238,
0.03161882236599922,
0.020403465256094933,
0.05223492905497551,
0.02862836793065071,
0.023410845547914505,
0.02779720164835453,
0.04139299690723419,
-0.011223326437175274,
0.035128287971019745,
-0.036906804889440536,
0.03813856467604637,
-0.0204339437186718,
0.02439888007938862,
0.04570186138153076,
-0.018901830539107323,
-0.025633888319134712,
-0.012246220372617245,
0.013948949985206127,
-0.008875877596437931,
0.037298064678907394,
0.0214387234300375,
-0.01793782040476799,
0.02149152383208275,
0.01843065209686756,
-0.026350174099206924,
-0.07591841369867325,
-0.005326756741851568,
-0.04213539510965347,
0.021710529923439026,
-0.05937933921813965,
-0.05352630838751793,
0.027011845260858536,
0.05923016741871834,
-0.0055448575876653194,
0.04263041540980339,
0.02979440428316593,
0.00794125348329544,
0.01676459237933159,
0.024023106321692467,
0.038767796009778976,
-0.07024988532066345,
0.0384303480386734,
0.0642896294593811,
-0.015167991630733013,
-0.024268729612231255,
0.020181672647595406,
0.032505594193935394,
-0.05199825018644333,
0.024027138948440552,
0.03135993331670761,
-0.057117659598588943,
-0.07604518532752991,
-0.024331744760274887,
0.04412372037768364,
0.02879529818892479,
-0.05300881713628769,
-0.05877825990319252,
0.044848717749118805,
-0.0013807459035888314,
0.05979802459478378,
0.03189487010240555,
0.011865109205245972,
-0.013951136730611324,
0.019852297380566597,
0.02769036777317524,
-0.001108881551772356,
0.005271360743790865,
0.026965392753481865,
0.04234769195318222,
-0.04025278240442276,
-0.01978653483092785,
-0.043262772262096405,
-0.042758382856845856,
0.024327024817466736
] |
<p>One usually hears about graphene as a good thermal conductor, and good light absorber due to its tunable bandgap properties. But i haven't heard about its aplicability as an optical mirror. In fact, mostly the opposite is true: the optical transmissivity of monolayer graphene is very high ($\approx$ 98%)</p>
<p>Since there are material engineering tricks to tune the separation between two or more graphene layers, i would expect that multi-layer destructive interference can be achieved with optical wavelengths, enhancing reflectivity</p>
<p>I know that probably graphene is not the best material to do this, but allow me to insist. Why? Well, graphene mantains it's properties well over 3000K, and a couple of layers of it can be quite strong and very light. All these properties make it the ideal material for a laser-pushed sail. </p>
<p>By the way, i'm asking about optical and UV frequencies, i know that monolayer graphene is reflective on the microwave region, and i'm not asking about that. Thanks</p> | g1307 | [
0.01707741990685463,
0.022015420719981194,
0.014284024946391582,
0.0030364827252924442,
0.053088121116161346,
0.0015432107029482722,
-0.024343058466911316,
0.005311756394803524,
0.021426698192954063,
-0.018138503655791283,
0.02332981489598751,
0.009604740887880325,
0.047182854264974594,
-0.04081745073199272,
0.008268634788691998,
0.0022887676022946835,
-0.006318375002592802,
-0.0011941901175305247,
0.0059061190113425255,
0.04189301282167435,
-0.11553539335727692,
-0.1014849841594696,
0.012770367786288261,
-0.04397285357117653,
-0.009533541277050972,
0.030144011601805687,
0.013755986467003822,
-0.036931782960891724,
0.035739555954933167,
-0.025429371744394302,
0.014694060198962688,
-0.02506912127137184,
-0.006184798199683428,
-0.04668395221233368,
0.011195646598935127,
0.01344059407711029,
-0.02880212850868702,
-0.028079545125365257,
0.004691873677074909,
0.00039675322477705777,
-0.012076492421329021,
0.03951497748494148,
-0.023049652576446533,
0.02353558875620365,
0.08510655909776688,
0.021577537059783936,
-0.018657660111784935,
-0.05313093587756157,
0.027304014191031456,
-0.08845867961645126,
0.018128152936697006,
0.009211601689457893,
0.06451812386512756,
-0.009268106892704964,
-0.007551920600235462,
-0.04267770051956177,
-0.058640897274017334,
-0.0008658095612190664,
0.020773425698280334,
-0.03579462319612503,
-0.0375591441988945,
0.000642118277028203,
-0.0240881759673357,
0.02346358448266983,
0.013993566855788231,
0.011519339866936207,
-0.020679201930761337,
-0.011257566511631012,
-0.014588109217584133,
-0.0034873492550104856,
-0.0012098735896870494,
-0.018709233030676842,
-0.02368944324553013,
-0.05010705068707466,
0.05701245367527008,
-0.027829088270664215,
0.016110697761178017,
0.012017959728837013,
-0.018258601427078247,
0.01449253223836422,
-0.043190665543079376,
0.018733182922005653,
-0.05176885798573494,
-0.010375290177762508,
-0.03674499690532684,
-0.02474564127624035,
0.025751899927854538,
-0.013465344905853271,
-0.0028951202984899282,
0.03937210515141487,
0.08936943858861923,
0.020037584006786346,
0.05053839087486267,
0.036406051367521286,
0.02943306975066662,
0.02624443545937538,
0.0291302390396595,
0.012387306429445744,
-0.02807057835161686,
0.02949581854045391,
-0.012021091766655445,
-0.05402831733226776,
-0.02250456064939499,
0.034910254180431366,
0.02897508814930916,
0.002093377523124218,
-0.0050557819195091724,
-0.01156229805201292,
-0.026591794565320015,
-0.027409421280026436,
-0.046407558023929596,
-0.034807149320840836,
0.0008322224020957947,
0.0022606635466217995,
-0.028867239132523537,
-0.011823388747870922,
0.08262887597084045,
-0.048102401196956635,
0.014714539982378483,
0.07871337980031967,
0.09706664085388184,
0.03285966441035271,
-0.03552481532096863,
0.04433498904109001,
0.028031665831804276,
-0.03231629729270935,
0.04030323401093483,
0.02898545190691948,
0.019644804298877716,
0.0024459296837449074,
0.013282690197229385,
0.029253019019961357,
-0.041891053318977356,
0.044323619455099106,
0.01433106604963541,
-0.010187597945332527,
-0.02547978051006794,
-0.020666059106588364,
0.007816950790584087,
0.025234680622816086,
0.013066490180790424,
-0.022816622629761696,
0.0064566778019070625,
-0.008279651403427124,
0.00929050613194704,
0.018296455964446068,
-0.052209995687007904,
0.0028421510942280293,
-0.026433462277054787,
0.02612397074699402,
0.022127803415060043,
0.03571166470646858,
0.030715826898813248,
-0.0985020250082016,
0.010275972075760365,
-0.012854666449129581,
0.020413603633642197,
-0.02015101909637451,
0.0346018485724926,
0.04899131879210472,
0.04799828678369522,
0.022453520447015762,
-0.058409444987773895,
-0.011746804229915142,
-0.004157125949859619,
-0.013378312811255455,
-0.03798140957951546,
-0.053125567734241486,
-0.021314555779099464,
0.028804464265704155,
-0.04155239090323448,
0.04577841982245445,
-0.03219648078083992,
0.04630108177661896,
0.008827673271298409,
0.012826822698116302,
0.022511834278702736,
-0.01748393289744854,
-0.03213763236999512,
0.010529911145567894,
-0.057187244296073914,
-0.01634267345070839,
0.009900353848934174,
-0.05722753331065178,
0.021783092990517616,
-0.050725314766168594,
-0.021022062748670578,
-0.05690119415521622,
-0.009833183139562607,
0.07560678571462631,
-0.014544893056154251,
0.03926275670528412,
-0.04171553999185562,
-0.006939505226910114,
0.06376306712627411,
-0.015088485553860664,
0.02906547114253044,
-0.004838207270950079,
-0.05401085689663887,
0.026168502867221832,
-0.02292940579354763,
-0.0225367434322834,
0.06122802570462227,
-0.00027929083444178104,
0.02309567853808403,
0.08331424742937088,
-0.02113187685608864,
-0.011505412869155407,
0.011386899277567863,
-0.03503311052918434,
0.059725090861320496,
0.03351562097668648,
0.027518028393387794,
-0.01886202208697796,
0.021380798891186714,
-0.002491061808541417,
-0.06215418130159378,
0.015844348818063736,
0.0249906275421381,
-0.0027191280387341976,
-0.045144226402044296,
0.058056462556123734,
0.031667351722717285,
0.009251145645976067,
-0.045197032392024994,
0.02000417187809944,
-0.103522889316082,
0.03380272537469864,
0.01810297742486,
-0.004348833113908768,
0.07295254617929459,
-0.020161129534244537,
0.02077101357281208,
-0.03610343486070633,
0.027803929522633553,
0.025649499148130417,
-0.04209195077419281,
-0.00558604346588254,
-0.010582110844552517,
0.005863027181476355,
0.02327756956219673,
-0.033310145139694214,
-0.053464435040950775,
-0.052394699305295944,
-0.022726519033312798,
-0.01832643523812294,
-0.0793556272983551,
0.058596864342689514,
0.047531355172395706,
0.007113482803106308,
0.061115313321352005,
0.01801697537302971,
-0.0018256290350109339,
0.0239302609115839,
-0.019279716536402702,
0.0432635173201561,
0.024921201169490814,
-0.018819961696863174,
-0.0701562836766243,
-0.03287194296717644,
-0.0033896551467478275,
-0.0630258098244667,
-0.042159151285886765,
-0.016081711277365685,
-0.010266261175274849,
0.002826375188305974,
0.008356938138604164,
0.019204508513212204,
0.046655431389808655,
0.021469028666615486,
-0.0320865698158741,
0.03251735121011734,
0.03789820894598961,
-0.00034621040686033666,
-0.006047668866813183,
-0.051526881754398346,
0.009188780561089516,
-0.043174151331186295,
0.06091748923063278,
0.01193674560636282,
0.0005001584067940712,
-0.04656041041016579,
-0.017486747354269028,
0.014874925836920738,
0.020970234647393227,
-0.014235648326575756,
0.001022542011924088,
0.005174556747078896,
0.082678884267807,
0.0221655685454607,
0.0006723047117702663,
0.000926376786082983,
-0.007694416679441929,
0.0048055765219032764,
-0.02613569237291813,
-0.04099581018090248,
0.04037681221961975,
0.008057809434831142,
-0.011725220829248428,
-0.03855319693684578,
-0.00874660536646843,
0.029875097796320915,
0.007449640892446041,
0.0449715293943882,
-0.05348458141088486,
0.005593621172010899,
0.005520942155271769,
-0.006778184790164232,
0.04486462473869324,
0.03338313102722168,
0.02720007859170437,
-0.001487879897467792,
-0.016286242753267288,
0.052307840436697006,
0.012489275075495243,
0.0539025254547596,
-0.04121037572622299,
-0.008313478901982307,
0.006087100598961115,
-0.014964970760047436,
0.0062719425186514854,
0.011388491839170456,
0.022779690101742744,
-0.0834100991487503,
-0.05368505045771599,
0.025030886754393578,
0.01254377793520689,
-0.027968687936663628,
-0.0141393281519413,
0.0005405719857662916,
0.007504199165850878,
0.03264893591403961,
0.020488247275352478,
0.030701270326972008,
0.0320318266749382,
0.0265478678047657,
0.006645990535616875,
0.013975727371871471,
-0.018299097195267677,
0.03781219199299812,
0.044328875839710236,
-0.02090708538889885,
-0.03411512076854706,
-0.06001901254057884,
0.06874693930149078,
0.021455513313412666,
-0.023354509845376015,
0.02193247526884079,
-0.04274850711226463,
0.01570313610136509,
-0.010158343240618706,
-0.06137630715966225,
0.021677570417523384,
0.011236414313316345,
-0.034653324633836746,
-0.033118393272161484,
0.02648494578897953,
0.07999014854431152,
0.04708421230316162,
-0.03057926893234253,
-0.014581411145627499,
0.03264579921960831,
0.025109415873885155,
-0.0021612830460071564,
0.011795173399150372,
-0.027875320985913277,
0.024514390155673027,
0.036300744861364365,
0.010235906578600407,
0.0993756577372551,
-0.018953144550323486,
-0.013224266469478607,
-0.01936202310025692,
-0.008746329694986343,
0.027797657996416092,
-0.022390587255358696,
0.026992417871952057,
0.0018943261820822954,
0.01963871531188488,
0.005083305295556784,
0.0030998357106000185,
0.037235077470541,
0.03719611465930939,
0.02295108139514923,
0.006990928668528795,
-0.02380971796810627,
-0.009758736938238144,
-0.06533622741699219,
-0.0192117802798748,
-0.06091619282960892,
-0.0004669076588470489,
-0.015063547529280186,
0.010566881857812405,
-0.0007490132702514529,
-0.013096550479531288,
-0.032569535076618195,
-0.03768312186002731,
-0.022930197417736053,
-0.016644444316625595,
0.03756421059370041,
0.05133115127682686,
0.012276098132133484,
-0.0342487134039402,
-0.0010305093601346016,
-0.009019813500344753,
-0.0398523174226284,
0.04074905067682266,
0.0029878125060349703,
-0.024668987840414047,
-0.02554456889629364,
0.022367054596543312,
-0.08540857583284378,
-0.0061590769328176975,
-0.07402043789625168,
-0.0015259977662935853,
0.034646470099687576,
-0.006668248679488897,
-0.04802203178405762,
0.026572823524475098,
0.01607505790889263,
-0.0009712993050925434,
0.03917795047163963,
-0.022368211299180984,
0.04331406205892563,
0.03459489718079567,
0.0754823088645935,
0.019156131893396378,
-0.06252875179052353,
0.023022275418043137,
0.004195760004222393,
0.07447915524244308,
-0.013075750321149826,
0.002611092058941722,
-0.010662941262125969,
0.020886661484837532,
0.02861085720360279,
0.07217776030302048,
0.008040804415941238,
0.02765772119164467,
0.04307090863585472,
0.0594913512468338,
-0.02146027237176895,
0.08946052193641663,
-0.009187699295580387,
0.029016463086009026,
-0.028466852381825447,
-0.006621811538934708,
-0.0017865921836346388,
0.033696308732032776,
0.081685371696949,
-0.02566434256732464,
-0.08450067788362503,
-0.003642902011051774,
-0.030781229957938194,
-0.09169253706932068,
-0.010163949802517891,
-0.030934419482946396,
0.022543836385011673,
0.060816843062639236,
-0.02215106412768364,
0.05917608365416527,
-0.029526237398386,
-0.04008584842085838,
-0.024873003363609314,
0.007261526770889759,
0.08130156248807907,
-0.02680230513215065,
0.03557271882891655,
0.005928948987275362,
-0.027767501771450043,
-0.006680102087557316,
0.06135788932442665,
0.0422065369784832,
0.04812801629304886,
-0.049095671623945236,
-0.06645365804433823,
-0.05754374712705612,
0.0006422499427571893,
-0.02901308983564377,
-0.025451498106122017,
-0.022541942074894905,
-0.01212163083255291,
0.06969378143548965,
-0.03776828944683075,
-0.04507504031062126,
-0.060025040060281754,
-0.0022027890663594007,
0.02620331011712551,
-0.034902945160865784,
-0.03670041263103485,
-0.02239309251308441,
-0.0054189786314964294,
-0.06744883954524994,
-0.021612072363495827,
-0.01605752296745777,
0.013770965859293938,
0.02828720025718212,
0.02289988473057747,
0.03218251094222069,
0.021391836926341057,
0.004376964643597603,
0.0478486604988575,
0.027962911874055862,
0.006648203823715448,
-0.04091605916619301,
0.028308145701885223,
0.04705935716629028,
-0.008126390166580677,
0.0150517662987113,
0.016551557928323746,
-0.039611637592315674,
-0.04216257110238075,
-0.08160701394081116,
0.02883891761302948,
0.008978275582194328,
-0.05764611437916756,
0.027086429297924042,
-0.01975765824317932,
-0.017745904624462128,
0.03693985939025879,
-0.020197156816720963,
0.022350959479808807,
-0.09271541982889175,
0.03498927131295204,
0.02689550258219242,
0.025398872792720795,
0.018961351364850998,
-0.02003270946443081,
0.01929652690887451,
-0.049800433218479156,
0.056430306285619736,
0.03811415657401085,
0.004666860681027174,
-0.02241765521466732,
0.03631309047341347,
0.0030091856606304646,
0.02275778353214264,
0.03177435323596001,
0.020783664658665657,
-0.0337170772254467,
-0.0793674886226654,
0.033034201711416245,
-0.015911145135760307,
0.0977756679058075,
0.05520589277148247,
0.027363015338778496,
0.03887932747602463,
-0.007356920279562473,
-0.032336246222257614,
0.022950012236833572,
0.06180162355303764,
-0.018989793956279755,
0.032300397753715515,
-0.024964114651083946,
0.02908586524426937,
0.0004588556766975671,
-0.08338095247745514,
-0.027297379449009895,
0.03674846142530441,
-0.0066131604835391045,
0.026819348335266113,
0.002608428942039609,
0.013792508281767368,
-0.03555912896990776,
-0.0048387665301561356,
-0.034311868250370026,
0.030470361933112144,
-0.0478990375995636,
0.013809481635689735,
-0.017564542591571808,
-0.06547129154205322,
-0.02650068886578083,
-0.008585046976804733,
-0.028534943237900734,
-0.006068868562579155,
0.01051351148635149,
-0.0034136029426008463,
-0.04336085543036461,
0.005024288315325975,
-0.0312986858189106,
0.04036702960729599,
0.0011649435618892312,
-0.05172592028975487,
-0.0015994702698662877,
-0.06394612789154053,
-0.003419838845729828,
-0.007671216037124395,
-0.021168727427721024,
0.04167331010103226,
-0.05075710266828537,
-0.009495820850133896,
-0.02150183916091919,
0.0019063001964241266,
-0.0036535710096359253,
0.04030795022845268,
-0.058913156390190125,
-0.03222239762544632,
0.03137153759598732,
0.018893931061029434,
-0.0016212433110922575,
0.024548644199967384,
-0.05984566733241081,
-0.020333625376224518,
-0.010286024771630764,
0.012930002063512802,
0.07254283875226974,
0.053152941167354584,
-0.06245778873562813,
0.015925172716379166,
0.022261682897806168,
0.009281758219003677,
0.02263498678803444,
-0.005648960825055838,
-0.022015804424881935,
-0.06084776297211647,
0.0025255666114389896,
-0.056873440742492676,
-0.05433698371052742,
0.01615164428949356,
0.004298995714634657,
0.016616294160485268,
-0.04278872534632683,
-0.009289774112403393,
-0.030346067622303963,
0.021883385255932808,
0.0471828356385231,
-0.022696735337376595,
0.015362344682216644,
0.0435330793261528,
-0.013232840225100517,
0.02000352554023266,
-0.01079554669559002,
0.07348368316888809,
-0.012736370787024498,
0.0280260369181633,
0.003810882568359375,
-0.02801145240664482,
-0.026169074699282646,
-0.005564630962908268,
0.018394827842712402,
-0.0783790647983551,
-0.02627067267894745,
-0.01502392627298832,
0.037526488304138184,
0.001842774567194283,
0.025438982993364334,
0.009030460380017757,
-0.06343217939138412,
-0.020906178280711174,
0.025805596262216568,
-0.0657443106174469,
0.006023265887051821,
-0.04620090499520302,
-0.030659999698400497,
0.003991152159869671,
0.01305155735462904,
-0.04631628468632698,
0.05616844817996025,
-0.006624880246818066,
-0.011414109729230404,
-0.005374657455831766,
-0.01364982035011053,
-0.036432065069675446,
-0.030805211514234543,
0.011026553809642792,
-0.0012412850046530366,
-0.009610799141228199,
-0.021891841664910316,
-0.02785404957830906,
-0.03295173496007919,
-0.0030355900526046753,
-0.036844588816165924,
-0.009591163136065006,
0.0013272197684273124,
0.0009538111044093966,
-0.06010846421122551,
-0.06121569871902466,
-0.034787409007549286,
-0.0510791577398777,
0.02772420644760132,
-0.009927655570209026,
0.0030306661501526833,
0.11474069952964783,
-0.02539885602891445,
0.011507020331919193,
0.022807689383625984,
-0.007725007366389036,
0.025910155847668648,
-0.020957184955477715,
-0.0602230578660965,
-0.029612941667437553,
0.08156416565179825,
-0.023520004004240036,
-0.02524721436202526,
0.05184317007660866,
0.01798158511519432,
0.009707068093121052,
0.03117825649678707,
-0.026316754519939423,
0.012245702557265759,
-0.05371374264359474,
0.011973903514444828,
0.029081078246235847,
-0.04763524606823921,
0.012965260073542595,
0.0409693606197834,
0.0010280967690050602,
-0.0023811710998415947,
0.07294313609600067,
-0.02919837087392807,
-0.035915251821279526,
0.03987901657819748,
0.05196257308125496,
0.04562121629714966,
0.04939587041735649,
-0.06006237864494324,
-0.030385112389922142,
0.02381940931081772,
-0.0390082523226738,
0.039902444928884506,
0.03178749978542328,
0.018025081604719162,
0.005710300989449024,
0.012837184593081474,
0.011951337568461895,
-0.06315411627292633,
0.0055535645224153996,
-0.02589203231036663,
0.052698858082294464,
0.009068997576832771,
0.023416010662913322,
0.05320446565747261,
-0.09212676435709,
-0.013670898973941803,
-0.020614009350538254,
0.01671415939927101,
0.011559534817934036,
0.03683764487504959,
0.06469063460826874,
0.04900494962930679,
0.0496053583920002,
0.016257749870419502,
-0.04554298520088196,
-0.052880071103572845,
-0.009581105783581734,
0.03863444924354553,
-0.07222473621368408,
-0.03145848959684372,
-0.043569132685661316,
-0.003042779630050063,
-0.0036837158259004354,
0.07487163692712784,
0.021479440852999687,
-0.027983274310827255,
0.04385306313633919,
-0.03515579178929329,
0.0687658041715622,
0.033475689589977264,
0.02513967454433441,
0.011698490008711815,
0.004007849842309952,
-0.017060449346899986,
0.00771993538364768,
-0.028163351118564606,
-0.013214407488703728,
-0.04135033115744591,
0.020590363070368767,
-0.07095937430858612
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.