question
stringlengths 37
38.8k
| group_id
int64 0
74.5k
| sentence_embeddings
listlengths 1.02k
1.02k
|
|---|---|---|
<p>Why is it preferable to say that the doppler effect causes a shift in frequency rather than a shift in wavelength? I often read on websites that they define the doppler effect as a change in frequency. </p>
| 8,795 |
[
-0.03184499964118004,
-0.0014247593935579062,
-0.00269737234339118,
-0.03222539648413658,
0.03404008597135544,
0.01468185056000948,
-0.014848412945866585,
-0.012749518267810345,
0.016705745831131935,
-0.010436798445880413,
0.008809692226350307,
0.022265464067459106,
0.054728537797927856,
-0.012648725882172585,
0.025926459580659866,
0.04093112424015999,
-0.008455933071672916,
-0.004107062239199877,
-0.027102356776595116,
-0.005388401448726654,
-0.034555014222860336,
0.019748089835047722,
0.008371787145733833,
0.009168471209704876,
-0.014249118976294994,
0.01789122074842453,
0.0429447703063488,
0.03086291253566742,
0.03563740476965904,
0.008268361911177635,
0.016160951927304268,
-0.004661066457629204,
-0.01612488552927971,
0.06790678203105927,
0.028546364977955818,
-0.016647377982735634,
-0.03835882619023323,
0.0029671420343220234,
0.008407230488955975,
0.016284340992569923,
-0.0541011206805706,
0.0004888692637905478,
0.011074618436396122,
0.029715828597545624,
-0.026711808517575264,
0.006764139048755169,
0.012749104760587215,
-0.03146710246801376,
0.04631952941417694,
-0.028416240587830544,
0.07039738446474075,
-0.03187425434589386,
0.03172742575407028,
0.008855723775923252,
-0.012343558482825756,
0.020110007375478745,
0.09733626246452332,
0.07783821225166321,
-0.027746831998229027,
-0.04754824936389923,
-0.03158245608210564,
-0.027654334902763367,
-0.008210537023842335,
-0.011151421815156937,
-0.022720832377672195,
0.01734672673046589,
-0.032146964222192764,
-0.03570671007037163,
0.03650135174393654,
0.03080199845135212,
-0.027189940214157104,
-0.005208391230553389,
0.010615874081850052,
-0.03883516788482666,
0.0012935118284076452,
-0.07089844346046448,
-0.01058932114392519,
-0.0007625952712260187,
0.02305479161441326,
0.04320664331316948,
-0.026788191869854927,
0.005979893729090691,
0.026162436231970787,
-0.003617061534896493,
0.011194052174687386,
-0.030815986916422844,
0.09343096613883972,
-0.009710042737424374,
0.0015311335446313024,
0.04480602219700813,
-0.01489904336631298,
0.023670518770813942,
0.02131704054772854,
-0.007916899397969246,
0.0017477627843618393,
0.0411921963095665,
-0.018897458910942078,
0.03800663352012634,
0.01876198500394821,
-0.05414330214262009,
0.012522576376795769,
-0.02679828368127346,
0.06040309742093086,
0.06587773561477661,
-0.018806055188179016,
-0.013190234079957008,
-0.042818475514650345,
0.015228058211505413,
-0.030103445053100586,
-0.024764860048890114,
-0.010636771097779274,
0.021341092884540558,
-0.007786335423588753,
0.03014826960861683,
-0.00918870884925127,
-0.004710810258984566,
0.0450030192732811,
0.0048657990992069244,
0.04885454103350639,
0.09428742527961731,
0.04715941473841667,
-0.0554380938410759,
0.014843318611383438,
-0.00950413104146719,
-0.017045702785253525,
0.019686700776219368,
0.0004094911855645478,
0.0001117667998187244,
-0.00048368191346526146,
0.013007387518882751,
-0.003310898318886757,
-0.045746393501758575,
0.015025521628558636,
0.013523604720830917,
-0.01228601485490799,
0.0142140444368124,
-0.13795241713523865,
-0.04536285623908043,
0.04542603716254234,
-0.01939941942691803,
0.01716580241918564,
-0.09701823443174362,
-0.009096683003008366,
0.004208941478282213,
0.0681937038898468,
-0.001709290430881083,
0.01236376166343689,
-0.03469742089509964,
0.03138548135757446,
-0.0007330205990001559,
0.0038556416984647512,
-0.03388108313083649,
0.004923607222735882,
-0.05896541476249695,
-0.002227246295660734,
-0.038215842097997665,
-0.021087493747472763,
0.020055364817380905,
-0.013407200574874878,
-0.03847487270832062,
0.03231801092624664,
-0.043062593787908554,
-0.027410808950662613,
0.01568983867764473,
0.03956717997789383,
-0.02499694563448429,
0.059982653707265854,
0.03291494771838188,
-0.009387141093611717,
0.034608032554388046,
0.026895346119999886,
0.02570175752043724,
0.008618524298071861,
0.058177750557661057,
0.012849293649196625,
-0.0535869374871254,
0.013231690041720867,
-0.011205587536096573,
0.01659071072936058,
-0.03329119086265564,
0.002123090671375394,
-0.01765815168619156,
-0.011422804556787014,
0.00447557307779789,
0.002098575234413147,
0.05769633501768112,
-0.007668428588658571,
0.027685686945915222,
0.01688835397362709,
-0.04813792556524277,
0.022914033383131027,
-0.0274709053337574,
0.061993300914764404,
0.005027621518820524,
-0.018455442041158676,
0.01969296857714653,
0.020256604999303818,
0.03862085938453674,
-0.01902097649872303,
-0.01688625104725361,
0.004261571913957596,
0.021015718579292297,
0.00024265970569103956,
-0.031949546188116074,
0.015064838342368603,
0.07977849245071411,
0.02052532508969307,
0.021317094564437866,
0.020263398066163063,
-0.02289762906730175,
-0.027511391788721085,
0.01687169447541237,
0.017245830968022346,
0.019729452207684517,
-0.027738206088542938,
-0.014210361987352371,
-0.015822479501366615,
-0.03043816238641739,
-0.017696531489491463,
0.04440489038825035,
-0.0457700714468956,
0.09380215406417847,
0.06065191328525543,
-0.012819342315196991,
0.03023577481508255,
0.054176732897758484,
0.013663620688021183,
-0.01116099487990141,
0.009279919788241386,
-0.05604034289717674,
-0.05032552778720856,
0.012504124082624912,
0.03387967869639397,
0.02537110261619091,
-0.03173797205090523,
0.009352428838610649,
0.003604627214372158,
0.03801926225423813,
0.0281660333275795,
0.060544341802597046,
0.004822088405489922,
-0.06599603593349457,
-0.012125416658818722,
0.011225291527807713,
0.009350770153105259,
-0.014048044569790363,
0.03136029466986656,
0.015865009278059006,
0.04017481952905655,
-0.011877988465130329,
-0.022260632365942,
0.052804186940193176,
-0.015527356415987015,
0.001971209654584527,
0.018823787569999695,
-0.007643049117177725,
-0.01167247723788023,
-0.053492702543735504,
0.012285208329558372,
0.011046216823160648,
-0.029332546517252922,
0.00926897767931223,
0.013284534215927124,
-0.028205400332808495,
0.03273766487836838,
0.007037436589598656,
-0.02985025756061077,
0.018171943724155426,
0.03396087512373924,
-0.05981409177184105,
0.0053784954361617565,
-0.044248566031455994,
-0.018452566117048264,
-0.013409690000116825,
-0.021261725574731827,
0.007598927244544029,
0.01479595061391592,
0.04408808425068855,
-0.020752310752868652,
-0.020763592794537544,
0.019504176452755928,
-0.040302474051713943,
-0.004613574128597975,
-0.010178747586905956,
-0.0007717162952758372,
0.0008292914717458189,
-0.03210338205099106,
-0.03527570888400078,
0.02465815283358097,
-0.03343275189399719,
-0.005563391372561455,
-0.01922011375427246,
-0.00528978044167161,
-0.07118476927280426,
-0.022970138117671013,
-0.047178030014038086,
0.032948050647974014,
0.024701079353690147,
-0.028488624840974808,
0.07046298682689667,
-0.04492736607789993,
-0.011975700967013836,
0.011406575329601765,
-0.021194547414779663,
-0.027984056621789932,
-0.04049792140722275,
-0.005667505785822868,
-0.0015783917624503374,
-0.04075067117810249,
0.021041063591837883,
-0.02027641423046589,
-0.0790354311466217,
0.0008221841999329627,
0.010541132651269436,
-0.04602586850523949,
0.05012048780918121,
0.0005320088239386678,
0.05806226283311844,
-0.017629064619541168,
-0.0014583528973162174,
0.06455283612012863,
0.025295330211520195,
-0.028371579945087433,
-0.022101804614067078,
0.005111084785312414,
-0.01972131058573723,
-0.024393415078520775,
0.019249578937888145,
0.05995737016201019,
-0.0035618352703750134,
0.05452293902635574,
0.0030472392681986094,
-0.019413333386182785,
0.040156327188014984,
0.03558027744293213,
-0.025967063382267952,
-0.007471222430467606,
-0.008716425858438015,
-0.006753060035407543,
0.018206585198640823,
0.030939405784010887,
-0.033775996416807175,
0.006343790329992771,
-0.009700826369225979,
0.03259878605604172,
0.0031739743426442146,
-0.030423911288380623,
0.01992362178862095,
0.008618101477622986,
-0.021144695580005646,
-0.014577506110072136,
0.006318863946944475,
0.010587142780423164,
0.01881919801235199,
-0.0059755714610219,
0.01819031871855259,
0.031906288117170334,
-0.012259186245501041,
-0.019767707213759422,
0.04166257753968239,
0.033149346709251404,
-0.013250142335891724,
0.010621129535138607,
0.00581670505926013,
-0.029412103816866875,
0.03183886036276817,
-0.01962798275053501,
-0.01597200520336628,
0.04612056910991669,
0.02188269793987274,
0.009658458642661572,
-0.0079836156219244,
-0.03880276530981064,
0.006413976661860943,
-0.03560034930706024,
-0.001891521504148841,
0.03270627185702324,
0.0255271103233099,
-0.0005620429874397814,
0.09400828182697296,
0.03446264937520027,
0.033289674669504166,
-0.011894134804606438,
-0.0009689053404144943,
-0.08427248150110245,
0.0036467795725911856,
-0.034599028527736664,
-0.008890253491699696,
-0.0227363184094429,
-0.02052925154566765,
-0.014356463216245174,
-0.054028190672397614,
-0.026290498673915863,
-0.037553317844867706,
-0.04233739897608757,
-0.027125315740704536,
0.006262976676225662,
0.023184021934866905,
-0.032235037535429,
-0.0216529443860054,
0.021754156798124313,
0.03273459151387215,
-0.003371182130649686,
0.0375216007232666,
0.04057135432958603,
0.005291967187076807,
-0.015817835927009583,
-0.022910024970769882,
0.006657429039478302,
0.013111245818436146,
0.016519812867045403,
0.05400077998638153,
0.012580336071550846,
-0.03720937669277191,
0.017624905332922935,
0.013978460803627968,
0.012330634519457817,
-0.008801285177469254,
-0.030386660248041153,
-0.0351315513253212,
-0.04008901119232178,
0.018607890233397484,
-0.004467252176254988,
0.06325887888669968,
-0.016031214967370033,
0.0072347489185631275,
0.031126419082283974,
-0.016921432688832283,
0.0031116572208702564,
0.05452330410480499,
0.009725839830935001,
0.004551225807517767,
-0.011974272318184376,
-0.01730523630976677,
0.022425558418035507,
-0.03150833025574684,
-0.022358637303113937,
0.019975021481513977,
0.008441644720733166,
-0.0020013863686472178,
-0.005276608746498823,
0.030800480395555496,
-0.009154129773378372,
0.011061618104577065,
-0.02136930078268051,
0.005513085518032312,
-0.0021004846785217524,
-0.0014079007087275386,
0.007580715697258711,
-0.013020893558859825,
0.027605291455984116,
0.0321744903922081,
0.014650729484856129,
-0.0021475402172654867,
-0.11298389732837677,
-0.01870795525610447,
0.012501278892159462,
0.040417786687612534,
-0.03775479272007942,
-0.012079046107828617,
-0.03780417889356613,
-0.016960743814706802,
0.000930839916691184,
-0.040040966123342514,
-0.00141328654717654,
-0.03839948773384094,
-0.0015523763140663505,
-0.0206086877733469,
-0.032555822283029556,
-0.005611106753349304,
0.028594888746738434,
0.01174322608858347,
-0.014016632921993732,
-0.01824934221804142,
-0.019824322313070297,
-0.03763372078537941,
0.00004959182479069568,
0.02593027427792549,
0.030993066728115082,
-0.01875274069607258,
-0.016679130494594574,
-0.03859084099531174,
0.023387499153614044,
-0.03227462247014046,
-0.05011899396777153,
-0.011099237017333508,
0.019143516197800636,
0.03342551365494728,
0.04257702827453613,
-0.016856921836733818,
-0.05967305973172188,
-0.007459335029125214,
0.01953217200934887,
-0.02571307308971882,
-0.020873161032795906,
-0.021921060979366302,
0.04887358844280243,
0.013591499999165535,
-0.002230673097074032,
0.048299938440322876,
0.03883788734674454,
-0.016037877649068832,
0.010370737873017788,
0.01018800400197506,
0.05928001552820206,
-0.07259271293878555,
-0.0013316895347088575,
0.00026366079691797495,
0.017695758491754532,
-0.01919742487370968,
0.06819251924753189,
0.010113141499459743,
0.004572706297039986,
0.008942420594394207,
-0.00602875417098403,
-0.028834480792284012,
0.01956189051270485,
0.0021976514253765345,
0.006841716356575489,
-0.01081361435353756,
0.014496852643787861,
0.01866760291159153,
-0.011344862170517445,
0.02946942113339901,
0.016878388822078705,
-0.006884477101266384,
0.02770417183637619,
-0.005653339438140392,
0.0012545296922326088,
-0.03438873589038849,
-0.012436958029866219,
0.03605641424655914,
-0.041743602603673935,
0.0034194421023130417,
-0.04179693013429642,
0.003448760835453868,
-0.01624894328415394,
-0.07056985050439835,
-0.03176407888531685,
0.008939340710639954,
-0.00988929346203804,
0.05079701542854309,
-0.03985363245010376,
0.03258943185210228,
0.026810484007000923,
0.010995144955813885,
-0.07745163142681122,
-0.05704807862639427,
0.025476763024926186,
0.04775036498904228,
-0.004979705438017845,
-0.009309055283665657,
0.02947956696152687,
-0.045302506536245346,
-0.017270009964704514,
-0.004824209958314896,
0.04888181388378143,
-0.012549730949103832,
-0.0255457554012537,
-0.005776091478765011,
-0.008853890933096409,
0.042750343680381775,
-0.025465816259384155,
-0.035398706793785095,
-0.0020267271902412176,
-0.021251603960990906,
0.0039014043286442757,
-0.018346669152379036,
0.05080900713801384,
-0.02677355334162712,
-0.031899407505989075,
0.022070463746786118,
-0.015321129932999611,
0.024628303945064545,
-0.026341356337070465,
-0.005626345053315163,
0.04488951712846756,
0.003974966239184141,
0.01965026557445526,
-0.004364600870758295,
-0.01327554415911436,
-0.024062426760792732,
0.04466026648879051,
0.01584792509675026,
-0.0020971745252609253,
-0.023060064762830734,
-0.010880798101425171,
0.0011368951527401805,
0.033781588077545166,
0.010194889269769192,
0.015430532395839691,
0.05773760378360748,
-0.011376065202057362,
0.01947695203125477,
-0.016484694555401802,
-0.020660843700170517,
0.015964992344379425,
-0.013541649095714092,
0.010975164361298084,
-0.000286699942080304,
0.024786023423075676,
-0.031033804640173912,
-0.023717038333415985,
-0.007817705161869526,
0.013670843094587326,
0.0707104504108429,
-0.023096900433301926,
0.046027928590774536,
-0.00237831543199718,
-0.0025681620463728905,
0.012334550730884075,
-0.009709428995847702,
-0.002360174898058176,
-0.00992052536457777,
-0.045033447444438934,
0.01721196435391903,
-0.012432388961315155,
0.002984137274324894,
-0.004224376752972603,
0.04092983528971672,
0.026748746633529663,
0.005626521538943052,
0.04987433925271034,
0.03146394342184067,
0.027701150625944138,
-0.002653818577528,
-0.03475448861718178,
0.029018355533480644,
-0.02285546436905861,
0.016968008130788803,
-0.0014669977826997638,
0.013648532330989838,
0.05528165400028229,
-0.03392881155014038,
-0.005063857417553663,
-0.03301845118403435,
-0.0035103813279420137,
-0.038912463933229446,
-0.0007666591554880142,
-0.00530870771035552,
0.02088816650211811,
0.04838459566235542,
-0.05633271113038063,
0.024631749838590622,
0.004489208105951548,
-0.020752258598804474,
0.003187253139913082,
-0.051372237503528595,
-0.04754259064793587,
-0.02906619757413864,
-0.04612385481595993,
0.04618116840720177,
-0.023101530969142914,
-0.05520642548799515,
-0.003705316223204136,
-0.01680067554116249,
0.02099240943789482,
0.027121825143694878,
-0.005729342345148325,
-0.03330416604876518,
0.07828808575868607,
0.005970632191747427,
0.003594528418034315,
0.02210143581032753,
0.010397178120911121,
0.11315498501062393,
0.051226906478405,
0.022296251729130745,
-0.04272501915693283,
0.052539531141519547,
-0.023464560508728027,
0.03430279716849327,
-0.028325406834483147,
0.004855354782193899,
-0.0002452374610584229,
0.02156333066523075,
0.01755390129983425,
0.0653400868177414,
0.036841996014118195,
-0.01212283130735159,
0.028794681653380394,
-0.04615611955523491,
0.0008231684332713485,
0.01848861575126648,
-0.021228300407528877,
0.002663887571543455,
0.04445536434650421,
-0.014968830160796642,
-0.0023799859918653965,
-0.043464042246341705,
-0.021116985008120537,
-0.018344443291425705,
-0.024297084659337997,
0.020660167559981346,
0.00163937546312809,
-0.07600954920053482,
-0.004709613509476185,
0.03891788050532341,
-0.013322873041033745,
-0.07832410931587219,
0.030031122267246246,
0.030406642705202103,
-0.02422267384827137,
0.008882373571395874,
-0.02358306385576725,
-0.006129599642008543,
0.018686113879084587,
0.004945534747093916,
0.026645177975296974,
-0.037676479667425156,
0.007265646941959858,
-0.029101230204105377,
0.018756981939077377,
-0.0022187780123203993,
0.015733417123556137,
-0.01601995714008808,
-0.0009419182897545397,
-0.04624885320663452,
-0.06768789142370224,
-0.0165927205234766,
0.007752012461423874,
0.019255829975008965,
0.0015473106177523732,
-0.0518576055765152,
-0.021568287163972855,
0.02144257351756096,
0.019907521083950996,
0.0669756606221199,
0.02883877605199814,
0.0011252914555370808,
-0.012485499493777752,
0.046452514827251434,
0.04313613101840019,
-0.02085036039352417,
-0.017784947529435158,
0.02851174771785736,
0.05312184989452362,
-0.08647354692220688,
-0.015327828004956245,
0.016460653394460678,
0.023421334102749825,
0.034765440970659256,
0.005776145961135626,
-0.015096300281584263,
-0.01642373763024807,
-0.09914010763168335,
0.018452700227499008,
0.03999047353863716,
-0.02576843649148941,
-0.009739285334944725,
-0.007170679979026318,
0.018976910039782524,
0.018145231530070305,
-0.010477673262357712,
0.048266950994729996,
-0.039815038442611694,
0.03219682723283768,
0.034643590450286865,
-0.0267663411796093,
-0.029108788818120956,
0.02764941193163395,
-0.0015222150832414627,
-0.03192053735256195,
-0.005651325453072786,
0.05224118381738663,
0.023514367640018463,
0.02336052618920803,
-0.003344172379001975,
0.04037907347083092,
-0.054150719195604324,
-0.012474940158426762,
-0.018337635323405266,
0.0112548116594553,
-0.004997724667191505,
0.02738824672996998,
0.014388784766197205,
-0.03564576059579849,
-0.050537679344415665,
-0.040450792759656906,
-0.018518248572945595,
0.02368677407503128,
0.019725309684872627,
0.006134775001555681,
0.04525981470942497,
-0.03630326688289642,
0.016567686572670937,
-0.005895004607737064,
-0.023721665143966675,
-0.07186224311590195,
0.02958456613123417,
-0.000517344509717077,
-0.04431719332933426,
-0.00653067696839571,
0.014045730233192444,
-0.06050407886505127,
-0.034494590014219284,
0.046216707676649094,
0.02469109371304512,
0.006648665759712458,
0.03842253237962723,
0.015461764298379421,
-0.01797928288578987,
0.038604170083999634,
-0.019965600222349167,
-0.021344872191548347,
0.0683828592300415,
-0.05023878067731857,
-0.03472081571817398,
0.04440958425402641,
-0.006076600402593613,
0.03000159002840519,
0.016815723851323128,
0.02217452973127365,
0.007522381842136383,
0.035601723939180374,
-0.017569582909345627,
0.01435769721865654,
0.00315230805426836,
-0.01933290809392929,
0.006270092912018299,
-0.014384916052222252,
-0.024257641285657883,
0.0056665739975869656,
-0.004955939948558807,
0.05194534361362457,
0.039174165576696396,
0.01653249002993107,
0.009497898630797863,
-0.011189957149326801,
-0.020931189879775047,
0.05041835084557533,
0.046713896095752716,
0.038234297186136246,
0.03206131234765053,
0.020225651562213898,
-0.03395581990480423,
0.016769878566265106,
0.0010580997914075851,
-0.01919599436223507,
-0.10469058156013489,
-0.011563797481358051,
0.002702587516978383,
0.02340458706021309,
0.03527987003326416,
-0.04289622604846954,
0.016916101798415184,
-0.001645672251470387,
-0.05611909553408623,
0.028746163472533226,
-0.024529950693249702,
-0.021824508905410767,
-0.04276898130774498,
-0.021092846989631653,
-0.03834758326411247,
0.02086116187274456,
0.07803696393966675,
0.021852556616067886,
-0.0011487463489174843,
0.019121592864394188,
0.01021236926317215,
-0.006857267580926418,
0.01660369150340557,
0.02631346508860588,
0.0005716113955713809,
-0.025416439399123192,
0.03701471537351608,
0.018125060945749283,
-0.027206866070628166,
0.05408354476094246,
0.015539593063294888,
0.04878760129213333,
-0.003678589593619108,
0.01609899289906025,
-0.004482921678572893,
-0.0073270173743367195,
0.022172197699546814,
-0.03344642370939255,
-0.02721877582371235,
0.08364229649305344,
0.009566182270646095,
0.02368611842393875,
-0.013364946469664574,
-0.0274024847894907,
0.014545437879860401,
-0.06733538955450058,
-0.020939897745847702,
0.01865929365158081,
-0.012451637536287308,
0.005263394210487604,
0.02438577637076378,
-0.006845035590231419,
0.026506507769227028,
-0.029000870883464813,
-0.008052347227931023,
-0.061185963451862335,
-0.02715957723557949,
0.015542907640337944,
0.0216474998742342,
-0.015438144095242023,
0.016802458092570305,
0.009401104412972927,
-0.0361911840736866,
-0.007251661736518145,
-0.017893336713314056,
0.0012990686809644103,
-0.02106531523168087,
0.016314979642629623,
0.0005536846001632512,
-0.02658410184085369,
-0.01752512715756893,
0.007949044927954674,
-0.02792496792972088,
0.018560126423835754,
-0.011846210807561874,
-0.000005901231361349346,
-0.03990386798977852,
-0.02589905448257923,
-0.02580905891954899,
-0.04361320286989212,
0.055849120020866394,
0.031799234449863434,
-0.00889359600841999,
-0.055494312196969986,
-0.035500530153512955,
-0.01776791736483574,
0.04222451522946358,
0.08261170983314514,
0.008893163874745369,
-0.039924684911966324,
0.005552011076360941,
0.018137821927666664,
0.01319925207644701,
-0.021560611203312874,
-0.013415305875241756,
-0.00826979149132967,
-0.01802479662001133,
-0.015120839700102806,
-0.019176093861460686,
-0.0505606010556221,
0.015080477111041546,
-0.023518623784184456,
0.02222275175154209,
0.06673947721719742,
0.0003525351930875331,
-0.023236174136400223,
0.051630713045597076,
0.0440828800201416,
-0.01668904721736908,
0.0744866356253624,
-0.031101077795028687,
-0.004453299101442099,
-0.005532627925276756,
-0.024812376126646996,
-0.07100726664066315,
0.037550266832113266,
-0.01776871457695961,
0.03584509715437889,
0.009316175244748592,
0.015128512866795063,
0.022750532254576683,
-0.02416054904460907,
0.022130556404590607,
0.059023499488830566,
-0.05428285896778107,
-0.01018611155450344,
0.03946862369775772,
0.012150685302913189,
-0.007000344339758158,
0.003838945645838976,
-0.011715722270309925,
0.008448971435427666,
-0.010167917236685753,
-0.012686886824667454,
0.024095742031931877,
0.0051751527935266495,
-0.0008151321089826524,
0.03792541101574898,
0.033760640770196915,
-0.021552490070462227,
-0.0281367190182209,
0.03849705308675766,
0.023458026349544525,
-0.011911723762750626,
-0.04076700657606125,
-0.012894262559711933,
-0.026308996602892876,
-0.02803916111588478,
0.03845510631799698,
-0.015386071987450123,
0.06038084253668785,
-0.03746169060468674,
0.03415999189019203,
0.002885326510295272,
0.0026421991642564535,
-0.0107163917273283,
-0.0029611338395625353,
0.021189836785197258,
-0.00572114996612072,
-0.002590523799881339,
0.010794242843985558,
0.012350698001682758,
-0.03130270168185234,
0.019456986337900162,
-0.04231785237789154,
-0.018636135384440422,
-0.011011764407157898,
-0.027572309598326683,
-0.011848006397485733,
0.035619281232357025,
-0.024981927126646042,
0.018293611705303192,
-0.005287894979119301,
0.046643905341625214,
0.04093340039253235,
0.014230076223611832,
0.01670655980706215,
-0.021241797134280205,
0.03680965676903725,
-0.06803163886070251,
-0.004457947798073292,
-0.020906152203679085,
0.020870527252554893,
0.0030260314233601093,
0.005013476591557264
] |
<p>I haven't been taught tensor product in class but they have taught us addition of spin. I looked up online in this link-><a href="http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_7.pdf" rel="nofollow">http://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_7.pdf</a> (pg 148, pg 10 in the pdf) and found an explanation. I think I understand most of it except this step:</p>
<p>$$ \vec{S}^{(A)} \otimes \vec{S}^{(B)} = \frac{\hbar^2}{4}(\sigma_x \otimes \sigma_x + \sigma_y \otimes\sigma_y + \sigma_z \otimes \sigma_z). $$</p>
<p>I know that:</p>
<p>$$ S^{2} = \frac{\hbar^2}{4}((\sigma_x)^2 + (\sigma_y)^2 + (\sigma_z)^2), $$</p>
<p>but I don't see the connection.</p>
| 8,796 |
[
-0.006597595289349556,
-0.03429769352078438,
-0.001907448167912662,
-0.018002795055508614,
0.03866111487150192,
0.03778926655650139,
-0.0205642469227314,
0.007183601148426533,
0.038994867354631424,
-0.06635964661836624,
0.000611764844506979,
0.03486527502536774,
0.08773781359195709,
0.03612463176250458,
0.03989509120583534,
0.007399543654173613,
-0.015683291479945183,
-0.02393297851085663,
-0.001996329752728343,
-0.011201729997992516,
0.020822087302803993,
0.04090188816189766,
-0.012880629859864712,
0.009068984538316727,
0.028630124405026436,
0.041993651539087296,
-0.0005335923051461577,
0.008417884819209576,
0.016161708161234856,
0.0619320310652256,
-0.011034402996301651,
-0.06486888229846954,
0.03342542052268982,
0.009264370426535606,
0.0040399846620857716,
-0.02358190529048443,
-0.04382527247071266,
0.0074807931669056416,
-0.004858636762946844,
-0.0002676397853065282,
-0.049863506108522415,
0.02017209306359291,
-0.03424284979701042,
0.06486281007528305,
-0.00887724943459034,
0.02668173424899578,
-0.03853391483426094,
-0.010071268305182457,
0.06225549057126045,
-0.03490680456161499,
0.0662706270813942,
0.024642007425427437,
0.011226545087993145,
0.0033968808129429817,
-0.022556699812412262,
-0.0010043758666142821,
0.05446407198905945,
0.051620181649923325,
0.014421656727790833,
-0.029678333550691605,
0.004165906459093094,
-0.04389171674847603,
0.012667412869632244,
-0.04695938155055046,
-0.015048712491989136,
-0.00251513859257102,
0.03224187344312668,
-0.007008573040366173,
0.03628057986497879,
-0.0025096063036471605,
0.014036375097930431,
0.023018473759293556,
0.04859047383069992,
-0.03634312376379967,
0.003302273340523243,
-0.027415702119469643,
-0.004127496853470802,
0.021183688193559647,
0.044153325259685516,
0.0042855627834796906,
0.009028937667608261,
0.020592212677001953,
0.03108876198530197,
0.014140112325549126,
-0.006020891014486551,
-0.013217171654105186,
0.061631977558135986,
0.01731918565928936,
0.029067225754261017,
0.048289693892002106,
-0.007605042774230242,
0.004489060491323471,
0.06647666543722153,
-0.031132297590374947,
-0.037400078028440475,
0.061741191893815994,
0.005356723442673683,
0.048799850046634674,
0.025899875909090042,
-0.023615218698978424,
-0.012177039869129658,
-0.02822316624224186,
0.003987295553088188,
0.0859210342168808,
0.0012579611502587795,
0.02837059088051319,
-0.03873588889837265,
0.04914713650941849,
-0.030306298285722733,
-0.044629503041505814,
-0.06785032898187637,
-0.004432928282767534,
-0.02475138008594513,
-0.010459237731993198,
-0.04348684102296829,
-0.03171622380614281,
-0.0014718991005793214,
0.01948719471693039,
0.03303319588303566,
0.05033382400870323,
0.03565896674990654,
-0.0336349755525589,
-0.00449489988386631,
-0.013880617916584015,
-0.07821950316429138,
0.007742195390164852,
0.04047619551420212,
-0.04001007229089737,
-0.04068794846534729,
0.01993841677904129,
0.023604683578014374,
-0.021391049027442932,
0.009726581163704395,
0.005586428102105856,
-0.006854124832898378,
-0.04089561104774475,
-0.10660645365715027,
-0.054549820721149445,
0.03526897355914116,
-0.003925441298633814,
0.010572673752903938,
-0.07977652549743652,
0.014158018864691257,
0.026296624913811684,
0.07861147075891495,
-0.006977318786084652,
0.06460368633270264,
-0.0019045625813305378,
0.02352168597280979,
0.02873264066874981,
-0.03360017016530037,
-0.01538484264165163,
-0.02927934005856514,
-0.04067400097846985,
-0.008405816741287708,
-0.03630169853568077,
0.0011986520839855075,
0.04338468611240387,
0.001552679343149066,
-0.0008644479094073176,
0.07373792678117752,
-0.017784971743822098,
0.020588215440511703,
0.03251160308718681,
0.019283004105091095,
-0.009151092730462551,
0.05518020689487457,
0.01122833788394928,
0.00849147792905569,
0.016035057604312897,
-0.008287759497761726,
0.0060439868830144405,
-0.0012995885917916894,
0.06535601615905762,
0.010680071078240871,
-0.02747906744480133,
-0.013743475079536438,
-0.00306416186504066,
-0.0045294188894331455,
-0.014612369239330292,
-0.06173411384224892,
-0.045410871505737305,
-0.039160169661045074,
0.03161843121051788,
0.0031613304745405912,
0.03645294904708862,
0.03503703698515892,
-0.017111586406826973,
-0.0218745656311512,
-0.05341530963778496,
-0.014313200488686562,
-0.08287657052278519,
0.013125563971698284,
-0.026427024975419044,
-0.03465931862592697,
0.047975439578294754,
0.030965665355324745,
0.008489114232361317,
-0.0062077846378088,
-0.0667230486869812,
-0.006073204334825277,
0.026786144822835922,
0.05099273845553398,
-0.0033365285489708185,
0.011628837324678898,
0.030472131446003914,
0.04029785096645355,
0.013442791998386383,
0.036721646785736084,
-0.02763228863477707,
-0.005780221428722143,
0.00431958818808198,
0.02033291943371296,
0.012788097374141216,
0.013965310528874397,
-0.02463460899889469,
-0.019491322338581085,
0.012445274740457535,
-0.0035810470581054688,
0.033678870648145676,
-0.061218202114105225,
0.06163427606225014,
0.05891049653291702,
0.016648322343826294,
-0.00019160480587743223,
0.06331492215394974,
0.03358624503016472,
0.03270067647099495,
-0.023674752563238144,
-0.007468092255294323,
-0.028204254806041718,
0.0001915261527756229,
0.03893890976905823,
0.05447372794151306,
-0.048723816871643066,
0.015848301351070404,
0.015416464768350124,
0.03500371798872948,
0.01316781621426344,
0.008601208217442036,
-0.0054785870015621185,
-0.02693946100771427,
0.00004952800736646168,
-0.005390206351876259,
0.008457343094050884,
0.007328909356147051,
0.02535850927233696,
-0.013949641026556492,
0.020991632714867592,
0.039541974663734436,
-0.03948139026761055,
0.013870266266167164,
-0.044477857649326324,
0.03505253419280052,
0.0046302699483931065,
-0.01852862723171711,
0.04427767172455788,
-0.0116602573543787,
0.026433588936924934,
0.05891386419534683,
-0.004367053974419832,
-0.009545625187456608,
-0.031910914927721024,
-0.004073935095220804,
0.001738651073537767,
-0.03102310560643673,
-0.015726150944828987,
-0.0016286936588585377,
0.013162464834749699,
-0.05139020457863808,
-0.011941798031330109,
0.02447686530649662,
-0.025499925017356873,
-0.009829462505877018,
0.024592865258455276,
0.016974445432424545,
0.023635607212781906,
0.05504985898733139,
-0.010183960199356079,
-0.035996146500110626,
0.0009950228268280625,
0.012546449899673462,
0.03803340345621109,
-0.0048201559111475945,
-0.0701858401298523,
0.006014296319335699,
-0.057120807468891144,
-0.00699251564219594,
0.03129568323493004,
0.006277814041823149,
-0.027877090498805046,
-0.006945715751498938,
-0.009610040113329887,
-0.02360159531235695,
-0.04083762317895889,
0.0011982257710769773,
0.02603660710155964,
-0.04466071352362633,
0.017340321093797684,
0.005230740178376436,
-0.025796303525567055,
-0.006522037088871002,
0.006813582498580217,
0.004567350260913372,
-0.057538267225027084,
-0.019616400822997093,
-0.020620625466108322,
0.006876543164253235,
-0.027278626337647438,
0.007374508306384087,
0.02064107544720173,
-0.011658248491585255,
-0.012653359211981297,
-0.031125180423259735,
-0.03594249486923218,
0.014977271668612957,
-0.005867705214768648,
0.029725532978773117,
-0.01211567036807537,
-0.03340631350874901,
0.11393850296735764,
0.0065308972261846066,
-0.01015392504632473,
-0.018126389011740685,
0.026075521484017372,
-0.0062390659004449844,
-0.02703290991485119,
0.02040279284119606,
0.03151911497116089,
-0.019863087683916092,
0.07573366165161133,
0.001003048149868846,
0.0007807138608768582,
0.08265336602926254,
0.002223833231255412,
-0.0358799546957016,
-0.015540043823421001,
-0.0113090043887496,
-0.011599592864513397,
0.06819271296262741,
-0.0011382510419934988,
0.0020694639533758163,
-0.008850608952343464,
-0.00997371319681406,
0.013827302493155003,
0.018438521772623062,
-0.012894684448838234,
0.032059695571660995,
0.012310579419136047,
-0.01255496870726347,
-0.022814234718680382,
0.046409498900175095,
-0.013906112872064114,
-0.048253368586301804,
0.000003968690634792438,
0.007551700808107853,
0.01571497693657875,
-0.021603751927614212,
0.011826615780591965,
0.057983458042144775,
0.00904842559248209,
-0.040270205587148666,
-0.003165427828207612,
-0.010710928589105606,
-0.000749770610127598,
0.026669710874557495,
-0.02031358890235424,
-0.009580198675394058,
0.017004989087581635,
0.031125497072935104,
-0.007104531396180391,
-0.03766371309757233,
-0.045691896229982376,
0.01072870846837759,
-0.057039231061935425,
0.022227197885513306,
-0.015249636024236679,
0.03254324942827225,
0.03323898836970329,
0.042080920189619064,
-0.018934668973088264,
-0.0061034089885652065,
0.03513983264565468,
-0.03401826694607735,
-0.04245291277766228,
-0.006554577965289354,
-0.013495109044015408,
-0.030914679169654846,
0.02150648832321167,
-0.01641233265399933,
0.030128084123134613,
-0.03152872622013092,
-0.03243961185216904,
-0.03292199224233627,
-0.038805462419986725,
-0.02704102359712124,
0.011531924828886986,
-0.003930788487195969,
-0.017157679423689842,
-0.006150189321488142,
0.011432705447077751,
0.027806133031845093,
-0.009476994164288044,
-0.014842200092971325,
0.07018611580133438,
-0.03724981099367142,
0.03578212112188339,
-0.02608463726937771,
0.019300300627946854,
0.025663716718554497,
0.012784183025360107,
0.04098162055015564,
0.018068276345729828,
-0.023243632167577744,
-0.0016928180120885372,
0.015065141953527927,
0.06809490919113159,
-0.00015564486966468394,
0.002004592912271619,
-0.010811029933393002,
-0.05261142924427986,
-0.008094597607851028,
-0.03978252038359642,
0.06904249638319016,
-0.0022634363267570734,
0.03084016777575016,
0.05263557285070419,
0.008104398846626282,
-0.04494199529290199,
0.01990405097603798,
0.06081930547952652,
-0.010156030766665936,
-0.005385636352002621,
-0.03385315090417862,
-0.020586643368005753,
-0.03555574640631676,
-0.031646016985177994,
0.028410524129867554,
-0.024282773956656456,
-0.046100810170173645,
0.00008878028893377632,
0.03210800141096115,
-0.004085826221853495,
0.006376342382282019,
0.032577645033597946,
0.008761221542954445,
-0.0016822373727336526,
0.03716299310326576,
-0.019405918195843697,
-0.020433476194739342,
0.046142347157001495,
0.03282390907406807,
-0.004494979977607727,
-0.03087826631963253,
-0.06358250230550766,
-0.013942601159214973,
0.028780095279216766,
0.05597171187400818,
-0.013794616796076298,
0.0028418288566172123,
-0.016603050753474236,
-0.048331450670957565,
0.07044593244791031,
-0.022440332919359207,
0.049048393964767456,
-0.005512869916856289,
-0.014765676110982895,
0.004226854536682367,
0.002352310111746192,
-0.052293676882982254,
0.03528480976819992,
-0.005826370324939489,
0.015892934054136276,
-0.0076604182831943035,
0.0037619457580149174,
-0.007449156139045954,
-0.013060719706118107,
0.010501162149012089,
0.033193573355674744,
-0.009869630448520184,
-0.018521510064601898,
-0.005929894279688597,
0.0671750158071518,
-0.03466067090630531,
-0.09219644963741302,
-0.00011107268073828891,
-0.018327737227082253,
-0.05983053892850876,
0.022609056904911995,
-0.028054675087332726,
-0.01099730096757412,
0.048658546060323715,
0.004971945192664862,
0.023370757699012756,
0.02524617128074169,
-0.010139727964997292,
0.058892082422971725,
0.055797308683395386,
0.00671383086591959,
0.007117645815014839,
0.024441489949822426,
-0.01853865385055542,
0.019603842869400978,
-0.037878114730119705,
0.006422809325158596,
0.005461441352963448,
0.019548755139112473,
-0.05113833397626877,
0.01294978428632021,
0.010099870152771473,
0.04083669185638428,
-0.024573514237999916,
0.008999220095574856,
-0.03251412510871887,
-0.023377379402518272,
-0.018658924847841263,
-0.005157738458365202,
-0.014742032624781132,
-0.04309605434536934,
0.0036898935213685036,
0.033642709255218506,
0.013186141848564148,
-0.03907608985900879,
-0.025269104167819023,
-0.0031198759097605944,
-0.013148828409612179,
0.0026258444413542747,
0.0031467999797314405,
0.03183276206254959,
-0.012470883317291737,
-0.019937535747885704,
0.02651672437787056,
-0.06365884095430374,
0.017734838649630547,
-0.029735000804066658,
-0.014859403483569622,
-0.00025174434995278716,
-0.022329147905111313,
-0.012116503901779652,
-0.00036608363734558225,
-0.017383405938744545,
0.005190093070268631,
-0.04751976206898689,
0.013426819816231728,
0.03607705980539322,
0.014231575652956963,
-0.05008632689714432,
-0.06669023633003235,
0.008509989827871323,
0.00029153560171835124,
-0.021129043772816658,
-0.029291165992617607,
0.010507151484489441,
-0.024013275280594826,
-0.03976978361606598,
0.0075734760612249374,
0.0474090613424778,
-0.0716516375541687,
-0.0399634875357151,
0.014880262315273285,
0.014168228022754192,
0.0532323494553566,
-0.011687093414366245,
-0.008236614055931568,
0.011009651236236095,
0.01466946117579937,
-0.023920919746160507,
0.031740136444568634,
0.041962139308452606,
-0.034253161400556564,
-0.01732025295495987,
-0.010674326680600643,
-0.007403081748634577,
0.02539673075079918,
-0.0339968316257,
0.019438738003373146,
-0.01769881136715412,
0.035223230719566345,
0.015257108025252819,
-0.04762831702828407,
-0.022377926856279373,
0.008584710769355297,
0.04470784589648247,
-0.015377504751086235,
0.021637579426169395,
-0.014586172066628933,
-0.012823585420846939,
-0.004014225676655769,
0.013066863641142845,
0.005721337627619505,
-0.01847631111741066,
0.09435528516769409,
-0.002005574759095907,
0.01776651106774807,
0.02196616120636463,
-0.02010597288608551,
-0.0021017291583120823,
0.013095016591250896,
0.03261338546872139,
0.02555401623249054,
0.0020956448279321194,
-0.018271634355187416,
-0.01063514593988657,
-0.017036236822605133,
0.023579295724630356,
0.08495929092168808,
-0.04311798885464668,
0.03376893699169159,
0.048567671328783035,
-0.014099237509071827,
0.029742641374468803,
-0.0032351408153772354,
-0.009097453206777573,
0.032056279480457306,
-0.011400052346289158,
0.04433140531182289,
-0.009993449784815311,
-0.00855333637446165,
0.033646173775196075,
0.02240157313644886,
-0.049306854605674744,
0.015419570729136467,
0.027304058894515038,
-0.02909483015537262,
0.03827090933918953,
0.02223527431488037,
-0.06398040056228638,
0.039757151156663895,
-0.022138375788927078,
0.05270468071103096,
-0.02286458946764469,
-0.020375655964016914,
0.055401477962732315,
0.027973700314760208,
0.00645190617069602,
-0.03676668554544449,
-0.03581779822707176,
-0.05070125684142113,
-0.02766343392431736,
0.015011889860033989,
-0.0197610966861248,
0.029356321319937706,
0.012107599526643753,
0.04341646283864975,
0.014113737270236015,
0.03645549714565277,
-0.019466139376163483,
-0.07111325114965439,
-0.014874101616442204,
-0.0408158116042614,
-0.04731859639286995,
0.05361245572566986,
-0.009480023756623268,
-0.03041422739624977,
0.010451184585690498,
-0.04948623850941658,
0.02449793927371502,
-0.011583630926907063,
0.04396522790193558,
-0.010665017180144787,
0.052838847041130066,
0.01206850167363882,
0.02664279006421566,
-0.0015679035568609834,
-0.012221256271004677,
0.09518058598041534,
0.060451705008745193,
0.020149845629930496,
-0.06564370542764664,
0.0448918379843235,
-0.03024340607225895,
-0.014795178547501564,
-0.03448207303881645,
0.02894562855362892,
0.004839493427425623,
0.010651917196810246,
0.001761266845278442,
0.04691946506500244,
0.017431678250432014,
-0.03080175630748272,
0.017927411943674088,
-0.06386960297822952,
-0.01815205067396164,
-0.028859945014119148,
0.005872291512787342,
-0.005840706638991833,
-0.006420224905014038,
-0.08799218386411667,
-0.007930544205009937,
-0.04526031017303467,
0.01683596521615982,
-0.058058056980371475,
-0.029581474140286446,
-0.018186287954449654,
0.006906427443027496,
-0.01232793740928173,
0.0251237191259861,
-0.017061196267604828,
-0.031267035752534866,
-0.03399442881345749,
0.020084267482161522,
0.05708375200629234,
-0.0006860014982521534,
0.043240904808044434,
0.010978988371789455,
-0.0015180446207523346,
0.00030206769588403404,
0.026935551315546036,
0.04240912199020386,
-0.03372732177376747,
0.023634592071175575,
-0.0014906757278367877,
0.10628464818000793,
-0.02741481550037861,
-0.007389103062450886,
0.009573245421051979,
-0.023618916049599648,
0.03876200690865517,
-0.04242204502224922,
-0.03146367520093918,
-0.001368742436170578,
0.02961724065244198,
-0.011190789751708508,
0.0247156023979187,
0.0023612549994140863,
0.020577292889356613,
-0.011074199341237545,
0.033680882304906845,
0.0050733694806694984,
-0.008443810045719147,
-0.0016768027562648058,
-0.004601835273206234,
0.003830342087894678,
-0.012870753183960915,
-0.011856302618980408,
-0.0034896056167781353,
-0.008311000652611256,
-0.02889021299779415,
-0.012623133137822151,
0.02025516889989376,
0.018092192709445953,
0.03378316015005112,
-0.025659965351223946,
-0.026180043816566467,
0.011329038999974728,
-0.03041578270494938,
0.008186114951968193,
-0.02866620570421219,
-0.0009431648068130016,
-0.010067661292850971,
0.022043142467737198,
0.03943007066845894,
0.021328218281269073,
-0.03406991809606552,
-0.0025305263698101044,
0.011573280207812786,
0.0179685577750206,
0.044878143817186356,
-0.012373087927699089,
-0.003065564436838031,
0.03196309134364128,
0.007091803476214409,
-0.005740513559430838,
-0.01063123531639576,
-0.007756448350846767,
0.024046624079346657,
0.03507376089692116,
-0.0126640060916543,
0.027114510536193848,
-0.00013429956743493676,
-0.00243269931524992,
0.03826158493757248,
-0.03326328471302986,
0.0012347068404778838,
0.010015803389251232,
-0.01084375660866499,
-0.05109132453799248,
0.02096647396683693,
0.002096819691359997,
0.023859625682234764,
0.004112595226615667,
0.030174287036061287,
-0.05843164399266243,
-0.01843063347041607,
-0.025138432160019875,
0.028916051611304283,
-0.02144015021622181,
-0.008760797791182995,
-0.04105164855718613,
0.012390847317874432,
0.02692519873380661,
0.03533250465989113,
0.0074967495165765285,
0.03899567946791649,
0.007503202185034752,
-0.03514263033866882,
0.023797664791345596,
0.038500767201185226,
-0.025915278121829033,
-0.04104866832494736,
0.008675606921315193,
0.007594842463731766,
0.02766723744571209,
0.021202296018600464,
-0.045624446123838425,
0.032065361738204956,
-0.05068985000252724,
-0.01668725721538067,
0.03145463764667511,
-0.00472270930185914,
0.02635600045323372,
0.015479642897844315,
-0.02840142324566841,
-0.023984162136912346,
0.023756790906190872,
-0.02120267227292061,
0.007951823994517326,
-0.01430564932525158,
-0.04895370081067085,
-0.0013610501773655415,
-0.04015659540891647,
0.03390186280012131,
0.028373824432492256,
-0.0034406371414661407,
0.01243206299841404,
-0.00806344673037529,
-0.03527306765317917,
0.014182524755597115,
0.00993157085031271,
-0.02577362209558487,
0.010566070675849915,
0.0018486679764464498,
0.00017038178339134902,
0.03477306663990021,
0.052802007645368576,
-0.010014980100095272,
0.04207034036517143,
-0.0011698552407324314,
0.023896226659417152,
-0.08485420048236847,
0.012041359208524227,
0.018751759082078934,
-0.02419668808579445,
0.030063442885875702,
-0.05533984676003456,
0.021476687863469124,
0.02046847529709339,
-0.06878290325403214,
0.0162429828196764,
-0.05557502806186676,
-0.037021975964307785,
-0.00952677521854639,
-0.011057033203542233,
0.006791616789996624,
0.037730976939201355,
0.0009402299183420837,
0.05617634952068329,
0.04698910191655159,
0.023009493947029114,
-0.019814176484942436,
-0.028948398306965828,
-0.03251447528600693,
-0.0004736341070383787,
0.02811792492866516,
-0.05120491608977318,
0.053767528384923935,
0.0033801142126321793,
-0.026725275442004204,
0.020235590636730194,
-0.01694405823945999,
-0.008326895534992218,
-0.019074590876698494,
0.014473645947873592,
-0.007654780056327581,
0.05071944743394852,
-0.024209408089518547,
0.0034725386649370193,
0.02360873483121395,
-0.004083166364580393,
0.046769388020038605,
-0.007951815612614155,
-0.025096457451581955,
-0.013691993430256844,
-0.00984364002943039,
-0.01564655266702175,
-0.01605651155114174,
0.0499909445643425,
-0.004889373667538166,
-0.013020484708249569,
-0.03439289331436157,
-0.010783117264509201,
0.015933452174067497,
-0.0573296882212162,
0.013977102935314178,
-0.0573875829577446,
-0.0007632642518728971,
0.0373721569776535,
-0.00040044530760496855,
-0.017300643026828766,
0.02843792550265789,
-0.02855963632464409,
-0.017278078943490982,
0.01890583150088787,
-0.006073860917240381,
-0.04701709374785423,
-0.02788769081234932,
-0.007964440621435642,
0.02304667793214321,
-0.012919198721647263,
-0.005404218100011349,
-0.0301780104637146,
-0.02504655160009861,
0.036633990705013275,
0.004414389841258526,
0.03484802320599556,
-0.021929295733571053,
-0.021532757207751274,
0.007031287532299757,
-0.07373663783073425,
0.04078439250588417,
0.024278156459331512,
-0.022343551740050316,
-0.03737606108188629,
0.01521786954253912,
0.00855659693479538,
-0.0050897859036922455,
0.061736710369586945,
-0.007657536305487156,
-0.009345226921141148,
-0.009017872624099255,
0.024753764271736145,
0.02361234650015831,
-0.038404107093811035,
0.0040342495776712894,
0.012607782147824764,
-0.009633950889110565,
-0.021957626566290855,
-0.00242656865157187,
-0.02804100327193737,
0.005934334360063076,
0.02492697536945343,
-0.004700855817645788,
0.018474319949746132,
0.002182926516979933,
-0.03982025012373924,
0.03660757467150688,
-0.011840074323117733,
-0.045674946159124374,
0.07787729799747467,
0.029347054660320282,
-0.015086679719388485,
0.060476869344711304,
-0.026989160105586052,
-0.013719793409109116,
0.020423846319317818,
-0.011071152985095978,
-0.021288326010107994,
-0.030176758766174316,
-0.011461643502116203,
0.056851454079151154,
-0.047272633761167526,
-0.0057895067147910595,
0.052380770444869995,
-0.032097648829221725,
-0.01804869808256626,
0.02879195287823677,
0.01920543983578682,
0.01524175051599741,
-0.011835443787276745,
0.028681712225079536,
-0.009303329512476921,
-0.022246168926358223,
0.03928422927856445,
0.031607355922460556,
0.026267847046256065,
0.01905163936316967,
-0.006822903640568256,
0.040005385875701904,
-0.036755818873643875,
-0.008458890952169895,
-0.013140824623405933,
0.030137594789266586,
-0.046775877475738525,
-0.03279626742005348,
-0.0033928498160094023,
-0.040681008249521255,
0.041984982788562775,
0.03797869011759758,
-0.04742930456995964,
0.07807034999132156,
-0.05599519982933998,
0.011550137773156166,
-0.014412947930395603,
0.007155932951718569,
-0.0038250358775258064,
0.001613591448403895,
0.046392105519771576,
0.023432882502675056,
-0.007612151559442282,
-0.04540689289569855,
-0.02361832559108734,
-0.02990631014108658,
0.010168744251132011,
-0.005366698373109102,
0.03509404882788658,
-0.004369128029793501,
-0.01128453016281128,
-0.004296515136957169,
-0.03214941918849945,
-0.005244506988674402,
-0.03612103685736656,
0.059662576764822006,
0.038837023079395294,
-0.0019038550090044737,
-0.02865542843937874,
-0.02396703138947487,
-0.020602405071258545,
0.048682939261198044,
-0.06857279688119888,
-0.007809370756149292,
-0.004267704673111439,
0.014573792926967144,
-0.014171306975185871,
-0.01380396168678999
] |
<p>I've been reading about how black holes can effect both time and light with gravity. So I was wondering, doesn't something have to have mass to be effected by gravity? And if so, does this mean both light and time have mass? And if not, how can gravity effect something that has no mass?</p>
| 143 |
[
-0.013438450172543526,
-0.06300246715545654,
-0.010345259681344032,
-0.033349763602018356,
0.041400011628866196,
0.012583483941853046,
-0.05366424098610878,
-0.027364423498511314,
-0.028670692816376686,
-0.00984236504882574,
0.006050600204616785,
0.031243642792105675,
0.037997178733348846,
-0.015476257540285587,
0.0011683851480484009,
0.015289784409105778,
-0.016337215900421143,
-0.007457457948476076,
-0.01837804727256298,
-0.039958175271749496,
-0.00037809766945429146,
0.04545556753873825,
0.0341702476143837,
0.01787572167813778,
-0.01509973593056202,
0.01449635811150074,
0.036893345415592194,
-0.0025771763175725937,
0.022752685472369194,
0.04136798158288002,
-0.0033215407747775316,
-0.015949595719575882,
-0.021312864497303963,
0.05986453965306282,
0.000997483846731484,
-0.005596012342721224,
-0.04944514110684395,
-0.008098997175693512,
-0.0003345117438584566,
0.010702624917030334,
-0.01710025779902935,
-0.025076743215322495,
0.008565637283027172,
0.03324166685342789,
-0.05248027294874191,
0.006778412498533726,
0.0009709247970022261,
-0.002296303864568472,
0.045186616480350494,
-0.05750799551606178,
0.07263384014368057,
-0.0021681177895516157,
0.04911883920431137,
-0.0011129899648949504,
-0.03310906141996384,
0.024849778041243553,
0.09732808917760849,
0.0630682110786438,
-0.03543289378285408,
-0.04225676506757736,
-0.041284382343292236,
0.0250870231539011,
-0.003834798466414213,
-0.038064975291490555,
-0.004303834866732359,
0.021647941321134567,
-0.032342929393053055,
0.004973958246409893,
0.04467262700200081,
0.008167162537574768,
0.006208594422787428,
-0.011704047210514545,
0.03282255679368973,
0.032673515379428864,
-0.03894835710525513,
-0.0490725114941597,
0.02606094628572464,
-0.011380634270608425,
0.034338708966970444,
0.04305869713425636,
-0.01996784284710884,
0.001377177657559514,
0.028882373124361038,
0.031165331602096558,
0.023241138085722923,
0.0024116793647408485,
0.07941626757383347,
-0.00271334545686841,
0.01300754863768816,
0.006837247870862484,
-0.04662994295358658,
-0.025951191782951355,
-0.001227399567142129,
-0.030310068279504776,
-0.006991887930780649,
0.004500149749219418,
0.017022615298628807,
0.043146975338459015,
0.006482102908194065,
-0.0023617439437657595,
0.007313126232475042,
0.011259784922003746,
0.03717590123414993,
0.06757815182209015,
-0.0031266771256923676,
-0.01571754179894924,
-0.03452242538332939,
0.0317094624042511,
-0.006609964184463024,
0.014452789910137653,
-0.0429053008556366,
-0.015918603166937828,
-0.002888828981667757,
-0.05706285312771797,
0.0444684736430645,
-0.028874468058347702,
0.00820024125277996,
-0.009146803058683872,
0.06402371823787689,
0.048865534365177155,
0.04024939611554146,
-0.06100776046514511,
0.023161616176366806,
-0.03456606715917587,
-0.05086927488446236,
0.014495925977826118,
0.027789084240794182,
-0.011194520629942417,
-0.008469676598906517,
0.018752695992588997,
-0.00035446492256596684,
-0.013633335940539837,
0.004176599904894829,
-0.005172820296138525,
0.05533603951334953,
-0.028464289382100105,
-0.10262832045555115,
-0.044817935675382614,
0.01166130043566227,
0.001023516757413745,
-0.03561699390411377,
-0.053152285516262054,
-0.003322361037135124,
0.017275458201766014,
0.07030119746923447,
0.021384695544838905,
0.004720764700323343,
0.027437372133135796,
0.030061036348342896,
0.0084428321570158,
-0.01460170466452837,
-0.0036875223740935326,
0.020925898104906082,
-0.017702434211969376,
0.03182079270482063,
-0.07104693353176117,
0.004096476826816797,
0.019533952698111534,
0.004059040918946266,
-0.029126301407814026,
0.07550715655088425,
-0.018462810665369034,
0.021785274147987366,
0.05784297734498978,
0.005118845030665398,
-0.023933328688144684,
0.06606260687112808,
0.002307008719071746,
-0.015093405731022358,
0.061260540038347244,
0.043357204645872116,
0.03919104486703873,
0.0420464351773262,
0.04966731742024422,
0.02415655367076397,
-0.02095082961022854,
-0.041974328458309174,
-0.0034701970871537924,
0.0165102556347847,
-0.005723113194108009,
-0.024811526760458946,
-0.026062123477458954,
-0.008706285618245602,
-0.009673019871115685,
-0.022670933976769447,
0.06640679389238358,
0.0025038111489266157,
-0.011210974305868149,
-0.026996074244379997,
-0.0020843876991420984,
0.018020763993263245,
-0.06853151321411133,
0.013628805987536907,
0.0064290976151824,
0.009494572877883911,
0.014910142868757248,
0.027939507737755775,
0.033398132771253586,
-0.06428506970405579,
-0.03319312632083893,
-0.003036011941730976,
0.04741014540195465,
-0.029560178518295288,
-0.03424954041838646,
0.02428361587226391,
0.04579467698931694,
0.02599223144352436,
-0.0009848498739302158,
0.0025553470477461815,
0.010474760085344315,
-0.026853883638978004,
0.024844491854310036,
0.01254746038466692,
0.017949659377336502,
-0.023649895563721657,
0.0224875770509243,
0.03082425892353058,
-0.0016395578859373927,
-0.003072538413107395,
0.05914503335952759,
-0.03141827881336212,
0.08451031893491745,
0.019345832988619804,
-0.03622385114431381,
0.010412251576781273,
0.046586181968450546,
0.051252566277980804,
0.0011062556877732277,
0.0022813586983829737,
-0.019139038398861885,
-0.028737392276525497,
-0.012476157397031784,
0.02351357974112034,
0.005297755356878042,
-0.023521216586232185,
0.020664045587182045,
0.016709433868527412,
0.053411029279232025,
0.014984024688601494,
0.03954475000500679,
-0.028224768117070198,
-0.008887886069715023,
0.011073951609432697,
0.008586830459535122,
0.023932043462991714,
0.012743991799652576,
0.0633058100938797,
0.03464025631546974,
0.02442086674273014,
-0.012091264128684998,
-0.009315650910139084,
0.04384453967213631,
-0.02443857491016388,
0.03177756071090698,
0.0012903440510854125,
-0.027314908802509308,
0.047541841864585876,
-0.020782003179192543,
0.014741492457687855,
0.01949930377304554,
-0.004718920215964317,
-0.02345426380634308,
-0.0465613529086113,
-0.018788987770676613,
-0.006151759997010231,
0.010575677268207073,
-0.02227286621928215,
-0.00786046776920557,
0.015817765146493912,
-0.03880283236503601,
0.02054331824183464,
0.0039381422102451324,
-0.033718645572662354,
-0.0229352954775095,
0.011534607969224453,
0.00542297912761569,
-0.005775019992142916,
0.059100862592458725,
-0.01804627850651741,
-0.048339154571294785,
-0.01065553817898035,
-0.06486324965953827,
-0.03488100692629814,
0.02256927825510502,
-0.04700453579425812,
0.04510978236794472,
-0.04020870476961136,
-0.034911662340164185,
0.06507297605276108,
-0.02123338170349598,
0.020326834172010422,
0.03014316037297249,
-0.02929244562983513,
-0.008030352182686329,
0.002167867496609688,
-0.03806259110569954,
-0.004395144060254097,
-0.02732040360569954,
0.04077844321727753,
0.028110075742006302,
0.00885158684104681,
-0.051816683262586594,
0.005244350992143154,
-0.006788115482777357,
-0.04581031575798988,
-0.014325362630188465,
0.009298896417021751,
0.007709996774792671,
-0.0659618005156517,
0.003092739498242736,
0.0012510481756180525,
-0.07471422106027603,
0.026078637689352036,
-0.015338349156081676,
-0.03800780326128006,
0.045132268220186234,
-0.006630118936300278,
0.020961113274097443,
0.010690261609852314,
-0.042602572590112686,
0.060756899416446686,
0.03172700107097626,
0.01012260653078556,
-0.05175032466650009,
-0.03052588738501072,
-0.004979508463293314,
-0.003575446316972375,
0.01876145228743553,
0.010265904478728771,
0.016023579984903336,
-0.003737142775207758,
0.0611470527946949,
0.02618933469057083,
-0.005141615867614746,
0.02280973643064499,
-0.026014771312475204,
-0.014290791004896164,
0.02483365498483181,
-0.0013476323802024126,
0.01770530641078949,
0.0437578521668911,
0.004159586038440466,
0.01433570683002472,
-0.00308683468028903,
0.0661083459854126,
-0.01845589093863964,
-0.020492784678936005,
0.046666521579027176,
0.025172583758831024,
0.032768815755844116,
-0.009334406815469265,
0.03152064234018326,
-0.02727501466870308,
0.014794150367379189,
0.03034166619181633,
-0.02499004267156124,
0.06593629717826843,
0.0021447872277349234,
-0.000879584695212543,
0.022768335416913033,
0.05397700518369675,
-0.038237690925598145,
-0.02842777408659458,
0.0142967002466321,
-0.016731344163417816,
0.05085572972893715,
-0.02195998840034008,
-0.02068288065493107,
0.05152146890759468,
0.04664525389671326,
0.02384505607187748,
0.000010690802810131572,
-0.03355938196182251,
-0.023984234780073166,
-0.07035745680332184,
0.011431831866502762,
0.023714473471045494,
0.023910271003842354,
0.00012696717749349773,
0.04494693502783775,
0.03211187571287155,
0.009398439899086952,
0.02855610102415085,
-0.034626830369234085,
-0.07592293620109558,
0.01974928006529808,
-0.05883508920669556,
-0.028868775814771652,
-0.01974969357252121,
-0.02390218898653984,
-0.04173503816127777,
-0.026068754494190216,
-0.010495073162019253,
-0.014127377420663834,
-0.01315698865801096,
-0.059699248522520065,
-0.012978387996554375,
-0.03791674226522446,
-0.017626270651817322,
-0.011888083070516586,
0.02041228674352169,
0.017839713022112846,
-0.002850488293915987,
-0.005469631403684616,
0.035749588161706924,
-0.031213020905852318,
0.0019631648901849985,
-0.0008687392110005021,
0.005761096719652414,
-0.011106043122708797,
0.03303736075758934,
0.05383974686264992,
-0.005134951788932085,
-0.03858880326151848,
0.021350227296352386,
0.0370960608124733,
0.053210705518722534,
-0.0067213717848062515,
-0.0396234504878521,
-0.0504966638982296,
-0.04010257497429848,
-0.021056097000837326,
0.0020624331664294004,
0.06398311257362366,
-0.005394832231104374,
-0.0017707132501527667,
0.012393050827085972,
-0.013121983967721462,
-0.012140157632529736,
0.04069942608475685,
0.057277899235486984,
0.025883477181196213,
-0.03379089757800102,
-0.052556753158569336,
-0.02488836459815502,
-0.044434987008571625,
-0.007074830122292042,
0.027345214039087296,
0.01061371061950922,
-0.03785187378525734,
0.008991273120045662,
-0.030438875779509544,
-0.005757221486419439,
-0.014866597019135952,
-0.041329413652420044,
0.030681120231747627,
0.021733734756708145,
-0.01705249212682247,
0.025128526613116264,
0.0194880198687315,
0.04496920481324196,
0.04089442268013954,
-0.011710506863892078,
-0.004714182578027248,
-0.08078719675540924,
0.014329303056001663,
0.04196155443787575,
0.023223761469125748,
-0.007757676765322685,
-0.02552105486392975,
-0.045235734432935715,
0.008120071142911911,
0.026300646364688873,
-0.015778260305523872,
0.009244256652891636,
-0.005017170216888189,
0.0028041223995387554,
0.010628834366798401,
-0.01904449611902237,
0.04679730162024498,
0.03882378339767456,
-0.016155637800693512,
0.006668433081358671,
0.011851322837173939,
0.003502961015328765,
0.012012146413326263,
0.018863338977098465,
0.025539327412843704,
0.031661320477724075,
0.03675653040409088,
0.004696203395724297,
0.011741312220692635,
0.005542688071727753,
-0.03324328735470772,
-0.10042955726385117,
-0.022652363404631615,
0.005688743200153112,
-0.033016957342624664,
0.03755901753902435,
-0.022116396576166153,
-0.032070454210042953,
0.03774913027882576,
0.0005939393304288387,
-0.02054428867995739,
-0.011611592955887318,
-0.03955604135990143,
-0.031759560108184814,
0.026448238641023636,
-0.013828017748892307,
0.027319855988025665,
0.00612106965854764,
-0.017759107053279877,
-0.024504592642188072,
-0.03628707677125931,
0.07646884769201279,
-0.05129818990826607,
0.009558740071952343,
-0.018506942316889763,
-0.01849444955587387,
-0.028464876115322113,
0.05123588442802429,
0.011192399077117443,
-0.011058980599045753,
0.03244371712207794,
-0.029810309410095215,
-0.025331174954771996,
0.0358087383210659,
0.041613802313804626,
-0.018716132268309593,
-0.044881392270326614,
0.0012210252461954951,
-0.02133134752511978,
-0.02216300554573536,
0.012565232813358307,
0.028560353443026543,
-0.0363093838095665,
0.031901706010103226,
0.009111965075135231,
0.010777250863611698,
0.002093216171488166,
-0.019988881424069405,
0.016001399606466293,
-0.031094679608941078,
0.04629627987742424,
-0.0022310814820230007,
-0.03957728296518326,
0.021416794508695602,
-0.06409765034914017,
-0.036909498274326324,
-0.012414718978106976,
-0.009617608040571213,
0.030939225107431412,
-0.0734906941652298,
0.057514067739248276,
0.053348127752542496,
0.006637278012931347,
-0.0879381000995636,
-0.03622501343488693,
0.01836249977350235,
0.01573086343705654,
0.012274172157049179,
-0.007764625828713179,
0.04164213687181473,
-0.061650846153497696,
-0.02864532172679901,
-0.011603794060647488,
0.05384766310453415,
-0.00432463176548481,
-0.015361502766609192,
0.002323779044672847,
0.014072542078793049,
0.04093845933675766,
0.004700447898358107,
-0.03388344869017601,
0.009902906604111195,
0.006416427902877331,
-0.011019570752978325,
-0.0022546749096363783,
0.07199231535196304,
-0.015717577189207077,
-0.035564422607421875,
-0.03870377689599991,
-0.02459089644253254,
-0.002657127333804965,
-0.025125054642558098,
0.03463243693113327,
0.05991014465689659,
0.034306369721889496,
0.009599936194717884,
-0.04237225651741028,
0.03857173025608063,
-0.013686363585293293,
0.009482509456574917,
-0.0024030045606195927,
-0.004105649888515472,
-0.01414054911583662,
-0.04125777631998062,
0.0675634816288948,
0.010849172249436378,
0.012712434865534306,
-0.005684765987098217,
0.04223066195845604,
0.01992390863597393,
-0.005763484165072441,
-0.0009841517312452197,
-0.024279100820422173,
0.011637348681688309,
-0.012065889313817024,
0.00875762291252613,
0.0190985519438982,
-0.022948123514652252,
-0.021878715604543686,
0.006872360594570637,
-0.0108144860714674,
-0.024860668927431107,
0.08967133611440659,
-0.014369064942002296,
0.03806011751294136,
0.009822304360568523,
-0.030499285086989403,
-0.007219966035336256,
-0.04053546488285065,
-0.00032318811281584203,
0.022983476519584656,
0.01111659687012434,
0.007485910784453154,
-0.012122193351387978,
0.012624511495232582,
0.04013972729444504,
0.024025985971093178,
0.0012655011378228664,
0.029874145984649658,
0.059373240917921066,
0.023638464510440826,
-0.001736887963488698,
0.016224713996052742,
-0.04207286983728409,
0.01195011381059885,
-0.016765069216489792,
0.008476413786411285,
-0.03722263127565384,
0.008564700372517109,
0.023971879854798317,
0.008515364490449429,
0.037021324038505554,
-0.014215607196092606,
-0.04035509005188942,
-0.05197277292609215,
0.014521713368594646,
-0.014285211451351643,
0.014959845691919327,
0.002654601354151964,
0.025381792336702347,
0.035728342831134796,
0.0255107544362545,
0.006331812124699354,
0.001297843991778791,
-0.07209629565477371,
-0.038225967437028885,
-0.04061880707740784,
-0.03280020132660866,
0.05304184928536415,
0.01228429563343525,
-0.04184764623641968,
0.016693510115146637,
-0.03226708620786667,
0.01574430614709854,
0.03084917552769184,
0.04728953540325165,
-0.04826551675796509,
0.06124274432659149,
0.012237650342285633,
0.0070793102495372295,
-0.0026609383057802916,
0.007700547110289335,
0.07643410563468933,
0.043962955474853516,
0.005008775275200605,
-0.08306039869785309,
-0.0021704621613025665,
-0.02193904109299183,
0.02295416034758091,
-0.03652811050415039,
0.022300872951745987,
-0.038464758545160294,
0.0034152150619775057,
0.014535869471728802,
0.03965672850608826,
0.009246486239135265,
-0.036394499242305756,
0.055997736752033234,
-0.018701717257499695,
-0.028902176767587662,
-0.009615601040422916,
0.024316556751728058,
0.018343549221754074,
0.0308728888630867,
-0.044199138879776,
0.016843656077980995,
-0.03202955052256584,
0.00554503221064806,
-0.02294613979756832,
-0.026902243494987488,
-0.014166327193379402,
0.001314430614002049,
-0.05019380897283554,
0.0015654972521588206,
0.036821842193603516,
-0.03543604910373688,
-0.0571487620472908,
0.0071278163231909275,
0.008784893900156021,
-0.021337609738111496,
-0.0006634549936279655,
0.012999108992516994,
-0.008295809850096703,
0.017747478559613228,
-0.006934735924005508,
-0.022540036588907242,
-0.060239095240831375,
0.0016044770600274205,
-0.011179069057106972,
0.039898112416267395,
-0.004014879930764437,
0.02656700648367405,
0.015608101151883602,
0.004152379464358091,
-0.005820010788738728,
-0.05377998203039169,
-0.014809710904955864,
-0.020000925287604332,
0.01062603946775198,
0.013642661273479462,
-0.017320334911346436,
-0.01773044653236866,
0.03269383683800697,
0.006915660575032234,
0.04163939133286476,
-0.004970846697688103,
0.014104485511779785,
0.03941912576556206,
-0.03253459557890892,
0.011724009178578854,
-0.052508022636175156,
-0.02173258177936077,
0.008592061698436737,
0.00052120559848845,
-0.033372096717357635,
-0.016866764053702354,
0.04209830239415169,
0.049795180559158325,
-0.006967736873775721,
0.006221851799637079,
0.018288541585206985,
-0.0034728404134511948,
-0.05704548954963684,
0.031033284962177277,
-0.031696926802396774,
-0.04436077922582626,
-0.02867763303220272,
0.017988018691539764,
0.05033786967396736,
0.02600625902414322,
-0.015532056801021099,
0.022190693765878677,
-0.04310789331793785,
-0.010278867557644844,
0.00027481731376610696,
-0.015785256400704384,
0.020428117364645004,
0.04839596897363663,
0.008043203502893448,
-0.012688088230788708,
-0.017577048391103745,
-0.015441786497831345,
0.03507797792553902,
-0.01565507985651493,
-0.013015846721827984,
0.04547804594039917,
-0.018775176256895065,
0.007773275021463633,
0.017834041267633438,
-0.016906345263123512,
0.014280800707638264,
0.00447134068235755,
0.04306057468056679,
-0.03788980096578598,
-0.06371797621250153,
-0.04110635444521904,
0.0060418774373829365,
0.011386004276573658,
0.016507286578416824,
0.0003159941697958857,
0.041041117161512375,
-0.020372584462165833,
0.03120608627796173,
-0.054029740393161774,
0.018419476225972176,
-0.08889731019735336,
0.023724129423499107,
0.016975976526737213,
-0.04823775216937065,
0.0013916154857724905,
0.018493350595235825,
-0.0098338071256876,
-0.026085685938596725,
-0.005424330942332745,
0.021372729912400246,
-0.017117202281951904,
0.02347918041050434,
0.03807744383811951,
-0.04025806114077568,
0.056329529732465744,
0.014154200442135334,
-0.009773358702659607,
0.007417232263833284,
-0.04344059154391289,
-0.02159346267580986,
0.049915045499801636,
-0.025785673409700394,
0.01738068088889122,
0.017336484044790268,
-0.022426778450608253,
-0.011082438752055168,
0.07823284715414047,
-0.01649114489555359,
-0.008197221904993057,
0.012388673610985279,
-0.07064972072839737,
-0.03756910189986229,
0.008435253985226154,
0.007031900342553854,
-0.02414943091571331,
-0.04551571607589722,
0.0404345877468586,
0.0037920537870377302,
0.003003823570907116,
0.009307676926255226,
0.008303258568048477,
0.009227297268807888,
0.01968424580991268,
0.019743697717785835,
-0.016530904918909073,
0.029917612671852112,
0.06201688572764397,
-0.03139987587928772,
0.044618964195251465,
0.04622972011566162,
0.012509635649621487,
-0.10394783318042755,
-0.003376533044502139,
0.013990041799843311,
0.021289436146616936,
0.03322397544980049,
-0.03234218433499336,
0.013788142241537571,
-0.0177265964448452,
-0.03101629577577114,
0.025860555469989777,
-0.030190808698534966,
-0.03360104188323021,
0.018245872110128403,
0.004133220296353102,
-0.00477116834372282,
0.01217279676347971,
0.04854049161076546,
0.02426805905997753,
-0.025641927495598793,
0.007577098906040192,
-0.017796311527490616,
-0.01372179202735424,
-0.00907827913761139,
0.02899378538131714,
0.0008009983575902879,
-0.0069785043597221375,
0.06548967212438583,
-0.016212977468967438,
-0.005938804242759943,
0.015525841154158115,
0.014680738560855389,
0.004333892837166786,
-0.0013620901154354215,
-0.0009758396772667766,
0.010105375200510025,
0.013744563795626163,
0.0016827537911012769,
-0.018988845869898796,
-0.019785329699516296,
0.06529250741004944,
-0.01234461460262537,
0.026011478155851364,
-0.007979432120919228,
-0.0015656102914363146,
-0.029385417699813843,
-0.06810493022203445,
-0.035122476518154144,
-0.009423015639185905,
-0.033796824514865875,
-0.026038242504000664,
-0.015026851557195187,
0.03377305343747139,
0.0032919796649366617,
-0.02606390416622162,
-0.0039941673167049885,
-0.059118278324604034,
-0.012345859780907631,
0.04554842785000801,
0.010428494773805141,
-0.02198035828769207,
0.025217391550540924,
0.0012753928313031793,
0.0029323813505470753,
-0.018347477540373802,
0.002724295947700739,
0.001760011538863182,
-0.043328702449798584,
0.01730169914662838,
0.0037628316786140203,
0.0016916533932089806,
0.01988109014928341,
-0.041401397436857224,
-0.02048061043024063,
0.042578306049108505,
-0.004016975872218609,
0.008560308255255222,
-0.016983389854431152,
-0.02668735198676586,
-0.015810688957571983,
-0.055099230259656906,
0.024266261607408524,
0.0022811421658843756,
0.03889509290456772,
-0.06609005481004715,
-0.005173321347683668,
-0.012957683764398098,
0.0016274680383503437,
0.05566580966114998,
-0.01607002317905426,
-0.027767527848482132,
0.04876703768968582,
-0.00037741713458672166,
-0.014076466672122478,
-0.025134792551398277,
0.009248346090316772,
-0.017407238483428955,
-0.06070801615715027,
-0.0071054561994969845,
-0.009613432921469212,
-0.02994394861161709,
0.008920763619244099,
0.026165807619690895,
-0.02775931917130947,
0.05099964886903763,
-0.017113035544753075,
-0.02109469845890999,
0.08631344139575958,
0.036010000854730606,
0.00585178891196847,
0.05640905722975731,
0.012006648816168308,
0.03291953727602959,
0.060920797288417816,
-0.014640423469245434,
-0.027113327756524086,
0.03946349397301674,
-0.03539413958787918,
0.010773519985377789,
-0.0010552587918937206,
-0.006435960531234741,
0.011117816902697086,
-0.017143184319138527,
-0.004394174087792635,
0.02962997369468212,
-0.01480068825185299,
0.0011895367642864585,
0.06144709512591362,
-0.002059992402791977,
0.043371476233005524,
-0.03001619689166546,
-0.009100306779146194,
0.0046486263163387775,
0.019639939069747925,
0.01693778857588768,
0.02978675812482834,
0.020159469917416573,
0.02069277875125408,
-0.01777929812669754,
0.029076291248202324,
-0.012103530578315258,
-0.018813449889421463,
-0.012423539534211159,
0.06550202518701553,
-0.03257067874073982,
-0.04816049337387085,
-0.01666676439344883,
0.000735891459044069,
0.026012249290943146,
0.018241796642541885,
-0.026347586885094643,
0.05278118699789047,
0.0008502580458298326,
0.016901256516575813,
-0.02831299789249897,
-0.015619348734617233,
-0.0034522286150604486,
0.028370428830385208,
0.002801107708364725,
0.04677777737379074,
0.01423701923340559,
-0.007379190530627966,
-0.017608946189284325,
-0.03841196000576019,
0.013653673231601715,
-0.02956966869533062,
0.02131388708949089,
0.007556425407528877,
0.0014956736704334617,
0.004860812798142433,
-0.029599402099847794,
-0.031895291060209274,
-0.02310260944068432,
0.0160662941634655,
0.028637513518333435,
0.014203328639268875,
-0.048623163253068924,
-0.001530720037408173,
-0.030127856880426407,
0.05477499961853027,
-0.0803532600402832,
-0.0060291956178843975,
-0.04702190309762955,
0.027116915211081505,
-0.014350395649671555,
-0.012748431414365768
] |
<p>I have seen the "objects pull down on space-time" explanations, but they assume a "pull down" force themselves. Could anyone explain the space-time explanation without assuming gravity in the first place?</p>
<p><img src="http://i.stack.imgur.com/RVFrW.png" alt=""></p>
| 13 |
[
-0.029065610840916634,
-0.02224414423108101,
-0.007453789934515953,
-0.024725528433918953,
0.003129956079646945,
0.003920513670891523,
-0.015490001998841763,
0.001728574512526393,
0.013669292442500591,
-0.03108787350356579,
0.00872785970568657,
0.042350150644779205,
0.009863119572401047,
0.003740500658750534,
0.017575563862919807,
0.0364903062582016,
-0.014004215598106384,
-0.029424237087368965,
0.00017908128211274743,
-0.030486568808555603,
-0.007704815361648798,
0.04227873310446739,
-0.017865292727947235,
0.014866509474813938,
-0.02015412598848343,
-0.0157657228410244,
0.045063234865665436,
-0.009214941412210464,
0.024702448397874832,
0.07679624855518341,
0.008469469845294952,
-0.020868681371212006,
-0.019935088232159615,
0.039472103118896484,
0.003969728946685791,
-0.010104624554514885,
-0.019673284143209457,
-0.004663869272917509,
-0.0040817866101861,
0.02586192823946476,
-0.017640843987464905,
-0.01029142178595066,
-0.046802930533885956,
0.07004863768815994,
-0.04103126376867294,
0.043473854660987854,
0.023478254675865173,
-0.0049974918365478516,
0.052657850086688995,
-0.055630769580602646,
0.08863835036754608,
-0.004096220247447491,
0.045637115836143494,
0.03291662037372589,
-0.013337038457393646,
-0.010061387903988361,
0.08133985847234726,
0.05452750250697136,
-0.04171155393123627,
-0.06667003035545349,
-0.023537036031484604,
-0.02229994535446167,
-0.01915937475860119,
-0.012667971663177013,
0.0050508128479123116,
0.019784502685070038,
-0.03834466636180878,
-0.022315124049782753,
0.02080462872982025,
0.009159781038761139,
0.018913237378001213,
-0.002361764432862401,
0.03766847029328346,
-0.00800547655671835,
-0.01873117685317993,
-0.012893685139715672,
0.03790649026632309,
-0.015219313092529774,
0.05719902366399765,
0.01526375487446785,
-0.0013562923995777965,
-0.002387843793258071,
0.06431803852319717,
0.040452174842357635,
0.01002644281834364,
-0.009113913401961327,
0.06674200296401978,
0.0003444401954766363,
0.012088138610124588,
0.0468360111117363,
-0.03951523080468178,
-0.007997340522706509,
0.023247137665748596,
-0.01046601589769125,
-0.014634714461863041,
0.035985346883535385,
0.0020834701135754585,
0.0515853650867939,
0.04371784254908562,
-0.002810918027535081,
-0.020095542073249817,
-0.004413684830069542,
0.00331590767018497,
0.08671703189611435,
0.005190460477024317,
-0.01336592249572277,
-0.058140646666288376,
0.06993171572685242,
-0.03051021881401539,
-0.0024055580142885447,
-0.02762329950928688,
0.015624679625034332,
0.0071416981518268585,
-0.03008403442800045,
0.024013157933950424,
-0.012650460936129093,
0.012759794481098652,
-0.021417448297142982,
0.02185181714594364,
0.03442726284265518,
0.03699851781129837,
-0.04094667360186577,
-0.0003601020434871316,
-0.022837404161691666,
-0.04901637136936188,
0.028283551335334778,
0.04649520292878151,
-0.04353897273540497,
-0.000461172399809584,
0.028391119092702866,
-0.023399660363793373,
-0.019276300445199013,
0.0009637576877139509,
-0.00993951503187418,
0.05468672513961792,
0.022783206775784492,
-0.11443652957677841,
-0.03628058731555939,
0.03902668505907059,
-0.0000013319117897481192,
-0.005660033319145441,
-0.06467124074697495,
-0.00047696701949462295,
-0.012053829617798328,
0.09333199262619019,
-0.02011079713702202,
0.00316276284866035,
0.012659095227718353,
0.03196808323264122,
-0.015124818310141563,
0.011178801767528057,
-0.009964043274521828,
-0.017701970413327217,
-0.061775341629981995,
0.0017883600667119026,
-0.09402354806661606,
-0.0020123962312936783,
0.04660607874393463,
-0.0004945450928062201,
-0.042901743203401566,
0.03782740980386734,
-0.0031500470358878374,
-0.011174171231687069,
-0.01645374298095703,
-0.0011272039264440536,
-0.027459047734737396,
0.04694848507642746,
0.008608064614236355,
-0.031775638461112976,
0.0824493020772934,
0.020531674847006798,
0.05735842138528824,
0.005401177331805229,
0.05061417818069458,
-0.0041336906142532825,
-0.042557887732982635,
-0.03215653449296951,
-0.008402383886277676,
-0.018355293199419975,
-0.009984632022678852,
-0.04244192689657211,
-0.030154140666127205,
0.007366289850324392,
-0.001407823758199811,
0.004833695013076067,
0.02321031503379345,
-0.0047600725665688515,
-0.031077438965439796,
-0.03223421052098274,
-0.05068240314722061,
0.015421674586832523,
-0.10088596493005753,
0.027036145329475403,
-0.031017275527119637,
-0.006211083848029375,
0.009023131802678108,
0.022169144824147224,
0.018954090774059296,
-0.04020218923687935,
-0.03592252358794212,
-0.03643670305609703,
0.028805825859308243,
-0.02516109310090542,
-0.02147609181702137,
0.0023446031846106052,
0.06222531199455261,
0.04265288636088371,
0.022259483113884926,
0.009626093320548534,
-0.01155025977641344,
-0.016856055706739426,
0.01602921634912491,
0.005663011223077774,
0.0036840715911239386,
-0.021296536549925804,
0.01777857355773449,
-0.0028084174264222383,
0.008144514635205269,
-0.012280697003006935,
0.05559776350855827,
-0.029530063271522522,
0.09370337426662445,
0.03140228986740112,
0.012720874510705471,
-0.018815429881215096,
0.04113128036260605,
0.022929884493350983,
0.008665181696414948,
-0.008944100700318813,
-0.00013085105456411839,
-0.03848441317677498,
-0.008808846585452557,
0.024202991276979446,
0.025713756680488586,
-0.02784937061369419,
0.0027354934718459845,
0.014422792941331863,
0.06511843949556351,
-0.00285408110357821,
0.05387681722640991,
-0.013815385289490223,
-0.04152655601501465,
-0.011088781990110874,
-0.005948130507022142,
0.021009322255849838,
0.01660546287894249,
0.05261412262916565,
0.021551791578531265,
0.011017093434929848,
0.0032553598284721375,
-0.03474058955907822,
0.013944213278591633,
0.006881951820105314,
0.015366964973509312,
0.01782544143497944,
-0.028478410094976425,
0.03156810998916626,
-0.025063375011086464,
0.02584853395819664,
0.023867905139923096,
0.0033738575875759125,
0.0014042992843315005,
-0.07508067041635513,
-0.005827055312693119,
0.029190050438046455,
0.02486734837293625,
-0.021855803206562996,
0.006271168123930693,
0.03661050647497177,
-0.03629806265234947,
-0.01587008312344551,
-0.010403556749224663,
-0.012050628662109375,
-0.02685714326798916,
0.020592372864484787,
-0.009277312085032463,
0.04008612036705017,
0.04702024906873703,
-0.01475957129150629,
-0.019389688968658447,
0.010318403132259846,
-0.015479039400815964,
-0.015576990321278572,
-0.0014354924205690622,
-0.043054159730672836,
0.046699158847332,
-0.02829420380294323,
-0.029717227444052696,
0.06375037133693695,
0.015312060713768005,
0.024277206510305405,
0.005355344153940678,
-0.034885797649621964,
-0.029672954231500626,
-0.019452203065156937,
-0.04319231957197189,
0.01431742962449789,
-0.032190363854169846,
0.01585918851196766,
0.07280072569847107,
0.005792325362563133,
-0.036043159663677216,
0.030789827927947044,
-0.04554342105984688,
-0.04303806647658348,
-0.023664943873882294,
0.01952267624437809,
0.003862551413476467,
-0.040475033223629,
0.006277167238295078,
-0.005988352466374636,
-0.05896870046854019,
0.042250148952007294,
-0.02692052349448204,
-0.017423195764422417,
0.025468727573752403,
-0.007708600256592035,
0.05524735152721405,
-0.02564125694334507,
-0.04380056634545326,
0.0878230631351471,
0.0082308454439044,
-0.019089819863438606,
-0.039521947503089905,
-0.024348285049200058,
-0.003424982773140073,
0.010340994223952293,
0.016409436240792274,
0.0355529747903347,
0.012606040574610233,
0.02806396782398224,
0.018043402582406998,
0.02865111455321312,
0.006535119377076626,
0.02456922084093094,
-0.03214316442608833,
-0.009434293024241924,
0.016914501786231995,
-0.019974997267127037,
0.04734943062067032,
0.011781356297433376,
-0.034158457070589066,
0.004147518426179886,
-0.0160816740244627,
0.03202955797314644,
-0.011938485316932201,
-0.04702826961874962,
0.046807579696178436,
0.009996922686696053,
0.003869210369884968,
-0.013288288377225399,
0.010143292136490345,
-0.026603657752275467,
0.0004137782962061465,
0.030466869473457336,
-0.007157818414270878,
0.057525888085365295,
0.0009292488102801144,
-0.003975904081016779,
-0.0027904100716114044,
0.04186982288956642,
-0.05903543904423714,
-0.05181954801082611,
0.008984936401247978,
-0.014724720269441605,
0.03229781612753868,
0.006667978595942259,
0.013689168728888035,
0.03561849892139435,
0.01721811480820179,
0.040360622107982635,
0.008592254482209682,
-0.06305139511823654,
0.011246760375797749,
-0.08126723021268845,
0.03251979127526283,
0.0016489573754370213,
0.021092476323246956,
0.0006487086648121476,
0.04395267367362976,
0.013987261801958084,
0.013034410774707794,
0.03460685908794403,
0.004646156914532185,
-0.08640772849321365,
-0.0020782765932381153,
-0.024515599012374878,
-0.031291984021663666,
-0.020851727575063705,
0.004315464291721582,
-0.015846865251660347,
-0.02748287469148636,
0.004619323182851076,
-0.024546533823013306,
-0.001101271016523242,
-0.06957046687602997,
0.006204443983733654,
-0.021210165694355965,
-0.009219502098858356,
-0.006725101266056299,
0.00021302839741110802,
0.040202993899583817,
-0.03582211211323738,
0.01989991031587124,
0.04028492420911789,
0.0016955446917563677,
-0.02698662504553795,
-0.0002554664097260684,
-0.017111677676439285,
0.05291733890771866,
-0.02920515090227127,
0.01896456629037857,
0.022578055039048195,
-0.0282510407269001,
0.014012052677571774,
-0.003248467342928052,
0.03299934044480324,
0.010241820476949215,
-0.035719938576221466,
-0.05715622380375862,
-0.040959279984235764,
-0.020415669307112694,
-0.019775893539190292,
0.07057832181453705,
-0.0036251035053282976,
0.006614789832383394,
-0.0006897600251249969,
0.030688660219311714,
0.004625438712537289,
0.023003801703453064,
0.04187699407339096,
0.017554575577378273,
-0.01747087575495243,
-0.04210186377167702,
0.007473534904420376,
-0.03757329657673836,
0.003332728985697031,
0.029993750154972076,
-0.009225595742464066,
-0.04238368570804596,
0.027780041098594666,
-0.00017355587624479085,
-0.011572113260626793,
-0.00016750289069022983,
-0.007330379914492369,
0.0045204502530395985,
0.022396527230739594,
-0.01227977592498064,
0.016230391338467598,
0.03867992386221886,
0.05192505940794945,
0.0524505153298378,
0.012364741414785385,
-0.00949038565158844,
-0.11446336656808853,
-0.023259442299604416,
0.05041223764419556,
0.0054250149987638,
-0.021554047241806984,
-0.02543986402451992,
-0.049298644065856934,
-0.01578519307076931,
0.04778200760483742,
-0.029937202110886574,
0.01563112810254097,
0.019022714346647263,
0.02699286676943302,
-0.014751801267266273,
-0.006740644574165344,
0.0016895090229809284,
0.0058620767667889595,
-0.034961920231580734,
0.04238297417759895,
-0.000135672657052055,
0.006902121007442474,
-0.02433806285262108,
0.03220769762992859,
0.018568899482488632,
0.02873051166534424,
0.007737445179373026,
0.030428333207964897,
-0.020009173080325127,
0.022343162447214127,
-0.054378241300582886,
-0.07063720375299454,
-0.003970681689679623,
0.010262086987495422,
-0.029368475079536438,
0.035921111702919006,
-0.03381560742855072,
-0.02988734096288681,
-0.00002853417936421465,
-0.02434486895799637,
0.01187971606850624,
0.0035064106341451406,
-0.030765878036618233,
0.031086070463061333,
0.038267962634563446,
-0.02171967551112175,
0.0325489267706871,
0.03787052258849144,
-0.026252346113324165,
-0.032264403998851776,
-0.014086350798606873,
0.036483000963926315,
-0.009585118852555752,
0.01354846078902483,
-0.04190528020262718,
0.0011902617989107966,
-0.048298951238393784,
0.035588428378105164,
0.004311179276555777,
0.004912985488772392,
0.019549600780010223,
-0.04134353622794151,
-0.025979062542319298,
0.04503597319126129,
0.029763173311948776,
0.01639649085700512,
-0.010219408199191093,
-0.007888284511864185,
-0.008891659788787365,
-0.026950249448418617,
0.02900068275630474,
0.044397782534360886,
-0.021153923124074936,
0.01874512806534767,
0.010626154020428658,
0.008108279667794704,
-0.00410451227799058,
-0.029582001268863678,
0.026074018329381943,
-0.04614846408367157,
0.040391650050878525,
-0.036027949303388596,
-0.0187671035528183,
0.00952513050287962,
-0.031126758083701134,
-0.009036780335009098,
-0.026073632761836052,
-0.02483060397207737,
0.018604431301355362,
-0.03340112417936325,
0.01026550866663456,
0.02381710149347782,
0.01775401085615158,
-0.06892772018909454,
-0.04882948845624924,
0.06335102766752243,
0.0016189374728128314,
-0.016073964536190033,
-0.05176163464784622,
0.02424287423491478,
-0.05787183716893196,
-0.03403840214014053,
-0.004763413220643997,
0.07490289956331253,
-0.01946134679019451,
-0.010660462081432343,
0.02087256871163845,
-0.010134907439351082,
0.03659847751259804,
-0.005334893707185984,
-0.029606865718960762,
0.016251878812909126,
-0.02159865014255047,
-0.004857105668634176,
-0.004056520294398069,
0.07807982712984085,
-0.028142748400568962,
-0.02392476052045822,
-0.0013239773688837886,
-0.034913189709186554,
0.01727817766368389,
-0.044429998844861984,
0.001218052115291357,
0.0490536242723465,
0.03415636718273163,
0.009892676025629044,
-0.03526150435209274,
0.05719148740172386,
-0.001666629919782281,
0.017455030232667923,
-0.007497068960219622,
0.02014010213315487,
-0.01712646894156933,
-0.038523104041814804,
0.044517096132040024,
-0.015750590711832047,
0.018488163128495216,
0.020187173038721085,
0.05459832400083542,
-0.013065866194665432,
-0.0012007537297904491,
0.013133126311004162,
0.007357102818787098,
0.028369123116135597,
0.030115986242890358,
0.014291302300989628,
0.02911951392889023,
-0.008315786719322205,
-0.039661865681409836,
0.016656428575515747,
0.015021148137748241,
0.019792689010500908,
0.056259915232658386,
-0.03871980309486389,
0.07455234974622726,
0.025136802345514297,
-0.005759408697485924,
-0.004119214601814747,
0.004987500142306089,
0.007103686686605215,
0.004728806205093861,
0.0004408499808050692,
0.022257091477513313,
-0.025832481682300568,
0.029678942635655403,
0.022053666412830353,
0.039618682116270065,
-0.034005142748355865,
0.007939603179693222,
0.04375501722097397,
0.01225314661860466,
0.026032056659460068,
0.010124120861291885,
-0.03347622975707054,
0.014811339788138866,
-0.004083338193595409,
0.01039906032383442,
0.013628492131829262,
-0.00638815900310874,
0.03839249536395073,
0.007622402627021074,
0.03027571178972721,
-0.0280404444783926,
-0.008812385611236095,
-0.044585149735212326,
-0.022014832124114037,
0.01573699712753296,
0.017693523317575455,
-0.0029940190725028515,
0.00432160310447216,
0.026420528069138527,
0.022837279364466667,
0.03307073935866356,
0.005431934259831905,
-0.05670524761080742,
-0.023402834311127663,
-0.03480043262243271,
-0.031176842749118805,
0.02522866800427437,
0.03326566144824028,
-0.019228175282478333,
-0.0004551955498754978,
-0.0401509664952755,
0.006241597700864077,
0.028498664498329163,
0.04602651670575142,
-0.024891287088394165,
0.09505412727594376,
-0.014154509641230106,
-0.020373115316033363,
-0.010403217747807503,
-0.02202777750790119,
0.10272393375635147,
0.029689554125070572,
0.0006855022511444986,
-0.05558422580361366,
0.005687593948096037,
-0.022687435150146484,
0.0065715559758245945,
-0.05491407588124275,
0.024017134681344032,
-0.0031782325822860003,
0.03235814347863197,
0.01889347843825817,
0.04810328409075737,
-0.008687729947268963,
-0.02008776366710663,
0.044159021228551865,
-0.0657951608300209,
-0.03216306120157242,
0.000348676519934088,
0.034030646085739136,
-0.0025590602308511734,
0.02887471579015255,
-0.047168273478746414,
0.03546048700809479,
-0.037543054670095444,
0.0029595487285405397,
-0.0223237257450819,
-0.041471898555755615,
-0.01372539158910513,
-0.01630312018096447,
-0.08041137456893921,
0.03165557608008385,
0.027233298867940903,
-0.035750579088926315,
-0.07075637578964233,
0.027372300624847412,
0.016933836042881012,
-0.0352889746427536,
0.016057109460234642,
-0.009270837530493736,
0.0001792498369468376,
0.023300040513277054,
-0.006722650490701199,
0.01188698224723339,
-0.04941441863775253,
0.010145914740860462,
-0.050671763718128204,
0.05963164567947388,
-0.03389633074402809,
0.012149298563599586,
0.0014280042378231883,
-0.002025169087573886,
0.0036515947431325912,
-0.06473668664693832,
-0.0030687276739627123,
-0.002819412387907505,
0.02487434446811676,
0.029149910435080528,
-0.030628731474280357,
-0.01553480513393879,
0.030987296253442764,
-0.0023164311423897743,
0.03164336085319519,
0.012417523190379143,
0.010349491611123085,
0.06013233959674835,
0.0012804900761693716,
0.03589541092514992,
-0.02843702770769596,
-0.0014007913414388895,
-0.027388030663132668,
-0.008644893765449524,
-0.044251251965761185,
0.0259995199739933,
0.01776345819234848,
0.04520222172141075,
0.010210728272795677,
-0.0025916898157447577,
0.0048601580783724785,
-0.0093797342851758,
-0.050786107778549194,
0.020561736077070236,
-0.04902278631925583,
-0.02487228624522686,
-0.039313964545726776,
0.011890513822436333,
0.0058072092942893505,
0.04553785175085068,
-0.0003036186099052429,
0.02658490277826786,
-0.030948199331760406,
0.02120038866996765,
-0.011115041561424732,
-0.01861158199608326,
-0.024828879162669182,
0.004240213427692652,
0.0015112289693206549,
-0.01256394013762474,
-0.010727102868258953,
0.0022254858631640673,
0.01521230023354292,
-0.008921614848077297,
0.002876952290534973,
0.034731533378362656,
-0.0070933997631073,
0.004674190655350685,
0.01978388987481594,
-0.03476984053850174,
-0.004111096728593111,
0.0166554544121027,
-0.019182484596967697,
-0.042165644466876984,
-0.008732609450817108,
-0.006254678126424551,
-0.009061964228749275,
-0.0012103905901312828,
0.05650455504655838,
-0.018116427585482597,
0.025075312703847885,
-0.03042200766503811,
0.02692611888051033,
-0.045752935111522675,
-0.0027789336163550615,
-0.06360418349504471,
0.01259410846978426,
-0.02518177591264248,
-0.022355319932103157,
-0.004726656246930361,
0.027763385325670242,
-0.04397379606962204,
-0.0033831230830401182,
0.006989386864006519,
-0.0028589563444256783,
-0.03109559789299965,
0.012204723432660103,
0.05343197286128998,
-0.013442623429000378,
0.03978018835186958,
0.005247561261057854,
-0.04001579061150551,
0.021958788856863976,
-0.041983816772699356,
-0.06954251229763031,
0.031133374199271202,
-0.020589271560311317,
0.03199445456266403,
0.024323876947164536,
-0.04573779180645943,
-0.025930678471922874,
0.07309436053037643,
-0.045184068381786346,
-0.01622195541858673,
-0.0037549640983343124,
-0.0194776002317667,
0.0004947782726958394,
-0.004858812317252159,
0.00048272349522449076,
-0.03379003703594208,
-0.03032710589468479,
0.010297609493136406,
0.011680718511343002,
-0.01606847159564495,
-0.004386757500469685,
0.03533736616373062,
-0.041058722883462906,
0.003387843957170844,
0.015059576369822025,
-0.018871093168854713,
0.017481999471783638,
0.045403722673654556,
-0.05191155895590782,
0.040152765810489655,
0.030184024944901466,
-0.012155651114881039,
-0.07806354761123657,
0.027995401993393898,
0.006031513679772615,
-0.01217199582606554,
0.053622979670763016,
-0.04924424737691879,
0.022094877436757088,
0.013260511681437492,
-0.05953799933195114,
0.03889910504221916,
-0.03766307979822159,
-0.01355384849011898,
-0.017552001401782036,
-0.031021956354379654,
0.042555879801511765,
0.07692375034093857,
0.023844121024012566,
0.06332821398973465,
-0.02104293368756771,
0.0080131646245718,
-0.02440750040113926,
-0.025974074378609657,
-0.00641821650788188,
0.04400337114930153,
-0.03346952795982361,
0.0050119501538574696,
0.053040843456983566,
0.01098699402064085,
0.0025434261187911034,
0.014526475220918655,
0.017743991687893867,
0.009851385839283466,
0.007554330863058567,
0.021061543375253677,
-0.013697502203285694,
-0.010192472487688065,
0.007636449299752712,
-0.02322857640683651,
-0.018554825335741043,
0.07008689641952515,
0.013387096114456654,
0.027883321046829224,
-0.017756978049874306,
-0.013631727546453476,
-0.0036453616339713335,
-0.06017467752099037,
-0.017092784866690636,
0.014104356057941914,
-0.034512411803007126,
0.01698409579694271,
0.008793544955551624,
0.015034783631563187,
0.019884809851646423,
-0.010917222127318382,
-0.014860508032143116,
-0.033172961324453354,
-0.00012432369112502784,
0.04193461686372757,
-0.015868067741394043,
-0.04502684250473976,
0.03274313360452652,
0.0006608836119994521,
-0.00605019461363554,
-0.024002887308597565,
0.002109095687046647,
0.015771299600601196,
-0.05212858319282532,
-0.00965462252497673,
0.022061875090003014,
-0.026953890919685364,
-0.013923927210271358,
-0.05274990200996399,
-0.027842985466122627,
0.06109268590807915,
0.04906347021460533,
0.0034716816153377295,
0.03191419690847397,
-0.05261965095996857,
-0.025967352092266083,
-0.0854579284787178,
0.042439572513103485,
-0.022972632199525833,
-0.003653022227808833,
-0.026341231539845467,
-0.014324166812002659,
-0.003128018695861101,
0.01600492373108864,
0.05272644758224487,
-0.0154477059841156,
-0.006727552507072687,
0.04440011829137802,
0.0072678872384130955,
-0.002518384251743555,
-0.03622303530573845,
0.007652833592146635,
0.020491527393460274,
-0.04147033020853996,
0.007198388688266277,
-0.0013950373977422714,
-0.0087678711861372,
0.016789298504590988,
0.0042111435905098915,
-0.02043025754392147,
0.06466047465801239,
0.007161137647926807,
-0.03007035329937935,
0.04221262410283089,
0.02848847769200802,
0.007422948721796274,
0.049355462193489075,
0.0009429581696167588,
-0.00250108796171844,
0.03215312957763672,
-0.01284912507981062,
-0.012796727009117603,
0.01861158199608326,
-0.02779489755630493,
0.006200764328241348,
-0.04006600007414818,
-0.035551559180021286,
0.030899103730916977,
-0.034559085965156555,
-0.025401340797543526,
0.035091184079647064,
-0.057514872401952744,
0.01005205512046814,
0.03726827725768089,
0.025678027421236038,
0.031169725582003593,
-0.026785017922520638,
0.026289956644177437,
0.012454054318368435,
-0.003548579989001155,
0.007983902469277382,
0.04019010439515114,
0.03286600857973099,
0.00011136352986795828,
0.0012865997850894928,
0.05012764781713486,
0.023666847497224808,
0.023719659075140953,
0.010007239878177643,
0.03319352865219116,
-0.026478106155991554,
-0.01344685535877943,
-0.0218537338078022,
0.003071530256420374,
0.011213840916752815,
0.02130514197051525,
-0.020215220749378204,
0.06783246994018555,
-0.020690347999334335,
-0.004041397478431463,
-0.011947561986744404,
-0.00982943270355463,
0.026593372225761414,
0.025324640795588493,
0.006309872958809137,
0.013313082978129387,
-0.0024061775766313076,
-0.03778167441487312,
0.021017467603087425,
0.00335772056132555,
0.02297208458185196,
0.01844947785139084,
0.029488788917660713,
-0.011267252266407013,
-0.0015775784850120544,
-0.007618720177561045,
-0.00878005102276802,
-0.03482671082019806,
-0.020419739186763763,
0.047595638781785965,
0.03558550402522087,
0.00563400611281395,
-0.032138802111148834,
0.018350359052419662,
-0.035830967128276825,
0.03973378986120224,
-0.06228642910718918,
-0.03239728510379791,
-0.017789892852306366,
0.06024168059229851,
-0.022960690781474113,
-0.007410271093249321
] |
<p>Until what point can the <a href="http://en.wikipedia.org/wiki/Matter_wave" rel="nofollow">de Broglie wave</a> be thought as a real wave?</p>
<p>I mean, is it made of something?
What amplitude does it have? Is it a sine wave? </p>
<p>How can it be related to the wavefunction of the particle?</p>
| 8,797 |
[
-0.015310613438487053,
-0.006372825708240271,
0.022069089114665985,
-0.06460043787956238,
0.053616736084222794,
0.014470120891928673,
-0.02859048917889595,
-0.055119626224040985,
-0.007967040874063969,
-0.019837500527501106,
0.04031410813331604,
0.04681926593184471,
0.026187552139163017,
0.03637244179844856,
0.02479024976491928,
0.0221246425062418,
-0.0036644553765654564,
-0.03936825320124626,
-0.027126673609018326,
-0.02357317879796028,
-0.0034639397636055946,
0.013814780861139297,
0.008288764394819736,
-0.0006492737447842956,
-0.015877187252044678,
0.01826789230108261,
0.06737565249204636,
0.028832940384745598,
0.012802002020180225,
0.05619765445590019,
0.017897462472319603,
-0.025379732251167297,
0.007644984405487776,
-0.002433394780382514,
0.022346442565321922,
-0.028976649045944214,
0.0082258190959692,
-0.015465229749679565,
-0.00834553875029087,
-0.016911804676055908,
-0.02508416771888733,
-0.031084803864359856,
-0.014803464524447918,
0.04596107453107834,
-0.027599621564149857,
-0.012452088296413422,
0.01566074602305889,
-0.05338404327630997,
0.05171627178788185,
-0.06975812464952469,
0.07722378522157669,
-0.015213778242468834,
0.05229222774505615,
-0.01755400002002716,
0.0117441825568676,
-0.03991470858454704,
0.07155704498291016,
0.05144699290394783,
-0.022637760266661644,
-0.06007115915417671,
-0.025914862751960754,
-0.00477102305740118,
-0.027193792164325714,
-0.021023280918598175,
-0.04053175076842308,
0.024567656219005585,
-0.02441159076988697,
-0.018899081274867058,
0.02659725397825241,
0.008540314622223377,
-0.019837288185954094,
0.008852793835103512,
0.03823721781373024,
-0.0034883192274719477,
0.020763998851180077,
-0.020291944965720177,
0.014707070775330067,
0.02121906727552414,
0.011613119393587112,
0.046593163162469864,
0.002493389183655381,
0.01910027116537094,
0.01820128783583641,
0.021707922220230103,
0.004209054633975029,
-0.011926647275686264,
0.07760883122682571,
-0.005295474547892809,
-0.007556015159934759,
0.03450290486216545,
0.010260775685310364,
0.01609227806329727,
0.02636471576988697,
0.003935377579182386,
-0.021078115329146385,
0.03192010149359703,
-0.0004880372143816203,
0.04150387644767761,
0.00834667682647705,
-0.06272275745868683,
0.027858451008796692,
-0.009693963453173637,
0.03579336404800415,
0.06438325345516205,
-0.013704872690141201,
-0.011495954357087612,
-0.06282070279121399,
0.029975906014442444,
0.004061939660459757,
-0.04838835820555687,
-0.016113808378577232,
0.04739474132657051,
0.0003512662078719586,
0.005613403394818306,
-0.003483625128865242,
-0.0034130108542740345,
0.01018909178674221,
-0.007549046538770199,
0.05737423524260521,
0.06452178955078125,
0.04737803339958191,
-0.029811445623636246,
0.03942350298166275,
-0.02274504490196705,
-0.07585606724023819,
-0.0031955153681337833,
0.0316275954246521,
-0.007355538662523031,
-0.020043831318616867,
0.020447121933102608,
0.003353646257892251,
0.006153739057481289,
0.013357582502067089,
-0.006676646880805492,
0.04390610754489899,
-0.011160320602357388,
-0.10852551460266113,
-0.06053164228796959,
0.03501647710800171,
-0.01721075363457203,
-0.03675302863121033,
-0.06814146786928177,
0.00886643398553133,
0.04175401106476784,
0.09807109832763672,
-0.00015196745516732335,
0.006261058151721954,
-0.012822838500142097,
0.03765628859400749,
-0.002264429582282901,
-0.0005962337600067258,
-0.021198492497205734,
0.014510098844766617,
-0.041976314038038254,
-0.008320571854710579,
-0.03151918575167656,
0.0055412123911082745,
0.03793107345700264,
-0.011287461966276169,
-0.033333901315927505,
0.06529109179973602,
-0.031717341393232346,
-0.009521694853901863,
0.015055556781589985,
-0.03855535015463829,
-0.032062940299510956,
0.08324899524450302,
0.02826073206961155,
-0.022547226399183273,
0.03568640723824501,
-0.000992265879176557,
0.006220635026693344,
0.005900782998651266,
0.024192869663238525,
0.021600501611828804,
-0.017217183485627174,
-0.056559037417173386,
-0.015180478803813457,
0.03553320840001106,
-0.013057238422334194,
0.01424061506986618,
-0.021766837686300278,
0.018236329779028893,
0.05872247368097305,
-0.009650073014199734,
0.04761987179517746,
-0.034707292914390564,
0.005900547374039888,
-0.02611895278096199,
-0.06635522842407227,
-0.014176815748214722,
-0.045589856803417206,
0.032151952385902405,
-0.015198242850601673,
0.01509024202823639,
0.0211460143327713,
0.027455559000372887,
0.01988622546195984,
-0.03876549378037453,
-0.015625473111867905,
-0.029872281476855278,
0.07303082197904587,
-0.013275304809212685,
0.014678622595965862,
0.04874638095498085,
0.05975254625082016,
0.011291568167507648,
-0.030694562941789627,
0.010165545158088207,
-0.015825480222702026,
-0.011473305523395538,
-0.021194733679294586,
-0.029315566644072533,
0.01787532866001129,
0.00031569323618896306,
0.038363710045814514,
-0.00007992378232302144,
-0.0358247235417366,
-0.02190271206200123,
0.01715807616710663,
-0.019413581117987633,
0.07164936512708664,
0.021414106711745262,
-0.0015214851591736078,
-0.0005951366620138288,
0.05170249566435814,
0.01397623959928751,
0.026104982942342758,
0.02636578306555748,
-0.02307708002626896,
-0.04376957193017006,
0.001081462251022458,
0.035645730793476105,
0.040413759648799896,
-0.029935713857412338,
0.01980222389101982,
-0.0017613942036405206,
0.04207747057080269,
0.04451606050133705,
0.04026688635349274,
-0.021116182208061218,
-0.023707685992121696,
-0.001317471731454134,
0.010158838704228401,
-0.0349414087831974,
-0.011480658315122128,
0.03976186737418175,
0.020486610010266304,
-0.009368943981826305,
-0.03432467579841614,
-0.02649890072643757,
0.04006243869662285,
-0.009065564721822739,
-0.00219466770067811,
-0.00900996383279562,
-0.04699293524026871,
0.03280334174633026,
-0.04120462387800217,
-0.002005711430683732,
0.0027214696165174246,
-0.029414227232336998,
-0.032831139862537384,
-0.029472624883055687,
-0.03245225548744202,
0.01455561351031065,
0.006142148282378912,
-0.04467965289950371,
-0.06297452002763748,
0.012633362784981728,
-0.019941886886954308,
0.015244940295815468,
0.0008412988390773535,
-0.019531698897480965,
-0.008364961482584476,
-0.004061626736074686,
0.04311239346861839,
0.02437286451458931,
0.050783250480890274,
-0.014158089645206928,
-0.07713459432125092,
0.013690405525267124,
-0.05395844206213951,
-0.007571607828140259,
-0.0037270563188940287,
-0.02581862360239029,
0.014440699480473995,
-0.029772954061627388,
-0.020221520215272903,
0.02054927684366703,
0.0028199597727507353,
-0.002445818390697241,
0.00871345680207014,
-0.03766295686364174,
-0.060737285763025284,
-0.002719886600971222,
-0.018784010782837868,
0.015015050768852234,
-0.03988996148109436,
0.009063602425158024,
0.01204824447631836,
-0.009495288133621216,
-0.014365103095769882,
0.014252551831305027,
0.011316709220409393,
-0.033372558653354645,
0.0004717367410194129,
-0.01772662252187729,
0.03372708708047867,
-0.043670590966939926,
0.012062483467161655,
0.024718059226870537,
-0.05582306906580925,
0.06948874890804291,
-0.0379522368311882,
-0.06357277184724808,
0.02857597917318344,
0.004251088947057724,
0.020590392872691154,
0.0077238380908966064,
-0.016762500628829002,
0.059036314487457275,
0.02979973517358303,
-0.06999482959508896,
0.0005390839651226997,
0.0017012280877679586,
0.00578903965651989,
-0.008053760044276714,
0.0019833543337881565,
0.05581488460302353,
-0.014208110980689526,
0.038382627069950104,
0.01757879927754402,
0.035185061395168304,
0.010753548704087734,
0.03828470781445503,
0.011269220151007175,
0.004553254693746567,
0.015899769961833954,
-0.015643492341041565,
0.04650937393307686,
-0.0057792565785348415,
-0.048859335482120514,
0.047970615327358246,
-0.01723247580230236,
0.018524378538131714,
0.01366730872541666,
-0.013771598227322102,
0.06194491684436798,
0.002973701572045684,
0.027049284428358078,
-0.037766050547361374,
0.04348314553499222,
0.004443020094186068,
-0.015590240247547626,
0.006835557986050844,
0.007938509806990623,
0.016328459605574608,
0.015041413716971874,
-0.023330945521593094,
0.04297104850411415,
0.008764408528804779,
-0.04426054283976555,
-0.03787975385785103,
-0.009566056542098522,
0.0022632027976214886,
0.01780310645699501,
-0.026804640889167786,
-0.06089198961853981,
0.03747587651014328,
0.03171399235725403,
0.03487144410610199,
-0.028240464627742767,
-0.02650383859872818,
-0.014819460920989513,
-0.049715813249349594,
-0.014603601768612862,
0.011983856558799744,
0.03201838582754135,
0.005001184996217489,
0.07410193979740143,
0.033592358231544495,
0.02293999306857586,
0.03056672029197216,
0.021488210186362267,
-0.09408703446388245,
0.019663158804178238,
-0.048684995621442795,
0.02024315483868122,
-0.029185360297560692,
-0.019061874598264694,
-0.013896340504288673,
-0.03284434974193573,
-0.03244682773947716,
-0.014512413181364536,
-0.021883804351091385,
-0.060314394533634186,
0.017879227176308632,
-0.023195745423436165,
-0.02249026484787464,
-0.03354310616850853,
0.029532015323638916,
0.03183094784617424,
0.026950428262352943,
-0.007476418744772673,
0.046998001635074615,
-0.023690231144428253,
0.020886702463030815,
0.020794911310076714,
-0.007403491996228695,
0.01332603208720684,
0.02680942229926586,
0.047157321125268936,
0.010632329620420933,
-0.04027235880494118,
0.011859641410410404,
0.027740946039557457,
0.04917027801275253,
0.012137160636484623,
-0.015314941294491291,
-0.013847763650119305,
-0.07123421132564545,
0.011590410955250263,
-0.028204243630170822,
0.04510827735066414,
0.015742262825369835,
0.014830355532467365,
0.009572549723088741,
-0.02412034571170807,
-0.03643130511045456,
0.05148538202047348,
0.06142621487379074,
-0.0011893085902556777,
-0.013291018083691597,
-0.03125252574682236,
0.001102894195355475,
-0.061550796031951904,
-0.013048438355326653,
0.024042639881372452,
-0.0005053758504800498,
-0.014238614588975906,
0.03873223438858986,
-0.005273953080177307,
0.0001461045176256448,
-0.0038066774141043425,
-0.02421724423766136,
-0.03859584778547287,
-0.02255488745868206,
-0.014047435484826565,
-0.006018012762069702,
0.024984151124954224,
0.054437410086393356,
0.0408969409763813,
0.00658164219930768,
-0.025852501392364502,
-0.07022496312856674,
0.0024077557027339935,
0.0454355925321579,
0.04683326184749603,
-0.023095520213246346,
-0.02819405123591423,
-0.07326342165470123,
-0.03141843527555466,
0.05469665676355362,
-0.06357608735561371,
0.004521872848272324,
-0.041085634380578995,
0.000010046210263681132,
-0.019029401242733,
-0.002929460722953081,
-0.00868913158774376,
0.023130031302571297,
-0.014523348771035671,
-0.010203670710325241,
-0.03160436451435089,
-0.0009155786829069257,
-0.02759740687906742,
0.0342002734541893,
0.00646558590233326,
0.04805007949471474,
0.035265542566776276,
0.021943621337413788,
0.0016162358224391937,
-0.0037690470926463604,
-0.04406961053609848,
-0.06891148537397385,
0.012122237123548985,
0.0011453720508143306,
-0.008727939799427986,
0.03124636970460415,
-0.014599491842091084,
-0.04471788555383682,
-0.005790261551737785,
-0.0038670178037136793,
0.024007193744182587,
0.029378918930888176,
-0.05530957877635956,
0.0568392388522625,
0.012546123936772346,
-0.006346112582832575,
0.012679548002779484,
0.02437981776893139,
-0.00158830510918051,
0.009363135322928429,
-0.018266085535287857,
0.012116795405745506,
-0.04491477459669113,
0.026072757318615913,
-0.01880861446261406,
0.003981127869337797,
-0.019377531483769417,
0.030746782198548317,
-0.03594670444726944,
-0.023035528138279915,
-0.01824377104640007,
-0.00313196680508554,
-0.03436825051903725,
0.01557003054767847,
0.010274039581418037,
-0.018642349168658257,
-0.014394699595868587,
0.021167511120438576,
0.011260074563324451,
-0.015203679911792278,
0.027994373813271523,
-0.0029404114466160536,
0.012724525295197964,
0.037220969796180725,
0.001497904653660953,
0.04392486810684204,
-0.013346066698431969,
-0.01103496365249157,
0.017093762755393982,
-0.061360087245702744,
0.03567764535546303,
-0.020882755517959595,
0.0026025802362710238,
0.009921384043991566,
-0.05874206870794296,
-0.03321355581283569,
0.012711949646472931,
0.016512393951416016,
0.03920235484838486,
-0.038858797401189804,
0.0256574135273695,
0.017728518694639206,
-0.0004698810516856611,
-0.06955630332231522,
-0.04832621291279793,
0.024129075929522514,
0.0279549453407526,
-0.006700433790683746,
-0.030559198930859566,
0.031511418521404266,
-0.02604532800614834,
0.0032235002145171165,
0.0024102330207824707,
0.022161388769745827,
-0.03689255565404892,
-0.016951831057667732,
0.015387962572276592,
-0.002537471940740943,
0.0817517340183258,
0.013290511444211006,
-0.035209957510232925,
0.015984611585736275,
-0.030186012387275696,
0.015602649189531803,
0.005962323863059282,
0.058621082454919815,
-0.01683991774916649,
-0.014371030032634735,
-0.0020521744154393673,
-0.0034203240647912025,
0.043353062123060226,
-0.013275657780468464,
0.012036551721394062,
0.012839742936193943,
0.017746586352586746,
-0.021983377635478973,
-0.016050776466727257,
0.01725032366812229,
-0.017493749037384987,
0.01956142671406269,
-0.002298761159181595,
-0.007240697275847197,
-0.057408470660448074,
-0.061257362365722656,
0.03428725153207779,
0.010216254740953445,
0.035750631242990494,
0.01957395300269127,
0.029172435402870178,
-0.006976217497140169,
0.011204728856682777,
0.0013769258512184024,
-0.01639235019683838,
-0.01050140243023634,
-0.024532465264201164,
0.005694148596376181,
-0.0011908404994755983,
0.01143701933324337,
-0.026095429435372353,
-0.008379871025681496,
-0.035559359937906265,
-0.007203215267509222,
0.04912293329834938,
-0.0063201189041137695,
0.043879810720682144,
0.0036997462157160044,
-0.004313786048442125,
-0.028532370924949646,
-0.0035756253637373447,
-0.012999214231967926,
-0.02099507674574852,
0.0011986687313765287,
0.008411804214119911,
-0.05153188481926918,
0.009734033606946468,
-0.011685887351632118,
0.0376090370118618,
-0.0010164562845602632,
0.019020352512598038,
0.03673824667930603,
0.02905472368001938,
0.013030650094151497,
0.013937417417764664,
-0.03756700083613396,
0.008424750529229641,
0.0031927479431033134,
0.05043894425034523,
0.005524668842554092,
-0.011093508452177048,
0.03208121657371521,
-0.00011125090532004833,
0.007040178403258324,
0.0019680378027260303,
-0.0036053387448191643,
-0.03312120959162712,
0.02104128897190094,
0.028009170666337013,
0.010503603145480156,
0.020761804655194283,
0.0020618310663849115,
-0.0035288240760564804,
0.032334987074136734,
0.009599929675459862,
0.009139561094343662,
-0.05126640573143959,
-0.024938195943832397,
-0.027815861627459526,
-0.04935411736369133,
0.05942869931459427,
0.01109580509364605,
-0.02831200137734413,
-0.006641180720180273,
-0.023952852934598923,
0.005326593294739723,
0.016432803124189377,
0.007737454026937485,
-0.035541944205760956,
0.045270808041095734,
-0.011935535818338394,
0.037763603031635284,
0.015957914292812347,
0.03583621233701706,
0.10935033857822418,
0.04698541387915611,
-0.004562336020171642,
-0.0644235834479332,
0.0008208606741391122,
-0.024292930960655212,
0.04797115549445152,
-0.020795386284589767,
0.009081950411200523,
-0.040396545082330704,
-0.006460933946073055,
-0.018033457919955254,
0.04545188322663307,
0.002694985130801797,
0.07498542964458466,
0.04771580174565315,
-0.07869960367679596,
-0.07633213698863983,
-0.0004037466424051672,
0.02437208965420723,
-0.007241296116262674,
0.027644596993923187,
-0.03499501571059227,
0.01925789751112461,
-0.03535780310630798,
-0.0068051014095544815,
-0.0011904140701517463,
-0.024037007242441177,
0.022855916991829872,
-0.0076522245071828365,
-0.05188952758908272,
-0.017991991713643074,
-0.0032629140187054873,
-0.007802407722920179,
-0.05087283253669739,
0.03676442801952362,
0.047114964574575424,
-0.00968359224498272,
0.010044490918517113,
0.008712058886885643,
-0.012682936154305935,
-0.010149095207452774,
0.008737691678106785,
0.011422363109886646,
-0.021058904007077217,
-0.014863749966025352,
-0.0013533473247662187,
0.04013362526893616,
-0.008607237599790096,
0.010190051048994064,
0.01829809509217739,
0.0068156179040670395,
-0.0007760621374472976,
-0.06555584818124771,
-0.018646499142050743,
-0.008738082833588123,
0.039222151041030884,
0.00235168868675828,
-0.042946502566337585,
-0.02149929851293564,
0.03493836149573326,
-0.03155696764588356,
0.01668585278093815,
0.0021280311048030853,
0.02139374241232872,
0.00789026077836752,
-0.01811208203434944,
0.024717800319194794,
0.002263552974909544,
-0.027809664607048035,
-0.014448391273617744,
-0.030339861288666725,
-0.049250997602939606,
-0.009886623360216618,
0.04443005099892616,
0.0402592197060585,
0.045415252447128296,
-0.0059306006878614426,
-0.006950684357434511,
-0.0322066992521286,
-0.06128288805484772,
0.01799355074763298,
-0.016733704134821892,
-0.03500739485025406,
-0.0023251944221556187,
0.0181873869150877,
0.05225587636232376,
0.08374013751745224,
-0.04695151001214981,
0.031270045787096024,
0.00019825658819172531,
-0.01301682647317648,
0.037980400025844574,
-0.013568062335252762,
0.0011220364831387997,
0.045570965856313705,
-0.00507831247523427,
0.01877780444920063,
-0.000744552118703723,
0.013834658078849316,
0.017315471544861794,
0.013576560653746128,
-0.0045308382250368595,
0.056170541793107986,
-0.03807345777750015,
-0.003083168063312769,
-0.0032790713012218475,
-0.004540165886282921,
0.008451131172478199,
0.03656816855072975,
0.005871585104614496,
-0.04858212545514107,
-0.05985359847545624,
-0.05099312216043472,
-0.012951775453984737,
0.002572408178821206,
0.042344942688941956,
-0.030681362375617027,
0.0015877147670835257,
0.04194819554686546,
0.004846394993364811,
-0.054512251168489456,
-0.008451152592897415,
-0.06035298481583595,
0.009060109965503216,
-0.018656205385923386,
-0.032620325684547424,
-0.015471860766410828,
0.0611453540623188,
-0.01840091310441494,
-0.022914933040738106,
0.018189869821071625,
0.041155386716127396,
-0.03230048343539238,
-0.00517423078417778,
-0.0028878573793917894,
0.0017672859830781817,
0.02422337792813778,
-0.008758297190070152,
-0.034496765583753586,
0.0213922131806612,
-0.06804527342319489,
-0.02316652424633503,
0.007335445377975702,
-0.007129129488021135,
0.02964325062930584,
0.045670051127672195,
-0.019176732748746872,
0.02773320861160755,
0.0421457514166832,
0.004127297084778547,
0.002756195142865181,
0.004555737599730492,
-0.03461327403783798,
-0.031942371279001236,
-0.0018923983443528414,
-0.002659351099282503,
0.011734525673091412,
-0.01502048596739769,
0.05853002518415451,
0.02894991636276245,
-0.0026952577754855156,
0.043761126697063446,
-0.003912684973329306,
0.008852365426719189,
0.0032723869662731886,
0.039362549781799316,
-0.0042953090742230415,
-0.0004649188194889575,
0.039261795580387115,
-0.0394979864358902,
0.021185999736189842,
-0.0004639050457626581,
-0.016515139490365982,
-0.0991581603884697,
0.012332722544670105,
0.012353947386145592,
0.0066139972768723965,
0.03466777503490448,
-0.02249745838344097,
0.027835264801979065,
0.025243274867534637,
-0.07660168409347534,
0.019879713654518127,
-0.031290337443351746,
0.004210211336612701,
0.000301858875900507,
0.014994285069406033,
-0.04228487238287926,
0.053763363510370255,
0.01974465884268284,
0.07374151796102524,
0.019262097775936127,
0.00045861967373639345,
0.004083908163011074,
-0.03528771176934242,
0.011392287909984589,
0.06188369169831276,
-0.006284711416810751,
0.002897640923038125,
0.07123129814863205,
-0.03255600482225418,
-0.008948794566094875,
0.031567078083753586,
-0.00707601010799408,
0.03351413458585739,
-0.0025900527834892273,
0.032523173838853836,
0.018513543531298637,
0.00761711411178112,
-0.0027432648930698633,
-0.024651676416397095,
-0.012472359463572502,
0.037812136113643646,
0.024457955732941628,
0.02482185885310173,
-0.0008067377493716776,
-0.009653589688241482,
0.015487417578697205,
-0.04866285249590874,
-0.05024995654821396,
0.02631225995719433,
-0.0014593357918784022,
-0.023017358034849167,
-0.03269943594932556,
-0.008937946520745754,
0.015569078736007214,
-0.01886723004281521,
0.014172183349728584,
-0.06864632666110992,
0.003833409398794174,
0.018020568415522575,
-0.0138227054849267,
-0.02713003382086754,
0.03427411988377571,
0.0008013931219466031,
-0.03986026719212532,
0.050578054040670395,
-0.00838699284940958,
-0.02228931151330471,
-0.02301383577287197,
-0.009019874967634678,
0.031477343291044235,
0.03862134367227554,
0.03492007777094841,
-0.028029391542077065,
-0.040871232748031616,
-0.006129877176135778,
-0.0079342070966959,
-0.0027937039267271757,
0.008249564096331596,
-0.04700925201177597,
-0.03225823491811752,
-0.08335206657648087,
0.055258896201848984,
0.00922192819416523,
-0.023637089878320694,
-0.015102177858352661,
0.006613542325794697,
0.018455352634191513,
0.03778710216283798,
0.05618543550372124,
-0.025287462398409843,
-0.01112922839820385,
0.011529471725225449,
-0.012055734172463417,
0.02081374265253544,
-0.026513371616601944,
-0.025220919400453568,
-0.02202063612639904,
-0.06061243638396263,
-0.025837114080786705,
0.0020081729162484407,
-0.03466082736849785,
0.024579644203186035,
0.029950523748993874,
0.031266264617443085,
0.010772911831736565,
-0.03556946665048599,
-0.027008209377527237,
0.04274448752403259,
0.024232903495430946,
-0.006855520885437727,
0.07326067984104156,
-0.02890993468463421,
0.011213933117687702,
0.02460687793791294,
-0.03472592681646347,
-0.025745484977960587,
0.014966601505875587,
-0.016549183055758476,
-0.001650670194067061,
0.0009031599620357156,
0.007677041459828615,
0.022892626002430916,
-0.043982356786727905,
-0.0049101985059678555,
0.042442549020051956,
-0.022305909544229507,
-0.013107862323522568,
0.08406857401132584,
0.024419602006673813,
0.020648539066314697,
0.021216191351413727,
0.00025167432613670826,
-0.0060441442765295506,
0.03404272347688675,
0.008351779542863369,
0.042841386049985886,
0.04688272997736931,
-0.02444051392376423,
0.011467444710433483,
0.0454983152449131,
-0.02369021251797676,
-0.00041770111420191824,
0.008551770821213722,
0.029344623908400536,
-0.03390505537390709,
-0.01780577003955841,
0.016449222341179848,
-0.029239078983664513,
0.006441539619117975,
0.04804130271077156,
-0.016397781670093536,
0.09944309294223785,
-0.00008164182509062812,
0.040898632258176804,
0.0297071635723114,
-0.0057988581247627735,
-0.03067462146282196,
-0.017137542366981506,
0.042439136654138565,
0.03193511441349983,
0.0032819993793964386,
-0.019039727747440338,
-0.038383759558200836,
-0.018079882487654686,
0.037615954875946045,
-0.06316277384757996,
-0.016488678753376007,
-0.02142769657075405,
-0.0313851460814476,
-0.012988394126296043,
0.011123918928205967,
-0.023142704740166664,
0.0071473391726613045,
0.03237709030508995,
0.025475576519966125,
-0.011179765686392784,
0.003681045025587082,
0.0013628307497128844,
0.00396268256008625,
0.030064458027482033,
-0.04611852020025253,
0.02915099635720253,
-0.030197685584425926,
0.012338383123278618,
-0.017335070297122,
-0.014321199618279934
] |
<p>I just want to calculate the derivative of epsilon for the following <a href="http://en.wikipedia.org/wiki/Lennard-Jones_potential" rel="nofollow">Lennard-Jones</a> equation:</p>
<p>LJ = $4\sqrt{\epsilon_{ii} \epsilon_{jj}}$ $[(\sigma/ r)^{12}-(\sigma/r)^{6}]$ with respect to $\epsilon_{ij}$</p>
<p>I am very glad if anyone explains this.</p>
| 8,798 |
[
0.011052234098315239,
-0.02962007373571396,
0.005295909941196442,
-0.006744692102074623,
0.01126187015324831,
0.01386804599314928,
-0.02181347645819187,
0.0025105541571974754,
0.018365420401096344,
-0.06454899907112122,
0.06736556440591812,
0.012040062807500362,
0.06593780964612961,
-0.0059263198636472225,
0.02128603868186474,
-0.009047698229551315,
-0.002043461427092552,
0.022888917475938797,
0.02188061736524105,
-0.013091422617435455,
0.007747693918645382,
-0.0060240658931434155,
0.00466417009010911,
-0.02537231706082821,
-0.03804325684905052,
0.033499825745821,
0.0013963815290480852,
-0.020525895059108734,
0.014440014027059078,
0.039854925125837326,
-0.029007049277424812,
-0.05055302008986473,
0.05984603613615036,
0.009674031287431717,
0.00015430530766025186,
0.030201401561498642,
-0.02168002724647522,
-0.028342727571725845,
-0.04668388143181801,
0.03844767436385155,
-0.06264569610357285,
-0.0009227288537658751,
0.0133334556594491,
0.05657000094652176,
-0.019865889102220535,
0.03611660748720169,
-0.01906779780983925,
-0.024494098499417305,
0.045946091413497925,
-0.03584323823451996,
0.0587037056684494,
0.017054377123713493,
0.037656672298908234,
0.01647172123193741,
-0.013674570247530937,
0.01945914886891842,
0.051910027861595154,
0.0794268473982811,
-0.005124704912304878,
-0.05857718735933304,
-0.01948440633714199,
-0.0060223788022994995,
0.0012759009841829538,
-0.017665274441242218,
-0.012117148377001286,
-0.018616171553730965,
0.005485584028065205,
-0.013999436050653458,
0.028043607249855995,
0.018143117427825928,
0.020455244928598404,
0.06102578714489937,
0.04938613995909691,
-0.017531249672174454,
0.03582786023616791,
-0.012342499569058418,
0.006089999806135893,
0.02878745272755623,
-0.008872690610587597,
-0.004270355682820082,
-0.009230135940015316,
0.008168745785951614,
0.012120276689529419,
0.03497270867228508,
-0.0147361159324646,
-0.013152687810361385,
0.054222386330366135,
-0.018329398706555367,
0.015888359397649765,
0.04077402874827385,
-0.020747248083353043,
0.01555666234344244,
0.04219872131943703,
-0.0236118882894516,
-0.03409803658723831,
0.045320842415094376,
0.0006847064942121506,
0.06164606288075447,
-0.01288251206278801,
-0.05139881744980812,
-0.0010394998826086521,
-0.05928714573383331,
0.006180223077535629,
0.05065338313579559,
0.017486965283751488,
0.00408779876306653,
0.011744953691959381,
0.013500810600817204,
0.010573222301900387,
-0.0337059460580349,
-0.05072467029094696,
0.0063828821294009686,
-0.014388437382876873,
-0.02523256465792656,
0.0039293053559958935,
-0.017999550327658653,
-0.0702340379357338,
-0.015017149038612843,
0.011096004396677017,
0.04637737572193146,
0.043222032487392426,
-0.02984626218676567,
-0.005483551416546106,
-0.025292042642831802,
-0.06735698133707047,
0.05343509837985039,
0.029763424769043922,
-0.024185024201869965,
-0.022702213376760483,
0.015790337696671486,
0.009231784380972385,
0.0029626048635691404,
0.0030540369916707277,
0.035897426307201385,
0.019105101004242897,
-0.02062470279633999,
-0.10564450919628143,
-0.06694993376731873,
0.01973191276192665,
-0.004162164404988289,
-0.016348151490092278,
-0.08729556947946548,
0.014891810715198517,
0.02536911331117153,
0.06798071414232254,
0.001257142168469727,
-0.007556956261396408,
0.0031853134278208017,
0.016434330493211746,
0.008946678601205349,
0.004713525529950857,
-0.03775668516755104,
-0.00854597520083189,
-0.03223366290330887,
0.014762742444872856,
-0.039967186748981476,
-0.011275180615484715,
0.022009115666151047,
-0.028542043641209602,
-0.030362311750650406,
0.06679636240005493,
-0.018475133925676346,
-0.0016757890116423368,
-0.004010513424873352,
0.028911232948303223,
-0.044481754302978516,
0.0950237289071083,
0.0477701872587204,
0.025040583685040474,
-0.01696685515344143,
0.01435611117631197,
0.011164842173457146,
-0.007505970075726509,
0.0534418523311615,
0.06405913829803467,
-0.02144628018140793,
0.00875374861061573,
-0.03684607148170471,
0.03813667967915535,
0.0037733237259089947,
-0.07871291786432266,
-0.024501724168658257,
-0.004294296260923147,
0.01138292532414198,
0.003821016289293766,
0.024583909660577774,
-0.0011207766365259886,
0.019016999751329422,
-0.015224792994558811,
-0.07932932674884796,
0.006629501469433308,
-0.07189676910638809,
0.023861443623900414,
-0.021067678928375244,
-0.049036767333745956,
0.013278338126838207,
-0.004528719931840897,
0.022826965898275375,
0.0030061721336096525,
-0.02277068980038166,
-0.01338252890855074,
0.025506727397441864,
0.01601421646773815,
0.005444136448204517,
0.021376430988311768,
0.038072630763053894,
0.04841833561658859,
0.015054727904498577,
0.05399530753493309,
-0.03385437652468681,
-0.022022707387804985,
0.008990148082375526,
-0.02621738612651825,
0.042713772505521774,
0.00597733911126852,
-0.0034269930329173803,
0.003487907350063324,
0.011077661998569965,
-0.008370529860258102,
0.027949832379817963,
-0.03232541307806969,
0.082609161734581,
0.06332218647003174,
0.03731916472315788,
-0.017901616171002388,
0.03373928368091583,
-0.010322736576199532,
0.04686293005943298,
-0.007805011235177517,
-0.028384754434227943,
-0.029438594356179237,
-0.019053488969802856,
0.03885184973478317,
0.03073536790907383,
-0.06021594628691673,
-0.0194263756275177,
0.048539720475673676,
0.006677802186459303,
0.04992702975869179,
0.023804478347301483,
-0.031745702028274536,
-0.012216643430292606,
0.00033161480678245425,
-0.030328182503581047,
-0.0330238938331604,
0.022309642285108566,
0.04396891966462135,
0.018777277320623398,
0.06929480284452438,
-0.043608687818050385,
-0.045045770704746246,
0.05489756166934967,
-0.00996360182762146,
-0.013304931111633778,
-0.006826572585850954,
-0.024024643003940582,
0.07414450496435165,
-0.023945381864905357,
0.01297423429787159,
0.059402573853731155,
-0.015673702582716942,
0.03886830061674118,
-0.001526938285678625,
-0.021359147503972054,
0.032505325973033905,
-0.019794529303908348,
-0.026909343898296356,
0.00005737206811318174,
0.0004493730084504932,
-0.034839533269405365,
0.01832103542983532,
-0.018515989184379578,
0.054484911262989044,
-0.0019847929943352938,
0.024595024064183235,
-0.005612567532807589,
0.03528183698654175,
-0.0027032485231757164,
0.016185129061341286,
-0.04065502807497978,
0.015975559130311012,
-0.03402017056941986,
0.035275574773550034,
0.0248789694160223,
-0.03513087332248688,
-0.003938861191272736,
0.013218720443546772,
-0.052559994161129,
0.01184549368917942,
0.008689375594258308,
-0.012187573127448559,
0.023412207141518593,
-0.010064243339002132,
-0.017590126022696495,
-0.026762360706925392,
0.017376458272337914,
0.01628749631345272,
-0.021565735340118408,
-0.0005025197751820087,
0.04153910651803017,
-0.016798578202724457,
-0.017653504386544228,
0.03330373764038086,
-0.031736619770526886,
-0.023810941725969315,
-0.03229772672057152,
-0.024899162352085114,
0.02593119814991951,
-0.004072125069797039,
-0.004796987399458885,
0.03258267790079117,
-0.018813813105225563,
-0.025346189737319946,
-0.039464302361011505,
-0.057532526552677155,
0.017855362966656685,
-0.008847870863974094,
0.025661397725343704,
-0.005348636768758297,
-0.05036275088787079,
0.12287432700395584,
-0.007193914148956537,
-0.01590980403125286,
-0.01516447402536869,
-0.01628563180565834,
-0.03073352389037609,
0.005065178498625755,
0.009463639929890633,
0.016306046396493912,
-0.031288549304008484,
0.003563839942216873,
-0.005121817346662283,
0.056211259216070175,
0.05454062670469284,
-0.02515551634132862,
-0.04729721322655678,
0.007465512491762638,
-0.024909399449825287,
-0.012016598135232925,
0.08806735277175903,
-0.016424991190433502,
0.013868982903659344,
0.02781786397099495,
0.011698986403644085,
0.03371511027216911,
0.019820723682641983,
-0.05513627827167511,
0.035305604338645935,
0.012334453873336315,
-0.03217792883515358,
-0.00555904395878315,
0.04815817251801491,
0.006092182360589504,
-0.03573931008577347,
0.0415811762213707,
0.022815795615315437,
0.07097560167312622,
-0.031420882791280746,
-0.015231828205287457,
0.04098494350910187,
0.005007641855627298,
-0.029188940301537514,
-0.03518036752939224,
0.019509591162204742,
-0.00401694281026721,
0.04923705756664276,
0.0021061066072434187,
-0.028709454461932182,
0.03575526550412178,
0.0001320630981354043,
0.03530660271644592,
-0.056489817798137665,
-0.039964042603969574,
-0.004050279501825571,
-0.06407881528139114,
0.008623139932751656,
0.004356699530035257,
0.06219782680273056,
0.015500690788030624,
0.07294599711894989,
-0.006558350753039122,
-0.00840900931507349,
0.04023440182209015,
0.021535223349928856,
-0.062402717769145966,
0.037180110812187195,
-0.01708025299012661,
-0.016309821978211403,
-0.023052290081977844,
-0.004669950343668461,
0.0005013311165384948,
0.0013286455068737268,
0.001791729824617505,
-0.05122409015893936,
-0.01182431261986494,
-0.020488524809479713,
-0.005390360485762358,
-0.05089105665683746,
0.0015237268526107073,
-0.042261216789484024,
0.029325569048523903,
0.0030148890800774097,
-0.02044088765978813,
0.008993271738290787,
0.041403695940971375,
0.0038501392118632793,
-0.004089054651558399,
-0.004502037074416876,
-0.002054912503808737,
0.011381545104086399,
0.02885862998664379,
0.02787671610713005,
0.003252452937886119,
0.03826828673481941,
0.011892742477357388,
-0.00704504270106554,
0.03176846727728844,
0.03615335002541542,
0.024337975308299065,
0.007690682075917721,
-0.049027226865291595,
-0.001452849479392171,
-0.025078928098082542,
0.050158750265836716,
-0.020643487572669983,
0.0435635969042778,
0.03290016949176788,
-0.0057018836960196495,
-0.01812688075006008,
0.012930300086736679,
0.07756493240594864,
0.017527500167489052,
-0.031166303902864456,
-0.050279077142477036,
0.010959723964333534,
-0.015187418088316917,
-0.0027827839367091656,
0.016436615958809853,
0.038423892110586166,
-0.0254677627235651,
-0.025576017796993256,
-0.004352286458015442,
-0.003931255545467138,
-0.016032768413424492,
0.0010602917755022645,
-0.007994860410690308,
0.02810506336390972,
-0.03256871923804283,
-0.008094673976302147,
0.005686790682375431,
0.031235508620738983,
0.04802936315536499,
-0.044571563601493835,
0.02231479622423649,
-0.054081398993730545,
-0.008387383073568344,
0.01877702958881855,
0.028472043573856354,
-0.018757911399006844,
0.011357467621564865,
-0.04746958240866661,
-0.039368901401758194,
0.0657125785946846,
-0.03502611815929413,
0.006928517483174801,
0.00029496714705601335,
-0.020516715943813324,
0.010143487714231014,
0.004310512449592352,
-0.0165861826390028,
0.01087021455168724,
-0.00020374383893795311,
0.018905336037278175,
-0.04950747266411781,
0.015234054066240788,
-0.03138760104775429,
0.007444589864462614,
-0.009707637131214142,
0.060823891311883926,
0.000009367833627038635,
0.001525256084278226,
-0.002593941753730178,
-0.007735645864158869,
-0.030166370794177055,
-0.03173714503645897,
-0.01321853045374155,
-0.002682151971384883,
-0.0039125410839915276,
0.035492073744535446,
-0.04963099583983421,
-0.0264685470610857,
0.03581466153264046,
0.040737785398960114,
-0.022645991295576096,
-0.03739088028669357,
-0.0066997031681239605,
0.022842345759272575,
0.04944058507680893,
0.0011700545437633991,
0.05798431485891342,
0.0840766578912735,
-0.029709044843912125,
-0.001340206596069038,
-0.056110870093107224,
0.04620566964149475,
0.030192412436008453,
-0.02662966214120388,
-0.029137518256902695,
0.012590774334967136,
-0.026692410930991173,
0.001050034537911415,
-0.03579363226890564,
0.04706846922636032,
-0.0016905710799619555,
-0.014307953417301178,
0.0017364753875881433,
-0.009953835979104042,
-0.010767744854092598,
-0.011815767735242844,
0.031029900535941124,
0.024458521977066994,
0.050619084388017654,
-0.02105885185301304,
0.009905565530061722,
-0.0026391136925667524,
-0.005745733622461557,
0.035384926944971085,
-0.042506881058216095,
0.012300713919103146,
0.004945419728755951,
-0.01734013482928276,
0.004998799413442612,
-0.04869656637310982,
0.03519880399107933,
-0.019720008596777916,
-0.017858268693089485,
0.03233962878584862,
-0.05305315554141998,
-0.0028056076262146235,
-0.007302092853933573,
-0.01737901195883751,
0.027033574879169464,
-0.05876621603965759,
0.04203861579298973,
0.022724539041519165,
0.009767375886440277,
-0.09073848277330399,
-0.031055165454745293,
0.015895595774054527,
-0.017294997349381447,
-0.03981870785355568,
-0.04257281869649887,
-0.02594425156712532,
0.02435368113219738,
-0.013543516397476196,
0.002371880691498518,
0.029832614585757256,
-0.005703155416995287,
-0.04340353235602379,
0.03141796216368675,
0.005796288605779409,
0.045122578740119934,
0.01292003970593214,
-0.007829598151147366,
0.01642715558409691,
-0.03336720168590546,
-0.023252107203006744,
0.025172626599669456,
0.08386428654193878,
-0.0526307076215744,
0.007417979184538126,
0.006372513249516487,
-0.024483665823936462,
0.012942509725689888,
-0.043071385473012924,
-0.009951090440154076,
-0.01525646448135376,
0.02033448964357376,
0.026567310094833374,
-0.029098914936184883,
-0.009175724349915981,
-0.017601806670427322,
0.005153350997716188,
-0.009785444475710392,
0.017071213573217392,
-0.02249835804104805,
-0.01805470883846283,
-0.00833401270210743,
0.03316429257392883,
0.028903119266033173,
0.006213937886059284,
0.09690729528665543,
-0.03523053973913193,
-0.020779499784111977,
0.04939563199877739,
0.015409259125590324,
-0.008446071296930313,
0.006854754872620106,
-0.001293049892410636,
0.02421051822602749,
0.0033532772213220596,
-0.0010406830115243793,
-0.037350304424762726,
-0.052577823400497437,
0.02017148956656456,
0.059560377150774,
-0.05815895274281502,
0.03822933882474899,
0.009055111557245255,
0.024106662720441818,
0.004556071013212204,
-0.02278364822268486,
-0.006980827543884516,
0.012578137218952179,
-0.0261961929500103,
0.043530404567718506,
-0.012047961354255676,
0.026797646656632423,
0.004998430609703064,
0.02247106097638607,
-0.04594160243868828,
0.005444013047963381,
0.016059720888733864,
0.04512553662061691,
0.03531081974506378,
-0.0006607747636735439,
-0.02299571968615055,
0.05855870991945267,
-0.014875129796564579,
0.063343346118927,
-0.019486956298351288,
-0.05016135051846504,
0.05721530318260193,
0.012355023063719273,
0.00333214458078146,
-0.02889222279191017,
-0.011210576631128788,
0.03403144329786301,
0.019787177443504333,
0.04669122397899628,
0.005775380879640579,
0.02930346131324768,
0.037669967859983444,
0.03940315917134285,
0.02976074256002903,
0.03396747633814812,
-0.050395604223012924,
-0.05373487249016762,
0.002851297380402684,
-0.029794927686452866,
-0.04902851581573486,
0.03126559779047966,
0.021706270053982735,
-0.04565626010298729,
0.001989939482882619,
0.005325654987245798,
0.04601781815290451,
0.02828431874513626,
-0.008405403234064579,
0.011897164396941662,
0.10377198457717896,
-0.02654844895005226,
0.028933705762028694,
0.009270494803786278,
0.005034697242081165,
0.1003655269742012,
0.05829671770334244,
0.010561750270426273,
-0.055472493171691895,
0.000431278080213815,
-0.008304320275783539,
-0.004819944500923157,
0.0019569946452975273,
0.026135314255952835,
-0.00686760013923049,
-0.006969218607991934,
0.009208274073898792,
0.015695098787546158,
0.015189370140433311,
0.021186405792832375,
0.04348736256361008,
-0.0033415870275348425,
-0.04950783774256706,
0.030519139021635056,
-0.0003380189009476453,
0.006259214598685503,
-0.0170066487044096,
-0.04320516809821129,
0.042816005647182465,
-0.061739444732666016,
0.009912986308336258,
-0.049981191754341125,
-0.05247561261057854,
0.002594050718471408,
0.007392171770334244,
-0.02074289321899414,
0.01614603027701378,
0.01330459676682949,
0.029173554852604866,
-0.0048678661696612835,
0.04534098133444786,
0.04138610139489174,
0.00477299839258194,
0.012414664961397648,
0.045348819345235825,
-0.007021691184490919,
0.024098196998238564,
0.023796597495675087,
0.04175840690732002,
-0.020790070295333862,
-0.019649993628263474,
-0.039820123463869095,
0.02546883560717106,
0.010644103400409222,
-0.01489188801497221,
0.023686014115810394,
0.0092479782178998,
0.021751966327428818,
-0.032344572246074677,
-0.04211616888642311,
0.0020898806396871805,
0.01652977429330349,
-0.04407265782356262,
-0.018587425351142883,
0.004131278954446316,
0.034310922026634216,
-0.014547093771398067,
0.034824807196855545,
-0.03876231983304024,
-0.03503594174981117,
-0.012994580902159214,
-0.02218320220708847,
0.007100961171090603,
-0.01389621663838625,
-0.014374240301549435,
-0.032775770872831345,
-0.011971759609878063,
-0.003882631426677108,
-0.011868109926581383,
-0.009889536537230015,
0.0392083078622818,
0.03242037072777748,
-0.026222068816423416,
-0.012813386507332325,
0.00459280563518405,
-0.06643229722976685,
0.030867403373122215,
-0.031279489398002625,
0.006631659809499979,
-0.034657422453165054,
-0.034342966973781586,
0.054747000336647034,
0.03063167631626129,
-0.029605263844132423,
0.01488751545548439,
0.018304800614714622,
0.024791007861495018,
0.04998268559575081,
-0.049996115267276764,
-0.010739799588918686,
0.026050345972180367,
-0.02230755425989628,
0.058623962104320526,
-0.010361983440816402,
0.04205749183893204,
0.019887663424015045,
0.0076604122295975685,
-0.0005778048653155565,
0.026806510984897614,
-0.07950527966022491,
0.010600783862173557,
0.013048022985458374,
0.017033590003848076,
-0.021031323820352554,
-0.013160591945052147,
-0.006387240253388882,
-0.011370653286576271,
0.016773251816630363,
-0.03453183174133301,
-0.027806691825389862,
0.009190204553306103,
0.00916141364723444,
-0.036091677844524384,
-0.024874189868569374,
-0.0338895358145237,
-0.011158651672303677,
-0.0031855041161179543,
-0.010161464102566242,
-0.018430666998028755,
-0.012501305900514126,
0.00441002519801259,
0.049872905015945435,
-0.05341677740216255,
-0.0034421139862388372,
-0.021755948662757874,
-0.013384798541665077,
0.008344671688973904,
0.02869913913309574,
0.003132882993668318,
-0.010639083571732044,
0.038663286715745926,
-0.0316101536154747,
0.05127400904893875,
-0.01744943857192993,
-0.03709246963262558,
0.031035041436553,
-0.06714718043804169,
-0.05301060900092125,
0.01772332936525345,
-0.003632401814684272,
0.03703151270747185,
0.00772983580827713,
-0.0036603191401809454,
-0.03069506213068962,
0.04894848167896271,
0.014011330902576447,
0.022019142284989357,
-0.002114395145326853,
-0.03468978777527809,
-0.01027402002364397,
-0.040128469467163086,
-0.03335491195321083,
-0.022830279543995857,
0.013741342350840569,
0.014929024502635002,
0.025738971307873726,
-0.055334217846393585,
-0.017390090972185135,
0.008149707689881325,
0.0007173538906499743,
0.009239127859473228,
0.007199724204838276,
0.030141567811369896,
0.028359808027744293,
0.011283328756690025,
-0.014933131635189056,
0.037282053381204605,
0.0008064376306720078,
0.022585764527320862,
-0.07638073712587357,
0.010319272056221962,
-0.04365627095103264,
-0.007003446109592915,
0.0452127568423748,
-0.0741429403424263,
0.023630596697330475,
0.03957144916057587,
-0.03134399652481079,
-0.004343283828347921,
-0.02793198451399803,
-0.017117084935307503,
-0.015465132892131805,
-0.009622517041862011,
0.0171828456223011,
0.02788553200662136,
0.00865079928189516,
0.0194574985653162,
0.035373952239751816,
-0.008813682943582535,
-0.0023837604094296694,
-0.002193002961575985,
0.0060047851875424385,
0.019130703061819077,
0.007710416801273823,
-0.023186830803751945,
0.016002945601940155,
-0.002945102285593748,
-0.07552769035100937,
0.022106174379587173,
-0.03382572904229164,
0.002493093255907297,
-0.004589947871863842,
-0.0029398142360150814,
0.006323247216641903,
0.04298122599720955,
-0.0007582138641737401,
-0.026794221252202988,
-0.00446725869551301,
0.007651177700608969,
0.012888997793197632,
0.03536370024085045,
0.016428980976343155,
-0.007314753718674183,
0.028670020401477814,
-0.0012412290088832378,
-0.06160900741815567,
0.059516292065382004,
-0.011968056671321392,
-0.00027633280842565,
-0.040155284106731415,
-0.006637423764914274,
0.0045980592258274555,
-0.07078356295824051,
0.017236530780792236,
-0.023811625316739082,
0.01515220943838358,
0.03246340528130531,
0.011874456889927387,
-0.022282034158706665,
0.020439404994249344,
-0.04246382787823677,
-0.02932553179562092,
0.016211966052651405,
0.0017508207820355892,
-0.029284970834851265,
-0.06129838153719902,
-0.01455971971154213,
-0.009933583438396454,
-0.022495664656162262,
-0.014654790982604027,
-0.02199077606201172,
-0.0476696640253067,
0.006425734609365463,
0.031698208302259445,
0.028926270082592964,
-0.003564343322068453,
-0.023734064772725105,
0.019142301753163338,
-0.05553733557462692,
0.02703990414738655,
-0.011557461693882942,
-0.038631122559309006,
-0.01596190221607685,
-0.02429235726594925,
-0.003175986697897315,
-0.007549963891506195,
0.055788129568099976,
-0.008526576682925224,
-0.020890802145004272,
-0.015734223648905754,
-0.0028875316493213177,
0.010147767141461372,
-0.04191308841109276,
-0.004532304592430592,
-0.01488837506622076,
0.006397627294063568,
-0.02718854881823063,
-0.003036832669749856,
-0.031075147911906242,
0.027857603505253792,
0.0013342613819986582,
0.05305302143096924,
0.015548809431493282,
-0.0039757173508405685,
-0.04061732441186905,
0.009243622422218323,
-0.037333279848098755,
-0.008325283415615559,
0.08709895610809326,
0.0028959084302186966,
-0.016683267429471016,
0.006750296801328659,
-0.014893212355673313,
-0.01595115475356579,
0.00689498707652092,
-0.016867168247699738,
-0.013387421146035194,
-0.019623413681983948,
-0.050435908138751984,
0.05474553257226944,
-0.04278068244457245,
-0.0033019930124282837,
0.03900629281997681,
-0.023433854803442955,
-0.005281281191855669,
0.04421679675579071,
0.011464442126452923,
0.014148182235658169,
0.02298903465270996,
0.01423050370067358,
0.0034867911599576473,
-0.007568522822111845,
0.005256691947579384,
0.003155124606564641,
0.013087909668684006,
-0.014087358489632607,
0.014815721660852432,
0.04219691455364227,
-0.019457140937447548,
-0.006915193051099777,
0.00027609962853603065,
-0.0033168166410177946,
-0.01684555597603321,
-0.018120519816875458,
0.03368448466062546,
-0.042130663990974426,
0.04551094397902489,
0.0012168296379968524,
-0.022678740322589874,
0.05895441770553589,
-0.016121437773108482,
0.02194465696811676,
-0.013869953341782093,
-0.01387600414454937,
-0.016770079731941223,
-0.02766641229391098,
0.025906888768076897,
-0.002117678290233016,
-0.02396075613796711,
0.0011029993183910847,
-0.026221558451652527,
-0.01687551848590374,
0.02560500241816044,
-0.06009675934910774,
0.010813050903379917,
0.025221502408385277,
-0.006788922939449549,
-0.03195410221815109,
-0.0036917056422680616,
-0.009988267906010151,
-0.02461186982691288,
0.020038383081555367,
0.0350397452712059,
0.018583418801426888,
-0.010559025220572948,
0.012624545022845268,
-0.0041323029436171055,
0.08510176092386246,
-0.04776976257562637,
0.019218215718865395,
-0.02060818299651146,
0.0148339057341218,
-0.03249891847372055,
-0.02641034871339798
] |
<p>Let's say point $P$ is the center of mass of an irregularly shaped object. </p>
<ol>
<li><p>If I make a straight cut trough point $P$ and split the object in two, is it possible for the two pieces to have the same mass? This would be possible if the centers of mass of each piece was the same distance from $P$, but is this possible with an irregularly shaped object of uniform density? </p></li>
<li><p>What about non-uniform density? </p></li>
</ol>
<p>This is just a question I thought about.</p>
| 8,799 |
[
-0.018400974571704865,
0.025689920410513878,
0.006892812438309193,
-0.05586545914411545,
0.040515102446079254,
0.011103889904916286,
-0.030484706163406372,
-0.03471370413899422,
0.01982029899954796,
-0.04078223183751106,
0.01705075055360794,
0.03612940385937691,
0.05587844178080559,
0.04235348850488663,
-0.009640698321163654,
-0.0027293642051517963,
0.013655686751008034,
-0.0016016799490898848,
-0.0027541061863303185,
-0.04553188383579254,
-0.0072578005492687225,
-0.0006526014767587185,
0.024432530626654625,
-0.020170200616121292,
-0.0023795212619006634,
0.040749356150627136,
0.017615245655179024,
-0.013793902471661568,
0.015328840352594852,
0.05243951827287674,
-0.01781248301267624,
-0.062383491545915604,
0.021392110735177994,
0.03653234243392944,
0.0466148667037487,
-0.011622675694525242,
-0.014192648231983185,
0.00392119400203228,
-0.007561819162219763,
0.029315052554011345,
-0.04301086813211441,
0.0015671121655032039,
-0.021072041243314743,
0.03494009003043175,
-0.004945315420627594,
0.018803132697939873,
0.011238684877753258,
-0.05844873562455177,
0.050245270133018494,
-0.04418712109327316,
0.07588313519954681,
0.0037732250057160854,
0.03248079493641853,
0.03352587670087814,
-0.016252800822257996,
0.0027363095432519913,
0.040901802480220795,
0.04404519125819206,
-0.02566773071885109,
-0.026481980457901955,
-0.006916513200849295,
0.005589109379798174,
0.026839356869459152,
-0.020992999896407127,
-0.03752423822879791,
-0.006964682601392269,
-0.024963458999991417,
-0.0009540074970573187,
0.007837587036192417,
-0.00007228645699797198,
-0.007485547568649054,
0.03188902139663696,
0.029031140729784966,
-0.021188296377658844,
0.028078874573111534,
-0.017911812290549278,
0.05130285769701004,
-0.007602950558066368,
0.05337892100214958,
0.00762517424300313,
0.03816710785031319,
0.010612084530293941,
0.03055015578866005,
0.006701957900077105,
0.01964796707034111,
-0.018954116851091385,
0.04948579892516136,
-0.012846413068473339,
0.00842017401009798,
0.047310177236795425,
0.006982365623116493,
-0.023570775985717773,
0.02860853262245655,
-0.015045723877847195,
0.00962991826236248,
0.025961650535464287,
-0.010709112510085106,
0.03221975266933441,
-0.00042721719364635646,
-0.00461680069565773,
0.004309334326535463,
-0.020977789536118507,
0.02511008270084858,
0.08838055282831192,
0.02816801145672798,
-0.028501765802502632,
-0.03761114925146103,
0.020015083253383636,
0.008920199237763882,
0.013467258773744106,
-0.040585365146398544,
0.003704795381054282,
0.018569335341453552,
-0.01911887153983116,
0.06166422367095947,
0.01923774555325508,
0.00955596100538969,
-0.03694693371653557,
0.03183453157544136,
0.031330060213804245,
0.03428567945957184,
-0.040648430585861206,
0.021123412996530533,
-0.0783277079463005,
-0.046326056122779846,
0.01605987176299095,
0.04520338028669357,
-0.004494052845984697,
-0.019199974834918976,
0.02207104302942753,
0.009549048729240894,
0.0054491800256073475,
0.036173850297927856,
-0.0071215396746993065,
0.021615276113152504,
-0.0016875738510861993,
-0.053702592849731445,
-0.0497320182621479,
0.02605810947716236,
0.022272903472185135,
-0.03798399865627289,
-0.04433011636137962,
-0.02035185694694519,
0.03684760257601738,
0.024439247325062752,
0.004010386299341917,
-0.0016228966414928436,
0.003622188698500395,
0.07756250351667404,
-0.009956101886928082,
0.0013097714399918914,
-0.021057743579149246,
-0.004583536647260189,
-0.04886966571211815,
0.011126692406833172,
-0.07718037068843842,
0.0320860780775547,
0.035789817571640015,
-0.007255482487380505,
-0.022309424355626106,
0.03431432694196701,
-0.021246513351798058,
0.008497224189341068,
0.027871398255228996,
-0.006415331270545721,
-0.024106722325086594,
0.056778717786073685,
0.027524448931217194,
-0.017168747261166573,
0.038126129657030106,
0.031124994158744812,
0.017646903172135353,
0.017893923446536064,
0.010692284442484379,
0.04202025383710861,
-0.03499646112322807,
-0.016634738072752953,
-0.00280696339905262,
0.03582420572638512,
0.014982001855969429,
-0.037758976221084595,
0.0009762530098669231,
0.007713080383837223,
-0.0031826996710151434,
0.02113969437777996,
0.061567384749650955,
0.010741102509200573,
-0.02854311652481556,
-0.009892166592180729,
-0.03163883090019226,
-0.009586530737578869,
-0.0331682451069355,
0.033474721014499664,
-0.002816129010170698,
-0.003153442172333598,
0.015861455351114273,
0.042519353330135345,
0.011716064997017384,
-0.05170337110757828,
-0.005186955910176039,
-0.006965561304241419,
0.02150367759168148,
0.010685976594686508,
-0.030515111982822418,
0.00799383781850338,
0.07094762474298477,
0.013840717263519764,
0.003959992900490761,
0.03104010596871376,
-0.024503912776708603,
-0.035031504929065704,
-0.008419608697295189,
-0.016309523954987526,
-0.007881310768425465,
-0.018040845170617104,
0.019030800089240074,
0.03532620519399643,
0.021176446229219437,
-0.006346685811877251,
0.062412116676568985,
-0.015390207059681416,
0.08705348521471024,
0.05393248796463013,
-0.022237736731767654,
0.02738768793642521,
0.01130180899053812,
0.04509270191192627,
0.036279499530792236,
-0.010266647674143314,
-0.04683864489197731,
-0.03610365837812424,
-0.006561970338225365,
0.0012764519779011607,
0.03310668468475342,
-0.04595740884542465,
0.029078762978315353,
0.03425729647278786,
0.034879062324762344,
0.018232805654406548,
-0.010556874796748161,
-0.004640697501599789,
-0.02916877530515194,
0.03720289468765259,
0.00917161162942648,
0.02379223145544529,
-0.009857281111180782,
0.002815314568579197,
0.002033595461398363,
0.01859774813055992,
-0.018863528966903687,
0.01684671826660633,
0.032192762941122055,
-0.011843670159578323,
-0.007262235041707754,
0.018985988572239876,
0.0018005139427259564,
0.018551668152213097,
-0.014809760265052319,
0.014207635074853897,
0.04654001444578171,
-0.003686622716486454,
-0.06570399552583694,
-0.05879149213433266,
-0.0163881853222847,
0.014262337237596512,
0.05775213614106178,
0.010766405612230301,
-0.001702960580587387,
0.021518193185329437,
-0.02341880276799202,
0.009646995924413204,
-0.02583736926317215,
0.004630845505744219,
-0.009264864027500153,
-0.010425154119729996,
0.008091400377452374,
-0.001472588861361146,
0.006164942402392626,
-0.03338316082954407,
0.027339186519384384,
-0.035200294107198715,
-0.02207360789179802,
-0.03222467750310898,
-0.005688105709850788,
-0.07709945738315582,
0.008596961386501789,
-0.025366881862282753,
-0.00391880888491869,
0.010453369468450546,
0.04681014642119408,
0.006389386020600796,
0.0013048907276242971,
-0.017312156036496162,
-0.048809416592121124,
0.014662781730294228,
-0.03071439079940319,
-0.003685713978484273,
-0.040121592581272125,
0.0028735469095408916,
0.02402120642364025,
0.0034645753912627697,
-0.0375170037150383,
0.015037828125059605,
-0.01860874891281128,
-0.024763204157352448,
-0.03487840294837952,
-0.03937314823269844,
0.04816146939992905,
-0.012094678357243538,
0.02690444327890873,
0.026196083053946495,
-0.028704751282930374,
0.04319432005286217,
-0.04272914677858353,
-0.037873342633247375,
0.026406826451420784,
-0.0526069737970829,
0.046451110392808914,
0.02086293138563633,
-0.03775089234113693,
0.08419214189052582,
0.017772821709513664,
-0.04954647272825241,
-0.017900843173265457,
0.021916786208748817,
0.004478893242776394,
0.022323882207274437,
0.0050237346440553665,
0.014249544590711594,
-0.06117212399840355,
0.005525609012693167,
0.04591401293873787,
-0.00029939666274003685,
0.016642263159155846,
0.03264946490526199,
-0.008038043975830078,
0.017602642998099327,
0.03561434522271156,
-0.00025773592642508447,
0.036085065454244614,
0.031293924897909164,
-0.03649340197443962,
0.02625153958797455,
-0.02576258033514023,
0.023821303620934486,
0.019627561792731285,
-0.042599551379680634,
0.04156479611992836,
0.023384939879179,
0.007746815215796232,
-0.02014058828353882,
0.0487147755920887,
0.031381845474243164,
-0.038670822978019714,
-0.012159832753241062,
0.017456838861107826,
0.06707483530044556,
-0.008519480004906654,
-0.03557970002293587,
0.047644153237342834,
0.04545924812555313,
0.0032631719950586557,
-0.04434405639767647,
0.00880376249551773,
0.004028520546853542,
0.024380963295698166,
-0.021107792854309082,
-0.03484584763646126,
0.04464762657880783,
0.03290274739265442,
0.039884019643068314,
0.005725480150431395,
-0.03360731527209282,
-0.0018092261161655188,
-0.08515726029872894,
0.0017456563655287027,
0.0111821498721838,
0.008490579202771187,
-0.02343790978193283,
0.06203221157193184,
0.042736608535051346,
-0.008105259388685226,
-0.0056717353872954845,
0.010075511410832405,
-0.08813467621803284,
0.007270707283169031,
-0.03196325525641441,
-0.0011220838641747832,
-0.013712932355701923,
-0.021326029673218727,
-0.03194337338209152,
-0.03354225680232048,
-0.008928676135838032,
-0.015423029661178589,
0.017881449311971664,
-0.05380029231309891,
-0.0020446728449314833,
-0.04380515217781067,
-0.046245474368333817,
0.008488896302878857,
0.06276852637529373,
0.027278045192360878,
-0.029953017830848694,
0.04568038880825043,
-0.007331983186304569,
-0.024840859696269035,
-0.0026871035806834698,
-0.025812558829784393,
0.008560801856219769,
-0.020367562770843506,
0.03996232897043228,
0.005998987704515457,
0.024203427135944366,
0.007993143051862717,
0.030258625745773315,
0.005070059094578028,
0.0704183429479599,
-0.027770282700657845,
-0.053383905440568924,
-0.05091681331396103,
-0.026961511000990868,
-0.03587779775261879,
-0.013891110196709633,
0.0545484721660614,
-0.03792265057563782,
-0.008233165368437767,
0.014526803977787495,
0.011536515317857265,
-0.020178109407424927,
0.04922933503985405,
0.05606739595532417,
0.04210367798805237,
-0.016603928059339523,
-0.07832467555999756,
-0.015519851818680763,
-0.005508823320269585,
-0.01585373654961586,
0.009132935665547848,
-0.015334263443946838,
-0.007427767850458622,
0.04181499779224396,
0.009742715395987034,
0.04058198258280754,
-0.016970129683613777,
-0.029500043019652367,
-0.01341584138572216,
0.008727919310331345,
-0.05217412859201431,
-0.005744770634919405,
-0.0021661361679434776,
0.009487359784543514,
0.040722522884607315,
0.0024196566082537174,
-0.01612941548228264,
-0.07203707098960876,
-0.012066462077200413,
0.02074653096497059,
0.019899049773812294,
-0.008997606113553047,
0.049817588180303574,
-0.039160825312137604,
-0.03531000390648842,
0.07533461600542068,
-0.026226671412587166,
0.008289201185107231,
-0.045466985553503036,
0.00032753494451753795,
0.02442435920238495,
0.019284427165985107,
-0.0504450798034668,
-0.00004579402593662962,
-0.015244930982589722,
0.019366523250937462,
-0.02172672376036644,
-0.01500664185732603,
0.005430926103144884,
0.021754059940576553,
0.04000987485051155,
0.04221612587571144,
0.02635643444955349,
-0.03414371609687805,
-0.025751611217856407,
0.03802961856126785,
0.004008514806628227,
-0.07188946008682251,
-0.02192000113427639,
0.020301366224884987,
-0.003290690714493394,
-0.0010531202424317598,
-0.018949976190924644,
-0.044961683452129364,
0.029348410665988922,
-0.014985702000558376,
-0.019352443516254425,
0.02534271776676178,
-0.01580911874771118,
0.06264014542102814,
0.053330227732658386,
0.005636726040393114,
0.0609620101749897,
0.016239825636148453,
-0.01266171783208847,
-0.03364846110343933,
-0.057933054864406586,
0.050932761281728745,
-0.02429831214249134,
-0.00003601282514864579,
-0.05049852281808853,
0.02360517345368862,
-0.033070504665374756,
0.00976450927555561,
0.02186405099928379,
0.02195495180785656,
0.002519048284739256,
-0.02811112441122532,
0.026108138263225555,
0.03658471629023552,
0.026315223425626755,
0.024553237482905388,
-0.006172478199005127,
0.03506045043468475,
0.02782566286623478,
-0.011256800033152103,
0.009053352288901806,
0.020001476630568504,
0.03355494886636734,
-0.01843840815126896,
-0.004966236650943756,
0.04600163921713829,
-0.07595552504062653,
-0.00274848029948771,
0.025573983788490295,
-0.038051579147577286,
0.06076783314347267,
0.009107543155550957,
0.045290857553482056,
0.012613722123205662,
-0.04269195348024368,
-0.026201894506812096,
0.00989935640245676,
-0.011719789355993271,
0.032943110913038254,
-0.0718763917684555,
0.050693560391664505,
-0.006736903917044401,
0.020123735070228577,
-0.04276782274246216,
-0.024367714300751686,
0.039034876972436905,
0.015496840700507164,
0.025567151606082916,
-0.028396666049957275,
-0.02065393514931202,
-0.0017001524101942778,
-0.03503316268324852,
-0.023784710094332695,
0.03648490831255913,
-0.028607027605175972,
-0.033117979764938354,
0.04904646798968315,
0.02956787869334221,
0.07458485662937164,
0.020109999924898148,
-0.03343728184700012,
-0.02325526624917984,
0.0032648828346282244,
-0.0052696517668664455,
-0.016149740666151047,
0.05241997167468071,
-0.035325635224580765,
-0.059403128921985626,
-0.0032900262158364058,
-0.03581603243947029,
0.05450788885354996,
-0.03662131726741791,
-0.005149737000465393,
0.030294720083475113,
0.020655905827879906,
-0.01003746222704649,
0.008377421647310257,
0.007317382842302322,
-0.004475854802876711,
0.003446889342740178,
-0.011564638465642929,
0.018536237999796867,
-0.02447415702044964,
-0.05432036146521568,
0.00861935131251812,
-0.026769010350108147,
-0.0020083305425941944,
0.00017444576951675117,
0.038200877606868744,
-0.015492257662117481,
-0.012239781208336353,
0.010160764679312706,
-0.03666115179657936,
0.05033300444483757,
0.007014198694378138,
-0.03906377777457237,
0.012923259288072586,
0.019675295799970627,
-0.029326489195227623,
0.0054902308620512486,
-0.022062743082642555,
-0.012769223190844059,
0.03547985479235649,
0.006027074530720711,
0.043502070009708405,
0.03683500364422798,
0.004028024151921272,
0.00042449653847143054,
-0.025730187073349953,
0.02170662023127079,
-0.013513656333088875,
0.016383377835154533,
0.060620374977588654,
-0.04330384358763695,
-0.03067792020738125,
0.0716245025396347,
0.06996335089206696,
-0.03717218339443207,
0.039544813334941864,
0.004913779441267252,
0.021982142701745033,
0.008390344679355621,
-0.01679157093167305,
-0.024378696456551552,
0.03508877009153366,
-0.02904897928237915,
0.004557579290121794,
-0.06084277853369713,
-0.03134869411587715,
0.01582806371152401,
0.011080135591328144,
0.025889622047543526,
-0.027126869186758995,
-0.01586073637008667,
-0.021187715232372284,
0.04782898351550102,
-0.016791120171546936,
-0.010047770105302334,
-0.0006234610336832702,
-0.010547294281423092,
0.027121076360344887,
-0.007665745913982391,
-0.013445151038467884,
-0.03871582821011543,
-0.042317748069763184,
-0.024624353274703026,
-0.02845148742198944,
-0.057839978486299515,
0.010982852429151535,
-0.02426903136074543,
-0.04762353003025055,
0.07331597059965134,
0.0014131836360320449,
0.03819234296679497,
0.05332082137465477,
0.037558235228061676,
-0.03263932839035988,
0.05119327828288078,
-0.009534657001495361,
0.03512457758188248,
-0.04742460697889328,
-0.007453132886439562,
0.11995016783475876,
0.024874407798051834,
0.04169566556811333,
-0.01879918947815895,
0.006458505522459745,
-0.0028245728462934494,
0.00853645522147417,
-0.001625192235223949,
0.02020329236984253,
-0.01112891174852848,
0.008783225901424885,
0.018037205561995506,
0.04996539279818535,
-0.015934063121676445,
-0.013024283573031425,
0.04904365539550781,
-0.02136540226638317,
-0.020724350586533546,
-0.027143552899360657,
0.020007535815238953,
-0.03612036630511284,
-0.006093897856771946,
-0.021148333325982094,
0.034251194447278976,
-0.027311380952596664,
0.008927073329687119,
-0.04523633420467377,
-0.029505733400583267,
0.005369643680751324,
0.008416080847382545,
-0.012797047384083271,
0.018018381670117378,
0.013243856839835644,
-0.05364663153886795,
-0.030073141679167747,
0.04053635895252228,
0.013803653419017792,
-0.047435954213142395,
-0.012115038000047207,
0.03467882424592972,
0.019176853820681572,
0.008970610797405243,
0.0038313562981784344,
-0.0030552009120583534,
-0.07278542220592499,
0.0005886463331989944,
-0.020228475332260132,
0.0064320433884859085,
-0.025063373148441315,
0.0070597510784864426,
-0.00029367353999987245,
0.0013817817671224475,
0.04043644666671753,
-0.0487203374505043,
-0.014886527322232723,
0.007527116220444441,
-0.008038763888180256,
0.03838459774851799,
0.006835116073489189,
-0.02020874433219433,
0.02159038744866848,
-0.02634173445403576,
-0.009774105623364449,
-0.022938549518585205,
-0.032297778874635696,
-0.02566879242658615,
0.01702924072742462,
0.05514916405081749,
-0.01080233883112669,
-0.013528235256671906,
-0.053539980202913284,
-0.007597577758133411,
-0.02075665257871151,
-0.027166003361344337,
-0.04044507443904877,
0.008344855159521103,
0.029972150921821594,
0.02345285937190056,
-0.01566738449037075,
-0.007573534268885851,
-0.022618765011429787,
0.027688421308994293,
-0.018954185768961906,
-0.01679980382323265,
-0.010855097323656082,
0.00036034287768416107,
0.015762677416205406,
0.050401266664266586,
-0.01865115761756897,
-0.00446447404101491,
-0.005481906700879335,
0.03249499201774597,
-0.004627026151865721,
-0.027986135333776474,
-0.04579136520624161,
0.0022888577077537775,
-0.009438781067728996,
0.030141953378915787,
-0.027861688286066055,
0.008682564832270145,
0.019404569640755653,
0.018900340422987938,
-0.008464392274618149,
0.03229864314198494,
-0.015282428823411465,
0.015476358123123646,
0.0034033425617963076,
-0.026278194040060043,
-0.0036158072762191296,
0.029255041852593422,
0.029855508357286453,
-0.029401328414678574,
-0.024965491145849228,
0.002468480495736003,
-0.03292441368103027,
-0.013843984343111515,
0.011556238867342472,
-0.017789173871278763,
-0.011470011435449123,
-0.043232135474681854,
0.002171706175431609,
-0.028497204184532166,
-0.004880709573626518,
-0.06256481260061264,
-0.02436370588839054,
0.02412388101220131,
-0.0017617734847590327,
-0.01108680572360754,
0.02702387422323227,
0.004653284326195717,
-0.0026101816911250353,
0.016055326908826828,
0.01968315616250038,
-0.00546418409794569,
-0.011961844749748707,
0.06559383869171143,
0.0032095264177769423,
0.049650028347969055,
-0.01689925044775009,
-0.019148098304867744,
0.04342374578118324,
-0.002652514260262251,
-0.0656084194779396,
0.006383417174220085,
-0.05118337273597717,
0.03373156115412712,
0.003018431831151247,
-0.020505161955952644,
-0.004865844268351793,
0.07149910926818848,
-0.007733593229204416,
-0.014311343431472778,
-0.016335641965270042,
-0.032978419214487076,
-0.022736774757504463,
0.006507841404527426,
0.02053980901837349,
-0.0016127164708450437,
-0.04892885312438011,
0.02790645696222782,
-0.00004612510747392662,
-0.01750839315354824,
0.00754380039870739,
0.03504697233438492,
-0.03908463194966316,
0.015613345429301262,
0.017390750348567963,
0.013897128403186798,
0.026246804744005203,
0.043481454253196716,
-0.03002098947763443,
0.005384406540542841,
0.01851952262222767,
-0.0039350916631519794,
-0.1067143902182579,
-0.06126601621508598,
0.01107263658195734,
-0.023099619895219803,
0.018114164471626282,
-0.0117838429287076,
0.004185506142675877,
0.001717028790153563,
-0.06298375874757767,
0.027829961851239204,
-0.03926447778940201,
-0.03475739434361458,
-0.05121966078877449,
-0.017578722909092903,
-0.04420213773846626,
0.04783909395337105,
0.007406569551676512,
0.054988227784633636,
-0.004611880052834749,
0.04095881059765816,
-0.029458114877343178,
-0.010910249315202236,
-0.012565084733068943,
-0.0066893501207232475,
-0.010872923769056797,
-0.028764529153704643,
0.08245829492807388,
-0.025803884491324425,
-0.014254485256969929,
-0.001078948494978249,
-0.053092602640390396,
-0.016087893396615982,
-0.0017152167856693268,
-0.026232801377773285,
-0.01039362233132124,
0.002004683483392,
-0.005609672050923109,
0.0339253768324852,
0.0072417291812598705,
0.009217463433742523,
-0.016826719045639038,
-0.016707831993699074,
-0.0370648056268692,
-0.012709975242614746,
-0.006345468107610941,
-0.03905005380511284,
0.0015872940421104431,
0.006788643077015877,
-0.033329326659440994,
-0.03922351077198982,
0.0016432116972282529,
0.04158638045191765,
0.029701977968215942,
-0.021766098216176033,
0.04124072194099426,
-0.052418965846300125,
0.002566527109593153,
0.03825732320547104,
0.020809318870306015,
-0.013930568471550941,
0.04171419143676758,
0.024558786302804947,
-0.025808060541749,
0.018600350245833397,
0.025987105444073677,
-0.06473349034786224,
-0.06334210187196732,
-0.016335925087332726,
-0.0052294423803687096,
0.02304771915078163,
0.03629834204912186,
-0.04472026601433754,
-0.0057868510484695435,
0.02525923401117325,
-0.008940786123275757,
0.013196952641010284,
0.011273457668721676,
-0.016020236536860466,
-0.03743375837802887,
-0.09605465084314346,
0.02296888642013073,
0.005259898025542498,
-0.01676095277070999,
-0.02681266888976097,
-0.0035172635689377785,
-0.026802197098731995,
0.01169681642204523,
0.060199152678251266,
0.051380470395088196,
0.04248157888650894,
0.05435499921441078,
-0.014744269661605358,
0.017051775008440018,
-0.053073178976774216,
-0.024530531838536263,
0.01800684817135334,
-0.0329761765897274,
0.029850546270608902,
0.014315684325993061,
-0.0007310776854865253,
0.02688707783818245,
0.03128993138670921,
0.005543945822864771,
0.002883925335481763,
-0.0074048275128006935,
-0.004507031757384539,
0.04313407093286514,
-0.00815772544592619,
0.016641484573483467,
0.054928578436374664,
-0.01764020137488842,
0.03409609943628311,
-0.0023256265558302402,
-0.05196167528629303,
-0.042823608964681625,
-0.012599977664649487,
-0.040218621492385864,
-0.032520174980163574,
-0.06781914085149765,
-0.005618693307042122,
0.017622385174036026,
-0.04402294382452965,
-0.00013540871441364288,
0.00893036462366581,
-0.03386320918798447,
-0.029473448172211647,
0.03227510675787926,
0.03604688122868538,
0.06523830443620682,
-0.010610155761241913,
-0.004712715279310942,
0.031194059178233147,
-0.04767804965376854,
0.06285074353218079,
0.009786972776055336,
0.04293042793869972,
0.024230996146798134,
-0.042997974902391434,
0.029869724065065384,
0.008885233663022518,
0.011127087287604809,
0.009219448082149029,
0.0259527750313282,
0.013503016903996468,
-0.05448078736662865,
0.012752057984471321,
-0.009393774904310703,
0.012710701674222946,
0.015827767550945282,
-0.018826015293598175,
0.06689555197954178,
0.06849426031112671,
0.009547462686896324,
-0.026171578094363213,
0.010036407969892025,
0.012404963374137878,
0.008385743014514446,
-0.00032345743966288865,
0.02545478567481041,
0.018471593037247658,
-0.007122464943677187,
-0.025140780955553055,
0.003245196072384715,
0.014341996982693672,
-0.008222395554184914,
0.030162904411554337,
-0.014534602873027325,
0.03506050631403923,
-0.01443410012871027,
-0.024409044533967972,
-0.0002418608928564936,
-0.056702498346567154,
0.036443889141082764,
0.04809834063053131,
0.02710583247244358,
0.011483263224363327,
-0.04143287241458893,
-0.007379924412816763,
0.06812010705471039,
-0.06762095540761948,
-0.06337197124958038,
-0.018365146592259407,
0.030590787529945374,
-0.01010379008948803,
-0.022716781124472618
] |
<p>I'm reading through Seiberg and Witten's paper "<a href="http://arxiv.org/abs/hep--th/9908142">String Theory and Noncommutative Geometry</a>," and one part in $\S$2.1 isn't quite clear to me. (Sorry, in advance, for the length.)</p>
<p>My question is about equation (2.7) on page 9, where they say:</p>
<blockquote>
<p>The coefficient $\theta^{ij}$ in the propagator also has a simple intuitive interpretation, suggested in <a href="http://arxiv.org/abs/hep-th/9903205">[15]</a>. In conformal field theory, one can compute commutators of operators from the short distance behavior of operator products by interpreting time ordering as operator
ordering. Interpreting $\tau$ as time, we see that</p>
<p>$$ [x^i(\tau),x^j(\tau)]=T(x^i(\tau)x^j(\tau^-)-x^i(\tau)x^j(\tau^+))=i\theta^{ij}. \tag{2.7} $$</p>
</blockquote>
<p>${}$</p>
<p><strong>Question: How did they get the first equality?</strong></p>
<p>I'm sure that there is probably some really simple argument I'm not seeing, but, as this equation is the crucial step in which noncommutativity of coordinates appears, I figure I should probably understand it. Any help?</p>
<hr>
<p>The context is: consider a flat space (with metric $g_{ij}$) in the presence of a constant NS $B$-field with $Dp$-branes. Further, for simplicity, they assume that $B_{0i}=0$, $B_{ij}\neq 0$ for $i,j=1,\cdots,r$, and $g_{ij}=0$ for $i=1,\cdots,r$ and $j\neq 1,\cdots,r$, where $r$ is the rank of the matrix $B_{ij}$. Then one can obtain the action</p>
<p>$$ S=\frac{1}{4\pi\alpha'}\int_{\Sigma}\big(g_{ij}\partial_ax^i\partial^ax^j-2\pi i\alpha'B_{ij}\epsilon^{ab}\partial_ax^i\partial_bx^j\big) $$</p>
<p>(with $\Sigma$: the string worldsheet), which leads to the boundary conditions (along the $Dp$-branes): $g_{ij}\partial_nx^j+2\pi i\alpha'B_{ij}\partial_tx^j\big|_{\partial\Sigma}=0$ (where $n$ is the normal to $\partial\Sigma$).</p>
<p>Taking $\Sigma$ to be a disc, these become:</p>
<p>$$ g_{ij}(\partial-\bar{\partial})x^j+2\pi\alpha' B_{ij}(\partial+\bar{\partial})x^j\big|_{z=\bar{z}}=0. $$</p>
<p>Then, it was shown elsewhere that the propagator can be written:</p>
<p>$$ \langle x^i(z)x^j(z') \rangle = -\alpha'\bigg[g^{ij}\log|z-z'|-g^{ij}\log|z-\bar{z}'|+G^{ij}\log|z-\bar{z}'|^2 $$
$$ \hspace{3.4in}+\frac{1}{2\pi\alpha'}\theta^{ij}\log\frac{z-\bar{z}'}{\bar{z}-z'}+D^{ij}\bigg], $$</p>
<p>where $G_{ij}$ is the open string metric given by</p>
<p>$$ G_{ij}=g_{ij}-(2\pi\alpha')^2(Bg^{-1}B)_{ij} $$</p>
<p>so that</p>
<p>$$ G^{ij}= \bigg( \frac{1}{g+2\pi\alpha'B}g\frac{1}{g-2\pi\alpha'B} \bigg)^{ij}, $$</p>
<p>the constants $D^{ij}$ depend only on $B$ and "play no essential role and can be set to a convenient value," and</p>
<p>$$ \theta^{ij}=-(2\pi\alpha')^2\bigg( \frac{1}{g+2\pi\alpha'B}B\frac{1}{g-2\pi\alpha'B} \bigg)^{ij}. $$</p>
<p>Finally, they focus on open string vertex operators, restrict to real $z$ and $z'$ (which they then denote by $\tau$ and $\tau'$), and make a convenient choice of $D^{ij}$ so that the above propagator reduces to</p>
<p>$$ \langle x^i(\tau)x^j(\tau')\rangle = -\alpha'G^{ij}\log(\tau-\tau')^2+\frac{i}{2}\theta^{ij}\epsilon(\tau-\tau'). $$</p>
<p>Then the above claim about the commutator is made.</p>
| 8,800 |
[
0.0023581860587000847,
-0.04114599898457527,
0.012499880976974964,
-0.07959836721420288,
0.03635897859930992,
0.0004974242765456438,
-0.041298117488622665,
0.02687213383615017,
-0.005506929941475391,
-0.05231095105409622,
0.03654199838638306,
0.01584715023636818,
0.07278569042682648,
0.03779017925262451,
0.016901297494769096,
-0.0017660013400018215,
-0.02500087395310402,
-0.01000241283327341,
-0.023656124249100685,
-0.0034525624942034483,
0.06320776045322418,
0.037861935794353485,
-0.025656841695308685,
-0.01576818712055683,
0.032275088131427765,
-0.022558819502592087,
-0.027852674946188927,
0.01921931840479374,
-0.03639691323041916,
0.06737697124481201,
0.0117198396474123,
-0.024563826620578766,
0.00361427734605968,
-0.01178010180592537,
0.015061975456774235,
0.010646967217326164,
0.00912249181419611,
-0.04219380393624306,
0.03309221193194389,
0.002927197143435478,
-0.016139186918735504,
-0.02935280092060566,
-0.024522190913558006,
0.02993497997522354,
0.003456127131357789,
0.03966600075364113,
-0.03327382355928421,
0.003054384607821703,
0.0558488704264164,
-0.040176961570978165,
0.06928090006113052,
0.0006980883190408349,
-0.00028542702784761786,
0.0016555397305637598,
-0.05172688513994217,
0.004452453460544348,
0.06353814899921417,
0.05014520883560181,
0.004398487973958254,
-0.07302077859640121,
-0.03486424311995506,
-0.037096042186021805,
-0.01709684170782566,
-0.0018951353849843144,
0.015240277163684368,
-0.013254348188638687,
0.01023697666823864,
0.014947324059903622,
0.044103801250457764,
-0.03990891948342323,
0.011796032078564167,
-0.0076735857874155045,
0.0671873465180397,
-0.05166777968406677,
0.015413295477628708,
-0.026465047150850296,
0.00840301625430584,
0.02317073568701744,
0.039247218519449234,
0.04124448075890541,
-0.04406752437353134,
0.01764412224292755,
0.01641191728413105,
0.019220029935240746,
-0.008024278096854687,
0.028322773054242134,
0.06381899118423462,
-0.02735096588730812,
0.011835047043859959,
0.06182410940527916,
-0.003322489093989134,
0.028810052201151848,
0.03145447000861168,
-0.03990638628602028,
0.024263624101877213,
0.028841793537139893,
0.0018921896116808057,
0.05127844586968422,
0.017244435846805573,
-0.021044926717877388,
-0.030218403786420822,
-0.04844401031732559,
-0.0022480953484773636,
0.0445278026163578,
0.020168716087937355,
0.030008114874362946,
-0.05544952303171158,
0.019064003601670265,
-0.05009402334690094,
-0.051679424941539764,
-0.05228757485747337,
-0.00437350757420063,
-0.017970090731978416,
0.026215868070721626,
-0.026640785858035088,
-0.03297152370214462,
0.010956703685224056,
0.035016030073165894,
0.06214673072099686,
0.05968109518289566,
0.03503379970788956,
0.006689218804240227,
0.003230425762012601,
-0.051470931619405746,
-0.02209383063018322,
-0.0204760879278183,
0.021223682910203934,
-0.023404238745570183,
-0.061819370836019516,
-0.023128289729356766,
0.02832040563225746,
-0.014839299023151398,
0.030560189858078957,
0.01822621561586857,
0.04392632842063904,
-0.0002888777235057205,
-0.06451763212680817,
-0.04487680271267891,
0.033639341592788696,
-0.004674156196415424,
-0.012507835403084755,
-0.06137806177139282,
-0.005886532831937075,
0.024172723293304443,
0.0903659462928772,
-0.010436401702463627,
0.021200384944677353,
0.015369145199656487,
0.024927711114287376,
0.014598608948290348,
-0.022444361820816994,
-0.0491115003824234,
0.002449300605803728,
-0.03304833546280861,
-0.007568483706563711,
-0.024607563391327858,
0.0347219780087471,
0.04953308030962944,
-0.00703738396987319,
-0.0008289873949252069,
0.09477991610765457,
-0.02350018173456192,
-0.004046091344207525,
0.023915475234389305,
-0.01930246129631996,
-0.013411280699074268,
0.062496285885572433,
0.010873454622924328,
0.015062692575156689,
0.00822766125202179,
0.02550593949854374,
-0.005981084890663624,
-0.0031779049895703793,
0.04001486301422119,
0.009282772429287434,
-0.04802138730883598,
-0.013163282535970211,
-0.0164148211479187,
-0.03196759521961212,
-0.0013595070922747254,
-0.023913588374853134,
-0.03539447486400604,
-0.03190465644001961,
0.026193493977189064,
0.0039949980564415455,
-0.0016092106234282255,
-0.005778440739959478,
0.006640661042183638,
0.02184128202497959,
-0.03855717554688454,
0.019682742655277252,
-0.08586104214191437,
0.021825242787599564,
0.03624362871050835,
-0.02970590442419052,
0.06308568269014359,
-0.007312846835702658,
0.003963646944612265,
-0.0016940346686169505,
-0.03910792991518974,
-0.004238931927829981,
0.023774027824401855,
0.038341205567121506,
0.020257052034139633,
0.006899554748088121,
0.03494089096784592,
0.04224822670221329,
0.009371213614940643,
0.05246252566576004,
-0.020831352099776268,
-0.02697012387216091,
0.02889137528836727,
-0.02054540626704693,
0.038205333054065704,
-0.039026618003845215,
0.019712703302502632,
0.007394801825284958,
-0.021612070500850677,
-0.03453304246068001,
0.04873167350888252,
-0.05005607008934021,
0.024016819894313812,
0.038056209683418274,
-0.013132669031620026,
-0.00823068805038929,
0.07031191140413284,
0.02056955359876156,
0.03179219737648964,
0.026363130658864975,
-0.06842775642871857,
-0.04274656996130943,
-0.021992193534970284,
0.028724459931254387,
0.06053991988301277,
-0.019055649638175964,
0.023110652342438698,
0.015224561095237732,
0.03455689921975136,
0.013603698462247849,
0.020048554986715317,
-0.010746723040938377,
-0.019289718940854073,
0.0077696326188743114,
-0.012898690067231655,
-0.015811679884791374,
0.013110498897731304,
0.01039434690028429,
-0.04301448538899422,
0.03448982536792755,
-0.0091267554089427,
-0.030985619872808456,
0.014957500621676445,
0.006611316464841366,
-0.018524454906582832,
0.013883990235626698,
0.004864088725298643,
0.07016091793775558,
-0.011273919604718685,
0.003971582744270563,
0.02481517754495144,
0.003438002662733197,
0.02002561092376709,
-0.020345257595181465,
-0.017154108732938766,
0.008158785291016102,
-0.019757455214858055,
-0.018873700872063637,
-0.010665351524949074,
-0.00274466210976243,
-0.022188611328601837,
-0.0037322945427149534,
-0.013891784474253654,
-0.007855268195271492,
0.01984241046011448,
-0.0010586399585008621,
0.027743030339479446,
0.02255244553089142,
0.023067371919751167,
-0.009489919990301132,
-0.02756393328309059,
0.02577286586165428,
-0.022246254608035088,
0.03633464500308037,
0.011858506128191948,
-0.03613177686929703,
0.002048908732831478,
-0.08908282220363617,
-0.018946971744298935,
0.049799297004938126,
0.017621280625462532,
0.023981118574738503,
0.031740400940179825,
-0.02025073580443859,
-0.024229131639003754,
-0.0612245611846447,
0.0020027244463562965,
0.027212858200073242,
-0.04753193259239197,
0.009470422752201557,
0.04109002277255058,
0.003889039158821106,
-0.034177228808403015,
-0.01604299061000347,
-0.019700638949871063,
-0.05045102909207344,
0.013906022533774376,
-0.00609439006075263,
0.00797564908862114,
-0.06047849357128143,
0.029606560245156288,
0.019152436405420303,
-0.01762666180729866,
-0.012747838161885738,
-0.05141366645693779,
-0.04781227186322212,
0.009498133324086666,
-0.010388826951384544,
0.021718909963965416,
-0.010030089877545834,
-0.05478530004620552,
0.10536013543605804,
0.0225966963917017,
0.023198140785098076,
-0.033649057149887085,
-0.010076758451759815,
-0.007748590316623449,
-0.038041044026613235,
-0.00046320486580953,
0.017909005284309387,
-0.011918568052351475,
-0.009789565578103065,
0.018282897770404816,
0.04986880347132683,
0.07422138005495071,
-0.0030164069030433893,
-0.01251103077083826,
-0.0045015765354037285,
0.005491605028510094,
0.019471116364002228,
0.03363215550780296,
-0.02053731121122837,
0.012190206907689571,
0.008521020412445068,
-0.009868627414107323,
0.00862169824540615,
-0.007836350239813328,
-0.07601696252822876,
0.028383752331137657,
0.029978882521390915,
-0.006420186720788479,
-0.00032840666244737804,
0.029678555205464363,
-0.01690749265253544,
-0.05864224582910538,
-0.010847916826605797,
0.00015171240374911577,
0.03952647000551224,
-0.01928999461233616,
0.011354578658938408,
0.021295325830578804,
0.031785592436790466,
-0.03686937317252159,
-0.0035377449821680784,
-0.02623753622174263,
-0.006053318735212088,
0.022347258403897285,
-0.03665696457028389,
-0.026277827098965645,
0.030358590185642242,
0.028204796835780144,
-0.010807502083480358,
-0.026644950732588768,
-0.029984649270772934,
-0.01819700188934803,
-0.029113562777638435,
0.008352885022759438,
0.009633194655179977,
0.023530354723334312,
0.009824437089264393,
0.0377364419400692,
-0.005226133856922388,
0.009245001710951328,
0.032092414796352386,
-0.006818709895014763,
-0.05878160521388054,
-0.017223117873072624,
-0.030263902619481087,
0.02431451342999935,
0.03076857514679432,
-0.03213087469339371,
-0.007703782524913549,
0.01135870162397623,
-0.01794818416237831,
-0.03769517317414284,
0.028555473312735558,
-0.056239720433950424,
0.05787433311343193,
-0.06265391409397125,
-0.06486475467681885,
-0.015553032979369164,
0.025885233655571938,
0.059142280369997025,
-0.02278411202132702,
0.03206581994891167,
0.02919524908065796,
-0.03770415857434273,
0.005376538261771202,
-0.00048785863327793777,
0.01653425581753254,
0.005524687934666872,
-0.011669505387544632,
0.013096221722662449,
0.015425235033035278,
-0.016445934772491455,
-0.00717949727550149,
0.007106923498213291,
0.06637845933437347,
0.024115653708577156,
-0.0471457801759243,
0.0038503368850797415,
-0.05125471577048302,
0.005804599728435278,
0.004708550870418549,
0.07534046471118927,
-0.01049734279513359,
0.004214768763631582,
0.05281508341431618,
0.037547409534454346,
0.03297848999500275,
0.017754532396793365,
0.061926744878292084,
0.022396115586161613,
-0.03809235617518425,
-0.021703362464904785,
-0.0036305554676800966,
0.007816966623067856,
0.015110181644558907,
-0.03857641667127609,
-0.014131560921669006,
-0.011505872011184692,
-0.01189013198018074,
0.009870433248579502,
0.01778075285255909,
-0.0416061095893383,
-0.016441918909549713,
0.015720529481768608,
-0.03394485265016556,
-0.003267883788794279,
-0.02641303278505802,
0.011697026900947094,
0.05370142310857773,
0.034612104296684265,
0.02046150341629982,
0.05784594640135765,
-0.036127302795648575,
-0.04817451164126396,
0.004296650178730488,
0.021404068917036057,
0.008294462226331234,
-0.04033226892352104,
-0.06429214030504227,
-0.010710678994655609,
0.03834832087159157,
-0.00534425675868988,
0.05807255581021309,
0.00933898240327835,
-0.0092018349096179,
-0.04616996645927429,
-0.009415744803845882,
-0.030323544517159462,
0.05690658092498779,
0.004759634379297495,
0.02160193771123886,
-0.02424437925219536,
0.0007551807211712003,
-0.012705143541097641,
0.02466275729238987,
0.02144581638276577,
-0.011546948924660683,
0.03683330491185188,
0.04734737426042557,
0.024492723867297173,
0.03510298952460289,
-0.02262725494801998,
-0.03623432293534279,
0.038942284882068634,
0.023325731977820396,
-0.034268561750650406,
0.012642241083085537,
-0.023971756920218468,
-0.01707865297794342,
0.030850689858198166,
-0.002451731124892831,
-0.012837270274758339,
0.05237865075469017,
-0.05223369225859642,
0.08710452169179916,
0.021640243008732796,
-0.005529416725039482,
0.03795964643359184,
0.004003188572824001,
0.0011217353167012334,
0.02323797345161438,
-0.05789517983794212,
0.0475662462413311,
0.019402090460062027,
0.00034358762786723673,
-0.048695243895053864,
-0.03664230555295944,
-0.04913761839270592,
0.013861212879419327,
-0.020679010078310966,
-0.006581463385373354,
0.012536648660898209,
-0.03583506867289543,
-0.005201990716159344,
0.012252375483512878,
-0.04187646135687828,
0.0019230025354772806,
0.026727477088570595,
0.029898175969719887,
0.02200666256248951,
0.0063333092257380486,
0.030925195664167404,
-0.03435532748699188,
0.008387547917664051,
0.048814624547958374,
0.005038275383412838,
-0.006674147676676512,
-0.014685651287436485,
0.02769511751830578,
0.001194948679767549,
-0.011303090490400791,
0.02194071188569069,
0.00910001341253519,
-0.014975860714912415,
0.0008108814363367856,
0.0031791171059012413,
-0.02396906353533268,
-0.02681039646267891,
-0.01404251903295517,
-0.0028257856611162424,
-0.015725519508123398,
-0.025941798463463783,
0.062254536896944046,
-0.021412182599306107,
-0.06922304630279541,
-0.05014917999505997,
0.006251944229006767,
-0.003073644358664751,
-0.03230779245495796,
-0.03229336068034172,
0.01654321514070034,
-0.024028772488236427,
-0.03151888772845268,
0.002260375302284956,
0.036702223122119904,
-0.030165420845150948,
0.012787497602403164,
0.0019434081623330712,
0.04884227737784386,
0.0083476472645998,
0.011924385093152523,
-0.03943350166082382,
0.01260116882622242,
-0.003586080390959978,
0.009204456582665443,
0.02438385598361492,
0.05095003917813301,
-0.03758900985121727,
-0.01598411612212658,
-0.014836237765848637,
0.010705058462917805,
-0.007477634586393833,
0.030859775841236115,
-0.038818903267383575,
0.028241688385605812,
0.00973578728735447,
0.009101681411266327,
-0.041227471083402634,
0.0021904846653342247,
0.018980680033564568,
0.008322695270180702,
-0.03701648488640785,
-0.01681116223335266,
-0.028175674378871918,
-0.024119673296809196,
0.03685564547777176,
-0.04442194476723671,
-0.021111885085701942,
-0.022340714931488037,
0.06725702434778214,
0.015193537808954716,
-0.0016979185165837407,
0.042679257690906525,
0.012270023114979267,
0.0066787865944206715,
-0.007289174012839794,
-0.009999079629778862,
0.029878199100494385,
-0.03108915127813816,
-0.033940739929676056,
-0.0074746981263160706,
-0.036439135670661926,
0.04492457956075668,
0.05790424346923828,
0.008416841737926006,
0.04126226529479027,
0.023515472188591957,
-0.004437877330929041,
0.005164665635675192,
-0.022696584463119507,
-0.03718320652842522,
-0.012632460333406925,
-0.001392095466144383,
0.010893073864281178,
-0.045385390520095825,
-0.014911247417330742,
0.052161477506160736,
0.0431722067296505,
-0.06856279820203781,
-0.0016256483504548669,
0.0256798155605793,
-0.021275794133543968,
0.007050564046949148,
-0.00499588530510664,
-0.04651878401637077,
0.03395787626504898,
-0.010063059628009796,
0.02822878025472164,
-0.00301478523761034,
-0.011387578211724758,
-0.0005425013951025903,
0.035560719668865204,
0.011007110588252544,
-0.007748199626803398,
-0.01022364106029272,
-0.04525761678814888,
-0.001131177879869938,
0.02736814320087433,
0.001750377705320716,
0.027971867471933365,
-0.01327733974903822,
0.04306838661432266,
-0.005856991279870272,
0.012759876437485218,
-0.022694461047649384,
-0.018293922767043114,
0.032327089458703995,
-0.04317205399274826,
-0.03755275160074234,
0.057548634707927704,
-0.0012752171605825424,
-0.016117103397846222,
-0.010258134454488754,
-0.04447806626558304,
0.030264753848314285,
-0.010414802469313145,
0.04301237687468529,
-0.007988388650119305,
0.0760827362537384,
-0.022943640127778053,
0.01772044040262699,
0.020784534513950348,
0.002134674694389105,
0.11575289070606232,
0.024341007694602013,
0.006737757474184036,
-0.05268723890185356,
0.01137489452958107,
0.028075076639652252,
0.02448953501880169,
-0.020219000056385994,
0.03151356056332588,
0.024396667256951332,
-0.04613065347075462,
0.04552130401134491,
0.020194293931126595,
0.006669749040156603,
-0.02187032252550125,
0.02986116148531437,
-0.07973800599575043,
-0.05433427542448044,
0.025484533980488777,
0.004056131932884455,
-0.005165846552699804,
-0.022645559161901474,
-0.05074324458837509,
0.0006447439664043486,
-0.020253511145710945,
0.03620026260614395,
-0.025623448193073273,
-0.02765684947371483,
0.009019562043249607,
-0.014508530497550964,
-0.023275086656212807,
0.019931610673666,
-0.0026455658953636885,
-0.0052348533645272255,
-0.016609707847237587,
0.028106631711125374,
0.011978221125900745,
0.0365208238363266,
0.03584444895386696,
0.033052291721105576,
-0.006317521911114454,
0.013970552012324333,
0.0077226352877914906,
0.030301785096526146,
-0.039919864386320114,
-0.0015841576969251037,
-0.010555152781307697,
0.049701958894729614,
-0.008193324320018291,
-0.006990032270550728,
0.0035849600099027157,
-0.018341800197958946,
-0.000809871475212276,
-0.03711557015776634,
0.001019241870380938,
0.02772495336830616,
0.028132721781730652,
-0.038377631455659866,
0.01372718345373869,
-0.0002168826322304085,
0.020112140104174614,
0.018076250329613686,
0.02518818899989128,
-0.018954908475279808,
-0.054397162050008774,
-0.005678425543010235,
-0.03347008302807808,
0.031801819801330566,
0.012516220100224018,
0.0017618678975850344,
0.004871427081525326,
0.010188625194132328,
-0.04892313852906227,
-0.04489566385746002,
-0.013190564699470997,
0.027394350618124008,
0.03619539365172386,
0.034791313111782074,
-0.020892739295959473,
-0.00011186643678229302,
-0.021013185381889343,
0.008472966961562634,
-0.00034534154110588133,
-0.018950210884213448,
-0.027903230860829353,
0.014635044150054455,
0.0006805703160353005,
0.04084915295243263,
-0.010369637981057167,
0.004955494776368141,
0.003992324694991112,
0.03842540830373764,
0.041140105575323105,
-0.002367323497310281,
-0.031396135687828064,
0.02486236020922661,
-0.014245619997382164,
-0.022949907928705215,
0.001335846958681941,
-0.008869199082255363,
0.031095977872610092,
0.02263822592794895,
-0.024251678958535194,
0.03475490212440491,
-0.026173284277319908,
-0.050319112837314606,
-0.00018373780767433345,
-0.03046196885406971,
0.0074793510138988495,
0.03471476584672928,
0.004050185903906822,
-0.011633581481873989,
-0.028375599533319473,
-0.004107350949198008,
0.03523976355791092,
0.03436630964279175,
-0.01531910803169012,
-0.07626804709434509,
-0.024912450462579727,
0.0059188054874539375,
0.024472137913107872,
-0.03133746236562729,
-0.00022670849284622818,
-0.04536382853984833,
0.06535996496677399,
-0.011728432960808277,
0.033396460115909576,
-0.011241687461733818,
0.038011129945516586,
-0.030941979959607124,
-0.03943841531872749,
0.026975754648447037,
0.01295230071991682,
-0.014099343679845333,
-0.006382955238223076,
0.0056320177391171455,
-0.03150349110364914,
0.0505838468670845,
0.04278917983174324,
-0.06887893378734589,
-0.033378344029188156,
-0.009765541180968285,
-0.03804541751742363,
0.07206223160028458,
-0.02436871826648712,
0.008310874924063683,
0.026584822684526443,
-0.024853935465216637,
-0.03972344473004341,
0.04356895387172699,
-0.03225286677479744,
-0.008868832141160965,
-0.001976838568225503,
-0.03577183559536934,
-0.0028542769141495228,
-0.004729477688670158,
0.044257860630750656,
-0.0036196797154843807,
-0.005713558755815029,
-0.007633592467755079,
0.0025099327322095633,
-0.026040082797408104,
-0.03822227567434311,
-0.013623987324535847,
-0.004160409327596426,
0.012561032548546791,
0.002110891742631793,
-0.00945784617215395,
-0.008898480795323849,
0.05297668278217316,
-0.02039327844977379,
0.03776808828115463,
0.00931685883551836,
0.02765030786395073,
-0.07671177387237549,
-0.004581877496093512,
0.030039172619581223,
0.055376145988702774,
0.04801158234477043,
-0.02434396743774414,
-0.022798409685492516,
0.02570316009223461,
-0.036299899220466614,
0.030634693801403046,
0.010386832058429718,
0.003045883262529969,
-0.028365708887577057,
0.025078272446990013,
-0.06388501077890396,
0.01714598946273327,
0.06201627478003502,
0.039262935519218445,
-0.028068289160728455,
0.016587741672992706,
-0.025383522734045982,
-0.07637087255716324,
-0.015952518209815025,
-0.0010602123802527785,
0.04292088374495506,
-0.019861359149217606,
0.07542499154806137,
-0.007960738614201546,
-0.029652247205376625,
0.04845148324966431,
-0.006583710201084614,
-0.033309049904346466,
-0.027994470670819283,
0.02780815400183201,
0.05627642571926117,
0.03421330079436302,
0.022357532754540443,
-0.028297383338212967,
-0.013797272928059101,
-0.03856765851378441,
0.010955985635519028,
0.01990494318306446,
0.005891825538128614,
0.008359512314200401,
0.012488088570535183,
-0.01745525561273098,
-0.008547167293727398,
0.006097508128732443,
-0.028768476098775864,
-0.04546823725104332,
-0.0031367193441838026,
-0.0072474307380616665,
0.017235595732927322,
0.02521968074142933,
0.01957554928958416,
-0.014652132987976074,
-0.01991969347000122,
0.012959176674485207,
0.008487177081406116,
-0.06542231887578964,
0.01709013618528843,
-0.026902971789240837,
-0.024519246071577072,
0.004220076836645603,
0.027735363692045212,
-0.02763856016099453,
-0.004684689920395613,
-0.039034489542245865,
-0.003055831417441368,
0.033532340079545975,
-0.016213182359933853,
-0.010571924969553947,
-0.039255574345588684,
0.010217038914561272,
0.0130357900634408,
0.042757418006658554,
-0.05592384561896324,
-0.005084540229290724,
0.003070525825023651,
-0.07834476232528687,
0.030942481011152267,
0.01145890261977911,
-0.017068175598978996,
-0.03000275045633316,
-0.026706678792834282,
-0.012990305200219154,
0.039607416838407516,
0.023239895701408386,
0.01020801905542612,
-0.036926962435245514,
0.028965523466467857,
-0.005208316259086132,
0.008486918173730373,
-0.02283058501780033,
0.0023183864541351795,
0.022882094606757164,
0.007085684221237898,
0.008098253980278969,
0.012279536575078964,
-0.03629933297634125,
0.03988489508628845,
0.01846412941813469,
-0.03453216329216957,
0.002174421213567257,
-0.018877539783716202,
-0.027844559401273727,
0.052007220685482025,
0.0011763280490413308,
-0.0020302485208958387,
0.04431934654712677,
0.0238435510545969,
0.025956492871046066,
0.03374641016125679,
-0.0010322767775505781,
-0.0510752908885479,
0.008735324256122112,
-0.02143150381743908,
-0.034245941787958145,
0.01689077727496624,
-0.0072546969167888165,
0.018600789830088615,
-0.018892094492912292,
0.0006712736212648451,
0.05958175286650658,
-0.001191636547446251,
-0.025087222456932068,
0.04899899289011955,
0.027193361893296242,
0.003104361006990075,
0.07207226753234863,
0.03420957922935486,
0.039278365671634674,
0.004569160286337137,
0.05191606655716896,
0.022080006077885628,
0.008711100555956364,
0.0034664375707507133,
-0.018156735226511955,
-0.04974132031202316,
-0.011015400290489197,
0.021168863400816917,
-0.01637493073940277,
0.03792070969939232,
-0.02045227773487568,
-0.019806651398539543,
0.027786972001194954,
0.0033603201154619455,
0.008243762888014317,
0.044874321669340134,
-0.0390949547290802,
0.09673051536083221,
-0.005302787758409977,
0.018067361786961555,
-0.05604610964655876,
0.010166839696466923,
-0.0006090224487707019,
-0.029669294133782387,
0.03345357999205589,
0.03652190417051315,
-0.054456546902656555,
-0.00015893924864940345,
-0.0076558589935302734,
-0.08445762097835541,
0.007640200667083263,
-0.051714103668928146,
-0.03117777407169342,
0.07985509186983109,
-0.017667245119810104,
0.029025748372077942,
-0.06670650094747543,
-0.04158925265073776,
-0.022504495456814766,
0.013740507885813713,
0.0026316854637116194,
-0.011887366883456707,
-0.024013083428144455,
0.0020599181298166513,
0.007005343679338694,
0.041516147553920746,
-0.03876576945185661,
0.006804435979574919,
-0.01196589320898056,
0.023940885439515114,
-0.005889132618904114,
-0.021457968279719353
] |
<p>In pseudo-thermal ghost imaging using a laser beam passing through a rotating ground glass plate, the temporal coherence is important since the intensities in both scanning and bucket detectors have to be measured within the coherence time of the beam. However, in computational ghost imaging this requirement is obviously not enforced (since the scanning detector intensity is calculated using the phase added by the spatial light modulator). I wanted to know what is the basic difference between these two approaches? Why is it that the phase fluctuations of laser (giving rise to finite coherence time) are important in conventional pseudo-thermal ghost imaging but is not important in computational ghost imaging.
Any help would be wonderful.
Thanks.</p>
| 8,801 |
[
-0.009194986894726753,
-0.040229521691799164,
-0.022426867857575417,
-0.04243785887956619,
0.05609634146094322,
0.008337460458278656,
-0.0178813636302948,
-0.06120870262384415,
0.010334831662476063,
0.0381464846432209,
0.05770585313439369,
0.02614540606737137,
0.029024355113506317,
-0.0069537293165922165,
0.04076248034834862,
0.0027118115685880184,
-0.021079396829009056,
-0.005890600383281708,
-0.03679336979985237,
-0.017483161762356758,
-0.025864265859127045,
0.038156669586896896,
0.00012389427865855396,
-0.015301564708352089,
-0.019937880337238312,
-0.0038778993766754866,
-0.005701026879251003,
0.008657930418848991,
0.038459017872810364,
0.030025888234376907,
-0.03917283937335014,
-0.02177056483924389,
-0.05693145841360092,
0.0310656800866127,
0.021504009142518044,
-0.02715892903506756,
-0.07447811961174011,
-0.047854892909526825,
-0.004275382962077856,
0.02023923583328724,
-0.05823304131627083,
-0.024043221026659012,
0.005885298363864422,
0.051418039947748184,
-0.009293911047279835,
0.020884914323687553,
-0.019219623878598213,
-0.009331331588327885,
0.01162817794829607,
-0.073990099132061,
0.04780784621834755,
-0.0015091850655153394,
0.04053639993071556,
0.006247744895517826,
0.0026024114340543747,
0.03536935895681381,
0.057334527373313904,
0.10426165163516998,
-0.019644271582365036,
-0.06363510340452194,
-0.030885450541973114,
-0.003567122621461749,
0.006307724863290787,
-0.030841005966067314,
-0.019164059311151505,
-0.003946441691368818,
0.03186897188425064,
-0.023250004276633263,
0.02977096289396286,
-0.008470679633319378,
-0.0209652092307806,
-0.03787277266383171,
0.06447290629148483,
-0.0022269145119935274,
0.010298271663486958,
-0.0166318416595459,
-0.0003938926965929568,
0.04861288517713547,
0.01945921778678894,
0.007567174732685089,
0.023007387295365334,
-0.02677975594997406,
0.0064093368127942085,
0.041701048612594604,
-0.023568371310830116,
0.006266580894589424,
0.06447052210569382,
0.0005241572507657111,
0.0013797300634905696,
0.014386946335434914,
-0.016207292675971985,
0.03647186979651451,
0.024486759677529335,
0.018475208431482315,
-0.050445761531591415,
0.020814968273043633,
0.0046991994604468346,
0.04379483684897423,
-0.029731355607509613,
-0.0334588848054409,
-0.004663755651563406,
-0.0076960613951087,
0.03408316150307655,
0.039475154131650925,
-0.015352649614214897,
0.007647156715393066,
-0.006272295024245977,
0.045570243149995804,
-0.010112457908689976,
0.0002040671679424122,
-0.023615632206201553,
0.008088720962405205,
-0.006796850822865963,
0.016127901151776314,
0.048323605209589005,
-0.007960320450365543,
0.03241743519902229,
-0.0005940473638474941,
0.04280402511358261,
0.08042381703853607,
0.015624713152647018,
0.0070739127695560455,
-0.0010539969662204385,
-0.018058689311146736,
-0.06972870230674744,
0.014048771001398563,
0.057955991476774216,
-0.02544393390417099,
-0.04605373740196228,
0.04274941608309746,
0.03882179781794548,
0.025851815938949585,
0.054473914206027985,
-0.031040016561746597,
0.02234145812690258,
-0.04586316645145416,
-0.09738244861364365,
0.007240422535687685,
0.04076915606856346,
-0.017255952581763268,
0.02731763757765293,
-0.0663682222366333,
0.05160156637430191,
0.013541183434426785,
0.06743387877941132,
0.005969835910946131,
0.01631235145032406,
-0.023278160020709038,
0.03895463049411774,
-0.02846241369843483,
-0.04195771738886833,
-0.01987924426794052,
0.001821399899199605,
-0.016143223270773888,
-0.035265009850263596,
-0.032323963940143585,
0.01010777149349451,
0.04086216911673546,
-0.018480883911252022,
-0.03240000829100609,
0.026792455464601517,
-0.002266873372718692,
-0.019903108477592468,
0.04422521963715553,
-0.0050381566397845745,
-0.016510142013430595,
0.035255104303359985,
0.015356996096670628,
0.013707736507058144,
0.03012694977223873,
-0.01594564877450466,
0.005766450893133879,
0.02315763756632805,
0.013452575542032719,
0.04431464895606041,
-0.0315934419631958,
0.02639913000166416,
0.0355149544775486,
0.00284069892950356,
0.028254302218556404,
-0.02328537218272686,
-0.0007206790614873171,
-0.01627199351787567,
0.014148061163723469,
0.009579485282301903,
0.016059452667832375,
0.00649042846634984,
-0.010361912660300732,
0.02736973576247692,
-0.05833939462900162,
-0.05538494512438774,
-0.051437858492136,
-0.007708258926868439,
0.035541683435440063,
-0.011264204047620296,
0.018398858606815338,
0.003215314820408821,
0.03579005226492882,
0.026308663189411163,
-0.03185335546731949,
0.0054572452791035175,
0.028745325282216072,
-0.0048306486569345,
-0.01083336677402258,
0.04683900997042656,
0.050001952797174454,
0.025014879181981087,
-0.04034935683012009,
0.04389678314328194,
-0.005595693830400705,
-0.034121375530958176,
0.007143818307667971,
-0.01567627675831318,
0.025086238980293274,
-0.009755287319421768,
-0.01759691908955574,
0.028541777282953262,
0.03625962883234024,
-0.009291472844779491,
-0.003731922712177038,
-0.027845364063978195,
0.05095938965678215,
0.08997748792171478,
0.006339594721794128,
-0.00768302334472537,
0.02057621069252491,
-0.009824497625231743,
-0.01471385546028614,
-0.0067980121821165085,
-0.04438668489456177,
-0.05360577628016472,
-0.027917461469769478,
0.056017789989709854,
0.025864940136671066,
-0.03936866670846939,
0.031259216368198395,
0.037216782569885254,
0.056862395256757736,
0.030622340738773346,
0.02059958316385746,
-0.04052083566784859,
-0.053405482321977615,
0.021886274218559265,
-0.0025038626044988632,
0.010703546926379204,
-0.017551228404045105,
0.015799276530742645,
0.002564553404226899,
0.015795288607478142,
0.0040680645033717155,
-0.03378288075327873,
0.04337366297841072,
-0.058359868824481964,
-0.022782472893595695,
-0.021030137315392494,
-0.03618818148970604,
-0.00007146078860387206,
-0.004005275201052427,
0.008793477900326252,
0.01622118055820465,
-0.045895978808403015,
0.02549630217254162,
-0.06392499804496765,
-0.06404092162847519,
0.04091833904385567,
0.010220030322670937,
-0.01695890910923481,
-0.02633063681423664,
0.01552110817283392,
-0.00012756740034092218,
0.020664408802986145,
-0.04954826459288597,
0.03346617892384529,
-0.046027105301618576,
0.009058929048478603,
0.0592532716691494,
-0.025820547714829445,
0.06080736964941025,
-0.03599206358194351,
-0.042288485914468765,
-0.022292280569672585,
-0.0011738920584321022,
0.019136324524879456,
0.031247079372406006,
-0.08973807841539383,
-0.005248531699180603,
0.010246357880532742,
-0.03159713372588158,
0.030485814437270164,
-0.0374591238796711,
0.0066932435147464275,
-0.024970026686787605,
0.004998927470296621,
-0.06939419358968735,
-0.002827236196026206,
0.009691272862255573,
0.016449134796857834,
-0.014468483626842499,
0.0029190077912062407,
0.044419948011636734,
0.00995405949652195,
-0.06551098823547363,
0.001979249995201826,
-0.02151210606098175,
-0.039152033627033234,
-0.004867657087743282,
-0.006400240585207939,
0.00294675724580884,
-0.03486477956175804,
0.007230206858366728,
0.0027646925300359726,
-0.05560421198606491,
0.0042573087848722935,
-0.018729528412222862,
-0.04251085966825485,
0.04147667437791824,
-0.004344792105257511,
0.021958163008093834,
-0.04252948611974716,
-0.0037794404197484255,
0.05270003527402878,
0.016868187114596367,
-0.036995746195316315,
-0.02892019972205162,
0.017886219546198845,
0.018014561384916306,
0.027646008878946304,
-0.009303754195570946,
-0.009898120537400246,
-0.0003939607704523951,
0.03302647918462753,
0.00843803957104683,
0.009769272059202194,
0.07487215101718903,
0.03903883695602417,
-0.007234037388116121,
0.004620356019586325,
0.012195921503007412,
0.005352351348847151,
0.05449492111802101,
0.0146536435931921,
-0.053627513349056244,
-0.0008915223297663033,
-0.04482312127947807,
-0.02561877854168415,
0.025266561657190323,
-0.06831426173448563,
0.042764220386743546,
-0.019567998126149178,
-0.004441468045115471,
-0.010166484862565994,
0.046808142215013504,
-0.03735141456127167,
-0.017091190442442894,
-0.02774951048195362,
0.054657865315675735,
0.028169510886073112,
0.011753996834158897,
-0.02657328173518181,
0.016843780875205994,
0.023090103641152382,
0.0005478786770254374,
0.01966124214231968,
0.013149510137736797,
-0.03455856442451477,
0.057199377566576004,
-0.03898083418607712,
-0.04351480305194855,
0.06830506771802902,
0.02744242362678051,
0.002289144555106759,
-0.010526486672461033,
0.014261641539633274,
-0.03991321101784706,
-0.028091365471482277,
-0.0017207798082381487,
-0.0169184822589159,
0.047904130071401596,
0.020541273057460785,
0.03081672638654709,
0.0715179517865181,
-0.00902166124433279,
0.0195190217345953,
0.0012270576553419232,
-0.08415447175502777,
-0.006155850365757942,
0.01650233380496502,
-0.002078964142128825,
-0.012406076304614544,
0.0022532097063958645,
0.00028175703482702374,
-0.01327428501099348,
-0.010988086462020874,
-0.007114260923117399,
0.01842062920331955,
-0.042535487562417984,
0.01255810633301735,
-0.015617250464856625,
-0.009624755010008812,
-0.04517031088471413,
0.05042325705289841,
-0.0005766681861132383,
-0.02749769203364849,
0.030920308083295822,
0.039541274309158325,
0.011465657502412796,
0.021010223776102066,
-0.0026147968601435423,
0.02533057890832424,
-0.004135848954319954,
0.02251657284796238,
0.03869195282459259,
0.03564121946692467,
-0.031588003039360046,
0.006969076581299305,
0.029902560636401176,
0.06315089017152786,
-0.008636348880827427,
-0.016981255263090134,
-0.005325054284185171,
-0.025374313816428185,
0.03202299773693085,
0.005756747908890247,
0.06883621215820312,
0.021839281544089317,
-0.04360194131731987,
0.016888221725821495,
0.05072053149342537,
-0.00826413556933403,
0.033300284296274185,
0.04471643269062042,
0.005457656923681498,
0.01748282089829445,
-0.0641358345746994,
-0.01248164102435112,
-0.03385770320892334,
-0.005152656231075525,
0.06979811936616898,
0.02305521070957184,
0.019833741709589958,
0.020308444276452065,
0.0000945048377616331,
-0.03883904218673706,
0.014672426506876945,
-0.0038042247761040926,
0.034085068851709366,
-0.003308637533336878,
0.009209679439663887,
0.02598705142736435,
-0.043160226196050644,
0.05228418856859207,
0.024378687143325806,
0.00898788683116436,
-0.01300191693007946,
-0.06218915060162544,
-0.03989633917808533,
0.049975473433732986,
0.012326553463935852,
-0.014730038121342659,
-0.05007006600499153,
-0.036149121820926666,
-0.05044816806912422,
0.03665853664278984,
-0.028454532846808434,
0.0167818795889616,
-0.03125471994280815,
-0.013442369177937508,
0.00048252136912196875,
-0.021509181708097458,
0.013054859824478626,
0.031236233189702034,
0.0027152046095579863,
0.030179915949702263,
-0.05887237936258316,
-0.040383584797382355,
-0.0015547251095995307,
0.0035964930430054665,
-0.017833756282925606,
0.032114554196596146,
-0.04116096720099449,
-0.006667523644864559,
-0.0033178068697452545,
0.013798223808407784,
-0.01846151053905487,
-0.034613803029060364,
0.0012396284146234393,
0.010773636400699615,
0.009850312024354935,
0.08204002678394318,
-0.0388394333422184,
-0.04063216224312782,
0.011909405700862408,
0.01924872025847435,
-0.00042793076136149466,
-0.005525051616132259,
-0.007840902544558048,
0.023338716477155685,
0.010397600010037422,
0.012180308811366558,
0.08098169416189194,
0.00544173875823617,
-0.019275950267910957,
0.009837772697210312,
-0.010260225273668766,
0.0619347020983696,
-0.025384364649653435,
0.020244233310222626,
-0.04174819961190224,
0.009141338057816029,
-0.04029032215476036,
0.08746737241744995,
-0.019656533375382423,
0.013521365821361542,
-0.02053597941994667,
-0.033389072865247726,
0.030325021594762802,
0.07404262572526932,
0.00794946774840355,
0.010105418972671032,
-0.011477280408143997,
0.03160764276981354,
0.02408134751021862,
0.023089446127414703,
-0.011548424139618874,
-0.02121998928487301,
-0.004438409116119146,
0.05535762012004852,
0.027622997760772705,
0.03259146586060524,
-0.062448397278785706,
0.004384968895465136,
-0.0057876878418028355,
-0.039655476808547974,
-0.005533165298402309,
0.014709265902638435,
0.035134993493556976,
0.0027765382546931505,
-0.08311250060796738,
0.012699531391263008,
-0.0278486255556345,
-0.038682930171489716,
0.0596870481967926,
-0.05435193330049515,
0.006298305932432413,
0.011083784513175488,
0.01906057447195053,
-0.06603539735078812,
-0.054485924541950226,
-0.021381938830018044,
0.024502966552972794,
-0.031131397932767868,
-0.022665858268737793,
0.023912521079182625,
-0.033803943544626236,
-0.0313076376914978,
0.006310637108981609,
0.007659452967345715,
0.019510336220264435,
-0.014448245987296104,
0.03448948264122009,
-0.0069118523970246315,
0.01727931573987007,
-0.020133957266807556,
0.02239755541086197,
0.030627744272351265,
-0.005357806570827961,
-0.056767769157886505,
-0.009343826211988926,
0.032845936715602875,
-0.017837123945355415,
-0.03604799881577492,
-0.06449209153652191,
0.011169061996042728,
0.05187750607728958,
-0.001287663821130991,
-0.032139312475919724,
-0.003713088808581233,
-0.01747533492743969,
-0.0058043161407113075,
-0.032902732491493225,
0.010020206682384014,
-0.0012981857871636748,
0.019753703847527504,
0.0004505062534008175,
-0.025956450030207634,
-0.018886344507336617,
-0.02493988908827305,
0.024168023839592934,
0.027957892045378685,
-0.0020260890014469624,
0.034883204847574234,
0.043807558715343475,
-0.02993669919669628,
0.006253852974623442,
0.018213380128145218,
-0.04079478606581688,
0.02344212867319584,
0.005342391319572926,
0.03380581736564636,
0.009096384979784489,
0.04256707802414894,
-0.027039695531129837,
-0.02423996664583683,
-0.018721673637628555,
-0.006277854088693857,
0.060833267867565155,
-0.009826206602156162,
0.06281272321939468,
-0.0026649157516658306,
-0.03543714061379433,
-0.011430179700255394,
-0.013645341619849205,
-0.014311005361378193,
0.06296764314174652,
-0.022888731211423874,
0.028732415288686752,
-0.048071131110191345,
-0.02183990180492401,
0.02979428693652153,
0.029734449461102486,
0.03192097693681717,
0.03999466449022293,
0.00980747863650322,
0.0387604795396328,
-0.011557063087821007,
-0.046272166073322296,
-0.02617822028696537,
0.059567902237176895,
-0.06251772493124008,
0.03369108960032463,
0.003224683692678809,
-0.001115143415518105,
0.02401874214410782,
-0.0033243156503885984,
-0.025762902572751045,
-0.0537073090672493,
0.004662142600864172,
-0.04845603182911873,
0.030524389818310738,
-0.015568645671010017,
-0.004046208690851927,
-0.0089940894395113,
0.010514402762055397,
-0.004393365699797869,
-0.014560080133378506,
0.010653723031282425,
0.023086387664079666,
-0.11774235963821411,
-0.0440058633685112,
0.004956012591719627,
-0.024315739050507545,
0.04790299013257027,
-0.016938496381044388,
-0.002099703997373581,
0.011269809678196907,
-0.030019238591194153,
0.012168314307928085,
0.008317781612277031,
0.030824461951851845,
-0.042887624353170395,
0.04095016047358513,
-0.0010227011516690254,
0.030458716675639153,
0.005008792504668236,
0.03653719648718834,
0.11092408746480942,
0.04001963883638382,
0.017888450995087624,
-0.04384152218699455,
0.008048690855503082,
0.0039051994681358337,
0.035423435270786285,
-0.037491146475076675,
0.03523874655365944,
0.006348239723592997,
0.020474091172218323,
0.0177509393543005,
0.02490716613829136,
-0.00909572932869196,
-0.031713422387838364,
0.012990400195121765,
-0.013472385704517365,
-0.012592014856636524,
0.02909051440656185,
0.017713813111186028,
0.002522350288927555,
0.019245842471718788,
-0.0060590896755456924,
-0.0021660723723471165,
-0.03817195072770119,
-0.008859995752573013,
-0.026950476691126823,
-0.042062338441610336,
-0.013777852058410645,
0.017378967255353928,
-0.03618592768907547,
0.008451620116829872,
-0.016244828701019287,
0.01255496870726347,
-0.026275141164660454,
-0.009620248340070248,
-0.00923852901905775,
0.013303857296705246,
0.033471763134002686,
0.035752732306718826,
0.025355923920869827,
-0.03882487863302231,
0.006970008835196495,
0.05288359895348549,
-0.034811533987522125,
-0.01241717766970396,
-0.0007427494856528938,
0.044338371604681015,
-0.013456831686198711,
0.00017159753770101815,
0.0045132823288440704,
-0.021552681922912598,
0.043478384613990784,
-0.0305376797914505,
-0.04027536138892174,
0.0031517695169895887,
0.01584511809051037,
-0.021845847368240356,
-0.024553781375288963,
-0.027288882061839104,
0.015187120996415615,
0.024173738434910774,
0.044510990381240845,
-0.029266223311424255,
0.015909980982542038,
-0.010544524528086185,
0.010562187060713768,
0.037726130336523056,
-0.014225071296095848,
-0.01722630113363266,
0.005972394719719887,
-0.003214518539607525,
-0.010864509269595146,
-0.00045049606706015766,
0.014142997562885284,
-0.013211563229560852,
0.033934205770492554,
-0.015749551355838776,
-0.02457660436630249,
0.027903230860829353,
-0.041061680763959885,
-0.013257928192615509,
0.010215021669864655,
-0.0263057928532362,
-0.007887917570769787,
-0.009973467327654362,
0.0593816377222538,
0.00962590891867876,
-0.028455747291445732,
-0.008724603801965714,
0.0030204569920897484,
0.039413176476955414,
0.033259257674217224,
-0.009257694706320763,
-0.026744447648525238,
-0.029103346168994904,
0.005531840026378632,
0.01836448907852173,
-0.03285659849643707,
-0.014489366672933102,
0.020134318619966507,
0.003759056329727173,
0.03129340708255768,
0.035261061042547226,
-0.013144289143383503,
-0.0006496781716123223,
0.002848774893209338,
-0.0011835576733574271,
-0.02110113762319088,
-0.01735028065741062,
0.02998119220137596,
-0.0301032904535532,
-0.015236114151775837,
-0.023449677973985672,
0.01181875355541706,
0.003561505815014243,
0.0017231496749445796,
-0.00899534672498703,
-0.029897356405854225,
-0.012925117276608944,
0.004649993497878313,
-0.04525471851229668,
-0.01943458430469036,
-0.03223535418510437,
0.06365718692541122,
0.01732603646814823,
-0.016835521906614304,
-0.0286834966391325,
0.03360545635223389,
-0.004168279934674501,
-0.05460236966609955,
0.0013444747310131788,
0.014437672682106495,
-0.025233957916498184,
0.022859273478388786,
0.04625394567847252,
-0.016008539125323296,
0.047466084361076355,
0.0077891964465379715,
0.00978664867579937,
0.025006456300616264,
-0.0375974215567112,
-0.04874547943472862,
0.06309662759304047,
0.0008270472171716392,
-0.008233374916017056,
0.04003526642918587,
-0.015558554790914059,
-0.0005907776649110019,
0.0478331595659256,
0.004365665838122368,
-0.02450411766767502,
-0.020979618653655052,
0.0016868060920387506,
-0.006401111837476492,
0.004641833249479532,
0.015498015098273754,
-0.06652327626943588,
-0.022221926599740982,
0.05279944837093353,
0.049879640340805054,
-0.025074996054172516,
0.007749033160507679,
-0.005620486102998257,
-0.024872850626707077,
-0.005277201067656279,
-0.0019770641811192036,
0.027448298409581184,
0.04951834678649902,
0.05877416580915451,
-0.012260827235877514,
-0.0011508006136864424,
0.0071915071457624435,
0.001505055814050138,
-0.08676999807357788,
-0.019528204575181007,
0.0019513947190716863,
0.009303777478635311,
0.015767961740493774,
-0.005040476098656654,
0.010546437464654446,
0.04320476949214935,
-0.06408068537712097,
0.03739804029464722,
-0.0360165536403656,
-0.026350611820816994,
-0.06582703441381454,
-0.00033729863935150206,
-0.020972611382603645,
0.00980420783162117,
0.014222766272723675,
0.004792851395905018,
0.04311635345220566,
0.004013844300061464,
-0.017869384959340096,
-0.0004481677897274494,
-0.0301053486764431,
0.0020494498312473297,
-0.008921677246689796,
-0.017316270619630814,
0.04414075240492821,
0.02375827170908451,
-0.05474701151251793,
-0.001461731269955635,
-0.030070733278989792,
0.01335606724023819,
0.01004310604184866,
0.031678397208452225,
-0.03359366953372955,
0.010471788235008717,
0.018723145127296448,
-0.008204618468880653,
0.04001002758741379,
0.017430320382118225,
-0.014912866987287998,
0.0638512521982193,
0.0068959142081439495,
0.026171863079071045,
-0.013510648161172867,
-0.04274245724081993,
-0.03703279048204422,
0.01638292521238327,
-0.002460071351379156,
-0.03456060215830803,
0.02262618951499462,
-0.01371516939252615,
0.03304251655936241,
-0.024755418300628662,
0.028964277356863022,
-0.05695221945643425,
-0.03122618794441223,
-0.0006365537410601974,
0.025188514962792397,
-0.03204157575964928,
-0.007850338704884052,
-0.021189887076616287,
-0.049858395010232925,
0.02099589630961418,
0.01797075942158699,
-0.003571468871086836,
-0.03962399810552597,
-0.025508735328912735,
0.01843850500881672,
0.013672210276126862,
0.0047008441761136055,
-0.017785971984267235,
-0.02538016252219677,
0.04545586183667183,
-0.022477587684988976,
0.01823868788778782,
-0.01311374269425869,
0.010780885815620422,
-0.0709751695394516,
-0.0704948678612709,
-0.006548549514263868,
0.00940976943820715,
0.009440627880394459,
-0.06644684076309204,
0.0029197942931205034,
-0.03621242195367813,
0.03086070343852043,
0.018970850855112076,
-0.0148765929043293,
-0.010920141823589802,
0.03141189366579056,
-0.02608671225607395,
0.018582254648208618,
-0.0316397100687027,
-0.003677563276141882,
-0.029530860483646393,
-0.005870933178812265,
0.01906430535018444,
-0.02983866259455681,
-0.018031945452094078,
0.031153688207268715,
0.03399568796157837,
-0.007384824566543102,
0.05006982386112213,
-0.020539164543151855,
-0.03533078357577324,
0.03425730764865875,
0.005063856951892376,
0.024619808420538902,
0.060469210147857666,
0.0026524323038756847,
0.04518536105751991,
0.01087531540542841,
0.006479241885244846,
-0.016015540808439255,
0.025210313498973846,
-0.041865695267915726,
-0.005715017206966877,
0.023161550983786583,
-0.005254516378045082,
0.004108686465770006,
-0.037400126457214355,
-0.02765650860965252,
0.028939681127667427,
-0.02638026513159275,
0.019947050139307976,
0.037491779774427414,
0.008628358133137226,
0.02290273644030094,
-0.01364611741155386,
0.05524008348584175,
0.0022103525698184967,
0.009904091246426105,
-0.01685676909983158,
0.04846952110528946,
-0.018183378502726555,
0.02303757332265377,
0.028455568477511406,
0.017470939084887505,
-0.012547844089567661,
0.010105334222316742,
-0.001160612446255982,
0.03875832259654999,
-0.046564068645238876,
-0.01643546111881733,
0.040703512728214264,
-0.01663932017982006,
0.01122212503105402,
0.024807708337903023,
0.008394588716328144,
0.07111009955406189,
-0.04052872210741043,
0.012549607083201408,
-0.006195727735757828,
-0.037458375096321106,
-0.0286712609231472,
0.034595925360918045,
0.006357051432132721,
0.04551011696457863,
-0.004071489442139864,
0.015623326413333416,
-0.01110613252967596,
0.0038554964121431112,
0.00726285157725215,
-0.09176545590162277,
0.017320608720183372,
-0.013800117187201977,
0.008574643172323704,
0.011115898378193378,
-0.01374772284179926,
-0.043566200882196426,
0.012917113490402699,
-0.0027731796726584435,
0.039513882249593735,
0.016926830634474754,
-0.012431931681931019,
-0.01747857965528965,
-0.009624718688428402,
0.04138629138469696,
-0.0957312285900116,
0.009755725041031837,
0.012283767573535442,
0.010807250626385212,
0.011579220183193684,
0.016529608517885208
] |
<p>I just read <a href="http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-S2" rel="nofollow">http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-S2</a></p>
<p>In my opinion, in this chapter the equations 18.6 and 18.7 are wrong. Have a look at the Picture <a href="http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-F1" rel="nofollow">http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-F1</a> . </p>
<blockquote>
<p>If $OP$ is called $r$, then the length $PQ$ is $rΔθ$, because of the way angles are defined. The change in $x$, then, is simply the projection of $rΔθ$ in the $x$-direction: $$\Delta x=-PQ\sin\theta=-r\,\Delta\theta\cdot(y/r)=-y\,\Delta\theta$$</p>
</blockquote>
<p>That is equation 18.6. <em>It is wrong because $\Delta\theta$ doesn't mean that $\theta_{Q}-\theta_{P}$ is infinitesimally small and equation 18.6 is only valid for infinitesimally small $\Delta\theta$.</em></p>
<p>An example is: I take $P$ to be $(1|0)$ and $Q$ to be $(0|1)$ than $\Delta x$ is $-1$ but calculated using equation 18.6 it should have been $-y\Delta\theta=(-1)(\pi /2)\approx -1,57$, which is wrong.</p>
<p>In the equations $d\theta$ should have be used instead of $\Delta\theta$.</p>
<p><strong>Is my reasoning correct?</strong></p>
| 8,802 |
[
0.012125670909881592,
-0.016788966953754425,
-0.0073587847873568535,
-0.029562262818217278,
0.021707693114876747,
0.03231286257505417,
-0.051898565143346786,
-0.04489153251051903,
0.011374755762517452,
-0.030835922807455063,
0.010645806789398193,
0.0149526447057724,
0.0565137043595314,
0.04118373990058899,
0.013154065236449242,
0.026228277012705803,
-0.013337851502001286,
-0.01697969250380993,
0.00858378130942583,
-0.030312776565551758,
0.02564573474228382,
0.05353077873587608,
0.011832416988909245,
-0.012011627666652203,
-0.02120182290673256,
0.04042891040444374,
0.04841871187090874,
-0.009120154194533825,
-0.026715505868196487,
0.0652933344244957,
-0.006172369234263897,
-0.020840059965848923,
-0.01650116592645645,
0.022761806845664978,
-0.022010348737239838,
-0.008081814274191856,
0.0057915449142456055,
-0.02685580961406231,
-0.008238440379500389,
0.026244385167956352,
-0.06578081101179123,
0.02535570226609707,
-0.021270006895065308,
0.0505899041891098,
-0.029859118163585663,
0.0033785924315452576,
-0.0046823774464428425,
-0.002894280944019556,
0.08929170668125153,
-0.02725932188332081,
0.08532080799341202,
0.0039260839112102985,
-0.01468139048665762,
0.01521483063697815,
-0.011256642639636993,
-0.025631243363022804,
0.029683172702789307,
0.04453130066394806,
-0.010277731344103813,
-0.07791294157505035,
-0.027307353913784027,
-0.059276510030031204,
0.004837868269532919,
-0.01605953462421894,
-0.002222623210400343,
-0.016389401629567146,
0.016619717702269554,
-0.020827382802963257,
0.015673071146011353,
-0.024879520758986473,
0.043073613196611404,
0.013685829937458038,
0.007128895726054907,
0.018874749541282654,
0.016266213729977608,
0.004798520356416702,
-0.017747681587934494,
0.024885540828108788,
0.0013954078312963247,
0.06507313996553421,
-0.047384247183799744,
-0.00001308470109506743,
0.016159888356924057,
0.016496673226356506,
-0.00528567424044013,
-0.010709330439567566,
0.06995601207017899,
-0.010161453858017921,
0.004904165398329496,
0.04083293303847313,
0.006950752809643745,
0.024725232273340225,
0.014144297689199448,
-0.037364136427640915,
-0.014056774787604809,
0.054110147058963776,
0.01056688092648983,
0.027650045230984688,
-0.016660412773489952,
-0.041505031287670135,
0.0019164358964189887,
-0.05113756284117699,
-0.012579519301652908,
0.08025921881198883,
-0.006329533644020557,
-0.01860031485557556,
-0.021492566913366318,
-0.0054331892170012,
-0.010665536858141422,
-0.020167378708720207,
-0.05105697363615036,
0.015850776806473732,
-0.04021339863538742,
0.019075924530625343,
-0.009749036282300949,
-0.011042912490665913,
-0.011197962798178196,
0.01635434851050377,
0.044271789491176605,
0.07428993284702301,
0.028211258351802826,
-0.03184175118803978,
-0.001590623753145337,
-0.03501557931303978,
-0.05989787355065346,
0.016100851818919182,
0.015552100725471973,
-0.005864266771823168,
-0.040689460933208466,
0.0015334145864471793,
0.04195130616426468,
0.020273510366678238,
0.013072218745946884,
0.03717372938990593,
0.028016580268740654,
0.019197694957256317,
-0.08013814687728882,
-0.06668229401111603,
0.024184873327612877,
-0.0023953712079674006,
0.018038222566246986,
-0.030506547540426254,
0.00016092834994196892,
0.012689605355262756,
0.07255019247531891,
-0.009717918001115322,
0.04020146653056145,
-0.0004082273517269641,
0.012517119757831097,
0.00855239387601614,
-0.0006944632041268051,
0.045670464634895325,
-0.011114922352135181,
-0.04158038645982742,
-0.058708157390356064,
-0.051631249487400055,
0.06204244866967201,
0.025395378470420837,
0.005598423536866903,
-0.003896405454725027,
0.0864245668053627,
-0.024585070088505745,
0.01783343218266964,
0.010099931620061398,
-0.042487576603889465,
-0.0280404444783926,
0.10345935076475143,
0.038830652832984924,
0.014104717411100864,
0.011843464337289333,
-0.031049057841300964,
-0.01178879663348198,
-0.04128085449337959,
-0.01887095719575882,
0.03343610465526581,
-0.006687510292977095,
-0.012103560380637646,
-0.04033788666129112,
-0.013924172148108482,
0.012126619927585125,
-0.03087836690247059,
-0.029220962896943092,
-0.026069102808833122,
-0.005264539737254381,
-0.01734928973019123,
0.05433689057826996,
-0.0013430335093289614,
-0.016006018966436386,
0.011996503919363022,
-0.042719192802906036,
-0.002637839876115322,
-0.030237479135394096,
0.03251349925994873,
0.033214423805475235,
0.0017282258486375213,
0.03262944519519806,
0.01627310924232006,
-0.012727589346468449,
-0.02862534299492836,
-0.012734390795230865,
-0.011959495022892952,
0.04525052383542061,
0.003003660822287202,
0.025534071028232574,
0.019628869369626045,
0.056785717606544495,
0.03804238140583038,
0.03324354439973831,
0.0001898802729556337,
-0.04318241775035858,
0.024897728115320206,
0.01104045007377863,
-0.017636099830269814,
0.006076525431126356,
0.008524884469807148,
-0.014486425556242466,
-0.004453946370631456,
0.010724533349275589,
-0.016647404059767723,
0.0038791862316429615,
-0.0378192663192749,
0.05346611142158508,
0.018400922417640686,
0.0013509029522538185,
0.01641414687037468,
0.030967099592089653,
0.017887266352772713,
0.05303226038813591,
0.0059018125757575035,
-0.036815889179706573,
-0.036298297345638275,
0.0028930562548339367,
0.0404222272336483,
0.0020562075078487396,
-0.034537822008132935,
0.008778019808232784,
0.01220531202852726,
0.006965742912143469,
0.012510840781033039,
-0.00838320143520832,
-0.00048126463661901653,
-0.050168320536613464,
-0.008002229034900665,
0.005491947289556265,
0.008269386366009712,
-0.024469878524541855,
-0.0010148986475542188,
-0.026532592251896858,
0.05088378116488457,
-0.0247306227684021,
0.009743927046656609,
0.013348226435482502,
-0.0007106951670721173,
-0.00400911970064044,
0.007537951692938805,
0.0011934337671846151,
0.04215610772371292,
0.005948735401034355,
0.030192263424396515,
0.011592724360525608,
-0.028487659990787506,
0.0034120979253202677,
-0.017620962113142014,
-0.005824057850986719,
0.0020496200304478407,
0.012665708549320698,
0.04147130623459816,
0.012787744402885437,
0.03195694088935852,
-0.027110733091831207,
-0.024625159800052643,
-0.036863431334495544,
-0.05827036127448082,
-0.017953677102923393,
-0.015387930907309055,
0.04471682384610176,
0.05779373645782471,
-0.0173158198595047,
-0.03563375398516655,
-0.019781241193413734,
-0.013492540456354618,
0.03184761479496956,
0.024733392521739006,
0.033996012061834335,
-0.007143524941056967,
0.002359086414799094,
-0.05519000440835953,
-0.018245579674839973,
0.013917980715632439,
0.02444647066295147,
0.006152952555567026,
-0.013134373351931572,
-0.0035085915587842464,
-0.04693049564957619,
-0.03226238116621971,
-0.021750833839178085,
-0.009132166393101215,
-0.02676793746650219,
-0.023204665631055832,
0.04145848751068115,
0.00041394177242182195,
-0.015619945712387562,
0.054797738790512085,
-0.03915046155452728,
-0.019383015111088753,
-0.015131262131035328,
0.002648435765877366,
-0.0010348379146307707,
0.028930865228176117,
0.030559882521629333,
0.02049577608704567,
0.004537105560302734,
-0.01301310770213604,
-0.08041275292634964,
-0.04466920346021652,
0.012655696831643581,
-0.012972456403076649,
0.0019832528196275234,
0.0014283073833212256,
-0.02006641775369644,
0.07377196848392487,
0.03380646929144859,
-0.050472866743803024,
-0.02733943983912468,
0.042806871235370636,
-0.02506171353161335,
-0.05007193982601166,
-0.009990462101995945,
0.029048923403024673,
-0.005417372565716505,
0.03856544569134712,
0.002230287529528141,
0.023001017048954964,
0.004207412246614695,
0.006766596343368292,
-0.00704811979085207,
0.028462084010243416,
0.015041311271488667,
-0.03733893483877182,
0.04287264123558998,
0.02739318460226059,
0.014433899894356728,
0.011092958971858025,
0.013172442093491554,
0.03160295635461807,
0.01739741861820221,
-0.061838969588279724,
0.034456752240657806,
0.012806907296180725,
0.008907560259103775,
0.005092204082757235,
0.022802181541919708,
-0.007033009082078934,
-0.05053321272134781,
-0.025903062894940376,
0.02096662111580372,
0.042526885867118835,
-0.02554835006594658,
-0.025049829855561256,
0.030006784945726395,
0.04242069274187088,
-0.01669212616980076,
-0.023499447852373123,
-0.01440419815480709,
-0.016261985525488853,
0.03653716668486595,
-0.026309171691536903,
-0.033992666751146317,
0.03409232199192047,
0.04541155323386192,
-0.009734747931361198,
-0.010611351579427719,
-0.01908063516020775,
-0.01859818957746029,
-0.03971710801124573,
0.024387476965785027,
-0.043310754001140594,
0.03871138393878937,
0.04553952440619469,
0.039637237787246704,
0.01859007589519024,
0.00918419100344181,
-0.014787165448069572,
-0.024185819551348686,
-0.09037243574857712,
0.015165322460234165,
-0.015458566136658192,
-0.04224042966961861,
-0.0010491641005501151,
0.010849162004888058,
0.04546530172228813,
0.0029159567784518003,
0.033164866268634796,
-0.03103785403072834,
-0.031802717596292496,
-0.02918640524148941,
0.02793733961880207,
-0.026270432397723198,
-0.05552496016025543,
-0.04188605025410652,
0.05532078072428703,
0.07777191698551178,
-0.034320101141929626,
-0.003383499337360263,
0.02880069799721241,
-0.04360262304544449,
0.0016189683228731155,
-0.005943431053310633,
0.023732857778668404,
-0.017060864716768265,
0.023536359891295433,
0.015947848558425903,
-0.0039148470386862755,
0.02590275928378105,
0.03227471560239792,
0.029634961858391762,
0.05624259635806084,
0.037158332765102386,
-0.038591932505369186,
0.016088373959064484,
-0.04451124742627144,
-0.018438057973980904,
-0.008109141141176224,
0.06097179651260376,
0.0025870855897665024,
-0.009241199120879173,
0.05310545489192009,
0.02528935670852661,
0.008332300931215286,
0.026398776099085808,
0.030498327687382698,
0.017798107117414474,
-0.013135763816535473,
-0.054280899465084076,
0.017306365072727203,
-0.02368105575442314,
0.00396176241338253,
-0.019882597029209137,
-0.002972477814182639,
-0.029279286041855812,
-0.021723324432969093,
0.04063190892338753,
0.022731753066182137,
-0.029471540823578835,
0.011447898112237453,
-0.00787016935646534,
0.01062700618058443,
-0.021372079849243164,
0.013913722708821297,
0.01662176288664341,
0.0392627976834774,
0.04245031625032425,
-0.00626313965767622,
-0.008042793720960617,
-0.04429970681667328,
-0.0022775151301175356,
0.05124415457248688,
0.06514675170183182,
0.04640725255012512,
0.012347092851996422,
-0.0777202770113945,
-0.04704347997903824,
0.027823299169540405,
-0.009474053047597408,
0.03848179802298546,
-0.035784803330898285,
-0.01671886071562767,
-0.03693549707531929,
-0.057781003415584564,
-0.05081995949149132,
-0.00719780009239912,
-0.0006360889528878033,
0.03636749088764191,
-0.018941115587949753,
-0.026497315615415573,
0.02009720169007778,
0.005656789988279343,
0.024584416300058365,
0.03654151409864426,
0.007165643386542797,
-0.0022923729848116636,
-0.004082049243152142,
0.00057494908105582,
0.00330450851470232,
-0.08040956407785416,
0.06028526648879051,
0.009517297148704529,
0.017679011449217796,
0.047563470900058746,
-0.02396794594824314,
-0.04399824142456055,
0.07892629504203796,
-0.004648357629776001,
0.016355711966753006,
0.05133479833602905,
-0.061139367520809174,
0.04636053368449211,
0.044672466814517975,
-0.010289838537573814,
0.05701737478375435,
0.013518321327865124,
0.00688690971583128,
-0.00626318110153079,
-0.03999601677060127,
-0.010066196322441101,
0.01583043485879898,
-0.019802028313279152,
-0.0474335178732872,
0.015669675543904305,
0.029005520045757294,
0.03329847380518913,
-0.02023915760219097,
0.023319905623793602,
-0.02141599729657173,
-0.028045281767845154,
-0.0062904818914830685,
0.01469787210226059,
0.0043031261302530766,
-0.00479845330119133,
0.024797068908810616,
-0.009181172586977482,
0.03349844366312027,
0.028332950547337532,
0.0013311521615833044,
-0.02830878458917141,
0.01782514899969101,
0.026248948648571968,
-0.03411824628710747,
-0.025479601696133614,
-0.028357649222016335,
-0.01670544408261776,
-0.0034324449952691793,
-0.06913138926029205,
0.05101949721574783,
-0.015186728909611702,
-0.0030620614998042583,
0.022041287273168564,
-0.015739943832159042,
-0.036635275930166245,
-0.002505418611690402,
-0.025373047217726707,
-0.00373161886818707,
-0.027914760634303093,
0.0023818386252969503,
0.036162592470645905,
0.0031747694592922926,
-0.03437549248337746,
-0.016761431470513344,
0.007883124984800816,
-0.029365351423621178,
-0.06927251815795898,
0.03956396505236626,
-0.010452945716679096,
0.04618072137236595,
-0.032328296452760696,
-0.032328370958566666,
0.011442907154560089,
-0.04522773250937462,
0.00375434011220932,
0.010307692922651768,
0.041614457964897156,
0.05378042906522751,
-0.020041804760694504,
0.003917352762073278,
0.03212917223572731,
-0.00003105369978584349,
-0.011712451465427876,
0.01225791871547699,
0.03378283977508545,
-0.046889528632164,
-0.026979297399520874,
-0.007844422943890095,
-0.015671908855438232,
0.01641554944217205,
-0.006684239488095045,
-0.03613346815109253,
0.0023946836590766907,
-0.016775663942098618,
0.00026931604952551425,
0.018521949648857117,
-0.0172797292470932,
0.0030757971107959747,
-0.00810051616281271,
0.008426223881542683,
0.012798107229173183,
-0.012935470789670944,
-0.024137992411851883,
0.023689305409789085,
-0.02779310755431652,
-0.011512918397784233,
0.00385817838832736,
0.06620823591947556,
-0.03207831084728241,
-0.013673335313796997,
0.054437097162008286,
0.0158239658921957,
0.022955672815442085,
-0.000002980962108267704,
0.03226681053638458,
0.011693715117871761,
-0.0017801685025915504,
-0.011215785518288612,
-0.04273306578397751,
-0.0677281990647316,
0.0002827645221259445,
0.07618514448404312,
0.03602128103375435,
0.021564403548836708,
-0.0010429925750941038,
-0.043373532593250275,
-0.0026369793340563774,
-0.021924784407019615,
-0.03196626901626587,
-0.028401058167219162,
0.005039353854954243,
0.011736792512238026,
-0.07102024555206299,
-0.03714669495820999,
0.003844010177999735,
0.01340925507247448,
-0.03935404121875763,
-0.01324400957673788,
0.025707677006721497,
0.0032503397669643164,
0.023511208593845367,
-0.010472373105585575,
-0.03274006024003029,
0.0615699477493763,
-0.01494693011045456,
0.05350853502750397,
-0.005641588941216469,
-0.011225102469325066,
0.02656669355928898,
0.008960449136793613,
0.036040570586919785,
-0.04759383946657181,
0.009058704599738121,
-0.020989280194044113,
-0.027948517352342606,
0.00123318238183856,
-0.0029573088977485895,
-0.011981277726590633,
-0.02194187417626381,
0.06724654883146286,
0.0033386859577149153,
0.033223021775484085,
-0.040735192596912384,
-0.03450382128357887,
-0.04132552444934845,
-0.019781755283474922,
-0.053877074271440506,
0.08187603205442429,
-0.03689994663000107,
-0.004819672089070082,
0.02168581262230873,
-0.04897278547286987,
0.03162304311990738,
0.031360775232315063,
0.01796329952776432,
-0.04233144596219063,
0.0277751162648201,
-0.04696791246533394,
0.0012774127535521984,
-0.03198574110865593,
-0.04382338374853134,
0.12586134672164917,
0.035373903810977936,
0.008079573512077332,
-0.00863631907850504,
0.07061754912137985,
-0.018245922401547432,
0.03371565416455269,
-0.03912721946835518,
0.0013929067645221949,
-0.02762920781970024,
-0.030003610998392105,
0.0016908443067222834,
0.0221936646848917,
-0.011886993423104286,
-0.02421339601278305,
0.0178462415933609,
-0.05438893288373947,
-0.0706111416220665,
-0.014348910190165043,
-0.00956436526030302,
-0.018373742699623108,
0.023561427369713783,
-0.0064960685558617115,
0.008548206649720669,
-0.047882016748189926,
0.01815740205347538,
0.0016441971529275179,
-0.037418875843286514,
0.01647471822798252,
0.015979178249835968,
-0.03464515507221222,
0.004148977342993021,
-0.009839332662522793,
-0.024414436891674995,
0.0066412873566150665,
0.011064993217587471,
0.031688008457422256,
-0.03652092441916466,
0.021802954375743866,
0.057508938014507294,
0.044495902955532074,
0.011611534282565117,
0.039625126868486404,
0.0007538854260928929,
-0.06519386917352676,
-0.03609459102153778,
-0.027254465967416763,
0.0729224681854248,
-0.007588553242385387,
0.005871572066098452,
-0.014651189558207989,
0.045875709503889084,
-0.018415020778775215,
-0.06089576333761215,
0.011464792303740978,
-0.009426850825548172,
0.012999067083001137,
0.015655290335416794,
0.025758171454072,
0.0035050425212830305,
0.03500856086611748,
0.013688714243471622,
0.0230817012488842,
0.0025916784070432186,
0.001315280911512673,
0.010845538228750229,
-0.010276577435433865,
0.05573353171348572,
0.010320320725440979,
0.007413625717163086,
-0.05752413719892502,
0.00784363318234682,
-0.019548628479242325,
0.013183985836803913,
-0.001361572532914579,
0.01810142956674099,
0.04229739308357239,
0.013063700869679451,
-0.004631728865206242,
-0.026729503646492958,
-0.046362511813640594,
0.01579328626394272,
-0.0038393684662878513,
-0.05521097779273987,
-0.026202257722616196,
-0.00875539518892765,
0.01611916907131672,
0.027804335579276085,
-0.0076008145697414875,
-0.020566901192069054,
-0.004304999485611916,
0.04459602013230324,
0.041360046714544296,
0.008036281913518906,
-0.08664515614509583,
-0.003632734762504697,
-0.00040067528607323766,
-0.04742100462317467,
0.023412803187966347,
-0.0050658732652664185,
0.04318546503782272,
0.03994372487068176,
0.0344080775976181,
0.0407637320458889,
-0.027234455570578575,
-0.014753307215869427,
0.012333756312727928,
-0.012260773219168186,
0.017172353342175484,
-0.010590058751404285,
0.007541431579738855,
-0.05067422240972519,
0.006271147634834051,
0.0002745020901784301,
-0.020404499024152756,
0.016889430582523346,
0.0000823028531158343,
-0.03768749162554741,
-0.02094295434653759,
-0.04277941957116127,
-0.015698915347456932,
-0.019772110506892204,
0.0011693426640704274,
-0.015322204679250717,
-0.02700103633105755,
-0.03261934965848923,
0.024697549641132355,
-0.024061890318989754,
0.02188650332391262,
-0.006980205420404673,
-0.017384842038154602,
0.00891126785427332,
-0.0007767838542349637,
0.009695133194327354,
-0.04526715353131294,
-0.014146631583571434,
0.049828771501779556,
0.02132605016231537,
-0.04587959125638008,
-0.06987934559583664,
0.029407629743218422,
-0.03021853044629097,
-0.02628714218735695,
0.04220493882894516,
0.00045147238415665925,
0.01810108684003353,
0.004698385018855333,
-0.009609081782400608,
0.010125369764864445,
0.043426092714071274,
0.012754864059388638,
-0.02531147003173828,
0.0087867621332407,
-0.05113935098052025,
0.008228432387113571,
-0.039253924041986465,
0.018281418830156326,
-0.028381099924445152,
0.04006349667906761,
0.03233756870031357,
-0.0022007031366229057,
-0.023500539362430573,
-0.011551831848919392,
-0.009448008611798286,
-0.0032617170363664627,
0.01323617622256279,
-0.03247428312897682,
-0.0019777745474129915,
0.026582224294543266,
-0.005421264562755823,
-0.02323058247566223,
0.047430843114852905,
0.007757409941405058,
-0.009940613061189651,
-0.07476149499416351,
-0.008262724615633488,
0.004172904416918755,
0.06522855907678604,
0.025494880974292755,
-0.08462558686733246,
-0.004208240658044815,
0.0379459522664547,
-0.07243932783603668,
0.03129483386874199,
0.002010288182646036,
-0.002942791674286127,
-0.00045605949708260596,
0.005208591464906931,
-0.0029295794665813446,
0.06076950952410698,
0.05090608820319176,
0.0802086815237999,
0.006920373998582363,
0.008587789721786976,
-0.0037778238765895367,
-0.05565211549401283,
-0.023635568097233772,
0.026012243703007698,
0.009702890180051327,
-0.010932357050478458,
0.04901041090488434,
-0.019802570343017578,
-0.01348580326884985,
0.037602704018354416,
0.014823571778833866,
0.017184851691126823,
0.009866924025118351,
-0.006169170141220093,
0.036346860229969025,
0.040083255618810654,
0.04495169594883919,
-0.005597574170678854,
0.004686709493398666,
-0.018040666356682777,
0.0058234091848134995,
0.020540887489914894,
-0.0014345323434099555,
-0.010249670594930649,
-0.005337580572813749,
-0.05461324751377106,
-0.019483651965856552,
0.021885946393013,
-0.03307918459177017,
-0.0010283993324264884,
0.0033675297163426876,
0.006135403644293547,
-0.0063430569134652615,
-0.03812577202916145,
0.01019126083701849,
-0.04873330146074295,
0.008211260661482811,
0.04851941019296646,
-0.02271401323378086,
-0.003993263002485037,
0.04144415631890297,
0.0015259130159392953,
-0.03314829617738724,
0.02361314371228218,
-0.006514957640320063,
0.009273681789636612,
-0.04059979319572449,
0.03532746806740761,
-0.019955798983573914,
0.004163844510912895,
0.016651106998324394,
0.00021956335694994777,
-0.06880281865596771,
-0.021981840953230858,
0.006343423388898373,
0.015939561650156975,
-0.019122524186968803,
-0.03318742662668228,
-0.017828093841671944,
-0.06725091487169266,
0.014046277850866318,
0.03234347701072693,
-0.01886802725493908,
-0.033267077058553696,
-0.031328435987234116,
-0.017540520057082176,
0.03886637091636658,
0.046858545392751694,
0.017830513417720795,
-0.041524771600961685,
0.03706430271267891,
0.024259615689516068,
0.007011457346379757,
-0.06267400085926056,
-0.0025745464954525232,
-0.0064326319843530655,
0.035530608147382736,
0.03304506093263626,
-0.0002886364236474037,
0.006912069860845804,
-0.0014138459227979183,
-0.016262877732515335,
0.0012825705343857408,
0.037984490394592285,
0.02480899728834629,
-0.05075429379940033,
0.030083391815423965,
-0.02570790797472,
-0.0003988445096183568,
0.07828490436077118,
0.0564284510910511,
0.033294927328825,
0.02537393942475319,
-0.048232294619083405,
-0.04480196163058281,
-0.026853440329432487,
-0.046925317496061325,
-0.010585114359855652,
-0.01913834922015667,
-0.028670968487858772,
0.05540718510746956,
-0.02258448675274849,
-0.014280213974416256,
0.06413517892360687,
0.01289890706539154,
-0.03472007066011429,
0.049643319100141525,
0.006795620545744896,
0.035664383322000504,
-0.012652781791985035,
0.009537294507026672,
0.03456423431634903,
-0.004872804041951895,
0.023883488029241562,
0.04571220278739929,
0.04641911759972572,
-0.021761290729045868,
0.013771340250968933,
0.02121672034263611,
-0.018911371007561684,
0.029172848910093307,
0.013323402963578701,
0.04494686424732208,
0.018793001770973206,
0.006234540604054928,
0.03325299173593521,
-0.01390877179801464,
-0.043738752603530884,
0.027212362736463547,
-0.018339509144425392,
0.03377610445022583,
-0.020868908613920212,
0.0406961552798748,
-0.007804820314049721,
-0.004280958790332079,
-0.021784545853734016,
0.015833469107747078,
-0.009473827667534351,
0.04569270461797714,
0.003110403660684824,
-0.02610810287296772,
-0.015006275847554207,
-0.005187103059142828,
0.007469995878636837,
-0.06244909018278122,
-0.025690600275993347,
0.05215614661574364,
0.0131635507568717,
0.012711328454315662,
0.0022693672217428684,
-0.031161759048700333,
-0.010896108113229275,
0.024460600689053535,
0.03540574014186859,
0.027866732329130173,
-0.015214016661047935,
0.014109091833233833,
-0.0094827339053154,
0.06712060421705246,
-0.04822327196598053,
0.007052457891404629,
0.022168900817632675,
0.0031932950951159,
0.004773100838065147,
-0.04283767566084862
] |
<p>there is a relation between time and space in special theory of relativity:
$$t^2c^2-L^2=\tau^2.c^2$$
what is relation between time and space in general relativity?</p>
| 8,803 |
[
0.010226580314338207,
-0.035168468952178955,
-0.011471997946500778,
-0.028607359156012535,
0.056216008961200714,
0.007495757658034563,
-0.023249976336956024,
-0.037564966827631,
-0.026744240894913673,
-0.02896617166697979,
0.022806614637374878,
0.02370193414390087,
0.039769794791936874,
0.012262964621186256,
0.010922969318926334,
-0.012316022999584675,
-0.03397408872842789,
-0.0030868540052324533,
-0.019315408542752266,
-0.02570534311234951,
0.04729805514216423,
-0.003907790407538414,
-0.004961960017681122,
-0.0025070123374462128,
-0.0425855778157711,
0.04468417540192604,
0.035790424793958664,
0.003456008853390813,
0.003362964605912566,
0.0691526010632515,
-0.013972600921988487,
-0.02441425807774067,
0.00923300813883543,
0.02268051914870739,
0.008572469465434551,
-0.04202510043978691,
-0.032291870564222336,
-0.03770430013537407,
0.02899046055972576,
0.0049046180211007595,
-0.06129471957683563,
-0.052375469356775284,
-0.015255840495228767,
0.07116920500993729,
-0.0038646480534225702,
0.02917051687836647,
-0.013464082963764668,
-0.011763748712837696,
0.036368876695632935,
-0.05339707434177399,
0.05241462215781212,
-0.01788799837231636,
0.021451525390148163,
-0.039576031267642975,
-0.014519010670483112,
0.025043847039341927,
0.07856059819459915,
0.046811141073703766,
0.011901091784238815,
-0.03645175322890282,
0.0011479504173621535,
0.0036392088513821363,
0.049581129103899,
-0.0026620374992489815,
-0.005900202319025993,
0.031911302357912064,
-0.05588535964488983,
0.002841107314452529,
-0.002207414945587516,
-0.0231059268116951,
-0.029728077352046967,
0.024524599313735962,
0.02333325333893299,
-0.00924687273800373,
0.002427845261991024,
-0.033831387758255005,
0.006885118316859007,
0.014772419817745686,
0.0636259987950325,
0.035988129675388336,
0.026040710508823395,
0.011993925087153912,
0.038413748145103455,
0.0033476408571004868,
0.009188096038997173,
0.009114416316151619,
0.05636075511574745,
-0.004170238971710205,
-0.004106779117137194,
0.01869906298816204,
-0.005020949058234692,
0.01587345078587532,
0.012941813096404076,
-0.011440384201705456,
-0.01584867388010025,
0.030631590634584427,
0.0003658281348180026,
0.0023013867903500795,
0.01928316429257393,
-0.01683235354721546,
0.0016941786743700504,
-0.021241171285510063,
0.01140952855348587,
0.06337092816829681,
0.026365645229816437,
-0.015281319618225098,
-0.03355276957154274,
0.003992417361587286,
-0.014806544408202171,
0.0014521307311952114,
-0.03424401581287384,
-0.0015148901147767901,
-0.01299461629241705,
0.017023108899593353,
0.008451449684798717,
-0.0290481336414814,
0.02620088681578636,
-0.008446965366601944,
0.054912764579057693,
0.08012820035219193,
0.03350444138050079,
-0.033710770308971405,
0.027179937809705734,
0.0033340458758175373,
-0.07320510596036911,
0.013840845786035061,
0.05544297769665718,
-0.04885231330990791,
-0.023646868765354156,
0.009253921918570995,
-0.002596238860860467,
-0.036366261541843414,
0.013454028405249119,
0.015313787385821342,
0.051776595413684845,
0.0028610320296138525,
-0.1055159717798233,
-0.038764603435993195,
0.04825334995985031,
-0.006763131823390722,
-0.01686422899365425,
-0.06281234323978424,
0.04413033649325371,
-0.0203421451151371,
0.06862261146306992,
0.04532618448138237,
0.001254136092029512,
0.019726216793060303,
0.02200132980942726,
-0.014038404449820518,
-0.037094246596097946,
0.02583598718047142,
0.02409244328737259,
-0.03209191560745239,
0.035481005907058716,
-0.07312101870775223,
-0.013660076074302197,
0.04290922358632088,
0.008537747897207737,
-0.02443951740860939,
0.08867477625608444,
-0.0442904494702816,
-0.0030544218607246876,
0.04978877678513527,
0.013155180960893631,
-0.029108555987477303,
0.07673439383506775,
0.030321704223752022,
0.009014072827994823,
0.04623831436038017,
0.006307362578809261,
0.023797031491994858,
0.03597274050116539,
0.03263647481799126,
0.025708196684718132,
-0.026999006047844887,
-0.04400934278964996,
0.048733189702034,
-0.03422245383262634,
0.0012695200275629759,
-0.05782857909798622,
-0.017403965815901756,
-0.014645633287727833,
0.01759975031018257,
-0.006861645262688398,
0.05679543316364288,
-0.013828601688146591,
0.028791237622499466,
-0.01714172028005123,
-0.030943159013986588,
0.017848743125796318,
-0.07461380958557129,
-0.016590433195233345,
-0.004589966963976622,
-0.0032843872904777527,
0.003723638830706477,
0.0016454034484922886,
0.029593363404273987,
-0.021070308983325958,
-0.027678173035383224,
-0.020487653091549873,
0.045867759734392166,
-0.013941816985607147,
-0.007641164120286703,
0.0285326074808836,
0.04257006198167801,
0.05259868502616882,
-0.010664914734661579,
-0.008473649621009827,
0.004430335946381092,
-0.017521915957331657,
0.030788222327828407,
0.01587493345141411,
0.030260233208537102,
-0.020903917029500008,
0.00041071567102335393,
0.00817381963133812,
0.009683621115982533,
-0.010914170183241367,
0.05389929935336113,
-0.014385971240699291,
0.05093039944767952,
0.06887897849082947,
0.011744832620024681,
0.03137081861495972,
0.048571184277534485,
0.008717638440430164,
0.01815403439104557,
0.020549742504954338,
-0.04116714000701904,
-0.019416961818933487,
-0.017102351412177086,
0.031057076528668404,
0.04899652302265167,
-0.0266153234988451,
0.013288061134517193,
-0.0020263404585421085,
0.03610299900174141,
-0.0011849735165014863,
0.019330816343426704,
-0.019222136586904526,
-0.055943358689546585,
0.002188832964748144,
-0.014064938761293888,
0.03915213793516159,
0.013264513574540615,
-0.0024562906473875046,
0.023317446932196617,
0.013907080516219139,
-0.022517383098602295,
-0.015330273658037186,
0.04805280640721321,
-0.03212488442659378,
-0.0044461400248110294,
0.051387932151556015,
-0.033465947955846786,
0.03946539759635925,
-0.024890217930078506,
-0.00015600128972437233,
0.015495753847062588,
-0.0013788084033876657,
0.012055576778948307,
-0.029971951618790627,
-0.014466188848018646,
0.010672585107386112,
-0.013918746262788773,
-0.0042163049802184105,
-0.020616058260202408,
0.029516596347093582,
-0.029971901327371597,
0.008866636082530022,
0.010447394102811813,
-0.034934695810079575,
-0.022487258538603783,
0.0077378395944833755,
0.0385197214782238,
-0.009528016671538353,
0.025820275768637657,
0.011806584894657135,
-0.05200463905930519,
0.01266558188945055,
-0.011156630702316761,
-0.021499913185834885,
0.008517645299434662,
-0.044698283076286316,
0.06727758049964905,
-0.01966167241334915,
-0.027921045199036598,
0.015409338288009167,
-0.015642037615180016,
0.05274463817477226,
0.02938719093799591,
-0.01957828737795353,
-0.04867708310484886,
-0.04884658381342888,
-0.03844394534826279,
0.005056212190538645,
-0.031075235456228256,
0.017312441021203995,
0.04893221706151962,
0.0010131321614608169,
-0.057290218770504,
-0.0034180006477981806,
-0.02959943562746048,
-0.04637666419148445,
-0.04810976982116699,
0.0038636871613562107,
0.025020474568009377,
-0.05991192162036896,
0.017554033547639847,
0.032495807856321335,
-0.06203317642211914,
-0.007161449640989304,
-0.04527871683239937,
-0.0032870210707187653,
0.05872707441449165,
0.01954510621726513,
0.03602302074432373,
-0.024308668449521065,
-0.0317341610789299,
0.06027113273739815,
0.017736198380589485,
0.006507143843919039,
-0.03888733312487602,
-0.015588141977787018,
-0.009465089999139309,
-0.024574944749474525,
0.006291673053056002,
0.01132411602884531,
-0.002736755646765232,
-0.007428679149597883,
0.0398225262761116,
0.042963821440935135,
0.018191104754805565,
0.021351078525185585,
-0.010409965179860592,
-0.029999257996678352,
0.008227014914155006,
0.007894786074757576,
0.01940036751329899,
-0.009629764594137669,
-0.023339953273534775,
0.010763716883957386,
0.016398373991250992,
0.04772478714585304,
0.012819318100810051,
-0.05748001113533974,
0.032604433596134186,
-0.027765661478042603,
0.004621194675564766,
-0.015401454642415047,
0.040561120957136154,
-0.009660663083195686,
0.012462224811315536,
0.033457688987255096,
0.0038431009743362665,
0.029807424172759056,
0.009136326611042023,
-0.006174657493829727,
0.02556470036506653,
0.04419960081577301,
-0.03693768382072449,
-0.040857650339603424,
-0.02077130414545536,
-0.0020210398361086845,
0.06258781254291534,
-0.05129485949873924,
0.007617360446602106,
0.03600991517305374,
0.0680931955575943,
0.002065781271085143,
0.018348289653658867,
-0.038513146340847015,
-0.004586841445416212,
-0.0901193842291832,
-0.01639886386692524,
0.009229373186826706,
0.0341351144015789,
0.007545804604887962,
0.025685150176286697,
0.03563343361020088,
-0.016457291319966316,
0.06177639961242676,
-0.021790552884340286,
-0.07715169340372086,
0.0003529774257913232,
-0.04388149455189705,
-0.0057455324567854404,
0.011219124309718609,
0.003658855566754937,
-0.006183823570609093,
-0.01595538668334484,
-0.011281130835413933,
-0.02476959116756916,
-0.015299202874302864,
-0.0822710245847702,
0.027906417846679688,
-0.03606386482715607,
-0.030123639851808548,
-0.02892903983592987,
0.027580128982663155,
0.046468622982501984,
0.007953890599310398,
0.0062496173195540905,
0.08069497346878052,
-0.021403122693300247,
0.009791633114218712,
0.011704494245350361,
-0.015632255002856255,
0.03990091010928154,
0.015228879638016224,
0.04057282581925392,
-0.0011337799951434135,
-0.025951461866497993,
0.005725590046495199,
-0.0014776911120861769,
0.01955660618841648,
0.0225229412317276,
-0.028231285512447357,
-0.0501508004963398,
-0.0584576241672039,
-0.018744533881545067,
-0.022403892129659653,
0.05364653468132019,
0.002755091292783618,
-0.011282461695373058,
0.032417766749858856,
-0.0020949854515492916,
0.01421278901398182,
0.030197670683264732,
0.031985264271497726,
-0.004460840951651335,
-0.034509044140577316,
-0.029248084872961044,
-0.04569683596491814,
-0.03621726483106613,
-0.029232680797576904,
0.04075288400053978,
-0.015615555457770824,
-0.047239746898412704,
-0.004460056312382221,
0.010440378449857235,
0.001223237020894885,
-0.028689701110124588,
-0.04869019612669945,
0.026953397318720818,
-0.00021588467643596232,
0.02920994721353054,
-0.010559825226664543,
-0.009461985900998116,
0.03050401248037815,
0.04398619011044502,
-0.001632055500522256,
-0.0029585359152406454,
-0.07122016698122025,
-0.008763588964939117,
0.01325843296945095,
0.0034387391060590744,
-0.0009769635507836938,
-0.02493227832019329,
-0.05131414160132408,
-0.001679504057392478,
0.018462302163243294,
-0.03316116705536842,
0.027928246185183525,
-0.022110821679234505,
-0.0008385586552321911,
-0.025291334837675095,
-0.02410595491528511,
0.019083796069025993,
0.06288249045610428,
0.004407299216836691,
-0.006029471755027771,
-0.03949173539876938,
0.02989225834608078,
-0.017514653503894806,
-0.0037973481230437756,
0.017209699377417564,
0.009914631024003029,
0.04984814673662186,
0.03384193405508995,
-0.0032220978755503893,
0.04701592028141022,
-0.04903070628643036,
-0.07805982232093811,
-0.008645029738545418,
0.04646600782871246,
-0.026004837825894356,
0.01481744647026062,
-0.047227200120687485,
-0.019550183787941933,
0.0265657901763916,
0.01654471643269062,
-0.01922626607120037,
-0.004834232851862907,
-0.04850202798843384,
-0.0009981264593079686,
0.01498500443994999,
-0.009262067265808582,
0.03931327909231186,
-0.012190792709589005,
-0.0008170580258592963,
-0.018668698146939278,
-0.005558658856898546,
0.04880848899483681,
-0.02970263361930847,
0.005307741463184357,
0.0048184748739004135,
-0.023966079577803612,
-0.045981816947460175,
0.039987895637750626,
-0.04648192971944809,
-0.001464313012547791,
0.006335515528917313,
-0.0037035406567156315,
-0.04147007316350937,
0.04251748323440552,
0.029958248138427734,
0.003615542082116008,
-0.01501765102148056,
0.004165742080658674,
0.025517569854855537,
-0.025515219196677208,
0.0005768077680841088,
-0.0020344657823443413,
-0.014611070044338703,
0.008793353103101254,
0.023214301094412804,
0.021442221477627754,
-0.0008477108203805983,
-0.015770098194479942,
0.00523556862026453,
-0.025698643177747726,
0.025616826489567757,
-0.01278193760663271,
-0.03907255828380585,
0.03745820000767708,
-0.03773213550448418,
-0.028845611959695816,
0.027919070795178413,
-0.01553866546601057,
0.025791382417082787,
-0.05978282913565636,
0.029793675988912582,
0.03799682855606079,
-0.005433815997093916,
-0.10323632508516312,
-0.041791725903749466,
0.015482029877603054,
0.009689688682556152,
-0.010908341966569424,
-0.046512454748153687,
0.004986973013728857,
-0.06672969460487366,
-0.02880910597741604,
-0.006284553557634354,
0.09848135709762573,
-0.014795771799981594,
-0.05079702287912369,
-0.04192529618740082,
0.003292936598882079,
0.0320911779999733,
-0.009461811743676662,
0.00635707750916481,
-0.03196606785058975,
0.012488176114857197,
0.016039351001381874,
-0.021746771410107613,
0.07423631846904755,
-0.015957096591591835,
-0.013863024301826954,
-0.04233798757195473,
-0.008341246284544468,
-0.006142823491245508,
-0.017732327803969383,
0.011378556489944458,
0.04486377164721489,
0.035420987755060196,
-0.029606744647026062,
-0.03365367650985718,
0.020552372559905052,
0.0040716687217354774,
0.04295181483030319,
-0.021970028057694435,
-0.005078070797026157,
-0.020464861765503883,
-0.025817107409238815,
0.036858342587947845,
-0.010799636133015156,
-0.014936813153326511,
-0.022097647190093994,
0.03973279148340225,
-0.0145669961348176,
-0.0005360727082006633,
0.0031540615018457174,
0.0008472962654195726,
-0.0018495535477995872,
0.006106780841946602,
-0.006578600965440273,
0.04700847342610359,
0.006368717644363642,
-0.03007565066218376,
0.0019578200299292803,
-0.010229380801320076,
-0.030275549739599228,
0.07095927000045776,
-0.037822552025318146,
0.049177564680576324,
0.04379364475607872,
-0.026025686413049698,
0.00008633465768070891,
-0.02078551985323429,
-0.0011276720324531198,
0.0032760570757091045,
0.0051801265217363834,
0.04117080569267273,
-0.028833668678998947,
-0.014919302426278591,
0.05086279660463333,
0.030658023431897163,
-0.02446337230503559,
0.004003250040113926,
0.019558226689696312,
-0.004864107351750135,
0.0009579742909409106,
-0.005594517104327679,
-0.04299122840166092,
0.041197262704372406,
-0.0051373871974647045,
0.028561262413859367,
0.0016323861200362444,
0.012179607525467873,
0.024179430678486824,
0.009955990128219128,
0.011364198289811611,
-0.02573969028890133,
-0.02076851949095726,
-0.06135430559515953,
0.0016930215060710907,
0.031110350042581558,
0.003923289477825165,
0.0057799541391432285,
0.030274085700511932,
0.031582411378622055,
-0.015758931636810303,
0.013564666733145714,
0.0291046854108572,
-0.06272275000810623,
-0.008736646734178066,
-0.04851650819182396,
-0.0353337861597538,
0.045238181948661804,
-0.010256924666464329,
-0.038874492049217224,
-0.02640252560377121,
-0.019131477922201157,
-0.007668722420930862,
0.019443267956376076,
0.042410798370838165,
-0.042984191328287125,
0.07220887392759323,
0.006552534177899361,
0.008458391763269901,
-0.008124389685690403,
0.016552086919546127,
0.11041291803121567,
0.031048333272337914,
-0.011677886359393597,
-0.07138755172491074,
0.02850601077079773,
-0.010684569366276264,
-0.0063861338421702385,
-0.063054159283638,
0.03779926151037216,
-0.00893857330083847,
0.00885301548987627,
0.021530570462346077,
0.051388371735811234,
0.015059585683047771,
-0.03950490802526474,
0.047297123819589615,
-0.035975247621536255,
-0.03491276502609253,
-0.01894785836338997,
0.03146940842270851,
-0.003876760834828019,
0.021355943754315376,
-0.0212404765188694,
0.03644765540957451,
-0.03379041701555252,
0.06428692489862442,
-0.0480823777616024,
-0.046531450003385544,
0.02270832471549511,
-0.014735533855855465,
-0.07345657050609589,
0.004346455913037062,
0.025533482432365417,
-0.005395557731389999,
-0.061849694699048996,
0.022367801517248154,
-0.007797342259436846,
0.013465394265949726,
-0.007474193815141916,
0.01379486359655857,
-0.004063155502080917,
0.025506779551506042,
-0.0140629718080163,
-0.0061379787512123585,
-0.05506947636604309,
0.008168539963662624,
-0.023497015237808228,
0.037378136068582535,
-0.02816561795771122,
0.026938261464238167,
0.021007975563406944,
0.01682475581765175,
0.015164037235081196,
-0.027894072234630585,
-0.012100908905267715,
0.015328810550272465,
0.04609144851565361,
-0.011511907912790775,
0.002907451940700412,
-0.04841560497879982,
0.029787234961986542,
-0.015772609040141106,
0.025159383192658424,
-0.00913170911371708,
0.002793397754430771,
0.05089716613292694,
-0.004929906222969294,
0.011034748516976833,
-0.05094986781477928,
-0.0022965669631958008,
-0.0239721592515707,
-0.004331481177359819,
-0.018291955813765526,
0.008253817446529865,
0.029393086209893227,
0.047397103160619736,
0.011645948514342308,
-0.009684678167104721,
-0.010804859921336174,
-0.007907331921160221,
-0.07679887115955353,
0.038996368646621704,
-0.024186179041862488,
-0.016398916020989418,
-0.008826402947306633,
0.013466660864651203,
0.04721726104617119,
0.055349308997392654,
-0.0370919331908226,
0.01136571541428566,
-0.035759586840867996,
0.01023941021412611,
0.013231835328042507,
0.002211695071309805,
0.02360396459698677,
0.005616324953734875,
0.0013377584982663393,
0.0028119683265686035,
-0.02616536244750023,
0.019411450251936913,
0.0644959807395935,
0.017746509984135628,
-0.0020144109148532152,
0.03438485786318779,
-0.021440589800477028,
-0.006322486326098442,
0.030528418719768524,
-0.028881294652819633,
0.023448139429092407,
0.008455634117126465,
0.03590213507413864,
-0.038663677871227264,
0.0012300243834033608,
0.001401933142915368,
-0.005350782070308924,
0.013706440106034279,
0.0028499651234596968,
-0.002577674575150013,
0.02922115847468376,
-0.005435926374047995,
0.01929820142686367,
-0.07118701189756393,
0.01381695456802845,
-0.06280553340911865,
0.05253300443291664,
-0.0024079550057649612,
-0.0571013018488884,
0.0020600941497832537,
0.029993778094649315,
-0.0039372751489281654,
0.003205730812624097,
0.01549583300948143,
0.009239770472049713,
-0.03563808277249336,
-0.0074426885694265366,
0.0319385901093483,
-0.02478286810219288,
0.04911940544843674,
0.009734068065881729,
-0.008591611869633198,
0.008742662146687508,
-0.035115040838718414,
-0.0377933494746685,
0.05907341092824936,
-0.008281276561319828,
0.022500919178128242,
0.024123044684529305,
-0.017070164903998375,
0.010443734005093575,
0.09172346442937851,
-0.04348139464855194,
0.003247881541028619,
0.014581034891307354,
-0.03324879705905914,
0.007570871151983738,
-0.024629797786474228,
0.05355245620012283,
-0.009428009390830994,
-0.024384932592511177,
-0.00036376513889990747,
0.029998190701007843,
-0.00901790615171194,
0.019806664437055588,
0.00001646880991756916,
-0.027684064581990242,
0.014391633681952953,
0.014116693288087845,
-0.025213196873664856,
0.037408627569675446,
0.04445771500468254,
-0.00989086925983429,
0.015888363122940063,
0.0501866415143013,
0.010320295579731464,
-0.09491440653800964,
0.0033050968777388334,
0.042738936841487885,
0.011658811941742897,
0.0586894229054451,
-0.012412002310156822,
0.024017779156565666,
0.03705816715955734,
-0.03711298853158951,
0.047317422926425934,
-0.017126474529504776,
-0.01878412812948227,
0.010869420133531094,
-0.01647467166185379,
-0.02228904515504837,
0.0619950108230114,
0.05572015792131424,
0.02522614784538746,
0.004637264180928469,
0.026932088658213615,
-0.008967301808297634,
-0.023746110498905182,
-0.0346895195543766,
0.004970346111804247,
-0.0087890001013875,
-0.0032708565704524517,
0.05499669909477234,
0.010241633281111717,
-0.007753673940896988,
0.0019503383664414287,
0.018564486876130104,
0.020099807530641556,
-0.000858701765537262,
0.014983169734477997,
0.0024037554394453764,
0.01767391711473465,
0.007580653298646212,
-0.028959989547729492,
-0.024427063763141632,
0.02918812818825245,
0.0023505890276283026,
-0.002783239120617509,
-0.016342930495738983,
-0.0009316024952568114,
-0.016076015308499336,
-0.05432301387190819,
-0.014072359539568424,
0.033334024250507355,
-0.015719087794423103,
-0.04578410089015961,
-0.009875829331576824,
0.009961641393601894,
-0.004384322091937065,
-0.04359937086701393,
-0.019013719633221626,
-0.02512996271252632,
-0.015350757166743279,
0.028185652568936348,
-0.010747813619673252,
-0.013305850327014923,
-0.006046731024980545,
-0.007195168640464544,
-0.03153533861041069,
0.0009194253361783922,
0.01771065592765808,
0.008144443854689598,
-0.03642364218831062,
-0.016792085021734238,
0.0067167687229812145,
-0.002930073067545891,
0.005470394156873226,
-0.03878629952669144,
-0.015439054928719997,
0.04656263068318367,
0.04329502955079079,
0.01101349014788866,
-0.013695609755814075,
0.012957464903593063,
0.006570128723978996,
-0.04866321384906769,
0.011506732553243637,
-0.013709228485822678,
-0.015090744011104107,
-0.05973176285624504,
0.01189504936337471,
-0.025388380512595177,
0.022895576432347298,
0.05593445524573326,
0.008568629622459412,
-0.004910659976303577,
0.007058229297399521,
0.017646877095103264,
0.013989767991006374,
-0.021917147561907768,
-0.028681863099336624,
0.009902695193886757,
-0.04808295518159866,
0.00485076243057847,
-0.024065567180514336,
-0.01862550899386406,
0.0149652985855937,
0.011860807426273823,
-0.03553112596273422,
0.06197715178132057,
0.010350524447858334,
-0.024317491799592972,
0.05338501185178757,
0.03973499312996864,
-0.026106087490916252,
0.06809988617897034,
-0.011971193365752697,
0.017268169671297073,
0.03926566615700722,
-0.027139771729707718,
-0.004665127489715815,
0.003287100698798895,
-0.05429937317967415,
-0.009373628534376621,
-0.02511841058731079,
-0.018566548824310303,
0.014261843636631966,
-0.04108276590704918,
-0.02375836670398712,
0.07248128950595856,
-0.03305358812212944,
0.009186016395688057,
0.04762312024831772,
0.008180910721421242,
0.01799371838569641,
-0.013923175632953644,
-0.00027893722290173173,
0.030017534270882607,
0.03250111639499664,
0.014155477285385132,
0.012002222239971161,
0.01802857778966427,
-0.021301250904798508,
-0.023587750270962715,
0.016779156401753426,
0.008057779632508755,
0.003749741706997156,
0.008616320788860321,
0.05066128075122833,
-0.02588523179292679,
0.014120783656835556,
0.004268405959010124,
-0.0033769879955798388,
0.046698201447725296,
0.02082280069589615,
-0.021054498851299286,
0.08066452294588089,
-0.060945119708776474,
0.014272754080593586,
-0.03156013786792755,
-0.022555368021130562,
-0.05769358202815056,
0.0232390146702528,
0.029345901682972908,
0.026206402108073235,
0.011186833493411541,
0.007833125069737434,
-0.014544639736413956,
-0.02189922332763672,
0.049274906516075134,
-0.03294255957007408,
0.0117232296615839,
-0.00001847896237450186,
-0.014626868069171906,
-0.011784883216023445,
-0.039675671607255936,
-0.03154964745044708,
-0.044118382036685944,
0.030426139011979103,
0.023171208798885345,
0.0575949028134346,
-0.03654582053422928,
0.0002523039875086397,
-0.017217958346009254,
0.04910627007484436,
-0.08618472516536713,
-0.02133488655090332,
-0.02264164574444294,
0.016087869182229042,
-0.043855465948581696,
-0.021066399291157722
] |
<p>If there were a particle in a box, how could one measure its energy?</p>
<p>I understand the theory behind quantum measurements: the Hamiltonian operator represents the energy observable, so you perform an "energy measurement" that returns an eigenvalue of the operator, and that eigenvalue is the energy. But how would you actually physically do this?</p>
| 8,804 |
[
-0.02996484376490116,
-0.025890931487083435,
0.021556733176112175,
-0.057644207030534744,
0.03246275708079338,
0.019452659413218498,
-0.024596404284238815,
-0.022950557991862297,
0.015350454486906528,
0.01363502535969019,
0.044202595949172974,
0.044081300497055054,
0.01583639346063137,
0.0008027305593714118,
0.009648247621953487,
0.009745076298713684,
-0.019745223224163055,
-0.023336315527558327,
-0.026986442506313324,
-0.06079046055674553,
0.00821367185562849,
0.00576762342825532,
0.0061104195192456245,
0.0023030180018395185,
-0.0019093480659648776,
0.032127294689416885,
0.032217152416706085,
-0.01613094098865986,
0.046293921768665314,
0.05867647007107735,
0.00968948658555746,
-0.03923787176609039,
0.01897634193301201,
0.005282077472656965,
0.02582002803683281,
-0.030400050804018974,
-0.034533701837062836,
-0.03463555872440338,
-0.016247224062681198,
0.032664328813552856,
-0.024575261399149895,
-0.019613174721598625,
0.008923834189772606,
0.0377371646463871,
-0.020177962258458138,
0.0024490102659910917,
0.0016910923877730966,
-0.03250352293252945,
0.03859034553170204,
-0.055002592504024506,
0.06283991038799286,
0.015656741335988045,
0.034015875309705734,
0.02982877939939499,
-0.021167682483792305,
-0.00030308967689052224,
0.08174794912338257,
0.07795050740242004,
-0.007227365858852863,
-0.05523255839943886,
-0.04883969575166702,
-0.01179516315460205,
-0.007218659855425358,
-0.05149191990494728,
-0.011970428749918938,
0.007615165319293737,
-0.010975641198456287,
-0.041174184530973434,
0.016922244802117348,
-0.02043902315199375,
0.0007311812951229513,
0.0233071930706501,
0.04001918062567711,
-0.018528368324041367,
-0.00007925702084321529,
-0.02977903001010418,
0.021111344918608665,
0.051067233085632324,
0.07968097925186157,
0.02571636624634266,
-0.01636418141424656,
-0.016602102667093277,
0.029990041628479958,
0.06841184943914413,
0.006629396229982376,
-0.012799226678907871,
0.0472620353102684,
-0.0009143241913989186,
-0.017082424834370613,
0.04954207316040993,
0.003226565197110176,
0.02679302543401718,
0.026636634021997452,
-0.017746273428201675,
-0.02981868013739586,
0.020123904570937157,
-0.0010873549617826939,
0.06653139740228653,
-0.013122374191880226,
-0.03410777077078819,
0.048434238880872726,
0.006145946681499481,
0.025107022374868393,
0.06943965703248978,
-0.02767680399119854,
-0.02648729644715786,
-0.00956769473850727,
0.03165947273373604,
0.028521336615085602,
0.01320081576704979,
-0.025506505742669106,
0.0011623541358858347,
0.016685444861650467,
0.023136764764785767,
0.05194243788719177,
-0.0004953977768309414,
-0.011324724182486534,
-0.04079854488372803,
0.05399976670742035,
0.028027169406414032,
0.010680022649466991,
-0.02269730716943741,
-0.013058217242360115,
-0.04910227656364441,
-0.04417780414223671,
0.01687106303870678,
0.035533130168914795,
-0.0009468937641941011,
-0.03576422110199928,
-0.001803945517167449,
0.0017697466537356377,
-0.024615870788693428,
0.011588480323553085,
-0.02355014719069004,
0.0277878325432539,
-0.0024210673291236162,
-0.11352041363716125,
-0.05372711271047592,
0.03976084664463997,
-0.02019662596285343,
-0.07521238923072815,
-0.06957241147756577,
-0.02450333535671234,
0.03032861463725567,
0.05154645815491676,
0.007981408387422562,
-0.009754011407494545,
0.019552651792764664,
0.00011226540664210916,
0.017824634909629822,
-0.014525480568408966,
-0.02481764554977417,
-0.019950393587350845,
-0.0262107215821743,
0.03502602502703667,
-0.004556403495371342,
-0.010227693244814873,
0.015625569969415665,
-0.039665110409259796,
-0.007167060859501362,
0.045288391411304474,
-0.03544168546795845,
-0.025263052433729172,
0.03436490148305893,
-0.0228069256991148,
-0.04409339651465416,
0.06747892498970032,
0.01519425492733717,
-0.004135638941079378,
0.008394364267587662,
0.011589482426643372,
0.024248316884040833,
0.026389341801404953,
-0.006311772856861353,
0.045070502907037735,
-0.023924244567751884,
-0.059054333716630936,
-0.030155226588249207,
0.025602519512176514,
-0.008060582913458347,
-0.060173045843839645,
-0.05229753255844116,
0.05379517376422882,
0.01014233659952879,
0.012349565513432026,
0.019924867898225784,
-0.013722224161028862,
-0.016234159469604492,
-0.004563816823065281,
-0.04135332256555557,
0.0032721979077905416,
-0.07900001853704453,
0.05853567272424698,
0.013390317559242249,
0.0020748237147927284,
0.023878930136561394,
0.027201149612665176,
0.007480429019778967,
-0.04211641475558281,
-0.03542459011077881,
0.013256940059363842,
0.042691998183727264,
-0.0009004347957670689,
-0.03986603766679764,
0.0006322611006908119,
0.04436749964952469,
0.050934311002492905,
0.018978387117385864,
0.02686179056763649,
-0.007998536340892315,
-0.05334589630365372,
-0.013430280610918999,
-0.030902205035090446,
-0.009539088234305382,
0.013401650823652744,
-0.014618019573390484,
0.003992901649326086,
-0.03747057914733887,
-0.020896878093481064,
0.021985329687595367,
0.014743467792868614,
0.05806082859635353,
0.023248400539159775,
-0.002905429108068347,
-0.009851371869444847,
0.02857460454106331,
-0.013080017641186714,
0.027855711057782173,
0.018215689808130264,
-0.023424681276082993,
-0.06309281289577484,
-0.022640973329544067,
0.02026178501546383,
0.021525684744119644,
-0.0373036153614521,
0.02046617679297924,
0.02767319791018963,
0.01278576161712408,
-0.00704423151910305,
0.008150989189743996,
-0.012973448261618614,
0.014107606373727322,
0.0046743289567530155,
0.03617769852280617,
0.001882938900962472,
0.0166811291128397,
0.02411073073744774,
0.034133341163396835,
-0.0018387110903859138,
0.011171531863510609,
0.00025477283634245396,
0.0343831405043602,
-0.02795214019715786,
0.023373287171125412,
0.0122364591807127,
-0.04082111269235611,
-0.007698533125221729,
-0.024651894345879555,
0.02682853303849697,
-0.0013716977555304766,
-0.023275570943951607,
-0.0017463380936533213,
-0.017141345888376236,
-0.032332129776477814,
0.007843787781894207,
0.029562175273895264,
-0.0415702685713768,
-0.00018283924146089703,
0.03257601708173752,
-0.011495612561702728,
0.046508464962244034,
-0.009686514735221863,
0.0094620231539011,
-0.011120917275547981,
0.021142587065696716,
0.027578219771385193,
-0.01974925398826599,
0.02482421323657036,
-0.03153038024902344,
-0.056279681622982025,
0.004201028496026993,
-0.07433751970529556,
0.007087792735546827,
0.016404513269662857,
-0.059985797852277756,
0.0139492591843009,
-0.07214058190584183,
-0.014149464666843414,
0.006689027417451143,
-0.013674854300916195,
0.02000424638390541,
0.05269651859998703,
0.010051297023892403,
-0.05976855754852295,
0.0116654047742486,
0.030908746644854546,
-0.011694040149450302,
-0.012688415125012398,
0.02051091007888317,
0.035378023982048035,
-0.04109395667910576,
-0.028787536546587944,
0.01803029701113701,
-0.012393629178404808,
-0.033719804137945175,
-0.011984264478087425,
-0.046618249267339706,
0.029156610369682312,
-0.01213458739221096,
0.04193558543920517,
0.030066676437854767,
-0.04738396033644676,
0.0044093867763876915,
-0.058684658259153366,
-0.050240349024534225,
0.013275707140564919,
0.018424492329359055,
0.030147096142172813,
-0.0044402857311069965,
0.012101571075618267,
0.0833243653178215,
0.004521098919212818,
-0.04296348989009857,
0.00327439047396183,
-0.00462347874417901,
-0.00004704781895270571,
-0.02973029762506485,
-0.010374906472861767,
0.01723695918917656,
0.002983376383781433,
0.014143448323011398,
0.0038117351941764355,
-0.002579091116786003,
0.014755036681890488,
0.027994049713015556,
-0.02937711589038372,
-0.01980954222381115,
0.005522210616618395,
0.01995757222175598,
0.04767439886927605,
-0.0004114386683795601,
-0.04014260321855545,
0.00869808904826641,
0.008525862358510494,
0.009879863820970058,
0.017550265416502953,
-0.05040707439184189,
0.04916120693087578,
0.001349231111817062,
0.008068123832345009,
-0.02037527784705162,
0.023408886045217514,
-0.0028186864219605923,
-0.00239113112911582,
0.015369142405688763,
0.030704403296113014,
0.05480961874127388,
0.02887786366045475,
0.001302504912018776,
0.047834914177656174,
0.024181166663765907,
-0.013836017809808254,
-0.035994693636894226,
0.013101881369948387,
0.015017169527709484,
-0.0005076429806649685,
0.002462791046127677,
-0.05985059216618538,
0.03018934838473797,
0.028637384995818138,
0.06282199919223785,
-0.010070680640637875,
-0.022707931697368622,
-0.027099166065454483,
-0.028145089745521545,
-0.0287166740745306,
0.020160727202892303,
0.04985813423991203,
0.01061319001019001,
0.06722932308912277,
0.026556149125099182,
-0.00984642282128334,
0.04143776744604111,
-0.03048192895948887,
-0.06097990646958351,
0.004845763090997934,
-0.045878101140260696,
-0.004524609539657831,
-0.01004208717495203,
0.006184769794344902,
0.013606211170554161,
-0.05903398245573044,
-0.012034288607537746,
-0.018721217289566994,
0.003259139135479927,
-0.03416178375482559,
-0.002948222914710641,
-0.015248236246407032,
-0.028831928968429565,
-0.003216190729290247,
0.019801011309027672,
0.04682423919439316,
-0.014093843288719654,
-0.015328027307987213,
0.04056302458047867,
-0.029541505500674248,
0.008523899130523205,
-0.0013670274056494236,
-0.01631024293601513,
0.015034724026918411,
0.052928242832422256,
0.01761205494403839,
0.04115767404437065,
0.00016984602552838624,
0.013619397766888142,
0.018693437799811363,
0.05574794113636017,
-0.009564874693751335,
-0.039424095302820206,
-0.0038726688362658024,
-0.011993171647191048,
0.02518596313893795,
-0.007026434410363436,
0.06152411922812462,
-0.04221812263131142,
0.020540772005915642,
0.007909960113465786,
0.04557625204324722,
-0.03207661584019661,
0.04615182802081108,
0.04536304250359535,
0.014484632760286331,
-0.04247980937361717,
-0.05238320678472519,
0.0038680860307067633,
-0.04102829098701477,
-0.02547251060605049,
-0.013021762482821941,
-0.03309008479118347,
-0.007997374050319195,
0.02576056495308876,
0.024370944127440453,
-0.0032158938702195883,
-0.02358383499085903,
-0.009093782864511013,
-0.015351012349128723,
0.01707093045115471,
-0.021750178188085556,
-0.010953639633953571,
-0.00009636321192374453,
0.04182033613324165,
0.028797483071684837,
-0.008823833428323269,
-0.0012226587859913707,
-0.07482476532459259,
-0.0015362396370619535,
0.027039168402552605,
0.01015464123338461,
0.011750798672437668,
-0.009263924323022366,
-0.02310306765139103,
-0.025753291323781013,
0.07238795608282089,
-0.006093947682529688,
0.023349100723862648,
-0.02357522025704384,
-0.009331944398581982,
-0.042031724005937576,
0.0005532917566597462,
-0.004287233110517263,
0.030166832730174065,
0.009031453169882298,
-0.018218016251921654,
-0.023354627192020416,
-0.02138753980398178,
-0.030662694945931435,
0.04490569233894348,
0.023111015558242798,
0.06808803230524063,
-0.004180321469902992,
0.0240996852517128,
-0.0012307999422773719,
0.002784362528473139,
-0.014347923919558525,
-0.06339406967163086,
-0.012733000330626965,
0.010916869156062603,
-0.014573595486581326,
0.04218941554427147,
-0.024819117039442062,
-0.07061942666769028,
0.0050083608366549015,
-0.030369697138667107,
-0.005739927291870117,
0.0074340542778372765,
-0.06906474381685257,
0.06313546746969223,
0.020269647240638733,
0.023767564445734024,
0.039865944534540176,
0.025376196950674057,
-0.024145595729351044,
0.02218911424279213,
-0.01700570061802864,
0.0191793330013752,
-0.03560764715075493,
0.0008262548362836242,
-0.044468123465776443,
0.02227332629263401,
-0.021632252261042595,
0.013607800006866455,
0.023420337587594986,
0.02206454426050186,
0.01570434495806694,
-0.06434541940689087,
-0.03486158698797226,
0.03839728608727455,
-0.0010165863204747438,
-0.007520849350839853,
0.003682836191728711,
0.018320687115192413,
-0.020752912387251854,
-0.053699444979429245,
-0.025880053639411926,
0.01913994550704956,
0.023734217509627342,
0.015425685793161392,
-0.02258026786148548,
0.045409731566905975,
-0.04631003737449646,
0.008484450168907642,
0.05462739244103432,
-0.04425044730305672,
0.03175618499517441,
-0.04387335479259491,
-0.0101728904992342,
0.008280334062874317,
-0.04694569110870361,
-0.05232890695333481,
0.003258637385442853,
-0.013111002743244171,
0.00933976098895073,
-0.020830582827329636,
0.03772537410259247,
-0.002599741332232952,
0.002730419160798192,
-0.06575649976730347,
-0.0011999147245660424,
0.0071867480874061584,
-0.005138037260621786,
0.011837880127131939,
-0.032903704792261124,
0.03034120611846447,
-0.017708472907543182,
0.00294419564306736,
-0.02346068248152733,
-0.003326910547912121,
-0.020877009257674217,
-0.011876562610268593,
0.002075732219964266,
0.010778198018670082,
0.035286419093608856,
-0.007008736487478018,
-0.029690098017454147,
0.008441471494734287,
-0.013609710149466991,
-0.011485903523862362,
0.016942068934440613,
0.02014557458460331,
-0.01140818651765585,
-0.03793478384613991,
-0.004087874665856361,
0.01122805755585432,
0.03653101995587349,
-0.005352636333554983,
0.00829385221004486,
0.04671987146139145,
0.009088668040931225,
-0.03168686851859093,
0.012460391968488693,
0.026981929317116737,
0.002382769715040922,
0.018258163705468178,
0.002773716812953353,
-0.018285667523741722,
-0.043914586305618286,
-0.03092304617166519,
0.02926807850599289,
-0.006059151142835617,
0.015819640830159187,
-0.02406504936516285,
0.06393533200025558,
0.0032134046778082848,
0.005336315371096134,
0.01401547808200121,
-0.027247296646237373,
-0.01325103547424078,
-0.006932677235454321,
0.00973366666585207,
-0.007730178534984589,
-0.013687040656805038,
-0.02520989067852497,
-0.03790539130568504,
-0.04749636352062225,
-0.035504214465618134,
0.03580005094408989,
-0.004457492846995592,
0.07518180459737778,
0.032111093401908875,
0.010462645441293716,
0.0289104413241148,
0.01639700122177601,
-0.001960804918780923,
0.008022346533834934,
-0.009575339034199715,
0.056926362216472626,
-0.0027138025034219027,
0.002206724137067795,
0.030679194256663322,
0.050069790333509445,
-0.025343727320432663,
0.018441092222929,
0.04822644591331482,
0.07024074345827103,
0.05482349917292595,
-0.019128937274217606,
-0.028821978718042374,
0.024062108248472214,
-0.01258326880633831,
0.01093363668769598,
-0.00854483712464571,
-0.028847625479102135,
0.04157739132642746,
0.012159569188952446,
-0.038178928196430206,
-0.0000026127950150112156,
0.009872742928564548,
-0.06383898854255676,
0.04909193888306618,
0.02762039564549923,
0.011446511372923851,
-0.004365063272416592,
0.03297804296016693,
0.018605206161737442,
0.003868941916152835,
-0.0021999895107001066,
0.032414186745882034,
-0.08720475435256958,
-0.03463961184024811,
-0.02058369852602482,
-0.0764409527182579,
0.026650669053196907,
-0.01588115654885769,
-0.007894720882177353,
0.019874332472682,
-0.006751150358468294,
0.017915861681103706,
0.005271395202726126,
0.019398927688598633,
-0.04233196750283241,
0.01814842037856579,
-0.014645421877503395,
0.012887752614915371,
0.001100066234357655,
0.032253485172986984,
0.11207377910614014,
0.04437645524740219,
-0.004170773550868034,
-0.07061300426721573,
0.00843666773289442,
-0.02766958810389042,
0.015420466661453247,
-0.018503369763493538,
0.012247354723513126,
-0.0021774773485958576,
0.03043457306921482,
-0.03782451152801514,
0.06350419670343399,
-0.0019182184478268027,
0.0034229133743792772,
0.05181298404932022,
-0.04002629593014717,
-0.03467161953449249,
0.0274412352591753,
0.039845749735832214,
-0.00702975457534194,
-0.022182460874319077,
-0.019756298512220383,
0.03308606520295143,
-0.02258991450071335,
-0.028494492173194885,
-0.027126023545861244,
-0.057477302849292755,
0.0209946446120739,
0.002780274720862508,
-0.043879445642232895,
0.022180885076522827,
0.011077641509473324,
-0.01606503687798977,
-0.03491085395216942,
0.03525599092245102,
0.05072159692645073,
0.02620026469230652,
0.015102546662092209,
0.018683820962905884,
0.024527132511138916,
-0.006216138601303101,
-0.014619567431509495,
-0.000940157740842551,
-0.01434299722313881,
-0.04695112630724907,
-0.008293123915791512,
0.05978259816765785,
-0.006994079798460007,
-0.031201299279928207,
-0.03125358372926712,
-0.008434586226940155,
-0.027477478608489037,
-0.03784547373652458,
-0.011557969264686108,
0.013211161829531193,
0.04228128865361214,
-0.029413573443889618,
-0.016014892607927322,
-0.014347398653626442,
0.016889166086912155,
-0.03681885451078415,
0.017912037670612335,
-0.0038771345280110836,
0.0020694034174084663,
0.017812883481383324,
0.0013704696903005242,
0.01625417172908783,
-0.001855946029536426,
-0.02588343434035778,
-0.005652685184031725,
-0.03127148747444153,
-0.05722777545452118,
-0.03286917880177498,
0.0019278519321233034,
0.031171398237347603,
0.014606415294110775,
0.010929741896688938,
0.022531455382704735,
-0.023705866187810898,
-0.0852963849902153,
0.04444646090269089,
-0.04537426680326462,
-0.007374627981334925,
-0.02572708949446678,
-0.0000069181442086119205,
0.054140105843544006,
0.0651736781001091,
-0.010228196159005165,
0.016941377893090248,
0.027305101975798607,
-0.021401774138212204,
0.021090475842356682,
-0.0005794722237624228,
-0.0016223504208028316,
0.0398050993680954,
-0.010072991251945496,
0.001717069768346846,
-0.03569910675287247,
0.013357341289520264,
0.007885738275945187,
-0.0005773719167336822,
-0.02897658757865429,
0.004827600438147783,
-0.05474963039159775,
-0.028682447969913483,
0.007384787313640118,
-0.028890352696180344,
-0.019755277782678604,
0.002601033076643944,
0.038380205631256104,
-0.04674108326435089,
-0.04590580612421036,
-0.05213579535484314,
0.006786364130675793,
-0.017295997589826584,
0.041256628930568695,
-0.01025110762566328,
0.0016136175254359841,
-0.012144593521952629,
0.0434708446264267,
-0.029930798336863518,
0.011595292948186398,
-0.0467696376144886,
0.01994224265217781,
0.010238217189908028,
-0.01570647954940796,
-0.04764573648571968,
0.03333253040909767,
0.014037600718438625,
-0.049160607159137726,
0.02101011388003826,
0.04172179475426674,
0.011490787379443645,
0.014426695182919502,
0.029886627569794655,
-0.004375614691525698,
0.034104421734809875,
0.00421476736664772,
-0.04138587787747383,
0.031225277110934258,
-0.055393036454916,
-0.0050156996585428715,
0.0330679789185524,
-0.020533857867121696,
0.015617668628692627,
0.045421142131090164,
-0.028566574677824974,
-0.022518396377563477,
0.0029298709705471992,
-0.05074012279510498,
-0.007294182665646076,
0.011611043475568295,
-0.04334990680217743,
-0.046433545649051666,
0.02668502740561962,
0.04885294660925865,
-0.01674632541835308,
-0.03152715042233467,
0.05576912313699722,
-0.01692171022295952,
0.041031841188669205,
-0.00011733061546692625,
0.008876311592757702,
-0.015592754818499088,
0.03939555585384369,
0.019567694514989853,
-0.025479430332779884,
0.0005345710087567568,
0.06942330300807953,
-0.05961009860038757,
0.0256344061344862,
0.018720852211117744,
0.0026890423614531755,
-0.0900765210390091,
0.0008893365738913417,
-0.03416658192873001,
-0.016053183004260063,
0.041690465062856674,
-0.04981807619333267,
0.03213367983698845,
0.05168680101633072,
-0.043365657329559326,
0.04016082361340523,
-0.01670677214860916,
-0.00040922535117715597,
-0.005722451489418745,
0.026278745383024216,
-0.02845265157520771,
0.04645874723792076,
0.03780166059732437,
0.01113219279795885,
0.0013505417155101895,
0.035369258373975754,
-0.0015418994007632136,
-0.014222663827240467,
0.0005501142586581409,
0.04438550025224686,
0.008498669601976871,
0.00008562117727706209,
0.05725958198308945,
-0.03984624519944191,
0.013379634357988834,
0.013331284746527672,
-0.012879188172519207,
0.01028673816472292,
-0.020890148356556892,
-0.017533697187900543,
-0.023102780804038048,
0.049782004207372665,
0.03386552259325981,
0.008183264173567295,
-0.020618410781025887,
0.023283222690224648,
0.045998215675354004,
0.03906819596886635,
0.0015330436872318387,
-0.01253443956375122,
0.025079356506466866,
-0.001339225796982646,
-0.002697049407288432,
0.0396394319832325,
0.021639550104737282,
0.02325722761452198,
0.03377777338027954,
0.0009760100510902703,
0.03007357195019722,
-0.00257115182466805,
-0.015356523916125298,
-0.04176000878214836,
-0.016745757311582565,
0.020668083801865578,
0.007590988650918007,
-0.05025755241513252,
-0.008304955437779427,
-0.0329696387052536,
-0.037726402282714844,
0.04286107048392296,
0.049669574946165085,
-0.04105929657816887,
-0.06233203038573265,
-0.020276514813303947,
0.02254600264132023,
-0.0004038566257804632,
0.022118207067251205,
-0.055739160627126694,
-0.04371434822678566,
0.013762963004410267,
0.019024558365345,
0.005060709081590176,
-0.008881039917469025,
-0.02703789435327053,
-0.03179067373275757,
-0.05679917708039284,
0.030570244416594505,
0.013820096850395203,
-0.018272288143634796,
0.014828639104962349,
0.003498397534713149,
0.015520178712904453,
-0.027061155065894127,
0.07084894180297852,
0.0008531699422746897,
-0.040516845881938934,
-0.0054733906872570515,
-0.03520960733294487,
0.03351264074444771,
-0.023686129599809647,
0.02478158287703991,
-0.028808193281292915,
-0.015320586040616035,
-0.038047049194574356,
-0.013452565297484398,
-0.019123272970318794,
0.014134268276393414,
0.06597476452589035,
-0.006277375388890505,
-0.021602686494588852,
-0.03147142753005028,
-0.02108090929687023,
0.09823823720216751,
-0.0038090376183390617,
0.00410390505567193,
0.05934755504131317,
-0.005727128125727177,
0.045330360531806946,
0.04094293713569641,
-0.019343633204698563,
-0.018026307225227356,
-0.0014845432015135884,
-0.04436461254954338,
-0.006717927288264036,
-0.009547601453959942,
0.020125433802604675,
0.019729476422071457,
-0.018341707065701485,
-0.014539692550897598,
0.036090265959501266,
-0.05376075208187103,
-0.020233003422617912,
0.04639088362455368,
0.03048812784254551,
0.0022203074768185616,
0.012939637526869774,
0.03837364539504051,
0.042593296617269516,
0.038167376071214676,
0.013233725912868977,
0.0699753388762474,
0.05662964656949043,
0.003250953508540988,
0.048482269048690796,
0.06302031874656677,
-0.004082130268216133,
0.006059382576495409,
0.021485015749931335,
0.03697560727596283,
-0.029301341623067856,
-0.015176147222518921,
0.005917195230722427,
-0.009573131799697876,
-0.0025821072049438953,
0.004021310247480869,
-0.046863533556461334,
0.09020635485649109,
-0.021082783117890358,
-0.05251754820346832,
-0.036207038909196854,
-0.010536964982748032,
0.011308602057397366,
0.004695131443440914,
0.04636203125119209,
0.028468457981944084,
0.006098560988903046,
0.04894823580980301,
-0.053824350237846375,
0.016864480450749397,
0.0013911027926951647,
-0.05749604105949402,
0.018150901421904564,
-0.005985958501696587,
0.0009692503954283893,
-0.033666327595710754,
-0.01656820811331272,
-0.02490292675793171,
-0.033438075333833694,
0.014571837149560452,
0.03535398095846176,
0.04424421489238739,
0.020373480394482613,
0.00396706210449338,
-0.006391020491719246,
0.04601332172751427,
-0.05917155370116234,
-0.01613716036081314,
-0.02601715549826622,
0.014341484755277634,
-0.024617165327072144,
0.010085836984217167
] |
<p>I want to derive from first principles the proof for magnitude of torque about a point O = perpendicular distance from O to the line of action of the force * magnitude of the force. I want to derive this result for a general 3-D case for any arbitrary point O and force <strong><em>F</em></strong> .
I need to prove this mathematically without knowing the cross-product magnitude in terms of the angle between the vectors..... that is given any force F = Fx i + Fy j + Fz k and any point O and using torque= r cross F & using the determinant expansion for the same & also the expressions for magnitude of a vector, I need to prove this.... In other words, I need to prove that the magnitude of the cross-product is indeed F*r*sin(theta</p>
| 8,805 |
[
-0.04652629420161247,
-0.0005942529533058405,
-0.03333821892738342,
0.00874122604727745,
0.05318637564778328,
0.027871645987033844,
-0.027975479140877724,
0.00484224921092391,
0.017287326976656914,
-0.047545842826366425,
0.009920350275933743,
0.0027254363521933556,
0.07675755023956299,
0.016321638599038124,
0.01954028569161892,
-0.010732332244515419,
-0.03156996890902519,
-0.018450289964675903,
-0.016119273379445076,
-0.03591935709118843,
0.023716723546385765,
0.001397560234181583,
0.01432669349014759,
-0.018113723024725914,
-0.0027975235134363174,
0.02385520376265049,
0.05792464688420296,
-0.01860651932656765,
0.010454077273607254,
0.05577998608350754,
0.010029918514192104,
-0.018365921452641487,
0.017905231565237045,
0.023169035091996193,
0.01332736574113369,
0.035864852368831635,
-0.016094405204057693,
0.012470288202166557,
-0.005360138136893511,
0.03801467642188072,
-0.03982531279325485,
-0.00831765215843916,
0.009604639373719692,
0.05123671516776085,
-0.03148966282606125,
0.030796384438872337,
-0.023208241909742355,
0.021961193531751633,
0.03839171305298805,
-0.07058868557214737,
0.08507350832223892,
0.013231875374913216,
0.05224030837416649,
0.026795053854584694,
-0.01250203512609005,
-0.03298351541161537,
0.0684683546423912,
0.02639346569776535,
-0.012028343044221401,
-0.048370059579610825,
-0.021513571962714195,
-0.058692868798971176,
-0.031123440712690353,
-0.042109839618206024,
-0.009381419979035854,
0.039924513548612595,
-0.031220948323607445,
-0.026512185111641884,
0.04280513897538185,
0.017601272091269493,
-0.024134211242198944,
0.04171409457921982,
0.03603162243962288,
0.009856445714831352,
-0.009666704572737217,
-0.04078824818134308,
0.039702851325273514,
-0.003896743757650256,
0.027379337698221207,
0.0110061876475811,
-0.0457100011408329,
0.030059263110160828,
0.059038255363702774,
0.07602377235889435,
-0.003768119728192687,
-0.007023526821285486,
0.04873213171958923,
0.013294943608343601,
0.007286152336746454,
0.04595458507537842,
0.021672142669558525,
0.011298244819045067,
0.002782581141218543,
-0.02580942027270794,
-0.02668120712041855,
0.014657984487712383,
-0.021901017054915428,
0.035622190684080124,
0.028932737186551094,
-0.004519723355770111,
-0.004091285634785891,
-0.021971523761749268,
-0.006719171069562435,
0.03305217623710632,
-0.0022844455670565367,
-0.0067022209987044334,
-0.0025522795040160418,
0.02318526990711689,
-0.012738941237330437,
-0.024699006229639053,
-0.03297269716858864,
0.013647432439029217,
0.0012025381438434124,
0.011306182481348515,
-0.0067193033173680305,
-0.022845109924674034,
-0.013557479716837406,
0.016517767682671547,
0.07375995069742203,
0.06405246257781982,
0.026189368218183517,
-0.04223504289984703,
0.0115969805046916,
-0.05463882163167,
-0.05692404508590698,
0.004444771911948919,
-0.0163778904825449,
-0.04911235347390175,
-0.020819587633013725,
0.04222879931330681,
0.0022114531602710485,
-0.045901164412498474,
-0.04244603216648102,
0.012777040712535381,
0.03296370804309845,
-0.006141821853816509,
-0.08219267427921295,
-0.04306851327419281,
0.032648324966430664,
0.010985062457621098,
0.006073320750147104,
-0.034348540008068085,
0.02666299417614937,
0.029201721772551537,
0.07350476086139679,
0.02243189699947834,
0.02293228730559349,
-0.021446652710437775,
0.022696135565638542,
-0.018780294805765152,
-0.014688958413898945,
-0.010262233205139637,
0.004898530431091785,
-0.013990035280585289,
-0.023089494556188583,
-0.05430147796869278,
0.050316620618104935,
-0.007548676338046789,
0.018393049016594887,
-0.059354472905397415,
0.08555266261100769,
-0.034381479024887085,
0.02410048060119152,
0.017297513782978058,
-0.028795231133699417,
-0.03369611129164696,
0.07966440171003342,
-0.03064017742872238,
0.01649434119462967,
0.024879315868020058,
-0.0012320287059992552,
-0.0025670500472187996,
0.003713267622515559,
0.01986461505293846,
0.05708847567439079,
-0.06125149875879288,
-0.01376345381140709,
0.005813220050185919,
-0.0026357267051935196,
-0.009223980829119682,
-0.02091047540307045,
-0.04892432317137718,
-0.020010557025671005,
-0.010105893015861511,
-0.029561150819063187,
0.057557571679353714,
-0.0110460901632905,
0.0005283474456518888,
0.004866480827331543,
-0.015004361048340797,
0.012334296479821205,
-0.04713816940784454,
0.04022498056292534,
-0.006600997410714626,
-0.06541009992361069,
0.031110404059290886,
0.0010325276525691152,
0.04035135358572006,
-0.05805863067507744,
-0.035532526671886444,
-0.009895830415189266,
0.027547109872102737,
0.01874672807753086,
-0.01702861674129963,
0.05453846976161003,
0.05096414312720299,
0.06245192140340805,
-0.010660966858267784,
0.029206838458776474,
-0.002580311382189393,
0.0025120172649621964,
0.003774278564378619,
-0.051805268973112106,
0.006118949502706528,
0.03268657997250557,
0.01897340826690197,
-0.0009082958567887545,
0.0060379416681826115,
-0.02580511011183262,
0.031942419707775116,
-0.008898903615772724,
0.08481461554765701,
0.0832667127251625,
0.04778353497385979,
0.03131549060344696,
0.04336842522025108,
-0.0016799324657768011,
-0.0029144235886633396,
-0.017453216016292572,
-0.014383119530975819,
-0.05777635797858238,
-0.011332294903695583,
0.05352895334362984,
0.03352552279829979,
-0.040424637496471405,
-0.019390949979424477,
0.05332072824239731,
0.018402056768536568,
0.03919372335076332,
0.040618136525154114,
-0.013648536056280136,
-0.02765182964503765,
-0.0033995818812400103,
0.02203436754643917,
-0.022601183503866196,
0.017338279634714127,
0.026689687743782997,
0.021363982930779457,
0.01820847950875759,
0.043670155107975006,
-0.03684479743242264,
0.04258641600608826,
0.006168608088046312,
0.011773780919611454,
0.03578025475144386,
-0.010155712254345417,
0.06477222591638565,
0.005864138714969158,
0.023668386042118073,
-0.008815719746053219,
-0.022385120391845703,
0.013761712238192558,
-0.001602804521098733,
0.0033260066993534565,
0.02331768535077572,
-0.03423972800374031,
-0.02602320909500122,
0.01802636869251728,
0.022797785699367523,
-0.05468861386179924,
-0.011230213567614555,
-0.011571303009986877,
-0.017269866541028023,
-0.01722927764058113,
-0.02243093214929104,
-0.011038885451853275,
-0.006153515074402094,
0.03389979153871536,
0.01280627865344286,
-0.004207867197692394,
-0.012123920023441315,
-0.02760612592101097,
0.02032368630170822,
0.0153921814635396,
-0.05058566853404045,
0.00008247295045293868,
-0.035219889134168625,
-0.04803033918142319,
0.06155233457684517,
0.024925140663981438,
0.00029319533496163785,
0.002265955088660121,
0.019425589591264725,
-0.06399320065975189,
-0.0183140616863966,
-0.0005071006598882377,
0.0019834483973681927,
-0.03264148160815239,
0.01701505482196808,
0.02370445616543293,
-0.01624259538948536,
-0.014960043132305145,
0.013920824974775314,
-0.029144687578082085,
-0.03070400096476078,
0.015991386026144028,
0.010553678497672081,
0.004902749788016081,
-0.01228350680321455,
0.004221573006361723,
0.04920470342040062,
-0.039436690509319305,
-0.02269427292048931,
-0.05180498957633972,
-0.01179182343184948,
0.008313119411468506,
-0.0014070982579141855,
0.0551505908370018,
-0.021196871995925903,
-0.07174722850322723,
0.06227569282054901,
0.03510263189673424,
-0.050033923238515854,
-0.04350391775369644,
0.011981404386460781,
-0.031361546367406845,
-0.012025355361402035,
0.01195721235126257,
-0.02291710115969181,
-0.014456936158239841,
0.029409442096948624,
0.00422130711376667,
-0.005099870730191469,
0.030393395572900772,
0.037521135061979294,
-0.0020697361323982477,
-0.009893198497593403,
-0.022560615092515945,
-0.002647276036441326,
0.052806198596954346,
0.013165125623345375,
-0.048339538276195526,
0.01570187509059906,
0.029382770881056786,
0.05524253100156784,
0.00881043542176485,
-0.06345520913600922,
-0.007965208031237125,
0.01487118098884821,
0.008688007481396198,
-0.010827429592609406,
0.04642406851053238,
0.005927702412009239,
-0.01703684590756893,
0.03180655837059021,
0.016114648431539536,
0.03810406103730202,
-0.02774951048195362,
-0.012985545210540295,
0.010152543894946575,
0.004355140496045351,
-0.02609877474606037,
-0.008608158677816391,
-0.02938546985387802,
0.010265353135764599,
0.005591828376054764,
-0.014605439268052578,
-0.015866046771407127,
0.01904362067580223,
0.01989811286330223,
0.020361335948109627,
0.02969219535589218,
-0.008976020850241184,
0.027683094143867493,
-0.029019394889473915,
-0.005067487247288227,
0.0030052217189222574,
0.03249577805399895,
0.00426170788705349,
0.07550544291734695,
0.017628267407417297,
-0.008936130441725254,
-0.002535642357543111,
-0.0036677191965281963,
-0.08398483693599701,
0.046035557985305786,
-0.0246755238622427,
-0.0312991663813591,
0.014038382098078728,
0.009085185825824738,
-0.032720718532800674,
-0.023590099066495895,
-0.003903129603713751,
-0.034915801137685776,
0.0011184464674443007,
-0.04704927280545235,
-0.011747408658266068,
-0.01481968816369772,
-0.013767711818218231,
-0.014128821901977062,
0.054567087441682816,
0.03535798192024231,
-0.03865072876214981,
0.027742668986320496,
0.06698896735906601,
-0.05139840394258499,
0.014388540759682655,
-0.052367739379405975,
0.02431112714111805,
-0.002210210310295224,
-0.003124755574390292,
0.007460723631083965,
0.005960867740213871,
0.02309280075132847,
0.03150954842567444,
-0.062718465924263,
0.03822789341211319,
0.046153854578733444,
0.02471577189862728,
-0.03648263216018677,
-0.07068916410207748,
-0.02668098919093609,
0.007272105664014816,
0.06653095036745071,
-0.020754873752593994,
-0.004242719151079655,
0.04707561805844307,
-0.011803245171904564,
-0.0238789152354002,
0.04398491978645325,
0.06140374764800072,
0.029685137793421745,
-0.02517845295369625,
-0.0798095315694809,
-0.03701326996088028,
0.006179420743137598,
-0.041893985122442245,
0.03261616826057434,
-0.0030644205398857594,
-0.007345999591052532,
-0.039819467812776566,
-0.0037593019660562277,
0.004474530462175608,
-0.02060551568865776,
0.03480546921491623,
-0.0001049672209774144,
0.02110762521624565,
-0.0033110782969743013,
0.0022262618876993656,
0.030194057151675224,
0.024703938513994217,
0.050522614270448685,
-0.005728950724005699,
-0.008633258752524853,
-0.053804535418748856,
0.009789220988750458,
0.0059781670570373535,
0.027533311396837234,
0.0072922296822071075,
0.001234909170307219,
0.015947801992297173,
-0.021290743723511696,
0.0429346077144146,
-0.04151094704866409,
0.040953170508146286,
-0.013277841731905937,
-0.01314549334347248,
-0.0530984103679657,
-0.021764349192380905,
-0.05253605172038078,
0.010118833743035793,
-0.060324233025312424,
0.03557400032877922,
-0.038817379623651505,
-0.0033051734790205956,
-0.012898482382297516,
0.005474493373185396,
0.03926101699471474,
0.013677424751222134,
0.06186334788799286,
-0.04121475666761398,
0.0024346380960196257,
0.04452629014849663,
-0.02350407838821411,
-0.039290327578783035,
-0.00257835048250854,
0.004607314709573984,
-0.012274151667952538,
0.03179015964269638,
-0.02579200081527233,
-0.054604969918727875,
-0.006570871453732252,
0.006142519414424896,
0.010801837779581547,
0.0037032966502010822,
-0.04438997060060501,
0.001938649802468717,
0.015310237184166908,
-0.005770888179540634,
0.034715067595243454,
0.0418061763048172,
-0.008707317523658276,
-0.009948711842298508,
-0.010635127313435078,
0.02834162674844265,
0.018289554864168167,
-0.01685996539890766,
-0.022231873124837875,
0.059067245572805405,
-0.013053586706519127,
0.0436820313334465,
0.00428194273263216,
0.00459399726241827,
-0.03585461527109146,
-0.02048015594482422,
-0.033090636134147644,
0.012523990124464035,
-0.00790052954107523,
-0.0031503518112003803,
0.03279947116971016,
0.0445689931511879,
0.008510442450642586,
-0.025267163291573524,
-0.016996854916214943,
-0.0073733278550207615,
0.007129678037017584,
0.013504995964467525,
0.014122127555310726,
0.008606085553765297,
-0.02730162814259529,
-0.013486260548233986,
-0.0006412575603462756,
-0.06914564222097397,
0.05704685300588608,
-0.01845056749880314,
0.035680949687957764,
-0.0009328358573839068,
-0.06345294415950775,
-0.02670595981180668,
0.028934594243764877,
0.026942573487758636,
0.04431460425257683,
-0.021170184016227722,
-0.01520531065762043,
0.00897846557199955,
-0.0012439851416274905,
-0.01182152796536684,
-0.08159362524747849,
-0.006340270861983299,
0.03501201048493385,
0.0026939590461552143,
0.006924361456185579,
-0.016613401472568512,
-0.010424801148474216,
-0.011014939285814762,
0.03007250279188156,
0.048914290964603424,
-0.019070716574788094,
0.023916257545351982,
0.049645792692899704,
-0.019008850678801537,
0.04966210946440697,
-0.04380778595805168,
-0.02591339685022831,
0.0006757489172741771,
-0.020855406299233437,
0.013476391322910786,
0.0008847762364894152,
0.026745643466711044,
-0.021667208522558212,
-0.006205009296536446,
-0.01575308106839657,
0.012349561788141727,
0.02014925889670849,
-0.003132052719593048,
-0.01814931072294712,
-0.01024659164249897,
0.021620430052280426,
-0.010850686579942703,
-0.04885336384177208,
0.03118707239627838,
0.010179339908063412,
0.017056602984666824,
-0.021983372047543526,
0.008255469612777233,
-0.06950635462999344,
-0.025058871135115623,
-0.003306416794657707,
0.03181258589029312,
0.028507376089692116,
0.00427060853689909,
0.06701018661260605,
-0.025957491248846054,
0.02695964276790619,
0.02788449265062809,
0.02430478110909462,
0.008414174430072308,
0.014506971463561058,
0.00969049520790577,
0.025827830657362938,
0.009319785051047802,
-0.03380245342850685,
-0.028930088505148888,
-0.03839854896068573,
0.06456005573272705,
0.09195711463689804,
-0.03087555803358555,
0.05040200799703598,
0.021819287911057472,
-0.0024536806158721447,
-0.014534047804772854,
0.007380909286439419,
-0.008502279408276081,
-0.0013570472365245223,
0.0027310820296406746,
0.017683081328868866,
-0.01584923267364502,
0.005745342001318932,
0.03822768107056618,
0.04698193445801735,
-0.0574774406850338,
-0.007819375954568386,
0.019535774365067482,
-0.004899255465716124,
0.029934454709291458,
0.0227994155138731,
-0.02475590817630291,
0.01935982145369053,
-0.012982230633497238,
0.04209945350885391,
-0.005056262947618961,
0.006390816532075405,
0.05906252935528755,
0.012888102792203426,
0.02263719029724598,
-0.018877578899264336,
-0.04693322628736496,
-0.029064271599054337,
0.04762859642505646,
0.028362832963466644,
-0.004966337699443102,
-0.011993193067610264,
0.016471298411488533,
0.08432434499263763,
-0.026344677433371544,
-0.017840806394815445,
-0.02407093159854412,
-0.023626962676644325,
-0.021065643057227135,
-0.028132617473602295,
-0.04636811465024948,
0.058417826890945435,
0.007851703092455864,
-0.054140932857990265,
0.03481411561369896,
-0.011482970789074898,
0.05072500929236412,
0.05308228358626366,
0.04798698425292969,
-0.0026681902818381786,
0.07036669552326202,
-0.008420174941420555,
0.031853366643190384,
0.002719616750255227,
-0.010728689841926098,
0.11809054017066956,
0.055307626724243164,
0.014848443679511547,
-0.040637847036123276,
0.050920404493808746,
-0.002921906765550375,
-0.041486192494630814,
-0.04105604439973831,
0.029934192076325417,
-0.015102751553058624,
-0.021490132436156273,
0.011972283013164997,
0.06752890348434448,
-0.03562816604971886,
-0.019094841554760933,
0.03857702761888504,
-0.023466574028134346,
-0.04514985531568527,
0.010105193592607975,
0.014550484716892242,
0.001433975761756301,
-0.03126683086156845,
-0.052823517471551895,
0.024434475228190422,
-0.06150633841753006,
-0.06229661405086517,
-0.00916687585413456,
-0.00048597354907542467,
0.024424655362963676,
-0.017965100705623627,
-0.047289520502090454,
0.0321572944521904,
0.021319210529327393,
-0.008595448918640614,
-0.042026348412036896,
0.04364614561200142,
-0.003525783307850361,
-0.007009552791714668,
0.034449514001607895,
0.007911426946520805,
0.014600461348891258,
0.01922709308564663,
0.00031869299709796906,
-0.002610463183373213,
-0.019512439146637917,
0.0016817740397527814,
-0.030637690797448158,
0.057596221566200256,
-0.0031183965038508177,
0.029451753944158554,
0.014252327382564545,
0.023511726409196854,
-0.00921173207461834,
-0.07287478446960449,
0.006273841485381126,
-0.004217503592371941,
0.02961142174899578,
-0.0332581028342247,
-0.002160916570574045,
-0.011891425587236881,
0.05462772026658058,
0.022321557626128197,
0.007283467333763838,
-0.009006882086396217,
-0.017611872404813766,
0.017542380839586258,
-0.012597738765180111,
0.06690476089715958,
-0.017474738880991936,
-0.029492707923054695,
-0.01815640553832054,
-0.01543769333511591,
-0.014734537340700626,
0.004436977673321962,
-0.014659526757895947,
0.00987320952117443,
-0.0021153048146516085,
-0.010692069306969643,
-0.027617746964097023,
-0.0035680278670042753,
-0.056331295520067215,
0.0011190813966095448,
-0.006634615361690521,
-0.0436100959777832,
-0.013774258084595203,
0.006088861729949713,
0.016331929713487625,
0.030882980674505234,
0.003669091733172536,
-0.00487367482855916,
-0.006911617703735828,
-0.009873569943010807,
0.028231767937541008,
-0.020509613677859306,
-0.03787128999829292,
-0.007546681445091963,
-0.015155482105910778,
-0.013790392316877842,
0.009403073228895664,
0.00952532421797514,
0.06612105667591095,
0.01294129528105259,
-0.009364896453917027,
0.03798608481884003,
-0.007274063304066658,
-0.021503586322069168,
0.02122393809258938,
-0.02079041488468647,
-0.010413196869194508,
0.006497856695204973,
-0.04191751405596733,
-0.02656039409339428,
-0.014952655881643295,
-0.04110609367489815,
-0.03067118674516678,
-0.00012833518849220127,
0.005114693194627762,
-0.016203222796320915,
-0.030083222314715385,
-0.055433548986911774,
0.02311561070382595,
-0.035585444420576096,
-0.007847491651773453,
-0.011607189662754536,
-0.009715978056192398,
-0.002995917806401849,
-0.029766904190182686,
-0.03528983145952225,
0.01605411432683468,
-0.011902790516614914,
-0.023089086636900902,
-0.013531746342778206,
-0.012694109231233597,
-0.003944655880331993,
-0.016098977997899055,
0.017402587458491325,
-0.040272656828165054,
0.03414032980799675,
-0.010201587341725826,
-0.020590752363204956,
0.01682802475988865,
-0.04069625958800316,
-0.006938423961400986,
0.01141335442662239,
-0.05567603558301926,
0.062167100608348846,
-0.007274478208273649,
-0.007992385886609554,
-0.027421141043305397,
0.028306877240538597,
0.0030051853973418474,
-0.00857495702803135,
0.003468631999567151,
-0.013217485509812832,
-0.03950401395559311,
-0.01583489403128624,
0.03777925670146942,
-0.04449421912431717,
0.01978822983801365,
-0.003994660917669535,
0.035118743777275085,
-0.0017041417304426432,
-0.009478425607085228,
0.043720792979002,
0.0271354578435421,
-0.003210528986528516,
0.054639626294374466,
-0.015423762612044811,
0.005063519813120365,
0.07069385796785355,
-0.014937430620193481,
0.018165627494454384,
-0.017240120097994804,
0.04389971122145653,
-0.12100327759981155,
-0.001901867683045566,
0.030797142535448074,
-0.018150975927710533,
0.057311054319143295,
-0.07090632617473602,
0.013030066154897213,
0.045093607157468796,
-0.08690980076789856,
-0.004171750508248806,
-0.025624729692935944,
0.020065072923898697,
-0.011710152961313725,
-0.04260937124490738,
0.06443192064762115,
0.0173955038189888,
-0.007185648661106825,
0.03885183855891228,
0.02891785278916359,
0.004321947228163481,
-0.035880330950021744,
-0.035691194236278534,
-0.0048733665607869625,
0.04968595132231712,
-0.0019100733334198594,
-0.03334513306617737,
0.04394431412220001,
0.0058470857329666615,
-0.018984828144311905,
0.023311879485845566,
-0.026637261733412743,
-0.016981782391667366,
-0.0024698572233319283,
0.0362495481967926,
-0.006485641468316317,
0.03945038095116615,
-0.010139181278645992,
0.001017050351947546,
0.013315273448824883,
-0.006890944670885801,
-0.01731790415942669,
0.012077733874320984,
-0.04542187228798866,
0.0037323101423680782,
0.05354846641421318,
-0.03781392052769661,
-0.04024428129196167,
0.019364723935723305,
-0.007367858663201332,
0.0050805676728487015,
-0.014132543466985226,
-0.009375265799462795,
-0.021202705800533295,
-0.03378975763916969,
0.0268796905875206,
-0.034230783581733704,
-0.005263971164822578,
0.0162359531968832,
-0.009816390462219715,
0.009462814778089523,
0.022799653932452202,
0.0004674781230278313,
-0.019715718924999237,
0.013121702708303928,
-0.0412931852042675,
0.02012796886265278,
-0.06681864708662033,
-0.012903516180813313,
0.04053105413913727,
-0.02105034328997135,
-0.012823114171624184,
-0.03670835122466087,
-0.021956684067845345,
0.0399896577000618,
0.027393780648708344,
-0.008215379901230335,
0.024351540952920914,
-0.02649698592722416,
0.011023741215467453,
-0.0632178857922554,
0.024623246863484383,
0.04152528941631317,
-0.0334320068359375,
-0.009936732240021229,
-0.0158274844288826,
-0.00064941740129143,
-0.0011108738835901022,
0.031816791743040085,
0.0018645166419446468,
-0.015389771200716496,
-0.006860135123133659,
-0.013131239451467991,
-0.00045989645877853036,
-0.0363042838871479,
0.011152302846312523,
-0.028141658753156662,
-0.009402253665030003,
0.0014557059621438384,
-0.006819922011345625,
0.010032057762145996,
-0.014585907571017742,
0.002075228374451399,
0.024682648479938507,
0.019369792193174362,
-0.029856786131858826,
-0.06420842558145523,
0.016197973862290382,
-0.016472578048706055,
-0.0154653275385499,
0.04514097422361374,
0.006463350262492895,
0.017205895856022835,
0.030856870114803314,
-0.0036655734293162823,
-0.037525828927755356,
0.037252988666296005,
-0.05743309482932091,
0.001982797170057893,
-0.031486835330724716,
-0.008360804989933968,
0.0339227057993412,
-0.06909829378128052,
0.008262225426733494,
0.03184458240866661,
-0.023180745542049408,
0.004012370947748423,
0.044893018901348114,
0.011386595666408539,
0.03547126427292824,
-0.00403348496183753,
0.027277376502752304,
0.03134045749902725,
-0.04166646674275398,
0.03980918601155281,
0.031034670770168304,
0.00818624161183834,
0.0009795761434361339,
-0.023968806490302086,
0.03926966339349747,
-0.031244557350873947,
0.01876751147210598,
0.011143791489303112,
0.04337525740265846,
-0.009395867586135864,
-0.02937409095466137,
0.004800808150321245,
-0.019762946292757988,
0.010340503416955471,
0.022110553458333015,
0.007201709784567356,
0.06625824421644211,
-0.030487850308418274,
0.0031399999279528856,
-0.0330040417611599,
-0.017519691959023476,
-0.02636285498738289,
-0.026152504608035088,
0.020144479349255562,
0.05671392008662224,
-0.05593913793563843,
0.011237476021051407,
-0.0005211984971538186,
-0.01889127679169178,
0.011743687093257904,
0.01857324317097664,
0.02014879137277603,
0.01735919900238514,
-0.004490197636187077,
0.003267863532528281,
-0.030121123418211937,
-0.025873325765132904,
-0.0080622723326087,
0.040565550327301025,
0.01874765381217003,
0.010949019342660904,
-0.005427320022135973,
0.005787933245301247,
-0.03253070265054703,
0.031017418950796127,
-0.06280027329921722,
-0.01928979530930519,
-0.020951030775904655,
0.04443841800093651,
-0.01272532157599926,
0.02490163780748844
] |
<p>I am very interested by <a href="http://journals.aps.org/prl/pdf/10.1103/PhysRevLett.110.210403" rel="nofollow">this paper</a> on entanglement swapping and timelike entanglement. </p>
<p>The one thing I get really tripped up with is the whole idea of a projection onto a bell basis. I understand the whole idea of projecting into different basises, but I am not sure what the authors are doing. From the article:</p>
<pre><code>When the two photons of time (photons 2 and 3) are
projected onto any Bell state, the first and last photons
(1 and 4) collapse also into the same state and entanglement
is swapped. The first and last photons, that did not share
between them any correlations, become entangled.
</code></pre>
<p>I am trying to see how that is the case from Equation 3. I am missing the way to mathematically take the projection and then see what is happening with photons 1 and 4. Any help in understanding how to project onto the bell basis would be very much appreciated!</p>
| 8,806 |
[
-0.014264384284615517,
-0.03219898045063019,
-0.017049068585038185,
-0.020659485831856728,
0.007596550043672323,
0.012640660628676414,
-0.021038973703980446,
-0.006715182214975357,
0.013518656603991985,
-0.01659758947789669,
0.04315619170665741,
0.04143373295664787,
0.019026197493076324,
0.011934252455830574,
0.015772391110658646,
-0.00030438744579441845,
-0.016672488301992416,
-0.003234290750697255,
-0.027282848954200745,
-0.036413345485925674,
0.0305789727717638,
0.029782447963953018,
-0.0035018264316022396,
0.007989028468728065,
-0.009147308766841888,
0.02694302797317505,
0.004279184155166149,
-0.011111547239124775,
0.025154460221529007,
0.07498298585414886,
-0.02835150621831417,
-0.03978116437792778,
-0.010717003606259823,
0.00585782527923584,
-0.013878673315048218,
-0.01696624793112278,
-0.04993802681565285,
-0.04134732484817505,
0.0072465804405510426,
0.012997841462492943,
-0.041823409497737885,
-0.0009119239985011518,
-0.012138983234763145,
0.05238616093993187,
0.0014707674272358418,
-0.00999131053686142,
-0.011919201351702213,
0.02282293327152729,
0.04552138224244118,
-0.0646689385175705,
0.08097430318593979,
0.016816817224025726,
0.006657760590314865,
-0.0023124199360609055,
-0.025172356516122818,
0.005171139724552631,
0.06427178531885147,
0.0630454421043396,
-0.010223792865872383,
-0.03524506837129593,
-0.04227452352643013,
-0.0032685494516044855,
0.0052672275342047215,
-0.03413661569356918,
-0.03096221759915352,
0.0017323418287560344,
-0.008012155070900917,
-0.0048166983760893345,
0.003901215735822916,
-0.061754755675792694,
0.010156399570405483,
0.0005710757686756551,
0.07918150722980499,
-0.024793479591608047,
0.008499416522681713,
0.0031250775791704655,
0.011776713654398918,
0.034153956919908524,
0.03524655103683472,
0.051466405391693115,
-0.0187876857817173,
0.02376587688922882,
0.00857181940227747,
0.016688883304595947,
-0.005165856797248125,
-0.02458629012107849,
0.04517423361539841,
-0.012213313952088356,
-0.0015637235483154655,
0.05377485230565071,
0.0005589238135144114,
0.02699911594390869,
0.0463363416492939,
0.0017980107804760337,
-0.029801014810800552,
0.01222863607108593,
0.020675120875239372,
0.06216097250580788,
-0.0087200328707695,
-0.030149077996611595,
0.01193724013864994,
-0.017100496217608452,
0.004675905220210552,
0.04252690076828003,
-0.027638133615255356,
0.003458828665316105,
-0.016634585335850716,
0.05958440154790878,
0.009266768582165241,
-0.038729049265384674,
-0.039897266775369644,
-0.015596786513924599,
0.026973042637109756,
0.008441980928182602,
0.003324847435578704,
-0.053776562213897705,
0.003086521290242672,
0.018413757905364037,
0.05876559391617775,
0.0663064643740654,
0.008224514313042164,
-0.0034044519998133183,
0.0023012508172541857,
-0.02947091870009899,
-0.05512601509690285,
-0.021563449874520302,
0.025435909628868103,
0.004815489053726196,
-0.03202294930815697,
0.0553971603512764,
0.01672668196260929,
-0.03441237658262253,
0.014211569912731647,
0.021161910146474838,
0.037612371146678925,
-0.034658852964639664,
-0.16687345504760742,
-0.048040155321359634,
0.0464785061776638,
-0.02497521974146366,
-0.008640213869512081,
-0.06577209383249283,
0.06492041051387787,
0.038652848452329636,
0.07303319126367569,
-0.025451498106122017,
0.015148719772696495,
0.011766127310693264,
0.031090060248970985,
0.041348062455654144,
0.000017286884030909277,
0.006841300521045923,
-0.008957569487392902,
-0.02607431448996067,
-0.04075494036078453,
-0.03690192475914955,
0.01333281397819519,
0.05722632259130478,
-0.0036908674519509077,
-0.02711784653365612,
0.08912614732980728,
0.0011620760196819901,
0.004245305433869362,
0.031253352761268616,
-0.036660488694906235,
-0.02250800095498562,
0.08055305480957031,
0.01539927814155817,
-0.03723374754190445,
0.04150860756635666,
-0.020464982837438583,
0.037232521921396255,
-0.023213889449834824,
0.03481398895382881,
0.0020320015028119087,
-0.023077355697751045,
-0.01652451977133751,
0.006586581934243441,
0.0070231300778687,
-0.020826110616326332,
-0.011131636798381805,
-0.038810260593891144,
-0.011449085548520088,
-0.003262569895014167,
0.01684529148042202,
0.0136228296905756,
-0.015829848125576973,
-0.014977328479290009,
-0.03534268960356712,
-0.07162543386220932,
-0.022977832704782486,
-0.06127526983618736,
0.029962725937366486,
0.018430326133966446,
-0.00972630362957716,
-0.006979701574891806,
0.007976771332323551,
0.03821681812405586,
-0.01678677834570408,
-0.02186633087694645,
-0.038364626467227936,
0.01969739980995655,
0.00969703122973442,
-0.010112310759723186,
0.027493810281157494,
0.05405851826071739,
0.02548784203827381,
0.011526960879564285,
0.00997779332101345,
-0.03294944763183594,
-0.018564734607934952,
0.052959755063056946,
0.010079807601869106,
0.016447335481643677,
-0.006832518614828587,
-0.0035273635294288397,
-0.003961557522416115,
0.035018160939216614,
0.0024775471538305283,
-0.013450597412884235,
-0.03498498350381851,
0.06043427437543869,
0.034727632999420166,
-0.003980492241680622,
-0.0036381410900503397,
0.047826092690229416,
0.022934257984161377,
0.02704307809472084,
0.001195327378809452,
-0.041606780141592026,
-0.025894390419125557,
-0.01660439372062683,
-0.010684429667890072,
0.050877250730991364,
-0.03156176954507828,
0.020183918997645378,
0.029295679181814194,
0.040508680045604706,
0.005531006027013063,
0.029564175754785538,
-0.01799943298101425,
-0.013290651142597198,
-0.011820615269243717,
-0.0016728645423427224,
-0.00013324270548764616,
0.013419676572084427,
0.012440348975360394,
0.01690194196999073,
0.016862165182828903,
-0.008205784484744072,
-0.04470451548695564,
0.027495425194501877,
-0.06950019299983978,
0.02702789194881916,
-0.04873645678162575,
-0.03636891022324562,
0.022799788042902946,
-0.03227098658680916,
0.023339705541729927,
-0.0008931743213906884,
-0.005447479896247387,
-0.03196929767727852,
-0.007269907742738724,
-0.04984087124466896,
-0.00518791051581502,
0.020993245765566826,
-0.014734598807990551,
-0.003743107197806239,
0.010062315501272678,
-0.03477369621396065,
0.03841833397746086,
-0.02213207259774208,
-0.010630467906594276,
-0.013351202011108398,
0.009203808382153511,
0.03492254391312599,
-0.0010905326344072819,
0.02922305464744568,
-0.060446206480264664,
-0.05919678509235382,
-0.001287349034100771,
0.006731735076755285,
0.005310040898621082,
0.0061106388457119465,
-0.07513302564620972,
0.01565573178231716,
-0.028157711029052734,
0.0037327392492443323,
0.029674163088202477,
0.004617931321263313,
0.021155603229999542,
0.02442367561161518,
0.0014279952738434076,
-0.04731791839003563,
-0.0347570963203907,
-0.007886803708970547,
-0.00920623354613781,
-0.007809191942214966,
-0.0044542415998876095,
0.06507154554128647,
-0.006565266288816929,
-0.05295293405652046,
-0.032681386917829514,
-0.021481921896338463,
-0.031646858900785446,
0.015705125406384468,
-0.002935617696493864,
-0.00159316451754421,
-0.03454740345478058,
0.02823847159743309,
0.012870479375123978,
-0.03476997837424278,
0.00469256192445755,
-0.04874083399772644,
-0.06799648702144623,
0.02554585039615631,
0.021490510553121567,
0.02761320024728775,
0.0009481180459260941,
-0.022390682250261307,
0.10103128105401993,
0.005702835042029619,
-0.024280041456222534,
-0.03517989441752434,
0.021029546856880188,
-0.012979957275092602,
-0.009204338304698467,
0.013143818825483322,
0.01712935045361519,
0.0026773102581501007,
0.04009146988391876,
-0.015774885192513466,
0.02116117626428604,
0.07818496972322464,
0.017005667090415955,
-0.0066632237285375595,
-0.014670118689537048,
0.008132405579090118,
-0.01507094968110323,
0.026657046750187874,
-0.036139022558927536,
-0.025035299360752106,
-0.006738463416695595,
0.018781419843435287,
-0.005161806475371122,
-0.03521629050374031,
-0.013132437132298946,
0.030185112729668617,
0.017657261341810226,
-0.004062730818986893,
-0.0324876494705677,
0.04402657225728035,
-0.005242520477622747,
-0.03658725693821907,
-0.008031324483454227,
0.040814679116010666,
0.05679057911038399,
-0.0249966848641634,
0.0043398598209023476,
0.05210698023438454,
0.01685195416212082,
-0.025898924097418785,
-0.04268086329102516,
0.0021239875350147486,
-0.024225106462836266,
0.06045134738087654,
-0.02766861580312252,
0.00044830385013483465,
0.07502737641334534,
0.014552210457623005,
0.02833317592740059,
0.004436596762388945,
-0.022020671516656876,
-0.016886724159121513,
-0.026271486654877663,
0.01510692946612835,
0.009026676416397095,
0.06369708478450775,
0.012470534071326256,
0.04623402655124664,
0.04247928038239479,
0.017187004908919334,
0.015035002492368221,
-0.017480261623859406,
-0.0757366344332695,
0.02363126166164875,
0.002341339597478509,
0.0024332415778189898,
0.007190126460045576,
-0.022019915282726288,
0.0009657763293944299,
-0.0039178901351988316,
-0.03616064041852951,
-0.011132471263408661,
-0.013942914083600044,
-0.05248298868536949,
0.017344312742352486,
-0.03962717205286026,
-0.0006606631795875728,
-0.0029292034450918436,
0.041204456239938736,
0.05243634805083275,
-0.008652511052787304,
0.0184174794703722,
0.03108063153922558,
-0.048931002616882324,
0.03165743127465248,
-0.007243067491799593,
0.017515402287244797,
0.01572432741522789,
0.035627931356430054,
0.023159610107541084,
0.056335218250751495,
-0.0134356040507555,
0.0247457604855299,
-0.00029119057580828667,
0.043629441410303116,
0.021871475502848625,
-0.02686750330030918,
0.003626925637945533,
-0.007068847771733999,
0.016498416662216187,
0.01079852320253849,
0.06287319958209991,
0.007357459980994463,
-0.006528779398649931,
0.04069085419178009,
0.033751990646123886,
-0.011158186011016369,
0.04849924519658089,
0.08267972618341446,
-0.023028310388326645,
0.012210249900817871,
-0.04928479716181755,
-0.027379555627703667,
-0.0005874322378076613,
0.0022506355307996273,
0.04748516157269478,
-0.01231648214161396,
-0.03912154585123062,
-0.008172664791345596,
0.03662312403321266,
0.006095594260841608,
-0.022318370640277863,
-0.013497737236320972,
-0.0034801566507667303,
0.001922374009154737,
0.03098893351852894,
-0.008733679540455341,
-0.015523784793913364,
0.04477005824446678,
0.049453794956207275,
0.023218458518385887,
0.013625427149236202,
-0.06470388174057007,
-0.0343109555542469,
0.03303822875022888,
0.0367237851023674,
0.041185878217220306,
-0.00009608225082047284,
-0.047096796333789825,
-0.023815808817744255,
0.01898292824625969,
-0.011582424864172935,
0.058042991906404495,
0.016026820987462997,
-0.009562536142766476,
-0.014932006597518921,
-0.016738206148147583,
0.0056469859555363655,
0.010903160087764263,
-0.036307644098997116,
0.01615193858742714,
-0.007276780903339386,
-0.009032193571329117,
-0.032682985067367554,
0.017825212329626083,
0.006600236054509878,
0.04885340854525566,
-0.013883241452276707,
0.02114848606288433,
-0.013590602204203606,
0.04306480288505554,
-0.027662750333547592,
-0.08087169378995895,
0.03000030480325222,
-0.009009568952023983,
-0.011203708127140999,
0.06685536354780197,
-0.0314754880964756,
-0.04028640687465668,
0.012812912464141846,
0.0026787053793668747,
-0.0013871646951884031,
0.0011321516940370202,
-0.0504024401307106,
0.03531228005886078,
0.014007460325956345,
-0.03300366923213005,
0.0650801882147789,
0.03811809793114662,
0.01006606686860323,
0.004006598144769669,
-0.01756099984049797,
0.039948318153619766,
-0.03311275318264961,
0.05619755759835243,
-0.006993172224611044,
0.030515141785144806,
-0.02462873049080372,
0.048991333693265915,
-0.03691531717777252,
0.03074035421013832,
0.008739378303289413,
-0.021207351237535477,
-0.016535375267267227,
0.0030411668121814728,
-0.009921281598508358,
0.027363643050193787,
0.00715795811265707,
-0.009198879823088646,
-0.003436334664002061,
-0.031037021428346634,
0.016360143199563026,
-0.02358732931315899,
0.0235111266374588,
0.017455536872148514,
-0.008425943553447723,
0.01664802059531212,
-0.03232786804437637,
-0.017183464020490646,
0.028510024771094322,
-0.055466972291469574,
0.029798494651913643,
-0.007466730661690235,
0.02873142436146736,
0.030707160010933876,
-0.06690194457769394,
-0.04681340605020523,
-0.015323701314628124,
-0.010606680065393448,
0.032712168991565704,
-0.07798441499471664,
0.01688530668616295,
0.021220920607447624,
-0.025713171809911728,
-0.08383643627166748,
-0.05236799269914627,
0.0396430678665638,
-0.005861049983650446,
-0.041047148406505585,
-0.032766442745923996,
0.0009491472155787051,
-0.016515467315912247,
0.006008962169289589,
-0.032993100583553314,
0.032509732991456985,
-0.027018576860427856,
-0.008708128705620766,
0.030798904597759247,
-0.005679133348166943,
0.04160449653863907,
-0.023050863295793533,
-0.016808615997433662,
0.0037035117857158184,
-0.00456968042999506,
-0.01091238297522068,
-0.01686909794807434,
0.0467473641037941,
-0.03187379613518715,
-0.058992888778448105,
-0.031958840787410736,
0.03126663714647293,
0.04226616770029068,
-0.04839221015572548,
0.0019367123022675514,
-0.03126686066389084,
0.041929155588150024,
-0.0030942633748054504,
-0.03148894011974335,
-0.013512330129742622,
0.017880069091916084,
0.030691834166646004,
-0.0018072203965857625,
0.004693640395998955,
-0.010048561729490757,
-0.051391106098890305,
0.01934422180056572,
-0.0013310166541486979,
0.012896322645246983,
0.030888058245182037,
0.06908787041902542,
0.013724752701818943,
0.0075683025643229485,
0.029984652996063232,
-0.02887124940752983,
-0.008390759117901325,
0.022107314318418503,
0.012902673333883286,
0.015704648569226265,
0.0030032049398869276,
-0.01075678039342165,
-0.02645641192793846,
-0.05179387703537941,
-0.010019458830356598,
0.08326821774244308,
-0.010299669578671455,
0.04930480197072029,
0.06025885418057442,
-0.009570503607392311,
-0.0013890728587284684,
-0.02221180684864521,
-0.012126078829169273,
0.0066431984305381775,
0.0011962089920416474,
0.033150192350149155,
-0.04253844544291496,
0.003958040848374367,
-0.011015674099326134,
0.036383964121341705,
-0.008441789075732231,
0.041728176176548004,
0.030756359919905663,
0.022864503785967827,
0.012293518520891666,
0.0022772671654820442,
-0.03234436362981796,
0.039762310683727264,
-0.04076572135090828,
-0.0014934366336092353,
0.0073026446625590324,
-0.01215307042002678,
0.02810331992805004,
0.022786926478147507,
0.04748387634754181,
-0.04313213378190994,
-0.055728647857904434,
-0.03705297037959099,
-0.003316308371722698,
0.008792353793978691,
0.021459756419062614,
0.007619479205459356,
0.020487353205680847,
0.04490237310528755,
-0.0194220170378685,
0.02208343893289566,
-0.009670590981841087,
-0.015581116080284119,
-0.0667136162519455,
-0.02341473288834095,
-0.0265012476593256,
0.019915757700800896,
-0.01181636843830347,
-0.008754313923418522,
0.017120927572250366,
-0.03836056962609291,
-0.0005182591266930103,
0.014157895930111408,
0.06070192903280258,
-0.004296749364584684,
0.06774739176034927,
0.022683650255203247,
-0.004242150578647852,
-0.025186380371451378,
0.01122451014816761,
0.10130657255649567,
0.054771214723587036,
0.019696414470672607,
-0.07799217849969864,
0.030907223001122475,
0.0001736455160425976,
0.0403418205678463,
-0.055559203028678894,
0.015542575158178806,
-0.014380233362317085,
0.04543370380997658,
-0.013443552888929844,
0.04067021235823631,
0.003770492970943451,
-0.02652120031416416,
0.012413066811859608,
-0.03843851760029793,
-0.05083295330405235,
0.002532540587708354,
0.025919124484062195,
0.017663178965449333,
-0.034965548664331436,
-0.046629928052425385,
0.005655504297465086,
-0.004330476745963097,
-0.03773728758096695,
-0.03829741105437279,
-0.003477380145341158,
0.013263700529932976,
-0.023670664057135582,
-0.008900380693376064,
0.00953949149698019,
-0.013905945234000683,
-0.014979955740272999,
-0.008625568822026253,
0.017256787046790123,
0.017154013738036156,
-0.01915886066854,
0.04888065159320831,
0.020069580525159836,
0.016267593950033188,
-0.01708412915468216,
0.044125307351350784,
0.026671865954995155,
-0.040417011827230453,
-0.019452739506959915,
-0.0071134972386062145,
0.06110384315252304,
-0.02632589265704155,
-0.04923713207244873,
0.0011233565164729953,
-0.038816340267658234,
0.023702358826994896,
-0.06961475312709808,
-0.039432793855667114,
0.010246353223919868,
0.009016974829137325,
0.0012413986260071397,
-0.011971923522651196,
0.0026289205998182297,
-0.01354328915476799,
-0.022556675598025322,
0.016792159527540207,
-0.04131510481238365,
0.026851151138544083,
-0.0069778780452907085,
-0.05447692051529884,
-0.007162065245211124,
-0.012392651289701462,
-0.012562165968120098,
-0.021597320213913918,
0.0022189668379724026,
-0.04637548327445984,
-0.03802293539047241,
0.032403506338596344,
0.007784656714648008,
0.036579329520463943,
0.01708764210343361,
-0.028146978467702866,
0.0077185845002532005,
-0.0793573260307312,
0.005557025782763958,
-0.01221050787717104,
-0.047797754406929016,
-0.0017009687144309282,
0.013261131942272186,
0.05411691591143608,
0.04030937701463699,
-0.00973980687558651,
-0.005662191659212112,
0.01846005953848362,
-0.005995265673846006,
0.04181579500436783,
-0.013282560743391514,
-0.0025311775971204042,
0.025214040651917458,
0.017138345167040825,
-0.031307004392147064,
-0.0550021231174469,
0.029666047543287277,
0.019078563898801804,
-0.01801658608019352,
-0.01969149336218834,
0.02613680809736252,
-0.007698348257690668,
-0.025319967418909073,
0.018966007977724075,
-0.002695683157071471,
0.011910644359886646,
0.011093077249825,
0.02681463398039341,
-0.03599018231034279,
0.0009219805360771716,
0.011995743960142136,
-0.004151852335780859,
-0.001006729551590979,
-0.022890035063028336,
-0.03452781215310097,
-0.02164810709655285,
0.00905513484030962,
0.02967473305761814,
-0.005889002699404955,
-0.02038162387907505,
-0.0452658087015152,
-0.004177712835371494,
-0.0024060276336967945,
-0.00482161296531558,
-0.02580132894217968,
0.04836590215563774,
0.009207792580127716,
-0.014306483790278435,
0.05033530294895172,
0.0420113243162632,
-0.02411128394305706,
0.0006836706888861954,
0.015065107494592667,
0.042346589267253876,
0.0342039093375206,
0.003948564175516367,
-0.05521353334188461,
0.04063280299305916,
-0.04228630289435387,
-0.012155156582593918,
0.06544215977191925,
0.011563686653971672,
0.01204175129532814,
0.02746576815843582,
-0.005880525801330805,
-0.03615109995007515,
0.05824144557118416,
-0.010770294815301895,
-0.004532705992460251,
0.02764277718961239,
-0.02043246105313301,
-0.015179765410721302,
0.0072574373334646225,
-0.029862605035305023,
0.006412072107195854,
-0.009055432863533497,
0.008541831746697426,
0.03017584979534149,
0.026787452399730682,
0.02433307282626629,
-0.02602251060307026,
-0.00035408002440817654,
0.027677340433001518,
0.013506902381777763,
-0.006691137794405222,
0.007622081320732832,
0.07140026241540909,
-0.01026341412216425,
0.03564413636922836,
0.015495073050260544,
-0.0011652554385364056,
-0.08423078060150146,
-0.010402591899037361,
0.018953092396259308,
0.003368042642250657,
0.0516851469874382,
-0.05631239339709282,
0.02080327272415161,
0.0524093322455883,
-0.03173552453517914,
0.04068485274910927,
0.008506200276315212,
-0.01043512299656868,
-0.010343334637582302,
0.05703971907496452,
-0.02021617814898491,
0.08364146202802658,
0.05376049876213074,
0.044022612273693085,
-0.0027910408098250628,
-0.013109569437801838,
-0.02538752742111683,
-0.05168609321117401,
-0.039218079298734665,
0.04668577015399933,
-0.00908073503524065,
0.00037064572097733617,
0.08272866904735565,
-0.01590479165315628,
-0.05156182497739792,
0.04874856024980545,
-0.02847396582365036,
-0.024800289422273636,
-0.013782329857349396,
-0.006173861213028431,
0.011263317428529263,
0.014566034078598022,
0.008659045211970806,
-0.02451634220778942,
-0.0009816443780437112,
0.030133919790387154,
0.03315756469964981,
0.007543498184531927,
-0.0026041369419544935,
0.009054542519152164,
0.02795318327844143,
-0.04415121302008629,
-0.029107531532645226,
0.027044178918004036,
0.017399834468960762,
0.01142972707748413,
-0.03374527394771576,
0.003116393694654107,
0.025260400027036667,
-0.04134714975953102,
0.007026578765362501,
-0.04705891013145447,
-0.006483605597168207,
0.03939906135201454,
-0.007064316887408495,
-0.010778400115668774,
0.021397707983851433,
-0.03661560267210007,
-0.05012546107172966,
0.03995182737708092,
-0.0055608851835131645,
0.0037647762801498175,
-0.05500952526926994,
-0.009980017319321632,
0.04585863649845123,
-0.018698018044233322,
0.009348600171506405,
-0.048303235322237015,
-0.04184664040803909,
0.004646708257496357,
-0.02580157294869423,
0.014427748508751392,
-0.01883195899426937,
-0.032505810260772705,
-0.03589027374982834,
-0.07492313534021378,
0.017020881175994873,
0.019251368939876556,
-0.02838876284658909,
-0.0423702672123909,
-0.016219016164541245,
-0.041405610740184784,
0.04626081511378288,
0.03513437509536743,
-0.013572757132351398,
-0.009145454503595829,
-0.005417661275714636,
0.013362396508455276,
0.02863844484090805,
-0.014660235494375229,
-0.008079188875854015,
0.013507039286196232,
-0.013822348788380623,
-0.008739681914448738,
-0.0008286698721349239,
-0.037346210330724716,
0.012168506160378456,
-0.012300863862037659,
-0.03399818390607834,
0.014562500640749931,
-0.005487203132361174,
-0.0527963824570179,
0.03887070342898369,
0.006743492092937231,
-0.012982540763914585,
0.04563872888684273,
-0.013600749894976616,
0.021167661994695663,
0.011709026992321014,
0.002481479663401842,
-0.042409271001815796,
-0.00002266735100420192,
-0.03079402633011341,
-0.03419576212763786,
0.009199672378599644,
0.02736019529402256,
0.03486509621143341,
-0.045636821538209915,
0.003267796942964196,
0.015975527465343475,
-0.029098987579345703,
-0.004060923121869564,
0.08836094290018082,
-0.0023828158155083656,
0.01904478296637535,
0.010524704121053219,
0.029386792331933975,
0.010729419067502022,
-0.02876182459294796,
0.01960725709795952,
0.043509591370821,
-0.01355037558823824,
-0.006052655633538961,
0.017731860280036926,
0.031229542568325996,
-0.020068282261490822,
0.0051359748467803,
-0.0015958005096763372,
0.03018711879849434,
-0.02495568059384823,
0.02066236361861229,
0.010405274108052254,
0.011332492344081402,
-0.01824946142733097,
-0.00282729952596128,
-0.016885977238416672,
0.056240346282720566,
-0.048780422657728195,
0.013018281199038029,
-0.04304765164852142,
0.023587733507156372,
-0.015147251076996326,
0.027974246069788933,
-0.01059617381542921,
0.07233574241399765,
-0.021426189690828323,
-0.0048705218359827995,
-0.03091040626168251,
-0.006172179710119963,
0.0014151623472571373,
-0.049931906163692474,
0.008242340758442879,
-0.012350622564554214,
-0.0003501527535263449,
-0.0006508529768325388,
-0.047086674720048904,
-0.0080265486612916,
-0.030951732769608498,
0.006831911392509937,
0.011322994716465473,
0.026611996814608574,
-0.026600323617458344,
0.02438417077064514,
-0.015518377535045147,
0.057652682065963745,
-0.0405970923602581,
-0.009424064308404922,
-0.03184777870774269,
0.03998382017016411,
0.0050825271755456924,
0.003452459117397666
] |
<p>Does exists a geometry (3d for example) which is Euclidean in 2 dimensions (x and y coordinates) and non-Euclidean when the third dimension (z) is taken into account? In other words a space where it is possible to construct a <em>square</em> but not a <em>cube</em>? </p>
| 8,807 |
[
-0.02781313844025135,
-0.0008510751649737358,
0.012252689339220524,
-0.034854546189308167,
0.06273995339870453,
0.029729802161455154,
-0.044757816940546036,
-0.049552351236343384,
0.00417832937091589,
-0.05483030900359154,
0.019710274413228035,
0.009584148414433002,
0.05687190964818001,
0.03320552781224251,
0.009108532220125198,
0.007948014885187149,
-0.0012070416705682874,
0.013022522442042828,
-0.01567930355668068,
-0.03461180254817009,
0.03526952490210533,
0.01004103198647499,
0.00950583815574646,
0.017521515488624573,
-0.029757676646113396,
0.03310629725456238,
0.02418469451367855,
0.00027351899188943207,
0.013731380924582481,
0.0537404865026474,
-0.0013686994789168239,
-0.020727401599287987,
-0.008201655931770802,
0.053893014788627625,
0.030111024156212807,
-0.034583929926157,
-0.029434531927108765,
0.002411348046734929,
0.010775603353977203,
0.020759504288434982,
-0.015233227051794529,
-0.008469395339488983,
-0.010856001637876034,
0.04832518845796585,
-0.03238551318645477,
0.04829900339245796,
-0.014900272712111473,
-0.04796721413731575,
0.021200407296419144,
-0.04747290164232254,
0.06922226399183273,
0.02223380096256733,
0.019519416615366936,
0.011789020150899887,
-0.008337878622114658,
-0.0029509246814996004,
0.06263909488916397,
0.056809067726135254,
-0.018972504884004593,
-0.016843486577272415,
-0.03127295896410942,
-0.012091897428035736,
0.03002765215933323,
-0.05247946456074715,
-0.04652298986911774,
0.022793544456362724,
-0.022100944072008133,
-0.025378890335559845,
-0.009117383509874344,
-0.0032306862995028496,
-0.011427692137658596,
0.04825356975197792,
0.04197772964835167,
-0.05131139978766441,
0.0028779844287782907,
-0.009511461481451988,
0.006928841583430767,
-0.0017433229368180037,
0.054292112588882446,
-0.013186176307499409,
0.012971509248018265,
-0.010382185690104961,
0.009045146405696869,
0.009168490767478943,
0.020144255831837654,
-0.01620822213590145,
0.037278685718774796,
-0.01896306499838829,
-0.01994476653635502,
0.02549162320792675,
0.015573155134916306,
-0.03422030434012413,
0.058567412197589874,
-0.026812903583049774,
-0.027214864268898964,
0.026008542627096176,
0.0073355380445718765,
0.05148069187998772,
0.010171993635594845,
-0.014285181649029255,
0.02242376282811165,
-0.0022689644247293472,
0.010210325941443443,
0.03549352288246155,
0.0072112479247152805,
-0.0015531312674283981,
-0.0303806122392416,
0.04593559727072716,
-0.0024886461906135082,
0.012866342440247536,
-0.01830855943262577,
0.0359649732708931,
-0.011973745189607143,
0.04880377650260925,
0.021425727754831314,
-0.005974911153316498,
-0.007626770995557308,
-0.02932274341583252,
0.021805502474308014,
0.08907534927129745,
0.027633365243673325,
-0.025284534320235252,
0.01896478421986103,
-0.032816335558891296,
-0.1083291620016098,
0.014736805111169815,
0.02273191697895527,
0.00041757646249607205,
-0.019262943416833878,
0.0312625989317894,
0.014189562760293484,
0.0017583321314305067,
0.02016683667898178,
0.005889432039111853,
0.05588383972644806,
-0.015991484746336937,
-0.06896121054887772,
-0.072841577231884,
0.037033017724752426,
0.034809187054634094,
-0.04336166009306908,
-0.0433545783162117,
0.03134138882160187,
0.03609386086463928,
0.07458581030368805,
0.02526656910777092,
0.016227439045906067,
0.020631980150938034,
0.03511437028646469,
0.01720300503075123,
-0.03740164265036583,
-0.003880951786413789,
0.019384849816560745,
-0.062174271792173386,
0.03409057855606079,
-0.042976271361112595,
0.05140114948153496,
0.012668986804783344,
0.036904823035001755,
-0.0367719791829586,
0.03312494605779648,
-0.012047889642417431,
-0.01734156720340252,
0.027509780600667,
-0.02132335864007473,
-0.013907619751989841,
0.07907993346452713,
0.0062975105829536915,
0.02616121619939804,
0.023444203659892082,
-0.006942312233150005,
0.03900420665740967,
0.03016999550163746,
0.054130252450704575,
0.06494063138961792,
0.008510182611644268,
-0.018793834373354912,
0.004775987006723881,
0.02167006954550743,
0.02915641851723194,
-0.05561574921011925,
-0.008007457479834557,
-0.019026033580303192,
0.01926433853805065,
-0.009443472139537334,
0.038374967873096466,
0.012823538854718208,
-0.017677219584584236,
0.04923423379659653,
-0.03512369841337204,
0.0033969746436923742,
-0.07145429402589798,
0.015200460329651833,
0.03757856786251068,
-0.029106851667165756,
-0.008437840268015862,
0.04283088073134422,
0.003309880383312702,
-0.07408609241247177,
-0.048038557171821594,
-0.011089234612882137,
0.03897581249475479,
0.02651214972138405,
-0.01701601967215538,
0.004035438876599073,
0.06686432659626007,
0.050573982298374176,
-0.018844211474061012,
0.0004366382781881839,
0.01904655620455742,
-0.0184504222124815,
-0.019506894052028656,
-0.009252096526324749,
0.007426753640174866,
-0.023271000012755394,
0.000058481498854234815,
0.02960735373198986,
0.0218636617064476,
-0.041684649884700775,
0.04865244776010513,
-0.06463111191987991,
0.05100053921341896,
0.04551716521382332,
-0.009388266131281853,
0.000854133628308773,
0.024253036826848984,
0.002327348105609417,
0.01018127053976059,
0.030389845371246338,
-0.03447148948907852,
-0.027517832815647125,
-0.0004599090898409486,
0.03881599381566048,
0.03259030729532242,
-0.07977201789617538,
0.013878176920115948,
0.01295082364231348,
0.036709658801555634,
0.002336307195946574,
0.01613985188305378,
-0.011207870207726955,
-0.03134603798389435,
-0.008169696666300297,
-0.010800471529364586,
0.058384496718645096,
0.049301259219646454,
0.007777063641697168,
-0.005152493249624968,
-0.03875890374183655,
-0.03363543748855591,
-0.03491698578000069,
0.04551125317811966,
-0.03204704821109772,
-0.009448411874473095,
0.019100451841950417,
-0.008729729801416397,
0.0245133675634861,
-0.010389733128249645,
0.014128037728369236,
0.02769605629146099,
0.01425932813435793,
-0.019531739875674248,
-0.030887078493833542,
-0.006707552820444107,
-0.0009719959925860167,
0.03091851994395256,
-0.021213049069046974,
-0.011196548119187355,
0.04032417759299278,
-0.0028172519523650408,
-0.038074493408203125,
-0.02930741384625435,
0.007150216028094292,
-0.008691915310919285,
-0.027696337550878525,
0.043332599103450775,
-0.019965466111898422,
0.03384151682257652,
0.0029919063672423363,
-0.019113102927803993,
-0.01165720447897911,
-0.029361244291067123,
-0.024254724383354187,
-0.0006442186422646046,
-0.043365925550460815,
0.03361711651086807,
-0.022858627140522003,
-0.023921912536025047,
-0.0045073311775922775,
-0.016170663759112358,
0.05702798068523407,
0.014536092057824135,
-0.010560409165918827,
-0.02122240886092186,
-0.023527080193161964,
-0.03982362896203995,
0.024839354678988457,
-0.012728892266750336,
0.006035464815795422,
0.007262043654918671,
-0.01086918730288744,
-0.05946008116006851,
0.025157082825899124,
-0.02039271406829357,
-0.04732498899102211,
-0.053213369101285934,
0.009506411850452423,
0.02520432136952877,
-0.06716956198215485,
-0.005815113428980112,
0.05449962615966797,
-0.029209690168499947,
0.01794218271970749,
-0.04583316296339035,
-0.05334893614053726,
0.005199602339416742,
-0.03362854942679405,
0.038192808628082275,
-0.02968062274158001,
-0.03143521025776863,
0.06198952719569206,
0.013330298475921154,
-0.024016132578253746,
-0.018467053771018982,
-0.0018066675402224064,
-0.011796548031270504,
-0.044999297708272934,
0.02144651673734188,
-0.0068155271001160145,
-0.015234493650496006,
0.0080709895119071,
0.018119409680366516,
0.01887991838157177,
0.029290052130818367,
-0.0008450049790553749,
-0.028823744505643845,
0.019512245431542397,
0.046610843390226364,
0.012646131217479706,
0.029856959357857704,
0.02925446443259716,
-0.05604023113846779,
0.029018208384513855,
0.017324920743703842,
0.020893288776278496,
0.026487233117222786,
-0.07616668939590454,
0.025477590039372444,
-0.02367267943918705,
0.04187461733818054,
0.016794638708233833,
0.032434187829494476,
0.016553709283471107,
-0.005967543926090002,
0.004605851601809263,
0.043522439897060394,
0.015643233433365822,
-0.02395179308950901,
0.004203840158879757,
0.023989062756299973,
0.022165730595588684,
-0.044845737516880035,
0.009365973994135857,
0.008288095705211163,
0.042238954454660416,
0.056114669889211655,
0.01930181123316288,
-0.01661675237119198,
0.05293283984065056,
0.042154934257268906,
0.0043940762989223,
0.04263358563184738,
-0.002123716054484248,
0.017985641956329346,
-0.06916522234678268,
-0.012916095554828644,
0.006503873039036989,
0.0334971658885479,
-0.021333662793040276,
-0.00021610193653032184,
0.0009135850705206394,
0.004403191152960062,
0.011127511970698833,
-0.02009573206305504,
-0.07071932405233383,
-0.030537119135260582,
-0.03737470135092735,
0.0017133144428953528,
-0.010140386410057545,
-0.02172918990254402,
-0.025027843192219734,
-0.03426285460591316,
-0.026258930563926697,
0.017346376553177834,
-0.011853695847094059,
-0.0824250727891922,
0.01929016038775444,
-0.017044533044099808,
-0.021878333762288094,
0.03742658719420433,
0.026646442711353302,
0.033988744020462036,
-0.02814543806016445,
0.02790805883705616,
0.031706809997558594,
-0.01341310329735279,
0.0102153979241848,
0.028986139222979546,
0.023436248302459717,
0.014100749045610428,
0.028780672699213028,
-0.029501527547836304,
0.04024963080883026,
0.022162331268191338,
0.012462968938052654,
-0.0218953937292099,
0.056718431413173676,
-0.03466077148914337,
0.020094500854611397,
-0.03407921642065048,
-0.036709971725940704,
-0.02883058786392212,
-0.01217705849558115,
0.043406013399362564,
0.00201340951025486,
0.0064207399263978004,
0.03672349825501442,
0.02345414087176323,
-0.03326783329248428,
0.002176311332732439,
0.051744185388088226,
0.0035785194486379623,
-0.06383662670850754,
-0.0164710134267807,
-0.048718567937612534,
-0.028809506446123123,
-0.04118683934211731,
0.050905242562294006,
0.010344932787120342,
-0.003639190923422575,
-0.009711602702736855,
0.020807554945349693,
-0.018551064655184746,
-0.017844459041953087,
0.005880207289010286,
0.01975109614431858,
-0.012186937965452671,
-0.0019432194530963898,
0.0033187714871019125,
-0.0027110353112220764,
0.016874486580491066,
0.0414913110435009,
0.00882276427000761,
-0.049557387828826904,
-0.060893669724464417,
0.01395360380411148,
0.0533977672457695,
0.020381608977913857,
0.014036103151738644,
-0.011282315477728844,
-0.05043737590312958,
-0.0420634001493454,
0.04253404587507248,
-0.017105694860219955,
-0.006311540026217699,
-0.04454977810382843,
-0.01923893205821514,
-0.04474299028515816,
-0.00025111157447099686,
-0.019010817632079124,
-0.052299369126558304,
-0.0070307329297065735,
0.008554416708648205,
0.019375400617718697,
0.019945453852415085,
0.0047441101633012295,
0.022649010643363,
0.03648297116160393,
-0.001910849823616445,
0.04379795864224434,
0.0075089395977556705,
-0.007880904711782932,
0.03816696256399155,
-0.018581952899694443,
-0.056047797203063965,
0.015241758897900581,
0.059101030230522156,
-0.009061980992555618,
0.05042286962270737,
-0.03007849119603634,
-0.02051541954278946,
0.026732636615633965,
-0.031709227710962296,
-0.006388647016137838,
0.06847593933343887,
0.013485198840498924,
0.017722032964229584,
0.04885787516832352,
0.011677934788167477,
0.025820430368185043,
0.01848655752837658,
0.008094506338238716,
-0.039692990481853485,
-0.06739415228366852,
0.03357020765542984,
-0.033861033618450165,
0.014310156926512718,
-0.03977103903889656,
-0.015665991231799126,
-0.006788123864680529,
0.020187262445688248,
0.0018685280811041594,
0.003555960487574339,
-0.015182318165898323,
-0.037597544491291046,
-0.021419333294034004,
0.009846667759120464,
0.023158954456448555,
0.017909737303853035,
-0.03764611855149269,
0.005250968970358372,
-0.0019735852256417274,
-0.025512516498565674,
-0.010201950557529926,
0.00030979019356891513,
-0.012043886817991734,
0.009250029921531677,
-0.013025397434830666,
0.01094650849699974,
0.0007831754046492279,
0.006720563862472773,
0.0008694752468727529,
-0.025206679478287697,
0.05549188330769539,
-0.028414588421583176,
0.01300548855215311,
0.022723019123077393,
-0.04629506915807724,
0.005018691997975111,
-0.01451182272285223,
0.013649077154695988,
0.005248296074569225,
-0.04905961826443672,
0.05259997397661209,
-0.0047497195191681385,
0.007073111366480589,
-0.08220989257097244,
-0.03201092779636383,
0.00940609723329544,
0.011397120542824268,
-0.01477373018860817,
-0.0444461815059185,
-0.023065662011504173,
-0.022509586066007614,
-0.04807347059249878,
0.012195306830108166,
0.06506064534187317,
-0.027202419936656952,
-0.03522171825170517,
0.019322238862514496,
0.05552936717867851,
0.02117711305618286,
-0.027849582955241203,
0.008502098731696606,
0.011242331936955452,
0.011404860764741898,
0.01929849199950695,
-0.007359946146607399,
0.05730527639389038,
-0.01205447968095541,
-0.00502212718129158,
-0.03721078857779503,
0.002683595521375537,
0.02078346163034439,
-0.048318538814783096,
-0.02822093293070793,
0.038631781935691833,
-0.022869061678647995,
-0.005057475995272398,
-0.01961999200284481,
0.009704524651169777,
-0.003854853566735983,
-0.0018070582300424576,
-0.0537443533539772,
0.016599735245108604,
-0.0023005763068795204,
-0.00712566077709198,
0.039302293211221695,
0.010294778272509575,
0.015562341548502445,
-0.000590172247029841,
0.029718009755015373,
0.01909743621945381,
0.0012235210742801428,
-0.00810976605862379,
-0.018501466140151024,
0.013467531651258469,
-0.008827604353427887,
-0.03652624040842056,
0.029650641605257988,
0.04541290923953056,
-0.04657003656029701,
-0.016918053850531578,
0.006153566762804985,
0.031091313809156418,
0.0562032051384449,
-0.040792256593704224,
0.058622024953365326,
0.04194216430187225,
-0.02309350110590458,
0.007203774992376566,
-0.018662510439753532,
0.004531218204647303,
0.033255256712436676,
-0.0022979285567998886,
0.07067704200744629,
-0.01887737587094307,
0.019370876252651215,
0.04924897849559784,
0.03618571162223816,
-0.02115355059504509,
0.03082985058426857,
-0.003331470536068082,
-0.0031043526250869036,
0.014885236509144306,
-0.01688196510076523,
-0.05743136629462242,
0.06638670712709427,
-0.014305935241281986,
0.015167739242315292,
0.014981863088905811,
-0.024670490995049477,
0.04074399545788765,
0.0025205654092133045,
0.010162056423723698,
-0.01483744103461504,
-0.019069399684667587,
-0.05066878721117973,
-0.014917968772351742,
-0.0064327288419008255,
0.05144565925002098,
-0.01613367348909378,
-0.05394623801112175,
0.053065840154886246,
-0.019363857805728912,
-0.024216527119278908,
0.00753943482413888,
-0.0774112269282341,
-0.01964692957699299,
-0.03888927772641182,
0.005479529500007629,
0.03526941314339638,
0.02723098173737526,
-0.019944392144680023,
-0.015627123415470123,
-0.023582471534609795,
0.008667814545333385,
0.011869060806930065,
0.05566498264670372,
-0.03340408205986023,
0.014164471067488194,
0.004943122621625662,
0.03352808579802513,
-0.04565398022532463,
0.011069764383137226,
0.08981885761022568,
0.04633811488747597,
0.024663131684064865,
-0.05496126040816307,
0.06392721086740494,
-0.06323656439781189,
-0.01914750412106514,
-0.0375235415995121,
0.027594005689024925,
0.012326905503869057,
0.009375845082104206,
0.02354501187801361,
0.08126382529735565,
0.006854984909296036,
-0.056292541325092316,
0.06819203495979309,
-0.041982848197221756,
-0.0418446846306324,
-0.013278977014124393,
0.01146283932030201,
-0.007082856725901365,
-0.001627533813007176,
-0.009610871784389019,
0.046315696090459824,
-0.01574256829917431,
-0.02351761795580387,
-0.03152493014931679,
-0.006493262946605682,
0.03221994265913963,
0.017255403101444244,
-0.04985162988305092,
-0.009031989611685276,
0.01808478683233261,
-0.00008316207095049322,
-0.04497508704662323,
0.009209315292537212,
-0.006195691414177418,
-0.016157856211066246,
-0.0027290964499115944,
0.03928495943546295,
0.034494154155254364,
0.01494787447154522,
0.006947466172277927,
0.002676971023902297,
-0.07757445424795151,
0.01810365915298462,
-0.0038361833430826664,
0.02529173344373703,
-0.01695987582206726,
0.015605922788381577,
-0.013162435963749886,
-0.004344748333096504,
0.018830278888344765,
-0.05284607782959938,
-0.027059027925133705,
-0.01459371205419302,
0.021022386848926544,
0.016375504434108734,
-0.017747102305293083,
0.0328206792473793,
0.028915811330080032,
-0.026509996503591537,
0.036083512008190155,
-0.011061631143093109,
-0.025745214894413948,
0.02400164306163788,
0.0006709664012305439,
0.04226091131567955,
-0.012352267280220985,
-0.005711220670491457,
-0.03231050819158554,
0.006382214371114969,
0.004598256666213274,
0.003000041237100959,
-0.010058988817036152,
0.021843817085027695,
0.0418996624648571,
0.0010365560883656144,
-0.020957235246896744,
0.006167888641357422,
-0.024391252547502518,
0.021338358521461487,
-0.06700290739536285,
0.041748352348804474,
-0.05265555530786514,
0.02645278349518776,
0.05977965146303177,
0.02564684860408306,
-0.02230624109506607,
-0.01977183111011982,
-0.04686559736728668,
-0.0025274506770074368,
0.014762837439775467,
-0.01531275361776352,
0.007312700152397156,
-0.03522063419222832,
-0.03911381959915161,
-0.01885734498500824,
-0.042566828429698944,
0.008141468279063702,
0.04123006761074066,
0.0433109812438488,
0.0055183665826916695,
0.04959646612405777,
-0.009967640973627567,
-0.012592876330018044,
0.023015407845377922,
-0.03273645415902138,
-0.005824795458465815,
0.017265312373638153,
0.03402940556406975,
-0.06510528177022934,
-0.02704680897295475,
-0.03192173317074776,
-0.014118652790784836,
-0.02970835193991661,
0.029285676777362823,
-0.01514776237308979,
-0.036905623972415924,
0.007687792647629976,
0.0029345653019845486,
-0.023233456537127495,
-0.02089950442314148,
-0.03121189959347248,
-0.01650572381913662,
0.02812160737812519,
-0.006114260293543339,
0.005572895985096693,
-0.011160374619066715,
-0.036717489361763,
-0.01781189627945423,
0.010857068933546543,
-0.010646414943039417,
-0.02751372568309307,
-0.015279857441782951,
-0.0051773544400930405,
0.014267722144722939,
0.03946065902709961,
-0.032625798135995865,
-0.013421828858554363,
0.021005703136324883,
-0.04556730017066002,
-0.04724382236599922,
0.017096811905503273,
-0.05122622475028038,
0.007088645361363888,
0.015977006405591965,
-0.012536577880382538,
-0.020623505115509033,
0.04267796501517296,
-0.013141607865691185,
0.01643477752804756,
0.017466237768530846,
-0.024434858933091164,
-0.020480073988437653,
-0.03152542561292648,
0.027280576527118683,
-0.0488915890455246,
-0.03783418610692024,
0.03614337742328644,
0.04352058097720146,
0.016935506835579872,
-0.020811758935451508,
0.0017773974686861038,
-0.0373658761382103,
0.0080498568713665,
0.018229197710752487,
0.010813876986503601,
0.01879129186272621,
0.023393236100673676,
-0.040028590708971024,
0.046282943338155746,
0.07350340485572815,
0.0008312491117976606,
-0.097004234790802,
-0.01787903532385826,
0.04500921443104744,
0.007706489413976669,
0.04604288563132286,
-0.06722304224967957,
0.0011443031253293157,
0.001225941115990281,
-0.1183730736374855,
0.027804454788565636,
-0.017092430964112282,
-0.05293780192732811,
-0.0426899679005146,
-0.0341637060046196,
0.006476695649325848,
0.024729469791054726,
0.0347643680870533,
0.047039635479450226,
0.018171217292547226,
0.033448636531829834,
-0.06220234930515289,
-0.02486264333128929,
0.017404697835445404,
-0.004557534120976925,
-0.031219255179166794,
-0.01994110271334648,
0.02621743083000183,
-0.025087308138608932,
-0.02944520115852356,
0.027082541957497597,
-0.004330596420913935,
0.01697828806936741,
0.01898142509162426,
-0.018386296927928925,
0.020585520192980766,
0.008944956585764885,
0.03507453203201294,
-0.0042758905328810215,
-0.03248954936861992,
-0.003910834435373545,
0.009315421804785728,
0.003814677707850933,
0.005590289365500212,
0.008164266124367714,
0.0020084544084966183,
-0.003826685482636094,
0.009662597440183163,
0.013086012564599514,
0.00018577407172415406,
-0.0037746867164969444,
0.005692422389984131,
0.018238773569464684,
0.028930556029081345,
-0.00704893609508872,
0.004249670542776585,
-0.0563473105430603,
-0.006156029645353556,
0.019440196454524994,
0.0023655612021684647,
-0.03884781152009964,
0.019457757472991943,
-0.016878144815564156,
-0.02685639262199402,
0.001567772007547319,
-0.032433923333883286,
0.016741368919610977,
-0.042225342243909836,
-0.0033601969480514526,
-0.0050301626324653625,
-0.04546790197491646,
0.03949180245399475,
-0.025301704183220863,
-0.007883390411734581,
0.04903681203722954,
0.022960690781474113,
0.022986890748143196,
-0.006500802934169769,
-0.0027322135865688324,
-0.027959294617176056,
-0.08032188564538956,
0.041050173342227936,
-0.014366093091666698,
-0.0036990928929299116,
-0.017161071300506592,
0.026364780962467194,
-0.03812290355563164,
-0.002894324017688632,
0.07158054411411285,
-0.01956222392618656,
0.03646249696612358,
-0.008456284180283546,
0.04583046957850456,
0.02148265391588211,
-0.024029573425650597,
-0.015310744754970074,
0.009222621098160744,
-0.04060937464237213,
-0.019078917801380157,
-0.010394847951829433,
0.0009044532780535519,
-0.020014967769384384,
0.019587213173508644,
-0.027081215754151344,
0.03697439655661583,
0.02391904406249523,
-0.0206222515553236,
0.04546867683529854,
0.003832279471680522,
-0.03185725957155228,
0.0710965096950531,
-0.02258404903113842,
0.015581552870571613,
0.012430199421942234,
0.004806703422218561,
-0.003180108033120632,
-0.0014470494352281094,
-0.008959587663412094,
-0.030885005369782448,
-0.04390450567007065,
-0.004148419480770826,
0.0319816991686821,
-0.014985296875238419,
-0.023747295141220093,
0.041898954659700394,
-0.0345129519701004,
-0.015097454190254211,
0.04778061807155609,
0.03518589958548546,
0.03565451502799988,
-0.03133101016283035,
-0.002343339379876852,
0.03420542925596237,
0.00831815879791975,
0.033223770558834076,
0.007008012849837542,
0.021228309720754623,
-0.002728293417021632,
-0.011410081759095192,
0.03522346168756485,
-0.024645984172821045,
0.016482139006257057,
0.021206730976700783,
0.07791411876678467,
-0.015605713240802288,
-0.010575564578175545,
0.01994040049612522,
-0.0019267579773440957,
0.062292855232954025,
-0.011469613760709763,
-0.01885652355849743,
0.08500684052705765,
-0.00034870332456193864,
0.019123336300253868,
-0.05684632435441017,
0.02116328664124012,
-0.027517639100551605,
-0.0014717776793986559,
0.024540234357118607,
0.04297942295670509,
-0.022969599813222885,
0.00045644602505490184,
-0.0224777702242136,
0.015598002821207047,
0.02047375962138176,
0.009376798756420612,
0.01549203135073185,
-0.01269303634762764,
-0.012501112185418606,
-0.0012621949426829815,
-0.011326953768730164,
-0.014941267669200897,
0.003352251835167408,
0.05213030055165291,
0.04749339073896408,
0.0670720562338829,
-0.04136021062731743,
0.0035679135471582413,
-0.033066526055336,
0.026217307895421982,
-0.06829211115837097,
-0.04063964635133743,
0.003538923105224967,
0.034327082335948944,
0.0015527431387454271,
-0.003721791785210371
] |
<p>during an undergrad experiment we have to estimate the finesse of an <a href="http://en.wikipedia.org/wiki/Fabry%E2%80%93P%C3%A9rot_interferometer" rel="nofollow">Fabry-Pérot interferometer</a>.</p>
<p>The reflectance $R$ is given so the theoretical value can be calculated by $\mathcal{F} = \frac{\pi\sqrt{R}}{1-R}$. For an estimation of the practical value we can use the definition $\mathcal{F} = \frac{\Delta\lambda}{\delta\lambda}$, where $\delta\lambda$ is the full-width half-maximum of an transmission band and $\Delta\lambda$ is the free spectral range (FSR).</p>
<p>In our experiment we had an expandet, monochromatic source in an magnetic field, so due to the Zeeman effect we had in fact an splitted line.
How can we get the FSR? Or is there another way to calculate the finesse?</p>
| 8,808 |
[
0.01351609081029892,
-0.013139038346707821,
-0.026141786947846413,
-0.010109007358551025,
0.06875907629728317,
0.016845347359776497,
-0.016618864610791206,
-0.0380873866379261,
0.03676033765077591,
0.0034041432663798332,
0.03696037456393242,
0.046244777739048004,
0.04860096424818039,
0.04704318195581436,
-0.0030936230905354023,
-0.01112375222146511,
0.0014246278442442417,
-0.007407382596284151,
-0.009305588901042938,
-0.03806900605559349,
0.013104254379868507,
-0.002693076618015766,
-0.011559674516320229,
-0.017351655289530754,
-0.05993707478046417,
0.01569376513361931,
0.03035695292055607,
-0.018660981208086014,
0.014213901944458485,
0.004876679740846157,
-0.011500975117087364,
-0.012406354770064354,
0.034292496740818024,
0.029211832210421562,
0.03421667590737343,
-0.005768273025751114,
0.006254328414797783,
-0.026753487065434456,
-0.00468679191544652,
0.055619146674871445,
-0.0350496768951416,
0.013963920995593071,
0.00041576253715902567,
-0.015123299323022366,
-0.022075317800045013,
-0.02746514230966568,
-0.004275246523320675,
-0.07330011576414108,
0.06429232656955719,
-0.0649833157658577,
0.05031541362404823,
-0.04222490265965462,
0.05441223457455635,
0.005007573869079351,
-0.013157720677554607,
0.019387803971767426,
0.06148741394281387,
0.07568087428808212,
0.0017153304070234299,
-0.03135368973016739,
-0.004160989075899124,
-0.06185078248381615,
-0.01822744309902191,
0.010151275433599949,
-0.056071262806653976,
-0.0017012988682836294,
-0.01908739097416401,
-0.06017998978495598,
0.07312842458486557,
0.03093794919550419,
-0.005371186416596174,
-0.004118384327739477,
0.025425851345062256,
0.012479686178267002,
0.04168976470828056,
-0.03863990306854248,
0.026309164240956306,
0.047770529985427856,
0.04070524871349335,
0.04815252870321274,
-0.020376965403556824,
0.04027533158659935,
0.008527817204594612,
0.05311586707830429,
0.013893879018723965,
-0.01695997081696987,
0.042104192078113556,
-0.022464962676167488,
0.02037077210843563,
0.005236465949565172,
0.0037249289453029633,
0.0009768608724698424,
0.03402215242385864,
0.010273975320160389,
-0.015426755882799625,
0.022205812856554985,
-0.014443464577198029,
0.013338840566575527,
-0.002728519029915333,
-0.03787977248430252,
0.026760919019579887,
-0.018653590232133865,
0.031012600287795067,
0.10629067569971085,
-0.00166404212359339,
0.0247013121843338,
-0.0016561561496928334,
-0.022839825600385666,
-0.036230962723493576,
-0.0007093106396496296,
-0.00724987406283617,
0.02124403789639473,
0.0050056506879627705,
0.033994369208812714,
-0.01102761086076498,
-0.019352542236447334,
0.021516410633921623,
-0.0386388897895813,
0.08274976909160614,
0.09357675909996033,
-0.011637796647846699,
-0.001632300321944058,
-0.0108977435156703,
-0.00472418824210763,
-0.04855756089091301,
0.03405158221721649,
0.03533271327614784,
0.027403203770518303,
-0.037381548434495926,
0.02145194448530674,
0.004021949600428343,
0.013410473242402077,
0.007005936000496149,
-0.0010380862513557076,
-0.03240647539496422,
0.00576617568731308,
-0.08508290350437164,
-0.06076735258102417,
0.04255497828125954,
0.019093802198767662,
0.020234618335962296,
-0.08178077638149261,
-0.011784551665186882,
0.029074668884277344,
0.10264269262552261,
0.02342400513589382,
0.01939011737704277,
-0.0559697151184082,
0.0007404495845548809,
-0.009690599516034126,
-0.058484625071287155,
-0.01284374576061964,
0.009465409442782402,
-0.031302180141210556,
-0.019779175519943237,
-0.031609274446964264,
-0.004621878731995821,
-0.0025365441106259823,
-0.0387483648955822,
0.01734396629035473,
0.04913434386253357,
0.004633880686014891,
-0.015562999993562698,
0.04218770191073418,
0.0016457217279821634,
-0.046830225735902786,
0.08813781291246414,
0.03617384657263756,
0.0013470924459397793,
-0.010363966226577759,
-0.020741846412420273,
-0.04372869059443474,
-0.034044910222291946,
-0.007256107870489359,
0.03345610201358795,
-0.005035544745624065,
0.008934983983635902,
-0.023420164361596107,
0.006635264493525028,
0.020782895386219025,
-0.017722882330417633,
-0.006262688897550106,
-0.02704857476055622,
0.051053982228040695,
0.07073178887367249,
0.059081047773361206,
0.0007806592038832605,
-0.011062721721827984,
0.03908302262425423,
-0.06480139493942261,
-0.0019862509798258543,
0.006935914047062397,
0.015130015090107918,
0.039188362658023834,
-0.05007898062467575,
0.021806832402944565,
-0.012170104309916496,
-0.0030575369019061327,
0.0026417758781462908,
-0.04563428461551666,
-0.014130303636193275,
0.016048109158873558,
0.04230973869562149,
0.0033735784236341715,
0.031808122992515564,
0.04521237313747406,
0.026016196236014366,
-0.03361804410815239,
0.024241184815764427,
-0.027481289580464363,
-0.04869978129863739,
-0.027943188324570656,
-0.02116488665342331,
0.025509322062134743,
0.03498011827468872,
0.028937924653291702,
0.025415118783712387,
-0.01097309123724699,
-0.012576929293572903,
-0.006279929541051388,
0.007423158269375563,
0.04156551510095596,
0.05425954610109329,
0.02509954757988453,
-0.0023851008154451847,
0.00815605465322733,
0.0023940347600728273,
0.02211468480527401,
-0.005569678731262684,
-0.0362638495862484,
-0.05542442947626114,
0.005300099961459637,
0.03484612703323364,
-0.02136555314064026,
-0.017500663176178932,
-0.03821251168847084,
0.05299852043390274,
-0.003567613661289215,
0.08923839032649994,
0.01976601965725422,
-0.06852707266807556,
-0.015329121612012386,
0.013845526613295078,
0.026447512209415436,
0.015243313275277615,
-0.0006328477757051587,
-0.000889405666384846,
0.052409399300813675,
0.04257267713546753,
0.03129652515053749,
0.01867835596203804,
0.03149515762925148,
0.014954338781535625,
0.000985251390375197,
0.012115810066461563,
-0.004532535094767809,
0.024516073986887932,
-0.03024926222860813,
0.0366048663854599,
0.05675441026687622,
-0.018626363947987556,
0.004003404639661312,
-0.029376866295933723,
0.007745108567178249,
0.011925651691854,
-0.023958273231983185,
-0.006987551227211952,
-0.0007941347430460155,
0.0377211719751358,
-0.00849203858524561,
0.025154106318950653,
-0.037883684039115906,
0.00013769064389634877,
-0.06932894885540009,
0.01820211298763752,
0.0016802923055365682,
-0.012305848300457,
0.022165749222040176,
-0.023512480780482292,
-0.019718332216143608,
0.025633180513978004,
-0.007085990160703659,
0.025728244334459305,
0.030616531148552895,
-0.01683778315782547,
-0.008465494960546494,
-0.0015835108933970332,
-0.01370906364172697,
-0.007465221453458071,
-0.001010218751616776,
-0.02054518647491932,
-0.014316800981760025,
-0.01078434195369482,
-0.06621144711971283,
-0.013849548064172268,
-0.004471500404179096,
-0.012471322901546955,
-0.010704525746405125,
-0.013003360480070114,
0.0004873504221905023,
-0.005973818711936474,
-0.021225130185484886,
0.013353747315704823,
-0.09053271263837814,
0.009547468274831772,
-0.023449309170246124,
-0.010493987239897251,
-0.008231114596128464,
-0.012737885117530823,
0.017944075167179108,
0.012565340846776962,
0.016383033245801926,
0.016381116583943367,
-0.048361483961343765,
-0.0804954394698143,
0.025886261835694313,
-0.02571345493197441,
-0.0039027142338454723,
-0.028212150558829308,
-0.018057608976960182,
0.05469032749533653,
0.03081432916224003,
-0.030895719304680824,
-0.05606731027364731,
0.01358137745410204,
0.010092862881720066,
-0.05827462300658226,
0.022634629160165787,
0.017088664695620537,
-0.009419302456080914,
0.0271593127399683,
-0.03386571258306503,
0.04089353606104851,
0.019968517124652863,
0.0077162329107522964,
-0.02220354974269867,
0.019929151982069016,
-0.024389619007706642,
0.007191753014922142,
0.0788615494966507,
0.036126162856817245,
-0.021024009212851524,
0.01391263585537672,
-0.003089071484282613,
0.07618072628974915,
0.016539987176656723,
-0.08273705095052719,
0.005257739685475826,
0.006065286695957184,
0.02641039714217186,
-0.02001560665667057,
0.02573884092271328,
0.00973608996719122,
0.011805896647274494,
0.010346155613660812,
0.024790914729237556,
0.033503301441669464,
-0.018930625170469284,
-0.018671339377760887,
0.0582854300737381,
0.02539924532175064,
0.023709964007139206,
-0.009730341844260693,
-0.02588159404695034,
-0.029179057106375694,
0.012737228535115719,
-0.05846940353512764,
-0.06571881473064423,
0.029116390272974968,
0.05996398627758026,
0.02018771506845951,
-0.040921203792095184,
-0.026225024834275246,
0.002706584520637989,
-0.03088158741593361,
-0.03844441473484039,
-0.026426181197166443,
0.07640589773654938,
0.025106366723775864,
0.030517520383000374,
0.011872678063809872,
0.012094945646822453,
-0.015861235558986664,
-0.014037763699889183,
-0.07965703308582306,
0.039883170276880264,
0.038349300622940063,
-0.04947775974869728,
-0.02470867522060871,
0.008166983723640442,
-0.014825545251369476,
-0.07782452553510666,
0.007530984468758106,
-0.04447651654481888,
0.011751826852560043,
-0.039219751954078674,
0.0038733722176402807,
0.0015854757511988282,
-0.019653303548693657,
-0.030097944661974907,
0.053967781364917755,
0.0347554087638855,
0.011772346682846546,
0.012700458988547325,
-0.00035095529165118933,
-0.0010211407206952572,
-0.0006501718307845294,
-0.02507152408361435,
-0.017565956339240074,
-0.005684776231646538,
0.01651056297123432,
0.03660139814019203,
0.016073420643806458,
-0.0435611754655838,
0.024459030479192734,
0.0053337085992097855,
0.028140509501099586,
0.012783624231815338,
-0.016765547916293144,
0.007537449710071087,
-0.019785694777965546,
0.01239222101867199,
-0.0013890843838453293,
0.06494387239217758,
-0.05107581242918968,
-0.015240456908941269,
0.031245017424225807,
0.002321939216926694,
-0.04409299045801163,
0.05487152934074402,
0.0260342787951231,
-0.038716915994882584,
0.011622190475463867,
-0.04198670759797096,
0.01774619147181511,
-0.036690548062324524,
0.0243294108659029,
0.014864862896502018,
0.02470530942082405,
-0.022456269711256027,
-0.0029163563158363104,
0.009152911603450775,
0.02240801230072975,
-0.015076407231390476,
-0.020343314856290817,
-0.022590504959225655,
0.004628384485840797,
-0.01453313883394003,
0.00610900716856122,
0.018508436158299446,
-0.0012874488020315766,
0.03449445962905884,
-0.021933523938059807,
0.003025090554729104,
-0.08886594325304031,
-0.04928016662597656,
0.01171823963522911,
0.00509793683886528,
0.01386902667582035,
-0.009280435740947723,
-0.016104556620121002,
-0.03276530280709267,
0.02335006557404995,
-0.008548307232558727,
0.03174510970711708,
0.006263784132897854,
-0.02300511859357357,
-0.04391755163669586,
-0.011672459542751312,
-0.05946182459592819,
0.03394008427858353,
-0.003150031203404069,
-0.0013882287312299013,
-0.030614133924245834,
0.005857900250703096,
0.030324019491672516,
0.03224862366914749,
0.04872141033411026,
0.04597369581460953,
0.0004407750675454736,
-0.030689846724271774,
-0.003755624871701002,
0.014787380583584309,
-0.02770775929093361,
-0.025272738188505173,
0.014807351864874363,
0.01164363045245409,
0.009042983874678612,
0.0661851242184639,
-0.019111424684524536,
-0.03581428527832031,
0.043183833360672,
0.0386703722178936,
-0.02168447896838188,
0.013718312606215477,
0.011132939718663692,
0.03705977648496628,
0.030604638159275055,
-0.008099674247205257,
0.03430603817105293,
0.012619109824299812,
-0.0010802578181028366,
0.033965710550546646,
-0.02262730337679386,
0.06072816997766495,
-0.029148688539862633,
-0.012482290156185627,
-0.01274918857961893,
-0.004780441988259554,
-0.010290774516761303,
0.010955662466585636,
0.0078660286962986,
0.027612389996647835,
-0.030483568087220192,
-0.04209262877702713,
0.00013131812738720328,
0.026575889438390732,
-0.03964662551879883,
0.01027942169457674,
0.008056393824517727,
0.035104330629110336,
0.01658237911760807,
0.015115589834749699,
0.03981361165642738,
-0.013322057202458382,
-0.022176144644618034,
0.012232844717800617,
-0.019139723852276802,
0.03947536274790764,
-0.033536069095134735,
-0.029309090226888657,
0.007608042564243078,
-0.061197679489851,
0.07187339663505554,
-0.014311933889985085,
0.026276538148522377,
-0.03177037462592125,
-0.0343221053481102,
-0.020586084574460983,
0.0328446589410305,
-0.006274894345551729,
-0.0006168559775687754,
-0.04055097699165344,
0.03982439264655113,
-0.013528186827898026,
-0.03592114895582199,
-0.07377120852470398,
-0.004658290185034275,
0.01369496714323759,
0.02539799176156521,
-0.05199597403407097,
0.01144320983439684,
-0.010104683227837086,
0.03245201334357262,
-0.008830339647829533,
0.008597630076110363,
0.011519009247422218,
-0.014392168261110783,
-0.023968307301402092,
0.01051122136414051,
-0.002147004706785083,
0.06914903968572617,
-0.017089825123548508,
-0.024787480011582375,
0.009278146550059319,
-0.007583285681903362,
-0.017772739753127098,
0.01264442689716816,
0.004342430271208286,
-0.04217829927802086,
-0.05160342901945114,
-0.037785496562719345,
0.013124175369739532,
0.05190347135066986,
0.0064860456623137,
-0.007735998369753361,
0.01405425276607275,
0.027832167223095894,
0.02297854796051979,
0.00787810143083334,
-0.02747160755097866,
-0.00011996254761470482,
0.01675783470273018,
-0.034800443798303604,
0.0002851736207958311,
-0.06202347204089165,
-0.003007745835930109,
0.014374271035194397,
-0.02581111714243889,
0.02939174696803093,
-0.0574209988117218,
0.08028516918420792,
0.012792326509952545,
-0.02571725659072399,
0.0453869104385376,
0.019898660480976105,
-0.011680797673761845,
0.027454078197479248,
-0.0063706315122544765,
0.0340355783700943,
0.022925717756152153,
-0.022792980074882507,
-0.02960045076906681,
-0.04561539739370346,
-0.04475274309515953,
0.07865756005048752,
-0.04337550699710846,
0.03513379022479057,
0.008437782526016235,
-0.026413699612021446,
-0.032229430973529816,
-0.025076964870095253,
-0.03243722394108772,
0.0028353920206427574,
-0.0144953653216362,
0.05652065947651863,
-0.05988546833395958,
-0.04354066029191017,
-0.0006902006571181118,
0.05002307519316673,
-0.01876680552959442,
-0.014371072873473167,
0.030086712911725044,
0.07508469372987747,
0.017740152776241302,
-0.05306357890367508,
-0.030658192932605743,
0.039260149002075195,
-0.011371146887540817,
0.01587785966694355,
0.07681827247142792,
-0.003065573750063777,
0.0380864255130291,
0.022418323904275894,
0.03585347533226013,
-0.043584536761045456,
0.0018600913463160396,
-0.0036898155231028795,
0.020661771297454834,
0.003548956476151943,
-0.028095850721001625,
0.033193301409482956,
-0.04247097671031952,
0.010531434789299965,
0.017683781683444977,
0.044488485902547836,
-0.0383325032889843,
-0.050693877041339874,
-0.0029967566952109337,
-0.019452067092061043,
-0.0492410808801651,
0.0802445039153099,
-0.040718868374824524,
-0.011911436915397644,
0.04923978075385094,
-0.033069685101509094,
0.041506312787532806,
0.025123240426182747,
0.04741812124848366,
-0.024763481691479683,
0.029018305242061615,
-0.047499511390924454,
0.050315771251916885,
0.032713938504457474,
0.01877656951546669,
0.11232229322195053,
0.03335953131318092,
0.017978783696889877,
-0.06445303559303284,
0.01249944232404232,
-0.007625210098922253,
0.012603740207850933,
-0.03777271509170532,
0.021981822326779366,
-0.019896654412150383,
0.005234197713434696,
0.009001319296658039,
0.04511890187859535,
-0.031114445999264717,
0.0018072879174724221,
0.009526250883936882,
-0.028730370104312897,
0.03777225315570831,
0.05086637660861015,
0.016948480159044266,
0.010635063983500004,
0.012736181728541851,
-0.03619048744440079,
0.03705041483044624,
-0.03522210195660591,
-0.010452201589941978,
-0.0288391150534153,
0.00757115613669157,
0.01488454733043909,
-0.009146486409008503,
-0.03152662143111229,
0.027460291981697083,
0.00022357988927979022,
0.013365129940211773,
0.021840762346982956,
0.036117881536483765,
0.018756037577986717,
0.01099217776209116,
0.0032993953209370375,
0.021946314722299576,
0.020312383770942688,
-0.03717565909028053,
0.04943491891026497,
0.03512169420719147,
0.00029084307607263327,
-0.03591146692633629,
-0.02940279059112072,
0.03800070285797119,
-0.0038945127744227648,
0.010447797365486622,
-0.038096725940704346,
0.03708568215370178,
-0.01891280710697174,
-0.03500198572874069,
-0.02057572454214096,
-0.013840182684361935,
-0.005710429046303034,
-0.022650206461548805,
-0.009193414822220802,
0.003963910974562168,
0.022971585392951965,
0.012794780544936657,
-0.022633712738752365,
-0.026058927178382874,
0.030971715226769447,
0.005784804001450539,
0.04967955872416496,
0.05404480919241905,
0.05355605110526085,
-0.035738758742809296,
-0.006874338258057833,
-0.0020691100507974625,
-0.03209276869893074,
-0.013126702979207039,
0.03639649599790573,
-0.018185190856456757,
0.023085152730345726,
-0.013384685851633549,
-0.04511255398392677,
-0.04914000630378723,
-0.06327155232429504,
0.013353397138416767,
-0.027828874066472054,
-0.025969302281737328,
0.007202538195997477,
-0.04148513451218605,
0.01724115014076233,
0.03214406594634056,
-0.01694764941930771,
-0.006115911994129419,
0.04911495000123978,
0.05756131932139397,
0.03455445170402527,
-0.019006336107850075,
-0.061605554074048996,
-0.010099739767611027,
-0.0042465063743293285,
0.005120852496474981,
0.008420044556260109,
0.04173898324370384,
0.013352369889616966,
0.017339613288640976,
0.011763500981032848,
0.020779268816113472,
-0.04961822181940079,
-0.0038364531937986612,
0.007370098028331995,
-0.02531595714390278,
0.002279438776895404,
-0.0348472036421299,
0.02884718030691147,
-0.030601661652326584,
-0.02146720141172409,
-0.015167836099863052,
-0.02200605720281601,
0.05008819326758385,
-0.0094715915620327,
-0.0020478961523622274,
0.017681894823908806,
0.00514609320089221,
-0.036935556679964066,
-0.017296452075242996,
0.016629213467240334,
0.009610427543520927,
0.018200458958745003,
-0.013828229159116745,
0.03787429258227348,
-0.03869317099452019,
0.025593452155590057,
-0.02409515529870987,
-0.03577280789613724,
0.005737979430705309,
0.05099606513977051,
0.03352305293083191,
-0.019543839618563652,
-0.009222134947776794,
0.011605359613895416,
0.03792865574359894,
-0.013867405243217945,
0.014629735611379147,
0.0225868858397007,
-0.027622653171420097,
-0.039124324917793274,
0.014192539267241955,
-0.01021555345505476,
0.021271413192152977,
0.01462888065725565,
-0.010846490040421486,
0.016215793788433075,
0.025932608172297478,
-0.02511277236044407,
-0.031567420810461044,
0.007545193657279015,
0.006757493130862713,
0.03126109018921852,
-0.04400469362735748,
0.0071163056418299675,
0.006123489700257778,
-0.010547316633164883,
-0.0041201477870345116,
0.0025716747622936964,
-0.04253301024436951,
0.03055819310247898,
-0.022575868293642998,
-0.032835934311151505,
-0.04422254115343094,
0.0006224695243872702,
-0.036095041781663895,
-0.0016718391561880708,
0.024039164185523987,
-0.008537331596016884,
-0.009658434428274632,
0.010909651406109333,
0.0014968941686674953,
-0.0650395080447197,
-0.012802316807210445,
-0.013955701142549515,
0.0375196747481823,
0.03106597624719143,
-0.042542509734630585,
0.0028717797249555588,
0.06391208618879318,
-0.04216974973678589,
-0.006983086932450533,
-0.024828488007187843,
-0.006837706547230482,
-0.0643116682767868,
-0.0030779619701206684,
-0.04749200865626335,
0.01916927844285965,
0.015607733279466629,
0.0006257555796764791,
0.031613629311323166,
0.016933945938944817,
-0.024941401556134224,
-0.037632379680871964,
0.01157753448933363,
-0.007463280577212572,
0.018139012157917023,
-0.028949076309800148,
0.04478929564356804,
-0.025125816464424133,
-0.006756237708032131,
0.015735376626253128,
-0.03776358440518379,
0.03702816367149353,
-0.012018454261124134,
-0.014883778057992458,
-0.013219529762864113,
0.012906546704471111,
0.013886173255741596,
-0.02610776200890541,
0.025380650535225868,
0.017231596633791924,
0.01859845407307148,
0.018088120967149734,
0.0075912075117230415,
-0.019816627725958824,
0.03854524344205856,
-0.052857886999845505,
-0.01755136251449585,
0.02902594767510891,
-0.017095012590289116,
-0.011821365915238857,
0.04656391963362694,
0.0014479223173111677,
0.005160685628652573,
-0.07678315043449402,
-0.006179040297865868,
-0.061565250158309937,
-0.010124280117452145,
0.012487252242863178,
0.04955730587244034,
-0.011045984923839569,
-0.01448028814047575,
-0.04395531490445137,
-0.057817455381155014,
0.046701449900865555,
-0.01895209774374962,
-0.04856279119849205,
-0.006896084640175104,
-0.023614568635821342,
0.017184007912874222,
0.000011011116839654278,
0.011053693480789661,
0.0012290736194700003,
-0.025057701393961906,
0.02452881820499897,
-0.01631264202296734,
-0.007109721656888723,
-0.03359371796250343,
-0.031188957393169403,
0.00837541650980711,
-0.02098080888390541,
0.02347405068576336,
0.009221899323165417,
0.024931790307164192,
-0.02693111076951027,
-0.03829719498753548,
0.007020735181868076,
0.035891130566596985,
0.050712913274765015,
0.02242080308496952,
-0.015016380697488785,
-0.0015562938060611486,
-0.016635606065392494,
0.021154167130589485,
-0.024594586342573166,
0.012856344692409039,
-0.031368184834718704,
-0.012643315829336643,
-0.01639407128095627,
-0.01110097300261259,
-0.011014120653271675,
-0.008197340182960033,
0.01218554750084877,
0.03638826310634613,
0.015000147745013237,
0.026496030390262604,
0.0010113464668393135,
0.036244045943021774,
-0.013901660218834877,
0.005522736348211765,
0.05624041706323624,
0.005675440654158592,
0.025121236220002174,
0.022225821390748024,
0.006055518519133329,
-0.030832091346383095,
-0.009623868390917778,
-0.023706015199422836,
0.02702021785080433,
-0.034353747963905334,
0.0051531302742660046,
-0.018542973324656487,
-0.04547073319554329,
0.013776194304227829,
0.02733897604048252,
-0.02607918716967106,
-0.028886456042528152,
0.06252902001142502,
-0.026134729385375977,
0.00037529136170633137,
-0.011892907321453094,
0.0006600750493817031,
0.01234288327395916,
-0.020339716225862503,
-0.04371925815939903,
0.033983174711465836,
-0.00003075552376685664,
0.031118256971240044,
0.022401941940188408,
0.030346553772687912,
-0.012887734919786453,
-0.005066407844424248,
0.03261738643050194,
0.006459927186369896,
0.008595120161771774,
-0.015461543574929237,
-0.015259130857884884,
0.02436749078333378,
-0.01219291239976883,
0.026022063568234444,
0.0009390495833940804,
0.06602945178747177,
0.010949741117656231,
0.061714839190244675,
-0.036812674254179,
0.025402873754501343,
-0.04784809425473213,
0.04709517955780029,
0.0178902018815279,
0.021646473556756973,
-0.006282371934503317,
0.0051555391401052475,
-0.05497555062174797,
0.01977509818971157,
0.025796284899115562,
-0.05960066244006157,
0.013166850432753563,
0.015114443376660347,
-0.031188832595944405,
-0.00911285076290369,
-0.007455397397279739,
-0.008752240799367428,
-0.00081781973131001,
-0.027640454471111298,
0.011659235693514347,
-0.020126160234212875,
0.01394115760922432,
0.012480171397328377,
-0.011163230054080486,
0.03868342936038971,
-0.06700868159532547,
-0.02593032829463482,
-0.020735012367367744,
0.021662600338459015,
-0.004953351803123951,
0.015352348797023296
] |
<p><strong>What is quantum entanglement?</strong></p>
<p>Please be pedagogical.</p>
<p><strong>Edit:</strong> I have updated my background under my profile.</p>
| 8,809 |
[
-0.0003996878513135016,
-0.026557307690382004,
0.0006791118066757917,
-0.014143010601401329,
0.021211035549640656,
0.01086116861552,
-0.00417041452601552,
-0.021189693361520767,
-0.006298160646110773,
-0.034215111285448074,
0.05278146639466286,
0.04903508350253105,
0.007225112523883581,
0.039575282484292984,
-0.014610068872570992,
0.014166994951665401,
0.03900618106126785,
-0.014808171428740025,
-0.004716312047094107,
0.012058254331350327,
-0.012993993237614632,
0.011096972040832043,
-0.0042684501968324184,
0.015473800711333752,
-0.002604367909952998,
0.025970716029405594,
0.04961571842432022,
-0.00527499383315444,
0.03694821149110794,
0.08823327720165253,
-0.009631753899157047,
-0.011472410522401333,
0.002627116395160556,
0.01061163004487753,
0.00692460173740983,
-0.03099512867629528,
-0.040584784001111984,
-0.007603992708027363,
0.02239488996565342,
-0.00392599031329155,
0.0059699323028326035,
-0.021478332579135895,
-0.003859300632029772,
0.0643647313117981,
-0.04801686480641365,
-0.004510970786213875,
0.02964635007083416,
-0.041355881839990616,
0.030557287856936455,
-0.07070428878068924,
0.03359660506248474,
0.009139671921730042,
0.01567804254591465,
-0.0012590826954692602,
-0.014847774989902973,
0.009764102287590504,
0.06857948750257492,
0.08179385960102081,
-0.016258059069514275,
-0.04201218858361244,
-0.015805134549736977,
-0.011374958790838718,
0.015933675691485405,
-0.012337182648479939,
-0.058437857776880264,
0.027440927922725677,
-0.005144347902387381,
0.009106558747589588,
0.011192257516086102,
-0.006770234555006027,
-0.02007785066962242,
0.03526821732521057,
0.07541078329086304,
0.00518075143918395,
0.025879643857479095,
-0.05822862684726715,
0.026315661147236824,
0.03977154567837715,
0.028188155964016914,
0.04716864228248596,
0.00022798085410613567,
-0.0035098399966955185,
0.03896245360374451,
-0.016223175451159477,
-0.0041428725235164165,
-0.03697875887155533,
0.10454081743955612,
-0.004521339200437069,
-0.04767362028360367,
0.030859658494591713,
0.005792359355837107,
0.014258752577006817,
0.018219800665974617,
-0.0055017173290252686,
-0.012042200192809105,
0.015122268348932266,
-0.007936542853713036,
0.03960995748639107,
0.012615352869033813,
-0.021099431440234184,
0.016120970249176025,
-0.013967497274279594,
0.04752359166741371,
0.059701427817344666,
0.010327067226171494,
-0.000565798080060631,
0.0005659887101501226,
0.02799208275973797,
0.023950856178998947,
-0.010629205033183098,
-0.046160973608493805,
0.014083960093557835,
0.002476730849593878,
-0.016929613426327705,
-0.007454976439476013,
-0.034949157387018204,
-0.0002091498172376305,
0.00031811583903618157,
0.06070810928940773,
0.04508616402745247,
0.02613789774477482,
-0.03868311643600464,
0.02021939866244793,
-0.028355928137898445,
-0.0759105458855629,
0.02758154459297657,
0.028170466423034668,
-0.004643912892788649,
-0.0592811144888401,
0.05891038477420807,
-0.021171964704990387,
0.0020561337005347013,
-0.009722243063151836,
0.000964912585914135,
0.025274643674492836,
-0.023079583421349525,
-0.1329198181629181,
-0.07992175221443176,
0.07211513817310333,
-0.004437643568962812,
-0.026886990293860435,
-0.0785161480307579,
0.04797388240695,
0.03138937056064606,
0.08219245821237564,
0.00879044272005558,
0.006023549009114504,
0.007015884388238192,
-0.006727708503603935,
0.03756735473871231,
-0.022732505574822426,
0.0030485091265290976,
-0.006871581543236971,
-0.04041089117527008,
0.02162785269320011,
-0.05495066195726395,
0.015493681654334068,
0.06298188865184784,
-0.02395184524357319,
-0.03460109233856201,
0.07268901914358139,
-0.018571985885500908,
0.010393218137323856,
0.024307237938046455,
-0.041014280170202255,
-0.032829876989126205,
0.0701252892613411,
0.011167832650244236,
0.008306811563670635,
0.0541703924536705,
-0.012298272922635078,
0.02178211510181427,
-0.017653195187449455,
0.014281973242759705,
-0.011833660304546356,
-0.009396257810294628,
-0.0031420623417943716,
0.0035289248917251825,
0.004040148574858904,
-0.012639770284295082,
-0.06054281070828438,
-0.03254492208361626,
-0.024714726954698563,
0.036840975284576416,
-0.016508495435118675,
0.02739236317574978,
-0.012068607844412327,
-0.022908229380846024,
-0.02960069477558136,
-0.04415065795183182,
-0.023958947509527206,
-0.05923924967646599,
0.048019152134656906,
0.00014583436131943017,
-0.024450179189443588,
0.0010063109220936894,
0.028655052185058594,
0.028537031263113022,
-0.031168898567557335,
-0.03213229030370712,
-0.03285856917500496,
0.034187883138656616,
0.04270303621888161,
-0.015758240595459938,
-0.007875245995819569,
0.0729905217885971,
0.00909811444580555,
-0.030903704464435577,
0.023789754137396812,
-0.02709195576608181,
0.0019605138804763556,
-0.010825163684785366,
-0.0009998532477766275,
0.030615435913205147,
-0.012388193048536777,
-0.006150837522000074,
-0.007370680570602417,
0.008001585491001606,
-0.007881827652454376,
0.028613878414034843,
-0.021862754598259926,
0.06870939582586288,
-0.009473641403019428,
-0.011258351616561413,
-0.015802565962076187,
0.021114839240908623,
0.014083520509302616,
-0.006007621996104717,
-0.010220560245215893,
0.01693718694150448,
-0.04340451955795288,
0.02326834760606289,
-0.010794887319207191,
0.0018816590309143066,
-0.04015900939702988,
0.01969045400619507,
-0.01922232285141945,
0.050681259483098984,
0.00894105900079012,
0.01006555650383234,
-0.04766851291060448,
-0.001682473812252283,
0.007407311350107193,
-0.03650250658392906,
0.007563956547528505,
0.028411224484443665,
0.002594346646219492,
0.03303724154829979,
0.03068186528980732,
-0.014205142855644226,
-0.0428340882062912,
0.05527040362358093,
-0.027758698910474777,
0.0038914154283702374,
-0.004826189484447241,
-0.02028745226562023,
-0.002321295440196991,
-0.03619246929883957,
0.022333968430757523,
-0.005445499438792467,
-0.006275225430727005,
-0.033009156584739685,
-0.0034476188011467457,
-0.0488082654774189,
0.001417022431269288,
-0.015638142824172974,
-0.010062512010335922,
0.013862096704542637,
0.04545051231980324,
-0.006917300168424845,
0.018802473321557045,
-0.006887244526296854,
0.0009910856606438756,
-0.0012171360431239009,
0.0071329157799482346,
0.022748563438653946,
-0.0053476328030228615,
0.03531371429562569,
-0.04808807000517845,
-0.07024539262056351,
-0.024507999420166016,
-0.03519187867641449,
0.03038179688155651,
-0.003085828386247158,
-0.054326727986335754,
0.028938550502061844,
-0.025057634338736534,
-0.01676231063902378,
0.005216929130256176,
-0.015553553588688374,
0.0017110659973695874,
0.01234931405633688,
-0.008695798926055431,
-0.020570805296301842,
-0.017557961866259575,
-0.04840591922402382,
0.0256910789757967,
-0.051858581602573395,
-0.020373404026031494,
0.030074799433350563,
-0.04077698662877083,
-0.02944713458418846,
-0.002996902447193861,
-0.026574162766337395,
-0.03315262869000435,
-0.018029384315013885,
-0.009544010274112225,
0.0236118845641613,
-0.026534048840403557,
-0.05000454932451248,
0.013398031704127789,
-0.01812998577952385,
-0.009316541254520416,
-0.03725621476769447,
-0.06033029034733772,
0.042842425405979156,
0.016399996355175972,
0.04755792394280434,
0.0076183234341442585,
-0.017321251332759857,
0.08255298435688019,
0.006602747831493616,
-0.03270971029996872,
-0.029754698276519775,
-0.019962189719080925,
-0.016776273027062416,
-0.036842960864305496,
0.036100950092077255,
0.02499683015048504,
-0.020326798781752586,
0.03140045702457428,
0.020391346886754036,
0.008435132913291454,
0.04395482689142227,
0.016942109912633896,
-0.05004481226205826,
-0.007000352256000042,
-0.020145611837506294,
-0.0032292779069393873,
0.06175849214196205,
0.02176189422607422,
-0.058997366577386856,
-0.0026463172398507595,
0.014676413498818874,
0.022129368036985397,
0.00829620473086834,
-0.016177119687199593,
0.06995195895433426,
0.0063225263729691505,
0.00632814085111022,
-0.033492449671030045,
0.053235672414302826,
-0.03520554304122925,
-0.012726189568638802,
-0.012218168005347252,
-0.0003584246151149273,
0.009174507111310959,
-0.013826738111674786,
0.004881821107119322,
0.03178635239601135,
0.04188373312354088,
-0.04084646701812744,
-0.02138446271419525,
-0.010979198850691319,
0.011782671324908733,
0.01884567178785801,
0.0032931023743003607,
-0.032556477934122086,
0.07340491563081741,
0.028571315109729767,
0.032990846782922745,
-0.0025512967258691788,
-0.03754403069615364,
-0.04082901403307915,
-0.08064988255500793,
0.02362135238945484,
0.020948821678757668,
0.05077757686376572,
0.005014521069824696,
0.06292374432086945,
0.03979482874274254,
0.002569622127339244,
0.009908770211040974,
0.0057509480975568295,
-0.05397006869316101,
0.01827896386384964,
-0.039021387696266174,
-0.011570013128221035,
0.02168041095137596,
-0.02173968032002449,
-0.03956351429224014,
-0.05687108635902405,
-0.06292996555566788,
-0.01893162913620472,
-0.015825165435671806,
-0.04777053743600845,
-0.02205468900501728,
-0.0028298241086304188,
0.027935286983847618,
0.008960158564150333,
0.04779296740889549,
0.04469335824251175,
-0.002094441093504429,
0.017618536949157715,
0.08685941249132156,
-0.027603602036833763,
0.03062668815255165,
0.011497843079268932,
0.004222719464451075,
0.006320107262581587,
0.03990495949983597,
0.015132485888898373,
0.030304405838251114,
-0.0021516140550374985,
0.00108836789149791,
-0.02039339765906334,
0.01663004420697689,
-0.010800720192492008,
-0.002236524596810341,
0.0077454932034015656,
-0.02814459055662155,
-0.003241791622713208,
-0.01989302970468998,
0.050326939672231674,
-0.03564514219760895,
0.02909582108259201,
0.015116671100258827,
0.02502766065299511,
-0.04444948211312294,
0.019280217587947845,
0.07286801189184189,
0.006289810407906771,
-0.0184391550719738,
-0.0180568415671587,
-0.03623060882091522,
-0.030910789966583252,
-0.0015619326150044799,
-0.01821940764784813,
0.009545172564685345,
-0.026615208014845848,
0.014023842290043831,
0.009527702815830708,
0.010822247713804245,
-0.026412086561322212,
-0.026666292920708656,
-0.03804055601358414,
-0.018299099057912827,
-0.0032953775953501463,
-0.0008759231423027813,
-0.011147004552185535,
0.014544142410159111,
-0.0008642537868581712,
0.010885044932365417,
-0.034345440566539764,
-0.07009395211935043,
-0.021386900916695595,
0.03905760869383812,
0.031759899109601974,
0.011638110503554344,
-0.004569016396999359,
-0.05835706740617752,
-0.054552968591451645,
0.019191855564713478,
-0.025405772030353546,
0.04871174693107605,
-0.026041917502880096,
0.00497397780418396,
-0.037924908101558685,
0.010104031302034855,
0.027942337095737457,
0.030205950140953064,
-0.01706889271736145,
0.03996570035815239,
-0.009440317749977112,
0.005283986683934927,
-0.030011961236596107,
0.018719572573900223,
0.01939651370048523,
0.050187982618808746,
-0.011609802022576332,
0.005286943633109331,
-0.01718490570783615,
0.02845732308924198,
-0.020751073956489563,
-0.09639506787061691,
-0.0006839917623437941,
-0.016431085765361786,
-0.026949582621455193,
0.05260806158185005,
-0.032842718064785004,
-0.03642652556300163,
-0.01858667843043804,
0.0006526844226755202,
-0.019288744777441025,
0.006796301808208227,
-0.03162512555718422,
0.061389584094285965,
0.009335626848042011,
0.015370003879070282,
0.02035832591354847,
0.03988230228424072,
-0.061940956860780716,
0.013548905029892921,
-0.02450043149292469,
0.051236629486083984,
-0.035640470683574677,
0.028959505259990692,
-0.0022287669125944376,
0.009719845838844776,
-0.054846372455358505,
0.04816224426031113,
-0.036845698952674866,
-0.00757240317761898,
-0.025333115831017494,
-0.042612358927726746,
-0.01884416863322258,
0.011389479972422123,
-0.00989458803087473,
0.0023740639444440603,
0.006414466071873903,
-0.024921851232647896,
-0.012804406695067883,
-0.004521566908806562,
0.007552846800535917,
0.026055291295051575,
-0.008585835807025433,
0.018080053851008415,
0.013991985470056534,
0.031047478318214417,
-0.040355175733566284,
-0.04808743670582771,
-0.007583339232951403,
-0.05961545184254646,
0.028072385117411613,
-0.013781778514385223,
0.013116748072206974,
0.035673588514328,
-0.07837789505720139,
-0.04227300360798836,
-0.0010971918236464262,
-0.04033274203538895,
-0.0029952668119221926,
-0.03201136738061905,
0.04565928503870964,
0.010164107196033001,
-0.010844586417078972,
-0.0370667465031147,
-0.06963876634836197,
-0.004179338924586773,
0.018412737175822258,
0.00609299773350358,
-0.005843294318765402,
0.026413220912218094,
-0.011571023613214493,
-0.028376733884215355,
-0.03997492417693138,
0.016469091176986694,
-0.025653576478362083,
-0.029528720304369926,
0.024719728156924248,
-0.023505324497818947,
0.026654906570911407,
0.0074079944752156734,
0.005309766158461571,
-0.02395990677177906,
-0.021760335192084312,
-0.004929257556796074,
-0.013830744661390781,
0.02991083823144436,
-0.030383775010704994,
-0.058116599917411804,
-0.015413886867463589,
0.01652541011571884,
0.021243352442979813,
-0.039389774203300476,
-0.004515316803008318,
-0.00028689534519799054,
0.037247102707624435,
-0.02885681949555874,
-0.0419163703918457,
0.00957157090306282,
-0.012321025133132935,
0.028793977573513985,
0.004475296474993229,
0.005990075413137674,
-0.01308088656514883,
-0.05037200450897217,
0.015975724905729294,
0.02236035279929638,
-0.029768813401460648,
-0.0071790157817304134,
0.06846355646848679,
0.01147462334483862,
0.01700948178768158,
-0.009124808013439178,
-0.05514347925782204,
0.004077581223100424,
-0.0047346362844109535,
0.007542148698121309,
0.014945621602237225,
0.005049184430390596,
-0.018452635034918785,
-0.012326888740062714,
-0.03723948076367378,
-0.013846289366483688,
0.030644671991467476,
-0.014707022346556187,
0.01565525308251381,
0.03640832006931305,
-0.012436355464160442,
0.021906038746237755,
-0.00516887940466404,
-0.009700368158519268,
0.012193377129733562,
0.011990518309175968,
0.025336917489767075,
-0.005004603881388903,
0.0179448239505291,
0.011988397687673569,
0.0714687779545784,
-0.007532134652137756,
0.00968018639832735,
0.04131514951586723,
0.02602333575487137,
0.033380769193172455,
-0.003517981618642807,
-0.03144951909780502,
0.038441553711891174,
-0.03413242846727371,
0.03043122962117195,
-0.0015613053692504764,
-0.011634250171482563,
0.04206030070781708,
-0.028255494311451912,
0.003979674074798822,
-0.016606273129582405,
-0.016799747943878174,
-0.031680669635534286,
-0.003562506753951311,
-0.018002333119511604,
0.02075040340423584,
-0.02489735744893551,
0.004415096249431372,
0.015850795432925224,
-0.006836993619799614,
0.02056060917675495,
-0.014219230972230434,
-0.07340391725301743,
-0.0346706323325634,
0.001592306885868311,
-0.029589520767331123,
0.03368861973285675,
-0.005231859628111124,
-0.036188483238220215,
0.04025870934128761,
-0.029454350471496582,
0.04584876820445061,
0.00912091787904501,
0.05201251059770584,
-0.04653025045990944,
0.05381246656179428,
-0.0034427170176059008,
0.019241342321038246,
0.00758374622091651,
-0.004060076083987951,
0.11231230944395065,
0.05528740957379341,
0.008202401921153069,
-0.07091142982244492,
0.009628154337406158,
-0.01593996211886406,
0.03432590886950493,
-0.007707521319389343,
0.007815268822014332,
-0.01890713721513748,
0.06946312636137009,
0.012304630130529404,
0.03916190192103386,
0.058682844042778015,
-0.008607503026723862,
0.04374600574374199,
-0.028490351513028145,
-0.06570687890052795,
-0.0005222996114753187,
0.01972370408475399,
-0.01438653003424406,
0.023576224222779274,
-0.03806683421134949,
-0.018420634791254997,
-0.016001872718334198,
-0.019849654287099838,
-0.02912740409374237,
-0.019967345520853996,
0.06597286462783813,
0.002595581579953432,
-0.01833055540919304,
0.04263376444578171,
0.008103983476758003,
-0.008095993660390377,
-0.03629953786730766,
0.010134460404515266,
0.04032410681247711,
-0.009086204692721367,
0.02612297795712948,
0.023902632296085358,
0.017236271873116493,
-0.027338381856679916,
0.029019728302955627,
0.005747268442064524,
-0.061617378145456314,
0.000526469957549125,
-0.010102377273142338,
0.054265640676021576,
-0.024976851418614388,
-0.014189548790454865,
-0.020939132198691368,
-0.009801014326512814,
0.018824821338057518,
-0.03749817982316017,
-0.01920393668115139,
0.04236256331205368,
0.029668843373656273,
-0.0217779278755188,
-0.004174660425633192,
-0.037752680480480194,
-0.003429532516747713,
-0.03747652843594551,
0.0320671983063221,
-0.03951558843255043,
0.03058634325861931,
0.0020729938987642527,
0.0031847001519054174,
0.0056678978726267815,
-0.018732400611042976,
0.023898134008049965,
-0.038399651646614075,
-0.012004717253148556,
-0.03266521543264389,
-0.041947316378355026,
0.02255624160170555,
0.02724110148847103,
0.040336642414331436,
0.0038480220828205347,
-0.019422199577093124,
0.006204462144523859,
-0.03889084234833717,
0.04612208902835846,
-0.012475650757551193,
-0.00750200729817152,
-0.013634339906275272,
0.023924099281430244,
0.04647573083639145,
0.03727968782186508,
0.0003394688537809998,
0.016960429027676582,
0.005786720663309097,
-0.021219611167907715,
0.04800504073500633,
0.005779916886240244,
0.012197247706353664,
0.038488127291202545,
-0.05115445703268051,
-0.02393132634460926,
-0.0311935655772686,
0.007971599698066711,
0.016501713544130325,
0.009539471007883549,
-0.007974582724273205,
-0.00538412481546402,
-0.029101189225912094,
-0.011891894042491913,
0.005629478022456169,
-0.016104917973279953,
-0.018314644694328308,
0.03784448280930519,
0.03545458987355232,
-0.02129507064819336,
-0.005823785904794931,
-0.017922915518283844,
0.005191665142774582,
0.007837256416678429,
0.05057811364531517,
-0.011047953739762306,
0.007673284038901329,
0.0235176682472229,
0.06967145204544067,
-0.03416236490011215,
-0.02045368403196335,
-0.03888965770602226,
-0.018955500796437263,
0.03105868399143219,
0.017948154360055923,
0.0009326133877038956,
0.0162665918469429,
0.007022839039564133,
0.023034682497382164,
0.034923091530799866,
0.025446217507123947,
0.010781762190163136,
0.0008081560372374952,
0.040658071637153625,
0.023356860503554344,
0.031942468136548996,
0.004521248396486044,
-0.04096674919128418,
0.05503202974796295,
-0.04797741025686264,
-0.0219881609082222,
0.018358895555138588,
-0.022234659641981125,
0.04749242588877678,
0.05973874777555466,
-0.018323486670851707,
-0.02134576253592968,
0.008770158514380455,
0.00145006796810776,
-0.016969110816717148,
0.02635974995791912,
-0.028133520856499672,
-0.01532694324851036,
0.005740104243159294,
-0.04671275243163109,
-0.004608237650245428,
-0.014080486260354519,
0.0408238060772419,
0.042755745351314545,
0.031265608966350555,
0.011888373643159866,
0.003544778097420931,
0.03683784604072571,
0.03201967850327492,
0.03586835786700249,
-0.004142033867537975,
0.01110862661153078,
0.057102981954813004,
-0.023826871067285538,
0.03850347176194191,
0.004361864645034075,
-0.018330655992031097,
-0.10114012658596039,
0.008547632023692131,
0.013838192448019981,
-0.029437528923153877,
0.040496572852134705,
-0.040647003799676895,
0.06415857374668121,
0.053923919796943665,
-0.06374526768922806,
0.05646480992436409,
-0.030752461403608322,
-0.02361631579697132,
0.0046090660616755486,
0.05574114993214607,
-0.022939013317227364,
0.08565276861190796,
0.02510005794465542,
0.06351081281900406,
0.021604081615805626,
0.02835831418633461,
0.004637903068214655,
-0.012648675590753555,
-0.014045833609998226,
0.0020456903148442507,
-0.026594286784529686,
0.00884872954338789,
0.042302194982767105,
0.007801738101989031,
-0.013809746131300926,
0.03067694790661335,
-0.0418393574655056,
0.006214279681444168,
0.009931991808116436,
0.004912182223051786,
0.01873907446861267,
0.008090678602457047,
0.004310716409236193,
-0.024811692535877228,
-0.03181716427206993,
0.026775861158967018,
0.040014103055000305,
0.06617669016122818,
0.042611632496118546,
-0.00935949757695198,
0.002381875878199935,
-0.038272738456726074,
-0.03299185633659363,
0.03742510452866554,
-0.019081177189946175,
0.02196258120238781,
-0.0209035761654377,
-0.006740770768374205,
0.00395300704985857,
-0.04527992755174637,
-0.014583569020032883,
-0.0523553267121315,
0.015599638223648071,
0.014383634552359581,
0.0104120634496212,
-0.005881814286112785,
0.030342046171426773,
-0.005392592865973711,
-0.03685186058282852,
0.035918768495321274,
-0.0041230712085962296,
0.004640655126422644,
-0.046222005039453506,
-0.0340048111975193,
0.033933669328689575,
-0.0005864574341103435,
0.028212659060955048,
-0.010709223337471485,
-0.02127789333462715,
0.024358626455068588,
0.003586339531466365,
0.0163472518324852,
-0.005804410204291344,
-0.05545613542199135,
-0.03725017234683037,
-0.03476451709866524,
0.05205465108156204,
0.030832570046186447,
0.007718728855252266,
-0.07724998146295547,
-0.012251472100615501,
-0.0024827567394822836,
0.03928063437342644,
0.032780230045318604,
-0.011629738844931126,
-0.012956702150404453,
-0.01835082843899727,
0.020104743540287018,
0.03556397557258606,
-0.004992847330868244,
-0.012185093946754932,
-0.004789533093571663,
-0.01838383637368679,
-0.021942202001810074,
0.003562356112524867,
-0.019236832857131958,
0.01980898529291153,
0.03777886554598808,
-0.009852653369307518,
0.0077634453773498535,
-0.0027906063478440046,
-0.03479774296283722,
0.04347062110900879,
-0.01860429160296917,
-0.0045052142813801765,
0.06726506352424622,
-0.015291222371160984,
0.021344205364584923,
0.02525610290467739,
-0.02677101083099842,
-0.04381321370601654,
0.023009544238448143,
-0.013067861087620258,
-0.020321102812886238,
0.0153072290122509,
-0.0027636606246232986,
0.034765057265758514,
-0.060272179543972015,
-0.016986379399895668,
0.030914103612303734,
-0.06761448830366135,
-0.0017482582479715347,
0.06017876788973808,
0.016740597784519196,
0.029333699494600296,
-0.006378211546689272,
0.018535034731030464,
-0.0012399847619235516,
-0.015447353012859821,
0.0013258024118840694,
0.0600634403526783,
0.01998727209866047,
-0.009604188613593578,
0.057267941534519196,
0.007621330674737692,
-0.008616111241281033,
0.026220371946692467,
0.005140096880495548,
0.03350788354873657,
-0.0313565768301487,
-0.012519897893071175,
0.011669207364320755,
-0.008999203331768513,
0.03364100307226181,
0.028328808024525642,
-0.033337753266096115,
0.07423233985900879,
-0.047103434801101685,
-0.005851240828633308,
0.02155609056353569,
0.02503182739019394,
-0.03728025034070015,
-0.010599089786410332,
0.02614324539899826,
0.0665445327758789,
-0.016941960901021957,
-0.010707160457968712,
-0.019802773371338844,
-0.005620965268462896,
0.0054280562326312065,
-0.038335517048835754,
0.036822400987148285,
-0.004947070498019457,
-0.024858660995960236,
0.005867354571819305,
-0.01100283395498991,
-0.009137572720646858,
-0.012992127798497677,
0.03585025295615196,
0.017851784825325012,
-0.007561278063803911,
-0.026765020564198494,
-0.004934913944453001,
-0.005312889814376831,
0.06078610196709633,
-0.05789347365498543,
0.021998517215251923,
-0.03752343729138374,
0.012083727866411209,
-0.029191702604293823,
-0.0048705837689340115
] |
<p>As you see things that are far smaller, a funny question about this:</p>
<p>Imagine there are many people in a row (all are same height)</p>
<pre><code> A Other Guy B C D
|
you | distance | distance distance
| <--------> | <-------> | <------->
| | | |
| | | |
------------------------------------------------------ floor
</code></pre>
<p>From your point of View you see D much smaller than you, then..
Remember, if this is an "effect" then D is not smaller than you, it's just far away
(and this is not earth curvature, because D is smaller in all sense not only in height)</p>
<p>so..</p>
<p>Imagine you have a laser pointer and want to point your partner's face to annoy him
so
how do you target it?
do you align the laser with the floor at the height of your own face believing in geometry? or do you point directly at the "little person" D ?</p>
<pre><code> A B C D
|. . . . Laser path . . . . . . >. . . . . . >. . . . . . >. . . . >
| ^ |
you | |parallel | |
| | | | |
| v | | |
------------------------------------------------------ floor
</code></pre>
<p>Then you don't hit him, and the "visual effect" became so real that you start to think D is for Dwarf. </p>
<p>There is something Wrong? Physics opinions are welcome!</p>
<p>I think the answer is that floor itself will seem not aligned eigther
so targeting the Dwarf you will be really aligned with floor
because floor itself will have perspective effect.</p>
<pre><code> A B C D
|. . . . Laser path . . .
| | ''''''''''''......
you | | | ......>|
| | | _______|___floor
| | ___________|------
--------------------------
</code></pre>
<p>Anyway its weird</p>
| 8,810 |
[
-0.015046305023133755,
-0.043061140924692154,
-0.009526131674647331,
-0.05447838827967644,
0.044391099363565445,
0.01271646749228239,
-0.036455489695072174,
-0.010803052224218845,
-0.005018658936023712,
-0.0035273218527436256,
0.04788835719227791,
-0.002473748056218028,
0.05365125089883804,
0.031146248802542686,
0.048823628574609756,
0.00849800556898117,
0.018274571746587753,
-0.013110323809087276,
-0.0005401946255005896,
-0.07376161962747574,
0.013414131477475166,
0.008207897655665874,
0.018113605678081512,
-0.04483645036816597,
-0.050060637295246124,
0.0492340624332428,
0.03224637731909752,
-0.03796698898077011,
-0.023338470607995987,
0.02084626816213131,
-0.017087187618017197,
-0.018613876774907112,
-0.024755800142884254,
-0.016784382984042168,
0.015846064314246178,
0.01946033164858818,
-0.016204556450247765,
0.013469504192471504,
0.011079932563006878,
0.018719302490353584,
0.005688876379281282,
0.022144446149468422,
-0.00918044988065958,
0.08315503597259521,
-0.016691328957676888,
0.01781184785068035,
-0.031276870518922806,
0.0013243270805105567,
0.0734921470284462,
-0.07233301550149918,
0.0512065589427948,
-0.012253770604729652,
0.026793139055371284,
-0.01722760684788227,
-0.0025795851834118366,
0.0006233675521798432,
0.04482577368617058,
0.06893080472946167,
-0.018875356763601303,
-0.03451515734195709,
0.003512535011395812,
0.008491197600960732,
-0.019835589453577995,
-0.02241654135286808,
0.03130197152495384,
0.0003770973125938326,
-0.03433092683553696,
-0.009500525891780853,
0.010741762816905975,
0.00024207818205468357,
-0.02635408565402031,
0.016676709055900574,
0.03308992460370064,
0.005899923387914896,
0.053520336747169495,
-0.007651643827557564,
-0.0017962788697332144,
0.019796600565314293,
0.018434865400195122,
0.03033067286014557,
-0.026113083586096764,
-0.021131567656993866,
0.014571086503565311,
0.03506052866578102,
0.025225350633263588,
-0.001128197181969881,
0.05624314770102501,
-0.007050932385027409,
-0.01784346252679825,
0.026702990755438805,
-0.010471475310623646,
-0.007989764213562012,
0.03620360046625137,
0.03603314608335495,
-0.009125025011599064,
-0.002277763094753027,
0.021869990974664688,
0.022841306403279305,
0.00782974436879158,
0.0034213035833090544,
-0.0650990754365921,
0.006219232454895973,
-0.01660841889679432,
0.015437537804245949,
-0.007009541615843773,
-0.019335418939590454,
-0.007978581823408604,
0.04256248101592064,
-0.007035722024738789,
-0.020396364852786064,
-0.04851353541016579,
0.0122935576364398,
0.001633521169424057,
0.007182979956269264,
0.010065947659313679,
-0.049321383237838745,
0.034934476017951965,
-0.013481711968779564,
0.08129290491342545,
0.04905780777335167,
0.014180084690451622,
-0.019124550744891167,
0.033128999173641205,
-0.010831671766936779,
-0.05093897879123688,
0.01869271509349346,
0.032859914004802704,
-0.003080895869061351,
-0.012799401767551899,
0.023724375292658806,
0.0009705909760668874,
0.023762961849570274,
-0.0021943128667771816,
0.007415631785988808,
0.036709610372781754,
0.03267327696084976,
-0.08593656867742538,
-0.052053432911634445,
0.05415412783622742,
0.05093115568161011,
-0.012201509438455105,
-0.09356450289487839,
-0.019587917253375053,
0.02848316915333271,
0.058353181928396225,
-0.006646658759564161,
0.0031994441524147987,
0.01377173326909542,
0.022036368027329445,
0.00469367578625679,
-0.0011155290994793177,
0.02376726269721985,
-0.04966813325881958,
-0.04569946974515915,
0.019424280151724815,
-0.03633580356836319,
-0.0051567512564361095,
0.04355539754033089,
-0.01528907846659422,
-0.006600517313927412,
0.046290408819913864,
-0.012810352258384228,
0.015116509981453419,
0.034078288823366165,
-0.021817998960614204,
0.0038609576877206564,
0.1293182522058487,
0.0300653874874115,
-0.010235613211989403,
0.047072846442461014,
-0.009250838309526443,
0.014399339444935322,
0.0044687893241643906,
-0.00025332265067845583,
0.07041183114051819,
-0.038147177547216415,
0.011949416249990463,
-0.004477114882320166,
0.006967656314373016,
-0.003651432925835252,
-0.05566691607236862,
-0.051131471991539,
-0.026244424283504486,
0.024934940040111542,
0.013565417379140854,
0.03481600061058998,
-0.008073071949183941,
0.015508410520851612,
0.02659076824784279,
-0.039314236491918564,
-0.016140274703502655,
-0.07407108694314957,
-0.005357398651540279,
0.008891426958143711,
-0.0263344869017601,
-0.01563483476638794,
0.0025964416563510895,
-0.008156470023095608,
-0.029951196163892746,
-0.008172130212187767,
0.0182638019323349,
0.03659411892294884,
0.04815809801220894,
-0.02548791654407978,
0.016387686133384705,
0.0801091119647026,
0.05937814339995384,
-0.019304439425468445,
-0.005561153404414654,
-0.02389249950647354,
0.04690973460674286,
0.004151534289121628,
0.019195860251784325,
0.024619942530989647,
0.02065110392868519,
0.019638996571302414,
0.009564310312271118,
0.04979537054896355,
-0.018810704350471497,
-0.009196747094392776,
-0.05776166915893555,
0.04631945863366127,
0.05815529823303223,
-0.034562285989522934,
-0.008272618055343628,
0.014657470397651196,
0.002157671842724085,
-0.0030898863915354013,
0.057119738310575485,
-0.0028783997986465693,
-0.029820729047060013,
0.011259115301072598,
-0.003459544852375984,
0.0012972843833267689,
-0.03987503424286842,
-0.008831311017274857,
0.05358932539820671,
0.010225472040474415,
0.007808870170265436,
0.008170515298843384,
-0.02343205362558365,
-0.017341721802949905,
0.035630613565444946,
0.006139869801700115,
0.02961764484643936,
-0.003005623584613204,
0.01716233417391777,
0.05430781841278076,
-0.00006697130447719246,
-0.004795084707438946,
-0.007127718068659306,
-0.028325680643320084,
-0.011554665863513947,
0.04600595310330391,
0.016673538833856583,
-0.011501557193696499,
0.02890690416097641,
0.018801391124725342,
-0.026687001809477806,
0.0381220281124115,
-0.05580592900514603,
-0.05316069722175598,
-0.07920772582292557,
-0.03242809697985649,
-0.01813795603811741,
0.06087905541062355,
-0.01565324142575264,
-0.0002743142540566623,
0.027279220521450043,
-0.012261156924068928,
0.015338440425693989,
0.022046733647584915,
-0.037820104509592056,
-0.04650444537401199,
-0.0016449885442852974,
0.015416214242577553,
0.023011768236756325,
0.015299712307751179,
-0.05915547534823418,
-0.024761302396655083,
-0.058701884001493454,
0.01664196141064167,
0.020548947155475616,
-0.005955283995717764,
-0.07291089743375778,
0.0012721348321065307,
-0.0019705593585968018,
-0.04755313694477081,
0.029737655073404312,
-0.011386305093765259,
-0.015647079795598984,
0.033582065254449844,
0.007210478652268648,
-0.019364280626177788,
-0.0217155609279871,
-0.0216674841940403,
0.013736018911004066,
-0.027384957298636436,
0.009561157785356045,
0.04081143066287041,
-0.0008171640220098197,
-0.06334798038005829,
0.02256631851196289,
-0.038250990211963654,
-0.033465832471847534,
0.0022861077450215816,
-0.015667108818888664,
-0.04484518617391586,
-0.007681443355977535,
-0.040508680045604706,
0.007882158271968365,
0.027601925656199455,
0.006556422915309668,
-0.06725796312093735,
-0.053683098405599594,
0.008993399329483509,
0.03561127558350563,
0.05966142192482948,
-0.0031855457928031683,
-0.014400521293282509,
0.0762556940317154,
0.0046352786011993885,
-0.03745175898075104,
-0.04247409105300903,
-0.016043396666646004,
0.010784197598695755,
0.004860378801822662,
0.04907660931348801,
0.05656422674655914,
-0.0458965040743351,
-0.008283605799078941,
0.013080958276987076,
0.03674882650375366,
0.007779474835842848,
0.025688381865620613,
-0.015053534880280495,
0.0006029815413057804,
-0.00473959743976593,
-0.014272269792854786,
0.04107062146067619,
0.035703323781490326,
-0.052905935794115067,
0.0010024462826550007,
-0.006221361458301544,
0.003199101658537984,
0.02447591722011566,
-0.058371737599372864,
0.028165342286229134,
-0.02275702729821205,
-0.028726503252983093,
-0.00014037724758964032,
0.009230214171111584,
0.013710031285881996,
-0.04055630788207054,
0.005121051333844662,
-0.013294651173055172,
0.003968016244471073,
-0.024850212037563324,
-0.00979745015501976,
0.053709305822849274,
0.013720064423978329,
0.002897873055189848,
-0.006188984960317612,
0.04319300875067711,
0.025384332984685898,
0.0046938941814005375,
-0.025641530752182007,
-0.009746890515089035,
0.0651470348238945,
0.05122275650501251,
0.005753401201218367,
0.0348522812128067,
-0.005286436527967453,
-0.0005869125598110259,
-0.06188551336526871,
0.021494075655937195,
-0.025201132521033287,
0.04965737834572792,
-0.003369387239217758,
0.03294207155704498,
0.04154777526855469,
0.021946780383586884,
0.0022510054986923933,
0.001974289771169424,
-0.057110175490379333,
-0.04634302482008934,
-0.007660293951630592,
-0.010357269085943699,
-0.016143908724188805,
-0.03123406507074833,
-0.014739342033863068,
-0.041486091911792755,
0.010391347110271454,
-0.0016067969845607877,
0.00971841998398304,
-0.010130123235285282,
-0.013053243979811668,
0.002244200324639678,
-0.0336478129029274,
0.0020317111629992723,
0.017856398597359657,
0.02126982994377613,
-0.016766516491770744,
0.01065637357532978,
0.044617392122745514,
-0.029278066009283066,
-0.027882732450962067,
0.006371098570525646,
-0.0017734554130584002,
0.028091678395867348,
0.04719066992402077,
-0.027226565405726433,
0.020736418664455414,
-0.022158600389957428,
-0.005780974868685007,
0.033094801008701324,
0.01878732442855835,
-0.010271166451275349,
-0.021684665232896805,
-0.003935921937227249,
-0.021478058770298958,
-0.02105419524013996,
-0.007466168142855167,
0.07054004818201065,
-0.005330963525921106,
0.01836644485592842,
0.021918147802352905,
0.020295271649956703,
-0.02715272456407547,
0.0215787123888731,
0.04638037085533142,
-0.008750217035412788,
-0.05095525458455086,
-0.06552650034427643,
-0.017326747998595238,
-0.024084562435746193,
0.016203055158257484,
0.046091023832559586,
0.034482017159461975,
-0.01269228383898735,
-0.01922059804201126,
0.03656229004263878,
0.014927713200449944,
-0.0185588076710701,
0.042621564120054245,
-0.02714092843234539,
-0.011854216456413269,
0.0034290743060410023,
0.04523879662156105,
0.00988084264099598,
0.01410166546702385,
0.01959417201578617,
-0.0027622729539871216,
-0.004186361562460661,
-0.09681814908981323,
-0.007181114051491022,
0.052642252296209335,
0.06511176377534866,
-0.023428553715348244,
0.0022413653787225485,
-0.05207031965255737,
-0.033947449177503586,
0.025313150137662888,
-0.06833908706903458,
0.022569317370653152,
-0.02248607948422432,
0.010236578993499279,
-0.03720107674598694,
-0.021863620728254318,
-0.033641114830970764,
0.0026906209532171488,
-0.02963780239224434,
0.009817555546760559,
-0.024842606857419014,
-0.040620867162942886,
0.041916705667972565,
0.016994033008813858,
0.06145578995347023,
0.035019345581531525,
-0.04595328867435455,
-0.07559950649738312,
-0.012166881933808327,
0.017285311594605446,
-0.03102750889956951,
-0.02515443041920662,
0.03670678287744522,
0.02431465871632099,
-0.02808803878724575,
0.07956255972385406,
-0.011464426293969154,
-0.03264717385172844,
0.017028216272592545,
0.00913010723888874,
0.007505468092858791,
0.00047758553409948945,
-0.023334985598921776,
0.03482305631041527,
0.016121473163366318,
-0.028365440666675568,
-0.010302679613232613,
-0.004089170601218939,
-0.05480523779988289,
-0.02016579732298851,
-0.010504246689379215,
0.029693324118852615,
-0.011016910895705223,
0.014241152442991734,
-0.029991697520017624,
0.024962516501545906,
-0.04442538693547249,
0.03973889350891113,
-0.016207680106163025,
-0.008071014657616615,
-0.018516521900892258,
-0.030275318771600723,
-0.007381629664450884,
0.02681737393140793,
0.017997264862060547,
0.006239135749638081,
-0.01772952266037464,
-0.015084199607372284,
0.04782089963555336,
0.007989248260855675,
0.02589605748653412,
-0.018620939925312996,
0.007200880907475948,
-0.004140584729611874,
-0.012372455559670925,
-0.006869104690849781,
-0.055000510066747665,
0.008704339154064655,
-0.005454474128782749,
-0.08362779021263123,
0.027392838150262833,
0.00266357883810997,
0.016419323161244392,
0.0705406442284584,
-0.020589781925082207,
0.002852817066013813,
-0.0031558158807456493,
-0.008934617042541504,
0.03471970185637474,
-0.010324184782803059,
-0.006627549882978201,
-0.0274191927164793,
0.007493988145142794,
-0.031804196536540985,
-0.0070921871811151505,
0.0012061937013641,
0.0015653861919417977,
-0.011860503815114498,
-0.02365783043205738,
-0.04789154976606369,
-0.015305341221392155,
-0.021190369501709938,
0.021628180518746376,
0.05804438889026642,
-0.014549368061125278,
0.01255415752530098,
0.016748471185564995,
0.0027528060600161552,
0.03034195303916931,
0.0008702579070813954,
0.0071168565191328526,
-0.026434773579239845,
-0.006042962893843651,
-0.0050366343930363655,
0.013913261704146862,
0.06729137897491455,
-0.039843760430812836,
-0.043365076184272766,
-0.017030708491802216,
0.009174211882054806,
0.02640116587281227,
-0.016661781817674637,
0.007230577524751425,
-0.03617134317755699,
-0.005530812777578831,
-0.02088378369808197,
-0.018464893102645874,
-0.030994132161140442,
-0.02853345312178135,
-0.0036683448124676943,
-0.022269675508141518,
0.023339325562119484,
0.00574524188414216,
0.000716807262506336,
0.010566811077296734,
0.0609964020550251,
-0.025776579976081848,
0.002131587127223611,
0.027841592207551003,
-0.029125932604074478,
-0.007266147527843714,
0.04575783759355545,
-0.032583966851234436,
0.034274227917194366,
-0.02426140196621418,
-0.013420776464045048,
0.03923032805323601,
-0.0028173241298645735,
-0.008294740691781044,
-0.008534989319741726,
-0.033472999930381775,
0.020061546936631203,
0.06174680218100548,
0.009652192704379559,
0.06926070153713226,
-0.004739088471978903,
-0.005409390199929476,
-0.0017730558756738901,
-0.026657456532120705,
-0.015180232934653759,
-0.004769006744027138,
0.010375766083598137,
0.03563576564192772,
-0.04227438569068909,
-0.013263536617159843,
0.07477974891662598,
0.029300378635525703,
0.0016346924239769578,
0.009041263721883297,
0.013689044862985611,
-0.0028326157480478287,
0.00226624240167439,
-0.05526605248451233,
0.004851314704865217,
0.06542012095451355,
-0.08157698810100555,
0.017100241035223007,
-0.0017959692049771547,
0.014888430945575237,
0.030203750357031822,
0.00680159917101264,
-0.0018366931471973658,
-0.05993156507611275,
-0.03388475626707077,
-0.06606161594390869,
-0.017077822238206863,
0.036727339029312134,
0.030915888026356697,
0.006923852022737265,
-0.020497947931289673,
0.029379189014434814,
-0.02542107179760933,
0.00396224670112133,
-0.05402925983071327,
-0.06409315764904022,
-0.06153596565127373,
-0.025266770273447037,
-0.02521893009543419,
0.05593685433268547,
0.007479687687009573,
-0.029321961104869843,
-0.003450873540714383,
-0.05403541028499603,
0.01744958758354187,
0.02166210673749447,
0.013373145833611488,
0.006152601446956396,
0.00940350815653801,
-0.003774617100134492,
0.026360828429460526,
-0.016908425837755203,
-0.020377613604068756,
0.17095746099948883,
0.015526730567216873,
-0.005203247535973787,
-0.03084125556051731,
0.04536789283156395,
0.03127948194742203,
-0.005242332816123962,
0.003303700825199485,
0.016532959416508675,
-0.026892373338341713,
0.0009659929783083498,
0.008426311425864697,
0.0250734593719244,
0.05354035273194313,
0.0034449875820428133,
0.005427813157439232,
-0.01859261468052864,
-0.028420142829418182,
0.06864066421985626,
0.0016767779598012567,
-0.014955144375562668,
0.026072239503264427,
-0.009696634486317635,
-0.008575106970965862,
0.019353557378053665,
0.012099072337150574,
-0.053922589868307114,
-0.003171014366671443,
-0.0018485443433746696,
0.03739600256085396,
-0.052464809268713,
0.02141607739031315,
0.007256025914102793,
-0.04846389591693878,
-0.026183240115642548,
-0.013993963599205017,
-0.0240078866481781,
-0.03050643764436245,
0.0009702373645268381,
0.011640140786767006,
0.0035287716891616583,
0.0178978368639946,
0.004511520732194185,
0.010172494687139988,
-0.042043041437864304,
-0.015516810119152069,
-0.035060297697782516,
0.030909597873687744,
0.009716375730931759,
0.01691884733736515,
0.006545897573232651,
0.02682155929505825,
-0.01880466192960739,
-0.0880851224064827,
0.0025483553763478994,
0.0005689554964192212,
0.029592666774988174,
0.009675150737166405,
-0.000233805098105222,
0.047190383076667786,
0.059362057596445084,
0.017120180651545525,
-0.019652171060442924,
-0.017942868173122406,
0.018038665875792503,
-0.017731841653585434,
-0.021930312737822533,
0.06556826829910278,
-0.005827561020851135,
-0.0057911197654902935,
-0.044053319841623306,
0.020216744393110275,
0.00822978001087904,
0.00025345003814436495,
-0.007168531883507967,
0.04391852021217346,
-0.012537322007119656,
0.02320699393749237,
-0.020530356094241142,
-0.03897376358509064,
-0.02698584459722042,
0.04779196158051491,
-0.05931995436549187,
-0.010781989432871342,
-0.03255177289247513,
-0.0036051843781024218,
0.029383789747953415,
0.02732398360967636,
0.007159034255892038,
0.006847591605037451,
-0.0026816087774932384,
0.09803356975317001,
-0.01105463970452547,
-0.01740414835512638,
-0.02213257923722267,
0.019138403236865997,
-0.016705971211194992,
0.004394348710775375,
0.014780395664274693,
0.028942564502358437,
0.021244894713163376,
-0.03055661730468273,
0.024895353242754936,
0.008379289880394936,
-0.07129167020320892,
-0.01637968234717846,
-0.01239794958382845,
-0.040772419422864914,
0.00396531680598855,
0.027372419834136963,
-0.018506819382309914,
-0.042728595435619354,
0.004130784422159195,
-0.00869676936417818,
-0.04447123035788536,
-0.018248924985527992,
0.0497967004776001,
-0.028935156762599945,
0.02366059087216854,
0.015970641747117043,
-0.02312413975596428,
-0.014900241047143936,
-0.013146714307367802,
-0.019118566066026688,
-0.023483863100409508,
-0.032902710139751434,
0.0008122220751829445,
-0.020695306360721588,
0.01537625677883625,
-0.062012314796447754,
0.01669764705002308,
-0.021173542365431786,
0.02381155453622341,
-0.020063458010554314,
-0.01577254757285118,
0.012804399244487286,
-0.033912017941474915,
0.008900978602468967,
-0.006020980421453714,
-0.056395966559648514,
-0.001430927193723619,
-0.013862048275768757,
-0.06435871124267578,
0.03990943729877472,
-0.009113490581512451,
0.06400249153375626,
0.03144760802388191,
0.02841709926724434,
0.020226435735821724,
0.05155549570918083,
-0.0021228641271591187,
-0.0071538700722157955,
-0.01435146015137434,
-0.022974615916609764,
0.018128730356693268,
-0.03322485089302063,
0.015242687426507473,
-0.029833350330591202,
-0.02353951707482338,
0.011292149312794209,
0.021778767928481102,
-0.017468566074967384,
0.02021164260804653,
0.015928037464618683,
-0.025402044877409935,
-0.03687450289726257,
-0.021609114482998848,
0.002369444351643324,
-0.001211195020005107,
0.0018191393464803696,
0.01462640892714262,
0.003044268349185586,
-0.008508512750267982,
0.007334766909480095,
-0.12002748996019363,
0.0053263502195477486,
0.05161263793706894,
0.023920202627778053,
0.04290750250220299,
-0.05586032569408417,
0.00751880370080471,
0.03309134021401405,
-0.07553273439407349,
0.06134537607431412,
0.008851787075400352,
0.013358044438064098,
-0.028351066634058952,
0.030101628974080086,
-0.0171009823679924,
0.03692282363772392,
-0.019258489832282066,
0.02628842554986477,
0.03698616847395897,
0.005925162695348263,
-0.020424529910087585,
-0.043865613639354706,
0.011049889959394932,
0.038980647921562195,
-0.011204702779650688,
0.005654234904795885,
0.04227111488580704,
-0.007087345235049725,
0.025084955617785454,
0.04361715167760849,
0.00562415411695838,
0.02565775439143181,
-0.02351934276521206,
0.043034445494413376,
0.046652838587760925,
0.03602643311023712,
0.0269160158932209,
-0.004725663457065821,
-0.027861187234520912,
-0.0012560351751744747,
-0.04350607842206955,
0.027269380167126656,
0.012768693268299103,
-0.009506198577582836,
0.014741872437298298,
-0.03302072361111641,
0.0000962017584242858,
0.013241029344499111,
-0.029143212363123894,
-0.019264988601207733,
-0.014499460346996784,
0.01363014243543148,
0.021966824308037758,
-0.04745760187506676,
-0.01585591398179531,
-0.05782714858651161,
0.02529081329703331,
0.00044599626562558115,
0.011924144811928272,
0.009477769955992699,
0.01617184467613697,
-0.019484059885144234,
0.0033624833449721336,
-0.008674104698002338,
0.02745278738439083,
-0.016292503103613853,
-0.000701701850630343,
0.005248889327049255,
-0.04017074406147003,
-0.002128427615389228,
0.01338204089552164,
-0.02307877130806446,
-0.02549939788877964,
0.00650503346696496,
-0.017249053344130516,
0.022540293633937836,
0.006715721916407347,
-0.010488621890544891,
-0.008643439039587975,
-0.07543016225099564,
0.03967976197600365,
-0.023685092106461525,
0.007158239837735891,
-0.06308916211128235,
-0.02184406667947769,
0.006238438189029694,
0.043731678277254105,
0.021351374685764313,
0.018434878438711166,
-0.009772436693310738,
0.021943606436252594,
-0.02230099029839039,
-0.006134190130978823,
-0.03752174600958824,
0.002811878453940153,
0.032057952135801315,
0.026454158127307892,
-0.016811057925224304,
0.0034534514416009188,
-0.018017303198575974,
0.004271668381989002,
0.02540411800146103,
0.026085762307047844,
0.04158661141991615,
-0.02804347313940525,
-0.05067586526274681,
0.016575323417782784,
0.014348207972943783,
0.0039395419880747795,
0.024900216609239578,
0.040030237287282944,
-0.02935607172548771,
0.0549454391002655,
-0.044020120054483414,
-0.013767480850219727,
0.020545342937111855,
0.0061441152356565,
-0.022088022902607918,
-0.032851722091436386,
-0.01407665852457285,
0.06141631677746773,
-0.02160438522696495,
0.005704604089260101,
0.014443897642195225,
-0.02368832193315029,
-0.03072255663573742,
0.03837205097079277,
-0.01500045508146286,
0.004758977331221104,
-0.013315885327756405,
0.05854196846485138,
-0.00329593219794333,
-0.00031112265423871577,
0.019987789914011955,
0.024567406624555588,
0.0062690912745893,
0.012071711011230946,
0.015181224793195724,
0.03876316174864769,
-0.0019438600866124034,
0.01480343658477068,
-0.009613760747015476,
0.04880140349268913,
0.03130197152495384,
0.014437859877943993,
0.041123099625110626,
0.03925807774066925,
-0.03336448222398758,
0.08419255912303925,
0.003233999013900757,
0.05557049810886383,
0.006632129196077585,
0.002966273110359907,
-0.028803415596485138,
0.00782639067620039,
0.004601734224706888,
0.01589009165763855,
0.01582600548863411,
0.01309826597571373,
-0.003334786742925644,
-0.018568987026810646,
0.009785034693777561,
0.0031184288673102856,
-0.0000378144541173242,
-0.036028698086738586,
0.03638944402337074,
-0.006570944096893072,
-0.005014609079807997,
0.027205923572182655,
-0.016049014404416084,
-0.011703474447131157,
-0.028934700414538383,
0.07208140939474106,
0.01818576268851757,
0.03445250168442726,
-0.0031468095257878304,
-0.002351107308641076,
-0.0156495813280344,
0.03886372223496437,
-0.07207871228456497,
-0.054733287543058395,
-0.009519308805465698,
0.03763578459620476,
0.013799527660012245,
-0.006327467504888773
] |
<p><strong>How far would my bullet fly with the following characteristics?</strong></p>
<ul>
<li>1.2km/second initial velocity</li>
<li>45 degree angle into the sky</li>
<li>'Normal' atmospheric conditions</li>
<li>No wind</li>
<li>Typical high-powered rifles have 5-10 gram bullets</li>
</ul>
<p>I've tried various <a href="http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html" rel="nofollow">online calculators</a> but they only do vacuum, not normal atmospheric conditions, so the range is 102km.</p>
| 8,811 |
[
-0.024317732080817223,
-0.03443949669599533,
0.0038796712178736925,
0.008944278582930565,
0.05125196650624275,
-0.028195761144161224,
-0.02559858001768589,
-0.010680928826332092,
0.02712666615843773,
-0.032934270799160004,
0.030149806290864944,
0.04786441847681999,
0.027183713391423225,
0.023084113374352455,
-0.0017100609838962555,
0.009229845367372036,
-0.013046943582594395,
0.004569053649902344,
0.013951851055026054,
-0.04796280339360237,
-0.012113122269511223,
-0.0029759714379906654,
0.0045446306467056274,
-0.004319855943322182,
-0.023693813011050224,
0.005124794784933329,
0.045083146542310715,
-0.013170907273888588,
0.017196541652083397,
0.029639456421136856,
-0.012905649840831757,
-0.00336251687258482,
0.06627487391233444,
0.015114570036530495,
-0.004019220359623432,
0.01014685072004795,
-0.02855335734784603,
-0.019957678392529488,
-0.03552105650305748,
-0.01131332665681839,
-0.02175280451774597,
0.003918197005987167,
0.018254011869430542,
0.05351615324616432,
-0.020222431048750877,
0.02683349698781967,
-0.042274586856365204,
-0.03291261941194534,
0.06672202050685883,
-0.07398153841495514,
0.048450153321027756,
0.01987331733107567,
0.05683157965540886,
0.04921058937907219,
0.033983197063207626,
-0.0484243705868721,
0.07790464907884598,
0.07055062055587769,
-0.01733550988137722,
-0.06673221290111542,
-0.01398884691298008,
-0.04091612249612808,
-0.02343795634806156,
-0.007703876588493586,
-0.0019798860885202885,
0.03543258085846901,
-0.02458314225077629,
-0.018873397260904312,
0.03542713075876236,
0.000916610995773226,
0.02192889153957367,
0.02160693146288395,
-0.001489965245127678,
-0.003449412062764168,
0.01151256263256073,
-0.025688955560326576,
0.03980330750346184,
0.01912543922662735,
0.03417080268263817,
0.059641655534505844,
-0.04350131377577782,
0.012336897663772106,
0.04814938083291054,
0.0021875076927244663,
0.03904490917921066,
-0.0307786725461483,
0.09442904591560364,
0.024351371452212334,
-0.007560379337519407,
0.026461200788617134,
-0.005930477753281593,
0.013783697970211506,
0.03627534955739975,
0.008767137303948402,
-0.024258293211460114,
0.05690176412463188,
-0.011132261715829372,
0.08313044160604477,
-0.0012602469651028514,
-0.03544297814369202,
0.00599416671320796,
-0.02155822329223156,
0.041317395865917206,
0.06227852404117584,
0.008470846340060234,
-0.010693206451833248,
0.006231524050235748,
-0.014727740548551083,
-0.018084479495882988,
0.0064817736856639385,
-0.024036625400185585,
0.04195427894592285,
0.0073430659249424934,
-0.020677536725997925,
-0.02580663561820984,
-0.045283157378435135,
0.01993749290704727,
-0.018601730465888977,
0.003043393837288022,
0.030756985768675804,
0.052803363651037216,
-0.02626395784318447,
-0.005464368965476751,
-0.015490297228097916,
-0.015076994895935059,
0.003186267800629139,
0.029709873721003532,
-0.008844013325870037,
-0.010542849078774452,
-0.007353098597377539,
-0.029701054096221924,
-0.02730095200240612,
0.023397833108901978,
-0.027067624032497406,
0.04943065345287323,
-0.01911480352282524,
-0.11175332963466644,
-0.03896940499544144,
0.03329324722290039,
0.011842490173876286,
-0.02399507910013199,
-0.07422403991222382,
0.026158396154642105,
0.02205631136894226,
0.05611737444996834,
0.022908007726073265,
0.03661596402525902,
0.0008623002795502543,
0.005875055678188801,
-0.010881684720516205,
-0.051403675228357315,
0.014189209789037704,
-0.012605706229805946,
-0.03369297459721565,
0.008983294479548931,
-0.033082760870456696,
0.020930275321006775,
0.012104210443794727,
0.0027657225728034973,
-0.03479054942727089,
0.03766724839806557,
-0.021033773198723793,
-0.0069288634695112705,
-0.022609610110521317,
0.034933533519506454,
-0.021723255515098572,
0.060001008212566376,
0.03308426961302757,
-0.04200908914208412,
0.014234568923711777,
-0.01879909820854664,
-0.0020148532930761576,
0.009954686276614666,
-0.055514443665742874,
0.0715504065155983,
-0.019092636182904243,
0.009159636683762074,
-0.035367291420698166,
0.0060449279844760895,
0.010445743799209595,
-0.04329252615571022,
-0.03702786564826965,
-0.009807084687054157,
0.04238593205809593,
0.017085976898670197,
0.048029690980911255,
-0.000005672631232300773,
0.006436169147491455,
-0.03469129279255867,
-0.010357087478041649,
-0.03105749562382698,
-0.0519588328897953,
0.03833501413464546,
0.019604450091719627,
-0.0030222332570701838,
0.014524489641189575,
0.021270636469125748,
0.03135526925325394,
-0.011564463376998901,
0.005850762594491243,
-0.032880526036024094,
0.03849992901086807,
0.021194856613874435,
0.008267934434115887,
-0.01413937471807003,
0.06815555691719055,
0.026036880910396576,
-0.013122566044330597,
0.003941303119063377,
-0.008826428093016148,
-0.027444269508123398,
-0.03894863277673721,
-0.04374221712350845,
0.0009355738293379545,
0.011590970680117607,
0.009061536751687527,
0.01605037786066532,
0.01583407074213028,
0.026657717302441597,
-0.0066721499897539616,
-0.02519416995346546,
0.08798409253358841,
0.05396106466650963,
-0.005954999476671219,
-0.005858617834746838,
0.057743072509765625,
-0.010460766963660717,
-0.04303329810500145,
0.0008989907219074667,
-0.01787988655269146,
-0.06438379734754562,
-0.013974142260849476,
0.030534453690052032,
0.005704828538000584,
-0.03791940584778786,
0.0282144732773304,
0.03802761808037758,
0.011642339639365673,
0.041959553956985474,
0.05780830606818199,
-0.043030787259340286,
-0.048533301800489426,
0.026212066411972046,
-0.00632040249183774,
-0.018775369971990585,
0.007163930684328079,
0.0007868733373470604,
0.02587789297103882,
-0.018665550276637077,
-0.010782296769320965,
-0.011443817988038063,
0.054011810570955276,
0.020364852622151375,
-0.012642143294215202,
0.017497727647423744,
-0.04019168019294739,
0.06864618510007858,
0.0008520007249899209,
-0.002448756480589509,
0.0469200424849987,
-0.011881872080266476,
0.0086048049852252,
-0.03235600143671036,
0.016185710206627846,
-0.011415845714509487,
0.025744153186678886,
0.008458162657916546,
-0.016305170953273773,
0.023699333891272545,
-0.08372204005718231,
-0.023459529504179955,
-0.043226826936006546,
0.006779125891625881,
-0.02304423600435257,
-0.001997873652726412,
0.022512691095471382,
0.05864718183875084,
-0.010889938101172447,
0.006484930403530598,
-0.04723833128809929,
0.014160322025418282,
-0.05263436958193779,
-0.016236210241913795,
-0.040232934057712555,
-0.018606780096888542,
0.016173982992768288,
-0.0008428876753896475,
-0.03126845136284828,
0.06342088431119919,
-0.020934365689754486,
-0.00949359592050314,
0.016635196283459663,
-0.03998229652643204,
-0.038563888520002365,
0.024931078776717186,
-0.04213902726769447,
-0.001495105098001659,
-0.031209275126457214,
-0.01147183496505022,
0.05078712850809097,
0.003503252752125263,
-0.0370139516890049,
0.04065180569887161,
-0.04169715568423271,
-0.047066088765859604,
-0.05144987627863884,
0.029441049322485924,
0.0003345388686284423,
-0.022317398339509964,
0.0028364781755954027,
0.015998078510165215,
0.000403027719585225,
0.008088096976280212,
-0.050022102892398834,
-0.022124875336885452,
0.027599912136793137,
0.015363592654466629,
0.0368482880294323,
0.022650770843029022,
-0.03363357484340668,
0.06243392452597618,
0.029080325737595558,
-0.019769631326198578,
-0.015542685985565186,
-0.034066393971443176,
-0.007517498452216387,
-0.020066218450665474,
-0.019320758059620857,
0.00849780160933733,
-0.012113720178604126,
0.026327144354581833,
0.015105756931006908,
0.028925573453307152,
0.04620944708585739,
-0.001882444485090673,
-0.003424867521971464,
-0.03481662645936012,
-0.01040630228817463,
0.00023455158225260675,
0.06575170904397964,
0.01609606295824051,
-0.02513512596487999,
0.022574322298169136,
-0.021884040907025337,
0.03804222121834755,
0.026762204244732857,
-0.07660673558712006,
0.04676063731312752,
0.003671544836834073,
-0.026946766301989555,
-0.0364178791642189,
0.03311138227581978,
-0.02411513403058052,
-0.01775379851460457,
-0.012638009153306484,
0.025222865864634514,
0.07630184292793274,
0.027095919474959373,
0.008627901785075665,
0.013254024088382721,
0.059534117579460144,
0.001177108264528215,
-0.020748630166053772,
-0.011907394044101238,
0.010859760455787182,
0.00027403683634474874,
0.007974205538630486,
0.0005167986964806914,
0.048284806311130524,
0.03150860220193863,
0.04289962351322174,
0.011508896946907043,
-0.023936782032251358,
0.024237193167209625,
-0.05160769820213318,
0.011794128455221653,
-0.04967834800481796,
0.05080752074718475,
-0.0022446417715400457,
0.0611177459359169,
0.010728471912443638,
0.027081822976469994,
0.026860712096095085,
0.018659261986613274,
-0.086936354637146,
0.06809291988611221,
-0.015984006226062775,
-0.06791184097528458,
0.012894543819129467,
0.014885364100337029,
-0.04549757018685341,
-0.010212212800979614,
-0.01323043555021286,
0.01822197251021862,
-0.023509778082370758,
-0.018895119428634644,
0.006749027408659458,
-0.017689058557152748,
-0.01262423861771822,
-0.01605680212378502,
0.04178951308131218,
0.029398927465081215,
-0.0019525046227499843,
0.034711070358753204,
0.04521103948354721,
-0.01182540226727724,
-0.004536043852567673,
-0.021119028329849243,
0.030766209587454796,
-0.014437897130846977,
0.056966133415699005,
-0.008812455460429192,
-0.0036351107992231846,
0.01762770488858223,
0.004585724789649248,
0.00009883271559374407,
0.015822216868400574,
-0.005830737762153149,
0.021369991824030876,
-0.04510156065225601,
-0.059985674917697906,
0.028841888532042503,
-0.005544239655137062,
0.025202851742506027,
-0.02563079446554184,
0.034885283559560776,
0.0391630120575428,
-0.019499624148011208,
-0.01841788925230503,
0.030459089204669,
0.04966219887137413,
-0.013545770198106766,
0.013265438377857208,
-0.031133471056818962,
-0.01327475719153881,
-0.04630187898874283,
-0.021186858415603638,
0.017371853813529015,
-0.004496518988162279,
-0.004993048496544361,
0.01650816947221756,
0.026331473141908646,
-0.013568202033638954,
-0.01965807005763054,
0.0428713820874691,
-0.009207670576870441,
0.024637985974550247,
-0.03414478898048401,
-0.022171156480908394,
0.010962980799376965,
0.029394909739494324,
0.04925011843442917,
0.007151211611926556,
-0.005755490157753229,
-0.10539162904024124,
-0.005858884658664465,
0.030196448788046837,
0.03126925975084305,
-0.0015590639086440206,
-0.027956845238804817,
-0.07267069816589355,
-0.03518824651837349,
0.03595147654414177,
-0.027131035923957825,
0.029328668490052223,
-0.0077223628759384155,
0.016087975353002548,
0.018821682780981064,
-0.03259025514125824,
-0.038944799453020096,
0.015261033549904823,
0.019570060074329376,
0.007650773972272873,
-0.014450226910412312,
0.016857320442795753,
0.009674342349171638,
0.05610731616616249,
0.03366335108876228,
0.08373390883207321,
0.01764613389968872,
0.010846924968063831,
-0.003340610070154071,
-0.054475344717502594,
-0.003953222651034594,
-0.062036484479904175,
0.005200852639973164,
-0.002761153969913721,
0.0050093913450837135,
0.004381598439067602,
0.003985282965004444,
-0.007264143321663141,
0.0640726163983345,
-0.01660795323550701,
-0.011776845902204514,
-0.012213986366987228,
-0.04392322897911072,
-0.028935635462403297,
0.016505111008882523,
-0.020006977021694183,
0.028791459277272224,
0.05315485969185829,
-0.010358895175158978,
0.014550751075148582,
-0.016766782850027084,
0.03144162893295288,
-0.022505497559905052,
-0.05456532537937164,
-0.040378324687480927,
0.002682898659259081,
-0.03388034179806709,
0.03898758441209793,
-0.011282629333436489,
0.01736820861697197,
-0.005362734664231539,
0.0032727974466979504,
-0.013074292801320553,
0.01584174670279026,
0.013562793843448162,
0.04187888279557228,
-0.010104448534548283,
0.024632520973682404,
-0.009631043300032616,
-0.003098926041275263,
0.004244004376232624,
0.027036715298891068,
-0.0006169461994431913,
0.03669542446732521,
-0.01711011677980423,
-0.028106721118092537,
-0.02169434353709221,
-0.005735266022384167,
-0.0014401882654055953,
-0.06781978160142899,
0.11439326405525208,
-0.006930558010935783,
-0.007823492400348186,
0.04905020073056221,
-0.0549267902970314,
-0.06430044025182724,
0.014854409731924534,
0.01432129554450512,
0.02764453925192356,
-0.0275528933852911,
0.038014549762010574,
-0.01902869902551174,
0.007981713861227036,
-0.03677869588136673,
-0.011500734835863113,
0.041977036744356155,
0.019360573962330818,
-0.02234555594623089,
-0.04059051722288132,
-0.0049676429480314255,
-0.03748676925897598,
-0.013470936566591263,
0.024370208382606506,
0.014236519113183022,
-0.0006776503287255764,
-0.032218750566244125,
-0.0008484006393700838,
-0.020813332870602608,
0.05188221484422684,
0.0142593402415514,
-0.02643846534192562,
0.02232552319765091,
-0.006082913372665644,
-0.03169830143451691,
-0.0015536765567958355,
0.03043408878147602,
-0.03477336838841438,
-0.008879895322024822,
-0.0032683913595974445,
-0.020242618396878242,
0.04048564285039902,
-0.018780812621116638,
0.03186480328440666,
-0.0007458204636350274,
-0.014498133212327957,
-0.002101161051541567,
0.0010465175146237016,
0.03531016409397125,
-0.026759136468172073,
0.009916670620441437,
-0.046370990574359894,
0.01556609757244587,
-0.05674559995532036,
-0.020071053877472878,
0.050594549626111984,
-0.004092392511665821,
0.042032625526189804,
0.011135227046906948,
0.05334600806236267,
-0.00929304026067257,
0.0012939218431711197,
0.026068663224577904,
0.007858977653086185,
0.010344713926315308,
-0.011277611367404461,
-0.02754654921591282,
0.03053578920662403,
0.014308926649391651,
-0.01702481135725975,
-0.049334876239299774,
-0.016668464988470078,
0.01616613380610943,
0.0672805905342102,
-0.03556252643465996,
0.02469615824520588,
-0.003032389096915722,
0.030401619151234627,
0.020614957436919212,
-0.005368904210627079,
0.027675088495016098,
-0.0009170316625386477,
0.00443445798009634,
0.005231659859418869,
-0.014997947961091995,
0.017957491800189018,
-0.012602191418409348,
0.03690211474895477,
0.016633056104183197,
-0.020146628841757774,
0.008555907756090164,
0.009042496792972088,
0.025705911219120026,
-0.05511035770177841,
-0.008083698339760303,
0.02076503075659275,
-0.05017995461821556,
0.04910288751125336,
0.016552332788705826,
-0.016185598447918892,
0.019560886546969414,
-0.013144179247319698,
-0.03016582876443863,
-0.0328281931579113,
0.010773024521768093,
-0.007992723025381565,
-0.0013491959543898702,
0.031174547970294952,
-0.013262898661196232,
0.01661284826695919,
0.015131690539419651,
0.017638694494962692,
-0.022425688803195953,
0.030556026846170425,
-0.032873399555683136,
-0.03559349849820137,
-0.014830497093498707,
-0.04895801469683647,
-0.05447183921933174,
0.05957605317234993,
0.026604007929563522,
-0.03737478330731392,
0.040747251361608505,
-0.023710375651717186,
0.028443770483136177,
0.033005423843860626,
0.023304399102926254,
-0.0023708909284323454,
0.08244340866804123,
-0.019137730821967125,
-0.006824599113315344,
-0.01575852930545807,
0.033058807253837585,
0.11256491392850876,
0.06778028607368469,
-0.0021684987004846334,
-0.012245513498783112,
-0.009767284616827965,
-0.009282919578254223,
0.04393542930483818,
-0.005041527561843395,
0.007472057361155748,
-0.027310555800795555,
-0.022108882665634155,
0.032251205295324326,
0.017656195908784866,
-0.007954607717692852,
-0.0019182804971933365,
0.038881704211235046,
-0.042853035032749176,
-0.023833053186535835,
0.007493908982723951,
-0.001683951006270945,
0.00620042672380805,
0.008112219162285328,
-0.0069359662011265755,
0.06140130013227463,
-0.012680654413998127,
-0.020805122330784798,
-0.03219860419631004,
-0.05091435834765434,
0.03471456095576286,
0.022780729457736015,
-0.038261301815509796,
-0.006039394531399012,
0.004694618750363588,
-0.02765650674700737,
-0.014537189155817032,
0.004980600904673338,
0.03988449275493622,
-0.024936366826295853,
-0.01891697756946087,
0.03070938028395176,
0.03679453209042549,
0.005064492113888264,
0.013816972263157368,
0.018681475892663002,
-0.06750809401273727,
-0.01131394412368536,
-0.03381448984146118,
0.0018644609954208136,
-0.006137625314295292,
0.0029565617442131042,
-0.029019735753536224,
0.04880767688155174,
0.0067674568854272366,
-0.08588716387748718,
-0.011277924291789532,
-0.00654370104894042,
0.045576032251119614,
-0.015470492653548717,
-0.046923235058784485,
-0.0227414071559906,
0.032948460429906845,
0.03667334467172623,
-0.0018041040748357773,
-0.040598563849925995,
0.03443525731563568,
-0.01420174166560173,
-0.02430545538663864,
0.0695490762591362,
-0.044783130288124084,
-0.025118930265307426,
0.0006494285771623254,
-0.01557003054767847,
-0.044794075191020966,
-0.003129574004560709,
0.024178557097911835,
0.023022828623652458,
0.01588585041463375,
0.03199111670255661,
0.002143787918612361,
-0.03812650963664055,
-0.0580989308655262,
0.019771473482251167,
0.022110413759946823,
-0.0031273062340915203,
-0.02499893680214882,
-0.0437794029712677,
0.011879809200763702,
0.024962767958641052,
0.009685884229838848,
0.010891205631196499,
-0.027569476515054703,
0.03325723856687546,
0.023782474920153618,
-0.043163102120161057,
-0.04135133698582649,
0.048573754727840424,
-0.033265355974435806,
0.04546915739774704,
-0.024803513661026955,
0.05570777878165245,
0.024060960859060287,
0.030653072521090508,
0.012213358655571938,
0.016438104212284088,
-0.053757622838020325,
0.015241851098835468,
-0.005345528479665518,
-0.042088788002729416,
-0.02998862788081169,
0.028022050857543945,
0.012810436077415943,
-0.008631101809442043,
0.01867799647152424,
-0.023054521530866623,
-0.041617169976234436,
0.0063686734065413475,
0.0115979528054595,
-0.013917493633925915,
0.0367557667195797,
-0.0339801125228405,
-0.0032542969565838575,
-0.05389600247144699,
0.026422949507832527,
-0.01065877452492714,
0.025127161294221878,
-0.02079988270998001,
-0.0024621179327368736,
-0.014397542923688889,
0.006700674071907997,
-0.053071439266204834,
-0.0138843460008502,
0.01933395303785801,
0.009028101339936256,
0.022367099300026894,
0.013155205175280571,
-0.007519173435866833,
0.004037615843117237,
0.03458161652088165,
-0.02608533762395382,
-0.013272101990878582,
0.010694482363760471,
-0.025006160140037537,
-0.050745464861392975,
0.02535741589963436,
0.01182449609041214,
0.08273657411336899,
0.024425163865089417,
-0.03262007609009743,
-0.00700526824221015,
0.11005423218011856,
0.0045219650492072105,
0.003594360314309597,
0.009431995451450348,
-0.03151840716600418,
0.049758102744817734,
-0.011564762331545353,
-0.010510660707950592,
-0.020077630877494812,
-0.016888262704014778,
0.05203481391072273,
0.00871811993420124,
-0.020656509324908257,
0.013629568740725517,
0.06530609726905823,
-0.020585685968399048,
-0.03300727158784866,
0.019657809287309647,
0.011033541522920132,
0.02230360358953476,
0.0204556193202734,
0.012926486320793629,
0.04685007035732269,
0.0071151722222566605,
-0.00457407021895051,
-0.13027483224868774,
0.020151372998952866,
-0.020887764170765877,
0.003987947944551706,
0.06461590528488159,
-0.06420682370662689,
0.0164999607950449,
0.053232673555612564,
-0.06362032890319824,
-0.04156028479337692,
-0.019069945439696312,
-0.0023192798253148794,
-0.033058565109968185,
-0.012183042243123055,
0.003580074291676283,
0.004573586862534285,
0.0249042809009552,
0.013820738531649113,
0.0220921840518713,
0.034077029675245285,
0.006283922586590052,
-0.01710284687578678,
0.010867432691156864,
0.028938520699739456,
0.0005053401691839099,
0.0056716944091022015,
-0.00004172118497081101,
-0.008378749713301659,
0.023904507979750633,
0.01085803471505642,
-0.02987031266093254,
0.054432883858680725,
-0.006499136332422495,
0.02777220867574215,
0.010677051730453968,
0.04293014854192734,
0.009598062373697758,
-0.007692994084209204,
-0.02300027385354042,
-0.014602039940655231,
-0.003934729844331741,
0.01152688730508089,
-0.029304547235369682,
-0.0007019290933385491,
0.022045129910111427,
-0.03046700358390808,
-0.048659615218639374,
0.012374443002045155,
-0.01750447228550911,
-0.029999269172549248,
-0.0007575557683594525,
-0.009905250743031502,
0.0057925330474972725,
-0.028109235689044,
-0.019719040021300316,
-0.05538076534867287,
0.02411005087196827,
0.023589057847857475,
-0.008700238540768623,
-0.011333196423947811,
0.025214670225977898,
-0.04401010647416115,
-0.013936112634837627,
0.011618801392614841,
-0.01239551231265068,
0.0023560014087706804,
-0.03651285171508789,
-0.017794709652662277,
0.006054999306797981,
0.022077716886997223,
0.006860149092972279,
-0.02603137120604515,
-0.017098093405365944,
0.03262908011674881,
0.03857528045773506,
0.018265150487422943,
0.010399255901575089,
0.008063172921538353,
-0.009099282324314117,
-0.04777107760310173,
0.031076285988092422,
-0.01132497750222683,
-0.030641596764326096,
-0.06361369043588638,
-0.06859063357114792,
0.036579929292201996,
0.009002970531582832,
0.0356910303235054,
-0.0443112775683403,
-0.02636103332042694,
0.006191207095980644,
-0.021876344457268715,
-0.026943886652588844,
-0.039719898253679276,
-0.0160418339073658,
0.007056295871734619,
-0.05847422778606415,
-0.036756228655576706,
-0.02542131394147873,
-0.04182475060224533,
0.02680433914065361,
0.04970098286867142,
0.0035185860469937325,
-0.027772674337029457,
-0.0036341347731649876,
-0.026813929900527,
0.007735041901469231,
0.03860306739807129,
-0.0069187902845442295,
0.06798108667135239,
-0.0049927569925785065,
-0.03103248029947281,
0.02038690261542797,
-0.003458942286670208,
-0.003466945141553879,
0.020283332094550133,
-0.010548539459705353,
-0.030675973743200302,
-0.022186510264873505,
-0.01758326031267643,
0.00799419917166233,
-0.07469600439071655,
-0.009085462428629398,
0.038040753453969955,
-0.006790918298065662,
-0.03232497349381447,
0.060636769980192184,
0.017610179260373116,
0.06015211343765259,
-0.013993455097079277,
0.02193828858435154,
0.03129422292113304,
-0.020249446853995323,
-0.010864747688174248,
-0.003291219938546419,
0.03475369140505791,
-0.02419857494533062,
0.004026319831609726,
0.009415795095264912,
-0.0006015755352564156,
0.012639375403523445,
0.026774324476718903,
0.02332681603729725,
-0.028562719002366066,
-0.017200034111738205,
0.010877244174480438,
0.0021985145285725594,
-0.0022011729888617992,
0.0021219064947217703,
-0.01875569298863411,
0.0667869970202446,
-0.018855705857276917,
0.002888499526306987,
0.003978514112532139,
-0.014761315658688545,
-0.023059964179992676,
0.04117119684815407,
-0.03010515682399273,
0.0007687282050028443,
0.01839675009250641,
-0.011815113015472889,
-0.013403586111962795,
0.009406687691807747,
0.025073541328310966,
-0.0041427817195653915,
0.004882492125034332,
-0.015929754823446274,
0.009970239363610744,
-0.03405037149786949,
-0.005953099578619003,
0.0046088784001767635,
-0.004472475498914719,
0.013464592397212982,
0.041206054389476776,
-0.0006288297008723021,
-0.015055954456329346,
-0.007711612153798342,
-0.013376136310398579,
0.03577667474746704,
-0.047693654894828796,
-0.0015360766556113958,
-0.03434278070926666,
0.012688161805272102,
-0.021982792764902115,
-0.028986603021621704
] |
<p>I would like to know how much speed is loss when a baseball is pitched. When a pitcher hurls the ball, it must lose speed before the catcher catches it because of the air resistance. So, if the catcher catches a 90 mph fastball, what speed was it going when it left the pitchers hand? The drag coefficient for a ball is 0.47 and the distance traveled is 60.5 feet. Let's make it easier by ignoring gravity. </p>
<p>How do I figure this out?</p>
| 8,812 |
[
-0.04957263916730881,
-0.03131242096424103,
-0.00984686054289341,
-0.0018883096054196358,
-0.0022801505401730537,
-0.0214837659150362,
-0.0032072970643639565,
0.00041586245060898364,
0.0028575006872415543,
0.04672326147556305,
0.013023311272263527,
0.048998937010765076,
0.04240666702389717,
0.03655948117375374,
0.037466276437044144,
0.009495043195784092,
-0.025014981627464294,
0.03398387134075165,
0.026184014976024628,
-0.026820996776223183,
-0.034514378756284714,
-0.02909100614488125,
0.03367423638701439,
-0.0007028022664599121,
0.0073778340592980385,
0.005227015353739262,
0.03686065599322319,
-0.021894387900829315,
-0.008044399321079254,
0.056168220937252045,
0.04567865654826164,
-0.010951812379062176,
0.007997789420187473,
0.01706564985215664,
0.0328555703163147,
0.0252548698335886,
-0.06260070949792862,
-0.017359288409352303,
-0.023609908297657967,
0.001291566644795239,
-0.022248705849051476,
-0.020072445273399353,
0.015307087451219559,
0.03591998293995857,
0.009974301792681217,
0.01700231060385704,
-0.009250362403690815,
0.004414158407598734,
0.073033407330513,
-0.04966292902827263,
0.046264562755823135,
0.02474702149629593,
0.05212213099002838,
0.012646409682929516,
-0.02334742061793804,
-0.002290903590619564,
0.045815788209438324,
0.056369245052337646,
-0.03573692962527275,
-0.07603167742490768,
-0.004506255500018597,
-0.046050455421209335,
-0.034100499004125595,
-0.05744483321905136,
-0.03173837065696716,
0.01713079959154129,
-0.05505126714706421,
-0.027032122015953064,
0.012841857969760895,
0.004085588734596968,
0.01993282325565815,
0.0051741586066782475,
0.02919677086174488,
0.009110046550631523,
0.0026854434981942177,
-0.013901470229029655,
0.01095726527273655,
0.034990549087524414,
0.0333918072283268,
0.059101652354002,
-0.03662537410855293,
0.019075991585850716,
0.07492094486951828,
0.023745344951748848,
-0.005769141484051943,
-0.010616072453558445,
0.06408499926328659,
-0.014242906123399734,
0.009834042750298977,
0.020632954314351082,
0.013323689810931683,
-0.02200883999466896,
-0.0021640195045620203,
-0.001190712209790945,
-0.018887687474489212,
0.019516373053193092,
-0.013172908686101437,
0.05401674658060074,
0.023889347910881042,
-0.05509892851114273,
-0.0007886785897426307,
-0.022640937939286232,
0.018260430544614792,
0.057841990143060684,
-0.0029587536118924618,
0.012002653442323208,
-0.026246896013617516,
-0.010097133927047253,
0.006591754034161568,
-0.020667877048254013,
-0.02927127666771412,
0.0229044109582901,
-0.0008882643887773156,
0.006515842396765947,
0.0074151004664599895,
-0.023743966594338417,
-0.020202236250042915,
0.012359299696981907,
0.02287953719496727,
0.028429606929421425,
0.08097653090953827,
-0.04351653903722763,
0.006239305250346661,
0.021028192713856697,
-0.014246668666601181,
0.025977972894906998,
0.02353947050869465,
-0.011872540228068829,
-0.010640358552336693,
0.026109294965863228,
-0.015585942193865776,
-0.005728801246732473,
0.003683987073600292,
-0.04033647105097771,
0.010140486992895603,
0.004914663732051849,
-0.0845721960067749,
-0.06961935013532639,
0.007286590524017811,
-0.00924055278301239,
-0.01783544383943081,
-0.0525953434407711,
-0.014802496880292892,
0.007374187465757132,
0.06571844965219498,
0.032716378569602966,
0.025000201538205147,
-0.010852205567061901,
0.031165992841124535,
0.007641808595508337,
-0.01944650709629059,
-0.026540838181972504,
0.011424263939261436,
-0.016424313187599182,
0.0059228031896054745,
-0.04556075111031532,
-0.025404982268810272,
0.04160405695438385,
-0.04275456815958023,
-0.04752982407808304,
-0.006205791607499123,
-0.013763323426246643,
0.013299193233251572,
-0.01182684488594532,
-0.00914821308106184,
-0.034857675433158875,
0.046636395156383514,
0.03558908775448799,
-0.021688362583518028,
0.013667500577867031,
0.0002889673341996968,
0.04410688579082489,
-0.004227707162499428,
-0.03612065315246582,
0.07731059938669205,
0.00413470808416605,
-0.003751976415514946,
-0.014324183575809002,
-0.020973099395632744,
0.0004351225506979972,
-0.025282539427280426,
-0.021852737292647362,
0.043610941618680954,
0.010765953920781612,
-0.00634066853672266,
0.03365769609808922,
0.02308260276913643,
0.00411472050473094,
0.012720237486064434,
-0.028134237974882126,
-0.059844255447387695,
-0.0883294865489006,
0.016273800283670425,
0.012035214342176914,
0.03620864450931549,
0.008817457593977451,
0.04673672094941139,
0.02130730450153351,
-0.024532701820135117,
-0.017290230840444565,
0.016688678413629532,
0.03831670433282852,
0.010267584584653378,
-0.004395306576043367,
-0.0018888366175815463,
0.052772101014852524,
0.06306859105825424,
-0.016842078417539597,
0.016879282891750336,
-0.008391482755541801,
-0.009477849118411541,
-0.013231693767011166,
-0.03883345425128937,
-0.0032373361755162477,
-0.0005703726783394814,
0.00940709374845028,
0.03663337230682373,
-0.012283988296985626,
0.013348110020160675,
-0.013468177989125252,
-0.01628088392317295,
0.0529107004404068,
0.03411128371953964,
-0.01702743023633957,
0.014101257547736168,
0.04026668891310692,
-0.008388816379010677,
-0.007319506723433733,
-0.005444030277431011,
-0.003402422182261944,
-0.016589779406785965,
-0.02470913715660572,
0.018571721389889717,
0.025371016934514046,
-0.01889944076538086,
0.008768931031227112,
0.021504659205675125,
0.012307201512157917,
0.051007043570280075,
0.04591013491153717,
-0.028356418013572693,
-0.06736490875482559,
-0.01774601824581623,
-0.005934494081884623,
-0.007066408172249794,
0.018295178189873695,
0.0323595255613327,
0.06294195353984833,
0.02522309310734272,
-0.0034230633173137903,
-0.035847242921590805,
0.009546685963869095,
0.05075858160853386,
0.010856814682483673,
0.02149014174938202,
-0.027763260528445244,
0.035527363419532776,
-0.023139959201216698,
0.018585115671157837,
0.03308163955807686,
0.013743503950536251,
0.03190014138817787,
-0.03403418883681297,
0.010970228351652622,
0.05614027380943298,
0.021032599732279778,
0.009492249228060246,
0.036062438040971756,
0.03620847687125206,
-0.058485474437475204,
-0.005379546899348497,
0.00426300847902894,
0.033776454627513885,
-0.03756120800971985,
0.004016061779111624,
0.01699521392583847,
0.031100261956453323,
0.04571668803691864,
-0.012672952376306057,
-0.026972221210598946,
0.01659756526350975,
-0.027049092575907707,
-0.017970871180295944,
0.013715819455683231,
-0.0510605163872242,
0.011137105524539948,
-0.01275576464831829,
-0.024265440180897713,
0.06250450015068054,
0.017777452245354652,
-0.03060644306242466,
0.050406865775585175,
-0.01908431388437748,
-0.04685480520129204,
-0.0061793457716703415,
-0.005023873411118984,
0.02407664805650711,
-0.05189403146505356,
0.04040268063545227,
0.037658821791410446,
0.007321204990148544,
-0.00018632641877047718,
0.023504698649048805,
-0.056829456239938736,
-0.0629667267203331,
-0.029783055186271667,
0.0016597947105765343,
0.03258095309138298,
-0.03737740218639374,
-0.007684110198169947,
-0.020185688510537148,
-0.008380875922739506,
0.004465776961296797,
-0.04471440240740776,
-0.05007871985435486,
0.0034018175210803747,
0.001922126510180533,
0.020370833575725555,
0.03188413754105568,
-0.05304080247879028,
0.07123899459838867,
0.04819241538643837,
-0.027736280113458633,
-0.026988515630364418,
0.001987785566598177,
0.003239350626245141,
-0.05071820318698883,
-0.007921232841908932,
0.03336092084646225,
-0.031217200681567192,
0.014067474752664566,
-0.009612212888896465,
0.02641136571764946,
0.04672340676188469,
0.002463173121213913,
0.02624140866100788,
-0.027424000203609467,
0.0061792777851223946,
-0.011067342944443226,
0.05124706029891968,
-0.014973695389926434,
-0.040430765599012375,
0.02438443712890148,
-0.037166256457567215,
0.05386536940932274,
-0.01000821590423584,
-0.04599877819418907,
0.013876841403543949,
-0.021813957020640373,
-0.02119210921227932,
0.009891536086797714,
0.00827334076166153,
-0.012479729950428009,
0.0210710559040308,
0.007469327189028263,
0.030548719689249992,
0.03268361836671829,
0.01920655369758606,
0.013595194555819035,
0.019255265593528748,
0.04556294530630112,
-0.028287233784794807,
-0.0620378740131855,
-0.06531820446252823,
-0.009912243112921715,
0.048123959451913834,
-0.03252856433391571,
-0.028030460700392723,
0.014347615651786327,
0.0009911303641274571,
0.04193321615457535,
-0.013469663448631763,
-0.03336082026362419,
-0.005681999493390322,
-0.02288387157022953,
-0.0019589203875511885,
0.005061676260083914,
0.039918724447488785,
-0.0005182349705137312,
0.04747765511274338,
0.03045847825706005,
0.02797500230371952,
0.015471021644771099,
0.015468072146177292,
-0.09523086994886398,
0.06755857169628143,
-0.026593906804919243,
-0.054893068969249725,
-0.013135825283825397,
0.013778695836663246,
0.010441135615110397,
-0.054112136363983154,
0.01749926060438156,
0.010304088704288006,
-0.02361278049647808,
-0.03686480596661568,
0.019794318825006485,
-0.009191720746457577,
-0.014878792688250542,
-0.01003748644143343,
0.02741403877735138,
0.03168955817818642,
0.0008378292550332844,
0.026051150634884834,
0.04376671090722084,
-0.017874740064144135,
-0.03398514911532402,
-0.05629339441657066,
-0.0242778193205595,
-0.028973672538995743,
0.03327185660600662,
0.05928344652056694,
0.006937472149729729,
-0.01348902191966772,
0.008464508689939976,
-0.015962515026330948,
0.03324537351727486,
-0.0005921655101701617,
0.01690099947154522,
-0.06039636954665184,
-0.09355493634939194,
-0.01060380320996046,
-0.022622713819146156,
0.04344196245074272,
-0.01495861355215311,
-0.014900283887982368,
0.044560376554727554,
0.015450861304998398,
-0.028899842873215675,
0.04146619886159897,
0.0632423534989357,
0.020899245515465736,
0.014956649392843246,
-0.05733403563499451,
0.005949485581368208,
-0.011799333617091179,
-0.01761055178940296,
0.037533897906541824,
-0.0015309156151488423,
-0.023045428097248077,
-0.013437749817967415,
0.03851251304149628,
0.007404983509331942,
-0.00543004646897316,
0.03162099048495293,
0.015839112922549248,
0.029405055567622185,
-0.01827438361942768,
-0.01906716264784336,
0.026756178587675095,
0.05455821380019188,
0.03010719269514084,
-0.00686542596668005,
0.012103755958378315,
-0.05119795352220535,
-0.03264901787042618,
0.014890498481690884,
0.03460993990302086,
-0.018122488632798195,
0.03102566860616207,
-0.031492121517658234,
-0.018755000084638596,
0.03946639224886894,
-0.04569995775818825,
0.032086655497550964,
-0.00987283792346716,
-0.0018348607700318098,
-0.00013694673543795943,
-0.037172362208366394,
-0.03670806810259819,
0.03565389662981033,
-0.039552439004182816,
-0.001276190858334303,
-0.040271203964948654,
-0.008387227542698383,
-0.03095286898314953,
-0.004298526328057051,
-0.017300602048635483,
0.06111614406108856,
0.023296060040593147,
-0.0029665064066648483,
-0.009033010341227055,
-0.02544841729104519,
-0.06504267454147339,
-0.05320961773395538,
-0.004994200076907873,
-0.02894512377679348,
0.0020595898386090994,
0.021978920325636864,
-0.008630344644188881,
-0.024681083858013153,
0.03810012713074684,
0.01836365833878517,
-0.013834209181368351,
0.029223086312413216,
-0.043817464262247086,
0.020573604851961136,
0.01154258195310831,
0.018702983856201172,
0.029972892254590988,
-0.022703317925333977,
-0.010823307558894157,
0.00982236210256815,
-0.005217313300818205,
0.04704086855053902,
0.006714479066431522,
0.003223501145839691,
-0.02602013759315014,
-0.022855903953313828,
-0.020033283159136772,
0.04976046830415726,
0.02497781068086624,
0.040507882833480835,
-0.03373413160443306,
-0.04439564049243927,
-0.024030392989516258,
-0.015339680947363377,
0.007940171286463737,
-0.008338741958141327,
0.025406235828995705,
0.007217677775770426,
-0.021378861740231514,
0.0003833655791822821,
-0.004608933348208666,
0.053299374878406525,
0.012236622162163258,
0.03373917564749718,
0.012165565975010395,
0.03293116018176079,
-0.030925031751394272,
-0.030668724328279495,
-0.00932565238326788,
-0.06269373744726181,
0.05816151201725006,
-0.019457297399640083,
-0.0056701782159507275,
0.007805280853062868,
-0.0691399946808815,
-0.05545148253440857,
0.010644080117344856,
0.021192634478211403,
0.007080067880451679,
-0.047113798558712006,
0.008334323763847351,
0.020259514451026917,
0.01847909949719906,
-0.04917769879102707,
-0.014141160994768143,
0.01591799408197403,
0.044786471873521805,
-0.027919908985495567,
-0.009436184540390968,
-0.014421441592276096,
-0.07272516191005707,
-0.06706144660711288,
0.007677841931581497,
0.027824852615594864,
-0.02758348360657692,
-0.0032403150107711554,
0.062137942761182785,
-0.031966209411621094,
0.06638749688863754,
0.04608900099992752,
0.003973240032792091,
0.0170493945479393,
-0.017292287200689316,
-0.02079744264483452,
-0.00017090108303818852,
0.06717173010110855,
-0.016316205263137817,
-0.02297125943005085,
0.02656496688723564,
-0.02213539369404316,
0.029661281034350395,
0.004545630421489477,
0.02778123877942562,
-0.004995597992092371,
0.009884568862617016,
0.010039457120001316,
-0.011149648576974869,
0.04901725798845291,
-0.007413675542920828,
0.05394972488284111,
0.004471173044294119,
0.015137411653995514,
-0.04142298921942711,
-0.026751330122351646,
0.007716277614235878,
0.03805256262421608,
0.04223873093724251,
0.0005804958054795861,
0.045080721378326416,
-0.024310575798153877,
-0.045519206672906876,
0.03049418516457081,
-0.00025693606585264206,
0.061327531933784485,
0.0361831933259964,
-0.001634307554922998,
0.009602842852473259,
-0.013847419060766697,
-0.02101271040737629,
-0.017948390915989876,
-0.028377361595630646,
-0.004886195529252291,
0.08935653418302536,
-0.029777850955724716,
0.0716838538646698,
0.015460174530744553,
0.03479631617665291,
-0.00752727035433054,
0.012222598306834698,
-0.0024071410298347473,
0.024404482915997505,
-0.003220738610252738,
0.00999442394822836,
0.02879338525235653,
0.02122030220925808,
0.013580900616943836,
-0.00463875662535429,
0.01356494426727295,
0.04943292215466499,
0.018787385895848274,
0.009733743965625763,
0.04957040399312973,
-0.0306214839220047,
0.005630153231322765,
-0.02050335519015789,
-0.006949364207684994,
0.0681389793753624,
-0.0458710677921772,
-0.0483800433576107,
0.08991917222738266,
0.024568574503064156,
-0.008484482765197754,
-0.01239489484578371,
-0.01216250192373991,
-0.02286756969988346,
-0.02833961695432663,
0.008246171288192272,
-0.02772180177271366,
0.001073686289601028,
0.023377688601613045,
0.04670964926481247,
0.015271171927452087,
0.06836240738630295,
-0.015071076340973377,
-0.024752911180257797,
-0.013574043288826942,
-0.031001001596450806,
-0.038263943046331406,
0.013585370033979416,
0.01586570218205452,
0.0023331071715801954,
0.02555011585354805,
-0.006815757602453232,
-0.017182137817144394,
0.024910079315304756,
-0.01953401044011116,
-0.05873854458332062,
0.12937872111797333,
-0.012266482226550579,
0.013210000470280647,
-0.02161390893161297,
0.005999486893415451,
0.10775606334209442,
0.042089805006980896,
0.030850179493427277,
-0.02213015966117382,
0.005965013988316059,
-0.007421488407999277,
0.019251510500907898,
-0.05612552538514137,
0.00012519105803221464,
-0.015101682394742966,
0.0469694659113884,
0.029258383437991142,
0.026027625426650047,
-0.017482208088040352,
-0.006855383515357971,
0.0249458160251379,
-0.03565293550491333,
-0.006856052204966545,
0.010795141570270061,
-0.01765473559498787,
-0.03824201226234436,
0.03411150723695755,
-0.03994673117995262,
0.03105754777789116,
0.010089308954775333,
-0.01834774576127529,
-0.036093153059482574,
-0.04684925079345703,
-0.01218795869499445,
-0.004344931337982416,
-0.07061612606048584,
0.027057910338044167,
-0.009311319328844547,
-0.017676815390586853,
-0.06103603169322014,
0.013202237896621227,
0.057213615626096725,
-0.03244667500257492,
-0.017740808427333832,
0.038266539573669434,
0.015014872886240482,
0.01498942356556654,
0.008770189248025417,
0.03119044378399849,
-0.05742601677775383,
-0.03268174082040787,
-0.030905555933713913,
0.04080480709671974,
-0.010529187507927418,
0.008495677262544632,
0.006139600649476051,
-0.003738151863217354,
-0.004620731342583895,
-0.05667942389845848,
0.013026757165789604,
0.00803876481950283,
0.04677470400929451,
-0.022859767079353333,
-0.005974662024527788,
-0.027688343077898026,
0.016070876270532608,
0.0008625434129498899,
0.0051891012117266655,
-0.004720006138086319,
0.016602452844381332,
-0.03734573349356651,
0.007604930549860001,
0.029802238568663597,
-0.030331503599882126,
-0.02434166707098484,
0.01487966813147068,
0.019531887024641037,
-0.03110671043395996,
0.016771825030446053,
0.04304589703679085,
0.005718771368265152,
-0.04560906067490578,
0.016500160098075867,
-0.007906910963356495,
-0.022005362436175346,
-0.044474441558122635,
0.039178717881441116,
-0.039394255727529526,
0.002428283914923668,
-0.05545506253838539,
-0.04106574505567551,
0.015226688235998154,
0.03150137513875961,
-0.014150086790323257,
-0.008237907662987709,
-0.02808193303644657,
0.03889795020222664,
0.007879341021180153,
-0.018980009481310844,
-0.019867420196533203,
0.03288174420595169,
-0.03397262096405029,
0.00434172572568059,
-0.01081617921590805,
0.08569972962141037,
0.040268655866384506,
0.018994467332959175,
-0.015946002677083015,
-0.017132993787527084,
-0.009109333157539368,
0.024090949445962906,
0.00448171142488718,
-0.032427072525024414,
-0.027586231008172035,
0.03227381035685539,
-0.008491934277117252,
-0.023430028930306435,
-0.02586394175887108,
-0.06688638776540756,
-0.01533400546759367,
-0.026994097977876663,
0.036431048065423965,
-0.041654739528894424,
0.02227468602359295,
-0.0025168920401483774,
0.016322799026966095,
-0.05263406038284302,
0.05829394608736038,
-0.046563103795051575,
-0.03551316633820534,
0.0030553345568478107,
0.010770094580948353,
-0.003998578526079655,
0.012894432991743088,
-0.0416337326169014,
0.010221236385405064,
-0.012445272877812386,
0.003187804715707898,
0.038612861186265945,
-0.003766541602090001,
0.008059893734753132,
-0.03013022057712078,
0.04787927493453026,
-0.030873149633407593,
-0.027126504108309746,
0.06541195511817932,
-0.04213432967662811,
-0.012313646264374256,
0.03715375065803528,
-0.00795383844524622,
0.07090454548597336,
-0.011183946393430233,
-0.021564358845353127,
-0.012525555677711964,
0.06474946439266205,
-0.0287051722407341,
0.002402444602921605,
-0.022413469851017,
-0.05298483371734619,
0.004627111833542585,
-0.020285841077566147,
0.006938470993191004,
-0.026893291622400284,
-0.0020453245379030704,
0.026774123311042786,
-0.009761764667928219,
-0.022225352004170418,
0.05328618362545967,
0.029708199203014374,
0.016087453812360764,
-0.03198547288775444,
0.03188387677073479,
-0.022651299834251404,
0.026499666273593903,
0.04383651912212372,
-0.017917443066835403,
0.06177562102675438,
-0.0009108683443628252,
-0.0010272188810631633,
-0.09135697782039642,
0.02909477986395359,
-0.027345679700374603,
0.05904713273048401,
0.04496234655380249,
-0.08168491721153259,
-0.013568498194217682,
0.0277942456305027,
-0.04564690217375755,
0.011028454639017582,
-0.05694545432925224,
0.014293458312749863,
-0.012466910295188427,
-0.03378932550549507,
0.01677638106048107,
0.021849442273378372,
0.038542233407497406,
0.004155212547630072,
0.006706700194627047,
0.022986650466918945,
-0.009214851073920727,
-0.026267440989613533,
-0.012124157510697842,
0.016449179500341415,
-0.014963800087571144,
0.0009744783164933324,
0.02845350094139576,
-0.016383294016122818,
0.01094529777765274,
0.02108258381485939,
-0.03869256749749184,
0.03699615225195885,
0.0046014986000955105,
-0.019896993413567543,
0.013353335671126842,
0.01434369757771492,
0.006679118610918522,
0.007339861243963242,
-0.02632158435881138,
0.03095218352973461,
0.009251624345779419,
0.04548957943916321,
-0.04203447327017784,
-0.01258593425154686,
0.0060613034293055534,
-0.0264036413282156,
-0.040101632475852966,
0.015539545565843582,
-0.03651685640215874,
0.012021076865494251,
-0.00030907453037798405,
-0.011457319371402264,
0.011628109030425549,
-0.014913822524249554,
-0.01613699086010456,
-0.01862064190208912,
-0.003219400532543659,
0.06372655183076859,
-0.027204575017094612,
-0.03575998544692993,
0.030007237568497658,
-0.023166557773947716,
-0.013195624575018883,
-0.013386200182139874,
-0.0156899131834507,
-0.00038608969771303236,
-0.014629014767706394,
-0.024480683729052544,
0.0029668535571545362,
-0.010886231437325478,
-0.01726776547729969,
-0.028600968420505524,
-0.01166987419128418,
0.0052106380462646484,
0.040280282497406006,
0.017480622977018356,
0.0007430477417074144,
0.004221823066473007,
0.016727518290281296,
-0.06995496898889542,
0.000851066317409277,
0.04377134516835213,
-0.04442176967859268,
-0.020205890759825706,
-0.010639220476150513,
0.02152050845324993,
0.011054505594074726,
0.05056022107601166,
-0.03710256144404411,
-0.044190119951963425,
0.014992930926382542,
-0.02732502482831478,
-0.011409149505198002,
-0.05263988673686981,
0.023958345875144005,
-0.0025403830222785473,
-0.05616983771324158,
0.008360921405255795,
-0.006606401409953833,
0.01654740795493126,
0.0059170201420784,
-0.00011819197970908135,
0.02687148191034794,
-0.02512967772781849,
-0.007540898863226175,
-0.04495774954557419,
0.013851203955709934,
0.05172298848628998,
0.026528356596827507,
0.0666554793715477,
-0.01493984553962946,
-0.010082541033625603,
0.026798982173204422,
-0.040590010583400726,
-0.027803592383861542,
0.06706937402486801,
-0.02700275182723999,
-0.006031627766788006,
-0.011456513777375221,
0.004578450694680214,
-0.004146431107074022,
-0.03322039544582367,
0.021700890734791756,
0.011050218716263771,
-0.013172858394682407,
-0.032001081854104996,
0.05532853305339813,
0.04213272035121918,
0.03069331683218479,
-0.022399846464395523,
-0.014465151354670525,
0.00022955592430662364,
-0.03840037062764168,
-0.015260881744325161,
0.021629853174090385,
0.006632224656641483,
0.02205590344965458,
-0.012757763266563416,
0.03686286881566048,
-0.006669879425317049,
0.02753565087914467,
0.02367541939020157,
0.002762953517958522,
-0.0219816192984581,
-0.033149246126413345,
-0.023874573409557343,
-0.0019437349401414394,
0.010218298994004726,
0.027296157553792,
-0.02937641181051731,
0.06441827118396759,
-0.024098847061395645,
-0.004162706900388002,
0.0062635899521410465,
0.011654948815703392,
-0.042739689350128174,
0.007258561439812183,
0.0253618061542511,
-0.013948812149465084,
0.011769099161028862,
-0.0252117570489645,
-0.0027105258777737617,
0.0015046342741698027,
0.02317444235086441,
0.011830338276922703,
-0.010373854078352451,
0.0005977142718620598,
0.0037308193277567625,
-0.03987313434481621,
-0.03166436776518822,
-0.039419353008270264,
-0.005691778380423784,
0.0012953082332387567,
0.03892172873020172,
0.021652229130268097,
-0.028954502195119858,
-0.007978935725986958,
-0.00751881068572402,
0.05422411486506462,
-0.06552567332983017,
-0.021269913762807846,
-0.020599840208888054,
0.05639335513114929,
-0.0023290503304451704,
0.021914521232247353
] |
<p>This theory states that at relative velocities exceeding 3^-0.5 c, gravitational repulsion ensues. The relevant papers are on arXiv by Franklin Felber. Here's one of them
<a href="http://arxiv.org/abs/0910.1084" rel="nofollow">http://arxiv.org/abs/0910.1084</a></p>
<p>I have seen two interesting critiques thus far. The first is that the effect is an artifact of the choice of coordinates:
<a href="http://arxiv.org/abs/1102.2870" rel="nofollow">http://arxiv.org/abs/1102.2870</a>
and rebutted by Felber here
<a href="http://arxiv.org/abs/1111.6564" rel="nofollow">http://arxiv.org/abs/1111.6564</a>
This answer also seems germane
<a href="http://physics.stackexchange.com/a/83175/11633">http://physics.stackexchange.com/a/83175/11633</a></p>
<p>The second critique involves the feasibility of the proposed LHC experiment:
<a href="http://arxiv.org/abs/0912.1323v1" rel="nofollow">http://arxiv.org/abs/0912.1323v1</a></p>
| 8,813 |
[
-0.03181910887360573,
-0.02776806429028511,
0.00011088525934610516,
-0.03598645702004433,
0.05017651244997978,
0.022807195782661438,
-0.026369797065854073,
-0.010501844808459282,
0.003782034618780017,
-0.012036983855068684,
0.004176615737378597,
0.06670816987752914,
0.032019469887018204,
0.015603083185851574,
0.011422302573919296,
0.018543243408203125,
0.0038527220021933317,
0.003828558372333646,
-0.005414334591478109,
-0.071123406291008,
0.03975372761487961,
0.03410480543971062,
0.01904281973838806,
-0.01871383562684059,
-0.013219483196735382,
-0.008262495510280132,
0.0169130340218544,
0.0035403647925704718,
-0.03233997896313667,
0.05788722261786461,
-0.018570074811577797,
0.005580383352935314,
-0.009846680797636509,
0.002748030237853527,
0.002671563997864723,
0.05809909477829933,
0.0015772631159052253,
-0.04147283732891083,
-0.012598593719303608,
0.019419848918914795,
-0.04983767494559288,
-0.004483677912503481,
-0.037092939019203186,
0.04613746330142021,
0.005929193925112486,
0.00047137492219917476,
0.0009178100735880435,
0.00607468094676733,
0.08654026687145233,
-0.06993072479963303,
0.04802819713950157,
0.01283515989780426,
-0.00886385329067707,
0.012689366936683655,
-0.014881571754813194,
-0.03544037044048309,
0.055300209671258926,
0.07952643930912018,
-0.015531430952250957,
-0.05360515043139458,
-0.02312232181429863,
-0.02877996489405632,
0.014621344394981861,
0.0022451363038271666,
-0.012586231343448162,
0.03601105138659477,
-0.009083081968128681,
-0.00112060341052711,
0.015455341897904873,
0.009939298965036869,
0.05266731232404709,
0.019638720899820328,
0.0049550761468708515,
-0.00038432946894317865,
0.03036734275519848,
-0.0015630628913640976,
0.012375155463814735,
-0.012259017676115036,
-0.005558159202337265,
0.049403492361307144,
-0.045735351741313934,
0.0004959520883858204,
0.05325760692358017,
0.052061162889003754,
0.010657630860805511,
-0.02360200323164463,
0.04457998648285866,
-0.01945251226425171,
-0.016698284074664116,
0.0496545247733593,
-0.029842883348464966,
-0.003422441426664591,
0.014875938184559345,
0.011058197356760502,
-0.019068030640482903,
0.04022786021232605,
0.00471191992983222,
0.07222335040569305,
-0.017492104321718216,
-0.018660034984350204,
-0.02505083940923214,
-0.006288195960223675,
-0.00835501030087471,
0.058334831148386,
0.009762289933860302,
-0.0471712090075016,
-0.03658054396510124,
-0.001713119330815971,
-0.0476522222161293,
-0.01329333521425724,
-0.03492202237248421,
-0.007021353580057621,
-0.0036539447028189898,
-0.00491189444437623,
0.02617371827363968,
-0.060322199016809464,
0.006282501388341188,
-0.011049272492527962,
0.07843571901321411,
0.025383340194821358,
0.04768188297748566,
-0.009673424065113068,
0.012206905521452427,
-0.009378684684634209,
-0.07554566860198975,
0.006236327812075615,
0.04710285738110542,
-0.02698466181755066,
-0.01884717494249344,
0.015767671167850494,
0.016210539266467094,
0.02669854275882244,
0.00035757015575654805,
0.008296280167996883,
0.05168838053941727,
-0.007099537644535303,
-0.12489499151706696,
-0.06482969224452972,
0.06214476749300957,
0.008411092683672905,
0.0012095948914065957,
-0.08135166764259338,
0.006509896833449602,
0.02650710754096508,
0.08106380701065063,
-0.023291001096367836,
-0.006052888464182615,
-0.031114844605326653,
0.05048515275120735,
-0.005656994879245758,
-0.013821977190673351,
-0.028376534581184387,
0.008336635306477547,
-0.05083497241139412,
-0.032709602266550064,
-0.07923325896263123,
0.005431278143078089,
0.02341526560485363,
-0.009631036780774593,
-0.017716800794005394,
0.05262681096792221,
-0.014851059764623642,
0.023911787196993828,
0.0001446396781830117,
-0.01062791794538498,
-0.008964461274445057,
0.08809014409780502,
0.015850014984607697,
-0.023975912481546402,
0.032479532063007355,
-0.008742902427911758,
0.047822531312704086,
-0.002458212897181511,
-0.02912423573434353,
0.029854774475097656,
-0.06453291326761246,
-0.00806419551372528,
-0.007668103091418743,
0.01817929744720459,
-0.027394670993089676,
-0.012548609636723995,
-0.018187545239925385,
-0.015537112951278687,
0.0050435252487659454,
-0.016738971695303917,
0.02134324051439762,
-0.009660640731453896,
0.024980563670396805,
0.031030643731355667,
-0.021641593426465988,
-0.025861956179142,
-0.07769526541233063,
-0.028432931751012802,
0.006170264910906553,
-0.0017520332476124167,
0.03089311718940735,
0.01775224506855011,
0.009396051056683064,
-0.015405110083520412,
-0.012170699425041676,
-0.011050163768231869,
0.03730003163218498,
0.005183713510632515,
0.012994423508644104,
0.013933361507952213,
0.07407446950674057,
0.04317350685596466,
0.01028306782245636,
0.0004250304482411593,
0.02541264146566391,
-0.0509188175201416,
0.014264031313359737,
-0.01231787633150816,
0.005675985012203455,
0.010798200964927673,
0.032872144132852554,
-0.01259556319564581,
0.018085326999425888,
0.001419508014805615,
0.027567550539970398,
-0.03133942186832428,
0.10970617830753326,
-0.0009209159761667252,
0.043460018932819366,
0.007860363461077213,
0.06558369845151901,
-0.00390973687171936,
0.03273084759712219,
-0.0004979466320946813,
-0.027479669079184532,
-0.061610858887434006,
-0.015445724129676819,
0.003917980473488569,
0.021817121654748917,
-0.03500164672732353,
0.054337646812200546,
0.04179844632744789,
0.04130105301737785,
0.004099904093891382,
0.009018556214869022,
-0.0030113577377051115,
-0.07146384567022324,
0.015077211894094944,
0.015252006240189075,
0.007786385715007782,
-0.0016377951251342893,
0.016314269974827766,
-0.007914300076663494,
-0.012921235524117947,
-0.029940785840153694,
-0.027178026735782623,
0.009853409603238106,
0.008238409645855427,
-0.021322719752788544,
0.005499253980815411,
-0.0052545988000929356,
0.054307885468006134,
0.006238223984837532,
0.027265004813671112,
0.03840593248605728,
-0.03101152554154396,
0.0054936460219323635,
-0.0441104955971241,
-0.025777002796530724,
-0.011285997927188873,
0.030146067962050438,
-0.010091248899698257,
-0.01116421539336443,
0.007568384055048227,
-0.09732624143362045,
0.002621456515043974,
-0.05213150009512901,
-0.0013290047645568848,
-0.011832859367132187,
-0.011181860230863094,
0.011710656806826591,
0.005553402937948704,
0.007298145908862352,
-0.014821646735072136,
-0.030481727793812752,
0.04087063670158386,
-0.002694532508030534,
-0.03305133059620857,
0.018407853320240974,
-0.016361385583877563,
0.010756962932646275,
-0.059968315064907074,
-0.022112052887678146,
0.04129679501056671,
-0.0014909416204318404,
0.028866199776530266,
0.0019116875482723117,
-0.008454011753201485,
-0.06815887242555618,
-0.022301800549030304,
-0.024864355102181435,
0.009251214563846588,
-0.01852397620677948,
-0.005425863899290562,
0.05625314265489578,
0.0287201926112175,
-0.036317791789770126,
0.01002398133277893,
-0.036071423441171646,
-0.023624299094080925,
0.008561119437217712,
0.018572017550468445,
-0.018828202039003372,
-0.0303388312458992,
0.056255120784044266,
-0.015341036021709442,
-0.027353327721357346,
-0.014525077305734158,
-0.03511986881494522,
-0.018860982730984688,
0.03900691494345665,
0.014402286149561405,
0.035401951521635056,
-0.019800281152129173,
-0.0220488253980875,
0.07209279388189316,
0.026323337107896805,
-0.0038330648094415665,
-0.03539391979575157,
-0.011675556190311909,
-0.014268982224166393,
0.013057876378297806,
-0.009316597133874893,
0.0103231156244874,
0.011893722228705883,
0.012516701593995094,
0.015165546908974648,
0.01235590223222971,
0.010157429613173008,
0.012421444989740849,
-0.024631833657622337,
-0.0037095830775797367,
0.01598045788705349,
-0.020824598148465157,
0.05188176780939102,
0.013755390420556068,
-0.05155050754547119,
-0.01315302774310112,
-0.005388949066400528,
0.02542722411453724,
-0.020808300003409386,
-0.07682884484529495,
0.07159975171089172,
0.020556703209877014,
0.02358824759721756,
-0.006215893197804689,
-0.012097936123609543,
-0.01386695820838213,
0.004495729226619005,
0.022171443328261375,
0.02526206709444523,
0.05422712489962578,
0.029353579506278038,
0.02364242821931839,
0.03126053884625435,
0.06300243735313416,
-0.011512449942529202,
-0.04853993281722069,
-0.01518456730991602,
-0.020981362089514732,
0.017785876989364624,
-0.0047178869135677814,
-0.02556713856756687,
0.02903156913816929,
0.02530011720955372,
0.025205649435520172,
0.00666182953864336,
-0.02112894505262375,
0.005698080640286207,
-0.07910614460706711,
0.032271984964609146,
-0.010437414050102234,
0.036052197217941284,
0.024532141163945198,
0.01274076383560896,
0.05827418714761734,
0.005195125937461853,
0.007148053962737322,
-0.018931686878204346,
-0.12594732642173767,
0.003343607299029827,
-0.05375425145030022,
-0.021876389160752296,
0.004904043860733509,
-0.030964942649006844,
-0.020366311073303223,
-0.018531816080212593,
-0.018700482323765755,
-0.026435792446136475,
0.02436317875981331,
-0.043738339096307755,
0.009509948082268238,
-0.03471323475241661,
-0.03894876316189766,
-0.01854921691119671,
0.04232325777411461,
0.02582588419318199,
-0.02845594845712185,
0.026335548609495163,
0.009662777185440063,
-0.05550020933151245,
-0.03872730955481529,
-0.0008374791359528899,
0.040557365864515305,
-0.0001901864307001233,
0.05104583874344826,
0.014794819056987762,
0.013943302445113659,
-0.028063390403985977,
0.010596051812171936,
0.04316384717822075,
0.006653536111116409,
0.022552167996764183,
-0.012748008593916893,
-0.031760189682245255,
-0.027112508192658424,
-0.03212343156337738,
0.017008241266012192,
0.04051967337727547,
0.0024767627473920584,
-0.004974363371729851,
0.02189520373940468,
0.030311429873108864,
0.02130613848567009,
0.02780000865459442,
0.03746112808585167,
-0.017103223130106926,
-0.03056379407644272,
-0.02712942473590374,
-0.03623306006193161,
0.009469817392528057,
-0.010642249137163162,
0.05925867706537247,
0.01050350721925497,
-0.04865817725658417,
-0.011697337962687016,
0.016442127525806427,
0.03988413140177727,
-0.04747908562421799,
0.010582760907709599,
0.0005086266319267452,
0.015610872767865658,
-0.030716819688677788,
0.011949191801249981,
-0.012242794968187809,
0.03718281537294388,
0.03293827176094055,
0.007637786213308573,
0.00745196919888258,
-0.0815049558877945,
-0.022814033553004265,
0.040668290108442307,
0.06417626142501831,
-0.015813207253813744,
-0.005376798566430807,
-0.04048796370625496,
0.006319698877632618,
0.042641766369342804,
-0.05301525816321373,
0.025928670540452003,
-0.0014202655293047428,
0.0255290437489748,
-0.0001393140119034797,
0.0019979327917099,
-0.007794604636728764,
0.02777821011841297,
-0.030291475355625153,
-0.012782114557921886,
-0.03393308073282242,
-0.01822047494351864,
-0.0004095317854080349,
-0.01356500107795,
0.03731556609272957,
0.04761884734034538,
0.03724538907408714,
0.04282592982053757,
-0.024695051833987236,
-0.01594109646975994,
-0.040598686784505844,
-0.0847369059920311,
-0.0016485822852700949,
-0.0079070208594203,
-0.012054480612277985,
0.04110853001475334,
-0.05842290818691254,
-0.025163434445858,
0.0508095920085907,
0.03707978501915932,
0.0022599592339247465,
0.011980409733951092,
-0.047759514302015305,
-0.004913755226880312,
0.047889914363622665,
-0.008576815016567707,
0.050183553248643875,
0.0017488887533545494,
-0.029858097434043884,
0.01149203535169363,
0.01635054498910904,
0.02724200300872326,
-0.031415510922670364,
0.01735304854810238,
-0.015229923650622368,
0.027328718453645706,
-0.05733257904648781,
0.035811495035886765,
-0.02028721757233143,
0.004400220699608326,
-0.0028366046026349068,
-0.03373020514845848,
-0.013863864354789257,
0.005666779354214668,
-0.01164109818637371,
0.003325647208839655,
-0.00568533968180418,
0.03551369532942772,
-0.010289136320352554,
-0.003016800619661808,
0.02850175090134144,
0.00010424896754557267,
0.010709627531468868,
0.00980362668633461,
-0.015567043796181679,
0.009131173603236675,
0.010412471368908882,
-0.0032796580344438553,
0.02662755735218525,
-0.03661279007792473,
0.035325609147548676,
-0.026700157672166824,
0.011776687577366829,
0.033743567764759064,
-0.01715238019824028,
-0.03301147744059563,
0.012327405624091625,
-0.02792258746922016,
0.038047417998313904,
-0.044740159064531326,
-0.004781221970915794,
0.002648066496476531,
0.03570361062884331,
-0.06270994991064072,
-0.043341681361198425,
0.038034405559301376,
0.003377954475581646,
-0.018762527033686638,
-0.028648031875491142,
-0.04002576321363449,
-0.03725988790392876,
-0.02639116533100605,
-0.039533596485853195,
0.05939924716949463,
-0.0237901471555233,
0.005351846106350422,
0.0007062637596391141,
0.011178581975400448,
0.03863466531038284,
0.011698480695486069,
0.02581637166440487,
0.013402950949966908,
0.0077529908157885075,
-0.002201528986915946,
0.00561393890529871,
0.0854455754160881,
-0.02038206346333027,
-0.03880927339196205,
-0.0013499412452802062,
0.016240164637565613,
0.009876826778054237,
-0.009259712882339954,
-0.025937387719750404,
0.047499191015958786,
0.015239368192851543,
0.011763767339289188,
-0.004197132308036089,
0.04276216775178909,
0.005096070934087038,
0.007443588227033615,
-0.02638157084584236,
0.020122094079852104,
-0.0003686189593281597,
-0.018019849434494972,
0.04371374472975731,
0.014638311229646206,
-0.013656162656843662,
-0.015955928713083267,
0.051130615174770355,
0.02352866716682911,
-0.021035179495811462,
0.012424592860043049,
-0.0008134205709211528,
0.01767861098051071,
-0.029112132266163826,
0.0434998944401741,
0.011973774991929531,
-0.009962694719433784,
-0.008160269819200039,
-0.03878333419561386,
-0.015028451569378376,
0.0023209915962070227,
0.06109717860817909,
-0.0008689573151059449,
0.07313655316829681,
0.001528332126326859,
-0.02675957791507244,
-0.003330248175188899,
-0.006068884395062923,
-0.0054836273193359375,
-0.006265634670853615,
0.023935526609420776,
0.013252794742584229,
-0.05133714899420738,
-0.041746653616428375,
0.01592368073761463,
0.011212541721761227,
0.002442997181788087,
-0.005289872642606497,
0.0479726605117321,
0.01586679369211197,
0.01181167270988226,
-0.003983770497143269,
-0.019430730491876602,
0.04697640985250473,
-0.01530238427221775,
0.030988996848464012,
0.019392838701605797,
-0.016366034746170044,
0.017842361703515053,
0.011020992882549763,
0.02667461335659027,
-0.026023361831903458,
-0.04157287999987602,
-0.07611265778541565,
0.0019576975610107183,
0.0052099875174462795,
0.025993043556809425,
0.012853250838816166,
-0.009588005021214485,
0.013116316869854927,
0.040205877274274826,
0.03349229320883751,
-0.014799881726503372,
-0.09890462458133698,
-0.012376907281577587,
-0.021578708663582802,
-0.017215101048350334,
0.04806094244122505,
0.005322199314832687,
-0.025437206029891968,
0.03186728432774544,
-0.0424305722117424,
-0.007512921467423439,
0.0418628565967083,
0.002629006514325738,
-0.016020525246858597,
0.058658529072999954,
-0.006463754456490278,
-0.002125739585608244,
-0.044171042740345,
0.00192371872253716,
0.10329409688711166,
0.02973245456814766,
0.005402136128395796,
-0.06871602684259415,
0.0660371482372284,
0.013716270215809345,
0.0043782759457826614,
-0.05150994658470154,
0.021855447441339493,
-0.0031864286866039038,
0.0017579308478161693,
0.03272417560219765,
0.01977563090622425,
-0.003270395565778017,
-0.051796697080135345,
0.029103919863700867,
-0.037420764565467834,
-0.06578889489173889,
0.02785545028746128,
0.02038436010479927,
-0.012049279175698757,
-0.02928217686712742,
-0.010637861676514149,
0.003798118559643626,
-0.019864926114678383,
0.0002509142505005002,
0.008977814577519894,
-0.06072761118412018,
0.022551044821739197,
0.002019319450482726,
-0.0353807732462883,
0.023950079455971718,
0.02507137507200241,
-0.025420861318707466,
-0.04472585394978523,
-0.002855981932953,
-0.007515801582485437,
-0.014680231921374798,
0.030353853479027748,
0.04254583641886711,
0.02117123268544674,
0.00495330523699522,
-0.006035313475877047,
0.023394213989377022,
-0.04926437884569168,
-0.03061896190047264,
-0.006338655017316341,
0.07323070615530014,
0.003808899549767375,
-0.018656311556696892,
-0.022464673966169357,
0.00786816980689764,
0.015141629613935947,
-0.04038669541478157,
0.011813719756901264,
-0.02013530395925045,
0.01462699193507433,
0.024142468348145485,
-0.033073198050260544,
-0.01018431130796671,
0.060917433351278305,
-0.03189723193645477,
0.000010387507245468441,
0.0053746518678963184,
0.002653250703588128,
-0.0004731986846309155,
-0.012475419789552689,
0.06209123134613037,
0.011665386147797108,
0.006236084271222353,
-0.04093869775533676,
0.03242915868759155,
-0.0678815022110939,
0.010762575082480907,
-0.025581371039152145,
0.015632525086402893,
0.015997178852558136,
0.025103218853473663,
0.024744311347603798,
-0.04303929954767227,
-0.041727036237716675,
0.03491659089922905,
-0.021923763677477837,
-0.031021567061543465,
-0.024852367118000984,
0.001828324398957193,
0.02526238188147545,
0.026163194328546524,
-0.03178470954298973,
-0.021436873823404312,
-0.026399018242955208,
0.035246483981609344,
-0.024404745548963547,
-0.02813783288002014,
-0.02730013243854046,
-0.02167080156505108,
-0.06030068174004555,
-0.011577179655432701,
-0.02272428572177887,
0.029934190213680267,
0.003449053270742297,
0.025111813098192215,
0.025708792731165886,
0.01542389765381813,
-0.011348474770784378,
-0.018160147592425346,
0.04410519450902939,
0.0034896484576165676,
-0.03610287606716156,
0.03381512314081192,
0.013016055338084698,
-0.014377056621015072,
-0.031310901045799255,
0.02436000294983387,
0.0011919232783839107,
-0.011064533144235611,
0.03525235876441002,
-0.03378941863775253,
0.021492822095751762,
-0.025790149345993996,
0.0051229605451226234,
-0.04449177905917168,
0.015245826914906502,
-0.04253534600138664,
0.018951186910271645,
-0.04507776349782944,
-0.018508629873394966,
-0.0029321464244276285,
0.04288157820701599,
-0.0264164749532938,
-0.0020933973137289286,
0.013718589209020138,
-0.007250584661960602,
-0.026167815551161766,
0.004817403387278318,
0.013287232257425785,
0.038145218044519424,
0.025105053558945656,
-0.02207743376493454,
-0.018559489399194717,
0.02314813807606697,
-0.024683771654963493,
-0.06831948459148407,
0.03452254459261894,
-0.05561031028628349,
0.01902211643755436,
-0.007064477074891329,
-0.019702544435858727,
-0.012350447475910187,
0.09583677351474762,
0.004389975685626268,
-0.000391407054848969,
-0.005873509682714939,
-0.036119263619184494,
0.0031138788908720016,
0.012007939629256725,
0.0021081422455608845,
-0.04816053435206413,
0.0027427105233073235,
0.037367403507232666,
0.02565215714275837,
-0.041388366371393204,
0.044251974672079086,
-0.03570646047592163,
-0.011818721890449524,
0.022589365020394325,
-0.005804791115224361,
-0.018741877749562263,
-0.008270053192973137,
0.013089283369481564,
-0.07091151922941208,
0.03341435268521309,
0.03234056010842323,
0.03078896924853325,
-0.1111685037612915,
0.012359834276139736,
-0.014606679789721966,
0.00669162068516016,
0.05263222008943558,
-0.05680399015545845,
0.0319800078868866,
0.0253989789634943,
-0.05411793291568756,
0.014944505877792835,
-0.048247840255498886,
-0.029365185648202896,
-0.04468776658177376,
-0.02366001158952713,
0.01791568100452423,
0.05388860031962395,
0.033465880900621414,
0.037666719406843185,
-0.019191794097423553,
0.006558086257427931,
-0.01691017858684063,
-0.027462463825941086,
-0.004311290103942156,
0.032375480979681015,
-0.01610286720097065,
0.0004823187773581594,
0.08233501762151718,
-0.008813456632196903,
-0.02798363007605076,
0.04080064967274666,
0.03013293445110321,
-0.001774297095835209,
-0.014154067263007164,
0.002411345951259136,
0.006039060186594725,
0.020742131397128105,
0.029401928186416626,
-0.0017787318211048841,
0.009946201927959919,
-0.010138126090168953,
0.0016623775009065866,
0.029295295476913452,
0.008144916966557503,
-0.00014578540867660195,
-0.015806496143341064,
-0.020052902400493622,
0.0009654095629230142,
0.04359040781855583,
-0.029663078486919403,
-0.010783555917441845,
-0.016876086592674255,
0.013001922518014908,
0.016029974445700645,
-0.04426097497344017,
0.0025781725998967886,
-0.026219729334115982,
-0.012198151089251041,
0.036419570446014404,
0.0027959635481238365,
-0.02065695822238922,
-0.0041418056935071945,
-0.013589128851890564,
0.03714350238442421,
-0.003949608188122511,
-0.024660760536789894,
0.02038496546447277,
-0.04372779279947281,
-0.00798928365111351,
0.010489673353731632,
0.02988220751285553,
0.0016921010101214051,
-0.051987044513225555,
-0.03553938865661621,
0.05622600391507149,
-0.023571781814098358,
0.016560731455683708,
-0.012898294255137444,
-0.0043030064553022385,
-0.022825583815574646,
-0.07202064990997314,
0.01838650554418564,
0.024037593975663185,
0.009579414501786232,
-0.04780443757772446,
-0.04517778754234314,
0.00720336614176631,
0.050067491829395294,
0.036070629954338074,
0.0018258941126987338,
-0.015107150189578533,
0.03394778072834015,
-0.01100305374711752,
-0.009219870902597904,
-0.023823948577046394,
-0.02373490296304226,
-0.004261041060090065,
-0.018824219703674316,
0.017647454515099525,
-0.015022718347609043,
-0.019568925723433495,
0.018688248470425606,
0.038339901715517044,
-0.011092192493379116,
0.03555259108543396,
0.04366227239370346,
-0.026261810213327408,
0.04743035510182381,
0.01583941839635372,
0.039841778576374054,
0.06627723574638367,
0.01926511339843273,
0.032951340079307556,
-0.001564229722134769,
0.0028795916587114334,
-0.017850911244750023,
0.04549812152981758,
-0.013478328473865986,
-0.011864453554153442,
-0.03466121107339859,
-0.009088938124477863,
-0.02118668518960476,
-0.04658237099647522,
0.011835016310214996,
0.0384354405105114,
-0.025390125811100006,
-0.023615999147295952,
0.02244727686047554,
0.03808947652578354,
0.03636261820793152,
0.006967467255890369,
0.010890118777751923,
-0.0025566453114151955,
-0.014409118331968784,
-0.011916102841496468,
0.02587251551449299,
0.03428513556718826,
0.02803024835884571,
0.012094604782760143,
0.030386092141270638,
-0.015546749345958233,
0.03412225842475891,
0.030388787388801575,
0.04729628190398216,
-0.01610620506107807,
-0.010725239291787148,
0.022054173052310944,
0.0051468475721776485,
0.00903646182268858,
0.03651197999715805,
-0.016575580462813377,
0.0806533545255661,
-0.013380822725594044,
-0.006341058760881424,
0.0004307931521907449,
-0.03971404209733009,
0.03349418193101883,
0.03310796618461609,
-0.02303248830139637,
0.05514582619071007,
-0.015080012381076813,
-0.019459746778011322,
-0.002496595261618495,
0.010120650753378868,
-0.005966775119304657,
-0.02432994171977043,
-0.024246878921985626,
-0.03361620381474495,
0.027156485244631767,
0.004537108354270458,
-0.008609054610133171,
-0.0247211791574955,
0.0004186871228739619,
0.021103577688336372,
0.0635431706905365,
0.021993469446897507,
-0.019932784140110016,
0.010431593284010887,
-0.013647987507283688,
0.040835440158843994,
-0.011402707546949387,
-0.027141887694597244,
-0.003928530029952526,
0.040995579212903976,
-0.031041527166962624,
0.01910131610929966
] |
<p>When working with linearized gravity, is Poincaré symetry assumed to be the symmetry of space-time?</p>
| 8,814 |
[
-0.021404065191745758,
0.0018834038637578487,
-0.01992509327828884,
-0.0018945436459034681,
0.056967977434396744,
0.03845362365245819,
-0.03286953642964363,
-0.015218611806631088,
-0.017684217542409897,
-0.013690710067749023,
-0.005137087311595678,
0.003956116270273924,
0.03248673677444458,
-0.008797693066298962,
0.04127643629908562,
-0.0029895645566284657,
-0.0020015581976622343,
0.00343592232093215,
-0.0018525853520259261,
-0.03450869396328926,
0.006095120683312416,
0.026941470801830292,
-0.001012022839859128,
-0.010047643445432186,
-0.030495770275592804,
0.03999762982130051,
0.02868879772722721,
0.01622440665960312,
0.007519076578319073,
0.053570035845041275,
-0.01613233983516693,
-0.003724233480170369,
0.00809467863291502,
0.038729649037122726,
-0.015313645824790001,
-0.011977056041359901,
-0.019306601956486702,
-0.0412229485809803,
0.01460504811257124,
0.008184741251170635,
-0.037397369742393494,
-0.01861133798956871,
-0.009600848890841007,
0.0673527717590332,
-0.01624043844640255,
0.043067462742328644,
-0.017282608896493912,
0.018306992948055267,
0.047338154166936874,
-0.03815176710486412,
0.0990571603178978,
0.017453117296099663,
0.018324365839362144,
-0.024458544328808784,
-0.02565932087600231,
0.012080777436494827,
0.06161016225814819,
0.0485619455575943,
0.00995028205215931,
-0.06298016756772995,
-0.047773268073797226,
-0.006661714054644108,
0.008596159517765045,
-0.03289926052093506,
-0.020631123334169388,
0.03126455098390579,
0.0029766527004539967,
-0.014616369269788265,
0.003920435439795256,
-0.004074280150234699,
-0.039515260607004166,
0.002012447454035282,
0.03861940652132034,
-0.03750705346465111,
-0.017086029052734375,
0.005582693964242935,
0.005877151153981686,
-0.016353189945220947,
0.04404154419898987,
-0.017166582867503166,
0.010436199605464935,
0.022196147590875626,
0.011802329681813717,
0.0474640354514122,
0.0025779344141483307,
0.00935370847582817,
0.06049739196896553,
-0.008834288455545902,
0.011440025642514229,
0.04045401141047478,
-0.011965072713792324,
-0.020351726561784744,
0.011040827259421349,
-0.02602626197040081,
-0.033392615616321564,
0.029225818812847137,
0.006462720688432455,
0.04414653033018112,
0.013882539235055447,
0.007023562211543322,
-0.005719760898500681,
-0.019298313185572624,
-0.017804928123950958,
0.053285617381334305,
0.03363965451717377,
-0.004275431390851736,
-0.01825578510761261,
0.03772193193435669,
-0.022315973415970802,
-0.004269400145858526,
-0.04039064049720764,
-0.013261617161333561,
-0.021482830867171288,
-0.0036965294275432825,
0.04169504716992378,
-0.010719756595790386,
0.0030182981863617897,
-0.029200900346040726,
0.03654294088482857,
0.06378276646137238,
0.01441370788961649,
0.003221564693376422,
0.04116176813840866,
0.005956508684903383,
-0.04321766644716263,
0.012780336663126945,
0.02984451875090599,
-0.010114576667547226,
-0.03761260211467743,
0.0029936672654002905,
0.02420882321894169,
-0.04205847531557083,
-0.010444526560604572,
-0.00721186026930809,
0.0560448132455349,
-0.007515797391533852,
-0.08892510831356049,
-0.05396723747253418,
0.019699420779943466,
0.005804973188787699,
-0.0019822032190859318,
-0.05313676595687866,
-0.0018886496545746922,
0.008507329039275646,
0.06770812720060349,
-0.0227790679782629,
0.01784045808017254,
0.01429652702063322,
0.030951928347349167,
0.013865680433809757,
-0.017129503190517426,
-0.019088873639702797,
0.029868215322494507,
-0.08123030513525009,
0.0022064577788114548,
-0.10016854852437973,
-0.026679208502173424,
0.005920650437474251,
0.007337420713156462,
-0.027195831760764122,
0.05157683789730072,
-0.019432418048381805,
0.0001660392590565607,
0.02572362869977951,
0.0062113795429468155,
0.005948218051344156,
0.04055347293615341,
0.007657208479940891,
0.013045430183410645,
-0.007223325781524181,
-0.008945390582084656,
0.04585147276520729,
0.009510437026619911,
0.04812012240290642,
0.04021940380334854,
-0.03512014448642731,
-0.01649351976811886,
-0.0005233230185694993,
0.013514995574951172,
-0.005004026927053928,
-0.023217983543872833,
-0.0382327176630497,
0.004115053918212652,
0.006348486989736557,
-0.029405396431684494,
0.058831341564655304,
0.0049147531390190125,
-0.0143533144146204,
-0.021303098648786545,
-0.021382970735430717,
0.004346420522779226,
-0.03815598040819168,
-0.0023034694604575634,
0.02360573410987854,
-0.03675496578216553,
0.0217159241437912,
0.04779811203479767,
0.014639736153185368,
-0.05906575173139572,
-0.051922671496868134,
0.016536889597773552,
0.05691951885819435,
-0.02114904299378395,
-0.03587513789534569,
0.036392319947481155,
0.033351004123687744,
0.04656590521335602,
0.0060278852470219135,
0.029633238911628723,
-0.017953122034668922,
-0.015006118454039097,
-0.0008663006592541933,
0.006100854836404324,
0.0007855611620470881,
-0.010190455242991447,
0.011805993504822254,
0.0019831720273941755,
0.018894553184509277,
0.012609702534973621,
0.057218510657548904,
-0.02533802017569542,
0.06587143987417221,
0.04295817390084267,
-0.0026913881301879883,
-0.004321834072470665,
0.05952112004160881,
0.018400656059384346,
0.013962425291538239,
0.0032785641960799694,
-0.005385515745729208,
-0.02316751889884472,
-0.02116210013628006,
0.02642630599439144,
0.03399055451154709,
-0.013363060541450977,
0.015690729022026062,
0.04520442336797714,
0.057089097797870636,
0.014905237592756748,
-0.0008315296145156026,
-0.04015398025512695,
-0.06277977675199509,
0.029590174555778503,
-0.012269444763660431,
0.05275484547019005,
0.0050094942562282085,
0.05145857483148575,
-0.0026816532481461763,
-0.0019555529579520226,
-0.013862153515219688,
-0.01510846707969904,
0.03399117663502693,
0.013738779351115227,
-0.00024809781461954117,
0.02382691390812397,
-0.01697358302772045,
0.03150423243641853,
0.011389950290322304,
0.0422358438372612,
0.03285056725144386,
-0.006613115780055523,
-0.012899857014417648,
-0.025829007849097252,
0.004007600713521242,
-0.006261111237108707,
-0.029246896505355835,
-0.005771467927843332,
-0.02234497107565403,
0.043713461607694626,
-0.05794534459710121,
0.002743331715464592,
-0.050339072942733765,
-0.012786300852894783,
0.0020677309948951006,
-0.0023200016003102064,
0.04584873467683792,
-0.02473980374634266,
0.04459507390856743,
-0.034298304468393326,
-0.02588971145451069,
0.0026630330830812454,
-0.0028389780782163143,
0.00015443853044416755,
0.0295538492500782,
-0.051118943840265274,
0.0243181511759758,
-0.06190838664770126,
-0.014056875370442867,
0.012055469676852226,
0.011478016152977943,
0.06411345303058624,
0.01621166057884693,
-0.02367788925766945,
-0.003945518750697374,
-0.016351141035556793,
-0.043927814811468124,
-0.000700657838024199,
-0.023359037935733795,
0.02991955541074276,
0.011993421241641045,
0.016718227416276932,
-0.02899198792874813,
-0.010464045219123363,
-0.028200801461935043,
-0.024971164762973785,
-0.019291266798973083,
-0.0003943890333175659,
-0.005516573321074247,
-0.04505165293812752,
0.01677374728024006,
0.027745110914111137,
-0.049064863473176956,
0.031523197889328,
-0.05037016049027443,
-0.049044400453567505,
0.03048952855169773,
0.012897276319563389,
0.014306777156889439,
0.026106709614396095,
-0.06595860421657562,
0.09059838205575943,
0.040948428213596344,
0.004249141085892916,
-0.026597989723086357,
0.01619911938905716,
0.010939335450530052,
-0.03056102804839611,
0.03844458982348442,
-0.002080105245113373,
0.006435888819396496,
0.02749093994498253,
0.046557147055864334,
0.01558808982372284,
0.002617931691929698,
-0.0010161974932998419,
-0.03548947349190712,
-0.00850821752101183,
0.01864778995513916,
0.0480070523917675,
0.014044596813619137,
0.04264107719063759,
-0.008356657810509205,
0.0018077909480780363,
0.026005173102021217,
0.006828798912465572,
0.00211554067209363,
-0.05286682769656181,
0.060450535267591476,
-0.011226565577089787,
0.042334336787462234,
-0.02264518477022648,
0.02598015032708645,
0.00281920051202178,
-0.017932584509253502,
0.023688238114118576,
0.015961898490786552,
0.040244460105895996,
0.0003235839249100536,
0.006987234577536583,
0.004521891474723816,
0.05478176847100258,
-0.02260706014931202,
-0.02473967894911766,
0.021624784916639328,
-0.015231779776513577,
0.030635498464107513,
0.012356983497738838,
-0.03280235454440117,
0.05194868892431259,
0.04374720901250839,
-0.010926195420324802,
0.015950314700603485,
-0.04983924701809883,
0.021014710888266563,
-0.07459075003862381,
0.001593029242940247,
0.0030774169135838747,
0.011187548749148846,
0.01013158354908228,
0.027134306728839874,
0.018830643966794014,
0.017816735431551933,
-0.004590701777487993,
0.023853465914726257,
-0.06849535554647446,
0.030551472678780556,
-0.0718097984790802,
-0.02602379024028778,
-0.01659807749092579,
-0.014971468597650528,
-0.01713639311492443,
-0.04445650801062584,
-0.010648570954799652,
-0.006449878215789795,
-0.012133973650634289,
-0.05346905440092087,
-0.008527209982275963,
-0.009330665692687035,
-0.05256667360663414,
-0.02262435294687748,
0.0325373038649559,
0.035523511469364166,
-0.02022370509803295,
0.02788603864610195,
0.04123707115650177,
0.011428768746554852,
-0.0022137900814414024,
0.0364009328186512,
0.04939459636807442,
0.0023334044963121414,
0.03216773271560669,
-0.00376197905279696,
0.0025622949469834566,
-0.03175545856356621,
-0.013410949148237705,
0.037526797503232956,
0.047920115292072296,
0.009843036532402039,
-0.008703157305717468,
-0.02791815996170044,
-0.05701293796300888,
-0.009096355177462101,
-0.019386233761906624,
0.05801015347242355,
0.01368691399693489,
0.013472145423293114,
0.019941091537475586,
0.057035814970731735,
-0.035660646855831146,
0.049267351627349854,
0.05533279851078987,
0.0030080624856054783,
-0.028925789520144463,
-0.02889510989189148,
-0.03852108493447304,
-0.038243427872657776,
-0.011606767773628235,
0.005433396901935339,
-0.0029010288417339325,
-0.056815724819898605,
0.025284543633461,
0.010654828511178493,
-0.00618975842371583,
-0.03893451392650604,
-0.015617561526596546,
-0.0020277865696698427,
0.028475023806095123,
0.01741812936961651,
0.019705194979906082,
0.027389472350478172,
0.049501992762088776,
0.07134351134300232,
0.02016906999051571,
-0.017387237399816513,
-0.07548446208238602,
0.00901092030107975,
0.008087975904345512,
-0.00588393397629261,
0.0057245590724051,
-0.02291974239051342,
-0.04339073970913887,
-0.027037186548113823,
0.07309351116418839,
0.003082639304921031,
0.03221011161804199,
-0.00686999037861824,
0.0012778943637385964,
-0.02945827692747116,
-0.004427189938724041,
-0.0402381531894207,
-0.0014550910564139485,
-0.01717383787035942,
-0.00014272815315052867,
-0.012294264510273933,
0.015334962867200375,
-0.024649597704410553,
0.029597144573926926,
0.015753651037812233,
0.030829191207885742,
0.03991946950554848,
0.007534225471317768,
-0.021246690303087234,
0.03845815360546112,
-0.04507766664028168,
-0.08321547508239746,
0.0029277715366333723,
0.02439739741384983,
-0.006730867549777031,
0.0315776988863945,
-0.010113898664712906,
-0.016180003061890602,
0.04721161350607872,
0.0062176864594221115,
0.03252037614583969,
0.01475885696709156,
-0.025610534474253654,
-0.00789884477853775,
0.020353326573967934,
0.0067123896442353725,
0.02280401438474655,
0.0023423386737704277,
-0.02497635968029499,
-0.060235925018787384,
-0.03924129158258438,
0.033957429230213165,
-0.0739813968539238,
-0.01921526901423931,
-0.01640837825834751,
0.003111894242465496,
-0.04629082232713699,
0.04604068398475647,
0.010639596730470657,
0.017630284652113914,
0.02358100935816765,
-0.03221665695309639,
-0.0059435307048261166,
0.039495792239904404,
0.04766726866364479,
-0.017206482589244843,
-0.004939606413245201,
0.00938419345766306,
0.006885323207825422,
-0.0334380678832531,
-0.016886243596673012,
-0.007736810017377138,
-0.04562769830226898,
0.038140956312417984,
0.01986510306596756,
0.019495462998747826,
0.021238496527075768,
-0.025124074891209602,
0.012893945910036564,
-0.05110299959778786,
0.01528081577271223,
-0.028126927092671394,
-0.054984692484140396,
0.030473999679088593,
-0.05279011279344559,
-0.005618286319077015,
0.006706476677209139,
-0.055266231298446655,
0.03652333468198776,
-0.050620995461940765,
0.04523301124572754,
0.0351654514670372,
-0.0017193675739690661,
-0.10548143088817596,
-0.04096977785229683,
0.03541922941803932,
-0.014299417845904827,
-0.028854219242930412,
-0.042728304862976074,
-0.0038336620200425386,
-0.05928754806518555,
-0.03757760301232338,
0.008397357538342476,
0.06291376054286957,
-0.04371507093310356,
-0.0038375575095415115,
-0.037590887397527695,
-0.021285634487867355,
0.021449686959385872,
-0.03856195881962776,
-0.025340581312775612,
0.014872229658067226,
-0.021337328478693962,
0.021810995414853096,
-0.03450097143650055,
0.06154898181557655,
-0.01081173773854971,
0.011741690337657928,
-0.04697147756814957,
-0.03985564038157463,
-0.0008972373907454312,
0.004420036915689707,
-0.025473495945334435,
0.07005514949560165,
0.02174217253923416,
-0.015827402472496033,
-0.023395538330078125,
-0.006800125818699598,
-0.021673152223229408,
0.014911020174622536,
-0.03761555254459381,
0.005295173730701208,
0.02379510924220085,
-0.026496751233935356,
0.07656057924032211,
0.0007006658706814051,
-0.024412022903561592,
0.00030253289151005447,
0.07447344064712524,
0.002852159086614847,
-0.023077823221683502,
-0.008096088655292988,
-0.02697524055838585,
-0.021058078855276108,
-0.011811059899628162,
0.0005622944445349276,
0.016420071944594383,
0.012011890299618244,
-0.030651696026325226,
-0.023128202185034752,
-0.007623826619237661,
0.011763284914195538,
0.07226934283971786,
-0.031402792781591415,
0.04869392514228821,
0.05282372981309891,
-0.005464155692607164,
-0.0028496598824858665,
-0.03244679048657417,
0.00020089824101887643,
0.009158739820122719,
0.008851207792758942,
0.04441111907362938,
-0.02590077370405197,
0.014117969200015068,
0.027938250452280045,
0.029058435931801796,
-0.028569413349032402,
0.01976286619901657,
0.015801124274730682,
0.024817608296871185,
0.024938590824604034,
0.0246774610131979,
-0.0683872401714325,
0.019043514505028725,
-0.02043185941874981,
0.040921393781900406,
0.02102317102253437,
-0.052117910236120224,
0.005505186039954424,
0.012274960055947304,
0.035371460020542145,
-0.006540108472108841,
-0.02175839990377426,
-0.04432268813252449,
0.019004875794053078,
0.030448157340288162,
0.0600498728454113,
0.001948787015862763,
0.008657523430883884,
0.03300454840064049,
-0.006576940417289734,
-0.00947482232004404,
-0.000009543705346004572,
-0.052951086312532425,
-0.02957061678171158,
-0.018740706145763397,
-0.026203490793704987,
0.048986371606588364,
0.0027059761341661215,
0.0009070948581211269,
-0.001236009644344449,
-0.029633458703756332,
0.0076823607087135315,
0.021867375820875168,
0.07335737347602844,
-0.025032920762896538,
0.046961843967437744,
-0.017444660887122154,
0.013128612190485,
-0.02442144602537155,
-0.010147817432880402,
0.1246369257569313,
0.05175870284438133,
0.005609461106359959,
-0.05961611866950989,
0.05669606104493141,
-0.02662990801036358,
-0.020457716658711433,
-0.02409319579601288,
0.040345072746276855,
-0.020177587866783142,
0.006276115775108337,
-0.006454696878790855,
0.054440878331661224,
-0.020191103219985962,
-0.05896897614002228,
0.06273588538169861,
-0.03279697149991989,
-0.024886058643460274,
0.03114781342446804,
0.033552248030900955,
0.005596840754151344,
0.012404123321175575,
-0.019795741885900497,
0.02349703386425972,
-0.02708335593342781,
0.01654127985239029,
-0.020466729998588562,
-0.043808359652757645,
-0.014680393971502781,
-0.005730293225497007,
-0.043131086975336075,
0.031541090458631516,
0.04253806546330452,
-0.044229790568351746,
-0.08597484976053238,
-0.017068056389689445,
-0.011390283703804016,
-0.005638789385557175,
0.04805120825767517,
0.015551561489701271,
-0.010339721105992794,
0.03227771818637848,
-0.012264897115528584,
-0.00925587397068739,
-0.07354562729597092,
0.04510529339313507,
-0.0034823003225028515,
0.057199690490961075,
-0.01621289737522602,
0.02527928166091442,
0.008536744862794876,
-0.020597374066710472,
0.008002512156963348,
-0.07839446514844894,
-0.03163672238588333,
-0.02397789992392063,
0.021284857764840126,
0.010779532603919506,
-0.007132977247238159,
-0.021955890581011772,
-0.00872541218996048,
0.00027334029437042773,
0.0373137928545475,
0.00554318493232131,
-0.006405118387192488,
0.05108898878097534,
0.007080599199980497,
0.04558887705206871,
-0.002550913719460368,
-0.023863865062594414,
-0.025846466422080994,
-0.029521038755774498,
-0.014898118562996387,
0.0022239862009882927,
0.02853957749903202,
0.02059732936322689,
0.03650176152586937,
-0.01966526173055172,
0.0011766973184421659,
-0.015984343364834785,
-0.05399172380566597,
0.03298129886388779,
-0.04010149836540222,
0.014344953931868076,
-0.03060232475399971,
0.018081145361065865,
0.06523215025663376,
0.06864045560359955,
-0.060161441564559937,
0.011534621007740498,
-0.0031809438951313496,
-0.016620531678199768,
-0.0002528262266423553,
-0.00786213856190443,
0.014600707218050957,
0.014623412862420082,
-0.0057217031717300415,
-0.0029122501146048307,
-0.03611575439572334,
0.0033553666435182095,
0.03921385481953621,
0.019779035821557045,
-0.017707012593746185,
0.02056770585477352,
-0.0024426195304840803,
0.0042455485090613365,
0.02029598504304886,
-0.03852005675435066,
0.015910780057311058,
0.032074011862277985,
0.007877216674387455,
-0.03336808457970619,
-0.031628578901290894,
-0.03218540549278259,
0.0030902030412107706,
0.014454154297709465,
0.012269467115402222,
-0.019793570041656494,
0.016415026038885117,
-0.0038053656462579966,
0.003647411474958062,
-0.048790138214826584,
-0.012553764507174492,
-0.06150145083665848,
0.0086599076166749,
0.0028209625743329525,
-0.02730623260140419,
0.010041717439889908,
0.017025232315063477,
-0.012849200516939163,
-0.027274487540125847,
0.030275268480181694,
0.01890186220407486,
-0.03721373528242111,
-0.002427243161946535,
0.055691175162792206,
0.009957892820239067,
0.06232716888189316,
-0.00066606723703444,
-0.00521719828248024,
0.025644196197390556,
-0.040652524679899216,
-0.03676997497677803,
0.05503728985786438,
0.005724700167775154,
0.00036893386277370155,
0.028173889964818954,
-0.017136573791503906,
0.0028663347475230694,
0.020198862999677658,
-0.01808503270149231,
0.010450542904436588,
0.017791902646422386,
-0.054110679775476456,
0.008972601033747196,
-0.006879990454763174,
0.009629221633076668,
-0.019516240805387497,
-0.021014530211687088,
0.023448830470442772,
-0.009047234430909157,
-0.025973167270421982,
0.005239499267190695,
-0.004640230443328619,
-0.013620756566524506,
0.002810634206980467,
0.03898567706346512,
-0.013291941024363041,
0.006179529242217541,
0.030730735510587692,
-0.05452306941151619,
0.015680629760026932,
0.05365808308124542,
0.0003566774248611182,
-0.10134340077638626,
-0.0146418996155262,
0.004602466244250536,
0.009963052347302437,
0.05706537514925003,
-0.0711321234703064,
0.0063230544328689575,
-0.0008874839404597878,
-0.04902634024620056,
0.04100509732961655,
-0.037737227976322174,
-0.027053123340010643,
0.0014064655406400561,
-0.01077798381447792,
0.015900639817118645,
0.05664176866412163,
0.05928818881511688,
0.03076695278286934,
-0.005851181223988533,
0.004212977830320597,
-0.00308622675947845,
0.009673905558884144,
-0.019048115238547325,
0.012316630221903324,
-0.0026685004122555256,
-0.03497462347149849,
0.03541990742087364,
-0.017220448702573776,
-0.0293328445404768,
0.012741466984152794,
-0.01316241268068552,
-0.02949671447277069,
0.0011205964256078005,
-0.00006703787221340463,
-0.0006208484410308301,
0.024886904284358025,
0.016566835343837738,
-0.021448230370879173,
-0.018085448071360588,
0.026576319709420204,
0.020911848172545433,
0.06027346849441528,
-0.02741127647459507,
-0.010867281816899776,
-0.024157632142305374,
-0.052542828023433685,
-0.022597670555114746,
0.014007295481860638,
-0.029204051941633224,
-0.032124076038599014,
-0.023623540997505188,
-0.01523030735552311,
-0.011603149585425854,
-0.011074639856815338,
0.0060290126129984856,
-0.04953591153025627,
0.021339738741517067,
0.029133759438991547,
-0.011969043873250484,
-0.025499381124973297,
0.024749699980020523,
0.0036854788195341825,
-0.02752399630844593,
-0.00031601134105585515,
0.022990891709923744,
0.03622519597411156,
-0.06806088238954544,
0.0034505955409258604,
0.003489208407700062,
-0.04488217830657959,
0.005030599422752857,
-0.046570394188165665,
-0.0046288687735795975,
0.051070086658000946,
0.038210272789001465,
0.022887960076332092,
0.003956642933189869,
-0.04238129407167435,
-0.0007063504890538752,
-0.06900117546319962,
0.042636938393116,
0.016269344836473465,
0.014819247648119926,
-0.011595687828958035,
0.022094957530498505,
-0.037262674421072006,
0.005807509645819664,
0.026318589225411415,
-0.007397696375846863,
-0.023785090073943138,
0.047885384410619736,
-0.003504163818433881,
0.009990556165575981,
-0.015242616645991802,
-0.00630085077136755,
-0.025849515572190285,
-0.016432970762252808,
-0.000976905575953424,
-0.007886821404099464,
-0.03562462702393532,
0.0008642287575639784,
-0.015775606036186218,
-0.006231154315173626,
0.038182519376277924,
0.012444104067981243,
-0.05859065055847168,
0.05033469572663307,
0.04161812737584114,
-0.026135185733437538,
0.05006173998117447,
0.007867035456001759,
-0.010452726855874062,
0.04876786470413208,
-0.022301755845546722,
-0.03882009536027908,
-0.0034684375859797,
-0.03818025067448616,
-0.02597055397927761,
-0.012423478998243809,
-0.004102463833987713,
0.003979152999818325,
-0.03736303001642227,
0.00028530266718007624,
0.05731843784451485,
-0.028320232406258583,
-0.03006858378648758,
0.036245718598365784,
-0.008563756942749023,
0.01435681339353323,
-0.016594063490629196,
0.019243234768509865,
0.048873115330934525,
0.002075380878522992,
0.029795829206705093,
0.03839877247810364,
0.03357496112585068,
0.03448786959052086,
-0.02208353951573372,
0.008978946134448051,
-0.018152408301830292,
0.026410454884171486,
0.01889663189649582,
0.06265140324831009,
-0.07666756957769394,
0.004398760385811329,
0.04172895476222038,
-0.008502724580466747,
0.06491315364837646,
0.008614128455519676,
-0.013527077622711658,
0.05761241167783737,
-0.018991008400917053,
-0.007141411770135164,
-0.016854172572493553,
-0.005740878637880087,
-0.0021233917213976383,
-0.009611591696739197,
0.034121859818696976,
0.07278155535459518,
-0.0003739334351848811,
-0.007662815507501364,
-0.033917706459760666,
0.023041673004627228,
0.020683081820607185,
-0.04429830238223076,
-0.0014999174745753407,
0.009569665417075157,
-0.004061834886670113,
0.006965789943933487,
-0.030400333926081657,
-0.02015993371605873,
-0.0053790961392223835,
0.012228180654346943,
0.01865929737687111,
0.04813766106963158,
-0.034064650535583496,
0.030753731727600098,
-0.05612184479832649,
0.025336533784866333,
-0.05615725368261337,
-0.040119070559740067,
-0.012965644709765911,
-0.006029293406754732,
0.019640158861875534,
0.00432628346607089
] |
<p>Consider a tube with two different diameters (one section wider than the other). Because what comes in must go out (conservation of mass), the flow rate in the wider section must be the same as the flow rate in the smaller section (you can't loses some or what your put in or gain some of what you've not put in). Also, the flow of a liquid follows the pressure gradient (liquid flows from high pressure to low pressure in the tube). The left end of the tube is at a high pressure and the right end is at a lower pressure (consider the fluid moving from left to right). According to continuity,</p>
<p>$\Phi_1$ = flow rate 1 $= \Phi_2$ = flow rate 2 </p>
<p>or</p>
<p>$A_1v_1 = A_2v_2$</p>
<p>where $A$ and $v$ are the cross sectional area and velocity respectively. Now consider the a disease/condition where the blood vessels are contracted (think of a normal blood vessel as the bigger diameter tube and the contracted blood vessel as the smaller diameter tube above). I forgot what this disease is called but that's beside the point. The main thing is that blood flow is reduced in the bad section of the blood vessel (small diameter section), requiring surgery to change out the bad section for a normal one. Does this not contradict the continuity equation, which states that the flow rate should be the same in each section?</p>
<p>My response: After talking to a professor, he gave the response (I didn't follow but goes something like) the continuity equation does not take into account the amount of pressure in the bigger diameter section and the amount of pressure in the smaller diameter section (it just takes into account the difference in pressure between the two ends). Can anyone help shed light on this? Please discuss what the continuity equation does and does not do as well as what's going on in the blood vessel please. Final note: </p>
<p>$\phi = \frac{\pi (P_A -P_B)}{8\eta L}R^4$</p>
<p>This equation describes flow rate taking into account the viscous drag force. It was derived considering a cylindrical tube. The derivation starts (I'm giving you this because even if you don't know what the equation is, I'm giving you context. I don't understand this equation either. It considers a tube all with a single diameter. $A = \pi r^2$, $SA$ stands for surface area. Note, velocity is greatest at the center and smallest along the tube walls due to friction)</p>
<p>(driving force) - ($F_{viscous}$) = 0 (at equilibrium)</p>
<p>$\Delta PA$ - $\eta (SA)\frac{dv}{dr}$ = 0</p>
<p>Anyways, the final equation for flow rate shows that $\phi \propto R^4$. I thought flow rate was constant? In summary, why is blood flow reduced in the contracted blood vessel and said to be the same in a pipe with different cross sectional areas?</p>
| 8,815 |
[
-0.02176377922296524,
0.010548184625804424,
-0.01509848516434431,
-0.02600688673555851,
0.03696977719664574,
0.0011990094790235162,
-0.007954069413244724,
-0.007366118021309376,
-0.005880431737750769,
0.011386110447347164,
0.03270581737160683,
0.005917938891798258,
0.03211227059364319,
-0.00008097013051155955,
-0.015569454059004784,
0.015425481833517551,
0.01664144918322563,
-0.018009847030043602,
0.0041888561099767685,
-0.01990705169737339,
0.014978695660829544,
-0.006966800894588232,
0.00018543594342190772,
0.014340909197926521,
-0.039243489503860474,
0.04545712098479271,
0.0072346031665802,
-0.017022011801600456,
-0.02727341279387474,
0.020768756046891212,
-0.04591045156121254,
-0.0212634839117527,
-0.004047222901135683,
0.017184365540742874,
-0.006773662753403187,
0.025721192359924316,
-0.04032096639275551,
0.0005814891774207354,
-0.012844488024711609,
0.049455005675554276,
-0.04223358631134033,
0.002574310638010502,
0.00042289288830943406,
0.019145572558045387,
-0.03207368403673172,
0.023675203323364258,
0.005251870956271887,
-0.02513648383319378,
0.03936165198683739,
-0.06398796290159225,
0.04013246297836304,
-0.023551233112812042,
0.08203623443841934,
0.02254667691886425,
0.014853152446448803,
-0.01010171603411436,
0.028568541631102562,
0.07386092096567154,
-0.01685766875743866,
-0.054402127861976624,
-0.003785905195400119,
0.03254106640815735,
-0.026354683563113213,
0.002774201799184084,
-0.011425120756030083,
-0.010171715170145035,
-0.04754728451371193,
-0.04152144119143486,
-0.0016880102921277285,
-0.0038338738959282637,
0.007582367397844791,
-0.007477193139493465,
0.01667890138924122,
-0.0036257694009691477,
0.05351630970835686,
0.004255564883351326,
-0.014287201687693596,
0.001055444241501391,
0.027524223551154137,
0.050512101501226425,
-0.04134190455079079,
-0.006372271105647087,
0.04819338768720627,
0.04042946547269821,
0.013324106112122536,
-0.019766060635447502,
0.07667722553014755,
0.007081270683556795,
0.03940991312265396,
0.02776397205889225,
0.0026838714256882668,
0.02359110303223133,
-0.0026659369468688965,
-0.009816788136959076,
0.05230975151062012,
0.06836988031864166,
-0.017105869948863983,
0.025818772614002228,
0.018173282966017723,
-0.008859730325639248,
-0.00299778557382524,
-0.05095349997282028,
0.0299200639128685,
0.10526658594608307,
-0.005932443775236607,
-0.03896811977028847,
-0.013345016166567802,
0.013055357150733471,
-0.016382304951548576,
0.014251100830733776,
-0.055665839463472366,
-0.026791084557771683,
0.009605204686522484,
0.019809260964393616,
-0.03967082127928734,
-0.001419172389432788,
0.004267683252692223,
-0.0204074177891016,
0.022919220849871635,
0.06386537104845047,
0.06264308840036392,
-0.022229669615626335,
0.01837531104683876,
-0.0016419439343735576,
-0.020019536837935448,
0.019718514755368233,
-0.008848742581903934,
-0.027134643867611885,
-0.02259800396859646,
0.023470131680369377,
0.04894532263278961,
-0.008381071500480175,
0.010837250389158726,
0.03841424360871315,
0.04180073365569115,
0.0030101356096565723,
-0.07544323056936264,
-0.06035130098462105,
0.06867127120494843,
0.019472315907478333,
-0.04002321511507034,
-0.08026023954153061,
0.019673116505146027,
0.024114584550261497,
0.09787943214178085,
-0.023548167198896408,
-0.03489013388752937,
0.0043148803524672985,
0.04136624187231064,
-0.013216645456850529,
-0.0049317264929413795,
0.03964652493596077,
-0.0042471508495509624,
-0.03460490331053734,
-0.001574952038936317,
-0.05938265100121498,
-0.0026005972176790237,
0.019647207111120224,
0.025348901748657227,
-0.031429827213287354,
0.029721427708864212,
-0.016133179888129234,
0.00792051199823618,
0.013132719323039055,
-0.011368301697075367,
0.01598234288394451,
0.0661473274230957,
0.003282536519691348,
-0.011455349624156952,
0.007312780246138573,
0.04224194958806038,
-0.0035531711764633656,
-0.019604284316301346,
0.02737322263419628,
0.02125568315386772,
-0.02354801818728447,
0.00030046256142668426,
-0.03200128301978111,
-0.01826094277203083,
0.028523094952106476,
0.003507081652060151,
-0.04050416126847267,
-0.033494096249341965,
-0.002751690335571766,
0.05306878685951233,
0.04585971310734749,
0.02634500153362751,
0.009377186186611652,
0.03734005615115166,
-0.04404423385858536,
-0.00941353477537632,
-0.018747597932815552,
0.005693935789167881,
-0.03890397027134895,
-0.024096978828310966,
0.0009740527020767331,
-0.021971214562654495,
-0.0005839289515279233,
-0.009009753353893757,
-0.011785442940890789,
-0.01568700559437275,
-0.003977559972554445,
0.028467144817113876,
0.012869741767644882,
0.010752732865512371,
0.05903811380267143,
0.01797749474644661,
0.025340408086776733,
0.013494297862052917,
-0.00420058099552989,
0.004546805284917355,
0.027903718873858452,
-0.0074104624800384045,
0.05213583633303642,
-0.03421957045793533,
-0.02875613048672676,
-0.0036864127032458782,
-0.0003344242868479341,
0.012998566962778568,
0.029072552919387817,
-0.06777513027191162,
0.08164399862289429,
0.06157762184739113,
-0.004553583916276693,
0.02675541490316391,
-0.005883322097361088,
-0.008848677389323711,
0.012251057662069798,
0.003201845334842801,
-0.03713104501366615,
-0.014269246719777584,
-0.0016425451030954719,
0.026412708684802055,
-0.0061652944423258305,
0.003171993652358651,
-0.0023903551045805216,
0.03366001695394516,
0.015091837383806705,
0.04171031713485718,
-0.017537856474518776,
0.007819758728146553,
-0.03988080844283104,
0.0037936242297291756,
0.0335436575114727,
-0.004730459302663803,
0.03331858664751053,
0.019710300490260124,
-0.03712477162480354,
0.07905318588018417,
-0.02957581914961338,
0.001529838889837265,
0.011124204844236374,
0.02470698207616806,
0.020239973440766335,
-0.00510413059964776,
0.003517861245200038,
0.04128844663500786,
-0.0024120931047946215,
0.026300353929400444,
0.03487640991806984,
-0.025281157344579697,
0.020295679569244385,
-0.04820532724261284,
0.01355866901576519,
0.02463623322546482,
0.02193683385848999,
0.020159702748060226,
-0.008376930840313435,
0.015761807560920715,
-0.03202709183096886,
-0.019393272697925568,
-0.04653151333332062,
-0.004206151235848665,
-0.06512409448623657,
-0.017289642244577408,
-0.0047392165288329124,
0.02968968078494072,
0.016696805134415627,
-0.024815693497657776,
-0.01713859848678112,
0.020765181630849838,
0.012512659654021263,
-0.011450694873929024,
-0.009958446957170963,
-0.040064748376607895,
0.03430445119738579,
-0.0037723530549556017,
0.01144225150346756,
0.07207317650318146,
0.011874131858348846,
-0.014740136452019215,
0.012516750022768974,
0.027850355952978134,
-0.05207153037190437,
0.003486206056550145,
-0.05891598388552666,
0.027026589959859848,
0.027233576402068138,
0.0018771681934595108,
0.0597083605825901,
-0.008945765905082226,
-0.06647204607725143,
0.029985448345541954,
-0.03257234767079353,
-0.02326810546219349,
-0.028565673157572746,
0.005479683633893728,
0.024223465472459793,
-0.005016160197556019,
0.007322448305785656,
0.00462214183062315,
-0.020723611116409302,
-0.014877726323902607,
-0.0358731672167778,
-0.01045267190784216,
0.0425461083650589,
-0.008737461641430855,
0.059174198657274246,
-0.009021923877298832,
-0.04244445264339447,
0.052851736545562744,
0.0004241912974976003,
-0.029159709811210632,
0.012123451568186283,
0.037139374762773514,
-0.02855876088142395,
-0.042512405663728714,
0.02143890969455242,
0.07847606390714645,
-0.04378698393702507,
0.016649259254336357,
0.00774458609521389,
0.06439477950334549,
0.04882650822401047,
0.02847271040081978,
-0.008049833588302135,
0.046828798949718475,
0.032698821276426315,
-0.03305208310484886,
0.043379105627536774,
0.022596143186092377,
0.021344825625419617,
-0.0012785108992829919,
-0.01005521509796381,
0.03842654079198837,
0.04210927337408066,
-0.06959965080022812,
0.039383213967084885,
0.024640416726469994,
-0.015043995343148708,
-0.03293197602033615,
-0.014746606349945068,
-0.008322218433022499,
-0.00606963224709034,
0.00017334806034341455,
0.02303381636738777,
0.03619812801480293,
-0.014994470402598381,
-0.025855490937829018,
0.05525455251336098,
0.018068816512823105,
-0.008112223818898201,
0.007534188684076071,
-0.0075803776271641254,
-0.01700630597770214,
0.05965733155608177,
-0.043622083961963654,
0.0069960602559149265,
0.05572788044810295,
0.03606927767395973,
-0.013802874833345413,
-0.009191184304654598,
-0.016936764121055603,
-0.0044744666665792465,
-0.06714627891778946,
-0.0030455298256129026,
-0.027093566954135895,
0.057232484221458435,
-0.007828881964087486,
0.05213643237948418,
0.0006505221244879067,
0.01532403938472271,
0.008227932266891003,
0.013850009068846703,
-0.08398333936929703,
0.009260434657335281,
0.01730501279234886,
-0.02874232642352581,
0.03044298104941845,
-0.010913782753050327,
0.009952989406883717,
-0.027507828548550606,
-0.02042856439948082,
-0.002932117087766528,
0.011015841737389565,
-0.035367127507925034,
0.05420733243227005,
-0.00925245601683855,
-0.032474059611558914,
-0.020838677883148193,
0.020207423716783524,
0.07473189383745193,
-0.005010202992707491,
0.05089950188994408,
0.02760542370378971,
0.010804940015077591,
0.0020189161878079176,
-0.004912234377115965,
0.011854940094053745,
0.06778943538665771,
0.045326609164476395,
0.007099661510437727,
0.0014941905392333865,
-0.02346276491880417,
0.017468225210905075,
0.020845554769039154,
0.009140546433627605,
0.0073439376428723335,
0.005083128344267607,
-0.014038026332855225,
-0.042363397777080536,
-0.04777296632528305,
0.011621949262917042,
0.08315537869930267,
0.02238217554986477,
0.02369213104248047,
0.0195111483335495,
-0.026082534343004227,
-0.029139121994376183,
0.026795024052262306,
0.0440494678914547,
-0.007099732756614685,
-0.015227061696350574,
-0.04260266572237015,
-0.002091486006975174,
-0.03143926337361336,
-0.03177988529205322,
0.015610773116350174,
0.025785677134990692,
-0.03985610604286194,
-0.03956988826394081,
0.023776870220899582,
0.013052635826170444,
-0.020145168527960777,
-0.016392001882195473,
-0.022193118929862976,
-0.02786090597510338,
0.015204165130853653,
0.011121324263513088,
0.05518469214439392,
0.02995625138282776,
0.0073510948568582535,
0.037116363644599915,
0.006748309824615717,
-0.10141000151634216,
-0.06288522481918335,
0.001580073032528162,
0.019734127447009087,
-0.018139975145459175,
0.011810492724180222,
-0.055750783532857895,
-0.016644909977912903,
0.027175363153219223,
-0.027601053938269615,
0.03488703444600105,
-0.028570907190442085,
0.013811113312840462,
0.010003015398979187,
-0.0901838019490242,
-0.013875202275812626,
-0.006314771715551615,
-0.03678044676780701,
-0.014930859208106995,
-0.007799412589520216,
0.015378748066723347,
-0.025900810956954956,
-0.029643209651112556,
0.02895442023873329,
0.04948017746210098,
-0.023388948291540146,
-0.0434018112719059,
0.020982131361961365,
0.04116271808743477,
-0.037651658058166504,
-0.0721050426363945,
0.044479768723249435,
-0.013175725936889648,
0.005149393808096647,
0.015427768230438232,
-0.01831742189824581,
-0.02996286377310753,
0.04167938232421875,
0.00692955544218421,
-0.022449897602200508,
0.034187354147434235,
-0.040026355534791946,
0.07258498668670654,
0.052298497408628464,
-0.004303234629333019,
0.055415257811546326,
0.017031414434313774,
-0.028682326897978783,
-0.03920712321996689,
-0.04598868638277054,
0.0037571231368929148,
0.00840763933956623,
-0.0257536880671978,
-0.05843210592865944,
0.022711116820573807,
-0.003697621403262019,
0.05944672226905823,
-0.006247243843972683,
0.02861449122428894,
-0.0006471745437011123,
-0.004202912095934153,
0.05314343050122261,
-0.00029473548056557775,
0.01720021292567253,
-0.029377073049545288,
0.0031430949456989765,
-0.007974018342792988,
0.05257508531212807,
-0.005260503850877285,
0.05179896578192711,
-0.0055293673649430275,
0.007216012571007013,
0.007471871562302113,
-0.031018974259495735,
-0.04352101311087608,
-0.024822348728775978,
-0.018970100209116936,
0.003972356673330069,
-0.031383365392684937,
0.05112902447581291,
0.010980598628520966,
0.029527047649025917,
-0.023603912442922592,
-0.009341050870716572,
-0.04762333631515503,
0.0188971646130085,
-0.01148616336286068,
0.0013176165521144867,
-0.040118709206581116,
0.000707462546415627,
-0.01355314813554287,
0.000522804562933743,
-0.0863751769065857,
-0.04042743891477585,
0.05920029804110527,
0.0011422804091125727,
-0.028730111196637154,
-0.0074470206163823605,
-0.02645987458527088,
0.006851456128060818,
-0.06436455994844437,
0.013959407806396484,
0.0298745259642601,
-0.041183918714523315,
-0.004855661187320948,
-0.012449769303202629,
0.02503468655049801,
0.05895940214395523,
0.024804580956697464,
0.0009846023749560118,
-0.01696484535932541,
-0.05288597196340561,
-0.013815240934491158,
-0.00309484894387424,
0.021633518859744072,
-0.049882709980010986,
0.014508496038615704,
0.0072003984823822975,
-0.009001553989946842,
0.044083356857299805,
0.006999939680099487,
-0.005605592858046293,
0.022863183170557022,
-0.01216951571404934,
-0.0038600557018071413,
0.0010841134935617447,
-0.016246305778622627,
0.00633616978302598,
0.04309449344873428,
-0.0010682404972612858,
-0.0022351862862706184,
-0.00930909626185894,
-0.061741314828395844,
-0.016146665439009666,
-0.0042540146969258785,
-0.021589146926999092,
-0.008994454517960548,
0.04835220053792,
-0.040256235748529434,
0.020970135927200317,
-0.005810103844851255,
0.004371421877294779,
0.04393318295478821,
0.011159617453813553,
-0.014928636141121387,
-0.017583847045898438,
-0.00018556737632025033,
-0.04706466570496559,
-0.016618365421891212,
-0.029826516285538673,
0.0019512390717864037,
0.02356545813381672,
0.018571902066469193,
0.03983628377318382,
-0.007979010231792927,
-0.007219721097499132,
0.00985364243388176,
-0.007502667140215635,
-0.02609093114733696,
-0.01804248057305813,
-0.038899559527635574,
0.037147846072912216,
-0.03500533476471901,
-0.029877034947276115,
0.051075443625450134,
0.03266104310750961,
-0.007842548191547394,
-0.010874979197978973,
0.028338324278593063,
-0.03929314389824867,
-0.021534275263547897,
0.030155902728438377,
-0.014682493172585964,
0.051219966262578964,
-0.03220963478088379,
0.0372452549636364,
-0.023470398038625717,
0.00012101348693249747,
0.07205425202846527,
0.02786201424896717,
0.003395628184080124,
-0.05000251904129982,
0.013513504527509212,
-0.043966226279735565,
-0.006322720553725958,
-0.007095053791999817,
-0.027614492923021317,
0.028703909367322922,
0.00010343665053369477,
0.011278858408331871,
-0.01699969545006752,
0.0438043549656868,
-0.05001053214073181,
-0.020806824788451195,
0.006345185451209545,
-0.02081095054745674,
-0.03659578785300255,
0.04597859084606171,
-0.008425897918641567,
-0.010228053666651249,
-0.006604516878724098,
-0.02145535685122013,
0.021784301847219467,
0.027306949719786644,
0.024515777826309204,
-0.03138582780957222,
0.03568458929657936,
-0.038180090487003326,
0.03699896112084389,
-0.04044075310230255,
0.02724481001496315,
0.11987955868244171,
0.05408525839447975,
0.006145660299807787,
-0.019556142389774323,
0.04206197336316109,
-0.014241578057408333,
0.021668704226613045,
-0.03215987607836723,
0.04679211229085922,
0.006645326502621174,
-0.011917902156710625,
0.038082055747509,
0.07533823698759079,
0.0013266101013869047,
-0.02347787283360958,
0.05491923913359642,
-0.03384633734822273,
-0.020735884085297585,
-0.0019384726183488965,
-0.0014695413410663605,
-0.05356614664196968,
0.031744569540023804,
0.019502267241477966,
0.05022590234875679,
-0.008368910290300846,
-0.009908419102430344,
-0.05469090864062309,
-0.026220958679914474,
0.006889342796057463,
-0.017140306532382965,
-0.04689498618245125,
0.02681722864508629,
-0.013469991274178028,
-0.03854949027299881,
-0.001554036163724959,
0.004441917408257723,
-0.0030934419482946396,
-0.05598748102784157,
0.0033018405083566904,
0.051297418773174286,
0.005261596757918596,
0.01910620741546154,
-0.00435034092515707,
0.028669243678450584,
-0.04836881533265114,
-0.028168853372335434,
-0.03747749701142311,
0.04672962427139282,
0.014232004061341286,
0.012638531625270844,
0.011799975298345089,
-0.0027904619928449392,
-0.0003440392029006034,
-0.069783054292202,
-0.05168059095740318,
-0.003467110451310873,
-0.020042799413204193,
0.023519190028309822,
-0.016269659623503685,
0.029247190803289413,
0.0416901558637619,
0.0038897492922842503,
0.007536685094237328,
-0.0025658293161541224,
-0.030444294214248657,
-0.01682979054749012,
0.004933592863380909,
0.02448166161775589,
-0.015857703983783722,
0.023802807554602623,
-0.04145323112607002,
0.025955121964216232,
-0.04580456390976906,
0.023476416245102882,
-0.004906709771603346,
0.03362885117530823,
0.035888709127902985,
-0.0031036296859383583,
-0.03152861073613167,
-0.030017241835594177,
-0.07405402511358261,
0.02754707634449005,
0.005822622217237949,
-0.008114161901175976,
-0.02997009828686714,
-0.01497148908674717,
-0.024179838597774506,
0.058250948786735535,
-0.016608580946922302,
-0.033760737627744675,
-0.01795361563563347,
0.06792716681957245,
0.03270139917731285,
-0.034315917640924454,
-0.0733867809176445,
-0.015559467487037182,
-0.028457237407565117,
-0.0153367193415761,
0.014000272378325462,
0.05415349826216698,
0.042646538466215134,
0.04055988788604736,
-0.026799945160746574,
0.013655112124979496,
-0.004093531519174576,
0.019419701769948006,
0.004107036627829075,
-0.03586532175540924,
-0.004078790079802275,
0.013894333504140377,
0.017577487975358963,
-0.016972754150629044,
0.008605606853961945,
-0.0063624815084040165,
-0.006200721487402916,
0.004561149515211582,
-0.012923121452331543,
0.0094779497012496,
0.006952670402824879,
-0.02579204924404621,
-0.006241211201995611,
-0.01953074522316456,
0.030380774289369583,
-0.0454816110432148,
-0.007200846914201975,
0.0037531231064349413,
0.011807972565293312,
-0.0017180258873850107,
0.03634807839989662,
-0.01657232828438282,
0.01789548061788082,
-0.015664750710129738,
-0.03307676687836647,
-0.0007471673307009041,
0.02232322096824646,
0.028840525075793266,
0.05467603728175163,
0.029420625418424606,
0.020742759108543396,
-0.009789109230041504,
0.02200889214873314,
-0.00487479567527771,
-0.04100646823644638,
-0.005337451118975878,
-0.004147459752857685,
-0.014704360626637936,
-0.010021823458373547,
-0.009715473279356956,
0.006229921244084835,
0.08378012478351593,
0.0020695924758911133,
-0.01770091988146305,
-0.04575560241937637,
-0.032529521733522415,
0.011984618380665779,
-0.04983992129564285,
0.031043125316500664,
-0.01855829544365406,
0.02721554785966873,
0.007066985592246056,
0.029990125447511673,
0.004650970920920372,
-0.04004591703414917,
-0.010688829235732555,
0.0026146280579268932,
0.010043948888778687,
-0.013048524037003517,
0.016595393419265747,
0.02886708453297615,
0.030563611537218094,
0.017009079456329346,
0.004022638313472271,
-0.0009599471231922507,
-0.028716450557112694,
-0.09852685034275055,
-0.012645460665225983,
-0.02703275717794895,
0.0267658494412899,
-0.03668154776096344,
-0.037700481712818146,
-0.015175790525972843,
0.007490935735404491,
-0.05355328321456909,
-0.019215982407331467,
-0.025216316804289818,
0.013692019507288933,
-0.040854744613170624,
-0.0020277334842830896,
-0.018953464925289154,
0.04090357944369316,
0.031138168647885323,
0.030176809057593346,
-0.02070755325257778,
-0.0001218293109559454,
0.012207183986902237,
0.006929769646376371,
0.029186243191361427,
0.013096884824335575,
-0.018185090273618698,
-0.029868723824620247,
0.011814292520284653,
-0.03751697763800621,
0.008553978055715561,
0.015001125633716583,
-0.02615625411272049,
0.04996781423687935,
-0.010399163700640202,
-0.004937007557600737,
0.012494855560362339,
0.014247099868953228,
-0.004489143844693899,
0.061193980276584625,
-0.0015673201996833086,
0.002561685163527727,
0.00012034211977152154,
-0.009859468787908554,
-0.0542781762778759,
0.019687291234731674,
0.0507519394159317,
-0.0727190151810646,
-0.003514594864100218,
0.016106782481074333,
-0.06299211829900742,
-0.012792382389307022,
0.036799706518650055,
-0.036707986146211624,
0.030000248923897743,
-0.020765723660588264,
-0.010751026682555676,
-0.043095868080854416,
-0.002488676691427827,
0.02996201068162918,
0.023901687934994698,
0.005546962842345238,
0.005463716574013233,
0.035191044211387634,
-0.037300534546375275,
-0.0014529164182022214,
0.008208158425986767,
-0.005630313418805599,
-0.03139631450176239,
0.010648110881447792,
-0.03102070651948452,
-0.022676723077893257,
0.012945716269314289,
-0.051983628422021866,
-0.0026977325323969126,
0.004065265879034996,
0.018984152004122734,
0.019387051463127136,
-0.00423199450597167,
0.0008756725583225489,
-0.020631492137908936,
-0.0759950652718544,
0.014463379979133606,
0.008538907393813133,
-0.043969012796878815,
-0.03066861629486084,
-0.016483094543218613,
-0.014784188009798527,
0.03633261099457741,
0.05854904279112816,
0.026651699095964432,
-0.004560710862278938,
0.00932204071432352,
0.010867608711123466,
0.021306272596120834,
-0.052952639758586884,
-0.016227610409259796,
0.0025222194381058216,
0.003305114572867751,
-0.013979950919747353,
0.03141661360859871,
-0.028522998094558716,
0.01913456618785858,
0.03435245528817177,
-0.012837402522563934,
0.026967482641339302,
0.010570874437689781,
-0.010832266882061958,
-0.015407907776534557,
0.0028917815070599318,
-0.03611338511109352,
0.09085914492607117,
-0.044761788100004196,
-0.0028156819753348827,
-0.0025573605671525,
-0.00866474024951458,
-0.06422331929206848,
0.02501402422785759,
-0.049642425030469894,
-0.003115194384008646,
0.0009257021592929959,
-0.040454499423503876,
0.05302859842777252,
-0.0617758110165596,
0.03403070196509361,
0.054862264543771744,
-0.057134781032800674,
-0.022168155759572983,
0.03134738281369209,
0.02418786659836769,
0.004967052955180407,
-0.06441666930913925,
0.0049206861294806,
-0.00713541591539979,
-0.03131923824548721,
-0.008628490380942822,
0.007829581387341022,
0.04069165140390396,
0.017148476094007492,
-0.012159839272499084,
0.03395402058959007,
-0.020565614104270935,
0.01714937575161457,
-0.03625800460577011,
0.043999530375003815,
-0.015721473842859268,
-0.02927672304213047,
-0.022397568449378014,
-0.03294414281845093,
0.0022776692640036345,
0.059872765094041824,
0.010419044643640518,
0.07683093100786209,
0.002253592014312744,
0.028491230681538582,
-0.017060991376638412,
0.013831409625709057,
-0.030670279636979103,
0.033530283719301224,
0.030598316341638565,
-0.0001859285112004727,
0.025757210329174995,
-0.03909943625330925,
-0.025000685825943947,
-0.01384082529693842,
0.011491386219859123,
-0.03136912360787392,
0.003064910415560007,
0.015073924325406551,
-0.00756540521979332,
-0.027555903419852257,
-0.0267188660800457,
-0.007930275052785873,
-0.04129540175199509,
0.038735486567020416,
0.02528807893395424,
0.012092052958905697,
0.036934223026037216,
0.011838078498840332,
-0.003005094127729535,
0.05663250759243965,
-0.05970650166273117,
-0.016772262752056122,
0.026836322620511055,
0.00569547712802887,
0.009594409726560116,
-0.013173139654099941
] |
<p>In many articles and web pages I found people claiming that the maximum critical temperature for superconductivity in the BCS framework is about 40K.</p>
<p>Sometime, more accurate writers report that the above temperature is the maximum critical temperature achievable with electron-phonon coupling.</p>
<p>In both cases I never sow a reliable proof of these statements, so I'm asking if they are correct and where I can find a reference (a paper or simply few physical considerations)
leading to this result.</p>
| 8,816 |
[
-0.01568726636469364,
-0.035902414470911026,
0.02837633155286312,
-0.03466634079813957,
0.014980142936110497,
-0.0000021491473489732016,
-0.004718591459095478,
-0.02963639236986637,
-0.0017627375200390816,
-0.060857247561216354,
0.058856379240751266,
0.03767147287726402,
0.01627536490559578,
0.041277844458818436,
-0.020450307056307793,
0.00014681309403385967,
-0.006969762500375509,
0.009146252647042274,
-0.022544244304299355,
0.009419881738722324,
-0.00012885156320407987,
0.06276220083236694,
-0.01926892064511776,
0.004173875320702791,
-0.011001168750226498,
0.010726670734584332,
-0.01348693948239088,
0.026860492303967476,
0.036121029406785965,
0.032118264585733414,
-0.009261109866201878,
-0.024804214015603065,
0.03636416420340538,
0.0223423782736063,
0.059671949595212936,
-0.005861726123839617,
-0.041232530027627945,
-0.04128514230251312,
-0.015492016449570656,
0.022309718653559685,
-0.010012591257691383,
0.0072526996955275536,
0.033645596355199814,
0.03629515320062637,
0.008901918306946754,
-0.000022796952180215158,
-0.025326084345579147,
-0.03131023049354553,
0.02535908855497837,
-0.06518615782260895,
0.027600781992077827,
-0.02411535382270813,
0.06983360648155212,
0.026288311928510666,
0.015141308307647705,
-0.003904707496985793,
0.08877978473901749,
0.057429417967796326,
0.009462214075028896,
-0.051882773637771606,
-0.004628663882613182,
-0.03136219084262848,
0.018204307183623314,
0.012542368844151497,
-0.04372217878699303,
0.07629319280385971,
-0.01756858080625534,
-0.04352801293134689,
0.014847363345324993,
-0.014507696963846684,
0.022272860631346703,
-0.01751340739428997,
0.021932102739810944,
-0.005698774009943008,
0.01067627314478159,
-0.04028501361608505,
0.01841973513364792,
-0.00034476572182029486,
-0.006842850707471371,
0.05936063453555107,
-0.037709157913923264,
0.013126973062753677,
0.007955501787364483,
0.027963444590568542,
0.0026053886394947767,
-0.012175670824944973,
0.07787944376468658,
-0.013887299224734306,
0.01414716336876154,
0.04304800555109978,
-0.008581988513469696,
0.02248651161789894,
-0.0004233682993799448,
-0.03838355839252472,
-0.0396820567548275,
-0.03270702064037323,
0.024182772263884544,
0.08081245422363281,
-0.026944950222969055,
-0.019384073093533516,
0.014432556927204132,
-0.014039519242942333,
0.003725037444382906,
0.06570866703987122,
-0.0032930471934378147,
-0.03451366350054741,
-0.03227705880999565,
0.020429033786058426,
-0.0012075569247826934,
-0.013126314617693424,
-0.05696069076657295,
0.014107652008533478,
-0.004536858759820461,
0.030364708974957466,
0.0034626044798642397,
-0.03000064380466938,
0.00650124903768301,
-0.03273038566112518,
0.023443570360541344,
0.026765089482069016,
0.005020470358431339,
-0.026776136830449104,
-0.009109013713896275,
-0.049219150096178055,
-0.036776501685380936,
0.036635223776102066,
0.02601923793554306,
0.004105004481971264,
-0.0305447056889534,
0.000499994435813278,
-0.0037449891678988934,
-0.017163923010230064,
0.004492404405027628,
-0.04318968206644058,
0.021656757220625877,
-0.02173210307955742,
-0.07848119735717773,
-0.06187695264816284,
0.052673980593681335,
-0.018032101914286613,
-0.018566135317087173,
-0.0741315484046936,
0.04267588630318642,
0.04255896061658859,
0.05682729557156563,
-0.009200449101626873,
0.008747648447751999,
-0.017703188583254814,
0.021537689492106438,
0.009576477110385895,
-0.039263829588890076,
-0.04599360004067421,
-0.004528344143182039,
-0.032625939697027206,
-0.00824225228279829,
-0.06365446001291275,
0.026092540472745895,
0.018474889919161797,
0.05687415599822998,
-0.020961588248610497,
0.033740878105163574,
-0.029164060950279236,
0.00801361445337534,
-0.046143751591444016,
0.005280022509396076,
-0.02447996474802494,
0.09528293460607529,
0.004621563479304314,
0.008757339790463448,
0.017430700361728668,
-0.008970145136117935,
-0.012017537839710712,
0.02659277245402336,
0.011938377283513546,
0.006212412845343351,
-0.038796670734882355,
0.006765410304069519,
-0.05347311869263649,
-0.0010551676386967301,
0.007575587369501591,
-0.0511050708591938,
0.018373040482401848,
-0.016617393121123314,
0.0147867351770401,
-0.019879238680005074,
0.04153437912464142,
-0.008488752879202366,
-0.02350798435509205,
-0.007279832847416401,
-0.07356300204992294,
-0.023661192506551743,
-0.050355106592178345,
0.010617858730256557,
0.010997578501701355,
-0.0179489366710186,
0.05520861968398094,
0.0057601300068199635,
0.02888297103345394,
-0.07489517331123352,
-0.028289448469877243,
-0.01863713562488556,
0.01618042215704918,
0.011708770878612995,
-0.02757292240858078,
0.05551758036017418,
0.035772375762462616,
0.022601250559091568,
-0.003085044212639332,
0.03441309928894043,
-0.012582186609506607,
-0.07365617901086807,
0.02821400575339794,
-0.04710564389824867,
0.02568790316581726,
0.029551474377512932,
0.00847660843282938,
0.021797731518745422,
-0.007088948506861925,
-0.023031270131468773,
0.032865650951862335,
-0.011347352527081966,
0.07337398082017899,
0.007280548568814993,
0.049779221415519714,
-0.01801776885986328,
0.008923998102545738,
0.038026224821805954,
-0.009444799274206161,
-0.01897899992763996,
-0.0058905817568302155,
-0.06709584593772888,
0.008523044176399708,
0.037906985729932785,
0.045858267694711685,
-0.07997090369462967,
0.027246039360761642,
-0.011801451444625854,
0.022161316126585007,
0.032921209931373596,
0.014276798814535141,
-0.03683524951338768,
-0.004898665938526392,
0.030160482972860336,
0.006142437923699617,
0.01810331456363201,
0.02755533531308174,
0.02588609606027603,
-0.007306003477424383,
0.002757081761956215,
-0.03053707629442215,
-0.03885680437088013,
0.02127077616751194,
0.00752262445166707,
-0.022324685007333755,
-0.023034075275063515,
-0.06284403055906296,
0.05238138139247894,
-0.04068107157945633,
0.03901466354727745,
-0.004486531484872103,
-0.00422410573810339,
0.0408882200717926,
-0.02465992234647274,
-0.03159337490797043,
0.036762505769729614,
-0.01569773070514202,
-0.04837551712989807,
-0.03531939536333084,
0.026449939236044884,
-0.07222627103328705,
-0.007424518931657076,
-0.0437275692820549,
-0.004230833146721125,
-0.01704244315624237,
0.02965911291539669,
0.023857934400439262,
0.017168570309877396,
0.06201017275452614,
-0.02055511251091957,
-0.044469114392995834,
0.010767349973320961,
-0.031651079654693604,
0.03505782037973404,
0.00955406203866005,
-0.04147288203239441,
0.031400348991155624,
-0.014229106716811657,
-0.03780902549624443,
0.02941267564892769,
-0.005508020054548979,
0.014032588340342045,
-0.020863359794020653,
-0.027152057737112045,
-0.02460918016731739,
0.012754988856613636,
0.02814425900578499,
-0.02122662216424942,
-0.017071055248379707,
-0.0038662031292915344,
0.024298083037137985,
-0.0037619939539581537,
-0.016003435477614403,
0.010252576321363449,
-0.017381496727466583,
-0.030446449294686317,
0.024452807381749153,
-0.012816467322409153,
-0.0009964156197384,
-0.029730765148997307,
0.05736283212900162,
0.012882715091109276,
-0.04079382121562958,
-0.03196382895112038,
-0.03346800059080124,
-0.046461883932352066,
0.031312644481658936,
-0.010796846821904182,
0.054600443691015244,
-0.013367794454097748,
-0.04967370629310608,
0.07647097110748291,
0.008925165049731731,
-0.013615580275654793,
-0.004040527623146772,
-0.02328682690858841,
-0.0340113490819931,
-0.004612389486283064,
-0.025964971631765366,
0.04684281721711159,
-0.0014054338680580258,
0.017558204010128975,
-0.012956973165273666,
0.044578880071640015,
0.025543808937072754,
-0.001326346886344254,
-0.0034867897629737854,
0.025327041745185852,
-0.016766691580414772,
0.03224704787135124,
0.05739106610417366,
0.0020590913482010365,
-0.02943352796137333,
0.01879303902387619,
-0.0004285495087970048,
0.03235883265733719,
-0.01611415296792984,
-0.050863124430179596,
0.040544599294662476,
-0.013602059334516525,
0.032409053295850754,
-0.028357692062854767,
0.006299213040620089,
-0.001892837230116129,
0.004535354673862457,
-0.0033565338235348463,
0.03518272936344147,
-0.0038439733907580376,
0.013796327635645866,
-0.0008460382232442498,
-0.002776854671537876,
0.01970413140952587,
0.02068597450852394,
-0.03243955969810486,
0.006214866414666176,
-0.02391740307211876,
0.030951743945479393,
-0.006318484898656607,
-0.03266388550400734,
0.004307491239160299,
0.011037986725568771,
0.05256367847323418,
-0.008270486257970333,
-0.015533309429883957,
0.006989406421780586,
-0.08269171416759491,
-0.0029243971221148968,
-0.04360061511397362,
0.04039241001009941,
0.018028125166893005,
0.044686634093523026,
0.04364898055791855,
0.014511042274534702,
0.01617242768406868,
0.023984313011169434,
-0.10755506157875061,
0.018524939194321632,
-0.03283942490816116,
-0.022267328575253487,
-0.0017334208823740482,
-0.039037808775901794,
0.01571427285671234,
0.019191794097423553,
-0.040274880826473236,
-0.04071827605366707,
-0.009610005654394627,
-0.06834416091442108,
0.03884908929467201,
-0.03604481369256973,
0.009101019240915775,
-0.004142401274293661,
-0.003902303520590067,
0.03733958303928375,
-0.08741258084774017,
-0.011558011174201965,
0.051377419382333755,
-0.0385286919772625,
-0.0010254725348204374,
-0.007905310951173306,
0.07210004329681396,
0.014493848197162151,
0.030533507466316223,
0.041307609528303146,
0.01914403960108757,
-0.04358401522040367,
0.008640854619443417,
0.026599114760756493,
0.04610833153128624,
0.02822628803551197,
-0.025237105786800385,
-0.025400519371032715,
0.0012658765772357583,
-0.009321622550487518,
0.019364645704627037,
0.04325805604457855,
-0.020652778446674347,
0.015097977593541145,
0.05561525747179985,
0.012616894207894802,
-0.036130741238594055,
0.0344616137444973,
0.021464867517352104,
0.011791208758950233,
-0.030580047518014908,
-0.04280214011669159,
-0.0372195728123188,
-0.05176916345953941,
0.019625326618552208,
0.03662401810288429,
0.012863864190876484,
-0.02193676121532917,
0.031870294362306595,
0.021033983677625656,
-0.0149512505158782,
-0.03701363503932953,
-0.013715068809688091,
0.010557192377746105,
0.019056424498558044,
-0.004907817114144564,
0.012601278722286224,
0.015305882319808006,
-0.008350472897291183,
0.040982652455568314,
-0.0016860805917531252,
-0.010317896492779255,
-0.015226881019771099,
-0.003726636292412877,
0.02323591336607933,
0.023204751312732697,
0.003263501450419426,
0.003634061897173524,
-0.05711343511939049,
0.012945305556058884,
0.036814134567976,
0.013965853489935398,
0.05412789061665535,
0.0019658009987324476,
-0.013315796852111816,
-0.03112996555864811,
-0.016200382262468338,
0.020337188616394997,
0.003828727174550295,
0.042773012071847916,
0.037920523434877396,
-0.009023378603160381,
-0.012650721706449986,
0.005798934958875179,
0.0005010960157960653,
0.041615378111600876,
0.06889782845973969,
0.00548281567171216,
-0.006542009301483631,
0.01887599565088749,
-0.00605994276702404,
-0.0005312594003044069,
-0.08359476923942566,
0.010752562433481216,
0.013255113735795021,
-0.0023667393252253532,
-0.0038037069607526064,
-0.05162208527326584,
-0.03307079151272774,
0.04604888707399368,
-0.005565299186855555,
-0.013712839223444462,
-0.036175686866045,
-0.020099977031350136,
0.0749511569738388,
0.011639649979770184,
-0.017056038603186607,
0.08271375298500061,
-0.0167853981256485,
0.003837126074358821,
-0.004634016193449497,
-0.024045057594776154,
0.04306166619062424,
-0.020213574171066284,
0.014163549989461899,
0.005853563547134399,
0.021563231945037842,
-0.04417266324162483,
0.04389498755335808,
-0.044941291213035583,
0.02868911251425743,
-0.0437181256711483,
0.014116431586444378,
0.017401138320565224,
-0.010045163333415985,
-0.03268169239163399,
-0.020621176809072495,
-0.01010437123477459,
0.005857097450643778,
-0.008564860559999943,
-0.030289707705378532,
0.023180225864052773,
-0.0012986272340640426,
0.007302956655621529,
0.007542992010712624,
-0.014727870933711529,
0.029247166588902473,
-0.025800717994570732,
-0.009233782067894936,
0.027110299095511436,
-0.05920688807964325,
0.04553163796663284,
-0.043323367834091187,
0.018795195966959,
-0.002630539471283555,
-0.03281697630882263,
-0.01306460052728653,
0.022666404023766518,
0.022582605481147766,
0.023902500048279762,
-0.05328524112701416,
0.03495491296052933,
0.020984584465622902,
0.022611260414123535,
-0.06564158946275711,
-0.055288251489400864,
0.02498820424079895,
0.018752509728074074,
-0.02703946828842163,
-0.018987899646162987,
0.013143187388777733,
-0.044277794659137726,
-0.011807151138782501,
0.01301443949341774,
0.045311734080314636,
-0.03258899971842766,
-0.028262145817279816,
-0.003486465662717819,
0.007612003479152918,
0.019428318366408348,
0.009602567180991173,
-0.03999565169215202,
0.005663620308041573,
-0.009322800673544407,
-0.002495554042980075,
0.005777124315500259,
0.03972838819026947,
-0.028381360694766045,
-0.025199564173817635,
-0.0009798738174140453,
0.006279043387621641,
0.024477336555719376,
0.008344847708940506,
-0.016085462644696236,
0.045152999460697174,
0.024485459551215172,
0.021248729899525642,
-0.015530510805547237,
0.0064567215740680695,
0.005434898193925619,
-0.00009231414878740907,
-0.007123930379748344,
-0.02536769211292267,
-0.009664232842624187,
-0.03785683959722519,
0.02950741909444332,
0.015434288419783115,
0.03321816399693489,
0.012734467163681984,
0.106816366314888,
0.020526321604847908,
-0.024535782635211945,
-0.01993507891893387,
-0.022202476859092712,
-0.011223005130887032,
0.007154435850679874,
0.025179119780659676,
0.010040431283414364,
0.019684137776494026,
0.01607711985707283,
-0.05903717502951622,
-0.023204544559121132,
0.014530224725604057,
0.06204132363200188,
-0.017102081328630447,
0.022476203739643097,
0.015768608078360558,
-0.023627664893865585,
0.006708985194563866,
-0.01915198750793934,
-0.020486345514655113,
0.03687170892953873,
-0.02268322743475437,
0.03832051903009415,
-0.06496007740497589,
-0.04340014234185219,
0.012869495898485184,
0.02116282843053341,
-0.014978929422795773,
0.030475543811917305,
0.023942625150084496,
0.0062851011753082275,
0.022841690108180046,
-0.023663979023694992,
-0.02030610293149948,
0.057182181626558304,
-0.023604143410921097,
0.05034355819225311,
0.008730011992156506,
0.011551414616405964,
0.026440775021910667,
-0.0006267072749324143,
0.02121063508093357,
-0.008267579600214958,
-0.05498408153653145,
0.007775753736495972,
0.0467844232916832,
-0.017064189538359642,
-0.005259835626929998,
0.020079778507351875,
0.004668528214097023,
-0.010073669254779816,
0.02722105197608471,
0.02247370034456253,
-0.012321758083999157,
-0.03845452517271042,
-0.011105136014521122,
-0.008011539466679096,
-0.036733005195856094,
0.04954223334789276,
0.002731886925175786,
-0.026851050555706024,
-0.004873636644333601,
-0.024317875504493713,
0.03662329912185669,
0.015284812077879906,
0.018646925687789917,
0.035954758524894714,
0.05367700383067131,
0.007302587386220694,
0.04967363551259041,
0.018409298732876778,
0.03424885869026184,
0.10002152621746063,
0.08319622278213501,
0.005855513736605644,
-0.08258002996444702,
0.05118781700730324,
-0.009700758382678032,
0.02159172296524048,
-0.055396534502506256,
-0.008768635801970959,
-0.01157537754625082,
-0.007252990268170834,
0.011877579614520073,
0.04370058327913284,
0.00944560021162033,
-0.022901197895407677,
0.03748186305165291,
-0.04330352693796158,
-0.027510488405823708,
0.02717999927699566,
0.045038338750600815,
-0.01982078142464161,
-0.037296462804079056,
-0.013828872703015804,
-0.04580016806721687,
-0.03507938235998154,
-0.012404781766235828,
-0.03923483565449715,
0.004045850597321987,
0.03456106409430504,
-0.007610224187374115,
-0.002908999565988779,
-0.03035663440823555,
0.014808224514126778,
-0.014702712185680866,
0.010382993146777153,
-0.008689572103321552,
0.020257242023944855,
0.0451439805328846,
0.0440279059112072,
0.04204282537102699,
-0.007263299077749252,
0.009440792724490166,
0.037494100630283356,
0.05217282474040985,
-0.04315531626343727,
-0.006958702579140663,
-0.02818867191672325,
0.005053614731878042,
-0.033396411687135696,
-0.006464850623160601,
0.007010270841419697,
-0.009763169102370739,
0.030969256535172462,
0.0015883278101682663,
-0.007074237801134586,
-0.009657753631472588,
0.038361284881830215,
-0.058492984622716904,
-0.020264526829123497,
-0.048589665442705154,
0.014822336845099926,
-0.0016384852351620793,
0.012404167093336582,
-0.012327413074672222,
-0.009608038701117039,
0.006662177853286266,
0.02879965864121914,
-0.003855300135910511,
-0.03540971130132675,
-0.012188859283924103,
-0.010722282342612743,
0.003754089353606105,
-0.04793998599052429,
-0.020330000668764114,
0.01963048242032528,
0.014344340190291405,
0.03215578943490982,
0.012443553656339645,
-0.03894861787557602,
-0.029194744303822517,
-0.046224452555179596,
0.0020607267506420612,
0.017647316679358482,
-0.032053522765636444,
0.0018420134438201785,
0.003126325085759163,
0.011038481257855892,
0.055008415132761,
-0.0577443428337574,
-0.0011341925710439682,
-0.015820592641830444,
-0.021927470341324806,
0.05455491691827774,
-0.021321317180991173,
0.002204332733526826,
-0.017601221799850464,
-0.0741116851568222,
0.01390842068940401,
0.007132381666451693,
0.017066502943634987,
0.038927700370550156,
-0.0013533167075365782,
0.029888123273849487,
0.02455049380660057,
-0.0359310582280159,
-0.009744670242071152,
0.013967537321150303,
-0.02050469070672989,
0.02102215401828289,
0.04011733457446098,
0.0027434516232460737,
-0.016414213925600052,
-0.0384337455034256,
-0.0271693617105484,
0.03260338306427002,
0.008740821853280067,
0.011264102533459663,
-0.04898883402347565,
0.0031237585935741663,
-0.012289539910852909,
-0.04258200153708458,
-0.058806825429201126,
-0.01239339541643858,
-0.038273971527814865,
0.011528895236551762,
0.010067285969853401,
0.013713272288441658,
-0.010334925726056099,
0.020990045741200447,
0.019890977069735527,
-0.034861765801906586,
0.030053969472646713,
0.02666134014725685,
0.00024305896658916026,
-0.016790827736258507,
-0.02178141660988331,
0.0212104432284832,
0.027874387800693512,
-0.024893345311284065,
-0.02757776528596878,
0.029321866109967232,
-0.05331419035792351,
-0.006258492358028889,
0.0013295164098963141,
-0.023348599672317505,
-0.005961738992482424,
0.006355659570544958,
0.027751818299293518,
-0.028786011040210724,
0.04749392718076706,
-0.00873203668743372,
0.01500239409506321,
0.016034943982958794,
-0.008323915302753448,
-0.0019350915681570768,
0.009175910614430904,
0.011289519257843494,
-0.017798613756895065,
0.005791000556200743,
0.013512758538126945,
0.022146137431263924,
0.0255258921533823,
-0.005077659152448177,
-0.011755675077438354,
-0.01664111576974392,
0.049819108098745346,
0.037994079291820526,
0.011479041539132595,
0.029116742312908173,
0.058590032160282135,
-0.02621394582092762,
0.023625938221812248,
-0.002480647526681423,
0.01984059251844883,
-0.07327506691217422,
0.006787222810089588,
-0.011991274543106556,
-0.04738013446331024,
-0.01802128180861473,
-0.027389047667384148,
0.07717298716306686,
0.012188049033284187,
-0.05801399424672127,
0.02324453555047512,
-0.03154066577553749,
-0.020794566720724106,
-0.062396638095378876,
-0.009948862716555595,
-0.03425618261098862,
0.046549372375011444,
0.05008833855390549,
0.048343587666749954,
-0.01869148574769497,
-0.003586411476135254,
-0.014205701649188995,
0.018909597769379616,
-0.003689781529828906,
0.025812970474362373,
0.0006628661067225039,
-0.02163679711520672,
0.02781270630657673,
-0.00881871022284031,
-0.04580942168831825,
0.015633977949619293,
0.007545730099081993,
-0.030716802924871445,
0.017913002520799637,
0.03260766342282295,
0.020075058564543724,
0.04518912732601166,
0.02664540335536003,
-0.024605978280305862,
0.012827564030885696,
-0.007609633728861809,
0.02353787049651146,
0.03714440390467644,
-0.05553055554628372,
-0.0049814339727163315,
0.02373538166284561,
-0.031447265297174454,
-0.06436935812234879,
0.0557742640376091,
-0.0260491780936718,
-0.013277245685458183,
0.008508548140525818,
-0.010049688629806042,
0.04654872417449951,
-0.035045281052589417,
0.021814966574311256,
-0.05541572719812393,
-0.04968826845288277,
0.019786247983574867,
0.054155778139829636,
-0.026827026158571243,
0.008560935966670513,
-0.021873844787478447,
-0.019542213529348373,
0.020353827625513077,
0.01152705866843462,
-0.0014235134003683925,
-0.03361699357628822,
-0.030580122023820877,
0.03994229808449745,
-0.007942413911223412,
-0.013033282943069935,
-0.06558184325695038,
-0.04091320186853409,
0.038174089044332504,
0.001954397652298212,
0.0370933935046196,
-0.009483322501182556,
-0.017328940331935883,
0.002744993893429637,
-0.03465196117758751,
0.030474113300442696,
-0.043424975126981735,
0.02456510253250599,
-0.02328072115778923,
-0.03622700646519661,
0.037162091583013535,
-0.005267890635877848,
0.062045615166425705,
-0.0035450130235403776,
-0.010093563236296177,
0.003790586953982711,
-0.007219754625111818,
0.010431387461721897,
-0.03490609675645828,
0.0034151498693972826,
0.004174281843006611,
-0.039880331605672836,
-0.026103550568223,
-0.03718021884560585,
-0.01792093552649021,
0.04383870214223862,
0.03837314248085022,
-0.02203119918704033,
0.036198534071445465,
0.009723693132400513,
0.00007450711564160883,
0.05470855161547661,
0.02435438148677349,
-0.006324301473796368,
0.0662764310836792,
-0.00841846875846386,
0.0172125156968832,
0.02159026823937893,
-0.008789378218352795,
-0.05316074565052986,
0.03348194435238838,
-0.02574559673666954,
0.018248142674565315,
0.024280983954668045,
0.013409297913312912,
-0.002648264169692993,
-0.011280647478997707,
-0.00006285788549575955,
0.04859646037220955,
-0.02994404174387455,
0.010738183744251728,
0.06281299889087677,
-0.013886190950870514,
0.04285038635134697,
-0.04723929241299629,
-0.018425002694129944,
-0.01236847136169672,
0.019735516980290413,
0.007382538635283709,
0.02710762247443199,
0.03180505707859993,
-0.001313618617132306,
0.03837960958480835,
0.02892116643488407,
-0.015760550275444984,
0.021617133170366287,
-0.00808027759194374,
0.00311506655998528,
-0.03674646094441414,
-0.03090827353298664,
0.01615733653306961,
-0.03287375718355179,
0.034230247139930725,
0.03490201383829117,
-0.0396120660007,
0.09460381418466568,
-0.018824324011802673,
0.011491984128952026,
-0.006605216767638922,
-0.008431252092123032,
0.0018038857961073518,
-0.005216028541326523,
0.010018513537943363,
0.06816603243350983,
-0.053239550441503525,
0.01008167490363121,
0.011737287044525146,
-0.0032316783908754587,
0.04267909750342369,
-0.03879028931260109,
0.011386165395379066,
-0.021153099834918976,
0.0341244600713253,
-0.005931264255195856,
-0.012637586332857609,
-0.023168765008449554,
0.011184594593942165,
0.07091806083917618,
0.03091970831155777,
-0.031162254512310028,
-0.002989092841744423,
0.002139338757842779,
0.0018281692173331976,
0.06670115888118744,
-0.04567583650350571,
0.01777707040309906,
-0.028673941269516945,
0.024613680317997932,
-0.03540019318461418,
0.007520241662859917
] |
<p>Having read Wikipedia's <a href="https://en.wikipedia.org/wiki/Thermocouple#Type_K" rel="nofollow">current explanation</a> that certain types of thermocouple (specifically Type K thermocouples) experience a step-change in their potential when they reach the Curie point of the constituent iron, it does not explain the reason, nor why the Curie point is important for the thermoelectric properties of ferromagnets. There seems to be no more of a hint on Wikipedia's page about <a href="https://en.wikipedia.org/wiki/Thermoelectric_effect" rel="nofollow">the thermoelectric effect</a>, nor for the page on the Curie temperature. Searching the internet more generally for information only seems to find similar assertions without explanations, or abstracts from academic papers hidden behind paywalls.</p>
<p>Can anyone explain this connection in terms a layman reading Wikipedia would understand, or failing that an undergraduate physics student?</p>
| 8,817 |
[
-0.042508043348789215,
-0.04571705684065819,
0.01576051488518715,
-0.03237393498420715,
0.017312053591012955,
0.028805335983633995,
-0.00969897024333477,
0.013399544171988964,
0.03908133506774902,
-0.07319831103086472,
0.006826726719737053,
0.020778989419341087,
0.051049355417490005,
0.026148362085223198,
0.022366901859641075,
0.006838956382125616,
0.0035404167138040066,
-0.016424696892499924,
0.007114689331501722,
-0.02693590708076954,
-0.0011485914001241326,
0.04941314086318016,
-0.023851390928030014,
0.022818565368652344,
-0.019265661016106606,
0.008566203527152538,
0.0019476234447211027,
-0.006726935505867004,
0.028369838371872902,
0.054019853472709656,
-0.02399330399930477,
-0.007802827283740044,
0.019366631284356117,
-0.01200894732028246,
0.00227390811778605,
-0.00843039806932211,
0.009544147178530693,
-0.055252838879823685,
0.0003715103957802057,
0.020902371034026146,
-0.03522815927863121,
0.0042649214155972,
-0.017159396782517433,
0.023836245760321617,
-0.007341474760323763,
-0.007307646330446005,
-0.025818388909101486,
-0.04613946005702019,
0.009768689051270485,
-0.03802461549639702,
-0.0007031625136733055,
-0.008588461205363274,
0.041990604251623154,
0.05209052562713623,
-0.025424562394618988,
0.0293639674782753,
0.07646133750677109,
0.06324191391468048,
-0.030200205743312836,
-0.033819813281297684,
-0.019265567883849144,
-0.023054921999573708,
0.0005014421767555177,
-0.013361068442463875,
-0.029169922694563866,
0.04556630179286003,
-0.003634396009147167,
-0.024904562160372734,
0.046377308666706085,
0.005057942122220993,
0.028119463473558426,
0.017237672582268715,
0.026883672922849655,
0.01552816852927208,
0.03178101032972336,
-0.030754519626498222,
-0.013135218061506748,
0.0030146108474582434,
0.05828173831105232,
0.044053398072719574,
-0.008688739500939846,
0.039036598056554794,
0.05981992557644844,
0.03957543894648552,
0.01627836376428604,
0.01271133404225111,
0.043838635087013245,
-0.005260177422314882,
0.02984679490327835,
0.02512475475668907,
-0.0020095009822398424,
0.01735673099756241,
0.015043474733829498,
-0.05475540831685066,
-0.03891710937023163,
0.021587232127785683,
-0.011445540934801102,
0.03806605190038681,
0.016858398914337158,
-0.03705276548862457,
0.03564244881272316,
0.007001951802521944,
0.034930579364299774,
0.059545066207647324,
0.043346986174583435,
-0.03455953299999237,
-0.00796040240675211,
-0.0033306905534118414,
-0.019999828189611435,
-0.006808943580836058,
-0.04557889699935913,
0.028502466157078743,
-0.019315853714942932,
0.023513244464993477,
-0.008570993319153786,
-0.02133003994822502,
-0.02897760458290577,
-0.02052699588239193,
0.05026736855506897,
0.004871946293860674,
0.045029934495687485,
-0.030682329088449478,
-0.012546242214739323,
-0.05936197191476822,
-0.08671344071626663,
0.029439758509397507,
0.02281368523836136,
-0.04579898715019226,
0.010930938646197319,
0.02737978659570217,
-0.008789506740868092,
-0.023041406646370888,
0.011598607525229454,
-0.030274704098701477,
0.019527427852153778,
0.024623243138194084,
-0.09151163697242737,
-0.04366717487573624,
0.047029878944158554,
0.020127862691879272,
-0.004700148478150368,
-0.08708484470844269,
0.008634695783257484,
0.03353964537382126,
0.08171969652175903,
0.0022161260712891817,
-0.016643881797790527,
-0.046799954026937485,
0.025370396673679352,
0.007991276681423187,
-0.029580049216747284,
-0.035076968371868134,
0.024248627945780754,
-0.013590720482170582,
-0.009351017884910107,
-0.06793911010026932,
0.02640508860349655,
0.019255582243204117,
-0.0018558392766863108,
-0.01705433614552021,
0.05164548382163048,
-0.020284641534090042,
-0.017509015277028084,
-0.013585236854851246,
0.01216895505785942,
-0.032184895128011703,
0.09536606073379517,
0.0002467834856361151,
0.017778275534510612,
0.010581223294138908,
-0.005354608874768019,
0.035638876259326935,
-0.002825238509103656,
0.04055378958582878,
0.047723691910505295,
-0.04297763109207153,
-0.0019305649911984801,
-0.018499471247196198,
0.02557474561035633,
-0.01022719033062458,
-0.07943274825811386,
-0.030838530510663986,
-0.0007259221747517586,
0.016963480040431023,
0.026025623083114624,
0.05377033352851868,
-0.024076469242572784,
0.01252623088657856,
0.02095627412199974,
-0.06461263447999954,
-0.021849868819117546,
-0.046289294958114624,
0.018602751195430756,
-0.02219570241868496,
0.0002948975015897304,
0.06250929832458496,
0.0035227411426603794,
0.030867785215377808,
-0.03612532466650009,
-0.029920710250735283,
0.00968065857887268,
0.000020765095541719347,
0.03803085908293724,
0.0033357145730406046,
-0.006104668602347374,
0.02789236418902874,
0.041524916887283325,
0.006072686053812504,
0.048304472118616104,
-0.02840937301516533,
-0.021738745272159576,
0.011112343519926071,
0.0031728337053209543,
-0.0026184709277004004,
0.044547636061906815,
-0.041653674095869064,
-0.05103178694844246,
0.07098240405321121,
0.011801837012171745,
0.03528781607747078,
-0.05004432797431946,
0.056213777512311935,
0.026765182614326477,
0.0054368856362998486,
-0.012795159593224525,
0.04513850808143616,
0.02578493393957615,
0.041772808879613876,
-0.04306108132004738,
-0.007947837002575397,
-0.027997246012091637,
-0.023015545681118965,
0.06064734607934952,
0.036655545234680176,
-0.063261479139328,
0.012555013410747051,
-0.016746798530220985,
0.034707844257354736,
-0.014778693206608295,
0.0011832262389361858,
-0.004399038385599852,
-0.007642568089067936,
0.020128117874264717,
-0.01623314805328846,
-0.036005303263664246,
0.0023825769312679768,
0.03499606251716614,
-0.005581699311733246,
0.028642384335398674,
-0.010410814546048641,
-0.009532504715025425,
0.03827279433608055,
0.0074027846567332745,
-0.002796200569719076,
-0.011219882406294346,
-0.004519619047641754,
0.017276257276535034,
-0.01249212771654129,
0.010070974007248878,
0.013072947040200233,
0.012314214371144772,
0.03080337680876255,
-0.02426542527973652,
-0.02713252604007721,
0.017889007925987244,
-0.026893464848399162,
0.016612466424703598,
-0.03420858457684517,
0.012823967263102531,
-0.03573582321405411,
0.011421448551118374,
-0.02338389866054058,
-0.019723035395145416,
0.0002656008873600513,
-0.0208868570625782,
-0.047103576362133026,
0.002436365932226181,
0.033786214888095856,
-0.03916725143790245,
-0.03867685794830322,
-0.022200394421815872,
-0.025222916156053543,
0.044742316007614136,
0.044202376157045364,
-0.020487796515226364,
0.018583565950393677,
-0.004822411574423313,
-0.00833459384739399,
0.04236592724919319,
-0.006865365896373987,
0.011686219833791256,
-0.03362998366355896,
0.03054806962609291,
-0.04315101355314255,
0.0071736229583621025,
0.002285934053361416,
0.01494264043867588,
0.00031464258790947497,
-0.003559552598744631,
0.03856723755598068,
-0.060137227177619934,
-0.02558172680437565,
0.05447768419981003,
-0.03517068549990654,
-0.040489185601472855,
-0.019756102934479713,
-0.04805995151400566,
0.000042451392801012844,
-0.008166697807610035,
0.02749774046242237,
0.018356971442699432,
-0.08670435100793839,
-0.024292433634400368,
-0.013371605426073074,
-0.05045803263783455,
0.061442818492650986,
-0.04662620648741722,
0.01863163523375988,
-0.003534507704898715,
-0.03548498451709747,
0.06834930181503296,
0.03174978122115135,
-0.012526003643870354,
-0.03895998001098633,
-0.02741163969039917,
-0.026295393705368042,
-0.03764014691114426,
-0.018296947702765465,
0.04156501218676567,
-0.020264869555830956,
0.03302969038486481,
0.013128206133842468,
0.05643543228507042,
0.05711255967617035,
0.005450303666293621,
-0.025451792404055595,
-0.0051194229163229465,
-0.005900370888411999,
-0.02025660313665867,
0.067011259496212,
0.020792298018932343,
-0.02513364888727665,
0.03103436902165413,
-0.00002156183654733468,
0.016736986115574837,
0.0650518462061882,
-0.04122167080640793,
0.052498266100883484,
-0.002555073471739888,
-0.034834593534469604,
-0.08142180740833282,
0.022903606295585632,
0.00289438059553504,
-0.054108355194330215,
-0.00364405638538301,
0.041735392063856125,
0.07327163219451904,
-0.058782871812582016,
-0.019123820587992668,
-0.004599211737513542,
0.011559649370610714,
-0.004669164773076773,
-0.025804104283452034,
-0.002250918885692954,
-0.036676496267318726,
0.006562473252415657,
0.007210954558104277,
0.009579104371368885,
0.05207831785082817,
0.010402422398328781,
0.033360935747623444,
0.007064566947519779,
-0.02418459765613079,
-0.018217647448182106,
-0.05704522877931595,
-0.01304093562066555,
-0.021692702546715736,
0.06183592602610588,
0.023686189204454422,
0.015842217952013016,
0.018576744943857193,
-0.021774619817733765,
-0.005822069942951202,
0.003563191508874297,
-0.09755201637744904,
0.033652063459157944,
-0.051129743456840515,
-0.006630397867411375,
0.012240506708621979,
-0.0015880141872912645,
0.0007060079369693995,
-0.013306749053299427,
-0.013986799865961075,
-0.022738153114914894,
0.0032887179404497147,
-0.04372399300336838,
0.018893392756581306,
-0.01708216965198517,
-0.052364856004714966,
-0.018544575199484825,
0.015280974097549915,
0.046256158500909805,
-0.05541563034057617,
0.007544476073235273,
-0.010731461457908154,
-0.02120104245841503,
0.021486246958374977,
-0.020637385547161102,
0.02286766655743122,
0.03515863046050072,
-0.011225701309740543,
0.02292933501303196,
-0.03070172294974327,
-0.00011361804354237393,
0.013456557877361774,
0.04547075554728508,
0.04017838463187218,
0.007441753521561623,
-0.025475716218352318,
-0.04214593023061752,
-0.03964659199118614,
-0.029108792543411255,
-0.005873821210116148,
0.050216272473335266,
-0.0011502226116135716,
0.03992447257041931,
0.02237813174724579,
0.009332499466836452,
0.004338896367698908,
0.03614436835050583,
0.03365383669734001,
0.007217898964881897,
-0.03668932244181633,
-0.02772444300353527,
-0.016702760010957718,
-0.013360549695789814,
0.01859777234494686,
-0.006698633078485727,
0.021627359092235565,
-0.013870338909327984,
0.012803749181330204,
0.004630020819604397,
-0.015808310359716415,
-0.00695623317733407,
-0.022669274359941483,
0.05206341668963432,
0.022135168313980103,
-0.04184354096651077,
0.011571827344596386,
0.03145669028162956,
-0.012716233730316162,
0.04717564210295677,
-0.02744586020708084,
-0.01434976328164339,
-0.08116485923528671,
-0.0013382765464484692,
0.0237786453217268,
0.04262116178870201,
-0.007596959359943867,
-0.004105161875486374,
-0.07575977593660355,
0.00971174892038107,
-0.014330526813864708,
-0.04016124829649925,
0.032317858189344406,
-0.012469645589590073,
-0.039161063730716705,
-0.03136710822582245,
-0.012237942777574062,
-0.0068153394386172295,
0.015612097457051277,
-0.0005455882637761533,
0.056947365403175354,
-0.029913587495684624,
-0.0029080542735755444,
0.01747823879122734,
-0.007694555446505547,
0.028586778789758682,
0.05641942843794823,
-0.003683591727167368,
0.016051115468144417,
0.018421314656734467,
0.03660015016794205,
-0.03022208996117115,
-0.08665672689676285,
-0.009255134500563145,
-0.030291035771369934,
-0.015982121229171753,
0.028225479647517204,
-0.015082383528351784,
-0.05762245133519173,
0.030121970921754837,
0.03729366138577461,
-0.014709190465509892,
-0.013058975338935852,
-0.011268303729593754,
0.07482283562421799,
0.04446454718708992,
-0.006851387210190296,
0.047934483736753464,
0.045038480311632156,
-0.036044031381607056,
0.01172693632543087,
-0.007148056291043758,
0.05223756656050682,
-0.00743112713098526,
0.02455773577094078,
-0.032377585768699646,
0.03874889761209488,
-0.012296872213482857,
0.04595475643873215,
0.001536363153718412,
0.02139136753976345,
-0.056203730404376984,
-0.004428560845553875,
-0.02635977230966091,
-0.023772766813635826,
-0.013557260856032372,
-0.025486424565315247,
-0.00337974657304585,
0.05120043829083443,
0.009547739289700985,
0.005879627540707588,
0.021187899634242058,
-0.020827794447541237,
0.023446008563041687,
0.006383632309734821,
0.00308965309523046,
0.039553847163915634,
-0.010214066132903099,
-0.00919666700065136,
0.002632196992635727,
-0.0357234962284565,
0.0422862283885479,
-0.022924738004803658,
-0.014625083655118942,
0.020411241799592972,
-0.03146497905254364,
0.0013589025475084782,
-0.016587845981121063,
0.0030433645006269217,
0.04310280829668045,
-0.022717025130987167,
0.029134750366210938,
0.025614159181714058,
0.014260955154895782,
-0.04185379296541214,
-0.03306800127029419,
0.0383327454328537,
-0.009113776497542858,
-0.022752001881599426,
0.036468539386987686,
0.018498554825782776,
-0.03368758410215378,
-0.02610425464808941,
0.05201820284128189,
0.03257111832499504,
-0.04185200482606888,
-0.03004603087902069,
0.018961384892463684,
0.022884467616677284,
0.06253625452518463,
0.017566874623298645,
-0.023159245029091835,
0.05220995098352432,
0.0014846035046502948,
-0.030629944056272507,
0.015131328254938126,
0.048912160098552704,
-0.02664066106081009,
-0.027323562651872635,
0.011224876157939434,
0.02121693082153797,
0.04553911089897156,
-0.01955389603972435,
0.002491653896868229,
0.026933591812849045,
0.03733734041452408,
-0.027378074824810028,
-0.048047516494989395,
0.0395202562212944,
0.04620704427361488,
0.03526996076107025,
0.012695102021098137,
-0.024249587208032608,
-0.0018886622274294496,
-0.0050110165029764175,
0.041943974792957306,
-0.011783869005739689,
0.0025147569831460714,
-0.0022196578793227673,
0.06557641178369522,
-0.027576202526688576,
-0.017765283584594727,
0.01677817478775978,
-0.028547462075948715,
-0.0032489742152392864,
0.0010878322646021843,
0.0006412281654775143,
0.0004961227532476187,
0.00230922969058156,
-0.020391209051012993,
0.006606160197407007,
-0.03286050260066986,
0.03468295559287071,
0.06065879762172699,
-0.01380513608455658,
0.04370466247200966,
0.030829623341560364,
-0.05553286895155907,
-0.0061065880581736565,
-0.02291245386004448,
-0.026662088930606842,
-0.008002831600606441,
-0.00431264191865921,
0.01566229946911335,
-0.03875714913010597,
-0.0024846033193171024,
0.04070121794939041,
0.02005303092300892,
-0.061164963990449905,
-0.002432319102808833,
0.03547964245080948,
0.06380687654018402,
0.03635410591959953,
-0.014960533007979393,
-0.01568966545164585,
0.06718821823596954,
-0.02383950911462307,
0.030643051490187645,
-0.006901518441736698,
-0.02961779572069645,
0.03858503699302673,
-0.01976889744400978,
0.03898879140615463,
-0.050112318247556686,
-0.044439952820539474,
-0.03743991628289223,
0.013211812824010849,
0.020130285993218422,
-0.0060233245603740215,
-0.0006459912983700633,
0.004150523338466883,
0.030783694237470627,
0.018475541844964027,
-0.03924427181482315,
-0.009381091222167015,
-0.0578378289937973,
-0.026344159618020058,
-0.020504698157310486,
-0.05866513401269913,
0.02555876225233078,
-0.020168719813227654,
-0.059976257383823395,
0.01567160151898861,
-0.05080949142575264,
0.03207138925790787,
0.006511398125439882,
0.004488264676183462,
-0.03263058885931969,
0.07350192219018936,
-0.035832297056913376,
0.007846581749618053,
-0.0015991056570783257,
-0.033868588507175446,
0.14374323189258575,
0.04426383599638939,
0.011202190071344376,
-0.08415181189775467,
0.030903330072760582,
-0.014431498013436794,
0.009515045210719109,
-0.009052006527781487,
-0.020837834104895592,
-0.022188926115632057,
0.009548020549118519,
0.0178179033100605,
0.03832994028925896,
0.0061608776450157166,
0.04867968708276749,
0.02681083418428898,
-0.04854097217321396,
0.008908774703741074,
0.02272193320095539,
0.019896239042282104,
0.005990561563521624,
-0.019993005320429802,
-0.006378958933055401,
-0.03279963880777359,
-0.07276348769664764,
0.015931129455566406,
-0.022344518452882767,
-0.0052210986614227295,
0.01956593059003353,
0.02744900807738304,
-0.05608407035470009,
0.03268783539533615,
0.009581335820257664,
0.003385887248441577,
-0.009035788476467133,
0.02832399681210518,
0.025941647589206696,
0.011249309405684471,
0.03435647860169411,
0.007612628396600485,
0.04376201331615448,
0.0029967431910336018,
0.0348697192966938,
0.029246989637613297,
-0.03626100346446037,
0.014416185207664967,
0.00401232810690999,
0.029822196811437607,
-0.015477228909730911,
0.02416929043829441,
-0.016301829367876053,
-0.020353607833385468,
0.02010395936667919,
0.010173129849135876,
-0.03115140087902546,
-0.0006244987016543746,
0.018316784873604774,
-0.006470425520092249,
-0.02668898180127144,
-0.03765980899333954,
0.04292092099785805,
-0.024255789816379547,
0.030816690996289253,
0.005355327855795622,
-0.04346339777112007,
0.016726700589060783,
0.030586740002036095,
0.00100559345446527,
-0.012122558429837227,
-0.005239128600805998,
-0.012351046316325665,
0.023870937526226044,
-0.03829103708267212,
-0.02063349075615406,
0.004994179122149944,
-0.0002985661558341235,
0.03292199224233627,
-0.019591933116316795,
-0.018334951251745224,
0.050286661833524704,
-0.06793060153722763,
-0.006326186936348677,
-0.0016988241113722324,
-0.01414678804576397,
-0.02185729518532753,
0.0025900143664330244,
0.02541930228471756,
0.0227796770632267,
-0.016652237623929977,
-0.0009285953710786998,
0.006077664438635111,
-0.0005045614088885486,
0.005452900193631649,
-0.010087834671139717,
-0.012574481777846813,
0.04378073662519455,
-0.020550012588500977,
0.016728892922401428,
0.01281766314059496,
0.03811618313193321,
0.010872961021959782,
0.0050532142631709576,
0.03082200698554516,
0.0026808923576027155,
-0.03703848645091057,
-0.014615216292440891,
0.011136817745864391,
0.018092814832925797,
-0.03961426392197609,
-0.002743026940152049,
-0.04538143426179886,
-0.016543148085474968,
-0.05831054598093033,
-0.011557238176465034,
-0.016905775293707848,
0.0007757826242595911,
0.050005391240119934,
-0.02284577302634716,
-0.012895695865154266,
-0.07070640474557877,
0.016899000853300095,
-0.03783255070447922,
-0.031460899859666824,
-0.025747958570718765,
-0.04357510805130005,
0.03558199107646942,
0.01904251053929329,
0.02841903641819954,
0.01802290603518486,
0.004728628788143396,
0.009263205341994762,
0.026636721566319466,
0.012735717929899693,
-0.024329274892807007,
0.00026372462161816657,
-0.02557425945997238,
-0.006716671399772167,
0.0573279932141304,
-0.04603458568453789,
-0.045773860067129135,
0.030081652104854584,
-0.028569296002388,
-0.03869607299566269,
0.041448939591646194,
-0.0010509563144296408,
0.0015766104916110635,
-0.014593406580388546,
0.02260017581284046,
-0.01441994309425354,
0.026667410507798195,
-0.026547817513346672,
0.031815964728593826,
0.02856363169848919,
-0.0059297289699316025,
-0.013922741636633873,
-0.021691899746656418,
0.027579480782151222,
-0.010284495539963245,
0.0028155529871582985,
0.020694680511951447,
0.02413848601281643,
-0.014625589363276958,
-0.0023574605584144592,
0.013678185641765594,
0.008377866819500923,
-0.009692440740764141,
0.006794346030801535,
0.032193753868341446,
0.054745566099882126,
0.038009945303201675,
-0.03799467161297798,
0.029812879860401154,
0.0025352397933602333,
0.002337205223739147,
-0.07240746170282364,
0.004858493804931641,
0.006193267647176981,
-0.005787006113678217,
0.022790098562836647,
-0.017150696367025375,
0.0024667682591825724,
0.012019431218504906,
-0.057627931237220764,
0.019810380414128304,
0.006877819541841745,
-0.024344857782125473,
-0.057416271418333054,
-0.018050260841846466,
-0.0019931886345148087,
0.02593974582850933,
0.021804258227348328,
0.04035963490605354,
0.05839897319674492,
0.020911887288093567,
-0.006118916440755129,
-0.05099240690469742,
-0.03721773251891136,
0.014715970493853092,
-0.011432971805334091,
-0.01743187941610813,
0.04470814764499664,
-0.00547796068713069,
-0.024440446868538857,
0.013834585435688496,
-0.035450465977191925,
-0.025554001331329346,
0.013540653511881828,
0.010506757535040379,
-0.003513020696118474,
0.04505408555269241,
0.02382177859544754,
-0.023562289774417877,
-0.0009731522877700627,
0.020864512771368027,
0.023570187389850616,
0.06441137939691544,
0.024740327149629593,
0.0029935797210782766,
0.015818508341908455,
-0.03492070734500885,
0.00303764920681715,
0.03708842024207115,
-0.034632857888936996,
-0.013538258150219917,
0.022755498066544533,
0.027594326063990593,
-0.016499875113368034,
-0.04245008900761604,
0.018847312778234482,
-0.06715387850999832,
-0.045566607266664505,
-0.00534409936517477,
0.01407784502953291,
0.05797082185745239,
0.016713708639144897,
-0.039088163524866104,
-0.0005676771979779005,
0.02519654855132103,
-0.005246808286756277,
-0.028612183406949043,
-0.019177015870809555,
-0.004739242140203714,
0.026643162593245506,
-0.003279451746493578,
-0.016915034502744675,
-0.03337132930755615,
-0.0515935942530632,
0.0584077388048172,
0.027834894135594368,
0.025225043296813965,
-0.01173343788832426,
-0.016895515844225883,
-0.013279646635055542,
-0.05945965647697449,
0.04747334122657776,
-0.03640592098236084,
-0.013092031702399254,
-0.028356783092021942,
-0.047537751495838165,
0.0179765485227108,
0.005062392447143793,
0.07340414077043533,
-0.011513406410813332,
-0.01889006793498993,
-0.00029711410752497613,
-0.03620686009526253,
0.02871127240359783,
-0.04394294321537018,
0.027716485783457756,
-0.013899841345846653,
-0.005154704675078392,
0.023743918165564537,
-0.0306934155523777,
-0.010308832861483097,
0.017175834625959396,
0.04960140958428383,
-0.004488462582230568,
-0.0040251766331493855,
-0.00764890480786562,
-0.00043614281457848847,
0.0037442753091454506,
0.0025476166047155857,
-0.004127775318920612,
0.030182432383298874,
-0.016730105504393578,
0.01822786219418049,
0.012018625624477863,
0.011979704722762108,
-0.049296293407678604,
0.010136189870536327,
0.000689948268700391,
-0.01749042049050331,
-0.016585953533649445,
-0.02881702594459057,
0.024925770238041878,
-0.04990587383508682,
-0.014569146558642387,
0.039852891117334366,
-0.015586533583700657,
0.00455059576779604,
0.018109992146492004,
0.034537628293037415,
0.03287481889128685,
-0.019424906000494957,
-0.004060949198901653,
-0.022031936794519424,
-0.01772230491042137,
-0.00555277056992054,
0.04526323825120926,
0.0640057846903801,
0.00967269204556942,
0.00022868435189593583,
-0.014629078097641468,
-0.017563743516802788,
-0.010630860924720764,
-0.0014531321357935667,
0.020867107436060905,
-0.03345523774623871,
-0.0584896020591259,
0.05759916082024574,
0.002024514600634575,
0.03440115973353386,
0.03795382007956505,
-0.013513999991118908,
0.06970416754484177,
-0.029204364866018295,
-0.00046749450848437846,
-0.02755480632185936,
0.025427188724279404,
0.01818242482841015,
-0.019847145304083824,
0.038144551217556,
0.015556632541120052,
-0.02783285826444626,
0.00833456963300705,
-0.03025498241186142,
0.0377148874104023,
0.021282076835632324,
-0.013818129897117615,
0.0023120439145714045,
-0.037860047072172165,
-0.012585803866386414,
-0.009266241453588009,
-0.02674657665193081,
0.003961110021919012,
-0.015430563129484653,
0.011464038863778114,
0.03927619010210037,
0.04568420350551605,
-0.016818977892398834,
-0.03118625283241272,
-0.024212827906012535,
0.05122145637869835,
-0.05785578861832619,
0.04028943553566933,
-0.025488141924142838,
0.06408142298460007,
-0.006190127227455378,
-0.006033354438841343
] |
<p>I read occasionally popular science articles and from time to time encounter issues about quantum information teleportation. (this one for example <a href="http://www.physorg.com/news193551675.html" rel="nofollow">http://www.physorg.com/news193551675.html</a>)</p>
<p>So far I have the following understanding of basic principles:</p>
<ol>
<li>after measurement entangled particles have identical random state (i.e. we can not predict the result, but we know that it will be similar for both particles).</li>
<li>"decoding key" should be sent by traditional channel</li>
</ol>
<p>As I understand the underlying process is the following:</p>
<ol>
<li>Some amount of entangled particles is sent to A and B.</li>
<li>Particles are measured at A and B and results R (equal in both places) are recorded. </li>
<li>Knowing the results A computes a "decoding key" (some function F, that F(R) has some valuable meaning) which is sent by traditional means to B. </li>
<li>B applies key to it's copy of R, and thus receives information.</li>
</ol>
<p>The benefit is that amount of information that needs to be transmitted by traditional means is small.</p>
<p>In case everything stated before is correct, I have the question: how is this "quantum information teleportation" process differs from just sending two identical sets of random data to both destinations by traditional means?</p>
<p>I could be wrong about understanding of principles of quantum information teleportation, in this case, please, correct me.</p>
| 8,818 |
[
-0.0076761734671890736,
-0.04115290567278862,
-0.029124759137630463,
-0.01609940081834793,
0.02495715208351612,
0.026567935943603516,
0.023451771587133408,
0.008071715012192726,
0.017389455810189247,
-0.016004830598831177,
0.041105419397354126,
0.056110188364982605,
-0.005528892856091261,
0.018664158880710602,
0.026176663115620613,
-0.022901330143213272,
-0.019749462604522705,
-0.017049791291356087,
-0.006496311631053686,
-0.01017904095351696,
-0.0009854568634182215,
0.04497375339269638,
0.013028004206717014,
-0.0018225370440632105,
-0.005444546230137348,
0.02563357725739479,
0.003570178523659706,
-0.029260149225592613,
0.04593193903565407,
0.07057702541351318,
0.004231012426316738,
-0.02136196568608284,
-0.004097871482372284,
0.03829546272754669,
0.007287004496902227,
-0.01937509886920452,
-0.08472438156604767,
-0.019606541842222214,
0.02593698538839817,
-0.025716427713632584,
-0.027204599231481552,
-0.012455591931939125,
-0.019840316846966743,
0.07768484950065613,
-0.021750634536147118,
0.000986922299489379,
0.020544709637761116,
-0.014696233905851841,
0.009414080530405045,
-0.06793742626905441,
0.06814940273761749,
0.01785281114280224,
0.03007318079471588,
-0.006747362203896046,
-0.03118498995900154,
-0.011761635541915894,
0.07610158622264862,
0.07985711097717285,
-0.013453029096126556,
-0.03417256847023964,
-0.014949829317629337,
-0.023764893412590027,
-0.00903985183686018,
-0.013752521947026253,
-0.04451528191566467,
0.007961612194776535,
-0.024386698380112648,
-0.005326597485691309,
0.0399940088391304,
-0.029680512845516205,
0.04091832414269447,
0.03906848654150963,
0.03521174192428589,
0.0080239437520504,
0.03945862501859665,
-0.027518564835190773,
-0.010103068314492702,
0.004792868159711361,
0.03348546847701073,
0.04456644132733345,
0.014148022048175335,
0.006009585689753294,
0.033801618963479996,
0.06971742957830429,
0.012907187454402447,
-0.023147162050008774,
0.049097172915935516,
-0.03238631784915924,
-0.0158954206854105,
0.015452039428055286,
-0.013597545213997364,
0.027095582336187363,
0.04143732413649559,
0.0033117940183728933,
-0.04005879908800125,
0.010558437556028366,
-0.018924131989479065,
0.056084971874952316,
0.005025012418627739,
-0.04561574012041092,
0.013946672901511192,
-0.0568479560315609,
0.026885997503995895,
0.06666794419288635,
-0.013364293612539768,
-0.045846957713365555,
-0.011323608458042145,
0.04234793409705162,
0.008911614306271076,
0.027189528569579124,
-0.025640711188316345,
0.002195250941440463,
0.002692891051992774,
0.027407143265008926,
0.021890021860599518,
-0.045678842812776566,
-0.014933496713638306,
-0.014463778585195541,
0.09464521706104279,
0.0495525486767292,
0.035816676914691925,
-0.02099902182817459,
-0.0020727519877254963,
-0.04805701598525047,
-0.011644650250673294,
0.02194228209555149,
0.021698538213968277,
0.005059120245277882,
-0.038090821355581284,
0.06900634616613388,
-0.010038433596491814,
-0.0171512421220541,
0.015625568106770515,
0.02239963412284851,
-0.00933773908764124,
-0.013205238617956638,
-0.18153367936611176,
-0.03681030496954918,
0.07334865629673004,
0.012356392107903957,
-0.018371546640992165,
-0.08668941259384155,
0.02492966130375862,
0.04133915901184082,
0.07330649346113205,
0.0032342132180929184,
0.02084074728190899,
-0.004918196704238653,
0.026343056932091713,
0.014926182106137276,
-0.01410621963441372,
0.004354365170001984,
0.014442287385463715,
-0.03492177650332451,
0.0019045463996008039,
-0.04633791744709015,
0.0015589527320116758,
0.040031738579273224,
-0.02800317294895649,
-0.021001549437642097,
0.06207573413848877,
-0.019328158348798752,
-0.03328682854771614,
0.02297215349972248,
-0.018755828961730003,
-0.02614172361791134,
0.05528445169329643,
0.004492561798542738,
0.01567648909986019,
0.04351900890469551,
-0.015193329192698002,
0.0237593874335289,
-0.0033810168970376253,
0.01685967482626438,
0.020033949986100197,
-0.036072153598070145,
0.005683581344783306,
-0.004463039338588715,
0.004926666617393494,
-0.020001273602247238,
-0.021064383909106255,
-0.04424357786774635,
-0.01604454778134823,
0.019169865176081657,
0.01254584826529026,
0.0012591617414727807,
-0.010658139362931252,
-0.01001746580004692,
0.021156515926122665,
-0.04850213602185249,
-0.0168168768286705,
-0.056572720408439636,
0.012325575575232506,
-0.013766344636678696,
-0.03041020967066288,
0.018029190599918365,
0.014814790338277817,
0.02345171570777893,
-0.004477002192288637,
-0.03699389845132828,
-0.0179161187261343,
0.0032490654848515987,
0.02199956215918064,
-0.003889189101755619,
0.04262295737862587,
0.0678788274526596,
0.010204434394836426,
0.004201347474008799,
0.02361171506345272,
0.0056937518529593945,
-0.06631827354431152,
-0.027714919298887253,
0.024872228503227234,
0.02990136109292507,
0.016298895701766014,
-0.008079705759882927,
0.008627648465335369,
0.004121145233511925,
-0.022863062098622322,
-0.00006219454371603206,
-0.0611971840262413,
0.07735621929168701,
0.005064287688583136,
0.030531970784068108,
-0.03539188951253891,
0.046290505677461624,
0.04033828154206276,
-0.001592264510691166,
-0.013801719062030315,
-0.07236942648887634,
-0.055190637707710266,
0.004084371495991945,
0.004276195075362921,
0.01753327064216137,
-0.03107590787112713,
0.04392743110656738,
0.011019428260624409,
0.03541671112179756,
0.02309594675898552,
0.01638226956129074,
-0.020927390083670616,
-0.034400083124637604,
0.010832608677446842,
0.0024881514254957438,
-0.02027679607272148,
0.03998689725995064,
0.0080053536221385,
0.003763006767258048,
-0.00992785394191742,
0.0029688957147300243,
-0.028772292658686638,
0.01803472824394703,
-0.007990140467882156,
0.028448287397623062,
0.0005951800849288702,
-0.013262719847261906,
0.009506979957222939,
-0.015077810734510422,
-0.0009978075977414846,
-0.012154584750533104,
-0.017636191099882126,
-0.011356908828020096,
-0.01029661949723959,
-0.029889360070228577,
-0.019897256046533585,
0.022076360881328583,
-0.030315333977341652,
0.008243695832788944,
0.02074500545859337,
-0.03976742550730705,
0.021783774718642235,
-0.014917046763002872,
0.013223964720964432,
-0.014420505613088608,
-0.00006007775300531648,
-0.02475951425731182,
-0.0030520393047481775,
0.029914025217294693,
-0.0377037487924099,
-0.024921853095293045,
-0.012796134687960148,
-0.03208223730325699,
-0.003834577975794673,
0.02152365818619728,
-0.07144331187009811,
0.0321953222155571,
-0.047776613384485245,
-0.011993670836091042,
0.046300213783979416,
-0.0344187431037426,
0.025482039898633957,
-0.019105786457657814,
-0.0065818107686936855,
-0.03250368684530258,
-0.019551867619156837,
-0.02893516980111599,
0.0411946102976799,
-0.02098696492612362,
0.008151434361934662,
0.056295245885849,
-0.010047322139143944,
-0.014965412206947803,
-0.01745758205652237,
-0.04209156334400177,
-0.04654529690742493,
-0.002404929604381323,
0.0008290706318803132,
-0.016706930473446846,
-0.04314177483320236,
0.002054563257843256,
0.01633087731897831,
-0.05121820420026779,
-0.04390396177768707,
-0.08030055463314056,
-0.08498043566942215,
0.03809385374188423,
0.0010581394890323281,
0.032787423580884933,
-0.00964876264333725,
-0.019863294437527657,
0.0680839791893959,
0.008442934602499008,
-0.027858303859829903,
-0.006343914195895195,
-0.006106623914092779,
0.01256750151515007,
0.007583420258015394,
0.003732554381713271,
0.034912314265966415,
-0.026074247434735298,
0.05278836935758591,
0.029154455289244652,
-0.01264586579054594,
0.03858419135212898,
0.004151364788413048,
-0.02484249323606491,
0.012881757691502571,
0.04472004622220993,
-0.023403042927384377,
0.05059303343296051,
0.007845778949558735,
-0.06092407926917076,
0.0035963640548288822,
-0.014281285926699638,
0.013204601593315601,
0.016293469816446304,
-0.035442985594272614,
0.026139236986637115,
0.03446463868021965,
0.03807980939745903,
-0.009912574663758278,
0.03636578470468521,
-0.06116894632577896,
-0.0009551428374834359,
0.02249184623360634,
0.011020596139132977,
0.0390397347509861,
-0.015531649813055992,
-0.007443028502166271,
0.047946903854608536,
0.039645057171583176,
-0.010833638720214367,
-0.008065803907811642,
-0.038109421730041504,
0.01742112822830677,
0.008079278282821178,
-0.013074347749352455,
-0.030972924083471298,
0.02618393860757351,
0.023291831836104393,
0.03230368718504906,
-0.009076971560716629,
-0.015424072742462158,
-0.049163561314344406,
-0.027635082602500916,
0.011772602796554565,
0.0056032342836260796,
0.04365648701786995,
0.02880515716969967,
0.05260602384805679,
0.03296959400177002,
-0.0043068318627774715,
0.01448146253824234,
-0.00843797717243433,
-0.08731487393379211,
0.015482673421502113,
-0.02426769770681858,
-0.01985456794500351,
0.02179722860455513,
-0.029982753098011017,
0.01838728040456772,
-0.03326905146241188,
-0.0620507076382637,
0.004353418946266174,
-0.0065358770079910755,
-0.028172537684440613,
-0.007430776488035917,
0.003494508098810911,
-0.029480701312422752,
-0.01651669107377529,
0.01943141408264637,
0.010691097937524319,
0.0015500682638958097,
0.020387977361679077,
0.047239016741514206,
-0.02547026239335537,
0.015142761170864105,
-0.00034935312578454614,
0.007890724577009678,
0.019656654447317123,
0.02466241829097271,
0.023389676585793495,
0.013193775899708271,
-0.013260845094919205,
0.016146307811141014,
0.010175369679927826,
0.04047493264079094,
-0.030190251767635345,
-0.004573384299874306,
-0.004215805791318417,
-0.013166221790015697,
-0.0158388614654541,
-0.008035839535295963,
0.042447514832019806,
-0.014779387041926384,
0.017171109095215797,
0.02353588677942753,
0.020833192393183708,
-0.00949397124350071,
0.016826532781124115,
0.049355849623680115,
0.011871888302266598,
0.00798775628209114,
-0.027076665312051773,
0.0014962605200707912,
-0.0012779164826497436,
-0.0151599096134305,
0.02831345424056053,
-0.015253550373017788,
-0.00283017847687006,
0.00020402338122949004,
0.00535954162478447,
0.007582657504826784,
-0.038594361394643784,
-0.0011042203987017274,
-0.019684458151459694,
0.012996966019272804,
-0.0016020392067730427,
0.0033764545805752277,
-0.010724376887083054,
0.04227225482463837,
0.005865294951945543,
0.02272190898656845,
0.0013072805013507605,
-0.05993247404694557,
-0.030070992186665535,
0.02971508912742138,
0.04683014005422592,
-0.008209888823330402,
0.014176546595990658,
-0.06577780097723007,
-0.04125594720244408,
0.016293225809931755,
-0.02324497699737549,
0.05079951137304306,
-0.004984974395483732,
-0.009206391870975494,
-0.0255182683467865,
0.0036177849397063255,
0.009711986407637596,
0.023949038237333298,
-0.006468781735748053,
0.02685992605984211,
-0.002881098072975874,
-0.01741449348628521,
-0.027633454650640488,
-0.023516783490777016,
0.03690453618764877,
0.059029486030340195,
-0.0189812108874321,
-0.006129592657089233,
-0.011876403354108334,
0.008640890009701252,
-0.02210640348494053,
-0.08000408858060837,
0.017340684309601784,
-0.009506277740001678,
-0.02974567376077175,
0.03226940333843231,
-0.02633771114051342,
-0.058353446424007416,
0.009289411827921867,
-0.015259645879268646,
-0.005203102715313435,
-0.006025394890457392,
-0.03595663234591484,
0.062426283955574036,
0.031647659838199615,
-0.0020574925001710653,
0.054207414388656616,
0.0411485880613327,
-0.01131624635308981,
0.021981555968523026,
-0.032187726348638535,
0.03590987250208855,
-0.03597739338874817,
0.023704471066594124,
-0.010005136951804161,
0.017776867374777794,
-0.036937274038791656,
0.0637681782245636,
-0.0011346244718879461,
0.0026367248501628637,
-0.01973969303071499,
-0.04896632209420204,
-0.029343247413635254,
0.01789102703332901,
-0.007740978617221117,
0.004279992543160915,
-0.009181339293718338,
0.004197230562567711,
-0.02341628260910511,
-0.03341227024793625,
-0.017927387729287148,
0.00017418152128811926,
0.007856295444071293,
0.014744408428668976,
-0.0020958376117050648,
0.03905422240495682,
-0.04148580878973007,
-0.023648595437407494,
0.035020988434553146,
-0.07495086640119553,
0.008559420704841614,
-0.008038172498345375,
-0.0013526281109079719,
0.03049449808895588,
-0.07406867295503616,
-0.04337945953011513,
0.001574424677528441,
0.0007143800612539053,
-0.01799962855875492,
-0.053716883063316345,
0.030660530552268028,
-0.038798388093709946,
-0.031215518712997437,
-0.038037050515413284,
-0.036398615688085556,
0.019385816529393196,
-0.015175861306488514,
-0.013319444842636585,
-0.008827757090330124,
0.02704552933573723,
-0.02683141827583313,
-0.007872650399804115,
-0.06110791489481926,
0.03602832928299904,
0.011386067606508732,
-0.011967020109295845,
0.030317597091197968,
0.030177773907780647,
0.03456363454461098,
-0.009935193695127964,
-0.019383210688829422,
0.025496015325188637,
-0.005770069546997547,
0.009148553013801575,
0.003462459659203887,
0.03728727996349335,
-0.049079637974500656,
-0.04661547392606735,
-0.025702066719532013,
0.012528324499726295,
0.023680321872234344,
-0.026371454820036888,
0.008969844318926334,
0.009629194624722004,
0.02232813462615013,
-0.004705536644905806,
0.001763661508448422,
-0.012069478631019592,
0.037116002291440964,
0.028105147182941437,
-0.020773330703377724,
0.013673320412635803,
0.004757969174534082,
-0.04790283367037773,
0.026295095682144165,
-0.005795421078801155,
-0.0030675549060106277,
0.005357122514396906,
0.03537467122077942,
-0.008232969790697098,
0.02671184204518795,
0.00256607704795897,
-0.03027755208313465,
-0.00127560761757195,
-0.03424832969903946,
0.022438213229179382,
0.0221440177410841,
0.004832128062844276,
-0.0324859656393528,
-0.032456591725349426,
-0.03486604243516922,
0.005610089749097824,
0.049564801156520844,
0.006369597278535366,
0.04326365515589714,
0.027682730928063393,
0.0018636123277246952,
-0.01814241148531437,
-0.020958762615919113,
-0.01805780455470085,
-0.011043029837310314,
0.03208154812455177,
0.03551890701055527,
-0.032989878207445145,
-0.032384827733039856,
0.006132973358035088,
0.05882108584046364,
0.01885928399860859,
0.03361799940466881,
0.035620540380477905,
0.034071918576955795,
0.03692905232310295,
-0.027534693479537964,
-0.037800099700689316,
0.04231385514140129,
-0.05283663421869278,
0.05087978020310402,
0.004113056696951389,
0.013106144033372402,
0.0489531084895134,
0.011399179697036743,
0.010111895389854908,
-0.05724414810538292,
-0.00159184739459306,
-0.0716281309723854,
-0.0021130575332790613,
0.010913360863924026,
0.013074317015707493,
0.011554508469998837,
-0.024085426703095436,
0.014926345087587833,
-0.006211026106029749,
0.015604750253260136,
-0.013977904804050922,
-0.0967191830277443,
-0.03617403656244278,
-0.02403843216598034,
-0.06385701149702072,
0.03431259095668793,
0.00234169140458107,
-0.017451124265789986,
0.030913095921278,
-0.05662902817130089,
0.06871457397937775,
0.02151290327310562,
0.03200441598892212,
-0.058272846043109894,
0.08936519175767899,
-0.006001326721161604,
0.032761864364147186,
-0.013548444956541061,
-0.004371602088212967,
0.12088935077190399,
0.03934316709637642,
-0.005380622576922178,
-0.03870415315032005,
0.01972847804427147,
-0.01652923785150051,
0.021492572501301765,
-0.023537997156381607,
0.002959698671475053,
0.015790628269314766,
0.028653191402554512,
0.020374512299895287,
0.012126104906201363,
-0.007726855110377073,
-0.01879662647843361,
0.04720024764537811,
-0.0366637222468853,
-0.06411413103342056,
0.002150940941646695,
0.00009541540930513293,
0.000709849875420332,
-0.02319890633225441,
-0.014503645710647106,
-0.012213995680212975,
-0.04398084059357643,
-0.027161970734596252,
-0.013544064946472645,
-0.014910037629306316,
0.011310349218547344,
0.019106609746813774,
-0.012878069654107094,
-0.005111420061439276,
-0.003211262170225382,
0.010258001275360584,
-0.008613121695816517,
0.038326431065797806,
0.046508338302373886,
-0.014647621661424637,
0.020060544833540916,
0.04351656138896942,
0.010995607823133469,
-0.0026011154986917973,
0.009516059421002865,
0.02549746073782444,
-0.06583186984062195,
0.0037204064428806305,
-0.0303029902279377,
0.06117362901568413,
-0.04941496253013611,
-0.04016558825969696,
-0.02288035675883293,
0.010156792588531971,
0.015599768608808517,
-0.05420602485537529,
-0.009977682493627071,
0.05163457244634628,
0.005880332551896572,
-0.025498991832137108,
-0.011224072426557541,
-0.008671754039824009,
0.010438120923936367,
-0.03303017094731331,
0.008468122221529484,
-0.0074338242411613464,
0.017254985868930817,
0.019479207694530487,
-0.014958121813833714,
0.020416492596268654,
-0.003542270278558135,
-0.010088672861456871,
-0.0667116791009903,
0.03164050355553627,
-0.06545116007328033,
-0.017233168706297874,
0.03368505835533142,
0.02003592997789383,
0.025122474879026413,
-0.0020438358187675476,
0.003596867434680462,
0.05528957396745682,
-0.04228153079748154,
0.04677944630384445,
0.009505783207714558,
-0.024816811084747314,
-0.02576889470219612,
0.0036722850054502487,
0.017791209742426872,
0.05640599876642227,
0.00311595993116498,
0.01805141754448414,
0.009980414062738419,
0.006630111951380968,
0.029721835628151894,
-0.03419576212763786,
-0.00569197628647089,
0.0014260587049648166,
-0.03775165602564812,
-0.019887682050466537,
-0.020316123962402344,
0.008951154537498951,
0.029258083552122116,
0.022859346121549606,
-0.015301133506000042,
-0.003852666122838855,
-0.028946470469236374,
-0.009265697561204433,
-0.015559905208647251,
-0.018811510875821114,
-0.016144568100571632,
-0.006887596100568771,
0.0381295345723629,
-0.016770821064710617,
-0.012906909920275211,
-0.015678809955716133,
-0.00009593355207471177,
0.01347208209335804,
-0.0074372380040585995,
0.006181204225867987,
0.002755735069513321,
-0.026131542399525642,
0.03356509655714035,
-0.017215916886925697,
-0.012754851952195168,
-0.007211425341665745,
0.02579978108406067,
-0.015473129227757454,
0.004811089485883713,
-0.02732810378074646,
0.04295573756098747,
-0.0032791257835924625,
-0.0034189270809292793,
0.015824805945158005,
-0.0024334322661161423,
-0.02137359045445919,
0.031016414985060692,
0.01216916460543871,
-0.023236572742462158,
0.050837792456150055,
-0.03344175964593887,
-0.05427739396691322,
0.05295882746577263,
-0.022630736231803894,
-0.027970924973487854,
0.05441256985068321,
-0.03282032161951065,
0.0033753113821148872,
0.03819917142391205,
-0.03226139768958092,
-0.0027453573420643806,
0.022196631878614426,
0.022236831486225128,
-0.015153431333601475,
0.023245321586728096,
-0.0300669576972723,
-0.0010590731399133801,
-0.002037313301116228,
0.02020116336643696,
-0.01074453815817833,
-0.0024581504985690117,
0.02988681197166443,
0.03783943131566048,
0.025194957852363586,
0.04730485379695892,
-0.007490008138120174,
0.016338063403964043,
0.006696721073240042,
0.007125446107238531,
-0.015155208297073841,
0.01219527330249548,
0.06813792884349823,
-0.02259323187172413,
0.041640717536211014,
0.04586223512887955,
0.02318570204079151,
-0.090659499168396,
-0.010546109639108181,
0.014355395920574665,
-0.001831555156968534,
0.02219628170132637,
-0.04942623898386955,
0.00532298069447279,
0.02303488738834858,
-0.05884227901697159,
0.028282901272177696,
-0.017616039142012596,
-0.018503231927752495,
-0.0024905747268348932,
0.04287954792380333,
-0.04792720824480057,
0.06630872189998627,
0.03188109025359154,
0.03729121759533882,
0.03352700546383858,
0.001616750261746347,
-0.011369002051651478,
-0.020910609513521194,
-0.04222385585308075,
0.0228147991001606,
-0.02001463621854782,
0.013510230928659439,
0.0670165941119194,
-0.01847635582089424,
-0.03947414085268974,
0.04446050897240639,
-0.01754862442612648,
0.014041803777217865,
-0.002088218228891492,
-0.002422043588012457,
0.02626056782901287,
0.00782978255301714,
0.02181839570403099,
-0.04165703430771828,
0.006630520336329937,
0.01840933784842491,
0.051375310868024826,
0.02543995901942253,
0.02209611050784588,
-0.004228213801980019,
0.0054224636405706406,
-0.013612453825771809,
0.015230061486363411,
0.03317108750343323,
-0.020729126408696175,
0.0047560688108205795,
-0.020459361374378204,
0.01608416438102722,
0.011797364801168442,
-0.04035395011305809,
-0.008660818450152874,
-0.03713188320398331,
-0.004052812233567238,
0.03955630213022232,
0.0038638063706457615,
-0.028302045539021492,
0.02447628229856491,
-0.045128993690013885,
-0.026232099160552025,
0.04487505927681923,
0.013231944292783737,
0.0365581251680851,
-0.05524929612874985,
-0.03795866668224335,
0.00009277242497773841,
0.039457712322473526,
0.007442737929522991,
-0.0634981244802475,
-0.036200154572725296,
0.02290225774049759,
-0.005588558968156576,
0.038696981966495514,
-0.01464099157601595,
0.014504234306514263,
-0.053245387971401215,
-0.06192811205983162,
0.0384657122194767,
0.026634899899363518,
0.03486710414290428,
-0.07701826840639114,
-0.03562565892934799,
-0.012867026031017303,
0.029656656086444855,
0.08269824087619781,
0.03313345089554787,
0.004024319816380739,
0.025091731920838356,
0.023415494710206985,
0.04344205558300018,
-0.03848470747470856,
0.02374466136097908,
-0.02935161255300045,
0.004224963951855898,
-0.004873253870755434,
-0.017009887844324112,
-0.025401657447218895,
0.037184394896030426,
0.022289741784334183,
-0.022945815697312355,
0.019569559022784233,
0.010999741964042187,
-0.0008563828887417912,
0.06023607775568962,
0.0039098234847188,
0.023407716304063797,
0.033724814653396606,
0.004028248135000467,
0.04105981066823006,
0.01659524068236351,
-0.017858797684311867,
-0.019995898008346558,
0.020025737583637238,
-0.04200315847992897,
-0.01036821398884058,
0.025670235976576805,
-0.013011913746595383,
0.018943164497613907,
-0.062206756323575974,
0.0020781883504241705,
0.016685158014297485,
-0.05103763937950134,
0.00577134545892477,
0.061317507177591324,
-0.017537925392389297,
0.050718698650598526,
0.011174273677170277,
0.032320670783519745,
-0.010715534910559654,
-0.008330528624355793,
-0.022584998980164528,
0.03624482452869415,
0.039249613881111145,
-0.022403305396437645,
0.03639386221766472,
0.034657977521419525,
-0.010487575083971024,
0.03453996405005455,
-0.009977942332625389,
0.04089927300810814,
-0.04212213307619095,
-0.02284242957830429,
0.03459706902503967,
-0.018250789493322372,
-0.01757795922458172,
0.0314861498773098,
-0.01005447469651699,
0.08394717425107956,
-0.028970813378691673,
-0.009426059201359749,
-0.004129184875637293,
0.014107996597886086,
-0.026924122124910355,
0.007638526149094105,
0.018039189279079437,
0.04268911853432655,
0.005507947411388159,
-0.0034868407528847456,
-0.028181860223412514,
0.018428849056363106,
-0.01676330156624317,
-0.03284863382577896,
0.006145433522760868,
-0.021058449521660805,
-0.01987462118268013,
-0.030209951102733612,
-0.03143853321671486,
-0.008445806801319122,
-0.0165119506418705,
0.03771815076470375,
0.031247273087501526,
-0.008802171796560287,
0.004633910488337278,
-0.04375883936882019,
0.03019505739212036,
0.08336551487445831,
-0.05903072655200958,
0.044341254979372025,
-0.06012408807873726,
0.04509974643588066,
-0.026741275563836098,
0.0005734473816119134
] |
<p>I was using a program for simulating optical elements; mirrors, gratings, foils, crystals, slits, and zoneplates are what it mentioned. Does anyone know what a foil is in terms of optics? I know what aluminum foil is, obviously, but in terms of an optical system I don't know what a foil, or foil, would be, and what it's unique optical properties are.</p>
| 8,819 |
[
-0.017287807539105415,
-0.0530010387301445,
-0.010490728542208672,
-0.011708403937518597,
0.06985700875520706,
0.04075207933783531,
0.0032739134039729834,
-0.02093837410211563,
-0.015625298023223877,
-0.027492797002196312,
0.03174419328570366,
0.04016504064202309,
0.07012861967086792,
0.027126861736178398,
0.0012124318163841963,
0.01137362141162157,
0.0031597623601555824,
-0.009659801609814167,
-0.019243571907281876,
-0.03632262349128723,
-0.02000504732131958,
0.02238856814801693,
0.00017780564667191356,
-0.0005811150767840445,
-0.034448426216840744,
0.05611075460910797,
-0.013221937231719494,
-0.04217664524912834,
0.07717855274677277,
-0.010903322137892246,
-0.009001372382044792,
-0.00324763311073184,
0.009650971740484238,
-0.019610658288002014,
0.01245916448533535,
-0.04063458368182182,
-0.03707917407155037,
-0.03595929592847824,
-0.00612844992429018,
0.008429331704974174,
-0.02364315465092659,
-0.015456520952284336,
-0.023126594722270966,
0.05924295634031296,
-0.008117062039673328,
-0.031664181500673294,
-0.017999477684497833,
-0.0537949800491333,
0.008819646202027798,
-0.047317322343587875,
0.04028747230768204,
0.026529423892498016,
0.02638082765042782,
0.04920446127653122,
-0.012418530881404877,
0.001676844316534698,
0.07595740258693695,
0.07305776327848434,
-0.003641459858044982,
-0.055098529905080795,
-0.00686732167378068,
0.018787525594234467,
-0.012531321495771408,
-0.013215486891567707,
-0.026060648262500763,
0.0113817248493433,
-0.006034251302480698,
-0.04001675918698311,
0.010494953952729702,
0.029462041333317757,
0.011355267837643623,
0.04237053170800209,
0.0026820460334420204,
-0.01228851918131113,
-0.005345107987523079,
-0.02142612636089325,
-0.0027588014490902424,
0.02675807476043701,
0.050734784454107285,
0.02503226511180401,
0.018343377858400345,
0.040571022778749466,
-0.0217277854681015,
-0.00874420441687107,
-0.02044653333723545,
0.006103942636400461,
0.10459503531455994,
-0.014141225256025791,
0.0017409478314220905,
-0.014326019212603569,
-0.046154849231243134,
0.023373855277895927,
0.02530943788588047,
0.005390385165810585,
-0.019408468157052994,
-0.012808529660105705,
-0.013308791443705559,
0.03238232433795929,
0.013826292008161545,
-0.026831267401576042,
0.016224578022956848,
-0.008107856847345829,
0.017391685396432877,
0.07979855686426163,
0.008559186942875385,
-0.02780943550169468,
-0.02484102174639702,
0.011430187150835991,
0.0023113195784389973,
0.023341063410043716,
-0.028489574790000916,
0.05591310188174248,
-0.0029528005979955196,
0.021636998280882835,
0.028507597744464874,
-0.018430283293128014,
0.01933557167649269,
0.020107122138142586,
0.02632373757660389,
0.08978479355573654,
0.03205948695540428,
-0.04144126921892166,
0.03598139062523842,
0.0007043479126878083,
-0.12101583182811737,
0.01430104486644268,
0.02440676838159561,
0.004548852331936359,
-0.012384627014398575,
0.01706123910844326,
-0.0007003817008808255,
-0.019942574203014374,
0.04084015265107155,
-0.02301693707704544,
0.02219478227198124,
-0.033770691603422165,
-0.0567534975707531,
-0.07658760249614716,
-0.003890159772709012,
0.036085065454244614,
-0.020675597712397575,
-0.02572762779891491,
0.0022369602229446173,
0.02895149029791355,
0.08129454404115677,
-0.0030220402404665947,
0.007233146112412214,
-0.03730333223938942,
0.03524903580546379,
-0.018648309633135796,
-0.044074710458517075,
0.03446830436587334,
0.0005387507262639701,
-0.046142272651195526,
0.018253572285175323,
-0.045425381511449814,
0.00050867855316028,
0.03548628091812134,
-0.03164474293589592,
-0.03574495017528534,
0.05711035057902336,
-0.041550133377313614,
0.03585631027817726,
0.029374228790402412,
-0.044294197112321854,
-0.054467327892780304,
0.07588697969913483,
-0.005922300275415182,
0.040903378278017044,
0.06703922897577286,
0.0007632420747540891,
0.02377280406653881,
-0.021852461621165276,
0.020709475502371788,
0.09266483038663864,
-0.006527379620820284,
-0.04844760149717331,
-0.01961946114897728,
-0.001571408472955227,
0.017176197841763496,
-0.031210435554385185,
-0.035408053547143936,
0.04198325052857399,
0.009824550710618496,
0.03766907379031181,
0.06413929164409637,
0.004152987152338028,
-0.03353084251284599,
-0.0050935084000229836,
-0.035275448113679886,
-0.026015453040599823,
-0.02219020016491413,
0.019455648958683014,
-0.039789553731679916,
-0.003094535553827882,
0.01642734184861183,
0.005113061983138323,
-0.025966893881559372,
-0.0008260780014097691,
-0.0361819714307785,
-0.026020724326372147,
0.036469828337430954,
0.017356060445308685,
-0.013577619567513466,
0.04095224291086197,
0.04941709712147713,
0.009544345550239086,
-0.011758696287870407,
0.02387203834950924,
-0.061742618680000305,
-0.005947530269622803,
-0.011060475371778011,
-0.022572187706828117,
0.016953008249402046,
0.0027067733462899923,
-0.016656694933772087,
0.016701554879546165,
0.002752800937741995,
0.010408056899905205,
-0.0021669836714863777,
-0.017716364935040474,
0.04357844963669777,
0.06076648458838463,
0.023037077859044075,
0.028534140437841415,
0.010785115882754326,
-0.02366807870566845,
0.017064185813069344,
-0.01122796256095171,
-0.007886059582233429,
-0.03332092985510826,
0.004493678919970989,
0.06708575785160065,
0.018144767731428146,
-0.06165635958313942,
0.035510286688804626,
-0.0016978036146610975,
0.028389010578393936,
0.06729191541671753,
-0.02085050195455551,
-0.024735137820243835,
0.005851982161402702,
-0.00927769485861063,
-0.013065188191831112,
0.03469986096024513,
0.024511486291885376,
0.039227474480867386,
0.037780795246362686,
0.0002683281491044909,
-0.015623079612851143,
-0.0070096771232783794,
0.0678369402885437,
-0.004441294353455305,
0.01926804706454277,
-0.027142658829689026,
-0.0499328076839447,
0.04512776806950569,
-0.044318731874227524,
-0.0019648682791739702,
0.030781833454966545,
-0.004689889959990978,
-0.011775895021855831,
-0.03607535362243652,
0.0017384032253175974,
0.025321008637547493,
0.02229122444987297,
0.009959209710359573,
-0.021312182769179344,
0.025719651952385902,
-0.01619262620806694,
0.03520774468779564,
-0.01975950039923191,
0.0028398302383720875,
0.00008167687337845564,
0.009857757948338985,
0.025700759142637253,
0.03817719221115112,
0.0508258193731308,
-0.015283591113984585,
-0.04704148694872856,
-0.02224225364625454,
-0.028262652456760406,
0.000035534449125407264,
0.013696127571165562,
-0.04430082067847252,
-0.005779735278338194,
-0.028211001306772232,
-0.06080176681280136,
0.046946294605731964,
-0.02311285398900509,
-0.030235620215535164,
0.005578222218900919,
-0.04779502749443054,
-0.042201630771160126,
0.018100250512361526,
-0.028759663924574852,
-0.01820996031165123,
-0.05994078144431114,
0.0094371372833848,
-0.004024137742817402,
-0.010722656734287739,
0.0021321382373571396,
0.025800403207540512,
-0.050915174186229706,
-0.003401123220100999,
0.004976895172148943,
-0.0029365576338022947,
0.02392449416220188,
-0.015527184121310711,
-0.005743001122027636,
0.043039966374635696,
-0.012853826396167278,
0.029317939653992653,
-0.019106606021523476,
-0.04079703241586685,
-0.006403118837624788,
0.007846604101359844,
0.02148508094251156,
-0.011742545291781425,
-0.018569298088550568,
0.09201577305793762,
-0.003062539268285036,
-0.031137337908148766,
-0.006170605309307575,
-0.016688933596014977,
0.014210278168320656,
-0.04126458987593651,
0.04192041605710983,
-0.004574082791805267,
0.01183125376701355,
0.02567778155207634,
0.009339231997728348,
-0.004992836620658636,
0.04182228446006775,
0.025860775262117386,
0.001960637280717492,
0.002550845267251134,
0.0015235430328175426,
-0.014251557178795338,
0.04114258289337158,
0.027484003454446793,
-0.03637485206127167,
0.016081443056464195,
-0.02149774692952633,
0.03474782407283783,
0.026186304166913033,
-0.03084280714392662,
0.049436137080192566,
0.005167171359062195,
0.010530934669077396,
0.033125150948762894,
0.054782480001449585,
-0.01511665154248476,
0.030195588245987892,
-0.011794459074735641,
0.03365432843565941,
0.03294045105576515,
-0.007463988848030567,
-0.023195352405309677,
0.02150845341384411,
0.020362384617328644,
-0.029852211475372314,
0.015292538329958916,
-0.01802649348974228,
-0.018250709399580956,
-0.03977947309613228,
-0.022008748725056648,
-0.005583284888416529,
0.07983732968568802,
0.0374305360019207,
0.024441011250019073,
0.019695980474352837,
-0.0329231396317482,
0.010238146409392357,
-0.056283239275217056,
0.02563592977821827,
-0.018042592331767082,
0.06148083135485649,
-0.033280838280916214,
0.05527552589774132,
0.03532768413424492,
0.02452290616929531,
0.023439213633537292,
0.021053723990917206,
-0.04436001554131508,
0.0428091399371624,
-0.0008140355348587036,
-0.006050671450793743,
-0.049297939985990524,
0.005266071297228336,
-0.020345008000731468,
-0.0006849123165011406,
-0.0204043909907341,
0.0004271378566045314,
-0.026331445202231407,
-0.03679919242858887,
0.003586162580177188,
-0.01784207858145237,
-0.0242149718105793,
-0.01615241914987564,
0.03342488408088684,
0.01376822404563427,
0.0034543906804174185,
0.0072111827321350574,
0.03046223148703575,
-0.044665247201919556,
0.006319819483906031,
0.005487821064889431,
0.008993387222290039,
-0.00271275220438838,
0.05978349223732948,
0.03205412998795509,
0.011294088326394558,
-0.027429774403572083,
-0.0023754113353788853,
0.0033043844159692526,
0.0904543548822403,
0.004284960217773914,
-0.025603648275136948,
-0.010068411938846111,
-0.0700383260846138,
-0.014931355603039265,
-0.0075891874730587006,
0.03318905457854271,
-0.011375626549124718,
-0.003904517740011215,
0.019690416753292084,
0.029174990952014923,
-0.04084340110421181,
0.030428633093833923,
0.023322781547904015,
0.03970234841108322,
-0.0017022262327373028,
-0.02378728613257408,
-0.01026176568120718,
-0.02442329004406929,
-0.02915422059595585,
0.016113540157675743,
-0.0022432864643633366,
0.010713533498346806,
0.02677556686103344,
0.00903860293328762,
-0.013426064513623714,
-0.01429977547377348,
0.0007407988305203617,
-0.02366524562239647,
-0.008631481789052486,
-0.008763921447098255,
0.0237544234842062,
-0.014431635849177837,
0.05601261928677559,
0.04313281551003456,
0.01730366237461567,
0.0030355791095644236,
-0.08869452774524689,
0.0492008812725544,
0.041681356728076935,
0.028529668226838112,
-0.011106918565928936,
-0.03452051430940628,
-0.01058789249509573,
-0.011961697600781918,
0.013983073644340038,
-0.0006018025451339781,
0.03845199942588806,
-0.06882177293300629,
-0.0019905888475477695,
-0.009769669733941555,
0.012807424180209637,
-0.002394335111603141,
0.026903117075562477,
-0.004996063187718391,
0.017162544652819633,
-0.02494138479232788,
0.00681956484913826,
-0.006886154878884554,
0.008468981832265854,
0.025339065119624138,
0.04196637496352196,
0.03153638541698456,
-0.02317045070230961,
0.02929151989519596,
0.017248570919036865,
-0.028475403785705566,
-0.062275052070617676,
-0.013181681744754314,
0.033633798360824585,
-0.01282176561653614,
0.01561389397829771,
-0.033568158745765686,
-0.05087713524699211,
0.021200701594352722,
0.009716195985674858,
-0.013950531370937824,
0.001418764004483819,
-0.019977569580078125,
0.000887551752384752,
0.018773702904582024,
0.02290249988436699,
0.06569153815507889,
0.014496540650725365,
-0.043517716228961945,
0.0102088563144207,
-0.013325326144695282,
0.0571805015206337,
-0.010913178324699402,
0.020409997552633286,
-0.024153711274266243,
-0.03138154745101929,
-0.022037846967577934,
0.04119495674967766,
-0.03355815261602402,
0.02628910355269909,
-0.004278062377125025,
-0.0521988570690155,
-0.012963598594069481,
0.022281618788838387,
-0.02819923311471939,
-0.01958605833351612,
-0.024663737043738365,
-0.0069610546343028545,
0.004831868689507246,
-0.01373700238764286,
-0.020416930317878723,
-0.017677484080195427,
0.021727919578552246,
0.012265021912753582,
0.023615913465619087,
0.0023815808817744255,
-0.06812171638011932,
-0.02754569612443447,
0.012862095609307289,
-0.044880203902721405,
0.07948076725006104,
-0.017027661204338074,
-0.011399149894714355,
0.04447835311293602,
-0.09178377687931061,
-0.05457917973399162,
0.01006425078958273,
-0.026720697060227394,
0.031294241547584534,
-0.049980778247117996,
0.01651276834309101,
-0.023645782843232155,
0.0007412596023641527,
-0.050681937485933304,
-0.030455363914370537,
0.029903292655944824,
0.03713490068912506,
-0.00685662729665637,
-0.000446497171651572,
-0.02240537293255329,
-0.0011013905750587583,
-0.08172042667865753,
0.019380703568458557,
0.02368389070034027,
-0.04110604524612427,
-0.051261819899082184,
0.03655592352151871,
-0.027968918904662132,
0.05155664309859276,
0.0015631859423592687,
-0.04826563969254494,
-0.006856310181319714,
-0.01442311704158783,
-0.03410644829273224,
-0.032578933984041214,
0.016338560730218887,
-0.012096785008907318,
-0.03280288353562355,
-0.024463606998324394,
-0.006739766336977482,
0.055478405207395554,
-0.013064206577837467,
0.018119869753718376,
-0.006810866761952639,
-0.004843514878302813,
-0.03330102190375328,
-0.012473534792661667,
0.02474627085030079,
-0.03117966093122959,
-0.01380838081240654,
-0.03132658824324608,
-0.019909922033548355,
-0.04151764512062073,
-0.03690489009022713,
0.049557480961084366,
-0.021200506016612053,
0.028563866391777992,
0.0040598404593765736,
0.04996919631958008,
-0.032287903130054474,
0.029056819155812263,
0.010696514509618282,
-0.038550443947315216,
0.03265915438532829,
-0.00937442947179079,
0.016609270125627518,
0.03642963990569115,
0.02139424718916416,
-0.001790355541743338,
-0.027118228375911713,
-0.015021647326648235,
-0.006467750295996666,
0.054821982979774475,
-0.0436234325170517,
0.04113304242491722,
0.020483473315835,
-0.03618788719177246,
-0.015139192342758179,
-0.00998941995203495,
-0.003427698742598295,
0.043851517140865326,
-0.012769313529133797,
0.04280417785048485,
-0.007415367756038904,
-0.016331588849425316,
-0.005052291322499514,
0.046783819794654846,
-0.00007626677688676864,
0.00999252125620842,
0.009328106418251991,
0.06000038981437683,
0.009057608433067799,
-0.020439201965928078,
-0.07428431510925293,
0.04770790413022041,
-0.06592299789190292,
0.0070394244976341724,
-0.021668341010808945,
0.009743518196046352,
0.036646194756031036,
-0.00707291578873992,
0.03294897451996803,
-0.051398251205682755,
-0.001610773615539074,
-0.018029160797595978,
0.031942203640937805,
0.010779195465147495,
-0.006794400978833437,
0.003718514461070299,
0.0065578315407037735,
0.03300692141056061,
-0.0036801574751734734,
0.015168773010373116,
-0.003828266868367791,
-0.07735979557037354,
-0.0354057140648365,
-0.03362712636590004,
-0.021078472957015038,
0.03754197806119919,
-0.0011440515518188477,
0.007516427896916866,
-0.021245207637548447,
0.004463985562324524,
0.01634126901626587,
0.01783790811896324,
0.026235155761241913,
-0.018859706819057465,
0.056144557893276215,
-0.035207465291023254,
0.05454213544726372,
0.002075650030747056,
0.009737073443830013,
0.10455802083015442,
0.043843064457178116,
0.009161057882010937,
-0.054940737783908844,
-0.009465434588491917,
-0.05567947030067444,
-0.00466111721470952,
0.008130335249006748,
0.017368141561746597,
-0.02834889478981495,
0.01646963134407997,
-0.01749247871339321,
0.008540406823158264,
0.006552516017109156,
0.034021876752376556,
0.027740154415369034,
-0.01166026946157217,
-0.017690539360046387,
0.0021471597719937563,
0.010114172473549843,
-0.006183719728142023,
0.040583930909633636,
-0.08297645300626755,
0.009033646434545517,
0.0021490624640136957,
-0.0009138543391600251,
-0.00927924457937479,
-0.04657746106386185,
0.06276389956474304,
0.03793373703956604,
0.0015545082278549671,
-0.022615419700741768,
0.01528635248541832,
-0.02012784034013748,
-0.011259540915489197,
0.025153055787086487,
0.009643101133406162,
0.029917901381850243,
0.0104933250695467,
0.010255519300699234,
0.0053903223015367985,
-0.015074482187628746,
0.02994767762720585,
-0.007369563449174166,
-0.02050485461950302,
-0.023709598928689957,
0.000590802519582212,
0.014615844935178757,
-0.028086084872484207,
-0.008513974957168102,
-0.02228214405477047,
-0.003421142930164933,
0.0010177893564105034,
-0.04317454621195793,
0.0005678057787008584,
-0.000015593295756843872,
-0.0036346567794680595,
-0.02742714248597622,
-0.05157077684998512,
-0.003679965389892459,
0.03913062810897827,
-0.04761121794581413,
0.025566332042217255,
-0.024751100689172745,
-0.0007392790867015719,
0.04759896174073219,
-0.04701495170593262,
0.030500518158078194,
0.002593870274722576,
-0.04081554710865021,
-0.05330980196595192,
0.006246717646718025,
-0.0034355600364506245,
-0.02975298836827278,
0.011164256371557713,
0.04046713188290596,
0.0020232277456671,
-0.007763419765979052,
-0.008078435435891151,
-0.010608180426061153,
-0.013536871410906315,
0.0453893207013607,
-0.04519837349653244,
-0.04221512749791145,
-0.026288555935025215,
-0.018194714561104774,
0.05031636729836464,
0.03479418158531189,
-0.01971624232828617,
0.008832884021103382,
-0.029692761600017548,
-0.0222889743745327,
-0.006451915949583054,
-0.013316120952367783,
-0.04807167127728462,
0.020212195813655853,
-0.016433019191026688,
0.008342256769537926,
-0.016806652769446373,
0.04884623736143112,
0.04910406842827797,
-0.04426657408475876,
0.017729677259922028,
0.01996147818863392,
-0.031239677220582962,
0.016115082427859306,
-0.013700171373784542,
-0.029906028881669044,
0.047199591994285583,
-0.011834506876766682,
0.0026354994624853134,
-0.06403595209121704,
-0.01297727506607771,
-0.028269566595554352,
-0.04028177261352539,
-0.0217522531747818,
0.0403083898127079,
0.024209870025515556,
-0.009806602261960506,
-0.012150350958108902,
-0.008577058091759682,
-0.0030341879464685917,
0.0012355154613032937,
-0.026465075090527534,
0.021744774654507637,
0.03502977639436722,
0.012907755561172962,
-0.012691987678408623,
0.03627493977546692,
-0.004758818075060844,
-0.037800371646881104,
-0.0003886526683345437,
0.034815460443496704,
0.023384371772408485,
0.0017142753349617124,
0.013230197131633759,
0.018278291448950768,
0.03381616994738579,
-0.0013342933962121606,
0.026126766577363014,
0.0515405610203743,
-0.03155594691634178,
-0.038938701152801514,
0.019631264731287956,
0.0006151374545879662,
0.0342995785176754,
0.04812859371304512,
0.012417682446539402,
0.015279962681233883,
0.062191907316446304,
-0.002897962462157011,
-0.035058677196502686,
-0.028343267738819122,
-0.0032172154169529676,
0.025516362860798836,
-0.038740143179893494,
0.012560516595840454,
-0.015598472207784653,
-0.004707797896116972,
0.031326618045568466,
-0.04340529441833496,
-0.016806479543447495,
0.005714802537113428,
0.0058475034311413765,
0.0030773465987294912,
-0.07638001441955566,
-0.00857552420347929,
0.007171466946601868,
0.0059624179266393185,
0.016211820766329765,
-0.010437446646392345,
0.03912928327918053,
0.04962985962629318,
-0.002321437234058976,
-0.07507011294364929,
-0.009227867238223553,
0.019763696938753128,
0.01914331503212452,
0.009362583979964256,
-0.054117586463689804,
0.0191293153911829,
0.004016186576336622,
-0.06870920211076736,
-0.0037836863193660975,
-0.011833912692964077,
-0.06428591907024384,
-0.07186528295278549,
0.004570110235363245,
-0.0033665194641798735,
0.04229382425546646,
0.011809679679572582,
0.03130929917097092,
0.03343052417039871,
-0.008100063540041447,
-0.020301945507526398,
-0.002410627668723464,
0.003892843844369054,
0.01093930285423994,
-0.02713571861386299,
-0.0145442895591259,
0.049485258758068085,
-0.018766509369015694,
-0.025459524244070053,
0.007630389183759689,
0.008911811746656895,
0.018876126036047935,
0.012786188162863255,
-0.0009878926211968064,
-0.005263293161988258,
0.04086226969957352,
0.006206914316862822,
0.020524494349956512,
-0.04837397485971451,
-0.0084513695910573,
0.02403450943529606,
-0.002785008167847991,
-0.004581780638545752,
0.017312921583652496,
0.04346867650747299,
-0.024125009775161743,
-0.03561142459511757,
0.009657938964664936,
-0.002011419739574194,
-0.008008272387087345,
-0.019947396591305733,
0.0022194008342921734,
0.037702009081840515,
0.0005830147420056164,
-0.0014859031653031707,
-0.04185696691274643,
-0.03870691731572151,
0.0050320918671786785,
-0.01063191145658493,
-0.04466793313622475,
0.0032916886266320944,
-0.02992895431816578,
-0.07107768207788467,
0.04893455654382706,
0.030448928475379944,
-0.024774547666311264,
-0.0013015511212870479,
0.0042535108514130116,
-0.01037729810923338,
0.01930428296327591,
0.012439293786883354,
0.028542410582304,
-0.034397028386592865,
0.005326838232576847,
-0.012327002361416817,
-0.01071222685277462,
0.009743272326886654,
-0.05281658098101616,
0.011938512325286865,
-0.044707778841257095,
0.07117673754692078,
-0.018765060231089592,
-0.05743519216775894,
-0.018644003197550774,
-0.005170161370187998,
0.005268243607133627,
0.06408072263002396,
0.040588829666376114,
-0.0010145183186978102,
0.007944620214402676,
-0.004651736468076706,
-0.007754649501293898,
0.03127705305814743,
-0.05309620872139931,
0.002710114698857069,
0.027562696486711502,
-0.0633268654346466,
-0.0008392581949010491,
-0.004871306475251913,
-0.026121366769075394,
0.011505689471960068,
0.05985814332962036,
0.026217922568321228,
0.024827267974615097,
-0.019512154161930084,
-0.055048901587724686,
0.056962281465530396,
-0.024047309532761574,
0.0004052754957228899,
0.07382097095251083,
-0.021949248388409615,
0.010362047702074051,
0.01717793382704258,
-0.02198803424835205,
-0.030805369839072227,
0.010378445498645306,
-0.04396796226501465,
0.014289725571870804,
-0.028507500886917114,
-0.00044512111344374716,
0.020766986533999443,
-0.03659119829535484,
-0.002565261209383607,
0.012396987527608871,
-0.013035397045314312,
-0.006956994999200106,
0.05524052679538727,
-0.023114997893571854,
0.015552058815956116,
-0.008059641346335411,
0.003032742068171501,
0.022087885066866875,
-0.021990513429045677,
-0.01904275268316269,
0.07569601386785507,
0.04375813528895378,
0.02915290743112564,
0.05691411346197128,
0.048198796808719635,
0.010038313455879688,
-0.0048688133247196674,
-0.015540564432740211,
-0.012793421745300293,
-0.013574088923633099,
-0.010057630948722363,
0.022072602063417435,
0.015250176191329956,
0.010839906521141529,
0.04916060343384743,
-0.032994043081998825,
0.09507165849208832,
-0.03796202316880226,
0.011161158792674541,
-0.00870297197252512,
-0.003429706674069166,
-0.026686377823352814,
0.030300362035632133,
0.040649741888046265,
0.03438495099544525,
-0.007083757780492306,
-0.004142420832067728,
-0.028719745576381683,
-0.005332460161298513,
0.056979913264513016,
-0.043113816529512405,
0.04120897129178047,
-0.0035670583602041006,
-0.018456825986504555,
0.020131032913923264,
-0.004599712323397398,
-0.01700223982334137,
-0.012753235176205635,
0.013356289826333523,
0.0012609062250703573,
-0.01425106916576624,
0.04871685430407524,
0.002362700877711177,
0.010577770881354809,
0.03993583843111992,
-0.08534751087427139,
0.016204258427023888,
0.023744802922010422,
0.01602145843207836,
0.03590262308716774,
0.04833115264773369
] |
<p>If water, air of whatever fluid had a different viscosity, but the same density, would things fall/sink differently? </p>
| 8,820 |
[
-0.027817238122224808,
-0.014349064789712429,
-0.027783485129475594,
0.02057788334786892,
0.01816323958337307,
-0.0012585478834807873,
-0.04041915759444237,
-0.015439316630363464,
0.017414303496479988,
-0.0029053373727947474,
0.02831314317882061,
0.06326442956924438,
0.03927764669060707,
0.0021396023221313953,
0.019936200231313705,
-0.004182671196758747,
-0.0009304830455221236,
0.03147134929895401,
0.006483272649347782,
-0.03608548268675804,
-0.0088889691978693,
0.005429858807474375,
0.05000755935907364,
0.014210115186870098,
-0.02952219918370247,
0.0033700994681566954,
-0.002372736344113946,
-0.056650638580322266,
0.024233127012848854,
-0.00820186361670494,
0.014666561037302017,
-0.004033184144645929,
0.004977086093276739,
0.042690031230449677,
0.038329582661390305,
0.011820139363408089,
-0.046402785927057266,
-0.00907310750335455,
-0.04928354546427727,
0.04944201558828354,
-0.03573258966207504,
-0.03976014256477356,
-0.01808064989745617,
0.035154279321432114,
-0.017839204519987106,
0.011049753986299038,
0.04775039479136467,
-0.05488062649965286,
0.017001517117023468,
-0.08061132580041885,
0.049448829144239426,
0.00828319601714611,
0.04523564875125885,
0.08635128289461136,
-0.009697817265987396,
0.007229267619550228,
0.04182017222046852,
0.06413057446479797,
-0.02174687385559082,
-0.05961126089096069,
0.001182464067824185,
-0.0025481136981397867,
-0.023486092686653137,
-0.01228775829076767,
-0.025672579184174538,
0.03254476189613342,
-0.03815020993351936,
-0.029175758361816406,
0.019311193376779556,
0.012748493812978268,
-0.02462976612150669,
0.02168099954724312,
0.046169813722372055,
-0.007624647114425898,
0.03031056746840477,
-0.015191160142421722,
0.0006198299233801663,
0.0014190847286954522,
0.039913251996040344,
0.027451010420918465,
-0.005517443176358938,
-0.013401421718299389,
0.025893723592162132,
0.012192204594612122,
0.008333060890436172,
-0.009653905406594276,
0.0573616661131382,
-0.0339469313621521,
-0.020511247217655182,
0.042492639273405075,
-0.015677083283662796,
-0.02380399778485298,
0.0027388606686145067,
-0.004466662183403969,
0.0034911921247839928,
-0.03978303074836731,
-0.011919167824089527,
0.0458119697868824,
0.022215023636817932,
-0.01328309252858162,
0.0003223910753149539,
-0.005333526059985161,
0.02298821695148945,
0.0837392657995224,
0.028064332902431488,
-0.05032942816615105,
-0.07259451597929001,
0.01801910810172558,
-0.046778369694948196,
-0.028214512392878532,
0.01254227850586176,
-0.01690276712179184,
-0.03757259249687195,
-0.029154397547245026,
0.021876618266105652,
-0.017558924853801727,
0.026597056537866592,
-0.04958794638514519,
0.04574495553970337,
0.034126996994018555,
0.0720355287194252,
-0.03220335394144058,
0.03159713372588158,
-0.00009753372432896867,
-0.030530236661434174,
0.03216421604156494,
0.0034798462875187397,
-0.03208474814891815,
-0.03956746309995651,
0.004736593924462795,
-0.06620696187019348,
-0.019623465836048126,
-0.003228524699807167,
-0.032365791499614716,
0.04253634437918663,
-0.008381800726056099,
-0.07221464067697525,
-0.03427769988775253,
0.036519795656204224,
-0.005926147103309631,
-0.072785884141922,
-0.05651095509529114,
-0.00416207080706954,
0.010667339898645878,
0.05253557488322258,
0.02475389838218689,
0.034300193190574646,
0.0037901776377111673,
0.0357760451734066,
0.0006381639395840466,
0.021571330726146698,
0.011296729557216167,
-0.0008839555084705353,
-0.05103246122598648,
0.012234002351760864,
-0.05486611649394035,
-0.012563568539917469,
0.023435570299625397,
0.022082731127738953,
-0.01407975610345602,
-0.007114715408533812,
-0.0378931425511837,
0.018402250483632088,
0.00675240671262145,
0.018453426659107208,
-0.03376316651701927,
0.03262726962566376,
0.01589049957692623,
0.00026754121063277125,
0.008315612562000751,
-0.0013171016471460462,
0.027607828378677368,
-0.03375837579369545,
0.001370393205434084,
0.07444604486227036,
0.004271211568266153,
0.011717808432877064,
-0.0004142145626246929,
0.03941609337925911,
-0.004144981037825346,
-0.027286505326628685,
-0.031836722046136856,
-0.002939722267910838,
-0.015697665512561798,
-0.004316937644034624,
0.019663237035274506,
0.014629077166318893,
-0.02318591997027397,
0.008105623535811901,
-0.034071147441864014,
-0.0006506661884486675,
-0.04819014295935631,
0.015749963000416756,
-0.034882377833127975,
0.021753394976258278,
0.039182569831609726,
0.03685533627867699,
0.036247964948415756,
-0.053363628685474396,
0.010928699746727943,
-0.008688698522746563,
0.012121056206524372,
0.012404202483594418,
0.00646575354039669,
-0.006203359458595514,
0.017592133954167366,
0.029035964980721474,
0.00613502599298954,
-0.013798362575471401,
0.005852344911545515,
-0.03171781077980995,
-0.01083319541066885,
-0.015805033966898918,
0.024921653792262077,
-0.010418002493679523,
0.00623224675655365,
0.04929812252521515,
0.01509932242333889,
0.009567189030349255,
0.032400209456682205,
-0.023546289652585983,
0.06253460794687271,
0.051519110798835754,
-0.011592242866754532,
0.029279286041855812,
0.052673861384391785,
0.012531688436865807,
-0.010156943462789059,
0.024356799200177193,
-0.013936067931354046,
-0.03523729369044304,
0.007105571683496237,
0.027242233976721764,
0.04060063511133194,
-0.0451589934527874,
0.020288953557610512,
0.04631699249148369,
0.0324314683675766,
0.0523354709148407,
0.018307100981473923,
0.03371663764119148,
-0.0523272268474102,
0.007019029930233955,
0.012581433169543743,
0.04205193370580673,
0.018195360898971558,
0.04838116839528084,
0.0576111301779747,
0.04719972610473633,
-0.04488320276141167,
-0.028753625229001045,
-0.011702205054461956,
0.01618291810154915,
0.035588666796684265,
-0.04019305855035782,
-0.013752831146121025,
0.01606699824333191,
-0.02601328305900097,
0.01428305171430111,
0.005754514131695032,
0.006996398791670799,
-0.022198708727955818,
-0.0381467342376709,
-0.005798176396638155,
0.03658129647374153,
0.03647718206048012,
0.0049979230388998985,
-0.020426198840141296,
0.04029184207320213,
-0.026031263172626495,
0.0073130764067173,
-0.029345691204071045,
0.018728580325841904,
-0.023440998047590256,
-0.0009895332623273134,
-0.004732846282422543,
-0.00877054501324892,
0.02613741345703602,
-0.004125021398067474,
-0.04369029030203819,
-0.012054129503667355,
-0.0035961868707090616,
-0.04619834944605827,
0.02352095954120159,
-0.04805858060717583,
0.04462362825870514,
-0.005311623215675354,
-0.030797258019447327,
0.031781431287527084,
-0.0027398255188018084,
0.005772307515144348,
0.026779768988490105,
-0.024496404454112053,
-0.02140563726425171,
0.02220797911286354,
-0.020420752465724945,
-0.001836323644965887,
-0.023315811529755592,
0.013814653269946575,
0.04863642156124115,
-0.028461266309022903,
-0.015880776569247246,
0.015711791813373566,
-0.04501863196492195,
-0.07400695234537125,
-0.01173954177647829,
0.008525093086063862,
0.0205802284181118,
-0.06355703622102737,
0.011433559469878674,
0.047554973512887955,
-0.08643637597560883,
-0.021922990679740906,
-0.014782997779548168,
-0.04197263717651367,
0.036758966743946075,
-0.024484040215611458,
0.05644073337316513,
0.013834791257977486,
-0.018538493663072586,
0.045553795993328094,
0.013633402064442635,
-0.026944709941744804,
-0.01784653775393963,
-0.00394629267975688,
-0.032205212861299515,
-0.02495674043893814,
0.013807063922286034,
0.02884119190275669,
-0.03371158242225647,
-0.01787037029862404,
0.0555252842605114,
0.02031070552766323,
0.04142843931913376,
0.0006768347229808569,
-0.010333789512515068,
0.021031895652413368,
0.07563897967338562,
-0.006627916358411312,
0.04201095551252365,
-0.021876713261008263,
-0.016361117362976074,
0.017820386216044426,
0.009906377643346786,
0.03842351213097572,
0.043162524700164795,
-0.03083757311105728,
0.09123318642377853,
0.0067900000140070915,
0.00018305810226593167,
-0.048315227031707764,
0.008542057126760483,
-0.018284909427165985,
0.024902598932385445,
-0.016265764832496643,
0.04627189412713051,
0.05403529852628708,
0.03258182108402252,
-0.0036861104890704155,
0.03359682112932205,
0.07670948654413223,
-0.015051208436489105,
-0.05332305282354355,
0.00532920565456152,
-0.006668459624052048,
0.06673864275217056,
-0.0008983403677120805,
-0.014478323981165886,
0.07927419990301132,
-0.027362478896975517,
0.02648151107132435,
-0.007583138532936573,
-0.06174004077911377,
0.03818259760737419,
-0.04557007923722267,
0.007367623504251242,
0.00932596530765295,
-0.005064900498837233,
-0.003879179945215583,
0.056813959032297134,
0.017689647153019905,
0.03839954733848572,
-0.005327440332621336,
0.0032651370856910944,
-0.07549265772104263,
0.012938804924488068,
-0.03444123640656471,
0.010166925378143787,
-0.0029485186096280813,
-0.026293843984603882,
-0.00151433190330863,
-0.043300241231918335,
0.015519363805651665,
-0.013762940652668476,
-0.018406858667731285,
-0.04236273467540741,
0.020626183599233627,
0.000609384966082871,
-0.028094103559851646,
0.018776506185531616,
0.038232527673244476,
0.002536687534302473,
0.010937954299151897,
0.07099407911300659,
0.018672769889235497,
0.011720402166247368,
-0.025451678782701492,
-0.019739914685487747,
0.005793411284685135,
-0.007554988842457533,
-0.008149610832333565,
0.02081933245062828,
0.02064652368426323,
0.002004277426749468,
0.011384968645870686,
0.02037356235086918,
0.016518939286470413,
-0.034788984805345535,
0.004156555514782667,
-0.037422336637973785,
-0.063164122402668,
-0.03277915343642235,
0.005645614583045244,
0.04088504984974861,
-0.003814530558884144,
-0.000611704948823899,
-0.02617194689810276,
-0.018113650381565094,
0.0020273250993341208,
0.04676241800189018,
0.032930564135313034,
0.018790341913700104,
-0.03216343745589256,
-0.0340229794383049,
0.0031705780420452356,
-0.012543042190372944,
-0.008300240151584148,
0.020422613248229027,
0.03372304514050484,
-0.020057804882526398,
0.006243555806577206,
0.02267102710902691,
0.0008374289609491825,
-0.007126892916858196,
-0.020182287320494652,
0.002498519141227007,
0.0064740413799881935,
-0.030879884958267212,
-0.005961189046502113,
-0.004889943171292543,
0.01953309215605259,
0.01808915287256241,
-0.00004317025377531536,
-0.013630854897201061,
-0.10125818103551865,
0.0004849980177823454,
0.01910552568733692,
0.009191357530653477,
-0.012180293910205364,
0.020301219075918198,
-0.05784424766898155,
-0.04509103298187256,
0.05184945464134216,
-0.009519824758172035,
0.0081443190574646,
-0.007064851466566324,
0.03340351581573486,
-0.001410677912645042,
-0.01755687966942787,
0.022219974547624588,
0.03096969611942768,
-0.01174838189035654,
-0.00341125694103539,
-0.02053293213248253,
0.004694330971688032,
-0.0019734601955860853,
0.006127208936959505,
0.030191026628017426,
0.0434456467628479,
0.01750355400145054,
0.04478105902671814,
-0.04415149614214897,
-0.018385393545031548,
-0.0638570487499237,
-0.07019326835870743,
0.016349028795957565,
0.00216606049798429,
0.013930728659033775,
0.008289569057524204,
-0.007503125350922346,
-0.07169584929943085,
0.05157783627510071,
-0.02112181857228279,
-0.021811308339238167,
0.027178382501006126,
-0.04320662468671799,
0.040424514561891556,
0.031588636338710785,
0.014545368030667305,
0.023693952709436417,
0.020884908735752106,
-0.018058309331536293,
-0.0440601222217083,
-0.02879057265818119,
0.05563797801733017,
-0.04505066201090813,
-0.033471837639808655,
-0.016279499977827072,
-0.01132473349571228,
-0.00900206621736288,
0.03602619096636772,
0.022498859092593193,
0.02320188842713833,
0.03655402362346649,
-0.03189883753657341,
-0.02384607307612896,
0.005977522116154432,
0.05635353550314903,
-0.02815369889140129,
0.01110701635479927,
0.013957170769572258,
-0.019591806456446648,
-0.023943211883306503,
0.016920391470193863,
-0.0008704342180863023,
-0.0009676878689788282,
0.011692972853779793,
-0.015553905628621578,
0.03901658207178116,
-0.02050444483757019,
-0.021427258849143982,
0.009204428642988205,
-0.05616646260023117,
0.06718398630619049,
-0.002763516968116164,
0.023301824927330017,
0.02060803398489952,
-0.04974411800503731,
0.018342256546020508,
0.02689453586935997,
-0.005887187551707029,
0.04502750560641289,
-0.043997976928949356,
0.04270097240805626,
0.011676271446049213,
-0.0008811313891783357,
-0.06998346745967865,
-0.02714628353714943,
0.01974148489534855,
0.06009431928396225,
0.021910926327109337,
-0.036366116255521774,
0.015168140642344952,
-0.0553181953728199,
-0.0316280871629715,
-0.004895704332739115,
0.045445460826158524,
-0.012385169044137001,
-0.017710870131850243,
0.019308388233184814,
0.0015076602576300502,
0.03471081703901291,
-0.017510537058115005,
-0.020695773884654045,
0.00048112182412296534,
-0.027322260662913322,
-0.012877480126917362,
-0.044085390865802765,
0.05483081936836243,
-0.029877332970499992,
-0.012933067046105862,
-0.004152405541390181,
-0.054038431495428085,
0.03328200429677963,
-0.03023155778646469,
0.04172050207853317,
0.00920114666223526,
-0.0020857970230281353,
0.019763298332691193,
-0.02599371410906315,
0.03663080558180809,
-0.014297177083790302,
0.03409417346119881,
0.005071686580777168,
-0.015790071338415146,
-0.0021960127633064985,
-0.030532928183674812,
0.023589523509144783,
0.015567072667181492,
-0.010201645083725452,
-0.022786999121308327,
0.0963166281580925,
-0.01385042630136013,
-0.03917115554213524,
0.03288544714450836,
0.0021452384535223246,
0.03505507856607437,
-0.009536704048514366,
-0.04484093189239502,
0.020573483780026436,
0.03429381549358368,
-0.016926994547247887,
-0.04687077924609184,
-0.026035645976662636,
-0.0026749621611088514,
0.07398590445518494,
-0.016607778146862984,
0.020840968936681747,
0.019818997010588646,
-0.039393991231918335,
0.03608819842338562,
-0.03429286926984787,
0.004542957525700331,
0.03873160108923912,
-0.036145005375146866,
0.053388651460409164,
-0.006476348266005516,
-0.011713407002389431,
0.0178921427577734,
0.05985940620303154,
0.006376209668815136,
0.03268709033727646,
0.04135483503341675,
0.03351917490363121,
0.029043270274996758,
0.015354793518781662,
-0.05784085392951965,
0.020800622180104256,
-0.04251557216048241,
0.03887763246893883,
-0.0539611279964447,
-0.023360541090369225,
0.043379418551921844,
0.017570821568369865,
0.0015719302464276552,
-0.040556423366069794,
-0.012045253999531269,
-0.009768799878656864,
0.029887370765209198,
0.016361230984330177,
0.03831915557384491,
-0.006373730953782797,
0.0418112613260746,
0.02595927193760872,
0.007283573970198631,
0.0038917846977710724,
-0.0019416309660300612,
-0.06154543533921242,
0.005283172242343426,
-0.027403710409998894,
-0.025385338813066483,
0.023916713893413544,
0.017113210633397102,
-0.041683297604322433,
0.02491980791091919,
0.01749827340245247,
0.010888797231018543,
0.012856929562985897,
0.0042089782655239105,
-0.0209591593593359,
0.0385332852602005,
0.006503337528556585,
0.016071433201432228,
-0.023319188505411148,
-0.004138445481657982,
0.12554723024368286,
0.05307071655988693,
0.049087561666965485,
-0.026804547756910324,
-0.0034370222128927708,
-0.00654770340770483,
0.023704400286078453,
-0.029834719374775887,
-0.0007928417180664837,
0.01637536846101284,
0.034345731139183044,
-0.011066759005188942,
0.07222509384155273,
0.006048500072211027,
-0.02215040661394596,
0.024925407022237778,
-0.02797386236488819,
0.0018038812559098005,
-0.057494208216667175,
0.0038324156776070595,
-0.033486779779195786,
0.06080596521496773,
-0.043365053832530975,
0.028227342292666435,
-0.009583831764757633,
0.007871420122683048,
-0.01842624880373478,
-0.0339142344892025,
0.008058985695242882,
0.004469411913305521,
-0.056261032819747925,
0.0045965625904500484,
0.03385831415653229,
-0.013042132370173931,
-0.07230636477470398,
0.041478369385004044,
0.011553862132132053,
-0.04819409176707268,
0.0026009371504187584,
-0.0017765352968126535,
-0.0014686805661767721,
0.016667837277054787,
-0.022797197103500366,
-0.016042126342654228,
-0.04982127249240875,
-0.0019661893602460623,
-0.029630137607455254,
0.013024953193962574,
-0.018178002908825874,
-0.0015853062504902482,
-0.005388407036662102,
0.001382449408993125,
-0.0018573661800473928,
-0.0315384641289711,
-0.01703629270195961,
-0.030147787183523178,
0.0221794955432415,
0.012399151921272278,
0.001946549047715962,
-0.007297655567526817,
-0.0026879976503551006,
0.015174753032624722,
0.01762166991829872,
-0.022871943190693855,
0.0004669371119234711,
-0.020638227462768555,
0.010935114696621895,
0.042895905673503876,
-0.04383925348520279,
-0.02642524056136608,
-0.017816968262195587,
0.014991569332778454,
-0.022862985730171204,
-0.01593005284667015,
0.01352999359369278,
0.04456525668501854,
0.02597637102007866,
0.02449091710150242,
0.011154682375490665,
-0.013921371661126614,
-0.05846695974469185,
0.06946108490228653,
-0.020671594887971878,
0.01313098892569542,
-0.04114663600921631,
-0.01818113774061203,
0.01935899816453457,
0.03463676944375038,
-0.0344100259244442,
-0.007943723350763321,
-0.02816713973879814,
0.046908117830753326,
0.009046074002981186,
-0.02374184876680374,
-0.010216347873210907,
-0.008420967496931553,
-0.03549688681960106,
0.016016755253076553,
0.01561353076249361,
0.0478937067091465,
0.01527042593806982,
-0.01850185915827751,
-0.011587475426495075,
0.012158871628344059,
-0.02589615061879158,
0.021556008607149124,
-0.008524480275809765,
-0.031665775924921036,
-0.04022970050573349,
0.025664936751127243,
0.0006749258027411997,
-0.01637118309736252,
-0.04455180838704109,
-0.04752738028764725,
0.0009072531829588115,
-0.018984723836183548,
0.012919251807034016,
-0.006744985468685627,
0.0490589514374733,
-0.0352025143802166,
0.01818396896123886,
-0.011521732434630394,
-0.007856522686779499,
-0.07789280265569687,
-0.017659885808825493,
-0.0019253573846071959,
-0.023809989914298058,
0.012600536458194256,
0.0051543270237743855,
-0.07089859992265701,
0.029750322923064232,
-0.00392453046515584,
0.002997166942805052,
0.004977712407708168,
-0.0018576881848275661,
0.03847636282444,
0.00006899339496158063,
0.04051023721694946,
-0.016353169456124306,
-0.04701671749353409,
0.020438995212316513,
-0.01645362190902233,
-0.0653621032834053,
0.038739364594221115,
0.00007513124000979587,
0.04464683309197426,
0.03171904757618904,
-0.01204697135835886,
-0.022717885673046112,
0.10488000512123108,
-0.026061462238430977,
0.01697390526533127,
-0.011508427560329437,
-0.015929456800222397,
-0.02351999469101429,
0.02777254395186901,
0.0388500839471817,
-0.02962629683315754,
-0.03090693987905979,
0.03904866427183151,
0.029187919571995735,
0.0016069961711764336,
-0.003450765274465084,
0.023045429959893227,
-0.033667124807834625,
0.010177018120884895,
0.022017473354935646,
-0.0033805209677666426,
0.02005186304450035,
0.021690608933568,
-0.033267851918935776,
0.014361741952598095,
0.044868290424346924,
-0.003390895202755928,
-0.12306265532970428,
0.0180211141705513,
0.028582729399204254,
0.009113314561545849,
-0.002437516814097762,
-0.04566086083650589,
0.026207366958260536,
-0.01830839179456234,
-0.08617249876260757,
-0.022705301642417908,
-0.026020003482699394,
0.00442936597391963,
-0.029645806178450584,
0.008610155433416367,
0.008704359643161297,
0.07681181281805038,
0.006813827436417341,
0.022745437920093536,
-0.014923625625669956,
0.00590586569160223,
0.0018739638617262244,
0.009722555987536907,
-0.016540221869945526,
0.005465668626129627,
0.0027699670754373074,
-0.0006741193355992436,
0.028757145628333092,
-0.019518157467246056,
-0.030548417940735817,
0.003947143442928791,
-0.016171324998140335,
0.032255303114652634,
-0.021870121359825134,
-0.010052706114947796,
-0.013806215487420559,
-0.022450998425483704,
-0.008607079274952412,
0.020880762487649918,
-0.04041140899062157,
0.02064373902976513,
0.008980423212051392,
0.034338537603616714,
-0.02096063829958439,
-0.015502220951020718,
0.0161238182336092,
-0.04586596041917801,
-0.042442306876182556,
0.007310384884476662,
-0.03188450261950493,
-0.012011007405817509,
-0.0031286259181797504,
0.002655219053849578,
0.05325210466980934,
-0.007154084276407957,
-0.009606696665287018,
-0.03426150232553482,
-0.002307709539309144,
0.03212102875113487,
0.010037642903625965,
-0.02890937589108944,
0.03400477021932602,
0.013944401405751705,
0.00356435333378613,
-0.05431392043828964,
0.005968336481601,
-0.009709575213491917,
-0.026065684854984283,
-0.036301881074905396,
-0.028631094843149185,
-0.00641988031566143,
-0.01757935807108879,
-0.04452051967382431,
-0.0008342511719092727,
0.026328522711992264,
0.05848248675465584,
0.01750188134610653,
0.025690456852316856,
-0.033659953624010086,
-0.025646742433309555,
-0.07582856714725494,
0.040130868554115295,
-0.035212382674217224,
-0.004931505303829908,
-0.01227371022105217,
0.011767463758587837,
0.005788001697510481,
0.017300961539149284,
0.05667261406779289,
0.00009664578101364896,
0.019165078178048134,
-0.001680646906606853,
0.0018036874243989587,
-0.003649784019216895,
-0.009578847326338291,
-0.010593277402222157,
-0.0008768856641836464,
-0.05318179726600647,
0.032516829669475555,
0.010192688554525375,
0.01259162463247776,
-0.03063375875353813,
0.0059802052564918995,
-0.029488131403923035,
0.010750493966042995,
-0.01961028017103672,
-0.007771357893943787,
0.04894169792532921,
0.03200289234519005,
-0.03465384244918823,
0.049206092953681946,
-0.01664554513990879,
0.0045944927260279655,
-0.0060534668155014515,
-0.04570133611559868,
-0.05584029480814934,
0.07059603184461594,
-0.029915237799286842,
-0.027903081849217415,
0.010899228975176811,
-0.033106185495853424,
-0.024248849600553513,
-0.02620493806898594,
0.027759505435824394,
-0.01738032139837742,
-0.026323556900024414,
-0.003778034821152687,
0.04581316560506821,
0.04884164035320282,
0.025723213329911232,
-0.028044363483786583,
-0.008764763362705708,
0.02728387899696827,
-0.017564823850989342,
0.026080705225467682,
0.06034493073821068,
0.06831590086221695,
0.015556425787508488,
-0.02988877147436142,
0.011305460706353188,
0.022589227184653282,
0.018816079944372177,
0.046168286353349686,
-0.007023253943771124,
0.010468634776771069,
-0.03895651549100876,
0.0012466562911868095,
0.02124786376953125,
-0.004920339677482843,
0.009203014895319939,
0.004465972539037466,
0.09079642593860626,
-0.0031409040093421936,
-0.004111871588975191,
-0.020897453650832176,
-0.014479419216513634,
-0.009746147319674492,
0.03544001653790474,
0.004936842247843742,
0.02703281119465828,
0.005841348320245743,
-0.025567416101694107,
-0.030485419556498528,
-0.01397626381367445,
0.017867157235741615,
-0.00037036003777757287,
0.005249449517577887,
-0.01435793749988079,
0.02272389456629753,
0.02082349732518196,
0.002427287632599473,
-0.0431906133890152,
-0.01551403570920229,
0.010497444309294224,
0.011598659679293633,
0.039420999586582184,
0.008646885864436626,
-0.035440053790807724,
-0.02241850271821022,
0.0660000741481781,
-0.06396659463644028,
-0.05688852444291115,
0.011442789807915688,
0.0587574727833271,
0.009581862017512321,
-0.019676927477121353
] |
<p>Questions about nuclear fuel:</p>
<p>Does nuclear chain reaction start in fuel pellets even before they being installed in reactor? If not, why not? My understanding is that since the fuel pellets are uranium enriched, they should be enough to sustain chain reaction. It seems I am wrong (found no reference support me), but I don't know why.</p>
<p>Also, for fuel pellets and rods are radioactive, how do we transport them? There are plenty of articles about spent fuel rod transport, but I found almost zero about "fresh" fuel rod transport. According to <a href="http://en.wikipedia.org/wiki/Nuclear_fuel_cycle#Transport_of_radioactive_materials">Nuclear fuel cycle page of wikipedia</a>:</p>
<p><em><code>In the case of some materials, such as fresh uranium fuel assemblies, the radiation levels are negligible and no shielding is required.</code></em></p>
<p>Erruh. This is against my understanding of the first question. Can anyone help relieve my headache?</p>
| 8,821 |
[
0.009617303498089314,
-0.07041631639003754,
-0.019148828461766243,
0.005644135642796755,
-0.026812495663762093,
-0.0009362699347548187,
-0.026078995317220688,
-0.0408211424946785,
0.014977344311773777,
-0.05176959186792374,
0.03741757571697235,
0.016948098316788673,
0.03520973399281502,
-0.0058737643994390965,
0.03269704058766365,
-0.011111880652606487,
-0.0030922042205929756,
-0.056180864572525024,
-0.019200120121240616,
-0.025964127853512764,
0.005883268546313047,
-0.028329631313681602,
0.016095515340566635,
-0.01605713739991188,
-0.01275971531867981,
0.028814319521188736,
-0.0027884994633495808,
0.03426646813750267,
0.05385526269674301,
0.04804522171616554,
0.0122684296220541,
-0.03869501128792763,
0.015668582171201706,
0.00676683196797967,
0.013944791629910469,
0.013882484287023544,
-0.04429341107606888,
0.00257068476639688,
-0.033999960869550705,
0.005875694565474987,
-0.011048546992242336,
-0.0346638485789299,
0.0029362745117396116,
0.029978638514876366,
0.02468797378242016,
0.02077363058924675,
-0.014700922183692455,
0.025543782860040665,
0.061304859817028046,
-0.031354352831840515,
0.017279407009482384,
-0.011877459473907948,
0.03680422157049179,
0.013388793915510178,
0.03359265625476837,
-0.0036392270121723413,
0.07308650761842728,
0.03691345453262329,
-0.006235278677195311,
-0.009437709115445614,
-0.0007283583399839699,
-0.01730109192430973,
-0.007777506951242685,
-0.0002504618896637112,
0.008866343647241592,
0.015284157358109951,
-0.014460999518632889,
-0.024153942242264748,
0.007441684138029814,
0.006715311668813229,
-0.00005893478373764083,
0.0038454325404018164,
-0.016037840396165848,
-0.009886222891509533,
0.029873255640268326,
-0.019733954221010208,
0.040086451917886734,
-0.018651140853762627,
0.011630814522504807,
0.03637462854385376,
-0.03569844737648964,
0.02636902779340744,
0.005086296238005161,
0.028869055211544037,
0.0078076692298054695,
0.0010737681295722723,
0.09369691461324692,
-0.0003904751793015748,
0.05588764697313309,
-0.0018296788912266493,
0.018033290281891823,
0.006790744140744209,
0.038963425904512405,
0.024138983339071274,
0.02846408449113369,
0.028834551572799683,
0.0034985525999218225,
0.045391008257865906,
0.007022725883871317,
0.0013619158416986465,
0.0708363950252533,
-0.017873501405119896,
0.0635959729552269,
0.07272648066282272,
-0.0034607863053679466,
-0.01049688458442688,
-0.03560832515358925,
0.012790260836482048,
-0.012020819820463657,
-0.03044090047478676,
-0.07305146753787994,
0.003349460894241929,
-0.017941854894161224,
-0.020819613710045815,
-0.01773790270090103,
-0.029418054968118668,
0.01650361530482769,
-0.03531905636191368,
0.06385914981365204,
0.036297742277383804,
0.04328412190079689,
0.01596952974796295,
0.037367936223745346,
-0.030276689678430557,
-0.089933380484581,
-0.0013689158950001001,
0.01834731362760067,
-0.019285233691334724,
-0.026784153655171394,
0.03311672434210777,
-0.009845959953963757,
-0.004458886105567217,
0.0154110761359334,
0.020325850695371628,
0.05877073481678963,
0.030930709093809128,
-0.10965041816234589,
-0.07540187239646912,
0.034566108137369156,
0.000607611087616533,
-0.012314294464886189,
-0.09909725189208984,
0.026026247069239616,
0.010607810690999031,
0.031197786331176758,
-0.03538782522082329,
-0.026892349123954773,
-0.012774649076163769,
0.023137709125876427,
-0.011484367772936821,
-0.030848387628793716,
-0.030292058363556862,
0.03884461894631386,
-0.038489848375320435,
0.014546523801982403,
-0.07805273681879044,
0.026912512257695198,
0.041634153574705124,
0.017791956663131714,
-0.05827457830309868,
0.06197500228881836,
-0.0346955806016922,
0.026944570243358612,
0.0021613321732729673,
-0.0366470143198967,
-0.013394961133599281,
0.06339617818593979,
0.022354451939463615,
0.028401723131537437,
0.03153632581233978,
0.055893439799547195,
0.051679521799087524,
0.006819510366767645,
-0.0015241457149386406,
0.039145328104496,
-0.05824858322739601,
-0.013923635706305504,
-0.00668557221069932,
-0.017764922231435776,
0.0074362256564199924,
-0.03033406473696232,
-0.006540675647556782,
-0.02337283454835415,
-0.01473073847591877,
0.022089768201112747,
0.02552979625761509,
0.024791957810521126,
-0.007585445418953896,
-0.0059610349126160145,
-0.016766777262091637,
-0.02039320394396782,
-0.03549380600452423,
0.013948020525276661,
-0.045496709644794464,
-0.047223806381225586,
-0.029979338869452477,
-0.01283059548586607,
0.018822139129042625,
-0.026156658306717873,
-0.032705195248126984,
-0.0007105940021574497,
0.0008220127783715725,
0.0026971304323524237,
0.009241555817425251,
0.004483867436647415,
0.053011056035757065,
-0.016413189470767975,
-0.013486945070326328,
0.02401023358106613,
-0.02113327570259571,
-0.010924160480499268,
-0.030219782143831253,
-0.023135516792535782,
-0.01947876624763012,
-0.0040102009661495686,
-0.06386006623506546,
-0.018611354753375053,
-0.011616140604019165,
0.01113285031169653,
0.047480180859565735,
0.006390202324837446,
0.08633528649806976,
0.03744525462388992,
0.019505485892295837,
-0.018213726580142975,
-0.009803441353142262,
0.0007449596305377781,
0.02070305310189724,
-0.023502875119447708,
-0.035648226737976074,
-0.07208969444036484,
-0.03961314633488655,
0.022685304284095764,
-0.010468067601323128,
-0.03843061253428459,
0.020112430676817894,
0.015126672573387623,
0.02411225438117981,
0.007748238742351532,
-0.006378582213073969,
-0.04688037186861038,
-0.019562993198633194,
0.022136755287647247,
0.03547275811433792,
-0.004919832572340965,
0.004772706888616085,
-0.010482515208423138,
0.011385960504412651,
0.004395916126668453,
-0.008427408523857594,
0.014043226838111877,
0.02984382025897503,
-0.026547832414507866,
-0.013529335148632526,
0.0045117479749023914,
-0.04242194816470146,
0.0632786899805069,
-0.01722642406821251,
0.022268297150731087,
-0.016796205192804337,
0.02563275210559368,
0.001768234884366393,
0.016316603869199753,
-0.01923857256770134,
-0.001320382347330451,
0.038428910076618195,
-0.03328924998641014,
-0.027225565165281296,
0.01516699604690075,
-0.03157195821404457,
0.030499646440148354,
-0.012314907275140285,
-0.0010595147032290697,
-0.013559237122535706,
0.014127364382147789,
0.02598145790398121,
-0.010795059613883495,
0.058578070253133774,
-0.07166805863380432,
-0.02475261129438877,
-0.04728918522596359,
-0.04258100315928459,
-0.004621430765837431,
0.0016588675789535046,
-0.053982846438884735,
0.040148716419935226,
-0.0033078088890761137,
-0.005347591824829578,
0.033309243619441986,
-0.012054097838699818,
-0.03803568705916405,
0.03435870632529259,
-0.011897243559360504,
-0.05790366977453232,
-0.011573780328035355,
-0.01483626663684845,
0.019372928887605667,
-0.0013179827947169542,
-0.00028789506177417934,
0.0938422679901123,
-0.010561807081103325,
-0.041575610637664795,
0.004758141934871674,
-0.08385986089706421,
0.016449278220534325,
0.004204744938760996,
0.0038018636405467987,
-0.011385554447770119,
-0.023495418950915337,
0.0062360879965126514,
0.00975745264440775,
-0.05882895365357399,
0.009300866164267063,
-0.0361609123647213,
-0.03782442957162857,
0.04062362387776375,
-0.017385531216859818,
0.04491318762302399,
0.0032277237623929977,
-0.006079515907913446,
0.042590659111738205,
0.03624036908149719,
-0.025507546961307526,
-0.00609148945659399,
-0.01056398544460535,
-0.01640225574374199,
-0.015851708129048347,
0.012096567079424858,
0.03246438875794411,
0.03841587156057358,
-0.011411688290536404,
0.021211815997958183,
0.034642551094293594,
0.0004322364111430943,
0.00006999527977313846,
0.019775820896029472,
-0.012445321306586266,
0.049011945724487305,
0.00887085497379303,
0.02493748627603054,
0.0008262093178927898,
-0.020618533715605736,
0.01567831262946129,
-0.036528076976537704,
0.0409037210047245,
0.012488266453146935,
-0.044228795915842056,
0.037091150879859924,
0.018394669517874718,
-0.0004148275766056031,
-0.025114374235272408,
0.049850136041641235,
-0.0009997030720114708,
-0.017700504511594772,
0.017989631742239,
0.010608768090605736,
0.05542926490306854,
-0.008131410926580429,
0.008483574725687504,
0.0016309572383761406,
0.08670826256275177,
-0.01681847684085369,
-0.014385745860636234,
-0.009439290501177311,
-0.038243673741817474,
0.02212308533489704,
0.007987488992512226,
0.016552748158574104,
0.04667389765381813,
0.03714961186051369,
0.016722077503800392,
0.014784774743020535,
-0.019027283415198326,
-0.003209287766367197,
-0.10282044112682343,
-0.03187589719891548,
0.005693609360605478,
0.041448164731264114,
-0.005534195341169834,
0.047089945524930954,
0.012619293294847012,
0.00040173777961172163,
-0.013835839927196503,
-0.00398661894723773,
-0.06514208018779755,
0.01976051554083824,
-0.04183449596166611,
-0.020428352057933807,
0.014032667502760887,
-0.01990262232720852,
-0.07569056749343872,
-0.024863624945282936,
-0.057138919830322266,
0.021706951782107353,
-0.0026366261299699545,
-0.061935700476169586,
0.018202362582087517,
-0.03423098474740982,
-0.04557758569717407,
-0.007016764022409916,
-0.004075442906469107,
0.04203582555055618,
0.015845978632569313,
0.028339598327875137,
0.02416558563709259,
-0.050338514149188995,
0.0006986507796682417,
-0.02484383061528206,
0.017465414479374886,
0.006168069783598185,
0.04963391274213791,
0.027887534350156784,
0.02794758602976799,
-0.062011584639549255,
-0.0013669548789039254,
0.02130601368844509,
0.03939620032906532,
0.004010793752968311,
-0.024157539010047913,
0.0008140259305946529,
-0.04234126955270767,
0.005248024594038725,
-0.009367031045258045,
-0.007360830903053284,
-0.033401139080524445,
0.015556009486317635,
0.012563305906951427,
-0.022990349680185318,
-0.03873063996434212,
-0.0011831562733277678,
0.06614135205745697,
-0.021257467567920685,
0.008162850514054298,
-0.02545616775751114,
-0.027009665966033936,
-0.004130673129111528,
-0.009060097858309746,
0.00033099864958785474,
0.0069021559320390224,
-0.01000659167766571,
0.03230443224310875,
0.016940638422966003,
0.007896622642874718,
-0.01957022398710251,
0.014446421526372433,
0.0016774182440713048,
0.01806267350912094,
0.032710980623960495,
0.0018437531543895602,
0.055478960275650024,
0.0003827569307759404,
0.02361869625747204,
-0.006955575663596392,
0.0025621133390814066,
-0.07022900879383087,
-0.008994709700345993,
0.03516065329313278,
0.08056751638650894,
-0.035691265016794205,
-0.010231942869722843,
-0.03598827123641968,
-0.03524138033390045,
0.07020416110754013,
0.0028260110411792994,
0.06653385609388351,
-0.06684550642967224,
-0.029291104525327682,
-0.0036113576497882605,
-0.044198695570230484,
-0.03065737895667553,
-0.0013497297186404467,
-0.027298251166939735,
-0.006448701024055481,
-0.013703533448278904,
-0.021132949739694595,
-0.01789531670510769,
0.020881447941064835,
0.05435477942228317,
0.0505400113761425,
-0.014169293455779552,
0.022715553641319275,
-0.03989279642701149,
0.013324121944606304,
0.006934662815183401,
-0.05399753153324127,
0.012825963087379932,
0.0017924204003065825,
-0.024578016251325607,
0.04690057039260864,
-0.04368624463677406,
-0.03881753608584404,
0.050653208047151566,
0.045152973383665085,
0.004613126162439585,
-0.058717548847198486,
-0.06069439649581909,
0.05639863759279251,
0.05659590661525726,
-0.015405511483550072,
0.04623212292790413,
0.06491705030202866,
-0.03952762484550476,
0.017094392329454422,
-0.05079025775194168,
0.008808708749711514,
-0.01948135532438755,
0.023485930636525154,
0.006437782198190689,
0.025282131507992744,
-0.0068343947641551495,
0.046862341463565826,
0.004291422199457884,
-0.022831933572888374,
-0.0017890152521431446,
-0.014692753553390503,
0.017169658094644547,
0.00311466446146369,
0.008499966003000736,
0.015671314671635628,
-0.02816404029726982,
-0.009685741737484932,
-0.006258922629058361,
-0.04988454654812813,
-0.002221423899754882,
-0.013467550277709961,
0.020271990448236465,
-0.004510299302637577,
-0.014013417065143585,
0.01590832509100437,
-0.03445087745785713,
-0.007108176592737436,
0.035965148359537125,
-0.027141975238919258,
0.0485028401017189,
0.030374014750123024,
-0.010250185616314411,
0.03229527175426483,
-0.04426433891057968,
-0.008860765025019646,
0.050940364599227905,
-0.011449466459453106,
-0.006527922116219997,
0.0007819518214091659,
0.06381667405366898,
-0.016816982999444008,
0.008285821415483952,
-0.0587688647210598,
-0.06815668940544128,
0.038701269775629044,
-0.008621679618954659,
-0.029906168580055237,
-0.05113982409238815,
-0.0008746261009946465,
-0.016788119450211525,
-0.03437567502260208,
-0.0014911213656887412,
0.05832970514893532,
-0.03390498086810112,
-0.022185014560818672,
0.033220481127500534,
0.016340581700205803,
0.08728994429111481,
-0.015766562893986702,
-0.03554154187440872,
-0.009575467556715012,
0.002880834974348545,
-0.002718533854931593,
-0.001693693338893354,
0.039994336664676666,
-0.014093163423240185,
-0.03977108746767044,
0.0020652958191931248,
0.02677799202501774,
0.053825944662094116,
-0.008492357097566128,
-0.008249934762716293,
0.054969124495983124,
-0.017720000818371773,
-0.006820859853178263,
-0.004131781868636608,
0.013438686728477478,
-0.00557607552036643,
0.03268515318632126,
-0.01808563992381096,
-0.008543841540813446,
-0.04098276048898697,
-0.030749661847949028,
0.03392287343740463,
-0.0013323859311640263,
0.0069862063974142075,
0.0374634712934494,
0.023216374218463898,
-0.028171274811029434,
0.0072061046957969666,
0.01932649314403534,
-0.028059259057044983,
-0.004670095629990101,
-0.022355763241648674,
-0.013197745196521282,
0.020864402875304222,
-0.03965005651116371,
-0.029657630249857903,
-0.053570136427879333,
-0.02210576832294464,
-0.010506036691367626,
0.02500019036233425,
-0.022010507062077522,
0.04611833766102791,
-0.01618027687072754,
0.0006760531687177718,
0.01665417291224003,
0.015029900707304478,
-0.05192198604345322,
-0.00454819155856967,
-0.004628385882824659,
0.04428447410464287,
0.003972896374762058,
-0.011008954606950283,
0.012036818079650402,
0.04017988592386246,
0.0290831271559,
0.027672618627548218,
0.02617465704679489,
-0.012881498783826828,
0.02632906474173069,
0.015256748534739017,
-0.024727310985326767,
0.004835835192352533,
-0.04111425578594208,
0.024058407172560692,
0.030162686482071877,
-0.041188471019268036,
0.06227993220090866,
0.01565760374069214,
-0.00177905207965523,
-0.03512517362833023,
-0.017077740281820297,
-0.02563260681927204,
-0.011735307984054089,
-0.02523496188223362,
-0.01726258173584938,
-0.007124996278434992,
-0.0034866631031036377,
0.035533357411623,
-0.03671364113688469,
0.010497400537133217,
0.030725862830877304,
-0.07029572874307632,
-0.0353790819644928,
-0.001814987976104021,
-0.04914466664195061,
0.034941814839839935,
0.003016230883076787,
-0.04115787521004677,
-0.024190548807382584,
-0.03772493079304695,
0.03670515865087509,
0.017124513164162636,
0.06637805700302124,
-0.0031123838853091,
0.04480160027742386,
0.01064069103449583,
0.04247177764773369,
-0.018859757110476494,
0.022180020809173584,
0.11008382588624954,
0.008010301738977432,
-0.02907153032720089,
-0.04357096180319786,
-0.010479401797056198,
-0.02390941046178341,
0.03241973742842674,
-0.01859448477625847,
0.0002093916409648955,
0.019634772092103958,
0.011711405590176582,
0.0608569011092186,
0.05386149883270264,
-0.018053477630019188,
0.032843321561813354,
0.03737874701619148,
-0.039490118622779846,
-0.03342599421739578,
0.020897019654512405,
0.005547569133341312,
-0.03229275718331337,
0.0005363993695937097,
-0.04403931275010109,
0.019125066697597504,
0.03747528791427612,
-0.025896629318594933,
-0.0252238642424345,
-0.012499455362558365,
0.04740529507398605,
-0.0035804330836981535,
-0.015287998132407665,
-0.026854757219552994,
-0.015458863228559494,
-0.0315108560025692,
0.019347066059708595,
0.016373811289668083,
0.02487165853381157,
-0.009076145477592945,
0.02179807238280773,
0.01978369988501072,
0.018352393060922623,
0.003276168368756771,
-0.010450437664985657,
0.03426351025700569,
-0.025736453011631966,
0.015843968838453293,
0.023119652643799782,
-0.0034411035012453794,
-0.05277927964925766,
-0.006378760561347008,
-0.0059263333678245544,
-0.009563904255628586,
0.01856387034058571,
-0.024959217756986618,
-0.03449074551463127,
0.020789217203855515,
0.019865911453962326,
-0.007095053791999817,
-0.016390156000852585,
-0.05688318610191345,
-0.012517541646957397,
-0.026103196665644646,
0.030797258019447327,
0.011682085692882538,
0.005664271302521229,
0.017229581251740456,
-0.051401134580373764,
0.009179665707051754,
-0.010773043148219585,
0.016678478568792343,
-0.06082376837730408,
0.008885135874152184,
-0.05485333874821663,
-0.015737950801849365,
0.03782754763960838,
0.03232135251164436,
0.04134030640125275,
0.009052924811840057,
-0.010302705690264702,
0.02505585551261902,
-0.02697841450572014,
0.05706557258963585,
0.004954174626618624,
-0.028515176847577095,
-0.0756664052605629,
0.009725243784487247,
0.0024008408654481173,
0.04535161703824997,
0.023006372153759003,
-0.0007487332331947982,
-0.02174459397792816,
0.038140732795000076,
0.015200928784906864,
-0.02897706814110279,
-0.040823712944984436,
0.03188490495085716,
-0.014132258482277393,
0.00524640129879117,
-0.016015220433473587,
0.02876897156238556,
0.027979519218206406,
0.011806987226009369,
0.000007734633982181549,
0.022900231182575226,
-0.0019107410917058587,
0.022877918556332588,
0.011402497068047523,
0.003381722141057253,
-0.011592098511755466,
-0.0019231534097343683,
0.009212981909513474,
-0.0047689820639789104,
-0.012170779518783092,
0.006721263285726309,
-0.04368055611848831,
-0.0016638293163850904,
0.017459183931350708,
-0.027646299451589584,
0.01627550646662712,
-0.05822204798460007,
0.012759394943714142,
-0.008367604576051235,
0.02380542829632759,
-0.05726262927055359,
-0.005852514877915382,
0.009837854653596878,
0.010149378329515457,
-0.04071429744362831,
0.03419427201151848,
-0.009053914807736874,
0.01630529575049877,
0.02746974304318428,
-0.0004321236629039049,
0.002240303670987487,
0.002034873003140092,
-0.016297535970807076,
0.010179245844483376,
0.026843231171369553,
0.006452235858887434,
-0.008542971685528755,
0.03270096331834793,
0.0026050503365695477,
-0.040324464440345764,
0.028901375830173492,
-0.0011507398448884487,
0.01543122623115778,
0.0005822038510814309,
-0.015535089187324047,
0.024427201598882675,
0.09729298949241638,
0.0006019608117640018,
-0.01275321003049612,
-0.005878224968910217,
-0.006884757429361343,
0.009061096236109734,
0.0143324239179492,
0.008370215073227882,
-0.017674362286925316,
0.015390940010547638,
0.032081615179777145,
0.035796940326690674,
0.001643116818740964,
0.0115516921505332,
-0.033421944826841354,
0.03647442162036896,
0.010967070236802101,
0.040120162069797516,
0.05431654304265976,
-0.010325816459953785,
0.0584452860057354,
-0.017430175095796585,
0.08653786778450012,
0.01934814639389515,
-0.03277911990880966,
-0.045259326696395874,
-0.038179911673069,
-0.003056964138522744,
-0.006371482275426388,
0.01369551569223404,
-0.03440437093377113,
-0.005169568583369255,
0.024089312180876732,
-0.04338319972157478,
0.0013996957568451762,
-0.023070257157087326,
-0.05042755603790283,
-0.057246193289756775,
-0.005968098528683186,
-0.006339391227811575,
0.030530478805303574,
0.062025539577007294,
0.06532017886638641,
0.022459249943494797,
0.005287070292979479,
-0.009473397396504879,
0.02727433107793331,
-0.01755025051534176,
0.03237609937787056,
0.0014840324874967337,
0.009686578996479511,
0.08947932720184326,
-0.016555393114686012,
0.016948791220784187,
0.0023798439651727676,
0.003452592296525836,
0.020032048225402832,
-0.00045102598960511386,
-0.004895429126918316,
0.002350431401282549,
0.04325380548834801,
-0.0021329978480935097,
-0.005738186649978161,
-0.007260051090270281,
0.012312480248510838,
0.008546333760023117,
0.006349367089569569,
-0.04217352718114853,
0.038075581192970276,
0.013599533587694168,
-0.0034226798452436924,
-0.009013586677610874,
0.055134039372205734,
-0.00047847002861090004,
-0.01570276729762554,
-0.002833413891494274,
0.02317090891301632,
0.02498052455484867,
-0.019500143826007843,
0.0063662538304924965,
-0.03374160826206207,
-0.01471718866378069,
0.019206320866942406,
-0.015626903623342514,
0.013531736098229885,
0.019749624654650688,
0.009745086543262005,
0.005049761850386858,
-0.014264339581131935,
-0.009709923528134823,
0.0013290074421092868,
-0.021596865728497505,
0.01423620618879795,
0.010448772460222244,
0.02902442030608654,
0.0004964800900779665,
-0.03426743671298027,
-0.022254249081015587,
0.08124316483736038,
0.027712736278772354,
-0.003277120878919959,
0.022903045639395714,
-0.030289189890027046,
-0.020236743614077568,
-0.03349863365292549,
0.0285207387059927,
0.027557961642742157,
-0.035611867904663086,
-0.04778987914323807,
-0.03140762075781822,
-0.023002324625849724,
0.05006753280758858,
0.03665462136268616,
0.040019840002059937,
-0.027218034490942955,
0.018640683963894844,
0.006590855773538351,
0.04721516743302345,
-0.05154227092862129,
0.03449305146932602,
0.013584695756435394,
-0.04798204451799393,
-0.019746221601963043,
0.015379560180008411,
-0.03496440872550011,
0.027143456041812897,
0.02462749369442463,
-0.004853523336350918,
-0.024104779586195946,
-0.0393267497420311,
-0.022651810199022293,
0.04382285475730896,
0.012542901560664177,
0.01680191047489643,
0.06690553575754166,
-0.0031744136940687895,
0.026696782559156418,
0.03231470659375191,
0.007259638514369726,
-0.03218526765704155,
0.03738494962453842,
-0.05636903643608093,
0.006024892907589674,
0.016480958089232445,
-0.052746400237083435,
0.0290005374699831,
-0.06390243023633957,
0.026929039508104324,
0.041221167892217636,
-0.04688572511076927,
-0.0015642604557797313,
-0.010820712894201279,
0.03316551446914673,
0.04103325307369232,
-0.00014881504466757178,
0.004495933651924133,
0.017852777615189552,
-0.03572443872690201,
0.00461674714460969,
0.039741963148117065,
0.018442045897245407,
-0.03204524517059326,
0.027399379760026932,
0.009219660423696041,
-0.017967570573091507,
-0.018433574587106705,
-0.021833283826708794,
0.023648269474506378,
-0.03170318901538849,
-0.027139699086546898,
0.03659263998270035,
-0.044253915548324585,
-0.027990546077489853,
0.03379214555025101,
-0.04221170023083687,
0.06263065338134766,
-0.029096202924847603,
0.03997545316815376,
0.0002481836127117276,
-0.0006502358010038733,
-0.020915238186717033,
0.01333022303879261,
-0.010831707157194614,
0.004552522208541632,
-0.017633572220802307,
0.030790824443101883,
0.00989114586263895,
-0.002609638497233391,
0.05308404937386513,
-0.02104600891470909,
0.04647563397884369,
-0.04144054651260376,
-0.007779261097311974,
-0.02426816336810589,
-0.05954846367239952,
-0.03306349366903305,
-0.03620302677154541,
0.059584662318229675,
0.06236506998538971,
-0.017737291753292084,
-0.003516546217724681,
-0.04065176099538803,
-0.001043006544932723,
0.0691177099943161,
-0.03228118270635605,
0.00029406597604975104,
-0.04784780740737915,
-0.022497963160276413,
-0.017217764630913734,
-0.009633071720600128
] |
<p>I want to check on the validity of the following objective definition of order. Is it correct? Is there a more rigorous statement of this concept? </p>
<p>The further a system is from its maximum thermodynamic entropy, the more ordered it is and the lower its entropy. Specifically, if a system’s microstates are not of equal probability, which is usually the case because of interactions or correlations between the microstates, it is more ordered when it spends time in the less likely states. If the microstates are of equal probability, it can be constrained to remain in one of the states a disproportionate amount of time by imposing constraints on the system’s random fluctuations. </p>
<p>Thanks very much for the input.</p>
| 8,822 |
[
-0.018775716423988342,
-0.023151123896241188,
-0.017913905903697014,
-0.02014586329460144,
0.03400271758437157,
0.0001526572013972327,
-0.007803476881235838,
0.036348991096019745,
-0.008717970922589302,
-0.024528859183192253,
0.020275630056858063,
0.014245633967220783,
0.01704109087586403,
0.013722683303058147,
0.021746089681982994,
0.011417023837566376,
-0.021325591951608658,
0.005469720344990492,
-0.004146253690123558,
-0.006294864695519209,
-0.002522517694160342,
0.025594456121325493,
0.021691251546144485,
-0.026201490312814713,
-0.07089340686798096,
0.02018527314066887,
0.023677147924900055,
0.016712281852960587,
0.028016971424221992,
0.06460479646921158,
-0.010676121339201927,
-0.024572663009166718,
0.017202788963913918,
0.046614207327365875,
0.06189447641372681,
-0.01789734698832035,
-0.0294120404869318,
-0.0008304158109240234,
-0.018560921773314476,
0.003393488470464945,
-0.03388797119259834,
-0.01831868104636669,
-0.027579760178923607,
0.016465485095977783,
0.01215552818030119,
0.023505257442593575,
-0.002001209417358041,
-0.009262025356292725,
0.029393387958407402,
-0.060107216238975525,
0.08986722677946091,
-0.012216492556035519,
0.03913962468504906,
0.026800014078617096,
0.010541160590946674,
-0.02148023061454296,
0.05981307476758957,
0.10286368429660797,
-0.01255692820996046,
-0.0517549142241478,
-0.027145998552441597,
-0.023675013333559036,
-0.011136485263705254,
-0.0321122407913208,
-0.004522346425801516,
0.035988979041576385,
0.004934422671794891,
-0.011959081515669823,
0.05472354590892792,
0.042889319360256195,
-0.009777686558663845,
-0.0017219135770574212,
0.06183983385562897,
-0.021199069917201996,
0.001764911925420165,
-0.055037226527929306,
0.027385378256440163,
-0.014263045974075794,
0.004045973997563124,
0.04593759775161743,
0.008780013769865036,
0.01604527235031128,
0.0024774253834038973,
0.03686428442597389,
-0.01315804198384285,
-0.02340780198574066,
0.092729352414608,
-0.021702764555811882,
0.02298869751393795,
0.037074014544487,
-0.029125496745109558,
0.02461332082748413,
0.0346568338572979,
0.02232976257801056,
-0.052077751606702805,
-0.003381571965292096,
-0.010137952864170074,
0.03106599673628807,
-0.04406145587563515,
-0.015981633216142654,
0.010704915039241314,
-0.05116955190896988,
0.03848131000995636,
0.04987471178174019,
0.015344250947237015,
0.012310171499848366,
-0.07222456485033035,
0.034376081079244614,
-0.018169255927205086,
0.0008995846146717668,
0.005940851755440235,
0.011891823261976242,
0.03968469798564911,
-0.013410943560302258,
-0.02519897371530533,
0.0018831772031262517,
0.009984584525227547,
-0.018311448395252228,
0.031672704964876175,
0.08109686523675919,
0.03926600143313408,
-0.01487048715353012,
0.026386264711618423,
-0.017631370574235916,
-0.08501416444778442,
0.01337401196360588,
0.03664809837937355,
0.0024605372454971075,
-0.026376349851489067,
0.049377553164958954,
-0.005879518110305071,
0.02070990577340126,
0.028972331434488297,
-0.014596487395465374,
0.04184607416391373,
-0.047869499772787094,
-0.131168931722641,
-0.047929733991622925,
0.05342579632997513,
0.0063622635789215565,
0.009296792559325695,
-0.06675387918949127,
0.02041742578148842,
0.029392791911959648,
0.039123158901929855,
0.024908022955060005,
0.02209530770778656,
-0.010934155434370041,
0.03271730989217758,
-0.0035085256677120924,
-0.04459879919886589,
0.007230449467897415,
0.01378170121461153,
-0.05008011683821678,
-0.007226862944662571,
-0.058085937052965164,
0.03485671430826187,
0.03241105377674103,
0.004463548306375742,
-0.04057775065302849,
0.038447849452495575,
-0.00010488067346159369,
-0.005561196245253086,
-0.0026062338147312403,
0.032396718859672546,
-0.020926065742969513,
0.05975347012281418,
0.009877498261630535,
0.02258905954658985,
0.009200909174978733,
0.03562450781464577,
0.019644079729914665,
0.005816383752971888,
0.03738970682024956,
0.05044015869498253,
-0.04058851674199104,
0.006724309176206589,
-0.028804490342736244,
0.0026196404360234737,
0.01576579548418522,
-0.024515150114893913,
0.0029202939476817846,
-0.02606668509542942,
0.016036609187722206,
-0.010898233391344547,
0.0052098981104791164,
-0.003140354063361883,
0.003669983008876443,
0.0034400278236716986,
-0.05863956734538078,
-0.04895064979791641,
-0.08756134659051895,
0.005006290972232819,
0.010796240530908108,
-0.028178680688142776,
0.03847075253725052,
-0.0001996629434870556,
0.046576641499996185,
-0.015993520617485046,
-0.01390870288014412,
-0.023838801309466362,
-0.02080068737268448,
-0.00014711757830809802,
0.007780430838465691,
0.036769069731235504,
0.06132495030760765,
0.015326540917158127,
-0.021232249215245247,
0.02736293524503708,
0.008515420369803905,
-0.03719503432512283,
0.0024939400609582663,
-0.012776977382600307,
0.01820225454866886,
0.02510673552751541,
0.010764271020889282,
0.022467687726020813,
-0.005638965871185064,
0.00019464649085421115,
0.010245841927826405,
-0.022932998836040497,
0.07167559117078781,
0.041658613830804825,
0.034014418721199036,
-0.016308441758155823,
0.04924551025032997,
0.015010811388492584,
-0.016651708632707596,
-0.035868700593709946,
-0.05173441767692566,
-0.05123685300350189,
0.007552571129053831,
0.047565024346113205,
0.08703520894050598,
-0.052501380443573,
0.023941069841384888,
0.0004291512886993587,
0.038619816303253174,
0.019054194912314415,
0.01719377376139164,
-0.02264224924147129,
-0.03083706460893154,
0.03923594951629639,
-0.003613387933000922,
0.021119143813848495,
0.019194453954696655,
0.018178628757596016,
-0.031236298382282257,
0.014348325319588184,
0.00002157978087780066,
-0.013137639500200748,
0.016139686107635498,
-0.00466340035200119,
-0.015981975942850113,
0.005822429433465004,
-0.03184466436505318,
0.02359604462981224,
-0.023508794605731964,
0.04274194687604904,
0.02133389748632908,
-0.013837035745382309,
0.024655360728502274,
-0.034926027059555054,
0.0070360396057367325,
-0.00452694995328784,
-0.011301777325570583,
-0.03307401388883591,
-0.043228261172771454,
0.023832639679312706,
-0.0033652554266154766,
-0.020222598686814308,
-0.004243866074830294,
-0.01807885803282261,
-0.041253991425037384,
-0.0020199662540107965,
0.04025638848543167,
0.0011577503755688667,
0.006272893399000168,
-0.004711491521447897,
0.005038262810558081,
-0.029723994433879852,
-0.019165892153978348,
0.001114957733079791,
0.013736458495259285,
-0.04987139254808426,
0.008931560441851616,
0.0325690433382988,
-0.020319271832704544,
0.01686057262122631,
-0.04481210559606552,
0.009976306930184364,
-0.0018518755678087473,
-0.015007440000772476,
-0.03854944556951523,
-0.005277018062770367,
-0.01324971579015255,
0.002266072668135166,
-0.0029512585606426,
-0.022969556972384453,
0.041957952082157135,
-0.017934665083885193,
-0.05514238402247429,
0.02170182392001152,
-0.04827328771352768,
-0.05932211875915527,
-0.006918448489159346,
0.026872040703892708,
0.03848736733198166,
-0.00046444221516139805,
0.031245186924934387,
0.07197285443544388,
-0.03674149140715599,
-0.03564334288239479,
-0.04539564251899719,
-0.09611430764198303,
0.05329914763569832,
-0.045254163444042206,
0.03333999589085579,
-0.0070624095387756824,
-0.05721403285861015,
0.060968149453401566,
0.05279973894357681,
-0.030678005889058113,
-0.013811067678034306,
-0.004879327490925789,
-0.002819173038005829,
0.007397042587399483,
0.0191157478839159,
0.01582520268857479,
0.0089960265904665,
0.06694981455802917,
0.03258615732192993,
0.05675363540649414,
0.016898171976208687,
-0.04770319163799286,
-0.013733718544244766,
0.009045169688761234,
0.04263783246278763,
-0.007292445749044418,
0.013320548459887505,
0.008701536804437637,
-0.0035301409661769867,
0.025622133165597916,
-0.00570891285315156,
0.03370086848735809,
0.021142633631825447,
-0.0682540088891983,
0.05618356913328171,
-0.0031039484310895205,
0.01033105980604887,
-0.043719734996557236,
0.02720114029943943,
-0.006744007114320993,
-0.011172125115990639,
0.012856434099376202,
0.034428782761096954,
0.03161768242716789,
0.01376414019614458,
0.01545092836022377,
0.06964384764432907,
0.023339228704571724,
0.0020138234831392765,
0.025402838364243507,
0.009051196277141571,
-0.013212639838457108,
0.029252108186483383,
-0.0004925178945995867,
-0.010078593157231808,
0.035380806773900986,
0.008021162822842598,
0.021953849121928215,
-0.01688423752784729,
-0.03966430574655533,
0.0047685448080301285,
-0.0739314928650856,
0.030616596341133118,
-0.019313843920826912,
0.046702317893505096,
0.022809457033872604,
0.06708953529596329,
-0.0001357712462777272,
-0.016527462750673294,
0.018672147765755653,
-0.0031248931773006916,
-0.062334559857845306,
0.0398753359913826,
-0.021003376692533493,
0.01666032336652279,
-0.019431570544838905,
-0.01014332752674818,
0.026217006146907806,
-0.059326667338609695,
-0.007414068561047316,
-0.0060863858088850975,
0.010845505632460117,
-0.0659148097038269,
-0.018246198073029518,
-0.04853901267051697,
-0.016916168853640556,
0.014914465136826038,
-0.006712732836604118,
0.021762043237686157,
-0.04628540575504303,
0.058371517807245255,
0.04222577437758446,
-0.013109389692544937,
-0.0022464583162218332,
0.00995618849992752,
0.03980674967169762,
0.025526436045765877,
0.0010840654140338302,
0.01678103394806385,
-0.003804909298196435,
-0.003856138326227665,
0.02220836654305458,
-0.03119959868490696,
0.040912676602602005,
0.017841309309005737,
-0.030564911663532257,
-0.029586855322122574,
-0.02551705203950405,
-0.028294257819652557,
0.023936090990900993,
0.024175388738512993,
0.003511399496346712,
0.018737668171525,
0.04007681459188461,
0.009478108026087284,
-0.0372295156121254,
0.05212663859128952,
0.06075069680809975,
-0.004001557361334562,
-0.006458721589297056,
-0.030692707747220993,
-0.024237507954239845,
0.0066149309277534485,
0.006514673586934805,
0.028012847527861595,
-0.015320845879614353,
-0.0370333194732666,
0.01679469458758831,
-0.03227171301841736,
-0.014363894239068031,
-0.04278971254825592,
-0.02612166851758957,
-0.002858824795112014,
0.03694133087992668,
0.037415511906147,
0.0081196129322052,
0.014252359047532082,
0.009988260455429554,
0.01798725500702858,
0.047439806163311005,
-0.0020922981202602386,
-0.06478863209486008,
-0.02868467941880226,
0.036224547773599625,
0.022287458181381226,
-0.01883646287024021,
0.03706745058298111,
-0.04060567170381546,
-0.02199219912290573,
0.0745437741279602,
-0.02187967672944069,
0.051403485238552094,
-0.026280662044882774,
-0.0030556232668459415,
-0.007937437854707241,
-0.06025395169854164,
-0.02146483026444912,
0.00002771142499113921,
0.015311667695641518,
0.026838062331080437,
0.005600408185273409,
-0.029604366049170494,
-0.06408675014972687,
-0.010109844617545605,
0.03209659084677696,
0.03345726802945137,
-0.014609081670641899,
-0.00851175282150507,
-0.009637294337153435,
-0.008504246361553669,
-0.052529290318489075,
-0.059460416436195374,
0.02834164910018444,
-0.00382497301325202,
-0.00897139310836792,
-0.00026604835875332355,
-0.015124897472560406,
-0.004354819655418396,
-0.007077336311340332,
0.0032180820126086473,
-0.010625019669532776,
0.011545898392796516,
0.005212174262851477,
0.08752701431512833,
0.03410692512989044,
-0.004440947901457548,
0.023429380729794502,
0.05247817188501358,
0.009262927807867527,
0.008929485455155373,
-0.017827792093157768,
0.04531114548444748,
-0.05987716466188431,
0.03059527836740017,
-0.058391354978084564,
0.01099846139550209,
-0.04021706059575081,
0.03908127546310425,
-0.008143042214214802,
0.019137956202030182,
-0.021514061838388443,
-0.028674226254224777,
-0.014815443195402622,
0.016109649091959,
0.02813679166138172,
-0.009485498070716858,
-0.025532638654112816,
0.03120720013976097,
0.009566997177898884,
-0.005737887695431709,
0.012187058106064796,
-0.010039388202130795,
-0.014350480400025845,
0.009714850224554539,
-0.02324334718286991,
0.04425979033112526,
-0.03587893024086952,
-0.038604479283094406,
-0.024259570986032486,
-0.033830299973487854,
0.03498852625489235,
-0.04804171994328499,
-0.011006085202097893,
-0.018702100962400436,
-0.04291747137904167,
-0.03565021976828575,
0.0065641338005661964,
-0.021513834595680237,
0.03292272984981537,
-0.010973883792757988,
0.03696398809552193,
0.026457378640770912,
0.008400990627706051,
-0.10728782415390015,
-0.0507580004632473,
-0.011679586954414845,
-0.0073510147631168365,
-0.04827650636434555,
-0.036379631608724594,
0.03799682855606079,
-0.023105597123503685,
-0.007546176668256521,
-0.021064797416329384,
0.01563655212521553,
-0.004694055300205946,
-0.016325654461979866,
0.0007600783719681203,
-0.004530925303697586,
0.05880522355437279,
-0.0003903037286363542,
-0.0190048236399889,
0.0027098054997622967,
0.021996650844812393,
-0.02154381573200226,
0.00968086440116167,
0.0474921353161335,
-0.013530443422496319,
0.00031343664159066975,
-0.000710535270627588,
0.014765464700758457,
0.01843763329088688,
-0.001603875425644219,
-0.008713312447071075,
0.0031185424886643887,
0.009475148282945156,
-0.001458807848393917,
-0.021105436608195305,
-0.016403894871473312,
-0.00043394588283263147,
-0.008312612771987915,
0.0247047059237957,
0.0071942973881959915,
0.0015016173711046576,
-0.07150329649448395,
0.01897217333316803,
-0.01104354951530695,
0.003915546927601099,
0.020565664395689964,
0.08448535203933716,
0.022358069196343422,
0.013402885757386684,
0.005955790169537067,
-0.032452672719955444,
0.009001488797366619,
-0.0010827876394614577,
0.0026249985676258802,
0.007932846434414387,
0.004673901945352554,
-0.035473793745040894,
-0.017232704907655716,
-0.04394690692424774,
-0.014817893505096436,
0.06968905031681061,
-0.024978552013635635,
0.03696653991937637,
0.03167181462049484,
0.009422438219189644,
0.0014267110964283347,
-0.018865592777729034,
0.021495763212442398,
0.028229916468262672,
0.0224679633975029,
0.01551759522408247,
-0.042574115097522736,
-0.04280649125576019,
0.029488801956176758,
0.023289961740374565,
-0.03666998818516731,
0.03292204439640045,
0.012484132312238216,
0.0023312922567129135,
0.0032768177334219217,
-0.026800328865647316,
-0.04143219441175461,
0.051349662244319916,
-0.05656621232628822,
0.04228248447179794,
-0.015467561781406403,
-0.03178747743368149,
0.003557487390935421,
-0.004563563037663698,
-0.018393078818917274,
-0.035092175006866455,
-0.0273723341524601,
-0.03707657381892204,
0.04293585941195488,
-0.00529170036315918,
-0.005026776809245348,
0.02610621228814125,
-0.02895769663155079,
0.02567005157470703,
0.03822530061006546,
0.014156167395412922,
0.0005898305680602789,
-0.05468280613422394,
0.004533304367214441,
-0.002254297025501728,
-0.052601154893636703,
-0.012739535421133041,
-0.008316783234477043,
-0.030589375644922256,
-0.007970225065946579,
-0.01016142126172781,
-0.030871080234646797,
0.009976701810956001,
0.027725644409656525,
-0.002324531087651849,
0.09558498859405518,
0.02874007262289524,
0.019600238651037216,
0.015327309258282185,
-0.0039039698895066977,
0.10224039107561111,
0.09200815111398697,
0.00010521178046474233,
-0.05311163514852524,
0.035017918795347214,
0.007255218457430601,
-0.011658364906907082,
-0.018882334232330322,
0.04317200556397438,
0.0141787463799119,
0.0006836444372311234,
0.028713807463645935,
0.03322772681713104,
0.002885806141421199,
-0.02409469150006771,
0.06949929893016815,
-0.05866019055247307,
-0.042755771428346634,
0.005626470781862736,
0.03614984080195427,
0.00022897690359968692,
-0.010753266513347626,
-0.05013520270586014,
0.00022661173716187477,
-0.012246087193489075,
0.0062071774154901505,
-0.008250082843005657,
-0.03619491681456566,
0.004449686035513878,
0.005779101978987455,
0.007630462758243084,
-0.00756960129365325,
0.014487306587398052,
-0.022905832156538963,
-0.05275927484035492,
-0.016755767166614532,
-0.027510495856404305,
0.004621455911546946,
0.032980091869831085,
0.032208822667598724,
0.037525925785303116,
0.008856703527271748,
0.04009707272052765,
0.005095325876027346,
-0.056795116513967514,
0.006500587798655033,
0.0008733790018595755,
0.02064027078449726,
-0.028195789083838463,
0.00956961140036583,
-0.02131715416908264,
-0.00836124923080206,
-0.018364666029810905,
-0.046144649386405945,
-0.006864967755973339,
-0.007515877950936556,
0.07110368460416794,
-0.005746901500970125,
-0.043185800313949585,
-0.04762198030948639,
0.0018053575186058879,
-0.01645035669207573,
0.020348550751805305,
-0.005591758526861668,
0.0074041131883859634,
0.004811311140656471,
-0.013188900426030159,
0.050146084278821945,
-0.019686328247189522,
-0.015959061682224274,
-0.013963579200208187,
-0.008682855404913425,
-0.05509268864989281,
0.003061546478420496,
0.009172541089355946,
-0.03061426617205143,
0.041550230234861374,
0.03675399348139763,
-0.0011446265270933509,
-0.0028062756173312664,
-0.03293522074818611,
-0.01393993478268385,
-0.00017709519306663424,
-0.053662948310375214,
-0.02148205228149891,
-0.004068048670887947,
0.026552533730864525,
0.048218127340078354,
-0.00932731106877327,
0.012399964034557343,
0.02732379361987114,
-0.0001131062745116651,
0.0034337269607931376,
-0.02611101046204567,
0.00690435292199254,
-0.0010795206762850285,
-0.03927406668663025,
0.0001991575991269201,
0.028621351346373558,
0.03566759452223778,
0.027151329442858696,
0.012190954759716988,
-0.0025789442006498575,
0.05634573847055435,
0.0028016576543450356,
0.01889759674668312,
0.017561884596943855,
-0.03658777102828026,
-0.015651823952794075,
0.0030124024488031864,
-0.012432041577994823,
-0.047532204538583755,
-0.04289674013853073,
-0.03673296421766281,
0.026547476649284363,
0.007299917284399271,
-0.015984470024704933,
-0.007295722607523203,
-0.013168228790163994,
-0.006228558253496885,
0.023919278755784035,
-0.030843062326312065,
-0.012774749659001827,
-0.04386305436491966,
-0.015680698677897453,
0.020236030220985413,
0.02586531825363636,
-0.01299439650028944,
0.03302955627441406,
0.031022457405924797,
-0.024515539407730103,
0.04855263605713844,
0.03929470106959343,
-0.0059577166102826595,
-0.04186893254518509,
-0.0012455127434805036,
-0.01318986527621746,
0.08175733685493469,
-0.05417695641517639,
-0.02407689578831196,
0.010678823105990887,
-0.05247890576720238,
-0.02571379579603672,
0.014021983370184898,
0.0009840368293225765,
0.018354255706071854,
0.016998162493109703,
-0.021861333400011063,
-0.020834576338529587,
0.04091571271419525,
0.0005115267122164369,
0.011770015582442284,
0.013088425621390343,
-0.015619478188455105,
-0.009550088085234165,
-0.0324026420712471,
-0.02552143856883049,
0.01172855868935585,
-0.004502066411077976,
0.03203662112355232,
0.044336602091789246,
0.01428336650133133,
-0.022459831088781357,
-0.014254771173000336,
0.0044532036408782005,
0.015250762924551964,
-0.005716175306588411,
0.0068261949345469475,
0.03371758759021759,
0.03479788079857826,
-0.02770833671092987,
0.04685547575354576,
0.024641362950205803,
0.013943673111498356,
-0.08039990812540054,
0.01443309523165226,
-0.0008873222977854311,
-0.012596916407346725,
0.017261093482375145,
-0.014466723427176476,
0.02429722435772419,
0.009732902981340885,
-0.03127781301736832,
0.0023334999568760395,
-0.01136025507003069,
-0.024761030450463295,
-0.03228425234556198,
0.015454046428203583,
-0.05550418049097061,
0.032087791711091995,
0.04226936027407646,
0.04654126986861229,
0.04212768375873566,
0.005645562894642353,
-0.01865016482770443,
-0.01081489585340023,
-0.0029891598969697952,
0.06411627680063248,
0.006492915563285351,
-0.030682634562253952,
0.055329471826553345,
-0.00624090526252985,
-0.03365391120314598,
0.056535396724939346,
-0.031868111342191696,
0.0009064195328392088,
0.020697660744190216,
0.05526908487081528,
-0.01180505845695734,
0.03264794498682022,
0.016181426122784615,
-0.022431617602705956,
-0.021742645651102066,
0.01569276675581932,
0.005476232152432203,
0.017099754884839058,
0.0013300454011186957,
-0.00817697774618864,
0.030773397535085678,
-0.011358346790075302,
-0.042306505143642426,
0.04600231349468231,
-0.016872748732566833,
-0.0011625320184975863,
0.0055356742814183235,
-0.013359365984797478,
0.006687250919640064,
-0.03310108184814453,
0.04324878007173538,
-0.016619276255369186,
-0.01630851998925209,
0.04264799878001213,
0.05174044519662857,
-0.044868580996990204,
-0.030271612107753754,
-0.009633897803723812,
-0.02906481921672821,
0.006178845651447773,
0.01046943198889494,
-0.010990245267748833,
-0.06144443526864052,
0.00026338835596106946,
-0.023397410288453102,
-0.035785552114248276,
-0.039401888847351074,
-0.053110282868146896,
-0.015362601727247238,
0.05213737487792969,
0.011164037510752678,
-0.006562214810401201,
0.01987483538687229,
-0.04934436082839966,
-0.02437359094619751,
-0.061644092202186584,
0.036582160741090775,
-0.010383279994130135,
0.011477501131594181,
-0.06002940610051155,
-0.014261788688600063,
0.001969302073121071,
0.034187592566013336,
0.038372840732336044,
0.029480252414941788,
-0.033926792442798615,
-0.0035871616564691067,
0.03277662396430969,
0.03590220957994461,
-0.03136465698480606,
0.028661446645855904,
-0.04195665568113327,
-0.026519643142819405,
-0.008159355260431767,
-0.03342173621058464,
-0.01596391201019287,
0.0030679062474519014,
0.03703583404421806,
-0.041297197341918945,
-0.012938852421939373,
0.010014237836003304,
-0.022356828674674034,
0.04992486536502838,
-0.008406589739024639,
-0.016745898872613907,
0.06870856136083603,
-0.04194281995296478,
0.013602816499769688,
0.025227613747119904,
-0.018230749294161797,
-0.034018754959106445,
0.036566540598869324,
-0.034270353615283966,
-0.0014476788928732276,
-0.002525254851207137,
0.015611627139151096,
0.012777547352015972,
-0.030754031613469124,
-0.0067230346612632275,
0.011384372599422932,
-0.046530596911907196,
-0.018189342692494392,
0.02734272927045822,
0.035161811858415604,
0.05672305077314377,
-0.019016040489077568,
0.000820155197288841,
0.005418102256953716,
0.013996858149766922,
0.014900391921401024,
0.07225409150123596,
0.06038101390004158,
0.00790711585432291,
0.01792672649025917,
0.005938082002103329,
-0.03972843661904335,
0.019605690613389015,
0.015802616253495216,
0.01325374934822321,
0.0008519159164279699,
-0.017997313290834427,
0.03239545226097107,
0.003346087411046028,
0.010933587327599525,
0.000394741102354601,
0.004022647626698017,
0.028810985386371613,
-0.020859424024820328,
0.016422279179096222,
-0.03377087786793709,
0.0028741031419485807,
-0.057612597942352295,
0.00016595081251580268,
0.013308905996382236,
0.023765994235873222,
-0.029326722025871277,
0.00034333387156948447,
-0.017612533643841743,
0.009342669509351254,
0.03336455672979355,
-0.023764895275235176,
0.0004348284855950624,
0.00935459416359663,
-0.013031302019953728,
-0.008815869688987732,
-0.0043970816768705845,
-0.05253613740205765,
-0.01672261394560337,
0.01587558723986149,
0.03239273652434349,
0.02848699316382408,
-0.00033144879853352904,
-0.024323485791683197,
-0.04488341882824898,
0.09881405532360077,
-0.07355500012636185,
-0.010861760936677456,
-0.05958329886198044,
0.011595617048442364,
-0.025896960869431496,
-0.01870981976389885
] |
<p>In this article (and numerous others) <a href="http://phys.org/news/2011-04-scientists-spacetime-dimension.html" rel="nofollow">http://phys.org/news/2011-04-scientists-spacetime-dimension.html</a> and <a href="http://www.rebelscience.org/Crackpots/notorious.htm" rel="nofollow">http://www.rebelscience.org/Crackpots/notorious.htm</a> they suggest that there is no time dimension and even in the last one that there is no motion in space-time. Do you believe these theories, are they true?</p>
| 8,823 |
[
0.0067615085281431675,
-0.024969350546598434,
0.01907922700047493,
-0.062725730240345,
0.07900194078683853,
-0.018670471385121346,
-0.04787246882915497,
-0.03637613356113434,
0.0035392893478274345,
-0.05180548503994942,
0.022482341155409813,
0.024703171104192734,
0.008199243806302547,
0.048993829637765884,
0.015269050374627113,
0.024323634803295135,
-0.011566991917788982,
0.01827217824757099,
0.001838895259425044,
-0.03790046647191048,
0.006482723634690046,
0.022634828463196754,
0.00957575161010027,
0.0038969756569713354,
-0.040861062705516815,
0.025400077924132347,
0.04799174517393112,
0.03647376596927643,
0.011012324132025242,
0.04000698775053024,
0.005589042790234089,
0.00028629350708797574,
-0.008243493735790253,
0.011499793268740177,
-0.011594460345804691,
-0.03594338521361351,
-0.03473815694451332,
-0.012548704631626606,
0.001225361949764192,
0.016181746497750282,
-0.004216961562633514,
-0.004958267789334059,
-0.00910500530153513,
0.04861380159854889,
-0.03395448625087738,
0.04172316566109657,
0.01822805590927601,
-0.006970611400902271,
0.06692393869161606,
-0.043194420635700226,
0.05890905484557152,
-0.008968407288193703,
0.012738348916172981,
0.012691047042608261,
-0.006628966424614191,
0.013299040496349335,
0.06864435225725174,
0.06542264670133591,
-0.03563442826271057,
-0.05609055235981941,
0.010472536087036133,
0.01263363379985094,
0.03309627249836922,
0.010350765660405159,
-0.015021256171166897,
0.05478721484541893,
-0.02652512863278389,
0.018764616921544075,
0.011362159624695778,
0.019611883908510208,
0.01562889665365219,
0.0007774288533255458,
0.027782706543803215,
0.013748826459050179,
-0.0073514352552592754,
-0.02456953004002571,
0.02093789353966713,
0.020017923787236214,
0.03841078653931618,
0.06453976780176163,
0.0016000577015802264,
0.000508133030962199,
0.024612119421362877,
0.0047638979740440845,
0.014643973670899868,
-0.013360206969082355,
0.059857405722141266,
0.009569903835654259,
-0.005772655829787254,
0.03954669088125229,
-0.008752936497330666,
0.005565153434872627,
0.021753676235675812,
0.002035356592386961,
-0.021483419463038445,
0.05832277610898018,
0.01769457384943962,
0.05546793341636658,
-0.0008024717681109905,
-0.030729908496141434,
-0.0248170904815197,
0.019209804013371468,
0.03063277155160904,
0.0468742810189724,
-0.01103555504232645,
-0.017152057960629463,
-0.0012898929417133331,
0.027057144790887833,
-0.027584366500377655,
0.0028883395716547966,
-0.04569913446903229,
-0.00211967877112329,
0.013979651965200901,
-0.0005056989029981196,
-0.0017140459967777133,
-0.020230745896697044,
0.027377011254429817,
-0.015107139013707638,
0.03623396158218384,
0.08903025090694427,
0.01946607418358326,
-0.0501432903110981,
-0.008386099711060524,
-0.01370997354388237,
-0.0785064548254013,
-0.018103359267115593,
0.02618507854640484,
-0.01886691525578499,
-0.022654514759778976,
0.06805404275655746,
-0.012114252895116806,
-0.0017460385570302606,
0.03926558792591095,
0.012128214351832867,
0.0713517814874649,
0.009313798509538174,
-0.11222178488969803,
-0.06201082840561867,
0.07961315661668777,
-0.0075630624778568745,
-0.006806608289480209,
-0.05348876491189003,
0.015309648588299751,
-0.030786098912358284,
0.10181808471679688,
0.004025058820843697,
0.015194553881883621,
0.0045632412657141685,
0.05025087296962738,
-0.01604820415377617,
-0.017493445426225662,
0.012640725821256638,
0.02035893313586712,
-0.0560578852891922,
-0.01480620913207531,
-0.07259558141231537,
0.0069888923317193985,
0.03008701466023922,
-0.008058596402406693,
-0.019630197435617447,
0.035138003528118134,
0.01615643873810768,
0.0023853201419115067,
0.0008258310845121741,
-0.013272494077682495,
-0.008260523900389671,
0.06788785755634308,
0.003960075322538614,
0.019234007224440575,
0.04139832779765129,
-0.0005097972461953759,
0.03806668147444725,
0.021044151857495308,
0.0388047955930233,
0.017808912321925163,
0.008278648369014263,
-0.014444699510931969,
0.005479996558278799,
-0.012855703011155128,
-0.014965503476560116,
-0.08056429028511047,
-0.009336274117231369,
-0.019237970933318138,
-0.012196858413517475,
-0.017711054533720016,
0.07207463681697845,
-0.010060751810669899,
-0.010391618125140667,
0.022334018722176552,
-0.040886040776968,
0.01856050454080105,
-0.08675669878721237,
0.008746006526052952,
-0.014124198816716671,
-0.02056318335235119,
-0.0014937708619982004,
0.018925616517663002,
0.044721510261297226,
-0.07540380954742432,
-0.007065355312079191,
-0.05850306153297424,
0.041903238743543625,
-0.015104306861758232,
-0.011499789543449879,
0.012756970711052418,
0.044482387602329254,
0.024664072319865227,
-0.036862242966890335,
0.003519616089761257,
0.019665023311972618,
-0.021875711157917976,
0.027173569425940514,
-0.018496103584766388,
0.04362192377448082,
-0.004183000884950161,
-0.026969628408551216,
0.011559749953448772,
0.046121519058942795,
-0.03022102452814579,
0.021141765639185905,
-0.016350427642464638,
0.045987654477357864,
0.011054976843297482,
0.01560783851891756,
-0.027450961992144585,
0.05701301246881485,
0.0009296729112975299,
-0.003214752534404397,
0.025340428575873375,
-0.031062493100762367,
-0.03932751715183258,
-0.007371554151177406,
0.051441989839076996,
0.04139740765094757,
-0.030525483191013336,
0.04213164746761322,
0.011988917365670204,
0.04673260077834129,
0.020430216565728188,
0.023724647238850594,
-0.009398850612342358,
-0.06414264440536499,
-0.0345313623547554,
-0.006796671077609062,
0.02824290655553341,
0.024849165230989456,
0.02658132091164589,
0.005134320817887783,
0.02473420649766922,
-0.01902833767235279,
-0.008386465720832348,
0.043285418301820755,
-0.025475943461060524,
0.0029974107164889574,
0.050367120653390884,
-0.028528977185487747,
0.00904358085244894,
0.0089936014264822,
0.010445503517985344,
0.0033716948237270117,
-0.0066908965818583965,
0.01509036310017109,
-0.02623612992465496,
-0.005656392313539982,
-0.019361896440386772,
0.03034983202815056,
-0.035749342292547226,
-0.008925467729568481,
0.026440506801009178,
-0.03619766607880592,
-0.022331777960062027,
-0.04539032652974129,
0.006612402852624655,
-0.03507274389266968,
0.006818245630711317,
0.035016339272260666,
-0.01829778030514717,
0.04032426327466965,
-0.010411283001303673,
-0.03217903897166252,
0.033182159066200256,
-0.023093752562999725,
-0.02392417937517166,
0.009357094764709473,
-0.04673195630311966,
0.04397139698266983,
-0.03332088887691498,
-0.010967743583023548,
0.0640646293759346,
-0.006435238290578127,
0.034469615668058395,
0.030355161055922508,
-0.05905097350478172,
-0.0373167060315609,
-0.01625232771039009,
-0.022251741960644722,
0.03779644891619682,
-0.024495329707860947,
-0.006202740594744682,
0.04198157787322998,
-0.02841530367732048,
-0.03283894807100296,
0.008515064604580402,
-0.03606538102030754,
-0.040319301187992096,
-0.0182191114872694,
0.00930721778422594,
0.02378961443901062,
-0.021967781707644463,
0.004788027610629797,
0.02474217675626278,
-0.04608231782913208,
0.00114075664896518,
-0.027264777570962906,
-0.036543771624565125,
0.0418606698513031,
-0.010298115201294422,
0.05168435722589493,
-0.024251563474535942,
-0.013521759770810604,
0.04719001427292824,
0.026433251798152924,
-0.033906418830156326,
-0.024317264556884766,
-0.02960715815424919,
-0.01630459539592266,
0.019923603162169456,
0.008713736198842525,
0.05055653303861618,
0.00543076591566205,
-0.02052394300699234,
0.018857240676879883,
0.03270174190402031,
0.02347385510802269,
0.014913695864379406,
-0.013648421503603458,
-0.00646523293107748,
0.04444321244955063,
-0.01580110192298889,
0.04267425090074539,
0.019283412024378777,
-0.031077982857823372,
-0.022163622081279755,
-0.027505258098244667,
0.059736236929893494,
0.014293009415268898,
-0.073321133852005,
0.043557360768318176,
0.003916931338608265,
0.02629350870847702,
0.0059278118424117565,
-0.012498834170401096,
0.020458923652768135,
0.005248736590147018,
-0.008425080217421055,
0.007945452816784382,
0.02980090118944645,
0.025912653654813766,
0.00666098902001977,
0.018470177426934242,
-0.005274736322462559,
-0.0417761467397213,
0.013626166619360447,
-0.010901380330324173,
0.006118799559772015,
0.052230484783649445,
-0.012089340016245842,
-0.03141622990369797,
0.07558935135602951,
0.025062428787350655,
0.014816057868301868,
0.036894556134939194,
-0.029521171003580093,
0.007503630127757788,
-0.08926863223314285,
0.02901407517492771,
-0.008747574873268604,
0.05228465422987938,
0.03007536195218563,
0.025115376338362694,
-0.019344955682754517,
0.0035979931708425283,
0.0027564289048314095,
-0.021481292322278023,
-0.0692424550652504,
0.0024871109053492546,
-0.023477118462324142,
-0.004540532827377319,
-0.03193167597055435,
0.014042820781469345,
-0.024924177676439285,
-0.004162287339568138,
-0.02241974137723446,
-0.009381109848618507,
-0.021952012553811073,
-0.09415692090988159,
0.002608409384265542,
-0.04616478085517883,
-0.024225013330578804,
-0.02510034665465355,
0.01570560783147812,
0.056047286838293076,
-0.02103954181075096,
0.011055481620132923,
0.014554500579833984,
0.0013599646044895053,
-0.020986409857869148,
0.027963461354374886,
-0.030519984662532806,
0.013026276603341103,
0.035397667437791824,
0.0015040102880448103,
0.005961223505437374,
-0.043024394661188126,
0.011912815272808075,
0.00042119360296055675,
0.0356929711997509,
-0.032016776502132416,
-0.02622133120894432,
-0.03296743705868721,
-0.016281168907880783,
0.011343810707330704,
0.0016430809628218412,
0.057709380984306335,
0.01175692304968834,
-0.005037697032094002,
0.03760053217411041,
0.00742484163492918,
-0.0058444226160645485,
0.03141537308692932,
0.03727519512176514,
-0.007217940408736467,
0.017416607588529587,
-0.04079311713576317,
-0.03861929848790169,
-0.016504725441336632,
-0.027552219107747078,
0.021263400092720985,
-0.009137103334069252,
-0.01121008861809969,
0.015672096982598305,
0.008380717597901821,
0.01824854128062725,
-0.007779249921441078,
0.020188553258776665,
0.00505454046651721,
-0.007056491915136576,
-0.019000418484210968,
-0.003371975151821971,
0.012234136462211609,
0.04135369136929512,
0.04504331573843956,
-0.002724278252571821,
-0.026994159445166588,
-0.07764346897602081,
0.028040973469614983,
0.03267763927578926,
0.03361031785607338,
-0.029834100976586342,
-0.020930685102939606,
-0.06457184255123138,
-0.02607269585132599,
0.02301296405494213,
-0.040670428425073624,
0.042105212807655334,
0.002748932922258973,
0.007683519273996353,
-0.03454098477959633,
-0.014532649889588356,
0.03213966265320778,
-0.017535315826535225,
0.010823520831763744,
0.012144098058342934,
-0.00023411394795402884,
0.011233005672693253,
0.006247620098292828,
0.01971791684627533,
0.033882033079862595,
0.044464148581027985,
0.017380429431796074,
0.029798299074172974,
-0.016355033963918686,
0.010147546418011189,
-0.028726542368531227,
-0.07488256692886353,
-0.004017759580165148,
0.034499913454055786,
-0.03466879203915596,
0.05258824676275253,
-0.04153641685843468,
-0.046973127871751785,
0.0002794359752442688,
0.003197584766894579,
-0.0073838564567267895,
0.014416874386370182,
-0.040496084839105606,
-0.003478245111182332,
0.014634945429861546,
-0.01680905930697918,
0.016686417162418365,
0.04083451256155968,
-0.0330672562122345,
-0.022036191076040268,
-0.007683335337787867,
0.025407956913113594,
-0.01111852377653122,
0.022471047937870026,
-0.025555366650223732,
0.008826438337564468,
-0.04423478618264198,
0.03028174117207527,
-0.010267467238008976,
-0.011402900330722332,
-0.0006100237951613963,
0.01103974785655737,
-0.028107518330216408,
0.03507041931152344,
0.03608119487762451,
-0.0021478834096342325,
-0.04044116288423538,
0.019371377304196358,
-0.02299657091498375,
-0.014446578919887543,
0.01113034226000309,
0.02032499760389328,
-0.005641311872750521,
0.05846340209245682,
0.0022621219977736473,
0.013319754973053932,
-0.020952101796865463,
-0.0056249783374369144,
0.007803269196301699,
-0.06974354386329651,
0.024082379415631294,
-0.01620779186487198,
-0.023764342069625854,
0.019888605922460556,
-0.04086242988705635,
-0.04402255639433861,
-0.00016616967332083732,
-0.001691649085842073,
0.0177666787058115,
-0.044483382254838943,
0.031661197543144226,
0.018821878358721733,
-0.003783716354519129,
-0.0773448497056961,
-0.058808282017707825,
0.026143865659832954,
0.028462989255785942,
-0.03555818274617195,
-0.03943070024251938,
0.010572455823421478,
-0.07849055528640747,
-0.03503039851784706,
-0.030295319855213165,
0.05549228936433792,
-0.007297249045222998,
-0.03225256875157356,
0.005842131562530994,
0.002226293319836259,
0.04140665754675865,
0.004691524896770716,
0.01420732494443655,
0.005858476739376783,
-0.003621654585003853,
0.0009431093349121511,
-0.018057608976960182,
0.017413858324289322,
0.002800850197672844,
-0.018464425578713417,
-0.03344583883881569,
0.01624550111591816,
0.0002843932597897947,
-0.018857495859265327,
-0.012777919881045818,
0.03319916874170303,
0.026590481400489807,
0.0044860634952783585,
-0.04363590478897095,
0.05540883168578148,
-0.00232106726616621,
-0.00990669522434473,
-0.01602567732334137,
0.03615035116672516,
-0.026453375816345215,
-0.020519349724054337,
0.0304328054189682,
-0.021141106262803078,
0.010072014294564724,
-0.011456198059022427,
0.025704286992549896,
-0.012996206060051918,
0.031745847314596176,
0.023671407252550125,
-0.01478910818696022,
0.01861283928155899,
-0.00886659137904644,
0.008456970565021038,
0.021246036514639854,
0.013873489573597908,
-0.01595490239560604,
-0.03310738876461983,
-0.01563706062734127,
0.028391951695084572,
0.05132371932268143,
-0.03152325004339218,
0.03396894782781601,
0.03007398173213005,
-0.04122314602136612,
-0.008053886704146862,
-0.021159259602427483,
0.012103915214538574,
0.03170754387974739,
0.024268293753266335,
0.02361997961997986,
-0.06010642275214195,
-0.0025140957441180944,
0.04376355558633804,
0.04910562187433243,
-0.027482973411679268,
0.03757781535387039,
0.03585430234670639,
-0.017424460500478745,
0.015322443097829819,
0.01781093142926693,
-0.0389212891459465,
0.055339038372039795,
-0.022373972460627556,
0.030078953132033348,
0.007933234795928001,
0.0005224057822488248,
0.02162962034344673,
0.002967131556943059,
0.024033261463046074,
-0.020561065524816513,
-0.0012446566252037883,
-0.048265740275382996,
-0.004995725583285093,
-0.04369714483618736,
0.052563637495040894,
-0.016317594796419144,
-0.022332893684506416,
0.03949015215039253,
0.008767158724367619,
0.03436088562011719,
0.005475393496453762,
-0.06490645557641983,
-0.01719687320291996,
-0.026149433106184006,
-0.028762884438037872,
0.06784310191869736,
-0.004856220446527004,
-0.03838079050183296,
-0.0052260044030845165,
-0.04617677628993988,
0.008901109918951988,
0.02649243175983429,
0.060424722731113434,
-0.035383615642786026,
0.05679899826645851,
-0.007195452693849802,
-0.016000255942344666,
-0.025537896901369095,
0.01716621220111847,
0.10143681615591049,
0.059771787375211716,
0.011673422530293465,
-0.056785210967063904,
0.03721369802951813,
-0.012892390601336956,
0.019459355622529984,
-0.03442028537392616,
0.0197366364300251,
-0.010810513980686665,
0.026180872693657875,
0.0036823644768446684,
0.07346101850271225,
0.010657889768481255,
-0.029600121080875397,
0.0017226689960807562,
-0.004948209039866924,
-0.047913867980241776,
0.0004287527408450842,
0.000198214765987359,
-0.0002034025965258479,
-0.006948451511561871,
-0.007391763385385275,
0.038928307592868805,
-0.01091806311160326,
0.0037626344710588455,
-0.03362225368618965,
-0.03983131796121597,
0.004809486214071512,
0.03137829899787903,
-0.06287189573049545,
-0.025175321847200394,
0.05026603490114212,
-0.02088211290538311,
-0.04611871764063835,
-0.000888315960764885,
-0.011645996011793613,
-0.04713454097509384,
0.004247261211276054,
0.0492885522544384,
-0.013936937786638737,
-0.02457909844815731,
0.0000869990763021633,
0.037716615945100784,
-0.07595106214284897,
0.007857372984290123,
-0.003733020043000579,
0.013045222498476505,
-0.03758097067475319,
0.0053082979284226894,
-0.0017004196997731924,
-0.031253568828105927,
-0.025049079209566116,
-0.05707938224077225,
-0.0381418913602829,
-0.009842580184340477,
0.047783516347408295,
0.011268234811723232,
0.003236512653529644,
-0.01872646063566208,
-0.012047271244227886,
-0.014599652029573917,
0.03769148513674736,
-0.007772771641612053,
0.008103014901280403,
0.022921999916434288,
-0.009665601886808872,
0.055587343871593475,
-0.019053852185606956,
0.031913939863443375,
-0.06475625932216644,
0.0019490597769618034,
-0.04522286728024483,
0.02275124192237854,
0.02222691848874092,
0.0532509945333004,
-0.0034011206589639187,
0.0037097553722560406,
-0.012863594107329845,
-0.010738372802734375,
-0.031396280974149704,
0.017430054023861885,
-0.012431418523192406,
-0.00530899316072464,
-0.0025242380797863007,
0.02268540859222412,
0.04058000072836876,
0.04008546471595764,
-0.03216199949383736,
-0.0038216905668377876,
0.003690296085551381,
-0.003921297378838062,
-0.008427398279309273,
-0.032468270510435104,
0.01412544772028923,
-0.027560433372855186,
-0.015254898928105831,
0.0009470619261264801,
-0.029159558936953545,
0.02470168098807335,
0.022163117304444313,
-0.016103440895676613,
0.0237088892608881,
0.012561599723994732,
0.0017000546213239431,
-0.024628126993775368,
0.03407168388366699,
-0.04404353350400925,
-0.005033804103732109,
0.030893508344888687,
0.04254910722374916,
-0.02796589955687523,
-0.03401849791407585,
-0.0099340183660388,
0.028598183766007423,
0.004421093966811895,
0.03798162192106247,
-0.049646638333797455,
-0.008302479051053524,
-0.0037976631429046392,
0.02638774737715721,
-0.03533966466784477,
-0.021816272288560867,
-0.04693771153688431,
0.024081319570541382,
-0.024366509169340134,
0.006040454376488924,
-0.024502085521817207,
0.027919016778469086,
-0.034632060676813126,
-0.003739771666005254,
0.038064613938331604,
0.018117118626832962,
-0.06893669068813324,
-0.001886998419649899,
0.05150261148810387,
0.015710776671767235,
0.04348171502351761,
-0.021304016932845116,
-0.05228692293167114,
0.00824055541306734,
-0.04045768454670906,
-0.06569606065750122,
0.036477796733379364,
-0.04432423412799835,
0.004422093741595745,
0.01090755220502615,
-0.018601298332214355,
0.00392930069938302,
0.05804792419075966,
-0.026559457182884216,
-0.005759472027420998,
0.022073738276958466,
-0.02754964865744114,
-0.03542044013738632,
-0.015882059931755066,
0.024753371253609657,
-0.013951362110674381,
-0.035431474447250366,
0.026461973786354065,
0.04440608248114586,
0.029770266264677048,
-0.031633589416742325,
0.020166384056210518,
-0.022417917847633362,
0.015662536025047302,
-0.010703522711992264,
-0.03221651911735535,
-0.005747247487306595,
0.05721806734800339,
-0.04895778372883797,
0.049025993794202805,
0.01769139990210533,
-0.004063829313963652,
-0.09813333302736282,
-0.02926492877304554,
0.01229072269052267,
0.04153359681367874,
0.020870478823781013,
-0.043351445347070694,
-0.006232012994587421,
0.03966176509857178,
-0.09893504530191422,
0.0156669020652771,
-0.004731069318950176,
-0.012856267392635345,
-0.029666028916835785,
-0.02022329531610012,
-0.0005589902284555137,
0.05928919091820717,
0.052987731993198395,
0.06814580410718918,
-0.03562646731734276,
0.027765223756432533,
-0.04768654704093933,
-0.06495000422000885,
-0.028188087046146393,
0.02727317065000534,
-0.030462635681033134,
0.002361808205023408,
0.06222527101635933,
-0.030118338763713837,
-0.018952928483486176,
0.053480952978134155,
0.03972133249044418,
0.03947935998439789,
0.017968881875276566,
-0.012179961428046227,
-0.004455342423170805,
0.01486223191022873,
0.047130703926086426,
-0.01680390164256096,
-0.0052796327508986,
0.04007180780172348,
-0.03450998291373253,
0.02551058679819107,
0.040245700627565384,
-0.02107940800487995,
-0.012881654314696789,
-0.027492130175232887,
0.023686693981289864,
0.024233486503362656,
-0.001366496435366571,
-0.008037158288061619,
0.002797090681269765,
0.039044592529535294,
-0.011145470663905144,
-0.004531971178948879,
-0.01001793798059225,
-0.038519199937582016,
-0.020318035036325455,
0.009966464713215828,
-0.030113453045487404,
-0.0215265192091465,
0.031128523871302605,
0.002462381962686777,
-0.009518666192889214,
0.011678052134811878,
0.011243375018239021,
0.012294423766434193,
-0.02496332861483097,
0.0000769782200222835,
0.0015679936623200774,
0.019859306514263153,
-0.010404197499155998,
-0.026100892573595047,
-0.014550757594406605,
0.03707320615649223,
0.013940611854195595,
0.04032465070486069,
0.017404569312930107,
-0.04155857115983963,
-0.019227931275963783,
-0.03556961938738823,
0.0352359414100647,
0.01972806453704834,
0.0003975899307988584,
-0.060467224568128586,
-0.017572788521647453,
-0.010150304064154625,
0.024803217500448227,
0.04972631484270096,
-0.03572060912847519,
0.02085350640118122,
0.009132751263678074,
0.012925787828862667,
0.034174054861068726,
-0.047180142253637314,
-0.03242861479520798,
0.021932749077677727,
-0.07430322468280792,
-0.0057553453370928764,
-0.016499293968081474,
-0.0274825356900692,
0.0018387350719422102,
0.03900087997317314,
-0.04369042068719864,
0.0327390655875206,
0.04868265613913536,
-0.027084819972515106,
0.042741235345602036,
0.013858646154403687,
-0.0046227253042161465,
0.07324035465717316,
-0.014782244339585304,
0.024860277771949768,
0.019152699038386345,
-0.013340344652533531,
0.015120047144591808,
-0.0014747182140126824,
-0.036938246339559555,
0.014511906541883945,
-0.012094667181372643,
-0.030329151079058647,
0.03885401785373688,
-0.03088623844087124,
-0.013982522301375866,
0.06359713524580002,
0.0025935200974345207,
0.02262880839407444,
0.04624443128705025,
-0.0009348873281851411,
0.03209336847066879,
-0.012808036059141159,
0.027108116075396538,
0.02707960084080696,
-0.0018731890013441443,
-0.0050706020556390285,
0.04145407676696777,
0.01550737489014864,
-0.013562689535319805,
0.01060813944786787,
0.030712706968188286,
-0.006129642948508263,
0.032151319086551666,
-0.02179616130888462,
0.05758513882756233,
-0.03074471466243267,
0.01947418786585331,
-0.011712686158716679,
-0.03205892816185951,
0.009475847706198692,
0.012006297707557678,
-0.06038918346166611,
0.06715946644544601,
-0.02162984013557434,
-0.0010448393877595663,
-0.023707831278443336,
-0.036626920104026794,
-0.026117311790585518,
0.010282855480909348,
0.002630014205351472,
0.026675034314393997,
-0.0027145054191350937,
-0.022899672389030457,
0.014385276474058628,
0.03414945676922798,
0.020058611407876015,
-0.04067670553922653,
0.016521625220775604,
-0.02879999205470085,
0.0007309391512535512,
-0.0007695891545154154,
-0.029780320823192596,
-0.014825764112174511,
-0.004336646758019924,
0.03249496594071388,
0.011561079882085323,
0.0008418141514994204,
-0.07493007183074951,
0.005685236304998398,
-0.022534683346748352,
0.03923527151346207,
-0.054734550416469574,
0.011741375550627708,
-0.01215443853288889,
0.040070511400699615,
-0.011788317002356052,
-0.02407669648528099
] |
<p>One day it was raining outside and I was breathing on the glass of my window. I noticed that around the spots of fly poop there is a circle where vapor does not condense. With time the circle becomes larger and larger as the condensation slowly disappears. </p>
<p>Why does this happen? </p>
<p>Edit: Note that the poop is there from days ago, so it's not warmer than the glass. If the effect has something to do with the poop being warmer, please give me a motivation.</p>
<p>There is an image <a href="https://www.dropbox.com/sc/w3u7bpcadms9f9z/vJI2DH8KVh">here</a> which is also shown below. Sorry that it is out of focus; my phone's autofocus couldn't pick out the foreground image.</p>
<p><img src="http://i.stack.imgur.com/M3kw3.jpg" alt="enter image description here"></p>
| 8,824 |
[
-0.043704867362976074,
-0.03160449489951134,
0.031381670385599136,
0.006321159191429615,
-0.008084666915237904,
-0.02669139951467514,
-0.01621481031179428,
-0.008212215267121792,
0.004119958262890577,
-0.01364948321133852,
0.03880539909005165,
0.056342680007219315,
0.02348373830318451,
-0.013856010511517525,
-0.028023868799209595,
0.005224160384386778,
-0.003974147140979767,
-0.016021471470594406,
-0.01624230295419693,
-0.028807757422327995,
-0.061711933463811874,
0.024244099855422974,
-0.019649522379040718,
-0.03166097775101662,
-0.031948450952768326,
0.028539037331938744,
0.0027389000169932842,
-0.005242613144218922,
-0.021340586245059967,
0.0070494781248271465,
-0.055149272084236145,
0.005993384402245283,
-0.00041899512871168554,
-0.002568777883425355,
0.0087873674929142,
-0.026285000145435333,
-0.014869557693600655,
-0.007306826766580343,
-0.0036413322668522596,
0.020089995115995407,
0.022488277405500412,
-0.01920195110142231,
-0.015245910733938217,
0.02306401915848255,
-0.052938662469387054,
-0.02346804365515709,
-0.0059258174151182175,
0.03185456618666649,
0.08652438968420029,
-0.056445349007844925,
0.03340964764356613,
-0.014840509742498398,
0.05592271685600281,
0.040908172726631165,
0.0088422866538167,
0.011574489064514637,
0.04117181897163391,
0.07631409913301468,
-0.01912100985646248,
-0.06441356241703033,
-0.001514842384494841,
-0.03103935346007347,
-0.04228097200393677,
0.02458733320236206,
-0.021773118525743484,
-0.0012252087472006679,
0.007437289226800203,
-0.030352473258972168,
0.02105896733701229,
0.015398243442177773,
0.02450943924486637,
0.013860423117876053,
0.03866872563958168,
0.015068202279508114,
0.03587374836206436,
-0.024220487102866173,
0.004993947222828865,
0.005760863423347473,
0.04436885938048363,
0.036650825291872025,
-0.01260727271437645,
0.023998577147722244,
0.00958949699997902,
-0.01592743955552578,
0.029463259503245354,
0.001678692875429988,
0.10724224150180817,
-0.05594557896256447,
-0.014633458107709885,
0.05564727634191513,
0.030937129631638527,
0.02488495223224163,
0.027111373841762543,
0.018198583275079727,
-0.000709685729816556,
0.030827824026346207,
-0.03696146234869957,
0.0090235760435462,
-0.0033934798557311296,
-0.01907447539269924,
-0.02582577057182789,
0.0072550163604319096,
0.017874525859951973,
0.07661258429288864,
-0.000014301210285339039,
-0.027253316715359688,
-0.0639139860868454,
0.01384986937046051,
0.0069199190475046635,
-0.004996425472199917,
-0.09035293012857437,
-0.041669610887765884,
-0.011472453363239765,
-0.0013380851596593857,
0.012590131722390652,
-0.027327198535203934,
0.009412259794771671,
0.0008923316490836442,
0.02166949026286602,
0.05090723931789398,
0.0213613323867321,
-0.022431347519159317,
0.006627113092690706,
-0.056767962872982025,
-0.09212534874677658,
0.05414978042244911,
0.043859295547008514,
-0.005299900192767382,
-0.018029924482107162,
0.02741694264113903,
-0.020136890932917595,
-0.01637483388185501,
0.07331456989049911,
0.0046507734805345535,
-0.00009731582395033911,
-0.02037915401160717,
-0.0922984704375267,
-0.026391731575131416,
0.04595743864774704,
-0.00041559815872460604,
-0.01122540608048439,
-0.06925950944423676,
0.0023307695519179106,
0.049733906984329224,
0.07395987212657928,
0.019324295222759247,
-0.00003343739081174135,
-0.035766392946243286,
0.05692111328244209,
0.020884104073047638,
-0.0029108766466379166,
0.0017442242242395878,
0.018835242837667465,
-0.07194440066814423,
0.00289676571264863,
-0.021931730210781097,
0.02392149344086647,
0.08440276980400085,
0.01923462189733982,
-0.029341304674744606,
0.04174279421567917,
-0.015893206000328064,
0.002424552571028471,
-0.014320776797831059,
-0.010795694775879383,
-0.06461281329393387,
0.06981724500656128,
0.02557123266160488,
-0.011942549608647823,
-0.04642680287361145,
0.0007573463954031467,
0.053504545241594315,
-0.012335820123553276,
0.00858813151717186,
0.0587526299059391,
0.014894090592861176,
0.021438658237457275,
-0.03241543099284172,
0.02628987468779087,
0.04529331624507904,
-0.0057634832337498665,
-0.0004957778146490455,
-0.0409054234623909,
0.008825263008475304,
0.011071448214352131,
0.02155981957912445,
-0.002642744453623891,
-0.05578901618719101,
0.033051747828722,
-0.07068976014852524,
-0.057162921875715256,
-0.09831640124320984,
0.006440774537622929,
-0.011388699524104595,
-0.015698524191975594,
-0.021608293056488037,
0.016914354637265205,
0.02556629106402397,
-0.004803630989044905,
-0.033349767327308655,
0.009880954399704933,
0.018483946099877357,
0.035369858145713806,
-0.01611216552555561,
-0.02611834555864334,
0.02777375467121601,
0.013384620659053326,
-0.032203104346990585,
0.0038655672688037157,
-0.05470443516969681,
0.03665380924940109,
-0.02752409316599369,
0.012003364972770214,
-0.02710353210568428,
-0.06519192457199097,
-0.01952105574309826,
0.05959369242191315,
0.07022316753864288,
0.01858118735253811,
0.018674205988645554,
-0.025740372017025948,
0.03435831889510155,
0.04989860951900482,
-0.011368300765752792,
0.00047993205953389406,
-0.003579121781513095,
0.04358543083071709,
-0.0018183373613283038,
0.010118003934621811,
-0.018855437636375427,
-0.03546757251024246,
-0.012782317586243153,
0.018829036504030228,
-0.004473839420825243,
-0.00555789889767766,
-0.009616883471608162,
-0.013470391742885113,
0.04637329280376434,
-0.007267415057867765,
0.04994601756334305,
0.02950439229607582,
0.015798883512616158,
0.019198542460799217,
0.03500887006521225,
0.066663458943367,
0.011238142848014832,
0.03298786282539368,
-0.0128470528870821,
0.06260459870100021,
-0.04496525600552559,
-0.051047954708337784,
0.006478678900748491,
-0.027804818004369736,
-0.0056859273463487625,
-0.06853046268224716,
0.02997182123363018,
0.018954811617732048,
-0.033818624913692474,
-0.02362470142543316,
0.02686242386698723,
0.0033917108085006475,
0.035159192979335785,
-0.06948353350162506,
-0.038030240684747696,
0.006313308607786894,
0.0791386142373085,
-0.030912650749087334,
-0.019160710275173187,
0.026529816910624504,
-0.054674457758665085,
0.040658701211214066,
-0.04385681450366974,
-0.03507980331778526,
-0.03193041309714317,
0.01920408196747303,
0.02782534807920456,
0.022292282432317734,
-0.009681427851319313,
0.016361219808459282,
-0.03723256289958954,
-0.035572707653045654,
-0.013289605267345905,
-0.01940378174185753,
0.002880699699744582,
-0.010378334671258926,
-0.009785844013094902,
0.04084666818380356,
0.01016053557395935,
0.010630236007273197,
0.008449888788163662,
-0.02143365889787674,
-0.032414473593235016,
-0.0204171072691679,
-0.009495430625975132,
-0.022699205204844475,
-0.022387027740478516,
0.019164737313985825,
-0.013579081743955612,
0.02958470582962036,
-0.011248963885009289,
-0.019018080085515976,
-0.05112864822149277,
0.037497442215681076,
-0.059267234057188034,
-0.035236965864896774,
-0.036598630249500275,
-0.028958531096577644,
0.029508398845791817,
-0.014493420720100403,
-0.002666347660124302,
-0.029346244409680367,
0.015576324425637722,
-0.03726877272129059,
-0.027913773432374,
-0.02875026874244213,
0.019073529168963432,
-0.004315586294978857,
0.019604194909334183,
0.00603661360219121,
-0.007690052036195993,
0.06269911676645279,
0.0021185888908803463,
-0.01901581697165966,
-0.020840181037783623,
-0.014655113220214844,
-0.053784359246492386,
-0.04726182296872139,
-0.0036702363286167383,
0.042698848992586136,
-0.005851109977811575,
0.013430147431790829,
0.03524961322546005,
0.059744469821453094,
0.029353003948926926,
0.021416109055280685,
-0.023346522822976112,
-0.00582220871001482,
0.005203756969422102,
-0.026025157421827316,
0.030666770413517952,
0.010677254758775234,
0.0031404332257807255,
-0.027057049795985222,
0.00454523554071784,
-0.008700436912477016,
0.036562588065862656,
-0.08187117427587509,
0.0002663883497007191,
0.021597115322947502,
0.038312558084726334,
-0.040438421070575714,
0.05645286664366722,
-0.02817004919052124,
-0.026595791801810265,
-0.034539107233285904,
-0.014280886389315128,
0.05259917676448822,
0.008348440751433372,
-0.00798637792468071,
0.05475384369492531,
0.02690781094133854,
-0.04264168068766594,
-0.025239013135433197,
-0.016555145382881165,
-0.018194902688264847,
0.019677890464663506,
0.005779007915407419,
-0.013059703633189201,
0.06546048820018768,
0.016716964542865753,
0.036928389221429825,
0.030816005542874336,
-0.060628656297922134,
-0.0011257481528446078,
-0.02136600948870182,
0.002057267352938652,
0.006499553099274635,
0.04391030967235565,
-0.014613752253353596,
0.02581942081451416,
0.009779841639101505,
0.04032183438539505,
0.045713428407907486,
-0.025132954120635986,
-0.07064846903085709,
-0.006387661211192608,
0.030944768339395523,
-0.03214534744620323,
-0.007013504393398762,
-0.02436484955251217,
0.0010971162701025605,
-0.019660422578454018,
-0.006393211428076029,
0.0415501706302166,
0.020111817866563797,
-0.05634159594774246,
-0.004620403982698917,
-0.004937414545565844,
0.0018996321596205235,
-0.06178417429327965,
0.016950320452451706,
0.02634693868458271,
0.005974941421300173,
0.039236705750226974,
0.03640945255756378,
0.009166792035102844,
-0.00537529494613409,
-0.03624790534377098,
0.007970444858074188,
0.04480375349521637,
0.02114897221326828,
0.02730249986052513,
-0.015043314546346664,
-0.00007796522550052032,
-0.013140886090695858,
0.0007691120845265687,
0.0038430620916187763,
-0.022114383056759834,
0.005375595763325691,
-0.01594485156238079,
-0.02359917387366295,
-0.017781831324100494,
0.0028385743498802185,
0.025273818522691727,
-0.005822522100061178,
0.07254551351070404,
-0.006828614044934511,
-0.01464009378105402,
-0.0007232062052935362,
0.014713970944285393,
0.048672765493392944,
-0.000711204600520432,
0.005884689278900623,
-0.04274892061948776,
-0.01458309218287468,
-0.03249157592654228,
0.04667987301945686,
0.025951437652111053,
0.03417326509952545,
-0.01327578630298376,
-0.01799841970205307,
0.013541358523070812,
-0.018534453585743904,
0.01422688364982605,
0.016051948070526123,
-0.02432972937822342,
0.013705275021493435,
-0.0459880530834198,
-0.020454062148928642,
-0.009375347755849361,
0.018855756148695946,
0.028164472430944443,
0.008621717803180218,
-0.01250004954636097,
-0.07249722629785538,
-0.007655004970729351,
0.05944245681166649,
0.04831407591700554,
0.002029591938480735,
0.002383795101195574,
-0.07906585186719894,
-0.04323757439851761,
0.039331838488578796,
-0.05291095748543739,
0.024470951408147812,
-0.02178375795483589,
-0.012251108884811401,
0.00801019836217165,
-0.037277452647686005,
-0.018160726875066757,
0.026890896260738373,
-0.03678718954324722,
0.009001744911074638,
-0.024271920323371887,
-0.03490710258483887,
-0.0016775090480223298,
0.03140983730554581,
-0.016436398029327393,
0.022367848083376884,
0.017311621457338333,
0.006226100958883762,
-0.046073853969573975,
-0.0401938334107399,
-0.036350067704916,
-0.0671633630990982,
0.02213149704039097,
0.012685352936387062,
-0.03037255071103573,
0.04867802932858467,
-0.040334735065698624,
-0.012803031131625175,
0.01047598198056221,
-0.010325710289180279,
-0.05803690105676651,
-0.019551875069737434,
-0.04612065479159355,
0.003010316053405404,
0.01647701859474182,
-0.003998194821178913,
0.0181354321539402,
0.04425082728266716,
0.01435689814388752,
0.005156815983355045,
-0.019223587587475777,
0.053972769528627396,
-0.03430292755365372,
-0.028537649661302567,
-0.024206925183534622,
-0.043054766952991486,
-0.040042150765657425,
0.0815650001168251,
0.027091803029179573,
-0.0010550754377618432,
-0.004064683336764574,
-0.015213356353342533,
0.000370378780644387,
0.00022225524298846722,
-0.01724136434495449,
0.014093185774981976,
0.004586015362292528,
0.012737755663692951,
0.004648621194064617,
-0.016123438253998756,
0.03609795495867729,
-0.0022818907164037228,
0.011352003552019596,
0.05688396096229553,
0.0007782960310578346,
0.014506159350275993,
-0.052310310304164886,
-0.007531377952545881,
0.016528483480215073,
-0.03153599426150322,
0.042991604655981064,
-0.02116878144443035,
-0.0219286922365427,
0.04105689004063606,
-0.059965986758470535,
0.02842520922422409,
0.004720641300082207,
-0.00027464982122182846,
0.007437692955136299,
-0.0701194480061531,
0.035190969705581665,
0.032222066074609756,
0.002887129783630371,
-0.02855514921247959,
-0.07073084264993668,
0.05584026500582695,
0.034065570682287216,
-0.03745393455028534,
-0.06522248685359955,
-0.01830861158668995,
-0.016798073425889015,
-0.04910000413656235,
0.016896164044737816,
-0.022299518808722496,
-0.03202969953417778,
0.010334690101444721,
0.029803741723299026,
0.0019731526263058186,
0.05200660601258278,
0.007921366021037102,
0.0022867810912430286,
0.041103579103946686,
-0.004847551696002483,
-0.057293593883514404,
0.02129330486059189,
0.02512066625058651,
-0.024760408326983452,
-0.033913303166627884,
0.006122191436588764,
-0.00817512534558773,
0.03826136142015457,
0.014935488812625408,
-0.02494034916162491,
-0.003878014162182808,
0.02399032935500145,
0.006500191520899534,
-0.014511806890368462,
0.024712661281228065,
0.0052687800489366055,
0.003108951495960355,
-0.008492783643305302,
0.013118735514581203,
0.013469832949340343,
-0.03053242899477482,
0.0013043683720752597,
0.007899260148406029,
-0.04412465542554855,
0.01035270094871521,
0.06907147169113159,
-0.06004456803202629,
0.02096743881702423,
0.021868929266929626,
-0.03344845771789551,
0.004114176612347364,
-0.005993957165628672,
-0.020178472623229027,
0.016446935012936592,
0.03416319936513901,
-0.06233111396431923,
-0.0003064310585614294,
-0.03798876330256462,
-0.03772004321217537,
0.03362276405096054,
-0.018646009266376495,
0.02645518258213997,
0.02145305462181568,
-0.03879941999912262,
0.029677391052246094,
0.002882331144064665,
0.006605838425457478,
0.03152776136994362,
-0.023747529834508896,
-0.0007880107150413096,
-0.008348138071596622,
-0.001743648899719119,
0.03426877036690712,
0.04963789880275726,
-0.017437919974327087,
-0.00005694428546121344,
0.0060944706201553345,
-0.016498729586601257,
0.04176068305969238,
-0.03741135448217392,
-0.028180809691548347,
0.02748488448560238,
-0.036258816719055176,
0.044495727866888046,
0.0019569757860153913,
-0.018395284190773964,
0.041411563754081726,
0.023334017023444176,
0.010096646845340729,
-0.046827711164951324,
0.0018211735878139734,
-0.04413125663995743,
0.011212268844246864,
0.021941356360912323,
-0.025298701599240303,
-0.027148501947522163,
-0.007937056943774223,
0.011539367958903313,
0.016041304916143417,
0.016564015299081802,
-0.010675501078367233,
-0.0033870453480631113,
0.003680975642055273,
-0.030526749789714813,
-0.01763031631708145,
0.04651079326868057,
0.0037663416005671024,
-0.005407573189586401,
-0.007087664678692818,
-0.0312056764960289,
0.0017462738323956728,
0.016113106161355972,
-0.011661459691822529,
0.028794437646865845,
0.03842601925134659,
0.020567761734128,
-0.001575887086801231,
-0.003989246673882008,
0.025752076879143715,
0.1431596279144287,
0.015966935083270073,
0.00035009923158213496,
-0.021341217681765556,
0.0008593671955168247,
0.03200992941856384,
0.012992143630981445,
-0.02614022232592106,
-0.0006977292941883206,
-0.022429730743169785,
0.026386067271232605,
0.053673505783081055,
0.05092429369688034,
0.01358134113252163,
0.039287175983190536,
0.010571863502264023,
-0.03914425149559975,
-0.030099425464868546,
0.00525887543335557,
-0.024534888565540314,
-0.010996183380484581,
0.05165184661746025,
-0.05034497752785683,
0.03291473910212517,
-0.024763543158769608,
0.027167396619915962,
-0.03302071988582611,
-0.025178097188472748,
0.01552741788327694,
0.024413971230387688,
-0.030830372124910355,
0.02419961430132389,
0.011953583918511868,
-0.027476206421852112,
-0.04428154230117798,
-0.011916986666619778,
0.003880307776853442,
0.00003698346336022951,
0.016435973346233368,
0.008334748446941376,
0.042717937380075455,
0.0033439258113503456,
-0.0013558362843468785,
0.03168819472193718,
-0.036861762404441833,
0.00938564632087946,
-0.020795853808522224,
0.05914875119924545,
-0.009021700359880924,
0.008737390860915184,
-0.021213708445429802,
0.0034700012765824795,
0.01118779182434082,
-0.05104522407054901,
-0.02044382505118847,
0.009749671444296837,
0.014883109368383884,
0.006850781384855509,
-0.05095434933900833,
-0.03587717562913895,
-0.004468897823244333,
0.031091855838894844,
0.019024264067411423,
-0.006758904550224543,
-0.0023982799611985683,
-0.017438743263483047,
-0.028762970119714737,
0.05191227048635483,
-0.022613348439335823,
0.006059963256120682,
0.007184775546193123,
-0.026697024703025818,
0.002105948282405734,
0.011741318739950657,
0.0007367038051597774,
0.008094770833849907,
0.028398221358656883,
0.026554519310593605,
-0.026924949139356613,
0.01677996851503849,
-0.06654846668243408,
0.009794752113521099,
-0.012035720981657505,
0.006616793107241392,
-0.03163166716694832,
-0.011891272850334644,
-0.018705764785408974,
0.03213318809866905,
-0.023655496537685394,
-0.03170204907655716,
0.005930083338171244,
0.08559071272611618,
0.00048306109965778887,
-0.01046543475240469,
-0.03531273081898689,
0.03901980072259903,
0.022311411798000336,
-0.0023954291827976704,
-0.0025998828932642937,
0.06037340685725212,
0.0008970869239419699,
0.00931556336581707,
0.01633869670331478,
0.006272272672504187,
-0.025486933067440987,
0.017262965440750122,
0.009836437180638313,
-0.013839487917721272,
-0.023422274738550186,
0.009479307569563389,
-0.028421292081475258,
-0.028707487508654594,
-0.017954621464014053,
-0.03046785295009613,
0.02032250165939331,
-0.02719813771545887,
0.023008989170193672,
-0.012453976087272167,
0.030676623806357384,
-0.01126051414757967,
0.04849996417760849,
0.002869801362976432,
-0.039897024631500244,
-0.09145918488502502,
-0.038001637905836105,
0.021704446524381638,
-0.0016109482385218143,
-0.0039017274975776672,
0.052579499781131744,
-0.03379298001527786,
-0.00013445703370962292,
0.01621505245566368,
0.03823099285364151,
-0.0034504500217735767,
0.002905718283727765,
0.046721283346414566,
0.009142467752099037,
0.05067380890250206,
-0.0316220186650753,
-0.032334938645362854,
0.03558892756700516,
-0.03641762584447861,
-0.0567452609539032,
0.007240703795105219,
0.014505053870379925,
0.028330199420452118,
0.02721344493329525,
-0.01612577773630619,
0.034723151475191116,
0.060416605323553085,
-0.021645795553922653,
-0.017909569665789604,
-0.022873491048812866,
-0.02118176594376564,
0.041866615414619446,
0.025432325899600983,
0.006747223902493715,
-0.011808986775577068,
-0.017834004014730453,
0.05727466195821762,
0.04039651155471802,
0.01695571281015873,
-0.026899315416812897,
-0.0072135101072490215,
-0.06156420707702637,
0.032913900911808014,
0.015852157026529312,
0.010718391276896,
0.04169538989663124,
0.02007422037422657,
-0.04410679265856743,
0.013682388700544834,
0.0306716226041317,
-0.0291362926363945,
-0.10964184999465942,
0.029387138783931732,
0.02463696151971817,
0.02389395609498024,
0.028150437399744987,
-0.025910528376698494,
0.05489008501172066,
0.04022100195288658,
-0.02937415800988674,
0.004364058841019869,
-0.015057053416967392,
0.0003103416820522398,
-0.040543846786022186,
-0.010152267292141914,
-0.020155439153313637,
0.03152339532971382,
0.0457434356212616,
0.05271231010556221,
0.032114122062921524,
0.045031581073999405,
-0.03690088167786598,
-0.07948481291532516,
-0.022283438593149185,
0.03065238893032074,
0.005580288823693991,
0.0019201076356694102,
0.03761317580938339,
-0.023093227297067642,
0.04309057071805,
0.02475506067276001,
-0.02099057100713253,
-0.015125389210879803,
-0.0036908965557813644,
0.021321773529052734,
-0.021160084754228592,
0.02695510908961296,
0.04833700880408287,
0.019467812031507492,
-0.013497832231223583,
-0.0024051000364124775,
0.045329708606004715,
0.01784973219037056,
0.03572041168808937,
-0.02067100629210472,
-0.0016486658714711666,
-0.008089078590273857,
-0.011712811887264252,
0.045980677008628845,
-0.024564890190958977,
-0.027161480858922005,
0.023682154715061188,
0.029937928542494774,
0.0012749930610880256,
-0.006409207824617624,
-0.015061094425618649,
-0.05232836678624153,
0.030072299763560295,
-0.001916320063173771,
0.013535255566239357,
-0.0015604110667482018,
0.0069393012672662735,
0.0032397336326539516,
-0.013492672704160213,
-0.01712675392627716,
0.008053102530539036,
-0.030122002586722374,
0.0026226125191897154,
-0.012682267464697361,
-0.0017576630925759673,
0.02023700438439846,
0.010753628797829151,
-0.008152635768055916,
-0.03717600554227829,
0.018744220957159996,
0.007647456135600805,
-0.01213321927934885,
-0.016863061115145683,
-0.020002512261271477,
-0.022136596962809563,
-0.058867622166872025,
0.03582800179719925,
-0.016827916726469994,
-0.030807970091700554,
-0.05642601475119591,
0.028219616040587425,
-0.005398179404437542,
0.008311169221997261,
0.05981498956680298,
-0.027837222442030907,
0.025200651958584785,
0.023453136906027794,
0.02109927125275135,
0.014795844443142414,
-0.042720161378383636,
0.008087470196187496,
-0.031212054193019867,
-0.0059637650847435,
0.039846405386924744,
0.0068742576986551285,
-0.004104977007955313,
0.038590263575315475,
0.030692359432578087,
-0.026707101613283157,
0.01514595840126276,
-0.026865322142839432,
-0.01736712083220482,
0.035209644585847855,
0.027886219322681427,
-0.013662797398865223,
0.056934114545583725,
0.001587073551490903,
-0.003988001961261034,
0.01911400817334652,
0.0014730648836120963,
-0.032617487013339996,
0.043936051428318024,
-0.006807256024330854,
-0.016530439257621765,
-0.017870811745524406,
-0.004988376051187515,
0.025776375085115433,
-0.05958564952015877,
0.03181159868836403,
-0.010003671050071716,
-0.01893368922173977,
-0.0018099239096045494,
0.049361005425453186,
-0.006119879893958569,
0.023126132786273956,
0.01350011583417654,
0.017792334780097008,
0.0076286098919808865,
0.005784087814390659,
-0.008413577452301979,
0.0782313421368599,
0.019527580589056015,
0.007147421594709158,
0.022995932027697563,
0.005028465762734413,
0.017414970323443413,
0.0541471391916275,
-0.011064006946980953,
0.05486299842596054,
-0.017240241169929504,
-0.02097754180431366,
0.02408492937684059,
-0.023497510701417923,
-0.011080408468842506,
0.03525293245911598,
0.010561730712652206,
0.026226524263620377,
0.004273987840861082,
0.0135115971788764,
0.0014493829803541303,
-0.0011864957632496953,
-0.013720919378101826,
0.00900792982429266,
0.012515198439359665,
0.033369921147823334,
0.04422557353973389,
-0.026511840522289276,
0.007356060203164816,
0.010204974561929703,
-0.011784927919507027,
0.010708929970860481,
0.04859507456421852,
0.0065596215426921844,
0.03314829245209694,
-0.029886536300182343,
-0.006462856661528349,
0.013813736848533154,
0.0010383109329268336,
0.023512670770287514,
0.029333483427762985,
-0.0075467852875590324,
0.009570165537297726,
-0.012871132232248783,
-0.0415465272963047,
0.06544902175664902,
-0.027180159464478493,
-0.027919357642531395,
-0.01087075937539339,
0.02003043331205845,
-0.00541315833106637,
-0.04288741573691368
] |
<p>Let's have Dirac spinor $\Psi (x)$, which formally corresponds to
$$
\left( 0, \frac{1}{2} \right) \oplus \left( \frac{1}{2}, 0 \right)
$$
representation of the Lorentz group.</p>
<p>What representation is true for $\Psi (x) \Psi^{+}(x')$? I expect something like
$$
\left[\left(\frac{1}{2}, 0 \right) \oplus \left( 0, \frac{1}{2} \right)\right]\otimes \left[\left( 0, \frac{1}{2} \right) \oplus \left( \frac{1}{2}, 0\right)\right] =
$$
$$
=\left(\frac{1}{2}, 0 \right) \otimes \left(\frac{1}{2}, 0 \right) \oplus \left(\frac{1}{2}, 0 \right) \otimes \left( 0 , \frac{1}{2}\right) \oplus \left( 0, \frac{1}{2} \right) \otimes \left(0, \frac{1}{2} \right) =
$$
$$
\tag 1 =\left[\left( 0, 0\right)\oplus (1, 0) \right]\oplus \left( \frac{1}{2} , \frac{1}{2}\right) \oplus \left[\left( 0, 0\right)\oplus (0, 1) \right],
$$
but I'm not sure.</p>
<p>Also I know that
$$
\tag 2 [\Psi (x), \Psi^{+}(y)]_{+} = i\left( i\gamma^{\mu}\partial_{\mu} + m\right)\gamma_{0}D_{m}(x - y),
$$
where $D_{m}(x - y)$ is a lorentz scalar function, so formally $(2)$ doesn't coinside with $(1)$. How to
compare it with $(1)$?</p>
| 8,825 |
[
-0.00022252903727348894,
0.022171614691615105,
0.0014369268901646137,
-0.04061903432011604,
0.026564698666334152,
0.04031684994697571,
-0.04894338548183441,
-0.06455134600400925,
-0.0007353956461884081,
-0.06828948855400085,
0.04126482084393501,
0.008683976717293262,
0.04512668773531914,
0.006319150328636169,
0.018625186756253242,
0.03664322942495346,
-0.05320637300610542,
0.023135773837566376,
-0.001724723493680358,
-0.03592346981167793,
0.01117988396435976,
0.011818044818937778,
0.010403407737612724,
-0.0022487672977149487,
-0.012576458044350147,
0.0538904145359993,
-0.002828850643709302,
-0.007434134837239981,
-0.013796688057482243,
0.046824708580970764,
-0.03062758781015873,
-0.06502775102853775,
0.0006157075404189527,
0.0034957965835928917,
0.002095490926876664,
-0.013188640587031841,
-0.028376750648021698,
-0.035266704857349396,
0.030078738927841187,
0.0022161451634019613,
-0.02162237837910652,
-0.0288927610963583,
-0.024769118055701256,
0.011204644106328487,
-0.02045859396457672,
0.018254095688462257,
0.009742418304085732,
-0.01135231927037239,
0.06690020859241486,
-0.05170389264822006,
0.09211114048957825,
0.00988216046243906,
-0.0118241673335433,
-0.023116135969758034,
-0.004891241434961557,
-0.0135069964453578,
0.0751347467303276,
0.09449445456266403,
0.012995687313377857,
-0.0522761270403862,
-0.02045380510389805,
-0.008929594419896603,
0.03267447650432587,
-0.01617787405848503,
0.01634906604886055,
0.035319093614816666,
0.010319006629288197,
0.026958033442497253,
-0.0043666670098900795,
0.00861040037125349,
0.015206613577902317,
0.009555245749652386,
0.056032001972198486,
-0.00385867222212255,
0.013461468741297722,
0.00539854122325778,
-0.011735174804925919,
0.00036016033845953643,
0.04154729098081589,
0.0020304364152252674,
0.016227373853325844,
0.0066163195297122,
-0.02273392118513584,
0.005067304242402315,
-0.0021252892911434174,
-0.02225314825773239,
0.05433051660656929,
0.011761975474655628,
-0.002264921786263585,
0.02591826394200325,
0.005364495329558849,
0.0014587159967049956,
0.04844871535897255,
-0.023409822955727577,
-0.023921597748994827,
0.03722580522298813,
-0.0020874906331300735,
0.009473326615989208,
-0.0018386918818578124,
0.008777007460594177,
-0.02095036394894123,
-0.047146718949079514,
-0.033283334225416183,
0.08419103175401688,
0.010429061949253082,
0.019172193482518196,
-0.014631466008722782,
-0.0025859226007014513,
-0.04764924198389053,
-0.0369744673371315,
-0.024787839502096176,
0.05677245184779167,
-0.05059455335140228,
0.010771547444164753,
-0.027001911774277687,
-0.037997834384441376,
0.0030725596006959677,
-0.022762887179851532,
0.039734333753585815,
0.07506626099348068,
0.02925814501941204,
0.005953386425971985,
-0.004027245566248894,
-0.012613561004400253,
-0.08466650545597076,
0.008641071617603302,
0.04544214904308319,
0.004616123158484697,
-0.0411500483751297,
-0.012127917259931564,
0.03097013384103775,
-0.0004495992907322943,
0.036949366331100464,
0.03813754394650459,
-0.011238344945013523,
-0.04698210582137108,
-0.08464699983596802,
-0.017946423962712288,
-0.007845507934689522,
-0.03736021742224693,
0.0001789617963368073,
-0.082626573741436,
-0.024623949080705643,
0.002543837996199727,
0.09597998112440109,
-0.02763919159770012,
0.06520422548055649,
0.010255780071020126,
0.02283305488526821,
0.01653783954679966,
-0.012967381626367569,
-0.020897632464766502,
-0.019017398357391357,
-0.05614299699664116,
0.02360132336616516,
0.008647832088172436,
0.01902487315237522,
0.06639870256185532,
-0.026545511558651924,
0.0009568217792548239,
0.055841054767370224,
-0.029728002846240997,
0.010567019693553448,
0.03627541661262512,
-0.01705324836075306,
0.007765153888612986,
0.05667032673954964,
0.021930836141109467,
0.015484940260648727,
0.037986524403095245,
-0.009666581638157368,
-0.004851378966122866,
-0.014326087199151516,
0.030443308874964714,
-0.00211148033849895,
-0.0381234772503376,
-0.04759323224425316,
0.0067423558793962,
0.010748634114861488,
-0.019764212891459465,
-0.026564091444015503,
-0.01962216943502426,
-0.04882604256272316,
0.00029075329075567424,
-0.00037451027310453355,
-0.004352389834821224,
0.026935013011097908,
-0.04293089732527733,
-0.006510881241410971,
-0.052089475095272064,
0.01747627556324005,
-0.052884362637996674,
-0.005205706227570772,
-0.020128827542066574,
-0.05156945437192917,
0.0253844503313303,
-0.0045047360472381115,
-0.010047882795333862,
-0.003820710815489292,
-0.02291574329137802,
-0.020582184195518494,
0.037823691964149475,
0.008112824521958828,
-0.023613058030605316,
0.017993850633502007,
0.00672948220744729,
0.03946863114833832,
-0.022818954661488533,
0.023508140817284584,
-0.0023593709338456392,
0.00668021384626627,
-0.0006599188200198114,
0.022033773362636566,
0.004462165758013725,
0.0024440502747893333,
-0.009524242952466011,
-0.00920133013278246,
0.012333204969763756,
-0.011911130510270596,
0.01692625880241394,
-0.04913392663002014,
0.05443459749221802,
0.057807762175798416,
-0.03235143795609474,
-0.008250429295003414,
0.015511533245444298,
-0.019557161256670952,
0.01480310782790184,
-0.05726037546992302,
-0.03704804554581642,
-0.025038734078407288,
0.01395504828542471,
0.07032638788223267,
0.07595476508140564,
-0.05215864256024361,
0.028783416375517845,
0.012823802419006824,
0.03271012008190155,
0.023040587082505226,
0.003751592244952917,
-0.012285208329558372,
-0.05157799646258354,
0.029561534523963928,
-0.004784810356795788,
-0.01596834324300289,
0.019960850477218628,
0.04620778560638428,
-0.022096507251262665,
0.02598973549902439,
0.009973644278943539,
-0.019540734589099884,
0.057721007615327835,
-0.059664707630872726,
-0.018255485221743584,
-0.004725025501102209,
-0.0018050257349386811,
0.024431785568594933,
-0.00610358128324151,
-0.005534003023058176,
0.03709586337208748,
0.0108717679977417,
0.0007143617258407176,
-0.03162126615643501,
-0.011951788328588009,
0.003022188786417246,
-0.004720047116279602,
-0.028326239436864853,
-0.03080553375184536,
-0.0007773162215016782,
-0.01745194010436535,
0.027212100103497505,
0.010894016362726688,
-0.038017526268959045,
0.011997065506875515,
0.000014077771083975676,
0.03654836490750313,
0.018047252669930458,
0.002441460033878684,
-0.030719637870788574,
-0.005044430028647184,
0.022315246984362602,
0.048564594238996506,
0.047358814626932144,
0.02999609149992466,
-0.0435924157500267,
0.013415385037660599,
-0.08543969690799713,
-0.009326356463134289,
0.013529843650758266,
0.03546275570988655,
0.013215447776019573,
-0.0050196400843560696,
-0.025440633296966553,
-0.07133309543132782,
-0.04422687366604805,
-0.014251017943024635,
0.02480781078338623,
-0.039235640317201614,
0.006002106238156557,
0.039101652801036835,
0.012968956492841244,
-0.05148322507739067,
-0.048067983239889145,
-0.0009396542445756495,
-0.04792449623346329,
-0.018395327031612396,
-0.002896052086725831,
-0.0038518602959811687,
-0.02137766405940056,
0.026347201317548752,
-0.006183495279401541,
-0.03236324340105057,
0.0240654107183218,
-0.05898574739694595,
-0.02152824029326439,
0.0013063490623608232,
0.0024151054676622152,
-0.00159896828699857,
0.02968652918934822,
-0.027569295838475227,
0.0972653478384018,
0.01550717931240797,
0.006830235477536917,
-0.056870799511671066,
0.038884758949279785,
-0.013306365348398685,
-0.036575961858034134,
0.009697926230728626,
0.0352926105260849,
0.014259167946875095,
0.03325894474983215,
0.024655664339661598,
0.015080375596880913,
0.02240643836557865,
-0.01758342608809471,
0.00011127100879093632,
0.06972558796405792,
-0.018164319917559624,
0.007331084925681353,
0.04962969198822975,
0.018429134041070938,
0.012277446687221527,
0.006848308257758617,
0.010464231483638287,
-0.04291212931275368,
0.002396021271124482,
0.0006271771271713078,
0.018654169514775276,
0.003793585579842329,
0.009811156429350376,
0.021252671256661415,
0.026762548834085464,
0.009066243655979633,
-0.05734142288565636,
-0.018883787095546722,
0.006540733389556408,
0.003182588843628764,
-0.02185213379561901,
0.00023511541076004505,
0.044733088463544846,
0.004237405490130186,
-0.010790392756462097,
-0.0019427527440711856,
0.00242483988404274,
-0.006196161732077599,
0.001701949629932642,
-0.02888231724500656,
-0.03993317112326622,
0.01022189762443304,
0.030256401747465134,
0.014325210824608803,
-0.009135459549725056,
-0.004104378633201122,
-0.00037255336064845324,
-0.04011476784944534,
0.017304059118032455,
-0.035815607756376266,
0.041099391877651215,
0.015980364754796028,
0.01691954769194126,
0.007645842153578997,
-0.006545995827764273,
-0.018394893035292625,
0.006812733132392168,
-0.023294813930988312,
-0.00788783933967352,
-0.021339723840355873,
-0.005477784667164087,
-0.016629783436655998,
0.0045728255063295364,
0.008558552712202072,
-0.041367460042238235,
-0.03987837955355644,
-0.004318553488701582,
-0.04634610190987587,
-0.05959554389119148,
0.046457689255476,
-0.054629504680633545,
-0.01797095686197281,
-0.047213226556777954,
0.0635363906621933,
0.03803243860602379,
0.00570882810279727,
-0.0008026027353480458,
0.02948351390659809,
-0.047246165573596954,
0.04933249577879906,
0.001214987481944263,
0.009070220403373241,
0.04399149492383003,
-0.009578720666468143,
0.04900890216231346,
0.008202046155929565,
-0.008088359609246254,
-0.013525830581784248,
0.019280117005109787,
0.07611142098903656,
0.024645458906888962,
-0.04023762047290802,
0.003492464777082205,
-0.00866746250540018,
-0.021770521998405457,
-0.0019046125235036016,
0.07379700243473053,
-0.01634231023490429,
0.01593901962041855,
0.03742377460002899,
0.017408782616257668,
0.00216022995300591,
-0.0020369982812553644,
0.052968233823776245,
-0.01969160884618759,
0.0015561302425339818,
-0.030309077352285385,
-0.010991394519805908,
-0.016871685162186623,
0.017946111038327217,
-0.004774829838424921,
0.011334341019392014,
-0.014858321286737919,
0.01262267678976059,
0.030695805326104164,
0.020469211041927338,
-0.01486576534807682,
0.01309733372181654,
0.011262244544923306,
0.006059762556105852,
0.06699235737323761,
0.004042414482682943,
-0.023049386218190193,
0.03154068812727928,
0.027847735211253166,
0.023520827293395996,
-0.012956107035279274,
-0.0272394847124815,
-0.023441525176167488,
0.03015364333987236,
0.017832087352871895,
0.021322080865502357,
0.01085794810205698,
-0.04236189275979996,
-0.005748281721025705,
0.048543531447649,
-0.00869256816804409,
0.020296424627304077,
0.0006704305415041745,
-0.042695000767707825,
0.0020620636641979218,
-0.024686848744750023,
-0.05715423822402954,
0.03520688787102699,
-0.0006204116507433355,
0.02459191530942917,
-0.04098515957593918,
0.04706854745745659,
-0.029584666714072227,
0.02386513724923134,
-0.019921904429793358,
0.03485874831676483,
-0.009021740406751633,
-0.0012396322563290596,
0.009835503064095974,
0.04733608290553093,
0.01877756416797638,
-0.09951722621917725,
0.007324251811951399,
0.006822539027780294,
-0.01841266267001629,
0.03988461568951607,
-0.04049472138285637,
-0.014313487336039543,
0.02629230171442032,
-0.011434387415647507,
0.04045483097434044,
0.046255894005298615,
-0.07083506137132645,
0.052150897681713104,
0.025915879756212234,
-0.011726556345820427,
0.016386307775974274,
0.03541272506117821,
-0.02762456238269806,
-0.010286460630595684,
-0.05296511948108673,
-0.0011129736667498946,
-0.027392202988266945,
-0.006300411187112331,
-0.0010643720161169767,
0.01295088604092598,
-0.025471588596701622,
0.03709355369210243,
-0.02578900381922722,
-0.007573687005788088,
0.018940109759569168,
-0.027339689433574677,
-0.018795831128954887,
0.03518294915556908,
-0.04161849990487099,
-0.010273678228259087,
-0.03330869972705841,
0.03061465173959732,
0.00573977455496788,
-0.029150092974305153,
0.02752312831580639,
-0.02671782858669758,
0.008295689709484577,
0.0664091482758522,
-0.008645853959023952,
0.017931966111063957,
-0.039650123566389084,
0.007545271888375282,
0.003973850514739752,
-0.017567116767168045,
0.0077979243360459805,
0.014881689101457596,
-0.01926065981388092,
0.03572956472635269,
-0.005238426849246025,
-0.038851503282785416,
0.037191908806562424,
-0.043670445680618286,
-0.0026627355255186558,
-0.028011759743094444,
0.013355047442018986,
0.05271657928824425,
-0.0030961851589381695,
-0.07288054376840591,
-0.025905294343829155,
0.0286457147449255,
-0.027554964646697044,
-0.016476882621645927,
-0.03034833073616028,
0.0359114408493042,
-0.032943446189165115,
-0.04269234091043472,
0.02511301450431347,
0.03840399906039238,
-0.03261369466781616,
-0.011152011342346668,
-0.016766373068094254,
-0.0029072987381368876,
0.02050166018307209,
-0.05355527624487877,
-0.013022953644394875,
0.009359017014503479,
-0.016406655311584473,
-0.0004827737284358591,
-0.010165448300540447,
-0.010987688787281513,
-0.0193855632096529,
-0.03304759040474892,
-0.031092923134565353,
0.021548012271523476,
0.010232997126877308,
-0.044860176742076874,
-0.03699088841676712,
0.024071872234344482,
0.04927905276417732,
0.01203454565256834,
-0.03454022854566574,
-0.05037854611873627,
-0.010879578068852425,
0.017874035984277725,
0.02567336894571781,
-0.017363805323839188,
-0.02653767541050911,
-0.0401894710958004,
0.01856403797864914,
-0.055033616721630096,
-0.02011042833328247,
-0.008187622763216496,
0.06912660598754883,
0.008908758871257305,
0.005486750975251198,
0.012028793804347515,
-0.03049880638718605,
-0.0331752635538578,
-0.003187588881701231,
0.04476678743958473,
0.004341972526162863,
0.03460954874753952,
-0.012613225728273392,
-0.008661609143018723,
-0.04752287641167641,
0.036234285682439804,
0.035159915685653687,
0.02944418601691723,
0.005518503487110138,
0.033690065145492554,
-0.010743151418864727,
0.0011182622984051704,
0.005757729057222605,
-0.0246814526617527,
0.024057725444436073,
0.0019844905473291874,
0.05442473292350769,
-0.061853744089603424,
-0.00510937487706542,
0.04245063662528992,
0.03838866576552391,
-0.04097003489732742,
0.022896867245435715,
0.02194339409470558,
-0.014749545603990555,
0.039542049169540405,
-0.01890465058386326,
-0.0543346144258976,
0.04972570762038231,
-0.026330307126045227,
0.016949720680713654,
-0.00909191183745861,
-0.01963978260755539,
0.015206570737063885,
0.05653318390250206,
0.03788895532488823,
-0.015876231715083122,
-0.018331145867705345,
-0.06578488647937775,
0.01296407263725996,
0.020982930436730385,
0.019225630909204483,
0.010781439952552319,
0.0172042828053236,
0.030785096809267998,
0.012362996116280556,
0.01380606833845377,
0.022471044212579727,
-0.01959407702088356,
0.015832720324397087,
-0.032089926302433014,
-0.06836886703968048,
0.04397233575582504,
-0.010571232065558434,
-0.001910551218315959,
-0.00045733695151284337,
-0.030641548335552216,
-0.0005748147377744317,
0.020717352628707886,
0.04644569382071495,
-0.020055901259183884,
0.036032531410455704,
-0.016869718208909035,
-0.0010709468042477965,
-0.003575562499463558,
-0.038628753274679184,
0.14723901450634003,
0.05371128395199776,
0.00786664430052042,
-0.062357574701309204,
-0.024234237149357796,
-0.0022444510832428932,
0.009072607383131981,
-0.03434159234166145,
0.023587649688124657,
0.0025429546367377043,
-0.033471234142780304,
-0.022489992901682854,
0.06616336852312088,
0.0033489863853901625,
-0.02943306416273117,
0.036778949201107025,
-0.0327657088637352,
-0.028141196817159653,
0.028395311906933784,
0.03251197189092636,
-0.02664346806704998,
0.024822251871228218,
-0.07120992243289948,
0.006661470979452133,
-0.029942044988274574,
0.06342113763093948,
-0.017778124660253525,
-0.01816331222653389,
0.01383028645068407,
-0.012069176882505417,
-0.04381440952420235,
-0.012903488241136074,
-0.012428181245923042,
-0.016426201909780502,
-0.03634598106145859,
-0.03281614929437637,
0.027391308918595314,
-0.02443123795092106,
0.020851435139775276,
0.026510363444685936,
0.005526762455701828,
0.021991685032844543,
0.03313503786921501,
0.0014020331436768174,
-0.04676271975040436,
-0.009507461450994015,
-0.03440375626087189,
0.0576445646584034,
-0.02120354399085045,
-0.009545357897877693,
0.046012066304683685,
-0.0302879698574543,
-0.0008600868168286979,
-0.058206796646118164,
-0.007269124500453472,
-0.029611511155962944,
0.03340839222073555,
0.008556959219276905,
0.012470652349293232,
-0.03160752356052399,
0.003922721836715937,
0.0223357193171978,
0.028419241309165955,
-0.044737208634614944,
-0.02201993390917778,
-0.002803409704938531,
-0.011218609288334846,
0.0444885678589344,
0.004073318559676409,
0.01673423871397972,
0.007116809953004122,
-0.0696510374546051,
-0.019544029608368874,
-0.03373843804001808,
0.024104531854391098,
-0.006120676174759865,
0.02367260679602623,
0.03627590090036392,
-0.02423125132918358,
-0.005622663535177708,
-0.0732206180691719,
0.02507336251437664,
-0.01450975239276886,
0.006466912105679512,
-0.0008003400871530175,
-0.01962157152593136,
0.04495934024453163,
0.035699423402547836,
0.010029841214418411,
0.0006281700916588306,
0.019531531259417534,
0.015228555537760258,
0.03287893906235695,
-0.018960343673825264,
0.009965832345187664,
0.0015981157775968313,
-0.03216635808348656,
-0.0002390792651567608,
-0.03121989220380783,
-0.011963054537773132,
0.018773596733808517,
0.03184826299548149,
-0.010904486291110516,
0.04646577686071396,
-0.014637547545135021,
-0.014872600324451923,
0.0026052987668663263,
-0.02180636301636696,
0.02041955105960369,
0.01894901879131794,
0.0006152959540486336,
-0.04108641669154167,
-0.013004172593355179,
-0.010356167331337929,
0.011897572316229343,
0.0023362922947853804,
-0.009777155704796314,
-0.07540234923362732,
-0.042799632996320724,
0.004829620011150837,
0.004760915879160166,
0.01908024586737156,
-0.001867632963694632,
-0.038674380630254745,
0.0011302653001621366,
-0.0007158642983995378,
0.008266402408480644,
0.03185947611927986,
0.0251782089471817,
0.028766527771949768,
-0.03190173953771591,
0.021351905539631844,
0.07086103409528732,
-0.03562929108738899,
-0.010123148560523987,
0.04665285348892212,
0.02751217968761921,
0.02635152079164982,
0.022861244156956673,
-0.02308424562215805,
0.023365646600723267,
-0.02525371126830578,
-0.009779897518455982,
0.061752282083034515,
0.027118287980556488,
0.01602998375892639,
0.04674705117940903,
-0.00039050725172273815,
-0.046362120658159256,
0.04546190798282623,
-0.027540411800146103,
-0.000050581733376020566,
-0.00452626496553421,
-0.04045751690864563,
0.03661534935235977,
-0.04105403274297714,
0.005602431483566761,
0.032941583544015884,
-0.024279117584228516,
-0.0005184527835808694,
-0.011354321613907814,
-0.016201941296458244,
-0.0026685227639973164,
0.003475181059911847,
-0.023123903200030327,
0.04429306089878082,
0.03273417800664902,
-0.006963447201997042,
0.033730681985616684,
0.0333436019718647,
-0.0513945147395134,
0.03854135051369667,
-0.014738873578608036,
-0.006260767579078674,
-0.0845823585987091,
-0.024053627625107765,
0.005746840965002775,
0.03279499337077141,
0.05301743373274803,
-0.024165568873286247,
-0.00280455918982625,
0.019971219822764397,
-0.014322785660624504,
0.000920479535125196,
-0.026496417820453644,
-0.04476920887827873,
0.0037163919769227505,
-0.01217343658208847,
-0.03380206599831581,
0.09095446020364761,
0.018666159361600876,
0.01827329955995083,
0.04097023233771324,
0.0017093647038564086,
-0.017284411936998367,
-0.04562244191765785,
-0.016976241022348404,
0.00838724710047245,
-0.02873382158577442,
-0.0018091086531057954,
0.0906735211610794,
-0.003464246867224574,
0.006172785069793463,
0.05745389312505722,
0.023549111559987068,
-0.021640047430992126,
-0.011065676808357239,
0.04947137460112572,
0.013530182652175426,
0.04114788398146629,
-0.0033335350453853607,
0.01186845451593399,
0.026733167469501495,
0.0003105049836449325,
0.02284342050552368,
-0.002381741302087903,
-0.041366200894117355,
-0.015004734508693218,
-0.04096336290240288,
-0.02158198133111,
-0.008827779442071915,
0.05369018390774727,
-0.011793753132224083,
-0.048531316220760345,
-0.041292570531368256,
0.011905149556696415,
-0.013799170032143593,
-0.003694613929837942,
0.04353758320212364,
-0.016222413629293442,
0.007313943468034267,
0.03499216213822365,
0.004072829615324736,
-0.027867842465639114,
0.03699572756886482,
-0.017233897000551224,
-0.052461761981248856,
0.026043972000479698,
-0.0023627111222594976,
0.02726512961089611,
-0.0022890325635671616,
-0.017225388437509537,
0.022448277100920677,
0.03848463296890259,
0.021772686392068863,
-0.010168647393584251,
-0.05416777729988098,
0.024441827088594437,
-0.006586132105439901,
0.02783004753291607,
-0.01547973696142435,
-0.02264745905995369,
-0.004734152927994728,
-0.05923730880022049,
0.031889792531728745,
0.022221146151423454,
-0.026989342644810677,
0.011178940534591675,
-0.0018416309030726552,
0.030775152146816254,
0.011911779642105103,
0.04531080648303032,
0.02489330619573593,
-0.06425030529499054,
0.02992001548409462,
0.03155895695090294,
0.04347451776266098,
-0.04691299423575401,
-0.012118199840188026,
0.006947493180632591,
-0.0019797049462795258,
0.004701350815594196,
0.06229567900300026,
-0.010807874612510204,
0.05159944295883179,
0.024098580703139305,
0.03562051057815552,
-0.022016040980815887,
0.019618283957242966,
-0.020466342568397522,
0.026482680812478065,
0.021976297721266747,
-0.0063272868283092976,
0.05538858473300934,
0.033604253083467484,
-0.016125617548823357,
0.02553347498178482,
-0.015206816606223583,
-0.06307270377874374,
-0.031478848308324814,
-0.0022985530085861683,
-0.014590132981538773,
-0.010871181264519691,
-0.01680939644575119,
0.06641890853643417,
-0.05517358332872391,
-0.019162163138389587,
0.029798489063978195,
-0.020962387323379517,
-0.023823857307434082,
0.04751645401120186,
-0.0007877621101215482,
0.0034722350537776947,
0.017379578202962875,
0.018619762733578682,
-0.006462705321609974,
-0.018136141821742058,
0.06256241351366043,
0.01916053704917431,
0.01516807358711958,
-0.0034406427294015884,
-0.008939792402088642,
-0.002429182641208172,
-0.03862467035651207,
0.02100728452205658,
0.017040522769093513,
0.025944069027900696,
-0.030848374590277672,
0.025511018931865692,
0.04486366733908653,
-0.0391063317656517,
0.03684799000620842,
0.005355802830308676,
-0.015181584283709526,
0.10043831169605255,
-0.04364151880145073,
-0.002111587207764387,
-0.017215359956026077,
0.0033217987511307,
-0.010937401093542576,
0.008865260519087315,
0.0354037769138813,
0.07409156113862991,
0.0020818228367716074,
-0.021765384823083878,
-0.011349554173648357,
-0.029314469546079636,
0.026935717090964317,
-0.05927208065986633,
0.020035339519381523,
0.027032215148210526,
-0.013398727402091026,
-0.0038042000960558653,
-0.011458175256848335,
-0.005282297730445862,
-0.030128415673971176,
0.007249477319419384,
0.013237633742392063,
0.02669740468263626,
-0.02376088686287403,
0.0006751889595761895,
-0.03987816721200943,
0.015420726500451565,
-0.06106878072023392,
-0.007860226556658745,
-0.011857661418616772,
-0.005217839032411575,
-0.004849924240261316,
0.020572088658809662
] |
<p>Is there a possible explanation for the apparent equal size of sun and moon or is this a coincidence?</p>
<p>(An explanation can involve something like tide-lock effects or the anthropic principle.)</p>
| 8,826 |
[
-0.044196296483278275,
0.007654823828488588,
-0.01537627074867487,
0.004328382667154074,
0.0029378943145275116,
0.029357993975281715,
-0.012629973702132702,
-0.031426310539245605,
-0.03703753277659416,
-0.020997796207666397,
0.04797028377652168,
0.041821256279945374,
0.02088315412402153,
0.03190396726131439,
0.050447773188352585,
-0.0307678934186697,
0.012249534949660301,
0.0011839830549433827,
0.002446467522531748,
-0.03610798344016075,
-0.007332443725317717,
0.027434049174189568,
0.014949392527341843,
-0.014891891740262508,
-0.02483271434903145,
0.029940716922283173,
0.06058337539434433,
-0.015053383074700832,
0.011523853056132793,
0.07929112017154694,
0.006311978679150343,
-0.009517338126897812,
0.046486884355545044,
0.052454326301813126,
0.0020232535898685455,
-0.0039108917117118835,
0.039394743740558624,
-0.01495274342596531,
0.03126426413655281,
0.02167596109211445,
-0.026011651381850243,
-0.038502853363752365,
-0.016348423436284065,
0.017344418913125992,
-0.037866298109292984,
0.0192246176302433,
0.0017179305432364345,
-0.04434709995985031,
0.027890177443623543,
-0.052925579249858856,
0.09129340201616287,
0.026037197560071945,
0.040150947868824005,
0.015915201976895332,
-0.027220124378800392,
-0.027147015556693077,
0.05687154084444046,
0.05682101100683212,
-0.0034418022260069847,
-0.03963971138000488,
-0.007314585614949465,
-0.009654207155108452,
-0.02510720118880272,
0.0016094925813376904,
-0.003756575984880328,
0.025663988664746284,
-0.04311824589967728,
-0.02618413232266903,
0.01974787376821041,
-0.005160794593393803,
0.027860531583428383,
0.023898575454950333,
0.04844538867473602,
0.006327728740870953,
0.008800252340734005,
-0.06558754295110703,
0.02208074927330017,
0.03733428567647934,
0.036987341940402985,
0.02176677994430065,
0.012505660764873028,
0.018045824021100998,
0.06087924912571907,
0.013663455843925476,
0.07018181681632996,
0.025370260700583458,
0.04628681391477585,
-0.00070191640406847,
0.007352240849286318,
0.038701388984918594,
-0.016670726239681244,
0.027506187558174133,
0.06290694326162338,
-0.041601356118917465,
-0.03189860284328461,
0.047919388860464096,
-0.016953101381659508,
0.0354401059448719,
0.03455600515007973,
0.01258709467947483,
-0.007848423905670643,
-0.008827835321426392,
0.00699611147865653,
0.03994422405958176,
0.045254357159137726,
-0.026238538324832916,
-0.05016045644879341,
0.032628752291202545,
0.0023794835433363914,
0.025302905589342117,
-0.017072152346372604,
-0.007524719927459955,
0.01288397703319788,
0.015662577003240585,
0.011839494109153748,
0.013966063968837261,
0.03502519428730011,
-0.0011857465142384171,
0.0938723161816597,
0.08347705006599426,
0.01558429840952158,
0.00748943816870451,
0.01595841720700264,
-0.026428382843732834,
-0.009395771659910679,
0.045694660395383835,
-0.0014164992608129978,
-0.020949523895978928,
-0.02154291793704033,
0.03642694279551506,
0.02408149652183056,
-0.03691673278808594,
-0.02366902492940426,
-0.018644222989678383,
0.06486925482749939,
0.024616604670882225,
-0.07779371738433838,
-0.024656683206558228,
0.07108348608016968,
-0.01299007423222065,
-0.019771894440054893,
-0.061942778527736664,
0.03775600716471672,
0.006858321838080883,
0.054717615246772766,
-0.013455100357532501,
-0.004134241491556168,
0.016297675669193268,
0.03880207985639572,
-0.01162851881235838,
-0.006804303731769323,
0.010979677550494671,
0.05326024442911148,
-0.041278257966041565,
0.009727335534989834,
-0.09939789026975632,
-0.0028633475303649902,
0.04418110102415085,
0.008713451214134693,
-0.0015607135137543082,
0.07078570127487183,
0.014784691855311394,
-0.003128394018858671,
0.0060769845731556416,
0.02881644107401371,
-0.06463562697172165,
0.06980966776609421,
-0.028553972020745277,
-0.01744033955037594,
0.03949936106801033,
-0.005752016324549913,
0.04770191013813019,
0.03421289101243019,
0.03965361416339874,
-0.006148756947368383,
-0.03779768571257591,
-0.0065061356872320175,
-0.009209791198372841,
0.023485707119107246,
0.003416734281927347,
-0.038174401968717575,
-0.048095304518938065,
-0.015061710961163044,
-0.007747316733002663,
0.03937269002199173,
0.053700175136327744,
-0.02677888050675392,
-0.030118273571133614,
0.011984233744442463,
-0.04896605759859085,
0.016239874064922333,
-0.045767731964588165,
-0.010332201607525349,
-0.0017240328015759587,
-0.01977224089205265,
0.02843836322426796,
0.02788536064326763,
-0.001844109152443707,
-0.033442504703998566,
-0.014672299847006798,
-0.02187511697411537,
0.06454230099916458,
0.026329535990953445,
0.025563130155205727,
0.03216540813446045,
0.08248796314001083,
0.042312055826187134,
-0.013690515421330929,
-0.038646966218948364,
-0.010781175456941128,
-0.05628928542137146,
-0.007512240670621395,
-0.018391534686088562,
0.0033596602734178305,
-0.026195352897047997,
0.040664274245500565,
0.034374069422483444,
0.017573615536093712,
0.002073408802971244,
0.027479158714413643,
-0.026999175548553467,
0.06484749168157578,
-0.02059437707066536,
-0.04208924621343613,
0.03377215564250946,
0.03504624962806702,
0.04679764062166214,
-0.002475129207596183,
0.009946255013346672,
-0.0289077777415514,
-0.03017241507768631,
-0.005079728085547686,
0.033718135207891464,
0.010940746404230595,
0.018094193190336227,
0.01942363567650318,
0.0172905120998621,
0.06698745489120483,
-0.01627022959291935,
0.04617908596992493,
-0.010679361410439014,
-0.04348590970039368,
-0.01557835377752781,
-0.019375985488295555,
0.008679933845996857,
0.007341363932937384,
0.01514484267681837,
0.024287616834044456,
0.00185411237180233,
-0.03223291039466858,
-0.04546688497066498,
-0.003045533550903201,
0.0025840173475444317,
0.04289345443248749,
-0.006803030148148537,
0.010470887646079063,
0.022578075528144836,
-0.05200973153114319,
0.009710527956485748,
-0.002230278216302395,
-0.02631501480937004,
0.003572458168491721,
-0.05378595367074013,
-0.038232289254665375,
-0.023615635931491852,
0.029199011623859406,
0.002706937724724412,
0.013995123095810413,
0.050962869077920914,
-0.07020249962806702,
-0.010000111535191536,
-0.045432090759277344,
-0.05156399682164192,
0.00790672842413187,
-0.020015306770801544,
0.04510541632771492,
0.007226194720715284,
0.02766271121799946,
-0.028919298201799393,
-0.004691156093031168,
-0.01631060428917408,
-0.00840714666992426,
-0.010819030925631523,
-0.008408677764236927,
-0.03462231904268265,
0.03363625332713127,
-0.016560517251491547,
-0.018993757665157318,
0.03489292785525322,
0.015930308029055595,
0.06414296478033066,
-0.005196907091885805,
-0.0054381052032113075,
-0.025800585746765137,
-0.011815940961241722,
-0.04301837086677551,
-0.006794247310608625,
-0.020031198859214783,
0.010120589286088943,
0.06954243034124374,
-0.012707319110631943,
-0.05901552364230156,
0.0031600117217749357,
-0.050224095582962036,
-0.024769537150859833,
-0.0016639498062431812,
0.01231728307902813,
0.005077064968645573,
-0.019036924466490746,
-0.0269786324352026,
0.03756551817059517,
-0.052422989159822464,
-0.005421612411737442,
-0.05570727586746216,
-0.05178866535425186,
0.01288981270045042,
-0.01884925551712513,
0.05080996826291084,
-0.01866932213306427,
-0.02849734202027321,
0.08146116882562637,
0.018632283434271812,
0.010714573785662651,
-0.027127405628561974,
0.006516252178698778,
-0.019226539880037308,
-0.008494442328810692,
0.05343516916036606,
0.05205972492694855,
0.024840347468852997,
0.044046394526958466,
0.031271860003471375,
0.04092143848538399,
0.004659953992813826,
0.02489764802157879,
0.008921334519982338,
0.009034108370542526,
-0.01761886291205883,
-0.010764493606984615,
0.03284884989261627,
-0.003901295131072402,
-0.02541697956621647,
-0.002658459823578596,
0.014530736021697521,
0.034978896379470825,
0.006928977090865374,
-0.029928818345069885,
0.0566573366522789,
0.004320928826928139,
0.0023827338591217995,
-0.025444068014621735,
0.0191443283110857,
0.0290510430932045,
0.03042757883667946,
-0.01779996044933796,
-0.0062866550870239735,
0.058135855942964554,
-0.008994849398732185,
-0.025826966390013695,
0.039718352258205414,
0.0025724503211677074,
-0.041592076420784,
-0.023581936955451965,
-0.029560232535004616,
-0.013259834609925747,
-0.0069464463740587234,
-0.056992001831531525,
-0.011223232373595238,
0.04428541660308838,
0.0324065163731575,
0.03637473285198212,
0.009861878119409084,
-0.06314602494239807,
-0.017885316163301468,
-0.0791017934679985,
-0.03115164488554001,
-0.03438326716423035,
0.002918488346040249,
-0.0010008993558585644,
0.040108826011419296,
0.034102924168109894,
0.048986390233039856,
0.03351578488945961,
0.016400272026658058,
-0.06855365633964539,
-0.010652311146259308,
-0.06274927407503128,
-0.0019613115582615137,
-0.032743897289037704,
-0.03197268769145012,
-0.028104929253458977,
-0.023938242346048355,
-0.017987815663218498,
-0.036220893263816833,
0.01239900290966034,
-0.03186778724193573,
0.011936617083847523,
0.015351970680058002,
-0.053878601640462875,
-0.0017468666192144156,
0.05682167783379555,
-0.002906224224716425,
-0.02487592212855816,
0.03921147435903549,
0.0353819765150547,
-0.03982754051685333,
-0.03840763866901398,
0.00021516830020118505,
0.033769939094781876,
-0.04007894545793533,
0.012296217493712902,
0.005277699790894985,
0.014858161099255085,
-0.039124876260757446,
-0.01669524982571602,
0.00588530208915472,
0.04086580500006676,
0.024171151220798492,
-0.012720588594675064,
-0.028064588084816933,
-0.039593297988176346,
-0.008480485528707504,
0.0013310650829225779,
0.02381543628871441,
-0.022516313940286636,
-0.018036125227808952,
0.03482748195528984,
0.015597338788211346,
0.007437245920300484,
0.045893341302871704,
0.02445102669298649,
0.017052805051207542,
-0.0185540784150362,
-0.051321033388376236,
-0.006964602041989565,
-0.018428200855851173,
0.021703291684389114,
-0.015029232949018478,
-0.002515476895496249,
-0.03981281444430351,
-0.038168106228113174,
-0.0016311111394315958,
-0.001595191308297217,
-0.03562403470277786,
-0.027516834437847137,
-0.035203058272600174,
0.04297378286719322,
-0.007299896329641342,
0.0019102415535598993,
0.02346646599471569,
0.016809189692139626,
0.027273990213871002,
0.006768393330276012,
-0.01747780852019787,
-0.06181057542562485,
-0.0029175025410950184,
0.03744680806994438,
0.03887774795293808,
-0.02355557307600975,
0.0005119247944094241,
-0.0951564684510231,
-0.0038341698236763477,
0.032391153275966644,
-0.024667859077453613,
0.020327389240264893,
-0.019173143431544304,
0.011552580632269382,
-0.028644587844610214,
0.0018157786689698696,
-0.000013639883036375977,
0.037979114800691605,
0.0063371299766004086,
0.03338623046875,
-0.030589457601308823,
0.0031556892208755016,
-0.015310189686715603,
0.06949910521507263,
0.03348211944103241,
0.020776063203811646,
0.023949697613716125,
0.0002663055493030697,
-0.027832427993416786,
-0.0022880886681377888,
-0.023152802139520645,
-0.07867307960987091,
-0.008247995749115944,
0.005036541726440191,
-0.04224497824907303,
0.012859778478741646,
-0.02169002592563629,
-0.045697662979364395,
0.023621991276741028,
-0.015008178539574146,
-0.00771881639957428,
-0.012889256700873375,
-0.05770236998796463,
0.021766318008303642,
0.047590382397174835,
-0.017858341336250305,
0.012655936181545258,
0.009796733036637306,
-0.03233636915683746,
-0.02549736574292183,
-0.02813664637506008,
0.026214933022856712,
-0.05035499110817909,
-0.031440142542123795,
-0.003533682320266962,
-0.014289483428001404,
-0.04928206652402878,
0.0175120048224926,
-0.007748596370220184,
0.05206725373864174,
-0.01043191272765398,
-0.03925561159849167,
-0.012582777068018913,
-0.0006409597117453814,
0.03929072618484497,
-0.009751646779477596,
0.015924766659736633,
-0.0010968699352815747,
0.007576816249638796,
-0.018151042982935905,
0.049350306391716,
0.007761120796203613,
0.009773222729563713,
0.010736307129263878,
-0.00910296943038702,
0.0062748161144554615,
-0.004434559494256973,
-0.02350565791130066,
0.01455522608011961,
-0.032212644815444946,
0.05321618169546127,
-0.030972104519605637,
0.01596682518720627,
0.059885550290346146,
-0.047113802284002304,
-0.009815170429646969,
0.008813014253973961,
-0.012041210196912289,
0.05389733985066414,
-0.042149607092142105,
0.028466038405895233,
0.03820295259356499,
-0.01136835664510727,
-0.06404650211334229,
0.010314215905964375,
0.03344973921775818,
0.00795897375792265,
-0.018554257228970528,
-0.02325589582324028,
-0.013467502780258656,
-0.027151232585310936,
-0.026185164228081703,
0.012338189408183098,
0.01595117151737213,
-0.03122144192457199,
-0.020563282072544098,
-0.008126146160066128,
0.022375864908099174,
0.05477610602974892,
-0.018373865634202957,
-0.03249671310186386,
0.003883653786033392,
-0.037592120468616486,
-0.005296698771417141,
-0.019070958718657494,
0.05093915015459061,
-0.026156658306717873,
-0.049577560275793076,
-0.02968730591237545,
-0.027775339782238007,
0.0003887386410497129,
-0.02019711770117283,
-0.02309468947350979,
0.054484475404024124,
0.020852811634540558,
-0.012422642670571804,
-0.028489677235484123,
0.043894343078136444,
-0.0041695814579725266,
0.03796015679836273,
-0.008107578381896019,
0.01005299761891365,
-0.004420876502990723,
-0.05211402475833893,
0.008869893848896027,
-0.01605263538658619,
-0.023819575086236,
0.0035467895213514566,
0.046205129474401474,
-0.02065463550388813,
-0.0036993767134845257,
0.016048507764935493,
0.0009199834312312305,
-0.009804974310100079,
-0.004289308097213507,
0.006234356202185154,
-0.030477367341518402,
0.013788733631372452,
-0.0615575946867466,
-0.05607568845152855,
0.002202728996053338,
0.0007151018362492323,
0.04829847067594528,
-0.04320065677165985,
0.036345209926366806,
0.03193943202495575,
0.006152015645056963,
0.012587038800120354,
-0.027437178418040276,
0.0018043274758383632,
-0.022477198392152786,
0.00186730339191854,
0.03183407336473465,
-0.054535675793886185,
-0.007973702624440193,
0.04596465080976486,
0.07732190191745758,
-0.003256909316405654,
0.0410395972430706,
0.040381863713264465,
0.01872199773788452,
0.03971101716160774,
0.00792249571532011,
-0.0373833030462265,
0.015188517048954964,
-0.014873405918478966,
0.014778506942093372,
-0.007587949745357037,
0.014127474278211594,
0.049340441823005676,
0.0008594566606916487,
-0.00005667438745149411,
-0.02977384440600872,
-0.012691022828221321,
-0.014835122041404247,
-0.004432674963027239,
0.04482070356607437,
0.031305111944675446,
0.0030627052765339613,
-0.002127690240740776,
0.029506027698516846,
-0.014723651111125946,
-0.01074841246008873,
-0.024598004296422005,
-0.06955583393573761,
-0.02152162231504917,
-0.02627704106271267,
-0.04506514593958855,
0.07367043197154999,
-0.03509853035211563,
-0.03353104740381241,
0.00794652197510004,
-0.02687624841928482,
-0.00034393765963613987,
-0.008824692107737064,
0.02279464341700077,
-0.008750776760280132,
0.06704531610012054,
-0.02608942985534668,
0.003577440045773983,
-0.06554374098777771,
0.006206579972058535,
0.11971410363912582,
0.032057203352451324,
0.015993334352970123,
-0.01893826760351658,
0.03298644348978996,
-0.0023121710401028395,
-0.01875295862555504,
-0.00044490856816992164,
0.008113263174891472,
-0.013304846361279488,
-0.004988540429621935,
0.012487039901316166,
0.013815647922456264,
0.018148139119148254,
-0.04015341401100159,
0.025288907811045647,
-0.0007825096836313605,
-0.029806774109601974,
0.004284093156456947,
0.033218756318092346,
-0.001980141270905733,
0.0018317247740924358,
-0.04350825771689415,
0.007719865068793297,
-0.023073434829711914,
-0.0011302249040454626,
-0.05355778709053993,
-0.017708048224449158,
0.014733918011188507,
0.010739699006080627,
-0.07471810281276703,
0.03288860619068146,
0.02170703373849392,
-0.025179265066981316,
-0.037537310272455215,
-0.02826666459441185,
0.030108964070677757,
-0.0010188155574724078,
-0.015442118048667908,
0.03993099927902222,
0.0083457101136446,
0.026124222204089165,
-0.012746954336762428,
0.017773384228348732,
-0.05530451983213425,
-0.0032002171501517296,
0.0038900563959032297,
0.024698706343770027,
0.01087348721921444,
0.017654579132795334,
-0.019116144627332687,
0.03119611367583275,
-0.002090414287522435,
-0.05336986854672432,
0.012070760130882263,
-0.005106023512780666,
0.011741217225790024,
-0.010552057065069675,
-0.038439877331256866,
0.007396841887384653,
0.020075811073184013,
-0.009620057418942451,
0.05729168653488159,
-0.010354310274124146,
0.01602182537317276,
-0.014145326800644398,
-0.005094654392451048,
0.04819656163454056,
-0.0036921026185154915,
-0.02157304622232914,
-0.0364488922059536,
-0.02015971578657627,
-0.03509334474802017,
-0.02160610258579254,
0.0140968207269907,
0.0369097925722599,
0.03178481385111809,
0.06681791692972183,
-0.016242627054452896,
-0.056882090866565704,
-0.012007203884422779,
0.05326102674007416,
-0.005398647394031286,
-0.01611577533185482,
-0.016914306208491325,
-0.0072161611169576645,
0.055085793137550354,
0.005443078465759754,
0.00018963283218909055,
0.006895144935697317,
-0.02449675463140011,
0.03186643496155739,
-0.0032509237062186003,
-0.032560259103775024,
-0.018199462443590164,
-0.012763961218297482,
-0.008401447907090187,
-0.008295000530779362,
-0.017210718244314194,
0.008595047518610954,
0.029444124549627304,
0.019642207771539688,
0.024272115901112556,
0.016416069120168686,
-0.02491348423063755,
-0.014247209765017033,
-0.014913567341864109,
-0.028475278988480568,
-0.03371692821383476,
-0.001573351793922484,
-0.03683412820100784,
-0.013163008727133274,
0.024623366072773933,
-0.009804164990782738,
-0.004433725960552692,
-0.010162152349948883,
0.016416562721133232,
-0.021774403750896454,
0.03631049767136574,
-0.009041031822562218,
0.033062394708395004,
-0.04384980350732803,
-0.0326743945479393,
-0.0563647486269474,
-0.03484369441866875,
0.002916698344051838,
-0.01877073012292385,
-0.015294953249394894,
0.04094760864973068,
-0.0321977473795414,
-0.04626220092177391,
0.016565049067139626,
-0.023640012368559837,
0.009984981268644333,
0.01958135887980461,
0.02428394742310047,
-0.024879122152924538,
0.04114748165011406,
-0.03367665037512779,
-0.03329005837440491,
0.01816626638174057,
-0.013718953356146812,
-0.047983355820178986,
0.017157496884465218,
-0.050177231431007385,
0.046411119401454926,
0.013321810401976109,
-0.027734937146306038,
-0.029880767688155174,
0.04854436591267586,
-0.03915566951036453,
-0.01318480633199215,
-0.015820205211639404,
0.016567710787057877,
0.01819189451634884,
0.017833489924669266,
0.008794077672064304,
-0.03469182923436165,
-0.004844709765166044,
0.030045712366700172,
0.023012980818748474,
-0.01661418378353119,
-0.0080606983974576,
0.01510162465274334,
-0.013713897205889225,
-0.01908789947628975,
-0.02023104578256607,
-0.027028566226363182,
0.005533790681511164,
0.0024110341910272837,
-0.0037949567195028067,
0.08961018919944763,
0.024381065741181374,
-0.004094425588846207,
-0.0674249604344368,
-0.009338644333183765,
0.037149135023355484,
0.008320007473230362,
0.030597157776355743,
-0.04665358364582062,
-0.00892785843461752,
-0.009727063588798046,
-0.09075431525707245,
0.007457592524588108,
-0.0021174014545977116,
-0.012052047997713089,
-0.007343957666307688,
0.005291507113724947,
0.012281091883778572,
0.03475426882505417,
0.02686511166393757,
0.018085457384586334,
-0.03199536353349686,
0.03963170573115349,
0.009111275896430016,
-0.05009171739220619,
-0.05155831202864647,
0.04329875484108925,
0.0036088249180465937,
0.007002865895628929,
0.04535438120365143,
-0.019453827291727066,
-0.018794260919094086,
0.026393093168735504,
0.025789843872189522,
0.04819275438785553,
-0.020748699083924294,
0.009861720725893974,
-0.0009980612667277455,
0.01910240761935711,
0.021983854472637177,
-0.027278132736682892,
-0.04665686935186386,
0.0049939402379095554,
0.013684717938303947,
0.04184068739414215,
0.016457371413707733,
-0.010864618234336376,
0.019215799868106842,
-0.06053908169269562,
-0.0012939836597070098,
-0.00454329838976264,
-0.008248316124081612,
-0.001073904219083488,
-0.004817148204892874,
0.016692956909537315,
0.008844172582030296,
0.004874606151133776,
0.012551935389637947,
-0.03693639114499092,
-0.03595605120062828,
-0.013729267753660679,
0.01655431278049946,
-0.011768758296966553,
0.06498224288225174,
0.06130478158593178,
-0.0014208516804501414,
0.008977808058261871,
-0.004500777926295996,
0.025308137759566307,
-0.02636202611029148,
0.030541568994522095,
-0.005756457801908255,
0.027078067883849144,
0.016375869512557983,
-0.04411584138870239,
-0.03388471528887749,
0.010286564007401466,
0.00014896180073264986,
-0.0002771631989162415,
-0.013127586804330349,
-0.05149634927511215,
-0.013391506858170033,
-0.02591223642230034,
0.014837970957159996,
-0.033309634774923325,
0.016422409564256668,
-0.042156461626291275,
-0.04457349702715874,
-0.027236422523856163,
0.024290746077895164,
0.028583558276295662,
0.035134345293045044,
0.0013954761670902371,
0.03876607120037079,
-0.008892228826880455,
0.026615113019943237,
-0.06875332444906235,
-0.0034456525463610888,
0.014067711308598518,
-0.035981059074401855,
0.05926838889718056,
-0.037956833839416504,
0.01727527193725109,
-0.0009833574295043945,
0.012078192085027695,
-0.011186573654413223,
0.06470321118831635,
0.04210631921887398,
-0.004723053425550461,
0.07208610326051712,
0.032751426100730896,
-0.011653945781290531,
0.053133524954319,
0.02945355698466301,
-0.008237775415182114,
0.01993400789797306,
0.008264593780040741,
-0.08654581755399704,
-0.006304411217570305,
-0.03960494324564934,
-0.018478043377399445,
-0.01683121733367443,
0.002492262050509453,
0.02354304865002632,
-0.016652612015604973,
-0.0024566908832639456,
0.03459887206554413,
-0.005169435404241085,
-0.021001307293772697,
0.05445089563727379,
-0.01261928491294384,
0.021275687962770462,
-0.019102109596133232,
0.03602103143930435,
0.027165018022060394,
-0.011159763671457767,
-0.0031795522663742304,
0.023984694853425026,
0.051609981805086136,
-0.001392571721225977,
-0.005709430202841759,
0.020420515909790993,
0.0404646173119545,
0.038793038576841354,
-0.007734988816082478,
0.024959726259112358,
-0.010609216056764126,
-0.06254081428050995,
0.03130565956234932,
0.015977179631590843,
0.02581959217786789,
0.042741287499666214,
0.013192465528845787,
0.0780707597732544,
0.027568290010094643,
-0.0007215316873043776,
-0.013599129393696785,
-0.0009515021811239421,
-0.0031438700389117002,
0.013038595207035542,
-0.0017862921813502908,
-0.014648434706032276,
0.004188433289527893,
-0.005443267058581114,
0.011090449057519436,
0.01551957055926323,
0.003347435500472784,
-0.03000655211508274,
0.010995798744261265,
-0.018887126818299294,
0.011695641092956066,
0.0026499012019485235,
0.0024929202627390623,
-0.03886934742331505,
-0.025917476043105125,
0.054676491767168045,
0.03592311590909958,
0.01266925223171711,
-0.013322094455361366,
-0.03205382078886032,
-0.011656466871500015,
0.040750373154878616,
-0.08812265843153,
-0.05489985644817352,
-0.011922582983970642,
0.03572222962975502,
-0.003659297479316592,
-0.04254283756017685
] |
<p>I heard that the Earth rotation is slowing down, but I also heard the Earth's length of day is increasing.</p>
<p>Does the two theories go together or conflict with each other?</p>
| 8,827 |
[
-0.029440440237522125,
-0.03462934494018555,
-0.0032253051176667213,
-0.007187261246144772,
0.04816863313317299,
0.01502411812543869,
-0.004278882872313261,
-0.033130403608083725,
0.008591189980506897,
-0.036794327199459076,
0.0010345265036448836,
0.06912893801927567,
0.01824852265417576,
0.023212598636746407,
0.017630796879529953,
0.00866925623267889,
-0.0017320241313427687,
0.008616376668214798,
-0.005780546460300684,
-0.004819266498088837,
-0.01764705963432789,
-0.012021800503134727,
0.031027859076857567,
0.009170536883175373,
-0.03358209505677223,
0.028127703815698624,
0.05743730813264847,
0.007660397794097662,
-0.007385612465441227,
0.06405744701623917,
0.036940235644578934,
-0.013783174566924572,
-0.003565257415175438,
0.055691614747047424,
0.03482859954237938,
0.003118935041129589,
-0.018275676295161247,
-0.014493175782263279,
-0.02017129585146904,
0.06130614131689072,
-0.04002078250050545,
-0.008329399861395359,
-0.040130943059921265,
0.016917958855628967,
-0.0455256886780262,
0.03587127476930618,
0.01438701432198286,
-0.024351419880986214,
0.042168036103248596,
-0.06598464399576187,
0.07388687878847122,
-0.011676757596433163,
0.00783095508813858,
-0.0062425886280834675,
0.009320054203271866,
-0.0005611424567177892,
0.0904669463634491,
0.0382431298494339,
-0.011977526359260082,
-0.07689252495765686,
-0.007592886686325073,
0.002341562183573842,
0.019274715334177017,
0.010928639210760593,
0.003083934774622321,
0.040069375187158585,
-0.03232410550117493,
-0.020259832963347435,
0.03360337018966675,
0.001713558565825224,
0.01624281331896782,
0.02824736386537552,
0.04410868510603905,
0.0008025469724088907,
0.009457600302994251,
-0.05329451337456703,
0.004913534503430128,
0.017741063609719276,
0.014626150019466877,
0.03203512728214264,
0.0010550773004069924,
0.003512841649353504,
0.03872217610478401,
-0.0027121598832309246,
0.0388653464615345,
0.024808114394545555,
0.05121419206261635,
0.0025623831897974014,
-0.02182641625404358,
0.06515812873840332,
-0.022369693964719772,
0.02084701508283615,
0.03920215740799904,
-0.05605151131749153,
-0.02119157649576664,
0.0527859628200531,
0.001121725421398878,
0.02965063974261284,
0.024495093151926994,
0.01969231851398945,
-0.008043627254664898,
0.004048987291753292,
0.012550576590001583,
0.04015486314892769,
0.0029062973335385323,
-0.024034930393099785,
-0.04804113134741783,
-0.009289001114666462,
-0.027386538684368134,
-0.01694938912987709,
-0.04378950223326683,
-0.01899060793220997,
-0.013295866549015045,
0.008483901619911194,
-0.002716903807595372,
0.005256707780063152,
-0.002464013872668147,
-0.015039545483887196,
0.05121567100286484,
0.06060938164591789,
0.02610643208026886,
-0.023536408320069313,
0.016275573521852493,
-0.022954197600483894,
-0.03625643625855446,
0.025106756016612053,
0.014604753814637661,
-0.04538940638303757,
-0.046503257006406784,
0.05097367241978645,
0.02814676985144615,
-0.02395543083548546,
-0.018713904544711113,
-0.03240012004971504,
0.06062883511185646,
0.025191912427544594,
-0.08059268444776535,
-0.014744803309440613,
0.08476883918046951,
0.00866623129695654,
0.0019542910158634186,
-0.046633679419755936,
0.0019420272437855601,
-0.05691054090857506,
0.11026071757078171,
0.03509029373526573,
0.023236079141497612,
0.01800920069217682,
0.025290371850132942,
0.013735123910009861,
-0.00785872619599104,
-0.007172814570367336,
0.041399575769901276,
-0.03485223650932312,
-0.007696953136473894,
-0.11221807450056076,
0.009862800128757954,
0.04401668906211853,
0.005861344281584024,
-0.015343946404755116,
0.046236809343099594,
0.007554780226200819,
-0.01273412723094225,
-0.004707129206508398,
0.02135225012898445,
-0.06301048398017883,
0.04358512908220291,
-0.02107265219092369,
0.0016015095170587301,
0.04837213084101677,
0.017606636509299278,
0.0350986011326313,
0.04484739899635315,
0.03731021285057068,
0.03575258329510689,
-0.03695731237530708,
-0.0018278517527505755,
-0.019747745245695114,
-0.0226999893784523,
0.02388351783156395,
-0.018619924783706665,
-0.015659993514418602,
-0.015313835814595222,
-0.02018009126186371,
0.006413726601749659,
0.09984833747148514,
-0.04156307131052017,
-0.005423943046480417,
0.005056297406554222,
-0.058971475809812546,
0.014063812792301178,
-0.057357512414455414,
-0.015796847641468048,
-0.033064987510442734,
0.008638100698590279,
0.024516679346561432,
0.022551871836185455,
0.019684625789523125,
-0.016659660264849663,
-0.02119392342865467,
0.0012379215331748128,
0.06573255360126495,
0.014605332165956497,
-0.04277751222252846,
0.01631607487797737,
0.06992107629776001,
0.017839211970567703,
0.015771914273500443,
-0.0038643446750938892,
0.00009966209472622722,
-0.06347903609275818,
0.02526516653597355,
-0.024806514382362366,
0.033253010362386703,
-0.006088981404900551,
0.01598414033651352,
0.02691134624183178,
0.04016712307929993,
0.004693289287388325,
0.017177004367113113,
-0.036143381148576736,
0.05683540180325508,
0.031124943867325783,
-0.023750891909003258,
0.0028208063449710608,
0.048529673367738724,
0.034109361469745636,
0.00447835074737668,
-0.009666693396866322,
-0.025439731776714325,
-0.014969638548791409,
0.005102722439914942,
0.02669125609099865,
0.03959481790661812,
-0.014915748499333858,
0.033802080899477005,
0.04960743710398674,
0.08220444619655609,
0.0020968273747712374,
0.04550350829958916,
0.03743651136755943,
-0.03434418886899948,
-0.021535051986575127,
-0.014865376986563206,
-0.008511674590408802,
0.04058864712715149,
0.03658211976289749,
-0.019120071083307266,
0.013859405182301998,
-0.026657484471797943,
-0.056725241243839264,
0.014131098054349422,
0.0364835150539875,
0.030874084681272507,
0.01628425158560276,
-0.016812734305858612,
0.019377510994672775,
-0.042453475296497345,
-0.01995716616511345,
-0.002319427439942956,
-0.022188588976860046,
0.03033081255853176,
-0.02597576007246971,
-0.012233822606503963,
-0.005357523914426565,
-0.0075949919410049915,
-0.012628813274204731,
-0.0013326230691745877,
0.05924531817436218,
-0.04667180776596069,
-0.016608744859695435,
-0.02666514553129673,
-0.019391439855098724,
-0.02637898176908493,
-0.010198382660746574,
0.009489201940596104,
0.003935074433684349,
0.05043526366353035,
-0.02132711000740528,
-0.01716483384370804,
0.01857730560004711,
-0.046290330588817596,
-0.008452546782791615,
-0.012192446738481522,
-0.03424965962767601,
0.028251703828573227,
0.009186556562781334,
-0.029235314577817917,
0.07863657176494598,
-0.003953504841774702,
0.03764135017991066,
0.0037165828980505466,
-0.007131710648536682,
-0.05890623852610588,
-0.0037066901568323374,
-0.021109282970428467,
-0.002849367680028081,
-0.008847346529364586,
-0.029255274683237076,
0.03531550616025925,
0.0014509001048281789,
-0.009606467559933662,
0.011870651505887508,
-0.06387001276016235,
-0.038035571575164795,
-0.026627756655216217,
-0.0033411949407309294,
-0.0016848091036081314,
-0.023676712065935135,
-0.042276207357645035,
0.021128349006175995,
-0.039187513291835785,
0.006125675980001688,
-0.01862754113972187,
-0.0574079304933548,
0.04291839525103569,
-0.02763908915221691,
0.08093700557947159,
-0.016184436157345772,
-0.026851074770092964,
0.03219116851687431,
0.044848933815956116,
0.01001022569835186,
-0.02784591354429722,
0.00351912179030478,
-0.019040994346141815,
0.0039056201931089163,
0.019069718196988106,
0.0392773374915123,
0.0009624335216358304,
0.0018072626553475857,
0.01314949244260788,
-0.009252598509192467,
0.027948720380663872,
0.03721841424703598,
-0.012316355481743813,
0.028576107695698738,
-0.00010524661774979904,
0.00048394696204923093,
0.020377974957227707,
0.014550783671438694,
-0.009252991527318954,
-0.02673833630979061,
-0.03512415289878845,
0.050593432039022446,
0.020703863352537155,
-0.038940802216529846,
0.050188448280096054,
-0.016593579202890396,
-0.0054502105340361595,
0.0021507206838577986,
0.029718337580561638,
0.006203308701515198,
0.026757819578051567,
-0.00799547415226698,
0.008117018267512321,
0.058000367134809494,
0.017484590411186218,
-0.021353179588913918,
0.008691961877048016,
0.033791299909353256,
-0.04084149748086929,
-0.013510635122656822,
-0.01643972098827362,
0.013373312540352345,
0.061264969408512115,
-0.04645715653896332,
-0.01705283112823963,
0.03490457311272621,
0.00033680294291116297,
0.03160030022263527,
0.005665758159011602,
-0.028503770008683205,
0.01577823795378208,
-0.09149610996246338,
0.011297785677015781,
-0.014419794082641602,
0.03374054282903671,
0.014029041863977909,
0.02606748230755329,
-0.0013791181845590472,
0.010564601048827171,
0.03840883448719978,
0.01121742743998766,
-0.048113733530044556,
0.02478235401213169,
-0.04816773533821106,
-0.005322271957993507,
-0.036040663719177246,
0.025055069476366043,
-0.02415367215871811,
-0.004794901702553034,
-0.026026654988527298,
-0.074724942445755,
-0.024612901732325554,
-0.048499319702386856,
0.00024309183936566114,
-0.01864468865096569,
-0.04167187213897705,
-0.0003820626880042255,
0.011265977285802364,
0.030874062329530716,
-0.01961737498641014,
0.038164734840393066,
0.03783613070845604,
-0.018538404256105423,
-0.01090190652757883,
-0.01130563486367464,
0.0004027229151688516,
-0.004550276789814234,
0.00394669733941555,
-0.0036202273331582546,
0.0019283582223579288,
-0.03309428691864014,
0.019265269860625267,
0.018520845100283623,
-0.004715984221547842,
-0.00008071297634160146,
-0.00584425637498498,
-0.03089132159948349,
-0.009697990491986275,
-0.020076051354408264,
0.008030750788748264,
0.020030463114380836,
-0.009437091648578644,
0.02042311057448387,
0.03641366958618164,
-0.01897859200835228,
-0.011483064852654934,
0.00346173788420856,
0.03059331141412258,
0.0004965212428942323,
-0.025043943896889687,
-0.03484460711479187,
-0.02720976062119007,
-0.004650274757295847,
0.023736601695418358,
-0.01190529577434063,
-0.01673229970037937,
-0.04563789442181587,
-0.03303490951657295,
0.030801944434642792,
-0.04210444539785385,
0.014533184468746185,
-0.0008406630950048566,
0.008088842034339905,
0.033972639590501785,
0.000913725234568119,
-0.004703288432210684,
0.005835296586155891,
0.03668224811553955,
0.03076179139316082,
0.02795073762536049,
0.005729355849325657,
-0.09307287633419037,
-0.008258010260760784,
0.02890392765402794,
0.004862773232161999,
-0.04676666483283043,
0.007602001540362835,
-0.08254419267177582,
-0.030200887471437454,
0.01996101438999176,
-0.0017526174196973443,
0.03611059859395027,
-0.016901180148124695,
-0.015578706748783588,
-0.03260907530784607,
-0.01296953670680523,
0.0022391625680029392,
-0.009693654254078865,
-0.004290304146707058,
0.031098660081624985,
0.005713144317269325,
0.013568037189543247,
-0.030634712427854538,
0.005227067973464727,
0.050180770456790924,
0.00989518966525793,
0.012548389844596386,
-0.01966077648103237,
0.006415122654289007,
0.017599916085600853,
-0.02059427835047245,
-0.05289987474679947,
-0.025258643552660942,
0.028272079303860664,
-0.058815859258174896,
0.04242393374443054,
-0.01569661684334278,
-0.03713583946228027,
-0.007688111159950495,
0.012432540766894817,
-0.018651144579052925,
-0.02458583191037178,
-0.0767851397395134,
0.0143470773473382,
-0.014085523784160614,
-0.007951276376843452,
-0.009577726013958454,
0.04479077830910683,
-0.04336443170905113,
0.012255231849849224,
-0.007213883567601442,
0.054745569825172424,
-0.030176322907209396,
0.0129260728135705,
0.05438109487295151,
-0.02278057672083378,
-0.0412721261382103,
0.03300413489341736,
0.00891159288585186,
0.029017291963100433,
-0.03515470027923584,
-0.03409729152917862,
-0.021908534690737724,
-0.007554044481366873,
0.0020150074269622564,
-0.006208918523043394,
0.014644629321992397,
0.04990614578127861,
0.003643578151240945,
-0.022614549845457077,
0.0213308222591877,
0.014067352749407291,
-0.010805211029946804,
0.020180920138955116,
0.005832140799611807,
-0.007315600756555796,
-0.03586944192647934,
-0.04317191615700722,
0.00825760792940855,
-0.005262784659862518,
0.062147773802280426,
-0.029756709933280945,
-0.005124327261000872,
0.028985491022467613,
-0.05582226812839508,
-0.0005778099875897169,
0.011861155740916729,
-0.027914494276046753,
0.013304305262863636,
-0.031240012496709824,
0.05523135885596275,
0.034765347838401794,
0.00698102405294776,
-0.05601290240883827,
-0.05272893235087395,
0.02253134362399578,
0.00308423675596714,
-0.010321961715817451,
-0.05474357306957245,
0.0032574674114584923,
-0.057855214923620224,
-0.058031611144542694,
-0.05122296139597893,
0.04732935130596161,
-0.00813115481287241,
-0.002438625320792198,
0.0075677540153265,
-0.0047600348480045795,
0.07065720111131668,
-0.013252384960651398,
0.004047947004437447,
0.0006619825726374984,
-0.03293392434716225,
0.005919137503951788,
-0.02350708097219467,
0.08835206180810928,
-0.037753138691186905,
-0.00497177429497242,
-0.019219953566789627,
-0.021504340693354607,
0.027577761560678482,
-0.028650986030697823,
-0.03079923428595066,
0.0657927542924881,
0.014781606383621693,
0.020622050389647484,
-0.015533695928752422,
0.05136691406369209,
-0.00037541164783760905,
0.03824033960700035,
-0.014675069600343704,
0.006617780774831772,
0.014305195771157742,
-0.06396088004112244,
-0.00021689593268092722,
0.021597137674689293,
-0.025396335870027542,
0.012842301279306412,
0.05314727500081062,
-0.021616188809275627,
-0.015410554595291615,
0.01646408811211586,
0.021586066111922264,
0.01582993008196354,
0.013661719858646393,
0.019217733293771744,
0.013426655903458595,
-0.007194657810032368,
-0.008025597780942917,
-0.04541414603590965,
0.009993142448365688,
-0.021563062444329262,
0.036223284900188446,
-0.023307286202907562,
0.04399839788675308,
0.02495570108294487,
0.005299122538417578,
0.006752233020961285,
-0.04899267107248306,
0.014559973031282425,
-0.002749072154983878,
0.004494807682931423,
0.029375502839684486,
-0.03866424039006233,
-0.004926855675876141,
0.03364301845431328,
0.0253937728703022,
0.013244177214801311,
0.035659871995449066,
0.010212227702140808,
-0.004655844531953335,
-0.002117483178153634,
-0.004092446994036436,
-0.06517510116100311,
0.03619381785392761,
-0.02050560899078846,
0.057311441749334335,
0.011084118857979774,
0.015661874786019325,
0.040949221700429916,
0.006208507809787989,
-0.005454200319945812,
-0.023835645988583565,
-0.014303985983133316,
-0.050624486058950424,
-0.024866852909326553,
0.011915425769984722,
-0.003968305420130491,
-0.0028320299461483955,
-0.004283878020942211,
0.026566119864583015,
0.0295546967536211,
-0.009905691258609295,
-0.037463996559381485,
-0.09218423068523407,
-0.009775981307029724,
0.0033115611877292395,
-0.06758177280426025,
0.0634351298213005,
-0.014693884178996086,
-0.016872147098183632,
-0.008521405048668385,
0.019046397879719734,
0.0012131663970649242,
0.008466195315122604,
0.03031374327838421,
-0.05000392347574234,
0.07664310932159424,
0.005989688448607922,
-0.013553631491959095,
-0.029784109443426132,
0.0144313033670187,
0.12138654291629791,
0.0240385252982378,
0.01355660054832697,
-0.052579116076231,
0.06680507957935333,
-0.010605596005916595,
0.01169836800545454,
-0.03996832296252251,
-0.01894286647439003,
-0.0038776909932494164,
0.024358553811907768,
0.011554923839867115,
0.03660671412944794,
0.014540612697601318,
-0.06045627221465111,
0.05534769594669342,
0.02127707004547119,
-0.021060941740870476,
0.030920879915356636,
0.0324762687087059,
-0.0033547512721270323,
0.008959969505667686,
-0.023482853546738625,
0.02099018543958664,
-0.047397736459970474,
-0.023608960211277008,
-0.006212402135133743,
-0.045409832149744034,
0.012765512801706791,
-0.012170075438916683,
-0.08384954929351807,
0.017346076667308807,
0.03156791627407074,
-0.03045952133834362,
-0.0467204749584198,
0.029837457463145256,
-0.00882171094417572,
-0.013542727567255497,
0.011420835740864277,
0.019073788076639175,
-0.0148992370814085,
0.005941877141594887,
0.0013225821312516928,
0.027612939476966858,
-0.044820066541433334,
0.016814207658171654,
-0.01449388824403286,
-0.024262268096208572,
0.009305299259722233,
0.030940845608711243,
0.012504639104008675,
0.025184739381074905,
-0.0073300511576235294,
-0.0336315780878067,
0.004522078204900026,
-0.006710969377309084,
0.006216312292963266,
-0.017174305394291878,
-0.030350783839821815,
-0.03479262813925743,
0.01697380840778351,
-0.005141099914908409,
0.044253766536712646,
0.005415248218923807,
0.014964166097342968,
0.019971460103988647,
0.02467985823750496,
0.03127682954072952,
-0.03565318509936333,
-0.018334833905100822,
-0.03856078162789345,
0.017239699140191078,
-0.01500807423144579,
0.013878864236176014,
0.022376978769898415,
0.010560188442468643,
0.02420951798558235,
0.010486872866749763,
-0.04255428537726402,
-0.0535246767103672,
-0.005833582952618599,
0.05310709774494171,
0.014186727814376354,
-0.0031333996448665857,
-0.021020278334617615,
0.021091915667057037,
0.03643323853611946,
-0.004724842496216297,
-0.014087988063693047,
0.04851800948381424,
-0.02019484154880047,
0.027356909587979317,
0.027654606848955154,
-0.01634751632809639,
-0.013422949239611626,
-0.004361093044281006,
-0.0063809240236878395,
0.004264298360794783,
-0.03772304579615593,
0.03697401285171509,
0.018822720274329185,
-0.0033955073449760675,
-0.005859874188899994,
-0.006374056916683912,
-0.017627334222197533,
0.028391622006893158,
-0.01319331768900156,
-0.03304431587457657,
-0.023998992517590523,
0.029346028342843056,
-0.027761364355683327,
-0.022377902641892433,
-0.014406180940568447,
-0.016964873299002647,
0.021552424877882004,
0.008222689852118492,
0.004273303784430027,
-0.05253806337714195,
0.06446056067943573,
-0.03884343430399895,
0.041687484830617905,
-0.05419636890292168,
0.008121427148580551,
-0.08192354440689087,
0.0006768709281459451,
-0.028078541159629822,
-0.009162338450551033,
0.03460745885968208,
0.03746729716658592,
-0.016335206106305122,
-0.02075001783668995,
0.031491849571466446,
-0.013978235423564911,
-0.014275429770350456,
0.020822329446673393,
0.040458351373672485,
-0.023181213065981865,
0.0403914600610733,
-0.019545534625649452,
-0.06992129236459732,
0.051525428891181946,
-0.00435763830319047,
-0.04937050864100456,
0.061682041734457016,
-0.04451410472393036,
0.020154938101768494,
-0.002766469493508339,
-0.01923561841249466,
-0.02107076346874237,
0.042560506612062454,
-0.03763079643249512,
-0.005317221395671368,
-0.02243036963045597,
0.010073507204651833,
0.03156335651874542,
0.013437450863420963,
-0.014107590541243553,
-0.007454766891896725,
-0.026246758177876472,
0.04230019450187683,
0.05313962325453758,
-0.03925471752882004,
0.009614808484911919,
-0.022317785769701004,
-0.04811592772603035,
0.02468293532729149,
-0.014594831503927708,
-0.02514265663921833,
0.039716579020023346,
0.015994558110833168,
-0.01406772993505001,
0.02012249268591404,
0.011168143711984158,
-0.01376156136393547,
-0.03938546031713486,
0.03095630183815956,
0.023457728326320648,
-0.02365695871412754,
0.026528161019086838,
-0.0037378647830337286,
-0.03311438485980034,
0.022548088803887367,
-0.07601860165596008,
0.015738628804683685,
-0.02133794315159321,
-0.005777017213404179,
-0.036831729114055634,
-0.020017728209495544,
0.023104486986994743,
0.0019986694678664207,
0.046989016234874725,
0.031415652483701706,
-0.007835278287529945,
0.04357323423027992,
-0.02790285460650921,
-0.03134596720337868,
0.0206178929656744,
0.016386516392230988,
0.024589311331510544,
-0.003161081112921238,
0.03056979365646839,
-0.053784485906362534,
-0.03886125236749649,
0.03704463317990303,
-0.0013305509928613901,
0.06718867272138596,
0.0031884699128568172,
0.0008716575102880597,
0.01137213408946991,
-0.01017523743212223,
0.010712972842156887,
-0.05022536963224411,
0.000534778053406626,
0.04538138955831528,
-0.004077537450939417,
0.062831349670887,
0.010418565012514591,
-0.02199583128094673,
-0.023931358009576797,
-0.06600067019462585,
-0.004478294402360916,
0.019345471635460854,
0.013014673255383968,
0.021976642310619354,
-0.017272531986236572,
0.03327706828713417,
0.008415120653808117,
-0.005322950892150402,
-0.0019807599019259214,
-0.01807447522878647,
-0.027117758989334106,
0.01553040649741888,
-0.005012783221900463,
-0.006423745770007372,
0.047189533710479736,
0.03229891508817673,
-0.008456149138510227,
-0.02460627444088459,
-0.004751081112772226,
0.029107630252838135,
-0.030220091342926025,
0.024866951629519463,
0.0033444410655647516,
0.01989712007343769,
-0.05309775099158287,
0.006874370854347944,
-0.02505655400454998,
0.0149833420291543,
0.0041489871218800545,
0.011941737495362759,
0.02591554820537567,
-0.05326740816235542,
-0.03343714028596878,
-0.02949853427708149,
0.044997263699769974,
0.008742590434849262,
0.003107879078015685,
-0.03563722223043442,
-0.06070082262158394,
-0.03692324459552765,
0.007521204184740782,
0.06116262078285217,
-0.010980586521327496,
0.016500186175107956,
0.01201293058693409,
-0.008194265887141228,
0.016006095334887505,
-0.0313570499420166,
0.010669452138245106,
0.011682482436299324,
-0.022730432450771332,
0.04497816786170006,
-0.047021180391311646,
-0.023615339770913124,
-0.03500661998987198,
0.01463148184120655,
0.0050236983224749565,
0.0765276700258255,
0.025517357513308525,
-0.025198722258210182,
0.05317191407084465,
0.00457792216911912,
-0.011776595376431942,
0.06372758001089096,
-0.03960894048213959,
0.012042976915836334,
0.022629456594586372,
-0.019860271364450455,
-0.04639917612075806,
0.0528985969722271,
-0.03350721672177315,
0.007790030911564827,
0.025608446449041367,
-0.02918071672320366,
0.05533543601632118,
0.003641524352133274,
-0.030913136899471283,
0.04259329289197922,
-0.00474168686196208,
0.02709159068763256,
0.014786512590944767,
0.020245227962732315,
0.02654743194580078,
-0.03193746507167816,
0.019269945099949837,
0.0007114920881576836,
0.0034988748375326395,
-0.010625729337334633,
0.028833426535129547,
0.03487617149949074,
-0.01686885394155979,
-0.002484674332663417,
0.013485869392752647,
0.0354815348982811,
0.05644048750400543,
-0.023376144468784332,
0.04223506525158882,
-0.023885391652584076,
-0.04942408576607704,
-0.005173016339540482,
-0.02468165196478367,
0.0047630975022912025,
0.05208861827850342,
-0.007955130189657211,
0.038759928196668625,
-0.017086602747440338,
-0.027529288083314896,
-0.005505752749741077,
-0.06749433279037476,
-0.022073712199926376,
-0.0047525097616016865,
0.007134711369872093,
-0.008950631134212017,
0.015147260390222073,
-0.01577107608318329,
0.002031715353950858,
0.02152509242296219,
0.0006194093730300665,
-0.043276749551296234,
0.030943987891077995,
-0.03204089775681496,
0.02107466571033001,
-0.005229557864367962,
-0.0046050832606852055,
-0.03892539441585541,
-0.019914887845516205,
0.046640537679195404,
0.02935825102031231,
0.020022708922624588,
-0.014019404537975788,
-0.013471110723912716,
0.004978499375283718,
0.03038581646978855,
-0.07737887650728226,
-0.005887186620384455,
-0.022372445091605186,
0.04018426313996315,
-0.006874184589833021,
-0.04156595095992088
] |
<p>My son is getting interested in astronomy. I was thinking about getting him a scope when he gets a bit older, he is 4 now. At what age have other people gotten their kids telescopes? (I have a 10" dob that we use together) Also at what age is taking a kid on a dark sky camping trip start to make sense.</p>
| 8,828 |
[
-0.011057346127927303,
-0.06434265524148941,
0.007952527143061161,
-0.00004947495472151786,
0.07916074246168137,
0.028383459895849228,
-0.017787223681807518,
-0.023161904886364937,
0.032499268651008606,
-0.06736011058092117,
0.008036419749259949,
0.05640850588679314,
0.023246314376592636,
0.01880907453596592,
0.035753097385168076,
0.038424715399742126,
0.008323132060468197,
-0.04151962324976921,
-0.023113416507840157,
0.010923124849796295,
-0.024391960352659225,
-0.006190513260662556,
0.04838394373655319,
0.00895853340625763,
-0.01603497378528118,
0.016862189397215843,
0.035321060568094254,
0.006833773571997881,
0.021143807098269463,
0.015459896996617317,
0.0117402458563447,
-0.014348207041621208,
0.04275290668010712,
0.032192062586545944,
0.03119705058634281,
-0.016011519357562065,
0.01098254881799221,
0.0009152202401310205,
-0.03895018249750137,
-0.025339670479297638,
-0.045033764094114304,
0.006320694461464882,
-0.0019544416572898626,
0.011323204264044762,
-0.03906285762786865,
-0.02696828916668892,
-0.02127404883503914,
-0.05798961967229843,
0.04054791107773781,
-0.04740280285477638,
0.02956477180123329,
-0.016067907214164734,
0.02294863387942314,
0.02652648463845253,
-0.033301983028650284,
-0.005161478649824858,
0.06692536175251007,
0.05514417961239815,
0.00550117390230298,
-0.047557879239320755,
-0.03270471841096878,
0.006529492326080799,
0.018267732113599777,
0.0034171452280133963,
-0.019160952419042587,
0.0029694719705730677,
-0.02617257833480835,
-0.01881837472319603,
0.03454827144742012,
-0.019803758710622787,
0.017218733206391335,
0.022496795281767845,
0.042873404920101166,
-0.011517152190208435,
-0.058485355228185654,
-0.03896138072013855,
-0.009706614539027214,
0.0018425046000629663,
0.0558534599840641,
0.0428691990673542,
-0.015270829200744629,
0.017890501767396927,
-0.00699275080114603,
0.0034795450046658516,
-0.006065555848181248,
0.013545982539653778,
0.07961723208427429,
-0.0005898215458728373,
0.008431563153862953,
-0.018441379070281982,
-0.004961456172168255,
0.038501329720020294,
0.06598705798387527,
-0.028559362515807152,
0.015882432460784912,
0.031983934342861176,
-0.030540576204657555,
0.053676001727581024,
-0.020477423444390297,
-0.03837154060602188,
0.05213251709938049,
0.01188711728900671,
0.02089902199804783,
0.08773406594991684,
0.0032221178989857435,
-0.021731838583946228,
-0.04095142334699631,
0.0308312326669693,
-0.015455192886292934,
-0.011421050876379013,
-0.05200260877609253,
0.026740562170743942,
0.009687010198831558,
0.010030869394540787,
0.05360967293381691,
-0.04509438946843147,
0.006598371546715498,
0.008425747975707054,
0.05953283980488777,
0.04550210386514664,
0.03858440741896629,
-0.014095842838287354,
0.02412114478647709,
-0.006378352642059326,
-0.053967367857694626,
0.02896173484623432,
0.018737534061074257,
-0.007514626253396273,
0.026675986126065254,
-0.004884413443505764,
-0.017529837787151337,
0.024029871448874474,
0.01030967477709055,
-0.0021794543135911226,
0.01006154902279377,
0.021357906982302666,
-0.03976847603917122,
-0.06589469313621521,
0.03576282411813736,
0.016858123242855072,
-0.011532471515238285,
-0.05857343599200249,
0.02132665552198887,
0.021993575617671013,
0.040229324251413345,
-0.024600090458989143,
-0.011573636904358864,
0.0047067622654139996,
0.06029047816991806,
-0.026853250339627266,
-0.06521530449390411,
-0.00021965061023365706,
-0.0015246705152094364,
-0.022627608850598335,
0.005707092583179474,
-0.09347900003194809,
0.04885796085000038,
0.02284153364598751,
0.01314274687319994,
-0.07080888748168945,
0.05492914095520973,
-0.02754703164100647,
-0.0517483726143837,
-0.002647001761943102,
0.03399015590548515,
-0.036317914724349976,
0.07703512907028198,
-0.0028041217010468245,
-0.006141792982816696,
0.04494014009833336,
0.020095303654670715,
0.006105782464146614,
0.03974273428320885,
0.0001897425827337429,
0.05149540677666664,
-0.0016132075106725097,
-0.02791493386030197,
-0.006851727608591318,
0.040573906153440475,
-0.005825770553201437,
-0.030472517013549805,
-0.0001113035759772174,
-0.016452765092253685,
0.009617007337510586,
0.004768987651914358,
0.03834229335188866,
0.01870829239487648,
0.01391497440636158,
0.012402329593896866,
-0.0208513755351305,
-0.021450279280543327,
-0.028411272913217545,
0.008791930973529816,
-0.00036898275720886886,
0.013052255846560001,
0.007869505323469639,
0.020607396960258484,
0.043744754046201706,
0.00920797884464264,
-0.03926050290465355,
0.011011715047061443,
0.018467718735337257,
0.004893645644187927,
-0.0363621860742569,
0.0190435741096735,
0.05715525895357132,
0.02841952256858349,
-0.006597843952476978,
0.03563098609447479,
-0.03469550237059593,
-0.025594037026166916,
-0.03341040387749672,
-0.019659753888845444,
-0.01941033825278282,
0.015752822160720825,
0.017097508534789085,
0.021280720829963684,
-0.0032720486633479595,
-0.01621248945593834,
0.01359136775135994,
-0.030089234933257103,
0.09330133348703384,
0.022318454459309578,
0.0007575881900265813,
0.027805974707007408,
0.007921164855360985,
0.0002478150126989931,
0.009774163365364075,
0.022037634626030922,
-0.01892336830496788,
-0.06173991039395332,
0.01786980591714382,
0.02547276020050049,
0.030849387869238853,
-0.010328047908842564,
0.02855832129716873,
0.054102443158626556,
0.015083637088537216,
0.02501651830971241,
0.010362735018134117,
-0.01871350221335888,
-0.028492199257016182,
-0.045833487063646317,
0.021069394424557686,
-0.025291763246059418,
0.06002237647771835,
0.016757579520344734,
0.017315031960606575,
0.010090411640703678,
-0.00557731231674552,
-0.06566478312015533,
0.00034925490035675466,
-0.004533227998763323,
0.019742364063858986,
0.028633276000618935,
-0.018341422080993652,
0.04897277429699898,
-0.04117551073431969,
0.008408712223172188,
0.03986429423093796,
0.028668563812971115,
0.003273394890129566,
-0.026442907750606537,
-0.014165662229061127,
0.006610850803554058,
0.01354459673166275,
-0.02698596753180027,
-0.013917804695665836,
0.03162975236773491,
0.01380479708313942,
0.022117208689451218,
-0.03523813188076019,
0.01292479783296585,
-0.023912187665700912,
-0.03207054361701012,
-0.002201244467869401,
-0.014129833318293095,
0.003377396147698164,
-0.016582999378442764,
-0.05669199302792549,
-0.005950137507170439,
-0.0014742191415280104,
-0.003061956027522683,
0.007814533077180386,
-0.06279779225587845,
-0.01177183911204338,
0.017660493031144142,
-0.0030039288103580475,
0.05440281331539154,
0.043668314814567566,
-0.009479026310145855,
-0.009172842837870121,
-0.03621037304401398,
-0.03471159562468529,
-0.003939775284379721,
0.04273383691906929,
-0.006844738032668829,
-0.028483565896749496,
-0.03348539024591446,
0.018698852509260178,
-0.014293264597654343,
-0.020410705357789993,
-0.039937976747751236,
-0.04254099354147911,
-0.013748745433986187,
0.0005648577935062349,
-0.005164662841707468,
-0.012690887786448002,
-0.011065381579101086,
-0.04576893523335457,
-0.021040109917521477,
-0.013588842004537582,
0.04270651564002037,
-0.014550475403666496,
-0.025545109063386917,
0.06061570346355438,
0.015785692259669304,
0.019822165369987488,
0.002256250474601984,
0.008523971773684025,
0.002070080256089568,
0.05912068113684654,
0.025524022057652473,
-0.0449993796646595,
0.029329296201467514,
0.006177986040711403,
-0.015702208504080772,
0.016749968752264977,
0.004461984150111675,
-0.027269113808870316,
0.019312623888254166,
-0.023045729845762253,
0.009634383954107761,
-0.009661870077252388,
0.023520085960626602,
0.02733369544148445,
-0.02677902579307556,
-0.03017660230398178,
0.0032680321019142866,
0.0470903255045414,
0.017605535686016083,
-0.036475297063589096,
0.003105774987488985,
-0.08469980210065842,
0.055326007306575775,
0.026033932343125343,
-0.0013955900212749839,
0.014216464012861252,
-0.030264725908637047,
-0.047568172216415405,
0.01306090597063303,
0.010732083581387997,
0.0187238622456789,
0.005179200321435928,
-0.04715432599186897,
0.008451431058347225,
0.042546991258859634,
-0.007882862351834774,
-0.03642254322767258,
0.028662851080298424,
0.014971078373491764,
0.017293062061071396,
-0.024563312530517578,
0.01150085311383009,
-0.02515624277293682,
0.03556499257683754,
-0.025746311992406845,
-0.005274391733109951,
0.046527259051799774,
0.03655685856938362,
-0.003595965215936303,
-0.020094702020287514,
-0.027725933119654655,
0.04889034852385521,
-0.06168943643569946,
-0.014364073984324932,
-0.008145145140588284,
0.015313869342207909,
0.02049107290804386,
0.009720253758132458,
-0.018473267555236816,
-0.00002019754538196139,
0.0313619039952755,
0.016253717243671417,
-0.057280976325273514,
0.02157038077712059,
-0.08325085788965225,
0.010511595755815506,
-0.06376868486404419,
0.02225472964346409,
-0.03421420976519585,
0.025435250252485275,
-0.01460004597902298,
-0.0363321378827095,
-0.006899502128362656,
-0.026895208284258842,
0.0028853528201580048,
-0.003001714823767543,
-0.062291573733091354,
-0.014315384440124035,
0.026536984369158745,
0.012360290624201298,
0.018282828852534294,
0.0433017872273922,
-0.015007875859737396,
0.007238137070089579,
-0.0005589914508163929,
-0.01136471051722765,
0.0008612178498879075,
-0.017106611281633377,
0.005467530339956284,
0.019227586686611176,
-0.02699866332113743,
-0.017911287024617195,
-0.02114463970065117,
-0.01452703308314085,
0.016650527715682983,
-0.004934372846037149,
-0.010748417116701603,
-0.015058844350278378,
-0.0583905391395092,
-0.020876700058579445,
-0.014288771897554398,
0.01552822720259428,
-0.03487367928028107,
0.02519436553120613,
0.04494328796863556,
-0.04922474920749664,
-0.056430310010910034,
-0.0010527967242524028,
0.03685884177684784,
-0.027537032961845398,
0.0019887667149305344,
-0.002263589296489954,
-0.014465848915278912,
-0.07100380212068558,
0.010178443975746632,
0.03751427307724953,
0.03449149802327156,
-0.0628606528043747,
-0.013083705678582191,
0.014767549932003021,
-0.01666935905814171,
-0.02320723980665207,
0.06236233562231064,
-0.02186444215476513,
0.018182259052991867,
-0.0226393174380064,
-0.025051862001419067,
0.017956016585230827,
0.06263495981693268,
0.06844353675842285,
0.01261133886873722,
-0.020604753866791725,
-0.053872715681791306,
0.00745741929858923,
0.03925370052456856,
0.042745400220155716,
-0.016703346744179726,
0.004649443086236715,
-0.04578816518187523,
-0.031800851225852966,
0.021783607080578804,
0.01533316820859909,
0.024072950705885887,
-0.022521408274769783,
0.015984049066901207,
-0.01696736179292202,
-0.0487523153424263,
0.0011963862925767899,
0.026093367487192154,
0.007434075232595205,
0.04482725262641907,
-0.016912922263145447,
0.009747307747602463,
-0.03012058138847351,
0.0028768684715032578,
0.03674502670764923,
0.05679519101977348,
0.03201514855027199,
-0.04843703657388687,
0.005690842401236296,
-0.027939483523368835,
-0.0462258942425251,
-0.026311440393328667,
-0.011604095809161663,
-0.009983662515878677,
-0.027347318828105927,
0.03514305502176285,
-0.042796727269887924,
-0.03280634433031082,
0.017185190692543983,
-0.030675308778882027,
-0.011791020631790161,
-0.02373737096786499,
-0.03736891224980354,
-0.038463592529296875,
0.010846720077097416,
0.007374494802206755,
0.03367805480957031,
0.06103314831852913,
-0.020442049950361252,
0.01657724380493164,
-0.0055794077925384045,
0.05817735940217972,
-0.026651656255126,
-0.018849611282348633,
-0.004177503753453493,
-0.05488947033882141,
-0.0757414773106575,
0.027603741735219955,
-0.01794469729065895,
0.008231030777096748,
-0.013959068804979324,
-0.03226754441857338,
0.00552877364680171,
0.06699991971254349,
0.05456814914941788,
0.01836821250617504,
0.039403852075338364,
0.008045002818107605,
0.008020390756428242,
-0.023613134399056435,
0.03515758365392685,
0.01919611729681492,
0.02738654613494873,
0.01564572937786579,
-0.013225588947534561,
0.007773589808493853,
-0.04462600126862526,
-0.017063651233911514,
0.02447359263896942,
-0.02528841234743595,
0.04384319484233856,
-0.03550100326538086,
-0.01509108953177929,
0.040182944387197495,
-0.06670640408992767,
-0.014803510159254074,
0.013326686806976795,
-0.06210097670555115,
0.053236354142427444,
-0.05312807485461235,
0.035873815417289734,
-0.01581183448433876,
0.037218127399683,
-0.03510765731334686,
0.018082378432154655,
-0.012147604487836361,
0.014699744060635567,
-0.01688174344599247,
0.019504107534885406,
0.02975180186331272,
-0.023854082450270653,
-0.04289998486638069,
0.0011316898744553328,
0.0625324547290802,
-0.027876360341906548,
0.01965123601257801,
-0.010895254090428352,
-0.01915801502764225,
0.0876539796590805,
-0.009487975388765335,
-0.012012090533971786,
0.0023141817655414343,
-0.006727825850248337,
-0.006782264914363623,
-0.0136518320068717,
0.04383901506662369,
-0.03921254724264145,
-0.034777235239744186,
-0.012756271287798882,
-0.005747195333242416,
-0.0017577530816197395,
-0.042055487632751465,
0.002284425310790539,
0.026963897049427032,
-0.0021364749409258366,
0.010538267903029919,
-0.029081184417009354,
0.06470636278390884,
-0.07933416217565536,
-0.01935858465731144,
-0.054839979857206345,
0.007116919849067926,
-0.00739757576957345,
-0.03637810796499252,
-0.0065260715782642365,
0.003304031677544117,
0.07071700692176819,
-0.009657478891313076,
0.012343715876340866,
-0.0013109724968671799,
-0.011345443315804005,
0.034897930920124054,
-0.01097006443887949,
-0.013492761179804802,
-0.004278059583157301,
0.021674586459994316,
0.003608567174524069,
0.02655111253261566,
0.016249889507889748,
-0.011161326430737972,
0.003528703935444355,
-0.014218811877071857,
0.07154303044080734,
-0.02253972366452217,
0.05436244606971741,
0.018119845539331436,
-0.01495863776654005,
0.006359477993100882,
-0.05630031228065491,
-0.009688081219792366,
-0.03711867332458496,
-0.01689922995865345,
0.00036071561044082046,
-0.028045304119586945,
0.02702571451663971,
-0.017674114555120468,
0.02205287292599678,
0.031965337693691254,
0.04695608839392662,
0.06032480299472809,
0.002844335278496146,
0.003335480811074376,
-0.02546340599656105,
-0.03923152759671211,
0.006245327647775412,
0.014463675208389759,
0.028562333434820175,
0.017352713271975517,
-0.010553006082773209,
0.02983088791370392,
-0.00886574573814869,
-0.016262687742710114,
-0.04019569233059883,
-0.020503796637058258,
-0.05925019830465317,
0.009869157336652279,
0.057757794857025146,
0.006583268754184246,
-0.022481033578515053,
-0.006444057449698448,
0.010248017497360706,
0.0019629523158073425,
0.012584592215716839,
-0.04763917997479439,
-0.04928402230143547,
-0.06577042490243912,
0.010258001275360584,
-0.050756897777318954,
0.0369160957634449,
-0.0027931949589401484,
-0.06847350299358368,
-0.046795643866062164,
0.01468157209455967,
-0.008653558790683746,
0.02478155680000782,
0.04637972638010979,
-0.04376903548836708,
0.047793831676244736,
-0.025192303583025932,
-0.004308486822992563,
0.015210812911391258,
0.01573868840932846,
0.13717398047447205,
0.006633311975747347,
-0.02741127647459507,
-0.04308582469820976,
0.04872845858335495,
-0.033928025513887405,
0.02999831922352314,
-0.007965685799717903,
0.0234097708016634,
-0.01688380539417267,
0.0016065231757238507,
0.0030570465605705976,
0.038693562150001526,
0.014192463830113411,
-0.007829512469470501,
0.07505414634943008,
0.013389479368925095,
-0.038439445197582245,
-0.013993787579238415,
0.028372405096888542,
0.007608539424836636,
0.035789135843515396,
-0.017268702387809753,
0.00978440884500742,
-0.04283779114484787,
-0.004200262483209372,
0.0006331881741061807,
-0.033663127571344376,
0.02954636886715889,
-0.009716520085930824,
-0.009808231145143509,
0.02096882462501526,
-0.01130305603146553,
-0.025109482929110527,
0.0032287156209349632,
0.020363524556159973,
0.038810405880212784,
-0.006342931650578976,
-0.0033743767999112606,
0.04499927535653114,
-0.017422731965780258,
-0.014176963828504086,
-0.007144837640225887,
0.03486219793558121,
-0.031733833253383636,
-0.006304986774921417,
-0.01570679061114788,
0.031689368188381195,
0.013027098029851913,
0.00010298127017449588,
-0.025771798565983772,
-0.0012336424551904202,
0.008269431069493294,
-0.060044340789318085,
-0.004330021794885397,
0.026238055899739265,
0.03329175338149071,
-0.03818260505795479,
-0.02699325792491436,
-0.017882630228996277,
0.024585163220763206,
-0.007854175753891468,
0.04837433248758316,
-0.029705792665481567,
0.04094031825661659,
0.023690244182944298,
-0.049167193472385406,
0.0021267023403197527,
0.007017011754214764,
-0.041504696011543274,
-0.02758227474987507,
0.06608346849679947,
-0.060872770845890045,
0.012744938023388386,
-0.01312390249222517,
0.012819427996873856,
0.05097581446170807,
0.01379579771310091,
-0.027865633368492126,
-0.006943705957382917,
-0.03474031761288643,
-0.0005413850885815918,
-0.04200368747115135,
-0.03269588574767113,
-0.04391740262508392,
0.024715401232242584,
0.009844823740422726,
0.012656256556510925,
-0.022223368287086487,
0.04032306373119354,
-0.02753417193889618,
0.014860182069242,
0.03182034194469452,
0.000145526064443402,
0.011384384706616402,
0.010225243866443634,
-0.06581529974937439,
-0.012433468364179134,
-0.035126954317092896,
0.04310571029782295,
0.009813752956688404,
0.010114597156643867,
0.04920516535639763,
-0.0385589525103569,
-0.04149264842271805,
0.01823042891919613,
-0.007183711510151625,
-0.0242314450442791,
0.024564366787672043,
-0.04027187451720238,
0.010574039071798325,
-0.026270825415849686,
-0.02105882577598095,
-0.05413810536265373,
0.02148088812828064,
0.0060819052159786224,
0.004346685484051704,
-0.04384300485253334,
0.06261316686868668,
-0.04104025289416313,
0.02543921209871769,
-0.04188493639230728,
0.010349899530410767,
-0.050286609679460526,
0.028522895649075508,
0.019525066018104553,
0.01915016584098339,
0.026440801098942757,
0.012761803343892097,
-0.015975728631019592,
-0.06160010024905205,
0.01566530205309391,
-0.004159082192927599,
0.020906446501612663,
0.015116262249648571,
0.0004498394555412233,
-0.019991690292954445,
0.08911976218223572,
-0.02284173294901848,
-0.010056618601083755,
0.03847736120223999,
-0.026210803538560867,
-0.05107636749744415,
0.01618734933435917,
0.010300788097083569,
0.037789683789014816,
0.019557056948542595,
-0.02284327708184719,
-0.00625113770365715,
0.02367815375328064,
-0.012288725934922695,
-0.06484559923410416,
0.03967858478426933,
-0.0013493001461029053,
0.045987196266651154,
0.0341242179274559,
-0.004264187999069691,
-0.02952502854168415,
-0.012010949663817883,
0.02782769687473774,
-0.012256579473614693,
0.01835327409207821,
0.029622182250022888,
-0.00935443677008152,
-0.03456665948033333,
-0.015021208673715591,
-0.0010715817334130406,
-0.006531859282404184,
0.032085128128528595,
0.029480908066034317,
-0.02482658252120018,
0.06990458816289902,
0.0459197573363781,
-0.01012406125664711,
-0.03652433305978775,
-0.003554681083187461,
-0.0016105964314192533,
0.031361259520053864,
0.052899070084095,
-0.05284855514764786,
-0.002133483998477459,
0.046231288462877274,
-0.05782410129904747,
0.024678578600287437,
-0.008654114790260792,
-0.044329773634672165,
-0.04057220742106438,
-0.00703706219792366,
-0.0044010840356349945,
0.003590321633964777,
0.013998487032949924,
0.0035483494866639376,
-0.01948404312133789,
0.03123675286769867,
0.006378483958542347,
-0.03149337321519852,
0.02852005884051323,
0.01627795398235321,
0.005541067570447922,
0.028625983744859695,
0.03694331273436546,
-0.013911922462284565,
0.009416140615940094,
0.03719202056527138,
-0.004591013770550489,
0.015126658603549004,
0.01151843462139368,
0.022490890696644783,
-0.02264053374528885,
0.00478583388030529,
0.001263547339476645,
-0.031201833859086037,
0.010404434986412525,
0.045787591487169266,
0.002547060139477253,
0.0011729671387001872,
-0.01264627929776907,
-0.011469129472970963,
0.05286773294210434,
-0.04725217446684837,
-0.021245496347546577,
0.04001474380493164,
0.011601976118981838,
0.032718271017074585,
0.005674862768501043,
-0.019502531737089157,
-0.020157193765044212,
-0.00690423883497715,
-0.011085924692451954,
-0.029676899313926697,
-0.012377940118312836,
0.008781577460467815,
-0.02795664593577385,
0.03183435648679733,
-0.030065365135669708,
-0.020545341074466705,
-0.03550911694765091,
0.008449485525488853,
-0.02117830142378807,
0.018552672117948532,
-0.019744189456105232,
0.027760855853557587,
0.024176498875021935,
0.0271664597094059,
0.009535878896713257,
0.002346631372347474,
-0.02147444523870945,
0.028864508494734764,
-0.04834212735295296,
0.004643385298550129,
0.020129777491092682,
-0.013764557428658009,
-0.011421790346503258,
-0.025929907336831093,
0.049271587282419205,
0.005729254335165024,
-0.0023373737931251526,
-0.05221937596797943,
0.015656083822250366,
-0.0036834029015153646,
0.018248537555336952,
0.029225407168269157,
-0.025876881554722786,
-0.017898976802825928,
0.018742095679044724,
0.03710608929395676,
0.0052957297302782536,
-0.0742284432053566,
0.029752399772405624,
0.03041701205074787,
-0.029497859999537468,
-0.008464520797133446,
-0.032928816974163055,
-0.019661113619804382,
-0.024001115933060646,
0.0381903275847435,
0.005376332439482212,
0.0618678517639637,
0.015826085582375526,
0.0024030779022723436,
0.035572350025177,
0.025463612750172615,
0.006804951466619968,
0.053708650171756744,
-0.015409235842525959,
-0.015706731006503105,
0.028773225843906403,
0.007877543568611145,
-0.013962218537926674,
0.019226141273975372,
-0.047687381505966187,
-0.0037129814736545086,
-0.017285987734794617,
-0.01145466323941946,
0.01590658910572529,
-0.046419449150562286,
-0.030534176155924797,
0.013826792128384113,
0.013855280354619026,
-0.04312768578529358,
0.07346250861883163,
-0.00694060605019331,
0.05127006024122238,
-0.01317615620791912,
0.04292181134223938,
0.025152646005153656,
-0.02944893389940262,
-0.0012368190800771117,
0.03559885174036026,
0.03579758480191231,
-0.00968664325773716,
0.019587695598602295,
0.02831503562629223,
0.032342005521059036,
-0.008908906951546669,
-0.003654197556897998,
0.06242973357439041,
0.0014349062694236636,
-0.018538372591137886,
0.0011929812608286738,
0.02480860985815525,
-0.01123005710542202,
0.06607037782669067,
-0.016673773527145386,
0.06348632276058197,
-0.023510552942752838,
-0.023358143866062164,
-0.02996986173093319,
-0.019142258912324905,
-0.03420548141002655,
0.026690427213907242,
-0.022324638441205025,
0.04462014511227608,
-0.002473756205290556,
-0.010428872890770435,
-0.020497534424066544,
0.00677597476169467,
0.06854940950870514,
-0.052592091262340546,
0.05958714336156845,
-0.037260353565216064,
0.06214634329080582,
0.001836881274357438,
0.0013186066644266248,
0.00982749741524458,
-0.04780123755335808,
-0.0028123059310019016,
0.03285554051399231,
0.00927609670907259,
-0.010202932171523571,
-0.017929978668689728,
0.02828662469983101,
0.05530472844839096,
-0.08290869742631912,
0.004917864687740803,
-0.010849486105144024,
-0.005041383672505617,
0.015777649357914925,
0.013144186697900295
] |
<p>We all know that wing-propeller planes rely on air to create a thrust. They suck the air in and push them back hard that it's opposite reaction pushes the plane (Newton's law). </p>
<p>Does that mean wing-propeller struggles up at high altitude because of the low pressure of the air ?</p>
<p>Same question for jet engine.</p>
| 8,829 |
[
-0.04241462051868439,
0.006437001749873161,
-0.0040478757582604885,
-0.0027051453944295645,
0.03453180193901062,
0.007032729685306549,
-0.015870485454797745,
-0.00018954278493765742,
0.013694562949240208,
-0.0472581647336483,
0.01138414815068245,
0.07955703139305115,
0.044797156006097794,
-0.005353348329663277,
-0.057786766439676285,
0.00575623195618391,
-0.03240605816245079,
-0.04127996042370796,
0.020503463223576546,
-0.005992654711008072,
-0.051538076251745224,
0.03418898582458496,
-0.0023754409048706293,
0.019053170457482338,
-0.02200004644691944,
0.03551757335662842,
0.024303466081619263,
-0.03025134839117527,
-0.005814732983708382,
0.020320260897278786,
0.019687747582793236,
0.03878272697329521,
0.010458302684128284,
0.05984710156917572,
0.03154957666993141,
0.01181661058217287,
-0.035913676023483276,
-0.048904899507761,
-0.034962430596351624,
0.03432709351181984,
0.004122125916182995,
-0.017108557745814323,
-0.0030450846534222364,
0.0009982148185372353,
-0.021090207621455193,
0.048487383872270584,
0.0005711193080060184,
-0.017173469066619873,
0.050136495381593704,
-0.08976694196462631,
0.01548412349075079,
0.009785333648324013,
0.015080425888299942,
0.05295508727431297,
0.004391932860016823,
-0.006829090882092714,
0.08111830055713654,
0.06510406732559204,
-0.03399541974067688,
-0.049569688737392426,
-0.02061006985604763,
-0.007396584376692772,
-0.021457940340042114,
-0.012462547048926353,
-0.025774987414479256,
0.02461251989006996,
-0.01993260532617569,
-0.030787793919444084,
0.006246459670364857,
-0.0008190936641767621,
-0.007154011633247137,
0.009222738444805145,
0.02139761485159397,
-0.016215801239013672,
0.018397226929664612,
-0.023256005719304085,
0.013322622515261173,
0.01749390922486782,
0.04434098303318024,
0.07656193524599075,
-0.02926606871187687,
0.04832945391535759,
0.03180013969540596,
0.0029256432317197323,
0.012844479642808437,
0.026449432596564293,
0.10206541419029236,
-0.008231505751609802,
0.008517936803400517,
0.02854514680802822,
0.017302827909588814,
-0.0001615376240806654,
0.007343348115682602,
-0.029547730460762978,
-0.003104276256635785,
0.000022902071577846073,
-0.00984149519354105,
0.05936352536082268,
0.049409620463848114,
-0.013359918259084225,
0.018824666738510132,
-0.017435993999242783,
0.036204636096954346,
0.04125776141881943,
0.006860588677227497,
-0.004152502864599228,
-0.07269568741321564,
0.008687795139849186,
-0.03691459819674492,
0.005032287910580635,
-0.03826303035020828,
0.030903397127985954,
-0.04192114621400833,
-0.05794175714254379,
-0.004876397550106049,
0.0009719321387819946,
0.012999075464904308,
-0.009653063490986824,
0.048566851764917374,
0.04679708182811737,
0.056761398911476135,
-0.02186550199985504,
0.04383919760584831,
0.018591444939374924,
-0.02730274759232998,
0.017315644770860672,
0.019948873668909073,
-0.06927581131458282,
-0.05681218206882477,
0.012379856780171394,
-0.009736555628478527,
-0.03010852076113224,
0.014400512911379337,
0.016866397112607956,
0.04244613274931908,
0.0010186302242800593,
-0.0839335173368454,
-0.07158162444829941,
0.02050509676337242,
0.011844396591186523,
-0.00132693350315094,
-0.05711483955383301,
0.010578067041933537,
0.00008342655200976878,
0.08572619408369064,
-0.007850793190300465,
0.028557823970913887,
-0.010536668822169304,
0.011802964843809605,
-0.004579114727675915,
-0.012091944925487041,
0.01280716061592102,
0.03530418872833252,
-0.0626177191734314,
0.0009882253361865878,
-0.09680701047182083,
0.009407157078385353,
0.031118789687752724,
0.005954984109848738,
-0.03501024469733238,
0.010185209102928638,
-0.020559892058372498,
-0.024868063628673553,
-0.018462955951690674,
0.013201416470110416,
-0.025263363495469093,
0.04430500417947769,
0.04712657257914543,
0.0019572111777961254,
0.048712484538555145,
0.000023732320187264122,
0.02702517621219158,
-0.020829055458307266,
-0.011664951220154762,
0.04837505891919136,
0.003791234688833356,
-0.013057716190814972,
-0.04822850972414017,
-0.013251631520688534,
0.01828051172196865,
-0.04225776344537735,
-0.037226367741823196,
-0.017788970842957497,
0.02143285609781742,
-0.03739060088992119,
0.029990598559379578,
0.009754200465977192,
0.011960180476307869,
-0.00004069557326147333,
-0.016552794724702835,
-0.03293369337916374,
-0.07610685378313065,
0.04041365534067154,
-0.036393314599990845,
-0.014146791771054268,
0.01493752934038639,
0.029365766793489456,
0.05225320905447006,
-0.07467132061719894,
0.0074343811720609665,
-0.000038553484046133235,
0.007858791388571262,
0.02079673483967781,
0.009773916564881802,
0.03151816874742508,
0.0414309948682785,
0.029885081574320793,
0.006202320568263531,
0.03947468847036362,
-0.01808158867061138,
-0.034458111971616745,
0.017178375273942947,
-0.026844382286071777,
-0.010701678693294525,
0.02698608860373497,
0.022069362923502922,
0.026926269754767418,
0.008179067634046078,
0.010991455055773258,
0.01781294494867325,
-0.023826727643609047,
0.07489452511072159,
0.042963702231645584,
0.021755479276180267,
0.022145897150039673,
0.015945229679346085,
0.001747112488374114,
-0.0010401807958260179,
0.0057206288911402225,
0.018064387142658234,
-0.019495783373713493,
-0.02999676577746868,
0.012640098109841347,
0.018261587247252464,
-0.061833351850509644,
0.056633636355400085,
0.058171629905700684,
0.015990886837244034,
0.029265740886330605,
0.047218237072229385,
-0.021368924528360367,
-0.03497902676463127,
0.028630759567022324,
0.051459673792123795,
0.025498973205685616,
0.0493680015206337,
0.03184261545538902,
0.0339692048728466,
0.012993711046874523,
-0.060336705297231674,
-0.023629629984498024,
0.028485406190156937,
0.023113660514354706,
0.0006767337908968329,
-0.0015813306672498584,
-0.039658449590206146,
0.04079970717430115,
-0.022290924564003944,
0.020086992532014847,
-0.024608971551060677,
-0.01804407499730587,
0.02139953151345253,
-0.004115298390388489,
-0.02039583958685398,
0.017358465120196342,
-0.006397579796612263,
0.0026125956792384386,
0.020508572459220886,
0.04201195761561394,
-0.05499904975295067,
0.022568514570593834,
-0.05767689272761345,
0.008580682799220085,
-0.043057847768068314,
-0.01596863381564617,
0.013669113628566265,
-0.005693559069186449,
0.07292082905769348,
0.007877007126808167,
-0.026635926216840744,
0.011306817643344402,
-0.041884567588567734,
-0.008446548134088516,
0.011796501465141773,
0.008496415801346302,
0.015813983976840973,
-0.0345747247338295,
-0.00257458770647645,
0.03573662415146828,
0.0178812425583601,
0.015445259399712086,
0.004972976632416248,
-0.046777691692113876,
-0.049280665814876556,
0.022512586787343025,
-0.06712744385004044,
-0.019856169819831848,
0.009587664157152176,
-0.007260799407958984,
0.02008536085486412,
-0.018448084592819214,
0.017842603847384453,
0.012629681266844273,
-0.05340426415205002,
-0.029321907088160515,
-0.012202993035316467,
0.003655389416962862,
-0.01018388383090496,
-0.054930511862039566,
0.016508379951119423,
0.006594583857804537,
-0.08751607686281204,
0.001954580657184124,
-0.052233289927244186,
-0.014155138283967972,
0.0077294702641665936,
0.007539188023656607,
0.017756957560777664,
-0.0033030579797923565,
-0.025441136211156845,
0.06647824496030807,
-0.02850108966231346,
-0.04232535883784294,
-0.0062872800044715405,
-0.029701581224799156,
-0.014362084679305553,
0.021777579560875893,
-0.002020525746047497,
0.05423012375831604,
0.00016765853797551244,
-0.0001151097021647729,
0.019237510859966278,
0.01502558309584856,
0.03224745765328407,
0.010954436846077442,
-0.027521392330527306,
-0.0026586130261421204,
0.008021603338420391,
0.0024745832197368145,
0.0372471883893013,
0.008805862627923489,
0.005245482083410025,
0.03706411272287369,
-0.03284527733922005,
0.04110230505466461,
-0.00031170269357971847,
-0.038287390023469925,
0.04940880835056305,
-0.014718265272676945,
0.003191306022927165,
-0.03364822641015053,
0.02987533062696457,
0.01138133741915226,
0.01492194551974535,
-0.004825422074645758,
0.03024611994624138,
0.04720723628997803,
0.01391016598790884,
-0.03133188188076019,
0.043526604771614075,
0.04788994416594505,
-0.03001401573419571,
-0.04107227548956871,
0.011951002292335033,
-0.04831517115235329,
0.007995453663170338,
-0.00914100743830204,
-0.007720394060015678,
0.03839930519461632,
0.0023889420554041862,
0.042723774909973145,
0.06114295497536659,
-0.034025344997644424,
0.0765061005949974,
-0.06478983908891678,
0.0009970193495973945,
-0.011611571535468102,
0.028200507164001465,
-0.00949140079319477,
0.07003599405288696,
0.0062104384414851665,
0.033864349126815796,
0.04150836542248726,
-0.00381249887868762,
-0.09251309186220169,
-0.012849901802837849,
-0.025943705812096596,
-0.027922235429286957,
-0.0005560130230151117,
-0.00950942188501358,
-0.018464302644133568,
-0.051253315061330795,
-0.01287497952580452,
-0.018908800557255745,
0.017724132165312767,
-0.01583290658891201,
0.04268060624599457,
-0.028461875393986702,
-0.03585542365908623,
-0.009328383021056652,
-0.007204678375273943,
0.05203620716929436,
-0.021570127457380295,
0.05511150509119034,
0.06263010948896408,
-0.01597505807876587,
-0.012844529934227467,
0.00004232599894749001,
0.013010137714445591,
-0.019411634653806686,
0.005936786066740751,
-0.005712324753403664,
0.005964071489870548,
-0.012178728356957436,
0.0008148215711116791,
0.0050035943277180195,
0.024584466591477394,
0.0034710289910435677,
0.023782804608345032,
-0.03626692295074463,
-0.03500358387827873,
-0.03585061430931091,
0.009426324628293514,
0.02600744739174843,
0.007509145885705948,
0.03881172463297844,
-0.02618568204343319,
-0.023163096979260445,
-0.010929339565336704,
0.04757628217339516,
0.03336983919143677,
0.020487187430262566,
0.007014087401330471,
-0.03584664314985275,
-0.0008603113819845021,
-0.04410926625132561,
-0.013881560415029526,
0.014620685018599033,
-0.006395944859832525,
-0.040690600872039795,
-0.01222708448767662,
0.031714871525764465,
0.011332545429468155,
-0.02225635200738907,
0.02325413003563881,
-0.012914526276290417,
-0.03412621095776558,
-0.022112276405096054,
0.028558727353811264,
0.03527523949742317,
0.018296515569090843,
0.01899932138621807,
0.02366364188492298,
-0.021217888221144676,
-0.1006658524274826,
-0.024670293554663658,
0.04981069639325142,
-0.0004374856944195926,
-0.008476047776639462,
0.017935041338205338,
-0.0381249338388443,
-0.018399111926555634,
0.029481593519449234,
-0.036857690662145615,
0.0213325135409832,
-0.059159521013498306,
-0.00808637123554945,
-0.01180285308510065,
-0.029727470129728317,
-0.009993506595492363,
0.003306903876364231,
-0.03485611453652382,
-0.00014310196274891496,
-0.021861955523490906,
0.004724707920104265,
-0.019210129976272583,
0.006341291591525078,
0.003782357554882765,
0.041666608303785324,
0.02347867377102375,
-0.022330164909362793,
-0.04625052586197853,
-0.00042843117262236774,
-0.030600784346461296,
-0.05887927487492561,
-0.009822355583310127,
-0.007093125954270363,
0.01126457005739212,
0.007448130287230015,
-0.034009143710136414,
-0.016130762174725533,
0.03512571379542351,
-0.02948734723031521,
-0.03699055314064026,
-0.03750107064843178,
-0.04220101609826088,
-0.017088668420910835,
0.03425249829888344,
0.004541413392871618,
0.03483816981315613,
0.04092961177229881,
-0.04073590040206909,
0.009199254214763641,
-0.00337769091129303,
0.03423476591706276,
-0.014484095387160778,
-0.055243540555238724,
-0.003088668454438448,
-0.014925319701433182,
-0.004543287213891745,
0.07449112087488174,
-0.006487301550805569,
0.033482786267995834,
-0.020341118797659874,
0.009775811806321144,
0.006055884063243866,
0.002557894214987755,
0.011022204533219337,
-0.00857754610478878,
-0.025525221601128578,
0.04164601489901543,
0.00781825091689825,
-0.03340268135070801,
-0.010149486362934113,
0.006888129748404026,
0.021771961823105812,
0.02931896224617958,
0.0045897504314780235,
-0.006237608380615711,
-0.018900766968727112,
0.00949457660317421,
0.004400153178721666,
-0.043998051434755325,
0.048144176602363586,
-0.017819423228502274,
-0.017265560105443,
0.007486812304705381,
-0.006321294233202934,
-0.03890858590602875,
0.022261958569288254,
0.022441953420639038,
0.03526715561747551,
-0.0037149402778595686,
0.026880556717514992,
-0.008038795553147793,
-0.01041372213512659,
-0.03995402902364731,
-0.04932856559753418,
0.05396721512079239,
0.039684489369392395,
0.014854669570922852,
-0.013764936476945877,
-0.02541869506239891,
-0.010115436278283596,
-0.027439042925834656,
0.023621993139386177,
0.04168647155165672,
-0.033412035554647446,
-0.03961921110749245,
0.03409912809729576,
-0.03901548311114311,
0.03646954521536827,
-0.018929749727249146,
-0.03647727146744728,
0.013723569922149181,
-0.01001120824366808,
-0.010111499577760696,
-0.04669899865984917,
0.025782903656363487,
-0.015144937671720982,
-0.014167816378176212,
0.0055425516329705715,
-0.027409521862864494,
0.01033820491284132,
-0.025362860411405563,
0.04782671853899956,
0.019769230857491493,
-0.022951465100049973,
-0.002128457650542259,
-0.022380374372005463,
0.029769454151391983,
-0.005702853202819824,
0.030003247782588005,
0.009020027704536915,
-0.01191212609410286,
-0.023322133347392082,
-0.021787431091070175,
0.030800793319940567,
0.0017492342740297318,
-0.002974661998450756,
0.023759089410305023,
0.08339322358369827,
-0.0021349736489355564,
-0.012639787979424,
-0.006564181763678789,
-0.04561373218894005,
-0.007480759639292955,
0.037819914519786835,
-0.0038526959251612425,
0.015501183457672596,
0.030178306624293327,
-0.006629572249948978,
-0.02405240572988987,
0.011302587576210499,
0.011143024079501629,
0.03980972245335579,
0.028370678424835205,
0.04313046112656593,
-0.00007934877794468775,
0.0005588977364823222,
0.024344805628061295,
-0.0065065729431807995,
-0.018279414623975754,
-0.016068825498223305,
0.0036398975644260645,
0.01682334393262863,
0.011450767517089844,
0.03503060340881348,
0.06784046441316605,
0.011252878233790398,
0.029166046530008316,
-0.025989647954702377,
0.04323761165142059,
0.025533730164170265,
0.003742972621694207,
0.007676171604543924,
-0.05529555678367615,
0.04784761741757393,
-0.039938993752002716,
0.058166082948446274,
-0.01609111949801445,
-0.00008234303095377982,
0.02161255106329918,
0.04390556365251541,
0.028866244480013847,
-0.0606488361954689,
0.013259900733828545,
-0.025550436228513718,
0.01712188310921192,
-0.021826334297657013,
-0.014531035907566547,
0.01997806876897812,
0.04569944366812706,
0.03528963401913643,
-0.0034540146589279175,
0.025252483785152435,
0.015662429854273796,
-0.03725699707865715,
-0.03810315206646919,
-0.003492133691906929,
-0.01289453823119402,
0.010481585748493671,
-0.007046443410217762,
-0.021970786154270172,
0.03888896107673645,
0.012606529518961906,
0.03550858795642853,
-0.02092844992876053,
0.0361960344016552,
-0.013044966384768486,
0.02976667694747448,
0.004441950935870409,
-0.0076174489222466946,
-0.004692831542342901,
0.01704605668783188,
0.12643171846866608,
0.023908238857984543,
0.028597019612789154,
-0.05478334054350853,
-0.018987072631716728,
-0.027138911187648773,
-0.000516877043992281,
-0.01270252000540495,
-0.009555834345519543,
-0.008336574770510197,
0.012271854095160961,
0.04069873318076134,
0.029158471152186394,
0.014496078714728355,
0.0003633410669863224,
0.05122163146734238,
-0.07538675516843796,
-0.01918625831604004,
0.008840799331665039,
0.013683633878827095,
-0.025324605405330658,
0.012255795300006866,
0.022227345034480095,
0.017003396525979042,
-0.02787167951464653,
0.007769925519824028,
0.0063740345649421215,
-0.05010939761996269,
0.04135514050722122,
-0.002094751223921776,
-0.0631444975733757,
0.018538441509008408,
0.020844051614403725,
-0.01025619637221098,
-0.02622193656861782,
0.025990648195147514,
-0.027192750945687294,
-0.001218231744132936,
0.0014966598246246576,
0.010420670732855797,
0.003253285540267825,
0.018733065575361252,
0.003013686975464225,
-0.008174576796591282,
-0.045370932668447495,
-0.0021428971085697412,
-0.014966065064072609,
0.01079636625945568,
0.01812467910349369,
0.02896999381482601,
-0.02862168848514557,
0.012269056402146816,
0.02975357696413994,
-0.06234855577349663,
-0.015796765685081482,
-0.0018070386722683907,
-0.006988007575273514,
-0.02944887802004814,
-0.09710651636123657,
-0.0028573456220328808,
0.00696210004389286,
0.01134602352976799,
-0.008204507641494274,
-0.015038719400763512,
0.03238904848694801,
0.012867315672338009,
-0.00553426519036293,
0.02788289077579975,
-0.041286617517471313,
-0.0014914153143763542,
-0.018249036744236946,
-0.005613237619400024,
-0.04276866465806961,
-0.018612440675497055,
0.01915931887924671,
0.03938835859298706,
0.009627722203731537,
0.015517720021307468,
-0.017816511914134026,
-0.040056608617305756,
-0.08424197882413864,
0.058604441583156586,
-0.01815909333527088,
-0.020776137709617615,
-0.0037703621201217175,
-0.02449863590300083,
0.019844835624098778,
0.07521625608205795,
-0.009845583699643612,
0.011346149258315563,
-0.03871355578303337,
0.0448341891169548,
0.009504108689725399,
-0.0136342728510499,
-0.06324201077222824,
0.025290794670581818,
-0.045976873487234116,
-0.014941676519811153,
0.014508336782455444,
0.05290650948882103,
0.008190376684069633,
-0.002720580669119954,
-0.05030493065714836,
0.023409351706504822,
-0.030924871563911438,
0.006516971159726381,
0.024416616186499596,
-0.000980707467533648,
0.01985679380595684,
0.02412189543247223,
0.04414161294698715,
-0.052584726363420486,
-0.014622113667428493,
-0.01594255305826664,
-0.021055730059742928,
-0.03186171501874924,
0.017840435728430748,
0.015629669651389122,
0.01803959347307682,
-0.006372519303113222,
0.027185380458831787,
-0.0331319235265255,
0.0029590153135359287,
-0.08795769512653351,
0.03205214813351631,
0.003110320772975683,
0.010351784527301788,
0.010954473167657852,
0.024104362353682518,
-0.05657719820737839,
0.021859394386410713,
-0.021961795166134834,
0.005072072148323059,
-0.003152363235130906,
0.03325928747653961,
0.0313798263669014,
-0.030663786455988884,
0.0432787649333477,
-0.02969060279428959,
-0.03585309907793999,
0.020050087943673134,
-0.018853722140192986,
-0.05660305544734001,
0.017171528190374374,
-0.01467504445463419,
0.008244617842137814,
0.014810463413596153,
0.007357934955507517,
-0.022732896730303764,
0.026470046490430832,
-0.020795144140720367,
-0.01743617281317711,
-0.009810141287744045,
0.0005971178179606795,
0.024151859804987907,
0.015531671233475208,
0.009309923276305199,
-0.029341137036681175,
-0.024402286857366562,
0.041831791400909424,
0.04324604570865631,
0.01218837033957243,
-0.0012525336351245642,
0.04160594940185547,
0.011429197154939175,
0.022793786600232124,
-0.00687309168279171,
-0.007056997623294592,
0.048677049577236176,
0.0007565878913737833,
-0.008167087100446224,
0.025823913514614105,
0.0267763901501894,
-0.02745973877608776,
-0.1341133862733841,
-0.01193238329142332,
-0.019426673650741577,
0.02992573007941246,
0.01775141805410385,
-0.04355551674962044,
0.011972542852163315,
0.010666225105524063,
-0.09711252897977829,
-0.00788346491754055,
-0.02559749223291874,
-0.01800556853413582,
-0.03354441747069359,
0.02854996919631958,
0.04958004504442215,
0.05024079605937004,
-0.0012800312833860517,
0.01953747868537903,
0.007520819548517466,
-0.0015307303983718157,
0.018186820670962334,
0.030521754175424576,
0.021681705489754677,
-0.0062913005240261555,
0.0004944817046634853,
-0.009306485764682293,
0.028724942356348038,
-0.02982698753476143,
-0.031074585393071175,
0.04731866717338562,
0.009430701844394207,
0.0448494628071785,
-0.034396011382341385,
0.012990438379347324,
-0.018085841089487076,
0.015437657944858074,
0.0022942167706787586,
0.01358709204941988,
-0.007273256778717041,
0.022544508799910545,
-0.030278777703642845,
0.01072108093649149,
-0.015617120079696178,
0.02048625983297825,
0.008080328814685345,
-0.020458918064832687,
0.022448064759373665,
0.06024440377950668,
-0.02907087281346321,
-0.013147600926458836,
-0.01708882302045822,
0.022201357409358025,
-0.004412056878209114,
0.0012820876436308026,
0.012014112435281277,
-0.057237643748521805,
0.003864541882649064,
0.023248199373483658,
0.00233474955894053,
-0.04215804487466812,
0.020930275321006775,
0.014149711467325687,
-0.025825031101703644,
0.02164601720869541,
0.015240928158164024,
-0.020611783489584923,
-0.0343807153403759,
0.008043226785957813,
-0.017886636778712273,
-0.036460794508457184,
-0.027114948257803917,
-0.07164902985095978,
-0.017560726031661034,
0.03467690572142601,
0.028931638225913048,
0.00836568046361208,
0.038663994520902634,
-0.028889011591672897,
-0.03586561232805252,
-0.07454954832792282,
0.01986696757376194,
0.022448454052209854,
0.021590234711766243,
-0.03341345489025116,
-0.03105854243040085,
0.029056211933493614,
0.0027462176512926817,
0.030800266191363335,
0.00912377331405878,
0.005936018656939268,
0.008435261435806751,
-0.011419357731938362,
-0.019575422629714012,
-0.022714566439390182,
0.01853027381002903,
0.03677107021212578,
-0.052895475178956985,
-0.03074498102068901,
0.00786355510354042,
-0.049982622265815735,
0.022121412679553032,
0.056715209037065506,
-0.005801033694297075,
0.05549944192171097,
0.023677850142121315,
-0.05668272450566292,
0.01620909757912159,
0.06890930980443954,
0.025905271992087364,
0.06800037622451782,
-0.012411059811711311,
0.024961937218904495,
0.009377466514706612,
-0.0040952167473733425,
-0.04581788182258606,
0.04434878006577492,
-0.03939833119511604,
-0.02304230071604252,
0.0022600889205932617,
-0.005361120216548443,
0.024536337703466415,
-0.053693439811468124,
0.012095729820430279,
0.04175770282745361,
-0.02002018131315708,
0.002414108719676733,
0.05420335754752159,
0.036291319876909256,
0.007437159772962332,
-0.03676791489124298,
-0.03390910103917122,
0.03603368252515793,
-0.009252844378352165,
-0.011675686575472355,
0.041310667991638184,
0.041890714317560196,
0.023053165525197983,
-0.003632846986874938,
0.007486812770366669,
0.010846145451068878,
0.011386854574084282,
-0.0008073640055954456,
0.05518447235226631,
-0.025964662432670593,
-0.03507755324244499,
0.022013721987605095,
0.0070018470287323,
-0.01163395307958126,
0.034952327609062195,
-0.014379617758095264,
0.07601716369390488,
-0.048780836164951324,
0.03143865242600441,
-0.03815663605928421,
-0.0007379093440249562,
-0.007369982544332743,
0.0003087543591391295,
0.01049339585006237,
0.031299199908971786,
0.021454649046063423,
-0.02817261405289173,
0.003749931463971734,
-0.0019515646854415536,
0.022072818130254745,
-0.005353401880711317,
0.0015627291286364198,
-0.034092824906110764,
0.018873073160648346,
-0.035781946033239365,
-0.028525540605187416,
-0.05637509375810623,
-0.013459784910082817,
0.011701715178787708,
0.03175457939505577,
0.016429748386144638,
-0.0010719686979427934,
-0.016252998262643814,
-0.04420461505651474,
0.028631918132305145,
-0.07641033083200455,
-0.026262210682034492,
0.031119132414460182,
0.019528375938534737,
-0.018327994272112846,
-0.013048372231423855
] |
<p>As you can see below, the two pages attached describe how to obtain the final solution of orthonormality.</p>
<p>I do not completely follow the discussion but I will talk you through what I DO understand and then hopefully you could fill in the gaps ?</p>
<p>So, we consider a wavefunction $\psi$ which when measured has discrete eigenvalues $f_n$.</p>
<p>When we obtain $f_n$ we then have $\psi$=$\psi_n$</p>
<p>We assume the eigenfunction ($\psi_n$) is normalise as per eqn. 3.1.</p>
<p>Applyin the principle of superposition : Since we have multiple eigenfunctions which satisfy the wavefunction $\psi$ we must also be able to state these eigenfunction as a linear combination which in turn is also a solution.</p>
<p>Hence, we obtain 3.2.</p>
<p><strong>First problem :</strong> In 3.2 where did $a_n$ come from ?</p>
<p>This completes the first picture discussion. Now moving onto the second picture :</p>
<p><strong>Second problem :</strong> The first paragraph talks about bilinear expressions and what not. I do not follow the discussion in this section or how 3.3 was obtained.</p>
<p>If these two issues are explained to me I think I can work out the rest. :)</p>
<p><img src="http://i.stack.imgur.com/kdHBL.jpg" alt="enter image description here"></p>
<p><img src="http://i.stack.imgur.com/nOS5l.jpg" alt="enter image description here"></p>
| 8,830 |
[
-0.0022385278716683388,
0.002171822590753436,
-0.026891984045505524,
-0.012726604007184505,
0.04780793935060501,
-0.024550914764404297,
-0.054699212312698364,
-0.046571921557188034,
0.0349496528506279,
-0.01590876281261444,
0.05503047630190849,
0.0036664882209151983,
0.07288810610771179,
0.01825876347720623,
0.030069200322031975,
0.025936275720596313,
-0.022273004055023193,
-0.03556912764906883,
-0.012085098773241043,
0.0038850901182740927,
0.0021911640651524067,
0.042688895016908646,
0.002072421833872795,
-0.026414906606078148,
-0.022520996630191803,
0.026882240548729897,
0.03465341031551361,
0.003329335479065776,
0.056661538779735565,
0.06492364406585693,
-0.0020894301123917103,
-0.029226141050457954,
0.007291754242032766,
0.0490000955760479,
-0.024024907499551773,
-0.0037373672239482403,
-0.029068639501929283,
-0.026918144896626472,
0.004716206341981888,
-0.0015266855480149388,
-0.02422706037759781,
-0.02472471445798874,
-0.02000090666115284,
0.022512774914503098,
-0.020147448405623436,
-0.0025038179010152817,
0.0036162561737000942,
-0.012240641750395298,
0.018478868529200554,
-0.05584508553147316,
0.09136592596769333,
0.02397901378571987,
0.03986072540283203,
0.023098990321159363,
-0.009891418740153313,
-0.03976300358772278,
0.05451544374227524,
0.07099121809005737,
0.0042682490311563015,
-0.0746074840426445,
-0.0021787979640066624,
-0.027910742908716202,
0.004705645143985748,
0.004035742022097111,
-0.06285806745290756,
-0.007860972546041012,
0.019242221489548683,
-0.02747451700270176,
-0.005225640255957842,
-0.030573643743991852,
-0.010237284936010838,
0.028882833197712898,
0.059689607471227646,
-0.03525875136256218,
-0.005869025364518166,
-0.014185584150254726,
-0.0029637080151587725,
0.027725648134946823,
0.047547198832035065,
0.012257869355380535,
-0.03859071806073189,
0.01644897274672985,
-0.0018489075591787696,
0.012891772203147411,
0.0033241743221879005,
-0.03774627298116684,
0.08243294060230255,
-0.0038138788659125566,
0.00879918597638607,
-0.0013492614962160587,
0.018394609913229942,
0.003720093285664916,
0.06739132106304169,
-0.014271344989538193,
-0.03379998356103897,
0.04354192316532135,
0.027003005146980286,
0.04453428462147713,
-0.007249908056110144,
-0.03266172856092453,
-0.0062918164767324924,
-0.03901205584406853,
-0.014320111833512783,
0.07923626154661179,
0.00983312539756298,
0.029403582215309143,
-0.06361614912748337,
0.04490850120782852,
0.0025139988865703344,
-0.0005179758882150054,
-0.019583648070693016,
0.044077303260564804,
0.0023746390361338854,
0.005563582759350538,
-0.01626552641391754,
-0.006186870392411947,
-0.028265221044421196,
-0.013797804713249207,
0.07240843027830124,
0.10159718990325928,
0.01079433411359787,
-0.006937185302376747,
0.029831448569893837,
-0.03557513281702995,
-0.07263659685850143,
0.004628691356629133,
-0.00219991197809577,
0.011743390001356602,
-0.04932496324181557,
0.05374734476208687,
0.03497178480029106,
0.02070547454059124,
-0.002616858808323741,
-0.014817684888839722,
-0.0006701462552882731,
0.0036650842521339655,
-0.12864971160888672,
-0.06625007092952728,
0.038755372166633606,
-0.040223121643066406,
0.002437183866277337,
-0.05468957498669624,
0.0002643227344378829,
0.05389038100838661,
0.09190024435520172,
-0.015812693163752556,
0.019406631588935852,
-0.021836087107658386,
0.013516493141651154,
0.019920626655220985,
0.022073965519666672,
-0.027438225224614143,
-0.017536818981170654,
-0.035147808492183685,
-0.03503093123435974,
-0.06176217645406723,
0.02221684344112873,
0.03506873548030853,
0.00781967956572771,
-0.026272408664226532,
0.10824277251958847,
0.009195011109113693,
-0.008641756139695644,
0.004416810814291239,
0.03530529886484146,
-0.021514656022191048,
0.023319395259022713,
0.017431754618883133,
-0.0000012549500070235808,
0.06553999334573746,
-0.03444007411599159,
0.03451446071267128,
-0.015115713700652122,
0.020723119378089905,
0.019138650968670845,
-0.03284859657287598,
0.002236513188108802,
-0.021428383886814117,
0.012224669568240643,
0.029149070382118225,
-0.012462285347282887,
-0.03577236831188202,
0.006128809880465269,
0.010519348084926605,
-0.002252922859042883,
0.05153152346611023,
0.00845164805650711,
-0.013804247602820396,
0.0005732454592362046,
-0.05149030312895775,
0.02083948627114296,
-0.0767589583992958,
0.05800632759928703,
0.015892351046204567,
-0.0255080908536911,
0.04839758574962616,
-0.023751530796289444,
0.011158635839819908,
0.014880819246172905,
-0.024810265749692917,
-0.0004144746926613152,
0.045635536313056946,
0.014750329777598381,
-0.018526624888181686,
0.04753531515598297,
0.07266321778297424,
0.024801500141620636,
0.013241846114397049,
0.047819849103689194,
-0.01669331267476082,
0.0032810841221362352,
0.012179090641438961,
-0.005843583028763533,
0.007527828682214022,
-0.003947360906749964,
-0.0139551917091012,
-0.003556986805051565,
-0.00043473372352309525,
-0.023399127647280693,
0.02138594351708889,
-0.0724715143442154,
0.09785833209753036,
0.039393238723278046,
0.015242061577737331,
0.030589278787374496,
0.01764940656721592,
0.032446544617414474,
-0.006179424934089184,
0.0004890993586741388,
-0.018886936828494072,
-0.0511833056807518,
-0.016964487731456757,
-0.013742261566221714,
0.06604952365159988,
-0.02256094478070736,
0.026028495281934738,
0.018556375056505203,
0.017516931518912315,
0.02372565306723118,
0.006548685021698475,
-0.021802352741360664,
-0.014994688332080841,
0.004287417978048325,
0.03929432854056358,
0.021115679293870926,
0.013361969962716103,
-0.020460011437535286,
0.0019289172487333417,
0.04461269825696945,
0.011936912313103676,
-0.003175188321620226,
0.030760761350393295,
-0.030871454626321793,
0.00798227358609438,
-0.00793125294148922,
0.0057932669296860695,
0.022877102717757225,
-0.03232244774699211,
-0.020679786801338196,
0.0320802703499794,
-0.046495310962200165,
-0.008001499809324741,
0.0012423115549609065,
-0.008880456909537315,
0.021378083154559135,
-0.019150100648403168,
-0.04265033081173897,
0.0062444196082651615,
0.00943688489496708,
-0.012346644885838032,
-0.018686821684241295,
-0.06808631867170334,
-0.011656212620437145,
-0.0005215275450609624,
-0.020582569763064384,
0.05100870877504349,
0.007545530330389738,
0.044772155582904816,
-0.066087506711483,
-0.009861748665571213,
0.015690572559833527,
-0.007841444574296474,
0.01711195893585682,
0.009607592597603798,
-0.056901369243860245,
-0.014712449163198471,
-0.06296406686306,
-0.0018305846024304628,
0.006924373097717762,
0.005071568302810192,
0.016007257625460625,
0.008652225136756897,
-0.0009835516102612019,
-0.06120524927973747,
-0.0508810319006443,
-0.012488355860114098,
-0.00958978570997715,
-0.05734977871179581,
-0.01723191700875759,
0.07904046028852463,
-0.0019309063209220767,
0.008093195036053658,
0.005722712259739637,
0.003433836158365011,
-0.016805453225970268,
-0.004499665927141905,
-0.012770160101354122,
0.023531433194875717,
-0.020555833354592323,
0.030530868098139763,
0.0016650233883410692,
-0.02774273231625557,
0.0036829309538006783,
-0.056930091232061386,
-0.05079362541437149,
0.012091455049812794,
0.021165965124964714,
0.02836737409234047,
0.005214528646320105,
-0.024728069081902504,
0.0536358579993248,
0.030546335503458977,
-0.053469251841306686,
-0.023771336302161217,
0.03775886446237564,
-0.03860296681523323,
-0.028512077406048775,
-0.02300899103283882,
0.04043086618185043,
-0.005772752221673727,
0.04244738444685936,
0.009303418919444084,
-0.004370891023427248,
0.054292213171720505,
-0.004400179255753756,
-0.037232667207717896,
0.019276082515716553,
0.0014719887403771281,
0.01489673089236021,
0.05030560493469238,
-0.03214432671666145,
-0.007523092906922102,
-0.014924908056855202,
-0.015288571827113628,
-0.006977053824812174,
-0.012635169550776482,
-0.047561630606651306,
0.014930827543139458,
0.004839309025555849,
0.002063363790512085,
-0.04788420349359512,
0.07612337917089462,
0.0023593429941684008,
-0.005823904182761908,
-0.012083645910024643,
0.04135886952280998,
0.055603478103876114,
-0.051308512687683105,
0.025267833843827248,
0.036390770226716995,
0.01814868487417698,
-0.03696640953421593,
-0.02983120270073414,
0.018426639959216118,
-0.027719303965568542,
0.00921750906854868,
-0.026507997885346413,
-0.024260884150862694,
0.008964449167251587,
0.05305114760994911,
0.01675204001367092,
-0.02065039426088333,
-0.034507811069488525,
-0.0022911604028195143,
-0.02290031872689724,
-0.0014533280627802014,
-0.025303436443209648,
0.061656367033720016,
0.00276103219948709,
0.03408445417881012,
0.025232572108507156,
0.0032467457931488752,
0.0033968559000641108,
-0.019773276522755623,
-0.06732237339019775,
-0.012685556896030903,
0.020442284643650055,
0.0013777179410681129,
0.016909141093492508,
-0.020961297675967216,
0.01795918680727482,
-0.022407827898859978,
-0.031099557876586914,
-0.016067707911133766,
0.005817451048642397,
-0.04437258839607239,
-0.021009178832173347,
-0.05806749686598778,
-0.02045142464339733,
-0.02327262982726097,
0.024459239095449448,
0.01784130185842514,
-0.016197744756937027,
-0.01609484665095806,
0.024668199941515923,
-0.024119853973388672,
-0.009222370572388172,
-0.023695021867752075,
0.03763505071401596,
0.008981022983789444,
0.03757946565747261,
0.009723861701786518,
0.024266816675662994,
0.019077084958553314,
-0.008366596885025501,
-0.003918623551726341,
0.05782473087310791,
0.010122916661202908,
0.0013081597862765193,
0.004674321506172419,
-0.03184353560209274,
-0.018401050940155983,
0.009889718145132065,
0.06064973771572113,
0.016076423227787018,
-0.00985471997410059,
0.020482037216424942,
0.005653346423059702,
-0.031933195888996124,
0.027830060571432114,
0.044812481850385666,
0.0030892419163137674,
-0.0005862551624886692,
-0.045312389731407166,
-0.014934700913727283,
-0.005064127966761589,
-0.0307149775326252,
0.017013762146234512,
-0.03831521421670914,
-0.007372600957751274,
-0.001307099824771285,
0.04506821185350418,
-0.0005414118058979511,
-0.0033278255723416805,
0.01428825594484806,
-0.0026117293164134026,
-0.01432742364704609,
0.023349229246377945,
-0.03451855853199959,
0.007953032851219177,
0.05904102697968483,
0.029820939525961876,
-0.0042921700514853,
0.007432489190250635,
-0.05949372053146362,
0.0017084922874346375,
-0.004024471156299114,
0.04871826618909836,
0.025605259463191032,
-0.017056813463568687,
-0.053890008479356766,
0.012987233698368073,
-0.005852042231708765,
0.005498782731592655,
0.06464194506406784,
-0.0063108159229159355,
-0.023059461265802383,
-0.014194528572261333,
-0.05441267788410187,
-0.031400199979543686,
0.04124296084046364,
0.023830711841583252,
0.014373723417520523,
-0.013036447577178478,
0.002627777401357889,
0.0033107425551861525,
0.02161240577697754,
0.02188742533326149,
0.06542608886957169,
-0.00901823677122593,
-0.0188261941075325,
0.001240769517607987,
0.03789355605840683,
-0.021480737254023552,
-0.08257367461919785,
0.011594767682254314,
0.01162496767938137,
-0.01348804496228695,
0.03796520084142685,
-0.04521164298057556,
-0.04432452470064163,
0.03371628373861313,
0.023869141936302185,
-0.030440885573625565,
0.02440003491938114,
-0.018757333979010582,
0.0648636594414711,
0.03610968589782715,
-0.0005738333566114306,
0.03228064998984337,
0.04590344801545143,
-0.029062792658805847,
0.0064041223376989365,
-0.01245428342372179,
-0.008193532936275005,
-0.027491707354784012,
0.014064697548747063,
-0.025889083743095398,
0.0210407804697752,
-0.014670904725790024,
0.03000725992023945,
0.010695738717913628,
0.015791937708854675,
-0.0015375831862911582,
-0.03079289384186268,
0.013316120952367783,
0.0070671141147613525,
-0.03516653925180435,
-0.0003845425380859524,
0.008765675127506256,
0.04849177598953247,
0.013383270241320133,
-0.04344725236296654,
0.004580017179250717,
0.00489897420629859,
0.02809252217411995,
0.04105190187692642,
0.004327636677771807,
0.025570467114448547,
-0.03387875482439995,
-0.011266052722930908,
0.01075321901589632,
-0.0740804597735405,
0.026290303096175194,
0.01345516461879015,
0.019307374954223633,
0.022555498406291008,
-0.02228301204741001,
-0.033774252980947495,
0.006436177063733339,
-0.022863874211907387,
0.003943170886486769,
-0.021721381694078445,
-0.006788104306906462,
0.04117625206708908,
0.03222472965717316,
-0.05396771430969238,
-0.03523189574480057,
0.012810262851417065,
0.012741251848638058,
-0.012467365711927414,
0.003760342951864004,
-0.021113203838467598,
-0.015814950689673424,
-0.007614756468683481,
0.0005578781710937619,
0.017230991274118423,
-0.010508987121284008,
-0.04243417829275131,
0.03737226128578186,
0.025321656838059425,
0.057937510311603546,
-0.02401595748960972,
-0.006570702884346247,
0.009802620857954025,
-0.016464944928884506,
-0.01915961317718029,
0.012964746914803982,
0.06780118495225906,
-0.04223232343792915,
-0.04280220717191696,
-0.04495609179139137,
0.008190464228391647,
0.07583467662334442,
-0.04624754562973976,
-0.03919900208711624,
-0.03639165684580803,
0.0038318736478686333,
-0.010355138219892979,
-0.02455567754805088,
0.00488923117518425,
0.005931206047534943,
0.04451790824532509,
0.014200996607542038,
0.0017381428042426705,
-0.026073062792420387,
-0.04163491353392601,
0.020849397405982018,
0.005109745543450117,
-0.024364344775676727,
0.007811888121068478,
0.08193349093198776,
-0.006891647819429636,
0.0350288450717926,
0.0342666357755661,
0.002565388334915042,
0.029857974499464035,
0.0042040697298944,
0.019948994740843773,
0.035148557275533676,
0.0009460772853344679,
-0.04007034748792648,
-0.03398092836141586,
-0.045905701816082,
0.03436588868498802,
0.043025095015764236,
-0.013070828281342983,
0.03896356374025345,
0.014953643083572388,
0.007092075888067484,
-0.02388329803943634,
-0.010761640965938568,
-0.007542248349636793,
0.006713864393532276,
0.011739827692508698,
0.02435383014380932,
-0.023881791159510612,
-0.008664372377097607,
0.017644794657826424,
0.027463136240839958,
-0.007281642407178879,
-0.03329300135374069,
0.039226558059453964,
0.02481088787317276,
0.05145161226391792,
-0.021846165880560875,
-0.0274838637560606,
0.039266832172870636,
-0.004838115070015192,
0.03871367871761322,
0.02255377359688282,
-0.029247842729091644,
0.05374446138739586,
0.038328852504491806,
-0.000903299602214247,
-0.050450410693883896,
-0.004901015665382147,
-0.05081681162118912,
0.008161837235093117,
0.012723647058010101,
-0.004057006910443306,
0.030773969367146492,
-0.0033886730670928955,
0.02953793667256832,
0.02599843218922615,
0.012204395607113838,
-0.04260769858956337,
-0.055019132792949677,
-0.014055835083127022,
-0.008301007561385632,
-0.052818696945905685,
0.04347637668251991,
-0.01450344268232584,
-0.02025601640343666,
0.037911307066679,
-0.03603281080722809,
0.018304385244846344,
0.021092012524604797,
0.013763311319053173,
-0.030778290703892708,
0.06557878851890564,
0.027891861274838448,
0.002355056582018733,
0.036899298429489136,
0.025490518659353256,
0.0820736438035965,
0.10739687085151672,
0.023678546771407127,
-0.03911320120096207,
0.06868084520101547,
0.0006088880472816527,
-0.036461297422647476,
-0.03559526801109314,
0.05347633734345436,
-0.034233711659908295,
-0.011905387975275517,
-0.05019666999578476,
0.04467881843447685,
-0.023049406707286835,
0.008137418888509274,
0.004618982318788767,
-0.06005372107028961,
-0.05353369936347008,
0.03697706386446953,
0.026157770305871964,
0.02135690487921238,
-0.0048752594739198685,
-0.035141471773386,
0.015338128432631493,
-0.0222854632884264,
-0.026446737349033356,
-0.02895493619143963,
-0.03881065547466278,
0.030781539157032967,
0.0036792054306715727,
-0.006260592024773359,
0.023358795791864395,
0.0013126046396791935,
-0.007956454530358315,
-0.027879860252141953,
0.04791819676756859,
0.03156273812055588,
-0.02632782608270645,
0.05133345350623131,
0.0053741177543997765,
-0.0017901634564623237,
-0.022830333560705185,
0.023440955206751823,
0.008250749669969082,
-0.03525511920452118,
-0.03602006658911705,
-0.016300011426210403,
0.08178055286407471,
-0.018210770562291145,
-0.010262437164783478,
-0.007311313413083553,
-0.03094758279621601,
0.006225695367902517,
-0.07473884522914886,
-0.015273886732757092,
-0.025732871145009995,
0.027100583538413048,
-0.01714911125600338,
-0.021261421963572502,
-0.014776721596717834,
0.017283935099840164,
0.03240343928337097,
0.008514730259776115,
0.0027477629482746124,
0.017147408798336983,
-0.012970346957445145,
-0.015611453913152218,
0.05775563046336174,
0.016345839947462082,
0.037215378135442734,
-0.02516481839120388,
-0.03596845269203186,
-0.006835377309471369,
-0.01804426684975624,
0.03443361446261406,
-0.002248206175863743,
0.060152318328619,
0.006263109855353832,
-0.01430506631731987,
-0.03954153507947922,
-0.08106815069913864,
-0.008154104463756084,
-0.021642252802848816,
-0.03858628869056702,
-0.012974031269550323,
-0.03776688501238823,
-0.0014603560557588935,
0.02088160254061222,
-0.026462526991963387,
0.025459565222263336,
-0.013052509166300297,
0.05463492125272751,
0.0071172453463077545,
-0.019716013222932816,
-0.015147528611123562,
-0.012501748278737068,
-0.016361987218260765,
0.009028192609548569,
-0.02549438364803791,
-0.007151686120778322,
0.011150206439197063,
0.021643636748194695,
-0.003978646360337734,
0.0758075937628746,
-0.01232608500868082,
-0.010475793853402138,
-0.007181315217167139,
-0.040949076414108276,
0.043184321373701096,
0.02519378811120987,
0.016239408403635025,
-0.05576791986823082,
-0.017651759088039398,
-0.01339954137802124,
0.006697662174701691,
0.012687139213085175,
0.010879147797822952,
-0.023978376761078835,
-0.017711887136101723,
-0.020729482173919678,
0.022501150146126747,
-0.037457339465618134,
-0.022364730015397072,
-0.008566039614379406,
0.02322765253484249,
0.0025517132598906755,
-0.007069818209856749,
-0.04175833985209465,
0.028957175090909004,
0.001346872071735561,
-0.023071790114045143,
0.03170201927423477,
0.027984619140625,
-0.0075992681086063385,
-0.03967326506972313,
-0.006034032441675663,
0.022801222279667854,
0.04072089493274689,
0.014235416427254677,
-0.03936116397380829,
0.006434890907257795,
-0.012195679359138012,
-0.026139408349990845,
0.034869853407144547,
-0.018270649015903473,
0.017120957374572754,
0.021087314933538437,
-0.02928738482296467,
-0.034116435796022415,
0.04636285454034805,
-0.025319257751107216,
-0.006177151575684547,
-0.027126042172312737,
-0.013403931632637978,
0.010034829378128052,
-0.00572401937097311,
-0.01933876983821392,
-0.001022572279907763,
0.01268321368843317,
0.005631268490105867,
0.025818586349487305,
0.002491168212145567,
0.004273212980479002,
0.004020089749246836,
0.005273628514260054,
0.015197739005088806,
0.0182334091514349,
-0.019976112991571426,
-0.0208693016320467,
0.026180725544691086,
-0.04255164414644241,
0.019220659509301186,
0.00203690561465919,
0.001979952212423086,
-0.08837029337882996,
-0.009721014648675919,
0.012669289484620094,
0.00713623221963644,
0.04621812328696251,
-0.07269628345966339,
0.019801165908575058,
0.03889742121100426,
-0.062215689569711685,
0.04801172763109207,
-0.03318646177649498,
0.0003791092603933066,
-0.05267556011676788,
0.039565056562423706,
-0.04803190380334854,
0.02272605709731579,
0.019010696560144424,
0.049052510410547256,
0.017123278230428696,
0.023683471605181694,
0.004019465763121843,
-0.0038862060755491257,
-0.03050960972905159,
0.03290589898824692,
0.02739783190190792,
-0.051551468670368195,
0.07173407822847366,
-0.006167382001876831,
-0.02512400969862938,
0.011157244443893433,
-0.02253051847219467,
-0.024535739794373512,
-0.01897084154188633,
0.022629860788583755,
0.015767650678753853,
-0.0032821842469274998,
0.018517863005399704,
0.027312424033880234,
0.03535208851099014,
0.018654346466064453,
0.023680035024881363,
-0.00989385787397623,
0.007268048822879791,
-0.003844586666673422,
0.02443218044936657,
0.00207581021822989,
-0.03921850025653839,
0.023722847923636436,
-0.0021385482978075743,
0.008240541443228722,
-0.005357253830879927,
-0.018259547650814056,
-0.02436925284564495,
-0.03220396116375923,
-0.009836336597800255,
-0.034991007298231125,
-0.05455736070871353,
0.012642702087759972,
0.012754582799971104,
-0.024104060605168343,
0.030301274731755257,
-0.0013395429123193026,
-0.05771726369857788,
0.026126757264137268,
-0.03577045351266861,
-0.021552586928009987,
-0.0495535247027874,
-0.007917889393866062,
0.031710345298051834,
-0.00537729449570179,
0.021732725203037262,
-0.004759101662784815,
-0.03384482488036156,
0.035113248974084854,
-0.03750358149409294,
-0.007358626928180456,
-0.03258486092090607,
-0.037109825760126114,
-0.012295016087591648,
-0.08594376593828201,
0.06160568818449974,
0.03666286543011665,
-0.030232153832912445,
-0.014192895963788033,
-0.01788190007209778,
0.0033551508095115423,
0.020546970888972282,
0.04639115557074547,
-0.0031563504599034786,
-0.027337955310940742,
0.009676891379058361,
0.012378995306789875,
0.04470816254615784,
-0.0006361238774843514,
0.009816200472414494,
-0.0030158287845551968,
0.0322904959321022,
-0.016113709658384323,
-0.032767802476882935,
0.00865259487181902,
0.00872078351676464,
-0.000018706383343669586,
-0.008376755751669407,
0.023694144561886787,
-0.0032033801544457674,
-0.04052300006151199,
0.02001412957906723,
-0.024510977789759636,
-0.03427223861217499,
0.07309082895517349,
-0.01979992911219597,
-0.0012555394787341356,
0.029405249282717705,
-0.01673012785613537,
-0.054802145808935165,
0.009339582175016403,
-0.028210025280714035,
0.015221105888485909,
-0.02509017288684845,
-0.008298289962112904,
0.017652226611971855,
-0.068430595099926,
0.0016125766560435295,
0.04516981542110443,
-0.014757147990167141,
-0.003812967799603939,
0.045714370906353,
-0.006555359810590744,
0.031081832945346832,
0.03170720115303993,
0.017072174698114395,
0.036946460604667664,
-0.00245154881849885,
0.000910353846848011,
0.02062678523361683,
0.005292500834912062,
0.010801609605550766,
0.0037259163800626993,
0.011094561778008938,
-0.03742409870028496,
0.009425780735909939,
0.02553793601691723,
0.007004940882325172,
-0.033310092985630035,
0.011038405820727348,
0.04532302916049957,
-0.005663879215717316,
-0.008379927836358547,
0.006737284362316132,
-0.02903558872640133,
0.07877768576145172,
0.002767054131254554,
0.034925367683172226,
-0.02786385454237461,
0.027575550600886345,
0.0075704241171479225,
0.017399156466126442,
0.024304546415805817,
0.044832486659288406,
-0.007492674980312586,
-0.001799197169020772,
-0.05206303671002388,
0.006807990837842226,
-0.0075114392675459385,
-0.06008122116327286,
-0.0017283044289797544,
-0.005148271098732948,
-0.033030916005373,
0.010666551999747753,
-0.029091959819197655,
-0.021973079070448875,
-0.014837169088423252,
0.01773384027183056,
0.01003315206617117,
0.016969965770840645,
-0.009129206649959087,
-0.005214505363255739,
-0.0070749325677752495,
0.06490322202444077,
-0.046300895512104034,
-0.01850862428545952,
-0.0029045369010418653,
-0.014601667411625385,
0.009335729293525219,
-0.015328857116401196
] |
<p>I don't understand well CP-violation, but since it introduces a microscopic irreversible process, couldn't it be somehow exploited to decrease entropy? For instance, if we could somehow use it to bias average particle movement in a particular direction I suppose it could be used to extract work.</p>
| 8,831 |
[
0.020451979711651802,
0.014690299518406391,
-0.02158520743250847,
-0.02591133862733841,
0.045931678265333176,
0.04170989617705345,
-0.00045708281686529517,
-0.002476682187989354,
-0.03287506476044655,
-0.026700176298618317,
0.02976803295314312,
0.034245897084474564,
0.019548973068594933,
0.0029752422124147415,
0.012000582180917263,
0.02076772227883339,
0.015421312302350998,
-0.03566696494817734,
-0.0010645621223375201,
-0.025414204224944115,
-0.0038286156486719847,
0.018419092521071434,
-0.02854583039879799,
-0.006150888744741678,
-0.02589540183544159,
0.03809840977191925,
0.044235341250896454,
0.0093797342851758,
0.0032706945203244686,
0.06797770410776138,
0.003691473277285695,
-0.010470707900822163,
0.0011614453978836536,
0.022309686988592148,
0.023023899644613266,
-0.03355468809604645,
-0.025790123268961906,
-0.05055306479334831,
0.0016760668950155377,
0.028474772348999977,
-0.03750550374388695,
-0.0010001275222748518,
-0.01638765260577202,
0.038093339651823044,
-0.01745361089706421,
0.023158445954322815,
0.01982862874865532,
-0.00042780913645401597,
0.045915115624666214,
-0.05056038126349449,
0.034638479351997375,
-0.009085300378501415,
0.0008254146669059992,
-0.020780442282557487,
0.0066971988417208195,
0.021541399881243706,
0.08447720855474472,
0.07623852789402008,
-0.01717175729572773,
-0.03448920696973801,
-0.0341060534119606,
0.002129478845745325,
0.011596772819757462,
0.0001990928576560691,
-0.02112327516078949,
0.01813778281211853,
0.013411200605332851,
-0.011938119307160378,
0.033527832478284836,
0.024971218779683113,
0.020161181688308716,
-0.01373975072056055,
0.024838890880346298,
0.0033180343452841043,
0.007857938297092915,
-0.02752276137471199,
0.00876733660697937,
-0.0029362787026911974,
-0.01639370433986187,
0.05193175747990608,
0.004785297904163599,
0.0026103267446160316,
0.012298211455345154,
0.07437846064567566,
-0.031263697892427444,
-0.019894767552614212,
0.07582495361566544,
-0.0231795571744442,
0.023562204092741013,
0.06840447336435318,
0.005850974470376968,
-0.02132502943277359,
0.05305281654000282,
0.02999003790318966,
-0.047760892659425735,
0.004900556989014149,
0.009529044851660728,
0.0550934337079525,
0.011199095286428928,
-0.009760193526744843,
0.009503576904535294,
-0.018613845109939575,
0.007291833870112896,
0.06290127336978912,
-0.010096527636051178,
-0.007275219541043043,
-0.006777484435588121,
0.037254828959703445,
0.01635642535984516,
0.013129272498190403,
-0.05530570074915886,
-0.03526696935296059,
-0.00874576810747385,
-0.02752905897796154,
0.03633309528231621,
-0.0222060177475214,
-0.0288541242480278,
-0.026240255683660507,
0.0655360221862793,
0.06249242275953293,
0.02254733256995678,
-0.022410327568650246,
0.00562004279345274,
-0.017678381875157356,
-0.0659232884645462,
0.0006711782771162689,
0.04358832910656929,
-0.01776215434074402,
-0.023953668773174286,
0.0005011842586100101,
-0.01136596966534853,
-0.019454529508948326,
0.01078700739890337,
-0.055055294185876846,
0.03524307906627655,
-0.022957993671298027,
-0.08568064123392105,
-0.06863916665315628,
0.07474787533283234,
0.024826789274811745,
-0.04300876334309578,
-0.07180555909872055,
-0.032925963401794434,
-0.01408618688583374,
0.08013062924146652,
0.0007553833420388401,
0.007418829016387463,
-0.00022492263815365732,
0.015236464329063892,
0.021149689331650734,
-0.014442535117268562,
-0.0006571104167960584,
0.026502395048737526,
-0.019865209236741066,
-0.01149536482989788,
-0.03268987685441971,
-0.006788202561438084,
0.038477543741464615,
-0.013578864745795727,
-0.023120328783988953,
0.01870012655854225,
-0.019811496138572693,
0.024172503501176834,
-0.008751763962209225,
-0.025557126849889755,
-0.03354131057858467,
0.08283108472824097,
0.0030799151863902807,
0.0172599907964468,
0.03037785366177559,
0.034452348947525024,
0.03805874288082123,
0.0114322230219841,
-0.005548367742449045,
0.03631557896733284,
-0.06756515055894852,
-0.022115163505077362,
-0.010648624040186405,
0.009660907089710236,
-0.012446518987417221,
-0.034312449395656586,
-0.0038384406361728907,
-0.004793427884578705,
-0.010115914978086948,
-0.024788733571767807,
0.016271529719233513,
-0.004832838196307421,
0.01423716265708208,
0.011956627480685711,
-0.06034720689058304,
-0.03360891714692116,
-0.0837382897734642,
0.018203170970082283,
0.006632005330175161,
-0.027879400178790092,
0.036939796060323715,
0.014800863340497017,
0.03016563504934311,
-0.05265938490629196,
-0.04526126757264137,
-0.01055198349058628,
0.026385396718978882,
-0.01620354875922203,
0.012864669784903526,
0.002368730027228594,
0.06771285086870193,
0.029837526381015778,
0.03628338873386383,
0.032157644629478455,
0.01578088477253914,
-0.026336809620261192,
-0.0431106872856617,
-0.014405055902898312,
-0.010843773372471333,
0.006396221462637186,
0.007232486270368099,
0.041088756173849106,
-0.005581019911915064,
0.010172455571591854,
0.006272250786423683,
-0.018211090937256813,
0.10927672684192657,
0.031156066805124283,
0.0527329258620739,
-0.04626716673374176,
0.023928962647914886,
0.046463243663311005,
0.002965665189549327,
-0.022783689200878143,
-0.024403633549809456,
-0.03370795398950577,
-0.016227466985583305,
0.030654212459921837,
0.036279868334531784,
-0.05644683912396431,
0.024542346596717834,
0.01607457362115383,
0.03622444346547127,
0.02925327979028225,
-0.0068407864309847355,
-0.01780764013528824,
-0.010628675110638142,
0.03646669164299965,
-0.007749113719910383,
0.020139699801802635,
-0.006438455078750849,
0.026988213881850243,
0.006400236859917641,
0.0031915660947561264,
0.00045117110130377114,
-0.037820860743522644,
0.003421860048547387,
-0.0023676545824855566,
0.01165841706097126,
0.024171538650989532,
-0.04855024069547653,
0.0005730892880819738,
0.0029347799718379974,
0.028621498495340347,
0.024209756404161453,
-0.003574227448552847,
0.023560766130685806,
-0.021558145061135292,
-0.04687608778476715,
-0.013196180574595928,
-0.007934941910207272,
-0.015463004820048809,
-0.001751571660861373,
0.033911123871803284,
0.010304619558155537,
0.011555627919733524,
0.005000907927751541,
0.030745647847652435,
-0.047430504113435745,
-0.01866327039897442,
0.018056664615869522,
0.0011109086917713284,
0.03617492690682411,
-0.042071253061294556,
-0.027311237528920174,
0.01907382346689701,
-0.009415622800588608,
-0.023670334368944168,
0.04971066489815712,
-0.04409217834472656,
0.016891786828637123,
-0.011637656018137932,
-0.05340197682380676,
0.030909325927495956,
-0.006333957426249981,
0.0520298145711422,
0.004736395552754402,
-0.015597830526530743,
-0.04910804703831673,
-0.004518480040132999,
0.00790882483124733,
0.011097411625087261,
-0.06373770534992218,
-0.017805589362978935,
0.0419815294444561,
0.011548356153070927,
-0.03524686023592949,
-0.01388353668153286,
-0.03629085794091225,
-0.054462384432554245,
-0.01016863901168108,
-0.0003735427453648299,
-0.000766019569709897,
-0.029652852565050125,
0.04998532682657242,
0.02585115097463131,
-0.07090809941291809,
-0.013504288159310818,
-0.025599492713809013,
-0.06188433617353439,
0.05216704308986664,
-0.0376494862139225,
-0.0061232042498886585,
-0.024561438709497452,
-0.01378923375159502,
0.06776870787143707,
0.07984609156847,
-0.04564443975687027,
0.006636194419115782,
-0.03203103318810463,
-0.035374775528907776,
-0.01742243394255638,
-0.018523333594202995,
0.02453550510108471,
0.02020755223929882,
0.03091209940612316,
0.03553788736462593,
0.03477475047111511,
-0.021146275103092194,
0.00809174682945013,
-0.0740547627210617,
-0.014159202575683594,
-0.0009631644352339208,
0.02406124398112297,
0.006337137892842293,
0.001376739121042192,
-0.026455087587237358,
0.01246496383100748,
0.03916287422180176,
0.05035925284028053,
0.00008401412924285978,
-0.025654766708612442,
0.05421699211001396,
0.033744458109140396,
0.018865928053855896,
-0.029920559376478195,
0.0451379157602787,
-0.01248311996459961,
0.01063484512269497,
-0.01251179352402687,
-0.004666393157094717,
0.045085057616233826,
0.011911249719560146,
0.014073380269110203,
0.013409142382442951,
0.04197784140706062,
0.007364642806351185,
-0.0014028322184458375,
0.0011685295030474663,
0.019124647602438927,
0.0064441142603755,
0.03508252277970314,
-0.022929275408387184,
0.051034942269325256,
0.03658377379179001,
0.03795020282268524,
0.005636110436171293,
-0.026262430474162102,
0.03597000986337662,
-0.04486420005559921,
0.003984502051025629,
-0.02176601067185402,
0.04569824039936066,
0.010371619835495949,
0.043523456901311874,
0.03891695290803909,
0.0016324989264830947,
0.022723088040947914,
-0.020677054300904274,
-0.08064110577106476,
0.0602571927011013,
-0.050017863512039185,
-0.03377768397331238,
-0.00964471884071827,
0.0015182277420535684,
0.0195529293268919,
-0.04888195917010307,
-0.02333013154566288,
-0.018621835857629776,
0.0004230815975461155,
-0.027179516851902008,
-0.02379661053419113,
-0.030025102198123932,
-0.04106937348842621,
-0.03294317051768303,
0.0010452739661559463,
0.09526363760232925,
-0.04368068650364876,
0.013534128665924072,
0.0031058345921337605,
-0.06493045389652252,
0.0052461810410022736,
0.020596764981746674,
0.033299677073955536,
0.019243493676185608,
0.019910918548703194,
-0.0011487966403365135,
0.018913593143224716,
-0.007409216836094856,
-0.0014754077419638634,
0.008775356225669384,
0.02280515618622303,
-0.007840927690267563,
0.0045809377916157246,
-0.03160789608955383,
-0.057124629616737366,
-0.03029344417154789,
0.02673085778951645,
0.026312779635190964,
-0.017298325896263123,
0.050049856305122375,
0.023612922057509422,
0.008768844418227673,
-0.0821538120508194,
0.015955954790115356,
0.04574276879429817,
0.0028067417442798615,
-0.0369647853076458,
-0.005431021563708782,
-0.048602502793073654,
0.012611458078026772,
-0.028185073286294937,
0.008143621496856213,
-0.009180326014757156,
-0.042658429592847824,
0.005259913392364979,
-0.02508004754781723,
0.0206392090767622,
-0.02976301684975624,
-0.007727258838713169,
0.00604868121445179,
0.041622377932071686,
0.011178497225046158,
0.02672400139272213,
0.05324918404221535,
0.03138172626495361,
-0.00031547562684863806,
0.006217354908585548,
0.0041791172698140144,
-0.057475123554468155,
0.00247927731834352,
0.034878648817539215,
0.03050737828016281,
-0.006767663639038801,
-0.004936682526022196,
-0.049771688878536224,
-0.03738779574632645,
0.06813429296016693,
-0.002079744590446353,
0.049018729478120804,
0.01057142298668623,
-0.02125469036400318,
-0.019846204668283463,
-0.017523817718029022,
-0.01743033528327942,
0.03672366961836815,
-0.0056011793203651905,
-0.01184083241969347,
-0.028576185926795006,
-0.029941340908408165,
-0.014460067264735699,
0.0033780403900891542,
0.012667431496083736,
0.05303419008851051,
-0.006222798954695463,
0.030519114807248116,
0.004296054597944021,
0.038446273654699326,
0.00037022223114036024,
-0.09564980864524841,
-0.022590091452002525,
-0.009681603871285915,
-0.01714341901242733,
0.017082786187529564,
-0.030660005286335945,
-0.027750320732593536,
0.008734560571610928,
0.002252653008326888,
0.010029831901192665,
-0.029260098934173584,
-0.04665958881378174,
0.04413401335477829,
0.024225030094385147,
-0.0013889186084270477,
0.060697756707668304,
0.05709043890237808,
-0.013356813229620457,
-0.01132145430892706,
0.010969032533466816,
0.04048534482717514,
-0.03273998200893402,
0.018993953242897987,
-0.01192496158182621,
0.03478526696562767,
-0.021551579236984253,
0.04948581010103226,
0.035815924406051636,
0.014198342338204384,
0.014138315804302692,
-0.02944774553179741,
-0.038284629583358765,
0.03226049616932869,
0.03265044465661049,
-0.04226551949977875,
0.010523002594709396,
0.016027111560106277,
-0.005384119227528572,
-0.021748658269643784,
0.0058703310787677765,
-0.000548931653611362,
-0.012741204351186752,
0.02670055441558361,
-0.034739524126052856,
0.0005890316097065806,
-0.04019506648182869,
-0.023960763588547707,
0.0053946650587022305,
-0.019178684800863266,
0.05503826588392258,
-0.02773597091436386,
0.02077300287783146,
0.004773213993757963,
-0.049532338976860046,
-0.03133958950638771,
0.03287678584456444,
-0.034153491258621216,
0.012482418678700924,
-0.046148478984832764,
0.07718309760093689,
-0.030359774827957153,
0.03265441581606865,
-0.09378252923488617,
-0.04051778092980385,
-0.008097030222415924,
0.0014698003651574254,
0.006778750568628311,
-0.030065611004829407,
-0.04219929501414299,
-0.016657846048474312,
-0.03163744881749153,
-0.001915741479024291,
0.015341049060225487,
-0.016355225816369057,
0.020421141758561134,
0.025127120316028595,
0.010923204943537712,
0.025154711678624153,
-0.018090806901454926,
-0.03851991519331932,
0.02422199212014675,
0.002378463512286544,
-0.016715647652745247,
0.014369749464094639,
0.03051712177693844,
-0.02764507755637169,
-0.0013223884161561728,
0.020804276689887047,
0.0012017259141430259,
0.017652716487646103,
0.012471199035644531,
-0.027435192838311195,
0.044052254408597946,
0.009729473851621151,
-0.0033015457447618246,
-0.024892788380384445,
-0.009789927862584591,
0.01833103410899639,
-0.011194496415555477,
-0.004960677120834589,
-0.014573994092643261,
-0.01386718824505806,
-0.05070393532514572,
0.034052107483148575,
0.022478144615888596,
-0.019108785316348076,
-0.013673386536538601,
0.03581606224179268,
0.00284765986725688,
-0.053598061203956604,
-0.011211423203349113,
-0.005664919037371874,
0.01151404157280922,
-0.040638986974954605,
0.02070883847773075,
0.003045815508812666,
-0.014807429164648056,
-0.05522102862596512,
-0.04344526305794716,
-0.03733876720070839,
-0.025262579321861267,
0.05948179215192795,
-0.011747035197913647,
0.059624623507261276,
0.01677747629582882,
-0.01127408817410469,
-0.033045973628759384,
-0.018842510879039764,
0.0018278720090165734,
0.02936854586005211,
0.003898896975442767,
0.0002606264897622168,
0.009441477246582508,
0.00019882868218701333,
0.02297404035925865,
0.04629415273666382,
-0.05795101448893547,
0.03895530849695206,
0.018176982179284096,
0.04715881124138832,
0.025502417236566544,
-0.015780789777636528,
-0.04004747048020363,
0.04199010878801346,
-0.06790517270565033,
0.027023697271943092,
0.008213730528950691,
-0.030945289880037308,
0.06202170252799988,
-0.009721376933157444,
-0.017111677676439285,
-0.052362971007823944,
-0.012065228074789047,
-0.051567625254392624,
0.011084474623203278,
0.00999251939356327,
-0.036512814462184906,
0.026944320648908615,
-0.02311156690120697,
0.036848653107881546,
0.029076548293232918,
-0.021286191418766975,
-0.011610626243054867,
-0.08391273766756058,
-0.0106124272570014,
-0.03537532687187195,
-0.038426611572504044,
0.014334979467093945,
0.019677480682730675,
-0.0004487779224291444,
0.03700478747487068,
0.012096389196813107,
0.028193365782499313,
0.034224893897771835,
0.04157993197441101,
-0.014554372057318687,
0.0450764037668705,
-0.027171215042471886,
0.021837688982486725,
-0.02044636942446232,
-0.012442904524505138,
0.11991975456476212,
0.023107247427105904,
-0.02932669222354889,
-0.08496534079313278,
0.03416386619210243,
-0.021206926554441452,
0.01539640687406063,
-0.009991766884922981,
0.04814966768026352,
-0.002413226757198572,
0.005628478713333607,
-0.0007059892523102462,
0.06172632426023483,
0.044964902102947235,
-0.0026114466600120068,
0.054235413670539856,
-0.043330177664756775,
-0.03313760831952095,
0.04311739653348923,
0.014388775452971458,
-0.007131288293749094,
-0.01595965400338173,
-0.03491823747754097,
-0.0009153351420536637,
-0.02806091122329235,
-0.023262955248355865,
-0.009537402540445328,
-0.038193926215171814,
0.02082359790802002,
0.01693381741642952,
-0.018109681084752083,
-0.005354901310056448,
-0.014386630617082119,
-0.008291148580610752,
-0.02690010890364647,
0.0011634964030236006,
0.014717437326908112,
0.007065027020871639,
-0.0023715829011052847,
0.01936403103172779,
0.020449139177799225,
0.01117880828678608,
-0.0036459611728787422,
-0.020409734919667244,
-0.029803665354847908,
0.00599910831078887,
-0.029198862612247467,
0.030939698219299316,
-0.048138055950403214,
0.007625527214258909,
0.024779299274086952,
-0.009895325638353825,
-0.001082154456526041,
0.00412735715508461,
-0.009291406720876694,
-0.03266577422618866,
0.012388802133500576,
0.022306427359580994,
-0.01762843132019043,
-0.014512023888528347,
0.03212939202785492,
-0.02112611196935177,
0.040060341358184814,
-0.01927264966070652,
-0.033464811742305756,
-0.004458989482372999,
0.020718881860375404,
0.02901921421289444,
-0.0012609255500137806,
-0.03893864154815674,
-0.050149403512477875,
0.019900761544704437,
-0.04349297285079956,
-0.015650855377316475,
-0.018437296152114868,
0.00960607174783945,
0.014758739620447159,
-0.009460808709263802,
-0.01321585662662983,
-0.04613804817199707,
-0.021411126479506493,
0.06335727125406265,
-0.028244899585843086,
-0.006944398395717144,
-0.01737852580845356,
0.0009254853939637542,
0.03431568294763565,
0.054753001779317856,
-0.0067175221629440784,
-0.007431300822645426,
0.011075995862483978,
0.024802183732390404,
0.017396897077560425,
0.018147682771086693,
-0.019866619259119034,
-0.0018245115643367171,
-0.050184138119220734,
0.021633608266711235,
0.01804816909134388,
0.05144502595067024,
0.04754960536956787,
-0.03911907598376274,
0.015732090920209885,
0.01377835962921381,
-0.02749938890337944,
-0.004205470439046621,
0.025703538209199905,
-0.020624835044145584,
-0.042477600276470184,
0.025835925713181496,
0.004566105082631111,
-0.016178222373127937,
-0.051134753972291946,
-0.038415323942899704,
0.005204967223107815,
0.021252494305372238,
0.021160786971449852,
-0.0366116501390934,
0.009553258307278156,
-0.06127697229385376,
0.04707208275794983,
-0.04110017046332359,
-0.006052109878510237,
-0.038263775408267975,
-0.026983099058270454,
-0.014834272675216198,
0.009548421949148178,
0.007767704781144857,
0.015949390828609467,
0.04244539886713028,
0.01592615433037281,
0.026422834023833275,
0.038081180304288864,
0.0004279095446690917,
-0.020494947209954262,
0.06046537309885025,
0.028506992384791374,
0.04994982108473778,
-0.04102015867829323,
-0.012081868015229702,
0.06175440549850464,
-0.03951628506183624,
-0.06313285231590271,
0.02506757341325283,
-0.024777159094810486,
0.013421449810266495,
0.02072218805551529,
-0.007975486107170582,
-0.014671634882688522,
0.06306599825620651,
-0.010652745142579079,
0.013317395932972431,
-0.017747217789292336,
-0.01495568547397852,
-0.030518747866153717,
-0.01742078736424446,
-0.002935796743258834,
-0.03362484276294708,
-0.03066425397992134,
0.06356626749038696,
0.00987479742616415,
0.008064466528594494,
-0.007997357286512852,
-0.04645463079214096,
-0.020080197602510452,
0.010243674740195274,
0.025106020271778107,
-0.028646009042859077,
0.013967061415314674,
0.022243093699216843,
-0.04487675428390503,
0.0052252840250730515,
0.04314259812235832,
0.00995436031371355,
-0.08006438612937927,
0.0034365442115813494,
-0.01737118512392044,
-0.012126540765166283,
0.027729105204343796,
-0.042530544102191925,
0.05168113484978676,
0.016805877909064293,
-0.04293075576424599,
0.028159720823168755,
-0.05248159170150757,
-0.039393361657857895,
-0.034063927829265594,
0.01255834847688675,
-0.04602488875389099,
0.05174633115530014,
0.03937255218625069,
0.05336521193385124,
0.01531446073204279,
0.01703895442187786,
-0.0067705693654716015,
-0.03595295920968056,
0.004459626507014036,
-0.01192160788923502,
0.00482891546562314,
0.017436211928725243,
0.03604148328304291,
-0.02302739769220352,
-0.024123379960656166,
-0.006745392922312021,
-0.01957874372601509,
0.008886546827852726,
-0.014536906033754349,
0.04594999924302101,
0.011549089103937149,
0.04591769352555275,
0.010152650065720081,
0.000651968119200319,
0.011724795214831829,
-0.0049063460901379585,
0.002941180020570755,
0.02195761725306511,
0.008541719056665897,
0.028544554486870766,
-0.019128017127513885,
-0.004583079367876053,
-0.01839509792625904,
0.03298790752887726,
-0.04517491161823273,
-0.0148177370429039,
0.007400156930088997,
0.006840451620519161,
0.0220789834856987,
0.0003240189398638904,
0.01375521905720234,
-0.0246039479970932,
-0.0044732182286679745,
-0.007201491855084896,
0.021962037310004234,
-0.041458483785390854,
-0.008337032981216908,
-0.007832517847418785,
-0.03607785701751709,
0.012365290895104408,
0.049270063638687134,
-0.0013398948358371854,
-0.05709400400519371,
0.010541911236941814,
-0.001625502249225974,
0.008695082738995552,
0.02119225263595581,
-0.05091433227062225,
-0.03901470825076103,
0.012256397865712643,
0.03280999884009361,
0.013650822453200817,
-0.0065617989748716354,
-0.022068463265895844,
-0.01288849487900734,
-0.036946382373571396,
0.06420456618070602,
-0.002255856990814209,
0.07011670619249344,
-0.030635900795459747,
-0.011603095568716526,
-0.01302574947476387,
0.016406837850809097,
0.056392524391412735,
-0.030561847612261772,
-0.01543971337378025,
0.05516422912478447,
0.009875723160803318,
0.014005479402840137,
-0.010669984854757786,
0.009195900522172451,
-0.03518626466393471,
0.008152151480317116,
0.003160783089697361,
-0.019407154992222786,
-0.04757284000515938,
0.010815237648785114,
0.016955455765128136,
0.01219906471669674,
-0.018742170184850693,
0.007310633081942797,
-0.026439359411597252,
0.07844556123018265,
-0.004380819387733936,
-0.007112272549420595,
0.040755946189165115,
-0.00607808493077755,
0.059800975024700165,
0.021473167464137077,
-0.015292711555957794,
-0.016255147755146027,
0.04929913207888603,
-0.003295838600024581,
-0.000011278692909399979,
-0.008665611036121845,
0.0026804208755493164,
0.01885877177119255,
-0.025368953123688698,
0.00035866611870005727,
0.03680509328842163,
-0.08454222232103348,
0.017574310302734375,
0.02067089080810547,
0.010416344739496708,
0.0332486592233181,
-0.00055094895651564,
0.04236224293708801,
-0.008342627435922623,
0.05656734108924866,
0.012285145930945873,
0.0840359628200531,
0.02964608371257782,
-0.012865581549704075,
0.017048854380846024,
0.01981084607541561,
-0.015380973927676678,
0.007434840779751539,
0.05064243823289871,
0.012593721970915794,
-0.032243259251117706,
-0.014715388417243958,
0.011064177379012108,
-0.01782260648906231,
0.033549100160598755,
0.015608505345880985,
-0.018516454845666885,
0.0645388588309288,
0.006870533339679241,
0.0210447758436203,
-0.046182721853256226,
-0.02703670784831047,
0.007794118486344814,
-0.03202716261148453,
-0.008849733509123325,
0.03625462204217911,
-0.011877612210810184,
-0.02787594497203827,
-0.003600863041356206,
0.02483414113521576,
0.02208571322262287,
-0.06759676337242126,
0.016470490023493767,
-0.0036865859292447567,
-0.001450601383112371,
-0.029330184683203697,
-0.0034143247175961733,
-0.015013424679636955,
-0.019140413030982018,
-0.004208763595670462,
0.04432729631662369,
0.04814941808581352,
0.02004491351544857,
-0.03795593976974487,
-0.0024801252875477076,
0.049780264496803284,
-0.0348857156932354,
-0.0047356379218399525,
-0.0422566682100296,
0.04062430560588837,
-0.03694142773747444,
0.012063216418027878
] |
<p>Can we say that nanomaterials have higher cohesive energies compared to coarse-grained counterparts?</p>
| 8,832 |
[
-0.03964247927069664,
-0.0015671937726438046,
0.0004117460339330137,
-0.033639516681432724,
0.017094284296035767,
0.024002499878406525,
-0.02793252468109131,
-0.05560433119535446,
0.020454533398151398,
-0.05287162959575653,
0.04482651874423027,
0.025345299392938614,
0.01834154687821865,
0.031582172960042953,
0.01090211234986782,
-0.009225301444530487,
-0.03192849084734917,
-0.025411855429410934,
-0.014101543463766575,
-0.03658248111605644,
-0.019280295819044113,
0.0030308051500469446,
0.013487215153872967,
0.02176292985677719,
0.023544348776340485,
-0.0011605912586674094,
0.01087550725787878,
-0.04931722953915596,
0.042143482714891434,
0.04887719079852104,
0.0058263735845685005,
0.0008658141596242785,
0.030093034729361534,
0.0445198230445385,
0.013869578018784523,
-0.03850037232041359,
-0.016270697116851807,
-0.04519727826118469,
-0.03598498925566673,
0.026081420481204987,
-0.03121461719274521,
-0.030229438096284866,
-0.0059052882716059685,
0.05630721151828766,
-0.023466425016522408,
0.02613668330013752,
-0.018957076594233513,
-0.06313661485910416,
0.0099894218146801,
-0.03744032606482506,
0.050626225769519806,
0.021380385383963585,
0.0559547059237957,
0.04691695794463158,
0.006654697470366955,
-0.04837643727660179,
0.03988742083311081,
0.09459567070007324,
-0.03880899399518967,
-0.03460228815674782,
-0.029186323285102844,
-0.021307120099663734,
0.011885805986821651,
-0.025744324550032616,
-0.020631590858101845,
0.05215197801589966,
-0.023538971319794655,
-0.02724330499768257,
0.0013732383958995342,
-0.03572563827037811,
0.001990142511203885,
0.0162214208394289,
0.05414750799536705,
-0.002817256608977914,
-0.006509491242468357,
0.009665447287261486,
-0.014861220493912697,
-0.016806937754154205,
0.0405120849609375,
0.06677909940481186,
-0.007548839319497347,
0.011811420321464539,
0.038877177983522415,
0.024186214432120323,
0.01104867272078991,
-0.003702061017975211,
0.08239100128412247,
-0.022822175174951553,
-0.006708184722810984,
0.029905064031481743,
0.0018247850239276886,
-0.015356411226093769,
0.06250070035457611,
-0.010769449174404144,
-0.026573101058602333,
-0.015520725399255753,
0.007566534914076328,
0.034887589514255524,
0.002769354498013854,
0.004707000683993101,
-0.014108557254076004,
-0.03684665262699127,
0.0461847148835659,
0.0817997083067894,
0.01961199939250946,
-0.07902009040117264,
-0.035906389355659485,
0.001996036386117339,
-0.015642061829566956,
-0.0078033809550106525,
-0.008402347564697266,
0.00563705014064908,
0.0041312179528176785,
-0.013597923330962658,
0.032799649983644485,
0.016565807163715363,
0.0065230499021708965,
-0.028451262041926384,
0.01794762909412384,
0.05343370884656906,
0.023023750633001328,
-0.027898522093892097,
0.04173877835273743,
-0.029238838702440262,
-0.05023250728845596,
0.011065937578678131,
0.029567992314696312,
-0.02769404463469982,
-0.02876332961022854,
-0.004260975401848555,
-0.004212980158627033,
-0.00213174638338387,
-0.008348004892468452,
-0.019229797646403313,
0.026421554386615753,
-0.006134213414043188,
-0.08662059903144836,
-0.024137312546372414,
0.0578167550265789,
-0.005727160256356001,
-0.0103765819221735,
-0.06730115413665771,
-0.013775547966361046,
-0.017516201362013817,
0.05089578777551651,
0.025966443121433258,
0.03463122248649597,
0.0028605072293430567,
0.012796422466635704,
-0.011953646317124367,
-0.005749267525970936,
-0.009985823184251785,
0.0340031199157238,
-0.023704135790467262,
-0.0019189816666767001,
-0.04980830103158951,
0.0040724570862948895,
0.02762645296752453,
0.03128061443567276,
-0.029606958851218224,
0.01735232211649418,
-0.05160461738705635,
0.018455401062965393,
-0.009862257167696953,
0.017752710729837418,
-0.055539123713970184,
0.04263924062252045,
0.008805413730442524,
0.05058857426047325,
0.05855150893330574,
0.004662510473281145,
-0.015033717267215252,
0.021065080538392067,
0.0158859770745039,
0.0040071201510727406,
-0.013597932644188404,
0.0017107682069763541,
-0.02955637499690056,
0.017128631472587585,
0.02745744213461876,
-0.044629037380218506,
-0.05143172666430473,
0.012588730081915855,
0.010693784803152084,
-0.011112292297184467,
0.0350777767598629,
0.011092491447925568,
-0.06566519290208817,
-0.03221214562654495,
-0.0344451479613781,
-0.007457016501575708,
-0.07137495279312134,
0.06919296085834503,
0.014657236635684967,
-0.004048075992614031,
0.04626516252756119,
-0.019619178026914597,
0.021558711305260658,
-0.007554058451205492,
0.005523599684238434,
-0.034806106239557266,
0.04838624969124794,
0.0012741320533677936,
-0.015465869568288326,
0.0629960298538208,
0.033322472125291824,
0.005400326102972031,
-0.009756282903254032,
0.02323015406727791,
0.012629938311874866,
-0.056026674807071686,
0.038084402680397034,
-0.028941698372364044,
0.039704643189907074,
0.0031188263092190027,
-0.0489751473069191,
0.0337352529168129,
-0.016314079985022545,
-0.035259947180747986,
0.057327382266521454,
-0.000551072764210403,
0.05393579602241516,
-0.009402629919350147,
0.014417610131204128,
-0.010935021564364433,
-0.00785891618579626,
-0.011694896966218948,
0.015814220532774925,
-0.02936222404241562,
0.008995046839118004,
-0.04838088899850845,
0.00044172495836392045,
0.08788760006427765,
0.0998377725481987,
-0.04499661922454834,
-0.006762817036360502,
0.021456824615597725,
0.01664501242339611,
0.006788725033402443,
0.007083300035446882,
-0.043110303580760956,
-0.027472825720906258,
0.05528375133872032,
0.02967415563762188,
0.03431684523820877,
-0.01026027463376522,
-0.009958209469914436,
0.03940214589238167,
0.019324786961078644,
0.005617550108581781,
0.0018827210878953338,
0.009446351788938046,
0.019943274557590485,
-0.010420014150440693,
-0.0023204197641462088,
-0.0431576631963253,
0.012139580212533474,
-0.019565783441066742,
0.016336379572749138,
0.009855279698967934,
0.012127508409321308,
-0.004986937157809734,
-0.017257707193493843,
-0.06312678754329681,
0.03338400647044182,
-0.007559733930975199,
-0.012321671470999718,
-0.0034083693753927946,
0.02589166723191738,
-0.008758002892136574,
-0.022339990362524986,
-0.008015153929591179,
0.0004273227823432535,
0.0014784400118514895,
0.019227614626288414,
0.028270937502384186,
-0.00988160353153944,
0.042628414928913116,
-0.04949400573968887,
-0.01233366597443819,
0.017458979040384293,
-0.02857297845184803,
-0.004473984707146883,
0.01371831726282835,
-0.027771709486842155,
0.024158375337719917,
-0.01719287596642971,
-0.014909997582435608,
0.03492199629545212,
-0.0041313557885587215,
0.018011435866355896,
0.0007542032399214804,
0.0025579670909792185,
-0.04753157123923302,
0.017165688797831535,
0.013266532681882381,
-0.005377596244215965,
-0.04436253756284714,
-0.001501783961430192,
0.0032563386484980583,
-0.029618602246046066,
-0.03130623325705528,
0.007589397951960564,
0.029030151665210724,
-0.04102981463074684,
-0.013169746845960617,
-0.029004260897636414,
0.007635027635842562,
0.0020578098483383656,
0.05371842160820961,
0.04718279838562012,
-0.04116065800189972,
-0.014783008955419064,
-0.06626953929662704,
-0.022811077535152435,
0.014890552498400211,
-0.050194140523672104,
0.03645077720284462,
-0.01901707611978054,
-0.01012440212070942,
0.045577093958854675,
-0.0123515073210001,
-0.028178008273243904,
0.017350109294056892,
-0.0506729818880558,
-0.013631101697683334,
0.010524744167923927,
-0.0006898420979268849,
0.03244786709547043,
0.028103411197662354,
-0.01607460156083107,
0.018352916464209557,
0.03448501229286194,
0.02145490236580372,
0.0013347147032618523,
-0.01984480209648609,
0.02951616421341896,
0.010240405797958374,
-0.012909208424389362,
-0.003992232959717512,
-0.002064861822873354,
-0.035128142684698105,
0.028892172500491142,
-0.005948780570179224,
0.052109554409980774,
0.023352066054940224,
-0.07214246690273285,
0.05989987775683403,
-0.002148538362234831,
0.015609265305101871,
-0.04518492519855499,
0.04426945745944977,
0.014940285123884678,
-0.006661718711256981,
0.004021485336124897,
0.043823134154081345,
0.04314751178026199,
0.0273626446723938,
0.009696153923869133,
0.028221378102898598,
0.03510502725839615,
0.01150463242083788,
-0.0052030449733138084,
0.0017095967195928097,
-0.011151799000799656,
-0.0029177481774240732,
0.005585711915045977,
0.001068111159838736,
0.015987027436494827,
0.004769344814121723,
0.03475025296211243,
0.010560497641563416,
-0.031996723264455795,
0.023309316486120224,
-0.04270421341061592,
-0.021283304318785667,
-0.011137587949633598,
0.042197175323963165,
0.0021434666123241186,
0.05546478554606438,
0.03025268390774727,
0.0029351816046983004,
-0.01600530929863453,
-0.012753603048622608,
-0.057607825845479965,
0.015431324020028114,
-0.037326302379369736,
-0.012743140570819378,
-0.0012623926158994436,
-0.019659899175167084,
-0.03719025105237961,
-0.01906263269484043,
-0.01723857969045639,
-0.006299554370343685,
-0.005861359648406506,
-0.04091101139783859,
0.01216962095350027,
-0.04294382035732269,
-0.015963148325681686,
0.023763466626405716,
0.009974634274840355,
0.010948620736598969,
-0.036967623978853226,
-0.0016654673963785172,
0.03631329536437988,
-0.02025778777897358,
0.020204372704029083,
0.007617788389325142,
0.0247453935444355,
-0.017497504130005836,
0.03059646300971508,
-0.011570644564926624,
0.000327105401083827,
0.030929677188396454,
0.008110802620649338,
0.01143253967165947,
0.014565223827958107,
0.005095832049846649,
-0.019216567277908325,
-0.029899809509515762,
-0.050929829478263855,
-0.005356038920581341,
0.02061890810728073,
0.041657403111457825,
-0.023706065490841866,
0.015281385742127895,
0.014501781202852726,
0.01936747133731842,
-0.01831028237938881,
0.04899616166949272,
0.03158845379948616,
0.01405429095029831,
-0.06116694584488869,
-0.08676841109991074,
-0.026715904474258423,
-0.018615499138832092,
-0.004902227781713009,
0.04700940102338791,
-0.01326365303248167,
-0.031026288866996765,
0.030045194551348686,
0.0216449536383152,
-0.006877264007925987,
-0.040834806859493256,
-0.026827052235603333,
-0.032371725887060165,
0.038314174860715866,
-0.002843513386324048,
-0.0031782572623342276,
-0.005463534500449896,
0.021956928074359894,
0.02895190380513668,
0.05316343531012535,
-0.014094480313360691,
-0.06709592789411545,
0.039572931826114655,
0.028248056769371033,
0.02955617569386959,
-0.0014722015475854278,
0.01172715611755848,
-0.0245277788490057,
-0.03251522034406662,
0.06567578762769699,
-0.0008788682171143591,
-0.005074683576822281,
-0.020663883537054062,
0.013132452964782715,
-0.0656164288520813,
-0.0010425228392705321,
0.0003462325257714838,
0.012430918402969837,
0.051947589963674545,
0.02213183604180813,
-0.05087452754378319,
-0.018338609486818314,
-0.021856287494301796,
0.0395461767911911,
0.03221525624394417,
0.045482464134693146,
0.024896161630749702,
0.014702102169394493,
-0.03491353988647461,
-0.006467689760029316,
-0.0408540703356266,
-0.09744349122047424,
0.014166812412440777,
0.012830154970288277,
-0.011633072979748249,
0.006005183793604374,
-0.030379677191376686,
-0.029784753918647766,
0.04975532367825508,
-0.025652727112174034,
0.0030559974256902933,
0.0008085704757831991,
-0.04235401004552841,
0.08199327439069748,
0.021791305392980576,
-0.0016077718464657664,
0.02009763941168785,
0.03251247853040695,
-0.03983374312520027,
0.008404701948165894,
-0.04434342309832573,
0.025083331391215324,
-0.041965022683143616,
-0.0036721189972013235,
-0.03875859081745148,
-0.008471708744764328,
0.013879171572625637,
-0.0005745865637436509,
-0.004264947958290577,
0.0048875100910663605,
-0.004912729375064373,
-0.038345616310834885,
-0.019506286829710007,
-0.0043840566650033,
0.013797475025057793,
-0.02447269670665264,
-0.016950104385614395,
0.016598030924797058,
0.0040832096710801125,
-0.00360865774564445,
-0.0025883279740810394,
-0.0001841357589000836,
-0.019741322845220566,
0.028183167800307274,
0.006136602256447077,
-0.018390456214547157,
-0.06950360536575317,
-0.028862301260232925,
0.005122855771332979,
-0.03658421337604523,
0.034849539399147034,
-0.003963276278227568,
0.0175362229347229,
-0.010614288970828056,
-0.052018504589796066,
-0.017145374789834023,
0.022306310012936592,
0.0020517054945230484,
0.04167807474732399,
-0.024358384311199188,
0.024120209738612175,
0.020419476553797722,
-0.008877523243427277,
-0.07329089939594269,
-0.027157247066497803,
-0.021503888070583344,
0.026059681549668312,
-0.005367058329284191,
-0.010395136661827564,
0.036131683737039566,
-0.04343352094292641,
-0.004569910001009703,
-0.0030116343405097723,
0.03964010626077652,
-0.03746555373072624,
0.007157646585255861,
0.0034047735389322042,
-0.008057883940637112,
0.05915796756744385,
-0.015102479606866837,
-0.01406970527023077,
0.010911043733358383,
-0.023372456431388855,
-0.008464486338198185,
-0.02309378981590271,
0.03217038884758949,
-0.03200716897845268,
0.02656232938170433,
0.021343955770134926,
-0.03662745654582977,
0.06515935808420181,
-0.01078441459685564,
0.010631535202264786,
0.05740896612405777,
-0.006326910573989153,
-0.029486725106835365,
-0.027218999341130257,
0.034593481570482254,
0.047764431685209274,
0.03885866329073906,
0.01121221948415041,
0.006512498017400503,
-0.027736539021134377,
-0.04171327129006386,
0.0661625936627388,
0.01952032931149006,
-0.02664201147854328,
0.021567098796367645,
0.09344719350337982,
-0.010850836522877216,
0.004219561815261841,
0.032271742820739746,
-0.03310846537351608,
0.027246087789535522,
-0.033155348151922226,
0.02994026243686676,
-0.003471303964033723,
0.0026567287277430296,
-0.04644561931490898,
-0.03937150537967682,
-0.010115932673215866,
-0.0026151551865041256,
0.015207545831799507,
-0.051979973912239075,
0.015316528268158436,
-0.015715017914772034,
-0.030523652210831642,
0.006571159698069096,
-0.05066262185573578,
0.030243076384067535,
0.014289789833128452,
-0.030027806758880615,
0.043994106352329254,
-0.017239734530448914,
-0.02968456596136093,
0.03331771865487099,
0.03688948228955269,
-0.021681370213627815,
0.03080027550458908,
-0.006106973625719547,
0.00948537327349186,
-0.002332917647436261,
-0.026130393147468567,
-0.05730152502655983,
0.06850845366716385,
-0.08107738941907883,
0.026784660294651985,
-0.04315834864974022,
-0.02422081120312214,
0.018566027283668518,
-0.010116029530763626,
0.006568446289747953,
-0.003935334272682667,
0.002649937756359577,
-0.005808549001812935,
0.0693642720580101,
-0.010100198909640312,
0.00006939778540981933,
-0.02798718586564064,
0.01775890402495861,
0.008022921159863472,
0.041010670363903046,
-0.015385031700134277,
-0.007391244173049927,
-0.08485298603773117,
-0.009360224939882755,
-0.003824773011729121,
-0.037187106907367706,
0.014985952526330948,
0.01899646408855915,
-0.04728499799966812,
0.05915629863739014,
-0.014173404313623905,
0.05575719103217125,
-0.00953210424631834,
-0.004018210805952549,
-0.00006035690603312105,
0.06157693266868591,
-0.00330578931607306,
0.025521760806441307,
-0.001231763162650168,
0.019081128761172295,
0.14382535219192505,
0.07877862453460693,
0.009443827904760838,
-0.03871208801865578,
0.03938329592347145,
-0.009270388633012772,
0.014683125540614128,
-0.005029086489230394,
-0.022332530468702316,
0.01950766332447529,
0.005513314623385668,
-0.011458122171461582,
0.07828137278556824,
-0.02823539450764656,
-0.015919432044029236,
0.03125099837779999,
-0.03704647347331047,
-0.02976684272289276,
-0.024099940434098244,
0.006604675203561783,
0.007174205966293812,
-0.01990412175655365,
-0.044991109520196915,
-0.022395184263586998,
-0.017394140362739563,
-0.004221502225846052,
-0.01411142386496067,
-0.021693138405680656,
0.053525373339653015,
0.028908949345350266,
-0.03053024224936962,
-0.025455117225646973,
0.009954684413969517,
0.0154203986749053,
-0.029614301398396492,
-0.02413102798163891,
0.012215818278491497,
0.027847515419125557,
0.036356180906295776,
-0.018619608134031296,
0.014555126428604126,
0.01641177572309971,
-0.009122748859226704,
0.028074443340301514,
-0.040512312203645706,
-0.008669146336615086,
-0.04674167186021805,
0.01521300058811903,
-0.030585048720240593,
0.029123350977897644,
0.0052268123254179955,
-0.03524896875023842,
0.005921906791627407,
0.0017949658213183284,
-0.017444999888539314,
-0.006952076684683561,
0.020751820877194405,
0.004411219619214535,
-0.013519229367375374,
-0.01496435422450304,
0.0038578917738050222,
-0.01462700217962265,
0.011353620328009129,
0.014537094160914421,
-0.015064427629113197,
0.0255177803337574,
0.03346027433872223,
0.02248149923980236,
-0.03052307851612568,
-0.0006236472399905324,
-0.02836138941347599,
-0.028485862538218498,
-0.04649713635444641,
-0.054977864027023315,
-0.019470078870654106,
0.03086855821311474,
0.0546504445374012,
0.013965203426778316,
0.026168879121541977,
-0.024026921018958092,
-0.05097286403179169,
0.060448057949543,
-0.021837053820490837,
-0.011107445694506168,
-0.02332318015396595,
-0.02884950488805771,
0.03715425729751587,
0.05836739018559456,
-0.008566439151763916,
0.053509023040533066,
-0.05763598904013634,
-0.003928243648260832,
0.00706750201061368,
-0.007643560413271189,
-0.02154145948588848,
0.00019706255989149213,
-0.01274740882217884,
0.022317737340927124,
-0.00882293377071619,
0.00278122047893703,
-0.01793709769845009,
-0.0051394132897257805,
0.022543197497725487,
0.044414274394512177,
-0.015729455277323723,
0.040032558143138885,
0.019325993955135345,
-0.0044955662451684475,
-0.04132293164730072,
0.038465797901153564,
0.015825673937797546,
-0.012066511437296867,
-0.03204943984746933,
-0.04801760986447334,
-0.004631795920431614,
0.036972228437662125,
0.04212227836251259,
-0.029412543401122093,
0.0026978387031704187,
-0.026044584810733795,
0.022991694509983063,
-0.05457483232021332,
-0.02304539829492569,
-0.03365268185734749,
-0.035293277353048325,
0.002350695664063096,
-0.053519248962402344,
-0.007127238437533379,
0.038694120943546295,
-0.007363971322774887,
0.013192509301006794,
0.03664625436067581,
0.011218271218240261,
-0.008625755086541176,
-0.00744672492146492,
0.020805252715945244,
-0.0024394423235207796,
0.06742457300424576,
-0.036160677671432495,
-0.03941863775253296,
0.03071785345673561,
-0.01535142119973898,
-0.09424499422311783,
-0.013229127041995525,
-0.04997105896472931,
-0.005391441285610199,
0.04195338860154152,
0.008417297154664993,
-0.009396332316100597,
0.05915224552154541,
-0.04334312304854393,
-0.028796443715691566,
0.03868882358074188,
-0.008393327705562115,
0.00005178690480533987,
-0.014618455432355404,
-0.013540685176849365,
-0.026950722560286522,
-0.028864754363894463,
0.03941116854548454,
0.009069053456187248,
0.054424453526735306,
-0.00924313347786665,
0.03839472308754921,
-0.024323048070073128,
-0.0027814446948468685,
0.03024439886212349,
0.046355951577425,
-0.0021929393988102674,
0.05504017323255539,
-0.043236494064331055,
0.025571191683411598,
0.03227481245994568,
-0.0016459982143715024,
-0.07009071856737137,
0.005931890103965998,
-0.023179592564702034,
0.01527295634150505,
0.011237368918955326,
-0.05626314505934715,
0.030443886294960976,
-0.010218371637165546,
-0.07530047744512558,
0.055773358792066574,
-0.06476151198148727,
-0.012944701127707958,
-0.04243217408657074,
-0.008024484850466251,
-0.03088654950261116,
0.06976844370365143,
0.0045116799883544445,
0.07548568397760391,
0.031606897711753845,
0.05519397556781769,
-0.015413950197398663,
0.031850095838308334,
-0.00588176678866148,
0.014275037683546543,
-0.029124675318598747,
0.003411263460293412,
0.0627295970916748,
-0.001236084382981062,
-0.05121795833110809,
-0.0056501771323382854,
-0.0031585844699293375,
-0.00788931455463171,
0.02172696590423584,
0.015264424495398998,
-0.00897056795656681,
0.007773850113153458,
0.0017443745164200664,
-0.010839364491403103,
-0.015416990034282207,
0.018267914652824402,
-0.008842634968459606,
0.02071111463010311,
0.004848614800721407,
0.015117745846509933,
0.026363208889961243,
-0.021600572392344475,
-0.0017046694410964847,
0.04488871991634369,
-0.0021760447416454554,
0.006748946383595467,
-0.01784552074968815,
0.0037028691731393337,
0.05508597567677498,
-0.008157092146575451,
-0.005809462629258633,
-0.028287582099437714,
-0.01797325722873211,
0.04283309355378151,
0.003232950810343027,
-0.011049214750528336,
0.021104855462908745,
0.037985801696777344,
-0.01149282231926918,
-0.025445187464356422,
0.04107356816530228,
0.02496509812772274,
-0.03610264137387276,
0.008108080364763737,
0.014101735316216946,
0.0014126444002613425,
-0.020495178177952766,
-0.02436133846640587,
-0.009947137907147408,
0.061069875955581665,
0.006209300830960274,
0.03157992660999298,
0.031875450164079666,
-0.028529422357678413,
-0.025038791820406914,
-0.05987042188644409,
0.006706558633595705,
-0.0418274886906147,
0.0019140462391078472,
-0.007606140337884426,
-0.01621440052986145,
0.03659282252192497,
0.007587326690554619,
0.05038191005587578,
0.011022954247891903,
0.00034727135789580643,
-0.004046368878334761,
-0.021022925153374672,
0.03261556476354599,
-0.00736790569499135,
0.012170976959168911,
-0.03206640109419823,
0.022589724510908127,
0.006306400988250971,
-0.004768577869981527,
-0.00846196711063385,
0.02625877968966961,
0.062310997396707535,
-0.015046567656099796,
-0.012829135172069073,
-0.021178392693400383,
-0.015628134831786156,
0.0623055063188076,
-0.008623996749520302,
0.0012844480806961656,
0.09302090108394623,
-0.04022683575749397,
0.036747947335243225,
-0.0018032443476840854,
-0.006421665661036968,
-0.046693023294210434,
0.012733500450849533,
-0.03934650495648384,
-0.015133080072700977,
0.006265808828175068,
0.02625490352511406,
0.022814225405454636,
-0.028761141002178192,
-0.0007313882815651596,
0.009755147621035576,
-0.025327157229185104,
0.0029185423627495766,
0.013565153814852238,
0.028322409838438034,
0.04501286894083023,
-0.011287268251180649,
0.02528585121035576,
0.04289985075592995,
0.006460940930992365,
-0.003919796086847782,
0.04792406037449837,
0.036836177110672,
0.0062913550063967705,
0.01894908770918846,
0.011350812390446663,
-0.04918225482106209,
-0.015351933427155018,
0.00008856062049744651,
-0.0033613801933825016,
-0.03667747601866722,
-0.0454159639775753,
0.018328851088881493,
-0.02515598200261593,
0.0338321290910244,
0.018276775255799294,
-0.000725423451513052,
0.07753737270832062,
-0.043760377913713455,
-0.021045047789812088,
-0.0367562435567379,
-0.015207987278699875,
0.007214483805000782,
0.031120410189032555,
0.02306625060737133,
0.03452024608850479,
0.027220310643315315,
-0.013190961442887783,
-0.020148027688264847,
0.0009177293395623565,
0.026577532291412354,
-0.055206529796123505,
0.025286579504609108,
-0.02115309052169323,
0.033376533538103104,
-0.02815459854900837,
-0.002419453114271164,
-0.054189495742321014,
-0.022442150861024857,
-0.0013210033066570759,
0.033514752984046936,
0.038407281041145325,
0.01009907852858305,
0.006298749707639217,
-0.017287980765104294,
0.051455769687891006,
-0.05221176892518997,
0.011304354295134544,
-0.017125608399510384,
0.025940271094441414,
-0.03018062934279442,
0.010090438649058342
] |
<p>I am having the following problem understanding the <a href="http://en.wikipedia.org/wiki/Born_approximation" rel="nofollow">Born approximation</a> in the case of the <a href="http://en.wikipedia.org/wiki/Lippmann%E2%80%93Schwinger_equation" rel="nofollow">Lippmann-Schwinger equation</a>. This exercise is for something which is entitled "computational physics lab course" and the following equations are
all taken from the lab manual.</p>
<p>Following the derivation in Chapter 3 of Weinbergs <em>The Quantum Theory of Fields</em> in a similar fashion one obtains the Lippmann-Schwinger-Equation:
$$ |\Psi_\mathbf{k}^\pm\rangle = |\mathbf{k}\rangle + \lim_{\epsilon\rightarrow 0^+} [E_k\pm i\epsilon - H_0 ]^{-1} V |\Psi_\mathbf{k}^+\rangle.$$</p>
<p>From this one can obtain the tranfer matrix $T$ by defining $$T|\mathbf{k}\rangle = V | \Psi_\mathbf{k}^+\rangle.$$
Then following holds:
$$T|\mathbf{k}\rangle> = V|\mathbf{k}\rangle + V \lim_{\epsilon\rightarrow 0^+} [E+i\epsilon-H_0]^{-1} T|\mathbf{k}\rangle.$$
From which in turn an expression analogous to eq 3.5.1 in Weinberg can be obtained:</p>
<p>$$\langle\mathbf{l}| T |\mathbf{k}\rangle = T(l,k)=\hat{V}(\mathbf{l}-\mathbf{k}) + \lim_{\epsilon\rightarrow 0^+} \frac{1}{(2\pi)^3}\int_{\mathbb{R}^3} \hat{V}(\mathbf{l}
-\mathbf{p})\langle \mathbf{p}|[E+i\epsilon-H_0]^{-1} T|\mathbf{k}\rangle d^3p,$$</p>
<p>where $\hat{V}$ is the Fourier transformation of the potential.
After a partial-wave decomposition one obtains:</p>
<p>$$\hat{V}(\mathbf{k}'-\mathbf{k}) = 4\pi\sum_{l=0}^{\infty} (2l+1)\hat{V}_l(k',k) P_l(\cos\theta).$$</p>
<p>After further algebra we end up with the following expression for $T$:</p>
<p>$$T(k',k) = \hat{V}(k',k)+\frac{2}{\pi} \int_0^{\infty} \frac{2m/\hbar^2}{k^2-q^2}\left[ q^2\hat{V}(k',q)T(q,k) - k^2 \hat{V}(k',k)T(k,k)\right]dq - 2i\frac{mk}{\hbar^2}
\hat{V}(k',k)T(k,k).$$</p>
<p>Now a real kernel is defined by:</p>
<p>$$K(k',k)=\hat{V}(k',k)+\frac{2}{\pi} \int_0^{\infty} \frac{2m/\hbar^2}{k^2-q^2}\left[ q^2\hat{V}(k',q)T(q,k) - k^2 \hat{V}(k',k)T(k,k)\right]dq.$$</p>
<p>My problem lies with the following:</p>
<p>Given a potential </p>
<p>$$V(r) = V_0 \frac{1}{\mu r} \cdot (e^{-2\mu r} - e^{-\mu r})$$ </p>
<p>(where actually $r=||\mathbf{r}||_2$) and using the following expression:</p>
<p>$$\hat{V}(k',k) = \sum_i \frac{V_i}{\mu_i}\frac{1}{k'k}Q_l\left( \frac{k^2+k'^2+\mu_i^2}{2kk'}\right),$$</p>
<p>where the sum is in this case over just two components. I have to solve the equation for $K$ for $l=0,1$ in Born approximation.</p>
<p>Unfortunately the only expressions for a Born approximation I have are for a state $\Psi_\mathbf{k}^\pm(r)$(Wikipedia says essentially the same)
and not for a matrix equation.</p>
<p>Now it took me some time and the equation 3.5.3 from Weinberg </p>
<p>$$T_{\beta\alpha}^+ = V_{\beta\alpha}+\int\frac{V_{\beta\gamma}V_{\gamma\alpha} }{E_\alpha - E_\gamma +i\epsilon}+\dots$$ </p>
<p>to get to the following conclusion:</p>
<p><em>The Born approximation in physics is the same as one step of a <a href="http://www.google.com/search?as_q=Picard+iteration" rel="nofollow">Picard iteration</a> in mathematics.</em></p>
<p>Where the latter one is an iterative solution of a Cauchy problem
$y(0)=y_0, \dot{y}= f(t,y)$ in the form:</p>
<p>$$y^{(0)}(t) = y_0, y^{(n+1)}(t) = y_0 + \int_0^t f(t', y^{(n)}(t'))dt'.$$</p>
<p>So in this case I would obtain for $K$:</p>
<p>$$K(k',k)=\hat{V}(k',k)+\frac{2}{\pi} \int_0^{\infty} \frac{2m/\hbar^2}{k^2-q^2}\left[ q^2\hat{V}(k',q)\hat{V}(q,k) - k^2 \hat{V}(k',k)\hat{V}(k,k)\right]dq.$$</p>
<p><strong>Here my question then:</strong></p>
<p>Is this reasoning right or am I missing something fundamental?</p>
| 8,833 |
[
0.0010797323193401098,
-0.054594069719314575,
0.040173593908548355,
-0.04363498464226723,
0.04150252416729927,
-0.014665596187114716,
-0.03484434261918068,
0.021672194823622704,
-0.005441189743578434,
-0.012093264609575272,
0.0006332324701361358,
0.02184532769024372,
0.03330479562282562,
0.012097828090190887,
0.004309491720050573,
0.03493337705731392,
-0.019071035087108612,
0.011445142328739166,
-0.03761935234069824,
-0.03410559892654419,
0.02580234780907631,
0.05274295061826706,
-0.007649872452020645,
0.01105722039937973,
-0.03090892732143402,
0.00847629550844431,
0.007424446288496256,
-0.019984031096100807,
-0.021941829472780228,
0.04344791918992996,
0.003070470178499818,
-0.023405296728014946,
0.03189117833971977,
0.004108360968530178,
-0.007199427578598261,
0.03254023194313049,
-0.006698827724903822,
0.015337786637246609,
0.02522827684879303,
0.0018115572165697813,
-0.05140044912695885,
-0.027691137045621872,
-0.010350952856242657,
0.03004547208547592,
0.02383648045361042,
-0.016722653061151505,
-0.007077462039887905,
-0.01915779896080494,
0.06035034731030464,
-0.04465857148170471,
0.066241554915905,
0.004388343542814255,
0.03544200584292412,
-0.003921641036868095,
-0.028869520872831345,
0.006778500508517027,
0.07020904868841171,
0.04912948235869408,
-0.0027872032951563597,
-0.0742063820362091,
0.006122298073023558,
-0.04092384874820709,
-0.01956024207174778,
0.01227314118295908,
0.0015421535354107618,
0.007728868164122105,
0.009392207488417625,
0.022325100377202034,
-0.0005918479873798788,
-0.03832949697971344,
0.022016189992427826,
-0.019592946395277977,
0.046105898916721344,
-0.02408171072602272,
0.034194640815258026,
0.011055108159780502,
-0.012117705307900906,
0.002412007423117757,
0.0214479248970747,
0.03788581117987633,
-0.0030324249528348446,
0.023126395419239998,
0.0038874070160090923,
-0.0027696595061570406,
0.02254519611597061,
-0.00580328144133091,
0.05897204205393791,
-0.010293045081198215,
-0.009361007250845432,
0.024497656151652336,
-0.0156688429415226,
0.025197459384799004,
0.0015142789343371987,
-0.039236586540937424,
0.00034895807038992643,
0.06682436168193817,
-0.0007347752689383924,
0.03616488724946976,
0.008564204908907413,
-0.029137099161744118,
0.015527859330177307,
-0.05515188351273537,
-0.03551418334245682,
0.06423987448215485,
-0.0029239750001579523,
-0.02921140380203724,
-0.008119168691337109,
0.0020236517302691936,
-0.0329618975520134,
-0.04675300419330597,
-0.04809261113405228,
0.0159534253180027,
0.0038561206310987473,
0.029606448486447334,
-0.05202881619334221,
-0.06372222304344177,
0.012217109091579914,
0.017543623223900795,
0.05673244595527649,
0.08121617138385773,
0.045544810593128204,
-0.03276066482067108,
0.014749671332538128,
-0.03977716341614723,
-0.03233218938112259,
0.017493797466158867,
0.04515989124774933,
-0.012282890267670155,
-0.05698595941066742,
0.03179119527339935,
0.029256608337163925,
0.01004517450928688,
0.03346944972872734,
0.005311769433319569,
0.04580674692988396,
-0.031026801094412804,
-0.10768009722232819,
-0.05513765290379524,
0.032910823822021484,
-0.030005086213350296,
-0.01585545763373375,
-0.07672727853059769,
0.0000058042610362463165,
0.04164820909500122,
0.0910487174987793,
0.0453137569129467,
0.026090746745467186,
-0.0010706433095037937,
0.007345050107687712,
0.02227226085960865,
-0.02057063765823841,
-0.019515477120876312,
0.0025438566226512194,
-0.01832081936299801,
-0.005874688271433115,
-0.03670131787657738,
-0.00461422698572278,
0.030759086832404137,
-0.007099499460309744,
0.013839147053658962,
0.08134531229734421,
0.009922551922500134,
-0.02678929828107357,
0.032231494784355164,
-0.03049336187541485,
-0.05504922196269035,
0.029022296890616417,
0.02440388686954975,
0.01039254292845726,
0.042534470558166504,
-0.01909618452191353,
0.010927869938313961,
-0.009961258620023727,
0.018531620502471924,
0.03204125165939331,
-0.02282182313501835,
-0.009670908562839031,
-0.025996815413236618,
0.010174136608839035,
0.007310925051569939,
-0.020207034423947334,
-0.00008821176743367687,
0.005795324221253395,
0.056003671139478683,
0.03130964934825897,
0.019439788535237312,
0.004743197001516819,
0.01824425347149372,
0.018966004252433777,
-0.019981209188699722,
0.0314757339656353,
-0.017010996118187904,
-0.03417276218533516,
-0.01424829475581646,
0.0028681494295597076,
0.06334417313337326,
0.0019887203816324472,
-0.009509761817753315,
-0.0028248843736946583,
-0.020910318940877914,
-0.017848465591669083,
0.025631222873926163,
0.03086208738386631,
0.008682239800691605,
0.03593151271343231,
0.03834080323576927,
0.015676911920309067,
0.019035061821341515,
0.011573228053748608,
-0.03920112922787666,
0.0030388657469302416,
0.015730373561382294,
-0.003441804787144065,
0.02443786896765232,
0.043015263974666595,
0.007305109407752752,
0.00040716829244047403,
-0.007014584261924028,
0.010678174905478954,
0.008769680745899677,
-0.015303315594792366,
0.0341513454914093,
0.05677442625164986,
0.01635620929300785,
0.0014546671882271767,
0.034607820212841034,
-0.03814195469021797,
0.05743488669395447,
-0.014925857074558735,
-0.02644600160419941,
0.004426116123795509,
0.00918375700712204,
0.044861339032649994,
0.012706148438155651,
-0.037177808582782745,
0.008825330063700676,
0.004168108571320772,
0.007364748977124691,
0.036479804664850235,
0.03505020588636398,
-0.04320512339472771,
-0.012252223677933216,
0.0012573098065331578,
-0.009729075245559216,
-0.018851377069950104,
0.012848888523876667,
-0.0034040389582514763,
-0.016065437346696854,
0.029896527528762817,
0.013127213343977928,
-0.04444432631134987,
0.024696674197912216,
-0.046372395008802414,
-0.010965322144329548,
0.002740292577072978,
-0.03165248781442642,
0.04066743329167366,
-0.02411782369017601,
0.018660923466086388,
0.020513541996479034,
-0.05010003224015236,
-0.02342299371957779,
-0.03712647408246994,
-0.029427554458379745,
0.013784639537334442,
-0.013464927673339844,
-0.027243414893746376,
-0.0027790102176368237,
0.012166370637714863,
-0.0340547077357769,
-0.001967604039236903,
0.024965479969978333,
-0.038580272346735,
0.002636294811964035,
0.00301770749501884,
0.053604912012815475,
0.011062439531087875,
0.012566797435283661,
-0.038486234843730927,
0.018685495480895042,
0.0072403098456561565,
0.0033937266562134027,
0.04069298133254051,
0.02100363001227379,
-0.04217199981212616,
0.01785842888057232,
-0.04279544949531555,
-0.01865985430777073,
0.013217807747423649,
-0.0059176054783165455,
-0.0243971049785614,
-0.004919287748634815,
0.028200941160321236,
-0.04178287461400032,
-0.03450971841812134,
-0.04276297613978386,
0.017417604103684425,
-0.012481939978897572,
0.04975321143865585,
0.031060772016644478,
-0.00028304639272391796,
-0.0729520171880722,
0.0076657976023852825,
0.003954932559281588,
-0.06916438788175583,
-0.007075430825352669,
-0.030193058773875237,
-0.014761155471205711,
-0.029016301035881042,
0.04082733020186424,
0.0023532467894256115,
-0.03460436314344406,
0.005557202268391848,
-0.07480473816394806,
-0.031247274950146675,
0.011571810580790043,
0.0259387344121933,
0.050615955144166946,
0.04580054432153702,
-0.03266020864248276,
0.13510602712631226,
0.025195997208356857,
-0.00017457712965551764,
-0.032882530242204666,
0.01669030636548996,
-0.015764456242322922,
-0.04452913627028465,
0.006235495209693909,
0.033251650631427765,
0.0030785987619310617,
0.04673027619719505,
-0.036502592265605927,
0.04855319485068321,
0.06647181510925293,
-0.008852522820234299,
-0.011150646023452282,
0.0018801901023834944,
-0.03247586637735367,
-0.013671462424099445,
0.07387044280767441,
-0.02738039381802082,
-0.02575576677918434,
-0.006381516810506582,
0.008508666418492794,
0.029694898054003716,
0.007062637712806463,
-0.025348272174596786,
0.04879862070083618,
-0.006146355997771025,
-0.040955882519483566,
-0.035456910729408264,
0.028920693323016167,
-0.022444767877459526,
-0.0012350216275081038,
0.014465118758380413,
0.03062949702143669,
0.02713065966963768,
-0.06628124415874481,
0.00007976651977514848,
0.03587188199162483,
0.044838178902864456,
-0.01983470283448696,
0.00008773232548264787,
-0.001243906794115901,
-0.023388318717479706,
0.024864723905920982,
-0.0307854562997818,
0.005413300357758999,
0.011419834569096565,
0.043160781264305115,
0.0037736911326646805,
-0.007091362960636616,
-0.01850799284875393,
-0.03537462279200554,
-0.014605156145989895,
0.01764426939189434,
0.014737943187355995,
0.0538494698703289,
0.029102958738803864,
0.0727887973189354,
0.001599422306753695,
0.01057496014982462,
0.0044395397417247295,
-0.0009872997179627419,
-0.012764636427164078,
-0.018703466281294823,
-0.011456520296633244,
-0.048163801431655884,
0.007474867627024651,
-0.04048741236329079,
0.023408399894833565,
-0.009814081713557243,
-0.015052253380417824,
-0.033324725925922394,
-0.0338984914124012,
-0.038005419075489044,
0.012660295702517033,
-0.014329944737255573,
-0.008694610558450222,
-0.0038946557324379683,
0.020870370790362358,
0.052552707493305206,
-0.050720516592264175,
-0.013175374828279018,
0.04847460985183716,
-0.028664132580161095,
-0.0063526928424835205,
0.004854402970522642,
0.006058728788048029,
0.05115141719579697,
0.023683948442339897,
0.04927041754126549,
0.023256434127688408,
-0.03102639690041542,
-0.012972676195204258,
-0.020217645913362503,
0.050940949469804764,
0.04354260489344597,
0.016626492142677307,
0.02534198760986328,
-0.05366215482354164,
-0.0019984636455774307,
-0.003515962976962328,
0.061345018446445465,
-0.01502376887947321,
0.018334684893488884,
0.057652126997709274,
-0.016731038689613342,
-0.023683547973632812,
0.02148384042084217,
0.024183155968785286,
-0.025067567825317383,
0.03240612521767616,
-0.02888844907283783,
0.02188805304467678,
0.029446158558130264,
0.010188810527324677,
-0.004155614413321018,
-0.018140463158488274,
0.016178984194993973,
-0.00016649215831421316,
0.024382131174206734,
0.030208606272935867,
-0.01757030002772808,
0.010327083058655262,
0.022832101210951805,
0.0012380894040688872,
-0.026580795645713806,
0.0017861707601696253,
-0.032424196600914,
0.03907749056816101,
0.04151217266917229,
0.013461487367749214,
0.03995262831449509,
-0.0772724598646164,
-0.05730154737830162,
0.029356392100453377,
0.02114902250468731,
0.0013357690768316388,
-0.031791795045137405,
-0.046869371086359024,
-0.05379161983728409,
0.03006063774228096,
-0.03043333813548088,
0.042334284633398056,
0.007806708104908466,
-0.005317429546266794,
-0.02787734754383564,
-0.06533493101596832,
-0.008320249617099762,
0.02167358063161373,
-0.028835777193307877,
-0.013075090013444424,
-0.022626427933573723,
0.029036322608590126,
0.004880033899098635,
0.012057621031999588,
0.007239875383675098,
0.03801426663994789,
0.0070573752745985985,
-0.03027011640369892,
0.019490553066134453,
-0.002884992165490985,
-0.03143274411559105,
-0.08732578903436661,
0.011879156343638897,
0.031099073588848114,
0.006219090428203344,
0.026049038395285606,
-0.051114771515131,
-0.0401286743581295,
0.03125198557972908,
0.0010536342160776258,
0.00017835345352068543,
0.001980998320505023,
-0.05066806450486183,
0.07652942091226578,
0.037336621433496475,
-0.03776664286851883,
0.038474760949611664,
0.03481907770037651,
-0.015187365002930164,
0.007056436035782099,
-0.03754618391394615,
0.004910359159111977,
0.010065334849059582,
0.02527874894440174,
-0.0490870364010334,
-0.013672946952283382,
-0.012340485118329525,
0.0680696964263916,
-0.025851616635918617,
0.01529853604733944,
-0.017261696979403496,
-0.0075071146711707115,
0.007710384204983711,
0.016226600855588913,
-0.03300616517663002,
0.005378263536840677,
-0.00033021802664734423,
0.018357494845986366,
0.03788331523537636,
-0.014319019392132759,
0.06128103658556938,
-0.0022950079292058945,
-0.0007434397120960057,
0.025118105113506317,
0.012575695291161537,
0.04470793530344963,
-0.000084838924522046,
-0.03289737179875374,
0.013784130103886127,
-0.04838918522000313,
0.03641346096992493,
-0.008258429355919361,
-0.01525129098445177,
-0.005810934584587812,
-0.025468088686466217,
-0.024856964126229286,
-0.006405504420399666,
-0.01867646351456642,
0.04428648576140404,
-0.006926746107637882,
-0.025957411155104637,
0.034120477735996246,
0.0025353136006742716,
-0.06835752725601196,
-0.025842605158686638,
0.00985054112970829,
-0.018198762089014053,
-0.0344281867146492,
-0.002670824062079191,
-0.03155267983675003,
0.010066292248666286,
-0.04666384682059288,
0.057162586599588394,
0.027573537081480026,
-0.04577052965760231,
-0.018864978104829788,
0.004178324248641729,
0.0471363328397274,
0.03542868793010712,
0.00458159763365984,
0.015849795192480087,
0.00042597358697094023,
-0.03267034515738487,
0.014287639409303665,
0.051316842436790466,
0.04935213923454285,
-0.03450005128979683,
0.01068055722862482,
-0.041517943143844604,
0.0121500538662076,
0.04615531489253044,
-0.003363363677635789,
-0.03151504322886467,
0.021437907591462135,
0.005816963035613298,
-0.01273280382156372,
-0.05518646165728569,
-0.02980055660009384,
-0.007512224838137627,
0.010389205999672413,
-0.010394329205155373,
-0.0311855711042881,
-0.012452829629182816,
-0.02503831312060356,
0.019157465547323227,
0.012663488276302814,
0.02166423574090004,
-0.036071281880140305,
0.03550868481397629,
-0.011506757698953152,
0.004633159376680851,
0.03914568945765495,
-0.017145207151770592,
0.02239074371755123,
-0.009143410250544548,
0.009585137479007244,
0.013850145973265171,
0.03325343132019043,
-0.0241516325622797,
0.000604321132414043,
-0.08959411084651947,
0.03289162740111351,
0.05392037704586983,
0.05187802389264107,
0.043958719819784164,
-0.0013757190899923444,
-0.02244793064892292,
-0.013989036902785301,
-0.008189152926206589,
-0.03121333383023739,
0.015863830223679543,
-0.02320951223373413,
0.015793969854712486,
-0.03243401274085045,
-0.00003878202915075235,
0.020609175786376,
0.0541672520339489,
-0.08020137250423431,
0.006964814383536577,
0.01026278268545866,
0.0197922270745039,
0.00009648578998167068,
0.012025540694594383,
-0.030678464099764824,
0.03267163410782814,
0.002383876359090209,
0.04859492927789688,
-0.00932533759623766,
-0.0265498049557209,
0.012592943385243416,
0.026069076731801033,
0.01933746039867401,
-0.03884522244334221,
-0.051524341106414795,
-0.04744959622621536,
0.0037861312739551067,
-0.022687667980790138,
-0.008721006102859974,
0.016700435429811478,
0.052335456013679504,
0.011327609419822693,
0.026172704994678497,
0.012285108678042889,
-0.033410072326660156,
-0.03669070824980736,
-0.012880136258900166,
-0.0508156344294548,
-0.06169687956571579,
0.007088993676006794,
-0.024414939805865288,
-0.0007869984838180244,
0.02747488208115101,
-0.03426045551896095,
0.0533374585211277,
-0.008451183326542377,
0.0030235464219003916,
-0.01716994307935238,
0.0700986385345459,
0.0005077238893136382,
-0.003612701315432787,
-0.027993883937597275,
0.015519748441874981,
0.12373217195272446,
0.07414587587118149,
0.01882283389568329,
-0.06495776027441025,
0.029032345861196518,
-0.011944014579057693,
-0.00579052371904254,
-0.06758330762386322,
0.0197049081325531,
-0.03195992112159729,
-0.032638926059007645,
-0.01039019227027893,
0.03946515917778015,
-0.023603715002536774,
-0.015217559412121773,
0.023500479757785797,
-0.05334343761205673,
-0.0348849855363369,
0.0011842536041513085,
-0.006284660194069147,
0.00031367826159112155,
0.0018808154854923487,
-0.007375133223831654,
0.028666341677308083,
-0.024577755481004715,
0.01422992441803217,
-0.03653622791171074,
-0.002045790199190378,
0.0384783074259758,
-0.03978704288601875,
-0.07246851176023483,
0.017305264249444008,
-0.006425509694963694,
0.012041574344038963,
-0.021197190508246422,
0.02639813721179962,
-0.001655830186791718,
-0.01734420470893383,
0.054236553609371185,
0.03328622505068779,
0.012310663238167763,
-0.0041456762701272964,
0.028322987258434296,
-0.021414270624518394,
-0.00016261728887911886,
-0.0211854949593544,
-0.05337296053767204,
0.07366018742322922,
-0.001912403735332191,
-0.021471461281180382,
-0.020985713228583336,
0.009200078435242176,
0.027549469843506813,
-0.05746158957481384,
0.0031803131569176912,
0.018512645736336708,
0.005380947608500719,
-0.0038485568948090076,
0.01441153883934021,
-0.012101355008780956,
0.015142777003347874,
0.009207387454807758,
-0.0005817104247398674,
0.0005196283455006778,
-0.02249474637210369,
0.011738527566194534,
-0.01636657305061817,
0.0316394567489624,
0.006994547788053751,
0.002129835542291403,
-0.01821112632751465,
-0.014100402593612671,
-0.027153175324201584,
-0.059716805815696716,
0.023724235594272614,
0.0327783040702343,
0.024923570454120636,
0.004481620620936155,
-0.01380065269768238,
-0.050925303250551224,
-0.07590670138597488,
0.030298877507448196,
-0.011411537416279316,
-0.07400096207857132,
0.005704882554709911,
-0.0006309783784672618,
-0.0032483332324773073,
0.08882518112659454,
-0.014444870874285698,
0.0036282700020819902,
0.022213825955986977,
0.021510733291506767,
0.025447344407439232,
-0.054083243012428284,
-0.046874258667230606,
0.04511784017086029,
-0.013212478719651699,
0.025011539459228516,
-0.019616350531578064,
0.03227443993091583,
0.02635326236486435,
0.037025608122348785,
-0.031426627188920975,
0.023634575307369232,
-0.0289996899664402,
-0.012751645408570766,
-0.014389852993190289,
-0.015702413395047188,
0.030109917744994164,
0.018339969217777252,
0.022928714752197266,
-0.038312554359436035,
-0.006361515261232853,
0.0010341316228732467,
0.0003079180314671248,
0.00928029976785183,
-0.0024506303016096354,
-0.012369451113045216,
-0.003985920455306768,
-0.012757393531501293,
0.004003901965916157,
-0.01616506464779377,
-0.024246981367468834,
-0.037099145352840424,
0.04007144272327423,
-0.029818665236234665,
0.030621660873293877,
-0.008011015132069588,
0.039351481944322586,
-0.008544889278709888,
-0.030257219448685646,
0.05945977568626404,
0.06667675822973251,
-0.0053006382659077644,
-0.008466445840895176,
-0.02036215178668499,
-0.005028330720961094,
-0.005618902388960123,
0.017151350155472755,
-0.016948629170656204,
0.019913462921977043,
-0.050591371953487396,
-0.01929011382162571,
0.040500905364751816,
0.023691290989518166,
0.00926433876156807,
0.03067203052341938,
0.020724646747112274,
-0.029277298599481583,
0.04479218274354935,
0.00787701178342104,
-0.021814269945025444,
-0.007674483582377434,
-0.08690230548381805,
0.013177981600165367,
-0.05477824807167053,
-0.0032929531298577785,
0.05288736894726753,
-0.009922754019498825,
0.002542957430705428,
0.021473143249750137,
-0.05564329773187637,
-0.006405968219041824,
0.011290998198091984,
0.002305035712197423,
0.022463053464889526,
0.006904681213200092,
-0.006576595362275839,
0.003923692274838686,
0.046155717223882675,
-0.012505007907748222,
0.009650073014199734,
0.0071784090250730515,
0.01734428107738495,
-0.09826797991991043,
-0.034834638237953186,
0.002169245621189475,
0.03642899915575981,
0.027144838124513626,
-0.05929453670978546,
0.02713814750313759,
0.03256013244390488,
-0.023699721321463585,
0.04904652386903763,
0.0010156125063076615,
0.01605263352394104,
-0.02622891776263714,
0.04869107902050018,
-0.008182239718735218,
0.02459803596138954,
0.02380332350730896,
0.00571450125426054,
-0.008945980109274387,
0.007550709415227175,
-0.010267131961882114,
-0.0432724691927433,
-0.03870878741145134,
0.010931272991001606,
0.018907621502876282,
-0.03264041617512703,
0.09662110358476639,
-0.008071611635386944,
-0.0004072179435752332,
0.016404595226049423,
0.016612274572253227,
-0.0022204576525837183,
0.0037841550074517727,
0.032311081886291504,
0.012523346580564976,
0.045858994126319885,
-0.010660955682396889,
-0.01806565560400486,
0.022209150716662407,
0.014639563858509064,
0.03917093202471733,
0.011815879493951797,
0.00860818661749363,
0.0080542778596282,
-0.00046960808685980737,
-0.05578037351369858,
-0.0471956804394722,
0.019347233697772026,
0.018195949494838715,
-0.013793546706438065,
-0.0004298667481634766,
-0.009090032428503036,
-0.010667775757610798,
-0.03033895418047905,
0.0217550341039896,
-0.03924905136227608,
0.004003280308097601,
0.015490016900002956,
0.005543828476220369,
0.0017325045773759484,
0.051452573388814926,
-0.04819247126579285,
-0.03646674379706383,
0.04889034107327461,
0.001677738269791007,
-0.04186692088842392,
-0.051170654594898224,
-0.014518807642161846,
0.007748382166028023,
0.02764313481748104,
-0.01529327780008316,
-0.01570095866918564,
-0.05368519946932793,
0.017456624656915665,
-0.017475107684731483,
0.03674089163541794,
-0.055032264441251755,
-0.0021889840718358755,
-0.019933683797717094,
-0.047011714428663254,
0.020096609368920326,
0.0024323738180100918,
-0.053950462490320206,
-0.03585323691368103,
-0.014522996731102467,
0.042711041867733,
0.01999625377357006,
0.033780165016651154,
0.013158251531422138,
-0.04291200637817383,
-0.022766128182411194,
-0.02822789177298546,
0.004725331906229258,
-0.0627133920788765,
0.007816469296813011,
-0.002208102261647582,
0.004516637418419123,
0.007170952390879393,
0.0032398682087659836,
-0.015922317281365395,
0.03290117159485817,
0.04467624053359032,
0.02404494769871235,
0.014842167496681213,
0.004830404184758663,
-0.059726450592279434,
0.03635392710566521,
-0.004021414555609226,
-0.0006084300111979246,
0.05805375427007675,
0.007617667317390442,
0.005634951870888472,
0.024111110717058182,
-0.055796388536691666,
-0.015310813672840595,
0.028217768296599388,
-0.02507646195590496,
-0.017071213573217392,
-0.041201621294021606,
-0.023940272629261017,
0.025178255513310432,
-0.015969764441251755,
-0.019900688901543617,
0.05325998365879059,
0.016225889325141907,
-0.016567012295126915,
0.04625086858868599,
-0.00768473744392395,
0.02459479682147503,
0.024921836331486702,
0.028453471139073372,
-0.0005218429141677916,
-0.014219586737453938,
0.023087400943040848,
0.03934706002473831,
0.020187918096780777,
-0.02378087118268013,
0.0014055469073355198,
-0.008054705336689949,
0.016308801248669624,
0.011730285361409187,
-0.010646597482264042,
-0.00885851588100195,
-0.0205747839063406,
-0.019907403737306595,
0.009750704281032085,
0.008487015031278133,
0.009625107981264591,
0.055481355637311935,
-0.038068268448114395,
0.10410190373659134,
-0.032008565962314606,
0.027868453413248062,
-0.017627790570259094,
0.04338706284761429,
-0.024936219677329063,
0.02301795221865177,
0.0040776547975838184,
0.04247024655342102,
-0.03279321268200874,
-0.03220074623823166,
-0.04122805967926979,
-0.02092910371720791,
-0.030493346974253654,
-0.058054592460393906,
-0.028270786628127098,
0.05294274166226387,
-0.030980687588453293,
0.007133072707802057,
-0.006558290217071772,
-0.015821922570466995,
-0.0379403680562973,
0.010906641371548176,
0.026104914024472237,
-0.005994297564029694,
-0.0036783572286367416,
-0.013233990408480167,
-0.006116330157965422,
0.01930508390069008,
-0.02223004214465618,
0.033222880214452744,
0.010902680456638336,
0.014408714137971401,
-0.011975779198110104,
0.008310280740261078
] |
<p>I recently was given the task to create power using magnets, I would think that if I were to put some same poled magnets together, and they were facing the same poled magnets, they would repel and rotate around a shaft. </p>
| 292 |
[
-0.0584196038544178,
-0.005781760439276695,
-0.022578677162528038,
-0.01961180381476879,
0.05643660947680473,
0.010345936752855778,
-0.020108439028263092,
0.009261337108910084,
0.010896674357354641,
-0.02005258947610855,
0.03129124641418457,
0.042878761887550354,
0.055027466267347336,
0.015558948740363121,
0.023508090525865555,
-0.0009515617857687175,
-0.008379151113331318,
0.014416535384953022,
0.0033502362202852964,
-0.02212510257959366,
0.001612322754226625,
0.02920905128121376,
0.010079806670546532,
0.006893480662256479,
-0.027909353375434875,
0.03935527801513672,
0.004701158497482538,
-0.025284703820943832,
0.009403158910572529,
0.042670395225286484,
0.0010471316054463387,
-0.03380800783634186,
0.012663539499044418,
0.027595220133662224,
0.04457508772611618,
-0.0026812145952135324,
-0.035972923040390015,
-0.03875057399272919,
-0.028978029265999794,
0.04272846132516861,
-0.01858699508011341,
-0.016827521845698357,
-0.02680937759578228,
0.03925854712724686,
-0.020277895033359528,
0.00811340194195509,
-0.015097190625965595,
-0.002262357622385025,
0.05371707305312157,
-0.07651671767234802,
0.08440688252449036,
0.004957490134984255,
0.01935102418065071,
0.002003819914534688,
-0.017099130898714066,
-0.011125815100967884,
0.06572700291872025,
0.042770229279994965,
-0.01830422692000866,
-0.06517389416694641,
-0.011187388561666012,
0.006515808403491974,
-0.02057899907231331,
-0.05919073522090912,
-0.05901388078927994,
0.034406356513500214,
-0.0025295247323811054,
-0.015138626098632812,
0.047415994107723236,
0.010273722931742668,
0.02361297607421875,
0.05068863928318024,
0.04117381572723389,
-0.0038007376715540886,
-0.04244113713502884,
-0.02543584071099758,
0.02899187244474888,
0.0007932816515676677,
0.03403738513588905,
0.019014379009604454,
-0.04540371894836426,
0.018113382160663605,
0.03361326456069946,
0.0418119803071022,
0.015168556943535805,
-0.029436660930514336,
0.027369629591703415,
-0.030973121523857117,
0.01538263913244009,
0.006976088974624872,
0.018451597541570663,
0.014548487961292267,
0.030642865225672722,
-0.006095633376389742,
-0.01740582287311554,
0.009234433993697166,
-0.007319149561226368,
0.0340864397585392,
0.008609112352132797,
-0.026033377274870872,
0.011500893160700798,
0.013027268461883068,
-0.005708342418074608,
0.04262246564030647,
0.032253727316856384,
-0.05477007105946541,
-0.027237311005592346,
0.00658378703519702,
-0.042104560881853104,
-0.016326887533068657,
-0.01700420305132866,
0.01629495620727539,
0.009192708879709244,
-0.03439619019627571,
0.00913319457322359,
-0.029894689098000526,
0.007996614091098309,
-0.00024502218002453446,
0.05703379958868027,
0.06915014237165451,
0.002830685582011938,
-0.03996165096759796,
0.05391193553805351,
-0.043713971972465515,
-0.0507689043879509,
-0.015059662982821465,
0.051255472004413605,
-0.0036895598750561476,
-0.0371280163526535,
0.03852730616927147,
0.01143222488462925,
-0.039558324962854385,
-0.03232546150684357,
-0.0020571870263665915,
0.04954754188656807,
-0.0031621677335351706,
-0.0950046181678772,
-0.026476750150322914,
0.030515169724822044,
-0.05840121954679489,
0.019466206431388855,
-0.05773905664682388,
0.002358087571337819,
0.023097490891814232,
0.07010181993246078,
-0.009426704607903957,
0.009917895309627056,
-0.006782771088182926,
0.0756027102470398,
-0.008235483430325985,
-0.010680263862013817,
-0.044496651738882065,
-0.024558309465646744,
-0.059656087309122086,
-0.0028052902780473232,
-0.046507373452186584,
0.034629788249731064,
0.020043127238750458,
-0.01896732859313488,
-0.011545252986252308,
-0.0007001442718319595,
-0.013083601370453835,
0.024937555193901062,
0.04620559513568878,
-0.026154790073633194,
-0.03182346373796463,
0.040563326328992844,
0.002457965863868594,
0.005980036687105894,
0.04287205636501312,
-0.00992339476943016,
0.020520372316241264,
0.029883690178394318,
0.043587371706962585,
0.03737408295273781,
-0.03392653912305832,
-0.00009453271923121065,
-0.02301812916994095,
0.04083849862217903,
-0.006836034823209047,
-0.02797525003552437,
-0.03605194389820099,
-0.0005254359566606581,
0.00154253956861794,
-0.028509683907032013,
0.0799727514386177,
0.006201169919222593,
-0.04353504255414009,
-0.0264684297144413,
-0.022805340588092804,
-0.002792792161926627,
-0.051152803003787994,
0.031846992671489716,
-0.050009530037641525,
-0.020033493638038635,
-0.0049483152106404305,
0.03123030811548233,
0.03135537728667259,
-0.03618261590600014,
-0.01738804206252098,
-0.02145993895828724,
0.023932460695505142,
-0.006593315862119198,
0.006215364206582308,
-0.02627217397093773,
0.04762176796793938,
0.035481613129377365,
-0.008423680439591408,
0.054855916649103165,
-0.028984995558857918,
-0.017549768090248108,
-0.003863045945763588,
-0.010037527419626713,
0.0036676812451332808,
0.0586392879486084,
0.01302215177565813,
0.04763966053724289,
0.01884092018008232,
-0.013287686742842197,
0.030134709551930428,
0.01794903725385666,
0.05379932373762131,
0.04683992266654968,
0.015002892352640629,
0.02560865879058838,
0.01990565098822117,
0.02476312220096588,
-0.012161961756646633,
-0.011818964034318924,
-0.022814659401774406,
-0.06871932744979858,
0.03344267979264259,
0.02728881873190403,
0.03484119102358818,
-0.06455892324447632,
0.04239843785762787,
0.050113726407289505,
0.03583212196826935,
-0.012774442322552204,
0.028800765052437782,
-0.030868401750922203,
-0.0029205777682363987,
0.0164926927536726,
0.019339783117175102,
0.009146963246166706,
-0.0012839882401749492,
0.04468978941440582,
0.031725745648145676,
0.007217471953481436,
0.023297786712646484,
-0.03240441158413887,
0.038469500839710236,
-0.007736461702734232,
0.023600654676556587,
0.017883403226733208,
-0.04827188700437546,
0.029004758223891258,
-0.004135642666369677,
0.024287279695272446,
-0.023429058492183685,
0.02218797244131565,
-0.005213303957134485,
0.008923860266804695,
-0.009751095436513424,
-0.014858127571642399,
0.0007487242692150176,
-0.013527723960578442,
-0.028900042176246643,
0.04030492901802063,
-0.036508090794086456,
0.020844770595431328,
-0.0070236059837043285,
-0.005142097361385822,
0.0005110485944896936,
0.021177100017666817,
0.003813954070210457,
0.03155307099223137,
0.06701438874006271,
-0.03299945965409279,
-0.029994258657097816,
-0.024071838706731796,
-0.032289255410432816,
0.02209085039794445,
0.020807452499866486,
-0.05974163860082626,
-0.002604292705655098,
-0.042213551700115204,
-0.035699326545000076,
0.02259654551744461,
-0.007414583116769791,
0.010901018045842648,
-0.004553739447146654,
0.0034944736398756504,
-0.04641774669289589,
-0.004602636676281691,
-0.018000120297074318,
0.0007417844608426094,
-0.02421656623482704,
0.016074517741799355,
0.034312158823013306,
-0.023071829229593277,
-0.030220624059438705,
-0.01785905286669731,
-0.026632744818925858,
-0.02359311655163765,
0.020845981314778328,
-0.023919645696878433,
0.037472281605005264,
-0.04048094525933266,
0.030908426269888878,
0.02560492791235447,
-0.05542825534939766,
-0.008380844257771969,
-0.0635295957326889,
-0.041596654802560806,
0.01095165777951479,
0.002518094377592206,
0.04428789019584656,
-0.022815190255641937,
-0.03815901651978493,
0.055302221328020096,
-0.018342608585953712,
-0.04727392643690109,
-0.02866384945809841,
-0.03217923641204834,
-0.02264903485774994,
-0.03804486617445946,
0.02271907962858677,
0.05181300640106201,
-0.017520207911729813,
0.018131641671061516,
0.03713499754667282,
0.01604517363011837,
0.011573579162359238,
0.014416827820241451,
-0.0032540885731577873,
0.016259517520666122,
0.040717653930187225,
-0.007716805208474398,
0.037661757320165634,
-0.0008967187604866922,
-0.006431164685636759,
0.03241853788495064,
0.015777476131916046,
0.01730976812541485,
0.011970262974500656,
-0.03616148233413696,
0.062153175473213196,
-0.01709924452006817,
0.044829897582530975,
-0.02678339183330536,
0.06215735897421837,
0.0027419431135058403,
-0.010725712403655052,
-0.0014751995913684368,
0.03462701663374901,
0.07582209259271622,
-0.024108994752168655,
-0.019090009853243828,
0.03908831626176834,
0.013442866504192352,
0.0003864578902721405,
-0.041892629116773605,
-0.0218686331063509,
-0.010117262601852417,
-0.004189962055534124,
-0.01893746294081211,
-0.02755369432270527,
0.053385596722364426,
0.022953487932682037,
0.033585820347070694,
0.03647231683135033,
-0.0002906107110902667,
0.002885931171476841,
-0.08611699938774109,
0.0034726199228316545,
-0.024806620553135872,
0.03238451108336449,
-0.019694292917847633,
0.044413819909095764,
0.038856860250234604,
0.003427864285185933,
0.0048414310440421104,
-0.01696726121008396,
-0.09843683242797852,
0.03638825938105583,
-0.02775999903678894,
0.0032426619436591864,
-0.007054897956550121,
-0.03890654444694519,
-0.009785991162061691,
-0.011490468867123127,
-0.009708966128528118,
-0.007097676862031221,
-0.045948415994644165,
-0.04875963553786278,
-0.006810028571635485,
-0.020295312628149986,
-0.044656865298748016,
0.02489566244184971,
0.0406772717833519,
0.032093510031700134,
-0.02999015711247921,
0.027313033118844032,
0.0016068712575361133,
-0.039554163813591,
0.034522101283073425,
-0.015554401092231274,
0.006812720093876123,
-0.0019119628705084324,
0.013668974861502647,
0.020390011370182037,
0.019428901374340057,
-0.02110947109758854,
0.007855561561882496,
0.006164328195154667,
0.038213636726140976,
0.018351301550865173,
-0.025515872985124588,
-0.0274138655513525,
-0.040989506989717484,
-0.03052339144051075,
0.02656794711947441,
0.07050793617963791,
-0.034804437309503555,
0.0013420607428997755,
0.020034639164805412,
0.011654720641672611,
0.011240022256970406,
0.014940779656171799,
0.052293017506599426,
0.0385994017124176,
-0.032235074788331985,
-0.043764181435108185,
-0.017624743282794952,
0.003953482490032911,
-0.018581636250019073,
-0.0004985136329196393,
-0.003561850404366851,
-0.0414033867418766,
-0.020829010754823685,
0.011422528885304928,
0.0256157536059618,
-0.024051155894994736,
0.06804526597261429,
-0.021904058754444122,
0.00838280376046896,
-0.00935153104364872,
0.013631876558065414,
-0.0010262380819767714,
0.021100105717778206,
0.03078375943005085,
-0.0016321201110258698,
-0.05694642290472984,
-0.09224925190210342,
-0.011523300781846046,
0.04213542863726616,
0.021091923117637634,
-0.002673864597454667,
-0.0005892409244552255,
-0.003935912158340216,
-0.015693729743361473,
0.043570902198553085,
-0.08392120897769928,
0.047696396708488464,
-0.013110937550663948,
-0.0307623203843832,
-0.012050896883010864,
0.016771158203482628,
-0.02868795022368431,
0.02822270430624485,
-0.009579023346304893,
0.03475053980946541,
0.004667847417294979,
-0.022933008149266243,
0.0028744509909301996,
0.006841837894171476,
0.062239695340394974,
0.006080860737711191,
-0.0036686044186353683,
0.013136964291334152,
-0.012025539763271809,
0.033653374761343,
-0.013977938331663609,
-0.09129951149225235,
0.019004976376891136,
0.01711093634366989,
-0.04685873165726662,
0.04084889963269234,
-0.03562190756201744,
-0.056080080568790436,
0.00015017219993751496,
-0.025257209315896034,
0.05936634540557861,
-0.03390122577548027,
-0.05482744425535202,
0.0022242616396397352,
0.036216702312231064,
0.02586318366229534,
0.06673074513673782,
0.042675357311964035,
-0.05394139885902405,
-0.012528016231954098,
0.010710636153817177,
0.04192636162042618,
-0.001546861371025443,
0.007134963292628527,
0.004171119537204504,
0.03417103365063667,
-0.05819856375455856,
0.0861116275191307,
-0.04244398698210716,
-0.004055882338434458,
-0.028104912489652634,
0.009381269104778767,
-0.027220137417316437,
0.019056007266044617,
-0.0005923601565882564,
-0.04384392127394676,
0.002195144770666957,
0.024501150473952293,
-0.009588348679244518,
-0.002456935355439782,
0.03203180804848671,
-0.02926449291408062,
0.0019618081860244274,
0.006052633747458458,
-0.0026035530027002096,
-0.012431042268872261,
-0.015500405803322792,
-0.0023032717872411013,
0.0012556873261928558,
-0.02633998543024063,
0.06500320881605148,
-0.010612317360937595,
-0.01711145043373108,
0.04483194649219513,
-0.048750389367341995,
-0.032283976674079895,
0.0321175791323185,
-0.013625603169202805,
0.0300124641507864,
-0.021841494366526604,
-0.004348634742200375,
-0.006005926989018917,
-0.019475765526294708,
-0.01634579338133335,
-0.07777532190084457,
0.02903958596289158,
0.01635088585317135,
0.06162557750940323,
-0.012525844387710094,
-0.034277018159627914,
-0.012309295125305653,
-0.037959035485982895,
-0.034704990684986115,
0.05879375711083412,
-0.056214429438114166,
0.025804467499256134,
0.022457992658019066,
-0.0023439566139131784,
0.0754106417298317,
0.014446415938436985,
-0.05161331593990326,
0.028465015813708305,
-0.04716561362147331,
0.006517413537949324,
-0.012477247975766659,
0.026615647599101067,
-0.030263222754001617,
-0.05817551165819168,
-0.01518676895648241,
0.0015556972939521074,
0.04555024579167366,
-0.01779129169881344,
0.021824756637215614,
0.034553006291389465,
0.02561342529952526,
-0.009967256337404251,
-0.003719550557434559,
0.024854358285665512,
0.03986489027738571,
-0.0037093970458954573,
-0.007380679249763489,
-0.022294046357274055,
-0.003934155218303204,
-0.04582229629158974,
0.0378330834209919,
0.018732141703367233,
-0.04014258086681366,
0.01663934625685215,
0.09586209803819656,
0.0006730107706971467,
-0.029414769262075424,
0.013965725898742676,
-0.0239650197327137,
0.026483505964279175,
-0.014870468527078629,
0.008496438153088093,
-0.027956806123256683,
0.012826145626604557,
-0.008946099318563938,
-0.022673144936561584,
0.015860820189118385,
-0.017666859552264214,
0.06850124895572662,
-0.025048693642020226,
0.06109638139605522,
0.024648040533065796,
-0.015582787804305553,
-0.014780220575630665,
-0.013869737274944782,
0.015843302011489868,
-0.006945973262190819,
-0.008275466971099377,
0.04191930592060089,
-0.0013300107093527913,
0.0056783221662044525,
0.04875514283776283,
0.04000543802976608,
-0.014609045349061489,
-0.019617073237895966,
0.030775578692555428,
0.028771040961146355,
0.02763904444873333,
0.0376117043197155,
-0.036843087524175644,
0.0013557194033637643,
-0.06729714572429657,
0.017873672768473625,
-0.03673865273594856,
0.022641457617282867,
0.011246376670897007,
0.018366636708378792,
0.0019192207837477326,
-0.0404188372194767,
-0.011347238905727863,
-0.032971568405628204,
0.02095666155219078,
0.01493912748992443,
0.015914099290966988,
-0.013740479946136475,
0.024806024506688118,
0.03890429809689522,
0.014782936312258244,
-0.002920151222497225,
0.027476293966174126,
-0.05157674103975296,
-0.017196286469697952,
-0.021056273952126503,
-0.05760883539915085,
0.014871124178171158,
0.016780860722064972,
-0.01914479024708271,
0.0194525308907032,
0.0009359363466501236,
0.025375133380293846,
0.015279613435268402,
0.02904476597905159,
-0.03245024010539055,
0.0681515485048294,
0.005029115825891495,
0.028386138379573822,
-0.00619330070912838,
0.003001859411597252,
0.11946269124746323,
0.0049498542211949825,
0.05130356550216675,
-0.050879139453172684,
0.024414384737610817,
-0.04914035275578499,
-0.03001239150762558,
-0.010804170742630959,
0.014265619218349457,
-0.02439029887318611,
0.024128884077072144,
0.0006394864758476615,
0.021638300269842148,
-0.014163029380142689,
0.0055757067166268826,
0.05869593843817711,
-0.028307076543569565,
-0.00912049226462841,
-0.012397942133247852,
0.027681797742843628,
-0.010428614914417267,
-0.020487675443291664,
-0.05272171273827553,
-0.000579207728151232,
-0.03929835557937622,
-0.0038751803804188967,
0.00822096224874258,
-0.02532198652625084,
0.03845979645848274,
0.012066860683262348,
-0.03015432320535183,
0.022049428895115852,
0.010223664343357086,
-0.0344773530960083,
-0.03971155732870102,
0.009337600320577621,
0.0496571846306324,
0.00887051597237587,
0.01004212535917759,
0.00157118437346071,
0.025484202429652214,
0.03142504021525383,
-0.0028741462156176567,
0.010256004519760609,
-0.06801898032426834,
0.009821861051023006,
-0.03505511209368706,
0.02285768650472164,
0.00041932749445550144,
0.00774006824940443,
-0.007894114591181278,
0.006433043163269758,
0.03659534826874733,
-0.04844283312559128,
-0.0012113511329516768,
-0.009742901660501957,
0.0009941031457856297,
-0.012579970061779022,
0.010154413059353828,
-0.014713562093675137,
0.03015853464603424,
-0.028225857764482498,
0.017529601231217384,
-0.04085177183151245,
0.0020283295307308435,
0.030948881059885025,
0.01725846529006958,
0.04777081683278084,
-0.011815279722213745,
-0.01945355534553528,
-0.056242685765028,
-0.028884688392281532,
-0.016603995114564896,
0.003158580046147108,
-0.029704030603170395,
0.020450757816433907,
-0.006935234181582928,
-0.02877071127295494,
-0.006207222584635019,
-0.016545332968235016,
-0.054285936057567596,
0.04259808734059334,
0.018619442358613014,
-0.020937955006957054,
-0.0043962262570858,
-0.01503002643585205,
0.0358426496386528,
0.04305271431803703,
-0.040434375405311584,
0.00661871861666441,
-0.007447009906172752,
0.013650408945977688,
0.011339010670781136,
0.005833309143781662,
-0.021141165867447853,
0.022365059703588486,
-0.05980265513062477,
-0.02084999345242977,
-0.0046596406027674675,
0.0179654099047184,
0.025738967582583427,
-0.006325389724224806,
0.0013315664837136865,
0.04597268998622894,
-0.01349756121635437,
0.027822794392704964,
0.014529759995639324,
-0.01816149428486824,
-0.03495064750313759,
0.007901313714683056,
-0.044685255736112595,
-0.04512638971209526,
-0.017222970724105835,
0.0013139526126906276,
-0.012590342201292515,
0.02610081620514393,
0.01523067057132721,
-0.02824215032160282,
-0.011468719691038132,
-0.015327688306570053,
0.058009110391139984,
-0.015144795179367065,
-0.0022933136206120253,
-0.033973176032304764,
-0.0019058029865846038,
0.024800948798656464,
-0.004306879825890064,
0.005479459185153246,
0.024380266666412354,
-0.01717413403093815,
0.029392313212156296,
0.02048596553504467,
0.0027821131516247988,
-0.013525593094527721,
-0.004278436303138733,
0.042451176792383194,
0.020764177665114403,
0.02489420399069786,
-0.023343920707702637,
-0.020104458555579185,
0.063498854637146,
-0.019756294786930084,
-0.024653613567352295,
0.016897350549697876,
-0.013292556628584862,
0.023093124851584435,
0.056285254657268524,
-0.027757739648222923,
-0.0031204859260469675,
0.05842696875333786,
-0.015498139895498753,
-0.011502527631819248,
0.004597093444317579,
0.024487126618623734,
0.021069232374429703,
0.016826719045639038,
0.01069910079240799,
-0.039310455322265625,
-0.03126371651887894,
-0.006328493822365999,
0.031049422919750214,
-0.007508894428610802,
-0.03315632790327072,
-0.004187016747891903,
0.04882257804274559,
-0.025138534605503082,
0.020265832543373108,
-0.030448880046606064,
-0.013139243237674236,
0.044463980942964554,
-0.025013770908117294,
0.016833707690238953,
0.013964328914880753,
0.010373637080192566,
-0.0884236991405487,
-0.016557421535253525,
0.0010204347781836987,
-0.025510741397738457,
0.002937765559181571,
-0.03509783372282982,
-0.01900455355644226,
0.016719479113817215,
-0.0738895982503891,
0.011416151188313961,
0.0018020863644778728,
-0.04312620684504509,
-0.020837273448705673,
0.02940603345632553,
0.016935814172029495,
0.05238591507077217,
0.03677228465676308,
0.06397642195224762,
-0.0015798434615135193,
-0.020096637308597565,
-0.030971063300967216,
-0.007624252233654261,
0.016571421176195145,
0.024868428707122803,
-0.017396120354533195,
0.024498380720615387,
0.05149799585342407,
-0.019381847232580185,
-0.038085490465164185,
0.036944471299648285,
-0.022399259731173515,
0.005089807324111462,
-0.006621039472520351,
0.04407120123505592,
0.015085709281265736,
0.03367286175489426,
-0.01572093367576599,
-0.00119976291898638,
-0.014672484248876572,
0.03302998095750809,
0.04238205403089523,
0.024144073948264122,
-0.006432610563933849,
0.034706853330135345,
0.028487008064985275,
-0.015282414853572845,
0.04779159277677536,
0.01630120724439621,
-0.040083643049001694,
0.00280633638612926,
-0.023118840530514717,
0.019740616902709007,
-0.008992448449134827,
-0.0033469670452177525,
0.0033565619960427284,
-0.047398850321769714,
-0.005465905647724867,
0.0320134274661541,
-0.037365809082984924,
0.01565375179052353,
0.06168137863278389,
-0.01536878664046526,
-0.008737042546272278,
0.019858485087752342,
0.0022122818045318127,
-0.033151086419820786,
-0.0653371810913086,
0.020036479458212852,
0.02527955174446106,
0.016839195042848587,
-0.0023639812134206295,
-0.09291931986808777,
0.017868919298052788,
0.043088510632514954,
0.023424314334988594,
0.039881981909275055,
0.05294307321310043,
-0.04422060772776604,
-0.016910076141357422,
-0.01763029769062996,
0.05820802226662636,
-0.016869045794010162,
-0.008347844704985619,
-0.042308323085308075,
-0.05652580037713051,
-0.0023378501646220684,
0.005521848332136869,
0.021353071555495262,
-0.0005879740929231048,
0.00030340428929775953,
0.02862210012972355,
-0.06198495253920555,
0.0374867208302021,
-0.02586018294095993,
0.008360986597836018,
0.012096409685909748,
-0.01577363722026348,
0.04487849026918411,
-0.017835015431046486,
-0.008601765148341656,
-0.010046709328889847,
0.007673581130802631,
-0.008193504065275192,
0.00781951379030943,
0.00443677743896842,
-0.045600973069667816,
0.03359699249267578,
0.006947033107280731,
-0.005502492189407349,
0.016427526250481606,
-0.010497814044356346,
0.007257732562720776,
-0.021527821198105812,
-0.04509039595723152,
-0.046212438493967056,
0.041945815086364746,
-0.0481494665145874,
0.011939425021409988,
0.00807871762663126,
-0.03755364939570427,
0.0415530726313591,
-0.04220249503850937,
-0.01740645430982113,
0.02088741399347782,
-0.023540211841464043,
0.002868108684197068,
0.02964189648628235,
0.019427914172410965,
0.00015109169180504978,
-0.05773181840777397,
0.03135821968317032,
0.0036955776158720255,
-0.02499956265091896,
0.007406868040561676,
0.02210925705730915,
-0.012834838591516018,
0.022392332553863525,
-0.02671421691775322,
0.023178333416581154,
0.026100778952240944,
0.013448823243379593,
0.011852008290588856,
0.03247154876589775,
-0.03638974204659462,
-0.01929561048746109,
0.02486720308661461,
-0.009211603552103043,
-0.00986933521926403,
0.018573636189103127,
-0.006790319457650185,
0.08905912190675735,
-0.03598678857088089,
0.011054124683141708,
-0.0349140428006649,
0.008784020319581032,
0.03308901935815811,
-0.013347426429390907,
0.014944792725145817,
0.022793572396039963,
-0.004474029876291752,
-0.03913245350122452,
-0.008913364261388779,
-0.024218056350946426,
0.05635949224233627,
-0.016601135954260826,
0.029437407851219177,
-0.02879190444946289,
0.044351350516080856,
-0.021959057077765465,
-0.036284029483795166,
-0.060034096240997314,
-0.04008720815181732,
0.017697591334581375,
0.02581750974059105,
0.017405984923243523,
-0.02656395547091961,
-0.004504141863435507,
-0.008688152767717838,
0.03365107253193855,
-0.07358567416667938,
-0.020792819559574127,
-0.057339344173669815,
0.032291073352098465,
0.028377626091241837,
0.037018366158008575
] |
<p>Consider a block floating in a fluid. The force due to gravity balances the buoyant force exerted on the block. But there must be a third-law action pair to the buoyant force. If the block exerts a force on the fluid, that would mean that the pressure in fluid just below the block is more than that in other places that are on the same horizontal level. </p>
<p><img src="http://i.stack.imgur.com/TrHKq.png" alt="enter image description here"></p>
<p>I do not believe that to be the case, since it doesn't conform to real world observations. </p>
<p>Also, if the block has a $m$ and density $\rho$, and the fluid + the container has a mass $M$. What is the mass of the block + container + fluid (as in the picture), as measured by a weighing machine underneath the container. </p>
<p>According to my common sense, since the buoyant force is internal, the measured mass of the system should be $m + M$. Am I right?</p>
| 8,834 |
[
-0.04028298333287239,
-0.003704735543578863,
-0.03319142758846283,
-0.016696400940418243,
0.04314170032739639,
-0.00973035953938961,
-0.006551515311002731,
0.016160599887371063,
0.037792544811964035,
-0.0059667774476110935,
0.03639160469174385,
0.03652149811387062,
0.0779547169804573,
-0.010613473132252693,
0.04058073088526726,
0.034795187413692474,
-0.004753527697175741,
0.008517266251146793,
0.027836469933390617,
-0.016309639438986778,
-0.044588811695575714,
0.05301375687122345,
0.029507389292120934,
0.006573610007762909,
0.007342249155044556,
0.03216137737035751,
0.0360698364675045,
-0.026674717664718628,
0.03522491455078125,
0.022283820435404778,
0.015440599992871284,
-0.009705687873065472,
-0.027432821691036224,
0.028740348294377327,
0.04642438143491745,
0.036274224519729614,
-0.02959360182285309,
-0.00676782988011837,
-0.0016484182560816407,
0.048509903252124786,
-0.030736234039068222,
-0.016364412382245064,
0.0006783087737858295,
0.02168310061097145,
-0.04503905400633812,
0.008281940594315529,
0.013846787624061108,
0.014994622208178043,
0.037499018013477325,
-0.0727202370762825,
0.06241009384393692,
0.02810697816312313,
0.0588248148560524,
0.06685180217027664,
-0.01794133521616459,
-0.021438423544168472,
0.07957280427217484,
0.07668692618608475,
0.0003204655076842755,
-0.032400745898485184,
-0.021034611389040947,
0.007816556841135025,
-0.025123054161667824,
-0.028647636994719505,
-0.011095413006842136,
0.003174684476107359,
-0.03486461564898491,
-0.01445438526570797,
0.006141369231045246,
-0.007138311397284269,
-0.022375671193003654,
-0.010565108619630337,
0.05568215996026993,
-0.023515544831752777,
0.025406301021575928,
-0.035175442695617676,
0.003850530134513974,
0.046614162623882294,
0.019004380330443382,
0.002633352531120181,
-0.023027684539556503,
-0.0005781171494163573,
0.024368688464164734,
0.060219284147024155,
0.028311418369412422,
-0.029218312352895737,
0.050811249762773514,
0.0024776568170636892,
-0.010469627566635609,
0.041592083871364594,
-0.004589429125189781,
0.0155585752800107,
0.002915626158937812,
-0.03680001199245453,
0.0255835372954607,
0.013636940158903599,
-0.004989637527614832,
0.02398618683218956,
0.016602395102381706,
-0.004725264851003885,
0.010616574436426163,
-0.02433478832244873,
0.0016934690065681934,
0.08145274966955185,
-0.0010476626921445131,
-0.02411288395524025,
-0.04012438282370567,
-0.007554338779300451,
0.0019845175556838512,
0.0025228685699403286,
-0.02835438773036003,
0.008522547781467438,
-0.011473830789327621,
-0.04000489413738251,
-0.016134250909090042,
0.010169433429837227,
0.028271621093153954,
-0.0014442827086895704,
0.05610466003417969,
0.010095011442899704,
0.05315259471535683,
-0.006083528511226177,
0.004622504580765963,
-0.06493949890136719,
-0.08660422265529633,
0.04786408320069313,
-0.003100544912740588,
-0.035692524164915085,
-0.041941650211811066,
0.05097043886780739,
0.02499449998140335,
0.000027366502763470635,
-0.011307538487017155,
-0.014621881768107414,
0.04202321544289589,
-0.029507504776120186,
-0.08875078707933426,
-0.03444521501660347,
0.04637989401817322,
0.007631889544427395,
-0.02270626276731491,
-0.05971013382077217,
-0.0025158708449453115,
0.045037589967250824,
0.06236761435866356,
0.0045930687338113785,
-0.001579152885824442,
-0.020091377198696136,
0.04317358508706093,
-0.005014999303966761,
0.011132248677313328,
-0.006868299096822739,
0.002645827829837799,
-0.043055880814790726,
0.005588234402239323,
-0.0749930813908577,
0.004295745864510536,
0.00034991823486052454,
0.013789298012852669,
-0.0033911638893187046,
0.05063343793153763,
0.0009832782670855522,
0.006021734792739153,
-0.004457253497093916,
-0.008371206000447273,
-0.017408182844519615,
0.046985454857349396,
-0.021700304001569748,
0.018436823040246964,
0.008532223291695118,
0.03809978812932968,
0.04081936925649643,
-0.007362368516623974,
0.011542633175849915,
0.05633828416466713,
-0.004839516244828701,
-0.041334234178066254,
-0.045126207172870636,
0.025026651099324226,
0.01767771877348423,
-0.029126720502972603,
-0.06189138442277908,
-0.0161371361464262,
-0.028777284547686577,
0.023033954203128815,
0.026948124170303345,
-0.01102663204073906,
-0.01536979153752327,
0.03385357931256294,
-0.03265384957194328,
-0.022425364702939987,
-0.08924700319766998,
0.020886480808258057,
-0.015308799222111702,
0.0017002214444801211,
0.010375401936471462,
0.026027489453554153,
0.03376006707549095,
-0.06683296710252762,
-0.023653022944927216,
-0.005334330722689629,
0.01079131942242384,
0.02185751497745514,
-0.012749537825584412,
0.032708972692489624,
0.010330555960536003,
0.03200848773121834,
0.004118975251913071,
-0.017404258251190186,
-0.008819496259093285,
-0.021721981465816498,
0.018356896936893463,
-0.027263563126325607,
-0.02379460074007511,
-0.01323658972978592,
-0.008756238035857677,
0.019619211554527283,
0.016943229362368584,
-0.023513955995440483,
0.026887403801083565,
-0.04407600313425064,
0.0777805745601654,
0.04982900246977806,
0.00552081735804677,
0.022260839119553566,
0.018081780523061752,
0.03706680238246918,
0.02953481487929821,
-0.01907028630375862,
-0.03011881373822689,
-0.0399758480489254,
-0.008388550952076912,
-0.021120242774486542,
0.04045740142464638,
-0.012478661723434925,
0.030960671603679657,
0.024988315999507904,
0.03271011263132095,
0.015543652698397636,
-0.004778522532433271,
-0.0003326982259750366,
-0.022355683147907257,
0.013752525672316551,
0.06252387911081314,
-0.005601675249636173,
0.02279612608253956,
0.030959421768784523,
0.029595037922263145,
0.009159700013697147,
-0.0032888606656342745,
0.011413568630814552,
-0.006877164356410503,
-0.019361987709999084,
0.030592981725931168,
-0.03977621719241142,
-0.00532310176640749,
0.04244857281446457,
-0.02947131171822548,
0.026075106114149094,
0.018018098548054695,
-0.03672328218817711,
0.010805385187268257,
-0.05341847240924835,
-0.05160369724035263,
0.018783675506711006,
0.03056361712515354,
-0.0446958988904953,
-0.04197258502244949,
0.02945503033697605,
-0.06611323356628418,
-0.005905294790863991,
-0.05241481959819794,
0.01610725373029709,
-0.014884259551763535,
0.028031662106513977,
-0.0019591099116951227,
-0.001598152332007885,
0.05609262362122536,
-0.036511268466711044,
-0.017179807648062706,
-0.018716417253017426,
-0.04537700489163399,
-0.01510037574917078,
-0.01564800925552845,
-0.04704185947775841,
-0.003716157516464591,
-0.06326939910650253,
-0.014811581000685692,
0.04491661861538887,
0.019029179587960243,
-0.008908383548259735,
0.024925673380494118,
0.02042682282626629,
-0.0222186166793108,
-0.008144707418978214,
-0.02332100085914135,
-0.017759917303919792,
-0.009936335496604443,
-0.008858606219291687,
0.0101228728890419,
-0.004313871264457703,
-0.034063082188367844,
0.02040739916265011,
-0.06539656966924667,
-0.05158897489309311,
0.006196893751621246,
0.00365068344399333,
-0.003714853897690773,
-0.041500408202409744,
0.0016456004232168198,
0.03800735995173454,
-0.01355550717562437,
-0.023763295263051987,
-0.04593614488840103,
-0.054533835500478745,
0.015977362170815468,
0.0022671157494187355,
0.04839668050408363,
0.005425215698778629,
-0.03636679798364639,
0.08932548016309738,
0.009303185157477856,
-0.030650177970528603,
-0.011740220710635185,
-0.021875852718949318,
0.0007777964347042143,
-0.05360325798392296,
0.01572554185986519,
0.02355465106666088,
-0.009538613259792328,
0.004809989593923092,
0.04679520055651665,
0.0164452213793993,
-0.00008717076707398519,
0.03139035031199455,
-0.0038308119401335716,
0.021284107118844986,
0.05486564338207245,
-0.0026192578952759504,
0.09266123920679092,
-0.009354598820209503,
0.029170183464884758,
-0.0012729709269478917,
-0.02131715975701809,
0.018827052786946297,
-0.005895341746509075,
-0.0333692729473114,
0.07345224916934967,
0.018529221415519714,
0.008701447397470474,
-0.03214910998940468,
0.01916983164846897,
0.007661267649382353,
0.014830019325017929,
0.030614802613854408,
0.011624233797192574,
0.02934209257364273,
0.004016873426735401,
-0.005728202406316996,
0.057958103716373444,
0.048194196075201035,
0.001687296200543642,
-0.06982913613319397,
0.004092497285455465,
-0.008181722834706306,
0.03839794173836708,
0.00032457010820508003,
-0.014088296331465244,
0.03098011203110218,
0.005681727081537247,
0.018354320898652077,
-0.0222829207777977,
-0.028669964522123337,
-0.02853037789463997,
-0.07537467032670975,
-0.02159331925213337,
0.010065237060189247,
0.029417676851153374,
-0.016116267070174217,
0.039266522973775864,
0.006835440173745155,
-0.0024578699376434088,
0.029428986832499504,
0.033082522451877594,
-0.062004704028367996,
0.00779144000262022,
0.005746142473071814,
-0.0019201560644432902,
0.016924209892749786,
-0.02617833949625492,
-0.003489911323413253,
-0.03762698546051979,
0.014984015375375748,
0.007368544116616249,
0.01620086468756199,
-0.049192022532224655,
-0.023284947499632835,
-0.0049574594013392925,
-0.006997127551585436,
0.0208729300647974,
0.015719661489129066,
0.021057602018117905,
-0.04757025092840195,
0.021105803549289703,
0.027615055441856384,
-0.021146809682250023,
-0.0031266184523701668,
-0.023689495399594307,
-0.0009693162865005434,
0.0335436686873436,
0.006304265931248665,
0.037853822112083435,
0.047251153737306595,
-0.0029099450912326574,
0.03242776170372963,
0.0007145627168938518,
0.03562672808766365,
-0.015318785794079304,
-0.01935812458395958,
-0.0007444571820087731,
-0.03153570741415024,
-0.0161602720618248,
0.03322291746735573,
0.01758570410311222,
0.004884340800344944,
0.018139682710170746,
0.003354235552251339,
0.010355411097407341,
-0.04217110946774483,
0.06904566287994385,
0.055894430726766586,
0.021703466773033142,
-0.035283107310533524,
-0.07164758443832397,
0.001877134433016181,
-0.05208680033683777,
-0.02924216538667679,
0.037578292191028595,
0.01380244828760624,
-0.02180173061788082,
-0.004099765792489052,
0.01884562522172928,
0.026334313675761223,
-0.004084024112671614,
0.015740947797894478,
0.0076570045202970505,
0.021507887169718742,
-0.03807873651385307,
0.015017704106867313,
0.015695031732320786,
0.05470241978764534,
0.014650573022663593,
-0.012647080235183239,
0.023693565279245377,
-0.08717701584100723,
-0.017756635323166847,
0.028463158756494522,
0.049589917063713074,
-0.012211707420647144,
0.004799356684088707,
-0.05759458988904953,
-0.030342767015099525,
0.02683347836136818,
-0.03098123148083687,
0.04909646883606911,
-0.00975743681192398,
0.023114237934350967,
-0.00334038189612329,
-0.04649860039353371,
-0.021387066692113876,
-0.007502077613025904,
0.016331473365426064,
-0.011370883323252201,
-0.019164588302373886,
0.025134121999144554,
0.015567328780889511,
0.02711506374180317,
0.029054146260023117,
0.02302311547100544,
0.00931406207382679,
-0.03270239382982254,
-0.027876587584614754,
0.01593567244708538,
-0.04759238660335541,
-0.0614049918949604,
-0.04487800970673561,
-0.010224717669188976,
0.005461772903800011,
0.028563708066940308,
-0.034058649092912674,
-0.09968702495098114,
0.010812949389219284,
0.003869855310767889,
-0.01648406684398651,
0.014345656149089336,
-0.012461229227483273,
0.01805334910750389,
0.05281231552362442,
-0.009133254177868366,
0.06623128056526184,
0.0296423751860857,
-0.005636070854961872,
-0.0390743613243103,
-0.028012584894895554,
0.023697378113865852,
-0.019627856090664864,
-0.030645720660686493,
-0.03085910901427269,
0.012314094230532646,
-0.04000561311841011,
0.0180602315813303,
0.028982171788811684,
0.024540796875953674,
-0.005151922814548016,
-0.03389551490545273,
0.02667178399860859,
0.024080632254481316,
0.031191691756248474,
0.021574988961219788,
0.017781833186745644,
-0.00032946368446573615,
0.008800064213573933,
-0.03950896114110947,
0.016076352447271347,
0.023420879617333412,
0.01684328354895115,
0.0023661397863179445,
0.0029683250468224287,
0.03294290229678154,
0.008134701289236546,
-0.024220388382673264,
-0.02091611921787262,
-0.012779632583260536,
0.05430999770760536,
-0.0029771027620881796,
0.018590062856674194,
0.00801586452871561,
-0.024911021813750267,
-0.009848397225141525,
-0.016658196225762367,
-0.0027733989991247654,
0.013716553337872028,
-0.018563415855169296,
0.03523577004671097,
0.034463487565517426,
0.017993159592151642,
-0.05694667622447014,
-0.006032006349414587,
0.03900529444217682,
0.02079084888100624,
0.01301534753292799,
-0.021783698350191116,
-0.002288496121764183,
-0.024933138862252235,
-0.03525685891509056,
-0.021084614098072052,
0.05284591019153595,
-0.033211272209882736,
-0.040273211896419525,
0.028986981138586998,
0.017627587541937828,
0.058898136019706726,
-0.02996251732110977,
-0.017433984205126762,
0.0011905645951628685,
-0.004449638072401285,
-0.021043628454208374,
-0.007053144741803408,
0.050774283707141876,
-0.015146994031965733,
-0.017903082072734833,
-0.013545400463044643,
-0.010919284075498581,
0.03422652557492256,
-0.041061025112867355,
-0.011526055634021759,
0.040532760322093964,
0.01083784643560648,
0.007372473366558552,
-0.030515875667333603,
0.057883139699697495,
0.010695376433432102,
0.02942175790667534,
-0.011957064270973206,
0.008318960666656494,
-0.032371390610933304,
-0.02229379117488861,
0.01881108619272709,
-0.027890844270586967,
-0.01089180912822485,
-0.018099065870046616,
0.07606497406959534,
0.022790027782320976,
0.011744635179638863,
0.0017530478071421385,
0.006206837948411703,
0.02905253693461418,
-0.014089355245232582,
-0.02472558058798313,
0.024304786697030067,
0.0441594161093235,
-0.03566151484847069,
-0.03827892988920212,
-0.04919873923063278,
0.02044524997472763,
0.07753028720617294,
-0.03465519845485687,
0.07244758307933807,
-0.016756894066929817,
-0.024543417617678642,
0.03921471908688545,
-0.0020839518401771784,
-0.012505956925451756,
0.013111576437950134,
0.003787379711866379,
0.058771438896656036,
-0.04783378541469574,
0.010514933615922928,
0.03682408109307289,
0.028360547497868538,
-0.017633024603128433,
0.014326282776892185,
0.0555998720228672,
0.012478193268179893,
0.006432411260902882,
-0.012166407890617847,
-0.03208078444004059,
0.042767688632011414,
-0.05795930325984955,
0.01660882495343685,
-0.005197570193558931,
-0.048858292400836945,
0.06198061630129814,
0.02332240343093872,
-0.022146277129650116,
-0.05454227328300476,
-0.004435891751199961,
-0.013922905549407005,
0.011708434671163559,
0.002437787363305688,
0.018423032015562057,
-0.009299836121499538,
-0.01941589079797268,
0.03381325677037239,
0.025837000459432602,
0.019395314157009125,
-0.013332374393939972,
-0.07650569081306458,
-0.018841145560145378,
0.0036866432055830956,
-0.022754186764359474,
0.024940524250268936,
-0.010699250735342503,
-0.033559177070856094,
0.05436750873923302,
-0.03667666018009186,
0.038967400789260864,
0.03433781489729881,
0.017944566905498505,
-0.02833697386085987,
0.0574224591255188,
-0.017471017315983772,
0.019249387085437775,
-0.015377653762698174,
0.01467500813305378,
0.10685870051383972,
0.060991302132606506,
0.02558937296271324,
-0.04346756637096405,
0.02096801996231079,
-0.02147575654089451,
-0.009362847544252872,
-0.045802172273397446,
0.006827642675489187,
-0.020219530910253525,
0.010224038735032082,
-0.02791457809507847,
0.07583992928266525,
-0.023119786754250526,
-0.01624494418501854,
0.032315682619810104,
-0.03172212094068527,
-0.05018102005124092,
-0.001296148868277669,
0.014841830357909203,
-0.026107562705874443,
-0.001252303714863956,
-0.013600826263427734,
0.046070877462625504,
0.0034579019993543625,
-0.009486278519034386,
-0.017199993133544922,
-0.004641486797481775,
-0.012664558365941048,
0.012286699377000332,
-0.06285449862480164,
0.007835247553884983,
-0.023197615519165993,
-0.057711392641067505,
-0.06201644241809845,
0.029421312734484673,
-0.018575657159090042,
-0.019056541845202446,
0.018254272639751434,
0.010663291439414024,
-0.010596188716590405,
0.04069386050105095,
0.015966426581144333,
0.007104525342583656,
-0.06364364922046661,
0.020986193791031837,
-0.010083407163619995,
0.019732872024178505,
-0.010420756414532661,
-0.032165221869945526,
-0.0035709275398403406,
-0.0032211407087743282,
-0.004253879655152559,
-0.053984135389328,
-0.024594994261860847,
0.005142983980476856,
0.06413981318473816,
-0.008192972280085087,
-0.04038596525788307,
-0.005873735528439283,
0.03911907598376274,
-0.01573975384235382,
0.006796133704483509,
0.0014004583936184645,
0.010922353714704514,
-0.007308616768568754,
-0.00003371676575625315,
0.04006179794669151,
0.0016842244658619165,
0.010173872113227844,
-0.027922173961997032,
0.012965304777026176,
-0.045952435582876205,
-0.020822638645768166,
-0.005951425060629845,
0.023675352334976196,
0.052573271095752716,
0.010542287491261959,
0.0030323052778840065,
-0.01946677826344967,
-0.04801848530769348,
0.031774457544088364,
-0.02880958467721939,
-0.0034168174024671316,
-0.05353322997689247,
-0.005832843016833067,
-0.018863260746002197,
0.045295462012290955,
0.008078943938016891,
-0.022832149639725685,
0.004864959511905909,
0.04699491336941719,
-0.0003129116084892303,
-0.017043713480234146,
-0.0245987456291914,
-0.022439954802393913,
-0.028093134984374046,
-0.006345788482576609,
-0.009312787093222141,
-0.0222795270383358,
0.0446820892393589,
0.010902183130383492,
0.014969751238822937,
0.026529520750045776,
-0.013630080036818981,
0.002855918603017926,
0.013848209753632545,
-0.015784716233611107,
-0.004147240426391363,
0.033155202865600586,
-0.025272639468312263,
-0.016532469540834427,
-0.017401060089468956,
-0.02796739898622036,
-0.007590480148792267,
-0.024985987693071365,
0.0390252061188221,
-0.029256371781229973,
-0.019462507218122482,
-0.03196404129266739,
0.0043978565372526646,
-0.029378993436694145,
0.000005499650796991773,
-0.0972243919968605,
-0.04240857809782028,
0.008502203039824963,
-0.024343613535165787,
-0.06870550662279129,
0.023666711524128914,
-0.0410386398434639,
0.00588791910558939,
0.010458060540258884,
-0.00996345840394497,
0.004019313957542181,
-0.025285160169005394,
0.031768228858709335,
-0.0164560005068779,
0.04605148732662201,
-0.0052649471908807755,
-0.03910575062036514,
0.053284917026758194,
0.01440918818116188,
0.014725142158567905,
0.029078824445605278,
0.010722133331000805,
0.0014659177977591753,
0.012683859094977379,
-0.012193245813250542,
-0.04879901930689812,
0.07209104299545288,
-0.005996606312692165,
-0.00006485889753093943,
-0.04215823858976364,
-0.03291897475719452,
-0.030033288523554802,
-0.01551840454339981,
0.05277948081493378,
-0.03082398883998394,
-0.003604230936616659,
0.007323546800762415,
0.028347687795758247,
0.017529435455799103,
-0.0013362574391067028,
-0.0024894599337130785,
-0.01022802758961916,
0.021973421797156334,
0.015896815806627274,
0.021975303068757057,
-0.004223507363349199,
0.04935755580663681,
-0.05222667008638382,
0.008756767027080059,
0.013476909138262272,
-0.008828562684357166,
-0.1058088168501854,
-0.031448569148778915,
0.020482679829001427,
0.010585742071270943,
0.023464428260922432,
-0.062190085649490356,
0.011974962428212166,
0.026750314980745316,
-0.05150469020009041,
-0.01637633703649044,
-0.06285906583070755,
-0.0034412317909300327,
0.003235531272366643,
0.0036064297892153263,
0.0011375133180990815,
0.032146017998456955,
-0.013266646303236485,
-0.00813460536301136,
0.013607204891741276,
0.012923430651426315,
-0.011381473392248154,
-0.022435706108808517,
0.010610816068947315,
0.053182512521743774,
0.019079161807894707,
0.02081368863582611,
0.06650492548942566,
-0.019892778247594833,
-0.03622059151530266,
0.014647431671619415,
-0.031396057456731796,
0.016226351261138916,
-0.004518488422036171,
0.02646341174840927,
-0.030666619539260864,
0.05405592545866966,
-0.0020896480418741703,
0.01377799455076456,
-0.01077177096158266,
0.024372689425945282,
0.02098076418042183,
0.04646197333931923,
-0.022408006712794304,
-0.01970202662050724,
0.032069042325019836,
-0.03659621998667717,
-0.039686691015958786,
0.01907334290444851,
-0.030616285279393196,
0.03778328374028206,
0.018276004120707512,
-0.001180982100777328,
0.031506624072790146,
-0.041722193360328674,
0.019173528999090195,
-0.03344874829053879,
0.0016845623031258583,
0.07572358101606369,
-0.011383946985006332,
-0.04500874504446983,
-0.022817663848400116,
0.03665485605597496,
-0.018608547747135162,
-0.013858883641660213,
-0.023078838363289833,
-0.04115691035985947,
-0.06354369968175888,
-0.05814054235816002,
0.0014986454043537378,
-0.04418535530567169,
-0.017563991248607635,
-0.03661235794425011,
-0.048960380256175995,
0.06441646814346313,
0.01846824586391449,
0.020483311265707016,
0.00828466098755598,
-0.035208165645599365,
-0.022166617214679718,
-0.08113393932580948,
0.01875510811805725,
0.03552381694316864,
-0.0017396241892129183,
-0.02737029455602169,
-0.0008478938252665102,
0.027727210894227028,
-0.009740552864968777,
0.048717960715293884,
0.009071332402527332,
-0.01110661868005991,
0.012285560369491577,
0.010658263228833675,
0.01607411541044712,
-0.024327917024493217,
-0.0040962002240121365,
-0.005593942478299141,
-0.00021640588238369673,
0.01111933309584856,
0.0008017330546863377,
0.006857711356133223,
-0.018467841669917107,
0.018259644508361816,
-0.010406170040369034,
0.016610469669103622,
0.007496771868318319,
-0.00248637143522501,
0.05160829797387123,
0.02366778813302517,
-0.0020009782165288925,
0.07224379479885101,
0.009835708886384964,
0.023420291021466255,
0.05769792199134827,
-0.021210314705967903,
-0.06238346919417381,
0.029356330633163452,
-0.021071970462799072,
0.007677523419260979,
-0.03415323793888092,
0.0015195594169199467,
0.020432492718100548,
-0.01855620928108692,
0.01910269446671009,
0.04093581810593605,
-0.050578922033309937,
-0.013285642489790916,
0.02825649455189705,
0.04901871085166931,
0.05244907736778259,
-0.008904761634767056,
0.0383349284529686,
0.035975344479084015,
-0.018946385011076927,
0.014898051507771015,
0.0543869286775589,
0.05597490444779396,
0.009552253410220146,
0.0008475776994600892,
0.05338360741734505,
-0.008476934395730495,
-0.010427478700876236,
0.03633112460374832,
-0.0014160345308482647,
-0.015279024839401245,
-0.04025653749704361,
-0.007666135672479868,
-0.017620887607336044,
0.016442855820059776,
0.027476416900753975,
0.0006091665709391236,
0.07071743160486221,
-0.023693125694990158,
-0.0074730827473104,
-0.005618758033961058,
-0.00503383856266737,
0.02084362879395485,
0.021865004673600197,
0.010011902078986168,
0.020563049241900444,
-0.02172328718006611,
-0.003337644273415208,
-0.014941059984266758,
-0.020461738109588623,
-0.010834954679012299,
0.006391126662492752,
0.008367052301764488,
-0.0005537514807656407,
0.03398558124899864,
-0.01208950113505125,
-0.034410059452056885,
-0.05240361765027046,
-0.02108272910118103,
0.04171250760555267,
0.039781976491212845,
0.022836003452539444,
0.008341079577803612,
-0.0013373882975429296,
-0.03557056561112404,
0.04848913848400116,
-0.08426973968744278,
-0.020313506945967674,
-0.02918039821088314,
0.019574156031012535,
0.0014899938832968473,
-0.020265625789761543
] |
<p>I am wanting to build a microwave powered steamer for a reverse engineering project in university. I've read up some on this and know that its not as efficient as a heating element. I'm curious about the wavelength changes of trying to heat a container of water directly with the magnetron. Unlike in a microwave which has a larger volume than I want, the water container would be much smaller and therefore microwaves concentrated. I know that there are limitations to the size of the container I use to heat the water that are based on the wavelength of the microwaves (roughly 12.5 cm). Also the water would have to be stirred to have even heating to allow boiling overall. </p>
<p>I think my question is really over the possibility of something like this working and things you could see going wrong.</p>
<p>Thanks for any and all help :)</p>
| 8,835 |
[
-0.017403844743967056,
-0.03064739890396595,
-0.022339889779686928,
-0.04993676766753197,
0.028758198022842407,
0.008502821438014507,
-0.06888377666473389,
-0.01124393381178379,
0.007179260719567537,
-0.029436904937028885,
0.04580366238951683,
0.06966979056596756,
0.04581060633063316,
-0.02924898825585842,
0.004388364031910896,
0.04023077338933945,
0.00445267278701067,
-0.01271988544613123,
0.0036536555271595716,
-0.007893871515989304,
0.017100317403674126,
-0.002258260501548648,
-0.005192908924072981,
-0.011149255558848381,
-0.0392649881541729,
-0.006084304768592119,
0.023493703454732895,
0.00774953979998827,
0.02386505715548992,
-0.005543436389416456,
0.011650579050183296,
-0.03939129784703255,
0.0039304387755692005,
0.018754905089735985,
0.06163902208209038,
0.00045880948891863227,
-0.055969808250665665,
-0.04427962005138397,
-0.01758967898786068,
0.034955937415361404,
0.025924578309059143,
0.016404902562499046,
0.01565711759030819,
0.021930566057562828,
-0.007687127683311701,
0.000010962196938635316,
-0.036711446940898895,
-0.04721430316567421,
0.07252045720815659,
-0.07515154033899307,
0.025577234104275703,
-0.009208140894770622,
0.023853827267885208,
0.007497972343116999,
0.020254110917448997,
0.009887204505503178,
0.09645382314920425,
0.059252019971609116,
0.006678300444036722,
-0.025883382186293602,
0.032066162675619125,
0.00103647424839437,
-0.02799258753657341,
-0.00386817567050457,
-0.040905192494392395,
0.01075979508459568,
0.0025741257704794407,
-0.02622421644628048,
0.0017523143906146288,
0.01880790665745735,
0.011494849808514118,
-0.0025198012590408325,
0.06137925013899803,
-0.014318928122520447,
-0.00581824965775013,
-0.021492259576916695,
0.027133386582136154,
0.02968517132103443,
0.0030300517100840807,
0.04842822626233101,
-0.0241572055965662,
-0.006019793916493654,
0.008825186640024185,
-0.0055888015776872635,
0.020697016268968582,
-0.024546422064304352,
0.019021136686205864,
0.01650284044444561,
0.015839530155062675,
0.038919080048799515,
-0.015619855374097824,
0.001401276676915586,
0.02918257564306259,
0.01937364600598812,
-0.01411024946719408,
-0.018243353813886642,
-0.005279096309095621,
0.03936947137117386,
-0.0030904635787010193,
-0.02845616824924946,
0.021613653749227524,
0.016909096390008926,
-0.008400890976190567,
0.07028620690107346,
0.003723337547853589,
-0.04617154970765114,
-0.010663347318768501,
0.024784432724118233,
0.014729410409927368,
-0.007297714706510305,
-0.028268249705433846,
-0.027273915708065033,
0.03223366662859917,
-0.04341021925210953,
0.018077166751027107,
-0.011563311330974102,
-0.010210246779024601,
-0.027398688718676567,
0.04638214781880379,
0.06844434142112732,
0.016077371314167976,
0.026729045435786247,
0.048874638974666595,
-0.04578607156872749,
-0.053347956389188766,
0.025456473231315613,
-0.04154706001281738,
0.0015831696800887585,
-0.007518839091062546,
0.014605141244828701,
-0.012389492243528366,
-0.010186989791691303,
0.05390840023756027,
-0.016455013304948807,
0.015729965642094612,
-0.04489282891154289,
-0.04107365384697914,
-0.03711007907986641,
0.041131120175123215,
-0.029045915231108665,
-0.015361824072897434,
-0.05454268679022789,
-0.002470752689987421,
0.02438989281654358,
0.08291835337877274,
0.011285719461739063,
0.002101465128362179,
-0.053263530135154724,
0.03478427231311798,
-0.013948654755949974,
-0.039705563336610794,
0.028579125180840492,
-0.008030365221202374,
-0.039922311902046204,
-0.01694018393754959,
-0.037980712950229645,
0.01892319694161415,
0.03502395749092102,
0.003587122308090329,
-0.03442622348666191,
0.0681859701871872,
-0.0069234855473041534,
-0.001101775444112718,
0.017798785120248795,
0.005738654173910618,
-0.04047242924571037,
0.09747685492038727,
0.0011977514950558543,
-0.004959713667631149,
-0.027244189754128456,
-0.023830166086554527,
0.015097505412995815,
-0.01843659207224846,
0.0136237982660532,
0.028879115357995033,
-0.01719377562403679,
-0.013057720847427845,
0.008201636373996735,
0.07089688628911972,
0.00042597390711307526,
-0.02020939812064171,
0.0032511544413864613,
-0.01796877197921276,
-0.02370382659137249,
-0.016989631578326225,
0.08349408209323883,
-0.023761657997965813,
-0.02064300887286663,
-0.030339324846863747,
-0.04881890490651131,
0.0174745824187994,
-0.02000773698091507,
0.03478248044848442,
-0.009289787150919437,
0.007332946173846722,
0.0333394780755043,
0.0035821229685097933,
0.009935789741575718,
-0.007825342938303947,
-0.03712131828069687,
0.03407210856676102,
0.012457367032766342,
-0.012067744508385658,
0.005568729247897863,
0.006748429965227842,
0.05529436469078064,
0.030921082943677902,
-0.03635656461119652,
0.015595827251672745,
-0.029977792873978615,
-0.03738422319293022,
-0.014886914752423763,
-0.04447317123413086,
0.00326847517862916,
0.01809293031692505,
-0.03275490552186966,
0.019471226260066032,
-0.003264201572164893,
-0.01820681057870388,
0.028307683765888214,
-0.01793249510228634,
0.10795947909355164,
0.054706547409296036,
0.00496871629729867,
0.030315624549984932,
0.0031757724937051535,
0.04077145829796791,
0.00045325924293138087,
0.0320221446454525,
-0.027741599828004837,
-0.05232757329940796,
0.005003067664802074,
0.014407613314688206,
-0.002244912553578615,
-0.058299701660871506,
-0.003623225726187229,
0.006703147664666176,
0.029583511874079704,
0.04194596782326698,
0.04838675633072853,
-0.023241912946105003,
-0.002489011501893401,
0.018058694899082184,
0.008569959551095963,
0.01865626871585846,
0.004584789276123047,
0.005237228237092495,
0.036155715584754944,
0.01662333682179451,
0.007108692545443773,
-0.008834565989673138,
0.03255616873502731,
-0.016298603266477585,
-0.010702426545321941,
0.003950031008571386,
-0.020910363644361496,
0.008551070466637611,
-0.06342608481645584,
-0.010471183806657791,
-0.007160465698689222,
0.03894426301121712,
0.01944863237440586,
-0.00679840799421072,
-0.0265719685703516,
-0.036536529660224915,
-0.016196345910429955,
-0.036980047821998596,
-0.013284198008477688,
0.023085838183760643,
-0.06255783140659332,
0.0006037763669155538,
-0.014010404236614704,
0.05406714230775833,
0.009258715435862541,
0.009749297052621841,
-0.0010439130710437894,
0.019802914932370186,
0.03861914947628975,
-0.04196959733963013,
-0.021788161247968674,
0.020055633038282394,
-0.05111771449446678,
-0.007790560834109783,
-0.010961507447063923,
-0.024437759071588516,
-0.009333844296634197,
-0.0061794170178473,
-0.010079854167997837,
0.02408713288605213,
-0.025440862402319908,
-0.0041578542441129684,
-0.009467140771448612,
0.0001870859123300761,
-0.08175058662891388,
-0.02106238156557083,
-0.0019101983634755015,
0.01686757244169712,
-0.002298743464052677,
0.005717819090932608,
0.055680885910987854,
0.004650247283279896,
-0.04580942913889885,
0.01005538273602724,
-0.027005789801478386,
-0.025788825005292892,
0.01478627324104309,
-0.0053795939311385155,
0.010852258652448654,
-0.032752666622400284,
0.03688850626349449,
0.03856908529996872,
-0.07040674239397049,
0.01740364171564579,
-0.03687186911702156,
-0.046756815165281296,
0.04685499891638756,
-0.005004405044019222,
0.05024206265807152,
-0.021905362606048584,
-0.0010063272202387452,
0.01908179000020027,
-0.004411755595356226,
-0.07266286760568619,
-0.02152439020574093,
0.018266821280121803,
-0.007118283770978451,
-0.031193453818559647,
0.0015616541495546699,
0.054376132786273956,
-0.04207652434706688,
0.0212283693253994,
0.0022448264062404633,
0.0037368962075561285,
0.04445957392454147,
0.029239097610116005,
0.0059556844644248486,
0.010985909961163998,
-0.0024702914524823427,
0.011873935349285603,
0.04260023683309555,
-0.014442154206335545,
-0.0024937218986451626,
0.028111282736063004,
-0.022848397493362427,
0.022510185837745667,
0.036123424768447876,
-0.034136999398469925,
0.025194525718688965,
0.006092152092605829,
-0.0014834594912827015,
-0.007276582065969706,
0.032216086983680725,
-0.03736373409628868,
0.0033356761559844017,
0.04221051558852196,
0.041666533797979355,
0.050096020102500916,
-0.004525347147136927,
-0.026460014283657074,
0.039398591965436935,
0.049835920333862305,
0.024224966764450073,
-0.0013517688494175673,
0.01958020217716694,
0.022090358659625053,
0.013801817782223225,
-0.006268032360821962,
0.010529201477766037,
0.06026902422308922,
0.044909097254276276,
0.0029985823202878237,
0.019627049565315247,
0.01565110869705677,
-0.008643479086458683,
-0.05766356736421585,
-0.01578548550605774,
0.004997480660676956,
0.05463419109582901,
0.0021746838465332985,
0.0471048578619957,
0.0445835180580616,
-0.01889599673449993,
0.02884269505739212,
-0.004168184008449316,
-0.09312395751476288,
0.020087312906980515,
-0.01375218853354454,
-0.005898479372262955,
-0.011657224036753178,
-0.008968730457127094,
-0.06760518252849579,
-0.020651763305068016,
-0.017179202288389206,
0.042299460619688034,
0.03653867170214653,
-0.05055738613009453,
0.07781561464071274,
-0.006519646383821964,
-0.03499149531126022,
-0.014949273318052292,
0.019104700535535812,
0.019881004467606544,
0.011580770835280418,
-0.010845589451491833,
-0.012256475165486336,
-0.03319239988923073,
0.007749755866825581,
-0.035087455064058304,
0.040320102125406265,
0.012201046571135521,
0.07753146439790726,
0.03292584419250488,
0.042843129485845566,
-0.05134616047143936,
0.05024276301264763,
0.025683138519525528,
0.016867980360984802,
-0.019167205318808556,
-0.003429155331104994,
-0.059403013437986374,
-0.013955900445580482,
-0.011303992010653019,
0.03509364649653435,
0.05754396319389343,
-0.01958812214434147,
-0.028566448017954826,
-0.014067823067307472,
-0.05107008293271065,
0.007751007564365864,
0.005060951691120863,
0.06426499783992767,
-0.0386502705514431,
-0.027656536549329758,
-0.055549778044223785,
-0.014292213134467602,
-0.036166973412036896,
-0.014046764932572842,
0.028937626630067825,
0.02384234219789505,
-0.0029282623436301947,
-0.023424392566084862,
0.03532596677541733,
-0.021418824791908264,
-0.025806695222854614,
0.025165820494294167,
-0.00956774689257145,
0.01941339112818241,
0.03064153343439102,
-0.006635033991187811,
-0.0008563695009797812,
0.027107467874884605,
0.0286781694740057,
-0.004060942213982344,
-0.005858778487890959,
-0.07692689448595047,
-0.03525076434016228,
0.02964375726878643,
0.0455862320959568,
0.016468698158860207,
-0.012762336991727352,
-0.06256002932786942,
-0.005055306479334831,
0.06449971348047256,
-0.029299335554242134,
-0.001100086374208331,
-0.03048667311668396,
0.0007496468024328351,
-0.04407025873661041,
-0.0075705270282924175,
0.0008144367602653801,
-0.025410545989871025,
-0.022415710613131523,
0.024484064429998398,
-0.04482841119170189,
-0.05223766714334488,
0.0023778555914759636,
-0.0018577469745650887,
0.04645247757434845,
0.014783336780965328,
-0.0008243058109655976,
0.002351615345105529,
0.019627057015895844,
0.02335413172841072,
0.014576922170817852,
-0.061313264071941376,
-0.021676182746887207,
0.00947446096688509,
0.04536615312099457,
0.0697915181517601,
-0.03393034264445305,
0.014239851385354996,
0.03124981001019478,
0.0378287099301815,
-0.013758854940533638,
-0.035393428057432175,
-0.041277363896369934,
0.03944271057844162,
0.0012657102197408676,
-0.04076981171965599,
0.026577908545732498,
0.03297732025384903,
-0.027317795902490616,
-0.0102302310988307,
-0.029011406004428864,
0.03496477007865906,
-0.047707781195640564,
0.004115072079002857,
0.008972208015620708,
0.011709085665643215,
-0.0220112893730402,
0.03804997727274895,
-0.005557870026677847,
-0.03577921912074089,
0.020077845081686974,
-0.017643429338932037,
0.02785799279808998,
0.009308178909122944,
-0.006760290823876858,
-0.018659550696611404,
0.007852804847061634,
0.023174451664090157,
-0.01309316884726286,
-0.019652197137475014,
0.03977300971746445,
-0.004496115259826183,
0.02760203555226326,
-0.0008107290486805141,
-0.0245243851095438,
0.01243212353438139,
-0.043231602758169174,
0.014933694154024124,
0.000004703146259998903,
-0.05256836488842964,
0.02438674122095108,
-0.0083102285861969,
0.03101767599582672,
0.05626028776168823,
-0.07022354006767273,
0.00003691747770062648,
0.011144046671688557,
-0.0400523915886879,
0.009714155457913876,
-0.06699955463409424,
0.0059250881895422935,
0.02713937871158123,
0.023252686485648155,
-0.052673324942588806,
-0.050816092640161514,
0.017407327890396118,
0.009496296755969524,
-0.0035940567031502724,
-0.038509950041770935,
-0.013619285076856613,
-0.049070172011852264,
0.0021196899469941854,
-0.008805391378700733,
0.018993882462382317,
-0.03706120327115059,
0.010342280380427837,
0.017356615513563156,
0.00005820220030727796,
0.07482632249593735,
0.019561944529414177,
-0.039360325783491135,
0.016836177557706833,
-0.04219519719481468,
0.0020108064636588097,
-0.030457481741905212,
0.026332713663578033,
-0.026767820119857788,
-0.035001613199710846,
-0.004517530091106892,
-0.019260868430137634,
0.05311056226491928,
-0.012608785182237625,
-0.02227339893579483,
0.027095966041088104,
0.05556179955601692,
0.0025764985475689173,
-0.012266668491065502,
0.02716001309454441,
-0.002776702167466283,
0.016307219862937927,
-0.009454634040594101,
-0.004755727015435696,
-0.04637807235121727,
-0.013281947933137417,
-0.0017483439296483994,
-0.017067505046725273,
-0.017954489216208458,
0.008057082071900368,
0.08482129126787186,
0.00012314366176724434,
0.014161859638988972,
0.014727492816746235,
-0.03773806244134903,
-0.015931786969304085,
-0.01059824600815773,
-0.006087473127990961,
-0.014069220051169395,
0.011424233205616474,
-0.005091673228889704,
-0.0393635556101799,
-0.048261262476444244,
0.00559464655816555,
0.052027683705091476,
0.007414694409817457,
0.03799017146229744,
0.009557384997606277,
-0.0070088570937514305,
-0.014997867867350578,
0.02439298667013645,
0.01792227476835251,
0.02203432470560074,
-0.036836981773376465,
0.04961314797401428,
-0.0034827436320483685,
-0.027434999123215675,
0.00687273358926177,
0.01966158114373684,
0.03350492939352989,
0.008770939894020557,
0.04683256521821022,
0.015069430693984032,
0.03460679203271866,
-0.029640043154358864,
-0.04579679295420647,
0.0035549954045563936,
-0.0674554780125618,
0.02330935373902321,
-0.00017291450058110058,
0.02152520790696144,
0.010776981711387634,
0.022435203194618225,
-0.0019078606273978949,
-0.04701758548617363,
-0.006228066049516201,
0.00014381470100488514,
0.009792834520339966,
-0.0022167859133332968,
-0.028718197718262672,
0.0006896256818436086,
0.004448935389518738,
0.030124595388770103,
0.025621309876441956,
0.008370665833353996,
-0.01284755952656269,
-0.06987782567739487,
-0.00026248814538121223,
-0.02791501209139824,
-0.026617607101798058,
0.05581419914960861,
-0.017967673018574715,
-0.03656773641705513,
-0.002052983967587352,
-0.023434368893504143,
0.038642767816782,
0.02712344564497471,
0.03429973125457764,
-0.0010299114510416985,
0.05091632157564163,
-0.04364107921719551,
-0.012235520407557487,
0.012444674037396908,
0.01362544298171997,
0.10927984863519669,
0.04058878868818283,
-0.0013459145557135344,
-0.06572790443897247,
0.023362794890999794,
-0.048545390367507935,
-0.009796414524316788,
-0.04106500372290611,
-0.01337145920842886,
-0.015808220952749252,
-0.00034960932680405676,
0.006823267787694931,
0.06471264362335205,
-0.003058790462091565,
0.0441165529191494,
0.018856095150113106,
-0.01929429918527603,
-0.02724207006394863,
0.049217335879802704,
0.00846617016941309,
0.0006969845271669328,
0.03745352476835251,
-0.03796882927417755,
0.012722642160952091,
-0.06519581377506256,
-0.022199135273694992,
0.005461161024868488,
-0.013914749957621098,
0.06719963997602463,
0.0058810715563595295,
-0.04532372206449509,
0.0032195085659623146,
-0.03813065215945244,
-0.00692349299788475,
-0.03346305713057518,
0.01448984257876873,
0.0634729340672493,
0.024658789858222008,
-0.007025463040918112,
0.017589587718248367,
0.0456683374941349,
0.0012813664507120848,
0.012286560609936714,
0.04571254551410675,
-0.03802407160401344,
-0.010628407821059227,
-0.03176603466272354,
0.007116786669939756,
0.018329322338104248,
-0.03146623820066452,
0.003722648834809661,
0.007869346998631954,
0.0003186463436577469,
-0.0887218564748764,
-0.008241264149546623,
-0.014312135986983776,
0.02056383714079857,
-0.006556311156600714,
-0.026128068566322327,
-0.013511812314391136,
0.04142008721828461,
-0.03233518823981285,
-0.004808985628187656,
-0.008722750470042229,
0.017215624451637268,
-0.04786022752523422,
0.009857194498181343,
0.05293084681034088,
0.04405181109905243,
-0.04582412540912628,
-0.033413421362638474,
-0.02469455637037754,
-0.014943918213248253,
-0.003625382436439395,
0.03673168644309044,
0.005813752766698599,
0.02186005190014839,
0.006758497562259436,
-0.0040356176905334,
0.021982192993164062,
-0.07355345040559769,
0.01474602147936821,
-0.0191153846681118,
-0.013432526029646397,
-0.00825131218880415,
-0.026206381618976593,
0.019787520170211792,
0.02667192928493023,
-0.01655569113790989,
0.0033860178664326668,
0.0006555119762197137,
-0.010171839036047459,
0.042383719235658646,
-0.0036723187658935785,
-0.03861023858189583,
0.0015016640536487103,
-0.047553133219480515,
-0.028382472693920135,
-0.03170100972056389,
0.07728701829910278,
0.00020889744337182492,
-0.021843453869223595,
0.01546055544167757,
-0.022675300016999245,
-0.031366486102342606,
-0.013173340819776058,
0.0031608555000275373,
-0.023194728419184685,
-0.028042737394571304,
-0.010487883351743221,
-0.015718773007392883,
-0.011104538105428219,
-0.016846802085638046,
-0.04773646965622902,
-0.018592149019241333,
0.007063203491270542,
0.0062804147601127625,
0.0021210703998804092,
0.02862582355737686,
-0.005163263063877821,
0.006422373000532389,
0.001383985043503344,
-0.024084819480776787,
-0.017724638804793358,
-0.019480962306261063,
0.0032124025747179985,
-0.011149837635457516,
-0.028271546587347984,
0.03466743603348732,
-0.032847315073013306,
-0.01591579243540764,
0.012481585144996643,
0.07884455472230911,
-0.00888216495513916,
-0.00015219203487504274,
0.04112643748521805,
0.007726144976913929,
0.04666725918650627,
-0.08290953934192657,
-0.05046023055911064,
0.040900856256484985,
-0.009718694724142551,
0.0027210949920117855,
0.03632905334234238,
-0.028285028412938118,
0.02661830186843872,
0.04950813949108124,
-0.028659772127866745,
-0.012830129824578762,
0.08774799108505249,
-0.0014908545417711139,
0.059308718889951706,
0.0012224101228639483,
-0.0357036329805851,
0.03180447965860367,
0.010098026134073734,
0.011855842545628548,
-0.015504320152103901,
-0.007249791175127029,
0.022581305354833603,
0.04970141127705574,
0.04293016716837883,
0.010471316054463387,
-0.029854265972971916,
-0.02437615767121315,
0.020750287920236588,
0.02733471803367138,
-0.027857718989253044,
0.005653347820043564,
0.04174770787358284,
-0.09091442823410034,
-0.015419667586684227,
0.021701978519558907,
-0.023403402417898178,
-0.09797105193138123,
0.010336780920624733,
0.023588474839925766,
-0.01955810934305191,
0.04442958906292915,
-0.015402157790958881,
0.00753795774653554,
0.07760663330554962,
-0.07465250790119171,
-0.015024863183498383,
-0.012222695164382458,
-0.01212206482887268,
-0.054194699972867966,
-0.04563141241669655,
-0.017222587019205093,
0.04333045706152916,
0.005506311543285847,
0.05430947616696358,
0.036341916769742966,
0.036283157765865326,
-0.05689416453242302,
-0.022438950836658478,
0.026432570070028305,
0.022661220282316208,
0.009841863065958023,
0.0010039746994152665,
0.008593272417783737,
-0.03209908679127693,
-0.05451742559671402,
0.008993544615805149,
-0.03651553764939308,
0.009540681727230549,
-0.0194254070520401,
0.03347499668598175,
0.01197727955877781,
0.02405785210430622,
0.0413362942636013,
-0.016829095780849457,
0.031896691769361496,
0.04315945878624916,
0.03430784121155739,
0.011805038899183273,
0.027650216594338417,
0.02228613756597042,
0.035116046667099,
-0.007840803824365139,
0.022283943369984627,
0.025424063205718994,
-0.028898613527417183,
-0.029142161831259727,
0.021244559437036514,
-0.01355654001235962,
0.05590976029634476,
-0.022651929408311844,
0.010889084078371525,
-0.06124328449368477,
-0.004079101607203484,
0.0034160776995122433,
0.06099637225270271,
-0.013921649195253849,
-0.011763570830225945,
-0.0039191595278680325,
-0.035848453640937805,
0.0006716067437082529,
-0.027461053803563118,
-0.04073313996195793,
-0.012231499888002872,
0.026284294202923775,
0.0224711112678051,
-0.007300045341253281,
0.0017602697480469942,
-0.02398715913295746,
-0.017545495182275772,
0.04185742139816284,
-0.014208604581654072,
0.0182070042937994,
0.04846090078353882,
-0.014035718515515327,
0.003939276561141014,
-0.0030270093120634556,
0.013957805000245571,
0.011567704379558563,
-0.0002838768414221704,
0.01975756324827671,
-0.010976641438901424,
0.005095756612718105,
0.0418139323592186,
0.030040210112929344,
-0.0011368014384061098,
0.003951289225369692,
-0.004952124785631895,
-0.008119161240756512,
0.014161588624119759,
-0.05442497134208679,
0.016112837940454483,
0.003644497599452734,
-0.051887158304452896,
-0.022160639986395836,
-0.02456914633512497,
-0.029771264642477036,
-0.0007423797505907714,
0.04207821190357208,
0.010096962563693523,
-0.010033003985881805,
0.0017551013734191656,
-0.01723644882440567,
0.0338236428797245,
-0.005424955859780312,
-0.004364862106740475,
0.07686856389045715,
-0.0039952038787305355,
-0.061599526554346085,
-0.008697863668203354,
0.01145583763718605,
-0.029230263084173203,
-0.012822551652789116,
0.008117075078189373,
0.058348800987005234,
-0.009344839490950108,
-0.021819904446601868,
0.03615656495094299,
-0.02841990999877453,
-0.002892690245062113,
0.008068842813372612,
-0.026759209111332893,
-0.0051450966857373714,
0.052230045199394226,
0.021291781216859818,
-0.0002593975223135203,
0.0036886995658278465,
-0.006012891419231892,
-0.008993999101221561,
0.01721760630607605,
-0.016438132151961327,
0.06015343591570854,
-0.006627399940043688,
0.020140336826443672,
0.04501153528690338,
0.03250034525990486,
-0.04041006788611412,
-0.007854526862502098,
0.017756784334778786,
0.023327233269810677,
-0.005090455524623394,
-0.04546590521931648,
0.02707245759665966,
0.0005688556120730937,
-0.008106636814773083,
0.031469814479351044,
0.006777537055313587,
0.08174922317266464,
0.013097715564072132,
-0.005154579412192106,
-0.027524108067154884,
-0.016569558531045914,
0.034841421991586685,
0.011085957288742065,
0.0034147428814321756,
0.03440375253558159,
-0.024442151188850403,
0.014836662448942661,
0.01439540646970272,
-0.01566772162914276,
0.06839167326688766,
-0.044208817183971405,
0.03633159399032593,
-0.05094721168279648,
-0.008087052963674068,
-0.030673107132315636,
-0.023276034742593765,
-0.026822200044989586,
-0.029392564669251442,
-0.0020954450592398643,
0.042343225330114365,
-0.0024249046109616756,
0.0027632354758679867,
-0.01828833483159542,
0.005812952294945717,
0.040368735790252686,
-0.07774706929922104,
-0.000048418762162327766,
-0.01163680013269186,
-0.007557160686701536,
-0.009823818691074848,
0.013004730455577374
] |
<p>I have looked at various derivations of the Gibbs free energy equation and the underlying definition of the gibbs free energy.</p>
<p>However I have been unable to attain direct insight/intuition over the significance of entropy in the equation.</p>
<p>Specifically, lets take the case of 2 gases reacting to form a solid (the reaction, overall, releases energy as more stable bonds are formed than the ones present before the reaction). Clearly, the entropy change for the system will be negative as the solidification strips the atoms of much of their "freedom".</p>
<p>However, what does it mean (in terms of this scenario) that if the temperature were high enough, the reaction would not occur. How is it that the entropy change will determine the spontaneity of the reaction, especially at high temperatures.</p>
<p>I really am looking for a verbal answer please (rather than some mathematical derivations which often, at least to the novice (me), lack illuminative powers).</p>
<p>Thank you!</p>
| 8,836 |
[
-0.0037178120110183954,
-0.011325275525450706,
-0.007340259850025177,
0.0022994449827820063,
-0.005550539121031761,
-0.003751895623281598,
-0.04788225144147873,
0.017393790185451508,
-0.007324995938688517,
-0.04476037994027138,
0.009255402721464634,
0.020424189046025276,
0.024673953652381897,
0.013818024657666683,
0.006370569113641977,
-0.008278022520244122,
-0.012088744901120663,
-0.030100757256150246,
0.025627486407756805,
0.006675112992525101,
0.0008721963386051357,
0.011962400749325752,
-0.005202168598771095,
-0.0034395260736346245,
-0.053658876568078995,
0.0473925806581974,
0.014628646895289421,
-0.006804238073527813,
0.04151838272809982,
0.04843432828783989,
-0.012801909819245338,
-0.05149635300040245,
0.007512612733989954,
0.033522918820381165,
0.020557548850774765,
-0.009855955839157104,
-0.015375598333775997,
-0.01443698164075613,
-0.03121437318623066,
0.023972222581505775,
-0.03844946622848511,
-0.010373584926128387,
-0.012676608748733997,
0.029185369610786438,
-0.0306039210408926,
0.01750102825462818,
-0.004969227127730846,
-0.02269130013883114,
0.03617120534181595,
-0.04917615279555321,
0.020158061757683754,
0.01194113027304411,
0.0380341000854969,
0.05050201714038849,
-0.01379359420388937,
0.0138123519718647,
0.04894115775823593,
0.08391490578651428,
-0.010400359518826008,
-0.053087446838617325,
-0.03125801682472229,
-0.043831005692481995,
-0.01076545286923647,
-0.012127687223255634,
-0.034985631704330444,
0.02548336610198021,
0.02162623591721058,
-0.03513731062412262,
0.04696543514728546,
0.02926645055413246,
0.009098651818931103,
-0.0047026341781020164,
0.02741566114127636,
-0.017977790907025337,
0.017621135339140892,
-0.010624275542795658,
0.03282501921057701,
0.035490576177835464,
0.01008900348097086,
0.06871572881937027,
-0.029955321922898293,
0.009854256175458431,
0.014467049390077591,
0.03761876001954079,
-0.0043037887662649155,
-0.00998513214290142,
0.07783620804548264,
0.010815542191267014,
0.03532574325799942,
0.018951280042529106,
-0.004018139094114304,
0.018951373174786568,
0.007926645688712597,
-0.003424830036237836,
-0.029316551983356476,
0.0029351606499403715,
0.0046308524906635284,
0.04843968152999878,
0.007114760112017393,
-0.02529139816761017,
0.013388552702963352,
-0.04216792434453964,
0.039149340242147446,
0.05279320850968361,
0.0038579783868044615,
-0.012785634957253933,
-0.06617405265569687,
0.004580455832183361,
0.031729377806186676,
-0.026691187173128128,
-0.010954057797789574,
-0.010583213530480862,
0.0017222263850271702,
-0.02498195879161358,
-0.015423581935465336,
-0.02207595854997635,
-0.011734257452189922,
-0.018045874312520027,
0.0318814218044281,
0.036113981157541275,
0.030009090900421143,
-0.045395344495773315,
0.021403953433036804,
0.015582166612148285,
-0.06892599910497665,
0.02485540695488453,
0.003503144020214677,
-0.02796376869082451,
-0.0005038087838329375,
0.023966358974575996,
-0.02481432817876339,
-0.01966196671128273,
0.012998589314520359,
-0.005752353463321924,
0.01642291061580181,
-0.013327945955097675,
-0.07948359847068787,
-0.05203765630722046,
0.03868168592453003,
0.0013788866344839334,
-0.03264704346656799,
-0.08755813539028168,
0.0018007729668170214,
0.002823032671585679,
0.06630506366491318,
-0.037263691425323486,
0.02560865692794323,
-0.025445446372032166,
0.02252442017197609,
0.009284074418246746,
-0.02720760554075241,
-0.021341592073440552,
0.01139023806899786,
-0.040868498384952545,
-0.017432132735848427,
-0.057173941284418106,
0.04915841296315193,
0.04704558104276657,
0.015534128993749619,
-0.023950975388288498,
0.003986552823334932,
-0.030892157927155495,
-0.02834928035736084,
0.017885060980916023,
-0.006963153835386038,
-0.01459373626857996,
0.08613590896129608,
0.011564468964934349,
0.013439763337373734,
0.019018616527318954,
0.045773860067129135,
0.040876466780900955,
0.001772981253452599,
0.042946238070726395,
0.04703423008322716,
-0.011625821702182293,
0.00010652561468305066,
-0.016489798203110695,
0.007078471593558788,
0.006969671696424484,
-0.029955176636576653,
0.007235654164105654,
-0.023249207064509392,
-0.007128995377570391,
0.0020876768976449966,
0.027966883033514023,
0.004933402873575687,
-0.00012107375368941575,
0.0047004385851323605,
-0.04746844619512558,
-0.06927868723869324,
-0.10851258784532547,
0.05020454525947571,
0.013814792968332767,
-0.026634590700268745,
0.036227770149707794,
0.0403159074485302,
0.039061661809682846,
-0.03777896985411644,
-0.03606194257736206,
-0.019851218909025192,
0.0023438602220267057,
-0.007032585330307484,
-0.02928762137889862,
0.032321713864803314,
0.08268176019191742,
0.032560646533966064,
-0.004578993655741215,
0.050423651933670044,
-0.01649581454694271,
-0.026507241651415825,
0.012086577713489532,
-0.01653929054737091,
0.002300059422850609,
-0.0030246837995946407,
-0.07428788393735886,
-0.009633212350308895,
-0.013859091326594353,
0.010553857311606407,
0.02522164396941662,
-0.02610214799642563,
0.07888080924749374,
0.04211534187197685,
0.04144756495952606,
-0.008877365849912167,
0.059725821018218994,
0.021245010197162628,
-0.012934583239257336,
-0.028242072090506554,
-0.020337192341685295,
-0.028788292780518532,
-0.013484085910022259,
0.02432672120630741,
0.06581785529851913,
-0.04512149840593338,
-0.008728397078812122,
0.01858314499258995,
0.005930483341217041,
0.028018880635499954,
0.022161390632390976,
-0.002263931557536125,
-0.020163409411907196,
0.017250481992959976,
-0.021202385425567627,
0.02269693836569786,
0.0034959379117935896,
0.029928116127848625,
0.019936034455895424,
0.01740989275276661,
-0.02037978358566761,
-0.04078147932887077,
0.028078999370336533,
0.021028883755207062,
0.025306852534413338,
0.008107476867735386,
-0.00527856033295393,
0.011122951284050941,
-0.005588551517575979,
-0.006158463656902313,
-0.0017890901071950793,
0.024813061580061913,
0.01676756702363491,
-0.018702328205108643,
-0.011814253404736519,
0.006599211599677801,
0.019602416083216667,
-0.02265368588268757,
-0.01463242620229721,
0.008780139498412609,
-0.034067828208208084,
-0.0026507622096687555,
0.021372783929109573,
0.01082150824368,
-0.004766696598380804,
-0.011692207306623459,
0.001385956653393805,
-0.00452550919726491,
0.025949500501155853,
0.00010003554780269042,
-0.04107173532247543,
-0.013040817342698574,
-0.036394208669662476,
0.0002458924427628517,
0.023273708298802376,
-0.027125632390379906,
0.016716688871383667,
0.008738716132938862,
-0.028391297906637192,
0.027340998873114586,
-0.007104930002242327,
0.012460917234420776,
0.0017956193769350648,
-0.026759672909975052,
-0.03901088982820511,
-0.0023489906452596188,
-0.010749990120530128,
0.025002820417284966,
-0.0423579104244709,
0.006018404848873615,
0.038033343851566315,
-0.04609963297843933,
-0.03210906311869621,
0.01827230677008629,
-0.04687200114130974,
-0.042778629809617996,
-0.023494716733694077,
-0.007201806176453829,
0.028035780414938927,
-0.012651119381189346,
0.030878588557243347,
0.03738359734416008,
-0.055136583745479584,
-0.04152655228972435,
-0.04219474643468857,
-0.05962687358260155,
0.025131845846772194,
-0.0330813005566597,
0.04051918536424637,
-0.03200656175613403,
-0.0385199598968029,
0.04716683551669121,
0.02348887361586094,
-0.01660742610692978,
0.006328629795461893,
-0.0365300327539444,
-0.012635215185582638,
-0.02567601017653942,
0.037060171365737915,
0.006764134392142296,
-0.005483458749949932,
0.048902735114097595,
-0.007749281823635101,
0.0481264553964138,
0.02292170561850071,
0.005387906916439533,
-0.024273833259940147,
0.020216666162014008,
0.02463047206401825,
0.009068393148481846,
0.01973447948694229,
0.003969763871282339,
0.0003132105921395123,
0.01838446594774723,
0.006578626576811075,
0.044806692749261856,
0.05258980020880699,
-0.06824609637260437,
0.021016251295804977,
0.012645791284739971,
0.009074483998119831,
-0.09029599279165268,
0.05549406632781029,
-0.02217581681907177,
0.016409164294600487,
0.0405084453523159,
0.01328854076564312,
0.06354551762342453,
-0.01552039198577404,
-0.0035747061483561993,
0.0028218799270689487,
0.028970062732696533,
-0.008845117874443531,
-0.023128170520067215,
0.0007360500167123973,
-0.027150694280862808,
0.03178536146879196,
0.035863783210515976,
0.02159583382308483,
0.03479786962270737,
-0.005388349294662476,
0.017318179830908775,
-0.00898528192192316,
-0.03280416876077652,
-0.013707962818443775,
-0.0809161588549614,
-0.0019572714809328318,
0.017227422446012497,
0.04206957668066025,
-0.010407391004264355,
0.07587078958749771,
0.00635250611230731,
0.02086794003844261,
0.0295388363301754,
-0.01628389209508896,
-0.10286371409893036,
0.03214980661869049,
-0.03472111001610756,
-0.011783608235418797,
0.022123631089925766,
0.0019384112674742937,
0.05288923904299736,
-0.02453816682100296,
-0.02102641575038433,
-0.006062501110136509,
0.04273080825805664,
-0.07478374242782593,
-0.010302380658686161,
-0.06171635165810585,
-0.0016328302444890141,
0.0060384878888726234,
0.03154623508453369,
0.02916303463280201,
-0.017267003655433655,
0.02351364865899086,
0.0318756029009819,
-0.03304867818951607,
0.027667831629514694,
-0.0020241490565240383,
-0.008670466020703316,
0.05313635990023613,
0.01668785698711872,
0.022788075730204582,
0.016775287687778473,
0.03243348374962807,
0.04671488702297211,
0.03647656366229057,
0.05755361169576645,
-0.00870054867118597,
-0.0030034855008125305,
-0.02340765856206417,
-0.05922563374042511,
-0.03909997642040253,
0.008195578120648861,
0.04160262644290924,
-0.013094739057123661,
0.05206245183944702,
0.018342027440667152,
-0.0059160809032619,
-0.013428797014057636,
0.030565353110432625,
0.08465030044317245,
0.011208359152078629,
-0.017320385202765465,
-0.002732342341914773,
-0.027912946417927742,
-0.04060306027531624,
-0.02311709336936474,
0.04645533114671707,
0.01615576632320881,
-0.029171856120228767,
-0.01701826974749565,
-0.01563393883407116,
0.02600874751806259,
-0.01962178759276867,
-0.025502290576696396,
-0.0031502898782491684,
0.06688489019870758,
0.027911484241485596,
-0.01275116577744484,
0.008795049041509628,
0.015258057974278927,
0.011384968645870686,
-0.021248526871204376,
-0.0027307551354169846,
-0.049179162830114365,
-0.014872186817228794,
0.06490753591060638,
0.03880249708890915,
-0.0003858421405311674,
-0.002954131457954645,
-0.053123753517866135,
-0.015869511291384697,
0.043267011642456055,
-0.019245298579335213,
0.03555675223469734,
-0.007089454680681229,
0.018356667831540108,
0.02515711449086666,
-0.02227124758064747,
-0.0008540709386579692,
0.0018076663836836815,
0.035896237939596176,
0.029993055388331413,
0.002965436317026615,
-0.030949320644140244,
0.0014863634714856744,
-0.018997887149453163,
0.005835726857185364,
0.04827774316072464,
-0.018835455179214478,
-0.0025135602336376905,
0.007129570469260216,
0.0276231337338686,
0.016271429136395454,
-0.09368067979812622,
0.019141152501106262,
-0.035689178854227066,
0.008663935586810112,
0.04486630856990814,
-0.03343522921204567,
-0.061606280505657196,
0.02352496236562729,
0.013247889466583729,
-0.029197055846452713,
-0.01584732159972191,
0.004933900199830532,
0.042142316699028015,
0.056614480912685394,
-0.017634807154536247,
0.03014160692691803,
0.030663860961794853,
-0.01570957899093628,
0.012443599291145802,
-0.03539491444826126,
0.03440409153699875,
-0.04601096734404564,
0.03336743265390396,
-0.0508725680410862,
0.019911237061023712,
-0.01975865662097931,
0.025985347107052803,
-0.007914368994534016,
0.03268258646130562,
0.002620762912556529,
-0.04392069950699806,
0.022547263652086258,
0.0013272971846163273,
0.01645873486995697,
0.013372682966291904,
-0.004333190619945526,
0.029341114684939384,
-0.017031485214829445,
-0.019088825210928917,
0.014065398834645748,
-0.0014471706235781312,
-0.016089284792542458,
0.021819593384861946,
-0.02197037637233734,
0.004780483432114124,
-0.028332967311143875,
-0.04007130488753319,
-0.005536172538995743,
-0.02677054889500141,
0.0404118187725544,
-0.016099514439702034,
0.02287840098142624,
0.014909189194440842,
-0.06740209460258484,
0.009987159632146358,
0.004491264466196299,
0.008915798738598824,
0.026671016588807106,
-0.018275827169418335,
0.04596593230962753,
-0.010081164538860321,
-0.020307252183556557,
-0.09400481730699539,
-0.07966800034046173,
0.015502816066145897,
-0.005756668280810118,
-0.06398109346628189,
-0.03452187031507492,
-0.01939532160758972,
-0.03132205829024315,
-0.0234046820551157,
0.02730931155383587,
0.027272140607237816,
0.005937100853770971,
-0.001037461101077497,
0.05532015860080719,
0.03020872361958027,
0.051697246730327606,
-0.01843576692044735,
-0.039323411881923676,
0.04198726639151573,
-0.010457814671099186,
-0.027909567579627037,
0.017543483525514603,
0.03882436826825142,
-0.02416527085006237,
-0.02986174449324608,
0.027120178565382957,
-0.005485423840582371,
0.04433036968111992,
-0.027933979406952858,
-0.019713586196303368,
0.012372864410281181,
0.014935859479010105,
0.013725035823881626,
-0.01115355920046568,
0.01603979803621769,
-0.006751728244125843,
0.03022109717130661,
0.0037802287843078375,
-0.004696079064160585,
-0.012466831132769585,
-0.02878456562757492,
-0.01046754326671362,
0.009146740660071373,
0.008849941194057465,
0.022415408864617348,
0.06744223088026047,
-0.001204540953040123,
-0.01716921105980873,
0.0065754735842347145,
-0.02285659871995449,
0.05465998500585556,
0.0021649899426847696,
0.02632145956158638,
0.017364468425512314,
0.01912388950586319,
-0.054033469408750534,
-0.03394364193081856,
-0.05662986636161804,
0.006212151609361172,
0.05275134742259979,
-0.0432993620634079,
0.06267282366752625,
0.015827374532818794,
-0.005138312466442585,
0.0037753109354525805,
-0.024332856759428978,
-0.008062595501542091,
0.0349440835416317,
-0.012529331259429455,
0.007755725644528866,
0.001641842070966959,
-0.020180774852633476,
0.03410663083195686,
0.008705057203769684,
-0.019569378346204758,
0.03496731445193291,
0.020459529012441635,
0.007041684817522764,
0.0326220765709877,
-0.013045182451605797,
-0.06924281269311905,
0.04990961030125618,
-0.059112124145030975,
0.05350327491760254,
-0.03592131286859512,
-0.01617930456995964,
0.035139791667461395,
0.012127263471484184,
0.013643573969602585,
-0.08947501331567764,
-0.03508905693888664,
-0.018535783514380455,
0.0005045703146606684,
0.00659586675465107,
-0.024229710921645164,
0.03233176842331886,
-0.00020710717944893986,
0.011945671401917934,
0.0191392470151186,
-0.023511743173003197,
0.006290390156209469,
-0.053250379860401154,
0.010759486816823483,
-0.0032162778079509735,
-0.02591949887573719,
-0.008440988138318062,
0.006371577735990286,
-0.015755336731672287,
-0.018061455339193344,
-0.007030261214822531,
-0.004172160290181637,
0.011325874365866184,
0.01705450378358364,
0.010564754717051983,
0.07616019248962402,
0.003439761931076646,
0.04271761700510979,
0.007053926587104797,
0.03468697890639305,
0.09245147556066513,
0.030578622594475746,
0.018168751150369644,
-0.04428943619132042,
0.00014532655768562108,
-0.018777767196297646,
-0.020693223923444748,
0.01245244313031435,
0.03833676502108574,
0.0181598998606205,
0.014144730754196644,
0.05896500125527382,
0.0401521772146225,
-0.009797491133213043,
-0.00616294052451849,
0.049223482608795166,
-0.0614454485476017,
-0.0272257998585701,
-0.0048446343280375,
-0.012501812539994717,
-0.026154672726988792,
0.02043093368411064,
-0.01642800122499466,
0.006733754184097052,
-0.021674081683158875,
-0.008221299387514591,
-0.03549518808722496,
-0.03265432268381119,
0.026163477450609207,
0.03566689416766167,
-0.022911114618182182,
-0.0047518364153802395,
0.012386740185320377,
-0.008331818506121635,
-0.030154965817928314,
-0.0037840025033801794,
0.011823576875030994,
-0.01406874880194664,
-0.011286666616797447,
0.030132874846458435,
0.007015402894467115,
0.01602719910442829,
0.018372083082795143,
0.025620218366384506,
-0.04493706300854683,
-0.036310359835624695,
-0.029403463006019592,
0.05198698118329048,
-0.02477423846721649,
-0.024532392621040344,
-0.020805031061172485,
0.0042314426973462105,
0.0271295178681612,
-0.026367658749222755,
-0.028559738770127296,
-0.022084513679146767,
0.043941155076026917,
-0.014292318373918533,
-0.03217924013733864,
-0.01818503811955452,
0.003859241958707571,
-0.008070513606071472,
0.004419382195919752,
-0.018430979922413826,
-0.03268489986658096,
0.02036442793905735,
-0.029748445376753807,
0.011073976755142212,
-0.014204510487616062,
-0.015920748934149742,
-0.03995026648044586,
-0.0005900357500649989,
-0.029571594670414925,
-0.015976136550307274,
-0.003025227226316929,
0.014632468111813068,
0.03840455040335655,
0.007868565618991852,
-0.009515673853456974,
-0.010840064845979214,
-0.05142178386449814,
0.03512017801403999,
-0.007744321599602699,
-0.008870226331055164,
-0.027426747605204582,
0.0158894844353199,
0.014762352220714092,
0.043667055666446686,
-0.0032204806338995695,
0.00931734312325716,
0.005692559294402599,
0.0015247953124344349,
0.04288804903626442,
-0.026477623730897903,
-0.006861634086817503,
0.028975702822208405,
-0.06197420880198479,
-0.014320689253509045,
0.03816625103354454,
0.0503925085067749,
0.048366744071245193,
0.004529740195721388,
0.03125784546136856,
0.026177948340773582,
-0.004470117390155792,
0.016360390931367874,
-0.006953450385481119,
-0.000016332895029336214,
-0.03302457928657532,
0.007359102834016085,
-0.02972240187227726,
0.00457674078643322,
-0.02448819763958454,
-0.027356760576367378,
0.02983538806438446,
0.01615387573838234,
0.03959060460329056,
-0.005685218144208193,
0.010319708846509457,
-0.009252741932868958,
0.055847156792879105,
-0.02878808230161667,
-0.036404602229595184,
-0.043474335223436356,
-0.0030874672811478376,
0.055645015090703964,
0.028272930532693863,
0.0218699648976326,
0.013876339420676231,
0.024573758244514465,
-0.029339754953980446,
0.03688298165798187,
0.03301011770963669,
0.0022128932178020477,
-0.04785212501883507,
0.014863287098705769,
-0.01933358982205391,
0.06239888072013855,
-0.04952685534954071,
-0.028609314933419228,
0.027952181175351143,
-0.03128888085484505,
-0.07326821982860565,
0.00821443647146225,
-0.004809292498975992,
0.033135052770376205,
0.04362351447343826,
-0.008731349371373653,
-0.054016172885894775,
0.08141068369150162,
-0.004630289040505886,
0.00032555207144469023,
0.005825520027428865,
-0.012914537452161312,
-0.037977155297994614,
-0.010384333319962025,
-0.02331654541194439,
-0.03698882460594177,
0.013811961747705936,
0.04050289839506149,
0.05535144358873367,
-0.012805280275642872,
-0.02814648486673832,
0.022753844037652016,
-0.016052043065428734,
-0.016262926161289215,
0.03712289780378342,
-0.0010621167020872235,
0.04840163141489029,
0.05372081696987152,
0.003099688794463873,
0.03987463191151619,
0.04100661724805832,
0.012804539874196053,
-0.08049091696739197,
0.0056092520244419575,
0.025694500654935837,
-0.027516881003975868,
0.03163355588912964,
-0.04151264578104019,
0.02728482335805893,
0.03472471609711647,
-0.054243944585323334,
-0.03319410979747772,
-0.05216370150446892,
-0.057551220059394836,
-0.025126861408352852,
-0.0139043889939785,
-0.02205749973654747,
0.052245188504457474,
0.024351637810468674,
0.051223088055849075,
0.03192833811044693,
0.019319210201501846,
-0.03476598113775253,
-0.02609378471970558,
-0.0004967334098182619,
0.01899869553744793,
0.0006860651192255318,
-0.021351400762796402,
0.041095323860645294,
-0.041478950530290604,
-0.03451530635356903,
0.00517791835591197,
-0.03758041933178902,
-0.030857371166348457,
0.025140494108200073,
0.01610775850713253,
-0.011875316500663757,
0.027201270684599876,
0.010304339230060577,
-0.01476233545690775,
-0.01778372749686241,
0.03041185811161995,
0.007814139127731323,
0.009325127117335796,
-0.001953584374859929,
0.007364788092672825,
-0.006547772791236639,
-0.025398463010787964,
-0.007882997393608093,
0.03883347660303116,
-0.02571754902601242,
0.0024527108762413263,
0.014944827184081078,
0.00824510958045721,
0.029719144105911255,
-0.019975360482931137,
-0.0008547805482521653,
-0.014273758977651596,
-0.026673171669244766,
0.03755764663219452,
0.04472813382744789,
-0.016788940876722336,
-0.013913911767303944,
-0.02777072787284851,
-0.006072374992072582,
0.01637876406311989,
0.00558878667652607,
-0.013103574514389038,
-0.053241509944200516,
-0.037308380007743835,
-0.010888519696891308,
-0.023225313052535057,
-0.022530023008584976,
-0.046907585114240646,
-0.03349494934082031,
0.04943197965621948,
0.033409565687179565,
0.05171148106455803,
-0.03395180404186249,
-0.0848589688539505,
-0.023231148719787598,
-0.06335505843162537,
-0.006019181571900845,
-0.058245014399290085,
0.0051994784735143185,
-0.08104982227087021,
-0.011337081901729107,
-0.017654020339250565,
-0.02634730562567711,
0.053483158349990845,
0.0047863624058663845,
0.011426536366343498,
-0.013544646091759205,
0.02644178457558155,
0.022832877933979034,
-0.033401042222976685,
0.020546214655041695,
-0.01612382009625435,
-0.024528611451387405,
0.014858906157314777,
-0.015799807384610176,
-0.01857709139585495,
0.013970596715807915,
0.03826354816555977,
-0.06165994703769684,
0.013532020151615143,
0.012699387967586517,
-0.005406182259321213,
0.06274528801441193,
-0.004928288981318474,
-0.03839559108018875,
0.06985385715961456,
-0.03885626047849655,
0.02255902998149395,
0.04218033701181412,
0.014189201407134533,
-0.05101459473371506,
0.03023461252450943,
-0.017772691324353218,
-0.013718499802052975,
0.002846530405804515,
-0.010916228406131268,
-0.0006338542443700135,
-0.02280663140118122,
0.0072422814555466175,
0.01050719153136015,
-0.09801530838012695,
0.02021014131605625,
0.03741336613893509,
0.02110748551785946,
0.05309780687093735,
-0.03703995421528816,
-0.003136605257168412,
-0.0017398942727595568,
0.050647586584091187,
0.005169174633920193,
0.04279178008437157,
0.030073467642068863,
0.005052612163126469,
0.025311363860964775,
-0.004625190049409866,
-0.028547005727887154,
-0.008123990148305893,
0.0407598651945591,
0.031624358147382736,
-0.05741141736507416,
-0.03902091830968857,
0.006217631045728922,
-0.023215554654598236,
0.06105317920446396,
0.02209530770778656,
-0.005778132472187281,
0.06756248325109482,
0.0018400790868327022,
0.0075558749958872795,
-0.029504649341106415,
0.03020612522959709,
-0.033249564468860626,
0.00864160992205143,
0.024507615715265274,
0.055153872817754745,
0.013020111247897148,
0.012679564766585827,
0.008080437779426575,
0.014421140775084496,
0.024959243834018707,
-0.009573012590408325,
0.005619286559522152,
0.0064438884146511555,
-0.004184562247246504,
-0.03629186004400253,
0.00981693435460329,
-0.03501037135720253,
-0.020893797278404236,
0.007759958505630493,
0.06147999316453934,
0.018978150561451912,
0.04045597463846207,
-0.03940482437610626,
-0.006225786171853542,
0.027786480262875557,
-0.03506609797477722,
-0.012265091761946678,
-0.042542170733213425,
0.03120051883161068,
-0.04412280395627022,
-0.009293358772993088
] |
<p>I would like to know if a object is launched horizontally in the air at a lower speed and a higher speed, why does the higher speed keep it airborne longer. what are the forces and why does gravity suddenly take "longer"</p>
<p>And is this relevant to a pole dancer spinning around a pole? Why is it easier to stay high on the pole for longer if more momentum is used? </p>
| 8,837 |
[
-0.06623817980289459,
-0.03491688147187233,
-0.006660697981715202,
-0.004973723087459803,
0.028177186846733093,
-0.009289262816309929,
-0.008776677772402763,
-0.0216768030077219,
0.02228759229183197,
-0.02642505243420601,
0.005259327124804258,
0.07107376307249069,
0.03679654002189636,
0.014552148059010506,
0.026958448812365532,
-0.003908137790858746,
-0.007432748097926378,
0.0016742818988859653,
0.004679573234170675,
-0.020476484671235085,
-0.048829540610313416,
0.007991530001163483,
-0.001995111582800746,
0.00696000037714839,
-0.03935132548213005,
-0.01852579042315483,
0.06292994320392609,
-0.004402291961014271,
0.030870096758008003,
0.03898376226425171,
0.0009606771054677665,
0.0231376513838768,
-0.01119687408208847,
0.0048085846938192844,
0.029688512906432152,
0.012426288798451424,
-0.04090888053178787,
-0.021245945245027542,
-0.011443166993558407,
0.017181411385536194,
-0.04819032549858093,
0.0045613753609359264,
-0.03572751209139824,
0.031095167621970177,
-0.014897857792675495,
0.024788543581962585,
0.0011037569493055344,
-0.008318079635500908,
0.09513507038354874,
-0.05126110464334488,
0.06794832646846771,
-0.018383951857686043,
0.03652007877826691,
0.03729170560836792,
-0.0034392832312732935,
-0.00627162167802453,
0.07978085428476334,
0.06683817505836487,
-0.04724188148975372,
-0.0443582609295845,
-0.007605038117617369,
-0.03166802600026131,
-0.03995734453201294,
-0.022244339808821678,
-0.0028770025819540024,
0.02899315021932125,
-0.03563477471470833,
-0.02355622500181198,
0.008781836368143559,
-0.0014790468849241734,
-0.0021992530673742294,
-0.004950874485075474,
0.03867089003324509,
0.03277698531746864,
0.019675569608807564,
-0.039058469235897064,
0.03369170054793358,
0.004707658663392067,
0.05032933130860329,
0.05225388705730438,
-0.03428588807582855,
-0.008293326012790203,
0.04807004705071449,
0.00928341131657362,
0.01660434901714325,
0.013826734386384487,
0.06118791550397873,
0.004916341044008732,
-0.0003899007278960198,
0.06142032891511917,
-0.0137793542817235,
-0.0187993161380291,
0.008361415937542915,
0.00103473209310323,
-0.01703052781522274,
0.03231181204319,
0.013189981691539288,
0.044344160705804825,
0.02687739208340645,
0.01272900402545929,
-0.00024936377303674817,
-0.04872129112482071,
0.00861725676804781,
0.06814992427825928,
0.024320540949702263,
0.00583233404904604,
-0.036034971475601196,
-0.010273115709424019,
-0.05811740830540657,
0.013128665275871754,
-0.023246176540851593,
0.015507244504988194,
-0.019591867923736572,
-0.04323256015777588,
-0.02636469528079033,
0.0005491944029927254,
0.030232099816203117,
0.012154564261436462,
0.06698863208293915,
0.056949540972709656,
0.03315242752432823,
-0.01525738276541233,
0.019789664074778557,
0.014033238403499126,
-0.01851000264286995,
0.01856342703104019,
0.023211058229207993,
-0.017945479601621628,
-0.020283633843064308,
0.029996328055858612,
-0.006406179163604975,
-0.024007000029087067,
0.004929800517857075,
-0.023896999657154083,
0.041194163262844086,
0.005957454908639193,
-0.1096770167350769,
-0.018856773152947426,
0.0490773543715477,
0.011064696125686169,
-0.024100810289382935,
-0.09839920699596405,
0.0015750188613310456,
-0.0031106933020055294,
0.06368282437324524,
0.006518681067973375,
0.015110170468688011,
-0.019335122779011726,
0.010507138445973396,
0.005654859822243452,
-0.007007421460002661,
-0.0005895287613384426,
0.010496146976947784,
-0.02561468631029129,
-0.0011465132702142,
-0.06687362492084503,
-0.00839522946625948,
0.001294181915000081,
-0.013715935871005058,
-0.028727306053042412,
0.022942231968045235,
-0.01803625002503395,
0.0015592778800055385,
0.009458730928599834,
0.004061900544911623,
-0.001479271100834012,
0.04824935644865036,
0.015253273770213127,
-0.004232821986079216,
0.039217907935380936,
0.0032194501254707575,
0.025685209780931473,
-0.00918132159858942,
-0.013259037397801876,
0.03405556455254555,
-0.020827654749155045,
-0.03217869997024536,
0.007008382119238377,
0.00981825776398182,
-0.026231596246361732,
-0.03493861109018326,
-0.040054988116025925,
-0.024626703932881355,
0.012294981628656387,
-0.001072464743629098,
0.054662447422742844,
0.03438932076096535,
0.00878298282623291,
-0.011993635445833206,
-0.034687340259552,
-0.013149677775800228,
-0.08975519984960556,
0.02600216306746006,
-0.015530859120190144,
-0.010523046366870403,
0.042433857917785645,
0.008729479275643826,
0.035273194313049316,
-0.03715210035443306,
0.015486827120184898,
-0.008814280852675438,
0.02961060404777527,
-0.002577289007604122,
0.00028433435363695025,
-0.0031625821720808744,
0.06952636688947678,
0.026113536208868027,
-0.001868869992904365,
0.00937918946146965,
-0.016239089891314507,
-0.017807655036449432,
-0.0016127038979902864,
0.004814344923943281,
-0.00429191580042243,
0.01640072464942932,
0.012219746597111225,
0.05101453885436058,
-0.004368579480797052,
0.01915496587753296,
0.03107473999261856,
-0.02987619861960411,
0.08296071738004684,
0.06439828872680664,
-0.020595382899045944,
0.033030830323696136,
0.04885364696383476,
0.01321292296051979,
-0.009985915385186672,
0.02940068580210209,
-0.027714934200048447,
-0.013576220721006393,
0.009729509241878986,
-0.007386345416307449,
0.022392289713025093,
-0.011295587755739689,
-0.010031139478087425,
0.012249884195625782,
0.03900658339262009,
0.005284926854074001,
0.060333460569381714,
-0.010978701524436474,
-0.05355290323495865,
0.030552003532648087,
0.00020191929070279002,
-0.00927770510315895,
0.02365051582455635,
0.027494234964251518,
0.02250046655535698,
0.002128724940121174,
0.005165998358279467,
-0.015352975577116013,
0.03325691074132919,
0.04849863797426224,
-0.012873973697423935,
0.02045949548482895,
-0.0714050680398941,
0.033110301941633224,
-0.023574408143758774,
0.03182869032025337,
0.03357641398906708,
0.017032483592629433,
0.01605103351175785,
-0.05555480346083641,
-0.018204646185040474,
0.028579195961356163,
0.01927674561738968,
0.009197835810482502,
-0.033278003334999084,
0.035954151302576065,
-0.041054531931877136,
-0.010483983904123306,
-0.014179219491779804,
-0.03147377073764801,
-0.020582905039191246,
-0.008522541262209415,
0.012078998610377312,
0.030699338763952255,
0.044177860021591187,
0.0021230399142950773,
-0.00418787682428956,
-0.008107482455670834,
-0.05502115190029144,
-0.005174897611141205,
-0.036993253976106644,
-0.042824141681194305,
0.01315100584179163,
-0.03599093109369278,
-0.023185402154922485,
0.05218295007944107,
-0.014579965732991695,
0.01435315702110529,
0.02067496068775654,
-0.00879679899662733,
-0.02141680009663105,
-0.009008764289319515,
-0.030687058344483376,
0.01775689609348774,
-0.002330367686226964,
-0.013618229888379574,
0.0817779153585434,
-0.015116604045033455,
0.001832050271332264,
0.04083467274904251,
-0.05819382146000862,
-0.043976008892059326,
-0.011417637579143047,
0.05114473029971123,
-0.012681788764894009,
-0.019974639639258385,
-0.0196160227060318,
0.006187040824443102,
-0.012053301557898521,
0.011464189738035202,
-0.050809770822525024,
-0.0211100522428751,
-0.0011849747970700264,
-0.0024612697307020426,
0.014583559706807137,
-0.010724482126533985,
-0.028482863679528236,
0.11003950983285904,
0.023013757541775703,
-0.018922407180070877,
-0.058792658150196075,
-0.0013122371165081859,
0.00505574606359005,
-0.011866109445691109,
0.056467205286026,
0.012141156010329723,
-0.0346657820045948,
0.015413873828947544,
0.05223491042852402,
0.00878025684505701,
0.00988270714879036,
0.008181698620319366,
0.0017603861633688211,
-0.002744579454883933,
0.016269907355308533,
-0.042531341314315796,
0.013619624078273773,
0.03598581627011299,
-0.03562181815505028,
0.008284059353172779,
-0.0027663265354931355,
0.04186080023646355,
0.0037653138861060143,
-0.05365923047065735,
0.0558306910097599,
-0.030541837215423584,
-0.027351295575499535,
-0.008958596736192703,
0.04390081763267517,
-0.015267006121575832,
-0.03148004412651062,
0.010399041697382927,
0.01017211563885212,
0.03818157687783241,
-0.003210292663425207,
0.015404341742396355,
0.033805958926677704,
0.05711212754249573,
-0.08517781645059586,
-0.024734286591410637,
-0.020518973469734192,
0.013749382458627224,
0.046178076416254044,
-0.05544488504528999,
-0.012281450442969799,
0.01701468601822853,
0.011220374144613743,
0.0233090091496706,
0.037413664162158966,
-0.04495496302843094,
-0.009685665369033813,
-0.08091617375612259,
0.032463863492012024,
-0.009565831162035465,
0.04328746721148491,
-0.012166065163910389,
0.06536190956830978,
0.015017339028418064,
0.04868701100349426,
0.0007324974867515266,
-0.010713157244026661,
-0.1323772817850113,
0.04441359266638756,
-0.07043242454528809,
-0.010489104315638542,
0.0009440614376217127,
-0.0020579658448696136,
-0.008179298602044582,
-0.048771657049655914,
-0.034738607704639435,
-0.008732966147363186,
0.0055303070694208145,
-0.0506565235555172,
0.01240385603159666,
-0.033096447587013245,
-0.013442344963550568,
0.022366460412740707,
0.03247078135609627,
-0.005643383599817753,
-0.043975163251161575,
0.038993678987026215,
0.04460694268345833,
-0.025464573875069618,
-0.003513423493131995,
-0.019397085532546043,
0.012506196275353432,
0.008839163929224014,
-0.01067045982927084,
-0.008149391040205956,
0.00945564266294241,
0.01934652402997017,
0.019942011684179306,
-0.0049382662400603294,
0.04399556666612625,
0.02048872970044613,
0.014219164848327637,
-0.0312921367585659,
-0.09123453497886658,
-0.0163336843252182,
-0.00042053789366036654,
0.032608650624752045,
0.01300038117915392,
-0.0489824153482914,
0.02235414832830429,
-0.012857998721301556,
0.004880727268755436,
0.04892896115779877,
0.05645526200532913,
0.01232963614165783,
-0.007216992788016796,
-0.038629963994026184,
-0.03438544645905495,
-0.05724242702126503,
-0.005045123398303986,
0.002365218009799719,
-0.0310023445636034,
-0.03711391240358353,
-0.0008306739036925137,
0.03503783047199249,
-0.026878343895077705,
-0.0018905382603406906,
-0.004556686617434025,
-0.009040212258696556,
0.02011183835566044,
-0.023727478459477425,
0.0019351637456566095,
-0.00042368427966721356,
0.03130560740828514,
0.0570065975189209,
0.006898509804159403,
0.01065846998244524,
-0.049830514937639236,
-0.04818188026547432,
0.0355292446911335,
0.02892579697072506,
-0.05338247865438461,
0.022869599983096123,
-0.02796688862144947,
-0.014168531633913517,
0.04322773963212967,
-0.02688073366880417,
0.030393969267606735,
-0.03172242268919945,
0.027039816603064537,
-0.011355804279446602,
-0.03389605134725571,
-0.007477610372006893,
-0.0024077610578387976,
-0.005463378503918648,
0.0027470896020531654,
-0.03534131869673729,
0.025695135816931725,
0.01407313346862793,
0.02200327068567276,
0.03999001160264015,
0.006193818990141153,
0.028255315497517586,
0.019287750124931335,
0.003590123960748315,
-0.02399401366710663,
-0.06551321595907211,
-0.09136420488357544,
-0.013785077258944511,
-0.0029366679955273867,
-0.010361912660300732,
0.011820639483630657,
-0.0363580696284771,
-0.04899956285953522,
0.00706320209428668,
-0.010404392145574093,
-0.029006287455558777,
-0.0009949771920219064,
-0.02912515588104725,
-0.00796943623572588,
0.03331262990832329,
-0.003850742243230343,
-0.0014863264514133334,
0.0183879304677248,
-0.019846785813570023,
-0.018141649663448334,
0.020285477861762047,
0.041617024689912796,
-0.01527334563434124,
0.009581432677805424,
-0.044678766280412674,
-0.011124087497591972,
-0.02546612359583378,
0.08831492811441422,
0.008233866654336452,
0.00243261712603271,
-0.03933800756931305,
-0.05509582906961441,
-0.020628128200769424,
0.05107274278998375,
0.03579052910208702,
-0.027837581932544708,
0.02348008006811142,
-0.002790485741570592,
-0.00035103937261737883,
0.006686600856482983,
0.02040237747132778,
0.044733256101608276,
-0.006948492955416441,
0.008309918455779552,
0.01106923259794712,
-0.02927969954907894,
-0.020114202052354813,
-0.02525547333061695,
-0.0039804670959711075,
-0.04286257550120354,
0.060632169246673584,
-0.004711410496383905,
-0.02628973312675953,
0.020579177886247635,
-0.061240024864673615,
-0.00810633972287178,
0.01780589111149311,
-0.011542621068656445,
0.020304549485445023,
-0.03737260401248932,
0.0181387048214674,
-0.0027426863089203835,
0.017259251326322556,
-0.046670570969581604,
-0.03450528159737587,
0.04558280110359192,
0.02840934880077839,
0.0009596060262992978,
-0.01967492885887623,
0.006698135286569595,
-0.05505722388625145,
-0.01939799077808857,
0.001839950680732727,
0.028416791930794716,
-0.022443577647209167,
-0.011835796758532524,
0.04724667966365814,
-0.0015588079113513231,
0.04709978774189949,
0.011633416637778282,
-0.03593618795275688,
-0.015988092869520187,
0.010084676556289196,
-0.028922073543071747,
-0.04343557730317116,
0.059679996222257614,
-0.02267107367515564,
-0.046047478914260864,
0.021739022806286812,
0.023445410653948784,
0.017843812704086304,
-0.01351254153996706,
0.004044015426188707,
0.05796234309673309,
0.0037577359471470118,
0.018823469057679176,
-0.019217651337385178,
0.03127257153391838,
0.017079098150134087,
0.03758179023861885,
0.021053995937108994,
-0.0059533980675041676,
-0.03637217357754707,
-0.024604640901088715,
0.026272915303707123,
0.019581729546189308,
0.017957046627998352,
-0.007690215017646551,
0.06472937017679214,
-0.02740408666431904,
-0.029165176674723625,
0.005020305048674345,
-0.0026863752864301205,
0.015306787565350533,
0.022868892177939415,
-0.021733790636062622,
0.04478542134165764,
0.04792533814907074,
-0.013349306769669056,
-0.0209826473146677,
0.002439894713461399,
-0.00752774253487587,
0.051283176988363266,
-0.04666946083307266,
0.04557562991976738,
0.016433361917734146,
0.017885534092783928,
-0.019155342131853104,
-0.019579635933041573,
-0.045762982219457626,
-0.016677984967827797,
0.0041845678351819515,
0.007754880469292402,
-0.010126625187695026,
0.034452080726623535,
0.04061035066843033,
0.04412982612848282,
-0.024977101013064384,
-0.02537774108350277,
0.04318343475461006,
0.0032868883572518826,
0.03167072683572769,
0.0006306838477030396,
-0.047759100794792175,
0.030783791095018387,
-0.011300460435450077,
0.059837814420461655,
-0.028044037520885468,
0.0028350031934678555,
0.044772908091545105,
0.04143361374735832,
-0.0030725954566150904,
-0.04760902374982834,
0.0004715789691545069,
-0.04087462276220322,
-0.019562583416700363,
0.0009351689368486404,
-0.013038144446909428,
-0.005173798650503159,
0.0047857570461928844,
0.057355303317308426,
-0.0020212314557284117,
0.021443335339426994,
0.0024478589184582233,
-0.003150630509480834,
-0.05732415243983269,
-0.031381215900182724,
-0.043827321380376816,
0.028151487931609154,
0.012066202238202095,
-0.028757214546203613,
0.008201765827834606,
-0.0068538072519004345,
-0.015511752106249332,
-0.01938803680241108,
0.02921181172132492,
-0.00721344631165266,
0.0930873230099678,
-0.012628978118300438,
-0.024105623364448547,
-0.00180963019374758,
0.020736901089549065,
0.10780085623264313,
0.04594959691166878,
-0.014658289961516857,
-0.021770885214209557,
0.013823475688695908,
-0.015556298196315765,
0.011304548010230064,
-0.04782634228467941,
-0.0001077895358321257,
0.0039218878373503685,
0.02216164954006672,
0.028579989448189735,
0.040432095527648926,
-0.041779156774282455,
-0.014420011080801487,
0.05421937257051468,
-0.03617523983120918,
0.010156760923564434,
-0.026462649926543236,
0.0021969086956232786,
-0.01991824246942997,
0.008096258156001568,
-0.01915058307349682,
0.046514786779880524,
-0.023742256686091423,
-0.021990271285176277,
-0.00905317347496748,
-0.032689180225133896,
0.0034142981749027967,
-0.00883704237639904,
-0.05948507413268089,
0.02223699353635311,
0.028815485537052155,
-0.01718888431787491,
-0.08427570760250092,
0.018209747970104218,
-0.006134096533060074,
0.0021640118211507797,
0.009365611709654331,
0.048222679644823074,
0.02258525975048542,
0.031480103731155396,
0.00030687882099300623,
0.02481754869222641,
-0.046243343502283096,
0.002193208085373044,
-0.019718386232852936,
0.01994898170232773,
-0.010167974047362804,
0.027711637318134308,
0.0010817580623552203,
0.014996068552136421,
-0.007431696634739637,
-0.059573736041784286,
-0.0033329306170344353,
0.015283402055501938,
0.01610555313527584,
-0.010867496021091938,
-0.02908984012901783,
-0.0360075905919075,
0.0029156056698411703,
0.01715100184082985,
0.015974070876836777,
-0.014889081008732319,
-0.005226390901952982,
0.02450134977698326,
-0.010646244511008263,
0.03761555254459381,
-0.029940662905573845,
-0.01824921928346157,
-0.0021902183070778847,
-0.006810608319938183,
-0.03893910348415375,
0.008467240259051323,
0.03679469972848892,
0.027850419282913208,
-0.014426038600504398,
0.02644745446741581,
-0.04988043010234833,
-0.038852233439683914,
-0.00943317636847496,
0.024614766240119934,
0.03278404846787453,
-0.023273209109902382,
-0.011655199341475964,
-0.016209425404667854,
0.02577345073223114,
0.004900292493402958,
0.0019235366489738226,
0.033024583011865616,
-0.04117913171648979,
0.013643129728734493,
0.010705839842557907,
-0.032156240195035934,
-0.03723561763763428,
0.03476828336715698,
-0.020687110722064972,
-0.0010256224777549505,
-0.0006979946047067642,
0.0413951650261879,
0.007987894117832184,
0.004878251813352108,
-0.008558525703847408,
0.007979398593306541,
-0.014917584136128426,
0.01820266805589199,
0.04663985222578049,
-0.044017817825078964,
0.013357101939618587,
0.007965611293911934,
-0.00034280039835721254,
-0.047896284610033035,
-0.04253217205405235,
-0.004041824955493212,
-0.037950970232486725,
-0.010895432904362679,
0.018577352166175842,
-0.001413353020325303,
0.052274204790592194,
-0.03518027439713478,
0.030117111280560493,
-0.03060925379395485,
0.05443483218550682,
-0.08168016374111176,
0.024433664977550507,
-0.0027250514831393957,
-0.03586890920996666,
-0.005495667457580566,
0.024418290704488754,
-0.05739874020218849,
-0.014827249571681023,
-0.0021483353339135647,
0.0193179901689291,
0.004566651303321123,
-0.018645847216248512,
-0.0054531157948076725,
-0.025904998183250427,
0.044291626662015915,
-0.00047895536408759654,
-0.028294598683714867,
0.0312921367585659,
-0.04817603901028633,
-0.04062626138329506,
0.029346652328968048,
-0.017062893137335777,
0.047722313553094864,
0.03526458144187927,
-0.060271892696619034,
-0.006761153694242239,
0.043557751923799515,
0.009025377221405506,
-0.005358030553907156,
0.006074346601963043,
-0.012496291659772396,
0.0022796927951276302,
-0.013766569085419178,
0.005554871633648872,
-0.03168138489127159,
-0.007027848158031702,
0.029755014926195145,
0.014727151952683926,
-0.027823971584439278,
0.016858940944075584,
0.0009449092904105783,
-0.005250197369605303,
0.00552127230912447,
0.012690060772001743,
0.007077810354530811,
0.06669983267784119,
0.05251338705420494,
-0.020022785291075706,
0.017765402793884277,
-0.01830984838306904,
-0.009144848212599754,
-0.10916940867900848,
0.021698642522096634,
-0.015412374399602413,
0.0036718810442835093,
0.03547592833638191,
-0.03354475274682045,
-0.014453690499067307,
0.031035736203193665,
-0.06199837103486061,
0.010904086753726006,
-0.03866177424788475,
0.008182140067219734,
-0.02940952405333519,
-0.032010190188884735,
0.03787364065647125,
0.05577011778950691,
0.015978842973709106,
0.014429892413318157,
0.006257023196667433,
-0.023906566202640533,
0.0018194169970229268,
-0.020147845149040222,
0.01664130575954914,
0.023070672526955605,
-0.004092751536518335,
0.004467131569981575,
0.05820205435156822,
-0.028548598289489746,
-0.01898784004151821,
0.04353489726781845,
0.005665223114192486,
0.06156998127698898,
-0.0037588677369058132,
-0.012424911372363567,
-0.021808898076415062,
0.022839834913611412,
-0.012036524713039398,
-0.012730074115097523,
-0.02359697036445141,
0.054092902690172195,
-0.007700867485255003,
0.042089056223630905,
-0.01803707703948021,
0.023600773885846138,
0.008236291818320751,
-0.05604541301727295,
-0.017709096893668175,
0.02966506965458393,
-0.011914132162928581,
0.03117956966161728,
0.027617020532488823,
-0.006083345040678978,
0.03361920267343521,
-0.0363876074552536,
0.005507758352905512,
-0.006305390503257513,
-0.02197982184588909,
0.020321039482951164,
-0.023041075095534325,
-0.008411603979766369,
0.050871025770902634,
0.011495600454509258,
0.015688681975007057,
-0.023561829701066017,
-0.00874405913054943,
0.017644399777054787,
-0.02269566059112549,
-0.0165836401283741,
0.010275891982018948,
-0.023299433290958405,
-0.02550424635410309,
-0.0397246778011322,
0.0098223015666008,
0.024710623547434807,
0.0189081858843565,
0.007878978736698627,
-0.019026311114430428,
-0.022251809015870094,
-0.017671560868620872,
-0.07356885820627213,
0.03011040948331356,
-0.007982965558767319,
-0.032298244535923004,
-0.049860432744026184,
-0.025311393663287163,
0.02865605242550373,
0.004735552240163088,
0.03628389537334442,
-0.014012257568538189,
-0.008495187386870384,
0.04211028665304184,
-0.01096839364618063,
-0.01835339143872261,
-0.040434952825307846,
0.016948871314525604,
0.017854033038020134,
-0.04305103421211243,
0.006001220550388098,
-0.023919815197587013,
-0.005980568937957287,
0.0043926723301410675,
0.0024994302075356245,
0.0106547512114048,
0.058082614094018936,
0.0040549468249082565,
-0.011356725357472897,
0.05428975075483322,
0.04864589869976044,
-0.0007942394004203379,
0.052724048495292664,
0.003255981020629406,
-0.017083793878555298,
0.02152513712644577,
-0.025672782212495804,
-0.045496586710214615,
0.05165697634220123,
-0.025430193170905113,
0.002624501707032323,
-0.031911224126815796,
-0.030094819143414497,
-0.005615394562482834,
-0.03508856147527695,
0.02380809746682644,
0.05424067750573158,
-0.014963340945541859,
-0.001004688674584031,
0.02849498949944973,
0.06013252213597298,
0.029187990352511406,
-0.08045068383216858,
-0.005609837826341391,
0.034426286816596985,
-0.019571950659155846,
-0.005151971708983183,
0.06536778062582016,
0.024447211995720863,
0.013169362209737301,
-0.011277088895440102,
0.02774040959775448,
0.013566254638135433,
0.03133849427103996,
0.05245022475719452,
0.047168999910354614,
-0.01898776739835739,
-0.042831819504499435,
0.007805176544934511,
-0.013270806521177292,
0.00816727988421917,
0.05254657194018364,
-0.03527849540114403,
0.04466916248202324,
-0.028172077611088753,
-0.027466079220175743,
0.011975944973528385,
0.005279836244881153,
-0.004061817657202482,
0.0008520693518221378,
0.009988589212298393,
0.04549979045987129,
0.034048568457365036,
-0.00879440363496542,
-0.017776310443878174,
-0.012326521798968315,
0.010490860790014267,
0.005945988465100527,
0.030861156061291695,
0.003711832920089364,
0.010598708875477314,
0.012340286746621132,
-0.022715140134096146,
-0.06371151655912399,
-0.014707661233842373,
0.06530240923166275,
0.03400585800409317,
0.03184455633163452,
-0.005765220616012812,
-0.0008422489045187831,
-0.04521624371409416,
0.0367487333714962,
-0.06499835848808289,
-0.04197293147444725,
-0.053144145756959915,
0.02848472259938717,
0.009829161688685417,
0.02186300978064537
] |
<p>If the method for creating electrons and positrons from photons, as described in <a href="http://phys.org/news/2014-05-scientists-year-quest.html" rel="nofollow">this article</a>, were proven correct, would it be possible to use it for accelerating space ships – using only an energy source such as a nuclear fission reactor (as opposed to having to use a propellant)?</p>
| 8,838 |
[
0.015878239646553993,
-0.01225753128528595,
-0.01233594585210085,
-0.048554420471191406,
0.02466515451669693,
0.01536540873348713,
-0.06418152898550034,
-0.007373344153165817,
0.015124239027500153,
-0.060658834874629974,
0.02181992307305336,
0.05673455446958542,
0.025035936385393143,
0.0197632797062397,
-0.015481741167604923,
0.04938449710607529,
0.005057414062321186,
0.001499268924817443,
-0.03279300406575203,
-0.04145622253417969,
0.014877237379550934,
-0.025005768984556198,
-0.0123845674097538,
-0.01889338716864586,
-0.04178532212972641,
0.045260313898324966,
-0.00640759477391839,
-0.013269452378153801,
-0.0042264764197170734,
0.03337576612830162,
0.024938106536865234,
0.010720201767981052,
0.043486569076776505,
0.0009867254411801696,
0.004918267950415611,
0.027139775454998016,
-0.03626655042171478,
-0.03369894623756409,
0.013885562308132648,
-0.00280075054615736,
0.018131554126739502,
-0.018358316272497177,
0.013717737048864365,
0.05433734133839607,
-0.004748700186610222,
0.019328013062477112,
-0.02643042802810669,
-0.016255252063274384,
0.05305691808462143,
-0.07168374210596085,
0.0199111495167017,
-0.01185575220733881,
0.025240184739232063,
0.015274357981979847,
-0.0019946072716265917,
-0.01898200251162052,
0.08291391283273697,
0.08232280611991882,
0.019781339913606644,
-0.006873265374451876,
0.01308602374047041,
0.019270772114396095,
0.004298759158700705,
-0.029498692601919174,
-0.016904929652810097,
0.012458303943276405,
-0.05185386911034584,
-0.010206017643213272,
0.012728634290397167,
0.019475704059004784,
0.05746182054281235,
0.02422201819717884,
0.00694370549172163,
0.025947554036974907,
0.01608041301369667,
-0.01974966563284397,
0.058709148317575455,
-0.02271168865263462,
0.03469578176736832,
0.06342305988073349,
-0.02299540303647518,
-0.004169776104390621,
0.03523954004049301,
0.015661651268601418,
0.028939025476574898,
0.017500359565019608,
0.04931588098406792,
-0.00811046827584505,
0.04071153327822685,
-0.007601662073284388,
0.024866526946425438,
0.022268740460276604,
0.013078749179840088,
0.002644243882969022,
-0.004075388889759779,
0.035502515733242035,
-0.009267601184546947,
0.024532433599233627,
-0.003916619345545769,
0.017161808907985687,
0.04551476612687111,
0.016941186040639877,
0.008168826811015606,
0.05599775165319443,
0.008334866724908352,
-0.030359921976923943,
-0.029029887169599533,
0.02199784852564335,
-0.05141571909189224,
-0.026807038113474846,
-0.04536633566021919,
0.012276279740035534,
0.022414272651076317,
-0.017350934445858,
0.029575124382972717,
-0.023932326585054398,
-0.0037591008003801107,
-0.036794405430555344,
0.057782132178545,
0.03550374507904053,
0.02880205027759075,
0.0020823287777602673,
0.07484734058380127,
-0.03455529361963272,
-0.04533585533499718,
-0.005211347248405218,
0.010559591464698315,
-0.032016877084970474,
-0.047066692262887955,
-0.0008237095316872001,
-0.03349130600690842,
-0.056955400854349136,
0.020181933417916298,
0.006276168394833803,
0.03429026901721954,
0.02801818586885929,
-0.08929040282964706,
-0.07047344744205475,
0.00690386863425374,
-0.019193166866898537,
-0.02050681784749031,
-0.0896153599023819,
-0.00006662071245955303,
0.0397699810564518,
0.078708715736866,
-0.03677201643586159,
-0.046116895973682404,
-0.010445799678564072,
0.053269628435373306,
-0.03491871803998947,
-0.026770509779453278,
0.027182092890143394,
-0.025777079164981842,
-0.0636633038520813,
0.019642747938632965,
-0.07555113732814789,
0.016475463286042213,
0.03345268592238426,
0.013514814898371696,
-0.010609546676278114,
0.0589400976896286,
-0.029436051845550537,
0.024454554542899132,
-0.024265272542834282,
0.024405859410762787,
-0.016208237037062645,
0.08116786926984787,
0.05474281311035156,
-0.0030353404581546783,
0.023393739014863968,
-0.0024144016206264496,
0.0406649149954319,
0.007626735605299473,
0.01052941009402275,
0.028426554054021835,
-0.08370085805654526,
-0.027589406818151474,
-0.02594124712049961,
0.0317530483007431,
-0.021263761445879936,
-0.018995212391018867,
-0.029585307464003563,
-0.02616564743220806,
-0.018067942932248116,
0.040539272129535675,
0.08647232502698898,
0.01868571527302265,
0.009093518368899822,
-0.011536790989339352,
-0.030770577490329742,
-0.005414286162704229,
-0.07193557918071747,
0.021852871403098106,
0.00013441477494779974,
-0.00787165854126215,
0.009164482355117798,
-0.01911613531410694,
0.006474595051258802,
0.010445860214531422,
-0.016966218128800392,
0.002261458896100521,
0.04840361326932907,
-0.0106632886454463,
0.011861538514494896,
-0.01053115539252758,
0.05481205880641937,
0.02972984127700329,
-0.0034982075449079275,
-0.016802635043859482,
0.0005379131762310863,
-0.007844727486371994,
0.005834989249706268,
-0.034100234508514404,
0.02997678704559803,
0.015168985351920128,
0.009879030287265778,
0.02251400053501129,
-0.006015177350491285,
-0.03251254931092262,
0.04292327165603638,
0.00967708695679903,
0.0840650200843811,
0.032942261546850204,
0.011397029273211956,
0.010474875569343567,
0.020124154165387154,
0.031313881278038025,
0.03459350764751434,
0.015941448509693146,
-0.05886127054691315,
-0.05083949491381645,
0.002823299029842019,
0.04238850250840187,
-0.008739867247641087,
-0.03332885354757309,
0.05769377201795578,
0.014656046405434608,
-0.024745160713791847,
0.024220185354351997,
0.050569888204336166,
-0.049249615520238876,
0.00031851715175434947,
0.05054048076272011,
0.04141128808259964,
0.008057748898863792,
0.012894862331449986,
0.022821223363280296,
-0.023902636021375656,
-0.03749845549464226,
-0.0006125401123426855,
0.0018646745011210442,
0.011297425255179405,
0.005894778296351433,
-0.020586347207427025,
-0.033707115799188614,
-0.05339455232024193,
0.04706919565796852,
-0.01907966658473015,
0.0014925218420103192,
-0.005791766103357077,
-0.006054027937352657,
-0.000738834380172193,
0.0025422237813472748,
0.00953679159283638,
-0.021342553198337555,
-0.008474370464682579,
-0.010662108659744263,
-0.0037352193612605333,
0.03212737292051315,
-0.08871793001890182,
0.04606061056256294,
-0.025075538083910942,
0.0005788077251054347,
-0.005817404016852379,
-0.013255974277853966,
0.026592889800667763,
-0.01991533301770687,
0.029329979792237282,
-0.03780451416969299,
-0.03348928317427635,
-0.001081484486348927,
-0.037510424852371216,
-0.014468662440776825,
0.015082111582159996,
-0.04141047224402428,
0.023942705243825912,
-0.022292202338576317,
-0.036570120602846146,
0.027601996436715126,
-0.017792049795389175,
0.011243658140301704,
0.023877693340182304,
-0.01268004346638918,
-0.040894702076911926,
-0.00012797203089576215,
-0.029820673167705536,
-0.034261200577020645,
-0.007769936230033636,
0.0038654946256428957,
0.052361663430929184,
0.013941900804638863,
-0.03288247436285019,
-0.007050781045109034,
-0.03825264796614647,
-0.03402480110526085,
0.04017734155058861,
0.030633781105279922,
0.01043386198580265,
-0.03369458392262459,
0.06201235204935074,
0.026069598272442818,
-0.04100393131375313,
0.00209700595587492,
-0.06210944056510925,
-0.0336584597826004,
0.050007179379463196,
-0.015001244843006134,
0.01741458848118782,
-0.02322116680443287,
-0.04217245802283287,
0.08163253217935562,
0.01379428245127201,
-0.004683437757194042,
-0.030059384182095528,
0.002988874213770032,
-0.016046274453401566,
-0.00017630057118367404,
-0.0013117860071361065,
0.023383377119898796,
0.002310020849108696,
-0.002203788608312607,
-0.016504479572176933,
-0.021426796913146973,
0.04346461594104767,
0.014830836094915867,
0.008651841431856155,
-0.005479686893522739,
0.034416887909173965,
0.01688992790877819,
0.018370093777775764,
0.015927931293845177,
-0.040936969220638275,
0.024412045255303383,
0.01899203471839428,
-0.0031250272877514362,
-0.004690950270742178,
-0.04372425377368927,
0.04044211655855179,
0.026010720059275627,
0.013295616954565048,
-0.0054471055045723915,
0.019855545833706856,
0.010949515737593174,
-0.005979231558740139,
0.0027511680964380503,
0.04572360962629318,
0.005528336390852928,
-0.0033939352724701166,
-0.011779907159507275,
0.003424235386773944,
0.052541691809892654,
0.011171632446348667,
-0.0427994430065155,
0.01715521514415741,
-0.00926266424357891,
-0.0123472074046731,
0.007976707071065903,
0.011055069975554943,
0.05838962644338608,
0.019474944099783897,
0.028166502714157104,
0.031910501420497894,
0.010930371470749378,
0.0009625257225707173,
-0.0411025807261467,
0.023042533546686172,
-0.049316029995679855,
0.07445584237575531,
0.04212528467178345,
0.03592674806714058,
-0.0007903427467681468,
0.015525572933256626,
-0.004336055833846331,
0.0036638742312788963,
-0.09262280911207199,
-0.01604549214243889,
-0.023281661793589592,
-0.020704982802271843,
-0.003867443883791566,
-0.0246135126799345,
-0.08414044231176376,
-0.027939634397625923,
-0.04650210961699486,
-0.026248468086123466,
-0.03262623772025108,
-0.042606476694345474,
0.03670267388224602,
-0.03126079961657524,
-0.04782317206263542,
-0.0054791695438325405,
-0.005911415908485651,
0.05145488679409027,
-0.027526818215847015,
-0.012265864759683609,
-0.0029081380926072598,
-0.030872970819473267,
-0.010267375968396664,
-0.00027663930086418986,
0.009960751980543137,
-0.011135987006127834,
0.05592338368296623,
0.02099657617509365,
0.0481681302189827,
-0.037146199494600296,
0.0004404457868076861,
0.028269685804843903,
0.005950350314378738,
-0.011516219936311245,
-0.02972702495753765,
-0.07373286038637161,
-0.01006048358976841,
-0.004822288639843464,
0.03130236640572548,
0.03903919830918312,
0.0027457524556666613,
0.014867439866065979,
-0.007202791050076485,
0.02102769911289215,
-0.01102441269904375,
0.014586567878723145,
0.055915314704179764,
0.0024157133884727955,
0.01042097993195057,
-0.02178526110947132,
-0.005732514895498753,
-0.005009467247873545,
-0.03617215156555176,
-0.008727526292204857,
0.013005239889025688,
-0.04051416367292404,
-0.002277255291119218,
0.02255692332983017,
-0.000669530127197504,
-0.05825769156217575,
0.026327231898903847,
-0.02941594272851944,
-0.00808516051620245,
0.017743537202477455,
0.03669795021414757,
-0.008088909089565277,
0.002744413446635008,
0.050542064011096954,
-0.008761987090110779,
0.0031550624407827854,
-0.07084284722805023,
0.005562501028180122,
0.020914895460009575,
0.04760065674781799,
-0.016705436632037163,
-0.018960105255246162,
-0.04501297324895859,
0.0026337229646742344,
0.06155947595834732,
0.0027312461752444506,
0.05860498920083046,
-0.015117650851607323,
0.015985488891601562,
0.0007482000510208309,
-0.02360312081873417,
-0.013992791064083576,
0.0364934578537941,
-0.0061838277615606785,
-0.009503615088760853,
-0.02805727906525135,
-0.00046142665087245405,
0.0427587516605854,
0.02794976346194744,
0.03791792690753937,
0.0651492178440094,
-0.007642269600182772,
-0.003489844035357237,
-0.024819863960146904,
-0.0025076763704419136,
-0.0034980846103280783,
-0.07980455458164215,
-0.01166710164397955,
0.011601943522691727,
-0.0506170429289341,
0.05288005247712135,
-0.05555889382958412,
-0.05880621075630188,
0.001909476239234209,
0.0051954807713627815,
0.013645769096910954,
-0.058870624750852585,
-0.05455693230032921,
0.009297868236899376,
0.030548695474863052,
-0.005312922410666943,
0.044352903962135315,
0.08369210362434387,
-0.08373945951461792,
0.003410845762118697,
-0.06031771004199982,
-0.0086201848462224,
-0.04152305796742439,
-0.013886112719774246,
0.012768016196787357,
0.013838822022080421,
-0.025787845253944397,
0.02360430918633938,
-0.011262061074376106,
-0.01094807218760252,
0.01769096776843071,
0.0008580178837291896,
-0.008823537267744541,
-0.004791321698576212,
-0.025573046877980232,
-0.02386668510735035,
-0.07955091446638107,
0.016402073204517365,
0.003467594739049673,
-0.035367656499147415,
0.0139114735648036,
0.004039940889924765,
0.03398379683494568,
0.008769281208515167,
-0.018509017303586006,
0.015923932194709778,
-0.008384449407458305,
0.014086009003221989,
0.05318662151694298,
-0.023034367710351944,
0.07020639628171921,
-0.013346143998205662,
-0.021428454667329788,
0.020466096699237823,
-0.028321070596575737,
-0.020316079258918762,
0.012899450026452541,
-0.0040956707671284676,
0.029374826699495316,
-0.018735062330961227,
0.04010463133454323,
0.005613552872091532,
0.02496526762843132,
-0.07617609947919846,
-0.04747157171368599,
0.0029970547184348106,
-0.01809864491224289,
-0.0023724923375993967,
-0.047257114201784134,
-0.017294112592935562,
-0.05393718555569649,
-0.01625082641839981,
-0.011185229755938053,
0.0775974690914154,
-0.043789781630039215,
-0.05244644358754158,
-0.026319606229662895,
-0.01647263765335083,
0.0318274199962616,
0.009096873924136162,
-0.061388950794935226,
0.015835192054510117,
-0.023977234959602356,
0.03872302919626236,
-0.052016548812389374,
0.05857095122337341,
-0.00488396966829896,
-0.06867588311433792,
-0.02461666241288185,
0.005782990250736475,
0.016758538782596588,
-0.016717659309506416,
0.001144637819379568,
0.09959174692630768,
0.023985791951417923,
-0.012103703804314137,
0.0018779827514663339,
0.03176230564713478,
0.00030584275373257697,
0.019807778298854828,
0.01460643857717514,
-0.012358629144728184,
-0.03197295218706131,
0.00212081428617239,
0.05114884674549103,
-0.010183141566812992,
0.013527698814868927,
0.007392832078039646,
0.06702912598848343,
-0.012840415351092815,
-0.013546419329941273,
0.010580101050436497,
0.005316799506545067,
0.019308706745505333,
-0.03008262999355793,
0.02718479558825493,
-0.01025026012212038,
-0.02425490692257881,
-0.028367668390274048,
-0.04992310330271721,
-0.024883829057216644,
-0.02184385620057583,
0.07306166738271713,
-0.0348641611635685,
0.020684080198407173,
-0.008328299038112164,
0.006044298876076937,
0.01216182205826044,
0.001952173886820674,
-0.006599361076951027,
-0.008665953762829304,
-0.03176921606063843,
0.027750805020332336,
-0.025352098047733307,
-0.034549400210380554,
0.026049690321087837,
0.03051096759736538,
-0.0067680031061172485,
0.04446348547935486,
-0.008197369053959846,
0.019721945747733116,
0.006867587566375732,
-0.0004548154247459024,
-0.037496406584978104,
0.018353629857301712,
-0.0632297545671463,
0.023984597995877266,
0.017660461366176605,
0.01359817385673523,
0.019717015326023102,
-0.015163923613727093,
-0.022359594702720642,
-0.02263353019952774,
0.005606347229331732,
-0.04108443856239319,
0.04054239019751549,
0.007728972006589174,
-0.0005183376488275826,
-0.02871621586382389,
0.012591340579092503,
0.01413201354444027,
0.03284069523215294,
0.01690508984029293,
0.004655147902667522,
-0.04498720169067383,
-0.011378966271877289,
-0.04586150497198105,
-0.026466911658644676,
0.040660303086042404,
0.016810083761811256,
-0.018733197823166847,
0.0029971825424581766,
0.006342821754515171,
0.032022830098867416,
0.03729905188083649,
0.06818681955337524,
-0.029765494167804718,
0.03488532453775406,
-0.046630311757326126,
0.022076917812228203,
-0.037183985114097595,
0.04945007339119911,
0.11741329729557037,
0.04799379035830498,
-0.007018478121608496,
-0.040598589926958084,
0.02490844950079918,
-0.05194741487503052,
-0.01030297763645649,
0.0012323128757998347,
0.02437213622033596,
-0.002735265763476491,
-0.00780385872349143,
-0.0499323308467865,
0.05474380776286125,
-0.025993280112743378,
0.0337127186357975,
0.0169890858232975,
-0.03467971459031105,
-0.03985291346907616,
0.04896833747625351,
0.0036120221484452486,
0.029124142602086067,
0.0021315047051757574,
-0.002140369964763522,
0.010630162432789803,
-0.03015170991420746,
0.0029867496341466904,
-0.0036000998225063086,
-0.020703522488474846,
0.03714340925216675,
0.021844783797860146,
-0.03524074703454971,
-0.01331003475934267,
0.025404635816812515,
-0.014201444573700428,
-0.008577059023082256,
0.010329990647733212,
-0.023183267563581467,
-0.0011561342980712652,
0.016519082710146904,
0.011826368980109692,
0.041787706315517426,
-0.00019889319082722068,
-0.01759166643023491,
0.032139040529727936,
-0.045648712664842606,
0.043214425444602966,
-0.018045872449874878,
0.017601706087589264,
-0.025226159021258354,
0.002368330489844084,
-0.021391144022345543,
0.0019227226730436087,
0.0064737130887806416,
-0.031990934163331985,
-0.04456328600645065,
-0.0009422667790204287,
0.007699378300458193,
0.011229299940168858,
-0.02005813829600811,
-0.00609090831130743,
-0.009648628532886505,
-0.0006101097096689045,
0.043712276965379715,
0.02754833735525608,
0.009581762365996838,
0.014063172973692417,
-0.013975718058645725,
0.03134439140558243,
-0.018306611105799675,
-0.049811214208602905,
-0.07742980867624283,
0.0024283421225845814,
-0.042590755969285965,
-0.02089657261967659,
0.031011609360575676,
0.040944647043943405,
0.014260509051382542,
0.0244078878313303,
0.0004170079482719302,
-0.02183886244893074,
-0.06456421315670013,
0.06230057775974274,
0.003878599964082241,
-0.046323828399181366,
-0.014392917975783348,
-0.000007797235411999281,
0.008464370854198933,
0.05411389470100403,
-0.04975081980228424,
-0.004930784925818443,
0.016603298485279083,
0.030756734311580658,
0.00977319572120905,
-0.0050477636978030205,
-0.004162176046520472,
-0.015844527631998062,
0.015156214125454426,
0.002959301695227623,
-0.029245613142848015,
0.04348163679242134,
0.029056211933493614,
-0.0016426192596554756,
0.011408574879169464,
0.006798276212066412,
-0.0360877588391304,
0.004075947217643261,
0.03687143698334694,
0.008497829549014568,
-0.010527543723583221,
-0.003283948404714465,
-0.0016745282337069511,
-0.024035105481743813,
-0.00027231915737502277,
-0.025000276044011116,
-0.012391075491905212,
0.007626167498528957,
0.0005590676446445286,
-0.0015321237733587623,
0.002150482963770628,
-0.009783467277884483,
0.023919183760881424,
-0.02116154506802559,
-0.0012081179302185774,
-0.029424410313367844,
0.030583182349801064,
-0.03806842491030693,
-0.014956708997488022,
-0.03318047150969505,
0.044671837240457535,
0.01157408393919468,
0.012144823558628559,
0.053728990256786346,
0.02836441434919834,
-0.044146258383989334,
-0.005138793028891087,
0.013657708652317524,
0.026656411588191986,
0.020818142220377922,
-0.027011629194021225,
-0.018262464553117752,
0.013982981443405151,
-0.0554627925157547,
-0.04803067818284035,
0.02293701469898224,
-0.02383243665099144,
0.03215142711997032,
0.015215582214295864,
-0.005967931821942329,
0.0016830674139782786,
0.07379727810621262,
-0.02919282391667366,
-0.0030009534675627947,
0.018655166029930115,
0.00873483158648014,
-0.0028109566774219275,
-0.010540389455854893,
-0.0014524584403261542,
0.004982260521501303,
-0.04341687634587288,
0.025516854599118233,
-0.0005380166694521904,
0.0062683648429811,
0.02960086241364479,
-0.03192148357629776,
-0.01318641472607851,
-0.004580358508974314,
-0.001903511118143797,
-0.010359084233641624,
0.00026768684620037675,
0.03947558254003525,
-0.009352966211736202,
-0.013762122020125389,
0.003852661931887269,
-0.036807168275117874,
-0.09874886274337769,
-0.01786026544868946,
-0.007026458624750376,
-0.02368861809372902,
0.004120787605643272,
-0.019620392471551895,
0.050661809742450714,
0.027533359825611115,
-0.05787697434425354,
0.026362378150224686,
-0.025250542908906937,
-0.02637632004916668,
-0.046712134033441544,
-0.011805684305727482,
-0.04009705036878586,
0.02795334719121456,
0.019790001213550568,
0.0663025975227356,
0.0003834073431789875,
0.007546213921159506,
0.005343735683709383,
-0.02118055149912834,
0.004442058503627777,
0.008223041892051697,
-0.02806685119867325,
-0.008944755420088768,
0.06440529227256775,
-0.04479920119047165,
-0.0033032631035894156,
0.02459573745727539,
0.030675381422042847,
0.02317221648991108,
-0.02293091081082821,
0.027801506221294403,
0.0016550440341234207,
0.029417341575026512,
0.024203555658459663,
-0.011841378174722195,
0.007751439698040485,
0.015853775665163994,
0.014669769443571568,
0.031633440405130386,
-0.005449783988296986,
0.017853735014796257,
0.04396604746580124,
-0.0003164081717841327,
0.000068163666583132,
0.06583867967128754,
0.02254651114344597,
-0.03067522868514061,
0.011753770522773266,
0.02354837767779827,
-0.016441036015748978,
-0.011053699068725109,
-0.016767727211117744,
-0.08762297034263611,
-0.004485293757170439,
-0.023489510640501976,
-0.01770865172147751,
0.01183999516069889,
0.02124786376953125,
-0.028219902887940407,
-0.011537149548530579,
0.01590901054441929,
-0.0040551587007939816,
0.0004884738009423018,
-0.009331673383712769,
0.022408021613955498,
0.048631735146045685,
0.010163486935198307,
-0.008095474913716316,
-0.025458771735429764,
-0.015168807469308376,
0.06274261325597763,
0.014121092855930328,
0.04563739523291588,
0.01870817504823208,
-0.012659937143325806,
-0.002932339208200574,
-0.03913196548819542,
0.03225044533610344,
-0.001353012747131288,
-0.04396423324942589,
-0.005506508052349091,
-0.018300842493772507,
0.01627085544168949,
0.01318100281059742,
0.02913804166018963,
-0.036399517208337784,
-0.027494948357343674,
0.022853676229715347,
-0.020310891792178154,
-0.014521983452141285,
-0.04819449782371521,
0.00031498807948082685,
0.0064570303075015545,
-0.02280772477388382,
-0.041503991931676865,
0.0062234471552073956,
-0.08479250967502594,
0.023594746366143227,
0.007289791014045477,
-0.0064606391824781895,
-0.0019156137714162469,
0.03371346369385719,
-0.017103714868426323,
0.05804150179028511,
0.008574665524065495,
-0.014531610533595085,
0.03798605129122734,
-0.015723885968327522,
0.036292023956775665,
-0.0031484661158174276,
-0.0020986103918403387,
-0.022177843376994133,
0.025199662894010544,
-0.04343651980161667,
0.005459423642605543,
-0.020383033901453018,
-0.025430159643292427,
0.021703634411096573,
-0.008281026966869831,
0.036373354494571686,
0.07975336164236069,
-0.03387409821152687,
0.03312261402606964,
0.02860698662698269,
0.013805976137518883,
0.0018419461557641625,
0.002281145891174674,
0.04452117905020714,
0.018595587462186813,
-0.02294991910457611,
-0.05047200620174408,
0.033713895827531815,
0.007415985222905874,
0.011768611147999763,
0.03624765947461128,
0.04124683514237404,
0.007884678430855274,
0.005586125422269106,
0.04756008833646774,
0.013852798379957676,
0.00019014431745745242,
0.013606401160359383,
0.022176558151841164,
-0.0005298929754644632,
-0.01552572101354599,
0.030010003596544266,
-0.009728454053401947,
0.09055670350790024,
0.004818866960704327,
0.02747040055692196,
0.009085621684789658,
-0.02066461741924286,
-0.005401369649916887,
0.030088333413004875,
-0.017742816358804703,
0.060813434422016144,
0.005874646361917257,
-0.03214704245328903,
-0.006478389725089073,
0.0059356894344091415,
0.04575007036328316,
-0.03597671166062355,
0.03810190036892891,
-0.016396906226873398,
-0.0029865209944546223,
-0.012057366780936718,
-0.03614645451307297,
0.0173511803150177,
-0.04681567847728729,
0.009623403660953045,
0.011631499975919724,
0.015034282580018044,
-0.017586499452590942,
-0.012509865686297417,
-0.017630470916628838,
0.0491994209587574,
-0.030939536169171333,
0.016623465344309807,
0.01779966615140438,
-0.0008492127526551485,
-0.01951722614467144,
0.007470111828297377
] |
<p>This should be a very basic question. In introductory QFT books, often one of the first things we see is the following claim: for every Lorentz transformation $\Lambda$, we can associate an unitary operator $U(\Lambda)$ such that:
$$ U(\Lambda)^{-1} \varphi(x) U(\Lambda)= \varphi(\Lambda^{-1}x)$$
And we also demand it to be a homomorphism, $U(A)U(B)=U(AB)$.</p>
<p>Where of course, $\varphi$ is an operator-valued quantum field. </p>
<p>I want to know what guarantees the existence of mappings $U$ which satisfy these conditions.</p>
<p>It seems like it ought be possible to choose an operator field $\varphi$ such that no such set of operators $U(\Lambda)$ exist. Is the existence of $U$ given by some requirement on quantum fields, or am I missing something else?</p>
| 8,839 |
[
0.004904468543827534,
-0.006742678117007017,
-0.0033664549700915813,
-0.021180542185902596,
0.01495856512337923,
-0.0015834535006433725,
-0.03951840102672577,
-0.041731953620910645,
0.0020066711585968733,
-0.02565138414502144,
0.014179573394358158,
-0.0005433332407847047,
0.08079738914966583,
-0.026837216690182686,
-0.012049744836986065,
0.009650991298258305,
-0.020911823958158493,
-0.033070940524339676,
-0.06327872723340988,
-0.000478405476314947,
0.017147837206721306,
0.04734860733151436,
0.008126801811158657,
0.007181598339229822,
0.020979641005396843,
0.0007897299947217107,
-0.00282151997089386,
0.04394257813692093,
0.0003674554463941604,
0.08395197242498398,
-0.02708396315574646,
-0.050229184329509735,
-0.003420280758291483,
0.03779881075024605,
0.02327422797679901,
0.020477039739489555,
-0.04553283751010895,
-0.0495450422167778,
0.0008544836891815066,
-0.020877398550510406,
-0.056269463151693344,
-0.05110793560743332,
0.005267143715173006,
0.05379917472600937,
0.004910451825708151,
0.01067742332816124,
0.006532120052725077,
-0.0003670270671136677,
0.048463404178619385,
-0.032796572893857956,
0.03907142952084541,
0.0443275086581707,
0.02434355765581131,
0.019954923540353775,
0.0030252961441874504,
-0.042493611574172974,
0.0864516943693161,
0.043279990553855896,
-0.00237929611466825,
-0.04199272766709328,
-0.04442991316318512,
-0.0032289137598127127,
0.001032192725688219,
-0.007892255671322346,
-0.030547523871064186,
0.01981515623629093,
-0.023870980367064476,
0.024441713467240334,
0.025014404207468033,
-0.03995974734425545,
0.013730491511523724,
-0.028751641511917114,
0.033413466066122055,
-0.038637738674879074,
0.014908121898770332,
-0.01315619982779026,
0.0010414088610559702,
0.019501665607094765,
0.04987093806266785,
0.026244433596730232,
-0.012624074704945087,
0.02547202818095684,
0.00808370765298605,
0.0024721540976315737,
0.00561675475910306,
-0.01392090693116188,
0.05652811750769615,
-0.004604890942573547,
0.00003206908149877563,
0.020334850996732712,
-0.017747536301612854,
-0.00876186229288578,
0.01354179810732603,
-0.03114713914692402,
-0.02528488263487816,
0.011550839990377426,
0.005828255787491798,
0.012256866320967674,
0.0000895343764568679,
-0.02517487108707428,
-0.022584974765777588,
-0.024964213371276855,
0.01328948512673378,
0.04654376208782196,
0.008510330691933632,
0.003955581691116095,
-0.020383695140480995,
0.047035619616508484,
-0.04494096711277962,
-0.006898658815771341,
-0.041450172662734985,
0.0136207714676857,
-0.03533945977687836,
0.030541108921170235,
0.00502775190398097,
-0.04969559982419014,
0.006698775105178356,
-0.03194194287061691,
0.04859282076358795,
0.09357369691133499,
0.08276587724685669,
-0.02608003281056881,
0.023605765774846077,
-0.012524459511041641,
-0.0637253150343895,
-0.015437709167599678,
0.034596845507621765,
0.017749613150954247,
-0.047032155096530914,
-0.008253680542111397,
-0.0008283708011731505,
-0.02003999799489975,
0.012459922581911087,
0.04728490486741066,
0.03907739371061325,
-0.04346465319395065,
-0.14614154398441315,
-0.06208658963441849,
0.01350227277725935,
0.001879625371657312,
-0.006853313650935888,
-0.07800470292568207,
0.015151054598391056,
0.029727449640631676,
0.0823623538017273,
-0.03877854719758034,
0.011998931877315044,
0.02062145434319973,
0.024147745221853256,
0.028634170070290565,
0.03581789880990982,
-0.007033758331090212,
-0.026524201035499573,
-0.054804593324661255,
0.009382394142448902,
-0.018578607589006424,
0.01026392262428999,
0.02525204047560692,
0.00017964575090445578,
-0.010178814642131329,
0.056981757283210754,
-0.0043156747706234455,
0.018421195447444916,
0.0010673603974282742,
-0.004631190560758114,
-0.01177905686199665,
0.04822678491473198,
0.02809496596455574,
0.02260044775903225,
0.036705952137708664,
-0.030639059841632843,
0.009313869290053844,
0.036392372101545334,
0.04809000715613365,
0.03245006129145622,
-0.0498523935675621,
-0.04139973595738411,
-0.01953607238829136,
0.01648039184510708,
-0.006508603226393461,
-0.017490170896053314,
0.0003728395968209952,
-0.04624375328421593,
-0.0032307656947523355,
-0.024790503084659576,
0.01836972124874592,
-0.006894359830766916,
0.010967962443828583,
0.028530647978186607,
-0.07808580249547958,
0.015215895138680935,
-0.03177771344780922,
0.02056313306093216,
0.043351881206035614,
-0.020527319982647896,
0.06557492911815643,
0.021819468587636948,
0.0023111747577786446,
-0.03800816088914871,
-0.06961294263601303,
-0.011921575292944908,
0.02425464242696762,
0.02307339385151863,
-0.004358226899057627,
0.027948474511504173,
0.018853049725294113,
0.06639555096626282,
0.006593194790184498,
0.046671539545059204,
-0.013623344711959362,
-0.02186606079339981,
-0.00024498015409335494,
-0.009060179814696312,
-0.006362293381243944,
-0.051450278609991074,
-0.00618014158681035,
-0.003983460832387209,
-0.02423383668065071,
-0.030453486368060112,
0.011987804435193539,
-0.059068698436021805,
0.052746593952178955,
0.012868212535977364,
-0.022095564752817154,
0.02061288058757782,
0.05924420431256294,
0.0328071154654026,
0.020911389961838722,
-0.013324446976184845,
-0.061263274401426315,
-0.0378803089261055,
0.016965946182608604,
0.0510961152613163,
0.030052650719881058,
-0.042016223073005676,
0.036681581288576126,
-0.00036440076655708253,
0.064203180372715,
0.014652511104941368,
0.040161047130823135,
-0.04242092743515968,
-0.04383142665028572,
0.024052338674664497,
0.00549317616969347,
0.0309981070458889,
0.00626232847571373,
0.009706640616059303,
-0.01493067666888237,
0.005716528743505478,
0.00157251232303679,
-0.03134731203317642,
0.052280232310295105,
-0.047474998980760574,
-0.0038456458132714033,
-0.007991418242454529,
-0.009150899015367031,
0.01460783090442419,
-0.012390528805553913,
0.035071276128292084,
-0.006845179945230484,
-0.007717160973697901,
-0.014887755736708641,
0.0008096921956166625,
-0.009044875390827656,
0.027880728244781494,
-0.018429039046168327,
-0.04261710122227669,
-0.013710669241845608,
0.018304210156202316,
-0.04793898016214371,
-0.02377677895128727,
-0.022842565551400185,
-0.0004448656691238284,
-0.0018372538033872843,
-0.009498012252151966,
0.055894020944833755,
0.006669077556580305,
0.015576119534671307,
-0.048446714878082275,
-0.015419913455843925,
0.006346835754811764,
-0.011200672015547752,
0.03604905679821968,
0.02710213139653206,
-0.03249907121062279,
0.01899385079741478,
-0.07118229568004608,
-0.025355510413646698,
0.048020824790000916,
-0.022969746962189674,
0.03155234828591347,
-0.02970792166888714,
-0.020446304231882095,
-0.04503874108195305,
-0.010954932309687138,
-0.05094593018293381,
-0.013196337036788464,
-0.009016325697302818,
-0.0044646235182881355,
0.048893459141254425,
0.0026014361064881086,
-0.022501282393932343,
0.012575875036418438,
0.0029826390091329813,
-0.030209019780158997,
0.0012115733698010445,
0.018016746267676353,
0.04389112442731857,
-0.04349517822265625,
0.04844573512673378,
-0.007291377987712622,
-0.031896308064460754,
-0.008182184770703316,
-0.04317476227879524,
-0.029864508658647537,
-0.0030163382180035114,
0.03243955597281456,
0.031129678711295128,
0.018278613686561584,
-0.02390599437057972,
0.07417583465576172,
0.03401621803641319,
-0.07237589359283447,
-0.039143964648246765,
0.010360436514019966,
0.027167528867721558,
-0.03658955171704292,
-0.022183788940310478,
0.009267253801226616,
-0.04149504750967026,
0.0798894390463829,
0.014410443603992462,
-0.0059517063200473785,
0.03368683531880379,
0.03341105952858925,
-0.04762051999568939,
0.04220329970121384,
0.026363899931311607,
0.03161873295903206,
0.04398141801357269,
-0.010737783275544643,
-0.008140281774103642,
-0.014969796873629093,
0.01592574454843998,
-0.019307345151901245,
-0.007816435769200325,
-0.01712162047624588,
0.06213003769516945,
0.02766832895576954,
0.016089731827378273,
-0.03262125700712204,
0.030752211809158325,
-0.023896008729934692,
-0.019121652469038963,
-0.005016937851905823,
0.016093352809548378,
0.006296491250395775,
-0.013568637892603874,
0.029742205515503883,
0.009372653439640999,
0.015405828133225441,
-0.05965176969766617,
0.012260960415005684,
-0.030778614804148674,
-0.025420265272259712,
0.025901753455400467,
-0.0278191938996315,
-0.025276772677898407,
0.027364669367671013,
0.057053253054618835,
0.036744628101587296,
-0.013972818851470947,
-0.03942948952317238,
-0.00535508943721652,
-0.0005368257407099009,
-0.019327089190483093,
-0.009147911332547665,
0.04852108657360077,
0.009416893124580383,
0.03629027679562569,
0.04148436337709427,
0.01249444205313921,
-0.01966828852891922,
-0.008279585279524326,
-0.07039730250835419,
0.01478083897382021,
-0.008074171841144562,
0.003954376094043255,
-0.00062992685707286,
-0.025002285838127136,
0.021215593442320824,
0.004588640294969082,
-0.0449678972363472,
-0.01298178918659687,
-0.020792800933122635,
-0.04428631439805031,
0.018534889444708824,
-0.02126014605164528,
-0.047643475234508514,
-0.02222076803445816,
0.0011215023696422577,
0.04235415905714035,
-0.0329684354364872,
0.011355884373188019,
-0.01534871757030487,
-0.036881472915410995,
-0.004608446266502142,
-0.0019091926515102386,
0.021373266354203224,
-0.007859920151531696,
0.019049381837248802,
0.01798751763999462,
0.03229079768061638,
-0.04260776564478874,
0.001722700777463615,
0.03408743813633919,
0.04807308316230774,
0.008379150182008743,
-0.013550401665270329,
-0.013333199545741081,
-0.032813768833875656,
-0.027740713208913803,
0.03286367282271385,
0.10027546435594559,
0.011667093262076378,
0.013567405752837658,
0.029822729527950287,
0.04172911122441292,
-0.03851580619812012,
-0.026837844401597977,
0.06653686612844467,
0.015233383513987064,
-0.006968810688704252,
0.002973539987578988,
0.0031255593057721853,
-0.0023534628562629223,
-0.0020230477675795555,
-0.015772996470332146,
0.008758438751101494,
-0.016362501308321953,
-0.006425381638109684,
0.034654971212148666,
0.03574313968420029,
-0.02771434746682644,
0.01049133762717247,
0.014868534170091152,
0.005201298743486404,
0.0023932717740535736,
-0.008991312235593796,
0.009895486757159233,
0.0409875363111496,
0.10300645232200623,
0.05712553858757019,
0.01964665949344635,
-0.03435194119811058,
-0.003101637586951256,
0.02577093243598938,
0.010772441513836384,
0.020360074937343597,
-0.011560744605958462,
-0.02853468246757984,
-0.034273967146873474,
0.024999048560857773,
-0.03439965471625328,
0.03863522782921791,
0.010873658582568169,
-0.024779142811894417,
-0.004153579939156771,
-0.06010552868247032,
-0.01819724589586258,
0.04528957977890968,
0.012487008236348629,
-0.008614230901002884,
-0.033140819519758224,
0.013062688522040844,
-0.0029095460195094347,
0.03416058048605919,
-0.006825547199696302,
0.014934810809791088,
-0.010817524045705795,
-0.00106139259878546,
0.011671922169625759,
0.03796767070889473,
-0.003677451517432928,
-0.07779669761657715,
0.004074042197316885,
0.025756726041436195,
0.00008226696081692353,
0.02746797539293766,
-0.0011314775329083204,
-0.04558001086115837,
0.007845083251595497,
-0.006796261761337519,
-0.006075005978345871,
0.04578833281993866,
-0.045161135494709015,
0.035955775529146194,
0.012596647255122662,
0.04013744741678238,
0.06527847051620483,
0.02168635092675686,
-0.018567828461527824,
-0.001153713557869196,
-0.03646566718816757,
0.009046903811395168,
-0.025726329535245895,
0.04450758919119835,
-0.03812362253665924,
-0.027273908257484436,
-0.01222040131688118,
0.05854308605194092,
-0.03017120249569416,
-0.03730370104312897,
0.011289078742265701,
0.0004147505678702146,
-0.030479751527309418,
0.012271958403289318,
-0.020938439294695854,
-0.027251197025179863,
-0.04014212265610695,
0.032328639179468155,
-0.012016748078167439,
-0.01989317312836647,
0.00501900864765048,
0.004944180604070425,
0.004261181689798832,
0.012149582616984844,
-0.0021070882212370634,
0.03052721917629242,
-0.03221042454242706,
0.0007989707519300282,
-0.0009723952389322221,
-0.055586136877536774,
0.040358152240514755,
-0.01558199618011713,
-0.007565856445580721,
-0.010374504141509533,
-0.04272668436169624,
0.010952956974506378,
-0.012762953527271748,
-0.0004977642674930394,
0.009551526978611946,
-0.019161406904459,
-0.029539253562688828,
0.007645800244063139,
-0.00292978435754776,
-0.062062714248895645,
-0.05297800898551941,
0.017426319420337677,
-0.018007192760705948,
-0.0027959945145994425,
-0.03351902216672897,
0.026167549192905426,
-0.0401763878762722,
-0.04256972298026085,
0.015430009923875332,
0.0637948215007782,
-0.06337086111307144,
-0.002677667187526822,
0.026759173721075058,
0.05398494377732277,
0.015620972961187363,
-0.012620165012776852,
-0.015782158821821213,
0.05582596734166145,
0.00016403457266278565,
-0.022932227700948715,
0.03242022916674614,
0.0572725310921669,
-0.016366582363843918,
-0.044021125882864,
-0.016557127237319946,
-0.020841140300035477,
0.015141692943871021,
-0.006974620744585991,
-0.014802074991166592,
0.03532203286886215,
0.0159179475158453,
0.003060560207813978,
-0.0054884194396436214,
-0.002041558036580682,
-0.008849172852933407,
0.04911380261182785,
-0.02812880650162697,
0.008271888829767704,
-0.002313553122803569,
-0.03486553207039833,
0.05884675681591034,
0.0017904120031744242,
0.03131857141852379,
0.022631727159023285,
0.03751875460147858,
-0.024533303454518318,
0.014810300432145596,
0.01728321798145771,
-0.027411092072725296,
0.015874667093157768,
-0.0025842238683253527,
0.02455291710793972,
0.0323774553835392,
-0.012378738261759281,
-0.039342619478702545,
-0.039158184081315994,
-0.03473860025405884,
-0.006367853842675686,
0.05479993298649788,
0.008099103346467018,
0.06725671887397766,
0.04825286939740181,
-0.0063561806455254555,
-0.031876228749752045,
-0.009821618907153606,
-0.023270677775144577,
0.02972300723195076,
-0.006009664852172136,
0.012121409177780151,
-0.024136776104569435,
-0.012475802563130856,
0.0135610057041049,
0.02951914444565773,
0.013312839902937412,
0.01038093026727438,
0.00199035182595253,
0.04794475436210632,
0.023654794320464134,
-0.001078505883924663,
-0.06475072354078293,
0.02880382351577282,
-0.04646676778793335,
0.04204443469643593,
0.01986813172698021,
-0.00005452410186990164,
0.00833412166684866,
0.015965012833476067,
0.0345170721411705,
0.013127630576491356,
-0.028504321351647377,
-0.06556417793035507,
-0.005845821928232908,
0.014622865244746208,
0.01677035167813301,
-0.019963815808296204,
-0.008247192949056625,
0.03973255679011345,
-0.007392760831862688,
-0.0115257129073143,
0.010901535861194134,
-0.02575298212468624,
-0.012479505501687527,
-0.045352958142757416,
-0.03019481897354126,
0.04177089035511017,
-0.013049758970737457,
-0.01885710097849369,
-0.013554088771343231,
-0.01686738058924675,
0.014877366833388805,
-0.011192204430699348,
0.03995990380644798,
-0.036483753472566605,
0.0677138939499855,
0.006894347257912159,
0.026948075741529465,
-0.029556317254900932,
0.04042147845029831,
0.11025410890579224,
0.06548140943050385,
0.034038495272397995,
-0.06357524544000626,
0.0009767228038981557,
-0.024172894656658173,
-0.026851115748286247,
-0.046808499842882156,
0.06312444806098938,
-0.004309091717004776,
0.025429971516132355,
-0.04619662091135979,
0.057027965784072876,
0.01377074234187603,
-0.01654193177819252,
0.07121274620294571,
-0.05526399239897728,
-0.03615174442529678,
0.0005768854171037674,
0.017624299973249435,
-0.01342263538390398,
-0.009663673117756844,
-0.02916259877383709,
-0.0098198764026165,
-0.006302224472165108,
0.0109544163569808,
0.0013884942745789886,
-0.038581859320402145,
0.01665383391082287,
-0.012758086435496807,
-0.03037043660879135,
-0.035275403410196304,
0.006277414504438639,
-0.0038926948327571154,
-0.04551161080598831,
-0.0009860028512775898,
0.015783729031682014,
-0.01630326919257641,
0.03921065106987953,
0.03442477062344551,
0.02668427675962448,
0.025015607476234436,
0.019493188709020615,
0.0022020312026143074,
-0.0259864442050457,
-0.01520242914557457,
-0.049406636506319046,
0.045960571616888046,
-0.048167869448661804,
-0.0045081209391355515,
-0.005198187194764614,
0.009274027310311794,
0.005874968599528074,
-0.024917427450418472,
-0.014254022389650345,
-0.014551933854818344,
0.027788231149315834,
0.019822033122181892,
0.015335346572101116,
-0.023100020363926888,
0.03378571569919586,
-0.008043527603149414,
0.04751085489988327,
-0.018181797116994858,
-0.04183074086904526,
0.014994424767792225,
-0.011841285042464733,
0.04344269633293152,
0.015717558562755585,
0.02006908692419529,
-0.005739904474467039,
-0.007565638516098261,
-0.0009316263603977859,
-0.014941152185201645,
0.03295892849564552,
-0.003256739117205143,
0.08001187443733215,
0.02428828552365303,
-0.02540777437388897,
0.007693297229707241,
-0.07143255323171616,
0.0042053451761603355,
-0.0241444930434227,
-0.03602348268032074,
0.013617347925901413,
-0.0018687123665586114,
0.016364822164177895,
0.06165477633476257,
-0.0020705293864011765,
-0.029081858694553375,
0.016004463657736778,
-0.014116273261606693,
0.04004853218793869,
-0.0232230257242918,
-0.015865657478570938,
-0.0016394916456192732,
-0.0314265675842762,
0.0029631946235895157,
-0.02171851135790348,
-0.01762772724032402,
0.046522919088602066,
0.020467501133680344,
-0.009627235122025013,
0.03401704505085945,
-0.00633928831666708,
-0.004655990283936262,
0.010189776308834553,
-0.02230241894721985,
-0.010036876425147057,
0.02416364662349224,
0.03378569334745407,
-0.0233248770236969,
-0.06537991762161255,
-0.018100207671523094,
-0.0007701374706812203,
0.030137240886688232,
-0.012471268884837627,
-0.03955765813589096,
-0.047130174934864044,
-0.01050123292952776,
0.03529434651136398,
-0.054169442504644394,
0.0011593644740059972,
-0.0789041817188263,
0.028651133179664612,
0.0034682778641581535,
0.00842156633734703,
-0.016923172399401665,
0.03440634906291962,
0.005492165684700012,
-0.02637298032641411,
-0.00033165703644044697,
0.011419940739870071,
-0.027498185634613037,
0.03866647556424141,
0.008474336937069893,
0.016240909695625305,
0.02008228190243244,
0.038870688527822495,
-0.01301550678908825,
0.05521829053759575,
-0.04830092564225197,
-0.006307434290647507,
0.05460372194647789,
-0.010760527104139328,
0.022960251197218895,
0.04191538691520691,
-0.01782922074198723,
-0.04337015375494957,
0.011866617016494274,
-0.005722076632082462,
0.00034689909080043435,
-0.0019580083899199963,
-0.033096425235271454,
0.012972649186849594,
-0.02343132160604,
0.02438061125576496,
-0.01306262705475092,
-0.019269119948148727,
0.020236920565366745,
0.037316106259822845,
-0.011141308583319187,
-0.022606492042541504,
0.00985028874129057,
0.04477958008646965,
0.04795076698064804,
0.017627062276005745,
0.015266972593963146,
0.003140564076602459,
0.02217032015323639,
-0.03358165919780731,
-0.007547948509454727,
0.019806217402219772,
0.0270231980830431,
-0.09648264199495316,
-0.04523177072405815,
0.0315341092646122,
0.009893921203911304,
0.024732891470193863,
-0.04030151665210724,
0.019636422395706177,
0.024303415790200233,
-0.04274417832493782,
0.02931709960103035,
-0.030094731599092484,
-0.0169215127825737,
-0.031503114849328995,
-0.01102463062852621,
-0.0543278306722641,
0.05314718559384346,
0.020492324605584145,
0.012892108410596848,
-0.007071475498378277,
0.004192981868982315,
0.005814722273498774,
-0.0008055752841755748,
-0.012947285547852516,
0.018103940412402153,
0.0059191398322582245,
-0.016722247004508972,
0.07976613938808441,
0.003139717970043421,
-0.031343474984169006,
0.0243964996188879,
0.016757406294345856,
-0.027863813564181328,
-0.009535043500363827,
0.01616762951016426,
0.006298039108514786,
0.0037875892594456673,
0.040131375193595886,
-0.016964251175522804,
-0.0073413546197116375,
-0.0009207621333189309,
0.04198690503835678,
0.03579653054475784,
-0.03028835356235504,
-0.009618150070309639,
0.011531595140695572,
-0.04280534014105797,
-0.05650796741247177,
0.028503410518169403,
-0.029717033728957176,
0.001895232475362718,
-0.027288472279906273,
-0.04440576955676079,
-0.0002482763957232237,
0.0028367959894239902,
0.0032065485138446093,
-0.03447108343243599,
-0.02775959111750126,
0.01741480827331543,
-0.01469016820192337,
-0.00906507670879364,
0.012218360789120197,
-0.009165139868855476,
-0.013407230377197266,
0.05814789608120918,
0.04415629059076309,
0.013960168696939945,
-0.0684385672211647,
-0.025105591863393784,
0.011725137010216713,
-0.006953080650418997,
-0.0040575130842626095,
-0.033513981848955154,
-0.020283786579966545,
0.015675317496061325,
-0.005644349846988916,
0.020885217934846878,
-0.05366040766239166,
-0.02503976970911026,
-0.010804454796016216,
-0.031006911769509315,
0.057032108306884766,
0.024336062371730804,
0.0269588865339756,
-0.006481270771473646,
-0.055955059826374054,
0.006832781247794628,
-0.004186096601188183,
0.04575049877166748,
-0.020604323595762253,
-0.03136398643255234,
0.02652517892420292,
-0.007211573421955109,
0.028345003724098206,
0.0005606908816844225,
0.004574079066514969,
-0.0307406447827816,
0.017919842153787613,
-0.012179500423371792,
-0.021259160712361336,
0.010858580470085144,
0.024902628734707832,
0.02880035899579525,
-0.026221640408039093,
-0.0076814740896224976,
0.0005172215169295669,
-0.0658249706029892,
0.031787753105163574,
0.018927235156297684,
0.028369739651679993,
0.030923860147595406,
0.017249396070837975,
0.021565208211541176,
0.025506293401122093,
-0.020230183377861977,
-0.039146579802036285,
0.05106903985142708,
-0.04407684877514839,
-0.027685783803462982,
0.023085638880729675,
0.015706373378634453,
0.03736978396773338,
-0.02310483530163765,
-0.014434303157031536,
0.025768764317035675,
-0.04410253465175629,
-0.010955884121358395,
0.04912509396672249,
-0.012391164898872375,
0.03621203079819679,
0.014061430469155312,
0.0135696055367589,
0.028580263257026672,
0.01512113120406866,
0.005540797021239996,
0.021222149953246117,
0.039274655282497406,
0.02773301489651203,
0.0086733503267169,
0.016160164028406143,
-0.04262324795126915,
0.02570926956832409,
0.009885089471936226,
0.039209846407175064,
-0.04104430973529816,
0.018955295905470848,
0.03064044751226902,
-0.01641819067299366,
-0.010673447512090206,
0.015347191132605076,
-0.0331699475646019,
0.09362643212080002,
-0.03284163400530815,
0.00682849669829011,
-0.06647243350744247,
0.03882374241948128,
0.0023370597045868635,
0.05661861598491669,
0.028654608875513077,
0.07598131895065308,
-0.0398535281419754,
0.009565538726747036,
-0.026424627751111984,
0.005440619774162769,
-0.023549463599920273,
-0.022422395646572113,
-0.031895656138658524,
0.02259267121553421,
-0.02537967450916767,
-0.0026643010787665844,
-0.03015931323170662,
-0.03050771914422512,
-0.013720177114009857,
0.010042454116046429,
0.040513068437576294,
0.024682367220520973,
0.0014014274347573519,
-0.010117058642208576,
-0.030527131631970406,
0.023436304181814194,
-0.05692724138498306,
0.022473769262433052,
-0.024468813091516495,
-0.0017627414781600237,
-0.0003004944883286953,
0.0402219183743
] |
<p>Suppose we have the following Lagrangian:</p>
<p>$\mathcal{L} = \frac{1}{2} \phi \Box \phi + V(\phi)$,</p>
<p>where $\Box = \partial _ {\mu} \partial ^ {\mu}$ and $V$ is the interaction term. We use the $(-+++)$ signature.</p>
<p>Is it true that the propagator is
$- \frac{i}{k ^ 2 - i \epsilon}$?</p>
<p>If we used the $(+---)$ signature, would the propagator be
$- \frac{i}{k ^ 2 + i \epsilon}$ or $\frac{i}{k ^ 2 + i \epsilon}$?</p>
<p>I am not particularly sure about the sign in each case. Could someone please explain?</p>
| 8,840 |
[
-0.0022664170246571302,
-0.009938693605363369,
-0.009144553914666176,
-0.001701004570350051,
0.028346063569188118,
0.02840716578066349,
-0.015401652082800865,
0.00019944373343605548,
0.02056261897087097,
-0.03578773885965347,
0.04417591542005539,
0.005773514974862337,
0.06194300577044487,
0.006489474326372147,
-0.0027582987677305937,
0.03394826129078865,
-0.009880639612674713,
-0.015755442902445793,
0.018686484545469284,
-0.02505277656018734,
0.007156175095587969,
0.029862994328141212,
0.016836779192090034,
0.016279814764857292,
-0.04128265753388405,
0.03723050281405449,
0.015381483361124992,
-0.018606306985020638,
-0.0028366707265377045,
0.04581908881664276,
-0.0061166188679635525,
-0.023358242586255074,
0.01941772922873497,
0.030656857416033745,
-0.0014710992109030485,
-0.006840548012405634,
-0.007418395951390266,
-0.05542873591184616,
-0.005458094645291567,
0.02466362714767456,
-0.030458588153123856,
0.00865410640835762,
0.012555322609841824,
0.051021941006183624,
-0.030075956135988235,
-0.021251488476991653,
0.0010138758225366473,
-0.01783314347267151,
0.0722748413681984,
-0.06586240977048874,
0.032599519938230515,
-0.009554184041917324,
0.03504602238535881,
0.03461441770195961,
-0.03983065485954285,
-0.04263995215296745,
0.0792926773428917,
0.08489951491355896,
0.03114493563771248,
-0.05805298686027527,
0.005552586633712053,
-0.01450470183044672,
0.019250106066465378,
0.010926502756774426,
0.010746650397777557,
0.016491927206516266,
0.004171312320977449,
0.010430965572595596,
0.02851889282464981,
-0.0015257523627951741,
0.02388947457075119,
-0.0021616853773593903,
0.03485727682709694,
-0.03489728271961212,
0.025681007653474808,
0.0034315071534365416,
0.024463051930069923,
0.015198366716504097,
-0.00047642612480558455,
0.04478226602077484,
-0.004041784908622503,
0.001082616625353694,
0.013352292589843273,
0.004606609698385,
0.003610684536397457,
-0.02163553237915039,
0.02888534404337406,
0.006329320836812258,
-0.01586354710161686,
0.041375745087862015,
0.00647438270971179,
-0.0011810030555352569,
0.020455699414014816,
-0.021514056250452995,
-0.0003335409564897418,
0.021327579393982887,
0.03577098995447159,
0.0077386945486068726,
0.03164175897836685,
0.026233207434415817,
-0.07014238089323044,
-0.01556575857102871,
-0.01511218398809433,
0.07607001066207886,
-0.015569756738841534,
0.03949145972728729,
-0.06086081638932228,
0.00522424653172493,
-0.026194708421826363,
-0.04612545669078827,
-0.025553351268172264,
-0.009807964786887169,
-0.012012114748358727,
0.008684678934514523,
0.011698471382260323,
-0.037309255450963974,
-0.04100177809596062,
-0.01576506346464157,
0.030989691615104675,
0.028545940294861794,
0.051734913140535355,
-0.00825748685747385,
0.03776666149497032,
-0.003300057491287589,
-0.025054339319467545,
0.008606418035924435,
0.09616083651781082,
0.013141633942723274,
-0.025995684787631035,
0.009294983930885792,
0.054261334240436554,
-0.0028188335709273815,
-0.026562470942735672,
0.022594217211008072,
0.03987756371498108,
-0.027712775394320488,
-0.06735710054636002,
-0.06345952302217484,
0.030095171183347702,
-0.009689370170235634,
-0.010335034690797329,
-0.062290359288454056,
-0.043842241168022156,
0.06513276696205139,
0.11421748995780945,
-0.008582240901887417,
-0.002620890736579895,
0.0062356614507734776,
0.027023132890462875,
-0.0024349919985979795,
-0.007894899696111679,
-0.0068043493665754795,
-0.03545829653739929,
-0.01756744086742401,
-0.020302092656493187,
-0.055060967803001404,
-0.011194230057299137,
0.03884974122047424,
-0.0011530301999300718,
-0.013657866045832634,
0.10052251070737839,
-0.039458055049180984,
0.06616085022687912,
0.045365963131189346,
-0.029405994340777397,
-0.0047569237649440765,
0.07814206928014755,
0.06297177821397781,
0.027172032743692398,
0.026936618611216545,
0.0101894186809659,
0.028486153110861778,
-0.007678534369915724,
0.049330949783325195,
0.07671480625867844,
-0.009174509905278683,
-0.016405723989009857,
-0.05840494856238365,
0.008172404952347279,
-0.019786186516284943,
-0.043553490191698074,
-0.05230964720249176,
-0.06929954886436462,
-0.012449845671653748,
-0.007862783968448639,
0.023655563592910767,
-0.01178942434489727,
0.0183506328612566,
0.027207860723137856,
-0.05702798813581467,
-0.020664799958467484,
-0.03813543915748596,
0.02040897309780121,
0.02919650822877884,
-0.05370458588004112,
0.034772519022226334,
0.00375541509129107,
0.0072477757930755615,
-0.011960254982113838,
-0.04557875916361809,
0.002406819723546505,
0.011157683096826077,
0.0005168942734599113,
-0.024868978187441826,
0.04179316386580467,
0.042332474142313004,
0.02227608673274517,
-0.007560480386018753,
0.053624819964170456,
-0.05650738254189491,
-0.01431538350880146,
0.0555257648229599,
-0.002056571887806058,
0.025963176041841507,
0.006083671003580093,
0.01872347667813301,
-0.0075194453820586205,
-0.004442052450031042,
-0.024687377735972404,
0.021104056388139725,
-0.0650802031159401,
0.06006032973527908,
0.10430272668600082,
0.012558075599372387,
0.009120060130953789,
0.045313119888305664,
-0.025709277018904686,
0.03481835499405861,
-0.0030167687218636274,
-0.04665800929069519,
-0.0017070142785087228,
-0.04187383875250816,
0.03160858526825905,
0.01347903348505497,
-0.016579091548919678,
0.028538892045617104,
0.03227991610765457,
0.01201940793544054,
0.02685587666928768,
0.012296376749873161,
-0.024522366002202034,
-0.028243379667401314,
0.028916481882333755,
0.041588325053453445,
-0.01448432169854641,
0.01882489211857319,
0.05824677646160126,
0.004050373565405607,
0.016853079199790955,
-0.006546587683260441,
-0.051118601113557816,
0.015276435762643814,
-0.03934291750192642,
0.008434062823653221,
-0.012788242660462856,
-0.021176652982831,
0.06910791248083115,
-0.025155290961265564,
0.026591753587126732,
0.004936947021633387,
-0.0000997225652099587,
0.0022375877015292645,
-0.0319802425801754,
-0.016959596425294876,
-0.005068703088909388,
0.024018382653594017,
-0.01412312313914299,
-0.04096868634223938,
0.01249067671597004,
-0.032598093152046204,
0.008062649518251419,
-0.008011809550225735,
-0.023287493735551834,
-0.01526301447302103,
-0.011266594752669334,
0.03859153389930725,
0.022317660972476006,
0.007709910627454519,
-0.0014788175467401743,
-0.035815656185150146,
0.035646408796310425,
-0.013244574889540672,
0.056986089795827866,
0.021742699667811394,
-0.046918220818042755,
0.0029317738953977823,
-0.048938967287540436,
-0.008988050743937492,
0.029804639518260956,
0.014255275018513203,
-0.0190506000071764,
-0.008480772376060486,
0.0018597343005239964,
-0.052825313061475754,
-0.047986943274736404,
-0.02715766802430153,
-0.0021406817249953747,
-0.012341112829744816,
0.010080218315124512,
0.036456432193517685,
0.025729244574904442,
-0.028695156797766685,
-0.009189401753246784,
-0.022560663521289825,
-0.029368000105023384,
-0.03056139312684536,
-0.04072675481438637,
0.020383793860673904,
-0.005443517584353685,
0.01065643597394228,
0.02913937345147133,
-0.04314810037612915,
0.033170122653245926,
-0.043541423976421356,
-0.0405595488846302,
0.017942242324352264,
-0.01647125743329525,
0.004354098346084356,
0.011173822917044163,
-0.03476173058152199,
0.08894769102334976,
0.06630080193281174,
0.008620180189609528,
-0.01089195255190134,
-0.009306742809712887,
-0.029497265815734863,
-0.03398068994283676,
-0.011344516649842262,
-0.006801993120461702,
-0.009113997220993042,
0.06474501639604568,
0.009897541254758835,
0.02661292813718319,
-0.008746104314923286,
0.032349102199077606,
-0.0015570787945762277,
0.004223196767270565,
-0.02018113248050213,
-0.020392421633005142,
0.04976695403456688,
-0.00025006316718645394,
-0.018252413719892502,
-0.017234066501259804,
-0.0033026528544723988,
0.006100605707615614,
0.027633186429739,
-0.014782151207327843,
0.06473175436258316,
0.003587711602449417,
0.009433118626475334,
-0.011438942514359951,
0.041550371795892715,
-0.012638049200177193,
-0.03519162908196449,
-0.037989530712366104,
-0.01088663563132286,
0.03866397589445114,
-0.020695388317108154,
0.011883508414030075,
0.006753240711987019,
0.017518462613224983,
-0.034422364085912704,
-0.03552733361721039,
-0.00984360184520483,
-0.01127717737108469,
0.02623426541686058,
0.012726539745926857,
-0.018655193969607353,
0.021755026653409004,
0.010510297492146492,
-0.03620698302984238,
-0.02712404541671276,
-0.013360255397856236,
0.00010873516293941066,
-0.05936829000711441,
-0.036494869738817215,
-0.004020748194307089,
0.0008346422691829503,
0.004348026588559151,
0.013699932023882866,
0.010591021738946438,
-0.009016632102429867,
0.01944594271481037,
0.02107701450586319,
-0.06001294404268265,
0.03580048307776451,
-0.023566141724586487,
-0.032606981694698334,
-0.001228750916197896,
-0.013208836317062378,
0.0026987548917531967,
-0.03605445846915245,
-0.036029327660799026,
0.029148731380701065,
0.0036731017753481865,
-0.036567386239767075,
0.030959676951169968,
-0.059178464114665985,
-0.02714865654706955,
-0.011524401605129242,
0.0028597889468073845,
0.03588860109448433,
-0.013081076554954052,
0.01874355599284172,
0.03329794108867645,
-0.01783083751797676,
-0.0048326714895665646,
-0.034228235483169556,
0.020391106605529785,
0.04250795394182205,
-0.003289826214313507,
0.036708757281303406,
0.008115674369037151,
-0.021413316950201988,
0.042985204607248306,
0.006820673123002052,
0.039089135825634,
0.020905431360006332,
0.006906949449330568,
-0.021001506596803665,
-0.038709837943315506,
-0.007689984980970621,
0.018536318093538284,
0.054754626005887985,
0.032659776508808136,
0.0345027782022953,
0.04265942424535751,
-0.008127227425575256,
-0.005830361973494291,
0.041624099016189575,
0.04795030131936073,
-0.017633231356739998,
-0.022587357088923454,
-0.06793078780174255,
-0.0014260195894166827,
0.01336605753749609,
-0.004132608883082867,
-0.0014129114570096135,
-0.00686102919280529,
-0.012189734727144241,
0.026482459157705307,
0.02966121956706047,
-0.015111900866031647,
-0.00865324679762125,
0.022162361070513725,
-0.011967512778937817,
0.01935606263577938,
0.003404910210520029,
-0.012292630970478058,
0.015654629096388817,
0.07675010710954666,
0.006789506413042545,
0.04802991822361946,
0.011875047348439693,
-0.04678157716989517,
-0.022302739322185516,
0.03818561136722565,
0.04815177246928215,
-0.009450075216591358,
-0.02027086541056633,
-0.060679953545331955,
-0.03192871809005737,
0.07123202085494995,
0.0072617302648723125,
0.026566365733742714,
-0.0003878686693497002,
-0.0029668824281543493,
0.004845034796744585,
-0.05297907814383507,
-0.02699039690196514,
0.029477566480636597,
0.02286628633737564,
-0.017151271924376488,
-0.03347967565059662,
0.01444973610341549,
0.008217858150601387,
0.011760088615119457,
-0.009845142252743244,
0.08071623742580414,
0.03337899222970009,
-0.007927623577415943,
-0.01934412680566311,
-0.007272687274962664,
-0.00817110389471054,
-0.08719458431005478,
0.0039009221363812685,
0.020095258951187134,
-0.006454521790146828,
0.028369328007102013,
-0.008985370397567749,
-0.04055248945951462,
0.024081042036414146,
0.03554560989141464,
-0.04229564219713211,
-0.017706267535686493,
-0.05568665266036987,
0.05374302715063095,
0.0410781092941761,
0.01479269377887249,
0.05335593223571777,
0.03919539973139763,
-0.03889063373208046,
-0.007079428527504206,
-0.03921891376376152,
0.02317272312939167,
0.0032097636722028255,
0.027000322937965393,
-0.04229706898331642,
0.019139694049954414,
-0.01856900006532669,
0.013260815292596817,
-0.01664753258228302,
0.019351506605744362,
-0.04139413684606552,
-0.005170509684830904,
-0.03410565108060837,
0.05071026831865311,
-0.019259769469499588,
-0.01949465274810791,
0.04978208243846893,
0.011346258223056793,
0.02263362891972065,
-0.025502437725663185,
0.007015435490757227,
-0.02707720175385475,
0.002793580060824752,
0.050693072378635406,
-0.004250458441674709,
0.02226260118186474,
0.0014807044062763453,
-0.014033357612788677,
-0.014393499121069908,
-0.05706823989748955,
0.011140839196741581,
0.007752030156552792,
-0.015651049092411995,
0.007053382229059935,
-0.0046613323502242565,
-0.038286834955215454,
0.0012730492744594812,
-0.025861186906695366,
0.015066534280776978,
-0.04222952947020531,
0.054453156888484955,
0.03263140469789505,
-0.00863533467054367,
-0.10363112390041351,
-0.027155932039022446,
-0.018769674003124237,
-0.04319121688604355,
-0.015800323337316513,
-0.002484966069459915,
-0.013220077380537987,
-0.026432402431964874,
-0.01924987882375717,
0.015631109476089478,
0.057183243334293365,
-0.041313547641038895,
-0.03352610021829605,
0.020772425457835197,
0.027469737455248833,
0.0408732034265995,
-0.020122146233916283,
-0.001209814683534205,
0.01845034398138523,
-0.04472080618143082,
-0.02214566245675087,
0.01330605149269104,
0.06429097056388855,
-0.035250838845968246,
-0.009248525835573673,
-0.036978334188461304,
-0.0025190506130456924,
0.034026138484478,
0.02564854919910431,
-0.02807774767279625,
0.017376581206917763,
0.00028327235486358404,
0.012178327888250351,
-0.0010883432114496827,
-0.009423556737601757,
-0.02433263696730137,
0.008918743580579758,
0.0298710148781538,
-0.005249650217592716,
-0.03502780199050903,
-0.0075800600461661816,
0.03254798427224159,
-0.0029626607429236174,
-0.007971632294356823,
-0.015584789216518402,
0.04992002248764038,
-0.014322467148303986,
-0.008910775184631348,
0.015047049149870872,
0.00945320911705494,
-0.010585285723209381,
-0.024920735508203506,
-0.0037985965609550476,
-0.006978380028158426,
0.003314283676445484,
-0.03791883960366249,
0.0005229940288700163,
-0.018262075260281563,
-0.0028045056387782097,
0.06657993793487549,
0.005409738980233669,
0.0010262337746098638,
-0.014681362546980381,
-0.039147112518548965,
0.029019441455602646,
-0.003898385213688016,
-0.024159986525774002,
-0.025811195373535156,
-0.011304342187941074,
0.0410722941160202,
-0.057616136968135834,
0.03468849137425423,
0.006409272085875273,
0.046625372022390366,
-0.039080675691366196,
-0.03228972479701042,
-0.009702020324766636,
-0.01824392005801201,
0.02332073077559471,
-0.004439881071448326,
-0.046486251056194305,
0.06855370104312897,
-0.02306574583053589,
0.0653795525431633,
-0.035622112452983856,
-0.0331786647439003,
0.03654662147164345,
0.031318627297878265,
-0.012644121423363686,
-0.01977846398949623,
-0.0035714099649339914,
-0.04377593845129013,
0.009054694324731827,
0.036035243421792984,
-0.004790150560438633,
0.023614434525370598,
0.017460571601986885,
0.049460820853710175,
0.0023558959364891052,
0.008822443895041943,
-0.0076507339254021645,
-0.0656963363289833,
-0.01304186787456274,
-0.051420390605926514,
-0.052678242325782776,
0.052847690880298615,
-0.012842961587011814,
0.005494584329426289,
-0.02067996747791767,
-0.03164178505539894,
0.024830739945173264,
0.021042659878730774,
0.02003658190369606,
-0.014951441437005997,
0.07516922801733017,
0.0022953778970986605,
0.04247799143195152,
0.021225959062576294,
0.011638512834906578,
0.10674723982810974,
0.09336598217487335,
-0.02826754003763199,
-0.09018721431493759,
0.025396855548024178,
0.01995345763862133,
-0.01133797224611044,
-0.056805722415447235,
0.04130961745977402,
-0.031079284846782684,
-0.01887219212949276,
-0.009103844873607159,
0.04995681345462799,
-0.026629755273461342,
-0.024335917085409164,
0.032097622752189636,
-0.022383684292435646,
-0.07267997413873672,
-0.018969491124153137,
0.026443399488925934,
-0.004698569420725107,
0.027435362339019775,
-0.02486138790845871,
0.04383775219321251,
-0.019937479868531227,
0.016603803262114525,
-0.03919162228703499,
-0.027234142646193504,
0.03784623369574547,
0.01958552561700344,
-0.0336141362786293,
-0.030845826491713524,
0.042306993156671524,
-0.0016395434504374862,
-0.006984035484492779,
0.01380965020507574,
0.027343807741999626,
-0.032876674085855484,
0.06895162165164948,
0.05394062027335167,
-0.014014910906553268,
0.007560990285128355,
0.017800023779273033,
-0.018896231427788734,
-0.027231890708208084,
0.015319891273975372,
-0.00544672692194581,
0.05440828576683998,
0.0369175523519516,
0.009804305620491505,
0.008301382884383202,
0.0012928091455250978,
0.0338951051235199,
-0.053312111645936966,
-0.03299184516072273,
0.007207244168967009,
0.04884271323680878,
-0.04446643590927124,
0.013450004160404205,
-0.008627391420304775,
0.02102535218000412,
0.014148054644465446,
0.007835512980818748,
0.007311456371098757,
-0.019630638882517815,
-0.011272989213466644,
-0.039895348250865936,
0.020214375108480453,
-0.001981366891413927,
-0.018571309745311737,
0.014616487547755241,
-0.00008316521416418254,
-0.03292832896113396,
0.018855586647987366,
-0.03200024366378784,
0.059585895389318466,
0.038741644471883774,
-0.0074514467269182205,
0.00026661992887966335,
-0.01872331090271473,
-0.06929527223110199,
0.01947018876671791,
-0.038019247353076935,
-0.005163864232599735,
0.0018318553920835257,
0.003977734129875898,
-0.004827533382922411,
0.009731889702379704,
-0.009984618984162807,
0.014174231328070164,
0.004743844270706177,
0.05812966078519821,
0.018173018470406532,
-0.02708684280514717,
-0.06219637021422386,
0.01776213012635708,
-0.018208669498562813,
0.02520275115966797,
-0.05415627732872963,
0.01632995530962944,
-0.011689309030771255,
0.010685780085623264,
-0.011227179318666458,
0.014866393059492111,
-0.028560485690832138,
-0.036375176161527634,
0.011801203712821007,
-0.01900038868188858,
0.04154686629772186,
0.007689708843827248,
0.0282252449542284,
-0.03689061477780342,
-0.02825935371220112,
0.02117178402841091,
0.005145474802702665,
0.032435011118650436,
-0.009699752554297447,
-0.036827147006988525,
-0.010028411634266376,
-0.008844800293445587,
-0.005865233950316906,
-0.03151315823197365,
-0.023203685879707336,
-0.06720452010631561,
0.014646519906818867,
-0.021977264434099197,
0.012199599295854568,
0.0005357787595130503,
0.044692978262901306,
-0.026153564453125,
-0.013773385435342789,
0.00908671785145998,
0.03566878288984299,
-0.013062997721135616,
-0.01391104981303215,
0.025539103895425797,
-0.029880011454224586,
0.028255315497517586,
-0.005396893247961998,
-0.025554770603775978,
0.008099539205431938,
-0.01688426174223423,
-0.0070717185735702515,
0.04037689045071602,
0.0024759499356150627,
0.010695522651076317,
0.025532521307468414,
-0.0011070616310462356,
-0.023003192618489265,
0.04447285085916519,
-0.012221445329487324,
0.006866364274173975,
-0.02080509066581726,
-0.07005906105041504,
-0.03422261029481888,
-0.049329038709402084,
-0.009651580825448036,
0.03439166769385338,
-0.01183750107884407,
-0.014940071851015091,
0.014259089715778828,
-0.034302543848752975,
0.009381850250065327,
-0.027778038755059242,
-0.04329156503081322,
0.030768217518925667,
0.013583699241280556,
-0.012595229782164097,
-0.010673697106540203,
0.018449459224939346,
-0.006832582876086235,
0.012008164077997208,
0.004514199681580067,
-0.011077458038926125,
-0.06469415128231049,
0.006354927085340023,
0.013978173956274986,
0.05013992637395859,
0.06119334697723389,
-0.07070736587047577,
0.012937984429299831,
0.015170369297266006,
-0.0296469796448946,
0.05390990152955055,
-0.010112117044627666,
-0.002577180042862892,
-0.014588477090001106,
0.0037412522360682487,
-0.02366366982460022,
0.02545270323753357,
0.01015622541308403,
0.03241847828030586,
0.010741002857685089,
-0.017145011574029922,
-0.010280484333634377,
-0.009779258631169796,
-0.03259337693452835,
-0.005518942140042782,
0.0022336356341838837,
-0.009928926825523376,
0.07709619402885437,
-0.02654857002198696,
-0.04629942774772644,
0.014108479954302311,
0.01088243629783392,
0.004464893136173487,
0.030410651117563248,
0.021433766931295395,
0.02122333087027073,
0.03732340410351753,
-0.002748040249571204,
-0.008347607217729092,
0.0055421800352633,
0.0014743208885192871,
0.036295127123594284,
0.04992813244462013,
-0.026398470625281334,
0.012440896593034267,
-0.02016093023121357,
-0.025974582880735397,
-0.010731687769293785,
0.08934076130390167,
-0.04325627163052559,
-0.018299560993909836,
-0.01247807964682579,
-0.01924440637230873,
0.033647097647190094,
-0.002756078029051423,
0.009928393177688122,
-0.039879657328128815,
0.006112734321504831,
0.020914729684591293,
0.003911068197339773,
-0.007692802231758833,
-0.020505158230662346,
-0.0038944724947214127,
-0.0354938805103302,
0.012888367287814617,
0.00954395066946745,
0.018345506861805916,
-0.0554482638835907,
-0.03388173133134842,
-0.005611451808363199,
0.005799804348498583,
-0.00009550333925290033,
-0.02137858420610428,
-0.04043138399720192,
0.01950233243405819,
-0.008270671591162682,
0.04862744361162186,
-0.015326227061450481,
-0.028523052111268044,
-0.020805267617106438,
-0.06722860038280487,
-0.005053887143731117,
0.057455211877822876,
-0.030714845284819603,
-0.01660696417093277,
-0.029805606231093407,
-0.003515148302540183,
0.017394449561834335,
0.02050172910094261,
0.024894390255212784,
-0.021365411579608917,
0.0047546979039907455,
-0.028587019070982933,
0.015851914882659912,
-0.038711898028850555,
-0.008715995587408543,
0.0030982717871665955,
-0.009177601896226406,
0.00041984274866990745,
0.018558938056230545,
-0.03944709524512291,
0.06199059635400772,
0.037142544984817505,
0.012257595546543598,
0.008130388334393501,
-0.0007652506465092301,
-0.031706612557172775,
0.032591111958026886,
-0.009983904659748077,
-0.014895622618496418,
0.05893433466553688,
0.030573444440960884,
0.0383310541510582,
0.01730932667851448,
-0.021667294204235077,
-0.019409801810979843,
0.0408131368458271,
-0.03926965594291687,
0.0012645762180909514,
-0.011302787810564041,
-0.01005536038428545,
-0.000717060873284936,
-0.0557791106402874,
-0.0005575291579589248,
0.03722129389643669,
-0.018426505848765373,
-0.023134814575314522,
0.06133635714650154,
0.017970938235521317,
0.034325044602155685,
0.05248565971851349,
-0.008427059277892113,
0.05948243290185928,
0.029519017785787582,
0.02911802940070629,
0.039399925619363785,
0.006102951243519783,
-0.013843148946762085,
-0.03115794062614441,
-0.011160149239003658,
-0.019173134118318558,
-0.007458505220711231,
-0.032283488661050797,
0.006131273228675127,
-0.05141247808933258,
0.03086680732667446,
-0.003997448366135359,
-0.008882805705070496,
0.027860252186655998,
-0.0005823991377837956,
-0.024343522265553474,
0.0321807898581028,
-0.025725236162543297,
0.029922300949692726,
-0.018283655866980553,
0.007325851358473301,
-0.002599346684291959,
0.024047035723924637,
0.032980777323246,
0.05389399081468582,
0.0030220411717891693,
-0.008224141784012318,
-0.0359022356569767,
-0.02075882814824581,
0.018474815413355827,
-0.09097831696271896,
-0.011329928413033485,
0.011095410212874413,
-0.014666560105979443,
-0.010922852903604507,
-0.044731274247169495,
-0.026013275608420372,
-0.058847591280937195,
0.0114975580945611,
0.04205253720283508,
0.0006073547410778701,
0.009038747288286686,
0.0020888792350888252,
-0.010701151564717293,
0.061712879687547684,
-0.04357277974486351,
0.017124980688095093,
-0.02207275480031967,
-0.0025157160125672817,
-0.0073124123737216,
0.017484690994024277
] |
<p>I've read that neutrinos in supernova can be affected by "neutrino refraction." Is this analagous to the refraction of light, and if so, is the speed of these neutrinos similarly reduced from their near c speeds via this index of refraction? </p>
| 8,841 |
[
-0.013238233514130116,
-0.0259152390062809,
-0.013472221791744232,
-0.03045877255499363,
0.0685410276055336,
0.03013085201382637,
-0.026001956313848495,
-0.04711296781897545,
-0.011598337441682816,
-0.04144043102860451,
0.02552122063934803,
0.06273820996284485,
0.037642281502485275,
-0.005686675198376179,
0.018288491293787956,
-0.022033467888832092,
-0.03420836851000786,
0.005603363737463951,
0.002950700232759118,
-0.07088839262723923,
0.0027144053019583225,
0.016973713412880898,
-0.0036929540801793337,
0.017474066466093063,
-0.03919067606329918,
0.05341204255819321,
0.0014745767693966627,
0.005560012999922037,
0.03431959077715874,
-0.009790762327611446,
0.04577045142650604,
-0.008131181821227074,
0.0001028910992317833,
0.03410761430859566,
0.0020813625305891037,
0.004045356065034866,
-0.022654807195067406,
-0.0453159362077713,
-0.04962291568517685,
0.01906023919582367,
-0.005553713068366051,
-0.01830626092851162,
-0.031127406284213066,
0.024454927071928978,
-0.006545506417751312,
-0.01225213147699833,
0.0116291344165802,
-0.02858799882233143,
0.06489384919404984,
-0.05154595524072647,
0.05553459748625755,
-0.014447159133851528,
0.016933344304561615,
0.037234965711832047,
-0.026980146765708923,
-0.0018348493613302708,
0.10081660747528076,
0.09348543733358383,
-0.012796975672245026,
-0.05969122797250748,
0.003488810732960701,
-0.009192491881549358,
-0.0043514142744243145,
-0.0060378084890544415,
-0.016558000817894936,
0.05536825582385063,
-0.03064468689262867,
-0.049858447164297104,
0.002035456243902445,
0.00795971229672432,
0.008884312584996223,
-0.022491611540317535,
0.007580234669148922,
0.019481422379612923,
-0.00887606106698513,
-0.06040055304765701,
0.007748183328658342,
-0.01842186041176319,
0.02297612652182579,
0.06346652656793594,
-0.030519861727952957,
0.004427419509738684,
0.023465558886528015,
0.011327429674565792,
-0.029101142659783363,
0.00461524398997426,
0.06453602015972137,
-0.02214660495519638,
0.011306182481348515,
0.03159105405211449,
-0.013416473753750324,
-0.01797090657055378,
0.007323312573134899,
-0.003386190626770258,
-0.05265283212065697,
0.011094696819782257,
-0.008220454677939415,
0.05514999479055405,
0.014854386448860168,
-0.033092983067035675,
-0.027859866619110107,
0.002976062009111047,
0.009945687837898731,
0.06247621774673462,
0.022307995706796646,
-0.08267442882061005,
-0.0618278868496418,
0.03183559328317642,
-0.056110985577106476,
-0.0014804588863626122,
-0.025599246844649315,
-0.03537097945809364,
-0.02984544076025486,
0.011908667162060738,
0.0416940338909626,
-0.04310966655611992,
-0.011524848639965057,
-0.02114034816622734,
0.0915842354297638,
0.08559960871934891,
0.04067040607333183,
-0.0027039654087275267,
0.000254239042988047,
0.018129192292690277,
-0.04875943064689636,
0.04188786447048187,
0.01524041686207056,
-0.003364315489307046,
-0.008389420807361603,
-0.0033052507787942886,
-0.010677286423742771,
0.008328418247401714,
0.00025845749769359827,
-0.03501071408390999,
0.02091711387038231,
0.00013578949437942356,
-0.10129949450492859,
-0.09932423382997513,
0.055499833077192307,
0.010004407726228237,
-0.02828008122742176,
-0.09629117697477341,
0.024702446535229683,
0.008296031504869461,
0.10084021836519241,
0.027337372303009033,
-0.001963558839634061,
-0.03384846821427345,
0.033993639051914215,
0.011482197791337967,
-0.005501532461494207,
-0.028128717094659805,
0.027807263657450676,
-0.03788888081908226,
0.00902643520385027,
-0.07940686494112015,
0.018189847469329834,
0.030359983444213867,
-0.0063836523331701756,
-0.0418439581990242,
0.07566940039396286,
-0.0526411347091198,
0.04554741457104683,
0.024790789932012558,
0.0026118154637515545,
-0.06384659558534622,
0.09954919666051865,
0.03886309638619423,
0.0043330504558980465,
0.04362777993083,
-0.003003442659974098,
0.06251934915781021,
-0.01084616594016552,
0.03184901550412178,
0.04455474764108658,
-0.023765284568071365,
-0.015379838645458221,
-0.016303354874253273,
0.005457400809973478,
-0.003239270066842437,
0.003137910971418023,
-0.024279093369841576,
0.0037926214281469584,
0.003853836562484503,
-0.0011965330922976136,
0.04813796654343605,
-0.00824671145528555,
-0.025896837934851646,
0.023390740156173706,
-0.033257417380809784,
0.005686960648745298,
-0.021786414086818695,
-0.01563292369246483,
0.0045084464363753796,
-0.0027547692880034447,
0.011212971061468124,
0.025151267647743225,
0.007846723310649395,
-0.01807234436273575,
-0.039498452097177505,
0.003117593936622143,
0.04715605080127716,
0.012232187204062939,
-0.01928918994963169,
0.023805731907486916,
0.013801068998873234,
0.020314451307058334,
-0.025262633338570595,
0.0245179645717144,
0.0020835513714700937,
-0.03778645396232605,
-0.0050404672510921955,
0.011890281923115253,
0.027579234912991524,
-0.02928825654089451,
0.005646692123264074,
0.014553812332451344,
0.029462626203894615,
0.01567292958498001,
0.018844641745090485,
-0.016180453822016716,
0.07901749014854431,
0.01083470694720745,
0.032593101263046265,
0.008873220533132553,
0.028328193351626396,
0.018738700076937675,
0.021369248628616333,
-0.014688877388834953,
-0.03047388233244419,
-0.0259091816842556,
-0.00899774581193924,
0.03863091021776199,
0.010654921643435955,
-0.0485217422246933,
0.01536332257091999,
0.04271078482270241,
0.04262970760464668,
0.04889490082859993,
0.029756082221865654,
-0.026133740320801735,
-0.05265280231833458,
-0.030491003766655922,
-0.0021214671432971954,
0.02213236317038536,
0.0010227434104308486,
0.01862155832350254,
0.004562121815979481,
0.041167400777339935,
-0.05734700709581375,
-0.0007747315103188157,
-0.011964596807956696,
-0.0026641814038157463,
-0.03394322842359543,
0.005717609543353319,
-0.04228846728801727,
0.034583158791065216,
-0.030603811144828796,
0.01663745939731598,
0.023715097457170486,
0.008752337656915188,
0.02742350660264492,
-0.021133122965693474,
0.031878285109996796,
0.02756917104125023,
0.0026010959409177303,
-0.01970183476805687,
0.012807417660951614,
0.021640587598085403,
-0.041115667670965195,
0.019144488498568535,
-0.022427503019571304,
0.023065270856022835,
-0.014655456878244877,
-0.010382209904491901,
0.009735535830259323,
0.03736718371510506,
0.03797737881541252,
-0.015980707481503487,
-0.06447333842515945,
0.014258477836847305,
-0.027839157730340958,
-0.027911171317100525,
0.05286547541618347,
-0.0198073647916317,
0.029242606833577156,
0.0019438616000115871,
-0.0281257051974535,
0.008374212309718132,
-0.021590249612927437,
0.025499671697616577,
0.03916588053107262,
-0.03930017724633217,
-0.0559656023979187,
-0.024361010640859604,
-0.009752091020345688,
0.005516636651009321,
-0.047888968139886856,
0.012114958837628365,
0.05191522091627121,
0.009803769178688526,
-0.010045194067060947,
-0.03785053640604019,
-0.03092472068965435,
-0.06027354300022125,
-0.01231288444250822,
0.013302820734679699,
0.010531209409236908,
-0.048066362738609314,
0.007063704077154398,
0.033265724778175354,
-0.04268713295459747,
0.03488161414861679,
-0.01155088096857071,
-0.06768796592950821,
0.045007217675447464,
-0.02202562615275383,
0.018971484154462814,
-0.015996141359210014,
-0.027686743065714836,
0.058820080012083054,
0.05682262033224106,
-0.0004296132829040289,
-0.036963868886232376,
-0.003585126716643572,
-0.006143897771835327,
0.003970366902649403,
0.004279043059796095,
0.022434532642364502,
0.001984227914363146,
0.022546328604221344,
0.012463335879147053,
0.037148259580135345,
0.03783117234706879,
0.016788741573691368,
0.007496284786611795,
-0.013344819657504559,
0.007149778306484222,
0.011296632699668407,
0.017161859199404716,
0.02863362245261669,
-0.027282027527689934,
0.011635384522378445,
0.00649322010576725,
0.05919831618666649,
0.04198182001709938,
-0.02379087544977665,
0.05001617595553398,
0.018422625958919525,
0.018284562975168228,
0.01715538650751114,
0.021236050873994827,
0.007849447429180145,
0.044068172574043274,
-0.002180703217163682,
0.014290397986769676,
0.04140126332640648,
-0.016457295045256615,
0.0065575409680604935,
0.008959773927927017,
0.03051210567355156,
-0.01519404724240303,
-0.013696436770260334,
0.019976835697889328,
-0.02412247285246849,
-0.0017087541054934263,
-0.010604992508888245,
0.011812873184680939,
0.05930721387267113,
0.025038735941052437,
-0.001996715785935521,
-0.03076624684035778,
-0.022356880828738213,
0.004903009161353111,
-0.027995049953460693,
0.009695612825453281,
-0.004184335470199585,
0.015171146020293236,
0.01439613290131092,
0.03221214562654495,
0.01271789986640215,
0.0026431805454194546,
0.01656510680913925,
-0.018825845792889595,
-0.0854232907295227,
-0.0056234002113342285,
-0.05911761522293091,
-0.04590926319360733,
-0.020789537578821182,
-0.004848613403737545,
-0.025963764637708664,
0.009686117060482502,
-0.007273219060152769,
-0.045801740139722824,
-0.02551151067018509,
-0.031338609755039215,
0.019049325957894325,
-0.03022376261651516,
-0.0558386966586113,
-0.012910368852317333,
0.028408735990524292,
0.00030770141165703535,
-0.018917661160230637,
-0.00988103449344635,
0.01853400096297264,
-0.06830568611621857,
0.010347520932555199,
0.0110704330727458,
0.011642931029200554,
-0.0018452091608196497,
0.04070694372057915,
0.03858844190835953,
0.0033387208823114634,
-0.026377175003290176,
0.0250139981508255,
0.042687274515628815,
0.023022448644042015,
0.028759729117155075,
-0.015536272898316383,
-0.02026290073990822,
-0.02791764587163925,
-0.05193181708455086,
0.011392898857593536,
0.06086451932787895,
-0.019191471859812737,
-0.0007043927907943726,
0.057813722640275955,
-0.002991856774315238,
-0.030771955847740173,
0.019376827403903008,
0.022532058879733086,
0.03800828382372856,
-0.007801022846251726,
-0.01903170347213745,
-0.01296475250273943,
0.009414788335561752,
0.016171609982848167,
0.03179806470870972,
0.015781568363308907,
-0.03836020454764366,
-0.015483502298593521,
-0.007020554039627314,
-0.010048593394458294,
-0.045310962945222855,
0.015106607228517532,
-0.02147550880908966,
-0.007927088998258114,
-0.01788826659321785,
0.027493635192513466,
0.00012480713485274464,
0.030432740226387978,
0.04276374727487564,
-0.0009212805307470262,
-0.015475047752261162,
-0.05454934760928154,
-0.004415157716721296,
0.04677986353635788,
0.04763675481081009,
-0.009585680440068245,
-0.01587216928601265,
-0.07107923179864883,
-0.02348761446774006,
0.031947940587997437,
-0.04253621771931648,
0.013354374095797539,
0.006417496129870415,
0.0011797626502811909,
0.008394520729780197,
-0.026707513257861137,
0.020154446363449097,
0.06486404687166214,
0.013767086900770664,
-0.005989114288240671,
-0.03819120675325394,
0.02234921231865883,
-0.014582962729036808,
-0.028379514813423157,
0.033376581966876984,
0.05893230810761452,
0.029740363359451294,
-0.008591443300247192,
0.0027662483043968678,
0.009629187174141407,
-0.023801537230610847,
-0.08948107063770294,
0.0026726252399384975,
0.029934775084257126,
-0.008208077400922775,
0.0540238618850708,
-0.018880296498537064,
-0.015534454956650734,
0.04772103950381279,
0.044881172478199005,
-0.011331637389957905,
0.0013086367398500443,
-0.039785582572221756,
0.034733593463897705,
0.02829466201364994,
-0.01959696039557457,
0.024764148518443108,
0.015126646496355534,
-0.025149481371045113,
0.011731917969882488,
-0.012507102452218533,
0.052343424409627914,
-0.028825385496020317,
0.01197559479624033,
0.018080413341522217,
-0.02017083764076233,
-0.0036378242075443268,
0.06884665042161942,
-0.008111580274999142,
0.0066859908401966095,
0.04321666806936264,
-0.01821058616042137,
-0.025082828477025032,
0.02385658025741577,
0.027622167021036148,
-0.040259599685668945,
0.007155591156333685,
-0.006261847913265228,
0.020589234307408333,
-0.024031322449445724,
0.04561517387628555,
-0.013961604796350002,
0.009617183357477188,
0.021650969982147217,
0.0003251550660934299,
-0.016941068693995476,
-0.023868512362241745,
-0.025744294747710228,
-0.004596951883286238,
-0.04983273893594742,
0.0379672534763813,
-0.018046610057353973,
-0.0198376402258873,
0.023785531520843506,
-0.024466317147016525,
-0.02161317691206932,
0.02926846407353878,
-0.05142751336097717,
0.06721127033233643,
-0.07420197874307632,
0.04148325324058533,
0.014493542723357677,
0.026753725484013557,
-0.06313866376876831,
-0.013040616177022457,
0.026322023943066597,
-0.017446693032979965,
-0.0041882735677063465,
-0.026065902784466743,
-0.014030075632035732,
-0.03535265848040581,
-0.03274373337626457,
-0.0012465895852074027,
0.05799729377031326,
-0.04780644178390503,
-0.04661780223250389,
0.005027413833886385,
-0.007787535898387432,
0.07144854217767715,
-0.005575596820563078,
-0.04457471892237663,
0.026468830183148384,
-0.02042689546942711,
0.019690368324518204,
0.025003021582961082,
0.07745665311813354,
-0.013989537954330444,
-0.048021409660577774,
-0.034724537283182144,
0.004388417582958937,
0.007147870492190123,
0.0005539300036616623,
0.011002748273313046,
0.04444701597094536,
0.03272194415330887,
0.006560164038091898,
-0.0046327980235219,
0.02236349880695343,
0.032382555305957794,
0.021161682903766632,
-0.0026866018306463957,
0.007523064035922289,
-0.020847514271736145,
-0.033578064292669296,
0.029048552736639977,
-0.0064223939552903175,
0.02873072400689125,
-0.014456093311309814,
0.058182574808597565,
0.0008202033350244164,
-0.036460328847169876,
-0.003417465602979064,
-0.001853364403359592,
-0.01700798235833645,
-0.010395117104053497,
0.018761686980724335,
-0.007448859512805939,
0.009621916338801384,
-0.0024951561354100704,
-0.03998512029647827,
-0.03900459036231041,
-0.014488580636680126,
0.09560838341712952,
-0.057568904012441635,
0.021124960854649544,
-0.02368704043328762,
-0.0064383503049612045,
-0.021093010902404785,
-0.025407269597053528,
0.0029220827855169773,
0.006669793743640184,
-0.006564323324710131,
0.038668375462293625,
-0.024008313193917274,
-0.022951243445277214,
0.028876379132270813,
0.06568113714456558,
-0.0059252274222671986,
0.03314243257045746,
0.018988139927387238,
0.042492616921663284,
0.01849844492971897,
0.007483819965273142,
-0.05151214823126793,
0.025342823937535286,
-0.04352673515677452,
0.035838738083839417,
0.005834465380758047,
-0.0028198484797030687,
0.026473412290215492,
-0.03447645902633667,
0.029124878346920013,
-0.02181815914809704,
-0.05059804022312164,
-0.02725692093372345,
-0.00124911789316684,
-0.0031598317436873913,
0.004083912819623947,
-0.016744118183851242,
0.005133703351020813,
0.03413418307900429,
0.01931089721620083,
0.0163456741720438,
-0.018307799473404884,
-0.06981275975704193,
-0.04019800201058388,
-0.032194361090660095,
-0.017962701618671417,
0.021734241396188736,
0.0008040788234211504,
-0.036366451531648636,
-0.003597503760829568,
-0.035677120089530945,
0.00959793757647276,
0.026617826893925667,
0.030148115009069443,
0.0047126696445047855,
0.053274694830179214,
-0.006102048791944981,
-0.004706331063061953,
0.013992054387927055,
-0.022158732637763023,
0.1013861894607544,
0.028244394809007645,
-0.005286389030516148,
-0.050755441188812256,
0.0028519537299871445,
-0.014661276713013649,
0.022411365061998367,
-0.03380906954407692,
-0.005161616485565901,
-0.028536388650536537,
0.025675615295767784,
0.0480930358171463,
0.07917708158493042,
0.020959721878170967,
-0.017022352665662766,
0.024400833994150162,
-0.019484715536236763,
-0.021222976967692375,
0.02328553982079029,
0.016273945569992065,
0.003901194781064987,
0.03503676876425743,
-0.051442284137010574,
0.03960280120372772,
-0.04787202924489975,
0.007488238625228405,
-0.030010830610990524,
-0.011827980168163776,
0.02633878029882908,
-0.012401886284351349,
-0.05399271473288536,
-0.01344190165400505,
0.03124372288584709,
-0.03607442229986191,
-0.021601177752017975,
0.02349458821117878,
0.02628690004348755,
0.007724232040345669,
0.019992072135210037,
0.003853101283311844,
0.044876355677843094,
0.001215223572216928,
0.0008181399898603559,
0.014918447472155094,
-0.045359592884778976,
0.009381811134517193,
0.010239233262836933,
0.024540867656469345,
-0.0007035831804387271,
0.005416004918515682,
-0.003507903777062893,
0.015217619016766548,
0.022508054971694946,
-0.050067055970430374,
-0.003735715290531516,
-0.011922198347747326,
0.005116730462759733,
0.0002506579621694982,
-0.007178439758718014,
0.008564016781747341,
0.017556235194206238,
-0.008317858912050724,
0.049333855509757996,
-0.015187680721282959,
0.005351714324206114,
-0.006504322402179241,
-0.01352363359183073,
0.00009180137567454949,
-0.032713986933231354,
-0.06602013111114502,
-0.034556690603494644,
0.0046792528592050076,
-0.021871594712138176,
-0.018471885472536087,
0.021602466702461243,
0.015154415741562843,
-0.003370058024302125,
0.006146456114947796,
0.02425374463200569,
-0.011235133744776249,
-0.0649917870759964,
0.05275000259280205,
-0.04229264333844185,
-0.03434444218873978,
-0.03736108914017677,
-0.017613394185900688,
0.05540921166539192,
0.039680711925029755,
-0.03325336053967476,
-0.009506582282483578,
-0.03037562221288681,
0.01961355283856392,
0.03361516073346138,
-0.024022327736020088,
-0.03138752654194832,
0.0017510431353002787,
-0.01641572266817093,
0.004469248000532389,
-0.025821520015597343,
0.04561600834131241,
0.04543716460466385,
-0.027214176952838898,
0.047279052436351776,
0.02212308533489704,
-0.026659410446882248,
-0.002064466243609786,
-0.003715453203767538,
-0.042543888092041016,
0.00955041404813528,
-0.03090919367969036,
0.017207233235239983,
0.012794071808457375,
-0.037845347076654434,
-0.05235584080219269,
0.007231179159134626,
0.008498833514750004,
-0.005220168735831976,
0.010635881684720516,
0.030872417613863945,
-0.0228411927819252,
-0.0002005926362471655,
-0.03385419771075249,
-0.004029914736747742,
-0.006448040250688791,
0.008468088693916798,
-0.0031554359011352062,
-0.03412707895040512,
-0.011990932747721672,
0.014302516356110573,
-0.010251257568597794,
-0.00042982830200344324,
0.015851633623242378,
-0.007001555059105158,
0.0022593161556869745,
-0.00046676589408889413,
0.03328194469213486,
0.0007345735211856663,
0.042811088263988495,
-0.01589365117251873,
-0.01630452461540699,
0.032743677496910095,
-0.03948201611638069,
-0.083682119846344,
0.041887201368808746,
-0.03274841606616974,
0.029190998524427414,
0.007902643643319607,
0.007602586876600981,
-0.0009741704561747611,
0.10070762783288956,
-0.01326800137758255,
-0.02965628169476986,
-0.0014822750817984343,
-0.016866520047187805,
-0.007550070993602276,
-0.023347649723291397,
0.03247968852519989,
0.005018614698201418,
-0.03032192774116993,
0.0574457049369812,
0.025945361703634262,
-0.024467838928103447,
0.009025884792208672,
-0.025640074163675308,
-0.0571412555873394,
-0.03725628927350044,
-0.007295046932995319,
0.01103453803807497,
0.03669467940926552,
0.02504388615489006,
-0.03622861206531525,
0.06963381171226501,
0.054983951151371,
0.03027273714542389,
-0.1070648729801178,
0.014178461395204067,
-0.009541008621454239,
0.05199452489614487,
0.0162053145468235,
-0.04421437531709671,
0.07003599405288696,
-0.0015069060027599335,
-0.04064078629016876,
-0.00234251469373703,
-0.04565409570932388,
-0.045824769884347916,
-0.046148139983415604,
-0.0002402999234618619,
0.017063336446881294,
0.031478963792324066,
0.03938781097531319,
0.017059266567230225,
0.03389301523566246,
-0.003626293735578656,
-0.026678811758756638,
0.00850630085915327,
0.0009204813977703452,
0.020097024738788605,
0.01480487734079361,
-0.007161607965826988,
0.043533310294151306,
-0.012455686926841736,
-0.006382802501320839,
0.036578450351953506,
0.012954751960933208,
0.023194829002022743,
0.025290222838521004,
-0.006658713798969984,
0.02874572202563286,
0.018450690433382988,
0.001888907398097217,
0.000957450014539063,
-0.008399005979299545,
0.023035293444991112,
-0.00704888254404068,
0.02143099345266819,
0.002671067137271166,
-0.005740050692111254,
-0.010704472661018372,
-0.0802803784608841,
-0.003885204903781414,
0.005239512771368027,
-0.018965154886245728,
-0.0008207024075090885,
-0.00939109455794096,
-0.01711203157901764,
0.025275761261582375,
-0.0003477332938928157,
0.025407878682017326,
-0.05286019667983055,
-0.013841783627867699,
0.031694620847702026,
0.006383922882378101,
-0.025767821818590164,
0.0014478660887107253,
0.00843035988509655,
-0.05036415532231331,
-0.020805053412914276,
0.012440061196684837,
0.006502723321318626,
-0.040791332721710205,
0.007443558424711227,
0.023135824128985405,
-0.008355891332030296,
0.0021274590399116278,
-0.03194185718894005,
-0.007251061033457518,
0.057206135243177414,
0.018092401325702667,
0.011397640220820904,
0.02611338347196579,
-0.010500743985176086,
-0.032595694065093994,
-0.05285009741783142,
-0.0004838035092689097,
-0.011415218003094196,
0.05662187188863754,
-0.03819258138537407,
0.004367548041045666,
-0.03740733489394188,
0.02876301482319832,
0.035556014627218246,
-0.0391080342233181,
-0.014118792489171028,
0.02233107201755047,
-0.0082237608730793,
-0.01202304009348154,
-0.07657080888748169,
-0.02107161656022072,
-0.02497727796435356,
-0.04109527915716171,
-0.032326243817806244,
-0.010791018605232239,
-0.02605857513844967,
0.0017762082861736417,
0.010090775787830353,
0.032042015343904495,
0.021231144666671753,
0.020409945398569107,
-0.009762438014149666,
0.03958753123879433,
0.039574284106492996,
-0.014322912320494652,
0.05921311676502228,
0.00860361848026514,
-0.015295573510229588,
0.043777596205472946,
-0.017549946904182434,
-0.042785532772541046,
0.016590023413300514,
0.012837237678468227,
-0.008323095738887787,
0.0009076211717911065,
-0.042734529823064804,
-0.008097008801996708,
-0.009620899334549904,
0.02318207360804081,
0.04440486058592796,
-0.03820626810193062,
-0.014773016795516014,
0.03475861996412277,
0.0056481133215129375,
0.02363530732691288,
0.008438137359917164,
0.011195641942322254,
-0.0037281480617821217,
0.01634669490158558,
-0.02890772931277752,
0.04358400031924248,
0.013098587282001972,
0.022814106196165085,
0.015934383496642113,
0.002888769144192338,
0.007996597327291965,
0.011362253688275814,
-0.03565627336502075,
0.03834100067615509,
-0.04044407606124878,
-0.016158584505319595,
0.012068608775734901,
-0.024750836193561554,
0.0021863793954253197,
0.038624465465545654,
0.008203075267374516,
0.051830507814884186,
-0.017517732456326485,
0.03515338897705078,
-0.013123758137226105,
-0.007505185902118683,
-0.00014133080549072474,
0.0325455516576767,
0.011728203855454922,
0.02807105891406536,
-0.014162355102598667,
-0.006539038848131895,
0.026043491438031197,
-0.00627870811149478,
0.043000321835279465,
-0.07317350804805756,
0.0148254269734025,
0.010726665146648884,
-0.013200205750763416,
-0.024474581703543663,
-0.006297553889453411,
-0.0013815630227327347,
-0.005487852729856968,
-0.007554052863270044,
0.01363084651529789,
-0.028772545978426933,
0.010212132707238197,
-0.004998453892767429,
0.008395306766033173,
0.04558169096708298,
-0.052824798971414566,
0.018488328903913498,
-0.011562748812139034,
0.04288843274116516,
-0.04830031096935272,
-0.027329666540026665
] |
<p>If gravity is the curvature of spacetime it should bend everything equally. To clarify my point I would like you to imagine two scenarios. Think of a bird flying in the storm while the wind is blowing sideways. Because the wind is an active force and the bird is fighting against it, the amount by which it's trajectory is bent should depend on it's momentum for a given strength of wind. Qualitatively speaking, more the momentum the less it bends. Now think of a train moving on a curved track. It should always bend by a fixed degree regardless of it's velocity or mass because the path itself is bent by that precise degree.</p>
<p>I am aware that in my examples I have only considered curvature in SPACE but the theory of relativity talks about curvature in SPACETIME and I am guessing that every object's trajectory through spacetime is indeed equally bent due to gravity. Can someone explain?</p>
<p><strong>EDIT</strong>: After reading some comments, I have realized that perhaps my choice of words wasn't that great in the original question. I know that different object will follow different geodesic trajectories based on their initial conditions. What I was interested in is the CHANGE in trajectories due to spacetime curvature. The term I should have used in the question is acceleration. For example, the gravitational acceleration an object will experience near the surface of the earth is g regardless of it's mass or initial velocity. So it's natural to expect that every object will experience the same acceleration when they are moving sideways with respect to a gravitational body. In other words the "bending" should be equal. Hope it's a little clearer now.</p>
| 8,842 |
[
-0.032276399433612823,
-0.008996240794658661,
-0.009667935781180859,
-0.020605551078915596,
0.05305549502372742,
0.03883872553706169,
-0.03636888042092323,
-0.01456279307603836,
-0.010769532062113285,
-0.021865172311663628,
-0.005925680976361036,
0.054094795137643814,
0.04263551905751228,
0.027921246364712715,
0.0240484531968832,
0.00221365038305521,
-0.018586795777082443,
-0.022379521280527115,
-0.0009580421028658748,
-0.04302047938108444,
0.016604458913207054,
-0.00047636288218200207,
-0.0012579465983435512,
-0.0013877039309591055,
-0.029390012845396996,
0.00721631059423089,
0.04020264744758606,
0.006763956975191832,
0.012734881602227688,
0.029950464144349098,
-0.002569720381870866,
0.005376237444579601,
-0.027560293674468994,
0.06242536008358002,
0.05380457639694214,
0.002648663707077503,
-0.06590215861797333,
0.0024783604312688112,
-0.03119191899895668,
0.004669381305575371,
-0.04274889454245567,
-0.047271426767110825,
-0.03773918002843857,
0.0677066221833229,
-0.05429929122328758,
0.02471824362874031,
0.03932039067149162,
0.007022489327937365,
0.057384852319955826,
-0.0494762659072876,
0.08065862208604813,
0.008369720540940762,
0.03865322843194008,
-0.001593584194779396,
0.014246837235987186,
0.012330632656812668,
0.07338345050811768,
0.06728079915046692,
-0.0323270708322525,
-0.008135901764035225,
-0.028963377699255943,
-0.05082586035132408,
-0.020506778731942177,
-0.020524559542536736,
-0.0023928640875965357,
0.037322547286748886,
-0.021167997270822525,
-0.032127805054187775,
0.03843186795711517,
0.012033171020448208,
0.02277868241071701,
0.0017534130020067096,
0.03234625607728958,
0.007680203299969435,
-0.02686438523232937,
-0.02109433338046074,
0.05166956037282944,
0.021145222708582878,
0.040949948132038116,
0.005132055375725031,
-0.004895887803286314,
0.0021315421909093857,
0.05276763439178467,
0.041490599513053894,
0.024007219821214676,
-0.030385348945856094,
0.09342451393604279,
-0.0053263441659510136,
0.020005477592349052,
0.055367421358823776,
0.028720932081341743,
-0.023346759378910065,
0.007090594619512558,
-0.007544743828475475,
-0.0230275709182024,
0.034793734550476074,
-0.0037010693922638893,
0.025564782321453094,
-0.01399948075413704,
0.018067263066768646,
-0.016919778659939766,
-0.03743636608123779,
0.0462971068918705,
0.06945828348398209,
0.017487933859229088,
-0.023273847997188568,
-0.07014362514019012,
-0.0015228416305035353,
-0.0017052392940968275,
-0.02804415300488472,
-0.001953638158738613,
0.022273890674114227,
-0.02396964654326439,
-0.04646550118923187,
0.015658102929592133,
-0.012509647756814957,
0.0003056959540117532,
-0.016811007633805275,
0.037559930235147476,
0.07148712873458862,
0.062335215508937836,
-0.05173215642571449,
0.035011325031518936,
-0.03928856551647186,
-0.03980838507413864,
0.022771956399083138,
0.059786271303892136,
-0.034104373306035995,
-0.020772306248545647,
0.015568479895591736,
0.003457240527495742,
-0.02179494872689247,
0.0012836601817980409,
-0.010557852685451508,
0.03322829306125641,
-0.013765078969299793,
-0.1154579296708107,
-0.04244783893227577,
0.04063008725643158,
0.022741563618183136,
0.012772238813340664,
-0.05492820590734482,
0.011374954134225845,
0.010548555292189121,
0.08951850235462189,
-0.005302964244037867,
0.04144846647977829,
0.023856375366449356,
0.026682838797569275,
0.00786579679697752,
-0.010385480709373951,
0.0011617772979661822,
0.0026624395977705717,
-0.05217934027314186,
-0.01320330798625946,
-0.049614813178777695,
0.0004577364306896925,
0.02747119404375553,
0.00027554354164749384,
-0.04024827107787132,
0.06223279982805252,
-0.019400127232074738,
0.04136855527758598,
-0.008017955347895622,
-0.0029262700118124485,
-0.0017387800617143512,
0.055680807679891586,
0.024721786379814148,
-0.03472296893596649,
0.012717739678919315,
0.04004107415676117,
0.013391879387199879,
-0.013593912124633789,
0.025921015068888664,
0.08273105323314667,
-0.05897808447480202,
-0.01709100976586342,
-0.020260944962501526,
-0.01410889532417059,
-0.03544357419013977,
-0.02719227969646454,
-0.028329556807875633,
-0.008247056044638157,
-0.02907634526491165,
-0.026820501312613487,
0.03512345626950264,
0.013467314653098583,
0.029236014932394028,
-0.014621204696595669,
-0.03756685182452202,
-0.028168607503175735,
-0.07990974932909012,
0.04499971866607666,
-0.05967039614915848,
-0.017853830009698868,
0.006022165529429913,
0.018774710595607758,
0.02373512275516987,
-0.04606383293867111,
-0.006975930649787188,
-0.025538654997944832,
0.026982290670275688,
-0.031855788081884384,
-0.028824161738157272,
-0.02113947458565235,
0.049067165702581406,
-0.000010595547792036086,
0.017296219244599342,
-0.00008442541002295911,
0.017234530299901962,
-0.019455812871456146,
0.003272092202678323,
-0.017800074070692062,
0.0024766467977315187,
0.00022122121299616992,
0.0006030932418070734,
0.015071126632392406,
-0.01956949383020401,
-0.016649099066853523,
0.047529034316539764,
-0.062057722359895706,
0.05541225150227547,
0.07737265527248383,
-0.019793594256043434,
0.023717936128377914,
0.0520746186375618,
0.007217549253255129,
-0.00118858995847404,
-0.005664691794663668,
-0.026840023696422577,
-0.022360241040587425,
-0.0005898429662920535,
0.020725995302200317,
0.001665181596763432,
-0.018767569214105606,
-0.000734236091375351,
0.03165591508150101,
0.036920662969350815,
-0.001844859216362238,
0.012529564090073109,
0.04362571984529495,
-0.014241855591535568,
-0.003997415769845247,
0.017861027270555496,
0.04724800959229469,
0.010790837928652763,
0.023861726745963097,
0.0022943890653550625,
0.0053630853071808815,
0.00859876535832882,
-0.03615999594330788,
0.0426793098449707,
-0.0031657093204557896,
0.03696839511394501,
0.016678227111697197,
-0.026861531659960747,
0.04477724805474281,
0.0032771506812423468,
0.03140616789460182,
0.03850850090384483,
-0.01549164392054081,
-0.000949042965658009,
-0.036949388682842255,
0.00847155973315239,
0.017772262915968895,
0.005530096124857664,
-0.027417143806815147,
-0.009224947541952133,
0.03469960391521454,
-0.06146268919110298,
0.00794845912605524,
0.012043492868542671,
0.0008479945245198905,
-0.012158283032476902,
0.008686978369951248,
0.0266664270311594,
0.023051269352436066,
0.029645023867487907,
-0.016956668347120285,
-0.031220225617289543,
-0.009613093920052052,
-0.03026489168405533,
-0.017625275999307632,
0.013486414216458797,
-0.07892437279224396,
0.05201031640172005,
-0.026629451662302017,
-0.02457532472908497,
0.06477170437574387,
-0.0011033503105863929,
0.0037000125739723444,
0.0683581531047821,
-0.006591105833649635,
-0.047265563160181046,
-0.0024693384766578674,
-0.0714760422706604,
-0.03109688125550747,
-0.027226291596889496,
-0.009580456651747227,
0.02879321202635765,
0.02334531582891941,
-0.023229185491800308,
0.03813936188817024,
-0.06335262209177017,
-0.053378429263830185,
-0.029788624495267868,
-0.004425226245075464,
0.030253160744905472,
0.0076590003445744514,
0.009218689985573292,
0.05354270711541176,
-0.028640273958444595,
-0.05512148141860962,
-0.040311913937330246,
-0.060427792370319366,
0.04295208305120468,
0.012202667072415352,
0.03961027041077614,
-0.021915053948760033,
-0.01017211377620697,
0.07463537156581879,
0.04582676663994789,
-0.029096152633428574,
-0.05500916764140129,
-0.008024840615689754,
0.02199529856443405,
0.004768832586705685,
0.011308899149298668,
0.024636797606945038,
0.01526399701833725,
0.023687956854701042,
0.05625401809811592,
0.0367814302444458,
-0.018236193805933,
-0.02998027205467224,
0.00019226166477892548,
-0.01979186199605465,
0.023966502398252487,
-0.0016412175027653575,
0.0008004096453078091,
0.0534212589263916,
-0.005771576892584562,
0.013831740245223045,
0.002987896790727973,
0.042301226407289505,
-0.013252929784357548,
-0.022554226219654083,
0.05433383956551552,
0.016628289595246315,
-0.008560556918382645,
0.0020830126013606787,
0.023440027609467506,
-0.023770295083522797,
-0.018346058204770088,
0.015865938737988472,
0.026308849453926086,
0.03383525833487511,
0.009342079050838947,
-0.0033070575445890427,
0.03126077726483345,
0.02166546881198883,
-0.050622083246707916,
-0.04366443306207657,
0.0002433868939988315,
-0.012492616660892963,
0.04588881880044937,
0.00038154947105795145,
-0.015461205504834652,
0.05071429908275604,
0.06286747753620148,
0.02223045937716961,
-0.032633405178785324,
-0.046850766986608505,
0.004947267938405275,
-0.05672997608780861,
-0.02015046589076519,
0.008122959174215794,
0.02868684194982052,
0.003778755897656083,
0.04014156013727188,
0.01010152604430914,
0.042526356875896454,
0.0087510347366333,
0.021272270008921623,
-0.08335541188716888,
0.0448048897087574,
-0.04564179107546806,
-0.016017671674489975,
0.007100269664078951,
0.005343884229660034,
-0.012722289189696312,
-0.05696745589375496,
0.01063695177435875,
-0.008018841035664082,
-0.013843879103660583,
-0.044503532350063324,
0.006407783832401037,
-0.029043057933449745,
-0.05739232897758484,
0.0004894401645287871,
0.030872739851474762,
0.04313937947154045,
-0.034339096397161484,
0.006792151369154453,
0.016008134931325912,
-0.01892315410077572,
-0.029843391850590706,
-0.023643704131245613,
0.027331426739692688,
-0.0031433196272701025,
0.010957923717796803,
0.017830034717917442,
0.001239748322404921,
-0.010316899046301842,
0.033693376928567886,
0.013325052335858345,
0.029102271422743797,
0.0001982509857043624,
-0.011862317100167274,
-0.015902763232588768,
-0.06217765808105469,
-0.01258903183043003,
0.011542929336428642,
0.05028999596834183,
-0.008048886433243752,
-0.03115738183259964,
0.003424977418035269,
0.048807721585035324,
0.004769293125718832,
0.03832133486866951,
0.04051079601049423,
0.01108996756374836,
-0.0028959682676941156,
-0.03876834362745285,
0.018011951819062233,
-0.05302320793271065,
-0.026413965970277786,
0.020368168130517006,
-0.02983235940337181,
-0.02347254939377308,
0.04025476798415184,
0.003134094877168536,
-0.0347863994538784,
-0.012473628856241703,
0.005352946929633617,
-0.020582690834999084,
0.04089554771780968,
-0.01814371719956398,
-0.029571235179901123,
0.0008421273087151349,
0.07223179191350937,
0.042799606919288635,
0.009289971552789211,
-0.012712011113762856,
-0.0788201317191124,
-0.00847863219678402,
0.03819112852215767,
0.00517416512593627,
-0.02681749314069748,
-0.014446372166275978,
-0.011801555752754211,
-0.015629520639777184,
0.03546193614602089,
0.010964907705783844,
0.007788326591253281,
-0.006144999992102385,
0.0021400509867817163,
0.012477373704314232,
-0.011127320118248463,
-0.038653310388326645,
0.02453927882015705,
-0.007195358630269766,
-0.03263234719634056,
0.01343175582587719,
0.03265739604830742,
-0.013400468975305557,
-0.0017161078285425901,
-0.0011911105830222368,
0.010519959963858128,
0.03490538150072098,
0.011363494209945202,
0.0016071964055299759,
0.04209272935986519,
-0.03761602193117142,
-0.07706362754106522,
0.0038574961945414543,
0.030765706673264503,
-0.017468538135290146,
0.042452264577150345,
-0.026707664132118225,
0.009399830363690853,
0.028407113626599312,
-0.03951341286301613,
-0.007621126715093851,
-0.02002904936671257,
-0.024185897782444954,
0.011849548667669296,
0.04457378759980202,
0.004266335163265467,
0.033773016184568405,
0.02680743671953678,
-0.018498700112104416,
-0.021999845281243324,
0.011588400229811668,
0.05095892772078514,
-0.03764035180211067,
-0.013221604749560356,
-0.02880699373781681,
-0.014555041678249836,
-0.0361616425216198,
0.031163062900304794,
0.009491410106420517,
0.0003230092115700245,
-0.012215351685881615,
-0.0299949049949646,
-0.0471382774412632,
0.02363508939743042,
0.024242045357823372,
-0.009278705343604088,
0.009712989442050457,
0.02553601749241352,
0.008135623298585415,
0.00019144071848131716,
-0.010500450618565083,
0.019399812445044518,
-0.015799041837453842,
0.049954164773225784,
-0.0007275713142007589,
0.023996712639927864,
-0.022859161719679832,
-0.015541915781795979,
0.0071721430867910385,
-0.0377369299530983,
0.028381116688251495,
0.015205341391265392,
-0.012726674787700176,
0.06486937403678894,
-0.04969995468854904,
-0.0188395157456398,
0.009448674507439137,
-0.03499257564544678,
-0.004478608723729849,
-0.028848635032773018,
-0.022848177701234818,
0.032662346959114075,
0.027533814311027527,
-0.08966800570487976,
-0.039583172649145126,
0.024298779666423798,
-0.03555353358387947,
0.02290780283510685,
-0.029342718422412872,
0.021519098430871964,
-0.064277783036232,
-0.02615177445113659,
-0.02048717439174652,
0.022986233234405518,
-0.027849191799759865,
-0.013903283514082432,
0.004931006580591202,
-0.02611001767218113,
0.06333627551794052,
-0.025034120306372643,
-0.004893163219094276,
-0.013761374168097973,
-0.024776365607976913,
0.0019310753559693694,
-0.0010049152188003063,
0.07479770481586456,
-0.030524609610438347,
-0.01950061321258545,
-0.003453795099630952,
-0.015334912575781345,
0.023479923605918884,
-0.018508031964302063,
-0.0018067024648189545,
0.02410193718969822,
-0.010032928548753262,
-0.0030847874004393816,
-0.009096451103687286,
0.03029491752386093,
-0.025388820096850395,
-0.011145733296871185,
-0.021690918132662773,
0.008569239638745785,
0.013665792532265186,
-0.06446753442287445,
0.030000869184732437,
0.028943298384547234,
-0.006559973116964102,
0.01642676815390587,
0.061222344636917114,
0.008641590364277363,
-0.03773515298962593,
0.010611358098685741,
-0.03390336409211159,
0.03826707974076271,
-0.023541729897260666,
0.00017023606051225215,
-0.007009749300777912,
-0.010002766735851765,
-0.009592413902282715,
0.0006621060892939568,
-0.0004087706620339304,
0.028520559892058372,
0.07485166937112808,
0.000449068786110729,
0.04016650840640068,
0.03399938344955444,
0.013935142196714878,
-0.0064371200278401375,
-0.020792922005057335,
0.011190739460289478,
-0.022797679528594017,
-0.006690878886729479,
0.05575650930404663,
-0.026407582685351372,
-0.007799625862389803,
0.005955004133284092,
0.01095710601657629,
-0.03409428521990776,
0.00745612196624279,
0.01428158674389124,
0.01741422340273857,
0.037253689020872116,
0.01043512299656868,
-0.029110467061400414,
0.014813359826803207,
0.0066075497306883335,
0.029592616483569145,
-0.0285776536911726,
-0.007544412277638912,
0.037138450890779495,
0.015157795511186123,
0.009636366739869118,
-0.03643336147069931,
-0.006426459643989801,
-0.0584779754281044,
0.022326644510030746,
0.005432141479104757,
0.002586074871942401,
0.012386579066514969,
0.05303480476140976,
0.056789711117744446,
0.005092419683933258,
0.01318441517651081,
-0.006012126803398132,
-0.06391964107751846,
-0.028867846354842186,
-0.057621996849775314,
-0.03901765123009682,
0.012002602219581604,
-0.0028536131139844656,
-0.04328477010130882,
-0.001818618387915194,
-0.025266123935580254,
0.0005760467029176652,
0.03841409087181091,
0.03423279523849487,
0.004874176811426878,
0.0851096510887146,
-0.01239524781703949,
0.029187975451350212,
0.00612258818000555,
-0.027749473229050636,
0.11202845722436905,
0.04231218621134758,
0.00629453593865037,
-0.02931143157184124,
-0.014642341062426567,
-0.017025809735059738,
-0.024164479225873947,
-0.013907380402088165,
0.026975221931934357,
0.013609277084469795,
0.01029160339385271,
-0.006634589750319719,
0.032818276435136795,
0.010690032504498959,
-0.04237068444490433,
0.08583294600248337,
-0.06900092214345932,
-0.004208436701446772,
-0.011853864416480064,
-0.011094417423009872,
-0.014321953058242798,
0.0304441936314106,
-0.032700955867767334,
0.02989465743303299,
-0.017282702028751373,
0.0374542698264122,
0.004052772652357817,
-0.03191319480538368,
0.0015907477354630828,
0.025376351550221443,
-0.0454445444047451,
0.014756706543266773,
0.032801367342472076,
-0.03536410629749298,
-0.06471668928861618,
0.0071265422739088535,
0.0333259254693985,
-0.016777265816926956,
0.015799062326550484,
0.03610335662961006,
-0.01790023036301136,
0.02561246044933796,
0.031801629811525345,
0.010953115299344063,
-0.024368729442358017,
-0.018524345010519028,
-0.060337722301483154,
0.037618137896060944,
0.013463997282087803,
0.01222897693514824,
0.009406259283423424,
0.014274941757321358,
0.0420718751847744,
-0.06898349523544312,
0.0005264544161036611,
-0.02189655601978302,
0.019319359213113785,
0.01344315055757761,
-0.018430957570672035,
-0.0021884168963879347,
0.03832945600152016,
0.00046254799235612154,
0.015325869433581829,
0.006826979108154774,
-0.004768694750964642,
0.007159617729485035,
-0.03798060864210129,
0.04685356467962265,
-0.025403400883078575,
-0.006816401612013578,
-0.014062175527215004,
-0.026288799941539764,
-0.03795919194817543,
0.01676763966679573,
0.032068975269794464,
0.00029866021941415966,
0.01286980602890253,
-0.015342549420893192,
0.004373621661216021,
0.026763593778014183,
-0.04999984800815582,
0.03839166834950447,
-0.0004773855034727603,
-0.021379731595516205,
-0.010896225459873676,
0.004530593752861023,
0.03001183271408081,
0.01181002426892519,
-0.006447228603065014,
0.04197085648775101,
-0.013677427545189857,
0.00941930990666151,
-0.019919952377676964,
-0.009693908505141735,
-0.012192807160317898,
0.05277259275317192,
-0.03448633477091789,
0.002815099898725748,
-0.014242196455597878,
0.031090477481484413,
0.006696716882288456,
-0.020050594583153725,
-0.018192347139120102,
0.0436784066259861,
-0.003670032136142254,
0.017580365762114525,
0.03148489072918892,
-0.0038441093638539314,
-0.005990531295537949,
0.00999331846833229,
-0.01778913289308548,
-0.06933403015136719,
-0.029079841449856758,
-0.03585515543818474,
0.010805376805365086,
-0.024307647719979286,
0.011000228114426136,
0.01651878096163273,
0.06586245447397232,
-0.011558076366782188,
0.030229292809963226,
-0.04411883279681206,
0.004346494097262621,
-0.07980538159608841,
0.023664897307753563,
0.017673909664154053,
-0.02025926299393177,
0.02588239312171936,
0.0432971827685833,
-0.030249502509832382,
-0.037688981741666794,
0.014512406662106514,
0.022121576592326164,
0.01822894625365734,
0.004419409669935703,
0.04555559158325195,
-0.029769396409392357,
0.04347353056073189,
-0.0018839872209355235,
-0.03605010360479355,
0.02026117406785488,
-0.050077300518751144,
-0.052070003002882004,
0.01216182392090559,
0.007791360840201378,
0.01936325989663601,
0.0018253546440973878,
-0.027677396312355995,
-0.025389522314071655,
0.055294934660196304,
0.011632988229393959,
-0.003953551407903433,
0.0050428276881575584,
-0.038700539618730545,
-0.030812067911028862,
-0.017881279811263084,
0.03299565240740776,
-0.0469016470015049,
-0.021066416054964066,
0.010830068029463291,
0.0001365401258226484,
-0.029683811590075493,
-0.005433596670627594,
-0.004879045765846968,
-0.01752997748553753,
-0.012385067529976368,
-0.0019463319331407547,
0.023852979764342308,
0.03322308510541916,
0.07820562273263931,
-0.08724034577608109,
-0.00017598766135051847,
0.026880547404289246,
0.01373701635748148,
-0.09362172335386276,
-0.010564316995441914,
0.016973933205008507,
-0.025616640225052834,
0.012132156640291214,
-0.04377192631363869,
0.021560439839959145,
-0.010600559413433075,
-0.053167156875133514,
0.01191391795873642,
-0.02735045738518238,
0.0375819131731987,
-0.02230837009847164,
-0.02112157642841339,
-0.010618584230542183,
0.04651028290390968,
0.05395480990409851,
0.054305851459503174,
0.03620758652687073,
-0.019456494599580765,
-0.003290907945483923,
0.006625187583267689,
-0.007117449305951595,
0.038982003927230835,
-0.00814846158027649,
0.004276406019926071,
0.05065246671438217,
-0.006303037516772747,
-0.037042442709207535,
0.01917927712202072,
-0.0019420795142650604,
-0.0019471985287964344,
-0.024442696943879128,
0.012751110829412937,
0.019569074735045433,
-0.005201907828450203,
-0.01741175353527069,
-0.023447493091225624,
0.006290638819336891,
0.03509443625807762,
0.003963536582887173,
0.00792011059820652,
0.003544508945196867,
-0.02076169289648533,
-0.002811592537909746,
-0.037102650851011276,
-0.04535597562789917,
0.0216270312666893,
-0.007148470729589462,
-0.036519940942525864,
-0.034193120896816254,
0.023769987747073174,
0.009334401227533817,
-0.014524545520544052,
0.017928678542375565,
-0.033617112785577774,
0.01623005047440529,
0.018717236816883087,
-0.02057940699160099,
-0.04340992495417595,
0.023998809978365898,
-0.00931489933282137,
-0.0051063112914562225,
-0.02371281385421753,
-0.00628728186711669,
-0.007354584988206625,
-0.050509411841630936,
-0.0011088129831478,
-0.027242815122008324,
-0.008828948251903057,
-0.016043784096837044,
-0.043487876653671265,
-0.0090503403916955,
0.04651060327887535,
0.02276035025715828,
0.012872651219367981,
-0.007019642740488052,
-0.029997672885656357,
-0.01411467231810093,
-0.06521939486265182,
0.04694332182407379,
0.0030653318390250206,
0.013897519558668137,
-0.04924827441573143,
0.018450772389769554,
0.0029166804160922766,
0.02766028791666031,
0.015722475945949554,
-0.047185126692056656,
-0.02364874817430973,
0.05312880873680115,
0.009559765458106995,
-0.006733344867825508,
-0.045934803783893585,
-0.007409758400171995,
-0.0214838907122612,
-0.06967823207378387,
-0.013607056811451912,
-0.005771582946181297,
-0.006375066936016083,
0.00364629365503788,
-0.01370854303240776,
-0.007113100029528141,
0.046044789254665375,
0.005837682168930769,
-0.028233330696821213,
0.05222877487540245,
0.03892316296696663,
-0.000028804604880861007,
0.07425131648778915,
0.020902303978800774,
-0.0190094243735075,
0.030303580686450005,
-0.025810280814766884,
-0.015634573996067047,
0.03592149168252945,
-0.006155355367809534,
0.011130890808999538,
-0.032531578093767166,
-0.008837088942527771,
0.031135614961385727,
-0.030696053057909012,
-0.012748838402330875,
0.0275822002440691,
-0.06276581436395645,
0.01590658165514469,
0.03422942012548447,
0.014365891925990582,
0.03125336766242981,
-0.015349180437624454,
-0.01263789925724268,
0.03804156184196472,
-0.002010219730436802,
0.00797328632324934,
0.029146648943424225,
0.023769153282046318,
0.025797758251428604,
0.008388757705688477,
0.025975823402404785,
-0.015876969322562218,
0.03882310539484024,
-0.004406027030199766,
0.025873009115457535,
-0.0256667360663414,
0.026202905923128128,
0.0067923651076853275,
0.0006283239345066249,
-0.014036629348993301,
-0.002774203894659877,
-0.018015285953879356,
0.027979856356978416,
-0.0007814880809746683,
-0.020603163167834282,
0.030439171940088272,
0.002260760869830847,
0.0058499849401414394,
0.012581524439156055,
0.019869355484843254,
0.07111865282058716,
0.05814489722251892,
-0.035675980150699615,
0.0170268677175045,
-0.03654946759343147,
0.01769367605447769,
0.014267432503402233,
0.013596921227872372,
-0.013657355681061745,
-0.007066636346280575,
0.009741907939314842,
-0.023579871281981468,
-0.05395340174436569,
-0.029754966497421265,
0.051072340458631516,
0.008255423977971077,
0.03561105206608772,
-0.014872655272483826,
-0.013567783869802952,
-0.0327143631875515,
0.07136908918619156,
-0.09498867392539978,
-0.02470187284052372,
-0.03823300823569298,
0.0032959990203380585,
0.00310136703774333,
-0.013484510593116283
] |
<p>Background: I have written a pop-science book explaining quantum mechanics through <a href="http://dogphysics.com/">imaginary conversations with my dog</a>-- the dog serves as a sort of reader surrogate, popping in occasionally to ask questions that a non-scientist might ask-- and I am now working on a sequel. In the sequel, I find myself having to talk about particle physics a bit, which is not my field, and I've hit a dog-as-reader question that I don't have a good answer to, which is, basically, "What purpose, if any, do higher-generation particles serve?"</p>
<p>To put it in slightly more physics-y terms: The Standard Model contains twelve material particles: six leptons (the electron, muon, and tau, plus associated neutrinos) and six quarks (up-down, strange-charm, top-bottom). The observable universe only uses four, though: every material object we see is made up of electrons and up and down quarks, and electron neutrinos are generated in nuclear reactions that move between different arrangements of electrons and up and down quarks. The other eight turn up only in high-energy physics situation (whether in man-made accelerators, or natural occurances like cosmic ray collisions), and don't stick around for very long before they decay into the four common types. So, to the casual observer, there doesn't seem to be an obvious purpose to the more exotic particles. So why are they there?</p>
<p>I'm wondering if there is some good reason why the universe as we know it has to have twelve particles rather than just four. Something like "Without the second and third generations of quarks and leptons, it's impossible to generate enough CP violation to explain the matter-antimatter asymmetry we observe." Only probably not that exact thing, because as far as I know, there isn't any way to explain the matter-antimatter asymmetry we observe within the Standard Model. But something along those lines-- some fundamental feature of our universe that requires the existence of muons and strange quarks and all the rest, and would prevent a universe with only electrons and up and down quarks.</p>
<p>The question is not "why do we think there are there three generations rather than two or four?" I've seen the answers to that here and elsewhere. Rather, I'm asking "Why are there three generations rather than only one?" Is there some important process in the universe that requires there to be muons, strange quarks, etc. for things to end up like they are? Is there some reason beyond "we know they exist because they're there," something that would prevent us from making a universe like the one we observe at low energy using only electrons, up and down quarks, and electron neutrinos?</p>
<p>Any pointers you can give to an example of some effect that depends on the presence of the higher Standard Model generations would be much appreciated. Having it already in terms that would be comprehensible to a non-scientist would be a bonus.</p>
| 8,843 |
[
-0.009144975803792477,
-0.01983504183590412,
0.051072414964437485,
-0.04312574118375778,
0.037604134529829025,
0.04529600590467453,
-0.018221165984869003,
-0.019488412886857986,
-0.02010577917098999,
-0.01963423192501068,
0.04798125475645065,
0.016179993748664856,
-0.0022473621647804976,
0.00114283652510494,
0.007346452213823795,
0.034891944378614426,
-0.011213348247110844,
-0.05037562921643257,
-0.02344192937016487,
-0.039106421172618866,
0.01495412364602089,
-0.010466344654560089,
-0.02067684940993786,
0.008026203140616417,
-0.03780343756079674,
0.029618537053465843,
0.015117096714675426,
-0.012810821644961834,
0.010033356957137585,
0.04515397921204567,
0.019618941470980644,
-0.015639109537005424,
0.05016417056322098,
-0.00275033968500793,
0.03159521892666817,
0.015958266332745552,
0.02072071097791195,
-0.0528755784034729,
0.019383205100893974,
0.037038762122392654,
-0.051159121096134186,
0.004674559459090233,
-0.03018629178404808,
-0.0002282322820974514,
-0.0695904791355133,
0.01185317151248455,
-0.013677437789738178,
0.020957788452506065,
0.07234964519739151,
-0.05107406899333,
0.03754609823226929,
0.0364191010594368,
0.026130739599466324,
0.012730821967124939,
-0.00864227395504713,
-0.013865193352103233,
0.07485095411539078,
0.02465839497745037,
0.02827990986406803,
-0.08122476935386658,
-0.011316012591123581,
-0.011386007070541382,
-0.0005536071257665753,
0.022170063108205795,
-0.00026840411010198295,
0.01097746193408966,
-0.00020903874246869236,
0.009108318947255611,
0.013758831657469273,
-0.014514866285026073,
0.010280255228281021,
-0.0049077607691287994,
0.0045599858276546,
0.05203147232532501,
-0.0003015309921465814,
-0.027335233986377716,
0.010871032252907753,
0.01451954897493124,
0.03636394441127777,
0.012491214089095592,
-0.016965501010417938,
-0.004891554359346628,
0.007069886662065983,
0.00878499262034893,
0.00004890229320153594,
0.0020541311241686344,
0.07253847271203995,
-0.025253400206565857,
-0.013327671214938164,
0.06758741289377213,
-0.013672547414898872,
-0.00005400694863055833,
0.06618792563676834,
0.032636646181344986,
-0.03638632595539093,
0.031174080446362495,
0.005884664133191109,
0.023831380531191826,
0.017109669744968414,
0.02621537074446678,
0.003782446961849928,
-0.03772968426346779,
0.026458030566573143,
0.07763093709945679,
-0.01386741828173399,
-0.039071548730134964,
-0.03494694083929062,
0.009874684736132622,
-0.02744458243250847,
0.010675379075109959,
-0.02555467188358307,
0.000751621788367629,
0.0017661942401900887,
0.004651125054806471,
-0.0006809596088714898,
0.00822782889008522,
0.020359383895993233,
-0.013683057390153408,
0.06977521628141403,
0.060988154262304306,
0.02624170482158661,
-0.03554674983024597,
-0.02121542952954769,
-0.008100160397589207,
-0.07885805517435074,
-0.011253432370722294,
-0.018402177840471268,
-0.0034212018363177776,
-0.00855247676372528,
0.019625002518296242,
-0.005400749389082193,
0.011794477701187134,
0.0403372086584568,
0.0036047324538230896,
0.04374585673213005,
0.00815864559262991,
-0.053450774401426315,
-0.06800375133752823,
0.06834081560373306,
-0.035337064415216446,
-0.047837045043706894,
-0.07953616231679916,
-0.013053476810455322,
0.015424530021846294,
0.07276826351881027,
-0.027075206860899925,
-0.04495516046881676,
0.01012867409735918,
0.01472820620983839,
0.04025520384311676,
0.030775319784879684,
0.027762845158576965,
-0.03544587641954422,
-0.023627815768122673,
-0.023547712713479996,
-0.07078825682401657,
0.03095976635813713,
0.00860097911208868,
0.004248335026204586,
-0.00022583176905754954,
0.043501172214746475,
-0.007794592529535294,
-0.0017604734748601913,
-0.004081391729414463,
-0.027805252000689507,
-0.03958088159561157,
0.06960245966911316,
0.03494969755411148,
-0.017597205936908722,
0.02086356095969677,
-0.0031614021863788366,
0.009390614926815033,
-0.010651770047843456,
0.034774668514728546,
0.015397464856505394,
-0.015406991355121136,
-0.024346135556697845,
-0.03178631514310837,
-0.012753759510815144,
-0.02159278281033039,
-0.011987851932644844,
-0.028506428003311157,
-0.010350106284022331,
-0.0037434257101267576,
0.033254243433475494,
-0.0001646858436288312,
-0.019692888483405113,
-0.025141490623354912,
0.021529849618673325,
-0.032657090574502945,
-0.01965450681746006,
-0.0755729153752327,
-0.039696212857961655,
-0.03343204781413078,
-0.03137388825416565,
0.02073775790631771,
-0.027646774426102638,
-0.024258706718683243,
0.0006924652843736112,
-0.03511246666312218,
0.014218500815331936,
0.04919300973415375,
0.04018730670213699,
0.021409932523965836,
-0.01775899901986122,
0.05897209048271179,
0.026750119403004646,
-0.01750798523426056,
0.01973615027964115,
-0.018257448449730873,
-0.0354829803109169,
-0.015864478424191475,
-0.020165689289569855,
0.009543978609144688,
-0.013585420325398445,
-0.002683353843167424,
0.03265398368239403,
-0.03205478563904762,
-0.034570738673210144,
0.04740035533905029,
-0.017809178680181503,
0.09585428237915039,
-0.002481082221493125,
-0.0007306986954063177,
0.0004629902832675725,
0.04294334724545479,
0.010621459223330021,
0.05038168281316757,
-0.006179184187203646,
-0.017065444961190224,
-0.07292082160711288,
-0.03536077216267586,
0.027176113799214363,
0.024492191150784492,
-0.03443296253681183,
0.051085419952869415,
-0.004268466029316187,
0.057894427329301834,
0.004623724147677422,
-0.002057389123365283,
-0.05037286877632141,
-0.04984814301133156,
0.007111770566552877,
-0.01239759847521782,
0.011047345586121082,
0.03879416361451149,
0.026096342131495476,
-0.011395245790481567,
-0.03367312252521515,
-0.044540684670209885,
-0.025527065619826317,
0.018911253660917282,
0.022558892145752907,
0.004819236695766449,
-0.009055433794856071,
-0.05722862482070923,
0.017753897234797478,
-0.007873269729316235,
0.01297303568571806,
0.005439497530460358,
-0.0174400731921196,
0.00855063647031784,
-0.01525974366813898,
-0.026059964671730995,
-0.01542625017464161,
-0.006346946582198143,
0.008499696850776672,
-0.024211639538407326,
0.02702925354242325,
-0.035475753247737885,
0.016350390389561653,
-0.028115639463067055,
-0.030157264322042465,
0.018883755430579185,
-0.011114118620753288,
-0.004985988140106201,
0.007750861346721649,
0.05461020767688751,
-0.022911306470632553,
-0.023415422067046165,
0.025563418865203857,
0.004767157137393951,
-0.005255932919681072,
0.05439996346831322,
-0.05949743837118149,
-0.010784636251628399,
-0.04471057280898094,
-0.04021002724766731,
0.015751486644148827,
0.018772251904010773,
0.0030843988060951233,
0.02574946917593479,
-0.009334791451692581,
-0.045804139226675034,
-0.021595288068056107,
-0.020724570378661156,
-0.00955524668097496,
-0.05719723179936409,
0.01026526652276516,
0.06913500279188156,
0.02726157009601593,
-0.045142948627471924,
-0.038839034736156464,
-0.06168763339519501,
-0.044110849499702454,
0.0026966023724526167,
-0.023194143548607826,
0.006038317456841469,
-0.008218739181756973,
-0.022136051207780838,
0.03775224834680557,
-0.055206745862960815,
-0.0020858007483184338,
-0.07766461372375488,
-0.04439866915345192,
-0.01247834600508213,
-0.005442129448056221,
0.04864680767059326,
0.003404575400054455,
-0.015209834091365337,
0.07811642438173294,
0.037023816257715225,
-0.03688063845038414,
-0.00015421811258420348,
0.00938600953668356,
0.01259570848196745,
-0.05621736869215965,
0.04680987820029259,
0.04800250008702278,
0.009971343912184238,
-0.013699053786695004,
0.0013918414479121566,
0.05631386861205101,
-0.013613286428153515,
-0.028950951993465424,
-0.0355633869767189,
-0.007622442673891783,
-0.017006469890475273,
0.0012801127741113305,
0.03428016975522041,
0.01982804574072361,
-0.0024549735244363546,
-0.000048377984057879075,
-0.004401157144457102,
0.023440103977918625,
0.014162850566208363,
-0.04028179496526718,
0.08718792349100113,
0.0192527174949646,
0.008063597604632378,
0.013638286851346493,
0.018750539049506187,
0.008127059787511826,
-0.069939024746418,
-0.04239558428525925,
0.009852803312242031,
0.053168706595897675,
-0.014924956485629082,
-0.007269758265465498,
0.030646225437521935,
0.052486494183540344,
-0.03981693461537361,
-0.002954116789624095,
-0.016948774456977844,
0.008229290135204792,
-0.03967108950018883,
0.0015720194205641747,
0.030572522431612015,
0.06842058897018433,
0.04642326012253761,
0.05858026072382927,
0.014687974005937576,
-0.041532859206199646,
-0.02263287454843521,
-0.0012285927077755332,
-0.001958946231752634,
-0.04429815709590912,
0.03388282284140587,
-0.010516416281461716,
0.0319051519036293,
0.0022289271000772715,
0.009068641811609268,
-0.02567998878657818,
0.0010391483083367348,
-0.09613800793886185,
0.005197979509830475,
-0.05011964961886406,
0.025241326540708542,
-0.020888321101665497,
-0.011631295084953308,
0.005254251882433891,
-0.03414390981197357,
-0.02979440987110138,
-0.03643798828125,
-0.034845463931560516,
-0.03045005351305008,
0.028869332745671272,
-0.08405756950378418,
-0.06111525371670723,
-0.02348676696419716,
0.03573727235198021,
0.08171309530735016,
-0.02794664166867733,
-0.023546092212200165,
-0.025400348007678986,
-0.010838326066732407,
0.003887519706040621,
-0.0282646082341671,
0.028377288952469826,
0.0065422505140304565,
-0.011409918777644634,
0.005168568808585405,
0.02467888779938221,
-0.03147558495402336,
-0.011255170218646526,
0.023557469248771667,
0.06361433863639832,
-0.0025623771362006664,
0.030033152550458908,
-0.022244524210691452,
-0.04403400048613548,
-0.03276132419705391,
0.008490204811096191,
0.029996607452630997,
-0.015193610452115536,
0.013916484080255032,
0.04055185243487358,
0.02308606542646885,
-0.03287703916430473,
0.03855240345001221,
0.028745081275701523,
-0.012942059896886349,
-0.014713458716869354,
-0.00318264146335423,
0.0021438910625874996,
0.004907849710434675,
0.013986170291900635,
-0.01229366846382618,
0.0009088003425858915,
-0.018621155992150307,
-0.006855135317891836,
-0.024556538090109825,
0.0178182665258646,
-0.04014617204666138,
-0.007154377643018961,
-0.04276493564248085,
0.021628914400935173,
-0.038883525878190994,
-0.0031019283924251795,
0.004191871732473373,
0.029118401929736137,
0.030610209330916405,
0.035765450447797775,
-0.01367568876594305,
-0.041895803064107895,
0.0114185381680727,
0.04949105158448219,
0.09398140013217926,
-0.0070304544642567635,
-0.018504640087485313,
-0.06448373198509216,
-0.04053325578570366,
0.031019380316138268,
-0.021388377994298935,
0.02789301425218582,
-0.017495108768343925,
0.002932586008682847,
-0.03153868392109871,
-0.028115469962358475,
0.030218426138162613,
0.015658725053071976,
-0.03976469859480858,
0.00899638794362545,
-0.04996245354413986,
0.009992540813982487,
-0.035118427127599716,
0.05652068182826042,
0.018362265080213547,
0.03251873701810837,
0.004774684552103281,
0.025520266965031624,
0.022992389276623726,
-0.021997293457388878,
-0.0051149167120456696,
-0.07699967175722122,
0.013036377727985382,
-0.018487224355340004,
-0.012376794591546059,
0.04036371782422066,
-0.023901117965579033,
-0.04363091289997101,
-0.0018593515269458294,
-0.0031466393265873194,
-0.010193130932748318,
-0.015185503289103508,
-0.06800942867994308,
0.008481793105602264,
0.013674733228981495,
0.037874121218919754,
0.014310899190604687,
0.023516111075878143,
-0.050647832453250885,
0.006702209357172251,
-0.042625632137060165,
0.013749190606176853,
-0.0067033241502940655,
-0.0009258794598281384,
0.010705611668527126,
-0.02426571026444435,
-0.04561251401901245,
0.037208691239356995,
-0.018977457657456398,
0.01610807701945305,
0.04778219759464264,
-0.04611640051007271,
-0.030401727184653282,
-0.016724159941077232,
0.006066861562430859,
-0.01352380309253931,
-0.010451956652104855,
0.024735407903790474,
-0.014148122631013393,
0.006555669475346804,
0.027690088376402855,
-0.03961578384041786,
0.00665948586538434,
0.03623105585575104,
-0.006383650936186314,
-0.014434636570513248,
-0.059625376015901566,
-0.023113494738936424,
0.032589446753263474,
-0.012791767716407776,
0.03558911383152008,
0.0053478507325053215,
0.023994378745555878,
0.020756114274263382,
-0.057669322937726974,
-0.05933631211519241,
0.003805302083492279,
-0.024465467780828476,
0.0031711244955658913,
0.009967388585209846,
0.0341465137898922,
-0.022502314299345016,
0.01185053214430809,
-0.07025767117738724,
-0.009121823124587536,
-0.004065802786499262,
0.009085305966436863,
0.0004146081337239593,
0.006766362581402063,
-0.03567914292216301,
-0.004213722888380289,
-0.04737231507897377,
0.01692081242799759,
0.05751536041498184,
-0.05359327420592308,
-0.009138066321611404,
0.008251944556832314,
0.045241836458444595,
0.040950581431388855,
0.008776693604886532,
-0.020168783143162727,
0.039944976568222046,
0.015682945027947426,
0.04504440352320671,
-0.0024875865783542395,
0.024543043226003647,
0.014726043678820133,
-0.011897698044776917,
0.030237391591072083,
0.005970638711005449,
0.015645649284124374,
-0.03674069792032242,
-0.0021010502241551876,
0.0351884700357914,
0.0028356905095279217,
-0.0008300290792249143,
-0.014928678050637245,
-0.00007376907160505652,
0.004779542796313763,
0.03750254213809967,
-0.02763662301003933,
0.030468221753835678,
-0.007074312772601843,
-0.0353594608604908,
0.05748814716935158,
-0.003433762351050973,
0.04366496950387955,
0.028071997687220573,
0.0028320224955677986,
0.002970536472275853,
-0.04530186578631401,
0.015409901738166809,
-0.016159778460860252,
0.008497064933180809,
0.024073440581560135,
0.012204404920339584,
-0.002084980020299554,
0.019706541672348976,
0.008464374579489231,
-0.002841625129804015,
-0.014440689235925674,
0.008380871266126633,
0.03369223698973656,
-0.0047362432815134525,
0.015137610025703907,
0.027424920350313187,
0.0010709399357438087,
-0.0017594899982213974,
-0.051222093403339386,
-0.010968735441565514,
0.047821979969739914,
-0.0026505067944526672,
0.017260605469346046,
-0.021408269181847572,
0.011213753372430801,
0.023409241810441017,
0.0395035594701767,
-0.010460196994245052,
0.022281376644968987,
0.021373005583882332,
0.035503171384334564,
-0.03519093617796898,
-0.03912913799285889,
-0.042192816734313965,
0.04671580716967583,
-0.0697922483086586,
0.006751382257789373,
0.01078344788402319,
-0.013818511739373207,
0.005940866190940142,
0.018562354147434235,
0.012108142487704754,
-0.004234728403389454,
-0.022266589105129242,
-0.07878084480762482,
-0.004734502639621496,
0.02823440171778202,
-0.009721038863062859,
-0.0376763716340065,
0.0037662764079868793,
0.03153659403324127,
-0.007998676039278507,
0.007774162571877241,
-0.0162472166121006,
-0.07081598043441772,
0.0034282489214092493,
-0.005620873533189297,
-0.03025784157216549,
0.04826756939291954,
-0.02572167105972767,
0.013150621205568314,
-0.009920124895870686,
-0.03365824371576309,
0.016183681786060333,
0.022298254072666168,
0.05864349752664566,
-0.034904059022665024,
0.018116794526576996,
-0.03135991096496582,
-0.024833740666508675,
-0.02477765828371048,
-0.005671268329024315,
0.16231393814086914,
0.03315204009413719,
0.005393352825194597,
-0.01912333443760872,
0.012552734464406967,
-0.024946168065071106,
0.056797437369823456,
0.02948521263897419,
0.001929562189616263,
0.007149402052164078,
0.015029783360660076,
-0.021297164261341095,
0.03464532643556595,
0.01105239987373352,
-0.003113833023235202,
0.04460718482732773,
-0.06585153937339783,
-0.012924040667712688,
-0.003350734245032072,
0.05111582204699516,
0.0007054361631162465,
-0.009037496522068977,
-0.025900980457663536,
0.007068360690027475,
0.00776476226747036,
-0.00638093426823616,
-0.0114167220890522,
-0.009260454215109348,
-0.0314326286315918,
0.0030792199540883303,
-0.02044399082660675,
-0.01615847274661064,
0.015549217350780964,
-0.03721492365002632,
-0.019718697294592857,
0.03476785123348236,
0.021708378568291664,
-0.050698257982730865,
0.04760052263736725,
0.0245716143399477,
0.036833930760622025,
-0.020653126761317253,
0.022630341351032257,
0.027487101033329964,
-0.051509227603673935,
-0.01904573105275631,
0.014593658037483692,
0.07005682587623596,
-0.021427858620882034,
-0.014843299984931946,
0.011148292571306229,
0.01459078211337328,
0.04965721070766449,
-0.00936607364565134,
-0.005380319431424141,
-0.033169835805892944,
0.004446015227586031,
-0.017611529678106308,
-0.009165669791400433,
0.01720302738249302,
0.047407206147909164,
-0.03507257252931595,
0.02095222659409046,
-0.012904240749776363,
0.010455159470438957,
-0.0015920457663014531,
-0.04581542685627937,
-0.03950833901762962,
0.012623107992112637,
-0.00607552845031023,
-0.03976559638977051,
0.0077111017890274525,
-0.0550573356449604,
-0.00517980707809329,
0.002513856627047062,
0.03574075177311897,
0.03060608170926571,
0.023286355659365654,
-0.0040703569538891315,
-0.011041561141610146,
0.016411494463682175,
0.020920805633068085,
-0.005307342857122421,
-0.0005020996904931962,
0.023618126288056374,
-0.036775391548871994,
-0.004875395447015762,
0.036091290414333344,
-0.03472970426082611,
0.033810243010520935,
0.01666390709578991,
0.05219053849577904,
0.00020749935356434435,
-0.013377428986132145,
-0.018373534083366394,
0.04491836577653885,
0.0015168945537880063,
0.007363244891166687,
-0.026642972603440285,
0.015350759960711002,
0.00008456236537313089,
-0.015387135557830334,
0.01683640666306019,
0.06286638230085373,
0.008589405566453934,
-0.016721908003091812,
0.06139521300792694,
-0.012986542657017708,
0.0014907445292919874,
0.03908749669790268,
0.04126667231321335,
0.015017597004771233,
-0.022400127723813057,
-0.006513931788504124,
-0.00935391616076231,
0.001994167920202017,
0.028362203389406204,
-0.024583978578448296,
0.005687382072210312,
-0.04169730097055435,
0.005243816878646612,
0.003853769740089774,
0.047708529978990555,
-0.048929113894701004,
0.017175987362861633,
-0.016267763450741768,
-0.01813143864274025,
-0.016502555459737778,
0.0394778698682785,
-0.009954242967069149,
0.0003725936112459749,
0.016223300248384476,
0.006922845263034105,
-0.025203203782439232,
-0.018354032188653946,
-0.0005326402024365962,
-0.0028635405469685793,
0.00040063829510472715,
0.01711612194776535,
-0.014537184499204159,
0.051639117300510406,
-0.01878911256790161,
-0.05995035544037819,
0.04384761303663254,
-0.00472599733620882,
-0.001426856848411262,
0.037896301597356796,
-0.022905955091118813,
-0.02823091484606266,
0.02677614614367485,
-0.01706549897789955,
-0.0057161529548466206,
-0.015794606879353523,
0.0035159888211637735,
-0.009017794393002987,
-0.022124961018562317,
0.01145427580922842,
0.017067059874534607,
-0.020815903320908546,
0.039678189903497696,
0.014172128401696682,
0.00440051918849349,
-0.023715492337942123,
-0.04915662109851837,
-0.020157912746071815,
0.007558594923466444,
0.009150579571723938,
0.05628075823187828,
0.014849956147372723,
-0.006184224504977465,
-0.0066468724980950356,
0.07404299080371857,
0.019666431471705437,
0.0009144414798356593,
-0.0693245604634285,
-0.02702927216887474,
0.011420114897191525,
0.033250197768211365,
0.02085636928677559,
-0.02590862847864628,
0.0070252735167741776,
0.02176487445831299,
-0.05719658359885216,
0.007361096795648336,
-0.018846141174435616,
-0.01433767843991518,
-0.03795230761170387,
-0.03091387078166008,
-0.01857195794582367,
0.04986019432544708,
-0.015420743264257908,
0.027662741020321846,
0.019183265045285225,
0.01926032267510891,
-0.006872514728456736,
-0.09316186606884003,
-0.03320671245455742,
0.017214907333254814,
0.01033310778439045,
0.04421209171414375,
0.07673168927431107,
-0.023424658924341202,
-0.0034568055998533964,
0.041308168321847916,
0.0434543751180172,
-0.004970923997461796,
-0.011515462771058083,
0.0035182135179638863,
0.01597130112349987,
0.04402005672454834,
0.04178674519062042,
0.014593904837965965,
0.04156477749347687,
-0.024012863636016846,
0.031025812029838562,
0.017507214099168777,
0.018934084102511406,
0.04141324758529663,
-0.011489260010421276,
-0.02420082688331604,
-0.017275754362344742,
-0.007142810150980949,
-0.003239759709686041,
-0.008219661191105843,
0.018020177260041237,
0.03159986808896065,
0.03736235201358795,
-0.00631748279556632,
-0.0045014070346951485,
-0.04385964199900627,
0.00864915270358324,
-0.02385871112346649,
0.033869944512844086,
0.01319968607276678,
0.016484996303915977,
-0.00840325653553009,
0.007487484719604254,
-0.00048222675104625523,
0.07954257726669312,
-0.005128383170813322,
-0.020199894905090332,
-0.006648274604231119,
0.001833953196182847,
0.07344166189432144,
0.011649788357317448,
-0.005790750030428171,
-0.030639471486210823,
-0.025324886664748192,
0.022893574088811874,
0.04548051953315735,
-0.05014083534479141,
-0.0278975460678339,
0.02622944489121437,
-0.03702504187822342,
0.014665872789919376,
0.02750752866268158,
0.05468323081731796,
-0.03358254209160805,
-0.022013062611222267,
-0.009470254182815552,
0.053815849125385284,
0.051503486931324005,
0.024415306746959686,
0.007095088250935078,
0.03085545264184475,
-0.02492855302989483,
0.020247887820005417,
-0.05417955294251442,
0.009534306824207306,
0.036349207162857056,
0.027007199823856354,
-0.017365707084536552,
0.02345695160329342,
-0.02309822291135788,
0.02872747927904129,
0.016876807436347008,
-0.009163284674286842,
0.002569444477558136,
-0.009021361358463764,
-0.04577704519033432,
0.03089958243072033,
0.007845588028430939,
-0.028552599251270294,
0.06275495141744614,
-0.010352032259106636,
0.025631409138441086,
0.02304496057331562,
-0.0206149835139513,
-0.00014691482647322118,
0.016029484570026398,
0.00281077204272151,
-0.03450673073530197,
-0.009152129292488098,
-0.011342013254761696,
0.05572057515382767,
-0.04632251337170601,
-0.007024399936199188,
0.042459629476070404,
-0.012743969447910786,
-0.020027903839945793,
0.01946159265935421,
0.06402995437383652,
0.04890286177396774,
0.016044577583670616,
0.01766066811978817,
-0.029269102960824966,
-0.05075060948729515,
0.012445079162716866,
0.027647925540804863,
-0.015169958584010601,
0.02130797877907753,
-0.009227967821061611,
0.04396422952413559,
0.015225532464683056,
0.02292373962700367,
0.015614602714776993,
0.011651339009404182,
-0.008805370889604092,
0.04797515273094177,
0.031904157251119614,
0.011515600606799126,
0.05178925767540932,
0.04039088264107704,
-0.007729321252554655,
0.05116792768239975,
-0.019107643514871597,
0.0006124944775365293,
-0.03920946642756462,
0.0228800680488348,
-0.012732692994177341,
0.011671076528728008,
-0.035140760242938995,
0.03596043214201927,
-0.014878110028803349,
-0.03277057409286499,
-0.05706825852394104,
0.030381660908460617,
0.05833720415830612,
-0.08189479261636734,
-0.006315200589597225,
0.02768123894929886,
0.0006856189575046301,
0.009140253067016602,
-0.01012716256082058,
-0.010293959639966488,
-0.01990104466676712,
0.021600110456347466,
0.057638995349407196,
-0.002225438831374049,
-0.027505408972501755,
-0.03380598500370979,
-0.0206016693264246,
0.02473110891878605,
0.005091232713311911,
-0.035865578800439835,
-0.02211287058889866,
0.010043985210359097,
-0.06040654703974724,
-0.02449202723801136
] |
<p>When your body burns calories and you lose weight, obviously mass is leaving your body. In what form does it leave? In other words, what is the physical process by which the body loses weight when it burns its fuel? Someone asked this question on the whiteboard at work. Someone said it leaves the body in the form of heat but I knew this is wrong since heat is simply the internal kinetic energy of a lump of matter and doesn't have anything do with mass. Obviously the chemical reactions going on in the body cause it to produce heat but this alone won't reduce its mass.</p>
| 8,844 |
[
-0.03103984333574772,
-0.052498169243335724,
-0.03508752956986427,
-0.0365748405456543,
-0.023369720205664635,
0.024304445832967758,
-0.024232862517237663,
-0.033799029886722565,
-0.021613938733935356,
-0.008788359351456165,
0.007503889035433531,
0.037437621504068375,
0.04144710302352905,
-0.0015876173274591565,
0.020910656079649925,
-0.004863710608333349,
0.0005244038184173405,
-0.029533248394727707,
-0.008115082047879696,
-0.029056694358587265,
0.0014069146709516644,
-0.04705391079187393,
0.0054860846139490604,
0.006385492160916328,
-0.04586738720536232,
0.029163097962737083,
0.03250695392489433,
0.01289680227637291,
0.0302826389670372,
0.029324451461434364,
-0.01092320866882801,
-0.03994400426745415,
-0.023910069838166237,
0.013461649417877197,
0.012354306876659393,
-0.0007193915662355721,
-0.04606487601995468,
-0.020842265337705612,
-0.0295182466506958,
0.02798977680504322,
0.004334255121648312,
-0.01041104644536972,
-0.024379193782806396,
0.026626477017998695,
-0.011627322062849998,
0.010533241555094719,
-0.016696806997060776,
0.00999249704182148,
0.03885168209671974,
-0.08555129915475845,
0.05814971774816513,
-0.008207474835216999,
0.0398724339902401,
0.009770744480192661,
0.030038287863135338,
0.02096298523247242,
0.0728963166475296,
0.05061247944831848,
-0.02346186526119709,
-0.03990013524889946,
-0.020280756056308746,
0.008908556774258614,
-0.01902235858142376,
-0.0039717452600598335,
-0.0030018992256373167,
0.006847083102911711,
-0.028830943629145622,
-0.024539930745959282,
0.0508844256401062,
0.023682726547122,
0.022099347785115242,
0.012059416621923447,
0.0159462820738554,
0.019586291164159775,
0.033392615616321564,
-0.02758564054965973,
0.05437656491994858,
0.025281233713030815,
0.062325648963451385,
0.06810955703258514,
-0.01688305288553238,
-0.03156530112028122,
0.0008712250273674726,
0.028133688494563103,
-0.012178868986666203,
0.0029333115089684725,
0.08084692806005478,
0.011059851385653019,
0.0033449602779000998,
0.05791719630360603,
0.0012747501023113728,
0.006054432597011328,
-0.004726322367787361,
-0.025033866986632347,
0.047308046370744705,
0.03083384968340397,
-0.005743179935961962,
0.053413938730955124,
0.01862845942378044,
-0.018923640251159668,
0.003924525808542967,
0.005381529685109854,
0.04602213203907013,
0.07896769046783447,
0.005772583186626434,
-0.0006246945122256875,
-0.03369559720158577,
0.011028196662664413,
0.0011907742591574788,
0.007547174580395222,
-0.04298900440335274,
-0.01139923371374607,
0.014431635849177837,
-0.017145277932286263,
0.026579616591334343,
-0.03488101065158844,
-0.003036024048924446,
-0.019004857167601585,
0.03982158377766609,
0.053680408746004105,
0.020807966589927673,
-0.012834107503294945,
-0.009070211090147495,
-0.008618691004812717,
-0.03146524727344513,
0.002461299765855074,
0.026422375813126564,
-0.026471063494682312,
-0.04156215116381645,
0.03531954810023308,
-0.025375358760356903,
-0.03606400266289711,
0.05344733968377113,
-0.016645891591906548,
0.007684989832341671,
-0.007756553590297699,
-0.08060575276613235,
-0.007157372310757637,
0.04544835537672043,
-0.028360353782773018,
-0.019295664504170418,
-0.04384768381714821,
-0.020479081198573112,
0.025174088776111603,
0.04565088823437691,
0.00747179239988327,
-0.022076278924942017,
-0.012254773639142513,
0.019835567101836205,
-0.018882593140006065,
0.007663029246032238,
-0.057788655161857605,
-0.004023666027933359,
-0.01846015825867653,
0.03169731795787811,
-0.02612288109958172,
0.014228842221200466,
0.07207737118005753,
0.0002715520968195051,
-0.023474689573049545,
0.031366266310214996,
-0.04565763100981712,
-0.0029811833519488573,
0.04217543080449104,
-0.012247093953192234,
-0.03176511079072952,
0.056935373693704605,
0.023190153762698174,
-0.030195346102118492,
-0.0038754059933125973,
0.07132841646671295,
0.027449101209640503,
-0.009790262207388878,
0.039191290736198425,
0.026645217090845108,
-0.0011190607910975814,
-0.04139289632439613,
-0.00720934709534049,
-0.007949816063046455,
0.03709111735224724,
-0.07867135107517242,
-0.04974401742219925,
0.0038414280861616135,
-0.014136504381895065,
0.029066381976008415,
0.04547717049717903,
0.019912881776690483,
-0.040742095559835434,
0.03306663781404495,
-0.012504853308200836,
-0.037411369383335114,
-0.0622301809489727,
0.002888813614845276,
-0.012120179831981659,
0.02100541442632675,
-0.02340557426214218,
0.029139475896954536,
0.011406023055315018,
-0.04989241436123848,
-0.012417202815413475,
0.023705556988716125,
0.028427254408597946,
-0.017199523746967316,
-0.009958368726074696,
-0.018157651647925377,
0.08284435421228409,
0.024180181324481964,
-0.022259874269366264,
-0.009447360411286354,
-0.02206205390393734,
-0.001129051437601447,
-0.029940305277705193,
-0.015763819217681885,
-0.0008818709175102413,
-0.05882127955555916,
-0.03161107376217842,
0.007209728937596083,
-0.0176561176776886,
-0.005800445564091206,
0.03268766403198242,
-0.02414858154952526,
0.09881337732076645,
0.02831791713833809,
-0.014055494219064713,
-0.020278628915548325,
0.026891930028796196,
-0.017420310527086258,
0.019296934828162193,
-0.024856481701135635,
-0.043407682329416275,
-0.028215685859322548,
-0.04027397930622101,
0.029095301404595375,
-0.023203924298286438,
-0.03197271749377251,
0.02778768353164196,
0.006328974850475788,
0.047229692339897156,
0.011056764982640743,
0.012634985148906708,
-0.024088000878691673,
-0.00018999447638634592,
0.020737528800964355,
-0.01168961450457573,
0.00003120081601082347,
0.02858336828649044,
0.0018068335484713316,
0.04099429026246071,
0.001636717701330781,
-0.001314064604230225,
-0.019871622323989868,
0.04553679749369621,
0.029954668134450912,
0.022848108783364296,
-0.017165344208478928,
-0.05735833942890167,
0.04226725175976753,
-0.016624407842755318,
0.013410397805273533,
-0.010908812284469604,
0.003566746599972248,
0.01317712850868702,
-0.04329835623502731,
-0.028590982779860497,
-0.01293874066323042,
0.07193276286125183,
-0.000502796727232635,
0.0026650219224393368,
0.007297133095562458,
-0.044291090220212936,
0.023906083777546883,
-0.006951688323169947,
-0.004879762884229422,
-0.021096231415867805,
0.021340681239962578,
0.005612392909824848,
-0.004958455916494131,
-0.010642437264323235,
-0.04933404177427292,
-0.02360658347606659,
-0.01379870530217886,
-0.07835127413272858,
-0.0005245528882369399,
-0.005444662179797888,
-0.04869048669934273,
-0.0031093661673367023,
-0.05313676968216896,
-0.03440779820084572,
0.07867925614118576,
0.0066266655921936035,
0.023405618965625763,
0.05074197053909302,
-0.00862715020775795,
-0.07555591315031052,
-0.0014493432827293873,
0.007781334221363068,
-0.02670568972826004,
0.013654876500368118,
0.04691784083843231,
0.07790825515985489,
-0.008730541914701462,
-0.05396842211484909,
0.0031915961299091578,
-0.057634152472019196,
-0.05272316187620163,
-0.028321649879217148,
-0.010379234328866005,
0.0422370545566082,
0.008055511862039566,
0.02334090881049633,
0.023691575974225998,
-0.051826443523168564,
0.04565977305173874,
-0.04936402663588524,
-0.005730792880058289,
0.03568437322974205,
-0.002684907289221883,
0.009702369570732117,
0.01967259868979454,
-0.042507000267505646,
0.06345295906066895,
0.019906815141439438,
-0.04560963809490204,
0.0046019465662539005,
0.006705059669911861,
0.00576691934838891,
-0.00646150903776288,
0.025907378643751144,
-0.015360205434262753,
0.0002922093844972551,
-0.005398619454354048,
0.038499169051647186,
0.027004363015294075,
0.0028455581050366163,
0.008978473953902721,
-0.044687967747449875,
0.00701407203450799,
-0.006103689316660166,
-0.0217670239508152,
-0.01889326609671116,
-0.010950078256428242,
-0.041891299188137054,
0.049351662397384644,
-0.02037365734577179,
0.0555480495095253,
-0.018384018912911415,
-0.07147548347711563,
0.04524762183427811,
0.01815924607217312,
0.0023994650691747665,
-0.05075471103191376,
0.039885539561510086,
-0.025532595813274384,
-0.008221627213060856,
0.017708877101540565,
0.027986111119389534,
0.04699091985821724,
-0.010156817734241486,
0.03396693244576454,
-0.011409884318709373,
0.05391206964850426,
-0.02512473799288273,
-0.031808383762836456,
-0.017959030345082283,
-0.018871856853365898,
-0.013768970966339111,
0.01040023472160101,
-0.013784319162368774,
0.036001935601234436,
0.026202736422419548,
0.052522528916597366,
0.003120008623227477,
-0.03154664859175682,
-0.039459794759750366,
-0.07226067036390305,
-0.024490898475050926,
0.02713927812874317,
0.04651258513331413,
-0.02200213074684143,
0.06250376999378204,
0.019756635650992393,
0.05009744316339493,
0.031491100788116455,
0.006760152522474527,
-0.09423330426216125,
0.03176899626851082,
-0.028891684487462044,
-0.02106429822742939,
0.007050918415188789,
-0.0003417475672904402,
-0.0030753412283957005,
-0.014764349907636642,
-0.025296729058027267,
-0.0009273588075302541,
0.004220848903059959,
-0.04030245915055275,
-0.009289998561143875,
-0.011218425817787647,
-0.04793361574411392,
-0.008193736895918846,
-0.009994897060096264,
0.0769338458776474,
-0.02337191253900528,
-0.006249846424907446,
0.04251132532954216,
-0.0435524620115757,
-0.02561642974615097,
-0.05703626573085785,
-0.0005700589972548187,
0.004113399423658848,
-0.0029718999285250902,
0.029858022928237915,
0.005730270873755217,
-0.011194372549653053,
0.04029584303498268,
-0.019445279613137245,
0.01307091023772955,
-0.013473880477249622,
-0.04383835941553116,
-0.023343078792095184,
-0.04924154281616211,
0.004385678563266993,
-0.005754353944212198,
-0.013531695120036602,
-0.013814905658364296,
0.012172156944870949,
0.00021751287567894906,
0.0117194140329957,
-0.0187041275203228,
0.06768480688333511,
0.058283720165491104,
0.028673015534877777,
-0.01575462706387043,
-0.01946900598704815,
0.00309630180709064,
-0.02308720350265503,
-0.0019648380111902952,
0.035260360687971115,
-0.005119448062032461,
0.009165256284177303,
-0.016627440229058266,
0.003571557579562068,
0.01862175576388836,
0.015750400722026825,
-0.026627110317349434,
0.015036597847938538,
0.035963986068964005,
-0.030222304165363312,
0.00016318095731548965,
0.05258406698703766,
0.026131169870495796,
0.033927071839571,
-0.007683688309043646,
0.006292907986789942,
-0.05271579697728157,
0.019117670133709908,
0.03380792960524559,
0.05104195326566696,
-0.049837626516819,
0.004317814949899912,
-0.025836799293756485,
-0.012009712867438793,
0.04515044018626213,
-0.015614219941198826,
0.03386696055531502,
-0.033078599721193314,
-0.0006006229668855667,
0.04166417941451073,
-0.02516973204910755,
0.022200435400009155,
-0.02468811720609665,
-0.0013341271551325917,
-0.004050134681165218,
-0.004910821560770273,
-0.010322291404008865,
-0.007120196241885424,
0.042019832879304886,
0.019926108419895172,
0.0304623581469059,
0.00662580318748951,
-0.0040665422566235065,
-0.0006934510893188417,
0.019934719428420067,
-0.04264214262366295,
-0.08207309246063232,
-0.04727844148874283,
-0.002020798157900572,
-0.01056825090199709,
0.020745182409882545,
-0.038094423711299896,
-0.08576728403568268,
-0.012479718774557114,
0.030455829575657845,
-0.0253676176071167,
-0.03546029329299927,
-0.09142068028450012,
0.028806142508983612,
0.0115840844810009,
-0.02110498957335949,
0.051046162843704224,
0.01076419372111559,
-0.025080068036913872,
-0.038492802530527115,
-0.02232474274933338,
0.02713109739124775,
-0.021945983171463013,
-0.0303031038492918,
-0.04122800752520561,
0.0002977047406602651,
-0.01460761483758688,
0.01605239138007164,
0.009595065377652645,
-0.01870134100317955,
-0.037574511021375656,
-0.0629623532295227,
0.0005116850952617824,
0.00886099599301815,
0.021048355847597122,
0.0025436305440962315,
-0.021940825507044792,
0.02727685309946537,
-0.02220217138528824,
-0.02675805054605007,
0.027024921029806137,
0.044547345489263535,
-0.022146806120872498,
0.01345797535032034,
-0.006772755645215511,
0.020294472575187683,
-0.015611040405929089,
-0.022258006036281586,
0.052684929221868515,
-0.006191548891365528,
0.034415069967508316,
-0.006449135020375252,
0.00012771319597959518,
0.00705232797190547,
-0.08992356061935425,
-0.04157564043998718,
0.0036856085062026978,
0.017435740679502487,
0.011955776251852512,
-0.024353260174393654,
0.06057221442461014,
0.0020171143114566803,
-0.0036006271839141846,
-0.06742888689041138,
-0.06442119926214218,
0.03697295859456062,
0.034873608499765396,
-0.03336883708834648,
-0.017703725025057793,
0.010487576015293598,
-0.05208663269877434,
-0.0661977082490921,
-0.00417507067322731,
0.011455529369413853,
-0.02461371384561062,
0.03193506971001625,
0.04369495064020157,
0.0029591561760753393,
0.056234486401081085,
0.05345001816749573,
-0.04797962307929993,
0.0006828623590990901,
0.015327343717217445,
-0.02828964963555336,
-0.007891148328781128,
0.059909556061029434,
0.01558715384453535,
-0.006578192114830017,
-0.013308417052030563,
-0.009685717523097992,
0.03838269039988518,
-0.007169039454311132,
-0.0036947859916836023,
0.039913538843393326,
0.03190848231315613,
-0.008073756471276283,
-0.030269397422671318,
0.06672515720129013,
0.004249784629791975,
0.050859954208135605,
0.021880684420466423,
-0.017171673476696014,
0.037350282073020935,
-0.01246684417128563,
0.037391070276498795,
-0.013574954122304916,
0.011167469434440136,
0.010275216773152351,
0.013081120327115059,
-0.002899434417486191,
0.008631523698568344,
-0.003505377098917961,
-0.012232139706611633,
0.04779573157429695,
-0.004172356333583593,
0.013210867531597614,
0.01369532011449337,
-0.0027038692496716976,
-0.04469350352883339,
-0.03317085653543472,
-0.03917009010910988,
-0.023733997717499733,
0.035589661449193954,
-0.009471073746681213,
0.030156264081597328,
0.00407406548038125,
0.00718762306496501,
0.03044254146516323,
-0.02200675755739212,
-0.000023377908291877247,
0.042662180960178375,
-0.0006074208649806678,
0.05148838460445404,
-0.013928154483437538,
0.012279019691050053,
0.0494394414126873,
0.050355445593595505,
-0.035561297088861465,
0.019211681559681892,
0.032376356422901154,
-0.0015549809904769063,
0.008982311934232712,
-0.02042500115931034,
-0.04280383512377739,
-0.021359505131840706,
0.0011508414754644036,
0.03332208842039108,
-0.024869436398148537,
-0.011935151182115078,
0.058896295726299286,
0.028609778732061386,
0.015401402488350868,
-0.03326207771897316,
-0.0067415619269013405,
-0.02904217131435871,
0.008098865859210491,
-0.04255864769220352,
0.006153960712254047,
0.0075853909365832806,
-0.011749468743801117,
0.023015454411506653,
-0.0006421607104130089,
0.0021336288191378117,
0.010569410398602486,
-0.017897557467222214,
-0.025128353387117386,
-0.017453936859965324,
-0.03229374811053276,
0.031360406428575516,
-0.012947304174304008,
-0.0044496748596429825,
-0.0012245429679751396,
-0.024813076481223106,
0.017226485535502434,
0.027934515848755836,
0.04247039556503296,
-0.014754909090697765,
0.027345256879925728,
-0.01202540472149849,
0.019724704325199127,
-0.023243721574544907,
0.03937961906194687,
0.10185759514570236,
0.03615545481443405,
0.009553737938404083,
-0.06958749890327454,
-0.023768877610564232,
-0.0274070855230093,
0.010949241928756237,
-0.01146528497338295,
-0.006086211651563644,
-0.0004587810253724456,
0.05976828187704086,
0.04043984040617943,
0.05866273120045662,
-0.02001861110329628,
-0.03237300366163254,
0.029858846217393875,
-0.003913633059710264,
-0.017130129039287567,
0.005101193208247423,
-0.016122538596391678,
-0.044247739017009735,
0.03881875425577164,
-0.03876117989420891,
0.032812125980854034,
0.0088896993547678,
-0.024244733154773712,
-0.049448803067207336,
-0.014411996118724346,
-0.009972336702048779,
0.007945401594042778,
-0.06834150105714798,
0.005231514573097229,
-0.012514633126556873,
-0.0002642931358423084,
0.0054961927235126495,
0.02649950049817562,
0.02697613649070263,
-0.03623087331652641,
-0.012146402150392532,
0.009461970068514347,
0.03838209807872772,
0.006033251527696848,
0.010273854248225689,
-0.0025937147438526154,
-0.0376480408012867,
-0.025457605719566345,
-0.006893038284033537,
0.02517182193696499,
-0.04651862382888794,
0.005191629286855459,
0.004549901932477951,
-0.016968635842204094,
0.0044213104993104935,
-0.045132577419281006,
0.023788101971149445,
-0.002811760175973177,
0.05058450251817703,
-0.025180505588650703,
-0.029781540855765343,
-0.057878632098436356,
0.0041916752234101295,
-0.00531013635918498,
-0.01600280962884426,
0.04783472791314125,
0.01731773465871811,
-0.010639356449246407,
0.019072601571679115,
0.005354849621653557,
-0.02361634001135826,
0.005411966238170862,
-0.012440298683941364,
-0.016079334542155266,
-0.0071488311514258385,
-0.028733568266034126,
0.026337716728448868,
0.04057355225086212,
0.006551793776452541,
0.026393279433250427,
-0.0005953683285042644,
-0.03253990411758423,
-0.032339371740818024,
0.07632101327180862,
-0.009046206250786781,
-0.012109166942536831,
-0.0361887626349926,
-0.012535125948488712,
-0.00679505942389369,
0.027930516749620438,
-0.01997382566332817,
0.006311789620667696,
-0.009850230067968369,
0.018416855484247208,
-0.0012229045387357473,
-0.03169452026486397,
-0.005070006009191275,
0.06502020359039307,
-0.022472111508250237,
0.0034591667354106903,
0.0012706617126241326,
0.05540343001484871,
0.04611748084425926,
-0.00021173297136556357,
-0.02135125733911991,
-0.00364804919809103,
0.023411976173520088,
0.01938704587519169,
-0.009208383038640022,
-0.014352462254464626,
0.018037280067801476,
0.0169474259018898,
-0.01826077327132225,
0.0009255345794372261,
-0.008371195755898952,
-0.0043388656340539455,
-0.009898720309138298,
-0.02214084565639496,
0.07433605939149857,
-0.00378797366283834,
0.06825786828994751,
-0.046747732907533646,
0.04277274012565613,
-0.05182943120598793,
0.025407563894987106,
-0.09370303899049759,
-0.02564612589776516,
0.0568612702190876,
-0.021705666556954384,
-0.04297111555933952,
0.006071316543966532,
-0.004627277608960867,
0.006881418637931347,
0.03835146129131317,
-0.006172776687890291,
0.0041603888384997845,
-0.020217640325427055,
0.035909976810216904,
-0.024364501237869263,
0.041924018412828445,
0.004384767729789019,
-0.0048325927928090096,
0.056785792112350464,
-0.030767278745770454,
-0.03418450802564621,
0.001560765434987843,
-0.0478564091026783,
0.026593640446662903,
0.04061909765005112,
-0.005649517755955458,
0.0031522815115749836,
0.075978584587574,
-0.0009403002331964672,
-0.008330109529197216,
-0.036054015159606934,
-0.018976913765072823,
-0.016954442486166954,
0.03251051530241966,
0.003225924214348197,
-0.01878579892218113,
-0.04165733605623245,
0.06637291610240936,
0.015903044492006302,
-0.030357684940099716,
0.02744552120566368,
-0.005665500648319721,
-0.013759937137365341,
0.00476622860878706,
0.031496282666921616,
0.04024210199713707,
0.022144630551338196,
0.053008366376161575,
0.004398302640765905,
0.010986845940351486,
-0.018125509843230247,
-0.024065403267741203,
-0.07775594294071198,
-0.021701840683817863,
-0.026455048471689224,
0.004450006410479546,
0.010220171883702278,
-0.023600712418556213,
-0.01937112770974636,
0.019057955592870712,
-0.06435227394104004,
0.02224077470600605,
-0.03045736625790596,
0.0026887841522693634,
0.010604733601212502,
-0.00787330698221922,
0.006541422102600336,
0.041720304638147354,
0.02995629794895649,
0.06512626260519028,
0.00836779735982418,
0.029558485373854637,
0.000034745091397780925,
-0.014467816799879074,
0.004259950015693903,
0.027729174122214317,
-0.0251833014190197,
-0.02268144115805626,
0.06120383366942406,
-0.02027774229645729,
-0.013810982927680016,
0.029452001675963402,
-0.011404018849134445,
0.05088804289698601,
0.0007701516151428223,
-0.0032203823793679476,
-0.0109689487144351,
0.04158583655953407,
-0.013705644756555557,
-0.003501725848764181,
-0.004791236948221922,
0.05296272784471512,
0.014730376191437244,
0.04362514987587929,
-0.022943977266550064,
0.024133173748850822,
0.017214233055710793,
-0.042250074446201324,
-0.02062799036502838,
0.03772013634443283,
-0.031664684414863586,
-0.006233736407011747,
-0.003662729635834694,
0.02195991389453411,
-0.00023016773047856987,
-0.021243788301944733,
-0.03143502026796341,
-0.040511444211006165,
-0.013690227642655373,
0.034533143043518066,
0.009550545364618301,
0.003603174816817045,
0.018366742879152298,
0.021900558844208717,
0.02025529183447361,
0.022494429722428322,
-0.009621159173548222,
-0.0345856212079525,
-0.011122800409793854,
-0.007668973878026009,
0.0004081345396116376,
0.0115364333614707,
-0.008413443341851234,
-0.031228315085172653,
-0.035221148282289505,
0.01552389096468687,
0.04908188804984093,
0.014353329315781593,
-0.009631861932575703,
-0.04849006608128548,
-0.039440277963876724,
-0.04663794860243797,
-0.019422730430960655,
-0.010506577789783478,
-0.0111034344881773,
-0.05318240821361542,
-0.000626901863142848,
0.02761620655655861,
0.016695162281394005,
0.05981392413377762,
0.007630724459886551,
-0.020578522235155106,
0.01386589277535677,
-0.013004899956285954,
0.0169522687792778,
-0.055909425020217896,
0.04207494482398033,
-0.018748896196484566,
-0.016925593838095665,
-0.020214661955833435,
0.02600950375199318,
-0.04799569025635719,
0.012993798591196537,
0.040085166692733765,
-0.01808859407901764,
-0.0024301446974277496,
-0.049649279564619064,
0.025308936834335327,
0.06705008447170258,
0.040209878236055374,
0.013256644830107689,
0.06318680942058563,
-0.015879003331065178,
0.025968024507164955,
0.060660067945718765,
-0.018028682097792625,
-0.01781492866575718,
0.030470408499240875,
-0.004375846590846777,
0.012447766028344631,
0.018369214609265327,
-0.01669667288661003,
0.054560840129852295,
-0.03447718545794487,
0.018447812646627426,
0.019063377752900124,
-0.007068286184221506,
-0.041395943611860275,
0.029220672324299812,
0.03798491880297661,
0.02283438667654991,
0.025628095492720604,
0.010852372273802757,
0.009876674041152,
-0.00154341000597924,
0.0418245792388916,
0.06705799698829651,
0.02989771217107773,
-0.0197332464158535,
-0.01134060975164175,
0.0011801705695688725,
-0.0012207354884594679,
0.03392808139324188,
-0.010104546323418617,
0.03845195099711418,
-0.0594036728143692,
-0.03857346251606941,
-0.006805042736232281,
-0.028288107365369797,
0.037017837166786194,
-0.005633201915770769,
-0.04144316539168358,
0.09859263896942139,
-0.0008140763966366649,
0.010248898528516293,
-0.016300829127430916,
0.009402443654835224,
-0.02903539501130581,
0.011795934289693832,
-0.008288752287626266,
0.037310730665922165,
0.00045145064359530807,
0.005295537877827883,
0.014303560368716717,
0.026433592662215233,
-0.00046758598182350397,
0.021125076338648796,
0.02027374505996704,
0.011540108360350132,
-0.018739674240350723,
-0.05353473126888275,
-0.014939423650503159,
0.0019336544210091233,
-0.005732892546802759,
0.04421454295516014,
0.06167704239487648,
-0.003275468945503235,
0.043667983263731,
0.007520042825490236,
-0.02665814384818077,
0.022358210757374763,
-0.062119435518980026,
-0.01739054173231125,
-0.022997817024588585,
0.029243046417832375,
-0.0013917481992393732,
-0.007867145352065563
] |
<p>I'm in the process of trying to understand X-Ray Absorption Fine Structure (XAFS) spectroscopy, but I think this question is more fundamental than merely as it pertains to XAFS. I think I don't entirely understand the interplay between electronic, vibrational, and rotational excitations in molecules. I understand that vibrational fine structure can be seen in electronic spectra. But how do we know which vibrational state a transition will end up in? Is it a Boltzmann distribution?</p>
<p>So to my main question. I realize that on the energy scale of XAFS, vibrational energy levels are not resolved; I just want to know if these transitions lead to the same type of vibrational state distribution that valence electronic transitions yield. Is that the case? Or if not, why not?</p>
| 8,845 |
[
-0.044103533029556274,
-0.03700382634997368,
-0.00010046359966509044,
-0.025689641013741493,
0.019498400390148163,
0.018240034580230713,
-0.024753523990511894,
-0.03229716047644615,
0.015470118261873722,
-0.05924037843942642,
0.03262884542346001,
0.032918110489845276,
-0.00045054926886223257,
-0.011325706727802753,
0.03126409649848938,
0.021984271705150604,
-0.009950537234544754,
-0.010712708346545696,
-0.006935007870197296,
0.013444816693663597,
0.008690392598509789,
0.002324734115973115,
0.004729575011879206,
-0.005010862369090319,
-0.014061113819479942,
0.01913251355290413,
0.01755613088607788,
-0.0014305089134722948,
0.057568907737731934,
0.0009505203925073147,
0.009775216691195965,
-0.012614044360816479,
0.0051834541372954845,
0.037082377821207047,
0.02186424843966961,
-0.0004302738234400749,
-0.0025376484263688326,
-0.03880438953638077,
-0.002590910065919161,
0.05024665594100952,
-0.05740213394165039,
-0.012318423949182034,
-0.011888241395354271,
0.00886126235127449,
-0.008441529236733913,
-0.023852355778217316,
-0.01691157929599285,
-0.02448946051299572,
0.029487671330571175,
-0.087398461997509,
0.07902085781097412,
-0.018920838832855225,
0.013230017386376858,
0.04882091283798218,
0.00616427231580019,
0.010990558192133904,
0.06060897186398506,
0.08236251026391983,
-0.020021075382828712,
-0.04161503165960312,
0.0040676104836165905,
-0.032474249601364136,
-0.028793973848223686,
0.018464457243680954,
-0.048829615116119385,
-0.0072425478138029575,
0.0020738886669278145,
-0.06405793130397797,
0.05262359231710434,
0.034640103578567505,
0.03365045413374901,
0.031918078660964966,
0.03725099191069603,
-0.02568189986050129,
-0.011353217996656895,
-0.006498894654214382,
0.05574822053313255,
-0.0062606544233858585,
0.043126896023750305,
0.03383146598935127,
-0.036837320774793625,
0.008387131616473198,
-0.0007783959154039621,
-0.023504097014665604,
-0.047809451818466187,
0.01028117910027504,
0.07761388272047043,
-0.019795753061771393,
0.009379317983984947,
0.019051875919103622,
0.008052884601056576,
0.006448530126363039,
0.030253132805228233,
0.02818901278078556,
-0.016983740031719208,
0.011834880337119102,
-0.019667990505695343,
0.06273555755615234,
-0.01406284049153328,
-0.021193042397499084,
0.01571936346590519,
0.008053475059568882,
0.04035891965031624,
0.06944824010133743,
-0.03604378551244736,
0.010148110799491405,
-0.02577557973563671,
-0.00142136518843472,
-0.014724072068929672,
-0.008808047510683537,
-0.02291918732225895,
0.007780627813190222,
-0.013041208498179913,
0.0006026934133842587,
0.003399617038667202,
0.008143887855112553,
0.017322516068816185,
-0.057301223278045654,
0.03938199207186699,
0.08949701488018036,
0.04929260537028313,
-0.0187687948346138,
0.02611369453370571,
0.01681382954120636,
-0.031197547912597656,
-0.009040610864758492,
0.0028109936974942684,
0.024978650733828545,
-0.018932880833745003,
-0.002756226109340787,
-0.0322050079703331,
-0.04139380902051926,
0.0072701843455433846,
-0.0131711820140481,
0.0070719849318265915,
-0.02620469033718109,
-0.09997997432947159,
-0.04601539671421051,
0.02843300811946392,
-0.01744840294122696,
-0.00892864353954792,
-0.07669886201620102,
0.01952221244573593,
0.03032010607421398,
0.04817092418670654,
0.0024782405234873295,
-0.021917888894677162,
-0.044585924595594406,
0.030617620795965195,
0.007738026790320873,
-0.0038487750571221113,
-0.00434773089364171,
0.017984317615628242,
-0.030623557046055794,
0.012557171285152435,
-0.05036718025803566,
0.02158394455909729,
0.017573779448866844,
0.057452380657196045,
-0.027516013011336327,
0.054615382105112076,
0.011019537225365639,
-0.021084288135170937,
-0.019937152042984962,
0.051033079624176025,
-0.01361207664012909,
0.05483366549015045,
0.0032267095521092415,
-0.009503019042313099,
0.03326792269945145,
0.022503577172756195,
-0.0027327619027346373,
0.009504551067948341,
0.029287064447999,
0.02481693960726261,
-0.03304172307252884,
-0.016237927600741386,
-0.03873762488365173,
0.003615056863054633,
-0.008135083131492138,
-0.051585517823696136,
0.0025880858302116394,
0.0056776185519993305,
0.007558275479823351,
-0.0015573479468002915,
0.035370972007513046,
-0.014341801404953003,
-0.03475063666701317,
0.01209208369255066,
-0.07868094742298126,
0.001881047966890037,
-0.038923606276512146,
0.0210578516125679,
-0.0085456483066082,
-0.021463267505168915,
0.062013428658246994,
0.02118203416466713,
0.012852550484240055,
-0.004892171360552311,
-0.016846979036927223,
-0.03650849312543869,
0.021498730406165123,
0.01905825547873974,
-0.046652454882860184,
0.025569254532456398,
0.037629492580890656,
0.007576705422252417,
-0.016589686274528503,
0.027906544506549835,
-0.03217817842960358,
-0.0391494520008564,
-0.008817322552204132,
-0.03289123997092247,
0.0165721345692873,
0.007757231593132019,
0.013520840555429459,
-0.04027276113629341,
-0.005460015963762999,
-0.02080824039876461,
0.01815086603164673,
-0.05065881833434105,
0.07395841926336288,
0.06780912727117538,
0.014484611339867115,
-0.0270120557397604,
0.04843118414282799,
0.021838096901774406,
-0.01249389722943306,
-0.011315993033349514,
-0.030916722491383553,
-0.04333838075399399,
-0.009746766649186611,
0.03353767842054367,
0.0176372230052948,
-0.046749863773584366,
0.015105663798749447,
0.02528720535337925,
0.027271650731563568,
0.0502077117562294,
0.013481096364557743,
-0.0037452944088727236,
0.016548635438084602,
0.016034044325351715,
0.005533761810511351,
0.01770312339067459,
0.02693675085902214,
0.0065839216113090515,
0.03492379188537598,
0.03564531356096268,
-0.00620546517893672,
-0.005315565504133701,
0.03198840841650963,
-0.03701939061284065,
-0.02565886452794075,
-0.0018785238498821855,
-0.03616431728005409,
0.03617680072784424,
-0.0003535912255756557,
0.022471638396382332,
0.03294592723250389,
-0.018850235268473625,
0.013671322725713253,
0.012827884405851364,
-0.013558776117861271,
0.04448128864169121,
-0.013090990483760834,
-0.040465522557497025,
0.0007919927593320608,
0.004567937925457954,
-0.021720856428146362,
0.02500058524310589,
-0.03862346336245537,
-0.011196372099220753,
0.0010647575836628675,
0.0017936573131009936,
0.03153127431869507,
0.029640786349773407,
0.01778476871550083,
-0.03116890974342823,
-0.04211742803454399,
0.009817232377827168,
-0.045374058187007904,
0.0033619245514273643,
0.014979176223278046,
-0.011088406667113304,
0.01509132981300354,
-0.03229789063334465,
-0.036905013024806976,
0.010495796799659729,
-0.06017540767788887,
-0.009911389090120792,
-0.008425932377576828,
-0.04064563289284706,
-0.0595393106341362,
0.020972756668925285,
0.034364111721515656,
-0.0331566259264946,
-0.019361376762390137,
0.014642909169197083,
0.02566634491086006,
-0.02746960148215294,
-0.0019103100057691336,
0.015033853240311146,
-0.017581669613718987,
-0.011563749052584171,
0.0076047335751354694,
-0.026345117017626762,
0.032030992209911346,
-0.003671979298815131,
0.0614921934902668,
0.06315243989229202,
-0.05803151801228523,
-0.010221651755273342,
-0.011250891722738743,
-0.0148861613124609,
0.02341369353234768,
-0.007315348833799362,
0.022647710517048836,
-0.008281435817480087,
0.007178776431828737,
0.04643087461590767,
-0.018131932243704796,
-0.02553420513868332,
-0.006158522330224514,
-0.0009338787640444934,
0.01201757974922657,
0.000061014583479845896,
0.027821624651551247,
0.015416665002703667,
0.0036447313614189625,
0.018534360453486443,
0.03451598063111305,
0.051549281924963,
0.03614599257707596,
-0.007640494499355555,
-0.0021731967572122812,
0.011270670220255852,
0.038906894624233246,
0.03550809621810913,
0.02756327949464321,
0.002111575799062848,
-0.009752443991601467,
0.029284903779625893,
0.024529483169317245,
0.030474578961730003,
0.021326128393411636,
-0.0686030387878418,
0.03901578113436699,
0.01638386771082878,
0.03366605564951897,
-0.035298436880111694,
0.03016491048038006,
-0.03255757689476013,
0.006766351871192455,
0.013142230920493603,
0.03800908848643303,
0.05024673417210579,
0.008957779966294765,
0.0038322298787534237,
0.03185351938009262,
0.050385113805532455,
-0.007246553432196379,
-0.0068696169182658195,
0.002360334387049079,
-0.04270660877227783,
0.022191280499100685,
-0.01341067161411047,
-0.023578373715281487,
0.051776956766843796,
0.0235431008040905,
0.04748751223087311,
-0.008414107374846935,
-0.029413701966404915,
0.020182853564620018,
-0.08710542321205139,
0.007468218449503183,
0.011037337593734264,
0.030375387519598007,
0.01564732939004898,
0.08119478076696396,
0.011410345323383808,
0.016192903742194176,
-0.00726876687258482,
-0.0035676886327564716,
-0.08305229991674423,
0.016696184873580933,
-0.0007138120708987117,
0.009356648661196232,
-0.04026259854435921,
0.006851986050605774,
0.017511390149593353,
-0.019770435988903046,
-0.02393568679690361,
-0.017117222771048546,
-0.00503632752224803,
-0.04379716515541077,
-0.013813030906021595,
-0.02585061453282833,
-0.010639812797307968,
-0.03709160163998604,
0.03155443072319031,
0.037283387035131454,
-0.027458615601062775,
0.035347700119018555,
0.031636275351047516,
-0.015022752806544304,
0.02252599038183689,
-0.03770345821976662,
0.013356535695493221,
0.015964357182383537,
0.027328113093972206,
0.022799067199230194,
0.016103923320770264,
0.00043222063686698675,
-0.015517039224505424,
-0.006338492501527071,
0.07655566930770874,
0.01524485182017088,
-0.03505929559469223,
0.004937729798257351,
-0.02321118488907814,
-0.00803864561021328,
0.020524300634860992,
0.022127149626612663,
-0.007260995451360941,
0.020642906427383423,
0.018374571576714516,
-0.010117936879396439,
-0.049948785454034805,
0.04667072370648384,
0.009590747766196728,
0.014670697040855885,
-0.037543538957834244,
-0.06442994624376297,
0.008805464021861553,
-0.04090477526187897,
0.00037913225241936743,
0.023828167468309402,
0.006876974366605282,
0.008516416884958744,
0.03615526854991913,
0.00658523989841342,
0.010368797928094864,
-0.016130881384015083,
-0.03485769033432007,
-0.03548288345336914,
0.026488404721021652,
-0.010224562138319016,
-0.007595464587211609,
-0.002272943966090679,
0.0017524468712508678,
0.06268622726202011,
-0.009462849237024784,
0.026284389197826385,
-0.07566515356302261,
-0.011436624452471733,
0.03315936028957367,
-0.0007763024768792093,
-0.031700581312179565,
-0.02144453302025795,
-0.028311600908637047,
-0.016987666487693787,
0.05293620750308037,
-0.03338140621781349,
0.03344477340579033,
0.0010728142224252224,
0.020047543570399284,
-0.01570761390030384,
-0.013535828329622746,
-0.013340982608497143,
-0.002880849875509739,
0.0497959740459919,
-0.01859320141375065,
-0.03732447698712349,
0.012878923676908016,
-0.025764547288417816,
0.010579650290310383,
0.033562999218702316,
0.041253264993429184,
0.026764649897813797,
-0.006911131553351879,
0.03148671239614487,
0.03426992520689964,
-0.006390945985913277,
-0.08168052136898041,
0.010571734048426151,
0.031706999987363815,
0.01650942489504814,
0.04461348429322243,
-0.019871968775987625,
-0.07764548063278198,
0.04526565223932266,
0.03189622238278389,
-0.010090503841638565,
-0.00391806336119771,
-0.026520267128944397,
0.07186214625835419,
0.03322473168373108,
0.004165013320744038,
0.07006240636110306,
0.043505411595106125,
-0.00023878908541519195,
0.01150741521269083,
-0.01785869710147381,
0.07896319031715393,
-0.023843491449952126,
-0.018912388011813164,
-0.058410584926605225,
0.007280562072992325,
0.003919254057109356,
0.010570329613983631,
-0.015734927728772163,
0.03009665571153164,
0.010758616961538792,
-0.03515053540468216,
0.022506067529320717,
0.05020471289753914,
0.021644994616508484,
0.010154508985579014,
-0.03666144609451294,
0.044913336634635925,
-0.019616160541772842,
-0.024810735136270523,
0.004680064041167498,
0.0028292874339967966,
-0.01326692383736372,
0.02685941942036152,
-0.015251869335770607,
0.03538292646408081,
-0.07769234478473663,
-0.01223488338291645,
0.0077082375064492226,
-0.06660547852516174,
0.05517353489995003,
-0.007627141661942005,
-0.02129116654396057,
-0.0013832523254677653,
-0.0510452464222908,
0.010128187946975231,
0.0472891665995121,
-0.014373219572007656,
0.026918916031718254,
-0.003553583286702633,
0.04441160708665848,
-0.01612285152077675,
-0.00169719650875777,
-0.11083732545375824,
-0.04925932362675667,
-0.02000688761472702,
0.05711980536580086,
-0.03422243893146515,
-0.0465366430580616,
0.03716880828142166,
-0.030564431101083755,
0.004843335133045912,
0.02412066049873829,
0.03179682418704033,
-0.03924724832177162,
-0.004304432310163975,
0.034310199320316315,
0.016467340290546417,
0.057770099490880966,
-0.031588103622198105,
-0.020482273772358894,
-0.0027303241658955812,
-0.029861412942409515,
-0.03762245923280716,
0.005322986748069525,
0.03062209114432335,
-0.019561100751161575,
0.012244772166013718,
-0.0215645432472229,
0.0216513741761446,
0.05235155671834946,
-0.04319198057055473,
-0.020056413486599922,
0.012727285735309124,
0.0022018877789378166,
0.04382004588842392,
-0.0186882633715868,
-0.002948491834104061,
-0.022182542830705643,
0.013360610231757164,
0.02400808036327362,
-0.01085904985666275,
-0.012152635492384434,
-0.03132417052984238,
0.028192631900310516,
0.022896919399499893,
0.030886979773640633,
0.041251521557569504,
0.05278277024626732,
-0.018554462119936943,
0.03461994230747223,
0.002655335236340761,
-0.021938316524028778,
0.04229188710451126,
-0.03580578789114952,
0.002365764928981662,
0.034627899527549744,
0.022590473294258118,
-0.02642083913087845,
-0.04789656773209572,
-0.0531512051820755,
-0.019568076357245445,
0.05069071426987648,
-0.03627017140388489,
0.023326529189944267,
-0.018390100449323654,
-0.003308831015601754,
-0.016719583421945572,
-0.038345932960510254,
-0.015485202893614769,
-0.0070641920901834965,
-0.02903241105377674,
0.037316445261240005,
-0.021866561844944954,
0.004169798456132412,
0.006855218205600977,
0.024801842868328094,
-0.01777774654328823,
0.03186006098985672,
0.05727216228842735,
0.00728076184168458,
0.015701068565249443,
0.010166258551180363,
-0.036300480365753174,
0.04240802675485611,
-0.024228626862168312,
0.02718145027756691,
0.026085689663887024,
-0.009427099488675594,
0.041827693581581116,
0.029788604006171227,
0.03122112900018692,
-0.047081951051950455,
-0.038402821868658066,
-0.047246698290109634,
0.07107396423816681,
-0.030340399593114853,
0.01212067250162363,
0.009884585626423359,
0.0216403529047966,
0.03412647917866707,
0.0026733672711998224,
0.01931207999587059,
-0.0029332314152270555,
-0.04919061437249184,
0.0019299581181257963,
-0.003004366997629404,
-0.05113355442881584,
0.02054901234805584,
-0.02036096341907978,
-0.05069168657064438,
0.025058742612600327,
-0.021561959758400917,
0.05224919319152832,
-0.039688851684331894,
0.03259583190083504,
0.0015837987884879112,
0.037845075130462646,
-0.020650040358304977,
0.037035129964351654,
0.012877197936177254,
0.037502095103263855,
0.10344656556844711,
0.061203375458717346,
0.025645997375249863,
-0.04786009341478348,
-0.009705962613224983,
-0.004176530055701733,
0.009634112007915974,
0.0010671073105186224,
-0.028093133121728897,
0.04178896173834801,
0.029590541496872902,
-0.014721042476594448,
0.057107120752334595,
-0.04239603877067566,
0.00841979868710041,
0.0554305762052536,
-0.02159523405134678,
-0.015711260959506035,
0.014863086864352226,
-0.0022117646876722574,
-0.002290863310918212,
0.000132681816467084,
-0.08387571573257446,
-0.0031206831336021423,
-0.01961088739335537,
0.01383733656257391,
-0.03954390063881874,
-0.06227791681885719,
0.01577823795378208,
-0.0026233841199427843,
-0.0016840852331370115,
-0.006440027616918087,
0.027623387053608894,
-0.007578707300126553,
-0.02507881633937359,
0.010502094402909279,
0.010993153788149357,
-0.0045411475002765656,
0.02854958549141884,
0.03634088486433029,
-0.003092176513746381,
0.014652098529040813,
0.012161515653133392,
0.050216663628816605,
-0.02570580132305622,
-0.021995332092046738,
-0.03144232556223869,
-0.019648993387818336,
-0.033304888755083084,
-0.010515722446143627,
-0.04088791459798813,
-0.009307465516030788,
0.027037912979722023,
-0.01834764890372753,
-0.028892219066619873,
0.006528227590024471,
0.054240111261606216,
-0.010881079360842705,
-0.008723173290491104,
-0.03700285777449608,
0.008314268663525581,
0.012487058527767658,
0.0037406045012176037,
0.00656436150893569,
-0.0001873848377726972,
0.004766049794852734,
-0.004360485356301069,
0.010182949714362621,
-0.029737528413534164,
-0.03676901385188103,
-0.00015410697960760444,
-0.02844482846558094,
-0.01998770795762539,
-0.037163566797971725,
0.06149785965681076,
-0.010487754829227924,
0.07814332842826843,
-0.001069447142072022,
-0.023110520094633102,
-0.008633112534880638,
-0.05049153044819832,
0.003427485004067421,
0.008595827035605907,
-0.04063291847705841,
0.015115371905267239,
0.031983524560928345,
-0.0007396302535198629,
-0.004057700280100107,
-0.034448202699422836,
0.03831895813345909,
-0.007790818810462952,
0.0009863968007266521,
0.003874928457662463,
-0.030646881088614464,
-0.026374639943242073,
0.025979433208703995,
-0.012050044722855091,
-0.01536362525075674,
0.006893534678965807,
0.06194208189845085,
-0.010466213338077068,
-0.0042434269562363625,
0.021474448963999748,
0.04196662828326225,
-0.032531239092350006,
0.009354955516755581,
0.01204687263816595,
-0.03068305365741253,
0.007966294884681702,
0.015486080199480057,
0.01491824071854353,
-0.05771508812904358,
-0.04118679091334343,
-0.060008253902196884,
-0.009314771741628647,
0.011591345071792603,
0.011222069151699543,
-0.02484290301799774,
0.023725662380456924,
-0.028019186109304428,
0.01878359727561474,
-0.012705711647868156,
-0.03249629959464073,
-0.04690966382622719,
0.04019544646143913,
0.01775994896888733,
-0.03575466573238373,
0.023104652762413025,
0.015208804048597813,
-0.01314041018486023,
-0.027401182800531387,
0.03950686380267143,
0.037714701145887375,
0.0228134635835886,
-0.006326574832201004,
-0.005343751050531864,
-0.03224208205938339,
0.058041658252477646,
-0.015662262216210365,
-0.009790798649191856,
0.038260046392679214,
-0.027930088341236115,
-0.027012234553694725,
0.013810007832944393,
-0.0061717405915260315,
0.0027181508485227823,
0.0069539290852844715,
-0.017824532464146614,
-0.020104823634028435,
0.04805610328912735,
-0.032850682735443115,
0.003972258884459734,
0.018117086961865425,
0.01564260758459568,
-0.012564725242555141,
0.008369472809135914,
0.012921378016471863,
-0.03608458489179611,
-0.0003364112344570458,
0.04302123188972473,
0.028869710862636566,
-0.0292690247297287,
0.006677402649074793,
0.0009590409463271499,
-0.05493663251399994,
0.02945086546242237,
0.03265129774808884,
0.03876068815588951,
0.05120199918746948,
0.06275207549333572,
-0.03234115615487099,
0.052263423800468445,
0.02904861979186535,
0.023360183462500572,
-0.07302223891019821,
-0.004705773666501045,
0.027834974229335785,
-0.038917046040296555,
-0.006240091752260923,
-0.019929004833102226,
0.015875505283474922,
0.03413989767432213,
-0.0661836490035057,
-0.02442224882543087,
-0.019907740876078606,
-0.020627081394195557,
-0.040204305201768875,
0.01401499379426241,
-0.035768814384937286,
0.016658268868923187,
0.024403708055615425,
0.03515684977173805,
0.01111831609159708,
0.005128203425556421,
-0.012746494263410568,
0.004732193425297737,
-0.004892002325505018,
-0.005120386835187674,
0.011003534309566021,
-0.045139435678720474,
0.08731819689273834,
-0.010805122554302216,
-0.02520269714295864,
0.011926412582397461,
-0.018955731764435768,
0.029880698770284653,
-0.005888272076845169,
-0.020667748525738716,
-0.011472970247268677,
-0.004354126285761595,
0.010007558390498161,
-0.06161535531282425,
0.010548056103289127,
0.016174262389540672,
0.009568685665726662,
0.031878791749477386,
-0.015622032806277275,
0.002982284175232053,
0.031236574053764343,
-0.039556775242090225,
-0.025296565145254135,
0.021551745012402534,
0.010421671904623508,
-0.027287829667329788,
-0.011825483292341232,
0.03379794582724571,
0.016380617395043373,
-0.04056694358587265,
0.002540030749514699,
-0.05713555961847305,
-0.030655570328235626,
-0.005745963659137487,
0.03508768603205681,
0.0040656025521457195,
-0.0037584349047392607,
-0.009397429414093494,
-0.04368116706609726,
-0.03120523877441883,
0.005311443004757166,
-0.038683585822582245,
-0.048155203461647034,
-0.03171085566282272,
0.021672256290912628,
-0.015440452843904495,
-0.04164614900946617,
-0.028813248500227928,
-0.03922368213534355,
0.0669151246547699,
-0.018863722681999207,
0.04815787076950073,
-0.010598228313028812,
-0.05462223291397095,
-0.030495142564177513,
-0.07439030706882477,
0.01277963351458311,
-0.06139224395155907,
-0.014013214968144894,
-0.04359613358974457,
-0.01877017319202423,
0.04741169884800911,
-0.0015732288593426347,
0.05540359765291214,
0.018835389986634254,
0.01136074960231781,
-0.019533121958374977,
0.003837320487946272,
0.021306348964571953,
-0.021333135664463043,
0.011961168609559536,
-0.031553592532873154,
-0.035031627863645554,
-0.018918538466095924,
-0.022568577900528908,
-0.040468979626894,
0.015489201992750168,
0.02523813582956791,
-0.016667013987898827,
-0.001218263991177082,
-0.03469312936067581,
0.008239053189754486,
0.05965789780020714,
-0.006444243248552084,
-0.0065038008615374565,
0.03972718119621277,
-0.024196064099669456,
-0.0004777590511366725,
0.04839436337351799,
0.0012758240336552262,
-0.04937288165092468,
0.0411578044295311,
-0.050892751663923264,
-0.03973710909485817,
0.03653103858232498,
-0.01933114603161812,
0.02327372133731842,
-0.0355006642639637,
0.04325413703918457,
0.05415303260087967,
-0.07810135185718536,
0.008095575496554375,
0.028970668092370033,
0.008508100174367428,
0.02665001153945923,
0.026024816557765007,
0.020013477653265,
0.005083569325506687,
0.004027948249131441,
-0.00461630430072546,
0.06246500462293625,
0.0259549543261528,
0.05181024968624115,
0.04101695865392685,
-0.03705788031220436,
-0.02664365991950035,
-0.0030518367420881987,
0.015651004388928413,
0.03501493111252785,
-0.02140573225915432,
-0.021599354222416878,
0.019348297268152237,
0.005769926588982344,
0.012165538035333157,
-0.008249479345977306,
-0.027191225439310074,
0.08293626457452774,
-0.060811661183834076,
-0.012799836695194244,
-0.04148108512163162,
0.002283735666424036,
-0.02311652898788452,
0.0013612115290015936,
0.0038813843857496977,
0.03495262190699577,
-0.01968676783144474,
0.02196303755044937,
-0.021380510181188583,
0.03213929757475853,
0.06587212532758713,
-0.036045774817466736,
-0.010973365977406502,
-0.04413868486881256,
-0.006499913986772299,
-0.0038973945192992687,
-0.0059358589351177216,
-0.017939314246177673,
0.010333181358873844,
0.02299133874475956,
0.0386040061712265,
-0.003770899260416627,
0.007993295788764954,
-0.012293708510696888,
-0.04195185378193855,
0.04740315303206444,
-0.0670754462480545,
-0.005176781676709652,
0.0017027576686814427,
0.0038662918377667665,
-0.027818990871310234,
-0.0026410247664898634
] |
<p>Sorry if this is a silly question but I cant get my head around it.</p>
| 8,846 |
[
-0.06272058933973312,
-0.0699596256017685,
-0.012929626740515232,
-0.022480174899101257,
0.024562355130910873,
0.022076435387134552,
0.009680643677711487,
0.003185891080647707,
-0.0021031969226896763,
-0.009775698184967041,
-0.0005087329773232341,
0.0469822883605957,
0.06346864253282547,
0.02567140944302082,
0.005786948371678591,
0.021474312990903854,
0.009102236479520798,
0.0006214729510247707,
-0.01829107105731964,
-0.011876142583787441,
0.016031436622142792,
0.044819679111242294,
-0.0014497659867629409,
0.019303767010569572,
-0.012914886698126793,
0.02998790703713894,
0.049723733216524124,
0.000904250075109303,
0.02531401626765728,
0.051462769508361816,
-0.01242043450474739,
-0.012909548357129097,
0.02362617664039135,
0.034164488315582275,
0.051688652485609055,
-0.021438337862491608,
-0.044969018548727036,
-0.016357095912098885,
-0.011599011719226837,
0.013323226012289524,
-0.013482972048223019,
0.008734929375350475,
-0.008458646945655346,
0.04629092290997505,
-0.052122797816991806,
0.028981663286685944,
-0.023471249267458916,
-0.046216245740652084,
0.055011358112096786,
-0.05448240786790848,
0.07349766790866852,
-0.006239195819944143,
0.012698054313659668,
0.021727092564105988,
-0.013163290917873383,
0.034065257757902145,
0.09501159191131592,
0.06014852598309517,
-0.029899857938289642,
-0.032854821532964706,
0.02939295768737793,
-0.010271620936691761,
-0.019853057339787483,
-0.013091986067593098,
-0.009860779158771038,
-0.007216368801891804,
-0.02611716277897358,
-0.03943171724677086,
0.05108931288123131,
-0.011858895421028137,
-0.0180770605802536,
0.020946402102708817,
0.04486970975995064,
-0.020934371277689934,
0.060028158128261566,
-0.031569723039865494,
0.0414784699678421,
0.01236745622009039,
0.04634401202201843,
0.009332109242677689,
-0.014656293205916882,
-0.028309151530265808,
0.006185864098370075,
0.038454074412584305,
0.01697332225739956,
0.0005473056226037443,
0.05966771021485329,
-0.03317525237798691,
0.009598583914339542,
0.048971544951200485,
-0.04452229663729668,
-0.01819618046283722,
0.04833109304308891,
0.008866773918271065,
-0.017923645675182343,
0.007997967302799225,
-0.0005614309338852763,
0.043721962720155716,
0.010208137333393097,
-0.0234761293977499,
0.01986485905945301,
-0.008058371022343636,
0.02064286544919014,
0.018867127597332,
-0.011699150316417217,
-0.017769575119018555,
-0.035844914615154266,
0.007048635743558407,
0.034931354224681854,
0.009140321984887123,
-0.031106607988476753,
-0.014353145845234394,
0.005243115592747927,
-0.020580342039465904,
0.027441246435046196,
-0.04305768013000488,
-0.007783876731991768,
-0.004299714230000973,
0.03947965428233147,
0.07760298997163773,
0.02194293402135372,
-0.013149693608283997,
0.05776585265994072,
-0.02863222174346447,
-0.07289619743824005,
0.037997931241989136,
0.025310572236776352,
-0.005623075179755688,
-0.01821904443204403,
0.020922431722283363,
-0.018642107024788857,
-0.029712654650211334,
0.05482865497469902,
-0.003068511141464114,
0.02508929744362831,
-0.02283659391105175,
-0.10265292972326279,
-0.08537185192108154,
0.062112800776958466,
-0.017954573035240173,
0.01569819264113903,
-0.10748182237148285,
0.02273762971162796,
-0.033998094499111176,
0.06264778971672058,
-0.006075074430555105,
0.0010914945742115378,
0.012155178934335709,
-0.0059838551096618176,
0.017136991024017334,
-0.007432560436427593,
-0.022237328812479973,
-0.0039052411448210478,
-0.0556197464466095,
0.013026710599660873,
-0.07209623605012894,
0.022452298551797867,
0.009967826306819916,
-0.008127131499350071,
-0.05720686912536621,
0.021670904010534286,
-0.03390570357441902,
0.006516403518617153,
0.00016155262710526586,
-0.016917910426855087,
-0.041023410856723785,
0.07808606326580048,
0.034735772758722305,
-0.01894114352762699,
0.05451120063662529,
-0.013823043555021286,
0.06779920309782028,
0.007157245650887489,
0.06761270016431808,
0.03493233397603035,
-0.019564131274819374,
-0.019989915192127228,
-0.039776675403118134,
0.02359665185213089,
0.014862466603517532,
-0.061872512102127075,
-0.027286391705274582,
0.027606403455138206,
0.01462319865822792,
0.024504849687218666,
0.05599368363618851,
0.004628630820661783,
-0.026802169159054756,
0.0004628380120266229,
-0.06344563513994217,
-0.02850075252354145,
-0.06892988085746765,
0.0037072969134896994,
0.006078867707401514,
-0.002894947538152337,
-0.0009710631566122174,
0.03622685745358467,
0.03432193398475647,
-0.037136320024728775,
-0.009041573852300644,
-0.02978750504553318,
-0.009726584888994694,
0.06432600319385529,
-0.049805570393800735,
0.0010148044675588608,
0.07803164422512054,
0.04410115256905556,
-0.00044906119001097977,
0.04199719429016113,
-0.008659668266773224,
-0.009557082317769527,
0.0013227320741862059,
-0.009540705941617489,
0.018217815086245537,
-0.012362126260995865,
-0.014981769025325775,
0.028559349477291107,
0.02474307082593441,
-0.0030350524466484785,
0.049200065433979034,
-0.01501738652586937,
0.08672488480806351,
0.012822392396628857,
0.0027036250103265047,
-0.03367266803979874,
-0.0032851784490048885,
0.0039124321192502975,
0.02325630560517311,
0.013353122398257256,
-0.036340031772851944,
-0.04285469651222229,
0.007888684049248695,
0.02081880532205105,
-0.01873154565691948,
-0.005609908606857061,
0.010264948010444641,
0.033826448023319244,
0.055793195962905884,
-0.009429028257727623,
0.021156543865799904,
0.009477920830249786,
0.014334192499518394,
-0.00336603750474751,
0.014850364066660404,
0.003684349125251174,
0.022952059283852577,
0.042200177907943726,
0.009672243148088455,
0.020573953166604042,
-0.036466632038354874,
-0.041472677141427994,
0.04161446914076805,
-0.009588037617504597,
0.030781613662838936,
0.015725668519735336,
-0.013394487090408802,
0.05695696175098419,
-0.05189201980829239,
0.027355678379535675,
-0.008322304114699364,
0.0304083414375782,
-0.01883085072040558,
-0.03629558905959129,
-0.015337166376411915,
0.026197699829936028,
0.048245396465063095,
-0.031048467382788658,
-0.009693436324596405,
0.04416028410196304,
0.007410835009068251,
-0.004703952930867672,
-0.01865389570593834,
-0.029904769733548164,
-0.02151241898536682,
-0.013220434077084064,
0.019761815667152405,
-0.006091074086725712,
0.04232115298509598,
-0.011141670867800713,
-0.049276161938905716,
-0.05064092576503754,
-0.05674055963754654,
0.01287434808909893,
0.005172781180590391,
-0.05452375486493111,
-0.01152944378554821,
0.0011599792633205652,
-0.022725487127900124,
0.03140949830412865,
0.0009101819014176726,
0.016028299927711487,
0.009034588932991028,
-0.02262929454445839,
-0.010436810553073883,
-0.011921304278075695,
-0.022014524787664413,
0.0359606072306633,
-0.02167549729347229,
-0.01443455833941698,
0.04102514311671257,
-0.009956416673958302,
-0.020652422681450844,
0.03034941665828228,
-0.07351209968328476,
-0.043720792979002,
-0.008954565040767193,
-0.02445228584110737,
0.004249804187566042,
-0.05878789350390434,
0.014015051536262035,
0.006799438968300819,
-0.05718519538640976,
-0.0004644796426873654,
-0.024275535717606544,
-0.0577208586037159,
0.029445938766002655,
0.003888124832883477,
0.026843242347240448,
-0.006056133657693863,
-0.044636841863393784,
0.03141384944319725,
-0.000001517519194749184,
-0.06113041937351227,
-0.012842226773500443,
-0.017264166846871376,
-0.0021383888088166714,
-0.04023583605885506,
0.019021326676011086,
0.07039180397987366,
-0.03105846419930458,
0.017873283475637436,
0.048939380794763565,
-0.003129771910607815,
0.03579593449831009,
-0.0030946126207709312,
-0.02204548940062523,
0.006248713470995426,
0.027994463220238686,
-0.01054984051734209,
0.005989358760416508,
0.0015107901999726892,
-0.05305279791355133,
0.002483486430719495,
-0.02040942944586277,
0.025884250178933144,
-0.007297119591385126,
-0.04057711362838745,
0.04633131995797157,
0.01687830500304699,
0.015897540375590324,
-0.019565889611840248,
0.04716167598962784,
0.0004084635293111205,
-0.0026483458932489157,
-0.022048652172088623,
0.009216155856847763,
0.07057703286409378,
-0.0608254075050354,
-0.03423216938972473,
0.018400240689516068,
0.049077752977609634,
-0.03832714632153511,
-0.018120650202035904,
-0.02072141133248806,
0.00446014991030097,
0.019788041710853577,
-0.005141627509146929,
-0.012244914658367634,
0.0708477571606636,
0.037094131112098694,
0.016271254047751427,
0.023742856457829475,
-0.023787647485733032,
0.017169715836644173,
-0.09268056601285934,
0.0166619960218668,
0.023494452238082886,
0.021014204248785973,
-0.03450355306267738,
0.05735357850790024,
0.043137576431035995,
0.010022041387856007,
0.0031794544775038958,
0.012825635261833668,
-0.04137987270951271,
0.0010528757702559233,
-0.010700569488108158,
0.0004804595373570919,
0.0020076236687600613,
-0.03367258980870247,
-0.013822591863572598,
-0.0024727119598537683,
-0.044440463185310364,
-0.004102818667888641,
-0.02804204449057579,
-0.04888949915766716,
0.010815172456204891,
0.013567949645221233,
-0.01744435541331768,
-0.007189775351434946,
0.028746256604790688,
0.04460201412439346,
0.017462527379393578,
0.0106075843796134,
0.03380966931581497,
0.00932672806084156,
-0.03661313280463219,
-0.05416054278612137,
0.013786539435386658,
0.01226161327213049,
0.027001719921827316,
0.025397883728146553,
0.004965261556208134,
-0.033325184136629105,
0.005348860286176205,
-0.03804526850581169,
0.003914095461368561,
0.030391784384846687,
0.031176744028925896,
-0.05405528470873833,
-0.029242223128676414,
-0.00446512084454298,
0.005219305399805307,
0.029896557331085205,
-0.026066280901432037,
0.025426028296351433,
0.019510388374328613,
0.003580523654818535,
-0.015919258818030357,
-0.0013626900035887957,
0.05651743710041046,
-0.009187905117869377,
-0.04245740547776222,
-0.048598699271678925,
0.01078149676322937,
-0.02956623025238514,
-0.014875339344143867,
0.0049588545225560665,
0.027174055576324463,
-0.023439189419150352,
0.009252791292965412,
0.01755630411207676,
-0.026776548475027084,
-0.05692029744386673,
0.008757407777011395,
-0.020113850012421608,
0.001845681108534336,
0.012798954732716084,
0.00598032446578145,
0.01104788575321436,
0.013861095532774925,
0.03753327578306198,
0.004653832409530878,
-0.0234974417835474,
-0.10178109258413315,
-0.028700141236186028,
0.018090730533003807,
-0.004986290819942951,
-0.02851906791329384,
-0.02462059073150158,
-0.054640043526887894,
-0.01469288021326065,
0.029531575739383698,
0.001258881762623787,
0.03539438173174858,
-0.029308347031474113,
-0.0022442408371716738,
-0.011827284470200539,
-0.018082667142152786,
-0.011421761475503445,
-0.005117350723594427,
-0.006827354431152344,
0.022505059838294983,
0.006441819481551647,
0.01680517941713333,
-0.027883483096957207,
-0.012034589424729347,
0.017350105568766594,
0.040149472653865814,
-0.005310227628797293,
0.028651181608438492,
-0.010339601896703243,
0.05448383837938309,
-0.03866002708673477,
-0.07240995019674301,
-0.0032796449959278107,
0.018423138186335564,
0.009894900023937225,
0.03811508044600487,
-0.021674158051609993,
-0.019674910232424736,
0.02141505479812622,
-0.026779040694236755,
0.00021847293828614056,
0.0027457766700536013,
-0.02041446417570114,
0.006684874650090933,
0.038444384932518005,
0.03787810355424881,
0.029391881078481674,
0.016194799914956093,
-0.030123179778456688,
-0.02236815355718136,
-0.027957329526543617,
0.029367148876190186,
-0.03734941408038139,
-0.009741696529090405,
-0.03179146349430084,
0.03189803659915924,
-0.028511522337794304,
0.04126555845141411,
-0.004085030406713486,
-0.02503473311662674,
-0.014082000590860844,
-0.0380946584045887,
-0.017457254230976105,
-0.0066469223238527775,
0.010358292609453201,
-0.0037921012844890356,
-0.029756715521216393,
0.019472984597086906,
-0.0033529389183968306,
-0.028170863166451454,
0.050820980221033096,
-0.04615851491689682,
-0.0011542313732206821,
0.02259811945259571,
0.006682997569441795,
0.021806737408041954,
-0.010238591581583023,
-0.004408674314618111,
0.02838735468685627,
-0.020822420716285706,
0.02111564576625824,
-0.022446928545832634,
0.002541734604164958,
-0.0011057911906391382,
-0.09446286410093307,
-0.014826027676463127,
-0.001944440882652998,
-0.04377476125955582,
0.009741873480379581,
-0.017761563882231712,
0.03031705506145954,
0.011086375452578068,
-0.01427155639976263,
-0.0788085088133812,
-0.07888088375329971,
0.0463942289352417,
0.04193110764026642,
-0.00816348660737276,
-0.017810340970754623,
0.02001161500811577,
-0.0310258399695158,
-0.031246013939380646,
-0.013350051827728748,
0.02687658555805683,
-0.020899875089526176,
-0.00019097798212897032,
0.02675277180969715,
-0.015032057650387287,
0.058144327253103256,
0.052147768437862396,
0.005172912497073412,
0.01974795199930668,
-0.027996791526675224,
-0.016005082055926323,
-0.009853767231106758,
0.05023389682173729,
-0.05146336182951927,
0.0010294793173670769,
-0.009162073954939842,
-0.006216372363269329,
0.029794054105877876,
-0.0343412384390831,
0.033792026340961456,
0.007424109149724245,
0.01946803368628025,
0.0017934824572876096,
-0.034852202981710434,
0.03329266235232353,
-0.0022958877962082624,
0.005985868629068136,
0.002600347623229027,
-0.010484126396477222,
-0.014698498882353306,
-0.025031104683876038,
0.013401228003203869,
0.02307780086994171,
-0.010238638147711754,
0.0033890646882355213,
0.07017648220062256,
-0.0455506257712841,
-0.027721870690584183,
0.031895797699689865,
-0.0130003085359931,
0.02746662311255932,
0.03435943275690079,
-0.0296615120023489,
0.00316964415833354,
0.024621278047561646,
0.00808060821145773,
-0.005078769754618406,
-0.012296201661229134,
0.020055146887898445,
0.05887629836797714,
-0.035630758851766586,
0.037928786128759384,
0.021408502012491226,
-0.011305629275739193,
0.008488775230944157,
0.006995118223130703,
-0.00705072982236743,
0.013624072074890137,
-0.03210456669330597,
0.024876415729522705,
-0.02460150420665741,
0.003635684959590435,
0.04313356801867485,
0.020929038524627686,
0.02222835086286068,
0.011580809950828552,
0.06360503286123276,
-0.005514064338058233,
0.02351551316678524,
0.018631022423505783,
-0.04347066581249237,
0.04200700297951698,
-0.05440196767449379,
0.028265289962291718,
-0.01211028452962637,
-0.019447829574346542,
0.04437101632356644,
0.0007051944849081337,
0.006218252703547478,
-0.025691863149404526,
-0.06591197848320007,
-0.004938777536153793,
0.005542257335036993,
0.010400572791695595,
0.024846632033586502,
-0.0046420893631875515,
-0.010606887750327587,
0.016564153134822845,
0.004296846222132444,
0.024328814819455147,
-0.0082044443115592,
-0.09307660907506943,
-0.032931454479694366,
-0.0005901979166083038,
-0.04561849310994148,
0.036495137959718704,
-0.02081197313964367,
-0.00873086042702198,
0.022363854572176933,
-0.01971738040447235,
0.00009111723920796067,
0.00214485009200871,
0.06541896611452103,
-0.0040448131039738655,
0.05487620830535889,
0.030444076284766197,
0.03742290288209915,
-0.024545596912503242,
0.009036574512720108,
0.13366839289665222,
0.039164379239082336,
0.028183721005916595,
-0.0772591084241867,
-0.006449087057262659,
-0.04614352807402611,
0.017756808549165726,
0.012003163807094097,
0.05517221987247467,
0.01443540584295988,
-0.006893585901707411,
0.021298009902238846,
0.05882108956575394,
0.007713358383625746,
0.02115287259221077,
0.0744282677769661,
-0.041230179369449615,
-0.06801299005746841,
0.0074001154862344265,
-0.00814107060432434,
-0.01427421998232603,
0.003775518387556076,
-0.03399239853024483,
-0.013698938302695751,
-0.01785065233707428,
-0.017768973484635353,
0.003252423135563731,
-0.029180103912949562,
0.011629652231931686,
0.04752612113952637,
-0.03294339030981064,
0.021049007773399353,
0.002865644870325923,
0.01460935641080141,
-0.04077884927392006,
0.033953458070755005,
0.06402061134576797,
-0.024245504289865494,
-0.003065896686166525,
0.03057403862476349,
0.024203283712267876,
-0.012619615532457829,
-0.012735292315483093,
-0.02089826390147209,
-0.04809148982167244,
-0.008558695204555988,
-0.023795103654265404,
0.01723780296742916,
0.000028327041945885867,
0.005247689317911863,
0.0010876917513087392,
0.024556072428822517,
0.021480988711118698,
-0.054670777171850204,
-0.03065604344010353,
0.012692919932305813,
-0.0200620386749506,
0.020182039588689804,
-0.025608500465750694,
-0.03560851141810417,
0.0029313266277313232,
0.004491802304983139,
0.02336025796830654,
0.004227370023727417,
-0.0062424372881650925,
0.016816185787320137,
-0.005985503550618887,
0.0032783125061541796,
-0.03574657440185547,
-0.04264841228723526,
-0.007892727851867676,
-0.006490612868219614,
-0.025590401142835617,
-0.02011798322200775,
0.013889568857848644,
0.06435628980398178,
0.030602362006902695,
-0.025066325441002846,
-0.01667809672653675,
-0.0003279952798038721,
0.025127161294221878,
0.034639131277799606,
-0.008082004263997078,
-0.005320219323039055,
-0.041850559413433075,
-0.0016423588385805488,
0.017120111733675003,
0.01960829459130764,
-0.024272585287690163,
0.03438418358564377,
-0.038369856774806976,
0.05141916126012802,
-0.001878964714705944,
-0.016747431829571724,
-0.045299604535102844,
0.021590983495116234,
-0.04407835006713867,
0.01484075840562582,
0.007065259851515293,
0.020174359902739525,
0.022232137620449066,
0.010134793817996979,
0.010304405353963375,
0.00654092850163579,
-0.012714536860585213,
0.01165504939854145,
0.02838074415922165,
-0.04642506688833237,
-0.027691297233104706,
0.036222271621227264,
-0.02778187207877636,
0.009206471964716911,
-0.018220137804746628,
-0.027247566729784012,
0.025396673008799553,
0.008366529829800129,
0.05190146341919899,
-0.019978638738393784,
0.005931911524385214,
-0.015412659384310246,
-0.00019143948156852275,
-0.023124249652028084,
0.011037866584956646,
-0.061861030757427216,
-0.0083019332960248,
0.033969696611166,
0.014829346910119057,
-0.0045440299436450005,
0.023374292999505997,
-0.0112959835678339,
0.0022006677463650703,
0.04513004049658775,
0.008265631273388863,
-0.026842601597309113,
-0.002662012353539467,
0.023853113874793053,
0.017676942050457,
0.036983851343393326,
-0.03188081830739975,
-0.03845769912004471,
0.029551466926932335,
-0.0737178847193718,
-0.022022666409611702,
0.005348568316549063,
-0.014877582900226116,
0.03279559686779976,
0.02540147490799427,
-0.007749725133180618,
0.0011495945509523153,
0.09202683717012405,
-0.03634166717529297,
-0.01090596430003643,
0.0007106351549737155,
-0.0086663868278265,
0.028616974130272865,
0.01661757007241249,
-0.029936015605926514,
-0.017026320099830627,
-0.007707709446549416,
0.014683024026453495,
0.014383056201040745,
-0.027194056659936905,
-0.04106129705905914,
-0.017514463514089584,
0.033531781286001205,
-0.0010887110838666558,
0.026245199143886566,
0.005645299330353737,
0.0010138966608792543,
0.03665595129132271,
-0.03825090080499649,
0.003846516599878669,
0.007439893204718828,
-0.010487268678843975,
-0.07863687723875046,
-0.025384575128555298,
-0.011334419250488281,
-0.009877706877887249,
0.017907243221998215,
-0.030677810311317444,
0.012730895541608334,
-0.0022539827041327953,
-0.06771453469991684,
-0.0005876018549315631,
-0.0044804587960243225,
-0.03952083736658096,
-0.04555478319525719,
0.030090605840086937,
-0.000011694309250742663,
0.042111434042453766,
0.014215530827641487,
0.036579813808202744,
0.04181806370615959,
0.0026810569688677788,
-0.02715439535677433,
-0.013047697022557259,
0.018865928053855896,
0.015219924971461296,
-0.007439303677529097,
-0.01467493362724781,
0.03659585118293762,
-0.06694921851158142,
-0.03450051695108414,
0.0696038082242012,
-0.010329896584153175,
0.028724467381834984,
0.009503294713795185,
0.03472060710191727,
0.045637086033821106,
-0.013949383050203323,
0.0031433003023266792,
0.002061560982838273,
0.00860354769974947,
0.055307723581790924,
0.016531243920326233,
0.046517353504896164,
-0.001729999901726842,
0.009238164871931076,
-0.005267178639769554,
-0.049440499395132065,
-0.009503417648375034,
-0.007354697212576866,
-0.020721811801195145,
0.008789506740868092,
-0.01305148471146822,
0.02119331993162632,
0.013873524032533169,
-0.03307570517063141,
0.005873884540051222,
-0.0629313588142395,
0.002188426209613681,
0.010716764256358147,
-0.009104478172957897,
-0.013610239140689373,
0.02165868692100048,
-0.025365512818098068,
-0.039928123354911804,
-0.03609046712517738,
0.028160080313682556,
-0.01760026253759861,
-0.019832460209727287,
-0.011774186044931412,
-0.01336085144430399,
0.01862432435154915,
-0.005386473145335913,
-0.0286430474370718,
-0.047656137496232986,
0.024790383875370026,
0.038490019738674164,
0.026667170226573944,
0.022999195381999016,
-0.0611167773604393,
-0.0019322555745020509,
-0.043093763291835785,
0.06717023253440857,
-0.01989123225212097,
0.014039093628525734,
-0.038427773863077164,
-0.030884675681591034,
-0.007900509983301163,
0.02451552450656891,
0.07573752850294113,
-0.03746325522661209,
-0.016912657767534256,
-0.02635536715388298,
0.0155477961525321,
-0.013763003051280975,
-0.028061551973223686,
0.019710397347807884,
-0.006566008552908897,
-0.02185755781829357,
-0.015546110458672047,
-0.017047341912984848,
-0.036496080458164215,
0.018524298444390297,
0.03310708329081535,
-0.013706658966839314,
0.021415000781416893,
-0.050719793885946274,
0.01074204221367836,
0.0202427189797163,
0.024763889610767365,
0.0009169168188236654,
0.05745614320039749,
0.025574875995516777,
0.0022205973509699106,
0.049216676503419876,
-0.0007340366137214005,
-0.048616234213113785,
0.07231085747480392,
-0.015259929932653904,
0.0014708207454532385,
-0.015469207428395748,
-0.002508383709937334,
0.036458082497119904,
-0.004994829185307026,
0.012504120357334614,
0.034815091639757156,
-0.012665191665291786,
-0.007769694551825523,
0.03993779420852661,
0.04208513721823692,
0.008020692504942417,
-0.024373332038521767,
0.014196177013218403,
0.007044430356472731,
-0.04828430712223053,
0.006579422391951084,
0.042034950107336044,
0.013737033121287823,
0.013559610582888126,
0.0342232808470726,
-0.008425447158515453,
0.021251704543828964,
0.044893279671669006,
-0.009081640280783176,
0.042842213064432144,
-0.037944406270980835,
0.0035456011537462473,
-0.004645550157874823,
-0.04364795982837677,
0.032927505671978,
0.018703877925872803,
0.002171090105548501,
0.11436689645051956,
-0.007117155473679304,
0.045542120933532715,
0.01607668586075306,
0.029316723346710205,
-0.02409774251282215,
0.0015078096184879541,
0.035518135875463486,
-0.03112628124654293,
-0.020894557237625122,
-0.02286745421588421,
-0.023246245458722115,
-0.01726190187036991,
0.0377795472741127,
-0.002492442959919572,
0.023480255156755447,
-0.015388157218694687,
0.010752090252935886,
-0.020216310396790504,
0.012676777318120003,
-0.018682027235627174,
-0.0061387778259813786,
0.04203706979751587,
0.031026579439640045,
0.0017612562514841557,
0.0024122153408825397,
-0.009489589370787144,
-0.025523677468299866,
0.040541525930166245,
-0.05074531212449074,
-0.020042015239596367,
-0.02341284230351448,
0.02853395976126194,
0.0035143436398357153,
0.0033448566682636738
] |
<p>If you take two ideal gases at different temperatures, and allow them to share energy through heat, they'll eventually reach a thermodynamic equilibrium state that has higher entropy than the original. The time evolution of that entropy increase is easy to predict, because we know the time evolution of $T$ and $U$ for each of the gases (assuming we have the necessary constants). This is OK.</p>
<p>Now take a system beyond the scope of thermodynamics. A single box containing a gas that is not in thermodynamic equilibrium (doesn't follow the Boltzman distribution). One would expect that gas to quickly thermalise, and reach said equilibrium. Entropy can still be defined using statistical mechanics, and the final state will have higher entropy than the initial state. </p>
<p>I'm looking for quantitative experimental evidence of this effect.<br>
<strong>Ideally, I'd like references measuring the time a gas takes to thermalise.</strong></p>
<p>Obviously this time depends on many factors and is not always doable. I wasn't more specific because I don't want to be picky, I'm looking for any experiments that verify it.</p>
| 8,847 |
[
-0.03747754916548729,
-0.038771744817495346,
-0.01706559956073761,
-0.0021069434005767107,
0.002318825339898467,
0.0006927247741259634,
-0.025548724457621574,
-0.005276858806610107,
0.003549091285094619,
-0.01989864557981491,
0.02593105286359787,
0.08065037429332733,
0.01853536069393158,
-0.01121824886649847,
-0.006528014782816172,
-0.005968889687210321,
-0.005597210954874754,
-0.022236261516809464,
0.006739350967109203,
-0.008845916949212551,
0.0048795901238918304,
0.010633625090122223,
0.02115078829228878,
-0.014801057986915112,
-0.048171427100896835,
0.06051655113697052,
-0.011668435297906399,
-0.03067728690803051,
0.021090932190418243,
0.03931741043925285,
-0.022503692656755447,
0.004648893605917692,
0.009089920669794083,
0.006685432977974415,
0.04127609357237816,
-0.00420734565705061,
0.004814381245523691,
-0.023816073313355446,
-0.002461254596710205,
0.018130619078874588,
-0.06165556237101555,
-0.025182615965604782,
-0.016058791428804398,
0.01798737794160843,
-0.02763187326490879,
0.014347813092172146,
0.001828852342441678,
-0.020288648083806038,
0.03788233548402786,
-0.06867468357086182,
0.039590369910001755,
0.02244097739458084,
0.047673046588897705,
0.030429070815443993,
-0.02880214713513851,
0.027109460905194283,
0.054480090737342834,
0.08224213868379593,
0.015241687186062336,
-0.03109108656644821,
-0.013714666478335857,
-0.02185521274805069,
-0.01623070053756237,
-0.008521247655153275,
-0.06035677343606949,
0.03730307146906853,
-0.002418140647932887,
-0.02104794979095459,
0.02199944108724594,
-0.021618828177452087,
-0.002975940005853772,
0.004755967762321234,
0.0774330198764801,
0.010805233381688595,
-0.0006665490800514817,
-0.0026426182594150305,
0.02413032576441765,
-0.011331556364893913,
0.02467445097863674,
0.0649104118347168,
-0.030692344531416893,
-0.008527177385985851,
0.02047542855143547,
0.04039786010980606,
0.006476275622844696,
-0.0020554917864501476,
0.08022290468215942,
-0.03440264239907265,
0.016642887145280838,
0.05693165212869644,
0.003926828969269991,
-0.016109662130475044,
0.030730564147233963,
-0.0006192215951159596,
-0.0192127488553524,
0.012284035794436932,
-0.016968606039881706,
0.05657986178994179,
0.029926631599664688,
-0.0649215579032898,
0.009956847876310349,
-0.038042034953832626,
0.016761716455221176,
0.06317376345396042,
0.01844416745007038,
-0.04139089956879616,
-0.06340214610099792,
-0.0030595017597079277,
0.013876019045710564,
0.01643124222755432,
-0.04337825998663902,
-0.024767592549324036,
-0.008200892247259617,
-0.030225498601794243,
-0.0002758527116384357,
0.014064332470297813,
-0.002609024755656719,
-0.04475826770067215,
0.08349135518074036,
0.05865304917097092,
0.045602016150951385,
-0.023054292425513268,
0.0027699340134859085,
-0.03851659968495369,
-0.04849864915013313,
0.01272609829902649,
0.03243966028094292,
-0.04735150188207626,
-0.008665278553962708,
0.05047828331589699,
-0.0008756672614254057,
-0.014370864257216454,
-0.011051271110773087,
-0.0239611454308033,
0.022682707756757736,
-0.012125616893172264,
-0.06535106897354126,
-0.07233591377735138,
0.046416524797677994,
-0.027019819244742393,
-0.03003033809363842,
-0.05947096273303032,
-0.005322250537574291,
0.029465841129422188,
0.05332379415631294,
-0.002445900347083807,
0.009405961260199547,
-0.05152909457683563,
0.03384457528591156,
0.008948852308094501,
-0.009152945131063461,
-0.0194875355809927,
0.03543397784233093,
-0.012785610742866993,
0.005077923648059368,
-0.06522919982671738,
0.009155694395303726,
0.06260661035776138,
-0.017257023602724075,
0.0002276313753100112,
0.012027464807033539,
-0.01454886980354786,
-0.020645130425691605,
-0.005326349753886461,
0.0019945537205785513,
-0.03374132141470909,
0.10567153990268707,
0.007068198639899492,
0.0006082745967432857,
-0.010258716531097889,
0.026263527572155,
0.022372568026185036,
0.041026730090379715,
0.0027360268868505955,
0.0021491325460374355,
-0.040866196155548096,
-0.009617085568606853,
0.009490443393588066,
-0.00669354060664773,
0.019486654549837112,
-0.014370168559253216,
0.003518558107316494,
-0.000025326693503302522,
-0.029473567381501198,
-0.006927772890776396,
0.02783908136188984,
-0.01344284974038601,
0.005329627078026533,
0.008420023135840893,
-0.1008511483669281,
-0.03776620328426361,
-0.09257598966360092,
0.0028556904289871454,
0.016494404524564743,
-0.03070947341620922,
0.0254434272646904,
0.016907237470149994,
0.06381648778915405,
-0.040590427815914154,
-0.06600085645914078,
-0.028021279722452164,
0.013258231803774834,
0.015499915927648544,
-0.016233371570706367,
0.014714390970766544,
0.031863003969192505,
0.045931294560432434,
-0.022232932969927788,
0.033610641956329346,
-0.01394746359437704,
-0.0617838129401207,
0.01521394494920969,
-0.028161751106381416,
0.0033509661443531513,
-0.03996463865041733,
0.001501622493378818,
0.032078493386507034,
0.010039626620709896,
0.014400193467736244,
-0.006276363972574472,
-0.013991368003189564,
0.05183238908648491,
0.023806096985936165,
0.0380689799785614,
-0.01242119912058115,
0.05418062582612038,
0.03440215438604355,
-0.023287108168005943,
0.007458992302417755,
-0.06591345369815826,
-0.040793947875499725,
-0.019042961299419403,
0.055515777319669724,
0.07029066979885101,
-0.03374612331390381,
0.0171969011425972,
0.015443703159689903,
0.009250852279365063,
-0.002143105724826455,
0.013221485540270805,
-0.004158863797783852,
-0.019751328974962234,
0.032382551580667496,
0.019935889169573784,
0.02859445847570896,
0.032320477068424225,
0.03623015433549881,
-0.005001111887395382,
0.00588753167539835,
0.024847380816936493,
-0.014648115262389183,
-0.012031731195747852,
0.00958701130002737,
-0.002070442773401737,
-0.03153957799077034,
-0.031783975660800934,
0.025833630934357643,
-0.021674640476703644,
0.023059755563735962,
-0.01231921836733818,
0.0362173467874527,
0.06515964865684509,
-0.022411510348320007,
-0.049881692975759506,
-0.007258681580424309,
0.003853119909763336,
0.004589738789945841,
0.010448319837450981,
0.026309184730052948,
-0.036158252507448196,
0.03273722901940346,
0.0018308026483282447,
0.027577074244618416,
-0.02218673750758171,
-0.0032825490925461054,
-0.010030527599155903,
0.008642956614494324,
0.006255438085645437,
-0.031799592077732086,
-0.021453874185681343,
-0.026561185717582703,
-0.03101016767323017,
0.01737433671951294,
0.006234720814973116,
-0.015261393040418625,
0.030816083773970604,
-0.005680478177964687,
-0.05048827826976776,
0.01835937239229679,
-0.04403877258300781,
0.02632877044379711,
0.051625318825244904,
-0.024082913994789124,
-0.056267429143190384,
0.0024094039108604193,
-0.018306991085410118,
-0.0037592335138469934,
-0.03822123259305954,
0.03017655573785305,
0.0491381511092186,
-0.04586712643504143,
-0.07550543546676636,
0.04264841228723526,
-0.04408608004450798,
-0.026742439717054367,
-0.02199663408100605,
-0.013647577725350857,
0.01927119679749012,
-0.025423189625144005,
0.030307143926620483,
0.029093684628605843,
-0.0379398949444294,
-0.0545477569103241,
-0.05012398958206177,
-0.052624788135290146,
0.05456465110182762,
0.012079124338924885,
0.05011603981256485,
-0.033257924020290375,
-0.016601327806711197,
0.04366079717874527,
-0.010110819712281227,
-0.009022737853229046,
0.0005930308252573013,
0.006196037400513887,
0.0008384614484384656,
0.008943064138293266,
0.008572481572628021,
-0.016582177951931953,
-0.013036059215664864,
0.03235269710421562,
0.03836958482861519,
0.04475168138742447,
0.001531373243778944,
-0.0030202202033251524,
-0.01899666339159012,
0.0411367304623127,
0.004360662307590246,
0.020324937999248505,
0.03799542784690857,
0.005661002825945616,
-0.01007241103798151,
-0.012308354489505291,
0.01866908185184002,
0.023869555443525314,
0.033014245331287384,
-0.08823087066411972,
0.061832308769226074,
0.002153209177777171,
-0.0003679403162095696,
-0.052354637533426285,
0.006938766688108444,
-0.044917043298482895,
-0.008241274394094944,
0.020704325288534164,
0.058129504323005676,
0.04241648688912392,
0.029341917484998703,
0.017482982948422432,
0.052073728293180466,
0.058478064835071564,
0.003531656228005886,
-0.011944461613893509,
-0.017991550266742706,
-0.015718046575784683,
0.055256109684705734,
-0.01448315754532814,
-0.017202362418174744,
0.011487423442304134,
0.02001071721315384,
0.016610248014330864,
-0.017654327675700188,
-0.02582121640443802,
-0.004607339855283499,
-0.08600520342588425,
-0.013650601729750633,
-0.04030779004096985,
0.04882220923900604,
0.022742845118045807,
0.05979219824075699,
0.00040701660327613354,
0.00967548880726099,
0.015145630575716496,
-0.039184294641017914,
-0.08919639140367508,
0.020209264010190964,
-0.0290057435631752,
-0.019464483484625816,
0.003750329138711095,
0.01567430980503559,
0.01589610055088997,
-0.038374800235033035,
0.000015481095033464953,
-0.016083087772130966,
0.022253289818763733,
-0.06427789479494095,
-0.007965190336108208,
-0.03534753620624542,
-0.04348678141832352,
0.0009960077004507184,
0.017341015860438347,
0.005942164454609156,
-0.034113116562366486,
0.015109263360500336,
0.01974027045071125,
-0.03154752776026726,
0.03600356727838516,
-0.03318445384502411,
0.03415025398135185,
0.04055945202708244,
0.024063734337687492,
0.03843829780817032,
0.030869627371430397,
-0.005228153895586729,
0.02813124842941761,
0.0302752498537302,
0.02434113249182701,
-0.020518755540251732,
-0.0061933547258377075,
-0.006159372627735138,
-0.0112027982249856,
-0.03875802084803581,
0.015220414847135544,
0.034793607890605927,
0.014976225793361664,
0.04807373881340027,
-0.03002176620066166,
0.054871492087841034,
-0.012899772264063358,
0.016706660389900208,
0.047789912670850754,
-0.033266544342041016,
-0.014536255039274693,
-0.009593076072633266,
-0.05472233518958092,
-0.011119551956653595,
0.0073906006291508675,
0.017736932262778282,
0.0029654167592525482,
-0.025185182690620422,
0.00015250634169206023,
-0.0146035710349679,
0.035774149000644684,
-0.011401759460568428,
-0.011511996388435364,
-0.01385590247809887,
0.020345626398921013,
0.006602117791771889,
0.01613536849617958,
-0.004945714492350817,
0.012885581701993942,
0.013352968730032444,
0.009562619030475616,
-0.004604012705385685,
-0.04739592969417572,
0.011576180346310139,
0.03237675130367279,
0.02096451260149479,
-0.008168734610080719,
0.028027836233377457,
-0.010134296491742134,
0.01741444133222103,
0.07375892251729965,
-0.0020375314634293318,
0.02658247761428356,
-0.0185935590416193,
-0.032307010143995285,
-0.0021672197617590427,
-0.024367187172174454,
-0.010648105293512344,
0.026492102071642876,
0.041410256177186966,
-0.0019377581775188446,
-0.003255953546613455,
-0.0423438586294651,
0.007179387379437685,
0.008697401732206345,
0.03787992522120476,
0.03386493772268295,
-0.027995634824037552,
0.014657163992524147,
0.0008335976162925363,
-0.002543349750339985,
-0.009947333484888077,
-0.06261249631643295,
0.014158072881400585,
-0.008883016183972359,
-0.044986262917518616,
0.008603664115071297,
-0.05446166172623634,
-0.04531261697411537,
0.039548251777887344,
-0.017427071928977966,
-0.025982536375522614,
-0.00014465981803368777,
-0.005997331812977791,
0.06482551246881485,
0.022692846134305,
0.001164534012787044,
0.0343894325196743,
0.05657365173101425,
-0.002493141684681177,
0.012348102405667305,
0.002531123347580433,
0.05215290188789368,
-0.04403223842382431,
0.000042898274841718376,
-0.025000378489494324,
0.005106613505631685,
-0.014746293425559998,
0.03560357540845871,
0.0028588110581040382,
0.028694534674286842,
-0.006765871308743954,
-0.037067338824272156,
0.025992441922426224,
0.019801409915089607,
0.029067886993288994,
0.018022799864411354,
0.003207434667274356,
-0.021592721343040466,
0.004686253610998392,
-0.02695535309612751,
-0.003776109777390957,
0.0064164395444095135,
-0.011762888170778751,
0.02966930717229843,
-0.046434346586465836,
0.008843381889164448,
-0.047150079160928726,
-0.025679606944322586,
0.00017238585860468447,
0.005969613790512085,
0.037002842873334885,
-0.015908479690551758,
-0.012308471836149693,
0.02780626155436039,
-0.04238218441605568,
0.021880317479372025,
0.031018132343888283,
0.007967903278768063,
0.02453898824751377,
-0.05212913453578949,
0.022184666246175766,
-0.0028266184963285923,
0.005790622439235449,
-0.10259731113910675,
-0.03588350862264633,
0.06513069570064545,
-0.005263712257146835,
-0.0058537558652460575,
-0.0732264295220375,
0.0062179407104849815,
-0.0341557115316391,
-0.0019988943822681904,
-0.0023197156842797995,
0.04135773703455925,
0.018970970064401627,
-0.00420607253909111,
-0.005294319242238998,
0.026490969583392143,
0.027157124131917953,
-0.02415318600833416,
-0.026000414043664932,
-0.035735175013542175,
0.01105190347880125,
-0.028171779587864876,
0.030755391344428062,
0.013896518386900425,
-0.013784618116915226,
-0.01789761893451214,
0.024191085249185562,
-0.010076896287500858,
0.035748258233070374,
-0.04525677114725113,
-0.015020822174847126,
0.058676961809396744,
-0.02955479733645916,
0.014670797623693943,
-0.004220691975206137,
0.029228588566184044,
0.004090527538210154,
0.01621803641319275,
-0.006708338391035795,
-0.01699000969529152,
0.013331553898751736,
-0.051707491278648376,
0.00033309360151179135,
-0.007735550403594971,
-0.015202794224023819,
-0.01470195036381483,
0.07774386554956436,
0.04240645840764046,
-0.014457957819104195,
0.01890704408288002,
-0.03663292154669762,
0.029603248462080956,
-0.002632449148222804,
-0.010080930776894093,
-0.012456119060516357,
-0.007148789241909981,
-0.014330098405480385,
-0.04573977366089821,
-0.02875651977956295,
-0.020805222913622856,
0.050376322120428085,
-0.02127920091152191,
0.07302990555763245,
0.04396500810980797,
0.00132879544980824,
-0.0016194946365430951,
-0.016523202881217003,
-0.0031600294169038534,
0.012868628837168217,
0.005889168009161949,
0.02386459708213806,
-0.004103031940758228,
-0.005103403236716986,
0.010651465505361557,
0.03924695402383804,
-0.007001020945608616,
0.029860369861125946,
-0.005610109306871891,
0.012238552793860435,
0.06751756370067596,
-0.0518830344080925,
-0.05359260365366936,
0.05881586670875549,
-0.048152390867471695,
0.045434560626745224,
-0.033102694898843765,
-0.0060835229232907295,
0.011269614100456238,
0.0029336444567888975,
-0.012052945792675018,
-0.06664672493934631,
-0.03880860656499863,
-0.05596552789211273,
0.014567242935299873,
-0.009754066355526447,
-0.013467895798385143,
0.036948543041944504,
0.010476614348590374,
0.033028703182935715,
0.015062114223837852,
0.007855617441236973,
0.010399745777249336,
-0.045369796454906464,
-0.0016843058401718736,
-0.004218883812427521,
-0.03977038338780403,
0.03889144957065582,
0.0074173458851873875,
-0.010127579793334007,
0.011633147485554218,
-0.025292975828051567,
-0.009515071287751198,
-0.007492697797715664,
0.03846058249473572,
0.012662047520279884,
0.08360754698514938,
-0.023267902433872223,
0.03207891434431076,
-0.03398721665143967,
0.026833295822143555,
0.10831833630800247,
0.01795506849884987,
0.018904393538832664,
-0.0427350215613842,
0.04620654135942459,
-0.006247124634683132,
-0.003603144781664014,
-0.025462185963988304,
-0.013097107410430908,
0.011749479919672012,
-0.011311188340187073,
0.024839073419570923,
0.07228294759988785,
-0.0033799458760768175,
-0.017718037590384483,
0.030460283160209656,
-0.03180845081806183,
0.005821469239890575,
0.02545682154595852,
0.051547277718782425,
0.019831852987408638,
-0.017066149041056633,
-0.0402524508535862,
-0.005909181199967861,
-0.030536077916622162,
-0.0005792094743810594,
0.0029560851398855448,
-0.030011240392923355,
0.010957300662994385,
0.002877115737646818,
-0.028370974585413933,
0.007552339229732752,
0.013394760899245739,
-0.03962799161672592,
-0.02886335365474224,
0.004697615280747414,
-0.00246633542701602,
0.030619483441114426,
0.0016949366545304656,
0.0495339073240757,
0.018301285803318024,
0.02741517312824726,
0.027715764939785004,
0.027793096378445625,
-0.04031848534941673,
-0.027731727808713913,
-0.016481926664710045,
0.014989994466304779,
-0.0567849799990654,
-0.020909611135721207,
0.0020203778985887766,
-0.02158275619149208,
0.024427544325590134,
-0.0035126334987580776,
-0.04413800686597824,
0.0020126481540501118,
0.038719646632671356,
-0.02619287371635437,
0.020078936591744423,
-0.008365342393517494,
0.03502632677555084,
-0.004646921530365944,
0.009980382397770882,
0.006146614905446768,
-0.0361950621008873,
0.007583805359899998,
0.0014162721345201135,
0.017815573140978813,
-0.024327293038368225,
-0.01975618675351143,
-0.033161185681819916,
-0.0039426167495548725,
-0.05786542221903801,
-0.0013515946920961142,
0.019212055951356888,
0.011083436198532581,
0.03716824948787689,
0.020382989197969437,
-0.02428857423365116,
-0.00944577343761921,
-0.0671326294541359,
0.014216761104762554,
-0.011338882148265839,
-0.03222670033574104,
-0.01840510033071041,
0.002354877768084407,
0.031651996076107025,
0.028589747846126556,
-0.015277699567377567,
0.014860169030725956,
0.034054093062877655,
0.025439122691750526,
0.021216806024312973,
-0.030818872153759003,
0.008910061791539192,
-0.0008496942464262247,
-0.039820026606321335,
-0.009898673743009567,
-0.009104124270379543,
0.035127874463796616,
0.010234009474515915,
-0.012518435716629028,
0.006675491109490395,
0.0027522211894392967,
-0.0013650873443111777,
0.04310361668467522,
0.033214271068573,
-0.020177701488137245,
-0.05505503714084625,
-0.019279927015304565,
0.005746976938098669,
0.02060055546462536,
-0.04744265601038933,
-0.050613634288311005,
0.022485682740807533,
-0.004165224265307188,
-0.013147636316716671,
-0.009113666601479053,
0.02243581973016262,
-0.023942815139889717,
0.05223393440246582,
-0.05563409626483917,
-0.023316513746976852,
-0.05140532925724983,
-0.046203866600990295,
0.01187711488455534,
0.04808156564831734,
0.004690325353294611,
0.049965228885412216,
0.00851109903305769,
-0.039424408227205276,
0.03519251570105553,
0.06087642163038254,
0.003688246011734009,
-0.033260148018598557,
-0.0038640715647488832,
0.0016409772215411067,
0.03799107298254967,
-0.027856534346938133,
-0.04565843194723129,
0.03906376659870148,
-0.024138493463397026,
-0.017420882359147072,
0.02556432969868183,
-0.012304188683629036,
0.005962206982076168,
0.02793538011610508,
-0.0058095138520002365,
0.0016196983633562922,
0.057129696011543274,
-0.038228634744882584,
-0.0011234530247747898,
0.012452998198568821,
-0.008880176581442356,
-0.020815689116716385,
0.010986773297190666,
0.02909332513809204,
-0.041093673557043076,
-0.0376264713704586,
0.023627979680895805,
0.006268055643886328,
-0.0029318106826394796,
0.006973989307880402,
-0.0012118055019527674,
-0.0007085544639267027,
0.021799951791763306,
0.00973169133067131,
-0.009754742495715618,
0.07173794507980347,
0.07587647438049316,
-0.03619809076189995,
0.015424863435328007,
0.02975711226463318,
-0.011785789392888546,
-0.10182307660579681,
0.00799193512648344,
0.013056270778179169,
-0.010668642818927765,
0.010744522325694561,
-0.031413350254297256,
0.03449603170156479,
0.0160380806773901,
-0.06585302948951721,
0.030597291886806488,
-0.021101027727127075,
-0.0005934232613071799,
-0.02029363624751568,
-0.0018381028203293681,
-0.03160449117422104,
0.015035445801913738,
0.03499934449791908,
0.0321127288043499,
0.00866133626550436,
0.0697636604309082,
-0.02106572687625885,
-0.008817432448267937,
0.009524330496788025,
0.009224677458405495,
0.025127394124865532,
-0.01456555537879467,
0.045482490211725235,
-0.02810210920870304,
-0.007611026056110859,
0.01772783137857914,
-0.03153950721025467,
-0.02263161912560463,
-0.0026779205072671175,
0.004000438842922449,
-0.01768413372337818,
0.006692398339509964,
0.0517699271440506,
-0.02653813175857067,
0.020412545651197433,
0.02525240182876587,
0.01758049987256527,
0.01711423136293888,
-0.02645772323012352,
-0.001979530556127429,
0.0207509845495224,
0.0029259694274514914,
-0.020594697445631027,
0.06153653562068939,
-0.01164812222123146,
-0.03503798320889473,
0.04615885019302368,
-0.009048215113580227,
0.04692550376057625,
0.01911117136478424,
-0.007210388779640198,
-0.04167261719703674,
-0.010554821230471134,
0.008197830058634281,
0.02584601566195488,
-0.029171951115131378,
0.007836204953491688,
-0.02671341598033905,
0.010070951655507088,
0.045039381831884384,
0.011119721457362175,
0.03850722685456276,
-0.0462779775261879,
-0.042961884289979935,
-0.034929949790239334,
0.0009534198907203972,
-0.018626127392053604,
-0.07812362909317017,
-0.05212128162384033,
0.04567848891019821,
0.012220395728945732,
0.029857777059078217,
-0.012362852692604065,
-0.041578326374292374,
-0.009393345564603806,
-0.04933208227157593,
0.017283543944358826,
-0.033587370067834854,
0.018243327736854553,
-0.05186055228114128,
0.00287924543954432,
0.015794964507222176,
-0.00859995000064373,
0.07522350549697876,
-0.011795326136052608,
-0.01992490142583847,
0.012807777151465416,
0.0031789203640073538,
0.04147859290242195,
-0.026009218767285347,
0.017720019444823265,
-0.05193939805030823,
-0.021858029067516327,
0.014535263180732727,
-0.0056125386618077755,
0.02776862122118473,
-0.006190002895891666,
0.04685889929533005,
-0.03769044950604439,
-0.017286254093050957,
-0.012099181301891804,
-0.03135408088564873,
0.08481519669294357,
0.0031890319660305977,
-0.039129871875047684,
0.05458508059382439,
-0.017453636974096298,
0.04738752916455269,
0.0045484257861971855,
-0.005322650540620089,
-0.043218597769737244,
0.02212216518819332,
-0.027456024661660194,
-0.011257728561758995,
-0.04986077919602394,
-0.025988159701228142,
-0.026274748146533966,
-0.021427076309919357,
0.01092593278735876,
-0.0010819683084264398,
-0.04938923195004463,
0.02880127914249897,
0.02022474631667137,
0.015769710764288902,
0.042843516916036606,
-0.046916745603084564,
0.03698037564754486,
-0.007919438183307648,
0.04892190918326378,
-0.017179343849420547,
0.06550982594490051,
0.052144914865493774,
-0.001842889585532248,
0.03110911324620247,
-0.01012930367141962,
-0.027081141248345375,
-0.004352218937128782,
0.01396312564611435,
0.006591269746422768,
-0.01440466195344925,
-0.03192708641290665,
0.036719825118780136,
-0.009982649236917496,
0.007589495275169611,
0.008482092060148716,
-0.01471584290266037,
0.05607760325074196,
-0.0075659663416445255,
0.0058977301232516766,
-0.040269576013088226,
0.02695618011057377,
-0.0070235952734947205,
-0.00829602312296629,
0.032253023236989975,
0.049981046468019485,
-0.026164408773183823,
0.036842163652181625,
-0.01318723987787962,
-0.009314213879406452,
-0.006149936933070421,
-0.010303180664777756,
0.00690669659525156,
-0.01732424460351467,
0.03864147514104843,
-0.026794085279107094,
-0.009823129512369633,
-0.006701905280351639,
-0.02924000471830368,
0.014841558411717415,
0.06035809591412544,
0.02839098684489727,
-0.006688108202069998,
-0.0049561089836061,
0.02017870917916298,
0.07467307150363922,
-0.052788544446229935,
-0.015996241942048073,
-0.021505169570446014,
0.020201940089464188,
-0.02668312005698681,
0.02511870674788952
] |
<p>I was told to find the temperature distribution of a wire with a current going through it. So I found $$T(x)=T_{\infty}-\frac{\dot{q}}{km^{2}}[\frac{cosh(mx)}{cosh(mL)}-1]$$</p>
<p>I need to find the average temperature in the wire using this formula. I know I have to use some integral but I can't remember the formula. If someone could just give me the formula then I could probably integrate it myself.</p>
| 8,848 |
[
0.011344894766807556,
-0.02942773327231407,
0.00879809632897377,
-0.02842232957482338,
0.006575306877493858,
0.013117864727973938,
-0.057633742690086365,
-0.02021806314587593,
-0.01150401309132576,
-0.009653889574110508,
0.09617549926042557,
0.04930742830038071,
0.058461349457502365,
0.005919978953897953,
0.03185725212097168,
-0.01671127788722515,
-0.007208148017525673,
0.0011596534168347716,
-0.00102574797347188,
-0.04277105629444122,
-0.009788114577531815,
0.038063839077949524,
-0.002229694975540042,
-0.00917081069201231,
-0.026621874421834946,
0.05149707570672035,
0.021153999492526054,
-0.034978318959474564,
0.02230537310242653,
0.03411604464054108,
-0.02569526992738247,
-0.0383598655462265,
0.04224430397152901,
-0.003331715939566493,
0.030718732625246048,
-0.009765442460775375,
-0.035558465868234634,
-0.05000864714384079,
-0.012517116963863373,
0.03724479302763939,
-0.013018671423196793,
-0.03718375414609909,
0.01139767374843359,
0.014398705214262009,
0.00010408661182736978,
-0.012698645703494549,
0.005139678250998259,
-0.0523969829082489,
0.02153424546122551,
-0.0558818019926548,
0.05419088900089264,
-0.028525512665510178,
0.04257278889417648,
0.02093161828815937,
-0.008271877653896809,
0.002875261241570115,
0.05558954179286957,
0.029219062998890877,
0.020421437919139862,
-0.046256303787231445,
-0.0015838455874472857,
-0.011875909753143787,
-0.023440303280949593,
-0.0018950806697830558,
0.005572757683694363,
0.01845076121389866,
0.00570838525891304,
-0.005621476098895073,
0.007117263972759247,
-0.01764233037829399,
0.02069755084812641,
0.012167425826191902,
0.017663655802607536,
-0.004220036324113607,
-0.023765578866004944,
-0.0020911074243485928,
0.022562434896826744,
0.05286182463169098,
0.020464608445763588,
0.03147834539413452,
0.009437790140509605,
0.008421435952186584,
-0.0038726928178220987,
0.012844177894294262,
-0.007080301642417908,
-0.018251482397317886,
0.09556017816066742,
-0.0005526841850951314,
0.015213701874017715,
0.019606435671448708,
-0.00554840499535203,
0.037810228765010834,
0.000959617318585515,
0.013161493465304375,
-0.012818741612136364,
-0.000800456153228879,
0.02172243595123291,
0.03629906848073006,
-0.03480558842420578,
-0.037448324263095856,
0.0189785398542881,
-0.016832783818244934,
-0.0002977068943437189,
0.06338246166706085,
0.01396982278674841,
-0.021153660491108894,
0.024507954716682434,
-0.04001711308956146,
0.006354509387165308,
-0.02277563139796257,
-0.07648400217294693,
0.012634326703846455,
0.025953033939003944,
0.002357185585424304,
-0.018924690783023834,
-0.015537560917437077,
0.005010955035686493,
-0.025045573711395264,
-0.0007308353087864816,
0.03738073259592056,
0.023435834795236588,
-0.013157812878489494,
0.03547675535082817,
-0.01644655503332615,
-0.04108215123414993,
0.029049115255475044,
0.02012953720986843,
0.009316195733845234,
-0.01735399104654789,
0.05110841616988182,
-0.015425354242324829,
-0.011436477303504944,
0.01875806227326393,
0.0009388072066940367,
0.04451337084174156,
-0.04965584725141525,
-0.04910322278738022,
-0.05884335935115814,
0.013942115008831024,
-0.0063515217043459415,
-0.004427395761013031,
-0.05527718365192413,
-0.008234200067818165,
0.059793490916490555,
0.04698138311505318,
0.015433277003467083,
0.021232450380921364,
-0.03538369759917259,
0.0016815179260447621,
-0.014982216991484165,
-0.03838241472840309,
-0.05237745866179466,
0.01707608252763748,
-0.0003510337264742702,
0.00990797858685255,
-0.034501127898693085,
0.02618308924138546,
0.04117431491613388,
0.000427259219577536,
0.008986461907625198,
0.022393733263015747,
0.003664428135380149,
-0.02595791406929493,
0.039870236068964005,
0.006155627314001322,
-0.04518716037273407,
0.09581373631954193,
-0.006192573346197605,
0.02955777384340763,
-0.01414323691278696,
0.020237300544977188,
-0.01237520482391119,
-0.013218376785516739,
0.007757971063256264,
0.02284732647240162,
-0.022873809561133385,
0.022235946729779243,
0.0018193917348980904,
0.009063098579645157,
0.04569671303033829,
-0.07563215494155884,
-0.03340180218219757,
0.03505213186144829,
0.004593277350068092,
0.02036258764564991,
0.03444772958755493,
0.03192543983459473,
-0.016460906714200974,
0.01997918076813221,
-0.015603971667587757,
-0.052179064601659775,
-0.022308968007564545,
0.019097644835710526,
-0.007579267956316471,
-0.005953802261501551,
-0.047906193882226944,
-0.005949038080871105,
0.03488586097955704,
-0.009490154683589935,
0.0056975232437253,
0.007657055277377367,
0.007978077046573162,
-0.011272908188402653,
-0.044933855533599854,
0.01687396503984928,
0.06721765547990799,
0.036683302372694016,
-0.010227777063846588,
0.01028782594949007,
-0.04662230983376503,
0.027895567938685417,
-0.036765966564416885,
-0.06335840374231339,
0.03815934807062149,
-0.004308555740863085,
-0.04223195090889931,
0.03390814736485481,
-0.017809033393859863,
-0.022242983803153038,
0.0288427472114563,
-0.021344449371099472,
0.06218531355261803,
0.052644021809101105,
0.03780132532119751,
-0.02509153261780739,
0.02169099636375904,
-0.011112059466540813,
0.015016063116490841,
-0.0034797857515513897,
-0.04249691590666771,
-0.02817031741142273,
0.008393337018787861,
0.05924401059746742,
-0.008469879627227783,
-0.04251338541507721,
-0.005138582084327936,
0.045030828565359116,
0.02860776148736477,
0.031740326434373856,
-0.007814787328243256,
0.0053016613237559795,
-0.022459635511040688,
0.016394710168242455,
0.01999444141983986,
-0.023625187575817108,
0.010671895928680897,
-0.014339392073452473,
0.02417379803955555,
0.04322630167007446,
0.02791007049381733,
0.0048373728059232235,
0.043589308857917786,
-0.021085884422063828,
0.04619520530104637,
-0.006391929928213358,
-0.013339884579181671,
0.04776462912559509,
-0.0476716123521328,
0.02800566889345646,
-0.0072566852904856205,
-0.007864126935601234,
0.049947746098041534,
0.002567856339737773,
-0.04279818758368492,
0.019160645082592964,
0.004055367317050695,
-0.004788858816027641,
-0.031615305691957474,
0.0261423010379076,
-0.02765725366771221,
0.0033231463748961687,
-0.0033797561191022396,
-0.00486717326566577,
-0.030673565343022346,
0.00114621187094599,
-0.003048565471544862,
0.010864160023629665,
0.027207093313336372,
-0.037326131016016006,
-0.04248607158660889,
-0.006386446300894022,
0.00195375457406044,
0.024956393986940384,
0.0402994304895401,
-0.03919832408428192,
-0.009405679069459438,
-0.011162620969116688,
-0.04856650158762932,
0.05167650431394577,
0.001395774190314114,
-0.0027433002833276987,
0.02914857119321823,
-0.007501801010221243,
-0.06924144923686981,
0.018588101491332054,
-0.005668931175023317,
0.024201275780797005,
-0.07728292047977448,
0.0052982838824391365,
0.024554753676056862,
-0.010136274620890617,
-0.04948083311319351,
0.021854273974895477,
-0.06632476300001144,
-0.09013731777667999,
-0.02584858238697052,
0.005800330545753241,
0.02221566252410412,
0.012263468466699123,
0.07255440205335617,
-0.013301094062626362,
-0.005712759681046009,
-0.031607020646333694,
-0.08222141861915588,
-0.008294535800814629,
0.04259023442864418,
0.011870275251567364,
0.02284967340528965,
-0.011986179277300835,
-0.054797738790512085,
0.07032648473978043,
0.028095247223973274,
-0.025596503168344498,
-0.006645056884735823,
-0.005122071597725153,
-0.02447834610939026,
-0.019999487325549126,
0.022024691104888916,
0.017389623448252678,
-0.06146993860602379,
-0.02900954708456993,
0.03818640485405922,
0.06472724676132202,
0.05873643606901169,
-0.040425244718790054,
0.012175763957202435,
0.02204018086194992,
-0.031234871596097946,
0.023092161864042282,
0.08133464306592941,
0.02262093313038349,
-0.002629147609695792,
0.02525085210800171,
-0.008549757301807404,
0.016868360340595245,
0.04396272078156471,
-0.05757023021578789,
0.02240898832678795,
-0.02039072848856449,
0.00550999166443944,
-0.08325345814228058,
0.0482502356171608,
-0.003059373702853918,
-0.015558505430817604,
-0.010609649121761322,
0.0365338958799839,
0.008269189856946468,
-0.009066052734851837,
0.03169616684317589,
0.0314582921564579,
0.007130844052881002,
-0.011754030361771584,
-0.0194003414362669,
0.0018253109883517027,
-0.03303905948996544,
0.009072916582226753,
-0.03940318524837494,
-0.0369795560836792,
0.019477589055895805,
0.06912130117416382,
0.0297552403062582,
0.014513774774968624,
0.0022348049096763134,
0.011096964590251446,
-0.05844031646847725,
-0.04843873903155327,
0.00893407966941595,
0.07438644766807556,
0.016377203166484833,
0.04500161483883858,
0.042342592030763626,
0.005862073041498661,
0.05424448102712631,
0.02203303389251232,
-0.09339912980794907,
0.048693858087062836,
-0.036267369985580444,
-0.02881748229265213,
-0.014165474101901054,
-0.028964059427380562,
0.01030306238681078,
0.008739950135350227,
0.012437712401151657,
0.021089328452944756,
-0.00589246628805995,
-0.03137577325105667,
0.008189979940652847,
-0.020191233605146408,
0.010968457907438278,
-0.0215741079300642,
0.0061228168196976185,
0.04438449442386627,
-0.05379654839634895,
0.0027753845788538456,
0.020391354337334633,
-0.019347412511706352,
-0.02128463052213192,
-0.049558427184820175,
-0.013710259459912777,
0.04287870600819588,
0.01118036825209856,
0.008698462508618832,
0.003054463304579258,
-0.03380785882472992,
0.018811911344528198,
0.012317858636379242,
0.08148480206727982,
0.013651934452354908,
-0.03928374499082565,
-0.011481590569019318,
-0.05335865169763565,
0.0002564118185546249,
0.020830677822232246,
0.02101181447505951,
-0.020622815936803818,
-0.02915591187775135,
0.03851744532585144,
-0.025453941896557808,
-0.008876541629433632,
0.025792023167014122,
0.025418566539883614,
-0.01395058911293745,
0.002764543518424034,
-0.03549887239933014,
-0.003136571031063795,
-0.05756054073572159,
-0.005347800441086292,
0.012800781987607479,
-0.022076470777392387,
0.016234328970313072,
0.00003020083750016056,
0.05867450684309006,
0.029738502576947212,
0.037343379110097885,
-0.044248852878808975,
0.026431327685713768,
0.04124986752867699,
-0.018736984580755234,
-0.033829521387815475,
0.026364631950855255,
0.03876552730798721,
0.000058254521718481556,
-0.005072641186416149,
0.006650461349636316,
-0.07296741008758545,
-0.014561047777533531,
0.026066023856401443,
0.05551103875041008,
0.005940616596490145,
-0.02300369180738926,
-0.08070562779903412,
0.009136656299233437,
0.08050443977117538,
0.0004140495148021728,
0.01686471328139305,
-0.007619098760187626,
-0.013734742067754269,
-0.006427760235965252,
-0.019597018137574196,
-0.008453205227851868,
0.02805730327963829,
0.02866184711456299,
0.014354477636516094,
-0.05840710178017616,
-0.008014518767595291,
0.02323821745812893,
0.03242429718375206,
0.027677012607455254,
0.011617590673267841,
0.00616831798106432,
-0.009394844993948936,
0.018115537241101265,
0.011908828280866146,
-0.020188404247164726,
-0.06799246370792389,
-0.02397097647190094,
-0.005341928452253342,
0.025775402784347534,
0.03442927077412605,
0.006474203430116177,
0.0019118215423077345,
0.060484629124403,
0.01224365085363388,
0.0031315910164266825,
-0.009752737358212471,
-0.03642488643527031,
0.04792056977748871,
0.02760254219174385,
0.0004285869945306331,
0.05804503336548805,
0.00753345713019371,
0.017825869843363762,
0.007387659978121519,
0.001252292189747095,
0.045468807220458984,
-0.016447825357317924,
-0.02198747731745243,
-0.04420586675405502,
-0.022218741476535797,
-0.026735568419098854,
0.013315897434949875,
-0.06566321104764938,
0.02626342698931694,
-0.0642097070813179,
-0.0007113923784345388,
0.054493747651576996,
0.01112594734877348,
0.03195700794458389,
-0.007656753063201904,
-0.001535405870527029,
0.047081317752599716,
-0.015423513017594814,
-0.06278906762599945,
0.010764035396277905,
-0.016415730118751526,
0.009081793017685413,
-0.002889362396672368,
-0.020258797332644463,
-0.016099339351058006,
-0.046932172030210495,
-0.0329124741256237,
-0.016455383971333504,
-0.024651682004332542,
0.004936753306537867,
-0.045146048069000244,
0.002501959912478924,
0.04106782376766205,
-0.03160283342003822,
-0.034428104758262634,
-0.016729718074202538,
0.02496599219739437,
0.04639410600066185,
-0.06590794026851654,
0.016888391226530075,
-0.004561060108244419,
-0.015035595744848251,
-0.049968983978033066,
-0.06604286283254623,
0.036309726536273956,
0.0026229501236230135,
-0.024786170572042465,
-0.008044064976274967,
0.0031308841425925493,
-0.0342593714594841,
-0.041932009160518646,
0.014406902715563774,
0.01653372123837471,
0.016304204240441322,
0.028829317539930344,
-0.007472869474440813,
0.029606448486447334,
0.0134733896702528,
0.0003739283129107207,
0.0009175640298053622,
0.00778181990608573,
-0.018437916412949562,
-0.061319660395383835,
-0.008043952286243439,
0.03850315511226654,
-0.006243935786187649,
-0.013319618068635464,
-0.01683674566447735,
-0.015594866126775742,
0.0373275987803936,
-0.0036474624648690224,
-0.033667176961898804,
0.017586305737495422,
0.06782510876655579,
-0.01088187750428915,
-0.007699640933424234,
0.01407628133893013,
0.04423968121409416,
0.025524338707327843,
-0.029564306139945984,
0.008188252337276936,
-0.013781915418803692,
-0.00558013841509819,
-0.0015121338656172156,
-0.005444184876978397,
0.0016188077861443162,
0.00884687714278698,
0.06269774585962296,
-0.004636004101485014,
-0.0020842894446104765,
0.03268132731318474,
-0.017098257318139076,
-0.01574159599840641,
0.01788792759180069,
-0.044943712651729584,
0.007587244734168053,
-0.0264905896037817,
-0.014756959863007069,
-0.028378251940011978,
-0.048928454518318176,
0.000506632961332798,
0.06343317776918411,
-0.02857297658920288,
0.04753653332591057,
0.02459365874528885,
0.013665231876075268,
0.005333690904080868,
0.030901601538062096,
-0.03971389681100845,
0.024795249104499817,
0.007212361786514521,
0.013693279586732388,
-0.023351335898041725,
-0.0023083186242729425,
0.022793876007199287,
0.04588521271944046,
-0.043392736464738846,
0.04605407640337944,
-0.019996101036667824,
0.01842171885073185,
-0.024790357798337936,
0.005304617807269096,
-0.03788874298334122,
0.02484903670847416,
-0.012898065149784088,
0.03407637029886246,
-0.05414534732699394,
0.0017555761151015759,
0.06404628604650497,
0.02464970014989376,
-0.02503451704978943,
-0.039507780224084854,
0.0008163817110471427,
-0.01561017520725727,
0.022248245775699615,
0.02186788246035576,
-0.005350313149392605,
0.038659002631902695,
0.04663083702325821,
0.04220631346106529,
-0.02222696878015995,
0.01654692366719246,
-0.04318328946828842,
-0.04138634353876114,
0.002358093159273267,
-0.022375620901584625,
-0.0778777077794075,
0.03455420210957527,
0.007191058713942766,
0.0032135758083313704,
0.014168518595397472,
-0.050680387765169144,
0.01741875149309635,
0.061337511986494064,
-0.002888872055336833,
-0.019940046593546867,
0.08005708456039429,
0.0004717218689620495,
-0.015227319672703743,
-0.03271833807229996,
0.009037655778229237,
0.11109885573387146,
0.050445277243852615,
0.0007524259854108095,
-0.08435159176588058,
-0.017905378714203835,
-0.0262617077678442,
0.02163093537092209,
-0.0788462683558464,
-0.0007045607198961079,
-0.04909208044409752,
0.016182245686650276,
0.04272501543164253,
0.041776541620492935,
-0.026019349694252014,
-0.008182363584637642,
0.023382289335131645,
-0.004365986678749323,
-0.036171142011880875,
0.03575844690203667,
-0.009540489874780178,
0.007867378182709217,
0.03319245204329491,
-0.06930682808160782,
0.04478215426206589,
-0.0325281098484993,
0.027531474828720093,
-0.04350683465600014,
-0.024978121742606163,
0.01954725757241249,
-0.025082791224122047,
-0.04382515698671341,
0.013164615258574486,
0.03274533152580261,
-0.03370985761284828,
-0.009839230217039585,
-0.0045022740960121155,
0.04309931397438049,
0.00042458681855350733,
0.049329258501529694,
0.002983481390401721,
0.02058497443795204,
0.022398892790079117,
0.028667686507105827,
0.02430700697004795,
-0.014321335591375828,
-0.0326169915497303,
-0.023659134283661842,
0.016979193314909935,
-0.010707022622227669,
0.0029721015598624945,
0.01613328792154789,
0.016379041597247124,
0.016191182658076286,
-0.022600967437028885,
0.008001109585165977,
-0.022656332701444626,
0.0292117428034544,
-0.045802854001522064,
-0.020843692123889923,
-0.012794682756066322,
0.013468075543642044,
0.01734314300119877,
-0.002724479418247938,
0.003072364255785942,
0.001125665265135467,
0.014583981595933437,
0.010826438665390015,
0.05127305909991264,
-0.00336332805454731,
-0.014675775542855263,
-0.0271809920668602,
-0.016769930720329285,
0.003068596124649048,
-0.011857189238071442,
-0.006008639466017485,
-0.00438542990013957,
0.04171932488679886,
-0.006180476862937212,
-0.004321540705859661,
-0.03417867049574852,
-0.07692883163690567,
0.03895183652639389,
0.030945580452680588,
0.017125314101576805,
0.0051498631946742535,
-0.014006341807544231,
0.00028565595857799053,
0.050494104623794556,
-0.010126294568181038,
0.009511707350611687,
0.04338059574365616,
0.025169499218463898,
0.030616378411650658,
-0.02883044257760048,
-0.002211848273873329,
-0.01899859681725502,
-0.047431908547878265,
0.0037545072846114635,
-0.00253496621735394,
0.03464219719171524,
0.013811912387609482,
0.006092357914894819,
-0.035988517105579376,
0.015765521675348282,
-0.020348964259028435,
0.02192339114844799,
-0.011213269084692001,
-0.0211118645966053,
0.006048246752470732,
-0.002858891384676099,
0.008505772799253464,
-0.03509363532066345,
-0.010327283293008804,
-0.014484643936157227,
0.0012233392335474491,
0.028855474665760994,
0.03636859357357025,
-0.05748288705945015,
0.006692694965749979,
-0.02208469621837139,
-0.009988849051296711,
0.007337683346122503,
0.03859550505876541,
-0.02873704768717289,
-0.002802218310534954,
-0.014195011928677559,
0.021452708169817924,
-0.03631073608994484,
0.020103922113776207,
-0.04197060689330101,
0.0026110238395631313,
0.03250426799058914,
0.027883965522050858,
-0.01517832837998867,
-0.03206654638051987,
-0.01265648938715458,
0.015479418449103832,
0.03163786605000496,
-0.054506566375494,
0.010532109998166561,
0.05872397497296333,
-0.026681821793317795,
0.006498875096440315,
0.03477080911397934,
0.035613588988780975,
0.03138434514403343,
0.06481147557497025,
-0.021371573209762573,
-0.010359656997025013,
0.057615794241428375,
-0.019326774403452873,
-0.013889106921851635,
-0.020057156682014465,
-0.05952589213848114,
0.054138049483299255,
-0.011470720171928406,
-0.0000028861593364126747,
0.01588360406458378,
0.014745844528079033,
0.011102517135441303,
0.02914399281144142,
-0.010527407750487328,
0.01144065335392952,
0.02094455063343048,
0.024766182526946068,
0.005744976922869682,
0.024175161495804787,
0.02208409458398819,
0.049519602209329605,
0.05784381553530693,
-0.009200352244079113,
0.004415952600538731,
-0.035143621265888214,
-0.010335869155824184,
-0.09211145341396332,
-0.01413793582469225,
-0.0076113417744636536,
0.02972126379609108,
0.04371671751141548,
-0.059655603021383286,
-0.025183789432048798,
0.05366825312376022,
-0.05810745432972908,
0.034411393105983734,
-0.01874690316617489,
-0.04361214116215706,
-0.028670454397797585,
-0.0037931720726191998,
-0.006671588867902756,
0.05366697162389755,
0.06064937263727188,
0.03194433078169823,
0.03885537013411522,
0.03300977870821953,
-0.02297060936689377,
-0.05228203535079956,
0.03518254682421684,
0.03391845524311066,
0.011846225708723068,
-0.025632638484239578,
0.016909854486584663,
-0.03427761048078537,
-0.0026978682726621628,
0.04524585232138634,
-0.04313696548342705,
-0.002230478450655937,
-0.00887824222445488,
0.03596465662121773,
-0.015434011816978455,
0.05145340412855148,
0.02068924345076084,
0.015107872895896435,
0.03737941011786461,
0.006114178337156773,
0.07004988193511963,
-0.015615331940352917,
-0.0358804389834404,
0.005050385370850563,
0.04327169060707092,
-0.031180821359157562,
-0.06199135631322861,
0.037477172911167145,
-0.015958420932292938,
0.002151055261492729,
0.02903435193002224,
-0.013387689366936684,
0.030972035601735115,
-0.03135160729289055,
-0.03821995481848717,
-0.020412230864167213,
-0.007719371933490038,
0.02452966757118702,
-0.009902403689920902,
0.03265824541449547,
-0.006027292460203171,
0.012157033197581768,
-0.03368489071726799,
0.04402927681803703,
0.0273829884827137,
-0.0017778818728402257,
-0.04259932041168213,
0.00945712998509407,
-0.01732470467686653,
0.02452865242958069,
0.03247792646288872,
-0.0297550018876791,
-0.05927397683262825,
0.019297849386930466,
0.0280886422842741,
0.014002217911183834,
-0.0006838468252681196,
-0.004650367423892021,
-0.02868003398180008,
-0.049654826521873474,
-0.011460432782769203,
-0.026796046644449234,
-0.029987353831529617,
-0.021540705114603043,
-0.022911524400115013,
-0.012897930108010769,
0.019012050703167915,
0.04914142191410065,
0.015757426619529724,
-0.01365748606622219,
0.016985883936285973,
0.010913334786891937,
0.016031766310334206,
-0.07692693918943405,
0.023748863488435745,
-0.010500737465918064,
0.006300879642367363,
-0.009561988525092602,
0.021757615730166435,
0.01169100683182478,
-0.006503389682620764,
0.02574683539569378,
-0.042782433331012726,
0.0671011209487915,
-0.035948462784290314,
-0.021276211366057396,
-0.0011103992583230138,
0.008197221904993057,
-0.025343935936689377,
0.047643277794122696,
-0.0497308187186718,
-0.0011816503247246146,
-0.01974589377641678,
0.00011435974738560617,
-0.031901586800813675,
0.01715555042028427,
-0.034124091267585754,
0.0052226390689611435,
-0.02243802696466446,
0.0038775568827986717,
0.005896102637052536,
-0.045354172587394714,
-0.004576270468533039,
0.0007797532598488033,
-0.040546588599681854,
-0.025730658322572708,
0.054252851754426956,
0.0055666049011051655,
0.04088069126009941,
-0.004303928464651108,
0.022618843242526054,
-0.00540609285235405,
0.0015722645912319422,
0.016680460423231125,
0.012676427140831947,
0.007325922604650259,
-0.03253328427672386,
-0.0017014665063470602,
0.019502835348248482,
-0.022875944152474403,
0.004882571287453175,
-0.005327919963747263,
-0.006523217540234327,
-0.030543019995093346,
-0.030891891568899155,
-0.019874874502420425,
-0.020833902060985565,
0.0437813475728035,
0.0012346759904175997,
-0.01593226008117199,
0.055964596569538116,
-0.028377177193760872,
0.023502256721258163,
-0.013063167221844196,
-0.012758174911141396,
-0.035858381539583206,
0.03340581804513931,
0.0028476137667894363,
0.042883433401584625,
-0.04225900396704674,
-0.01223266962915659,
0.016149459406733513,
0.012776823714375496,
0.012839649803936481,
-0.02798900566995144,
0.02632218599319458,
-0.026892971247434616,
0.00014120408741291612,
-0.02902798168361187,
-0.01206403411924839,
-0.017264842987060547,
-0.012278098613023758,
-0.0026179959531873465,
0.03290308639407158,
0.03148616850376129,
-0.020944567397236824,
0.001167642418295145,
-0.010597006417810917,
0.050954222679138184,
-0.06549341976642609,
-0.006292324047535658,
-0.03379162400960922,
0.023188455030322075,
0.008950350806117058,
-0.016373367980122566
] |
<p>I am reading about some canonical transformations of the Hamiltonian (of a system consisting of an electron interacting with an ionic lattice) due to Tomanaga and Lee, Low and Pines. One of the important considerations should be translation invariance (momentum conservation). In a paper by Lee, Low and Pines ("Motion of Slow Electrons in a Polar Crystal", 1953), there is a frequent mention of low-lying energy levels. Intuitively, I would like to think they are referring to energy states close to the ground-state, but I don't think that is quite correct. </p>
<p>Do low-lying energy levels have to do with, perhaps, energy of the electron with small momentum? The title of the paper by Lee, Low, and Pines is after all about "Slow Electrons". </p>
<p>I'm confused. Some clarification could be helpful. </p>
| 8,849 |
[
-0.019707608968019485,
-0.038146696984767914,
0.003437499050050974,
-0.046153340488672256,
-0.004749821033328772,
-0.013380812481045723,
-0.0338810570538044,
-0.013003923930227757,
-0.017460964620113373,
-0.03888756409287453,
0.03492751717567444,
0.012133345939218998,
0.040637653321027756,
0.03548933565616608,
-0.002367441076785326,
0.009881401434540749,
-0.02673114277422428,
-0.008854794315993786,
-0.03895758464932442,
-0.023276321589946747,
0.020945783704519272,
0.006477524060755968,
0.0009552098927088082,
0.019383853301405907,
0.0040970053523778915,
0.014293631538748741,
0.004352269694209099,
-0.027710504829883575,
0.00980208907276392,
0.04317711666226387,
-0.01499092485755682,
-0.042928751558065414,
0.002905034925788641,
-0.018389862030744553,
0.014090092852711678,
-0.005449333228170872,
-0.04133695736527443,
-0.06453793495893478,
0.04411577433347702,
0.038381047546863556,
-0.04113279655575752,
-0.007731155026704073,
-0.020253097638487816,
0.009576172567903996,
-0.025204341858625412,
0.018985480070114136,
0.01307161059230566,
-0.03165113925933838,
0.03047017753124237,
-0.06154230982065201,
0.06576448678970337,
0.004277887288480997,
-0.00015983260527718812,
0.011917719617486,
0.012132917530834675,
-0.004244661424309015,
0.06424516439437866,
0.07822604477405548,
-0.019355447962880135,
-0.03399199992418289,
-0.006675757467746735,
-0.05753042548894882,
0.01705366186797619,
-0.006579863838851452,
0.018603967502713203,
0.007244003936648369,
0.01171430665999651,
-0.05654044821858406,
0.03331492841243744,
0.03212440386414528,
0.018941933289170265,
0.016358526423573494,
0.029804101213812828,
-0.010374355129897594,
0.04426146671175957,
-0.013597814366221428,
0.036142244935035706,
0.030925767496228218,
0.0020471091847866774,
0.040698979049921036,
0.00631673913449049,
0.003095685038715601,
0.02273513376712799,
0.06194230914115906,
-0.057501524686813354,
0.010890246368944645,
0.056260738521814346,
-0.027925079688429832,
-0.013075477443635464,
0.05017678439617157,
-0.0023120197001844645,
0.009624623693525791,
-0.005542751867324114,
0.0042245052754879,
-0.056656576693058014,
-0.0008524884469807148,
0.024381455034017563,
0.051275864243507385,
-0.015886807814240456,
0.017662271857261658,
0.03801412507891655,
-0.04551215097308159,
0.027792762964963913,
0.03196331486105919,
-0.02386193536221981,
-0.0324324294924736,
-0.05117751657962799,
0.0012542686890810728,
-0.01697455532848835,
-0.026939302682876587,
0.0037769689224660397,
0.00896768644452095,
0.02255702018737793,
0.007952308282256126,
-0.005386201199144125,
-0.006499088369309902,
0.0026703081093728542,
0.010941111482679844,
0.05936533957719803,
0.02718697115778923,
-0.0020766102243214846,
-0.015140911564230919,
0.04313607141375542,
-0.007658662740141153,
-0.10112714022397995,
0.02303672581911087,
0.033952586352825165,
0.02090638317167759,
-0.030588995665311813,
-0.0006881153676658869,
0.014665215276181698,
-0.0029250062070786953,
0.009345854632556438,
-0.0104744303971529,
0.059880830347537994,
-0.001687903655692935,
-0.10304450988769531,
-0.017772575840353966,
0.04465024918317795,
0.011031338013708591,
0.006490169558674097,
-0.09303472936153412,
-0.0170756746083498,
0.010733690112829208,
0.043080467730760574,
0.0001601094991201535,
0.01974565163254738,
-0.01826614886522293,
0.00681726448237896,
-0.0029070787131786346,
0.023367276415228844,
-0.0060318754985928535,
-0.008975984528660774,
-0.04484637454152107,
0.031718261539936066,
-0.04718606546521187,
0.046721793711185455,
0.015340527519583702,
0.017239399254322052,
0.0017523785354569554,
0.041112858802080154,
-0.04594755917787552,
0.011131108738481998,
-0.012056746520102024,
0.017792658880352974,
0.0185674000531435,
0.0519932359457016,
-0.00092672323808074,
0.005229535046964884,
0.024861963465809822,
0.026110168546438217,
0.023970915004611015,
-0.02867194451391697,
0.0298903938382864,
0.07335571199655533,
-0.046547066420316696,
-0.00908318255096674,
-0.03220637887716293,
0.014483770355582237,
-0.0036790345329791307,
-0.06727589666843414,
-0.00245875446125865,
0.035043325275182724,
0.012936858460307121,
-0.004279476590454578,
0.047852858901023865,
-0.012804308906197548,
-0.013502631336450577,
-0.026859600096940994,
-0.016039187088608742,
0.010213490575551987,
-0.0388520322740078,
0.029102787375450134,
-0.008938268758356571,
0.017713449895381927,
0.0935465469956398,
0.004239393398165703,
0.03464274853467941,
-0.03905978798866272,
-0.0007969189318828285,
-0.014387947507202625,
-0.01052900217473507,
-0.012743519619107246,
-0.05274183675646782,
0.05994076654314995,
0.029236769303679466,
0.015216657891869545,
0.0014435455668717623,
0.0008772096480242908,
-0.018692048266530037,
-0.008480721153318882,
0.01678067073225975,
0.009409205988049507,
0.06471681594848633,
0.07836711406707764,
0.011504781432449818,
-0.029123973101377487,
-0.024975638836622238,
0.002637525787577033,
0.035367004573345184,
-0.028119880706071854,
0.05355963483452797,
0.024058740586042404,
0.008969751186668873,
0.01128778513520956,
0.04977727681398392,
-0.00021053670207038522,
0.02648586593568325,
0.011704567819833755,
-0.035441700369119644,
-0.01417854055762291,
-0.04222627729177475,
0.0446968749165535,
0.011097234673798084,
-0.0436251126229763,
0.002785607473924756,
0.04262315854430199,
0.045009832829236984,
0.04383212327957153,
-0.010333620943129063,
-0.009486286900937557,
-0.03147024288773537,
0.03404439613223076,
0.018803615123033524,
-0.01905915141105652,
0.01766529306769371,
0.02787199430167675,
0.005406243726611137,
0.015226053074002266,
-0.030619794502854347,
-0.023157604038715363,
0.029922205954790115,
0.017473794519901276,
0.0035319961607456207,
-0.005031363107264042,
-0.046050745993852615,
0.018896572291851044,
-0.055307794362306595,
0.063463494181633,
0.010230575688183308,
-0.017282262444496155,
0.043363671749830246,
0.007607822306454182,
-0.04545732960104942,
0.01768476329743862,
0.020273692905902863,
-0.02790014259517193,
-0.026359863579273224,
0.017968494445085526,
-0.027148578315973282,
0.030088966712355614,
-0.010839173570275307,
-0.03234492614865303,
0.007258018013089895,
0.00394852738827467,
0.03015143796801567,
0.017514392733573914,
0.020882736891508102,
-0.04161112383008003,
-0.015487770549952984,
-0.05254559963941574,
-0.02905319817364216,
0.041651807725429535,
0.05386330187320709,
-0.028704917058348656,
0.010963434353470802,
-0.03941646218299866,
-0.04487602412700653,
0.04930567368865013,
0.00977224763482809,
-0.002443908480927348,
0.019915098324418068,
-0.0622919462621212,
-0.050107695162296295,
-0.004985342267900705,
-0.0034582847729325294,
0.005476643797010183,
-0.0005120521527715027,
-0.0080318758264184,
0.0762520581483841,
-0.013086730614304543,
-0.020170440897345543,
-0.018117543309926987,
-0.01512960996478796,
-0.03666685149073601,
-0.0010865990770980716,
-0.019688451662659645,
0.027950048446655273,
0.009285562671720982,
0.036259982734918594,
0.04519233480095863,
-0.059884242713451385,
-0.022752167657017708,
-0.04744879901409149,
-0.05698126554489136,
0.006613804958760738,
-0.0012321989051997662,
0.01996266283094883,
-0.024981172755360603,
-0.03136547654867172,
0.1069318950176239,
0.02544533647596836,
-0.023054298013448715,
-0.010807521641254425,
-0.04459612816572189,
-0.035201944410800934,
-0.027838237583637238,
-0.004692504182457924,
0.0540638193488121,
0.027856571599841118,
0.015895476564764977,
-0.00566556490957737,
0.08617987483739853,
0.014292554929852486,
-0.012617040425539017,
-0.005131739657372236,
0.03343767300248146,
0.02487950585782528,
0.008077042177319527,
0.015074919909238815,
0.02156340889632702,
-0.02767559513449669,
0.005264300387352705,
-0.015242650173604488,
0.07045110315084457,
0.02530539780855179,
-0.07454569637775421,
0.03391553834080696,
0.0023968564346432686,
-0.005791543982923031,
0.0083547318354249,
0.04047401249408722,
0.03721821680665016,
-0.008460797369480133,
-0.009499303065240383,
0.04049306735396385,
0.050981126725673676,
-0.01544436626136303,
0.006784829776734114,
0.0018857219256460667,
0.02413358725607395,
-0.02907295897603035,
-0.02346419170498848,
0.011214627884328365,
-0.025826482102274895,
0.04503060132265091,
-0.013106588274240494,
-0.03905491158366203,
0.044830117374658585,
-0.01962156593799591,
0.03185543417930603,
0.005000784061849117,
-0.059055134654045105,
0.0053293281234800816,
-0.03567823767662048,
0.01917586475610733,
0.018352709710597992,
0.036214429885149,
0.03361683338880539,
0.05563439056277275,
0.028215985745191574,
0.02710607834160328,
0.006574911996722221,
0.03240145370364189,
-0.048054758459329605,
-0.0018826423911377788,
-0.021031809970736504,
0.034639786928892136,
-0.000515249848831445,
0.02528637833893299,
0.020025217905640602,
-0.009059993550181389,
-0.036770179867744446,
-0.0195880476385355,
0.010969712398946285,
-0.01614757440984249,
-0.0077011785469949245,
-0.01129237562417984,
-0.0030409577302634716,
-0.0373137965798378,
0.006813829764723778,
0.03407873958349228,
-0.0412784218788147,
0.00017518595268484205,
0.05440221726894379,
-0.013547930866479874,
-0.001581263029947877,
-0.032956838607788086,
0.010527534410357475,
0.04868311807513237,
0.020089002326130867,
0.008032500743865967,
0.0034463033080101013,
0.003727295435965061,
-0.012150466442108154,
0.00647242646664381,
0.04678989201784134,
0.009671229869127274,
0.011455819942057133,
0.008416091091930866,
-0.013809005729854107,
-0.007626832462847233,
0.031135164201259613,
0.04435089975595474,
0.0257955901324749,
0.03630116581916809,
0.0191598329693079,
0.011403496377170086,
-0.0015826233429834247,
0.04276452213525772,
0.022347543388605118,
0.026684001088142395,
-0.012935427017509937,
-0.04270925745368004,
0.0021600541658699512,
-0.04222638159990311,
0.0037516606971621513,
0.03572699800133705,
-0.02057648077607155,
0.020589208230376244,
-0.004324616864323616,
0.02059335447847843,
0.00025907272356562316,
-0.02947891503572464,
-0.040803126990795135,
-0.03049672581255436,
-0.021615715697407722,
-0.018232617527246475,
-0.017862766981124878,
0.01905103214085102,
-0.02970631793141365,
0.029160339385271072,
0.021459829062223434,
0.0460626557469368,
-0.04569627717137337,
-0.018426494672894478,
0.043594956398010254,
0.016313787549734116,
0.004282785579562187,
-0.00025630564778111875,
-0.05134238302707672,
0.013749223202466965,
-0.010930965654551983,
-0.008815737441182137,
0.017109733074903488,
0.01604675129055977,
-0.01453124824911356,
-0.05167106166481972,
-0.06523442268371582,
-0.0007256542448885739,
-0.0005391251761466265,
-0.008466663770377636,
0.023498302325606346,
-0.032291095703840256,
-0.041005805134773254,
-0.016726205125451088,
-0.005578863900154829,
0.010473430156707764,
0.04561401158571243,
0.020589446648955345,
0.002366884844377637,
0.02151351422071457,
0.01119079627096653,
-0.030387189239263535,
-0.1115727350115776,
-0.010124683380126953,
0.007675275206565857,
0.028632869943976402,
0.05437510460615158,
-0.055844344198703766,
-0.06803572177886963,
0.0038593406789004803,
-0.012186004780232906,
-0.005904398392885923,
-0.03256271034479141,
-0.04186617210507393,
0.06380897760391235,
0.02195345237851143,
-0.023155227303504944,
0.0646393746137619,
0.022645842283964157,
-0.054552774876356125,
0.018345559015870094,
-0.036526236683130264,
0.036389146000146866,
-0.052789356559515,
0.011234460398554802,
-0.0569220632314682,
0.016454264521598816,
-0.03351306542754173,
0.06805897504091263,
-0.021526813507080078,
0.021253280341625214,
-0.014843634329736233,
-0.030375324189662933,
0.0003976427251473069,
-0.00039251960697583854,
0.03423644229769707,
-0.00951426476240158,
-0.023096363991498947,
0.01383896078914404,
-0.01898832432925701,
-0.03247279301285744,
0.003160283900797367,
-0.03323213383555412,
0.012000023387372494,
0.05836755782365799,
-0.004503344185650349,
-0.0060009281150996685,
-0.04024125635623932,
-0.045144110918045044,
0.03361058607697487,
-0.019636794924736023,
0.011074240319430828,
-0.0009228228009305894,
-0.028194449841976166,
0.02234669215977192,
-0.033629629760980606,
-0.016485700383782387,
0.04120694100856781,
-0.02363339252769947,
0.005820401944220066,
-0.05945877358317375,
0.030221665278077126,
0.033873677253723145,
0.021431393921375275,
-0.0651233047246933,
-0.038093335926532745,
-0.00823626946657896,
0.03292267769575119,
-0.024571072310209274,
-0.023904874920845032,
-0.010247776284813881,
-0.05085357651114464,
0.01062157191336155,
0.030434871092438698,
0.029343901202082634,
-0.034777041524648666,
0.005092647857964039,
0.007339810486882925,
-0.007913189940154552,
0.07593858987092972,
-0.007835407741367817,
-0.030756574124097824,
0.018364829942584038,
-0.004610072821378708,
-0.00039706629468128085,
-0.01819569803774357,
0.03223451226949692,
-0.017854813486337662,
-0.003198490710929036,
-0.011145741678774357,
-0.005164711270481348,
0.019721951335668564,
-0.0036760708317160606,
-0.029168857261538506,
0.05083886906504631,
-0.009276045486330986,
0.014280945993959904,
0.0009304796112701297,
0.0008494516951031983,
-0.011950896121561527,
0.018106713891029358,
0.01776895858347416,
-0.012759444303810596,
-0.01570662297308445,
0.0004804751370102167,
0.011197226122021675,
0.009197679348289967,
0.023158272728323936,
0.0015062777092680335,
0.08486156165599823,
0.013174007646739483,
0.03170626610517502,
0.053285691887140274,
-0.03443693369626999,
0.049604631960392,
0.0003666117263492197,
0.025300130248069763,
-0.020397692918777466,
0.04688514769077301,
0.0030559988226741552,
-0.0694035217165947,
-0.04098009318113327,
0.008633671328425407,
0.04777593910694122,
0.0006054500117897987,
0.011676132678985596,
0.020447710528969765,
-0.022772278636693954,
-0.003901235992088914,
-0.01484433189034462,
-0.04059316962957382,
-0.0056214164942502975,
-0.021430542692542076,
0.015961332246661186,
-0.0358077809214592,
0.013961637392640114,
0.021747060120105743,
0.04870501533150673,
-0.03711584955453873,
0.03601093962788582,
0.03498388081789017,
0.0070276870392262936,
-0.006528002675622702,
0.0013831574469804764,
-0.06487517803907394,
0.0697183683514595,
-0.003905916353687644,
0.037883058190345764,
0.010916423052549362,
-0.017056578770279884,
0.030740350484848022,
0.02639046125113964,
0.03422379493713379,
-0.037271201610565186,
0.0029267221689224243,
-0.026499679312109947,
0.07885433733463287,
-0.03644152358174324,
0.00486583961173892,
-0.04795810580253601,
0.004635246004909277,
0.004123969003558159,
0.015861136838793755,
0.020251810550689697,
-0.003241343889385462,
-0.026390166953206062,
-0.014380128122866154,
-0.05523841828107834,
-0.012264430522918701,
0.02018941007554531,
-0.0075666774064302444,
0.004046537913382053,
-0.007800641469657421,
-0.033193107694387436,
0.006264034658670425,
-0.007985771633684635,
0.009663776494562626,
0.024268409237265587,
0.059945881366729736,
0.01765694096684456,
0.01154336053878069,
-0.0010015734005719423,
0.028710467740893364,
0.12695106863975525,
0.05009404942393303,
-0.0005984019371680915,
-0.06733494251966476,
0.016197456046938896,
-0.02601751685142517,
0.02779650315642357,
-0.001449116040021181,
-0.04251678287982941,
-0.042341381311416626,
0.012808838859200478,
-0.01956099458038807,
0.05416792631149292,
-0.0018768628360703588,
0.016568342223763466,
0.04776506870985031,
-0.04973488301038742,
-0.03517938777804375,
0.03712782636284828,
0.006782637443393469,
-0.009208722971379757,
0.010191243141889572,
-0.007978530600667,
0.007214624900370836,
0.008371070958673954,
-0.022205058485269547,
-0.02029380202293396,
-0.051999155431985855,
0.017697516828775406,
0.013613314367830753,
-0.04635343328118324,
0.01438263151794672,
0.024145886301994324,
0.0002193021500715986,
-0.04320433363318443,
0.00751433614641428,
0.0016398841980844736,
-0.010028950870037079,
0.0482361800968647,
0.039751313626766205,
-0.008347569033503532,
0.0017195872496813536,
0.034931834787130356,
0.0037478292360901833,
-0.02722850814461708,
0.0004545577976386994,
-0.0006723528495058417,
0.007617355789989233,
-0.044202376157045364,
-0.04408648982644081,
-0.028983741998672485,
-0.016964023932814598,
-0.0002272386191179976,
-0.06290978193283081,
-0.002412420930340886,
-0.03751612827181816,
0.01848897710442543,
-0.013341891579329967,
0.011383701115846634,
-0.030463408678770065,
-0.029342595487833023,
0.023642543703317642,
-0.0166730098426342,
0.015015929937362671,
-0.024832583963871002,
0.0216660276055336,
-0.009077227674424648,
0.017333827912807465,
-0.004960241727530956,
-0.007375578861683607,
-0.028742754831910133,
0.002601555548608303,
-0.018699990585446358,
-0.04186844825744629,
0.007943099364638329,
0.014332584105432034,
0.051378510892391205,
-0.024272410199046135,
-0.02500997483730316,
-0.0374707393348217,
-0.1126619428396225,
0.05891158804297447,
0.019509831443428993,
-0.010934673249721527,
-0.01453718077391386,
0.0397954024374485,
0.006770154926925898,
0.06149899959564209,
-0.05105966329574585,
0.023517722263932228,
-0.015753988176584244,
0.021763525903224945,
0.03318578749895096,
-0.05396687239408493,
0.010394982993602753,
0.011255782097578049,
-0.015499391593039036,
-0.004456987138837576,
-0.0029495777562260628,
0.005596652626991272,
-0.00019229689496569335,
-0.05366140231490135,
-0.010077090002596378,
0.042048029601573944,
-0.03320496901869774,
-0.03490784764289856,
-0.002400242956355214,
-0.012777850963175297,
0.01748259924352169,
0.02847246453166008,
0.01757887937128544,
-0.008512928150594234,
-0.00861661322414875,
-0.06017374247312546,
0.023374639451503754,
0.0028655584901571274,
0.027277331799268723,
-0.005686386488378048,
0.025040075182914734,
-0.018534325063228607,
0.022773392498493195,
-0.019897714257240295,
-0.008593246340751648,
-0.02975420281291008,
0.04224767908453941,
0.019717348739504814,
0.017623551189899445,
-0.043471809476614,
0.03561362624168396,
-0.028929319232702255,
-0.029641125351190567,
0.05375124141573906,
0.03969478979706764,
-0.040342673659324646,
0.017190048471093178,
0.01641581580042839,
-0.030744116753339767,
0.03499685600399971,
-0.04125146567821503,
-0.0355868861079216,
0.011871879920363426,
-0.026532424613833427,
-0.04514108970761299,
0.026668649166822433,
-0.028588786721229553,
0.000545564922504127,
0.006913734599947929,
-0.029592324048280716,
-0.02988922782242298,
0.03306889906525612,
-0.0068900552578270435,
-0.02632063813507557,
-0.0069974567741155624,
-0.04589671641588211,
0.0050652544014155865,
-0.04312632605433464,
0.011855443008244038,
-0.027302490547299385,
0.017257191240787506,
0.04532400891184807,
0.047659870237112045,
-0.00410292437300086,
-0.038131289184093475,
-0.043880607932806015,
0.010891024954617023,
0.0015218532644212246,
0.0063384477980434895,
0.008349024690687656,
0.01387243252247572,
0.054827988147735596,
-0.03262036666274071,
0.02591755986213684,
-0.020213568583130836,
0.009847787208855152,
-0.0730731412768364,
-0.017177175730466843,
-0.026765473186969757,
0.006124262232333422,
0.040098272264003754,
-0.04758581519126892,
0.01091892272233963,
0.006279656197875738,
-0.08602841198444366,
0.0005955640808679163,
-0.02431156486272812,
-0.03308437392115593,
-0.009144073352217674,
-0.01478186622262001,
-0.014695553109049797,
0.03746630251407623,
-0.026640482246875763,
0.047745123505592346,
0.03769664466381073,
0.01038708258420229,
0.015379341319203377,
0.002612820826470852,
-0.046497318893671036,
0.027108492329716682,
0.023666569963097572,
-0.02078751102089882,
0.07666422426700592,
-0.042275168001651764,
-0.04356662184000015,
0.029255244880914688,
-0.012485608458518982,
-0.003056845860555768,
-0.011401105672121048,
0.015102611854672432,
-0.023519938811659813,
0.044216569513082504,
0.01687081716954708,
-0.012543940916657448,
0.002350166440010071,
0.008940408006310463,
-0.010850375518202782,
0.016968894749879837,
0.030760595574975014,
-0.007744939532130957,
0.003393032820895314,
-0.05109259858727455,
-0.04697320610284805,
0.03039298951625824,
-0.003076016204431653,
0.0196421779692173,
0.028253920376300812,
-0.002752249827608466,
0.05069972574710846,
-0.019789209589362144,
-0.0019373840186744928,
0.00015102878387551755,
-0.03447908163070679,
-0.01364173460751772,
-0.019799724221229553,
0.028014278039336205,
0.017089039087295532,
-0.014820247888565063,
-0.0367795005440712,
0.03794686868786812,
0.017369747161865234,
-0.03520683944225311,
-0.06721830368041992,
-0.005910768173635006,
-0.018918272107839584,
-0.016359727829694748,
-0.047803137451410294,
-0.0598839595913887,
-0.020789219066500664,
0.013505460694432259,
0.015963925048708916,
0.028364066034555435,
-0.0245863925665617,
-0.010595247149467468,
0.008153688162565231,
-0.01875734142959118,
0.018825547769665718,
0.0018967943033203483,
0.04732723906636238,
0.015124856494367123,
-0.021383969113230705,
0.016077920794487,
0.038512784987688065,
0.04755428805947304,
0.020838014781475067,
0.006082944571971893,
0.011240468360483646,
-0.03806987404823303,
0.013002260588109493,
-0.03213708475232124,
-0.011145235039293766,
-0.005240662023425102,
0.005693711806088686,
0.005086998455226421,
-0.023098818957805634,
-0.062412671744823456,
-0.00023665236949454993,
0.012545308098196983,
0.009456474334001541,
-0.002988506108522415,
-0.022729557007551193,
-0.025959007441997528,
0.0535903163254261,
0.03311537578701973,
-0.049858108162879944,
0.08032336086034775,
-0.002430642955005169,
0.01817241869866848,
0.0380065031349659,
-0.007936104200780392,
-0.047947514802217484,
0.0332452766597271,
-0.06930061429738998,
-0.0033831987529993057,
0.029498199000954628,
0.025955643504858017,
0.05041591823101044,
-0.026949230581521988,
-0.029201405122876167,
0.01477312482893467,
-0.02310994826257229,
-0.01957256719470024,
0.04097672551870346,
0.02899687923491001,
0.04370836541056633,
0.00038903672248125076,
0.019370611757040024,
-0.00973766203969717,
0.010071007534861565,
0.007200147025287151,
0.051920272409915924,
0.03326922655105591,
-0.01069952268153429,
0.047842614352703094,
-0.003109710058197379,
0.004730593413114548,
0.006037459243088961,
0.029669905081391335,
0.02769484557211399,
-0.00730664050206542,
0.03746578469872475,
0.06229834258556366,
0.012888312339782715,
-0.008988450281322002,
0.006671150680631399,
0.00406127143651247,
0.03271373733878136,
-0.02934245392680168,
-0.017127299681305885,
-0.00232597510330379,
0.030349530279636383,
-0.01786763034760952,
0.0036599580198526382,
0.025122009217739105,
0.042136240750551224,
-0.025961410254240036,
-0.010531490668654442,
-0.03614325821399689,
-0.0028022832702845335,
0.010720228776335716,
-0.056043364107608795,
-0.017088310793042183,
-0.0082987230271101,
-0.018773341551423073,
0.01971694640815258,
0.010089820250868797,
-0.03972833976149559,
0.003815711010247469,
0.02419855259358883,
0.005932679399847984,
0.06908402591943741,
-0.01799852028489113,
0.012160063721239567,
-0.03448565676808357,
0.04873143881559372,
-0.0450688898563385,
-0.014295845292508602,
-0.02531972900032997,
-0.0003144390066154301,
-0.02735741063952446,
0.008288964629173279
] |
<p>I have a basic question about the logic of renormalization in quantum field theory (QFT). We met the ultraviolet (UV) divergence in loop corrections. The standard argument is, our current field theory is incorrect at high-energy scale, we regularize and renomalize the theory to make it work. </p>
<p>My question is, why do we expect a correct theory will be capable for loop corrections without regularization? Is that possible that nature or saying a correct theory at high energy scale is non-perturbative from free particles? </p>
<p>P.S. non-perturbative from free particles mean (i) if one uses perturbative expansion from free particle, the "correct" theory still gives infinity; and (ii) if one uses perturbative expansion from a special interacting solvable system or by certain non-perturbative technique, the results from that theory always agrees with experiments.</p>
| 8,850 |
[
0.0200718492269516,
0.029860857874155045,
0.014574171975255013,
-0.019135842099785805,
0.021251242607831955,
0.008366190828382969,
-0.01849934458732605,
-0.00796814076602459,
0.003976899199187756,
-0.026850957423448563,
0.021960387006402016,
-0.01042203139513731,
0.0286554004997015,
0.01320662721991539,
-0.0037414426915347576,
0.021278291940689087,
0.0006417338736355305,
-0.04613166302442551,
0.01380856428295374,
-0.004521473310887814,
0.0030177487060427666,
0.06928978115320206,
-0.018489159643650055,
-0.009640272706747055,
-0.047723401337862015,
-0.014781882055103779,
0.014817629009485245,
0.07437111437320709,
-0.003114997176453471,
0.07132753729820251,
-0.0037297296803444624,
-0.02487722598016262,
-0.006578439846634865,
0.030904483050107956,
0.01528320275247097,
0.05306846648454666,
-0.023137886077165604,
-0.02576332353055477,
0.017984097823500633,
-0.0117647685110569,
-0.01023140549659729,
-0.031962040811777115,
0.013294453732669353,
0.04623771458864212,
-0.012571120634675026,
-0.005889860447496176,
-0.0054930136539042,
-0.023943686857819557,
0.07403941452503204,
-0.07056067883968353,
0.038812894374132156,
0.02725962921977043,
0.031537190079689026,
0.040634021162986755,
-0.017046406865119934,
-0.005390726495534182,
0.0678018257021904,
0.05020845681428909,
0.003961307927966118,
-0.07663977146148682,
-0.06359419226646423,
-0.0366523303091526,
0.00005865021012141369,
-0.01719004660844803,
-0.013928554020822048,
0.035058844834566116,
-0.026272404938936234,
0.016042836010456085,
0.004462334327399731,
-0.021349864080548286,
0.004358041565865278,
0.011493762955069542,
0.064084492623806,
0.0260994341224432,
0.018340710550546646,
0.027671916410326958,
0.005834013223648071,
-0.014364339411258698,
0.021359652280807495,
0.046494755893945694,
-0.020317956805229187,
0.014367305673658848,
0.03574460372328758,
0.032373521476984024,
0.012554069980978966,
-0.030927367508411407,
0.04374682530760765,
-0.008041500113904476,
0.0021832699421793222,
0.06167682260274887,
-0.026735441759228706,
-0.0015146869700402021,
0.044408369809389114,
-0.020080935209989548,
-0.016215432435274124,
0.05794186890125275,
-0.0041425530798733234,
0.04853637516498566,
-0.005510274786502123,
0.01508342381566763,
-0.012907826341688633,
-0.0074162958189845085,
0.016564466059207916,
0.055540427565574646,
-0.009096313267946243,
-0.02424471080303192,
-0.04080594331026077,
0.035828009247779846,
-0.020670507103204727,
-0.040642257779836655,
-0.017019731923937798,
0.009697256609797478,
-0.02574886940419674,
0.020065320655703545,
0.003249203786253929,
-0.04582454264163971,
-0.014286690391600132,
-0.03310278430581093,
0.09385685622692108,
0.06766031682491302,
0.011766969226300716,
-0.02786027267575264,
0.010580450296401978,
-0.04246651753783226,
-0.04123890399932861,
0.02486019767820835,
0.05472247675061226,
-0.02574407123029232,
-0.023338492959737778,
0.0008165091858245432,
0.01905783824622631,
-0.009915503673255444,
-0.025042716413736343,
0.005498926620930433,
0.05079079419374466,
-0.03907449543476105,
-0.10531459748744965,
-0.04844778776168823,
0.031077153980731964,
0.004420624580234289,
-0.018067697063088417,
-0.05488583445549011,
-0.003440326312556863,
0.05077405646443367,
0.09861025959253311,
-0.02886946313083172,
0.011560087092220783,
0.011156956665217876,
0.007372269872575998,
-0.011289993301033974,
-0.014525934122502804,
-0.031117910519242287,
-0.006563231814652681,
-0.03961030766367912,
-0.022541411221027374,
-0.07056790590286255,
0.02974715270102024,
0.01904328726232052,
0.026845822110772133,
0.024633560329675674,
0.05723441019654274,
-0.02023579180240631,
0.01244731992483139,
-0.012499451637268066,
-0.010750195942819118,
-0.013628524728119373,
0.08358317613601685,
0.0016049070982262492,
0.013120647519826889,
0.08122189342975616,
-0.010204042308032513,
-0.002334916265681386,
0.007195060607045889,
0.00474148616194725,
0.0384349524974823,
-0.039593134075403214,
-0.023622730746865273,
-0.053154848515987396,
0.03691650182008743,
-0.016552463173866272,
-0.02682824619114399,
0.02184239961206913,
-0.04288225993514061,
0.013235120102763176,
-0.0123518081381917,
0.01750674843788147,
-0.018056267872452736,
0.013277090154588223,
0.0258674006909132,
-0.0562908798456192,
-0.007086835335940123,
-0.07338161021471024,
-0.009845289401710033,
0.01270690094679594,
0.010510844178497791,
0.04698683321475983,
-0.02147504687309265,
-0.0021005566231906414,
-0.006340359337627888,
-0.054205410182476044,
-0.0233237836509943,
0.045489512383937836,
0.015518784523010254,
0.04670315608382225,
0.060313645750284195,
0.05797131732106209,
0.03830800577998161,
0.0272224061191082,
0.049822717905044556,
-0.030184004455804825,
-0.0505002997815609,
0.02324080653488636,
-0.021429715678095818,
0.0001626906159799546,
-0.007925073616206646,
0.006192981265485287,
0.012739316560328007,
-0.004994111601263285,
-0.01584719680249691,
0.04937964305281639,
-0.012799518182873726,
0.07174438238143921,
0.02598368562757969,
-0.0016919716726988554,
-0.0016843929188326001,
0.023135684430599213,
-0.012081083841621876,
0.018939008936285973,
0.012006131000816822,
-0.060875266790390015,
-0.08253619819879532,
-0.025127727538347244,
0.025712521746754646,
0.031876176595687866,
-0.006319831125438213,
-0.005999730434268713,
0.037506770342588425,
0.041492898017168045,
-0.009544432163238525,
0.04854794591665268,
-0.0062728822231292725,
-0.005990206729620695,
0.018873102962970734,
0.025950700044631958,
0.043264057487249374,
-0.010872391983866692,
-0.013130366802215576,
-0.01645924523472786,
0.023773739114403725,
-0.009569269604980946,
-0.02160615846514702,
0.005612233188003302,
-0.006825447082519531,
-0.041008833795785904,
0.009145303629338741,
-0.03253214806318283,
-0.005145899951457977,
-0.006085015367716551,
0.05131325498223305,
-0.0015809389296919107,
-0.042729925364255905,
-0.016085123643279076,
-0.03518934175372124,
-0.019129827618598938,
0.03094061091542244,
0.012045971117913723,
-0.055994365364313126,
-0.03387721627950668,
0.01635846309363842,
-0.052229396998882294,
-0.008705995045602322,
-0.027847642078995705,
-0.0164333488792181,
-0.011068803258240223,
0.04369942098855972,
0.011164216324687004,
0.005107464734464884,
0.005007205065339804,
-0.01833822950720787,
-0.0282894317060709,
0.040969233959913254,
-0.03944181650876999,
0.01242799311876297,
0.05250530689954758,
-0.02052805759012699,
-0.011750050820410252,
-0.0754295140504837,
-0.04077909141778946,
0.020061053335666656,
0.01029956340789795,
0.06000296398997307,
0.008192058652639389,
-0.01180590596050024,
-0.017627742141485214,
-0.024650000035762787,
-0.05368347093462944,
0.035975921899080276,
0.02420295774936676,
-0.02207564190030098,
0.045797497034072876,
0.029899878427386284,
-0.03288804367184639,
0.04839281737804413,
-0.014233613386750221,
-0.03273765742778778,
0.015472246333956718,
0.0088137686252594,
0.023579739034175873,
-0.027428392320871353,
0.050981421023607254,
0.014405729249119759,
-0.036974478513002396,
-0.02610158734023571,
-0.057118210941553116,
-0.06014543026685715,
-0.00110377068631351,
0.017142802476882935,
0.01983451284468174,
-0.0021033971570432186,
-0.061001770198345184,
0.06443558633327484,
0.05021244287490845,
-0.028425799682736397,
-0.03560611978173256,
-0.009581008926033974,
-0.025578698143363,
-0.015264429152011871,
-0.0022504455409944057,
-0.018003389239311218,
0.00874260999262333,
0.033672984689474106,
0.004802234936505556,
0.06921543926000595,
-0.011916257441043854,
0.019321702420711517,
-0.013360788114368916,
0.003229666268453002,
0.05174528434872627,
-0.013037040829658508,
0.03201087936758995,
0.0005081190029159188,
-0.02631196193397045,
0.006542964838445187,
0.0210006944835186,
0.012967593036592007,
0.020532606169581413,
-0.05073203146457672,
0.058982428163290024,
0.040531232953071594,
0.046074576675891876,
-0.061796918511390686,
0.01687396876513958,
-0.005406064912676811,
-0.04424094408750534,
0.0031942971982061863,
-0.003058517351746559,
0.01218911912292242,
-0.011693986132740974,
0.02728596329689026,
0.018608879297971725,
0.05850796774029732,
-0.046548888087272644,
-0.03870762139558792,
-0.02882399782538414,
-0.024748416617512703,
0.014503373764455318,
-0.01495710015296936,
-0.02575938031077385,
0.029423434287309647,
0.0400066077709198,
-0.0066202180460095406,
-0.037391260266304016,
-0.0298867579549551,
-0.0037286358419805765,
-0.07431366294622421,
0.008937947452068329,
-0.023194877430796623,
0.055955786257982254,
-0.006578529253602028,
0.04969042167067528,
0.007309527602046728,
0.020121099427342415,
0.0027816006913781166,
0.031623151153326035,
-0.0910598412156105,
0.03306914493441582,
-0.033614374697208405,
-0.02634759433567524,
-0.021775012835860252,
-0.02106315828859806,
0.030035290867090225,
-0.0027487867046147585,
-0.02968437410891056,
-0.015264959074556828,
-0.0034276212099939585,
-0.03660369664430618,
0.0026895038317888975,
-0.03535255417227745,
-0.04534643143415451,
-0.00656127231195569,
0.029170742258429527,
0.039163824170827866,
-0.017675595358014107,
0.01877899095416069,
0.019195448607206345,
-0.035752393305301666,
-0.026903469115495682,
-0.004312798846513033,
0.034622639417648315,
0.020617296919226646,
0.022265305742621422,
0.04131116345524788,
0.04266273230314255,
-0.06337643414735794,
0.0102609284222126,
0.05734067037701607,
0.037474531680345535,
0.013944080099463463,
0.007857224904000759,
-0.023989977315068245,
-0.06568325310945511,
-0.0029757164884358644,
0.013459666632115841,
0.0755225121974945,
0.03650897741317749,
0.01034421008080244,
0.029644295573234558,
-0.0018458433914929628,
-0.02679833024740219,
-0.00726134842261672,
0.04539184272289276,
-0.015356802381575108,
-0.023867495357990265,
-0.014059199020266533,
0.021143950521945953,
0.005276096984744072,
-0.004554183222353458,
-0.005155174061655998,
-0.003742251545190811,
-0.01451287604868412,
-0.020028594881296158,
0.02963916026055813,
-0.011762765236198902,
-0.04246896132826805,
0.015872692689299583,
-0.0026146688032895327,
-0.0027703880332410336,
-0.025830920785665512,
0.008195617236196995,
0.005874153226613998,
0.03891557827591896,
0.05978303402662277,
0.020140884444117546,
0.0030365127604454756,
-0.04548487439751625,
-0.004529363941401243,
0.05783272907137871,
0.05354227498173714,
0.024162307381629944,
-0.019175320863723755,
-0.028521912172436714,
-0.03654833137989044,
0.04275243729352951,
-0.022278176620602608,
0.02807660400867462,
0.002982191741466522,
0.015672676265239716,
-0.010312276892364025,
-0.028410136699676514,
-0.009232050739228725,
0.0035963619593530893,
-0.02953723631799221,
0.0038941004313528538,
-0.018935436382889748,
0.002908165566623211,
-0.016268571838736534,
-0.00036512460792437196,
0.0024192037526518106,
0.06480906903743744,
0.019718140363693237,
0.03053191304206848,
0.03160551190376282,
-0.006960165686905384,
-0.03320992365479469,
-0.07694783061742783,
0.025318017229437828,
0.01480043213814497,
-0.030448824167251587,
0.034407757222652435,
0.003531099995598197,
-0.06390554457902908,
-0.009372655302286148,
0.010290081612765789,
0.003972477279603481,
-0.01233740895986557,
-0.07015427947044373,
0.04968174546957016,
0.029827477410435677,
0.010098529048264027,
0.044414933770895004,
0.058721259236335754,
-0.007704480551183224,
-0.011711993254721165,
-0.023871958255767822,
0.016389016062021255,
0.001403432572260499,
0.03703279048204422,
-0.03470883518457413,
-0.01275321003049612,
-0.0013441991759464145,
0.026263367384672165,
-0.03402272239327431,
0.03583754971623421,
-0.023494381457567215,
-0.0553445890545845,
-0.0060347612015903,
0.022486397996544838,
-0.01901356503367424,
-0.014617938548326492,
-0.006965576205402613,
0.011644244194030762,
0.006033588666468859,
-0.032362569123506546,
0.010328651405870914,
0.02341674454510212,
-0.03261612355709076,
0.029497696086764336,
-0.00957178883254528,
-0.005030681379139423,
-0.012027177028357983,
-0.028613843023777008,
0.005303323734551668,
-0.030407100915908813,
0.013231883756816387,
-0.011555004864931107,
-0.015144157223403454,
-0.04611377790570259,
-0.04465393349528313,
-0.02125346101820469,
-0.020319513976573944,
-0.01226719282567501,
0.027360886335372925,
-0.03776572644710541,
0.026316404342651367,
0.02221970073878765,
0.00515712657943368,
-0.07338961958885193,
-0.06237931177020073,
0.0030293322633951902,
0.006511881481856108,
-0.014561084099113941,
-0.019695954397320747,
-0.013542182743549347,
-0.050320256501436234,
-0.025244563817977905,
-0.03866255655884743,
0.0370681993663311,
-0.043193891644477844,
-0.019744185730814934,
0.04340139776468277,
0.0420801006257534,
0.03202636167407036,
-0.02855798788368702,
-0.02096627466380596,
0.009721697308123112,
-0.011050881817936897,
-0.013265264220535755,
0.019628945738077164,
0.04555375501513481,
-0.018914172425866127,
-0.04324920102953911,
-0.01437443122267723,
0.006110555492341518,
0.02237815223634243,
-0.01490160170942545,
-0.02520306408405304,
0.04509209468960762,
0.026644140481948853,
0.02033170312643051,
-0.01322136353701353,
0.007510146126151085,
-0.007176809478551149,
0.0276155024766922,
0.00540641974657774,
-0.010697653517127037,
-0.00029370433185249567,
-0.021512195467948914,
0.060194797813892365,
0.007953242398798466,
-0.01982140727341175,
0.01926553249359131,
0.03745390102267265,
-0.0166952982544899,
-0.026087086647748947,
0.026643086224794388,
-0.03986039385199547,
0.004074754659086466,
0.00669831782579422,
0.04156817868351936,
-0.0016792226815596223,
0.03364462032914162,
-0.016755355522036552,
-0.014552846550941467,
-0.028707489371299744,
-0.010206605307757854,
0.04730921983718872,
-0.006277197040617466,
0.0047528669238090515,
0.02169489674270153,
-0.008432081900537014,
-0.028185486793518066,
-0.028947699815034866,
-0.03972621634602547,
0.013605918735265732,
-0.004204026889055967,
0.022896945476531982,
-0.03290615975856781,
-0.010481858626008034,
0.008374510332942009,
0.029581215232610703,
-0.029786663129925728,
0.005623387638479471,
0.03703780099749565,
0.0012218854390084743,
-0.00443335622549057,
0.013166439719498158,
-0.03707985579967499,
0.04849909245967865,
-0.03245457634329796,
0.01835479773581028,
0.027548743411898613,
0.0077347951009869576,
0.005800159648060799,
-0.006506727542728186,
0.03916217386722565,
0.0021051964722573757,
-0.03227856382727623,
-0.06161326915025711,
0.013721926137804985,
-0.019984891638159752,
0.01929391734302044,
0.0027181797195225954,
-0.010909901931881905,
0.014936602674424648,
0.01604016311466694,
0.02013513818383217,
-0.0016969551797956228,
-0.08242280036211014,
-0.04168429970741272,
-0.07125400006771088,
-0.021297210827469826,
0.05796963348984718,
-0.003977597691118717,
-0.043627236038446426,
-0.009200070984661579,
-0.02185838110744953,
0.0226167980581522,
-0.005362375173717737,
0.03038943000137806,
-0.031089257448911667,
0.01787000149488449,
0.0028574932366609573,
0.03875157609581947,
-0.019478267058730125,
0.02891731821000576,
0.11970783025026321,
0.07844102382659912,
-0.019652478396892548,
-0.05994129180908203,
0.00778330909088254,
-0.03953274339437485,
0.0006640861975029111,
-0.021094180643558502,
0.05544433742761612,
-0.000005016676368541084,
-0.03936836123466492,
0.015440575778484344,
0.05835213139653206,
0.02373068779706955,
-0.0013456785818561912,
0.06860940158367157,
-0.05670173093676567,
-0.06618201732635498,
0.030799126252532005,
0.016709908843040466,
-0.019754597917199135,
0.013372539542615414,
-0.03311213478446007,
-0.0005853365291841328,
-0.012148948386311531,
0.018938792869448662,
0.0064106835052371025,
-0.024909140542149544,
0.037174712866544724,
0.01954992301762104,
-0.0406372994184494,
-0.016105182468891144,
-0.019862709566950798,
-0.002298469888046384,
-0.05672860145568848,
0.00104863743763417,
0.0069319382309913635,
-0.03281543403863907,
0.024847157299518585,
0.07068237662315369,
0.035769786685705185,
-0.008722429163753986,
-0.01072212029248476,
-0.002882103668525815,
-0.03206457197666168,
-0.029039759188890457,
-0.033847518265247345,
0.04775109514594078,
-0.02791782282292843,
-0.013900154270231724,
-0.02482409030199051,
-0.011273406445980072,
0.014337535947561264,
-0.02585996314883232,
-0.01788337714970112,
0.03199823573231697,
0.02866038680076599,
-0.02918657660484314,
0.008606910705566406,
-0.015218215063214302,
0.03795788437128067,
0.0011086845770478249,
0.0004695933894254267,
0.013416326604783535,
-0.017166046425700188,
0.003125684568658471,
0.0016400758177042007,
0.043393030762672424,
-0.031625885516405106,
0.0006034671096131206,
-0.035778600722551346,
-0.0061677261255681515,
-0.03929814696311951,
-0.006109417416155338,
0.009057747200131416,
0.01649322919547558,
0.06217503175139427,
-0.011968311853706837,
0.05147454887628555,
-0.006152264308184385,
-0.020723160356283188,
0.04453181475400925,
-0.030973084270954132,
-0.02033090777695179,
-0.024783441796898842,
-0.0028706220909953117,
-0.009395407512784004,
0.05665295198559761,
-0.0020642965100705624,
-0.026755061000585556,
0.025153378024697304,
0.009302198886871338,
0.00924349669367075,
-0.041188787668943405,
-0.03726588934659958,
-0.02258576825261116,
-0.017785806208848953,
-0.03558087348937988,
-0.03671085461974144,
-0.0012572340201586485,
0.030838575214147568,
0.01434953324496746,
0.010234148241579533,
0.011060078628361225,
0.0008334199665114284,
0.008090648800134659,
0.02841307409107685,
0.017945043742656708,
0.026658043265342712,
0.02692197822034359,
0.00222100131213665,
-0.017305513843894005,
-0.057907212525606155,
-0.020198877900838852,
0.0026021553203463554,
0.011650796979665756,
0.006669466849416494,
-0.0100473091006279,
0.011905943043529987,
-0.004032081458717585,
0.027329904958605766,
-0.02103806659579277,
-0.03305922821164131,
-0.06732847541570663,
0.03224383667111397,
-0.014418801292777061,
-0.018188800662755966,
0.001260334742255509,
0.027154164388775826,
-0.038673918694257736,
-0.05443423241376877,
0.011461541056632996,
0.029289988800883293,
-0.01801455207169056,
0.0023525881115347147,
-0.01612020656466484,
0.009186387993395329,
0.02138998918235302,
-0.0030686662066727877,
-0.01905425265431404,
0.021162228658795357,
-0.06220260635018349,
-0.0821821466088295,
0.017173273488879204,
0.005759697873145342,
0.01894255168735981,
0.020945411175489426,
0.004437869414687157,
-0.04204132407903671,
0.018799804151058197,
-0.02582324855029583,
0.022527381777763367,
-0.005748807918280363,
-0.005345678422600031,
-0.003517136676236987,
-0.011301594786345959,
0.029411736875772476,
0.013618172146379948,
-0.0026934309862554073,
0.03318345919251442,
0.014947878196835518,
0.02186685800552368,
-0.02688361331820488,
0.02144601009786129,
-0.011863618157804012,
0.008510103449225426,
0.023067530244588852,
0.005242209415882826,
-0.010374212637543678,
0.06935145705938339,
-0.04147522523999214,
0.017029471695423126,
-0.03577246516942978,
0.0006473293760791421,
-0.08533711731433868,
-0.026653602719306946,
0.02839404158294201,
0.02650851011276245,
0.01252404972910881,
-0.028035257011651993,
0.016296474263072014,
0.002465921686962247,
-0.0668482854962349,
0.03315592557191849,
-0.03846517950296402,
-0.01642567291855812,
-0.017879869788885117,
0.028048310428857803,
-0.011565450578927994,
0.04548432677984238,
0.07542554289102554,
0.03832392394542694,
-0.007876062765717506,
-0.017971748486161232,
0.013295872136950493,
0.012952839955687523,
-0.01877426728606224,
0.007811462972313166,
0.0073831286281347275,
-0.012511322274804115,
0.05381643399596214,
-0.018356092274188995,
-0.019686024636030197,
-0.007373711559921503,
0.02192787081003189,
-0.0000743626878829673,
-0.013046211563050747,
-0.0062317876145243645,
0.00018421639106236398,
0.01541462354362011,
0.024677809327840805,
-0.007268799468874931,
-0.005220556631684303,
0.016460342332720757,
0.028871705755591393,
0.047028858214616776,
-0.015648238360881805,
0.018947439268231392,
-0.015190528705716133,
-0.026652701199054718,
-0.03604336455464363,
0.07983865588903427,
-0.00652712769806385,
-0.018393678590655327,
0.0010116329649463296,
0.05222117900848389,
-3.2701805707802123e-7,
-0.0004723845631815493,
0.01170538179576397,
-0.021887147799134254,
-0.013502825982868671,
0.0036371483001857996,
0.02125518210232258,
-0.007228110916912556,
0.034527529031038284,
-0.016141412779688835,
-0.02311975136399269,
0.006881217006593943,
0.004428309854120016,
-0.002069147303700447,
-0.04032469913363457,
-0.0025360367726534605,
-0.003090017009526491,
0.0021467749029397964,
0.010420811362564564,
-0.05941126123070717,
-0.020358484238386154,
0.011202623136341572,
0.004557072650641203,
0.04947660490870476,
-0.03400480002164841,
-0.020511368289589882,
-0.023837300017476082,
-0.06869086623191833,
0.03105000965297222,
0.0033538176212459803,
0.015112144872546196,
-0.06315183639526367,
-0.009421220049262047,
-0.015318219549953938,
0.012722056359052658,
0.049616362899541855,
-0.00370334112085402,
-0.015863874927163124,
0.003942991141229868,
-0.0010717804543673992,
0.00900223944336176,
-0.02260533533990383,
-0.0001742548047332093,
-0.012825488112866879,
-0.010552454739809036,
-0.01862362213432789,
-0.01558997854590416,
-0.01294614002108574,
0.06768088787794113,
0.028130847960710526,
-0.000246833311393857,
0.025275615975260735,
0.017102118581533432,
-0.06447932869195938,
0.06571223586797714,
-0.029603920876979828,
0.014413660392165184,
0.03725342079997063,
-0.006598659325391054,
0.03545352444052696,
0.02961219847202301,
-0.016148606315255165,
-0.02048005536198616,
0.04209253937005997,
-0.053603146225214005,
-0.007037072908133268,
-0.0020968203898519278,
0.006658147554844618,
0.00927224475890398,
-0.04279322549700737,
0.007388388738036156,
0.07541266828775406,
0.0028076795861124992,
-0.00970432162284851,
0.05987527593970299,
0.014872921630740166,
0.020901301875710487,
-0.022709781304001808,
-0.01106634084135294,
0.053420279175043106,
0.03327729180455208,
0.0018149189418181777,
0.040425047278404236,
0.043596331030130386,
0.009406400844454765,
0.03603711724281311,
0.039634305983781815,
0.017574293538928032,
0.0489499606192112,
0.017364641651511192,
0.0509449727833271,
-0.02348737046122551,
-0.007766297087073326,
0.016451919451355934,
-0.01915283314883709,
0.015621739439666271,
0.0234921146184206,
-0.041069578379392624,
0.08369728177785873,
-0.033814556896686554,
0.01461741141974926,
0.009964094497263432,
0.005844831466674805,
-0.005925539880990982,
-0.0031182197853922844,
-0.01210416667163372,
0.0648895874619484,
0.014424320310354233,
-0.019028600305318832,
0.00923190824687481,
0.012415784411132336,
0.008788779377937317,
-0.025699976831674576,
-0.018586620688438416,
0.0004831370315514505,
-0.027877788990736008,
-0.034175362437963486,
-0.010657328180968761,
-0.052481088787317276,
0.0006341810221783817,
0.03335190191864967,
0.04955476149916649,
0.018322493880987167,
0.008112305775284767,
-0.006344129331409931,
-0.020663218572735786,
0.053653910756111145,
-0.028794238343834877,
0.02838553488254547,
-0.005016509909182787,
-0.009584902785718441,
-0.0024479255080223083,
-0.014617957174777985
] |
<p>I notice yesterday that my neighbor’s car had water coming out of the exhaust pipe in the morning. My first response was since the hot exhaust is hotter than the cold tail pipe, heat is transferred from the hot exhaust through the pipe, and with enough moisture in the exhaust, enough heat leaves such that the humid air is condensed forming water drops. </p>
<ol>
<li>Is my thinking correct here? If not, please correct me.</li>
<li>Does the water come from (i) a chemical byproduct of gasoline combustion or (ii) the humidity of the air (i.e. I've only noticed this in the winter, not the summer so I assume that during the summer this would not happen since the tail pipe is “already warm enough.”)</li>
</ol>
| 8,851 |
[
-0.004827287979424,
-0.037950363010168076,
0.002816904103383422,
0.009159909561276436,
0.024844855070114136,
0.0023648531641811132,
-0.014101678505539894,
0.003653711872175336,
0.05077945068478584,
-0.011425378732383251,
0.04637926071882248,
0.06937150657176971,
0.01733899675309658,
-0.0007820890750735998,
0.03216554597020149,
0.014711858704686165,
0.01880609057843685,
-0.021184144541621208,
0.024698419496417046,
0.008950131945312023,
-0.03073148801922798,
-0.0057664671912789345,
0.021410426124930382,
-0.007518209051340818,
-0.043569907546043396,
0.02294006198644638,
-0.022632529959082603,
0.002767352620139718,
-0.006677827797830105,
-0.0000024439150365651585,
0.006412603426724672,
-0.02133674919605255,
0.004162915050983429,
0.02314835414290428,
0.003306892467662692,
0.01028754934668541,
0.0024285197723656893,
-0.01169225201010704,
-0.04366283863782883,
0.026966439560055733,
0.015335186384618282,
-0.012870335020124912,
-0.002211483661085367,
0.042951781302690506,
-0.062451571226119995,
-0.0033254032023251057,
0.02986765280365944,
0.0021442908328026533,
0.03555556386709213,
-0.0669650286436081,
0.013498201966285706,
0.006619292311370373,
0.007943682372570038,
0.03481127321720123,
-0.019830960780382156,
0.02215161733329296,
0.0642409399151802,
0.06337497383356094,
-0.03365449234843254,
-0.03022902086377144,
-0.009293421171605587,
0.01701047271490097,
-0.033578820526599884,
0.014324759133160114,
-0.03574527055025101,
-0.015782104805111885,
-0.00973834004253149,
-0.05096228048205376,
0.021077346056699753,
0.01179089117795229,
0.027077117934823036,
-0.03149117901921272,
0.011368545703589916,
0.018301500007510185,
0.014558622613549232,
-0.015266234055161476,
0.006784169003367424,
0.034332241863012314,
0.04239024594426155,
0.012348445132374763,
0.015072746202349663,
0.01792549341917038,
-0.012044656090438366,
0.014062373898923397,
-0.00534782512113452,
-0.020491665229201317,
0.11328944563865662,
-0.0016348938224837184,
0.02781914919614792,
0.02211437188088894,
0.017697378993034363,
0.037812165915966034,
-0.015832994133234024,
0.009557337500154972,
0.024903779849410057,
0.034023262560367584,
0.00496663386002183,
0.002772066043689847,
0.023960186168551445,
-0.012379433028399944,
0.003315896028652787,
-0.016604507341980934,
0.038921333849430084,
0.047434162348508835,
-0.011186731047928333,
-0.05450373888015747,
-0.036303821951150894,
0.031124642118811607,
-0.03034796193242073,
-0.023769766092300415,
-0.07089115679264069,
0.013964145444333553,
-0.017607437446713448,
-0.028132149949669838,
-0.0017012758180499077,
0.013501297682523727,
0.023045651614665985,
-0.02972671575844288,
0.06002319976687431,
0.049355361610651016,
0.015299778431653976,
-0.0031556871253997087,
-0.003200098406523466,
0.012431493028998375,
-0.07498564571142197,
0.03160668909549713,
-0.0065767508931458,
0.004260804504156113,
-0.03451133891940117,
0.034781623631715775,
-0.022893182933330536,
0.004121458623558283,
0.04070311784744263,
-0.0012098726583644748,
-0.032515477389097214,
-0.015420888550579548,
-0.10891720652580261,
-0.05589095875620842,
0.02086777612566948,
0.011368873529136181,
-0.02902079187333584,
-0.07997247576713562,
-0.01744958572089672,
0.014108051545917988,
0.05621982738375664,
-0.02240443043410778,
0.018066460266709328,
-0.0018200308550149202,
0.04154592007398605,
0.009183675050735474,
0.03253180533647537,
-0.051627274602651596,
0.01877238042652607,
-0.051701560616493225,
-0.026509810239076614,
-0.017893264070153236,
0.04744400084018707,
0.068961963057518,
0.01065303385257721,
-0.016450650990009308,
0.044642768800258636,
-0.0044539314694702625,
-0.005861055105924606,
0.04414728656411171,
0.02101117931306362,
-0.05312935262918472,
0.03196055814623833,
0.04896159842610359,
-0.01170327328145504,
0.013475839048624039,
0.04109426960349083,
0.03625068441033363,
0.013782869093120098,
0.04064907133579254,
0.033992063254117966,
-0.02899879775941372,
0.006928484421223402,
-0.04707581549882889,
0.056632742285728455,
0.010574616491794586,
-0.036667946726083755,
0.015592376701533794,
-0.024249544367194176,
0.030110104009509087,
0.015466874465346336,
0.02114954963326454,
0.0266561396420002,
-0.054324690252542496,
0.015057053416967392,
-0.049542587250471115,
-0.04066748544573784,
-0.05255343019962311,
-0.012832460924983025,
-0.027758251875638962,
-0.003258343320339918,
-0.014580599032342434,
0.006434678100049496,
0.030874060466885567,
-0.042343318462371826,
-0.05136246234178543,
0.017987418919801712,
0.0060725137591362,
0.020877541974186897,
-0.03292464464902878,
0.008607170544564724,
0.05736948549747467,
0.0318995863199234,
0.003521692706272006,
0.013351310044527054,
-0.052941448986530304,
-0.05216547101736069,
-0.03332144394516945,
0.0050519234500825405,
-0.016175437718629837,
-0.04431600868701935,
-0.00763187650591135,
0.020890722051262856,
-0.019176818430423737,
0.0018136880826205015,
0.014633162878453732,
-0.0591307133436203,
0.061864566057920456,
0.0874490886926651,
0.03065219335258007,
-0.027097702026367188,
0.027635658159852028,
0.02107173390686512,
-0.005564049351960421,
-0.00521803880110383,
-0.007181961555033922,
-0.027877289801836014,
-0.011052323505282402,
0.06785839051008224,
-0.021698761731386185,
-0.031621333211660385,
0.004504210315644741,
0.00141622731462121,
0.06401677429676056,
0.015208817087113857,
0.014884322881698608,
-0.017626063898205757,
-0.01462321262806654,
-0.002539056818932295,
0.036399513483047485,
0.023551730439066887,
0.026010485365986824,
0.06786559522151947,
0.025845680385828018,
0.04332108050584793,
-0.06126720458269119,
0.004664026200771332,
0.055383194237947464,
0.02999216690659523,
0.0401611290872097,
-0.029153911396861076,
-0.0339975580573082,
0.04416993632912636,
-0.028314175084233284,
-0.025974111631512642,
0.010068854317069054,
0.005256021860986948,
0.0472731851041317,
-0.018574340268969536,
-0.026864923536777496,
-0.0071854661218822,
0.01868824101984501,
-0.04674091935157776,
-0.003114081919193268,
0.03942229598760605,
-0.05361942574381828,
0.03587162867188454,
-0.040699154138565063,
-0.0016104275127872825,
-0.014991114847362041,
0.037853434681892395,
0.04761861264705658,
-0.014593647792935371,
0.01429901085793972,
-0.02512110210955143,
-0.06861317902803421,
-0.03826049715280533,
-0.001351444749161601,
-0.04071211814880371,
0.03211502358317375,
-0.028082599863409996,
0.0234183669090271,
0.0030007734894752502,
0.01953267492353916,
0.045775510370731354,
0.01838122494518757,
-0.03192422538995743,
0.01471957378089428,
-0.0019709146581590176,
-0.021512676030397415,
-0.027306988835334778,
-0.03402242437005043,
0.009289134293794632,
-0.03761923685669899,
0.004190565552562475,
0.014776666648685932,
-0.039365217089653015,
-0.020256616175174713,
-0.0005632761749438941,
-0.04843957722187042,
-0.014478308148682117,
0.015572652220726013,
-0.04062102735042572,
0.003565641585737467,
0.027133949100971222,
0.02167375385761261,
0.025166906416416168,
-0.0559702105820179,
-0.011158942244946957,
-0.04960734769701958,
-0.07661012560129166,
0.05356726050376892,
0.0028532070573419333,
0.04568856209516525,
0.01348715927451849,
-0.0360613688826561,
0.006597227416932583,
-0.023715386167168617,
-0.05303426831960678,
0.033219773322343826,
-0.0019321052823215723,
-0.0239412784576416,
-0.038462989032268524,
-0.012855755165219307,
0.04037180170416832,
-0.016908902674913406,
0.028757208958268166,
0.07512381672859192,
-0.003219251288101077,
0.002685247454792261,
0.023351870477199554,
-0.005008155945688486,
0.003975240979343653,
-0.03497081622481346,
0.006744876969605684,
0.033928610384464264,
0.0065230196341872215,
0.001366891316138208,
-0.003950759302824736,
-0.049939025193452835,
0.03155837953090668,
0.03696063160896301,
-0.05744114890694618,
0.03622722998261452,
0.03309232369065285,
-0.003278253600001335,
-0.06411468982696533,
0.05288510397076607,
-0.014246230944991112,
0.01871635392308235,
-0.014269751496613026,
-0.0099555142223835,
0.03805360570549965,
-0.002652559895068407,
0.008491100743412971,
0.024168280884623528,
0.03690458461642265,
-0.05368415638804436,
-0.03396951034665108,
0.008904331363737583,
-0.05322584882378578,
0.012041466310620308,
0.023466959595680237,
0.01662168838083744,
0.04403484985232353,
0.02487930655479431,
0.03988984599709511,
-0.005577763542532921,
-0.06080679967999458,
0.024618569761514664,
-0.05651937797665596,
0.010433128103613853,
0.006217263638973236,
0.03749644383788109,
-0.01080714538693428,
0.07162805646657944,
-0.018652334809303284,
0.02276839129626751,
0.04059195891022682,
-0.05824572965502739,
-0.044309359043836594,
0.010284318588674068,
-0.002580483676865697,
-0.05171402916312218,
-0.010456793941557407,
-0.05433124303817749,
-0.010413071140646935,
-0.04903314635157585,
-0.028272459283471107,
0.019308825954794884,
-0.022346215322613716,
-0.03823843225836754,
0.013443869538605213,
-0.03512385115027428,
-0.0661841556429863,
0.0004477242473512888,
0.013465343974530697,
0.04881412535905838,
-0.025335827842354774,
0.015132012777030468,
0.01444160658866167,
-0.03297264873981476,
-0.013072005473077297,
-0.03820601850748062,
0.022161612287163734,
0.022175371646881104,
0.006802613381296396,
0.00017597766418475658,
0.018495535477995872,
0.0051029701717197895,
0.02748776040971279,
-0.02776785008609295,
0.022145649418234825,
0.012572416104376316,
0.015172133222222328,
-0.016888733953237534,
-0.004463189747184515,
-0.025981221348047256,
0.04232269152998924,
0.010245902463793755,
-0.010086871683597565,
0.06871140748262405,
-0.01189312245696783,
-0.047462258487939835,
-0.009597430005669594,
0.03751647099852562,
0.02038034237921238,
0.019364776089787483,
0.027622340247035027,
-0.019505679607391357,
0.02060203067958355,
-0.017896289005875587,
0.022135334089398384,
0.05447836220264435,
0.05024827644228935,
-0.009429476223886013,
-0.041012153029441833,
-0.014028221368789673,
0.018663965165615082,
0.014943074434995651,
0.02292823977768421,
0.012931461445987225,
0.028612367808818817,
-0.00586029002442956,
-0.017222389578819275,
0.023688985034823418,
0.019286423921585083,
0.0517105758190155,
0.012995593249797821,
-0.026463273912668228,
-0.09607797861099243,
-0.020746292546391487,
0.03816401585936546,
0.015386275015771389,
-0.01569996029138565,
0.012234600260853767,
-0.07063082605600357,
-0.0092239361256361,
0.040710896253585815,
0.0035563884302973747,
0.04105132818222046,
0.005984591785818338,
0.007503881584852934,
-0.008623873814940453,
-0.01498865894973278,
0.022896140813827515,
0.003281682962551713,
-0.019779108464717865,
0.034614332020282745,
-0.025289762765169144,
-0.05936303362250328,
-0.019192475825548172,
0.03337569162249565,
0.03138422220945358,
-0.0030344256665557623,
0.001819677883759141,
-0.057719260454177856,
-0.04051918908953667,
0.02661261335015297,
-0.019915712997317314,
-0.07397691160440445,
0.012419602833688259,
-0.031236855313181877,
-0.023702500388026237,
0.06261204928159714,
-0.02766191028058529,
0.0017369436100125313,
0.039645005017519,
0.02404503896832466,
-0.03569338470697403,
-0.0065298862755298615,
-0.04794493317604065,
0.0282747820019722,
0.02190743014216423,
0.03907063603401184,
0.042226944118738174,
0.02366594225168228,
0.03468429297208786,
0.03207504004240036,
-0.002477864734828472,
0.027743754908442497,
-0.051166705787181854,
-0.016658388078212738,
-0.03096500225365162,
0.010212204419076443,
-0.025506047531962395,
0.012562830932438374,
0.022130075842142105,
0.0033264511730521917,
-0.007142394781112671,
-0.05630570650100708,
0.02994673326611519,
-0.04962538182735443,
-0.0006575369625352323,
-0.03203511983156204,
-0.05563284829258919,
0.03363128378987312,
-0.004618843551725149,
-0.0012347492156550288,
0.023562954738736153,
-0.025301437824964523,
0.014148719608783722,
0.020454850047826767,
-0.02757408283650875,
0.028231017291545868,
-0.015162435360252857,
0.005278236698359251,
0.0661587044596672,
-0.014018327929079533,
0.014750977046787739,
-0.020900120958685875,
0.01706562004983425,
0.03448799252510071,
-0.06780893355607986,
0.023511569947004318,
0.03990115225315094,
0.04036836698651314,
0.029852036386728287,
-0.022284872829914093,
0.05209517106413841,
0.022687509655952454,
-0.010478748008608818,
-0.026330696418881416,
-0.0436645969748497,
0.049076147377491,
0.01951352320611477,
-0.023982994258403778,
-0.06523079425096512,
0.0011737995082512498,
-0.05921866372227669,
-0.043535757809877396,
0.011367883533239365,
-0.013007097877562046,
-0.02746567502617836,
0.010076028294861317,
0.0434073731303215,
0.04463239014148712,
0.08263646066188812,
-0.02892363630235195,
0.008320135995745659,
0.01678478717803955,
-0.03718527406454086,
-0.015678124502301216,
-0.01331262569874525,
0.019218474626541138,
-0.014656485989689827,
0.014454645104706287,
0.009366740472614765,
0.013369010761380196,
0.08622481673955917,
-0.002400388941168785,
-0.0014123658183962107,
0.018192369490861893,
0.03744705393910408,
-0.02628905512392521,
-0.013236114755272865,
0.0411495678126812,
0.01165725477039814,
0.024725621566176414,
-0.03559151291847229,
0.001593917142599821,
0.014179195277392864,
0.005686177406460047,
-0.04734959080815315,
-0.015489165671169758,
-0.008475931361317635,
0.04623117297887802,
0.07010041177272797,
-0.025492142885923386,
0.017106983810663223,
0.020531803369522095,
-0.02158866822719574,
0.028198324143886566,
0.01765904575586319,
-0.002660029334947467,
0.012012897990643978,
0.010914507322013378,
0.0037806122563779354,
-0.029980327934026718,
-0.013072059489786625,
-0.03146643936634064,
0.03951951116323471,
-0.004249514080584049,
0.03682038187980652,
0.042186662554740906,
0.02964969538152218,
-0.005966887343674898,
-0.034605976194143295,
-0.021719345822930336,
0.01506201270967722,
-0.013631848618388176,
0.008627141825854778,
-0.016660042107105255,
-0.010218185372650623,
0.02065303921699524,
0.00698810862377286,
-0.007344684563577175,
0.014428188093006611,
0.009254575707018375,
-0.010069120675325394,
-0.0104339849203825,
-0.021674592047929764,
-0.06008203700184822,
0.013445035554468632,
-0.035041019320487976,
0.04676777869462967,
-0.017352353781461716,
0.0026283832266926765,
0.028540680184960365,
0.0015476358821615577,
-0.004631132818758488,
-0.07415161281824112,
0.018966518342494965,
-0.04827611893415451,
0.0064947414211928844,
-0.020286893472075462,
0.019068744033575058,
-0.0061231995932757854,
0.01794482208788395,
0.01812339574098587,
0.0036865309812128544,
0.03711024299263954,
-0.014054514467716217,
-0.03575369715690613,
0.04722198471426964,
0.02305312268435955,
-0.032172948122024536,
0.04523574560880661,
-0.0074446420185267925,
-0.035572636872529984,
0.0302286297082901,
-0.027973683550953865,
0.005422910675406456,
-0.022619185969233513,
0.0452081672847271,
0.030110007151961327,
0.05393616110086441,
-0.02264193817973137,
0.0052964347414672375,
0.0057305824011564255,
0.03694813698530197,
0.11519013345241547,
0.0323292501270771,
0.03317546099424362,
-0.022476039826869965,
-0.02923770807683468,
0.0012351858895272017,
-0.016842497512698174,
-0.0158231183886528,
0.00904944445937872,
-0.03992513567209244,
0.062387336045503616,
0.040020618587732315,
0.02869047410786152,
0.002267200965434313,
-0.009372872300446033,
0.025866834446787834,
-0.03245619311928749,
-0.042239945381879807,
-0.020157108083367348,
0.02273990586400032,
0.0032531488686800003,
0.006803408265113831,
-0.056096967309713364,
0.006024823524057865,
0.016540829092264175,
-0.010715382173657417,
-0.012917901389300823,
-0.05802931264042854,
0.02914024516940117,
-0.022230343893170357,
-0.05063715577125549,
0.04442853853106499,
0.03476261347532272,
-0.004276564344763756,
-0.02481798455119133,
-0.0044730352237820625,
0.03219328075647354,
-0.02488105744123459,
0.0040058558806777,
0.006561807822436094,
0.03634021431207657,
-0.028684919700026512,
-0.0014872826868668199,
0.069878950715065,
-0.07945384830236435,
0.026243338361382484,
-0.023493338376283646,
0.0030523526947945356,
-0.010518466122448444,
-0.017606178298592567,
-0.03029448166489601,
0.02144993096590042,
0.05113060772418976,
-0.042289335280656815,
-0.021173035725951195,
-0.0015338488155975938,
0.029991501942276955,
-0.011552391573786736,
-0.037228427827358246,
-0.049036622047424316,
0.04098602384328842,
-0.019635062664747238,
-0.04523526504635811,
0.05651777237653732,
0.00721640745177865,
-0.007318535353988409,
-0.021553823724389076,
0.023702815175056458,
-0.02548055350780487,
-0.015104426071047783,
-0.03974711522459984,
-0.002806610893458128,
0.0002106495958287269,
-0.01640203408896923,
0.004425819963216782,
0.031519025564193726,
0.035417743027210236,
0.030734412372112274,
0.01602363958954811,
-0.015175959095358849,
-0.06663365662097931,
0.01036615390330553,
0.018409494310617447,
-0.007918069139122963,
-0.04836020991206169,
0.04327281191945076,
-0.04307442903518677,
0.03255218639969826,
-0.020145758986473083,
0.01263614371418953,
0.03537968173623085,
0.10673726350069046,
0.008867031894624233,
-0.01268540509045124,
-0.007689924910664558,
0.020611826330423355,
0.0065812175162136555,
0.022678766399621964,
0.031217221170663834,
0.04443000629544258,
0.028077298775315285,
0.019899554550647736,
0.0038196039386093616,
0.020547857508063316,
0.010456043295562267,
0.030791211873292923,
0.020402800291776657,
0.0007270769565366209,
-0.010471845977008343,
-0.012301565147936344,
-0.008257693611085415,
-0.02892984077334404,
-0.0020500661339610815,
-0.02387591078877449,
0.0021821882110089064,
-0.018948933109641075,
0.0176071897149086,
-0.012595457024872303,
0.012348480522632599,
-0.006612336728721857,
0.0580461248755455,
-0.032571371644735336,
-0.005728567950427532,
-0.0610482320189476,
-0.039429306983947754,
0.015615889802575111,
0.003679045243188739,
-0.01065125036984682,
0.04952764883637428,
-0.03691834211349487,
-0.003415967570617795,
0.032921478152275085,
0.002122959354892373,
-0.021496888250112534,
-0.016450397670269012,
0.008337912149727345,
-0.0011978000402450562,
0.07771030813455582,
-0.028613848611712456,
0.009592489339411259,
0.035186752676963806,
-0.004919995553791523,
-0.01373316254466772,
-0.005724119022488594,
-0.025515545159578323,
0.01387188769876957,
-0.003701841924339533,
-0.018065737560391426,
0.008650562725961208,
0.05532296746969223,
-0.030918149277567863,
0.001504313200712204,
0.019429003819823265,
0.00009589399996912107,
0.011256909929215908,
-0.027655815705657005,
0.004984227009117603,
0.011621136218309402,
-0.016704309731721878,
0.029025722295045853,
0.03154199197888374,
-0.006597606930881739,
0.007243639789521694,
0.0018816362135112286,
-0.019718410447239876,
-0.004934109281748533,
0.006717266980558634,
0.02241947315633297,
0.030115658417344093,
0.02357005700469017,
-0.059745460748672485,
0.03158654645085335,
-0.031331129372119904,
-0.032976191490888596,
-0.08702293783426285,
-0.0010790122905746102,
0.03331899642944336,
-0.026132667437195778,
0.014200195670127869,
0.010966862551867962,
-0.011197899468243122,
0.02588220126926899,
-0.05603810399770737,
-0.030675508081912994,
-0.027903158217668533,
-0.02336442843079567,
-0.047271862626075745,
0.0073376307263970375,
-0.009923448786139488,
0.004788746125996113,
0.021305743604898453,
0.051255252212285995,
0.01686401665210724,
0.05369731783866882,
-0.01370740681886673,
-0.011346547864377499,
0.02247728779911995,
0.03202859312295914,
-0.011128137819468975,
-0.014842398464679718,
0.048456814140081406,
-0.053897157311439514,
0.01764298602938652,
0.012917380779981613,
-0.01735430210828781,
0.03502301871776581,
0.0004504204844124615,
-0.026620162650942802,
-0.000671977293677628,
-0.0002341549698030576,
0.01814429648220539,
-0.0004075388133060187,
0.0017988828476518393,
0.028474288061261177,
-0.00997476652264595,
0.027296630665659904,
0.0138297900557518,
-0.008051714859902859,
0.004344292916357517,
-0.02663622796535492,
-0.05645222216844559,
0.02713802084326744,
-0.04181354492902756,
-0.013525008223950863,
0.010683738626539707,
0.0006812033825553954,
-0.01236328762024641,
-0.01643907092511654,
-0.058026596903800964,
-0.02251891978085041,
-0.03376283869147301,
0.023718807846307755,
0.019640199840068817,
-0.004483652301132679,
0.0019475045846775174,
-0.02810143679380417,
-0.03304695338010788,
0.011264105327427387,
0.012053769081830978,
0.002547686453908682,
-0.024491168558597565,
-0.013104276731610298,
-0.0168825164437294,
-0.03316831961274147,
-0.01473325677216053,
-0.045284442603588104,
-0.0063751074485480785,
0.06849636137485504,
0.02502504177391529,
-0.03266077861189842,
-0.010439403355121613,
-0.020131336525082588,
0.014886281453073025,
-0.06448838859796524,
0.027911659330129623,
-0.009484264068305492,
-0.0036289782728999853,
-0.03966720029711723,
-0.028543177992105484,
0.0052344282157719135,
0.008579903282225132,
0.05184030160307884,
0.013117406517267227,
-0.005101697985082865,
0.018687380477786064,
0.005929081235080957,
0.003384003881365061,
-0.03437143191695213,
0.032225362956523895,
0.04156198725104332,
-0.0007833571871742606,
-0.00664542568847537,
-0.021754536777734756,
-0.02465149201452732,
0.000441170996055007,
0.03789343684911728,
-0.007020718418061733,
0.010752426460385323,
-0.030644165351986885,
-0.0031179566867649555,
0.00921662151813507,
0.009160907939076424,
-0.036178842186927795,
0.04676081985235214,
-0.026627736166119576,
0.02785472571849823,
0.0634816512465477,
-0.0021842520218342543,
-0.06817536056041718,
0.030601415783166885,
0.004567254800349474,
-0.014121891930699348,
0.005153526086360216,
-0.03888566419482231,
0.053727779537439346,
-0.03300577402114868,
0.03600030764937401,
-0.009007768705487251,
-0.029958048835396767,
-0.0035681098233908415,
0.012138580903410912,
0.008174794726073742,
0.021307237446308136,
0.015585718676447868,
0.01263592392206192,
0.018352560698986053,
-0.0045612528920173645,
-0.03687077760696411,
0.0625438392162323,
0.04231535643339157,
-0.01080390065908432,
-0.017429864034056664,
0.021313786506652832,
-0.009781773202121258,
0.020758621394634247,
-0.02371537685394287,
0.022157004103064537,
-0.04773954302072525,
-0.02829192578792572,
0.02650456875562668,
-0.008593518286943436,
-0.004454480484127998,
0.03856542333960533,
-0.014785616658627987,
0.02560495212674141,
0.004471056163311005,
0.02986592799425125,
-0.025433054193854332,
0.026945818215608597,
0.002700456418097019,
0.010219183750450611,
-0.005536934826523066,
0.024003872647881508,
0.02354096993803978,
-0.04141902178525925,
0.010938514955341816,
0.0006520954193547368,
-0.011517835780978203,
-0.004655893892049789,
0.03376308083534241,
-0.03848016634583473,
0.026103651151061058,
-0.05496268719434738,
-0.04356234148144722,
0.0030391786713153124,
-0.007935898378491402,
0.03285783901810646,
0.042056676000356674,
-0.04352835938334465,
-0.019516784697771072,
-0.019464384764432907,
-0.04051104560494423,
0.033695586025714874,
-0.05688236653804779,
0.019011639058589935,
-0.011480745859444141,
0.0035174195654690266,
-0.018158677965402603,
-0.061897747218608856
] |
<p>The stress-energy tensor derived from the ghost action of a bosonic string is:</p>
<p>$$
T_{\alpha \beta} = \frac{i}{4 \pi} \left ( b_{\alpha \gamma} \nabla_{\beta} c^{\gamma} + b_{\beta \gamma} \nabla_{\alpha} c^{\gamma} - c^\gamma \nabla_\gamma b_{\alpha \beta} - g_{\alpha \beta} b_{\gamma \delta} \nabla_\gamma c^{\delta} \right)
$$</p>
<p>My book says, but doesn't give the proof, that in light-cone coordinates, the only two non-trivial components are the diagonal ones, given by:</p>
<p>$$
T_{++} = \frac{i}{4 \pi} \left ( 2b_{++} \partial_+ c^+ - c^+ \partial b_{++} \right)
$$</p>
<p>and the same thing for $T_{--}$ but replacing all plus signs in the indices with minus signs.</p>
<p>But I can't derive this. I know that in light-cone coordinates, $g_{++} = g_{--} = 0$ and $g_{+-} = g_{-+} = -\tfrac{1}{2}$ and the covariant derivative is just the partial derivative.</p>
<p>Now for example, consider $T_{+-}$ and focus on the $c^\gamma \nabla_\gamma b_{\alpha \beta}$ term. In light-cone coordinates, it's:</p>
<p>$$
c^+ \partial_+ b_{+-} + c^- \partial_- b_{+-}
$$</p>
<p>Since these are the only terms involving partial derivatives of $b$, they must kill each other for $T_{+-}$ to be zero. I know that $b$ is symmetric and traceless, and that $b$ and $c$ anti-commute, but that's not enough to produce </p>
<p>$$
c^+ \partial_+ b_{+-} + c^- \partial_- b_{+-} = 0
$$</p>
<p>I don't see how it's possible.</p>
| 8,852 |
[
0.00744242500513792,
0.012498672120273113,
0.017722759395837784,
-0.06265754997730255,
0.02829119749367237,
0.03569268062710762,
-0.03419647738337517,
0.013852380216121674,
0.0133033636957407,
-0.07847806811332703,
0.022995516657829285,
0.021151505410671234,
0.02871125191450119,
0.039231155067682266,
-0.0056076752953231335,
-0.007015530485659838,
0.012855644337832928,
0.0033665834926068783,
-0.02427966333925724,
-0.053094908595085144,
0.015072262845933437,
0.02366345189511776,
-0.026107965037226677,
0.001214324147440493,
0.00824669934809208,
0.023623419925570488,
-0.007136367727071047,
-0.0007449586410075426,
-0.01993686892092228,
0.043538663536310196,
-0.042554959654808044,
-0.018243806436657906,
-0.0018737076316028833,
-0.003773806383833289,
0.011868402361869812,
0.010901658795773983,
-0.056043755263090134,
-0.028828859329223633,
-0.01350266020745039,
0.005765868350863457,
-0.025340592488646507,
0.03358636423945427,
-0.04927961155772209,
0.0662640854716301,
-0.0014594547683373094,
0.007785627152770758,
-0.0009523798944428563,
0.0028901409823447466,
0.054203249514102936,
-0.0687829852104187,
0.059093695133924484,
-0.004007737152278423,
0.03732863813638687,
-0.009172665886580944,
-0.03915613517165184,
-0.05840673670172691,
0.06545320153236389,
0.07688022404909134,
0.0075517804361879826,
-0.0820758119225502,
0.006759633310139179,
-0.0062761856243014336,
-0.002923691878095269,
-0.009331105276942253,
-0.015478852204978466,
0.009459407068789005,
0.043060801923274994,
-0.006745923776179552,
0.014653671532869339,
-0.044576968997716904,
-0.010983017273247242,
-0.04091286286711693,
0.0440535768866539,
-0.01397124957293272,
-0.016178246587514877,
-0.02506464719772339,
0.019907228648662567,
0.02875303290784359,
0.013571062125265598,
0.0233142226934433,
-0.00577987264841795,
0.024456359446048737,
0.015091796405613422,
0.05486467480659485,
-0.03219754621386528,
0.019264062866568565,
0.06315043568611145,
-0.0075120688416063786,
0.01494964212179184,
0.0490516796708107,
0.019992053508758545,
-0.008690489456057549,
0.01326560415327549,
-0.013546689413487911,
-0.021308155730366707,
0.03910369426012039,
0.02052184008061886,
0.03241480886936188,
0.00014073424972593784,
0.011741701513528824,
-0.04289411008358002,
-0.027799490839242935,
-0.0013144478434696794,
0.09067058563232422,
0.004506785422563553,
0.012242707423865795,
-0.026128698140382767,
0.01679249480366707,
-0.019461065530776978,
-0.019293352961540222,
-0.05945384502410889,
0.004312117118388414,
-0.015187522396445274,
-0.03478887677192688,
-0.008174717426300049,
-0.06142172962427139,
0.02383536845445633,
-0.006049490999430418,
0.05358085781335831,
0.042435284703969955,
0.054497454315423965,
-0.02367558516561985,
0.003431404707953334,
-0.010627951472997665,
-0.071891650557518,
-0.004592007026076317,
0.09032805263996124,
-0.015062886290252209,
-0.0427488312125206,
-0.013490471057593822,
0.040329061448574066,
-0.03312065824866295,
0.02115708589553833,
0.005182844586670399,
0.02340714819729328,
0.00931320060044527,
-0.09417100995779037,
-0.03617427125573158,
0.037717677652835846,
-0.002715025097131729,
-0.010898294858634472,
-0.07261472195386887,
-0.018352333456277847,
0.013135818764567375,
0.09462817013263702,
-0.037785615772008896,
0.03812115639448166,
0.024695027619600296,
0.01921047829091549,
0.0000584892877668608,
0.021922366693615913,
-0.028131380677223206,
-0.01815391704440117,
-0.045001063495874405,
-0.059987302869558334,
-0.05473116785287857,
-0.012265630066394806,
0.03954412415623665,
-0.017264874652028084,
0.028787806630134583,
0.07927587628364563,
-0.025142379105091095,
0.0244038887321949,
0.027001462876796722,
-0.011202302761375904,
-0.06737784296274185,
0.05718647316098213,
0.010121718980371952,
-0.011127972044050694,
0.012397758662700653,
-0.01900910586118698,
-0.019202325493097305,
-0.021702418103814125,
0.02539217099547386,
0.046857453882694244,
-0.05493837967514992,
-0.03304178640246391,
0.007315740454941988,
-0.017009397968649864,
0.019481083378195763,
-0.036376141011714935,
-0.045245323330163956,
-0.04409287869930267,
0.030672699213027954,
0.003895187983289361,
0.029577026143670082,
0.009237744845449924,
-0.0017128405161201954,
0.02298213727772236,
-0.04881074279546738,
-0.005276798736304045,
-0.037295009940862656,
-0.01306932233273983,
0.041185326874256134,
-0.043951842933893204,
0.01470644399523735,
0.0054159509018063545,
0.002951874164864421,
-0.010908612981438637,
-0.024219300597906113,
0.024309556931257248,
0.045431263744831085,
-0.010791515000164509,
-0.02070360630750656,
0.02725624106824398,
-0.003240926656872034,
0.047502920031547546,
0.01817205548286438,
0.049071911722421646,
-0.03407100588083267,
-0.0025006195064634085,
0.035413581877946854,
-0.017084479331970215,
0.03596353903412819,
-0.03369094058871269,
-0.000004832240392715903,
0.009543891064822674,
-0.018179070204496384,
-0.009721379727125168,
0.02690509334206581,
-0.04323515668511391,
0.019421251490712166,
0.0776907429099083,
0.010142795741558075,
-0.001268370426259935,
0.03408189117908478,
0.0008715778240002692,
0.054184459149837494,
-0.010137831792235374,
0.0027523546013981104,
-0.021726731210947037,
-0.026140393689274788,
0.02820494957268238,
-0.01978791505098343,
-0.047557905316352844,
0.013373490422964096,
0.027148960158228874,
0.03017251566052437,
0.03445356711745262,
0.0049423947930336,
-0.023700209334492683,
-0.038285985589027405,
0.02945629321038723,
0.013716010376811028,
-0.005389129277318716,
0.017978128045797348,
0.0487973652780056,
-0.010195539332926273,
0.045909300446510315,
-0.010965985246002674,
-0.0010817785514518619,
0.013550644740462303,
-0.040241215378046036,
-0.010883211158216,
0.0485573410987854,
0.0021620860788971186,
0.07074213027954102,
-0.022948533296585083,
0.047123853117227554,
0.04835020750761032,
-0.020664364099502563,
-0.0191164780408144,
0.004859711043536663,
-0.017904609441757202,
0.033271629363298416,
-0.007057194598019123,
-0.0075867571868002415,
-0.03136380389332771,
0.005790115334093571,
-0.03636675700545311,
0.00647521298378706,
0.002304361667484045,
-0.002127142855897546,
-0.017345761880278587,
-0.010105419903993607,
0.025309303775429726,
0.04102865234017372,
0.047665953636169434,
-0.034128859639167786,
-0.010887080803513527,
0.015167346224188805,
0.0007990642916411161,
0.014770456589758396,
0.026014402508735657,
-0.008867679163813591,
0.027330266311764717,
-0.08275923877954483,
-0.008044526912271976,
0.03295297175645828,
0.009708232246339321,
0.009761030785739422,
0.0019181121606379747,
-0.02934299223124981,
-0.02884766459465027,
-0.022779563441872597,
0.01702011004090309,
0.01779763586819172,
-0.10646050423383713,
0.0101176667958498,
0.0629071518778801,
0.02474423684179783,
-0.04698685556650162,
0.018102919682860374,
-0.00452833715826273,
-0.056546423584222794,
0.0192940142005682,
-0.0259565282613039,
-0.015902606770396233,
-0.0351562574505806,
0.05176354944705963,
-0.013952240347862244,
0.004119547083973885,
0.01846078410744667,
-0.06330101191997528,
-0.01648901216685772,
0.02165527641773224,
0.04046821966767311,
-0.00013976081390865147,
0.004148629028350115,
-0.0731830820441246,
0.10752144455909729,
0.02068011462688446,
-0.029838554561138153,
0.017786798998713493,
0.010294144973158836,
-0.01666495017707348,
-0.0278781745582819,
-0.002779470756649971,
-0.01087790634483099,
0.007242892403155565,
0.003165141213685274,
0.016896948218345642,
0.04806795343756676,
0.05767524242401123,
0.03795773163437843,
-0.019092123955488205,
0.010127266868948936,
-0.000568655610550195,
0.018165480345487595,
0.06663241237401962,
-0.004854476545006037,
0.010014120489358902,
0.00026991221238859,
0.009233630262315273,
-0.0006209136336110532,
0.003870853455737233,
-0.0421648733317852,
0.04397905245423317,
0.0047161392867565155,
0.003457595594227314,
0.0011227451032027602,
0.02679554559290409,
-0.003821405814960599,
-0.020468978211283684,
-0.0272205900400877,
0.011937899515032768,
0.050757575780153275,
-0.026841597631573677,
-0.0012698452919721603,
0.02233770303428173,
0.023271121084690094,
-0.013062167912721634,
-0.044340696185827255,
0.01616332121193409,
-0.007313485722988844,
0.02465020678937435,
-0.039010364562273026,
-0.016999702900648117,
0.021771833300590515,
0.028857188299298286,
-0.001153362449258566,
-0.0011221782770007849,
-0.0623936802148819,
0.004883844405412674,
-0.02777855098247528,
0.015121505595743656,
-0.039768218994140625,
0.050642065703868866,
-0.00356725649908185,
0.03733358159661293,
0.019496163353323936,
0.0350213386118412,
0.0718374028801918,
0.009725305251777172,
-0.06869997084140778,
0.009431845508515835,
-0.022282134741544724,
-0.013673561625182629,
-0.007812220137566328,
-0.015856973826885223,
-0.009442169219255447,
-0.00037847523344680667,
-0.032612480223178864,
-0.0321585088968277,
-0.024268867447972298,
-0.07082849740982056,
0.046080853790044785,
-0.0643574669957161,
-0.013331697322428226,
0.00042551959631964564,
0.03008558414876461,
0.047100767493247986,
-0.04087626561522484,
-0.021367255598306656,
0.06429668515920639,
-0.0030532313976436853,
0.009458844549953938,
-0.04184870794415474,
0.023506861180067062,
0.04240894690155983,
0.00476039107888937,
0.013929863460361958,
0.012854361906647682,
0.007947665639221668,
-0.02807324379682541,
0.03739260509610176,
0.03289302438497543,
0.009272697381675243,
-0.026335520669817924,
0.005330797750502825,
-0.019916478544473648,
0.014254157431423664,
0.008379955776035786,
0.0697350949048996,
0.010370584204792976,
0.012312879785895348,
0.010803165845572948,
0.04485814645886421,
-0.010718995705246925,
0.05653595179319382,
0.03452378883957863,
0.011783280409872532,
-0.02774147503077984,
-0.056615378707647324,
0.003973409067839384,
-0.033911414444446564,
-0.026603784412145615,
-0.023891421034932137,
0.00721548218280077,
-0.06802167743444443,
0.022270098328590393,
0.021258780732750893,
0.041469018906354904,
-0.012200548313558102,
-0.007665885146707296,
0.009093363769352436,
-0.017221929505467415,
0.008287857286632061,
0.010786660946905613,
0.02941093221306801,
0.03697235509753227,
0.0426548570394516,
-0.005669515114277601,
0.023076368495821953,
-0.021573202684521675,
-0.019063422456383705,
0.002639901591464877,
0.022375749424099922,
0.024479595944285393,
-0.027049116790294647,
-0.047181256115436554,
-0.022535119205713272,
0.046457380056381226,
-0.02184578962624073,
0.020628347992897034,
0.021732408553361893,
0.04799158126115799,
-0.031313322484493256,
-0.03593138977885246,
-0.016204915940761566,
0.06633695214986801,
-0.01018330454826355,
0.005180568899959326,
-0.019308794289827347,
-0.002787396078929305,
0.010915378108620644,
-0.00032820916385389864,
-0.003891052445396781,
0.05127180367708206,
-0.011836190707981586,
-0.0333184152841568,
-0.0068817767314612865,
0.011255668476223946,
-0.012608637101948261,
-0.06387298554182053,
-0.0031162146478891373,
-0.004661520477384329,
-0.0381397046148777,
0.03532829508185387,
-0.02910379320383072,
-0.037695545703172684,
0.040044933557510376,
0.01762205734848976,
-0.008505834266543388,
0.03432651609182358,
-0.041516710072755814,
0.027399390935897827,
0.004305017180740833,
-0.029200004413723946,
0.05519947037100792,
0.0021892241202294827,
-0.01729474775493145,
-0.019334036856889725,
-0.02666480280458927,
0.026547370478510857,
-0.03368852287530899,
0.01151344645768404,
-0.02584419585764408,
-0.011559130623936653,
-0.03458430618047714,
0.013108287006616592,
-0.04327321797609329,
-0.004086325876414776,
-0.012215404771268368,
-0.04411860182881355,
-0.011917904950678349,
0.030670881271362305,
0.008689448237419128,
0.0070019871927797794,
0.01133565790951252,
0.0019455819856375456,
0.011917431838810444,
0.00017361737263854593,
0.031748343259096146,
0.011420824564993382,
-0.039539139717817307,
0.057381514459848404,
0.002935622353106737,
0.03595681115984917,
-0.03484007716178894,
-0.00769586768001318,
0.008307864889502525,
-0.02494019828736782,
0.020256949588656425,
-0.0006942175095900893,
-0.005225182045251131,
0.007532630115747452,
0.0010354539845138788,
-0.006915274541825056,
-0.010839073918759823,
-0.047993164509534836,
0.005983859766274691,
-0.04923484846949577,
-0.013438161462545395,
0.050245173275470734,
-0.003438275773078203,
-0.05696525052189827,
-0.03350549936294556,
0.008851147256791592,
-0.0014716542791575193,
-0.02390127442777157,
0.026865802705287933,
0.012214184738695621,
-0.009491140954196453,
-0.05453692749142647,
0.016902929171919823,
0.03748251497745514,
-0.024949481710791588,
-0.009184456430375576,
0.013170325197279453,
0.02984994277358055,
0.010323205962777138,
0.004057663027197123,
-0.015325086191296577,
0.0031489823013544083,
-0.026992036029696465,
-0.02529282681643963,
-0.012665859423577785,
0.05678611621260643,
-0.0010685300221666694,
-0.02789933793246746,
0.008922227658331394,
0.019198467954993248,
0.024839947000145912,
0.029048310592770576,
0.006409948226064444,
-0.004581848159432411,
0.016237156465649605,
-0.02359931170940399,
-0.06063408777117729,
-0.00978449359536171,
0.01024271547794342,
0.020340876653790474,
-0.03231494128704071,
0.014880557544529438,
-0.044658102095127106,
-0.03719329461455345,
0.015258011408150196,
0.009171420708298683,
-0.002564577152952552,
-0.028389958664774895,
0.07121030986309052,
0.011795049533247948,
-0.019747966900467873,
0.03079892136156559,
-0.017097756266593933,
0.005719691980630159,
0.04192323610186577,
0.00719452602788806,
0.00032652655499987304,
-0.022785648703575134,
-0.05389002710580826,
-0.005605658981949091,
-0.03141734376549721,
0.033157091587781906,
0.060226477682590485,
0.0072532836347818375,
0.018439048901200294,
0.008243327029049397,
-0.010025992058217525,
0.0246177576482296,
0.02183261513710022,
-0.034152835607528687,
0.02379251830279827,
-0.007264934480190277,
0.020789336413145065,
-0.06916572153568268,
-0.028034182265400887,
0.0535939559340477,
0.0481431782245636,
-0.07526092976331711,
0.041124824434518814,
0.008401496335864067,
0.014120160602033138,
-0.012395498342812061,
-0.01054411195218563,
-0.047861650586128235,
0.07259365171194077,
0.0013331295922398567,
0.07638544589281082,
0.013057331554591656,
-0.0106460340321064,
0.026624485850334167,
0.016940122470259666,
0.018824247643351555,
0.003925548400729895,
-0.029825350269675255,
-0.04318488761782646,
0.0428205244243145,
0.025418436154723167,
-0.01113880705088377,
-0.005186190828680992,
-0.0020289006642997265,
0.017809735611081123,
-0.022999240085482597,
0.046555567532777786,
-0.014560531824827194,
-0.021431444212794304,
-0.0211197342723608,
-0.03972666338086128,
-0.040920406579971313,
0.058431483805179596,
-0.04639923945069313,
-0.019004393368959427,
-0.00288578262552619,
-0.006749509368091822,
0.018971357494592667,
0.007403873372823,
0.030977467074990273,
0.022857308387756348,
0.0593680776655674,
-0.0202657338231802,
0.006858535576611757,
0.01432498823851347,
-0.0033398286905139685,
0.13360600173473358,
0.030542459338903427,
-0.0018812773050740361,
-0.06917094439268112,
0.030844353139400482,
-0.022245116531848907,
0.022448331117630005,
-0.06335581094026566,
0.05059993639588356,
-0.0012417574180290103,
-0.028811803087592125,
-0.005303794983774424,
0.03988354653120041,
-0.03328995406627655,
-0.02479020692408085,
0.02248533070087433,
-0.025324184447526932,
-0.05661565065383911,
-0.021077344194054604,
0.0407215915620327,
-0.02847222611308098,
-0.012632775120437145,
-0.006348588969558477,
-0.012642371468245983,
-0.008074255660176277,
0.03507096692919731,
-0.06058670952916145,
-0.04425440728664398,
0.023385044187307358,
-0.016199491918087006,
-0.02190443128347397,
0.007797782309353352,
0.024334412068128586,
0.0059906295500695705,
-0.009631644934415817,
-0.010629678145051003,
0.020614905282855034,
0.010916122235357761,
0.040508463978767395,
0.034278471022844315,
-0.006930491887032986,
0.03727598115801811,
0.035489074885845184,
0.048104383051395416,
-0.012659127824008465,
-0.002742793643847108,
0.003763331798836589,
0.07838527858257294,
-0.010100390762090683,
-0.006184824742376804,
0.00588339613750577,
-0.031397901475429535,
0.020412646234035492,
-0.05172303318977356,
-0.0043960679322481155,
-0.009059222415089607,
0.0041153309866786,
-0.03050423413515091,
0.011937038041651249,
0.01808273233473301,
0.0064569138921797276,
0.03155416622757912,
0.0006846764008514583,
-0.016713691875338554,
-0.00025216658832505345,
-0.0174272283911705,
-0.03386656194925308,
0.02842937409877777,
-0.012372966855764389,
0.008719458244740963,
-0.01940786838531494,
-0.011990532279014587,
-0.025733519345521927,
-0.025053156539797783,
-0.0028348274063318968,
0.0324641615152359,
0.029402421787381172,
-0.019222037866711617,
-0.004044536035507917,
-0.0413585864007473,
-0.021603042259812355,
0.010213318280875683,
-0.0010998580837622285,
-0.04026200994849205,
0.014388242736458778,
0.0035088949371129274,
-0.00379605358466506,
0.07460179924964905,
-0.014982430264353752,
0.019121214747428894,
-0.0024040425196290016,
0.04164140298962593,
0.025624815374612808,
-0.021721743047237396,
-0.03367570415139198,
0.009897101670503616,
0.013642046600580215,
-0.015549217350780964,
0.0322844535112381,
-0.011797589249908924,
0.017641425132751465,
0.031168628484010696,
-0.0022284428123384714,
0.03504974767565727,
-0.018688585609197617,
-0.061997879296541214,
0.027763905003666878,
-0.03931863233447075,
-0.0015005373861640692,
0.045474059879779816,
0.010622537694871426,
-0.05552275478839874,
-0.02092267945408821,
0.0009506770293228328,
0.023609861731529236,
0.009329124353826046,
0.019665859639644623,
-0.04422867298126221,
-0.044330619275569916,
-0.007442930247634649,
-0.014445320703089237,
-0.08534607291221619,
0.012605756521224976,
-0.04086841642856598,
0.05522705614566803,
-0.004998443182557821,
0.027264738455414772,
-0.0363733246922493,
0.017669672146439552,
-0.021067189052700996,
-0.0347854383289814,
0.0479334220290184,
0.026795348152518272,
0.016612231731414795,
-0.005667134188115597,
0.02302909828722477,
-0.0061048115603625774,
0.004168120678514242,
0.049475133419036865,
-0.023883970454335213,
-0.0250535998493433,
-0.013534055091440678,
-0.03124948963522911,
0.03862378001213074,
0.010994710959494114,
0.04011552780866623,
0.013424395583570004,
-0.01859630085527897,
-0.012187117710709572,
0.04795490577816963,
-0.01505277305841446,
-0.022563651204109192,
-0.01678486540913582,
-0.06326815485954285,
-0.023570150136947632,
-0.05492355301976204,
0.012986734509468079,
-0.002980890218168497,
0.02958594262599945,
-0.0020482426043599844,
-0.0380212627351284,
-0.020668307319283485,
-0.01634952612221241,
0.00567267369478941,
0.0005267593078315258,
-0.000530528777744621,
0.00463117053732276,
-0.0020225485786795616,
-0.0037999888882040977,
0.06567387282848358,
0.009942758828401566,
0.04492679610848427,
0.017024194821715355,
0.034003306180238724,
-0.042351171374320984,
-0.03960692882537842,
0.010911979712545872,
0.001162846339866519,
0.054763779044151306,
-0.026316067203879356,
0.08252483606338501,
0.00409048842266202,
-0.046923015266656876,
0.03519738093018532,
-0.023457633331418037,
0.019922291859984398,
-0.010837019421160221,
0.0014390416909009218,
-0.03887317329645157,
0.0707717090845108,
0.05715984106063843,
0.050859805196523666,
0.017002109438180923,
0.026500681415200233,
-0.024008173495531082,
-0.02440248429775238,
-0.031161664053797722,
0.0376327708363533,
0.015397222712635994,
-0.008198298513889313,
0.0688232034444809,
0.006855792831629515,
-0.021653668954968452,
0.0024731007870286703,
0.016538504511117935,
-0.016382558271288872,
0.0006114173447713256,
0.04224218428134918,
0.018832560628652573,
0.023717401549220085,
0.0170967448502779,
-0.0056615606881678104,
-0.0027678655460476875,
0.0034582773223519325,
0.019926443696022034,
0.016251705586910248,
-0.03556414321064949,
0.001110769808292389,
-0.002110860077664256,
-0.05440209433436394,
-0.012302751652896404,
0.019301146268844604,
-0.04350758716464043,
-0.026105400174856186,
-0.028584394603967667,
-0.02841661125421524,
0.016764940693974495,
-0.007694506086409092,
0.014209511689841747,
-0.03972766175866127,
0.005518652033060789,
0.029560359194874763,
0.007668884936720133,
-0.046011969447135925,
0.015653373673558235,
0.004483567550778389,
-0.04678698256611824,
0.01223108172416687,
0.030943769961595535,
0.004553916398435831,
-0.026971669867634773,
-0.008115561679005623,
-0.011285466141998768,
-0.011962248012423515,
-0.030994446948170662,
-0.017626207321882248,
-0.0254154484719038,
0.02573144994676113,
0.03588341176509857,
-0.00291808950714767,
-0.03174878656864166,
-0.025876082479953766,
0.0012727954890578985,
-0.07287382334470749,
0.019976764917373657,
0.01499952469021082,
-0.012331738136708736,
-0.04218200221657753,
-0.003244705032557249,
-0.01090339757502079,
0.042593538761138916,
0.026511987671256065,
-0.044413529336452484,
-0.021328678354620934,
0.03455078601837158,
-0.0023761834017932415,
-0.030091475695371628,
-0.03195770084857941,
-0.010453689843416214,
0.004141089506447315,
-0.033430926501750946,
0.00047698942944407463,
0.04004552587866783,
-0.04879974573850632,
0.055789537727832794,
0.006756078451871872,
-0.0020410390570759773,
0.040927205234766006,
0.007880252785980701,
-0.039883390069007874,
0.01943705417215824,
-0.0102883605286479,
-0.014008193276822567,
0.03564975783228874,
0.008234450593590736,
0.035280369222164154,
0.06078073009848595,
-0.04693010449409485,
-0.0318116769194603,
0.03391638770699501,
-0.019889701157808304,
-0.018251249566674232,
-0.03752410411834717,
0.0020545399747788906,
0.01688271202147007,
-0.011802715249359608,
0.026913566514849663,
0.038283973932266235,
-0.0195013340562582,
-0.021799415349960327,
0.04537072032690048,
-0.01838427037000656,
0.014777506701648235,
0.0030241271015256643,
0.01169870886951685,
0.024763736873865128,
0.01577542908489704,
0.049694303423166275,
0.010189739987254143,
-0.019617844372987747,
0.019348306581377983,
-0.013315482996404171,
-0.013204953633248806,
-0.024258781224489212,
0.02111196331679821,
-0.031387511640787125,
-0.006622761022299528,
-0.030970394611358643,
0.001136514823883772,
0.036202192306518555,
0.0019893322605639696,
0.021339241415262222,
-0.00846631359308958,
-0.020291540771722794,
0.06988900154829025,
-0.023735973984003067,
0.02441188506782055,
0.00727070914581418,
0.02263704687356949,
-0.019905956462025642,
0.012904595583677292,
0.012257042340934277,
0.06616569310426712,
0.0003035747504327446,
-0.010645236819982529,
-0.034641675651073456,
-0.02285008691251278,
-0.006058163475245237,
-0.07573312520980835,
-0.030510663986206055,
0.022688085213303566,
-0.007988879457116127,
0.03465317562222481,
-0.03339491784572601,
-0.037181396037340164,
-0.020096303895115852,
0.00828387401998043,
0.003120815847069025,
-0.01289207860827446,
0.011503761634230614,
0.027399778366088867,
-0.025273902341723442,
0.06743098050355911,
-0.035979967564344406,
0.014347882010042667,
0.0071707358583807945,
-0.0021893950179219246,
-0.00530765438452363,
-0.0017002624226734042
] |
<p>We all know that gravity decreases as the distance b/w the two increases. Hence </p>
<p>$$ g = G \frac{Mm}{r^2} $$ </p>
<p>hence acceleration due to gravity is inversely proportional to the distance b/w the 2 bodies.</p>
<p>Then why the gravity decreases as we go deep into the earth?</p>
| 50 |
[
0.006234153639525175,
-0.02877761796116829,
-0.0016853886190801859,
0.0009305644198320806,
0.0022264791186898947,
0.02813265658915043,
-0.00335568911395967,
-0.04079320281744003,
0.02054424025118351,
-0.014059662818908691,
-0.004665008746087551,
0.038478951901197433,
0.03306747227907181,
0.015843110159039497,
0.018515560775995255,
0.003286022460088134,
-0.015085632912814617,
0.004018289968371391,
0.0099750692024827,
-0.03512512519955635,
-0.018775787204504013,
0.012227541767060757,
0.019816195592284203,
0.011903840117156506,
-0.012150516733527184,
0.016291696578264236,
0.02702266536653042,
-0.012458128854632378,
0.0023874405305832624,
0.053370099514722824,
0.03770999610424042,
0.01099491585046053,
0.028291095048189163,
0.030034534633159637,
0.010916327126324177,
-0.009535296820104122,
-0.038039594888687134,
-0.008841327391564846,
-0.003969190642237663,
0.041646264493465424,
-0.025285499170422554,
-0.022238165140151978,
-0.014014134183526039,
0.051846109330654144,
-0.016260139644145966,
0.027998503297567368,
0.039809487760066986,
-0.025431619957089424,
0.018303140997886658,
-0.06524938344955444,
0.03288356587290764,
-0.00009853368101175874,
0.05277792364358902,
0.005396320950239897,
0.02825341373682022,
-0.01220646034926176,
0.09252668917179108,
0.08362476527690887,
-0.00870836153626442,
-0.03793151676654816,
-0.008179889060556889,
-0.03331766277551651,
-0.02986944653093815,
-0.026941141113638878,
0.01199202612042427,
0.04060719907283783,
-0.06625243276357651,
-0.004221512004733086,
-0.006072662305086851,
0.0006649311981163919,
0.0038971896283328533,
0.009292562492191792,
0.008351135067641735,
-0.016499444842338562,
0.009762556292116642,
-0.04006253182888031,
0.011308223940432072,
0.02897256426513195,
0.001186455599963665,
0.040136661380529404,
-0.013768005184829235,
-0.010409434325993061,
0.07842934876680374,
0.04264875128865242,
0.029049161821603775,
0.011542991735041142,
0.04301317408680916,
0.009140386246144772,
-0.014226994477212429,
0.04069870710372925,
-0.019715690985322,
0.016267098486423492,
-0.02390415035188198,
-0.016837410628795624,
0.006273847073316574,
0.027143659070134163,
-0.006714335177093744,
0.049657613039016724,
0.007494570687413216,
-0.017312463372945786,
0.0018982323817908764,
-0.005547332111746073,
0.006398338824510574,
0.062140703201293945,
0.02761620096862316,
-0.009220938198268414,
-0.07875935733318329,
0.006984297651797533,
-0.0047064353711903095,
-0.01067131757736206,
-0.016413597390055656,
0.01000418420881033,
-0.012136987410485744,
-0.02414225973188877,
0.017557702958583832,
-0.009537819772958755,
0.014121802523732185,
-0.02958771586418152,
0.03678956255316734,
0.03231297433376312,
0.03348122537136078,
-0.002404743107035756,
0.02871854603290558,
-0.034473225474357605,
-0.06420744210481644,
0.016320960596203804,
0.03886590898036957,
-0.030071109533309937,
-0.02498520538210869,
0.017412668094038963,
0.007498960476368666,
-0.014891279861330986,
-0.02629595808684826,
0.002955460688099265,
0.05900118872523308,
0.030777951702475548,
-0.09979027509689331,
-0.07012365013360977,
0.06512679904699326,
0.023699648678302765,
0.006736268755048513,
-0.06547755002975464,
0.02845274843275547,
0.014977538958191872,
0.07933605462312698,
0.04072627052664757,
0.013122865930199623,
0.013237646780908108,
0.010588138364255428,
0.00876954197883606,
0.031085608527064323,
-0.030957886949181557,
0.010857193730771542,
-0.04003152996301651,
0.022749684751033783,
-0.10641541332006454,
0.010077439248561859,
0.010371520183980465,
0.007217887789011002,
-0.0254520270973444,
0.043050989508628845,
-0.05019856616854668,
-0.0057946969754993916,
-0.0005647741490975022,
-0.015976043418049812,
-0.02352782152593136,
0.07721281796693802,
0.030972613021731377,
-0.0018403831636533141,
0.04120723530650139,
0.026642026379704475,
0.03473838418722153,
0.012057223357260227,
0.004967488814145327,
0.0074816360138356686,
-0.03168409317731857,
-0.030451560392975807,
-0.007878854870796204,
0.0016815324779599905,
0.01778929866850376,
-0.04215708002448082,
-0.04425860941410065,
0.0036923273000866175,
-0.0033745202235877514,
0.011911360546946526,
0.037753939628601074,
0.0007882793433964252,
-0.034673452377319336,
-0.005283733829855919,
-0.007038519252091646,
-0.0015458728885278106,
-0.07719523459672928,
0.033419739454984665,
0.03768488019704819,
-0.00389137607999146,
-0.009064911864697933,
0.025378640741109848,
0.007536813151091337,
-0.026691842824220657,
0.000953143578954041,
-0.013002200983464718,
0.010468769818544388,
-0.0085574546828866,
-0.008705862797796726,
0.01569504104554653,
0.056096773594617844,
0.0516023226082325,
0.017225515097379684,
0.0020022252574563026,
0.004708483349531889,
-0.031615328043699265,
0.007773036137223244,
-0.0229277852922678,
0.003612448927015066,
-0.01414461713284254,
-0.0024847874883562326,
0.014271693304181099,
0.01058389525860548,
0.003408536547794938,
0.03589978814125061,
-0.056244052946567535,
0.11504529416561127,
0.04181167855858803,
0.016404161229729652,
0.014928006567060947,
0.017170460894703865,
0.018379494547843933,
0.010501948185265064,
-0.01936025731265545,
-0.006411213427782059,
-0.06984836608171463,
-0.03057900071144104,
-0.01866764947772026,
0.01919453777372837,
-0.035706933587789536,
0.022223081439733505,
0.021555909886956215,
0.04476506635546684,
0.004511284176260233,
0.008883591741323471,
0.001615531975403428,
-0.07462714612483978,
0.0169602669775486,
0.02961917407810688,
0.0038490230217576027,
0.02233796752989292,
0.026770561933517456,
0.031790345907211304,
-0.0026023159734904766,
-0.04043574631214142,
-0.012351158075034618,
0.015030531212687492,
0.016669493168592453,
0.04525768756866455,
0.028205322101712227,
-0.02594888024032116,
0.029003946110606194,
-0.019667191430926323,
0.001669586170464754,
0.017324233427643776,
-0.001144631183706224,
0.007859335280954838,
-0.05011129751801491,
-0.020072948187589645,
0.031143752858042717,
0.015755940228700638,
-0.005971097387373447,
0.010549776256084442,
0.029957961291074753,
-0.06210213899612427,
0.0014006935525685549,
-0.05019156634807587,
-0.0062707168981432915,
-0.06898613274097443,
0.0004630009352695197,
0.009116333909332752,
0.009497479535639286,
0.014852287247776985,
-0.004149615298956633,
-0.015663698315620422,
0.00010282934817951173,
-0.029003679752349854,
-0.017454156652092934,
0.0019197462825104594,
-0.024531468749046326,
0.0478040836751461,
-0.01623860001564026,
-0.01394603680819273,
0.05612152814865112,
0.04357036575675011,
0.04712216928601265,
0.02110898680984974,
-0.024050507694482803,
-0.01633455790579319,
-0.01166361290961504,
0.0047580040991306305,
0.00007643258868483827,
-0.0037728066090494394,
0.021281450986862183,
0.07433810830116272,
-0.019357070326805115,
-0.008257891051471233,
-0.018107272684574127,
-0.07531506568193436,
-0.03562207892537117,
-0.026938585564494133,
0.006591595709323883,
-0.001437013503164053,
-0.011292630806565285,
-0.016780443489551544,
-0.001849189167842269,
-0.0675959587097168,
-0.02852301299571991,
-0.06371959298849106,
-0.01824718527495861,
0.04512793570756912,
0.02629532665014267,
0.030234266072511673,
-0.015737516805529594,
-0.04434860870242119,
0.06689523905515671,
0.05547936260700226,
-0.0024743210524320602,
-0.03996860980987549,
-0.015129047445952892,
0.019239112734794617,
-0.006588967517018318,
0.001613032422028482,
0.045621585100889206,
-0.018091656267642975,
0.0033612684346735477,
0.02585570700466633,
0.03946009278297424,
0.014862285926938057,
0.015294441021978855,
0.0014285487122833729,
-0.02074614353477955,
0.025917964056134224,
-0.019717955961823463,
0.026646802201867104,
0.012313861399888992,
0.004508454818278551,
-0.006836370564997196,
-0.005531464237719774,
0.05109439045190811,
0.002720549935474992,
-0.05453256890177727,
0.01643310859799385,
-0.004460220690816641,
0.01942574232816696,
-0.024257799610495567,
0.013331358321011066,
0.01802809163928032,
0.025002682581543922,
-0.006085589993745089,
0.00917808897793293,
0.04234815016388893,
-0.019453557208180428,
-0.04830903932452202,
-0.007730672601610422,
0.03546677902340889,
-0.04728445038199425,
-0.05722450092434883,
0.006181292235851288,
-0.0006120337056927383,
0.051607243716716766,
-0.011570300906896591,
-0.007227165624499321,
0.0489797405898571,
0.030075758695602417,
0.014421145431697369,
-0.007961695082485676,
-0.036810893565416336,
0.007738006301224232,
-0.0617033950984478,
-0.0031527241226285696,
-0.015234989114105701,
0.045698948204517365,
-0.001697744824923575,
0.03978252410888672,
0.037690822035074234,
0.030962077900767326,
0.03164156153798103,
0.0073297712951898575,
-0.11932546645402908,
0.010341261513531208,
-0.07501523196697235,
-0.01908147893846035,
0.009191886521875858,
-0.00567657919600606,
-0.04818650335073471,
-0.04210656136274338,
-0.011379959061741829,
-0.013068160973489285,
0.013281160034239292,
-0.04468502849340439,
-0.0027318301144987345,
0.002215462038293481,
-0.04309610649943352,
-0.04997701942920685,
0.029222115874290466,
0.03093165159225464,
0.006359900813549757,
0.04099981486797333,
0.028573060408234596,
-0.004403627477586269,
-0.019849009811878204,
0.003465864807367325,
-0.004312113858759403,
0.02375706285238266,
0.01672443374991417,
0.014884857460856438,
0.0016892536077648401,
-0.004019018728286028,
0.0065800766460597515,
0.01312353927642107,
0.01658891700208187,
-0.029973896220326424,
-0.01694430224597454,
-0.015840008854866028,
-0.02624932862818241,
-0.037276364862918854,
0.0014657577266916633,
0.028107330203056335,
-0.009453547187149525,
-0.000700382748618722,
0.02782035432755947,
-0.004492329433560371,
-0.0017623218009248376,
0.031977590173482895,
0.05585271865129471,
0.010378711856901646,
-0.029274920001626015,
-0.03660604730248451,
-0.049446914345026016,
-0.06296339631080627,
-0.02309224382042885,
0.04344134032726288,
-0.002477359725162387,
-0.0364961102604866,
-0.001390778343193233,
0.043127547949552536,
0.02553454041481018,
0.00956722442060709,
-0.03422574698925018,
-0.011176199652254581,
0.04792928695678711,
0.0022924223449081182,
0.005517458077520132,
-0.004397351294755936,
0.025491977110505104,
0.05755109339952469,
-0.04020152613520622,
-0.020180266350507736,
-0.09850136935710907,
-0.005497216712683439,
0.011988308280706406,
0.02256392501294613,
-0.028218528255820274,
0.030076870694756508,
-0.04413884878158569,
-0.039825160056352615,
0.03040139563381672,
-0.016155242919921875,
0.047891128808259964,
-0.035084858536720276,
0.02237114869058132,
-0.012698845006525517,
-0.03937646374106407,
-0.019964221864938736,
0.010133680887520313,
0.005298983305692673,
0.012634143233299255,
-0.003704650327563286,
0.02398507669568062,
-0.0027414450887590647,
0.022173814475536346,
0.04519680142402649,
0.054339151829481125,
0.040692005306482315,
0.010525323450565338,
-0.023128511384129524,
-0.012362640351057053,
-0.04108837991952896,
-0.042108215391635895,
-0.0381690077483654,
-0.0009174773585982621,
-0.011649579741060734,
0.020704595372080803,
-0.02131560444831848,
-0.040822699666023254,
0.03945041075348854,
0.02089705318212509,
-0.01781289093196392,
-0.011222047731280327,
-0.047940004616975784,
0.020782021805644035,
0.023172296583652496,
-0.036308757960796356,
0.047364406287670135,
-0.019661795347929,
-0.044600144028663635,
-0.031166303902864456,
-0.011573324911296368,
0.042219970375299454,
-0.07278399914503098,
-0.006999210920184851,
0.021889308467507362,
0.015873311087489128,
-0.02282259240746498,
0.018345847725868225,
0.009639771655201912,
0.012963793240487576,
-0.0034571525175124407,
-0.050510574132204056,
0.00012817367678508162,
0.01735670492053032,
0.035669874399900436,
0.05152866616845131,
0.029365427792072296,
0.01388299185782671,
0.02186162769794464,
-0.046155206859111786,
0.0034412406384944916,
0.01743832230567932,
-0.03172490745782852,
0.021972686052322388,
0.0021593982819467783,
0.01797337457537651,
-0.009912501089274883,
-0.024288034066557884,
0.02018699049949646,
-0.03966179117560387,
0.053197719156742096,
-0.020460007712244987,
-0.02040601521730423,
0.02585890144109726,
-0.028255024924874306,
-0.00878316443413496,
-0.018348371610045433,
-0.01837773807346821,
0.019553041085600853,
-0.06864666938781738,
0.05684557184576988,
0.04853029549121857,
0.04684719443321228,
-0.08555185794830322,
-0.03159962594509125,
0.00852137990295887,
0.011319858022034168,
-0.014200431294739246,
-0.016017457470297813,
-0.0022990230936557055,
-0.05517008155584335,
-0.032534465193748474,
-0.009496589191257954,
0.05244006589055061,
-0.009802212938666344,
0.0078073469921946526,
0.019251883029937744,
-0.0032306683715432882,
0.05955559387803078,
0.00010452937567606568,
-0.01577923633158207,
0.0025507837999612093,
0.009758391417562962,
0.01883196271955967,
-0.024155480787158012,
0.0892215371131897,
-0.02904636599123478,
-0.027164289727807045,
-0.0030868942849338055,
-0.035779815167188644,
0.006049594841897488,
-0.01644044928252697,
0.009684231132268906,
0.03371233120560646,
0.018728649243712425,
-0.016580380499362946,
0.0031196584459394217,
0.05687102675437927,
-0.019681241363286972,
0.0490795373916626,
-0.010462998412549496,
-0.0041871205903589725,
-0.05199922248721123,
-0.028040610253810883,
0.005879205651581287,
-0.008928850293159485,
0.019549427554011345,
-0.0241249892860651,
0.09174679219722748,
-0.011974918656051159,
-0.03914761543273926,
0.019269559532403946,
0.003354265121743083,
0.0037786527536809444,
0.003526122774928808,
-0.031752634793519974,
0.05099284648895264,
0.011276578530669212,
-0.018477752804756165,
0.002881861524656415,
-0.012820674106478691,
-0.0022509268019348383,
0.0795578584074974,
-0.030333906412124634,
0.05973753705620766,
0.011816147714853287,
-0.023457415401935577,
0.03865553438663483,
-0.041764769703149796,
-0.012535600923001766,
-0.012764587998390198,
-0.010370231233537197,
0.015359411016106606,
-0.02139970101416111,
-0.006149694323539734,
0.030398141592741013,
0.05065367370843887,
-0.02672887220978737,
0.011146776378154755,
-0.0024193874560296535,
0.009867852553725243,
-0.0036452081985771656,
-0.014190729707479477,
-0.02654379978775978,
0.032380152493715286,
-0.009896636940538883,
0.04330368712544441,
0.0021275056060403585,
-0.004087045788764954,
0.05346010625362396,
0.0043382043950259686,
0.017414525151252747,
-0.0428692027926445,
-0.01224945392459631,
-0.016768189147114754,
0.0005566119216382504,
0.029768558219075203,
0.012258629314601421,
-0.03563862666487694,
0.041839078068733215,
0.015766974538564682,
-0.016428524628281593,
-0.00489726522937417,
0.004348112735897303,
-0.07834143191576004,
-0.024931788444519043,
-0.03849451243877411,
-0.04623446613550186,
0.019315330311655998,
-0.011654751375317574,
-0.03426111862063408,
0.004348620772361755,
-0.02186787687242031,
0.0037896307185292244,
0.03708168864250183,
0.0012251557782292366,
-0.021788595244288445,
0.10187840461730957,
-0.0016484789084643126,
0.00197666441090405,
0.016373395919799805,
-0.0046027484349906445,
0.10855040699243546,
0.047223031520843506,
0.0009767793817445636,
-0.039044033735990524,
0.03895300254225731,
-0.028446797281503677,
0.030122801661491394,
-0.04121536761522293,
0.02154674008488655,
-0.0031103428918868303,
0.02060258388519287,
0.01477006170898676,
0.04968564957380295,
-0.016738014295697212,
-0.042542465031147,
0.058898717164993286,
-0.033969197422266006,
-0.03906994313001633,
-0.015554901212453842,
0.010194397531449795,
-0.02298293076455593,
0.017407719045877457,
-0.002164339879527688,
0.036145228892564774,
-0.03413935378193855,
0.001271539949811995,
-0.029011864215135574,
-0.038873255252838135,
0.0036201211623847485,
-0.011874368414282799,
-0.08358648419380188,
0.019845008850097656,
0.005746499635279179,
-0.05072652921080589,
-0.05386658012866974,
0.032991018146276474,
0.021535713225603104,
-0.030079683288931847,
-0.022105369716882706,
-0.0039020918775349855,
-0.013721838593482971,
0.03749561682343483,
-0.01205568015575409,
0.03519270196557045,
-0.05876759812235832,
0.035340309143066406,
-0.01922331377863884,
0.052295975387096405,
-0.026303453370928764,
0.01241279672831297,
0.006853801663964987,
0.03096749261021614,
-0.01334409136325121,
-0.036850620061159134,
-0.004237307235598564,
-0.00041252360097132623,
0.021918216720223427,
-0.00390785513445735,
-0.04943886026740074,
-0.010171374306082726,
-0.007409242447465658,
0.018498284742236137,
0.022392645478248596,
-0.00672354269772768,
0.02328328602015972,
0.015565656125545502,
0.0021956057753413916,
0.04613741487264633,
-0.05271836370229721,
-0.010791751556098461,
-0.061905983835458755,
0.023555241525173187,
-0.038345105946063995,
-0.003510556183755398,
0.014907206408679485,
0.03536834940314293,
0.018956949934363365,
0.01879328303039074,
-0.015446805395185947,
-0.03264284133911133,
-0.043302346020936966,
0.05659446492791176,
-0.01350702065974474,
-0.0007985451957210898,
-0.06309425830841064,
0.002510913647711277,
0.01433473452925682,
0.01138635165989399,
-0.027168981730937958,
-0.022252894937992096,
-0.020095396786928177,
0.02604246884584427,
0.01181995589286089,
-0.02822173573076725,
-0.016837652772665024,
-0.00142852368298918,
-0.0060988967306911945,
-0.014610911719501019,
0.03171839192509651,
0.010153449140489101,
0.026405468583106995,
0.002042780164629221,
-0.005796606186777353,
0.010159055702388287,
-0.03652086853981018,
0.03005288727581501,
0.001991953467950225,
0.00230049854144454,
-0.006782557815313339,
0.02300359308719635,
0.005613924004137516,
-0.048838336020708084,
0.00733249681070447,
-0.011868201196193695,
-0.00025757894036360085,
0.0006044746842235327,
0.0396280437707901,
-0.0007808031514286995,
0.026171423494815826,
-0.022178715094923973,
0.022266225889325142,
-0.0591026172041893,
0.012201369740068913,
-0.05961281433701515,
-0.022944658994674683,
-0.004896753933280706,
-0.02139274775981903,
0.0034975199960172176,
0.01259351521730423,
-0.05282570421695709,
-0.007787778042256832,
0.029913509264588356,
-0.00044736452400684357,
0.00814168993383646,
0.012207498773932457,
0.04928421974182129,
-0.041531842201948166,
0.030528360977768898,
-0.02013658918440342,
-0.04735035449266434,
0.03250802680850029,
-0.020419884473085403,
-0.05639320984482765,
0.04431658610701561,
-0.024762434884905815,
0.03507804498076439,
-0.005839962512254715,
-0.031483620405197144,
-0.025328394025564194,
0.04503626003861427,
-0.01432221382856369,
-0.007853172719478607,
-0.0282390508800745,
-0.0151362968608737,
-0.025033192709088326,
0.0016822798643261194,
-0.012419584207236767,
-0.05267909914255142,
0.013410812243819237,
0.023534633219242096,
0.011969920247793198,
0.0016837420407682657,
0.023974847048521042,
0.008451582863926888,
-0.01155051589012146,
-0.008858615532517433,
0.01927170902490616,
0.0067063625901937485,
0.04152347892522812,
0.039076659828424454,
-0.02290952205657959,
0.038417600095272064,
0.02564583532512188,
0.004634729586541653,
-0.06793059408664703,
-0.012438420206308365,
0.0032435061875730753,
0.0000755689397919923,
0.04034503549337387,
-0.07395539432764053,
0.0032771355472505093,
0.01744089275598526,
-0.0966784730553627,
0.054562825709581375,
-0.03499731421470642,
-0.004063419997692108,
0.001355667132884264,
-0.01754455454647541,
0.030582936480641365,
0.04291068762540817,
0.03185046464204788,
0.03412160649895668,
-0.004536423832178116,
0.002055720193311572,
0.0016800588928163052,
-0.022403473034501076,
-0.01864222064614296,
0.02710178680717945,
-0.02617555297911167,
0.04974542185664177,
0.06319624930620193,
0.01832203008234501,
-0.0030365546699613333,
0.01184360682964325,
-0.014463839121162891,
0.02117701806128025,
0.006542838178575039,
-0.012600760906934738,
-0.010613217018544674,
0.02812192589044571,
-0.012443444691598415,
0.00043704514973796904,
-0.009725017473101616,
0.012083983980119228,
0.012217368930578232,
0.04203447699546814,
-0.005037951748818159,
-0.004460656084120274,
0.009656568989157677,
-0.03324242681264877,
0.006147143896669149,
0.03128833323717117,
-0.019735032692551613,
0.016320452094078064,
0.01262515690177679,
0.013576272875070572,
0.021126525476574898,
-0.043196555227041245,
-0.021042674779891968,
-0.019928421825170517,
-0.012868855148553848,
0.03930884972214699,
-0.02656679041683674,
-0.023769689723849297,
0.041909072548151016,
0.013084798119962215,
-0.006990530528128147,
-0.026696080341935158,
-0.006308089010417461,
-0.008762598037719727,
-0.029758501797914505,
-0.006509461440145969,
0.006815098226070404,
0.002574080368503928,
0.00885313656181097,
-0.042347751557826996,
-0.03331023082137108,
0.07973801344633102,
0.007854959927499294,
0.026702022179961205,
-0.008037700317800045,
-0.0242209080606699,
-0.03795377537608147,
-0.06815940886735916,
0.02110227197408676,
-0.009621568024158478,
-0.04640056565403938,
-0.023935021832585335,
-0.023662826046347618,
-0.0005822941893711686,
-0.014616651460528374,
0.06673746556043625,
0.03149895370006561,
0.020451582968235016,
0.012825238518416882,
0.026494067162275314,
0.006591149605810642,
-0.049713313579559326,
0.013445861637592316,
0.026026364415884018,
-0.04243026673793793,
-0.0005590192740783095,
0.005157030187547207,
-0.020397301763296127,
0.006824729032814503,
-0.03417044132947922,
-0.028022602200508118,
0.05606142431497574,
0.0208685714751482,
0.00598166324198246,
0.03509485349059105,
0.011708874255418777,
0.0026948400773108006,
0.092075414955616,
-0.016076745465397835,
0.0154148293659091,
0.005553764756768942,
0.003863021731376648,
-0.03150426596403122,
0.0321790911257267,
-0.006033934652805328,
0.025045758113265038,
-0.015864018350839615,
0.010133654810488224,
0.033222299069166183,
-0.03352062776684761,
-0.011409441940486431,
0.04222186282277107,
-0.04720413312315941,
-0.008644582703709602,
0.04509252682328224,
0.021068090572953224,
0.03181295841932297,
-0.02994750253856182,
0.051749978214502335,
0.004496805369853973,
-0.01522074081003666,
0.023622101172804832,
0.039193421602249146,
0.009159205481410027,
-0.003935034852474928,
-0.016665596514940262,
0.07808005064725876,
0.017057109624147415,
0.03235163912177086,
0.02294665388762951,
0.039927639067173004,
-0.03683141618967056,
-0.0356927327811718,
-0.03286588937044144,
-0.0492158867418766,
0.016235729679465294,
0.017202429473400116,
-0.014730584807693958,
0.07122354954481125,
-0.010335979983210564,
-0.0122491754591465,
0.010629330761730671,
-0.03888441249728203,
-0.02510477788746357,
0.009556208737194538,
0.011169836856424809,
0.024210333824157715,
0.026244793087244034,
-0.014470519497990608,
0.012727132998406887,
-0.039175208657979965,
0.008815951645374298,
0.01087264809757471,
0.021994752809405327,
0.011020355857908726,
-0.009613573551177979,
-0.00905633345246315,
-0.004694594070315361,
-0.026657765731215477,
-0.024925250560045242,
0.06380177289247513,
0.05659108608961105,
0.03134208917617798,
-0.01725979708135128,
0.00035744268097914755,
-0.017880616709589958,
0.06791786849498749,
-0.08070562034845352,
-0.03196103498339653,
-0.034805577248334885,
0.00042540644062682986,
-0.023685168474912643,
-0.029569333419203758
] |
<p>Within the framework of string theory, I have read in numerous articles such as the introduction of this <a href="http://arxiv.org/pdf/1305.3607.pdf" rel="nofollow">this</a> in which it is stated that the gauge theories living on a stack of D-branes can be used to <em>probe a spacetime singularity</em>, such as for example a <a href="http://en.wikipedia.org/wiki/Calabi%E2%80%93Yau_manifold" rel="nofollow">Calabi-Yau</a> or <a href="http://en.wikipedia.org/wiki/Toric_variety" rel="nofollow">toric</a> one.</p>
<p>What is exactly meant by that?</p>
| 8,853 |
[
-0.00035806879168376327,
-0.0036137502174824476,
0.014961672015488148,
-0.0718756914138794,
0.041672516614198685,
0.055844128131866455,
-0.006501701660454273,
-0.02498694695532322,
0.02754919044673443,
-0.03150187432765961,
0.01767301745712757,
0.011965482495725155,
0.0236678346991539,
0.012792766094207764,
0.011595216579735279,
0.023673666641116142,
-0.040875885635614395,
-0.03083549253642559,
0.0017871852032840252,
-0.04026849567890167,
0.029635114595294,
0.005450127180665731,
-0.02035451866686344,
0.03318068012595177,
0.000817334686871618,
-0.023491647094488144,
0.003831373294815421,
0.01631336286664009,
0.008248736150562763,
0.05944328382611275,
-0.0115791792050004,
-0.012154988013207912,
0.022081511095166206,
0.005915878340601921,
-0.0022178899962455034,
-0.007610938977450132,
-0.023983323946595192,
-0.02812119945883751,
0.01991947554051876,
0.02012682892382145,
0.00983879342675209,
-0.042544618248939514,
-0.017360616475343704,
0.08685877174139023,
-0.040811557322740555,
0.024474674835801125,
-0.028844378888607025,
-0.05693452060222626,
0.05933205783367157,
-0.10305080562829971,
0.05633692443370819,
-0.00481999758630991,
-0.013822026550769806,
0.033834490925073624,
0.005587490275502205,
0.015503010712563992,
0.05548279359936714,
0.07938003540039062,
-0.027959100902080536,
-0.040474556386470795,
-0.06215165928006172,
0.006111809518188238,
0.005802938248962164,
-0.03186532109975815,
-0.04697529226541519,
0.03770841658115387,
-0.01411342341452837,
-0.007310705259442329,
0.010679012164473534,
-0.04525697976350784,
-0.009949680417776108,
0.008410877548158169,
0.012998975813388824,
0.005780021660029888,
0.039285797625780106,
-0.01261668186634779,
0.00043229255243204534,
-0.024878347292542458,
0.06467117369174957,
0.03315625712275505,
0.02021673135459423,
-0.008492405526340008,
0.008808666840195656,
-0.004737746901810169,
0.02441726252436638,
-0.006665357854217291,
0.07304900884628296,
-0.02279219962656498,
0.0019926277454942465,
0.03727685287594795,
-0.014679627493023872,
-0.0337115041911602,
0.05974002182483673,
-0.017301300540566444,
-0.03241114318370819,
0.0034625758416950703,
0.01111743412911892,
0.04421976953744888,
-0.03756192699074745,
-0.025173550471663475,
-0.025719987228512764,
-0.011550160124897957,
0.022852901369333267,
0.0790625512599945,
0.016937311738729477,
-0.014836842194199562,
-0.01394196692854166,
0.018634604290127754,
-0.007060803938657045,
-0.010780064389109612,
-0.05101655423641205,
0.02100038342177868,
-0.016486240550875664,
0.0008888315642252564,
-0.006175115704536438,
0.0014460210222750902,
-0.00836229044944048,
-0.01773832179605961,
0.05527713894844055,
0.05356002599000931,
0.038149937987327576,
-0.020109422504901886,
0.01696092262864113,
-0.03798770159482956,
-0.07641898095607758,
0.04734128341078758,
0.05987925827503204,
0.010587390512228012,
-0.02964889444410801,
0.01843528263270855,
0.0042189680971205235,
-0.02134634740650654,
-0.0028745410963892937,
0.006882212124764919,
0.048546094447374344,
-0.03125006705522537,
-0.09059679508209229,
-0.033483657985925674,
0.0483664870262146,
0.025616636499762535,
-0.023608073592185974,
-0.05789020285010338,
-0.02177422121167183,
0.03300304338335991,
0.09393260627985,
-0.007056426722556353,
0.02300463803112507,
0.007681706920266151,
0.024658281356096268,
-0.006532674189656973,
-0.030368858948349953,
-0.024585383012890816,
-0.0012256649788469076,
-0.030281690880656242,
-0.015390097163617611,
-0.06507813185453415,
0.005867274012416601,
0.02804330550134182,
-0.006625331472605467,
-0.02287536859512329,
0.07541476935148239,
-0.02060732990503311,
-0.0053182803094387054,
0.05418890714645386,
-0.032012324780225754,
0.02792092226445675,
0.11041595786809921,
0.018770921975374222,
-0.01561915222555399,
0.05661972239613533,
-0.024749698117375374,
0.02008356712758541,
0.04141969233751297,
0.05697167292237282,
0.0033728850539773703,
-0.034099675714969635,
-0.02805403433740139,
0.00027655024314299226,
0.016104023903608322,
-0.00846830289810896,
-0.03580944612622261,
-0.028047911822795868,
0.0028750025667250156,
0.010642549954354763,
0.002759709255769849,
0.053849078714847565,
-0.036950938403606415,
-0.039337802678346634,
-0.006943278014659882,
-0.056122325360774994,
-0.009741241112351418,
-0.03850170224905014,
-0.004805362783372402,
-0.02642248198390007,
0.022535130381584167,
0.012482333928346634,
-0.0018192766001448035,
0.01909659616649151,
-0.029799582436680794,
-0.021463004872202873,
0.017074966803193092,
0.044191546738147736,
-0.002848860342055559,
0.015897123143076897,
0.01834779791533947,
0.025428470224142075,
0.03589879348874092,
-0.03640466928482056,
0.03471758961677551,
-0.0018957068677991629,
-0.001971712103113532,
0.004845202900469303,
-0.011083866469562054,
0.03694777190685272,
-0.014294599182903767,
0.017470229417085648,
0.02461249567568302,
0.029267573729157448,
-0.030032716691493988,
0.05177997797727585,
-0.047301262617111206,
0.04898221418261528,
0.03213917091488838,
0.044470470398664474,
-0.019290924072265625,
0.037684500217437744,
0.013601127080619335,
0.03938226401805878,
-0.017080800607800484,
-0.03510651737451553,
-0.058772873133420944,
-0.0033227328676730394,
0.05059327557682991,
0.037157829850912094,
-0.005967795383185148,
0.02040090784430504,
0.05451153963804245,
0.031316690146923065,
-0.008705544285476208,
0.0588875487446785,
-0.01703781820833683,
0.02303941920399666,
0.006859084591269493,
-0.015009823255240917,
0.0037250269670039415,
0.007610964123159647,
0.026692593470215797,
0.01693999394774437,
-0.022913601249456406,
-0.010434639640152454,
-0.023850707337260246,
0.08428886532783508,
-0.018653856590390205,
0.0062359971925616264,
0.03547893092036247,
-0.010640380904078484,
0.04258076101541519,
-0.007930951192975044,
0.027819829061627388,
0.035662345588207245,
0.024859942495822906,
0.02550378069281578,
-0.03195326030254364,
0.0029029627330601215,
0.03216484189033508,
0.04932110011577606,
0.002216141205281019,
-0.01737314462661743,
-0.0006391947972588241,
-0.045606426894664764,
0.013977857306599617,
0.02751120924949646,
-0.007704933639615774,
0.0008543295552954078,
0.027833834290504456,
0.01349970418959856,
0.007021828554570675,
0.04719823598861694,
-0.012414035387337208,
-0.03265228495001793,
0.03808852285146713,
-0.04959478974342346,
-0.001622798852622509,
0.01804225519299507,
-0.035413648933172226,
0.029815005138516426,
-0.053583208471536636,
-0.00145711877848953,
0.015912765637040138,
-0.015481610782444477,
0.028128406032919884,
-0.033668164163827896,
-0.01582009345293045,
-0.011200138367712498,
-0.028453795239329338,
0.013281496241688728,
0.021182170137763023,
-0.007711105514317751,
0.025514045730233192,
0.05411169305443764,
0.03093891404569149,
-0.017744652926921844,
0.002622123807668686,
-0.027947641909122467,
-0.026485159993171692,
-0.004165190737694502,
-0.019963227212429047,
0.0003262331010773778,
-0.0440286248922348,
0.03449859842658043,
0.004299374762922525,
-0.062279462814331055,
-0.007463760208338499,
-0.04735689237713814,
-0.06273836642503738,
0.014036889187991619,
0.003300194162875414,
0.031257305294275284,
-0.025202959775924683,
-0.07575186342000961,
0.04885312169790268,
-0.01353471726179123,
-0.028451764956116676,
0.010259291157126427,
-0.01501332689076662,
-0.040112387388944626,
-0.014506980776786804,
0.03978889063000679,
0.015643572434782982,
-0.040971361100673676,
0.003668061690405011,
0.05602524057030678,
0.04512724652886391,
0.026874752715229988,
0.02691253274679184,
-0.04526612535119057,
-0.012678618542850018,
0.03237021714448929,
-0.0008828920545056462,
0.02333819307386875,
0.0037454853300005198,
-0.01747710257768631,
-0.02194931171834469,
-0.019006650894880295,
-0.014082423411309719,
0.03316258639097214,
-0.039121925830841064,
0.029412711039185524,
-0.0005557602271437645,
-0.01824367418885231,
0.01906508393585682,
0.020293720066547394,
0.006987510249018669,
-0.030241383239626884,
0.0027771973982453346,
0.02725016511976719,
0.054979242384433746,
-0.015395796857774258,
-0.03641348332166672,
-0.0003906741621904075,
0.048549726605415344,
-0.03790755569934845,
-0.020124264061450958,
-0.01137419044971466,
-0.015121538192033768,
0.019633114337921143,
-0.024749254807829857,
-0.00922451727092266,
0.037905387580394745,
0.033859528601169586,
0.02447311021387577,
-0.038103580474853516,
-0.03461268171668053,
0.022847937420010567,
-0.06307541579008102,
0.023562058806419373,
0.020908528938889503,
0.0627497211098671,
0.016772791743278503,
0.019060200080275536,
0.024802030995488167,
-0.00999264232814312,
0.01356858666986227,
-0.03130416199564934,
-0.06347141414880753,
-0.022058431059122086,
-0.03536904603242874,
0.004642064683139324,
0.003874284913763404,
-0.026686519384384155,
0.03602488711476326,
0.03933527320623398,
-0.050859104841947556,
-0.04248642548918724,
-0.004302050918340683,
-0.07140102982521057,
0.02336724102497101,
-0.03357845917344093,
-0.05403778702020645,
-0.003600028809159994,
0.04128243401646614,
0.057782817631959915,
-0.0038488274440169334,
-0.02413884922862053,
0.025543203577399254,
-0.04018092155456543,
-0.030114522203803062,
0.021577948704361916,
0.03631950169801712,
0.01599641516804695,
0.04535611346364021,
0.022412080317735672,
0.007641134317964315,
-0.03870455548167229,
0.0357806570827961,
0.03780859336256981,
0.04114687815308571,
-0.03038826398551464,
-0.007363053970038891,
-0.025034833699464798,
-0.036013163626194,
-0.013508367352187634,
-0.04828539490699768,
0.06477248668670654,
-0.03351837024092674,
-0.023329969495534897,
0.041886940598487854,
0.01409941166639328,
-0.014295628294348717,
0.06169296056032181,
0.012564131990075111,
-0.010132966563105583,
-0.051993418484926224,
-0.05553695559501648,
-0.02339085564017296,
-0.029835816472768784,
-0.01623058132827282,
0.005661592353135347,
-0.024810491129755974,
-0.05640983581542969,
0.011890275403857231,
0.043636538088321686,
0.0026134802028536797,
-0.04175718128681183,
-0.009680246002972126,
0.011917524971067905,
-0.03127031773328781,
-0.020545586943626404,
0.0055645424872636795,
-0.01608649268746376,
0.0036907638423144817,
0.031214514747262,
0.013859846629202366,
0.003899485571309924,
-0.0931093692779541,
-0.0045533981174230576,
0.03127365931868553,
-0.0037039080634713173,
-0.005505342967808247,
-0.04263462498784065,
-0.041037969291210175,
-0.00544741889461875,
0.038327328860759735,
-0.014051742851734161,
0.028598980978131294,
-0.020068421959877014,
0.017124170437455177,
-0.02505718544125557,
-0.00077882717596367,
0.03313954174518585,
0.02474236860871315,
-0.01433197408914566,
0.03638770803809166,
-0.026629021391272545,
-0.0197360310703516,
-0.012178591452538967,
-0.00007775851554470137,
0.009285812266170979,
0.03864453360438347,
0.018023384734988213,
-0.0028045796789228916,
0.023958958685398102,
0.0421442985534668,
-0.008313392288982868,
-0.06646543741226196,
0.028865894302725792,
0.026863930746912956,
-0.03477685526013374,
0.054771117866039276,
-0.04332295060157776,
-0.015607686713337898,
0.02265237644314766,
0.02887352928519249,
0.021824678406119347,
-0.008898953907191753,
-0.030017254874110222,
0.023230984807014465,
0.06101999431848526,
-0.009433727711439133,
0.019453251734375954,
0.001253112917765975,
-0.008305621333420277,
-0.017828498035669327,
-0.035108841955661774,
0.033810198307037354,
-0.023019395768642426,
-0.009562879800796509,
-0.022871846333146095,
-0.011770465411245823,
-0.041311364620923996,
0.029348766431212425,
-0.008450178429484367,
0.02765687368810177,
-0.018217260017991066,
-0.0547814704477787,
-0.0166725292801857,
0.0071901967748999596,
0.03933829814195633,
-0.011852000840008259,
0.015425167046487331,
0.03526098653674126,
0.009198380634188652,
0.006464894860982895,
0.0014512140769511461,
-0.01226173248142004,
0.029466480016708374,
0.03531631827354431,
0.011027556844055653,
0.010647919028997421,
-0.014506553299725056,
-0.013069472275674343,
0.04905417934060097,
-0.057905491441488266,
0.03710220381617546,
-0.0026854851748794317,
-0.007897436618804932,
0.020077580586075783,
-0.03629802167415619,
-0.013145974837243557,
0.010231777094304562,
-0.015479444526135921,
0.011355854570865631,
-0.054639581590890884,
0.02126903645694256,
-0.002896660938858986,
0.008973455987870693,
-0.0820087343454361,
-0.029433434829115868,
0.0407748818397522,
0.006664873566478491,
-0.03371741995215416,
-0.029515665024518967,
0.02281966805458069,
-0.033076509833335876,
-0.023945998400449753,
-0.02633208967745304,
0.054877255111932755,
-0.048596158623695374,
-0.012294916436076164,
0.00035600370028987527,
0.053380269557237625,
0.01871524751186371,
0.004647738765925169,
-0.023085277527570724,
0.0001744549663271755,
-0.012358271516859531,
0.03505653142929077,
-0.019988980144262314,
0.010799936018884182,
-0.01731955073773861,
-0.023469557985663414,
-0.0433870404958725,
-0.0216356310993433,
0.012962444685399532,
-0.0143797118216753,
0.029331019148230553,
0.055976271629333496,
0.029344860464334488,
0.03848440572619438,
-0.029292644932866096,
0.011885706335306168,
0.012096051126718521,
-0.00207207421772182,
-0.045934177935123444,
0.008411003276705742,
-0.011433935724198818,
-0.027811886742711067,
0.046652741730213165,
-0.04458857327699661,
0.011974984779953957,
0.01896856538951397,
0.058602701872587204,
-0.007281856145709753,
-0.015655972063541412,
-0.0009145167423412204,
-0.030492905527353287,
-0.007126431446522474,
-0.009250921197235584,
0.022111190482974052,
0.0224141888320446,
0.015743331983685493,
-0.004980364348739386,
-0.05363155156373978,
-0.0121470857411623,
0.0255904383957386,
0.06048349663615227,
-0.010621638968586922,
0.04563805088400841,
0.034147921949625015,
-0.018652155995368958,
0.02103051170706749,
-0.021880662068724632,
-0.006691675633192062,
0.00528673967346549,
0.006195950321853161,
0.028968753293156624,
-0.03887397050857544,
-0.026625018566846848,
0.04680324345827103,
0.03495566174387932,
-0.04346621781587601,
0.03268161416053772,
0.05330077186226845,
0.0180561151355505,
0.031835876405239105,
0.0054861921817064285,
-0.043442580848932266,
0.05506046488881111,
-0.04286058247089386,
0.025207053869962692,
0.016407206654548645,
0.007509228773415089,
0.029214909300208092,
0.018632065504789352,
0.01928742416203022,
-0.004337810445576906,
-0.03248552978038788,
-0.0495726615190506,
0.060759905725717545,
0.03493041917681694,
0.018534818664193153,
0.018806451931595802,
-0.005973863415420055,
0.035357069224119186,
-0.00755351223051548,
0.01460378896445036,
0.006249073427170515,
-0.08114043623209,
-0.07056508958339691,
-0.03337423875927925,
-0.059536781162023544,
0.04740110784769058,
-0.00027726611006073654,
-0.0036220112815499306,
-0.01892300322651863,
-0.06733960658311844,
0.030367976054549217,
-0.011772345751523972,
0.06775697320699692,
-0.03241989389061928,
0.0473298616707325,
-0.019540250301361084,
0.00734555022791028,
-0.04434119910001755,
0.008295923471450806,
0.11437316238880157,
0.048597756773233414,
-0.014158441685140133,
-0.11453062295913696,
-0.010636497288942337,
-0.015441061928868294,
0.034247126430273056,
-0.04568392038345337,
0.00008286166848847643,
0.01633346825838089,
-0.00019005867943633348,
-0.019756902009248734,
0.034841734915971756,
-0.020132234320044518,
-0.009502728469669819,
0.023908313363790512,
-0.031578294932842255,
-0.06062699481844902,
0.029020870104432106,
0.04036472737789154,
-0.016643118113279343,
0.00753802340477705,
-0.05975580960512161,
0.009898514486849308,
-0.00624253461137414,
0.004887046292424202,
-0.022654904052615166,
-0.003704530419781804,
0.002356132725253701,
0.03854890912771225,
-0.022336801514029503,
0.02229432575404644,
-0.002236591186374426,
-0.00975516252219677,
-0.03750342130661011,
0.01682845689356327,
-0.011691083200275898,
0.021671347320079803,
0.015546634793281555,
0.04260457679629326,
-0.024538151919841766,
-0.01770785078406334,
-0.014038816094398499,
0.031997259706258774,
-0.03958364203572273,
-0.0016215977957472205,
-0.003653651336207986,
0.012005047872662544,
0.007742331828922033,
0.018331345170736313,
-0.025800973176956177,
-0.023049388080835342,
0.019456159323453903,
-0.003337734378874302,
-0.003291893983259797,
-0.00017448699509259313,
0.01006248313933611,
-0.044512029737234116,
-0.00737119372934103,
0.02873944491147995,
0.021155590191483498,
-0.006725708022713661,
0.011925116181373596,
-0.011595389805734158,
-0.019220534712076187,
-0.0024017756804823875,
-0.02265767753124237,
0.005436593201011419,
-0.019953526556491852,
0.011229845695197582,
-0.023164546117186546,
-0.00006232432497199625,
-0.02285398542881012,
0.021129587665200233,
0.012323785573244095,
0.060732826590538025,
0.03148476034402847,
0.009896557778120041,
-0.005956231150776148,
0.016753442585468292,
-0.008718257769942284,
0.03276101127266884,
-0.022142870351672173,
-0.02981342002749443,
-0.02653736248612404,
0.040319714695215225,
0.03907107189297676,
0.03285148739814758,
0.006166242994368076,
-0.001361529459245503,
0.018811924383044243,
0.02241465449333191,
0.017038587480783463,
-0.023999042809009552,
-0.00896333996206522,
0.0077796317636966705,
-0.019062098115682602,
-0.02664928510785103,
-0.010011308826506138,
0.026475628837943077,
0.03243545442819595,
-0.007374106906354427,
-0.000842131266836077,
0.06782252341508865,
-0.029863877221941948,
-0.00989440269768238,
0.03685138747096062,
-0.008457350544631481,
0.002735404996201396,
0.02042338065803051,
0.011099960654973984,
-0.03117852658033371,
-0.022994456812739372,
0.002500871429219842,
-0.01697366125881672,
-0.007531777024269104,
0.026120370253920555,
-0.0586298331618309,
0.023200595751404762,
-0.004653078503906727,
0.006264015566557646,
-0.05622684210538864,
-0.04643115773797035,
-0.02913530543446541,
0.04261011630296707,
-0.021441666409373283,
0.022184055298566818,
0.023356692865490913,
0.022112498059868813,
-0.032144200056791306,
-0.039680399000644684,
0.033160436898469925,
0.021281259134411812,
-0.05511470511555672,
0.004757876042276621,
-0.012533009983599186,
0.005529525224119425,
0.026391983032226562,
-0.01185397244989872,
-0.03737367317080498,
0.021112147718667984,
-0.050936177372932434,
-0.055623091757297516,
0.04912866652011871,
0.002215044805780053,
0.028870582580566406,
0.03279540315270424,
-0.017738208174705505,
-0.03946768492460251,
0.03994423896074295,
0.018232354894280434,
-0.020831771194934845,
0.032894205302000046,
-0.034641943871974945,
-0.04324037581682205,
-0.01987937092781067,
0.03074265457689762,
-0.006538414396345615,
0.004792706109583378,
-0.03878112509846687,
-0.0044649867340922356,
0.0002441883261781186,
-0.024483470246195793,
-0.010625429451465607,
-0.0506594255566597,
0.03443906083703041,
-0.014348004013299942,
0.0020269383676350117,
0.02655576355755329,
0.0631563737988472,
-0.040868423879146576,
0.004744985140860081,
0.013461671769618988,
-0.015569007024168968,
-0.0935797467827797,
-0.003956756554543972,
0.035013508051633835,
0.034135784953832626,
0.029805412515997887,
0.009286660701036453,
-0.007050658576190472,
0.047463517636060715,
-0.042913421988487244,
0.026058237999677658,
-0.014259199611842632,
-0.006302573252469301,
-0.007145993877202272,
0.008389221504330635,
-0.01652137190103531,
0.05456230044364929,
0.03962263837456703,
0.015554996207356453,
0.0020060925744473934,
0.008839157409965992,
-0.05238737910985947,
-0.030199924483895302,
0.002826252719387412,
0.04895726591348648,
-0.03481107950210571,
-0.035395167768001556,
0.08316310495138168,
-0.021456405520439148,
-0.04179548844695091,
0.025833776220679283,
0.01769029162824154,
-0.009908050298690796,
0.02586119808256626,
-0.010097263380885124,
0.027757924050092697,
0.004897990729659796,
0.05673561245203018,
-0.022244814783334732,
-0.004275857470929623,
-0.0014126808382570744,
-0.003716816660016775,
0.015184018760919571,
-0.020537493750452995,
-0.006034240126609802,
-0.0019878780003637075,
-0.024649351835250854,
0.006012899335473776,
0.042397551238536835,
-0.026363473385572433,
-0.0364246740937233,
-0.003500043647363782,
-0.001833469606935978,
0.03342978656291962,
-0.006038885097950697,
-0.03330302610993385,
-0.04355448856949806,
0.021982330828905106,
0.024038715288043022,
0.0004430497356224805,
0.007343940436840057,
0.05173075571656227,
-0.002400569152086973,
-0.04505881667137146,
0.06588679552078247,
-0.002377686556428671,
-0.032336000353097916,
-0.04397255927324295,
-0.007557117845863104,
-0.02858584001660347,
0.007251492701470852,
0.010542302392423153,
-0.006401160731911659,
-0.005531142465770245,
0.03102903440594673,
0.010443131439387798,
0.011474653147161007,
-0.015513350255787373,
-0.024648431688547134,
-0.015005627647042274,
-0.07139195501804352,
0.033537302166223526,
-0.024184050038456917,
-0.004142473451793194,
-0.00662083039060235,
0.011576772667467594,
0.011925313621759415,
0.0470668263733387,
0.03240351751446724,
-0.01017212588340044,
0.0056090205907821655,
0.03185955435037613,
-0.016896652057766914,
0.017470112070441246,
-0.007822799496352673,
-0.01039069052785635,
-0.005096249282360077,
-0.050994809716939926,
0.022598639130592346,
0.013826576061546803,
-0.015409007668495178,
0.010548518039286137,
0.03282919153571129,
-0.0004290154902264476,
0.04316774383187294,
-0.01878165453672409,
-0.033550161868333817,
0.03180311620235443,
0.029036959633231163,
-0.03648317605257034,
0.05497782677412033,
-0.0061490777879953384,
0.013650117442011833,
0.013746770098805428,
0.0035396830644458532,
0.002224524738267064,
0.004474733490496874,
-0.0217189472168684,
0.004200272262096405,
0.007478857878595591,
-0.043734680861234665,
0.008180776610970497,
-0.006773184984922409,
-0.03701233118772507,
0.04138414189219475,
-0.03320673108100891,
-0.01762140542268753,
0.053212009370326996,
0.0007024469668976963,
0.00678336713463068,
-0.02115495689213276,
0.017097003757953644,
0.03133247047662735,
-0.034481145441532135,
-0.000286775961285457,
0.04267365485429764,
0.024744823575019836,
0.005313360132277012,
-0.005475261714309454,
0.019768260419368744,
-0.016928426921367645,
0.008242708630859852,
0.0007500454084947705,
0.03456463664770126,
-0.04729229584336281,
0.007933728396892548,
-0.01665317453444004,
-0.013766158372163773,
0.03175586089491844,
0.04009580612182617,
-0.046970512717962265,
0.09473724663257599,
-0.001382148009724915,
0.00681898882612586,
-0.00022651063045486808,
-0.019464515149593353,
-0.001972018741071224,
0.03455077484250069,
-0.011218764819204807,
0.06684514135122299,
-0.009595043025910854,
-0.0019396566785871983,
0.025350447744131088,
0.0027572407852858305,
0.03174920752644539,
-0.020391158759593964,
0.01723869889974594,
-0.04862446337938309,
0.016086628660559654,
0.003180269617587328,
-0.038014546036720276,
-0.029195113107562065,
-0.02526695653796196,
0.015222028829157352,
0.012790941633284092,
-0.0023227622732520103,
-0.022654835134744644,
-0.02207445167005062,
-0.018845435231924057,
-0.004840110428631306,
-0.06128837913274765,
-0.0011358290212228894,
-0.02695230208337307,
0.028663985431194305,
-0.022014498710632324,
0.016487089917063713
] |
<p>Both matter and antimatter have mass and thus gravity, but since energy from annihilation has no mass what happens to the force of gravity that was previously present?
What about conservation of energy? Does it include gravity too?</p>
| 8,854 |
[
-0.03851046413183212,
-0.02554466389119625,
-0.04207314923405647,
-0.005652327090501785,
0.017904717475175858,
0.029741978272795677,
-0.049665458500385284,
-0.035435549914836884,
0.000636091164778918,
-0.013025837019085884,
-0.004414429888129234,
-0.003305518999695778,
0.04675013944506645,
-0.024210920557379723,
0.03495949134230614,
-0.0036788498982787132,
-0.007439356297254562,
-0.022429348900914192,
0.01847958192229271,
-0.04513037949800491,
-0.013285680674016476,
-0.009753160178661346,
-0.021539149805903435,
0.0043205139227211475,
-0.02132882922887802,
0.050836216658353806,
0.0246207807213068,
-0.013333485461771488,
0.0346466489136219,
0.046463485807180405,
0.026113351806998253,
-0.031530000269412994,
-0.007415324915200472,
0.032632648944854736,
0.004185555502772331,
0.01833241619169712,
-0.014517351984977722,
-0.030946994200348854,
-0.014490580186247826,
0.015766719356179237,
-0.06295742839574814,
-0.03405636176466942,
-0.009389197453856468,
0.04027484729886055,
-0.04617182910442352,
0.020649747923016548,
-0.00019522907678037882,
0.013268763199448586,
0.049714572727680206,
-0.05243979021906853,
0.07118483632802963,
0.018301021307706833,
0.06524743884801865,
-0.011865008622407913,
-0.022806892171502113,
0.0009054269758053124,
0.07704920321702957,
0.04710884764790535,
-0.015152674168348312,
-0.051362231373786926,
-0.0240832157433033,
0.015604075975716114,
-0.013913263566792011,
-0.03679756075143814,
-0.04066714271903038,
0.03104647994041443,
-0.0007191551267169416,
-0.0027409533504396677,
0.037630993872880936,
0.019024105742573738,
0.0163373164832592,
0.03390543907880783,
0.009303178638219833,
0.0226228479295969,
-0.002315194346010685,
-0.034268781542778015,
0.025898372754454613,
-0.0045171212404966354,
0.02344411611557007,
0.06312523037195206,
-0.006549896206706762,
0.008296074345707893,
0.039442624896764755,
0.04569363221526146,
0.01824752427637577,
0.02051207795739174,
0.07248128205537796,
0.008817123249173164,
0.0004141735553275794,
0.046881888061761856,
-0.0037593464367091656,
-0.00065753044327721,
0.008865810930728912,
-0.022677885368466377,
-0.030201302841305733,
0.04678342118859291,
-0.003183376044034958,
0.045348867774009705,
0.007458833046257496,
-0.00011815222387667745,
0.031721875071525574,
0.0023094378411769867,
0.026576755568385124,
0.05855250731110573,
0.03530193865299225,
-0.048641059547662735,
-0.04453759267926216,
0.04070892557501793,
-0.03539793938398361,
0.005054251290857792,
-0.020194241777062416,
-0.0011491096811369061,
-0.008583647198975086,
-0.06996048241853714,
0.03948359191417694,
-0.014726283960044384,
0.01923731155693531,
-0.018331928178668022,
0.05738656967878342,
0.05491417273879051,
0.034357573837041855,
0.001255833893083036,
0.018067743629217148,
-0.017771387472748756,
-0.04265688732266426,
-0.0020684862975031137,
0.048191942274570465,
-0.03302600607275963,
-0.047026243060827255,
0.010261202231049538,
-0.023035770282149315,
-0.013617324642837048,
-0.023883888497948647,
-0.017275122925639153,
0.03617122024297714,
-0.016380665823817253,
-0.08053833991289139,
-0.07048830389976501,
0.008474810980260372,
-0.038842685520648956,
-0.035425495356321335,
-0.03536381945014,
-0.02551855705678463,
0.014305362477898598,
0.053768523037433624,
-0.012642853893339634,
-0.03845100849866867,
0.0165544543415308,
0.027095463126897812,
-0.009224682115018368,
0.003360605565831065,
-0.03318408504128456,
0.018590204417705536,
-0.049196507781744,
-0.005278728902339935,
-0.07657679170370102,
0.004360174294561148,
0.025458792224526405,
0.0032385934609919786,
-0.017694324254989624,
0.04843633994460106,
-0.002595029305666685,
0.017509007826447487,
-0.0011335881426930428,
-0.0020863928366452456,
-0.0412755161523819,
0.04727312549948692,
0.034131377935409546,
-0.015588327310979366,
0.031139899045228958,
0.06584961712360382,
0.03766743466258049,
-0.0027630156837403774,
0.006982574239373207,
0.06354234367609024,
-0.03108793869614601,
-0.02914193645119667,
-0.011525287292897701,
0.005338472779840231,
0.008510535582900047,
-0.025586282834410667,
-0.03912227228283882,
-0.014323881827294827,
0.0036262718494981527,
0.01701054535806179,
0.04238646849989891,
-0.01417076401412487,
-0.024510324001312256,
-0.012750834226608276,
-0.024777496233582497,
0.000547167262993753,
-0.08653821051120758,
0.024252012372016907,
0.000010826873221958522,
-0.0024362048134207726,
-0.01737733744084835,
0.07391583174467087,
0.02072872780263424,
-0.04581212252378464,
-0.02517022006213665,
0.010751252062618732,
0.04695446044206619,
-0.05042897164821625,
-0.016658935695886612,
-0.003485732711851597,
0.03574115037918091,
0.05076169595122337,
-0.005414778832346201,
0.0246327705681324,
0.016427239403128624,
-0.01787140592932701,
0.010607234202325344,
-0.004022680688649416,
-0.0174623504281044,
-0.014984606765210629,
0.010764723643660545,
0.02996618114411831,
-0.0006843024748377502,
0.006406921893358231,
0.03967379778623581,
-0.01496818196028471,
0.07903991639614105,
0.011862684041261673,
-0.012397611513733864,
-0.011586884967982769,
0.037763986736536026,
0.04106202721595764,
0.05069025605916977,
-0.027715709060430527,
-0.013162428513169289,
-0.03724110126495361,
-0.02863204851746559,
-0.0004654155345633626,
0.02461102232336998,
-0.01543845608830452,
0.04224509373307228,
0.026066526770591736,
0.01649714820086956,
0.011124439537525177,
0.033756107091903687,
-0.015185711905360222,
-0.06296678632497787,
0.03667106851935387,
0.006682293489575386,
0.025575250387191772,
0.000005331567535904469,
0.038397327065467834,
0.03241264447569847,
-0.02721196785569191,
0.025994203984737396,
-0.015735004097223282,
0.025004420429468155,
0.007797047030180693,
0.021976668387651443,
-0.006798821967095137,
-0.06333331763744354,
0.02951432578265667,
-0.029242027550935745,
0.018302958458662033,
0.00409002834931016,
-0.020980393514037132,
-0.023972181603312492,
-0.04741811752319336,
-0.02203647419810295,
-0.0026058978401124477,
-0.0068741352297365665,
0.006915496662259102,
0.0038392695132642984,
0.02627514861524105,
-0.03479829430580139,
0.011625569313764572,
-0.031637273728847504,
-0.012853601947426796,
-0.0273500494658947,
0.01284854207187891,
0.016518961638212204,
0.0002451414766255766,
0.0684819370508194,
-0.025626104325056076,
-0.021816683933138847,
-0.015804221853613853,
-0.04338974133133888,
-0.02566913515329361,
0.04380958527326584,
-0.02492833137512207,
0.03404771536588669,
-0.06336373090744019,
-0.02024572342634201,
0.04758688062429428,
-0.009465450420975685,
0.01734849251806736,
0.03181096538901329,
-0.016816388815641403,
-0.025054574012756348,
-0.004066054243594408,
-0.04019871726632118,
-0.026323813945055008,
-0.016619041562080383,
0.040201276540756226,
0.05563787370920181,
0.005643091630190611,
-0.034435026347637177,
-0.007603008300065994,
-0.055098891258239746,
-0.0639139860868454,
-0.009619961492717266,
0.015744704753160477,
0.03968250751495361,
-0.04094627872109413,
0.030009528622031212,
0.02417020872235298,
-0.08820837736129761,
0.005622552242130041,
-0.03847551718354225,
-0.01178403664380312,
0.025983190163969994,
-0.011519720777869225,
-0.00019849331874866039,
-0.005822249222546816,
-0.025188781321048737,
0.07477045059204102,
0.034303802996873856,
-0.018763933330774307,
-0.01859014481306076,
0.01534656435251236,
0.0332680381834507,
-0.007020617835223675,
-0.006852737627923489,
0.00881633348762989,
0.02052745409309864,
-0.012941858731210232,
0.038120854645967484,
0.03857705369591713,
-0.00021721606026403606,
0.021338211372494698,
-0.03810355067253113,
-0.00419030524790287,
0.0486103892326355,
0.012012962251901627,
0.023842496797442436,
-0.0052843717858195305,
0.0007278036209754646,
0.01582261361181736,
0.02383153699338436,
0.06030573323369026,
-0.024241065606474876,
-0.03038538619875908,
0.07693707942962646,
0.013296998105943203,
0.01859637163579464,
-0.01841447688639164,
0.01872098073363304,
-0.02009000815451145,
-0.002930003684014082,
0.0626426711678505,
0.016766853630542755,
0.040501222014427185,
-0.0057236687280237675,
-0.016415590420365334,
0.005332889501005411,
0.053331173956394196,
-0.04828483238816261,
-0.06497043371200562,
0.02144530974328518,
-0.0033853407949209213,
0.013405779376626015,
0.004386842250823975,
0.0097234807908535,
0.013313280418515205,
0.024866947904229164,
0.022636890411376953,
0.013126015663146973,
-0.05697767809033394,
-0.017269471660256386,
-0.05347915366292,
0.015663953498005867,
0.014220849610865116,
0.03366197273135185,
-0.01160517055541277,
0.037920963019132614,
0.02192545123398304,
0.02726147323846817,
0.01536983996629715,
-0.0037024319171905518,
-0.10368477553129196,
0.056754015386104584,
-0.05412931367754936,
-0.024304313585162163,
0.0030097053386271,
-0.0045860446989536285,
-0.02140118181705475,
-0.025119010359048843,
0.0031893919222056866,
-0.011255379766225815,
-0.028003497049212456,
-0.045395493507385254,
0.0021278944332152605,
-0.07464532554149628,
-0.056527506560087204,
0.011238981038331985,
0.005316963419318199,
0.04243270680308342,
-0.009519253857433796,
-0.0011542914435267448,
0.044569503515958786,
-0.030191846191883087,
-0.026846490800380707,
-0.005460598971694708,
0.009306884370744228,
-0.030388323590159416,
0.04141441360116005,
0.07372443377971649,
0.006517223548144102,
-0.0226321779191494,
-0.0025524760130792856,
0.023259703069925308,
0.04214305430650711,
-0.0031233590561896563,
0.015627151355147362,
-0.0015546460635960102,
-0.053880609571933746,
-0.03875574469566345,
0.0026306351646780968,
0.02331913448870182,
-0.021048197522759438,
-0.0036728237755596638,
-0.0001893423468573019,
0.03667324781417847,
-0.01261628232896328,
0.0701448991894722,
0.0981280505657196,
0.032977763563394547,
-0.027642585337162018,
-0.03351391851902008,
0.00275795953348279,
-0.023767249658703804,
-0.008529867976903915,
0.006425447296351194,
-0.009152496233582497,
-0.07033860683441162,
0.00861391332000494,
-0.006960129830986261,
0.03570571169257164,
-0.055976372212171555,
-0.011401829309761524,
0.00045308677363209426,
0.018554065376520157,
0.005187958478927612,
-0.006531374994665384,
-0.0036764629185199738,
0.030534351244568825,
0.04865584522485733,
-0.013005558401346207,
0.021655185148119926,
-0.07933000475168228,
0.01547782402485609,
0.03871074691414833,
0.04919716715812683,
-0.010664474219083786,
-0.04389332979917526,
-0.08563652634620667,
-0.022906649857759476,
0.03159619867801666,
-0.030208254233002663,
0.004367517307400703,
-0.018100380897521973,
0.008990452624857426,
0.010268421843647957,
-0.038259219378232956,
0.00717620924115181,
0.029407108202576637,
-0.03938133269548416,
-0.009863344021141529,
0.00031036880682222545,
0.01267993077635765,
-0.014635658822953701,
0.01865193247795105,
0.015749387443065643,
0.027989378198981285,
0.03039686195552349,
0.008592491038143635,
-0.010755099356174469,
0.02158268913626671,
-0.03088103048503399,
-0.07907701283693314,
-0.051757924258708954,
0.008344369940459728,
-0.04731939360499382,
0.032854169607162476,
-0.013994600623846054,
-0.04976559802889824,
-0.004579942207783461,
0.0016392447287216783,
-0.013150474987924099,
-0.027466049417853355,
-0.05271129310131073,
0.022143874317407608,
0.028444180265069008,
-0.024993421509861946,
0.02329920046031475,
0.013825139962136745,
-0.004498370923101902,
-0.002842348301783204,
-0.03434116020798683,
0.05079855024814606,
-0.030855674296617508,
-0.016467908397316933,
-0.034185320138931274,
-0.008961266838014126,
-0.0290970578789711,
0.04170682281255722,
-0.022159991785883904,
-0.0029857109766453505,
0.008319695480167866,
-0.0478065088391304,
0.005379359237849712,
0.012131531722843647,
0.047321997582912445,
-0.02333812043070793,
0.01770981401205063,
0.00811382383108139,
-0.05212126299738884,
-0.02575654909014702,
0.03229418769478798,
0.036926399916410446,
-0.037922486662864685,
0.010370001196861267,
-0.0021899472922086716,
0.04616909474134445,
-0.0014301133342087269,
-0.03313467651605606,
0.04038995876908302,
-0.01917502097785473,
0.01947818137705326,
-0.013144892640411854,
-0.03135693445801735,
0.03364247828722,
-0.05714638903737068,
-0.047349873930215836,
0.01012960635125637,
0.00388128450140357,
0.011072796769440174,
-0.04001221805810928,
0.0632128119468689,
0.04754476621747017,
0.010147465392947197,
-0.10362561047077179,
-0.028486153110861778,
0.008089933544397354,
0.005966321565210819,
0.003510747803375125,
-0.01799478754401207,
-0.00421511335298419,
-0.04639240354299545,
-0.00972807314246893,
-0.005204315762966871,
0.03805996850132942,
-0.03619863837957382,
0.008088251575827599,
0.02888728864490986,
0.016791339963674545,
0.03734975680708885,
0.0025109092239290476,
-0.01820165105164051,
0.013254069723188877,
0.008934758603572845,
0.018881905823946,
0.017788881435990334,
0.07344979047775269,
-0.00017871342424768955,
-0.028192762285470963,
-0.006775044836103916,
-0.03370146080851555,
0.00860187504440546,
-0.022354496642947197,
0.01312505453824997,
0.04790343716740608,
0.025655681267380714,
-0.020823335275053978,
0.011605609208345413,
0.026589738205075264,
-0.042916327714920044,
0.060638297349214554,
-0.008501858450472355,
-0.011941355653107166,
0.006712160538882017,
-0.013220748864114285,
0.029040349647402763,
-0.001971032004803419,
0.010641888715326786,
-0.008020203560590744,
0.06450780481100082,
0.0233877282589674,
-0.013768739998340607,
0.003231519367545843,
-0.02217045985162258,
0.032066334038972855,
-0.0396118238568306,
0.007257305551320314,
0.021858016029000282,
-0.02141064591705799,
-0.005821010563522577,
-0.03691689297556877,
-0.023127766326069832,
-0.011731959879398346,
0.05243627727031708,
-0.0319761261343956,
0.047746509313583374,
-0.008194450289011002,
0.015125229023396969,
0.007285668980330229,
-0.05319506302475929,
0.02767881006002426,
0.009840360842645168,
0.002873646095395088,
0.020112577825784683,
0.01200717780739069,
-0.004974810406565666,
0.04828031361103058,
0.044041384011507034,
-0.02978299744427204,
0.007647133432328701,
0.020588258281350136,
0.01481196004897356,
0.008725538849830627,
-0.004550985060632229,
-0.054481763392686844,
-0.0015611081616953015,
-0.01926390640437603,
0.029062440618872643,
-0.017810411751270294,
-0.03924332186579704,
0.022558698430657387,
0.018837805837392807,
0.010407284833490849,
0.010516621172428131,
-0.04141802340745926,
-0.018700815737247467,
0.002818197477608919,
-0.005694471765309572,
0.021179482340812683,
-0.04337874427437782,
0.03900708630681038,
0.031401462852954865,
-0.005320570897310972,
0.006484427955001593,
0.0035210002679377794,
-0.08033071458339691,
-0.02627047337591648,
-0.04442722350358963,
-0.017641715705394745,
0.0333024263381958,
-0.013790284283459187,
-0.0030599867459386587,
0.029946228489279747,
-0.010479958727955818,
0.013082509860396385,
0.010820470750331879,
0.017076170071959496,
-0.017839616164565086,
0.08119279891252518,
-0.01843450218439102,
0.018364815041422844,
-0.002594117308035493,
0.042255718261003494,
0.111823171377182,
0.04460883140563965,
-0.005022831726819277,
-0.05362674966454506,
0.010736647993326187,
-0.016804883256554604,
-0.014147639274597168,
-0.03709452599287033,
0.021841589361429214,
-0.025148900225758553,
0.0020906913559883833,
0.017435327172279358,
0.05901579186320305,
-0.001614704029634595,
-0.031549908220767975,
0.06421969830989838,
-0.0278276726603508,
-0.05013863369822502,
-0.00913071259856224,
0.006351696327328682,
-0.020605215802788734,
0.022730547934770584,
-0.03276446834206581,
0.02766350656747818,
-0.016762394458055496,
0.022622551769018173,
-0.02040703594684601,
-0.033501919358968735,
-0.014932096004486084,
0.018405674025416374,
-0.05244049057364464,
0.024896088987588882,
0.006030633579939604,
-0.0105117317289114,
-0.05056597292423248,
0.005051149055361748,
0.0296091940253973,
-0.002595377154648304,
0.014399832114577293,
0.018237251788377762,
0.019845958799123764,
0.023417221382260323,
-0.019317559897899628,
0.007916979491710663,
-0.044963110238313675,
0.0026430014986544847,
-0.01181879173964262,
0.051949210464954376,
-0.0027811971958726645,
0.027384430170059204,
0.02167138084769249,
-0.010112482123076916,
-0.012239458039402962,
-0.02615462802350521,
-0.005397086497396231,
-0.02063172310590744,
0.004513276740908623,
0.006411074195057154,
-0.003425060771405697,
-0.02066762000322342,
0.015675175935029984,
-0.0007560673402622342,
0.040295008569955826,
-0.019477596506476402,
0.018372230231761932,
0.04209071397781372,
-0.009749267250299454,
0.021660028025507927,
-0.04950552061200142,
-0.025193270295858383,
0.0006760886171832681,
-0.03386054188013077,
-0.044604185968637466,
-0.019845113158226013,
0.05793420225381851,
0.057951074093580246,
0.02303047850728035,
0.015728481113910675,
0.011435062624514103,
-0.038029324263334274,
-0.04625803232192993,
0.06375536322593689,
-0.04216478019952774,
-0.039461731910705566,
-0.029699523001909256,
0.0009251503506675363,
0.010744958184659481,
0.032442208379507065,
-0.007107444107532501,
-0.01981925778090954,
-0.024832403287291527,
-0.005073540844023228,
0.01825253665447235,
-0.0019524998497217894,
0.014250678941607475,
0.01830483041703701,
-0.016612328588962555,
-0.008576298132538795,
-0.0435587577521801,
-0.0036173805128782988,
0.03552337363362312,
0.004019015934318304,
-0.003666195087134838,
0.024531900882720947,
0.006438363343477249,
0.0225017499178648,
0.006494258530437946,
-0.022581830620765686,
-0.003958039451390505,
0.0287537332624197,
0.012442206963896751,
-0.022993257269263268,
-0.003132573561742902,
-0.022062018513679504,
0.007364805322140455,
0.008399817161262035,
0.06447973102331161,
-0.038308240473270416,
0.041301559656858444,
-0.009783185087144375,
0.0429844968020916,
-0.042051367461681366,
0.009960642084479332,
-0.07907726615667343,
0.002248998498544097,
0.02867896296083927,
-0.07006581127643585,
-0.012128976173698902,
0.03351619839668274,
-0.009290479123592377,
0.00008557074033888057,
-0.0025014514103531837,
0.022869756445288658,
-0.017280811443924904,
-0.014181645587086678,
0.05088911950588226,
-0.034416113048791885,
0.08088795840740204,
0.012214582413434982,
0.004760045558214188,
0.04987380653619766,
-0.03235768526792526,
-0.04148212447762489,
0.0366690568625927,
-0.028575852513313293,
0.03675771504640579,
0.006156564224511385,
-0.04118068888783455,
-0.021626882255077362,
0.07589028775691986,
-0.030919149518013,
-0.004833560902625322,
-0.017341194674372673,
-0.046888649463653564,
-0.02729693613946438,
0.012824026867747307,
0.0013766272459179163,
-0.007603436708450317,
-0.012382740154862404,
0.04309907928109169,
0.012026687152683735,
-0.026475518941879272,
0.027985448017716408,
0.005427398253232241,
-0.009161265566945076,
-0.0041385190561413765,
0.02666638419032097,
-0.004363840911537409,
0.009792504832148552,
0.07308609783649445,
-0.02318992279469967,
0.016308121383190155,
0.037826091051101685,
0.02674430049955845,
-0.09251254051923752,
-0.014877837151288986,
-0.005845741834491491,
-0.013595201075077057,
0.025980893522500992,
-0.03332842141389847,
0.017681414261460304,
0.016610529273748398,
-0.04733404889702797,
0.04642689973115921,
-0.026479244232177734,
-0.03082379139959812,
0.013651571236550808,
-0.024258192628622055,
0.010869267396628857,
0.056701015681028366,
0.029587162658572197,
0.049587100744247437,
-0.018279843032360077,
-0.014035704545676708,
-0.0029218962881714106,
-0.011014207266271114,
-0.04729308933019638,
0.011671794578433037,
-0.03862844407558441,
0.017006436362862587,
0.048680730164051056,
-0.013160289265215397,
0.003896488808095455,
0.04081379622220993,
-0.0007359084556810558,
-0.030611552298069,
-0.019672725349664688,
-0.0026915729977190495,
0.0028269304893910885,
0.029648583382368088,
0.007406953256577253,
-0.014623600989580154,
-0.013815467245876789,
0.06119409576058388,
-0.0028333489317446947,
0.03243254870176315,
0.0033365697599947453,
0.011549408547580242,
-0.0026781009510159492,
-0.037520989775657654,
-0.00619225250557065,
0.013974301517009735,
-0.021037554368376732,
-0.032478295266628265,
-0.014273684471845627,
0.04381241649389267,
-0.0030893152579665184,
-0.014147729612886906,
-0.02535029500722885,
-0.04162899777293205,
-0.010876676999032497,
0.04794615879654884,
0.0027217944152653217,
0.0026996859814971685,
0.020611025393009186,
0.00826297514140606,
-0.0054002427496016026,
0.000999363837763667,
-0.02496686950325966,
0.005399169400334358,
-0.0008431870955973864,
0.011541013605892658,
0.018819501623511314,
0.03080086037516594,
-0.003345631528645754,
-0.0695950984954834,
-0.019976578652858734,
0.06053035706281662,
0.000749987259041518,
0.02004651539027691,
-0.015259601175785065,
-0.06624972075223923,
-0.01580270752310753,
-0.052888356149196625,
0.0029869459103792906,
-0.008456151932477951,
-0.0036814475897699594,
-0.03565487265586853,
-0.0033878469839692116,
0.016308320686221123,
-0.023668579757213593,
0.025003978982567787,
-0.02122284658253193,
-0.018980572000145912,
0.028943751007318497,
-0.008916591294109821,
0.0049232011660933495,
-0.02955847978591919,
0.020665019750595093,
-0.003012212226167321,
-0.03497914597392082,
-0.011037674732506275,
0.015463338233530521,
-0.026828227564692497,
0.021879004314541817,
0.003930229227989912,
-0.015071898698806763,
0.024496791884303093,
-0.012836873531341553,
-0.02090727910399437,
0.0627942606806755,
0.03880186378955841,
-0.008420003578066826,
0.06548650562763214,
-0.004044809378683567,
0.023355688899755478,
0.05425898730754852,
0.0006598848849534988,
-0.02598443254828453,
0.03303230553865433,
-0.02741244062781334,
-0.007837743498384953,
-0.006922230124473572,
-0.005398331210017204,
0.04788796231150627,
-0.025831710547208786,
0.00337183172814548,
0.03805052861571312,
-0.010542520321905613,
-0.013155225664377213,
0.04775848239660263,
0.03968495875597,
0.03297896310687065,
-0.017681406810879707,
0.015209916979074478,
0.031602662056684494,
0.04125567525625229,
-0.0056280833669006824,
0.054887522011995316,
0.008117581717669964,
0.05116131901741028,
-0.021949268877506256,
0.021679937839508057,
-0.016255995258688927,
-0.006909295450896025,
0.01627284474670887,
0.030743243172764778,
-0.0457378588616848,
-0.05146476998925209,
0.016111161559820175,
-0.015865713357925415,
0.054488588124513626,
0.039309654384851456,
-0.026302458718419075,
0.06690927594900131,
-0.031195160001516342,
0.03309916704893112,
0.014252999797463417,
-0.0078580966219306,
-0.016988953575491905,
0.006713320501148701,
-0.02580232545733452,
0.06053924188017845,
0.023182446137070656,
0.0024829821195453405,
-0.03169756382703781,
0.004388878121972084,
0.010465291328728199,
-0.02043876238167286,
0.0290426854044199,
0.029635315760970116,
-0.010017329826951027,
-0.02340785041451454,
-0.026030421257019043,
-0.054011307656764984,
-0.021597424522042274,
0.006068000569939613,
0.03906003013253212,
0.03468979895114899,
-0.03579331934452057,
-0.008132442831993103,
-0.024637598544359207,
0.037193603813648224,
-0.043291833251714706,
-0.01737426035106182,
-0.023536674678325653,
-0.009958000853657722,
-0.01360772829502821,
0.0057851579040288925
] |
<p>There is a claim often made about cold fusion, that it is excluded theoretically. The main theoretical argument is that electronic energies are too low to overcome the Coulomb barrier, since d-d fusion only takes place at KeV energies, while chemistry is at eV energies.</p>
<p>This is belied by inner shells, which in Palladium store 3 or 20 KeV of energy per ejected electron, depending on whether the first or second shell is excited. These inner shell vacancies can decay either by x-rays, or by absorbing an electron into the vacancy and simultaneously ejecting a different electron (this second process is electrostatic). The cross section for ejecting a deuteron with tens of KeV's instead of an electron should be larger, since a deuterium is heavier. So I believe deuterated metal with excited inner shells has KeV deuterons running around.</p>
<p>If two KeV deuterons do a fusion to an alpha in a dense environment, close to a nucleus or to an electron, I don't know why the process cannot end without a proton or neutron ejected. There are electrostatic matrix elements that allow an unstable alpha-resonance to decay by giving its energy to a charged particle nearby, instead of ejecting a constituent.</p>
<p>After a fusion, the resulting alpha leaves an energetic track behind, and charged particles leave behind trails of atoms with ejected inner-shell electrons. So the K-shell holes produce fast deuterons, and fusion in deuterons produces K-shell holes. I don't see why this can't make a chain reaction.</p>
<p>I have explained this idea before. I would like to know whether somebody knows a sound theoretical argument which rules it out. Can such a chain reaction in a Pd be excluded theoretically? I am not asking if it is likely, I am asking whether it can be firmly theoretically excluded.</p>
<p>Anna v. asks how this process gets started--- it requires a random charged particle to pass through the deuterated material, from spontaneous environmental radioactive decay, or a cosmic ray muon. Charged particles produce K-shell holes.</p>
<p>To make my biases clear: I can't exclude it. Regardless of the quality of the experiments, I don't see an argument against cold fusion.</p>
| 8,855 |
[
-0.039457015693187714,
-0.012825174257159233,
0.0498325452208519,
-0.046008817851543427,
-0.0008691259426996112,
0.002703040139749646,
-0.051059845834970474,
-0.030342591926455498,
-0.0004056358302477747,
-0.028845369815826416,
0.023241089656949043,
0.00754812965169549,
0.03093554452061653,
0.02248171903192997,
-0.04129123315215111,
0.023697229102253914,
0.02021748386323452,
-0.08299018442630768,
0.0002897118392866105,
-0.0461646132171154,
0.022259550169110298,
-0.01550938468426466,
-0.023421332240104675,
-0.011231795884668827,
-0.02751169539988041,
0.015965037047863007,
0.026910370215773582,
0.0018157835584133863,
0.029598722234368324,
0.047874487936496735,
0.010140073485672474,
-0.06051187589764595,
0.003634358523413539,
-0.0003811939968727529,
0.0057387202978134155,
0.0222785584628582,
0.006208903156220913,
-0.04223421961069107,
-0.04212091863155365,
0.04550846293568611,
-0.014163803309202194,
-0.005928975064307451,
-0.013591357506811619,
0.008603021502494812,
0.009014736860990524,
-0.02216765284538269,
0.049542635679244995,
-0.0223957821726799,
0.020189553499221802,
-0.029365748167037964,
-0.02635476179420948,
-0.026668820530176163,
0.04393532872200012,
-0.003959352616220713,
0.02997361123561859,
0.010863552801311016,
0.06955686211585999,
0.07254420220851898,
0.017538705840706825,
-0.04146439954638481,
-0.02574268914759159,
0.0026871091686189175,
-0.0014678561128675938,
0.050042614340782166,
-0.002289293333888054,
0.009306254796683788,
-0.01924680359661579,
-0.017333827912807465,
-0.0038681018631905317,
0.009741827845573425,
0.04626075178384781,
-0.0017047966830432415,
-0.016912495717406273,
-0.013724562712013721,
0.04470477253198624,
-0.019981537014245987,
0.028620732948184013,
-0.010977447964251041,
0.028913380578160286,
0.07000089436769485,
-0.033159367740154266,
0.011088334023952484,
0.03013291209936142,
0.01466306485235691,
0.02312302030622959,
0.032624781131744385,
0.07241852581501007,
-0.04548109695315361,
-0.0051180110312998295,
0.046015772968530655,
0.0026478704530745745,
0.007290933281183243,
0.02664116397500038,
0.012699874117970467,
-0.0230422206223011,
0.024395344778895378,
0.01553138718008995,
0.09780740737915039,
-0.021033642813563347,
0.03434276208281517,
0.0036959252320230007,
0.02256886102259159,
0.04398973286151886,
0.0985800176858902,
0.0474749319255352,
-0.027817800641059875,
-0.0013161482056602836,
0.008961944840848446,
-0.018454674631357193,
-0.01975109428167343,
-0.05755223333835602,
0.0026615310925990343,
0.00290421349927783,
-0.004859871696680784,
0.0219027791172266,
-0.03312266618013382,
-0.007529347203671932,
-0.00011239878222113475,
0.06250545382499695,
0.05799024924635887,
0.011112160049378872,
0.009299615398049355,
-0.017306122928857803,
-0.0665627270936966,
-0.05388033762574196,
-0.025953160598874092,
0.04182526469230652,
0.005032940302044153,
-0.013014528900384903,
-0.0013385273050516844,
-0.00565809803083539,
-0.008345331996679306,
0.023649020120501518,
-0.00859209056943655,
0.06840289384126663,
-0.017949972301721573,
-0.06593412905931473,
-0.061785370111465454,
0.049007829278707504,
-0.0009770231554284692,
-0.023732036352157593,
-0.07043132185935974,
0.00992551539093256,
0.002767517464235425,
0.053621601313352585,
-0.010718888603150845,
-0.05397139489650726,
-0.02303381636738777,
0.03787004575133324,
0.035692550241947174,
-0.017524903640151024,
-0.01946122758090496,
-0.00044700130820274353,
-0.03384746238589287,
-0.027918854728341103,
-0.030205311253666878,
0.046034831553697586,
0.0022208974696695805,
0.02499585784971714,
-0.0018504513427615166,
0.08092540502548218,
-0.03298255428671837,
0.03120356611907482,
0.01368996687233448,
0.02406366914510727,
-0.03303114324808121,
0.08545675873756409,
0.04687394201755524,
-0.006842783652245998,
0.03462173417210579,
0.0041973707266151905,
0.048015061765909195,
0.02663724683225155,
0.029935140162706375,
-0.0062696682289242744,
-0.05461066961288452,
-0.011585981585085392,
-0.03650821000337601,
-0.002337658079341054,
-0.0059172604233026505,
-0.05114692077040672,
0.005473537836223841,
-0.004629442933946848,
-0.003038533730432391,
0.0033918539993464947,
0.025513315573334694,
0.009531868621706963,
-0.00878088641911745,
-0.018263548612594604,
-0.01883392035961151,
-0.03779074549674988,
-0.034732550382614136,
0.003219848731532693,
0.019016727805137634,
-0.03178183361887932,
0.006398337427526712,
-0.02846739999949932,
0.0002692269627004862,
0.0012733309995383024,
-0.03926648199558258,
-0.000576875580009073,
-0.00047303191968239844,
0.009694705717265606,
-0.013549829833209515,
0.007307356223464012,
0.07600659877061844,
-0.006484732963144779,
-0.0020156754180788994,
0.02197420224547386,
0.011328011751174927,
-0.023105943575501442,
-0.024522127583622932,
-0.027196072041988373,
0.018954675644636154,
0.008971513248980045,
-0.01265542022883892,
0.034095291048288345,
-0.02693699486553669,
0.019842443987727165,
0.010273647494614124,
-0.010815877467393875,
0.08034855872392654,
0.019315999001264572,
0.0300734993070364,
-0.03403734788298607,
0.04839099943637848,
0.013852505013346672,
0.03402137756347656,
-0.004688173998147249,
-0.028762981295585632,
-0.07634025067090988,
-0.007730631623417139,
0.04311223328113556,
0.006968234665691853,
-0.060441479086875916,
0.032770052552223206,
-0.027140431106090546,
0.015841901302337646,
0.03910498321056366,
0.018922287970781326,
-0.010690202936530113,
0.00032463474781252444,
-0.012907370924949646,
0.009598244912922382,
0.0022138471249490976,
0.022119807079434395,
0.02426597662270069,
-0.011624532751739025,
0.008560805581510067,
-0.023911910131573677,
0.015422385185956955,
0.024693382903933525,
-0.023649197071790695,
0.000999688752926886,
0.001463492400944233,
-0.051061902195215225,
0.013947340659797192,
0.002736138179898262,
0.009090976789593697,
0.029868608340620995,
0.003762022126466036,
0.055953141301870346,
-0.003635246539488435,
-0.005990974139422178,
-0.007430039346218109,
0.021732177585363388,
0.014081482775509357,
-0.011605435982346535,
0.03408890590071678,
-0.036259766668081284,
0.038880713284015656,
-0.023943275213241577,
-0.005962746683508158,
-0.013304946944117546,
-0.00941385980695486,
0.011057996191084385,
-0.001745477318763733,
-0.00009478750871494412,
-0.04002872854471207,
-0.019282691180706024,
-0.023049885407090187,
-0.0012484835460782051,
-0.0012383147841319442,
0.01149657741189003,
-0.04941543564200401,
0.025870315730571747,
-0.04388546198606491,
-0.019573906436562538,
0.05152278393507004,
-0.0008224886259995401,
0.003660081187263131,
0.019581526517868042,
0.017498679459095,
-0.07799343764781952,
0.01297555211931467,
-0.01930762268602848,
-0.03612077236175537,
-0.06707977503538132,
-0.015902649611234665,
0.04812701791524887,
0.022310182452201843,
-0.04540996253490448,
0.041150014847517014,
-0.03186493739485741,
-0.027706729248166084,
-0.011029999703168869,
-0.021930575370788574,
0.0015482627786695957,
-0.002223336137831211,
0.007080128416419029,
0.034367647022008896,
-0.029834674671292305,
-0.00926760584115982,
-0.015378899872303009,
-0.03698529675602913,
0.035613179206848145,
-0.01779896579682827,
0.016199981793761253,
-0.03284653648734093,
-0.023408211767673492,
0.05494602397084236,
0.01604164019227028,
-0.016739031299948692,
0.024648522958159447,
-0.03711031377315521,
-0.021812671795487404,
-0.010369405150413513,
0.01918957754969597,
0.03589605167508125,
0.024245314300060272,
-0.012744437903165817,
-0.013905635103583336,
0.05214889720082283,
-0.013923076912760735,
-0.03872900456190109,
-0.020079774782061577,
0.02747279219329357,
0.0206949170678854,
0.00945764034986496,
0.02453511208295822,
-0.005857451818883419,
-0.04106825962662697,
0.008928819559514523,
-0.011173142120242119,
0.024466440081596375,
0.024154551327228546,
-0.08369958400726318,
0.032597869634628296,
-0.0031054888386279345,
0.013695979490876198,
-0.01676434651017189,
0.012283582240343094,
0.0014297860907390714,
-0.06057608127593994,
0.00494368514046073,
0.021332325413823128,
0.06300751864910126,
0.008518654853105545,
0.046919796615839005,
0.043889228254556656,
0.030050424858927727,
-0.00404305849224329,
-0.01916588470339775,
-0.013157407753169537,
-0.004307762254029512,
-0.005836389493197203,
-0.016553405672311783,
-0.007533470634371042,
0.03291260823607445,
0.041113343089818954,
0.021981365978717804,
-0.004580063279718161,
0.00021204094809945673,
-0.024854477494955063,
-0.0820874497294426,
-0.02047189325094223,
0.00594823295250535,
0.0608275942504406,
-0.010299500077962875,
0.043803900480270386,
0.045612022280693054,
0.011496290564537048,
-0.038384467363357544,
-0.032912809401750565,
-0.06633701920509338,
0.002405914943665266,
-0.002987123792991042,
-0.03938533365726471,
-0.019318152219057083,
-0.013842243701219559,
-0.056089576333761215,
0.0008037639781832695,
-0.06511747092008591,
0.0013719601556658745,
-0.01726343296468258,
-0.04816189035773277,
0.015508684329688549,
-0.007600865326821804,
-0.06720295548439026,
-0.03368794918060303,
0.030000654980540276,
0.10972234606742859,
-0.014076968654990196,
0.0025062523782253265,
-0.001602654461748898,
-0.07519190013408661,
-0.003734845668077469,
-0.026937339454889297,
0.034803375601768494,
0.001961048226803541,
0.04091325029730797,
0.01625923439860344,
0.0027294373139739037,
-0.023606274276971817,
-0.03717470169067383,
0.0460750050842762,
0.041730139404535294,
0.01651439070701599,
0.0009433747618459165,
0.015424000099301338,
-0.029244644567370415,
-0.01893703080713749,
0.02357937954366207,
0.029125379398465157,
-0.028016824275255203,
0.04433298110961914,
-0.0019169114530086517,
0.005464685615152121,
-0.028835315257310867,
0.05660643056035042,
0.008465058170258999,
0.03116816282272339,
-0.007609483785927296,
-0.03209235519170761,
-0.009241027757525444,
-0.00827035028487444,
-0.026237864047288895,
-0.014810220338404179,
-0.01529568899422884,
0.004103660583496094,
0.011116774752736092,
-0.008183078840374947,
-0.03271101787686348,
-0.01087420154362917,
-0.03406975418329239,
-0.05445130541920662,
-0.001646538614295423,
-0.01596904546022415,
0.0011888825101777911,
0.0828525647521019,
-0.008992709219455719,
0.06096307560801506,
0.0598013736307621,
0.03808274120092392,
-0.05798199772834778,
0.006734899710863829,
0.0647779107093811,
0.09007204324007034,
-0.01810014434158802,
-0.014430406503379345,
-0.06843545287847519,
-0.03609186410903931,
0.029992077499628067,
-0.004695662297308445,
0.03534214571118355,
-0.023775003850460052,
0.017936881631612778,
-0.0058427294716238976,
-0.04182850569486618,
-0.029143638908863068,
-0.009189343079924583,
0.005080211441963911,
-0.015668818727135658,
-0.037657011300325394,
-0.012609988451004028,
-0.01425117626786232,
0.014529475010931492,
0.05632751062512398,
0.018971774727106094,
-0.0019852120894938707,
-0.009880002588033676,
-0.020069880411028862,
-0.00010691503848647699,
-0.0013626778963953257,
-0.09163933247327805,
0.005731390789151192,
-0.025694897398352623,
0.016312310472130775,
0.03842741996049881,
-0.04497915506362915,
-0.04417796432971954,
0.005991243291646242,
0.02471146173775196,
0.024895064532756805,
-0.0018897977424785495,
-0.04463641345500946,
0.03903518617153168,
0.03678307682275772,
-0.00428818678483367,
0.045668404549360275,
0.027634423226118088,
-0.04662071168422699,
-0.0019121237564831972,
-0.034812428057193756,
-0.03329286724328995,
-0.02519298531115055,
0.035572394728660583,
-0.04828524962067604,
0.04069202020764351,
0.011697610840201378,
-0.006210711318999529,
-0.0199313722550869,
-0.009814353659749031,
0.0009638210176490247,
-0.018512386828660965,
0.007939541712403297,
0.020167920738458633,
-0.03604661300778389,
-0.0017226433847099543,
-0.026306569576263428,
0.030810605734586716,
0.016486406326293945,
-0.0019506068201735616,
0.022862838581204414,
0.004350912757217884,
0.015024496242403984,
0.004190158098936081,
-0.06026092916727066,
-0.04824589192867279,
-0.022597409784793854,
-0.030868329107761383,
0.03248826414346695,
-0.03161326423287392,
0.02374652959406376,
-0.02864646539092064,
0.01455533318221569,
0.017131179571151733,
-0.014736940152943134,
0.020580509677529335,
0.02238004468381405,
-0.00997733511030674,
0.023394953459501266,
0.0053167156875133514,
0.04593837633728981,
-0.004012772347778082,
0.000045552224037237465,
-0.1050897166132927,
-0.03056451492011547,
0.017413027584552765,
0.004825726617127657,
-0.05779425427317619,
-0.038366083055734634,
-0.03867250680923462,
-0.010962171480059624,
-0.01229061558842659,
0.012462417595088482,
0.04326007142663002,
-0.04659688472747803,
-0.008361372165381908,
0.02910780906677246,
0.0149622093886137,
0.06989206373691559,
-0.002907871501520276,
-0.022374551743268967,
-0.018046926707029343,
-0.013624228537082672,
0.011834636330604553,
-0.01591460220515728,
-0.015365121886134148,
0.005606930702924728,
-0.001342305331490934,
-0.022357339039444923,
0.009563311003148556,
0.04776805266737938,
-0.016716063022613525,
-0.029297472909092903,
0.07561992853879929,
0.006168536376208067,
0.027595311403274536,
-0.02700255997478962,
0.023656003177165985,
-0.03854053094983101,
0.03641175851225853,
-0.012309444136917591,
0.019487563520669937,
-0.017088470980525017,
-0.011751508340239525,
0.008799316361546516,
-0.004294851329177618,
0.00862120557576418,
-0.0017907817382365465,
0.029729625210165977,
-0.00446338951587677,
0.0176926851272583,
-0.004474102985113859,
-0.038252729922533035,
0.03506489470601082,
-0.02897137962281704,
-0.006754626985639334,
-0.01177707314491272,
-0.0010691066272556782,
0.00011051384353777394,
-0.02403746359050274,
-0.04982076957821846,
0.012616876512765884,
0.024166954681277275,
0.004974512383341789,
0.022763321176171303,
-0.03883950784802437,
0.010888044722378254,
-0.015049253590404987,
-0.04996120557188988,
-0.0013519985368475318,
-0.004330259747803211,
-0.020505668595433235,
-0.002792046405375004,
0.01491479855030775,
-0.033404652029275894,
0.03983452916145325,
0.05816560238599777,
-0.03286685794591904,
0.047329798340797424,
0.03964109718799591,
-0.002788024954497814,
0.00948461052030325,
-0.04344915971159935,
-0.04535476863384247,
0.00770168611779809,
-0.058593444526195526,
0.02625308372080326,
0.01033895555883646,
-0.04638904705643654,
0.02837061695754528,
0.023302283138036728,
0.03183910623192787,
-0.022387145087122917,
-0.045046817511320114,
-0.04537930712103844,
0.03453744202852249,
0.005279012024402618,
-0.00809412356466055,
-0.017932886257767677,
-0.019848942756652832,
0.049843840301036835,
0.007658311631530523,
-0.00948343612253666,
-0.013882182538509369,
-0.02901529334485531,
-0.02543366700410843,
-0.03491207957267761,
-0.0306447334587574,
0.050052013248205185,
-0.04476328566670418,
-0.05892205983400345,
0.007909328676760197,
-0.007422964554280043,
0.03628651425242424,
0.03468884155154228,
0.06186649575829506,
-0.01593182235956192,
0.0025922043714672327,
-0.00034748809412121773,
0.02410866506397724,
-0.04570981115102768,
0.0014343814691528678,
0.16641594469547272,
0.04256558045744896,
0.005054119508713484,
-0.03337956219911575,
-0.022952701896429062,
-0.01795659214258194,
0.020569512620568275,
0.020973198115825653,
0.022903066128492355,
0.012027887627482414,
-0.0014491240726783872,
0.029774125665426254,
0.06550291180610657,
-0.007625673431903124,
0.018809912726283073,
0.029083706438541412,
-0.00791114754974842,
-0.014626911841332912,
0.005330312997102737,
0.017167314887046814,
0.0006220560171641409,
0.004113943316042423,
-0.029994789510965347,
0.01927206479012966,
0.00567514868453145,
-0.011455078609287739,
-0.04868748411536217,
0.005145777948200703,
0.034956034272909164,
-0.015824727714061737,
-0.05879419296979904,
-0.021289272233843803,
0.023343972861766815,
0.025878624990582466,
0.026693904772400856,
0.01782887615263462,
0.023165985941886902,
-0.0013632129412144423,
-0.0001811981201171875,
0.015781914815306664,
0.016043011099100113,
-0.019748814404010773,
0.03943672403693199,
0.011896942742168903,
-0.01597660221159458,
0.005090378690510988,
-0.010890981182456017,
0.031012561172246933,
-0.07293768972158432,
-0.019817067310214043,
0.0013268734328448772,
-0.02957608737051487,
0.017563093453645706,
-0.004511242266744375,
-0.021525641903281212,
-0.0006951696705073118,
-0.00008622028690297157,
0.01651700586080551,
-0.0022751297801733017,
0.01034509763121605,
0.030804617330431938,
-0.01291862316429615,
0.010239170864224434,
-0.025548435747623444,
0.01435929536819458,
0.001459002960473299,
0.017601456493139267,
0.03057159297168255,
-0.0010638660751283169,
0.007902251556515694,
-0.059228941798210144,
0.019170371815562248,
-0.027077767997980118,
-0.01595335640013218,
0.008119289763271809,
0.00550921680405736,
0.0806119367480278,
0.03530285507440567,
0.000988527899608016,
-0.016298625618219376,
-0.047101810574531555,
0.05685184523463249,
0.042451441287994385,
-0.017692336812615395,
-0.011284487321972847,
0.024966441094875336,
0.00839297566562891,
0.028677135705947876,
-0.03848358616232872,
0.018728040158748627,
0.026788903400301933,
0.07761809974908829,
-0.03130844980478287,
-0.03852389380335808,
-0.048373136669397354,
-0.029573554173111916,
-0.050593238323926926,
0.027454713359475136,
-0.02988758683204651,
-0.01595459319651127,
-0.007169652264565229,
-0.005433154758065939,
0.025584416463971138,
0.023698611184954643,
0.014101913198828697,
0.008551591075956821,
0.02893449179828167,
0.0003229195426683873,
-0.006178547162562609,
0.002869145944714546,
-0.007836390286684036,
-0.025214534252882004,
0.006701856851577759,
0.001853416906669736,
-0.013126254081726074,
0.00841890275478363,
0.02694506198167801,
-0.028774093836545944,
0.024505333974957466,
-0.030107520520687103,
0.013714388012886047,
0.014768040738999844,
0.028575871139764786,
-0.027609165757894516,
-0.00499937916174531,
-0.0077569265849888325,
0.02389831468462944,
-0.03103063814342022,
0.021907806396484375,
-0.0016497098840773106,
0.016178281977772713,
0.01197834499180317,
-0.0012070470256730914,
-0.02481149323284626,
0.009974847547709942,
0.017393654212355614,
-0.011060664430260658,
0.0063059888780117035,
-0.00005075138687971048,
-0.009092926979064941,
0.01725989580154419,
-0.03359149768948555,
-0.047016941010951996,
0.002237164182588458,
0.008526807650923729,
-0.006116610020399094,
0.026104750111699104,
-0.012772091664373875,
-0.004292699508368969,
0.09551512449979782,
-0.03482700511813164,
-0.045190051198005676,
-0.0016786231426522136,
0.021296175196766853,
-0.0016470665577799082,
-0.0024464086163789034,
0.014789369888603687,
-0.02971735969185829,
0.029422231018543243,
0.013766149990260601,
0.006338923238217831,
-0.026783864945173264,
0.006942743435502052,
-0.05572865903377533,
-0.009106508456170559,
0.009250180795788765,
0.03784947469830513,
0.03434082493185997,
-0.0076632727868855,
0.025998687371611595,
-0.015456345863640308,
0.021629903465509415,
0.01425380352884531,
-0.010748517699539661,
-0.09184592962265015,
-0.04749219864606857,
-0.006324747111648321,
0.012041229754686356,
0.01537714060395956,
-0.010942801833152771,
0.009715749882161617,
-0.010043065994977951,
-0.09655670821666718,
0.008613892830908298,
-0.013471544720232487,
0.0247831791639328,
-0.06944655627012253,
-0.0000037122063076822087,
-0.059819579124450684,
0.016566576436161995,
0.0071335118263959885,
0.05470038577914238,
0.016484567895531654,
0.021332256495952606,
0.016467858105897903,
-0.011433248408138752,
-0.026570715010166168,
0.009454306215047836,
-0.00406956160441041,
0.024010155349969864,
0.08774720877408981,
-0.021964171901345253,
-0.0010791342938318849,
0.012824167497456074,
-0.008314911276102066,
0.03993216156959534,
-0.026391858235001564,
0.0026023222599178553,
0.0016278057591989636,
0.021546773612499237,
0.017044303938746452,
0.007497726008296013,
0.024237941950559616,
0.024109262973070145,
0.0160452201962471,
-0.008141796104609966,
-0.000392560992622748,
0.012732313014566898,
0.05421992763876915,
-0.028813300654292107,
-0.03851106017827988,
0.02783147245645523,
0.00029365502996370196,
-0.027764808386564255,
0.03770722076296806,
0.08001134544610977,
0.024326829239726067,
-0.0024263430386781693,
-0.03961111977696419,
-0.023169737309217453,
0.010731407441198826,
-0.01540387887507677,
0.041466474533081055,
0.02340167574584484,
0.0453808419406414,
-0.014485238119959831,
-0.017382783815264702,
0.00785584095865488,
0.04135794937610626,
-0.01602167636156082,
-0.035495053976774216,
-0.005469413008540869,
-0.014048435725271702,
0.05056232586503029,
0.008390816859900951,
-0.015236597508192062,
-0.048493642359972,
0.04846126213669777,
0.014997399412095547,
0.060382284224033356,
-0.02220170386135578,
-0.07069384306669235,
0.005945717915892601,
-0.030962638556957245,
0.04633792117238045,
-0.05117082968354225,
-0.0009540661121718585,
-0.016388261690735817,
-0.04629446193575859,
0.028728390112519264,
0.019035758450627327,
0.030621159821748734,
0.015814512968063354,
-0.021954301744699478,
0.06912904977798462,
-0.028416726738214493,
0.024064358323812485,
-0.05409994348883629,
0.03320426493883133,
-0.01895933598279953,
0.014802285470068455,
-0.007876483723521233,
-0.02213079109787941,
-0.051734887063503265,
0.04008999094367027,
0.050386447459459305,
-0.0237281434237957,
-0.01310275960713625,
0.021312488242983818,
0.007297846022993326,
0.07119645923376083,
0.03585357591509819,
0.010869309306144714,
0.06536474823951721,
-0.00840308889746666,
0.023233352228999138,
0.0063138315454125404,
-0.021094851195812225,
-0.026667160913348198,
0.025483064353466034,
-0.004257683642208576,
0.013494870625436306,
-0.012263478711247444,
-0.046050023287534714,
0.02472049556672573,
-0.026648078113794327,
0.017672166228294373,
0.036536216735839844,
-0.057695139199495316,
-0.028405604884028435,
0.019581306725740433,
-0.026711536571383476,
0.05241959169507027,
0.02007102593779564,
0.022265903651714325,
-0.011703171767294407,
-0.0018241654615849257,
-0.020980916917324066,
0.023055149242281914,
0.01742546074092388,
0.0019026582594960928,
0.028805429115891457,
0.0051980996504426,
0.03511589765548706,
0.0018111263634636998,
-0.011792032048106194,
-0.008257968351244926,
-0.015457957051694393,
0.003351155435666442,
0.05351529270410538,
-0.018898414447903633,
-0.017064180225133896,
0.01564052514731884,
-0.03722267597913742,
0.05505944788455963,
0.0016574604669585824,
0.016965312883257866,
-0.02595425583422184,
-0.023704657331109047,
0.027243560180068016,
0.028268059715628624,
0.006983455270528793,
0.038225073367357254,
-0.032620303332805634,
-0.009551646187901497,
0.005638198461383581,
0.02733885683119297,
0.022997582331299782,
-0.02797851152718067,
0.007429643999785185,
0.00920693576335907,
-0.012870047241449356,
0.015123054385185242,
0.014288674108684063,
-0.04297151044011116,
-0.015331697650253773,
0.021009331569075584,
0.01326367724686861,
-0.022207239642739296,
-0.0017631268128752708,
-0.017072072252631187,
-0.022889895364642143,
0.03463152050971985,
-0.022061515599489212,
0.01925947703421116,
-0.0163009874522686,
0.0025287687312811613,
-0.026405083015561104,
0.04179614409804344
] |
<p>We know that the spatial inversion parity for eigenfunctions of $\hat {L}_{z}$ operator (spherical functions) is $(-1)^{l}$, where $l$ refers to angular momentum. So for product of two eigenfunctions with definite summary angular momentum $L = l_{1} + l_{2}$ corresponding wavefunction has parity $(-1)^{L}$. </p>
<p>Also full wavefunction (in $\hat {L}_{z}$ representation) of two particles has parity $(-1)^{l_{1} + l_{2}}$ under their interchanging. For example, $l_{1} = l_{2} = l, L = 2l, m_{1} + m_{2} = 2l - 1$ in $\hat {L}_{z}$ it $\hat {L}_{z}$ representation is given as
$$
\langle l_{1}m_{1}, l_{2}m_{2}|L = 2l, M = 2l - 1\rangle = \frac{1}{\sqrt{2}}\left(\delta_{m_{1}l}\delta_{m_{2}(l - 1)} + \delta_{m_{1}(l - 1)}\delta_{m_{2}l} \right).
$$</p>
<p>The question: is it possible to establish a one-to-one correspondence between spatial inverse parity and interchange parity formally? One can imagine a bit classical mental experiment: let's have two particles with definite angular momentums. Let's use coordinate system with center in a middle of imaginary line which connects the particles. So in this case spatial inversion is equivalent to particles interchanging. I want to formalize it in a quantum case if this correspondence is true.</p>
| 8,856 |
[
-0.027156095951795578,
0.029967131093144417,
-0.03630506992340088,
0.01509618479758501,
0.050648003816604614,
0.015223628841340542,
-0.01151514332741499,
-0.02626090869307518,
0.03854050859808922,
-0.02223656140267849,
0.04402387887239456,
-0.0041708857752382755,
0.07943293452262878,
0.004329105373471975,
0.003554602852091193,
0.031395576894283295,
-0.04446641728281975,
0.01178587693721056,
-0.01105811819434166,
-0.010788362473249435,
0.015568138100206852,
0.03451298922300339,
0.021933799609541893,
0.003612792119383812,
-0.03244711831212044,
0.041796378791332245,
-0.0060007618740201,
-0.010348179377615452,
-0.0072593386285007,
0.083695188164711,
0.004626638256013393,
-0.0005501417326740921,
0.03935635834932327,
0.03405829146504402,
-0.044937293976545334,
0.0013805774506181479,
-0.029780099168419838,
-0.031282681971788406,
-0.0022645900025963783,
0.029428299516439438,
-0.04501233994960785,
-0.04617714881896973,
-0.05402348190546036,
0.059904035180807114,
0.008564723655581474,
-0.0027598983142524958,
-0.05611813813447952,
-0.004798757378011942,
0.04740392789244652,
-0.04890250787138939,
0.05902797356247902,
0.004862420726567507,
0.03447743505239487,
-0.017590388655662537,
-0.0013312478549778461,
0.015785260125994682,
0.0453004315495491,
0.07832705229520798,
0.03382449597120285,
-0.04908236116170883,
-0.04022865369915962,
-0.0501285083591938,
0.027583366259932518,
0.00700197322294116,
-0.03288445249199867,
-0.04501017555594444,
0.03086932934820652,
0.01700228452682495,
-0.006441468372941017,
-0.005805948283523321,
-0.03107951208949089,
-0.028531232848763466,
0.04818263277411461,
0.00790588278323412,
0.011508260853588581,
-0.016133476048707962,
0.017012521624565125,
-0.0007750550284981728,
-0.01530643180012703,
-0.003917173016816378,
-0.0397535115480423,
0.019621776416897774,
-0.011110534891486168,
0.01571529172360897,
0.0013699226547032595,
0.010474413633346558,
0.058361802250146866,
-0.0035453354939818382,
0.02792864851653576,
0.02006189525127411,
-0.00718064047396183,
-0.01252200547605753,
0.031975071877241135,
-0.0013102086959406734,
-0.04220592975616455,
0.03377519175410271,
0.01109043974429369,
0.018910638988018036,
-0.028152141720056534,
-0.05323219299316406,
0.006666408386081457,
0.02261524833738804,
0.017210744321346283,
0.057857923209667206,
-0.03121364302933216,
-0.027386829257011414,
-0.03481759876012802,
0.006501576863229275,
-0.015929533168673515,
-0.013394725508987904,
-0.024470064789056778,
0.011766736395657063,
-0.021802034229040146,
0.01319798082113266,
0.035914260894060135,
-0.046955324709415436,
-0.04570767283439636,
-0.006830345839262009,
0.055958814918994904,
0.07290209084749222,
0.05177272856235504,
-0.03536509349942207,
0.025944462046027184,
-0.0321337915956974,
-0.04216573014855385,
0.00243377685546875,
0.026439499109983444,
-0.0027012245263904333,
-0.048244658857584,
0.05446549504995346,
0.056096676737070084,
-0.038044583052396774,
0.030907975509762764,
-0.0022177950013428926,
0.02802238240838051,
-0.02515224553644657,
-0.0953480452299118,
-0.03423565998673439,
0.013555972836911678,
-0.05594593659043312,
-0.013217800296843052,
-0.07382615655660629,
-0.010483103804290295,
0.052090320736169815,
0.07636338472366333,
0.03571469336748123,
0.026840975508093834,
-0.01508015114814043,
0.019727908074855804,
0.046681925654411316,
-0.027300814166665077,
-0.02415699139237404,
0.017068780958652496,
-0.04166511446237564,
-0.014553109183907509,
-0.04430964216589928,
0.01958432048559189,
0.02999647706747055,
0.009718310087919235,
-0.01612589694559574,
0.0720941424369812,
-0.023244544863700867,
0.0018538773292675614,
0.041695576161146164,
0.012087102048099041,
-0.029362212866544724,
0.08995836973190308,
0.023297568783164024,
0.004902159795165062,
0.028362087905406952,
-0.023125022649765015,
-0.01338447630405426,
-0.010474690236151218,
0.028417712077498436,
0.023311058059334755,
-0.03729134425520897,
-0.05034714564681053,
-0.035125281661748886,
-0.01611023023724556,
-0.024941135197877884,
-0.04707751050591469,
0.003171520307660103,
-0.05836434289813042,
0.01758175529539585,
0.018458181992173195,
0.005414697807282209,
-0.019219115376472473,
-0.014428743161261082,
0.00918678566813469,
-0.04551713913679123,
0.006079799961298704,
-0.03766123950481415,
0.03277923911809921,
0.03705297037959099,
-0.029795920476317406,
0.05644566938281059,
0.0213487409055233,
0.04120640829205513,
-0.021089650690555573,
-0.04927029088139534,
-0.028753459453582764,
0.010590796358883381,
0.004141424782574177,
0.0022087479010224342,
-0.005881351884454489,
0.05606168508529663,
0.05717650428414345,
-0.008038348518311977,
0.008636509999632835,
-0.006463078316301107,
-0.012556454166769981,
-0.011649885214865208,
0.0013413159176707268,
0.0055522313341498375,
0.03933313116431236,
0.001200572936795652,
-0.02510003373026848,
0.006931918207556009,
-0.01494380459189415,
0.03254728764295578,
-0.037381161004304886,
0.04698915034532547,
0.05817658454179764,
0.00015436418470926583,
0.008867229335010052,
0.027494097128510475,
0.022934122011065483,
0.026709135621786118,
0.004772489424794912,
-0.05267605930566788,
0.0053108022548258305,
-0.009207096882164478,
0.017906326800584793,
0.041607700288295746,
-0.02461807057261467,
0.009142755530774593,
0.02115427516400814,
0.024858014658093452,
0.014958780258893967,
0.028023242950439453,
-0.013347754254937172,
-0.03611891344189644,
0.015200984664261341,
0.004499271512031555,
0.05079299956560135,
0.01464170590043068,
-0.006924973335117102,
0.008809031918644905,
0.001538743614219129,
0.04383600503206253,
-0.01389914657920599,
-0.00046561608905903995,
-0.036915041506290436,
-0.002729075262323022,
-0.01060882955789566,
-0.0023388692643493414,
0.02855658158659935,
0.004780486226081848,
0.019098103046417236,
0.029356544837355614,
-0.04073994979262352,
-0.014897839166224003,
-0.004782295785844326,
0.0018386344891041517,
0.013301020488142967,
-0.02217857539653778,
-0.044142577797174454,
-0.01113529596477747,
0.01017789077013731,
-0.01405929122120142,
0.012143497355282307,
0.027456680312752724,
-0.021558383479714394,
0.016896171495318413,
0.009401601739227772,
0.0466388538479805,
0.012255769222974777,
0.008390950970351696,
-0.009630555287003517,
-0.050084348767995834,
0.0194714218378067,
0.011273135431110859,
0.035723909735679626,
0.018106918781995773,
-0.06631717830896378,
0.023366158828139305,
-0.05955693498253822,
-0.01602037623524666,
0.014775584451854229,
0.008736846968531609,
0.013104371726512909,
-0.016531554982066154,
-0.013143177144229412,
-0.0830533504486084,
-0.029043521732091904,
-0.046679750084877014,
0.021867724135518074,
0.0028256301302462816,
0.002774918917566538,
0.01377004012465477,
-0.005767492577433586,
-0.017752697691321373,
-0.01937868446111679,
-0.02056465484201908,
-0.041181087493896484,
-0.018927281722426414,
-0.014545093290507793,
0.03882602974772453,
-0.024103477597236633,
0.04279658943414688,
0.023461133241653442,
-0.03594919666647911,
0.003296400886029005,
-0.08922691643238068,
-0.03451348841190338,
0.023652274161577225,
0.03941355645656586,
0.03962666913866997,
-0.0031253297347575426,
-0.02887081727385521,
0.05950210243463516,
-0.015836643055081367,
-0.03978155553340912,
-0.0051259747706353664,
0.015470866113901138,
-0.013267673552036285,
-0.0300784669816494,
0.01813354715704918,
-0.002361495280638337,
-0.010670909658074379,
0.07373494654893875,
0.02259976603090763,
-0.0033434818033128977,
0.019750701263546944,
0.006902677938342094,
-0.005517469719052315,
0.004466426093131304,
0.016153637319803238,
0.01296109240502119,
0.024952901527285576,
-0.029086919501423836,
-0.03677089512348175,
0.015116873197257519,
0.0328904427587986,
-0.017618851736187935,
0.003966311924159527,
-0.006926137022674084,
0.06432607024908066,
-0.0035458921920508146,
0.01916036382317543,
-0.0036674530711025,
0.05243118852376938,
0.018995149061083794,
0.01008310355246067,
0.0024806237779557705,
0.03978854790329933,
0.0436784103512764,
-0.030064819380640984,
-0.009027790278196335,
0.05755861476063728,
0.014417444355785847,
0.008178346790373325,
-0.0005577436531893909,
0.02149078994989395,
0.006182271987199783,
0.03649730607867241,
-0.030618540942668915,
-0.0424080491065979,
-0.00038295690319500864,
0.03169894963502884,
0.012381155043840408,
-0.004600815009325743,
-0.03180921822786331,
0.04781119152903557,
-0.007352572865784168,
0.02306998334825039,
-0.0008891602628864348,
0.024860071018338203,
-0.032235026359558105,
0.06215400621294975,
0.04283202067017555,
0.00006501676398329437,
-0.03957926481962204,
-0.00048652879195287824,
-0.04593244567513466,
-0.015929043292999268,
0.0021526473574340343,
0.04124060645699501,
-0.02832130528986454,
0.008568859659135342,
0.013896241784095764,
-0.04788236320018768,
-0.02571459487080574,
0.00208999402821064,
-0.034907158464193344,
-0.03604409098625183,
0.022646630182862282,
-0.04843393713235855,
0.006698670797049999,
-0.024181587621569633,
0.0700647383928299,
-0.0033769274596124887,
-0.021006133407354355,
0.02611653506755829,
0.07125578075647354,
-0.07113625854253769,
0.027478864416480064,
-0.03592051938176155,
0.01462467946112156,
0.017624009400606155,
0.02940947189927101,
0.04844541847705841,
0.039448484778404236,
-0.006982089020311832,
0.011435775086283684,
-0.03165340796113014,
0.03714665025472641,
0.025236470624804497,
0.0015727380523458123,
0.028708796948194504,
-0.033078014850616455,
-0.01046878844499588,
-0.021918419748544693,
0.07081210613250732,
0.0013150962768122554,
0.012026331387460232,
0.028444791212677956,
0.015121967531740665,
-0.014359851367771626,
0.024393673986196518,
0.04625936597585678,
-0.007186100818216801,
-0.014236178249120712,
-0.04143897444009781,
0.0003405460447538644,
0.010567525401711464,
-0.029511289671063423,
0.03682974353432655,
-0.011184087023139,
-0.01912548579275608,
0.0039253756403923035,
0.029974346980452538,
0.021267419680953026,
-0.020653553307056427,
0.013705814257264137,
-0.02867087908089161,
0.029913876205682755,
0.017989061772823334,
0.018470022827386856,
0.007837211713194847,
0.03582944720983505,
0.011847957968711853,
0.013213827274739742,
0.01743966154754162,
-0.046551428735256195,
0.016164062544703484,
0.025607002899050713,
0.0207829587161541,
-0.007419694680720568,
0.006744887679815292,
-0.040869660675525665,
-0.036897193640470505,
0.04875390604138374,
-0.02046826295554638,
0.04331342130899429,
-0.014961108565330505,
-0.021083977073431015,
0.000888609851244837,
-0.02899613045156002,
-0.00947327446192503,
0.05198701098561287,
-0.01720193773508072,
-0.014200827106833458,
-0.07826963812112808,
-0.010585270822048187,
-0.049425434321165085,
-0.0012590920086950064,
0.010331920348107815,
0.04079928621649742,
0.0037140240892767906,
0.02029481716454029,
-0.03554677963256836,
0.06660426408052444,
-0.005966969300061464,
-0.05323841795325279,
0.0016335492255166173,
0.03283163160085678,
-0.010285085998475552,
0.05741434171795845,
-0.03170048072934151,
-0.02869531698524952,
0.011826258152723312,
-0.00935661792755127,
-0.010435422882437706,
0.030458837747573853,
0.011246406473219395,
0.06363319605588913,
0.03956571966409683,
-0.01956864818930626,
0.07089948654174805,
-0.003399268491193652,
-0.003653700929135084,
-0.016212156042456627,
0.011116435751318932,
0.017942357808351517,
-0.01777876913547516,
0.004394390620291233,
-0.045254502445459366,
0.027805788442492485,
-0.035007916390895844,
0.07354433834552765,
-0.03940427303314209,
0.0021380679681897163,
0.016681266948580742,
-0.00273612211458385,
-0.04223841801285744,
0.0718676820397377,
-0.026769571006298065,
-0.008654100820422173,
-0.007712895981967449,
-0.0025770324282348156,
0.006204718723893166,
-0.029302790760993958,
-0.010005195625126362,
-0.013168723322451115,
-0.007037556730210781,
-0.013825653120875359,
-0.025027599185705185,
0.053858432918787,
-0.03515263646841049,
-0.015499217435717583,
-0.02530086785554886,
-0.05291273817420006,
0.0055832937359809875,
-0.0057046678848564625,
0.010494493879377842,
0.01185985654592514,
-0.06680771708488464,
-0.023143906146287918,
0.050853289663791656,
-0.011527623981237411,
-0.004541195463389158,
-0.03207661211490631,
-0.02454439178109169,
0.012086587026715279,
-0.006219231523573399,
-0.07676072418689728,
-0.032789189368486404,
0.023488419130444527,
-0.0022376172710210085,
-0.015402257442474365,
-0.020514683797955513,
-0.0003544001083355397,
0.02216694876551628,
-0.034781306982040405,
-0.000008660994353704154,
0.032482780516147614,
-0.038586150854825974,
-0.02788381837308407,
0.018813010305166245,
0.005289314314723015,
0.04714617505669594,
-0.049573469907045364,
-0.011244373396039009,
-0.0055197481997311115,
-0.005257079843431711,
0.003777927253395319,
0.02281244285404682,
0.01838623359799385,
-0.0024136172141879797,
-0.053016845136880875,
-0.031230119988322258,
0.00022182958491612226,
0.018275214359164238,
-0.041458915919065475,
-0.03501376137137413,
-0.000755010696593672,
-0.0035376788582652807,
0.0040802606381475925,
-0.009687217883765697,
-0.010303480550646782,
-0.04084708169102669,
0.0462622307240963,
-0.007316311821341515,
-0.01828545145690441,
-0.033331070095300674,
-0.01800747774541378,
-0.009406492114067078,
-0.008627831004559994,
-0.006966042798012495,
0.013908534310758114,
0.060124147683382034,
-0.007252519018948078,
0.0161226075142622,
0.054653100669384,
0.007664210628718138,
0.004615768790245056,
-0.011693873442709446,
0.007129318080842495,
-0.018188370391726494,
0.009167899377644062,
-0.048095595091581345,
-0.022893568500876427,
-0.00010514853784115985,
0.024924064055085182,
0.0356430858373642,
0.006359116639941931,
0.05041518062353134,
0.032252758741378784,
0.027425065636634827,
-0.03339190036058426,
-0.009702605195343494,
-0.0017348994733765721,
0.015785716474056244,
-0.00858992151916027,
0.05815485492348671,
-0.05998964607715607,
0.005296781193464994,
0.05620129778981209,
0.07785815000534058,
-0.011232767254114151,
0.01458596158772707,
0.0005774405435658991,
0.01042087934911251,
0.024739069864153862,
-0.008157068863511086,
-0.021281201392412186,
0.034684937447309494,
-0.05111638829112053,
0.02466481365263462,
-0.021735168993473053,
0.005508928559720516,
0.028255123645067215,
0.01415087841451168,
0.027868835255503654,
-0.03440186381340027,
-0.0419694222509861,
-0.042745549231767654,
0.02285711281001568,
0.022712262347340584,
-0.0017817470943555236,
0.010638453997671604,
-0.009492959827184677,
0.03345425799489021,
-0.015353204682469368,
0.00010698682308429852,
-0.06268144398927689,
-0.05946584790945053,
-0.0318281464278698,
-0.020570412278175354,
-0.03711170330643654,
0.0393010750412941,
-0.024643288925290108,
0.012855183333158493,
-0.0005592004745267332,
0.0006997809396125376,
0.008209403604269028,
0.019747259095311165,
0.050283949822187424,
-0.05101705715060234,
0.07407902926206589,
0.014940301887691021,
0.061515554785728455,
-0.011702503077685833,
0.012158123776316643,
0.11314114928245544,
-0.007524960674345493,
0.01503029465675354,
-0.08503700792789459,
0.02611391432583332,
-0.008043225854635239,
-0.0005614352994598448,
-0.05162817984819412,
0.03654801473021507,
0.010525443591177464,
-0.02508077584207058,
-0.019319280982017517,
0.06913723796606064,
0.0031790989451110363,
-0.0028446989599615335,
0.033276885747909546,
-0.030966971069574356,
-0.0402522012591362,
-0.028197428211569786,
0.007381435949355364,
0.005418913438916206,
0.026056913658976555,
-0.03076973930001259,
-0.014859936200082302,
-0.01922762766480446,
0.023857496678829193,
-0.006586612667888403,
-0.020946329459547997,
0.019861191511154175,
0.006466403137892485,
-0.03396403044462204,
0.00914071500301361,
0.010794896632432938,
-0.002754230285063386,
-0.009371884167194366,
0.009391739964485168,
-0.001193962525576353,
0.015817362815141678,
0.0236833356320858,
0.023259224370121956,
0.009428908117115498,
0.007879035547375679,
0.04824875295162201,
0.005499471910297871,
-0.03276291862130165,
0.011780906468629837,
-0.0046846214681863785,
0.046271633356809616,
-0.03750593960285187,
-0.013342774473130703,
-0.014032787643373013,
-0.04368757829070091,
0.004841740243136883,
-0.039030447602272034,
-0.009713774546980858,
0.013895435258746147,
0.03155619651079178,
-0.005238885525614023,
0.02374914102256298,
-0.0058797323144972324,
0.011744619347155094,
0.0350068099796772,
0.028362296521663666,
-0.05426201596856117,
-0.032829951494932175,
0.021121008321642876,
0.036647628992795944,
0.03687422722578049,
-0.009975798428058624,
-0.027494996786117554,
-0.03045027330517769,
0.002726214472204447,
-0.02646462991833687,
-0.030713222920894623,
0.04123660922050476,
-0.005972282961010933,
0.05005498602986336,
0.009708590805530548,
-0.024624019861221313,
-0.0010467305546626449,
-0.07758305221796036,
-0.039079710841178894,
-0.012019996531307697,
-0.04753595218062401,
0.025632105767726898,
0.014594389125704765,
0.044736240059137344,
0.046187762171030045,
-0.07084500044584274,
-0.02438354678452015,
-0.012578691355884075,
0.011198572814464569,
0.02027246728539467,
-0.049942824989557266,
-0.05152682960033417,
-0.006424325052648783,
-0.022644568234682083,
-0.012191139161586761,
-0.044072143733501434,
-0.00129824283067137,
0.015804104506969452,
0.039104949682950974,
-0.020189359784126282,
0.04714145138859749,
-0.028947358950972557,
0.021578174084424973,
-0.000990409287624061,
-0.03106033243238926,
-0.01816396415233612,
0.002486403100192547,
0.025743234902620316,
-0.00959485862404108,
-0.02313186414539814,
0.016718801110982895,
-0.01899304799735546,
0.0017564046429470181,
0.010139845311641693,
-0.03171568363904953,
-0.031851626932621,
-0.009687625803053379,
-0.008331172168254852,
-0.026377243921160698,
-0.009861532598733902,
-0.0138392997905612,
0.015218193642795086,
0.0053422958590090275,
-0.013724010437726974,
0.01454250980168581,
0.04166385531425476,
-0.021451901644468307,
-0.013973173685371876,
0.03533576801419258,
0.06756308674812317,
-0.021971872076392174,
0.012603018432855606,
0.02516733482480049,
0.026633819565176964,
0.06620501726865768,
-0.037392087280750275,
-0.03667626157402992,
0.02135762944817543,
-0.023226896300911903,
-0.04399445280432701,
0.04601676017045975,
-0.009733648039400578,
0.06863050907850266,
0.03458433970808983,
-0.00021540939633268863,
-0.025480397045612335,
0.05450597405433655,
-0.025263244286179543,
-0.0015787965385243297,
0.010533958673477173,
-0.013131576590240002,
-0.01226176880300045,
-0.0338984914124012,
0.028530539944767952,
-0.02535601519048214,
-0.023041343316435814,
0.0031789434142410755,
0.01740673929452896,
-0.020547684282064438,
-0.001581565011292696,
0.01178477331995964,
0.009743733331561089,
0.030424224212765694,
0.026639005169272423,
-0.02049075998365879,
0.027892950922250748,
0.03911871090531349,
-0.04161299392580986,
0.03334570303559303,
0.043861620128154755,
-0.00047874145093373954,
-0.06522230803966522,
0.0032435066532343626,
0.04348784685134888,
0.010633129626512527,
0.025729158893227577,
-0.05447099357843399,
0.050940729677677155,
0.03279031813144684,
-0.04971083626151085,
0.01150857750326395,
-0.046697866171598434,
-0.007865622639656067,
-0.033052630722522736,
-0.012677706778049469,
-0.05564086511731148,
0.03258180990815163,
0.011502962559461594,
0.035584956407547,
0.012733628042042255,
0.006025207694619894,
-0.005688753444701433,
-0.03361188992857933,
-0.04121804237365723,
-0.0040858108550310135,
-0.008235189132392406,
-0.03093518130481243,
0.09461314976215363,
-0.03513362258672714,
-0.03914527967572212,
0.033340759575366974,
-0.04476005584001541,
-0.021653970703482628,
-0.025360839441418648,
0.023492105305194855,
-0.008904495276510715,
0.022301724180579185,
-0.014188003726303577,
0.016027560457587242,
-0.011495925486087799,
-0.0017733459826558828,
0.04030781611800194,
0.003627046709880233,
-0.02938578836619854,
0.005614632274955511,
0.008756670169532299,
-0.02790891006588936,
-0.01970398612320423,
0.05341225862503052,
-0.011888646520674229,
-0.015140041708946228,
-0.01803085021674633,
0.008326803334057331,
0.04330867901444435,
-0.044963207095861435,
0.04683760553598404,
-0.04837635159492493,
-0.021795857697725296,
0.017188942059874535,
0.012703629210591316,
-0.017647473141551018,
0.0004503356758505106,
0.0004094263131264597,
-0.06756258755922318,
0.0699017122387886,
0.011987559497356415,
-0.03333370015025139,
-0.03550078347325325,
-0.025149744004011154,
0.03008023090660572,
-0.005598400719463825,
0.031330909579992294,
-0.0602235309779644,
-0.054302819073200226,
0.03506186604499817,
-0.039887621998786926,
0.04423709586262703,
-0.033542320132255554,
-0.0232789795845747,
-0.024184321984648705,
-0.0606490783393383,
0.021093256771564484,
0.015098657459020615,
0.014261482283473015,
0.02706533670425415,
-0.0019277272513136268,
-0.021801846101880074,
-0.010355962440371513,
0.053818292915821075,
0.014472349546849728,
-0.026628097519278526,
0.01527886651456356,
0.01606886461377144,
0.018261944875121117,
-0.005278388503938913,
-0.022863829508423805,
-0.02967924438416958,
-0.03435518220067024,
0.021334538236260414,
-0.008554988540709019,
-0.020314615219831467,
0.021586131304502487,
0.007832369767129421,
-0.014843557961285114,
-0.003158256644383073,
-0.010315122082829475,
-0.0835411548614502,
0.05335794389247894,
0.012669824995100498,
-0.014092518016695976,
0.045588914304971695,
0.02889975532889366,
0.001956666586920619,
0.013152875006198883,
0.005410353187471628,
-0.05056232959032059,
0.005556168500334024,
-0.02632306143641472,
-0.021874157711863518,
-0.023486481979489326,
0.03700389713048935,
0.02603626437485218,
-0.018568290397524834,
-0.013278577476739883,
0.02479931339621544,
-0.038077425211668015,
-0.017565274611115456,
0.04878753423690796,
0.00878298282623291,
0.023451674729585648,
0.009596881456673145,
0.024119403213262558,
0.017311790958046913,
0.013065486215054989,
0.04653507098555565,
0.0477866604924202,
0.02027723379433155,
0.01502565573900938,
0.001112069352529943,
0.010044635273516178,
-0.009307562373578548,
0.029888756573200226,
0.0015513774706050754,
0.05248917266726494,
0.018488341942429543,
0.021434735506772995,
0.05504949763417244,
-0.02019713819026947,
-0.011595114134252071,
0.01167166419327259,
0.00435310322791338,
0.04993044212460518,
-0.022897250950336456,
0.02825953997671604,
-0.06527484953403473,
0.02172301523387432,
0.011244605295360088,
0.021910740062594414,
0.029324522241950035,
0.013812355697154999,
-0.013793395832180977,
-0.012308135628700256,
-0.02554934471845627,
0.0009073512628674507,
-0.00286412937566638,
-0.044557735323905945,
0.012949408032000065,
-0.016435610130429268,
-0.050519853830337524,
0.008566870354115963,
-0.06760728359222412,
0.007309046573936939,
-0.039704568684101105,
0.011112378910183907,
0.0562874972820282,
0.06565724313259125,
-0.005676326807588339,
-0.018120214343070984,
-0.00392580684274435,
0.0432952381670475,
-0.04654856026172638,
-0.03755152225494385,
0.009250897914171219,
0.016582701355218887,
-0.027125263586640358,
0.032255519181489944
] |
<p>I am a rank amateur, so please forgive me if the answer to this is well-known.</p>
<p>The following quote can in a weekly update for an EdX course I am following in astrophysics:</p>
<blockquote>
<p>"And what a week it's been with the recent discovery of primordial gravitational waves from the epoch of inflation! This one observation has pushed back the earliest direct measurements of the Universe from about 1 second (the epoch of nucleosynthesis) to $10^{-35}$ seconds (the epoch of inflation)."</p>
</blockquote>
<p>I would appreciate any comments as to what it will take to close the gap.</p>
<p><strong>EDIT</strong>: Well, initially I asked this question with a few specific alternatives. Perhaps - respectfully and with moderators' approval -I should revert to that (as best as I can remember), in that any one of them could be answered with a "yes" or "no" and a few qualifying, suggestive sentences.</p>
<p>-- Would a viable GUT do the job.</p>
<p>-- Are there currently specifically directed experiments whose intended results will answer the question.</p>
<p>-- Can the gap be closed by correct extrapolation of know experimental and theoretical results.</p>
<p>If this is yet deemed unacceptable, I understand, and please feel free to restrict my question as deemed appropriate.</p>
| 8,857 |
[
-0.00793877337127924,
-0.04506893455982208,
-0.0010215654037892818,
-0.02863914519548416,
0.035955652594566345,
-0.01600850187242031,
-0.0271369107067585,
-0.059718430042266846,
-0.007420096546411514,
-0.02711057849228382,
0.009135260246694088,
0.04853568971157074,
0.04068080335855484,
0.012511735782027245,
0.0033606949727982283,
0.0326908715069294,
-0.005649936851114035,
-0.031949080526828766,
0.005235275719314814,
-0.02361867018043995,
0.023351900279521942,
0.02154371328651905,
-0.01526294182986021,
0.015754785388708115,
-0.03853117302060127,
0.022266283631324768,
0.05201103165745735,
0.0011565505992621183,
-0.012965970672667027,
0.07557926326990128,
-0.02822434902191162,
-0.04186791181564331,
0.008062795735895634,
0.04217424616217613,
0.03210972994565964,
-0.01713431067764759,
0.005584174767136574,
-0.04317573830485344,
-0.0236045029014349,
0.030745087191462517,
-0.05094523727893829,
0.0024427196476608515,
-0.006094431504607201,
0.020590191707015038,
-0.002830812241882086,
-0.00865992158651352,
0.01039951853454113,
0.007260762155056,
0.03997737541794777,
-0.02575650066137314,
0.03878573328256607,
-0.018177973106503487,
0.05200814828276634,
0.00840152706950903,
-0.0449967160820961,
-0.016084471717476845,
0.10532345622777939,
0.060757506638765335,
-0.000803582661319524,
-0.03841901943087578,
-0.02455659955739975,
0.019340675324201584,
-0.008613436482846737,
0.00737339723855257,
-0.05582970380783081,
0.04671351611614227,
-0.05324660614132881,
-0.02234559878706932,
0.014853590168058872,
-0.031645528972148895,
-0.005324139259755611,
0.015680264681577682,
0.06448447704315186,
0.030490143224596977,
0.027811693027615547,
-0.04072323068976402,
0.02311232127249241,
-0.00195659720338881,
0.0209648460149765,
0.05963868275284767,
-0.04146970435976982,
0.0006454483373090625,
0.05775199830532074,
0.06501948088407516,
0.023639803752303123,
0.020757250487804413,
0.08187264204025269,
-0.060996249318122864,
0.00016370842058677226,
0.05344120040535927,
-0.029114969074726105,
0.0073017640970647335,
0.040633030235767365,
0.010412044823169708,
-0.016181115061044693,
0.04310959577560425,
-0.010582336224615574,
0.052315790206193924,
-0.004549864213913679,
-0.05883420631289482,
0.04397394880652428,
-0.010604016482830048,
0.03938845545053482,
0.08925850689411163,
0.020934414118528366,
-0.002994301961734891,
-0.032016970217227936,
0.009669213555753231,
-0.04480506479740143,
-0.034402091056108475,
-0.03592242673039436,
0.017435826361179352,
-0.033980485051870346,
-0.01934119500219822,
-0.00015712776803411543,
-0.04792160540819168,
0.007500927429646254,
-0.04102586582303047,
0.070734903216362,
0.05560566484928131,
0.03944128006696701,
-0.0028786128386855125,
0.019017046317458153,
-0.0403667651116848,
-0.06698713451623917,
-0.010510195046663284,
0.035485051572322845,
-0.010074335150420666,
-0.02879662811756134,
0.01129263173788786,
-0.0144664840772748,
-0.005682441871613264,
0.018764324486255646,
-0.029860518872737885,
0.05722562596201897,
-0.0011477370280772448,
-0.08421451598405838,
-0.07220128178596497,
0.06424571573734283,
-0.003977468702942133,
-0.013971959240734577,
-0.07840530574321747,
0.008578328415751457,
0.014746556058526039,
0.03607059270143509,
0.029590675607323647,
-0.003539257450029254,
-0.046455420553684235,
0.04376506060361862,
0.016411831602454185,
-0.026981348171830177,
-0.004221591167151928,
0.012282956391572952,
-0.024795571342110634,
0.0015626674285158515,
-0.03496958687901497,
0.015873242169618607,
0.024601729586720467,
-0.0319305881857872,
-0.014627060852944851,
0.060749299824237823,
0.0013669714098796248,
-0.007355703506618738,
0.008092696778476238,
0.02417866513133049,
-0.03518759086728096,
0.08945148438215256,
0.05165030062198639,
-0.029903443530201912,
0.028940586373209953,
0.0017246271017938852,
0.006288639269769192,
0.024390721693634987,
-0.001841713092289865,
0.03628277778625488,
-0.05261163040995598,
-0.03487327694892883,
-0.004777401220053434,
-0.010103683918714523,
-0.01868022046983242,
-0.0032996400259435177,
0.010683991946280003,
-0.02704915963113308,
-0.009147859178483486,
0.007466953247785568,
0.036945492029190063,
-0.02220136672258377,
-0.006937909871339798,
0.009222525171935558,
-0.0341971255838871,
-0.020125823095440865,
-0.06246766448020935,
-0.024660354480147362,
0.02555834874510765,
-0.0008268191013485193,
0.01425428781658411,
-0.04403507336974144,
0.020389875397086143,
-0.01728171668946743,
-0.05814265459775925,
0.007459173444658518,
0.010397280566394329,
0.058918148279190063,
0.016019055619835854,
0.012253439985215664,
0.055183541029691696,
0.04954720661044121,
-0.03873971477150917,
0.002160185482352972,
0.013335427269339561,
-0.03898529335856438,
0.020553771406412125,
-0.017716586589813232,
0.029496753588318825,
-0.004342071246355772,
0.03079076111316681,
0.015439084731042385,
-0.007434540893882513,
0.015162467956542969,
0.042121902108192444,
-0.014978053979575634,
0.09432105720043182,
0.013238553889095783,
0.0332634374499321,
-0.032963208854198456,
0.02794761396944523,
0.03486241027712822,
0.06135806068778038,
-0.016534188762307167,
-0.011280165985226631,
-0.06329046934843063,
-0.026050053536891937,
0.020831041038036346,
0.007241313345730305,
-0.008309876546263695,
0.0384213961660862,
0.040896154940128326,
0.004813306499272585,
-0.0029107185546308756,
0.01664077118039131,
-0.012255732901394367,
-0.03545565903186798,
0.017850730568170547,
0.024910515174269676,
-0.002850338350981474,
0.02185453101992607,
0.023095011711120605,
-0.009891967289149761,
0.02620946243405342,
0.01474524475634098,
0.044153984636068344,
0.004222332499921322,
0.004716096445918083,
-0.03259050101041794,
-0.019946888089179993,
-0.03382565453648567,
0.030454237014055252,
-0.006072426214814186,
-0.01658172719180584,
0.02776304818689823,
0.014492761343717575,
-0.02509116195142269,
-0.02941107004880905,
0.012179084122180939,
0.010924399830400944,
0.015534209087491035,
-0.03340550512075424,
-0.01320775505155325,
0.02078544721007347,
-0.052129507064819336,
0.0002518789260648191,
-0.010440937243402004,
-0.02186264656484127,
-0.025377420708537102,
-0.024530824273824692,
0.018170874565839767,
0.00886945053935051,
0.003722209483385086,
-0.05508016049861908,
-0.037203434854745865,
0.0007630648906342685,
0.006609766744077206,
-0.0055127572268247604,
0.006528702564537525,
-0.022552797570824623,
0.017118455842137337,
-0.03086695447564125,
0.0032760307658463717,
-0.009624119848012924,
-0.032613709568977356,
0.02825351618230343,
0.007842246443033218,
-0.005225042346864939,
-0.031887974590063095,
-0.005639605689793825,
-0.052524734288454056,
0.01912650652229786,
-0.022554069757461548,
-0.003951781429350376,
0.054471954703330994,
-0.005640960298478603,
-0.05353592336177826,
0.0007440194603987038,
-0.009878918528556824,
-0.011838202364742756,
-0.03851398080587387,
0.01336976233869791,
-0.006254120264202356,
-0.055505525320768356,
0.027443483471870422,
-0.00858114194124937,
0.006922874599695206,
0.0257125124335289,
-0.06165219470858574,
-0.07468963414430618,
0.04124270752072334,
-0.008860846050083637,
0.02218150906264782,
-0.01922992616891861,
-0.009331949055194855,
0.03003033436834812,
0.017524011433124542,
-0.02488170564174652,
-0.02649056725203991,
0.016626253724098206,
0.03692181035876274,
-0.005325355567038059,
-0.002947648288682103,
0.0030551208183169365,
0.027146564796566963,
0.025392519310116768,
0.043565813452005386,
0.059944380074739456,
-0.011270958930253983,
0.03640662133693695,
-0.0044723316095769405,
-0.0069363415241241455,
0.00799024198204279,
0.02916465699672699,
0.017121849581599236,
0.03085201419889927,
-0.03227062150835991,
-0.009685871191322803,
-0.034650158137083054,
0.024828897789120674,
0.01777966134250164,
-0.0537879653275013,
0.03569536283612251,
-0.010678485967218876,
-0.005030647851526737,
-0.019746016710996628,
0.027695773169398308,
-0.007824700325727463,
-0.008306696079671383,
0.02860948257148266,
-0.01064328569918871,
0.0568694993853569,
0.02833297662436962,
0.007500867825001478,
0.02513798512518406,
0.016939014196395874,
0.025416826829314232,
-0.0003619518247433007,
-0.006612076889723539,
-0.042651209980249405,
0.019262759014964104,
-0.01962612010538578,
0.00689643993973732,
0.03367426246404648,
0.058773621916770935,
0.032580308616161346,
-0.012221590615808964,
-0.04577997699379921,
-0.005720315035432577,
-0.06742440909147263,
-0.00016817136202007532,
0.008473229594528675,
0.037254683673381805,
-0.010328831151127815,
0.06032431870698929,
0.03425345942378044,
-0.010629444383084774,
0.0010716402903199196,
-0.020869161933660507,
-0.10458038002252579,
0.009387516416609287,
-0.049903929233551025,
-0.003146726405248046,
-0.02385280467569828,
0.011902191676199436,
-0.0061708358116447926,
-0.01139803696423769,
-0.011584322899580002,
-0.0334869809448719,
0.006953687872737646,
-0.06711001694202423,
0.021694006398320198,
-0.0385967493057251,
-0.00657864473760128,
-0.010160845704376698,
-0.005029844120144844,
0.05795292183756828,
-0.005048931576311588,
0.024889791384339333,
0.015628546476364136,
0.007970747537910938,
-0.02240152470767498,
0.014281541109085083,
0.04807209596037865,
-0.022494567558169365,
0.0574696809053421,
0.041339561343193054,
0.015115704387426376,
-0.059051770716905594,
0.029076188802719116,
0.059698037803173065,
0.03198215365409851,
0.020001104101538658,
-0.009765632450580597,
-0.02745657041668892,
-0.03924911841750145,
-0.039793677628040314,
0.015545321628451347,
0.05769749730825424,
-0.005834776908159256,
0.004946116358041763,
0.023064790293574333,
0.043576743453741074,
-0.02258932776749134,
0.06298140436410904,
0.06774512678384781,
-0.053490009158849716,
-0.02722075767815113,
-0.055267542600631714,
-0.04928198084235191,
-0.039641156792640686,
0.010747247375547886,
0.014454785734415054,
0.009791366755962372,
0.0003916021669283509,
-0.0036458352115005255,
0.01925271935760975,
0.005198023281991482,
-0.014320824295282364,
-0.012811998836696148,
-0.018719611689448357,
0.03930392488837242,
-0.027175508439540863,
0.011129380203783512,
-0.011643010191619396,
0.0453653447329998,
0.09146374464035034,
-0.015128685161471367,
-0.010148228146135807,
-0.06338120996952057,
0.007807549089193344,
0.03237828239798546,
0.05086660012602806,
-0.015407178550958633,
-0.020228127017617226,
-0.05299849435687065,
-0.027695320546627045,
0.027058688923716545,
-0.010971187613904476,
0.017053620889782906,
-0.011884026229381561,
-0.024013688787817955,
0.01659427024424076,
-0.03635643422603607,
0.007686192635446787,
0.01479986310005188,
0.019372645765542984,
-0.004766747821122408,
0.0021257244516164064,
-0.0018962443573400378,
-0.0051627070643007755,
0.0026488741859793663,
0.03565307334065437,
0.06961991637945175,
0.007936416193842888,
-0.00040823969175107777,
0.007631020620465279,
-0.015438072383403778,
-0.025893036276102066,
-0.08528853207826614,
0.025879135355353355,
-0.03199121356010437,
-0.054152991622686386,
0.02481057681143284,
-0.04263000190258026,
-0.056637734174728394,
0.0342501737177372,
0.03224187716841698,
-0.03128295764327049,
0.013197963126003742,
-0.032268594950437546,
0.05132153630256653,
0.030029745772480965,
0.017979765310883522,
0.038824837654829025,
0.0335703119635582,
0.027171384543180466,
0.03181824833154678,
-0.012064200825989246,
-0.004731525667011738,
-0.03675965592265129,
-0.0072686998173594475,
-0.003537882585078478,
-0.00003944995114579797,
-0.04830263555049896,
0.023858390748500824,
-0.03455404192209244,
0.007546554319560528,
-0.0038982206024229527,
-0.0212422963231802,
0.007612690795212984,
0.04381702467799187,
-0.017627978697419167,
0.02363133244216442,
0.00022786115005146712,
0.018039487302303314,
0.0019653928466141224,
0.0006725026178173721,
0.016134565696120262,
-0.008509122766554356,
0.025302963331341743,
0.005089674610644579,
-0.0028712586499750614,
0.028718916699290276,
-0.0032641098368912935,
-0.008843095041811466,
0.04982144385576248,
-0.0057541741989552975,
0.05120906978845596,
-0.0030175698921084404,
0.01893814653158188,
-0.004563870839774609,
-0.05049644410610199,
-0.022147387266159058,
0.023581495508551598,
-0.005199131090193987,
0.039913441985845566,
-0.03431373089551926,
-0.0023711633402854204,
0.006327052600681782,
0.03393689543008804,
-0.1035231351852417,
-0.05210486426949501,
0.04286758229136467,
0.0391080304980278,
-0.02205190621316433,
-0.017077386379241943,
-0.01345745474100113,
-0.04187589883804321,
-0.003710248041898012,
-0.026803918182849884,
0.030533762648701668,
-0.014724505133926868,
-0.013900138437747955,
-0.009101261384785175,
0.01989678479731083,
0.047445692121982574,
-0.010170030407607555,
-0.014660150744020939,
-0.005653504282236099,
-0.007423392031341791,
0.010547807440161705,
0.012019667774438858,
0.027806691825389862,
-0.02881348878145218,
-0.024878811091184616,
-0.012467125430703163,
-0.010710112750530243,
0.016597455367445946,
-0.056948237121105194,
-0.008647821843624115,
0.07123115658760071,
-0.017842324450612068,
0.01968507282435894,
-0.03622613102197647,
0.03282961994409561,
-0.051221419125795364,
-0.024520298466086388,
-0.0053178174421191216,
-0.021389352157711983,
0.015538097359240055,
-0.02808135189116001,
0.041010960936546326,
-0.005896774120628834,
-0.011448132805526257,
-0.023747319355607033,
0.039246294647455215,
-0.014348583295941353,
-0.0370618999004364,
0.02396608702838421,
-0.019318923354148865,
0.027079816907644272,
-0.011274636723101139,
0.016463760286569595,
0.015658922493457794,
-0.00736130028963089,
-0.04535767063498497,
-0.04691265523433685,
-0.021040992811322212,
-0.02508561685681343,
0.07584651559591293,
-0.006322688888758421,
0.0368548184633255,
-0.023209230974316597,
0.004051363095641136,
-0.04325210303068161,
-0.03447191044688225,
-0.011696979403495789,
0.032088182866573334,
0.009215112775564194,
0.011139453388750553,
-0.02326480858027935,
0.00974335614591837,
0.0029902500100433826,
0.01975044421851635,
0.0075799222104251385,
0.026791000738739967,
0.03139788284897804,
0.04409024491906166,
0.03665010631084442,
-0.06314942985773087,
-0.02179136499762535,
-0.005157875828444958,
-0.04497813805937767,
0.025963956490159035,
-0.003060572547838092,
-0.012203896418213844,
0.022672759369015694,
0.0246892087161541,
0.025939244776964188,
0.0326465480029583,
-0.009223557077348232,
-0.040870070457458496,
-0.017641860991716385,
0.033719923347234726,
0.026727499440312386,
0.005502703133970499,
-0.01889677904546261,
0.01034859661012888,
0.012850876897573471,
0.0122958580031991,
0.006200683303177357,
-0.08129572123289108,
-0.04229298233985901,
-0.018376482650637627,
-0.04708915576338768,
0.07742135971784592,
-0.009488392621278763,
-0.05300214886665344,
0.021096279844641685,
0.007763606496155262,
-0.024858757853507996,
-0.014359469525516033,
0.030490510165691376,
-0.026750314980745316,
0.0465242974460125,
-0.0005596666014753282,
0.008314435370266438,
-0.015516940504312515,
0.02778029441833496,
0.1237054392695427,
0.06004604324698448,
0.018863486126065254,
-0.035331059247255325,
0.03829269856214523,
-0.025964276865124702,
-0.007023300975561142,
-0.017575165256857872,
0.030151793733239174,
-0.00489116832613945,
-0.02279834635555744,
0.0314750038087368,
0.05511653795838356,
0.0013763735769316554,
0.003350116079673171,
0.05823097378015518,
-0.03697596862912178,
-0.004215885419398546,
0.001165438094176352,
0.04775422066450119,
0.028517654165625572,
0.0028509802650660276,
-0.019789312034845352,
0.01904601790010929,
-0.03587445616722107,
-0.0005343850934877992,
0.0006708556320518255,
-0.028402887284755707,
0.017724841833114624,
-0.02010241150856018,
-0.03612040728330612,
0.0017935853684321046,
-0.0005964707816019654,
-0.0120517173781991,
-0.05416814610362053,
0.0005950024351477623,
0.010812554508447647,
0.006288089323788881,
0.006571547593921423,
0.025190742686390877,
0.03262954205274582,
0.0008244336931966245,
-0.008502953685820103,
-0.0010978803038597107,
-0.013481060974299908,
-0.00748080387711525,
-0.0009383343276567757,
0.050220537930727005,
-0.024260202422738075,
-0.031479984521865845,
-0.01609494350850582,
-0.03765607625246048,
-0.012931383214890957,
-0.013333979062736034,
-0.024717286229133606,
0.03793412446975708,
0.03863781690597534,
0.013653201051056385,
-0.03552684560418129,
-0.002229065867140889,
0.02892819419503212,
-0.023878905922174454,
0.02283414825797081,
-0.031809527426958084,
-0.0028314876835793257,
-0.005676578730344772,
-0.0022713171783834696,
0.038832053542137146,
-0.015557495877146721,
-0.006317385472357273,
-0.03505067154765129,
-0.02904583513736725,
-0.057199206203222275,
0.00041479707579128444,
0.020488901063799858,
0.0067947604693472385,
0.03682686388492584,
0.011110137216746807,
0.012586095370352268,
0.003620364936068654,
-0.022847268730401993,
0.013401631265878677,
0.002489627804607153,
-0.004376144148409367,
-0.019089670851826668,
-0.007609181571751833,
0.0018099397420883179,
0.03829619288444519,
-0.017897574231028557,
0.01720360480248928,
-0.0012762051774188876,
0.0695289745926857,
-0.00009219249477609992,
-0.02096390351653099,
-0.02739010937511921,
-0.01405754592269659,
-0.028298553079366684,
0.008990921080112457,
-0.015768827870488167,
0.03384996950626373,
-0.015246828086674213,
0.01020585373044014,
0.04055875539779663,
0.0015357605880126357,
-0.03322291001677513,
0.040233418345451355,
0.02956177107989788,
-0.0384892039000988,
-0.018083801493048668,
-0.020078735426068306,
0.03637457638978958,
-0.01305213663727045,
-0.028001708909869194,
-0.02393031120300293,
0.001988155534490943,
0.014026420190930367,
-0.0036930954083800316,
-0.043424129486083984,
0.04542986676096916,
-0.004621692933142185,
-0.04016108810901642,
-0.06569759547710419,
-0.003191288560628891,
-0.0497610829770565,
0.0077072624117136,
0.006522510666400194,
-0.03431320935487747,
0.04567691683769226,
0.05794013291597366,
-0.01673802360892296,
-0.03828443959355354,
0.030259739607572556,
0.023933246731758118,
-0.025583958253264427,
0.016828879714012146,
0.023727266117930412,
0.008676650002598763,
0.05859379842877388,
-0.01224445179104805,
-0.05284188315272331,
0.013489131815731525,
-0.06059307977557182,
-0.08021757006645203,
0.04915202036499977,
-0.005706068594008684,
0.02695438265800476,
0.04350881278514862,
-0.030746564269065857,
-0.015567511320114136,
0.07106759399175644,
-0.020672840997576714,
-0.029844962060451508,
0.025964027270674706,
0.021595707163214684,
-0.0037065763026475906,
0.003290407359600067,
-0.003852122463285923,
-0.010681194253265858,
-0.023353336378932,
0.020693257451057434,
0.010740213096141815,
0.006127818021923304,
-0.006969219073653221,
-0.008177933283150196,
-0.02699180878698826,
-0.009116506204009056,
-0.008971063420176506,
-0.004794580861926079,
0.0074929711408913136,
0.026258409023284912,
-0.05248000845313072,
0.031084898859262466,
0.031895946711301804,
-0.008083492517471313,
-0.08441058546304703,
0.011222632601857185,
-0.026510922238230705,
0.025667186826467514,
0.0022543754894286394,
-0.03006824105978012,
0.0540841706097126,
0.012105553410947323,
-0.03530902788043022,
0.01807173155248165,
-0.0022544304374605417,
-0.01583903655409813,
-0.013747901655733585,
-0.013639330863952637,
-0.0044776685535907745,
0.004285911563783884,
0.0258779376745224,
0.04281163960695267,
-0.009780637919902802,
0.022411970421671867,
0.011887182481586933,
-0.020318258553743362,
0.0016332854283973575,
0.028584809973835945,
0.013259314931929111,
0.0005632855463773012,
0.07483603060245514,
-0.009242394007742405,
-0.019318660721182823,
0.019773133099079132,
0.012160534039139748,
0.03755764290690422,
-0.023019075393676758,
-0.006186698097735643,
-0.016081664711236954,
0.01247447170317173,
0.02870034985244274,
-0.002916635014116764,
0.012954595498740673,
0.03575471043586731,
-0.016661424189805984,
0.024021755903959274,
-0.0033424803987145424,
-0.010639438405632973,
0.035427432507276535,
-0.026366081088781357,
-0.024149445816874504,
0.009590678848326206,
-0.010317248292267323,
0.046242713928222656,
0.03357405588030815,
0.030048219487071037,
0.016576621681451797,
-0.025553680956363678,
-0.035810686647892,
-0.04787449911236763,
-0.041054558008909225,
0.018373506143689156,
0.03419117629528046,
-0.07871589809656143,
0.025743627920746803,
-0.0047172000631690025,
-0.019662057980895042,
0.009060702286660671,
-0.01666419953107834,
-0.0043999855406582355,
-0.04811948537826538,
0.011829525232315063,
0.005712284240871668,
0.008631403557956219,
0.030347565189003944,
-0.04802209883928299,
-0.0455540306866169,
0.05163086950778961,
-0.013389675877988338,
0.024655146524310112,
0.0020290908869355917,
-0.03210261091589928,
0.002485604491084814,
-0.07622292637825012,
0.01241960097104311,
-0.006041120737791061,
0.04206811264157295,
-0.04081379249691963,
-0.014262133277952671,
-0.0157521590590477,
-0.030149754136800766,
0.05899146571755409,
-0.00891846138983965,
-0.03712991252541542,
0.013101819902658463,
-0.017905807122588158,
0.0040156240575015545,
-0.0649351179599762,
0.017114877700805664,
-0.016208045184612274,
-0.00343137769959867,
-0.0024774011690169573,
-0.01847027614712715,
-0.018129579722881317,
0.0022801635786890984,
0.039167147129774094,
0.010817276313900948,
0.02881573513150215,
0.019700387492775917,
-0.0030642517376691103,
0.06945047527551651,
0.006517090834677219,
0.026358207687735558,
0.06271982938051224,
-0.0027881660498678684,
-0.025142939761281013,
0.040837857872247696,
-0.0003906005003955215,
-0.07627946138381958,
0.05498465150594711,
-0.03090858832001686,
-0.00586657552048564,
-0.01350972056388855,
0.00472014956176281,
-0.005080609582364559,
-0.03735242038965225,
-0.025039486587047577,
0.07247607409954071,
-0.044020745903253555,
0.024263417348265648,
0.007765467278659344,
0.0009314737981185317,
0.035747021436691284,
-0.025084031745791435,
-0.012286245822906494,
0.004628401715308428,
0.025475718080997467,
-0.016890021041035652,
0.00644279457628727,
0.06118952855467796,
0.017881030216813087,
0.02945641241967678,
-0.009531867690384388,
-0.009925219230353832,
0.02359648235142231,
0.013954175636172295,
0.019617557525634766,
-0.02622266672551632,
-0.046096496284008026,
0.023161647841334343,
0.0015702508389949799,
0.0031178053468465805,
0.017167625948786736,
0.0026810888666659594,
0.07479862123727798,
0.007502248976379633,
0.024337995797395706,
0.003694622777402401,
-0.009273241274058819,
-0.027247706428170204,
0.020864320918917656,
-0.004334854427725077,
0.02222335897386074,
-0.01828816533088684,
0.009828170761466026,
-0.006413711700588465,
0.008697731420397758,
0.02254803292453289,
-0.05700959637761116,
-0.004998351447284222,
0.004745423793792725,
0.017803335562348366,
0.006157039664685726,
-0.0031504682265222073,
-0.025143012404441833,
-0.03625793755054474,
0.05181410536170006,
0.019437331706285477,
0.0041109188459813595,
-0.03529884293675423,
-0.006588369142264128,
-0.027679499238729477,
0.0505334809422493,
-0.02650652453303337,
-0.015516619198024273,
-0.04022372514009476,
0.019876224920153618,
-0.02526906318962574,
-0.015688059851527214
] |
<p>No viscosity means no friction between neighbouring particles. I think outer space is such a place. So a golfball or a tennis ball traveling in space with a large spinning such as <a href="http://en.wikipedia.org/wiki/Backspin" rel="nofollow">backspin</a> would not experience the <a href="http://en.wikipedia.org/wiki/Magnus_effect" rel="nofollow">Magnus effect</a> where the ball changes its direction due to spinning. </p>
<blockquote>
<p><strong>Is this correct? So a ball in outer space would not experience Magnus effect due to a large spinning? So is playing tennis in outer space a very directional game without spins and curvatures?</strong></p>
</blockquote>
| 8,858 |
[
-0.006154940463602543,
-0.02165929786860943,
-0.010719779878854752,
-0.010124917142093182,
0.028005633503198624,
0.011208842508494854,
-0.0268552303314209,
0.02606959268450737,
-0.026099393144249916,
-0.045176416635513306,
0.02876269817352295,
0.038564711809158325,
0.028831124305725098,
0.047780804336071014,
-0.003716799896210432,
-0.0208661500364542,
-0.02499503269791603,
0.010897823609411716,
0.008583895862102509,
-0.02930353209376335,
0.04308457300066948,
-0.03567364811897278,
0.007971961982548237,
0.006171063054352999,
-0.014122684486210346,
-0.007241967599838972,
0.005696727894246578,
-0.030190685763955116,
0.017055001109838486,
0.008399968966841698,
0.008419006131589413,
0.011865437962114811,
-0.017137881368398666,
-0.01402064599096775,
0.01880291849374771,
0.004959919024258852,
-0.04693617671728134,
0.003088219789788127,
0.02408314310014248,
-0.00878699030727148,
-0.027447093278169632,
-0.03319276496767998,
-0.022420059889554977,
0.06269080191850662,
-0.02925453893840313,
0.027608297765254974,
0.03841926530003548,
0.0000033367955438734498,
0.07544034719467163,
-0.05633946880698204,
0.03433486446738243,
-0.016392644494771957,
0.02350148744881153,
0.008234506472945213,
-0.021636955440044403,
0.00027375048375688493,
0.04833737760782242,
0.08399234712123871,
0.007265022955834866,
-0.044572267681360245,
0.02664763480424881,
-0.01341046579182148,
0.009447128511965275,
-0.008937554433941841,
-0.027540406212210655,
0.08120241016149521,
0.004446765407919884,
-0.06684944778680801,
0.054209012538194656,
0.03444630280137062,
0.007537519093602896,
0.049946870654821396,
0.01981094852089882,
0.008168291300535202,
0.0036671762354671955,
0.0029732289258390665,
0.03877151757478714,
-0.006353221368044615,
0.0293686855584383,
0.020907199010252953,
-0.014139230363070965,
-0.028007512912154198,
0.03392723947763443,
0.005171608179807663,
0.039344701915979385,
-0.0199943408370018,
0.08394629508256912,
-0.013710148632526398,
0.029580723494291306,
0.07727550715208054,
0.01898711360991001,
0.01091228798031807,
0.015434769913554192,
-0.02030918560922146,
-0.04832831770181656,
0.024067450314760208,
0.013096349313855171,
0.04166434332728386,
-0.03641652315855026,
-0.01675076223909855,
-0.033715225756168365,
-0.007071046158671379,
0.00767499441280961,
0.07413922250270844,
0.0009643280645832419,
-0.06877833604812622,
-0.037187736481428146,
0.006352575495839119,
-0.015953801572322845,
-0.002708189422264695,
-0.03150858357548714,
0.017144152894616127,
-0.036302581429481506,
-0.00506433704867959,
0.00977339781820774,
-0.010605227202177048,
-0.024824541062116623,
-0.003511236747726798,
0.017627570778131485,
0.060674116015434265,
0.05878404155373573,
-0.030656199902296066,
-0.006860844790935516,
-0.016336143016815186,
-0.062440160661935806,
0.029091447591781616,
0.06258687376976013,
0.0035137718077749014,
-0.0074288551695644855,
-0.013557765632867813,
-0.014786847867071629,
0.018912434577941895,
-0.0010697497054934502,
0.006735123693943024,
0.052563074976205826,
-0.028718365356326103,
-0.07807590812444687,
-0.025518245995044708,
0.10824485123157501,
0.011667460203170776,
-0.009698623791337013,
-0.05245239660143852,
-0.03370986133813858,
0.019771534949541092,
0.10817094892263412,
0.04107176139950752,
0.025219621136784554,
-0.000024682916773599572,
0.05503241717815399,
0.0009695882326923311,
-0.01990920677781105,
0.025138430297374725,
-0.009430300444364548,
-0.07234812527894974,
-0.0074423085898160934,
-0.0730195865035057,
0.03891851752996445,
0.04099404439330101,
0.017098547890782356,
-0.027246203273534775,
-0.002441649092361331,
-0.058443088084459305,
0.05450494587421417,
-0.019790759310126305,
-0.02777218259871006,
-0.019795073196291924,
0.07112773507833481,
0.014691031537950039,
0.02673967555165291,
0.01166303176432848,
-0.000996671966277063,
0.02418500743806362,
-0.020764237269759178,
-0.0003224126703571528,
0.0601334311068058,
-0.038767024874687195,
-0.012444169260561466,
0.03511297330260277,
-0.0287803765386343,
-0.036967191845178604,
-0.06599250435829163,
-0.012453536503016949,
0.0031716888770461082,
-0.0020462211687117815,
-0.02533886395394802,
0.027080731466412544,
0.005540014244616032,
0.031114885583519936,
0.003907356411218643,
-0.028072254732251167,
0.005554805509746075,
-0.03370409831404686,
0.0025966805405914783,
-0.004605043213814497,
-0.017451269552111626,
0.010687118396162987,
0.029619814828038216,
0.03243270143866539,
-0.03133479505777359,
-0.03632107377052307,
-0.010363818146288395,
0.039748258888721466,
-0.0018285029800608754,
-0.0013729751808568835,
-0.0077773043885827065,
0.028708219528198242,
0.002036635298281908,
-0.04130837693810463,
-0.016767054796218872,
0.009704935364425182,
-0.03373139351606369,
0.006829002406448126,
-0.030759982764720917,
0.04570985957980156,
0.019780602306127548,
-0.00996095035225153,
0.05036773532629013,
0.016059067100286484,
-0.008666153065860271,
0.007294393610209227,
-0.01983308047056198,
0.03582796826958656,
0.04733522981405258,
-0.01469993032515049,
0.043998878449201584,
0.041739631444215775,
0.003818148048594594,
-0.021629853174090385,
0.018237972632050514,
-0.02076549269258976,
-0.062269072979688644,
-0.00788962747901678,
0.018332589417696,
0.016101518645882607,
-0.041146088391542435,
0.02233075350522995,
0.04586617648601532,
0.03818900138139725,
0.004307707771658897,
0.014058489352464676,
-0.02797575667500496,
-0.02534632571041584,
0.013419178314507008,
0.03940607234835625,
0.042669627815485,
0.03249387815594673,
-0.0033510178327560425,
0.024977464228868484,
0.011880026198923588,
0.008109265007078648,
-0.024523837491869926,
0.007270279806107283,
0.010361693799495697,
0.03151685744524002,
0.029876243323087692,
-0.014901282265782356,
0.05601666867733002,
0.007874700240790844,
0.0246047955006361,
0.004940800368785858,
0.027730071917176247,
-0.0025503283832222223,
-0.03058885969221592,
-0.007615222595632076,
-0.015240008011460304,
0.009070213884115219,
-0.026799865067005157,
-0.012109894305467606,
0.03699794411659241,
-0.018898652866482735,
-0.017641834914684296,
0.02132345922291279,
0.05318944901227951,
-0.002357936231419444,
0.006980370730161667,
0.0313747376203537,
0.03645739331841469,
0.004715094808489084,
0.0014733111020177603,
0.0066914805211126804,
-0.01304367370903492,
-0.043593697249889374,
-0.01909373700618744,
-0.00040583001100458205,
-0.07735864073038101,
0.06204036623239517,
-0.06289016455411911,
0.0010252264328300953,
0.03147119656205177,
-0.03679104894399643,
0.008487645536661148,
0.03633378446102142,
0.003970084711909294,
-0.04331536218523979,
-0.00914798118174076,
-0.036426886916160583,
0.007439767476171255,
-0.0166243277490139,
0.0020747617818415165,
0.04144268110394478,
0.0371287539601326,
-0.008245262317359447,
0.04508332535624504,
-0.055581461638212204,
-0.05646270141005516,
-0.0014466068241745234,
0.014392358250916004,
0.0428197979927063,
-0.04707270488142967,
-0.013560906983911991,
0.02632269449532032,
-0.02102564089000225,
-0.033270128071308136,
-0.06988710910081863,
-0.037487734109163284,
0.043779607862234116,
0.007760229986160994,
0.009435515850782394,
-0.022607678547501564,
-0.009815779514610767,
0.0435052327811718,
0.03682878986001015,
-0.012299580499529839,
-0.02521267719566822,
0.0046363044530153275,
-0.03210686147212982,
-0.05296590179204941,
-0.00459859287366271,
-0.019230317324399948,
-0.0161434356123209,
-0.017437893897294998,
0.030515141785144806,
0.030825484544038773,
-0.006227931007742882,
-0.011929658241569996,
-0.013448387384414673,
-0.01702001318335533,
0.012473370879888535,
-0.007590166293084621,
0.04937097430229187,
0.031174466013908386,
-0.026973199099302292,
-0.005281116347759962,
-0.015823252499103546,
0.033647798001766205,
0.03188561648130417,
-0.04076851159334183,
0.05562545731663704,
0.0051644635386765,
-0.01608382910490036,
0.005866332910954952,
0.008965070359408855,
-0.03111145831644535,
0.04718197137117386,
0.012880743481218815,
0.0336637869477272,
0.006861178204417229,
0.050832636654376984,
0.043875765055418015,
0.04250728338956833,
0.017122691497206688,
-0.005357213784009218,
-0.017759140580892563,
-0.005530789028853178,
-0.010283124633133411,
0.023304564878344536,
-0.05020385608077049,
-0.012447895482182503,
-0.003848243970423937,
0.03355323523283005,
0.04251358285546303,
0.019962655380368233,
-0.03841536492109299,
0.025571977719664574,
-0.038865506649017334,
0.04050341621041298,
-0.038625556975603104,
0.012012967839837074,
0.02387448586523533,
0.04718602076172829,
0.021184761077165604,
0.027696626260876656,
0.029912205412983894,
0.005842925980687141,
-0.0911596417427063,
0.05591566115617752,
-0.004457553382962942,
-0.02178548090159893,
-0.007166143506765366,
-0.023039793595671654,
-0.03488500788807869,
-0.022282937541604042,
0.020332273095846176,
0.0020268901716917753,
-0.022316671907901764,
-0.0805983692407608,
0.009814339689910412,
-0.03644130006432533,
-0.03002612665295601,
0.00845708791166544,
0.03453856706619263,
0.03854650631546974,
-0.022199301049113274,
0.0353715643286705,
0.024556001648306847,
-0.030289340764284134,
-0.01475166343152523,
-0.01836034283041954,
0.024048389866948128,
0.024914933368563652,
0.018093764781951904,
0.03826932981610298,
0.04063835367560387,
-0.01737905852496624,
-0.006211575120687485,
0.019366716966032982,
0.023613540455698967,
0.0015582706546410918,
-0.0037928554229438305,
-0.030271310359239578,
-0.06784933805465698,
-0.013951551169157028,
0.018022321164608,
0.049202244728803635,
0.020766103640198708,
0.017038043588399887,
0.02236787974834442,
-0.023365000262856483,
0.022333310917019844,
-0.017002727836370468,
0.007348516024649143,
0.04285911098122597,
-0.049539148807525635,
-0.029324157163500786,
-0.048609744757413864,
-0.006065992172807455,
-0.0330934077501297,
0.025325322523713112,
0.021206850185990334,
-0.013294259086251259,
-0.005591820925474167,
0.009576594457030296,
0.05142506584525108,
0.0009016572730615735,
0.03651786223053932,
-0.02279362641274929,
0.025288745760917664,
-0.05071936920285225,
-0.021545525640249252,
0.002176256151869893,
0.005331740714609623,
0.009152225218713284,
0.008342334069311619,
-0.04370042681694031,
-0.07887400686740875,
0.005726465955376625,
0.024057039991021156,
0.03104078769683838,
0.018650371581315994,
-0.011134096421301365,
-0.03551508113741875,
-0.021719273179769516,
0.056650109589099884,
-0.03895273432135582,
0.04433901607990265,
-0.034982968121767044,
0.037171948701143265,
-0.01865367218852043,
-0.03884447365999222,
-0.005895528476685286,
0.0169766154140234,
-0.03984559327363968,
0.008955419063568115,
-0.030689934268593788,
-0.009747392497956753,
-0.015918994322419167,
-0.010866536758840084,
0.013498146086931229,
0.019630078226327896,
0.007190291304141283,
0.03011365421116352,
0.008345982059836388,
0.0165884830057621,
-0.03202972933650017,
-0.0747278556227684,
0.0220491923391819,
0.02384190820157528,
-0.0017850958975031972,
0.04184240475296974,
-0.02132318913936615,
-0.028435859829187393,
0.035401906818151474,
-0.024921316653490067,
0.019718974828720093,
0.008212056942284107,
-0.03661539405584335,
0.021962450817227364,
0.00047278605052269995,
0.009697115048766136,
0.03864610195159912,
0.023188896477222443,
-0.008102976717054844,
-0.012372293509542942,
-0.0022886176593601704,
0.016562137752771378,
-0.021177854388952255,
-0.0119845075532794,
-0.011878181248903275,
-0.012960566207766533,
-0.015941370278596878,
0.025334684178233147,
-0.0033779796212911606,
-0.014843405224382877,
0.012617995031177998,
-0.04654267057776451,
-0.05634090304374695,
0.016597498208284378,
0.043748050928115845,
-0.02317206561565399,
-0.0455033965408802,
0.016162006184458733,
-0.021073300391435623,
-0.0029584027361124754,
-0.008430182933807373,
0.004656306002289057,
-0.03885617479681969,
0.05540301278233528,
0.016636619344353676,
0.021151376888155937,
-0.009619439020752907,
-0.026235440745949745,
-0.022224998101592064,
-0.0751701220870018,
0.03968061879277229,
0.002045357134193182,
-0.0412161685526371,
0.07226531207561493,
-0.05583968386054039,
-0.011667643673717976,
0.004931268747895956,
-0.02537173219025135,
-0.03010619804263115,
-0.0599508062005043,
-0.006851284299045801,
-0.0012253629975020885,
0.02598278783261776,
-0.03547641262412071,
-0.08250876516103745,
0.007576220203191042,
0.022386880591511726,
0.02215665392577648,
0.004282828886061907,
-0.0007518339552916586,
-0.05531994253396988,
-0.021449938416481018,
0.005173234734684229,
0.01843186467885971,
-0.01809437945485115,
0.006281230133026838,
0.04372889921069145,
0.003469559596851468,
0.027821308001875877,
0.02978755347430706,
-0.026204440742731094,
0.00010735762043623254,
0.025587914511561394,
0.019026292487978935,
-0.033070456236600876,
0.055478233844041824,
-0.01610201969742775,
-0.06313153356313705,
-0.02596372552216053,
0.01415269449353218,
0.009774982929229736,
0.029542766511440277,
-0.04048539698123932,
0.01759876124560833,
-0.014489973895251751,
0.02067912556231022,
-0.00844251923263073,
0.030597353354096413,
-0.029786841943860054,
0.02627808041870594,
-0.004117236938327551,
-0.019801199436187744,
-0.007988505996763706,
-0.04359471797943115,
0.02467227727174759,
0.026226824149489403,
0.012494649738073349,
-0.011417803354561329,
0.08405489474534988,
-0.007091889623552561,
-0.027093268930912018,
0.013538879342377186,
-0.016206596046686172,
0.05024263635277748,
-0.04165717959403992,
-0.0357557088136673,
-0.02616170607507229,
0.03381677344441414,
-0.02643660642206669,
-0.03933176025748253,
-0.025005973875522614,
0.05487028509378433,
0.06035735085606575,
-0.04667079821228981,
0.030143529176712036,
0.021610010415315628,
0.007163477595895529,
-0.01619323529303074,
-0.04331137239933014,
0.021163245663046837,
0.030035683885216713,
-0.007506799418479204,
0.024742918089032173,
-0.052635472267866135,
0.005330923944711685,
0.035546377301216125,
0.05562933534383774,
-0.03242916986346245,
0.026434114202857018,
0.03690638020634651,
0.00014751909475307912,
0.000404332677135244,
-0.01535315252840519,
-0.0354866199195385,
0.001839212141931057,
-0.02022368460893631,
0.08721183985471725,
0.0046354299411177635,
-0.005009173881262541,
0.03284488990902901,
0.01458673644810915,
0.02808075211942196,
-0.043881483376026154,
-0.00676236255094409,
-0.031562499701976776,
0.01058326754719019,
0.002751655410975218,
0.005859760567545891,
-0.014721514657139778,
0.01320167537778616,
0.04266512021422386,
0.033418647944927216,
-0.006026320159435272,
-0.014819719828665257,
-0.06528677046298981,
-0.0063992817886173725,
-0.030675053596496582,
-0.05165810137987137,
0.06519854068756104,
0.02273101732134819,
-0.02983260154724121,
0.026748377829790115,
0.003769200760871172,
0.007294172886759043,
0.016724495217204094,
0.04601768031716347,
-0.004542680457234383,
0.05297777056694031,
-0.013522431254386902,
0.012699265033006668,
-0.04652190953493118,
0.0031742719002068043,
0.1287587732076645,
-0.005630090367048979,
0.002287216717377305,
-0.017157435417175293,
-0.01616642251610756,
-0.04636135697364807,
0.038583941757678986,
0.0056932163424789906,
-0.019383663311600685,
-0.024745551869273186,
0.011739248409867287,
0.013717027381062508,
0.05638645216822624,
-0.011319711804389954,
-0.021670514717698097,
0.03577955439686775,
-0.06863759458065033,
-0.013939823023974895,
-0.01800128072500229,
-0.006959265097975731,
0.01671072095632553,
0.008004508912563324,
-0.040701065212488174,
0.0311302300542593,
-0.008236909285187721,
0.036196090281009674,
-0.020936472341418266,
-0.0461762435734272,
-0.00018177737365476787,
0.019767021760344505,
-0.04361337795853615,
0.00009825777669902891,
0.015750978142023087,
-0.007516270037740469,
-0.06348547339439392,
-0.004743997938930988,
0.043313346803188324,
-0.06449713557958603,
0.007237269077450037,
0.03404121473431587,
-0.01052602007985115,
0.00876041129231453,
0.003851545276120305,
0.021690763533115387,
-0.04597524181008339,
-0.0024619847536087036,
-0.03706622123718262,
0.017409849911928177,
-0.010559437796473503,
0.014723616652190685,
0.006887538358569145,
-0.026558663696050644,
0.018645940348505974,
-0.039518509060144424,
-0.005402122624218464,
-0.018675582483410835,
0.0046646795235574245,
-0.016954628750681877,
0.024144001305103302,
-0.0031033814884722233,
-0.01126058492809534,
0.042671967297792435,
0.001707246177829802,
-0.015156237408518791,
0.024481870234012604,
0.009277865290641785,
0.009560702368617058,
0.04016492888331413,
-0.033897336572408676,
-0.0038319225423038006,
-0.056739360094070435,
0.018078915774822235,
-0.043497130274772644,
0.0283525213599205,
0.018079476431012154,
0.042888473719358444,
0.02347906306385994,
0.00535532645881176,
-0.002332862466573715,
0.005569525994360447,
0.0020960886031389236,
0.030812205746769905,
-0.059950198978185654,
0.007665850222110748,
0.005375910084694624,
-0.01702158898115158,
0.02199743129312992,
0.03008340485394001,
-0.03778235614299774,
-0.027427611872553825,
-0.0006995571893639863,
0.03337499499320984,
0.03303052484989166,
-0.03024262748658657,
-0.03425787016749382,
-0.002599911531433463,
-0.05634443089365959,
0.024398203939199448,
-0.00819795299321413,
0.05678965896368027,
0.02367349900305271,
-0.004372413270175457,
-0.005999671760946512,
-0.0014123243745416403,
-0.016178686171770096,
-0.01228500809520483,
0.0396416112780571,
-0.03378723934292793,
-0.030211996287107468,
0.02557828277349472,
0.0026914747431874275,
-0.03224952891469002,
-0.034255266189575195,
-0.028480615466833115,
0.005130360834300518,
-0.015631187707185745,
0.030229477211833,
-0.031765881925821304,
0.04861798509955406,
-0.001229232526384294,
0.02796717919409275,
-0.061020627617836,
0.010815370827913284,
-0.03255787491798401,
0.02414148487150669,
0.023980194702744484,
0.024248436093330383,
0.025163520127534866,
0.003698892891407013,
-0.06596037745475769,
-0.019883273169398308,
0.0038274815306067467,
0.03028292767703533,
0.005813299212604761,
0.03807985782623291,
0.017330758273601532,
0.0000673087197355926,
0.01196318306028843,
-0.02014542557299137,
-0.013670950196683407,
0.030493171885609627,
-0.055257648229599,
-0.07381308078765869,
-0.01006716676056385,
-0.03170459344983101,
0.019328683614730835,
0.01929447241127491,
-0.018675271421670914,
-0.028603509068489075,
0.07491325587034225,
-0.029444877058267593,
0.013276871293783188,
0.003080249298363924,
-0.04658995568752289,
-0.01831916533410549,
-0.0018513285322114825,
0.007364180870354176,
-0.03427918627858162,
-0.025479046627879143,
0.03609488531947136,
0.008649692870676517,
-0.016069315373897552,
-0.025297200307250023,
0.004042895510792732,
-0.01846025139093399,
-0.054267920553684235,
-0.008699036203324795,
-0.013679021038115025,
-0.01828167214989662,
0.05950291454792023,
-0.05469375103712082,
0.009298685006797314,
0.029373643919825554,
-0.0011646427446976304,
-0.10613934695720673,
0.0079188896343112,
0.01638779602944851,
-0.015300876460969448,
0.004667382687330246,
-0.07370513677597046,
0.0083884596824646,
0.0020193762611597776,
-0.10247024893760681,
0.032532528042793274,
-0.019677666947245598,
0.0019802944734692574,
-0.03993752971291542,
-0.009987303987145424,
-0.007446058560162783,
0.041423290967941284,
0.05551613122224808,
0.022710170596837997,
-0.019464749842882156,
0.029209483414888382,
-0.002029173308983445,
-0.006261809729039669,
-0.002071786904707551,
0.04236359894275665,
-0.007732176221907139,
-0.004817735403776169,
0.03574550896883011,
-0.011361130513250828,
-0.03282260522246361,
0.02572132833302021,
-0.0034453857224434614,
0.048585161566734314,
0.0020296780858188868,
-0.014549467712640762,
-0.00855803769081831,
-0.004924754146486521,
0.012282625772058964,
-0.009613375179469585,
0.01931549422442913,
0.0032463697716593742,
-0.00574907660484314,
0.007871762849390507,
0.0019615315832197666,
0.007503291592001915,
0.01336613018065691,
-0.037813700735569,
-0.03680630028247833,
-0.022130388766527176,
-0.038853757083415985,
0.008643820881843567,
0.004310289863497019,
0.03099389746785164,
0.016383199021220207,
0.014269895851612091,
-0.0019686140585690737,
-0.02916889823973179,
0.028240852057933807,
-0.0010109673021361232,
-0.014155678451061249,
-0.008658988401293755,
0.012234204448759556,
0.0224467683583498,
-0.020166020840406418,
-0.012212908826768398,
-0.01642002910375595,
-0.012009372003376484,
-0.011853725649416447,
0.002393650822341442,
-0.012376728467643261,
0.020432962104678154,
-0.022477760910987854,
-0.04849445819854736,
-0.01899533160030842,
0.04460102692246437,
0.0672532171010971,
0.021645542234182358,
-0.008822525851428509,
-0.012427050620317459,
0.0135530736297369,
-0.08021202683448792,
-0.018149076029658318,
-0.0126657048240304,
-0.005527978762984276,
-0.025894075632095337,
-0.02655446156859398,
-0.008258141577243805,
0.014958279207348824,
0.06408293545246124,
-0.05050770938396454,
0.005831072572618723,
0.03660663217306137,
0.026081852614879608,
0.01334849651902914,
-0.03051071986556053,
0.026202991604804993,
-0.005076057277619839,
-0.04427764192223549,
0.03127720579504967,
0.0006525432108901441,
-0.019192522391676903,
-0.008973918855190277,
0.05597652122378349,
-0.013794641010463238,
0.028838524594902992,
-0.0038158567622303963,
-0.0638706386089325,
0.033809684216976166,
0.03954686224460602,
0.0031903297640383244,
0.061922892928123474,
0.01038963533937931,
-0.011730964295566082,
0.01512384507805109,
-0.021440230309963226,
-0.02259952574968338,
0.04915956035256386,
-0.018922680988907814,
-0.0234831552952528,
-0.03321390599012375,
-0.03302912414073944,
-0.00020765031513292342,
-0.01741218939423561,
-0.012615451589226723,
0.030675694346427917,
-0.03177247941493988,
-0.02957559935748577,
0.025714945048093796,
0.00815119594335556,
0.014886729419231415,
-0.01955707184970379,
0.012023267336189747,
0.021711699664592743,
0.0012889486970379949,
-0.021929726004600525,
0.05622725188732147,
0.0409560427069664,
0.012844851240515709,
-0.010469263419508934,
0.03132762387394905,
0.00678904727101326,
0.03665687516331673,
0.015570007264614105,
0.079274483025074,
0.0006775045767426491,
-0.012917176820337772,
0.006484014913439751,
0.04250134155154228,
0.010755246505141258,
0.04799719527363777,
-0.01553467195481062,
0.06767687201499939,
-0.027054546400904655,
-0.01371840015053749,
-0.014465252868831158,
0.00035421771463006735,
-0.004806856159120798,
-0.006282787770032883,
0.00711282342672348,
-0.0142140481621027,
0.015038536861538887,
-0.0595749206840992,
0.0167514830827713,
-0.005021860357373953,
0.04852111265063286,
0.012116221711039543,
0.023734144866466522,
-0.0146394744515419,
0.01944461464881897,
0.03296062722802162,
-0.02488202229142189,
-0.001988318981602788,
0.0096907839179039,
0.023408126085996628,
0.007947564125061035,
0.017227325588464737,
-0.04080883041024208,
0.003671969287097454,
-0.00626538647338748,
0.06852502375841141,
-0.058126311749219894,
-0.0072504132986068726,
0.01428999099880457,
0.04479292407631874,
-0.018440326675772667,
0.022599035874009132
] |
<p>My professor told me that a 4-dimensional Minkowski - Space Integral I was working on can be written as the product of a metric tensor and a scalar:</p>
<p>$\int d^4 k \frac{k^\mu k^\nu}{(k^2-m_1^2)(k^2-m_2^2)} = g^{\mu \nu} B_2$ </p>
<p>where $B_2$ is a scalar. </p>
<p>I am surprised that apparently for $\mu = \nu = 0$ , the sign of the integral is opposite to the sign for, say, $\mu = \nu = 1$. This seems wrong to me, and in an Eucledian Space it certainly would be. If I had been asked to guess, I would have written the above equation with $ g^\mu_\nu B_2$ on the right hand side instead..</p>
<p>Can someone bring clarity?</p>
| 8,859 |
[
-0.027021341025829315,
-0.01037797424942255,
0.007332415785640478,
-0.03018151968717575,
0.0668063834309578,
0.0813552513718605,
0.02209273912012577,
-0.02318136766552925,
-0.000012335621249803808,
-0.03931621462106705,
0.04476810619235039,
0.013307641260325909,
0.09939184039831161,
0.018298901617527008,
0.022859107702970505,
-0.007546045817434788,
-0.019417745992541313,
-0.02479725331068039,
-0.014815358445048332,
-0.04685652256011963,
0.011764110065996647,
0.02582366019487381,
-0.03346365690231323,
-0.04668290540575981,
-0.0004266116884537041,
0.025969410315155983,
0.025828562676906586,
-0.018636086955666542,
0.012783071957528591,
0.06674373149871826,
-0.03271719068288803,
-0.010055727325379848,
0.030258437618613243,
0.022352423518896103,
0.0030484653543680906,
-0.01354410033673048,
-0.020705843344330788,
-0.004554910585284233,
0.001198417623527348,
0.008396829478442669,
-0.024373775348067284,
-0.0003011974331457168,
0.0015423238510265946,
0.0332677848637104,
-0.01818014495074749,
0.01885225810110569,
0.023617655038833618,
-0.007655375637114048,
0.033529046922922134,
-0.04088696092367172,
0.06691223382949829,
0.024231771007180214,
0.025303548201918602,
0.018675662577152252,
-0.0026210013311356306,
-0.009042114950716496,
0.07043873518705368,
0.05317546799778938,
-0.00932873971760273,
-0.040289610624313354,
-0.029983913525938988,
0.013470112346112728,
-0.00449968921020627,
0.001963687827810645,
0.023912671953439713,
0.04451780393719673,
0.00025286173331551254,
-0.026578867807984352,
0.026825405657291412,
-0.016158323734998703,
-0.0004494163440540433,
0.03606937825679779,
0.04382210224866867,
-0.04270128160715103,
0.022898005321621895,
0.007443721871823072,
0.026063133031129837,
0.01798372156918049,
0.03899600729346275,
0.028347386047244072,
-0.015549452975392342,
-0.011506456881761551,
0.005052862223237753,
0.001597591326572001,
0.0192115381360054,
0.029776040464639664,
0.021009724587202072,
-0.014280503615736961,
0.02432132698595524,
0.08070620894432068,
0.005334650166332722,
0.039373792707920074,
0.037655897438526154,
0.021189700812101364,
-0.02484559267759323,
0.036366768181324005,
0.004062922205775976,
0.024930721148848534,
0.0035217490512877703,
-0.03169136494398117,
-0.03775088116526604,
0.011493291705846786,
0.008339045569300652,
0.04731930047273636,
0.017591407522559166,
0.011586200445890427,
-0.03033861704170704,
0.03381076455116272,
-0.034981533885002136,
0.018150407820940018,
-0.04042433202266693,
0.0062743499875068665,
0.0016201758990064263,
-0.0001889384730020538,
0.030348042026162148,
-0.0404941663146019,
-0.018489331007003784,
0.006752719171345234,
0.011860794387757778,
0.05577407032251358,
0.044603921473026276,
-0.023552970960736275,
0.04922601580619812,
-0.038173858076334,
-0.06610415875911713,
0.020716402679681778,
0.015988243743777275,
0.009669752791523933,
-0.025608239695429802,
0.019296957179903984,
0.029150960966944695,
0.00813350174576044,
-0.0012338634114712477,
0.03625747933983803,
0.03506786748766899,
-0.03689832240343094,
-0.07105463743209839,
-0.08854550868272781,
0.051163457334041595,
-0.00790045503526926,
0.022441234439611435,
-0.09381692856550217,
-0.033779457211494446,
0.024294186383485794,
0.08884904533624649,
0.02155078575015068,
0.018014803528785706,
-0.0037949145771563053,
0.00493631511926651,
-0.0016717289108783007,
-0.020505500957369804,
0.0034024622291326523,
-0.043432530015707016,
-0.0409574955701828,
-0.001844758982770145,
-0.08323984593153,
0.006393653806298971,
0.03306109458208084,
-0.009429531171917915,
-0.02541472762823105,
0.08822310715913773,
0.03271186724305153,
0.025534164160490036,
0.019506171345710754,
0.010851836763322353,
0.000296675629215315,
0.05874069035053253,
0.05782143771648407,
0.007061287295073271,
-0.008209144696593285,
0.033882346004247665,
0.0014522081473842263,
-0.04030275717377663,
0.0770689994096756,
0.08014630526304245,
-0.015188203193247318,
0.0025091045536100864,
-0.023539511486887932,
0.03534478321671486,
-0.009951402433216572,
-0.01213066466152668,
-0.028286045417189598,
-0.03786458075046539,
-0.025139404460787773,
-0.018781907856464386,
0.015251514501869678,
0.023065689951181412,
0.01323135569691658,
0.026480907574295998,
-0.020832456648349762,
-0.0058916835114359856,
-0.027599569410085678,
0.04495558142662048,
0.04730096086859703,
-0.04035468026995659,
0.02285766787827015,
-0.018373295664787292,
0.026619315147399902,
-0.01685400679707527,
-0.07000008225440979,
-0.003266502870246768,
0.00642320467159152,
0.015992216765880585,
0.003157085971906781,
0.0023042927496135235,
0.020522840321063995,
0.028501082211732864,
-0.02040855400264263,
0.02622297964990139,
-0.00024087655765470117,
-0.0003351141349412501,
0.016427502036094666,
0.016702447086572647,
0.025752967223525047,
-0.013006961904466152,
-0.013720784336328506,
0.015119046904146671,
-0.0020228722132742405,
-0.01171879842877388,
0.05141429603099823,
-0.0839695930480957,
0.019588248804211617,
0.06511204689741135,
0.018585950136184692,
0.037700846791267395,
0.033618733286857605,
0.006220195442438126,
0.021235691383481026,
0.00011750082194339484,
-0.0365992970764637,
-0.019439103081822395,
-0.0034033998381346464,
0.016173170879483223,
0.012994108721613884,
-0.03978687524795532,
-0.011932261288166046,
0.01929790899157524,
0.028745373710989952,
-0.001592199900187552,
0.0005687601515091956,
0.0003840194549411535,
-0.03537587448954582,
0.003213847754523158,
-0.01575571298599243,
0.00033398697269149125,
0.020294399932026863,
0.005043880548328161,
-0.027027389034628868,
0.022079387679696083,
-0.02668464183807373,
-0.011423212476074696,
0.0018432444194331765,
-0.03191694617271423,
0.03579171001911163,
-0.008930033072829247,
-0.011888626031577587,
0.08271117508411407,
-0.009520665742456913,
0.02923303097486496,
0.03390667214989662,
0.010546354576945305,
-0.016984645277261734,
-0.053914375603199005,
-0.007805254776030779,
-0.0021440116688609123,
0.022018974646925926,
-0.008320645429193974,
-0.04158104211091995,
0.03246253356337547,
-0.030318910256028175,
0.005947825964540243,
-0.008175553753972054,
-0.025531886145472527,
-0.01550221536308527,
0.009217302314937115,
0.015559343621134758,
0.03956198692321777,
0.02457699552178383,
0.00012667647388298064,
-0.029068676754832268,
0.00646775308996439,
0.007683923002332449,
0.04041207209229469,
0.05218387395143509,
-0.038377851247787476,
0.03272527828812599,
-0.042646780610084534,
0.013441823422908783,
0.023938331753015518,
-0.0071192518807947636,
0.005076717585325241,
0.034638289362192154,
0.011870174668729305,
-0.0186766404658556,
-0.032227836549282074,
-0.030430544167757034,
0.001735030673444271,
-0.002219251124188304,
0.003702759277075529,
0.019794031977653503,
-0.01999797485768795,
-0.04834636300802231,
-0.0017164667369797826,
-0.050109654664993286,
-0.07052860409021378,
-0.036657992750406265,
-0.029758330434560776,
0.07207638025283813,
0.0032873405143618584,
0.00722168805077672,
0.04962770268321037,
0.013641891069710255,
-0.03345838561654091,
-0.07576457411050797,
-0.052782442420721054,
0.00460748840123415,
-0.014125402085483074,
0.026288118213415146,
-0.013546495698392391,
-0.019971709698438644,
0.07756524533033371,
0.03295285999774933,
-0.01291841734200716,
-0.00047473449376411736,
0.016535641625523567,
-0.002410688903182745,
-0.06874988228082657,
-0.02781539037823677,
-0.02646644413471222,
0.014716774225234985,
0.08116269111633301,
-0.00944606401026249,
0.025213204324245453,
0.040697287768125534,
0.017783276736736298,
-0.02931157872080803,
0.010678239166736603,
-0.04891812056303024,
-0.009652471169829369,
0.0591556541621685,
0.0399184487760067,
0.016304701566696167,
0.009421893395483494,
-0.028600817546248436,
0.008747569285333157,
0.018200647085905075,
-0.030029188841581345,
0.04591772332787514,
-0.005408698692917824,
-0.011100219562649727,
-0.045995745807886124,
0.021993983536958694,
-0.000819181150291115,
-0.03593095391988754,
0.019777294248342514,
-0.0004984014085493982,
0.02566797286272049,
-0.029102105647325516,
0.014084001071751118,
0.027326000854372978,
0.011691350489854813,
-0.009112884290516376,
0.01405323576182127,
0.013345449231564999,
-0.0035236438270658255,
-0.0013841716572642326,
-0.02006504498422146,
0.04003315046429634,
0.04427275434136391,
0.03467288613319397,
0.013913799077272415,
-0.0027290864381939173,
-0.05212609842419624,
-0.006659870035946369,
-0.059478163719177246,
-0.026758955791592598,
-0.002968413755297661,
0.018065426498651505,
0.029968617483973503,
0.0001271298824576661,
0.015370621345937252,
0.007663865573704243,
0.024114511907100677,
-0.01920514553785324,
-0.06721372157335281,
0.030240077525377274,
-0.04195181280374527,
-0.00792057253420353,
-0.01931324601173401,
-0.07483137398958206,
-0.011858697049319744,
-0.036154605448246,
-0.03960414230823517,
-0.007358592934906483,
-0.00248974678106606,
-0.06741126626729965,
0.05304209887981415,
-0.006731867790222168,
-0.08750567585229874,
-0.014311465434730053,
0.04089614003896713,
0.07470981031656265,
-0.01876629702746868,
-0.009524895809590816,
0.07200376689434052,
0.006216178182512522,
0.019582392647862434,
-0.03970323130488396,
0.005577526520937681,
0.010643492452800274,
0.005766832269728184,
0.019078919664025307,
0.007134316489100456,
-0.03833403065800667,
0.014336835592985153,
0.052874427288770676,
0.06723468750715256,
-0.018246876075863838,
-0.032768674194812775,
-0.045761995017528534,
-0.04208733141422272,
-0.02387959696352482,
-0.029982902109622955,
0.04505565017461777,
0.015374261885881424,
0.009257038123905659,
0.009419484995305538,
0.03426406532526016,
0.013471136800944805,
0.023974401876330376,
0.0727032944560051,
-0.03596627712249756,
0.0005929346662014723,
-0.028672242537140846,
-0.02295244112610817,
-0.002318433253094554,
-0.021899189800024033,
0.03546786308288574,
-0.0034462304320186377,
-0.03444245085120201,
-0.019551575183868408,
0.011263631284236908,
-0.0028861509636044502,
-0.0008907800074666739,
0.043235793709754944,
-0.020901165902614594,
-0.02765328623354435,
-0.00861948262900114,
-0.028224026784300804,
0.014829116873443127,
0.06690049171447754,
0.04314439743757248,
0.03567051887512207,
-0.026366639882326126,
-0.05216401442885399,
-0.03898780047893524,
-0.021651720628142357,
0.03736723214387894,
0.007703851908445358,
-0.017723217606544495,
-0.04089995101094246,
-0.021117037162184715,
0.04330834373831749,
-0.0010754027171060443,
0.023876061663031578,
0.02410324290394783,
0.0072323535569012165,
-0.010891384445130825,
0.004672565963119268,
-0.018611876294016838,
0.028107255697250366,
-0.036743368953466415,
0.001343300100415945,
-0.01422377210110426,
0.023405231535434723,
-0.015068668872117996,
0.03702954947948456,
-0.0293585192412138,
0.006268553901463747,
0.0023727077059447765,
-0.015286114066839218,
0.020147472620010376,
0.043281860649585724,
-0.019819147884845734,
-0.06947528570890427,
0.016665585339069366,
0.005221082363277674,
-0.036201830953359604,
0.03343482315540314,
-0.014978837221860886,
-0.04050912708044052,
0.03735136240720749,
-0.013276098296046257,
0.034212131053209305,
0.031087055802345276,
-0.04179581627249718,
0.0013889996334910393,
0.027398115023970604,
-0.004252398852258921,
0.028498144820332527,
0.014265588484704494,
0.013331982307136059,
-0.001076638582162559,
-0.04973583668470383,
0.035450149327516556,
-0.03609129786491394,
0.0026069534942507744,
0.025458984076976776,
-0.027881626039743423,
-0.04392574355006218,
0.03197723627090454,
-0.011250752955675125,
0.034537702798843384,
-0.011347860097885132,
-0.01718731038272381,
-0.009398534893989563,
0.013119363225996494,
0.005898868199437857,
-0.016990967094898224,
0.040723007172346115,
-0.007383657619357109,
0.024983225390315056,
-0.03653163090348244,
0.01771637797355652,
-0.006760249845683575,
-0.042190853506326675,
0.021224182099103928,
0.018244024366140366,
0.017079053446650505,
0.01657375507056713,
-0.022179294377565384,
0.030413947999477386,
-0.02770359069108963,
-0.013767991214990616,
-0.006391030270606279,
-0.008756834082305431,
0.023354165256023407,
-0.021197771653532982,
-0.040797244757413864,
-0.023308588191866875,
-0.005859639961272478,
0.016897471621632576,
-0.036971915513277054,
0.009199912659823895,
0.008733435533940792,
0.05133599415421486,
-0.08557157963514328,
-0.015783192589879036,
-0.026949243620038033,
-0.021597614511847496,
-0.00396717106923461,
-0.038065869361162186,
-0.005007847677916288,
-0.0010664339642971754,
-0.035107843577861786,
0.02329813875257969,
0.06442920118570328,
-0.030222725123167038,
-0.03462202847003937,
-0.011081032454967499,
0.03786028176546097,
0.039437662810087204,
-0.024580279365181923,
-0.010857902467250824,
0.052759166806936264,
-0.0009956223657354712,
-0.003104806412011385,
0.01090759877115488,
0.06681562215089798,
-0.02174895815551281,
-0.004268700256943703,
-0.021379824727773666,
-0.019609728828072548,
-0.015099771320819855,
0.011702480725944042,
-0.0030952070374041796,
0.025335997343063354,
0.01759614422917366,
0.000526909832842648,
-0.0246865414083004,
-0.008927613496780396,
-0.016996046528220177,
-0.0038611909840255976,
-0.005571698769927025,
-0.009257271885871887,
-0.005728477146476507,
-0.024990728124976158,
0.020719895139336586,
-0.01655232533812523,
0.038498781621456146,
-0.0483260378241539,
0.05070367082953453,
-0.008259252645075321,
-0.01680145040154457,
0.02693605050444603,
-0.022967586293816566,
0.02262832224369049,
-0.022392120212316513,
0.0004007426032330841,
-0.0015120971947908401,
0.023325713351368904,
-0.026235874742269516,
-0.012763705104589462,
-0.030358687043190002,
0.021960726007819176,
0.07191268354654312,
-0.05610018968582153,
0.025710711255669594,
0.029415974393486977,
-0.027485786005854607,
0.02338043414056301,
-0.03680570051074028,
-0.014928157441318035,
0.028955182060599327,
-0.0378929004073143,
0.01715213805437088,
-0.02714182808995247,
-0.002337346551939845,
0.00045764719834551215,
0.011662519536912441,
-0.050443440675735474,
-0.009109069593250751,
0.004787871614098549,
0.023388754576444626,
-0.012161754071712494,
0.010613590478897095,
-0.07792501896619797,
0.06706751883029938,
-0.012670056894421577,
0.035547446459531784,
-0.025522705167531967,
0.023620329797267914,
0.02253967709839344,
0.008522460237145424,
-0.016982145607471466,
-0.029547397047281265,
-0.00827083457261324,
-0.009588712826371193,
-0.020934931933879852,
0.04525194317102432,
-0.03718121722340584,
-0.02167026698589325,
0.01303173042833805,
0.05241130292415619,
-0.022870752960443497,
0.020048651844263077,
-0.013080314733088017,
-0.04156146198511124,
-0.020902486518025398,
-0.06025827303528786,
-0.052899911999702454,
0.06234441697597504,
-0.021581241860985756,
-0.006999193225055933,
-0.02339651994407177,
-0.037927769124507904,
0.008333203382790089,
-0.004466813988983631,
0.02416246011853218,
-0.016232328489422798,
0.048887018114328384,
0.013637745752930641,
0.004568453878164291,
-0.018191561102867126,
-0.007546501234173775,
0.12372174113988876,
0.0338079035282135,
-0.015706418082118034,
-0.07195611298084259,
-0.0010450140107423067,
-0.03662965074181557,
-0.009586961008608341,
-0.02407444268465042,
0.03662778064608574,
-0.02645847015082836,
0.011013907380402088,
-0.00396534102037549,
0.0589899867773056,
-0.005133024882525206,
-0.03754284232854843,
-0.0004774899862241,
-0.012265496887266636,
-0.03994739428162575,
0.011789906769990921,
0.022297510877251625,
-0.02227897010743618,
-0.01006521936506033,
-0.019478630274534225,
0.04325689747929573,
-0.01485615037381649,
0.04770664498209953,
-0.07255998998880386,
0.0059319292195141315,
0.01624702848494053,
0.038812968879938126,
-0.05719737708568573,
0.003919644746929407,
0.011172207072377205,
-0.013774475082755089,
-0.006790020037442446,
-0.01289396733045578,
0.04480602592229843,
-0.011172761209309101,
0.029457654803991318,
0.03390089049935341,
-0.016985544934868813,
0.015193155966699123,
0.020382767543196678,
0.012830257415771484,
-0.03376615792512894,
0.005814786069095135,
-0.0402311235666275,
0.09779178351163864,
0.010804755613207817,
0.014357885345816612,
0.013141158036887646,
0.005884169135242701,
0.013246148824691772,
-0.0887298658490181,
-0.024048127233982086,
-0.007850715890526772,
0.046465445309877396,
0.003134426660835743,
-0.01571895182132721,
0.014976578764617443,
0.03835436329245567,
0.006181858945637941,
0.00474651949480176,
-0.026569008827209473,
-0.014064973220229149,
0.011078929528594017,
-0.035828907042741776,
0.025717569515109062,
0.006039778236299753,
-0.04396665096282959,
-0.021240022033452988,
-0.030762290582060814,
-0.012519046664237976,
0.02002824656665325,
-0.03469951078295708,
0.021585706621408463,
0.07453534007072449,
-0.024041015654802322,
-0.015063668601214886,
0.019359078258275986,
-0.02512417919933796,
0.017963318154215813,
-0.04083548113703728,
0.009177977219223976,
-0.00890168733894825,
-0.014946706593036652,
0.0019453305285423994,
0.021333953365683556,
0.008089602924883366,
-0.0016154440818354487,
0.0008626197814010084,
0.0000877612765179947,
-0.005799274891614914,
-0.00627135019749403,
-0.026880905032157898,
0.014095073565840721,
-0.009961276315152645,
0.021466946229338646,
-0.04472175985574722,
-0.030697157606482506,
0.032858897000551224,
0.05404055863618851,
-0.013494407758116722,
0.042120400816202164,
0.002091307658702135,
-0.02084278129041195,
0.023490088060498238,
-0.010468465276062489,
0.01731833443045616,
-0.009108896367251873,
0.015732591971755028,
-0.05453578010201454,
0.008153540082275867,
-0.012899820692837238,
0.011515224352478981,
-0.02591121383011341,
0.0319838747382164,
-0.022379903122782707,
-0.010949688032269478,
-0.0024028944317251444,
0.003330767620354891,
-0.006510473787784576,
-0.010633333586156368,
-0.04280519485473633,
0.01929101161658764,
0.025101372972130775,
-0.0005428770673461258,
-0.01469935942441225,
0.02763265371322632,
-0.03220994770526886,
-0.002350754803046584,
0.060604277998209,
0.007034578826278448,
-0.0346544086933136,
-0.024211058393120766,
0.017003050073981285,
-0.011113815940916538,
0.03240031376481056,
0.05057874694466591,
-0.007674563676118851,
0.013012973591685295,
-0.0583956278860569,
-0.03492971509695053,
0.012080173939466476,
0.013521065935492516,
0.006813093554228544,
0.016535695642232895,
-0.00048338426859118044,
-0.04091271758079529,
0.06297948956489563,
-0.0063867573626339436,
0.013362444005906582,
0.023977529257535934,
-0.04404888302087784,
0.005479638930410147,
-0.054598335176706314,
-0.010962490923702717,
0.03967487812042236,
-0.00007879445183789358,
-0.028437355533242226,
-0.027822867035865784,
-0.02761244960129261,
0.006539633963257074,
-0.006457733456045389,
-0.017817294225096703,
-0.012196160852909088,
-0.012966434471309185,
0.005652870051562786,
0.009852021001279354,
0.04564715176820755,
-0.007266996894031763,
0.03137114271521568,
0.030146848410367966,
0.024323992431163788,
-0.0860636830329895,
-0.015118584036827087,
0.005434061400592327,
0.030191335827112198,
0.03126057982444763,
-0.07760397344827652,
0.010666439309716225,
0.017082136124372482,
-0.057476937770843506,
0.009213658981025219,
-0.013664421625435352,
-0.06414661556482315,
-0.03754495084285736,
-0.023364825174212456,
-0.017465081065893173,
0.04469656944274902,
0.06655464321374893,
0.03771863877773285,
-0.008921787142753601,
0.02207626774907112,
-0.020401520654559135,
0.001967202639207244,
-0.0010647105518728495,
0.0070016346871852875,
0.02409798838198185,
-0.026798421517014503,
0.0953773558139801,
-0.02023991011083126,
-0.017656324431300163,
0.06096389517188072,
-0.024077149108052254,
-0.009966721758246422,
0.00567991565912962,
0.011993921361863613,
0.03537871688604355,
0.015467355027794838,
0.033921610563993454,
-0.011533811688423157,
0.027666429057717323,
0.010128667578101158,
0.023506540805101395,
-0.005993611644953489,
-0.040753770619630814,
-0.004957915283739567,
0.0060671414248645306,
-0.04365459457039833,
-0.029998214915394783,
0.07492164522409439,
-0.005204964429140091,
-0.023870259523391724,
-0.0321374274790287,
-0.03768644109368324,
0.025285806506872177,
-0.04969091713428497,
0.044387247413396835,
-0.06184450536966324,
0.008212674409151077,
0.025103190913796425,
0.010836823843419552,
-0.018937282264232635,
0.014820748008787632,
-0.021653374657034874,
0.004109052941203117,
0.0014056183863431215,
-0.010276595130562782,
-0.032829754054546356,
-0.041961297392845154,
-0.03183732554316521,
-0.009481609798967838,
-0.0037810790818184614,
0.0074921101331710815,
-0.042747873812913895,
-0.02203361876308918,
0.023931540548801422,
0.03948940709233284,
0.04325781762599945,
0.0027208749670535326,
-0.04076400399208069,
-0.03236567974090576,
-0.08263906091451645,
0.012897343374788761,
0.024383511394262314,
-0.002829703502357006,
-0.009580458514392376,
0.00003484821354504675,
-0.013671071268618107,
-0.008092870935797691,
0.033561237156391144,
0.03615821152925491,
-0.012214012444019318,
0.022646578028798103,
0.02666129358112812,
0.010466770268976688,
-0.04787084460258484,
-0.012380802072584629,
0.018141111359000206,
-0.005819135345518589,
-0.00032949168235063553,
0.04239020124077797,
-0.03811522573232651,
0.032404422760009766,
0.005101971328258514,
-0.010028551332652569,
0.010706489905714989,
0.000028988448320887983,
-0.01381625421345234,
0.019662607461214066,
-0.008811155334115028,
-0.029396750032901764,
0.05575169622898102,
0.03703631833195686,
0.0006789773469790816,
0.051514629274606705,
-0.02692350745201111,
-0.0228160098195076,
0.013070556335151196,
-0.014366175048053265,
-0.03584008291363716,
-0.03168066218495369,
0.012994324788451195,
0.021378956735134125,
-0.010594206862151623,
-0.0331137590110302,
0.0542282834649086,
-0.028165725991129875,
-0.014371062628924847,
0.04317997768521309,
0.024878667667508125,
0.014856644906103611,
0.035294000059366226,
0.022677728906273842,
0.054496992379426956,
0.024984188377857208,
0.03155098110437393,
0.03840474411845207,
-0.0015892192022874951,
-0.004499385133385658,
-0.07087726145982742,
0.025273974984884262,
-0.06738840043544769,
-0.008641344495117664,
-0.01572151482105255,
0.0013338563730940223,
-0.04513043165206909,
0.016861751675605774,
0.023400818929076195,
-0.002109760418534279,
0.0418744720518589,
0.023935429751873016,
-0.012052896432578564,
0.062394607812166214,
-0.025619709864258766,
0.01495400257408619,
-0.052068449556827545,
0.02963016740977764,
-0.009526105597615242,
0.0493786558508873,
0.04085281118750572,
0.015195393934845924,
0.012750205583870411,
-0.024831967428326607,
-0.04390482231974602,
-0.020466536283493042,
0.020124344155192375,
-0.048180922865867615,
0.00005749943738919683,
0.02457333169877529,
-0.007820908911526203,
0.0006873281672596931,
-0.01629842072725296,
-0.0042992946691811085,
-0.01825757324695587,
0.00783891323953867,
-0.006315648090094328,
0.02345528081059456,
-0.00708374660462141,
-0.013303603045642376,
-0.02460751123726368,
0.04425497725605965,
-0.05908394977450371,
-0.01300035323947668,
-0.01720462553203106,
0.015407229773700237,
0.037776194512844086,
-0.012854444794356823
] |
<p>Here is a video presentation of infrared recordings of anomalous heating in a deuterium palladium cell: ( <a href="http://www.youtube.com/watch?v=Pb9V_qFKf2M&feature=relmfu" rel="nofollow">youtube video</a>) (see also <a href="http://www.youtube.com/watch?v=N2LV8rM7vn0" rel="nofollow">this presentation</a> if you want more detail, and have time). There are two papers referenced in the link, which give more detail. You can see with your own eyes sporadic localized bursts of energy, which show up as white flashes in the camera (I would like to encourage people to read the linked papers, which include thermal photos with a different color map, and also include piezoelectric detection of bursts)</p>
<p>Excluding cold fusion, what could possibly be causing this? Please try to account for the nature of the bursts--- the small radius, the qualitative amount of energy released, etc. </p>
<p>Just to be clear, I think the answer is <em>nothing</em>, that it is cold fusion, but I would like to see what explanations people come up with. I will also point out that this research group has been <a href="http://blog.newenergytimes.com/2012/03/01/navy-commander-halts-spawar-lenr-research/" rel="nofollow">politically shut down recently</a>.</p>
| 8,860 |
[
-0.024893496185541153,
-0.0072441743686795235,
-0.017136700451374054,
-0.06291466951370239,
0.0755319744348526,
0.0023584163282066584,
-0.0287272110581398,
-0.019243737682700157,
0.0032872918527573347,
-0.050214532762765884,
0.04155720770359039,
-0.003185597714036703,
0.028415268287062645,
0.0014457589713856578,
-0.0017684610793367028,
0.004524850286543369,
0.06800518929958344,
-0.06244368106126785,
0.015038810670375824,
-0.03262122720479965,
-0.0008439482771791518,
-0.0021492165978997946,
-0.012977025471627712,
-0.010362690314650536,
-0.04374797269701958,
0.012144136242568493,
0.011541294865310192,
0.007831202819943428,
-0.005282609723508358,
0.03799472749233246,
-0.010151980444788933,
-0.04142678156495094,
-0.05194157734513283,
-0.032905589789152145,
-0.01744222827255726,
0.013555308803915977,
-0.00961095280945301,
-0.019361918792128563,
0.00015775747306179255,
0.03944189101457596,
-0.026012146845459938,
-0.0049625420942902565,
-0.027777303010225296,
0.04116857796907425,
-0.04275652766227722,
-0.05283741652965546,
0.04384509101510048,
-0.028555115684866905,
0.03864459693431854,
-0.04925324022769928,
0.012168352492153645,
-0.01206118706613779,
0.039666797965765,
-0.020706521347165108,
-0.0014182185987010598,
0.04302695766091347,
0.037949200719594955,
0.07778481394052505,
-0.007207660935819149,
-0.04208351671695709,
0.0022750890348106623,
0.0273879561573267,
-0.008020841516554356,
0.0020815858151763678,
-0.03656698018312454,
0.026074189692735672,
-0.014084906317293644,
-0.05205453932285309,
0.0019207439618185163,
0.03115798905491829,
0.017158744856715202,
0.02832859940826893,
0.026765529066324234,
-0.014016050845384598,
0.032174691557884216,
-0.0362965352833271,
0.028874358162283897,
-0.00883745402097702,
0.04540400207042694,
0.0696064904332161,
-0.028884246945381165,
-0.0022583783138543367,
0.00332814222201705,
0.012306680902838707,
0.01581224612891674,
-0.012785322964191437,
0.08545801788568497,
-0.02698512189090252,
0.006064657121896744,
0.0117501150816679,
-0.03780197352170944,
0.022207733243703842,
0.015837520360946655,
0.039022210985422134,
-0.038479987531900406,
0.03817286342382431,
0.015078152529895306,
0.08516591787338257,
-0.022097239270806313,
-0.04388062655925751,
0.04441574588418007,
0.029447041451931,
0.05465494841337204,
0.07626080513000488,
0.008484739810228348,
-0.06836482137441635,
-0.02346169576048851,
0.02499874122440815,
-0.023810453712940216,
0.014463595114648342,
-0.07606647908687592,
0.016697578132152557,
0.008302728645503521,
-0.028148658573627472,
0.004011912737041712,
-0.023469069972634315,
0.0075933607295155525,
0.01576829142868519,
0.04054640978574753,
0.053213462233543396,
0.008652077056467533,
-0.02713329903781414,
0.01006040908396244,
-0.04691283777356148,
-0.025209207087755203,
0.02184073068201542,
0.032006729394197464,
-0.0029678530991077423,
-0.0017955885268747807,
0.022355157881975174,
-0.006811944767832756,
-0.01820226199924946,
0.003639209782704711,
-0.015521952882409096,
0.03092983365058899,
-0.007199985906481743,
-0.07697486132383347,
-0.0789012759923935,
0.09731869399547577,
0.001771125360392034,
-0.014560372568666935,
-0.10622883588075638,
-0.030755123123526573,
0.02477165311574936,
0.07578035444021225,
-0.022323500365018845,
-0.05982217937707901,
-0.0306873619556427,
0.0669359564781189,
0.004789436236023903,
-0.017086733132600784,
-0.011710754595696926,
0.013649099506437778,
-0.044612254947423935,
0.011179397813975811,
-0.058124788105487823,
0.03721849247813225,
0.0228989627212286,
-0.013586366549134254,
-0.02357122115790844,
0.05736422538757324,
0.0049555073492228985,
-0.0057973372749984264,
0.020048895850777626,
0.04357703775167465,
0.006725655868649483,
0.1101013720035553,
0.010944808833301067,
-0.05951306223869324,
0.05918953940272331,
0.005235848482698202,
0.04006374627351761,
0.040309276431798935,
0.05169660598039627,
0.0142458975315094,
-0.040762223303318024,
0.02898501418530941,
-0.02143603004515171,
0.00415555527433753,
0.004766850266605616,
-0.06032322347164154,
-0.015458449721336365,
0.0007297471165657043,
-0.018872689455747604,
0.007911793887615204,
0.06933165341615677,
-0.012487861327826977,
0.019172340631484985,
0.0353703573346138,
-0.060048628598451614,
-0.01628260128200054,
-0.02950773388147354,
0.005561972968280315,
-0.03033842332661152,
-0.026655808091163635,
0.012502966448664665,
-0.010939965955913067,
0.014481520280241966,
-0.0063148257322609425,
-0.06822383403778076,
0.02416856586933136,
0.024330459535121918,
0.03832119703292847,
0.02567373774945736,
-0.0028252878692001104,
0.04084905982017517,
-0.01821316033601761,
-0.010640807449817657,
-0.001775117707438767,
-0.037335652858018875,
-0.01541916560381651,
-0.011500540189445019,
-0.03788839280605316,
0.01851506344974041,
0.009550348855555058,
-0.024126293137669563,
-0.006583513226360083,
0.02250021882355213,
0.001068424666300416,
-0.007884752936661243,
-0.0015644560335204005,
0.05982774496078491,
-0.01766795665025711,
0.03539048507809639,
-0.02741829678416252,
0.054699551314115524,
0.03385356068611145,
0.0023370827548205853,
-0.020265130326151848,
-0.011689000762999058,
-0.07298806309700012,
-0.016392990946769714,
0.046454377472400665,
-0.0036122724413871765,
-0.06571463495492935,
0.050161730498075485,
-0.0216609388589859,
0.013480988331139088,
0.0389234833419323,
0.012363678775727749,
-0.016877824440598488,
-0.0016558209899812937,
-0.005290853790938854,
0.028758196160197258,
0.01031129714101553,
0.0008883088012225926,
0.008306754752993584,
0.04889055714011192,
0.02268160507082939,
0.00130745698697865,
0.01129493024200201,
0.002456540707498789,
-0.01931651122868061,
0.00475371303036809,
0.004838623106479645,
-0.012157939374446869,
0.021498285233974457,
0.007308459375053644,
0.013280385173857212,
0.031055031344294548,
0.003595428541302681,
0.059171296656131744,
-0.018619362264871597,
-0.02130611054599285,
-0.009086363948881626,
0.00023161170247476548,
0.0006391727365553379,
-0.018160106614232063,
0.022445140406489372,
-0.03128788247704506,
0.048368677496910095,
-0.02316056564450264,
0.019074570387601852,
-0.008044283837080002,
-0.005478803068399429,
0.003533138195052743,
0.007476085796952248,
0.016761479899287224,
-0.05282753333449364,
-0.03956907242536545,
0.004302917048335075,
-0.05758707970380783,
0.022921573370695114,
0.01384364441037178,
-0.043102458119392395,
0.006032405886799097,
-0.012035079300403595,
-0.02115979604423046,
0.032986197620630264,
-0.023693302646279335,
-0.0062442501075565815,
0.008206143043935299,
-0.004210298415273428,
-0.05919796973466873,
-0.010134118609130383,
-0.033154889941215515,
0.03348856046795845,
-0.046514805406332016,
0.0011885050917044282,
0.05185044929385185,
-0.05428683012723923,
-0.037554990500211716,
0.04298146069049835,
-0.006156753282994032,
0.009528130292892456,
-0.006149999797344208,
-0.02097037062048912,
0.0023236051201820374,
-0.013071473687887192,
0.018326515331864357,
0.009558938443660736,
-0.03090975619852543,
0.0017104719299823046,
-0.007755469065159559,
-0.037924669682979584,
0.012743069790303707,
-0.01043784897774458,
0.038726311177015305,
-0.018418561667203903,
-0.027833344414830208,
0.014554563909769058,
0.0017098928801715374,
-0.015954583883285522,
0.009989053942263126,
-0.02073112316429615,
-0.028339166194200516,
-0.010461808182299137,
0.0222425926476717,
0.06102905794978142,
0.021555431187152863,
0.012654082849621773,
0.010565249249339104,
0.0588197186589241,
0.05081770941615105,
-0.005843786988407373,
-0.05775775387883186,
0.01304859109222889,
-0.01726631447672844,
0.03045683167874813,
0.04217742383480072,
-0.00625718105584383,
-0.034286823123693466,
0.0073646255768835545,
0.00954021979123354,
0.023018240928649902,
0.05201833322644234,
-0.06307408213615417,
0.03091115690767765,
0.041575029492378235,
-0.010371736250817776,
-0.029647165909409523,
0.007460650056600571,
0.00021552831458393484,
-0.025763917714357376,
0.016430877149105072,
0.04864625632762909,
0.029036566615104675,
0.007830372080206871,
0.012584882788360119,
0.04980441555380821,
-0.0005618722061626613,
0.02258184924721718,
0.003969000186771154,
0.027867235243320465,
-0.0421467125415802,
-0.0008602234302088618,
0.0070687467232346535,
0.018425235524773598,
0.07545934617519379,
0.01865151710808277,
0.04082415997982025,
0.004705724306404591,
-0.017188554629683495,
0.001672900514677167,
-0.06411927938461304,
-0.028151242062449455,
0.008731319569051266,
0.06490601599216461,
0.0004143175610806793,
0.02172308973968029,
0.03558502346277237,
0.053865231573581696,
0.04190429672598839,
-0.04080018773674965,
-0.06332453340291977,
0.010583015158772469,
-0.0034051411785185337,
-0.02476165071129799,
-0.030472686514258385,
-0.006811727769672871,
-0.024789294227957726,
0.00890758540481329,
-0.029617981985211372,
-0.024161774665117264,
-0.004008083138614893,
-0.061281848698854446,
0.016085004433989525,
-0.00469577731564641,
-0.04292658343911171,
-0.04090111702680588,
-0.003108247183263302,
0.052627649158239365,
-0.014202791266143322,
0.011011487804353237,
0.017374098300933838,
-0.033362556248903275,
0.023069679737091064,
-0.026409268379211426,
0.004215911030769348,
0.0176825150847435,
0.03554341569542885,
0.003033079905435443,
0.0022407732903957367,
-0.011515573598444462,
-0.012808434665203094,
0.029865620657801628,
-0.00010797992581501603,
-0.01017172820866108,
0.018368246033787727,
-0.02560729719698429,
-0.0351472906768322,
0.0036980793811380863,
0.03186909109354019,
0.022484375163912773,
-0.029386969283223152,
0.07375730574131012,
-0.018541205674409866,
0.01596899703145027,
0.014777316711843014,
0.031765058636665344,
0.022372009232640266,
-0.01972326450049877,
0.004145391285419464,
-0.04294336959719658,
-0.01667998731136322,
-0.013977952301502228,
-0.016773313283920288,
0.021526502445340157,
-0.023470349609851837,
0.02224895916879177,
0.0022702771238982677,
0.0021902951411902905,
0.013811628334224224,
-0.021202875301241875,
-0.021387051790952682,
-0.032916344702243805,
-0.0024225248489528894,
0.002238168381154537,
-0.009533971548080444,
0.024455897510051727,
-0.0009699989459477365,
0.06804390996694565,
-0.0014467210276052356,
-0.009499609470367432,
-0.1212049201130867,
0.014872074127197266,
0.02889270894229412,
0.03522861376404762,
0.0029448361601680517,
0.00891044083982706,
-0.08205775916576385,
-0.02552533894777298,
0.03233430162072182,
-0.020325668156147003,
0.016550293192267418,
-0.03966563194990158,
-0.022179581224918365,
-0.01120542362332344,
-0.023201342672109604,
0.0027377926744520664,
-0.00810127891600132,
0.039289440959692,
0.012892935425043106,
-0.026130616664886475,
-0.03557781130075455,
0.02851775847375393,
-0.0013164005940780044,
0.029150106012821198,
0.0013481414644047618,
0.016601990908384323,
0.0037477524019777775,
0.002154208952561021,
0.028307097032666206,
-0.001245114835910499,
-0.10047953575849533,
0.015319284051656723,
-0.022712145000696182,
-0.007900606840848923,
0.06933958828449249,
-0.0657249242067337,
-0.04319499060511589,
0.016678638756275177,
0.006652132607996464,
0.002684216946363449,
-0.043723419308662415,
-0.030139746144413948,
0.03649761155247688,
0.04803933575749397,
0.01703016087412834,
0.01995101571083069,
0.08282865583896637,
-0.03180692344903946,
-0.004084523301571608,
-0.019563816487789154,
0.03145669400691986,
-0.02623174525797367,
0.002175965579226613,
0.0035342939663678408,
0.024016670882701874,
-0.033872462809085846,
0.04323038458824158,
-0.01545763574540615,
-0.008601194247603416,
0.0001145799906225875,
-0.025349438190460205,
0.0244658961892128,
0.007947216741740704,
-0.014783680438995361,
-0.009340549819171429,
-0.013313256204128265,
0.04740523174405098,
0.016053617000579834,
-0.0005216969875618815,
0.02294493466615677,
-0.010021992027759552,
0.012946372851729393,
0.018019607290625572,
-0.04515986517071724,
0.006749300751835108,
-0.04365866631269455,
0.020301641896367073,
0.052247557789087296,
-0.02175687439739704,
0.0052979206666350365,
-0.004637119825929403,
0.02029448002576828,
0.03538652881979942,
-0.042179450392723083,
-0.022953584790229797,
-0.013536297716200352,
0.0007516212062910199,
0.022387459874153137,
-0.033880285918712616,
0.029169268906116486,
-0.025609515607357025,
0.010015581734478474,
-0.08343160897493362,
-0.06042362004518509,
0.05112747848033905,
0.023394688963890076,
-0.04219206050038338,
-0.07160446047782898,
-0.03624865040183067,
-0.01880027912557125,
-0.020585117861628532,
-0.024669401347637177,
0.01566769927740097,
-0.011496889404952526,
-0.02222120761871338,
0.029051851481199265,
0.00789246242493391,
0.05242760106921196,
-0.0227960217744112,
-0.007375337183475494,
0.016443980857729912,
0.0023692294489592314,
-0.05625090375542641,
0.003405265510082245,
0.014505861327052116,
-0.022808196023106575,
-0.021191570907831192,
0.015545216389000416,
0.007094176020473242,
0.03996827453374863,
-0.0430934801697731,
0.015829185023903847,
0.056394319981336594,
0.03446565195918083,
0.020618541166186333,
-0.03910133242607117,
0.036727335304021835,
-0.010541087947785854,
0.005360875744372606,
-0.010551235638558865,
0.005316916853189468,
0.004327267408370972,
-0.04149435833096504,
0.00699841370806098,
-0.029974235221743584,
-0.012608812190592289,
-0.02348935976624489,
0.008068433962762356,
-0.009678603149950504,
0.0010605015559121966,
0.009928236715495586,
-0.005025016609579325,
0.05321484059095383,
-0.024110550060868263,
-0.003913271240890026,
-0.0155461011454463,
-0.007149942219257355,
-0.032164886593818665,
-0.047373704612255096,
-0.046623215079307556,
0.03514063358306885,
0.048292189836502075,
-0.025011351332068443,
0.026105372235178947,
-0.008078704588115215,
-0.010919054038822651,
0.02823747880756855,
-0.016734890639781952,
0.017949365079402924,
0.01649419777095318,
-0.011322502978146076,
-0.012384897097945213,
-0.004717964679002762,
0.004904072731733322,
0.01878597028553486,
0.07740521430969238,
0.008841266855597496,
0.017445916309952736,
0.06250572949647903,
0.038228124380111694,
0.029872044920921326,
-0.04737500846385956,
-0.06314802169799805,
0.042052313685417175,
-0.03761058673262596,
0.02123580314218998,
0.015882166102528572,
-0.012517520226538181,
0.06285072863101959,
0.005213919561356306,
0.0016172627219930291,
-0.04382738098502159,
-0.0030761619564145803,
-0.023601587861776352,
0.016090724617242813,
0.014482812955975533,
-0.01124956738203764,
0.0051614209078252316,
-0.006790433544665575,
0.029444022104144096,
0.01111888699233532,
0.001876972382888198,
-0.008402776904404163,
-0.05396288260817528,
-0.01827339641749859,
0.010332038626074791,
-0.03651181608438492,
0.06392095983028412,
-0.044703949242830276,
-0.046003714203834534,
-0.0018290492007508874,
-0.007719970773905516,
0.005815672222524881,
0.023521846160292625,
0.047222353518009186,
-0.0008558203699067235,
0.035387735813856125,
-0.005371851846575737,
0.023516228422522545,
-0.02903149276971817,
0.003182608401402831,
0.11807647347450256,
-0.00031239393865689635,
-0.011145222000777721,
-0.04130306467413902,
0.01793336123228073,
-0.004659545142203569,
0.020892305299639702,
0.006157792638987303,
0.0016612157924100757,
-0.00839326623827219,
0.027437033131718636,
0.042741578072309494,
0.061824698001146317,
0.022200381383299828,
0.030969547107815742,
0.024252938106656075,
0.00495109474286437,
-0.019832327961921692,
0.06643456965684891,
0.019878627732396126,
-0.016679607331752777,
-0.025132739916443825,
-0.023437095806002617,
0.024564441293478012,
-0.017987320199608803,
0.013419478200376034,
-0.010577155277132988,
-0.026661088690161705,
0.03494036942720413,
0.0305128563195467,
-0.049139026552438736,
0.01565602980554104,
-0.02148362435400486,
0.0031049640383571386,
-0.010960846208035946,
0.01151258498430252,
-0.0002849637239705771,
0.031002257019281387,
0.001013306900858879,
0.007492796052247286,
0.02958359569311142,
-0.025370342656970024,
0.01587049290537834,
0.04358397051692009,
0.006164036691188812,
-0.00723637081682682,
0.0035227967891842127,
0.008888071402907372,
-0.019066115841269493,
-0.002208925085142255,
-0.0004962274106219411,
-0.007530517876148224,
0.0127684585750103,
-0.0020134644582867622,
-0.044693171977996826,
-0.00870340596884489,
-0.0010578564833849669,
-0.002770513528957963,
-0.03716728091239929,
-0.02916502207517624,
0.033095527440309525,
-0.004533618688583374,
0.013763646595180035,
-0.022446006536483765,
0.02240043692290783,
0.017713556066155434,
0.0037763307336717844,
0.05866200104355812,
0.01889171451330185,
0.01911364309489727,
-0.03848780691623688,
-0.02723078988492489,
-0.008377248421311378,
-0.027314331382513046,
-0.0026042356621474028,
0.02112032286822796,
0.045740656554698944,
0.01664811186492443,
-0.036969736218452454,
0.013849747367203236,
-0.046469796448946,
0.039457082748413086,
0.003435641760006547,
-0.020089035853743553,
-0.013581315986812115,
-0.006044673267751932,
0.02822662703692913,
0.011677596718072891,
-0.0437733493745327,
-0.0013247813330963254,
0.0026467307470738888,
0.05186816304922104,
0.007137766573578119,
-0.01804123818874359,
-0.03065723180770874,
-0.014409178867936134,
-0.02827601507306099,
-0.000439189636381343,
-0.015229142270982265,
0.024706222116947174,
0.009816508740186691,
-0.006791818421334028,
0.03854987770318985,
0.004266833886504173,
-0.03778945654630661,
-0.016107656061649323,
0.022845352068543434,
-0.024126563221216202,
-0.03219865635037422,
-0.04206422343850136,
-0.013617774471640587,
-0.017375698313117027,
-0.019080225378274918,
0.015352768823504448,
0.00019735853129532188,
-0.013546627014875412,
0.06706995517015457,
-0.0135703319683671,
0.010527173988521099,
-0.01586642488837242,
0.011390965431928635,
0.006630118936300278,
0.011486425064504147,
-0.0481344498693943,
0.011514115147292614,
-0.024850117042660713,
0.02710052765905857,
-0.024269577115774155,
0.03058687224984169,
0.005656181834638119,
-0.007451065815985203,
0.023055346682667732,
0.01515000406652689,
0.006675933953374624,
0.019228599965572357,
0.007695992477238178,
0.0028421804308891296,
0.011482903733849525,
0.005420800764113665,
-0.06013217568397522,
0.05684686452150345,
-0.028779471293091774,
-0.061042483896017075,
0.048825785517692566,
-0.012168671004474163,
-0.0038552959449589252,
0.024012429639697075,
0.01001976989209652,
-0.004360179416835308,
0.0878036692738533,
-0.001962019130587578,
-0.03396645933389664,
0.021931981667876244,
0.004417138174176216,
0.024759650230407715,
0.019408350810408592,
-0.008210349828004837,
-0.041305240243673325,
-0.005481664557009935,
0.018898174166679382,
0.04824455827474594,
-0.019738586619496346,
0.01265295036137104,
-0.020664852112531662,
-0.029516326263546944,
0.027298517525196075,
0.002223534043878317,
0.049990151077508926,
0.0004228748148307204,
0.03968082368373871,
-0.04653247818350792,
-0.023221416398882866,
-0.012128754518926144,
0.013279968872666359,
-0.10896296799182892,
-0.025368811562657356,
-0.019025010988116264,
0.00003948992525693029,
0.006487686187028885,
-0.025316135957837105,
0.03331347927451134,
0.050780706107616425,
-0.07148242741823196,
-0.01889018528163433,
-0.03277578577399254,
-0.0270705483853817,
-0.042630601674318314,
0.016400596126914024,
-0.05138716474175453,
0.03689184412360191,
0.025610966607928276,
0.04460646212100983,
0.04119784012436867,
0.03967349976301193,
-0.01974106952548027,
-0.00009514798875898123,
0.017914434894919395,
0.018605448305606842,
0.05701382830739021,
-0.022762449458241463,
0.05913644656538963,
0.027341976761817932,
-0.01889670640230179,
0.02752680703997612,
-0.03744308650493622,
-0.013825719244778156,
0.01628137193620205,
-0.011955712921917439,
0.006086197216063738,
0.011266892775893211,
0.0321245975792408,
-0.024935882538557053,
-0.018646158277988434,
0.008517771027982235,
0.03117561899125576,
0.04439220577478409,
0.018401013687253,
0.026980213820934296,
0.027272922918200493,
-0.03891792148351669,
0.0006925981724634767,
0.026293428614735603,
-0.0310216024518013,
-0.0075665973126888275,
0.06058313325047493,
0.0233941450715065,
0.018258865922689438,
-0.045036815106868744,
-0.0033829326275736094,
-0.04349314048886299,
-0.0035899963695555925,
-0.012296704575419426,
0.03817441314458847,
0.015905573964118958,
0.030531568452715874,
-0.004504791460931301,
0.006620130036026239,
-0.002741412026807666,
-0.003588849911466241,
-0.025337453931570053,
-0.05280248448252678,
0.0114732151851058,
-0.013457166962325573,
-0.004512672312557697,
0.011314384639263153,
-0.01476489007472992,
-0.05728968605399132,
0.09660470485687256,
0.01261143572628498,
0.02595733478665352,
-0.01090153120458126,
-0.046224046498537064,
-0.027884431183338165,
-0.048343412578105927,
0.023525435477495193,
-0.03634743019938469,
0.008828059770166874,
-0.028073536232113838,
-0.046155840158462524,
-0.02255145087838173,
0.024960719048976898,
0.027143798768520355,
0.01887001283466816,
-0.04098924994468689,
0.05795874819159508,
-0.04493435099720955,
-0.00029182538855820894,
-0.05301181972026825,
0.036770980805158615,
-0.03246280923485756,
0.011653946712613106,
-0.007877347059547901,
-0.022064972668886185,
-0.014613104984164238,
-0.012789576314389706,
0.03536732867360115,
-0.00005965126911178231,
0.001368786906823516,
0.012057386338710785,
-0.010069768875837326,
0.04643428698182106,
0.0017433157190680504,
0.021410884335637093,
0.033833399415016174,
0.0017749769613146782,
-0.011854411102831364,
0.025737617164850235,
-0.014681128785014153,
-0.04201609641313553,
0.04261522367596626,
0.003697416977956891,
0.012283249758183956,
-0.006322158500552177,
-0.04357750713825226,
0.046391550451517105,
-0.041856907308101654,
0.034629445523023605,
0.0298034455627203,
-0.04914502426981926,
-0.01700778491795063,
0.03397756442427635,
-0.01012594997882843,
-0.003643629839643836,
0.0160349253565073,
0.031851474195718765,
-0.015438203699886799,
0.03582804650068283,
-0.01762962155044079,
0.05614959076046944,
0.015593068674206734,
-0.0056988210417330265,
0.022927356883883476,
-0.0032581444829702377,
0.006351923570036888,
0.0053961146622896194,
-0.003961880225688219,
-0.022625431418418884,
-0.017609139904379845,
-0.02061486430466175,
0.06294476985931396,
-0.050813689827919006,
-0.03843347728252411,
0.04496801272034645,
0.018649941310286522,
0.06889647990465164,
0.007891957648098469,
0.01405464019626379,
-0.0223604217171669,
-0.0013668789761140943,
-0.007968820631504059,
0.007068483624607325,
-0.010706692934036255,
0.031767189502716064,
-0.043683215975761414,
0.004343037959188223,
-0.01500723883509636,
0.024177270010113716,
0.011308230459690094,
-0.05122906714677811,
-0.020563125610351562,
-0.036439500749111176,
-0.010224489495158195,
0.012908627279102802,
0.015887562185525894,
-0.015529129654169083,
-0.018972130492329597,
0.0035552307963371277,
0.026722310110926628,
-0.017417509108781815,
0.008396578021347523,
-0.05027414485812187,
-0.02124728634953499,
0.03399810567498207,
-0.0524052195250988,
0.0160434078425169,
-0.014078851789236069,
0.0077908760868012905,
-0.0164923258125782,
0.007268835790455341
] |
<p>Let’s consider a pair of particles [with their signals] comprising an <em>isolated system</em>. Any change in some property of either particle is due to the signal/s received from the other. Each particle has the knowledge of the signals emitted by it and the consequences of such signals on the other. This is a “continuous process” which may go simultaneously with increasing separation between the particles. </p>
<p>The entanglement of some property ,between the particles, even in the highest level of non-locality seems to be intuitively “natural” <em>so long the system remains an isolated one</em>, comprising the two particles and the signals exchanged between them.</p>
<p>Would it be correct to say that the entanglement of properties in the non-local context should not be considered as an injury to commonsense perceptions?</p>
| 8,861 |
[
-0.004245982505381107,
-0.0021268485579639673,
0.014527890831232071,
0.0022781689185649157,
0.007985115982592106,
0.024033311754465103,
-0.036375656723976135,
0.007761950138956308,
0.010611314326524734,
-0.016847996041178703,
0.030155448243021965,
0.02312777191400528,
-0.013155639171600342,
0.025445550680160522,
-0.033497005701065063,
0.005204701796174049,
-0.022694982588291168,
-0.006600279826670885,
-0.007184579502791166,
-0.021461395546793938,
0.007774201687425375,
0.03306366875767708,
-0.014257242903113365,
-0.030417295172810555,
-0.004685681313276291,
0.038654010742902756,
-0.005018786992877722,
-0.01459664199501276,
0.016611937433481216,
0.068452388048172,
-0.00801464356482029,
-0.048188358545303345,
-0.04025557264685631,
0.0076135918498039246,
0.007501605898141861,
-0.007017407100647688,
-0.06894855201244354,
-0.020149176940321922,
0.04503660649061203,
-0.023122170940041542,
-0.03594326600432396,
-0.03422890603542328,
0.01062826905399561,
0.06368938088417053,
-0.03798286244273186,
-0.02712242491543293,
0.030674127861857414,
-0.012972325086593628,
0.015407427214086056,
-0.04294263571500778,
0.042992495000362396,
-0.02607959322631359,
-0.011532213538885117,
-0.014370416291058064,
-0.02066866122186184,
0.021809538826346397,
0.06917716562747955,
0.05959973856806755,
0.0026074752677232027,
-0.04761672392487526,
-0.021746426820755005,
-0.02988191694021225,
0.014556022360920906,
-0.03521844744682312,
-0.024128170683979988,
-0.00869469903409481,
0.04232503101229668,
0.002610338618978858,
0.019923048093914986,
0.007876737974584103,
-0.046643272042274475,
0.009075974114239216,
0.07767663896083832,
-0.001537030329927802,
0.026548530906438828,
-0.008342310786247253,
0.008536440320312977,
0.03241296112537384,
0.0023459563963115215,
0.04214668273925781,
0.021858757361769676,
-0.027380216866731644,
-0.014721737243235111,
-0.009815966710448265,
0.013220163993537426,
-0.03429286554455757,
0.09089148044586182,
-0.03203723952174187,
0.011272701434791088,
0.042019154876470566,
0.007986187003552914,
0.0069420249201357365,
0.026950307190418243,
0.025019453838467598,
-0.04871983081102371,
0.018273357301950455,
0.010931147262454033,
0.021063199266791344,
-0.01250823587179184,
-0.0580064132809639,
-0.02255810983479023,
-0.0505109578371048,
0.05425791069865227,
0.04926463961601257,
-0.00652062613517046,
-0.005312187597155571,
-0.038513071835041046,
0.015701543539762497,
0.003318610368296504,
-0.01974561996757984,
-0.04680141806602478,
0.03664252534508705,
0.021564103662967682,
0.05060034245252609,
0.023206517100334167,
-0.00943841878324747,
0.0031709517352283,
-0.005479826591908932,
0.099432572722435,
0.07955234497785568,
0.04017982259392738,
-0.03466872498393059,
0.016832157969474792,
-0.03587234020233154,
-0.06672479212284088,
0.07528029382228851,
0.012620468623936176,
-0.030247611925005913,
-0.03106735832989216,
-0.009549640119075775,
0.0037924847565591335,
0.012748358771204948,
-0.006437258794903755,
0.00027836146182380617,
0.018945569172501564,
-0.0023864193353801966,
-0.12460305541753769,
-0.043409571051597595,
0.046014342457056046,
0.016639739274978638,
0.00892670638859272,
-0.09476566314697266,
-0.0197020061314106,
0.027578167617321014,
0.10254698246717453,
-0.00695860804989934,
-0.014179868623614311,
0.007308510132133961,
0.02084968239068985,
0.00046206905972212553,
0.0009607778629288077,
-0.01175045408308506,
0.02755504660308361,
-0.019097432494163513,
-0.009033139795064926,
-0.03796220198273659,
0.038261380046606064,
0.0943867415189743,
-0.02048761211335659,
0.010358178988099098,
0.032672490924596786,
0.009690719656646252,
0.006654004566371441,
0.024867525324225426,
0.006156465969979763,
-0.05645628646016121,
0.08561789989471436,
-0.000005949616024736315,
0.03670001029968262,
0.050437454134225845,
0.037200771272182465,
0.029286783188581467,
-0.027604984119534492,
0.015545587986707687,
0.04267984256148338,
-0.03549552708864212,
0.01667129248380661,
0.003971777856349945,
0.0013660324038937688,
-0.011510711163282394,
-0.009978348389267921,
-0.001443047309294343,
-0.03967972844839096,
0.03504367172718048,
0.00637883460149169,
0.013386496342718601,
-0.022188827395439148,
-0.016766758635640144,
0.01573151908814907,
-0.03142398223280907,
-0.015625113621354103,
-0.0850970596075058,
0.02992400899529457,
0.00463512446731329,
-0.045252617448568344,
0.06049932539463043,
-0.02208208665251732,
0.023022927343845367,
-0.03371772915124893,
-0.030820000916719437,
-0.014187417924404144,
0.03666011244058609,
0.053574636578559875,
-0.06289862096309662,
-0.005283962935209274,
0.05739976838231087,
0.014702457934617996,
0.03606685996055603,
0.010166924446821213,
0.0148537065833807,
-0.08499330282211304,
0.029740463942289352,
0.017815565690398216,
0.034900542348623276,
-0.02260410785675049,
0.03291679173707962,
-0.012951791286468506,
0.011766633950173855,
-0.055436648428440094,
-0.005241599399596453,
-0.06855055689811707,
0.04401005804538727,
0.011866561137139797,
0.005454623606055975,
-0.010295618325471878,
0.016047492623329163,
0.035388123244047165,
-0.007530130445957184,
-0.013326942920684814,
-0.029415974393486977,
-0.06233552098274231,
0.008384048007428646,
-0.013536270707845688,
0.08450444787740707,
-0.008961262181401253,
-0.0063826702535152435,
-0.019141998142004013,
0.04457804560661316,
0.0071033900603652,
-0.018221072852611542,
-0.026038119569420815,
-0.015036508440971375,
0.031718287616968155,
0.008752863854169846,
0.013680825009942055,
0.006214842200279236,
-0.019401157274842262,
-0.001713308272883296,
0.04057494178414345,
-0.029378412291407585,
0.004765738267451525,
0.043319787830114365,
-0.03914548084139824,
0.058477602899074554,
-0.010815983638167381,
-0.008546932600438595,
0.03321032598614693,
-0.005931032355874777,
0.028192071244120598,
0.004044526256620884,
-0.03599834814667702,
-0.026505766436457634,
-0.03127644583582878,
-0.04186849296092987,
-0.02671990729868412,
-0.01504332385957241,
-0.07726655900478363,
-0.012280083261430264,
0.03159346431493759,
-0.02376824989914894,
-0.012698270380496979,
0.0037731132470071316,
-0.005014457739889622,
0.008659974671900272,
-0.0015157820889726281,
0.03977768123149872,
-0.02098076045513153,
0.01774776540696621,
-0.05129389464855194,
-0.015396136790513992,
0.03162068501114845,
-0.001186042558401823,
-0.016985831782221794,
0.04939582198858261,
-0.06067436560988426,
0.025919687002897263,
-0.0452907457947731,
0.0012724010739475489,
-0.0009857162367552519,
-0.026058336719870567,
0.05799373611807823,
0.005232236813753843,
-0.036135490983724594,
-0.046741072088479996,
-0.01142061222344637,
-0.034873973578214645,
-0.014209403656423092,
-0.01565438322722912,
-0.026449190452694893,
0.032067980617284775,
0.010218435898423195,
-0.04480734467506409,
-0.023153558373451233,
-0.01631917804479599,
-0.05469657853245735,
0.011538156308233738,
-0.02648869715631008,
-0.012588988058269024,
-0.03267728164792061,
-0.005198407918214798,
0.01270503643900156,
-0.05761179327964783,
-0.013959648087620735,
-0.0771820917725563,
-0.07776894420385361,
0.026010751724243164,
0.01998266391456127,
0.04145447164773941,
-0.011959484778344631,
-0.005121144466102123,
0.0377793088555336,
-0.01250707358121872,
-0.004324459005147219,
0.01238664984703064,
-0.021873872727155685,
-0.004959056153893471,
-0.014531816355884075,
-0.03631402552127838,
0.009367524646222591,
0.014344376511871815,
0.019730186089873314,
0.052443861961364746,
0.03468325734138489,
0.038597624748945236,
0.010985932312905788,
-0.028068741783499718,
-0.017126046121120453,
0.0287022665143013,
-0.02129160426557064,
0.04730922728776932,
0.016399262472987175,
-0.04166607931256294,
0.012570752762258053,
-0.0027242370415478945,
0.010352464392781258,
-0.012950267642736435,
-0.04454586282372475,
0.06321381032466888,
0.011050651781260967,
0.03800148516893387,
-0.023931868374347687,
0.015362975187599659,
-0.01873786933720112,
0.02324298769235611,
-0.017143841832876205,
0.019302401691675186,
0.012592955492436886,
0.0038836579769849777,
0.010831722058355808,
0.031003328040242195,
0.014684053137898445,
-0.009081280790269375,
-0.03033481538295746,
0.030649706721305847,
0.013407493010163307,
0.0358055904507637,
-0.001257017021998763,
0.00018440572603140026,
0.0019854314159601927,
0.00663919560611248,
0.0045813824981451035,
0.016241351142525673,
-0.05056069791316986,
-0.020008035004138947,
-0.05688194930553436,
0.014843553304672241,
0.016031021252274513,
0.004119060933589935,
0.0239213015884161,
0.02135368250310421,
0.03927885740995407,
-0.019463418051600456,
-0.01823173090815544,
0.0030834078788757324,
-0.0671992301940918,
-0.0037265627179294825,
-0.003730848664417863,
-0.004806910641491413,
0.004115148913115263,
-0.004285870585590601,
0.015414822846651077,
-0.040948472917079926,
-0.028647759929299355,
-0.013228130526840687,
0.026233689859509468,
-0.07054275274276733,
0.006481206510215998,
-0.049874197691679,
-0.047894079238176346,
-0.0390016995370388,
0.004807059187442064,
0.04212324321269989,
-0.02771458402276039,
0.0248879287391901,
0.01691686548292637,
-0.04062008112668991,
0.04107066988945007,
0.018397890031337738,
-0.003972000442445278,
0.05380730703473091,
-0.015310165472328663,
0.027162231504917145,
0.022467508912086487,
-0.022374402731657028,
0.03211255744099617,
0.015453658066689968,
0.01559666357934475,
-0.01252184621989727,
-0.011907149106264114,
-0.003710828023031354,
-0.039012353867292404,
-0.03733380138874054,
0.006010562647134066,
0.05928264558315277,
0.012680293060839176,
0.028731582686305046,
0.016699563711881638,
0.01445984747260809,
0.00013893816503696144,
-0.0034459985326975584,
0.03901061415672302,
0.0038126937579363585,
-0.04089426249265671,
-0.017078125849366188,
-0.00567244365811348,
0.00422284658998251,
-0.0037865075282752514,
0.007095739711076021,
0.0054530855268239975,
-0.015650250017642975,
-0.006228293292224407,
0.008315003477036953,
0.03790539503097534,
-0.00795811042189598,
-0.025563271716237068,
-0.017390772700309753,
-0.0013138167560100555,
-0.03187623620033264,
0.0034902303013950586,
0.021685995161533356,
0.039229847490787506,
0.002279519336298108,
0.03448840230703354,
-0.015867499634623528,
-0.0811329111456871,
-0.0016616707434877753,
0.04470081254839897,
-0.0038906680420041084,
0.020439326763153076,
-0.022398216649889946,
-0.06026258319616318,
-0.0411212295293808,
0.016143249347805977,
0.0005609193467535079,
0.02435949072241783,
-0.006743712816387415,
0.0033312295563519,
-0.04713766649365425,
-0.011597157455980778,
-0.007312198635190725,
0.03798124939203262,
0.02211565151810646,
0.03272167593240738,
-0.045388493686914444,
-0.017471350729465485,
0.0001190692710224539,
0.010431390255689621,
-0.010684873908758163,
0.03866147622466087,
0.005482604261487722,
-0.025865405797958374,
-0.0343577116727829,
0.011423403397202492,
0.016386156901717186,
-0.0286868866533041,
0.040368031710386276,
-0.0136764757335186,
-0.0238956231623888,
0.03260457143187523,
-0.004663548432290554,
-0.05125241354107857,
-0.014499110169708729,
-0.018893970176577568,
0.006181738339364529,
0.028169943019747734,
-0.025788070634007454,
0.07857869565486908,
0.015988439321517944,
-0.018742742016911507,
0.011828240007162094,
0.040690284222364426,
0.005797874182462692,
0.029106389731168747,
0.00039412410114891827,
0.06749587506055832,
-0.05634762719273567,
0.05904432013630867,
-0.06249351054430008,
0.0004652228963095695,
-0.04304049164056778,
0.045759137719869614,
0.010528946295380592,
-0.007988193072378635,
-0.011751005426049232,
-0.05297858640551567,
-0.005907355807721615,
0.00842232909053564,
-0.019382186233997345,
-0.014017071574926376,
-0.03243519738316536,
0.023991262540221214,
-0.033854544162750244,
-0.0072942376136779785,
-0.023037705570459366,
0.01412291917949915,
0.012897705659270287,
0.014320618472993374,
-0.018409723415970802,
0.0029533375054597855,
-0.032778311520814896,
-0.04273931309580803,
0.021647043526172638,
-0.07318597286939621,
0.019293982535600662,
-0.009017755277454853,
-0.014097041450440884,
-0.010467500425875187,
-0.035732995718717575,
-0.01732003316283226,
0.022762274369597435,
-0.0185844749212265,
0.025133395567536354,
-0.08101403713226318,
0.010564517229795456,
0.005273330025374889,
-0.015212924219667912,
-0.05872046574950218,
-0.04873691499233246,
0.028108248487114906,
-0.02155604213476181,
0.02194218337535858,
-0.01901654340326786,
0.005430643912404776,
-0.006037341430783272,
0.021011823788285255,
-0.025192636996507645,
0.03186102956533432,
0.009560372680425644,
-0.011358080431818962,
0.015908051282167435,
0.05350662022829056,
0.03877684846520424,
-0.01803886704146862,
0.02600143477320671,
-0.020386815071105957,
0.007668125908821821,
0.009351292625069618,
-0.00016622140537947416,
0.036578547209501266,
-0.0305878147482872,
-0.04688366875052452,
-0.02033364027738571,
-0.03874950855970383,
0.01083883922547102,
-0.008374576456844807,
-0.04098629578948021,
0.011252094991505146,
-0.0002639202284626663,
0.006952732335776091,
0.026333250105381012,
-0.0016876537119969726,
0.025831814855337143,
0.024215618148446083,
0.01540087629109621,
0.01711520552635193,
0.024086005985736847,
-0.027292245998978615,
0.019410451874136925,
0.033420342952013016,
-0.0376199372112751,
0.03908294439315796,
-0.006310697179287672,
0.01520455814898014,
0.0065881661139428616,
0.019493265077471733,
-0.01412591990083456,
0.024417651817202568,
-0.035250864923000336,
0.018993601202964783,
0.008087673224508762,
0.017911866307258606,
-0.04632400721311569,
-0.00922760833054781,
-0.04064919054508209,
-0.014718299731612206,
0.026691587641835213,
-0.01914098858833313,
0.03872727230191231,
0.03147771954536438,
-0.005173428449779749,
-0.022049568593502045,
-0.0359041653573513,
0.02562338300049305,
0.002853376790881157,
-0.018219418823719025,
0.047014787793159485,
-0.043763045221567154,
0.00737518398091197,
0.0023723975755274296,
0.06530988216400146,
-0.023503579199314117,
0.017759187147021294,
-0.010990101844072342,
0.024549802765250206,
0.01826917752623558,
-0.015146058984100819,
-0.020609701052308083,
0.015775542706251144,
-0.03656008839607239,
-0.013628987595438957,
-0.007181194610893726,
0.002258669352158904,
0.019472623243927956,
0.014875584281980991,
0.023634161800146103,
-0.007592621259391308,
-0.017329920083284378,
-0.04223327338695526,
0.01203351840376854,
-0.0030092173255980015,
-0.006141368765383959,
0.0015816588420420885,
-0.008880267851054668,
-0.004547229036688805,
0.01965012028813362,
0.015226592309772968,
-0.015903107821941376,
-0.0547889843583107,
-0.01859966851770878,
-0.036848243325948715,
0.003963946830481291,
0.03415137901902199,
-0.02319045178592205,
-0.006351325195282698,
0.060122109949588776,
-0.021568607538938522,
0.04118053987622261,
-0.006322345230728388,
0.012846349738538265,
-0.02885785885155201,
0.043127089738845825,
-0.0015735495835542679,
-0.005706059746444225,
-0.005337510723620653,
0.03220231831073761,
0.11315491050481796,
0.04617229104042053,
-0.006616599392145872,
-0.04638141393661499,
0.01816696859896183,
-0.010100218467414379,
0.014869210310280323,
-0.00078841473441571,
0.001724476576782763,
0.004292639903724194,
-0.008439037017524242,
0.015720298513770103,
0.00870649516582489,
0.0616547130048275,
-0.016398310661315918,
0.05595097690820694,
-0.03897756338119507,
-0.024355534464120865,
-0.003386714030057192,
0.02087571658194065,
0.0007660261471755803,
-0.03459782153367996,
-0.008794477209448814,
0.004271003417670727,
0.006832597777247429,
0.014855803921818733,
0.0012655023019760847,
-0.004613202065229416,
0.01033670362085104,
0.025311695411801338,
-0.012097801081836224,
0.015167715027928352,
-0.003803350729867816,
-0.0030275769531726837,
-0.009850290603935719,
-0.009881360456347466,
0.03639473021030426,
-0.02552378736436367,
0.028979947790503502,
-0.008353300392627716,
-0.004255103878676891,
0.0018356184009462595,
0.022576550021767616,
0.008968442678451538,
-0.07367581129074097,
-0.0049181245267391205,
0.016161473467946053,
0.0411808043718338,
0.007406997960060835,
0.00341200758703053,
0.02233566716313362,
-0.023646827787160873,
0.025118708610534668,
-0.03296034410595894,
-0.01618468575179577,
0.002062833169475198,
-0.005485699977725744,
0.018340403214097023,
-0.008829786442220211,
-0.0045976340770721436,
0.027512622997164726,
0.012140982784330845,
0.018693875521421432,
-0.0025016663130372763,
0.0004761490854434669,
0.0042833248153328896,
0.02386106364428997,
0.05345477908849716,
0.045281682163476944,
0.02488633804023266,
-0.06798914819955826,
-0.0008586638141423464,
-0.04103828966617584,
-0.000313112250296399,
-0.015559513121843338,
-0.008260363712906837,
0.06336824595928192,
0.019607488065958023,
-0.004552047699689865,
-0.013352597132325172,
-0.055289126932621,
0.03762274980545044,
-0.027470270171761513,
-0.011349632404744625,
-0.021198095753788948,
0.03265291452407837,
0.014158861711621284,
0.03393956646323204,
-0.02310270629823208,
-0.010701145976781845,
0.006994146388024092,
0.022517630830407143,
0.014036362059414387,
0.00171704962849617,
0.00959395244717598,
-0.024463223293423653,
-0.04800404980778694,
-0.037420809268951416,
-0.012438781559467316,
0.034653548151254654,
0.008417594246566296,
0.036817893385887146,
-0.00352392322383821,
0.044980280101299286,
-0.013278353027999401,
0.002970165340229869,
0.030476126819849014,
-0.009858455508947372,
-0.022477317601442337,
0.025338847190141678,
0.024790268391370773,
-0.015767183154821396,
0.015497436746954918,
-0.03206660971045494,
0.0003769471659325063,
-0.004803049378097057,
0.03131541237235069,
-0.009044032543897629,
-0.024088812991976738,
0.019713783636689186,
0.08270572125911713,
-0.003315687645226717,
-0.02413049340248108,
-0.06819433718919754,
-0.016289103776216507,
0.014417055062949657,
-0.026479613035917282,
-0.00765121728181839,
0.04092048853635788,
0.007857334800064564,
0.0006052893004380167,
0.028238724917173386,
0.03769942745566368,
0.0003004551399499178,
-0.017383525148034096,
0.008405737578868866,
0.0009662191732786596,
0.02782057225704193,
-0.010573025792837143,
-0.04501166194677353,
0.03963581100106239,
-0.008191986009478569,
-0.024743573740124702,
0.021567698568105698,
-0.007744744420051575,
0.026946743950247765,
0.03274962306022644,
0.025426242500543594,
-0.04347760230302811,
0.013860903680324554,
-0.007959680631756783,
0.025306185707449913,
0.01703757792711258,
0.008140955120325089,
-0.027131328359246254,
-0.01490670908242464,
-0.0021724586840718985,
0.0047551547177135944,
-0.02539467066526413,
0.04805370047688484,
0.045099034905433655,
0.04021453484892845,
0.06092323735356331,
0.038913704454898834,
-0.009035851806402206,
0.025081440806388855,
0.01929486356675625,
0.013631505891680717,
0.018107421696186066,
0.05327814817428589,
-0.021353019401431084,
0.005085622891783714,
0.034542862325906754,
-0.012107976712286472,
-0.09039884060621262,
-0.006216320209205151,
0.010543513111770153,
0.007708149030804634,
0.014560327865183353,
-0.03183846175670624,
0.03951466828584671,
0.02832445502281189,
-0.08227574825286865,
0.021350914612412453,
-0.006563100963830948,
-0.05475312098860741,
-0.036906905472278595,
0.050153765827417374,
-0.06861375272274017,
0.07551562041044235,
0.0017200297443196177,
0.023496223613619804,
0.004417935386300087,
0.02335534617304802,
-0.023969966918230057,
-0.022499920800328255,
-0.0405174158513546,
-0.003335450543090701,
-0.012087580747902393,
-0.021974625065922737,
0.09975630044937134,
-0.03241794928908348,
-0.009785981848835945,
0.03231411054730415,
-0.030064696446061134,
-0.033705420792102814,
-0.021079907193779945,
0.037002090364694595,
0.0352468304336071,
0.003228302812203765,
0.006056679878383875,
-0.012558906339108944,
0.009999576956033707,
-0.0003131878620479256,
0.0013183493865653872,
0.034170154482126236,
-0.018740851432085037,
-0.020567813888192177,
-0.01377083919942379,
-0.021415777504444122,
-0.03311177343130112,
0.017392732203006744,
-0.0267151091247797,
-0.014791871421039104,
-0.019182542338967323,
0.03917977213859558,
-0.01702166721224785,
-0.015940744429826736,
0.05361931771039963,
-0.04357025399804115,
-0.009668035432696342,
0.04400792345404625,
0.005380280781537294,
-0.03338102623820305,
-0.03798960521817207,
-0.0060303970240056515,
-0.04831938445568085,
0.015700438991189003,
0.005633195396512747,
0.015419689938426018,
-0.030912118032574654,
-0.0356111004948616,
0.014002057723701,
0.013003193773329258,
0.028712280094623566,
-0.07470965385437012,
-0.04278809577226639,
0.019665053114295006,
-0.013562241569161415,
0.019010717049241066,
0.00008198720752261579,
-0.026094578206539154,
-0.012367730028927326,
-0.07821162045001984,
0.057144127786159515,
-0.0006961413309909403,
0.02158668078482151,
-0.04440674930810928,
-0.022640932351350784,
-0.019394781440496445,
0.008869091980159283,
0.052389875054359436,
0.03711608052253723,
0.0008436182979494333,
0.0301272664219141,
0.04691767692565918,
0.022099005058407784,
0.033906616270542145,
0.005444904323667288,
-0.036439720541238785,
0.02375510148704052,
0.0061200582422316074,
-0.028730474412441254,
-0.03764151409268379,
0.03854221850633621,
0.03276285529136658,
-0.0018392117926850915,
-0.010220014490187168,
-0.002249235287308693,
-0.03593337535858154,
0.06642532348632812,
-0.007659262046217918,
0.011069190688431263,
0.03990243375301361,
-0.00626708846539259,
0.054178230464458466,
0.01740425080060959,
0.005468880292028189,
-0.06921198964118958,
-0.02132609859108925,
-0.010068429633975029,
-0.03557019308209419,
-0.02632785402238369,
0.006352439057081938,
0.022964367642998695,
-0.013239488005638123,
0.002819981426000595,
0.035371966660022736,
-0.07165516912937164,
0.013998248614370823,
0.02405763417482376,
0.02486930787563324,
0.014779498800635338,
0.04561691731214523,
0.03764455392956734,
0.045269519090652466,
0.020926443859934807,
-0.0077838473953306675,
0.06919951736927032,
0.07900023460388184,
-0.005817870143800974,
0.023108679801225662,
0.005367794074118137,
-0.06473295390605927,
0.031059781089425087,
0.002209059428423643,
0.040114324539899826,
0.012437550351023674,
-0.01225042250007391,
0.020593766123056412,
0.020543940365314484,
-0.004960573278367519,
0.03153207153081894,
0.017824850976467133,
0.07453574240207672,
-0.003999362699687481,
0.004324538167566061,
0.012520147487521172,
0.02605004608631134,
-0.023763258010149002,
-0.02331351488828659,
0.033396393060684204,
0.0372338630259037,
0.018434053286910057,
-0.037576835602521896,
-0.027495620772242546,
-0.028195006772875786,
0.0341559574007988,
-0.0742221400141716,
0.029700404033064842,
-0.014765117317438126,
0.009018095210194588,
0.00563293881714344,
-0.05233943462371826,
-0.0027259644120931625,
-0.03273817151784897,
0.044890690594911575,
0.02103571780025959,
0.06558586657047272,
-0.02584310621023178,
-0.013144937343895435,
-0.029039090499281883,
0.02524670399725437,
-0.07182200253009796,
0.023726193234324455,
0.0015995805151760578,
0.04245438426733017,
-0.021958937868475914,
-0.03195677697658539
] |
<p>How is Gauss' law related to permittivity?
I know that it equals $1/\epsilon_0$ times the magnitude of the charge enclosed. But, I'm unable to understand what it actually means.</p>
<p>Can someone intuitively explain it to me?</p>
| 8,862 |
[
-0.015641020610928535,
-0.00020957671222276986,
0.017574626952409744,
-0.015063348226249218,
0.024804692715406418,
0.022345557808876038,
-0.037939589470624924,
-0.009478408843278885,
-0.011149026453495026,
-0.010693051852285862,
0.03913680836558342,
0.054706960916519165,
0.062371548265218735,
-0.006452333647757769,
0.0064547318033874035,
0.016137929633259773,
-0.01378804724663496,
-0.011296955868601799,
0.0032825281377881765,
-0.02965044416487217,
-0.022268587723374367,
0.04294222965836525,
0.011685861274600029,
0.008884565904736519,
-0.03947827219963074,
0.03455503284931183,
0.020071856677532196,
0.006597863044589758,
0.05030091851949692,
0.043943971395492554,
-0.00120361743029207,
-0.0248543880879879,
0.01836683414876461,
-0.0009361138800159097,
0.01219777762889862,
-0.027562826871871948,
-0.010028045624494553,
-0.03251134976744652,
-0.0103861503303051,
0.028829138725996017,
-0.009377983398735523,
-0.04432963207364082,
-0.006755473557859659,
0.05249537527561188,
-0.01924877054989338,
-0.0009529156377539039,
-0.00810281839221716,
-0.04034631699323654,
0.05381392315030098,
-0.06714276969432831,
0.051591940224170685,
0.002824063180014491,
0.055264607071876526,
0.024738362058997154,
0.018239593133330345,
0.022617282345891,
0.10732534527778625,
0.05099713057279587,
-0.010034038685262203,
-0.04985698685050011,
-0.0037566074170172215,
-0.036377571523189545,
-0.01686585135757923,
-0.024930832907557487,
-0.01851440966129303,
0.02696082554757595,
-0.0322943776845932,
-0.023249810561537743,
0.02154318243265152,
0.016591690480709076,
0.011270123533904552,
0.03286292031407356,
0.023534473031759262,
-0.02199794352054596,
0.005895990412682295,
-0.0033132971730083227,
0.0039669605903327465,
0.016578303650021553,
0.04308551549911499,
0.034719422459602356,
-0.021047567948698997,
0.015263567678630352,
-0.010543025098741055,
0.05102090537548065,
0.019647035747766495,
-0.011456686072051525,
0.04405685514211655,
-0.04472942650318146,
0.03401261195540428,
0.002628703834488988,
-0.03260285034775734,
0.020945848897099495,
0.0054503073915839195,
-0.00950058177113533,
-0.011150859296321869,
0.03291940689086914,
-0.011227396316826344,
0.02250906266272068,
0.011725645512342453,
-0.024505339562892914,
0.023217400535941124,
-0.01560917031019926,
0.0005509370821528137,
0.056327782571315765,
-0.003580821678042412,
-0.05718056112527847,
-0.005051807034760714,
0.031747329980134964,
-0.021434908732771873,
-0.03821675106883049,
-0.035030048340559006,
0.03905614838004112,
0.018528470769524574,
0.005062969401478767,
0.02536671981215477,
-0.027407938614487648,
0.03331907466053963,
-0.02095675840973854,
0.027017168700695038,
0.07935518026351929,
0.04141852259635925,
-0.05871375650167465,
0.037388332188129425,
-0.006086952053010464,
-0.08604917675256729,
0.03156593441963196,
0.00017625610053073615,
-0.007666382007300854,
-0.03310349956154823,
0.00945842731744051,
-0.028721628710627556,
-0.035502467304468155,
-0.0016312304651364684,
0.016343245282769203,
0.016736950725317,
-0.03296390175819397,
-0.08456344157457352,
-0.04306923598051071,
0.017397204414010048,
-0.023842601105570793,
-0.017456693574786186,
-0.10251663625240326,
0.008265340700745583,
0.01984955370426178,
0.06407182663679123,
0.017797335982322693,
0.003266695188358426,
-0.006126416381448507,
0.03278146684169769,
0.003728737821802497,
-0.0048072971403598785,
-0.04036105051636696,
-0.001385089592076838,
-0.03152437135577202,
0.011136762797832489,
-0.05014047771692276,
0.033210087567567825,
0.038409363478422165,
-0.018416928127408028,
-0.02098170854151249,
0.05803103372454643,
-0.01791989989578724,
-0.013322192244231701,
0.001437115017324686,
-0.010238461196422577,
-0.03043040633201599,
0.08168743550777435,
0.02810259722173214,
0.04762953519821167,
0.0688822790980339,
0.0008554835803806782,
-0.0038243927992880344,
0.032438699156045914,
0.05273544043302536,
0.047973282635211945,
-0.024882428348064423,
-0.003802864346653223,
-0.04106799513101578,
0.013392355293035507,
0.012004230171442032,
-0.04510188847780228,
-0.060976166278123856,
0.025083160027861595,
0.03164812549948692,
-0.008799735456705093,
0.028084665536880493,
0.001442056498490274,
-0.012046695686876774,
-0.012741535902023315,
-0.06407967954874039,
-0.007613794878125191,
-0.058544132858514786,
0.06164906919002533,
0.031808268278837204,
-0.02111881785094738,
0.032127492129802704,
0.010723549872636795,
-0.0017960196128115058,
-0.05854881554841995,
-0.0369449220597744,
0.0016463269712403417,
0.02860279753804207,
-0.028906039893627167,
-0.03277292847633362,
0.02643440291285515,
0.033910948783159256,
0.03770992159843445,
0.01845947839319706,
0.052358269691467285,
-0.007581161800771952,
-0.016785655170679092,
0.028360463678836823,
-0.022813277319073677,
0.029938817024230957,
0.0037306714802980423,
-0.011449373327195644,
0.01125542726367712,
-0.025408200919628143,
-0.01545810978859663,
0.05934282764792442,
-0.021422231569886208,
0.07295826822519302,
0.08291824907064438,
0.01928207091987133,
-0.012708035297691822,
0.031071294099092484,
-0.013995141722261906,
-0.0168774276971817,
-0.024587897583842278,
-0.04190588742494583,
-0.047016553580760956,
0.01073288731276989,
0.03936376795172691,
0.043253093957901,
-0.010452980175614357,
-0.009937278926372528,
0.020709441974759102,
0.03575277328491211,
0.05244620516896248,
0.04112136736512184,
-0.027342384681105614,
-0.02553970366716385,
0.02093682251870632,
-0.008103610947728157,
-0.029164161533117294,
-0.020334668457508087,
0.004744395613670349,
0.02984974905848503,
0.030648939311504364,
0.02217741496860981,
0.008544281125068665,
0.02958681248128414,
0.0023546244483441114,
0.018419746309518814,
0.021394897252321243,
-0.02449887990951538,
-0.0059270309284329414,
-0.04869075119495392,
0.01395063754171133,
0.012006955221295357,
-0.02225901186466217,
0.01999306119978428,
-0.040060196071863174,
0.0027341165114194155,
0.04695238173007965,
-0.042745448648929596,
-0.04159118980169296,
-0.004671492148190737,
0.030852707102894783,
-0.06848526000976562,
0.007451609708368778,
0.01589677482843399,
-0.02347552217543125,
-0.03902295231819153,
-0.022394075989723206,
0.014991560019552708,
-0.015741383656859398,
0.04790385067462921,
-0.010709534399211407,
-0.04260661453008652,
-0.0028895095456391573,
-0.015828819945454597,
0.01374113280326128,
-0.002322985092177987,
-0.01615460030734539,
0.007511760573834181,
-0.036430951207876205,
-0.010291489772498608,
0.03834446147084236,
0.0001669350895099342,
-0.009765805676579475,
0.006991748232394457,
-0.0019149861764162779,
-0.036576248705387115,
-0.009534166194498539,
-0.011763431131839752,
0.029507620260119438,
-0.025208599865436554,
0.0037081630434840918,
0.04171687364578247,
-0.045539066195487976,
-0.042221665382385254,
0.01300870906561613,
-0.036753784865140915,
-0.042499225586652756,
-0.01438642293214798,
-0.013083202764391899,
0.0007105900440365076,
-0.02125687710940838,
0.022923381999135017,
-0.0034989595878869295,
-0.058842893689870834,
-0.018311170861124992,
-0.0257590189576149,
-0.040765512734651566,
0.03377613052725792,
-0.0034067933447659016,
0.06066565960645676,
-0.007937262766063213,
-0.05046101659536362,
0.0634087398648262,
0.02094913460314274,
-0.0037750727497041225,
0.004951418377459049,
-0.044553112238645554,
-0.014325943775475025,
-0.02569536864757538,
-0.00041349130333401263,
0.06448402255773544,
-0.019386261701583862,
-0.005784973502159119,
0.0384935699403286,
0.03365231677889824,
0.033115994185209274,
0.027214080095291138,
0.01596737653017044,
-0.016397127881646156,
-0.014920882880687714,
0.007960622198879719,
0.04925158619880676,
0.012420034036040306,
-0.013366585597395897,
0.010417891666293144,
0.02940642647445202,
0.04766419157385826,
0.03124873898923397,
0.009010843932628632,
0.024976499378681183,
0.0031387251801788807,
0.028803132474422455,
-0.030711833387613297,
0.041001349687576294,
0.016442568972706795,
-0.0028144288808107376,
0.04375183582305908,
0.03334615379571915,
0.022784512490034103,
-0.05823179706931114,
0.0008804400567896664,
0.020287225022912025,
0.0352269671857357,
-0.024716492742300034,
-0.026859812438488007,
-0.0076568955555558205,
-0.016020821407437325,
0.02656269446015358,
-0.014856449328362942,
-0.03040088340640068,
0.02842624858021736,
0.018716076388955116,
0.023567039519548416,
0.014859719201922417,
-0.032298557460308075,
0.0031391947995871305,
-0.03088807873427868,
-0.024980349466204643,
0.00015141034964472055,
0.045150935649871826,
0.01432543620467186,
0.07905268669128418,
0.025461748242378235,
0.015998538583517075,
0.018638109788298607,
-0.0045426334254443645,
-0.07875032722949982,
0.01389063149690628,
-0.051222752779722214,
0.005648803431540728,
-0.03346152603626251,
-0.0035656802356243134,
-0.00970369391143322,
-0.0038834139704704285,
-0.013256329111754894,
-0.023610113188624382,
-0.001117468229494989,
-0.051007963716983795,
0.021105628460645676,
-0.033795371651649475,
-0.016895411536097527,
-0.017901958897709846,
0.01227051392197609,
-0.007414764724671841,
-0.04667241498827934,
-0.015271603129804134,
0.04309726133942604,
-0.012695816345512867,
-0.013386078178882599,
0.007010027766227722,
0.013880478218197823,
0.03137127310037613,
0.026280734688043594,
0.04141642898321152,
-0.017100155353546143,
0.011953928507864475,
-0.0013431732077151537,
0.022709118202328682,
0.08593559265136719,
0.015657590702176094,
-0.020321795716881752,
-0.06008489057421684,
-0.06088617071509361,
-0.017483970150351524,
-0.03276214748620987,
0.05952256917953491,
-0.02182464860379696,
-0.001816064235754311,
0.02659926563501358,
0.0031891162507236004,
-0.0019551822915673256,
0.042442645877599716,
0.022897539660334587,
0.030801955610513687,
-0.02240854874253273,
-0.05411997064948082,
0.005688792560249567,
-0.04221414774656296,
0.0026658226270228624,
0.017684191465377808,
-0.0169692300260067,
-0.03240388631820679,
-0.015482663176953793,
0.019859954714775085,
-0.007484534755349159,
0.01438628975301981,
-0.014042171649634838,
0.006282349582761526,
-0.006318506319075823,
0.001140727661550045,
-0.030873844400048256,
-0.02485361136496067,
0.0539143905043602,
0.04773297905921936,
0.002230699174106121,
-0.026322199031710625,
-0.0911557674407959,
0.0021078188437968493,
0.03099668398499489,
0.006853554397821426,
-0.007219208404421806,
0.015054767020046711,
-0.03321375325322151,
-0.0016079373890534043,
0.03526104614138603,
-0.024986818432807922,
0.006233197636902332,
-0.016847578808665276,
-0.0009191141580231488,
-0.05617891252040863,
0.0002916574012488127,
-0.029694214463233948,
0.033962126821279526,
0.009269448928534985,
0.009837526828050613,
-0.0003526792861521244,
0.009271904826164246,
-0.022946549579501152,
0.059318527579307556,
0.015403361059725285,
0.057241812348365784,
-0.00031071933335624635,
-0.002775518922135234,
-0.006779819261282682,
0.034884482622146606,
-0.0039014362264424562,
-0.047585438936948776,
0.011204725131392479,
0.004879568703472614,
0.006841061171144247,
0.046689074486494064,
-0.025453772395849228,
-0.03451620042324066,
0.021933019161224365,
0.03329605236649513,
-0.016138041391968727,
-0.009996662847697735,
-0.006468663923442364,
0.05056626722216606,
0.012360401451587677,
0.024498334154486656,
0.044828809797763824,
0.021395601332187653,
-0.0020621565636247396,
-0.01995399035513401,
-0.023479964584112167,
0.07028059661388397,
-0.013110019266605377,
-0.028458276763558388,
-0.007748209871351719,
0.021405596286058426,
-0.06631767004728317,
0.057470954954624176,
-0.02271469123661518,
0.023397669196128845,
-0.026828907430171967,
-0.027144717052578926,
-0.008760693483054638,
-0.0010747505584731698,
0.0006882377783767879,
-0.019731000065803528,
0.0031390232034027576,
0.029270419850945473,
0.02600436843931675,
-0.030185505747795105,
0.007755191531032324,
-0.02068433351814747,
0.018185945227742195,
0.012192437425255775,
-0.00033058132976293564,
0.015479996800422668,
-0.042177487164735794,
-0.008107226341962814,
0.017290949821472168,
-0.029742881655693054,
0.04974978417158127,
-0.03179304301738739,
-0.002451496198773384,
-0.006252207327634096,
-0.06632984429597855,
-0.031139248982071877,
0.010322283953428268,
0.026375379413366318,
0.0465773306787014,
-0.05379050225019455,
-0.0011971803614869714,
0.008794158697128296,
0.018230104818940163,
-0.06963040679693222,
-0.06285098940134048,
0.024950791150331497,
0.018171772360801697,
-0.0017367955297231674,
-0.014155538752675056,
-0.009076952002942562,
-0.010485908947885036,
-0.05430600047111511,
0.03519569709897041,
0.02655835449695587,
-0.03247501701116562,
0.009033070877194405,
-0.010583681985735893,
-0.0007045156671665609,
0.0403178445994854,
-0.019318709149956703,
-0.020097561180591583,
0.012683517299592495,
-0.0340566411614418,
0.00043819870916195214,
-0.004971381276845932,
0.045060284435749054,
-0.029915818944573402,
-0.014137929305434227,
-0.020283665508031845,
-0.025666579604148865,
0.04305567964911461,
-0.03774958476424217,
0.003307660110294819,
0.016836892813444138,
0.01967654377222061,
-0.009083175100386143,
-0.010227967984974384,
0.0025638092774897814,
0.02330024726688862,
0.04772461578249931,
0.029710130766034126,
-0.024680376052856445,
-0.0706130862236023,
-0.01175419706851244,
0.01804123818874359,
0.024322127923369408,
0.04535917192697525,
-0.0004675661912187934,
0.06090693920850754,
-0.05291964113712311,
0.0038674084935337305,
0.01764533855021,
0.0002032504853559658,
0.016598854213953018,
0.019754650071263313,
-0.0202417504042387,
0.029659433290362358,
0.035529110580682755,
-0.028460506349802017,
0.005050822161138058,
-0.04027625918388367,
-0.00452672503888607,
0.0798344537615776,
-0.024295290932059288,
0.06306669116020203,
0.02952173352241516,
-0.02408447302877903,
0.010789155960083008,
0.013590700924396515,
-0.028878863900899887,
-0.01690254919230938,
-0.029240354895591736,
-0.02758384868502617,
-0.027741771191358566,
0.002711003879085183,
0.017762403935194016,
0.023473000153899193,
-0.023406412452459335,
-0.008349919691681862,
0.03712461143732071,
0.041572194546461105,
0.017625955864787102,
-0.03449809178709984,
-0.02794817090034485,
0.07135110348463058,
-0.039651207625865936,
0.027379214763641357,
-0.01473904587328434,
0.0050568608567118645,
0.04359564930200577,
-0.005705888848751783,
-0.014709034003317356,
-0.01669144071638584,
-0.014630604535341263,
-0.033367156982421875,
0.022299494594335556,
0.040099479258060455,
0.004854503087699413,
-0.02244701236486435,
0.01317556481808424,
-0.004947300534695387,
0.02909328229725361,
0.010285607539117336,
0.01760690100491047,
-0.05432860180735588,
-0.017014937475323677,
-0.031462378799915314,
-0.03327815979719162,
0.03286336362361908,
0.03707621619105339,
-0.03785395249724388,
0.022818686440587044,
-0.0457988865673542,
0.05208921805024147,
0.02717486396431923,
-0.01483726967126131,
-0.007420867215842009,
0.06236649304628372,
-0.01094900630414486,
0.017583053559064865,
-0.003372394945472479,
-0.011622363701462746,
0.09720906615257263,
0.044534362852573395,
0.007843926548957825,
-0.05045274645090103,
0.013037079945206642,
-0.02224307507276535,
-0.007877640426158905,
-0.0430867038667202,
0.01365259662270546,
-0.036138348281383514,
0.03122708573937416,
0.024982480332255363,
0.028431307524442673,
-0.004508966114372015,
0.014981193467974663,
0.06013009324669838,
-0.02362816222012043,
-0.027506064623594284,
0.006184007972478867,
0.03187955915927887,
-0.007804499007761478,
0.04763338342308998,
-0.04294222220778465,
0.03322053700685501,
-0.07595755159854889,
-0.017742032185196877,
-0.042100053280591965,
-0.014854378998279572,
0.009991465136408806,
0.005068715661764145,
-0.029077725484967232,
-0.007779343985021114,
0.010381757281720638,
-0.0004157163784839213,
-0.05061167851090431,
0.0481179915368557,
0.048584312200546265,
0.03359122574329376,
-0.02117045409977436,
-0.006950883660465479,
-0.0075859734788537025,
0.04153219237923622,
0.013774671591818333,
0.029834352433681488,
-0.04272386431694031,
0.008872900158166885,
-0.03136901184916496,
0.03887626901268959,
-0.011720973066985607,
0.02489105425775051,
0.005631488282233477,
0.055319271981716156,
0.01780763640999794,
-0.07295138388872147,
-0.040496326982975006,
-0.008917558006942272,
0.018070463091135025,
-0.032166555523872375,
-0.0064765275456011295,
-0.021851908415555954,
0.04368140548467636,
-0.01851227506995201,
0.03543183207511902,
0.00579819967970252,
-0.01941009610891342,
0.034582268446683884,
-0.008891700766980648,
0.034137774258852005,
-0.014543638564646244,
-0.03354579955339432,
-0.02037849836051464,
-0.017285043373703957,
-0.010814652778208256,
-0.031739819794893265,
-0.0008491527405567467,
0.02875116653740406,
0.025872262194752693,
-0.019662149250507355,
-0.010268570855259895,
-0.011771240271627903,
-0.07278186827898026,
0.06286831200122833,
-0.022333195433020592,
0.015402090735733509,
-0.03520544618368149,
-0.04067377373576164,
0.015358448028564453,
0.05743976682424545,
-0.027754981070756912,
0.03301864117383957,
0.0026325262151658535,
0.01202801987528801,
0.015335110947489738,
-0.016556544229388237,
-0.01501428335905075,
-0.0005080801784060895,
-0.03872903436422348,
0.008725877851247787,
0.03283271938562393,
0.033670827746391296,
0.03385598957538605,
0.03379150480031967,
0.005481131374835968,
0.0345432385802269,
-0.05996876582503319,
-0.01435967069119215,
0.00007009906403254718,
-0.02666659653186798,
0.01040750090032816,
0.02272879332304001,
-0.0036836103536188602,
-0.030519474297761917,
-0.023619351908564568,
-0.012676640413701534,
0.005416948348283768,
0.022594962269067764,
0.024060353636741638,
0.004077432677149773,
-0.02300553396344185,
-0.014848903752863407,
0.025467997416853905,
-0.025025881826877594,
-0.06200498715043068,
-0.04225200414657593,
0.013796982355415821,
-0.0018839843105524778,
-0.019910914823412895,
0.019573980942368507,
-0.0011682958574965596,
-0.02490486018359661,
0.007797498255968094,
0.03787536546587944,
0.005821391474455595,
0.010207449086010456,
-0.0005923726712353528,
0.03166420757770538,
-0.03968552500009537,
0.07148505747318268,
-0.06737463176250458,
-0.04343004152178764,
0.04400233179330826,
-0.05163723602890968,
-0.05058278888463974,
0.004492101725190878,
-0.010098095051944256,
0.0448375903069973,
0.00010843704512808472,
-0.013711554929614067,
-0.04097028076648712,
0.03186224773526192,
-0.027353649958968163,
0.013627453707158566,
-0.03153112903237343,
-0.042335089296102524,
0.0009731650934554636,
-0.041104890406131744,
0.0005206105997785926,
0.004006184637546539,
0.015943022444844246,
0.05528958514332771,
0.01922024041414261,
0.001622319919988513,
-0.021549373865127563,
0.03157239034771919,
0.016761967912316322,
-0.0022276381496340036,
0.04510943964123726,
0.004783929325640202,
0.01902146264910698,
0.04602499678730965,
-0.01033866312354803,
0.03282927721738815,
0.022728754207491875,
0.03501076623797417,
-0.09668021649122238,
-0.020004726946353912,
0.014485828578472137,
0.017972031608223915,
0.01775430329144001,
-0.048973873257637024,
-0.007708320394158363,
0.023343754932284355,
-0.05818300321698189,
-0.00421606982126832,
-0.02227407693862915,
-0.01848732866346836,
-0.02689965069293976,
-0.0025395534466952085,
0.0009261258528567851,
0.04002520814538002,
0.035901617258787155,
0.042753517627716064,
0.034611981362104416,
0.02651919610798359,
-0.00608369056135416,
-0.04285624995827675,
-0.03431224077939987,
0.03295065090060234,
-0.006679974962025881,
-0.022962499409914017,
0.040027521550655365,
0.001665017451159656,
0.004644299391657114,
0.033547382801771164,
0.01336918119341135,
-0.013129671104252338,
0.029037009924650192,
0.048546407371759415,
0.02039659209549427,
0.022544454783201218,
0.006233576685190201,
-0.0057699307799339294,
-0.03800090029835701,
0.02196611277759075,
0.05753162130713463,
0.015905555337667465,
0.01000895444303751,
-0.0194812323898077,
0.035316694527864456,
-0.02244030311703682,
-0.010532567277550697,
0.023925742134451866,
-0.03590148314833641,
-0.019385065883398056,
-0.003471673233434558,
0.014388008043169975,
0.0008306356612592936,
-0.03938538208603859,
0.009155744686722755,
-0.06436605006456375,
-0.03650447726249695,
0.04531039670109749,
0.009715015068650246,
-0.0038545008283108473,
0.021653132513165474,
0.018127061426639557,
-0.02830454893410206,
0.004901709035038948,
0.0330241359770298,
0.03308233618736267,
-0.04781261458992958,
-0.0036925035528838634,
0.004255068022757769,
-0.010489460080862045,
0.0353979617357254,
-0.03987910971045494,
-0.06286013126373291,
0.029179006814956665,
0.03299275040626526,
0.030203765258193016,
-0.00455608032643795,
-0.05149787291884422,
-0.029928235337138176,
-0.06267648190259933,
0.04459525644779205,
-0.02999616228044033,
-0.056542880833148956,
-0.03941398859024048,
-0.031141819432377815,
-0.019098857417702675,
0.003122694091871381,
0.06671708077192307,
0.0019750811625272036,
-0.03632909432053566,
0.0011804669629782438,
0.01806720532476902,
-0.00997676607221365,
-0.0658373013138771,
-0.017701739445328712,
0.027371332049369812,
-0.01909540221095085,
-0.011603938415646553,
0.011248860508203506,
-0.013820846565067768,
0.019528985023498535,
-0.015202302485704422,
0.00932785402983427,
0.005011825822293758,
-0.054208993911743164,
-0.03275212645530701,
0.056653738021850586,
0.040080539882183075,
-0.021128032356500626,
0.0739806517958641,
-0.04224236309528351,
0.014955964870750904,
0.009975573979318142,
-0.0209561325609684,
-0.03576543927192688,
0.011679966002702713,
-0.05500949174165726,
0.003666990203782916,
-0.011600559577345848,
0.02146809548139572,
0.04128106310963631,
-0.0461222305893898,
-0.005100889131426811,
0.06040976569056511,
-0.08167169243097305,
0.010906084440648556,
0.06886123865842819,
-0.008612453006207943,
0.02823895588517189,
0.005865210667252541,
-0.0072039645165205,
-0.0040632556192576885,
-0.015400419011712074,
-0.010991586372256279,
0.032019954174757004,
0.021013600751757622,
-0.02932657301425934,
0.008092631585896015,
0.07440714538097382,
-0.0005744739901274443,
0.004110482521355152,
0.009664943441748619,
0.021463658660650253,
-0.037820108234882355,
-0.04001754894852638,
-0.01516661699861288,
-0.029354115948081017,
0.005644424818456173,
0.018048709258437157,
-0.017384178936481476,
0.0699634775519371,
-0.03402768820524216,
0.001344691845588386,
0.017468959093093872,
0.02075018361210823,
-0.016547314822673798,
0.006495374720543623,
0.014582335948944092,
0.03903760388493538,
-0.025690097361803055,
-0.014856390655040741,
-0.007056321017444134,
-0.03025510162115097,
0.016505347564816475,
0.0012588826939463615,
0.02952372282743454,
0.021574750542640686,
-0.0013791134115308523,
-0.020629137754440308,
-0.006526256911456585,
-0.012281008064746857,
-0.015715213492512703,
0.001287568942643702,
0.002022044500336051,
0.015344133600592613,
0.020877106115221977,
-0.002343403175473213,
-0.020225772634148598,
0.05984644219279289,
-0.06376417726278305,
-0.011295794509351254,
-0.012387130409479141,
0.024031255394220352,
-0.00558006064966321,
-0.01017413567751646
] |
<p>Spectral emission by elements occurs in discrete wavelengths. There are only about 118 elements. My question is whether there are pure colors either disfavored in nature or even disallowed? </p>
<p>The sun (via prism) appears to generate a continuum of visible frequencies but of course that would probably appear to be the case, as the eye would mix adjacent spectral colors and the resultant (near-spectral) color would seem to fill in the gap (note: that is a question, not a statement).</p>
<p>It is often recited that "black bodies" (like the sun) emit a spectrum of radiation, but how would we notice small discontinuties, if they existed?</p>
<p>Red-shift might create visible frequencies that otherwise do not occur. But do we have some basis other than (prism + visual intuition) that all pure visible frequencies do in fact correspond to some possible natural or artificial source? </p>
<p>Apologies for the naivete of the question, if that is the case, and the likelihood that the answer may not have much practical significance. There were related question on the site and on Google but nothing directly on point.</p>
<p>Thanks. </p>
| 8,863 |
[
-0.018370024859905243,
-0.02860032021999359,
0.015340829268097878,
-0.04304962977766991,
0.03232249990105629,
0.012484092265367508,
-0.03286150470376015,
-0.013371542096138,
-0.013830849900841713,
-0.04044068977236748,
0.03791777044534683,
0.030003273859620094,
0.037437111139297485,
0.033046964555978775,
0.03811954706907272,
0.011658217757940292,
-0.0057312785647809505,
-0.03491341322660446,
-0.0029305049683898687,
-0.011251050978899002,
0.05083485692739487,
-0.003275069873780012,
0.0033174240961670876,
-0.004735865164548159,
-0.04229582101106644,
-0.008160756900906563,
0.019479900598526,
0.05670051649212837,
0.021215951070189476,
0.036704692989587784,
-0.026312755420804024,
-0.024429358541965485,
0.0050046322867274284,
0.03376112878322601,
0.03160536289215088,
0.0033472860231995583,
0.012160082347691059,
-0.010859066620469093,
-0.020929962396621704,
0.007304632104933262,
-0.03081950731575489,
-0.02828437276184559,
-0.002877421211451292,
0.027132676914334297,
-0.018617955967783928,
-0.02245594933629036,
0.00032938041840679944,
-0.032319698482751846,
0.07290232926607132,
-0.05851510539650917,
0.0944097563624382,
-0.019400853663682938,
0.06428540498018265,
0.010831956751644611,
-0.007873308844864368,
-0.0047769746743142605,
0.07668902724981308,
0.07216708362102509,
-0.02053423412144184,
-0.022046593949198723,
0.006145858205854893,
0.003490075236186385,
-0.000242727852310054,
-0.0026272295508533716,
-0.05502954497933388,
0.01625756174325943,
-0.017676005139946938,
-0.0325646698474884,
0.05619927495718002,
0.024078194051980972,
0.012873005121946335,
0.028787242248654366,
0.018459048122167587,
0.0030087297782301903,
0.010338454507291317,
-0.05959567055106163,
0.06215455010533333,
0.0067468564957380295,
0.011093908920884132,
0.029791906476020813,
-0.025005483999848366,
-0.03566606342792511,
-0.01195278950035572,
0.020412273705005646,
0.01403532363474369,
0.015706315636634827,
0.08083244413137436,
-0.028456075116991997,
0.027825498953461647,
-0.006678120698779821,
-0.0021859172265976667,
-0.004540244583040476,
0.05131309852004051,
0.047851502895355225,
-0.025411810725927353,
0.026430180296301842,
-0.04430742561817169,
0.047983188182115555,
-0.019615761935710907,
-0.04312184080481529,
0.03755400329828262,
0.014292865991592407,
0.07310730218887329,
0.08432750403881073,
-0.024879993870854378,
0.007731711957603693,
-0.0108622582629323,
0.006158455740660429,
0.003201673272997141,
-0.004452765919268131,
0.01410194393247366,
0.01406079437583685,
0.016911225393414497,
-0.008701265789568424,
-0.011222000233829021,
-0.0021841481793671846,
0.03749513998627663,
-0.04246006906032562,
0.07759370654821396,
0.10457739979028702,
0.02094205841422081,
-0.030680524185299873,
0.020158013328909874,
-0.0019366875058040023,
-0.036179568618535995,
-0.009904622100293636,
-0.0005563625600188971,
0.026288779452443123,
-0.018763255327939987,
-0.005186022724956274,
-0.02466714009642601,
-0.03738277778029442,
0.02534477971494198,
-0.021797172725200653,
0.014392142184078693,
-0.04807489365339279,
-0.09609660506248474,
-0.07394672185182571,
0.005822064355015755,
-0.014766691252589226,
-0.03536439314484596,
-0.03464049845933914,
0.015711046755313873,
0.0091704735532403,
0.057397037744522095,
0.006342671811580658,
-0.03263092413544655,
-0.021081503480672836,
0.059965308755636215,
-0.0028046967927366495,
-0.03083672747015953,
-0.010462204925715923,
0.031746964901685715,
-0.05816225707530975,
-0.010890522971749306,
-0.046696823090314865,
0.0017627760535106063,
0.024064190685749054,
0.042116135358810425,
-0.017585046589374542,
0.053796399384737015,
-0.018089132383465767,
0.009283031336963177,
0.026382502168416977,
0.017202487215399742,
-0.01729663461446762,
0.09556438028812408,
0.022781457751989365,
0.024022772908210754,
0.006995570845901966,
0.04680126905441284,
0.002946338150650263,
0.036677539348602295,
0.027617134153842926,
0.015263519249856472,
-0.06370038539171219,
-0.01537539903074503,
-0.04753632843494415,
0.048808421939611435,
-0.031208660453557968,
-0.047205399721860886,
0.0009918027790263295,
-0.0037271762266755104,
0.00821151863783598,
0.03166787698864937,
0.07509765774011612,
0.0033623541239649057,
-0.044575486332178116,
0.06318928301334381,
-0.058566316962242126,
0.038219235837459564,
-0.016056552529335022,
0.023176847025752068,
0.030433736741542816,
-0.01713307946920395,
0.03561458736658096,
-0.014953156933188438,
0.029610248282551765,
-0.022556865587830544,
-0.018916113302111626,
-0.017614535987377167,
0.0416441336274147,
0.03408462181687355,
-0.008962566033005714,
0.002842914080247283,
0.07232324779033661,
0.042624298483133316,
0.02013804018497467,
0.0181235671043396,
-0.014346327632665634,
-0.07593453675508499,
0.009389159269630909,
-0.04907714203000069,
0.04382823035120964,
0.00562118086963892,
0.03008393570780754,
0.0023370226845145226,
-0.0025166335981339216,
-0.020406574010849,
0.03347015008330345,
-0.05122191086411476,
0.06905291229486465,
-0.004513617604970932,
-0.0019210847094655037,
0.006049619987607002,
0.023695994168519974,
0.014122544787824154,
-0.012715348973870277,
-0.03228404000401497,
-0.03932711482048035,
-0.06601624190807343,
0.014453333802521229,
0.05552447959780693,
0.015227114781737328,
-0.04188749939203262,
0.029497098177671432,
-0.0026962850242853165,
0.06583578884601593,
0.03410636633634567,
0.027830788865685463,
-0.042408108711242676,
-0.03296859562397003,
0.01761944591999054,
0.01813310571014881,
0.05296994000673294,
0.03703296557068825,
0.0016443300992250443,
0.022578665986657143,
0.027819262817502022,
-0.026894938200712204,
0.018227795138955116,
0.033461760729551315,
-0.03262397274374962,
-0.0013192511396482587,
-0.04467345401644707,
0.004694452974945307,
0.04497440531849861,
-0.04931424558162689,
-0.014648730866611004,
0.016577353700995445,
-0.031671714037656784,
-0.011156785301864147,
0.0037915464490652084,
-0.027204761281609535,
0.014871975407004356,
0.0485716350376606,
-0.05884020775556564,
0.011874369345605373,
0.024961400777101517,
-0.0283983051776886,
0.023161133751273155,
-0.03671949729323387,
-0.00260336184874177,
-0.014975123107433319,
0.009680554270744324,
0.015958847478032112,
0.014462276361882687,
0.02235248312354088,
-0.06058453395962715,
-0.013439442031085491,
0.0012609368422999978,
-0.03763659670948982,
-0.011585953645408154,
0.020416345447301865,
-0.03359728306531906,
0.022036736831068993,
-0.03416275605559349,
-0.06056864932179451,
0.04013112932443619,
-0.00342765636742115,
-0.007597797550261021,
0.018872646614909172,
-0.051004476845264435,
-0.04873830825090408,
0.006278568878769875,
-0.00660619605332613,
0.015292450785636902,
-0.026769546791911125,
-0.023538431152701378,
0.044784724712371826,
-0.042284317314624786,
-0.03632493317127228,
-0.009027212858200073,
-0.0622452050447464,
-0.02592356503009796,
-0.04166959226131439,
-0.002519492292776704,
0.012106896378099918,
-0.03232474997639656,
0.008401100523769855,
0.03430035710334778,
-0.03910800814628601,
0.04002515599131584,
0.004116271156817675,
-0.047778137028217316,
0.005244513973593712,
-0.014317004941403866,
0.03449029475450516,
0.0064410497434437275,
0.014257349073886871,
0.051181238144636154,
0.05584975332021713,
-0.020481105893850327,
-0.01854441501200199,
-0.010626043193042278,
-0.0033923534210771322,
-0.03317181020975113,
0.018288223072886467,
0.02177337557077408,
0.009658229537308216,
0.0352284200489521,
0.012808379717171192,
0.04248536005616188,
0.0013200403191149235,
0.012467955239117146,
-0.03231492638587952,
0.009286356158554554,
0.0038161647971719503,
-0.0077453418634831905,
0.034692250192165375,
0.057282544672489166,
-0.03595409169793129,
0.03259223327040672,
-0.03667443245649338,
0.051995899528265,
0.042089276015758514,
-0.047365397214889526,
0.030947668477892876,
0.02639232575893402,
0.04795828461647034,
0.0021741497330367565,
0.025773625820875168,
0.012326247990131378,
0.015127754770219326,
-0.0333857499063015,
0.015464757569134235,
0.04007351025938988,
-0.0157353263348341,
-0.008862907066941261,
0.05238359421491623,
0.02396281063556671,
-0.008086691610515118,
0.029015354812145233,
0.01461172103881836,
0.009584123268723488,
0.02101845294237137,
-0.009765183553099632,
0.005830775480717421,
0.06568708270788193,
0.03758573532104492,
0.02511421963572502,
0.0023845599498599768,
-0.007753406651318073,
0.008859416469931602,
-0.025246039032936096,
-0.03708093613386154,
-0.0085148299112916,
0.04149093106389046,
0.004786294884979725,
0.05372604355216026,
0.030137045308947563,
0.014955089427530766,
-0.008288620039820671,
0.004522775299847126,
-0.11078939586877823,
0.00018034843378700316,
-0.016718167811632156,
0.013739014975726604,
-0.05193813145160675,
-0.018513444811105728,
-0.021780407056212425,
-0.01143538486212492,
-0.04860946163535118,
-0.003031620755791664,
-0.011036199517548084,
-0.038671545684337616,
0.032387908548116684,
-0.006451259832829237,
-0.05885670706629753,
-0.013494201935827732,
0.02373443730175495,
-0.008731924928724766,
0.005590826738625765,
0.002463112585246563,
-0.029669273644685745,
-0.02800055965781212,
-0.013676390051841736,
-0.03125160560011864,
0.019713738933205605,
-0.02571677789092064,
0.03462810441851616,
0.010391558520495892,
0.02939327247440815,
-0.03249427676200867,
-0.009358447976410389,
0.004621119238436222,
0.044386714696884155,
-0.044873591512441635,
-0.019138824194669724,
-0.011121148243546486,
-0.052809879183769226,
0.008103067986667156,
0.0009104115306399763,
0.03884453326463699,
-0.05006520822644234,
0.019002722576260567,
0.04566549137234688,
-0.0023050091695040464,
-0.008559457957744598,
0.04144874960184097,
-0.00040444760816171765,
0.013219429180026054,
-0.013140278868377209,
-0.0027772642206400633,
0.025727389380335808,
-0.0166977159678936,
0.03092331252992153,
0.0063248020596802235,
0.02513318508863449,
0.027628730982542038,
0.007819769904017448,
0.019576553255319595,
0.015371637418866158,
-0.018854588270187378,
0.006094571202993393,
-0.010179667733609676,
0.00331195630133152,
-0.06106479465961456,
-0.008596780709922314,
0.01030410174280405,
0.03148777782917023,
0.05534534156322479,
-0.03056837059557438,
0.0022572011221200228,
-0.10164826363325119,
0.011835101060569286,
0.03545169159770012,
0.0051458305679261684,
-0.01061218697577715,
-0.0009253981988877058,
-0.06259620189666748,
-0.02077449858188629,
0.03257707133889198,
-0.0009776251390576363,
0.009122410789132118,
-0.040053267031908035,
0.0066984910517930984,
0.004030293319374323,
-0.02434340864419937,
0.016034051775932312,
0.032281599938869476,
0.03436910733580589,
0.019646191969513893,
-0.023340372368693352,
-0.03452792018651962,
-0.010624979622662067,
0.0484035387635231,
0.04515010118484497,
0.04461587220430374,
0.011204398237168789,
-0.006519435904920101,
-0.004267212003469467,
-0.006741836201399565,
-0.005857788026332855,
-0.05903780460357666,
0.01040563639253378,
0.014847577549517155,
-0.0007234546937979758,
0.0634261816740036,
-0.046991024166345596,
-0.04641569405794144,
-0.006861668545752764,
0.022579701617360115,
0.0027475436218082905,
0.01895749941468239,
-0.037179626524448395,
0.04274464398622513,
0.017796888947486877,
0.0083153136074543,
0.020253289490938187,
0.02861310914158821,
-0.0052658687345683575,
0.010178760625422001,
-0.04492512717843056,
0.02668752335011959,
-0.016805831342935562,
-0.024473058059811592,
-0.008468970656394958,
-0.030775202438235283,
-0.02824626863002777,
0.06005936861038208,
0.012532166205346584,
-0.01359434425830841,
0.00916918646544218,
-0.04915884509682655,
-0.00801094900816679,
0.036477673798799515,
-0.002754131332039833,
0.01665395125746727,
-0.024795493111014366,
0.038398418575525284,
0.0021564660128206015,
0.01137341558933258,
0.020783046260476112,
-0.0031792428344488144,
-0.022044776007533073,
0.04317433759570122,
-0.01023012213408947,
0.034235816448926926,
-0.06415638327598572,
0.007493116892874241,
-0.006050131283700466,
-0.029224006459116936,
0.03830912709236145,
-0.015361933968961239,
0.05839267373085022,
0.01802399940788746,
-0.076484814286232,
-0.027914421632885933,
0.004076540935784578,
-0.009953659027814865,
0.055124398320913315,
-0.04415768384933472,
0.048145465552806854,
-0.0012584066716954112,
-0.017509542405605316,
-0.09484715759754181,
-0.035807184875011444,
-0.018241170793771744,
0.07514896243810654,
-0.024944856762886047,
-0.018844962120056152,
0.005143582355231047,
-0.034687627106904984,
-0.015939123928546906,
0.041396595537662506,
0.018813684582710266,
-0.02292928844690323,
-0.014446238987147808,
-0.013473489321768284,
-0.016812438145279884,
0.03588918223977089,
-0.02702922746539116,
-0.03225192055106163,
0.009556290693581104,
0.008272494189441204,
0.0074858348816633224,
-0.00555924978107214,
0.04598205164074898,
-0.03950812295079231,
-0.028157955035567284,
0.000022770089344703592,
-0.021169885993003845,
0.007070089690387249,
-0.025278262794017792,
-0.012848635204136372,
0.04121577739715576,
0.010568291880190372,
0.008808367885649204,
0.0001901008072309196,
0.05239303410053253,
-0.027027791365981102,
-0.02492702379822731,
-0.014304270967841148,
0.0007610839093104005,
-0.004551211837679148,
-0.028684018179774284,
0.0280207060277462,
-0.02455289289355278,
0.04877161607146263,
-0.00154076237231493,
0.05943960323929787,
-0.015502567403018475,
-0.007040195632725954,
0.003399032400920987,
-0.008337488397955894,
0.016780046746134758,
-0.022409984841942787,
0.020913366228342056,
-0.03670032322406769,
0.016167040914297104,
-0.02443169243633747,
-0.04297838732600212,
-0.017452837899327278,
-0.01229569036513567,
0.05827781930565834,
-0.022427674382925034,
0.03651851415634155,
0.005324371624737978,
0.005915876477956772,
0.00628898898139596,
-0.008118972182273865,
-0.0048001897521317005,
-0.00902387872338295,
0.006966189481317997,
0.024696797132492065,
-0.0032719692680984735,
0.028127556666731834,
-0.004027333576232195,
0.03387943655252457,
0.004549387842416763,
0.057735998183488846,
0.026675712317228317,
0.030987458303570747,
0.013160730712115765,
-0.04008015990257263,
-0.025727039203047752,
0.007905974984169006,
-0.027498554438352585,
0.004601242020726204,
0.04590799659490585,
-0.00952166598290205,
0.019052846357226372,
-0.0005878898082301021,
0.023491118103265762,
-0.02547275274991989,
-0.025402139872312546,
-0.03484399989247322,
0.01621127501130104,
-0.02652767114341259,
0.018183544278144836,
-0.023717330768704414,
-0.02915930561721325,
-0.0203465074300766,
-0.004430227447301149,
0.01412072591483593,
-0.024359146133065224,
-0.08008461445569992,
-0.05779026076197624,
-0.0666215792298317,
-0.02714335359632969,
0.04045560210943222,
-0.006761329714208841,
-0.03958464786410332,
-0.025921672582626343,
-0.02751237154006958,
0.03556133434176445,
0.007158117368817329,
0.025924334302544594,
-0.011724276468157768,
0.007099182344973087,
-0.0174542386084795,
0.038772836327552795,
0.006493458524346352,
0.0221114419400692,
0.1034470722079277,
0.05814419686794281,
0.00808676891028881,
-0.054988469928503036,
0.017947427928447723,
-0.03434441238641739,
0.020185561850667,
0.00829770416021347,
0.03182946890592575,
-0.006514657288789749,
0.029763229191303253,
0.009252024814486504,
0.026936087757349014,
0.04257917404174805,
-0.00741990702226758,
-0.000784192350693047,
-0.014300312846899033,
-0.01649150252342224,
-0.021384529769420624,
0.030627934262156487,
-0.025847196578979492,
0.018140999600291252,
-0.05560530349612236,
0.0051085250452160835,
-0.023007839918136597,
0.008122045546770096,
-0.014086224138736725,
-0.019166799262166023,
-0.0002364482352277264,
0.022383200004696846,
-0.034202899783849716,
-0.028273940086364746,
0.007375587709248066,
-0.02096524089574814,
-0.03657633438706398,
-0.0052103763446211815,
0.05668710172176361,
0.0031988315749913454,
0.022913528606295586,
0.0077284942381083965,
0.009734717197716236,
-0.011194844730198383,
-0.0050969431176781654,
0.011471627280116081,
-0.01466341968625784,
-0.007016226649284363,
-0.024637432768940926,
0.03700190782546997,
-0.03408520668745041,
-0.01519802212715149,
-0.019923822954297066,
-0.03291291743516922,
-0.02942710556089878,
-0.06070132926106453,
-0.00901664886623621,
-0.03441237658262253,
0.0240925382822752,
-0.023718461394309998,
-0.05196865648031235,
0.012089711613953114,
0.017125645652413368,
-0.012400939129292965,
0.022891294211149216,
0.027049176394939423,
-0.033833932131528854,
-0.021253090351819992,
0.034194592386484146,
0.06133756786584854,
0.03948386013507843,
-0.020805174484848976,
-0.030996542423963547,
-0.0578170008957386,
-0.015041743405163288,
-0.041327960789203644,
0.028958909213542938,
0.04830760881304741,
0.020162414759397507,
0.024922799319028854,
-0.026550989598035812,
-0.00554158678278327,
-0.012665040791034698,
0.04715568944811821,
0.028351599350571632,
-0.0331888385117054,
0.003331555984914303,
-0.001647566445171833,
0.02553674951195717,
0.012305685319006443,
-0.012146033346652985,
0.0012648403644561768,
0.020889807492494583,
0.03917130082845688,
0.04035503417253494,
-0.039830006659030914,
-0.022904297336935997,
0.022716093808412552,
-0.03982986882328987,
0.025715874508023262,
0.0056347972713410854,
0.03742797672748566,
-0.0027204903308302164,
0.017852533608675003,
0.03006621263921261,
0.04659295827150345,
-0.02806035801768303,
-0.005108594428747892,
0.02408849075436592,
-0.06101318076252937,
0.0075254919938743114,
-0.01472130324691534,
-0.02248513698577881,
-0.005637702066451311,
-0.06803883612155914,
-0.03734350576996803,
0.024213917553424835,
0.01485360972583294,
0.014528420753777027,
-0.029866693541407585,
0.008467904292047024,
-0.0016610031016170979,
-0.021204670891165733,
-0.016837041825056076,
-0.04063809663057327,
-0.042437806725502014,
0.0015902823070064187,
0.015168756246566772,
-0.02584056928753853,
-0.01280603650957346,
-0.000026041499950224534,
-0.031240127980709076,
-0.02991587296128273,
0.06598394364118576,
0.04162925109267235,
-0.016513925045728683,
0.00005633462205878459,
0.020320480689406395,
-0.011316155083477497,
0.030845370143651962,
-0.008338766172528267,
-0.013375732116401196,
0.028799254447221756,
-0.036488763988018036,
-0.019276201725006104,
0.021047895774245262,
-0.04999722167849541,
0.033895500004291534,
-0.004817849025130272,
-0.010113216005265713,
-0.017438383772969246,
0.06797860562801361,
-0.002860994078218937,
0.006784175988286734,
0.027928359806537628,
0.047029681503772736,
-0.017743689939379692,
-0.017724519595503807,
0.008927042596042156,
-0.01382925920188427,
-0.02083609439432621,
0.03515186160802841,
-0.020488452166318893,
-0.021494440734386444,
-0.0154957240447402,
0.000297393708024174,
-0.03782085329294205,
-0.0086103156208992,
0.020028753206133842,
0.03309033438563347,
-0.012666916474699974,
0.001611034502275288,
-0.06568371504545212,
0.060981687158346176,
0.026894448325037956,
-0.009418140165507793,
-0.0679340809583664,
-0.0062062302604317665,
0.019877538084983826,
0.023552821949124336,
-0.009342435747385025,
-0.06096382066607475,
-0.0011295992881059647,
0.04167168587446213,
-0.06980070471763611,
-0.005868386942893267,
0.0037118217442184687,
-0.025287237018346786,
-0.025562331080436707,
-0.010167558677494526,
-0.05801840126514435,
-0.033128999173641205,
0.019934846088290215,
0.051887184381484985,
0.01471065916121006,
0.03260158747434616,
-0.010329444892704487,
-0.01167047768831253,
-0.007424340583384037,
0.01808018423616886,
-0.001769529189914465,
0.006495775654911995,
0.06597165018320084,
-0.0010232435306534171,
-0.0072284359484910965,
-0.008474239148199558,
-0.005152280908077955,
0.02930622734129429,
-0.012151749804615974,
-0.019650869071483612,
-0.03828902170062065,
0.030567767098546028,
0.02347181737422943,
-0.0020849527791142464,
-0.028529386967420578,
0.006215209141373634,
0.01776181533932686,
0.0338657908141613,
-0.0037606481928378344,
0.027729585766792297,
0.044515643268823624,
-0.045650891959667206,
-0.03943141549825668,
-0.005366571247577667,
-0.004818839021027088,
-0.006166171282529831,
0.030324522405862808,
0.038193218410015106,
0.05151700973510742,
-0.037358805537223816,
0.01706324703991413,
-0.04793756827712059,
-0.01786380633711815,
-0.010698380880057812,
0.04671996086835861,
0.007700450252741575,
0.014372851699590683,
-0.024953095242381096,
-0.04601277410984039,
-0.006899221800267696,
0.008152434602379799,
-0.017238890752196312,
-0.022815566509962082,
0.017362333834171295,
0.035602763295173645,
0.008350024931132793,
-0.010793985798954964,
-0.01216147281229496,
-0.03457188606262207,
0.02049946039915085,
-0.016899460926651955,
0.007974955253303051,
-0.020615004003047943,
-0.04483618214726448,
-0.0247038584202528,
-0.03694581240415573,
0.03232792019844055,
-0.018766244873404503,
0.023115474730730057,
-0.0341157428920269,
0.0036976621486246586,
-0.028488030657172203,
0.04534487798810005,
0.006173257250338793,
-0.004686229862272739,
-0.024348951876163483,
-0.008413531817495823,
-0.0027331311721354723,
0.032765913754701614,
-0.011193427257239819,
0.005692675709724426,
-0.007945591583848,
-0.04188791662454605,
-0.033113062381744385,
-0.010091266594827175,
-0.025902368128299713,
0.0066374968737363815,
0.03388899192214012,
0.01947547309100628,
-0.0130021832883358,
-0.0015735889319330454,
-0.022476769983768463,
0.11130103468894958,
0.0012683722889050841,
-0.0051062763668596745,
0.06115478277206421,
0.008741000667214394,
0.021189015358686447,
0.036110032349824905,
-0.010133976116776466,
-0.040518078953027725,
0.018201477825641632,
0.0018870399799197912,
-0.0011415337212383747,
0.02299540676176548,
0.025039149448275566,
0.027696995064616203,
-0.0387568436563015,
0.04072319716215134,
0.03569613769650459,
-0.012551107443869114,
-0.01908751018345356,
0.01792415790259838,
-0.009043975733220577,
0.02055968903005123,
0.021049553528428078,
-0.020147258415818214,
0.019965846091508865,
0.0012406945461407304,
-0.015491669066250324,
0.03472619503736496,
0.01188418734818697,
-0.012433932162821293,
0.02638169750571251,
0.0077735017985105515,
-0.025322839617729187,
0.025228342041373253,
-0.001788909430615604,
0.021294819191098213,
-0.028117399662733078,
-0.003578724106773734,
0.004649620037525892,
0.04858240857720375,
0.034938208758831024,
0.012301306240260601,
-0.025195661932229996,
0.08214109390974045,
-0.011779074557125568,
0.02462594397366047,
-0.05157509818673134,
0.0135647626593709,
-0.01888987049460411,
-0.0071775903925299644,
0.008154739625751972,
0.01920943334698677,
-0.03256547451019287,
-0.010103422217071056,
0.003629208542406559,
0.009372946806252003,
0.0566822811961174,
-0.06959570199251175,
0.0010844598291441798,
-0.024463143199682236,
-0.036365676671266556,
0.001170451520010829,
0.010262117721140385,
0.01283142901957035,
-0.0010458683827891946,
0.012596193701028824,
0.039501022547483444,
0.014684321358799934,
-0.026750002056360245,
0.0019055160228163004,
-0.027765726670622826,
0.04116091877222061,
-0.060555122792720795,
-0.005537046585232019,
-0.0014964613365009427,
0.03406701982021332,
-0.054291121661663055,
-0.056671272963285446
] |
<p>I am a physics undergrad interested in stuff like dynamical systems, chaos theory etc. Is there ongoing research in these fields? I am talking about pure research and not applications to things like weather etc? I hope this question is appropriate for Physics SE. I asked this question, because I browsed through the websites of the physics departments of a few renowned universities (MIT, Princeton, Caltech) etc, but nowhere it mentioned research in these areas.</p>
| 8,864 |
[
-0.00023549016623292118,
-0.017226556316018105,
0.0011242498876526952,
-0.025374261662364006,
0.04778819903731346,
-0.016925334930419922,
-0.00710314093157649,
-0.054353028535842896,
-0.013237280771136284,
-0.04867236688733101,
-0.005182751454412937,
0.036128636449575424,
0.02884693071246147,
0.01833583042025566,
0.020413804799318314,
-0.010014905594289303,
-0.02954677864909172,
-0.02307366207242012,
-0.0005973139777779579,
0.023235201835632324,
-0.008076182566583157,
-0.014007805846631527,
0.04195694997906685,
0.020854070782661438,
-0.018846478313207626,
0.026181086897850037,
-0.020627956837415695,
0.0019459421746432781,
0.01207276526838541,
0.030328180640935898,
0.028542041778564453,
-0.008248729631304741,
0.010623781941831112,
0.029475877061486244,
0.031137878075242043,
0.012491803616285324,
-0.024227473884820938,
-0.05479525402188301,
-0.026105405762791634,
0.015307841822504997,
-0.07463326305150986,
-0.06243302673101425,
-0.05208774283528328,
0.002672194968909025,
-0.041753821074962616,
0.005576077848672867,
0.01448602881282568,
-0.017099134624004364,
0.059855878353118896,
-0.07927027344703674,
0.09938587993383408,
0.004115560557693243,
0.03081165999174118,
0.013112537562847137,
0.011641529388725758,
-0.0063929748721420765,
0.0814281776547432,
0.0580584742128849,
-0.007463949266821146,
-0.06278103590011597,
-0.012028301134705544,
-0.00019248397438786924,
-0.01425155345350504,
-0.03511393070220947,
-0.05459862947463989,
0.06654788553714752,
-0.03718484565615654,
-0.03625993803143501,
0.03531637042760849,
-0.004190513864159584,
-0.015760241076350212,
0.03106117993593216,
0.039062872529029846,
-0.012666980735957623,
0.002895145211368799,
-0.052156057208776474,
0.007862741127610207,
-0.04410966485738754,
0.004062815103679895,
0.03960244357585907,
-0.010644890367984772,
-0.00875423289835453,
-0.007860382087528706,
0.021502386778593063,
-0.027183998376131058,
-0.025198720395565033,
0.07053223252296448,
-0.04409677907824516,
-0.011387716978788376,
0.023091871291399002,
-0.02775115706026554,
-0.0034344501327723265,
0.007146446965634823,
0.02257850021123886,
-0.03790874406695366,
0.004968137014657259,
0.015700042247772217,
0.07270438224077225,
-0.019407501444220543,
-0.0241108275949955,
-0.005689311306923628,
-0.030812762677669525,
0.0032646534964442253,
0.0929369404911995,
-0.009879822842776775,
-0.029343290254473686,
-0.003467065980657935,
0.012992920354008675,
-0.02472720667719841,
0.0005021804827265441,
-0.03828536346554756,
0.0011798423947766423,
-0.01798257604241371,
-0.006457285489886999,
0.01074184849858284,
-0.01852956786751747,
-0.00775544811040163,
-0.028263695538043976,
0.008700638078153133,
0.09926123917102814,
0.00657892320305109,
-0.050730325281620026,
0.04139320179820061,
-0.03979784622788429,
-0.06487621366977692,
0.012035666033625603,
0.036074940115213394,
-0.0092046819627285,
-0.03727453574538231,
0.03447161614894867,
0.00924694538116455,
0.0033626474905759096,
-0.007532227318733931,
0.002460368210449815,
0.05411947891116142,
-0.02557746134698391,
-0.09428119659423828,
-0.05002070218324661,
0.06601319462060928,
0.01364684198051691,
-0.010887742042541504,
-0.03251587226986885,
-0.004888530354946852,
0.009383982978761196,
0.06570577621459961,
-0.001723059336654842,
-0.012325374409556389,
0.017110444605350494,
0.052629683166742325,
0.014503485523164272,
-0.004188519902527332,
-0.012349852360785007,
0.006285513751208782,
-0.016326919198036194,
0.052459973841905594,
-0.08351513743400574,
0.06299301981925964,
-0.0016680365661159158,
-0.017988549545407295,
-0.02732544019818306,
0.07977169007062912,
-0.005972644314169884,
0.026749251410365105,
0.013357379473745823,
0.001388590782880783,
0.008576331660151482,
0.06408002972602844,
-0.008996598422527313,
0.024832094088196754,
0.01362787839025259,
0.015451491810381413,
0.00397119764238596,
0.028024815022945404,
0.04119965806603432,
0.04860451817512512,
-0.04201967269182205,
-0.009963542222976685,
0.013669698499143124,
0.004353353288024664,
-0.0030230290722101927,
0.007426316849887371,
-0.009099694900214672,
-0.006675417069345713,
-0.007767864502966404,
-0.0036330523435026407,
0.0413317009806633,
0.0025219079107046127,
-0.016214115545153618,
0.02475026063621044,
-0.07187815755605698,
0.0018835205119103193,
-0.03562634810805321,
0.01492591667920351,
-0.03652733936905861,
-0.01063009724020958,
0.021344564855098724,
0.006908468436449766,
0.00945611484348774,
-0.04781109839677811,
-0.05476771667599678,
-0.004050825722515583,
0.030085640028119087,
0.014430645853281021,
0.0062484946101903915,
0.0058136931620538235,
0.009121197275817394,
0.015509248711168766,
-0.017740892246365547,
0.028123941272497177,
-0.06076880544424057,
-0.0409742072224617,
-0.0364447645843029,
-0.029778162017464638,
0.04288816824555397,
-0.011816728860139847,
-0.008671373128890991,
0.03780916705727577,
-0.01662173680961132,
-0.03912237659096718,
0.00610492704436183,
-0.0094813983887434,
0.05455690622329712,
0.04065045341849327,
0.05157329514622688,
0.018158450722694397,
0.053684454411268234,
0.002996109426021576,
0.003922115080058575,
0.01467258483171463,
-0.026698440313339233,
-0.06360311061143875,
0.04157702624797821,
0.03838881850242615,
0.021465828642249107,
-0.046001311391592026,
0.0556357316672802,
-0.003927712794393301,
0.028295712545514107,
0.049614448100328445,
0.02629747986793518,
-0.03623288497328758,
-0.03602157160639763,
0.011445132084190845,
0.028928019106388092,
0.006193454377353191,
0.02389245107769966,
0.05183330923318863,
-0.01300114206969738,
-0.01363426074385643,
0.029072178527712822,
-0.03324476256966591,
0.01947636529803276,
-0.006582050118595362,
-0.006533931940793991,
0.012202355079352856,
-0.04078654944896698,
0.024050772190093994,
-0.022370200604200363,
-0.0026927178259938955,
-0.0031062383204698563,
0.01833616942167282,
0.028689559549093246,
-0.012632342055439949,
-0.008058392442762852,
-0.017742324620485306,
-0.014119323343038559,
-0.03564434498548508,
-0.014319422654807568,
0.032570209354162216,
0.003499740967527032,
0.02258140593767166,
0.003994577098637819,
0.013315754011273384,
-0.06660465896129608,
0.004152858164161444,
0.03681548312306404,
0.009986866265535355,
0.026779012754559517,
-0.03352275490760803,
-0.016285793855786324,
0.02418077550828457,
-0.033922888338565826,
0.0007083159871399403,
0.03912835568189621,
-0.05460238829255104,
0.04669611528515816,
-0.0003906905185431242,
-0.02496299333870411,
0.041041966527700424,
-0.03607382997870445,
0.04271099716424942,
0.01006485614925623,
-0.014877072535455227,
-0.02332838997244835,
-0.0012335721403360367,
-0.020801281556487083,
0.002123301150277257,
-0.02504255436360836,
0.03582052141427994,
0.019702736288309097,
-0.007741712033748627,
0.0009446664480492473,
-0.011097480542957783,
-0.02985071949660778,
-0.016459081321954727,
-0.0258871428668499,
-0.012771598994731903,
0.019404016435146332,
-0.027642114087939262,
0.03164881467819214,
0.051882266998291016,
-0.05537797883152962,
0.0038450146093964577,
-0.04996123164892197,
-0.06522157043218613,
-0.015590418130159378,
-0.0030930680222809315,
0.03880993276834488,
-0.00002380625119258184,
-0.010064035654067993,
0.042902782559394836,
0.01370188407599926,
-0.02391304448246956,
-0.0010440866462886333,
-0.03544239699840546,
-0.00916537269949913,
-0.027062026783823967,
0.023391082882881165,
0.021657327190041542,
-0.0016110612777993083,
0.011871694587171078,
0.042218051850795746,
-0.0030296200420707464,
0.008854085579514503,
0.03718244656920433,
-0.023918652907013893,
0.025300942361354828,
-0.009476293809711933,
0.017331792041659355,
0.05761489272117615,
-0.0016942095244303346,
-0.07003820687532425,
0.001575796282850206,
0.010139690712094307,
0.012701811268925667,
0.020637409761548042,
-0.03819020465016365,
0.04318452253937721,
0.00783794280141592,
-0.0214921236038208,
-0.016150709241628647,
0.020863978192210197,
-0.010299799032509327,
0.017076270654797554,
-0.019325289875268936,
0.053076863288879395,
0.02476784959435463,
0.026931440457701683,
0.02114296145737171,
0.04886702075600624,
0.001107498537749052,
-0.04788874834775925,
-0.0037192986346781254,
-0.022853491827845573,
0.01061901543289423,
0.048093657940626144,
-0.020762614905834198,
-0.03598983585834503,
0.05196569859981537,
0.0024339258670806885,
0.030612168833613396,
0.0037474893033504486,
-0.03314177319407463,
0.019144555553793907,
-0.06251706182956696,
-0.012352271936833858,
-0.04430761560797691,
0.07156124711036682,
-0.004900044295936823,
0.018931522965431213,
-0.0011684580240398645,
0.02898847870528698,
0.019117511808872223,
-0.014317268505692482,
-0.06964563578367233,
0.0629212036728859,
-0.04754063859581947,
-0.0038977735675871372,
-0.02585865557193756,
0.01671171933412552,
0.03443577513098717,
0.006677611730992794,
-0.019527902826666832,
-0.031008709222078323,
-0.007230664603412151,
-0.06813143938779831,
-0.04683339595794678,
-0.09003794938325882,
-0.04105713218450546,
-0.03245769813656807,
-0.020152345299720764,
0.040251173079013824,
-0.0469624288380146,
0.03892068192362785,
0.02578858844935894,
-0.015374924056231976,
-0.023775432258844376,
-0.01030825637280941,
0.02397005632519722,
0.0036991266533732414,
0.02896057814359665,
0.035692568868398666,
0.01620985008776188,
-0.04190422222018242,
0.05369476228952408,
0.04389894753694534,
0.031275674700737,
-0.006374283693730831,
-0.019828911870718002,
0.0032499106600880623,
-0.027732765302062035,
-0.013070360757410526,
0.01973172090947628,
0.042932379990816116,
0.03721310570836067,
0.00018367584561929107,
0.04173402860760689,
0.0092668691650033,
-0.02457813359797001,
0.023657239973545074,
0.05103684589266777,
-0.050817620009183884,
0.001466092187911272,
-0.043247904628515244,
0.002934746677055955,
-0.024122850969433784,
0.00823566410690546,
-0.010578323155641556,
-0.006337814033031464,
0.016199031844735146,
0.027958732098340988,
0.03423536196351051,
0.027530668303370476,
-0.03247028589248657,
-0.032502759248018265,
-0.01900123804807663,
0.04651163890957832,
0.015658730641007423,
0.0021495448891073465,
-0.005770727526396513,
0.03826833888888359,
0.03854641318321228,
0.021624518558382988,
0.00958639569580555,
-0.06315737217664719,
0.027585741132497787,
0.031017854809761047,
0.005841095466166735,
-0.008320032618939877,
0.03360601142048836,
-0.05310492962598801,
-0.015117251314222813,
0.05237754434347153,
-0.015596440061926842,
0.051172900944948196,
-0.026714487001299858,
-0.021832387894392014,
-0.011383495293557644,
-0.01808495819568634,
0.006772369146347046,
0.016814973205327988,
0.009275716729462147,
0.004324701149016619,
0.007507195696234703,
-0.03228387609124184,
-0.04016045480966568,
0.038834404200315475,
0.026190923526883125,
0.04200315102934837,
0.008186123333871365,
0.01947251334786415,
0.00144817098043859,
0.009076728485524654,
-0.0023028289433568716,
-0.05782123655080795,
0.009466123767197132,
0.008271951228380203,
-0.04149755463004112,
0.04184793680906296,
-0.008778713643550873,
-0.005156235303729773,
0.013071510009467602,
-0.010688080452382565,
-0.0014241727767512202,
0.005209431983530521,
-0.02335510216653347,
0.014648356474936008,
0.02917901985347271,
0.009816417470574379,
0.014896295964717865,
0.07210340350866318,
-0.0012804740108549595,
-0.012571809813380241,
0.01661817729473114,
0.036134783178567886,
-0.012006261385977268,
0.003169980365782976,
0.026013854891061783,
-0.027452146634459496,
-0.03139536455273628,
0.06957091391086578,
-0.008163563907146454,
0.0024584513157606125,
-0.027705365791916847,
-0.018067870289087296,
-0.029055867344141006,
0.04181075841188431,
0.016241731122136116,
-0.024777019396424294,
0.030731957405805588,
0.03396226838231087,
0.008643561974167824,
-0.009935881942510605,
0.021103089675307274,
-0.007151634898036718,
-0.02153170108795166,
0.028905048966407776,
-0.043088383972644806,
0.0133524714037776,
-0.049763355404138565,
-0.037526123225688934,
0.024497944861650467,
0.014272059313952923,
0.03416041284799576,
0.002297407016158104,
-0.022503487765789032,
0.039846643805503845,
-0.06839076429605484,
0.003087481716647744,
0.0030719703063368797,
0.005614219233393669,
0.02316863462328911,
-0.04838292673230171,
0.0371733196079731,
-0.018392596393823624,
0.033655717968940735,
-0.06985954940319061,
-0.05090935900807381,
0.024521861225366592,
0.008356649428606033,
-0.02812149003148079,
-0.03173467144370079,
0.020656665787100792,
-0.03115171566605568,
-0.014437978155910969,
-0.0016077276086434722,
0.04163184389472008,
-0.026637623086571693,
-0.004326788708567619,
0.013456341810524464,
-0.011051490902900696,
0.0339067168533802,
-0.010262821801006794,
0.005810402799397707,
0.01525608915835619,
0.023314859718084335,
0.007081310264766216,
-0.01573282666504383,
0.052674248814582825,
-0.019175492227077484,
0.01306331716477871,
0.010919942520558834,
-0.0035865316167473793,
0.021737415343523026,
-0.06367703527212143,
-0.005951710045337677,
0.0240860003978014,
0.041318658739328384,
0.028365787118673325,
-0.01656760275363922,
0.03302956372499466,
0.016949690878391266,
-0.03810543566942215,
-0.005270870868116617,
0.01442968100309372,
0.010278169997036457,
-0.06843167543411255,
0.009446567855775356,
0.010542621836066246,
-0.00226405868306756,
-0.0017816474428400397,
0.040949080139398575,
0.02876315265893936,
-0.032679855823516846,
0.029756110161542892,
0.011909367516636848,
0.0014715230790898204,
-0.03609836474061012,
0.03001098334789276,
-0.018036995083093643,
-0.008767467923462391,
0.006087003741413355,
-0.09752481430768967,
-0.02121584489941597,
-0.009416081942617893,
0.08436044305562973,
-0.03019821271300316,
0.025637436658143997,
0.032178279012441635,
0.011404061689972878,
-0.008722605183720589,
0.006183873862028122,
0.026466427370905876,
0.018008699640631676,
-0.016951486468315125,
-0.011072537861764431,
-0.011208458803594112,
0.01558639109134674,
0.016993163153529167,
0.012527290731668472,
-0.022893130779266357,
0.020837174728512764,
0.007159155327826738,
0.04610304534435272,
0.02980884537100792,
-0.024060498923063278,
-0.03585916757583618,
0.06602408736944199,
-0.03998954966664314,
0.0438341423869133,
-0.020306887105107307,
-0.059911444783210754,
0.02610648423433304,
0.030711714178323746,
-0.002719488926231861,
-0.008845696225762367,
0.018317779526114464,
-0.019719481468200684,
0.026137245818972588,
0.0045179701410233974,
0.018800001591444016,
0.013917290605604649,
0.016886847093701363,
0.014173254370689392,
0.03529776260256767,
-0.0018176438752561808,
0.02074296958744526,
-0.061405107378959656,
-0.03530922904610634,
-0.026166409254074097,
-0.047563303261995316,
0.05104822665452957,
0.00032823943183757365,
-0.0015849991468712687,
0.003830092493444681,
-0.007644565310329199,
0.027976268902420998,
-0.008419504389166832,
0.018069500103592873,
-0.013442711904644966,
0.03664523735642433,
-0.005235881544649601,
0.04661470279097557,
-0.03172774240374565,
0.04146820679306984,
0.07612739503383636,
0.032237615436315536,
0.01859326846897602,
-0.05491618067026138,
0.024996159598231316,
-0.026050830259919167,
0.03154202550649643,
-0.04470880329608917,
0.026100531220436096,
0.029476851224899292,
0.007018908392637968,
0.00924224965274334,
0.061738111078739166,
0.04364655911922455,
-0.0038378636818379164,
0.053175460547208786,
-0.029138140380382538,
-0.046412739902734756,
0.019726954400539398,
0.026603329926729202,
0.0026568779721856117,
0.013839305378496647,
-0.049930110573768616,
0.03209275007247925,
-0.04820587858557701,
-0.0009743815171532333,
0.008690908551216125,
-0.05760568380355835,
0.028216267004609108,
-0.012320115230977535,
-0.01804371550679207,
-0.005344024859368801,
-0.01574847660958767,
0.008220475167036057,
-0.0449342206120491,
0.03463415056467056,
0.011854809708893299,
-0.005219604354351759,
0.014612494967877865,
0.03652128204703331,
0.023673806339502335,
-0.010493326000869274,
-0.02260435000061989,
-0.015975406393408775,
-0.029152216389775276,
0.012619143351912498,
-0.03393767774105072,
0.0023922654800117016,
-0.043288227170705795,
0.04358389228582382,
-0.01982119306921959,
-0.0005904894205741584,
-0.017177585512399673,
0.021193189546465874,
-0.020484047010540962,
-0.00745872687548399,
0.05706516280770302,
-0.039301201701164246,
0.0017020583618432283,
-0.004912670236080885,
0.004933788441121578,
-0.01828734576702118,
0.01568722166121006,
-0.020301392301917076,
-0.03630581125617027,
-0.029665986075997353,
0.0010734901297837496,
0.0272320955991745,
-0.031080175191164017,
-0.016476931050419807,
-0.03788982704281807,
0.03592366352677345,
-0.04171732813119888,
-0.025659510865807533,
0.008212022483348846,
-0.000049824076995719224,
0.01440794300287962,
0.02395850047469139,
-0.037443287670612335,
-0.017415553331375122,
-0.021215783432126045,
0.005647001322358847,
-0.010118905454874039,
-0.005949699319899082,
-0.0322745144367218,
-0.050297971814870834,
0.03609864041209221,
0.0012791623594239354,
-0.03028688207268715,
-0.024392373859882355,
0.01616872288286686,
-0.022501599043607712,
0.010997881181538105,
-0.02429063431918621,
-0.0033500418066978455,
-0.002148888073861599,
-0.03315942361950874,
0.021828722208738327,
-0.0010654532816261053,
0.023722009733319283,
0.00468412833288312,
0.01996447704732418,
-0.009027693420648575,
0.06311078369617462,
-0.016209686174988747,
0.03359457105398178,
0.05202395096421242,
-0.04625711962580681,
-0.031012987717986107,
-0.014376508072018623,
0.05195287987589836,
-0.011883490718901157,
-0.059641238301992416,
-0.01721825823187828,
0.0389484278857708,
-0.0298323892056942,
0.014032927341759205,
-0.024933911859989166,
-0.010517817921936512,
0.023149961605668068,
0.030249807983636856,
-0.07057175040245056,
-0.01695256121456623,
-0.07125178724527359,
-0.026879627257585526,
0.0017938886303454638,
-0.012295318767428398,
-0.011905302293598652,
0.03145728260278702,
-0.01436648704111576,
-0.00026123569114133716,
0.03310365229845047,
0.05256928130984306,
-0.025179801508784294,
-0.01640676148235798,
0.0355524905025959,
-0.0041184681467711926,
0.03500489518046379,
-0.03364451229572296,
-0.043426793068647385,
0.07747966051101685,
-0.04382135346531868,
-0.07124188542366028,
0.03693510591983795,
-0.04406329616904259,
-0.006343991961330175,
0.0451844222843647,
0.0026979718822985888,
-0.01566961593925953,
0.04029475525021553,
0.041072845458984375,
0.005267104599624872,
0.0031172491144388914,
0.0025327003095299006,
0.0025829928927123547,
0.008382834494113922,
0.0384928360581398,
-0.045980390161275864,
-0.0034436918795108795,
0.00981579627841711,
0.06212121248245239,
0.021439433097839355,
-0.01576252095401287,
0.0014570605708286166,
-0.009419167414307594,
0.0428043007850647,
-0.004652626346796751,
0.0027625341899693012,
0.049777802079916,
0.05511575564742088,
-0.024376211687922478,
0.03669305890798569,
0.013193758204579353,
0.012403173372149467,
-0.07538449019193649,
0.026481999084353447,
0.030525188893079758,
0.019674116745591164,
0.024473095312714577,
-0.019818387925624847,
-0.014071818441152573,
0.013143009506165981,
-0.05798329785466194,
0.020409295335412025,
-0.03523190692067146,
-0.03022337518632412,
0.009745082817971706,
0.023000312969088554,
0.0036381897516548634,
0.02853589504957199,
0.026696830987930298,
0.02026178129017353,
0.00845818780362606,
0.007262398488819599,
0.008729384280741215,
0.046143755316734314,
-0.007134771440178156,
0.0032930588349699974,
0.012586928904056549,
-0.015699882060289383,
0.04468420147895813,
-0.030454078689217567,
-0.042068999260663986,
0.030985422432422638,
0.009301857091486454,
-0.02008708193898201,
-0.028587276116013527,
0.01393524743616581,
-0.004453397821635008,
0.010198788717389107,
0.05874203145503998,
-0.01731354556977749,
0.0330766886472702,
0.006941250525414944,
-0.0014294524444267154,
0.04152446612715721,
-0.009469535201787949,
0.0191816296428442,
-0.010937516577541828,
-0.029105104506015778,
-0.014286826364696026,
-0.0060686031356453896,
-0.018784645944833755,
-0.004721242934465408,
0.008631253615021706,
0.010596651583909988,
-0.011090192012488842,
-0.0008897455991245806,
0.03295037895441055,
-0.04852887988090515,
-0.028214730322360992,
-0.017383703961968422,
0.022710153833031654,
0.017010647803544998,
0.04486303776502609,
0.009503860026597977,
-0.02262735925614834,
0.010579952970147133,
-0.010409452021121979,
0.04402774199843407,
-0.0691026821732521,
-0.011402742937207222,
0.01662948913872242,
0.004141641780734062,
-0.036185938864946365,
-0.04691086336970329,
-0.03793895244598389,
0.05684938654303551,
-0.01573834754526615,
0.03758480027318001,
0.007862858474254608,
-0.03867297247052193,
-0.011345817707479,
-0.047613948583602905,
0.051247451454401016,
0.003092218656092882,
0.020471084862947464,
-0.01537786703556776,
-0.007994391955435276,
-0.017569085583090782,
-0.030237864702939987,
0.0005731175187975168,
-0.06084061414003372,
0.0025613002944737673,
0.02754305675625801,
-0.024836698547005653,
0.0071008591912686825,
-0.0288865864276886,
-0.016090424731373787,
-0.05977381393313408,
-0.020896848291158676,
-0.012052330188453197,
-0.023684974759817123,
-0.004136681091040373,
0.00397432642057538,
0.03920283168554306,
0.010087789036333561,
0.038997117429971695,
0.019229192286729813,
-0.042212922126054764,
0.05869748815894127,
0.029249021783471107,
0.004706572741270065,
0.04822823405265808,
-0.03276686742901802,
0.042924121022224426,
0.02872881293296814,
-0.036370981484651566,
-0.004891078453511,
0.07757218182086945,
-0.035741351544857025,
-0.0025941883213818073,
-0.04558253288269043,
-0.054562512785196304,
0.0035594517830759287,
-0.03735356777906418,
-0.03135979548096657,
0.04867587983608246,
-0.03181791305541992,
-0.009803260676562786,
0.04118883237242699,
0.013645175844430923,
-0.02227373979985714,
0.005080634728074074,
0.0278769563883543,
0.040941379964351654,
0.006677407771348953,
-0.04226405546069145,
0.09197051078081131,
0.03210630640387535,
-0.011120056733489037,
0.01823176071047783,
-0.0007591211469843984,
-0.0046421559527516365,
0.023642197251319885,
0.01498021837323904,
0.02294611930847168,
-0.008522478863596916,
0.007577540818601847,
0.021284600719809532,
-0.008210035972297192,
0.0037158681079745293,
0.005074501037597656,
-0.020901180803775787,
0.06640532612800598,
-0.007975820451974869,
-0.010979228653013706,
0.005179145839065313,
-0.03728017210960388,
-0.02509920671582222,
-0.04109808802604675,
-0.0036139728035777807,
0.034841377288103104,
-0.018014075234532356,
0.017248792573809624,
-0.03894124552607536,
0.0170164555311203,
-0.012650439515709877,
-0.06416912376880646,
0.03671405091881752,
-0.009675080887973309,
0.02698935940861702,
-0.0012198827462270856,
-0.005587515886873007,
-0.04386718571186066,
-0.0519179031252861,
0.03374931588768959,
0.016425805166363716,
0.03413816913962364,
0.010073510929942131,
-0.030529504641890526,
-0.03430045768618584,
0.05372136831283569,
-0.025551272556185722,
-0.009344883263111115,
-0.04562649503350258,
0.0197280403226614,
-0.015534350648522377,
0.0012003722367808223
] |
<p>A few questions about the design of a common table fan, such as below.</p>
<ol>
<li>Does the round disc (silver in the image) in front of the blades serve any functional purpose?</li>
<li>Does the metal casing around the blades serve any functional purpose except protecting the blades?</li>
<li>What exactly are the sources of noise in a well-designed fan? Does the metal casing in a well-designed fan have an impact on the noise level? </li>
</ol>
<p><img src="http://img193.imageshack.us/img193/8081/60933751.gif"></p>
| 8,865 |
[
-0.06523199379444122,
-0.0331760048866272,
-0.004250477068126202,
0.00719107361510396,
0.033863939344882965,
0.026097334921360016,
-0.002441706135869026,
-0.015556516125798225,
0.016422148793935776,
-0.03886529803276062,
0.05341779440641403,
0.07263454049825668,
0.05830441042780876,
0.06585180014371872,
0.03643176332116127,
-0.014741971157491207,
-0.01127068791538477,
-0.03503195196390152,
-0.020340995863080025,
-0.00684871943667531,
-0.02790885791182518,
-0.00016419871826656163,
-0.0010926538379862905,
-0.02249833568930626,
-0.017215099185705185,
-0.0183697696775198,
-0.0024543500039726496,
-0.01632547937333584,
0.024438444525003433,
0.02377064898610115,
-0.030589450150728226,
-0.00832238607108593,
0.003191441297531128,
0.011913685128092766,
0.021127596497535706,
-0.028679700568318367,
-0.018921522423624992,
0.027495209127664566,
-0.029322410002350807,
0.0072518023662269115,
-0.040950216352939606,
-0.007388226222246885,
0.03229396790266037,
0.024413978680968285,
-0.0020702038891613483,
-0.008752919733524323,
0.015975860878825188,
-0.019043613225221634,
-0.0142826484516263,
-0.08177892863750458,
0.027695419266819954,
-0.0011562671279534698,
0.022104322910308838,
0.06416787207126617,
0.010196346789598465,
0.027649104595184326,
0.03148443251848221,
0.04795404151082039,
-0.02766226790845394,
-0.06826277077198029,
0.03075418993830681,
-0.016168059781193733,
-0.011419910937547684,
-0.02004309743642807,
-0.028998911380767822,
0.032219965010881424,
0.0029545899014919996,
-0.030685115605592728,
0.046099863946437836,
0.0021026574540883303,
0.013055910356342793,
0.025774352252483368,
-0.016552451997995377,
-0.009883114136755466,
0.018154656514525414,
-0.04741070419549942,
0.006560269743204117,
0.014694495126605034,
0.020419355481863022,
0.046808019280433655,
0.015753604471683502,
0.009652567096054554,
0.024625618010759354,
0.004761642310768366,
0.018749654293060303,
-0.005731632001698017,
0.08007192611694336,
-0.01440498512238264,
0.03260210156440735,
-0.0033751947339624166,
0.02632135897874832,
0.015141207724809647,
0.05566642805933952,
0.014589793048799038,
-0.021207613870501518,
0.029594063758850098,
-0.006874001584947109,
0.022315308451652527,
0.010772096924483776,
-0.03150163218379021,
0.011141310445964336,
0.03125583007931709,
0.023183584213256836,
0.06909631937742233,
-0.025221867486834526,
-0.010014316067099571,
-0.02517000027000904,
0.027890220284461975,
-0.01504566241055727,
-0.008671026676893234,
-0.05216282606124878,
0.020647596567869186,
0.0035063440445810556,
-0.006751911249011755,
0.006365993991494179,
0.003929701168090105,
0.01754039339721203,
0.019812120124697685,
0.030467936769127846,
0.0622309111058712,
0.026091773062944412,
-0.018927164375782013,
0.006775126326829195,
-0.01426677219569683,
-0.02860574796795845,
0.020767228677868843,
-0.0027456653770059347,
-0.030267219990491867,
-0.015622241422533989,
0.035943906754255295,
-0.01483490876853466,
-0.017216118052601814,
0.008847212418913841,
0.01284835860133171,
0.01694023236632347,
-0.02011200040578842,
-0.0875805988907814,
-0.06823528558015823,
0.05143481120467186,
-0.010511747561395168,
-0.04522465169429779,
-0.029315931722521782,
-0.0032097487710416317,
0.02560698427259922,
0.038111377507448196,
0.0005900642718188465,
-0.05767710134387016,
-0.025744479149580002,
0.03331628814339638,
0.004134256858378649,
-0.041311632841825485,
0.01872245967388153,
-0.02424001879990101,
-0.010729442350566387,
-0.020744383335113525,
-0.05684226006269455,
0.01338124368339777,
-0.00574827753007412,
0.03029666654765606,
-0.0464252308011055,
0.016776183620095253,
0.007356668822467327,
-0.028189508244395256,
-0.021082909777760506,
-0.0005059000104665756,
-0.02577815018594265,
0.0176760982722044,
-0.017468202859163284,
-0.009663684293627739,
0.04098556190729141,
0.002164797857403755,
0.027873026207089424,
0.0018858184339478612,
-0.03256015107035637,
0.030747458338737488,
-0.02433953434228897,
0.006230149883776903,
-0.022763293236494064,
0.011625290848314762,
-0.00939052365720272,
-0.04945656284689903,
-0.003446692368015647,
-0.0025999736972153187,
-0.031958263367414474,
0.012794938869774342,
0.07668406516313553,
0.0006348273600451648,
0.006332736928015947,
0.0026616882532835007,
-0.018374158069491386,
-0.030195018276572227,
-0.08990383893251419,
0.01795951835811138,
-0.04778095707297325,
-0.0161008071154356,
0.002535441890358925,
-0.010406018234789371,
0.03328366205096245,
-0.01825644075870514,
0.004206451587378979,
-0.024740517139434814,
0.024844693019986153,
0.03327876701951027,
0.004517650697380304,
0.04029400274157524,
0.04099494591355324,
0.03330076485872269,
-0.03575250506401062,
0.02579447813332081,
-0.04554302617907524,
-0.05962717905640602,
-0.00308759743347764,
-0.02630947157740593,
-0.018495744094252586,
0.042879875749349594,
0.014150436967611313,
0.03505197912454605,
0.03534549102187157,
0.018668459728360176,
0.02021237649023533,
-0.022849053144454956,
0.05778517201542854,
0.05140862241387367,
-0.00923861749470234,
0.03913319855928421,
0.007671652361750603,
0.007319294847548008,
-0.014961141161620617,
-0.0005315141170285642,
-0.0010278502013534307,
-0.09137847274541855,
-0.010149362497031689,
0.07679953426122665,
0.0036303799133747816,
-0.04011004790663719,
0.024093175306916237,
0.021599693223834038,
-0.024106433615088463,
0.0469895601272583,
-0.023503312841057777,
-0.0052288612350821495,
-0.003327810438349843,
-0.001754064462147653,
0.033267486840486526,
-0.028279835358262062,
0.0281155314296484,
0.03204777091741562,
0.04131721332669258,
0.029174823313951492,
-0.006076007150113583,
-0.023148057982325554,
0.07495350390672684,
0.006762941833585501,
0.03342336043715477,
-0.03888661786913872,
-0.0022504639346152544,
0.04707038030028343,
-0.0036552101373672485,
-0.009477159939706326,
-0.009702146984636784,
-0.004434115719050169,
0.0020986637100577354,
-0.024141838774085045,
-0.012154549360275269,
-0.023002520203590393,
0.009987808763980865,
-0.019851187244057655,
-0.005598049610853195,
0.028506897389888763,
-0.0034991800785064697,
0.025958355516195297,
-0.02396203950047493,
0.0034454416017979383,
0.005381041672080755,
0.003871180349960923,
0.05144133046269417,
-0.005101608578115702,
0.054829176515340805,
-0.006448750849813223,
-0.020343290641903877,
-0.0034121389035135508,
-0.03292505815625191,
-0.03195500746369362,
-0.006382405757904053,
-0.06717901676893234,
-0.017175894230604172,
-0.005458159372210503,
-0.029009409248828888,
0.020857466384768486,
-0.01642504706978798,
-0.00883637648075819,
0.0021097478456795216,
0.016381217166781425,
-0.06887934356927872,
0.013369356282055378,
0.0029694458935409784,
0.015515615232288837,
-0.03562725707888603,
-0.025490062311291695,
0.01730995625257492,
-0.030439652502536774,
0.0028196058701723814,
0.0138762928545475,
-0.05266851931810379,
-0.035658325999975204,
-0.002633302705362439,
-0.042047370225191116,
0.03276638314127922,
-0.022292787209153175,
-0.0256508681923151,
0.01441698707640171,
-0.02253280021250248,
-0.008660323917865753,
-0.051054976880550385,
0.0025211467873305082,
-0.0016698382096365094,
-0.023217536509037018,
0.08373276144266129,
-0.0032487621065229177,
-0.020700089633464813,
0.04967619106173515,
0.038832761347293854,
-0.04831070080399513,
-0.004752755630761385,
-0.048477403819561005,
-0.03593014180660248,
-0.07764305919408798,
0.029188605025410652,
0.04513050615787506,
-0.014801057986915112,
0.012938256375491619,
0.040352240204811096,
-0.022640403360128403,
0.027706153690814972,
0.0001919115602504462,
0.0025767358019948006,
-0.020837802439928055,
0.010999994352459908,
-0.03940843045711517,
0.06470878422260284,
-0.012219292111694813,
-0.02986833080649376,
0.0004324614710640162,
-0.043627358973026276,
0.038238849490880966,
0.043319348245859146,
-0.028700552880764008,
0.038127049803733826,
-0.015807224437594414,
0.029022542759776115,
-0.04778182506561279,
0.052211396396160126,
0.0004651029594242573,
-0.031477075070142746,
-0.026285424828529358,
0.02349347062408924,
0.02274559624493122,
0.010219407267868519,
-0.0005912504275329411,
0.05882210657000542,
0.020500902086496353,
-0.03754561394453049,
-0.0271847452968359,
-0.010670233517885208,
0.006405954249203205,
-0.0060822442173957825,
-0.006020190194249153,
-0.002849214943125844,
-0.009027520194649696,
0.06535431742668152,
0.008957475423812866,
0.0088739525526762,
-0.024318929761648178,
0.0007890611886978149,
-0.0800146609544754,
-0.006967088673263788,
-0.06771644949913025,
0.04760943725705147,
-0.014850418083369732,
0.024107348173856735,
0.016457712277770042,
-0.02752470225095749,
0.019822193309664726,
0.0015557287260890007,
-0.08436829596757889,
0.030741678550839424,
-0.0032836156897246838,
-0.016084782779216766,
-0.03207197040319443,
-0.008228711783885956,
-0.0034123086370527744,
0.010136457160115242,
-0.046779777854681015,
-0.012583315372467041,
0.023333601653575897,
-0.02117038145661354,
0.02133316546678543,
0.012833742424845695,
-0.03908584639430046,
0.001999177969992161,
0.02349880523979664,
0.002742114244028926,
-0.0018473478266969323,
0.04567477107048035,
0.016587119549512863,
-0.0027804195415228605,
-0.0012697558850049973,
-0.0011419018264859915,
-0.020942475646734238,
-0.04492134228348732,
0.00857554655522108,
0.014172828756272793,
0.020237982273101807,
-0.004481757991015911,
0.008220240473747253,
0.011961154639720917,
0.015691863372921944,
0.022754639387130737,
0.009756454266607761,
-0.021414950489997864,
-0.05422850698232651,
-0.005553356371819973,
0.010257476009428501,
0.03785576671361923,
-0.00306719564832747,
0.005058604292571545,
-0.008083275519311428,
-0.012528433464467525,
-0.037791527807712555,
0.001024013850837946,
0.014749574474990368,
0.02641209028661251,
-0.014489925466477871,
-0.04189973697066307,
-0.02460305392742157,
-0.007324642967432737,
-0.025614963844418526,
0.008040366694331169,
0.012831359170377254,
0.00595106091350317,
0.023943297564983368,
-0.017102036625146866,
-0.01112568099051714,
-0.03195127099752426,
0.03435991704463959,
0.03684470057487488,
0.02115178108215332,
-0.005911199375987053,
0.02151920273900032,
0.014774993993341923,
0.05135580897331238,
0.05588524788618088,
-0.0033281110227108,
-0.04908645153045654,
-0.07654127478599548,
-0.052900876849889755,
0.05777549743652344,
0.059932369738817215,
-0.024020276963710785,
0.046835266053676605,
-0.05520019307732582,
-0.05572136491537094,
0.051912494003772736,
0.003079706570133567,
0.042264729738235474,
-0.05993766337633133,
0.004330627620220184,
-0.035220686346292496,
0.002104545943439007,
-0.01844479888677597,
-0.0038079596124589443,
-0.015595261938869953,
0.02802055887877941,
-0.018095923587679863,
-0.033555980771780014,
-0.01806991547346115,
0.01928965002298355,
0.03285697102546692,
0.020004630088806152,
-0.015479414723813534,
0.0029499842785298824,
0.023545246571302414,
-0.0007890966953709722,
-0.021819351240992546,
-0.030750878155231476,
-0.0072083622217178345,
0.031174810603260994,
-0.0018625465454533696,
0.02717096172273159,
-0.030322972685098648,
-0.041871730238199234,
-0.014955449849367142,
0.013330533169209957,
-0.043760139495134354,
0.009066987782716751,
-0.024234898388385773,
0.03130001574754715,
0.029603200033307076,
0.015154818072915077,
0.06403098255395889,
0.06463340669870377,
-0.047455187886953354,
0.011220716871321201,
-0.012205975130200386,
-0.008495034649968147,
-0.00470720324665308,
0.005816321354359388,
-0.05109049007296562,
-0.012675665318965912,
-0.023783894255757332,
0.0531427264213562,
-0.019581960514187813,
0.04618139937520027,
-0.004227722063660622,
-0.042606420814991,
-0.0030457377433776855,
0.05600200220942497,
0.018646840006113052,
-0.026925789192318916,
0.010230868123471737,
0.0539390929043293,
-0.014222318306565285,
0.00993572548031807,
0.003629799000918865,
-0.03630347177386284,
0.052421290427446365,
0.02629491128027439,
-0.011538413353264332,
0.04889700934290886,
-0.05182356387376785,
-0.03070106916129589,
-0.009677153080701828,
-0.055635616183280945,
0.08596248179674149,
0.015446631237864494,
0.020855432376265526,
0.04571571201086044,
-0.041459470987319946,
-0.02483002096414566,
0.02126767300069332,
-0.008373442105948925,
0.021735649555921555,
-0.017127584666013718,
0.04612801969051361,
-0.01092545036226511,
-0.018159160390496254,
-0.025667479261755943,
0.026198064908385277,
0.01913658156991005,
0.0625474750995636,
0.0013794531114399433,
-0.02630486525595188,
-0.0020197168923914433,
0.007775499019771814,
-0.03944110870361328,
0.01660279743373394,
0.0036343189422041178,
-0.012870477512478828,
-0.010283764451742172,
0.053734809160232544,
0.002043628366664052,
0.10224048048257828,
0.028385858982801437,
-0.006944009102880955,
-0.0036891410127282143,
-0.039072901010513306,
-0.07394690811634064,
-0.05253063514828682,
-0.006774486042559147,
-0.04756586626172066,
-0.042042866349220276,
0.005461813881993294,
0.025549372658133507,
0.05334034562110901,
0.000983760110102594,
0.029439769685268402,
0.0017175468383356929,
-0.018979843705892563,
-0.02828630805015564,
-0.032909974455833435,
0.03815460205078125,
-0.024778861552476883,
0.04758840799331665,
0.019436417147517204,
0.009424535557627678,
-0.007583240512758493,
-0.023747315630316734,
0.032256145030260086,
0.003330974606797099,
-0.007414371706545353,
0.031204160302877426,
0.06396599858999252,
-0.027110373601317406,
0.027233516797423363,
-0.03196084871888161,
-0.03320326656103134,
0.07793089002370834,
0.010982186533510685,
0.0028436314314603806,
-0.00767734507098794,
0.03521845117211342,
0.004446099046617746,
-0.03470073267817497,
-0.005790663883090019,
-0.0264726709574461,
0.050869446247816086,
-0.0085522485896945,
0.042518630623817444,
0.01761290244758129,
-0.02936786599457264,
-0.04004281386733055,
-0.03222677856683731,
-0.011689623817801476,
-0.027123495936393738,
0.014224882237613201,
-0.005622392520308495,
-0.011457032524049282,
0.005751931574195623,
0.04150641709566116,
-0.005010890308767557,
0.02830491028726101,
0.029444286599755287,
0.06379564106464386,
0.018758179619908333,
0.021241910755634308,
0.007180243730545044,
-0.009233917109668255,
0.036858439445495605,
-0.040465038269758224,
0.019169818609952927,
-0.01071403082460165,
0.010759333148598671,
0.04337866231799126,
0.05706053599715233,
0.020766137167811394,
-0.047270484268665314,
0.05441184341907501,
-0.04018092900514603,
0.03425295650959015,
-0.0013072695583105087,
-0.010232361033558846,
0.0004276433610357344,
-0.02887594886124134,
0.018947996199131012,
-0.024009620770812035,
-0.0014240676537156105,
-0.011869720183312893,
-0.07144056260585785,
0.03491443023085594,
-0.010751977562904358,
-0.007525067310780287,
0.06032111123204231,
0.006957952864468098,
-0.0685923621058464,
0.02176477201282978,
-0.01169565599411726,
0.02768697217106819,
-0.0008405466796830297,
0.025860773399472237,
-0.05096133053302765,
0.050242263823747635,
-0.01568419113755226,
0.0313621461391449,
0.005631844978779554,
-0.0037087209057062864,
0.137050062417984,
0.025261884555220604,
0.017110327258706093,
-0.0252989511936903,
-0.00906571839004755,
0.020570214837789536,
-0.018534841015934944,
0.013056124560534954,
0.022853339090943336,
-0.04413722828030586,
0.08144563436508179,
0.05807047709822655,
0.042859189212322235,
-0.029309624806046486,
0.01887531206011772,
0.02506875991821289,
-0.018260452896356583,
-0.0207391194999218,
-0.003106517717242241,
0.019249463453888893,
-0.016661038622260094,
-0.0017122324788942933,
-0.049668390303850174,
-0.0022257270757108927,
0.00020693885744549334,
-0.014005642384290695,
-0.01328732818365097,
-0.03469162434339523,
0.03243698924779892,
-0.028850466012954712,
-0.034823399037122726,
0.0307101309299469,
0.025872742757201195,
-0.004153672140091658,
-0.018981976434588432,
-0.019813261926174164,
0.009087254293262959,
-0.025012848898768425,
0.0021435609087347984,
0.05896379053592682,
-0.013506080955266953,
-0.02645706757903099,
0.031231960281729698,
0.027164695784449577,
-0.0547642782330513,
-0.020332511514425278,
-0.026362325996160507,
-0.00500103086233139,
-0.01462335791438818,
-0.008882174268364906,
-0.02904665097594261,
0.024287458509206772,
0.010882807895541191,
-0.0603843629360199,
0.014191764406859875,
0.02484399825334549,
0.009631108492612839,
-0.016690947115421295,
-0.046313706785440445,
-0.057000089436769485,
0.038295190781354904,
0.005201462656259537,
-0.02523578330874443,
-0.0021798957604914904,
0.0158877931535244,
-0.010523458942770958,
-0.021697208285331726,
0.04108913242816925,
0.010040422901511192,
0.015489164739847183,
-0.04901256039738655,
-0.03181571885943413,
-0.029196977615356445,
0.028241051360964775,
-0.021644219756126404,
0.03272874280810356,
0.016151277348399162,
0.012465225532650948,
0.03282766044139862,
-0.0005550668574869633,
-0.04528217017650604,
0.041591543704271317,
0.012995082885026932,
-0.030009180307388306,
0.0018598642200231552,
-0.0035688672214746475,
0.006352376192808151,
0.00377711676992476,
0.00007672582432860509,
0.01214916817843914,
0.011176113970577717,
0.08356039971113205,
-0.0029147446621209383,
0.014117112383246422,
-0.01636757329106331,
-0.021373987197875977,
-0.03905409947037697,
0.012456601485610008,
0.005847744178026915,
0.060502197593450546,
0.035705115646123886,
0.010940509848296642,
0.015776535496115685,
0.010637500323355198,
-0.02690933085978031,
-0.010537797585129738,
0.033869314938783646,
-0.04183575138449669,
0.030844081193208694,
0.010284543968737125,
0.013663148507475853,
-0.058640915900468826,
-0.028050513938069344,
-0.025021420791745186,
-0.036350999027490616,
-0.02265785075724125,
0.03164426609873772,
-0.02961203083395958,
0.01779402419924736,
-0.02837820164859295,
0.009584703482687473,
-0.03898851200938225,
0.004592485725879669,
-0.050457678735256195,
0.0006162833306007087,
0.020666491240262985,
0.004663356114178896,
0.020811835303902626,
0.024652333930134773,
-0.01167953573167324,
0.012648800387978554,
-0.025342902168631554,
0.00638997508212924,
0.0069158426485955715,
0.023283880203962326,
-0.021921969950199127,
0.0017961033154278994,
0.0610235333442688,
-0.012743509374558926,
-0.01333529781550169,
0.04970870912075043,
0.005695933476090431,
-0.02598312869668007,
-0.006704624742269516,
-0.004562840331345797,
0.017052920535206795,
-0.02682294324040413,
-0.03162054717540741,
0.03326856717467308,
0.026856597512960434,
-0.0030028705950826406,
-0.018542708829045296,
-0.03589096665382385,
0.0035944932606071234,
0.04477252811193466,
-0.0038781207986176014,
-0.02689136378467083,
-0.03793768584728241,
0.012350675649940968,
0.03215261548757553,
0.010703016072511673,
-0.019408512860536575,
-0.029746102169156075,
-0.012425946071743965,
-0.03251143544912338,
-0.004185536876320839,
-0.014404439367353916,
0.050851669162511826,
0.009210021235048771,
0.01881423406302929,
-0.02691231109201908,
0.06066417321562767,
0.011174250394105911,
-0.04172956943511963,
-0.12258696556091309,
-0.010663113556802273,
0.010864919982850552,
0.014901379123330116,
-0.0022369292564690113,
-0.00413915840908885,
0.011904841288924217,
0.03260244429111481,
-0.0276422668248415,
0.03239499777555466,
0.005145537666976452,
-0.049113061279058456,
-0.05018286034464836,
0.030746690928936005,
0.01561809703707695,
0.010199075564742088,
-0.01861579343676567,
0.0046578035689890385,
0.018798217177391052,
0.011554792523384094,
0.0025527041871100664,
-0.013382984325289726,
0.006538406014442444,
0.01946464367210865,
-0.03233812004327774,
-0.015056807547807693,
0.06808983534574509,
-0.0007396691362373531,
-0.023602843284606934,
0.0276396032422781,
-0.02319796197116375,
0.018128329887986183,
-0.00437780050560832,
-0.0024061736185103655,
-0.016047783195972443,
0.00431571900844574,
0.04013475403189659,
0.008788412436842918,
-0.014353622682392597,
0.007105343043804169,
0.006864700932055712,
-0.005421153269708157,
0.012479616329073906,
0.04551193118095398,
0.04027695581316948,
-0.018616672605276108,
0.008075593970716,
-0.0042412071488797665,
-0.05015596002340317,
-0.00631720619276166,
0.0016945194220170379,
0.01003257930278778,
0.007739868015050888,
-0.011536665260791779,
0.029054012149572372,
-0.011696035042405128,
-0.017761079594492912,
0.032310593873262405,
0.014361364766955376,
-0.005610753782093525,
0.02258438616991043,
0.02041899412870407,
-0.037617020308971405,
-0.016476256772875786,
0.025571927428245544,
-0.043044086545705795,
-0.05313562601804733,
-0.008636696264147758,
0.01638583466410637,
-0.008734251372516155,
-0.00999181903898716,
-0.03250768408179283,
-0.01993553712964058,
0.013951561413705349,
-0.019729232415556908,
-0.00398030923679471,
0.0005549555644392967,
-0.02088931016623974,
-0.04953568056225777,
-0.053469378501176834,
0.03035455010831356,
0.03317967802286148,
-0.03644351288676262,
-0.028913550078868866,
-0.060549210757017136,
-0.03295663744211197,
0.04120961204171181,
0.07220151275396347,
0.04497293382883072,
-0.03528538718819618,
-0.006332428194582462,
-0.00765179144218564,
0.041686300188302994,
-0.04435426741838455,
0.08318954706192017,
-0.008703529834747314,
-0.010170774534344673,
0.018653016537427902,
-0.036718957126140594,
0.000140263611683622,
-0.006204746197909117,
0.06302206963300705,
-0.023679550737142563,
0.05409253388643265,
0.01598867028951645,
-0.008604925125837326,
0.04198921471834183,
0.03716159239411354,
-0.0012124774511903524,
0.041616328060626984,
-0.028525106608867645,
0.023670637980103493,
0.03687351942062378,
-0.02009611949324608,
-0.035425737500190735,
0.03885835409164429,
-0.03523635491728783,
-0.009664423763751984,
-0.01585477963089943,
0.018516140058636665,
0.019939519464969635,
-0.07776346802711487,
0.008498216047883034,
0.03802694380283356,
-0.0546368733048439,
-0.0187926534563303,
0.022493774071335793,
0.034601856023073196,
0.03773973509669304,
-0.003437663661316037,
-0.0021264199167490005,
0.007191414944827557,
-0.08025982975959778,
-0.04097605496644974,
0.03765891119837761,
0.02807111293077469,
0.013708511367440224,
-0.005678266752511263,
0.034307125955820084,
-0.023563914000988007,
0.013680894859135151,
0.014289770275354385,
0.014921804890036583,
-0.0408770814538002,
-0.003250963520258665,
0.05648129805922508,
0.03194770961999893,
-0.032458800822496414,
0.05509921535849571,
0.00014007075515110046,
0.08231130242347717,
-0.00863744504749775,
0.026145191863179207,
-0.04126770421862602,
-0.013694788329303265,
-0.03651523217558861,
-0.01708616316318512,
0.032041698694229126,
0.04502363130450249,
0.018968572840094566,
0.0048869457095861435,
-0.01222739927470684,
0.01785399205982685,
0.02904442511498928,
-0.04021677002310753,
0.012342915870249271,
-0.02449244260787964,
-0.004392159637063742,
-0.01899460330605507,
0.013309121131896973,
-0.0206486526876688,
-0.017545532435178757,
0.06369888782501221,
0.06122848764061928,
0.024932056665420532,
0.009382035583257675,
-0.012081149034202099,
-0.008894775994122028,
0.03173373267054558,
-0.07239710539579391,
0.0016451086848974228,
-0.012380669824779034,
0.00833759643137455,
-0.007503936067223549,
0.008233103901147842
] |
<p>I have often heard statements like, Continuum limit of Lattice Yang-Mills doesnot exist in dimensions higher then four. Is there a neat way to see this? or could some one point me to some relevant literature where this has been shown.
thanks</p>
| 8,866 |
[
-0.004681598860770464,
-0.010108068585395813,
0.0308527909219265,
-0.03889773413538933,
-0.004190478473901749,
0.048978306353092194,
-0.013776051811873913,
-0.027500448748469353,
-0.005031917244195938,
-0.060984641313552856,
0.030409809201955795,
0.008875559084117413,
0.06159043312072754,
0.011200019158422947,
0.0033910495694726706,
0.017397616058588028,
-0.03298831358551979,
-0.013406987302005291,
0.026463203132152557,
-0.006052292417734861,
0.00366478250361979,
0.03843090683221817,
-0.019783245399594307,
0.02490665577352047,
0.0028821402229368687,
-0.009836678393185139,
0.03053821437060833,
0.040594518184661865,
0.010338853113353252,
0.05120488256216049,
0.009385794401168823,
-0.02099432609975338,
0.03002369962632656,
0.03378651291131973,
0.027325641363859177,
-0.006567940581589937,
-0.0256100594997406,
-0.02522103674709797,
0.005826510488986969,
-0.009158289059996605,
-0.032122787088155746,
-0.011484591290354729,
0.017656806856393814,
0.08864989876747131,
-0.00024774979101493955,
0.02340100333094597,
-0.019271403551101685,
-0.05145817995071411,
0.10029695928096771,
-0.04911480098962784,
0.05992019176483154,
0.03316975757479668,
0.034693215042352676,
0.04063746705651283,
0.018357204273343086,
-0.01795506849884987,
0.03839218616485596,
0.03858375921845436,
-0.0028489609248936176,
-0.02809768356382847,
-0.04334638640284538,
-0.03791438415646553,
0.0075423819944262505,
-0.03768867999315262,
-0.02639106847345829,
0.018813151866197586,
-0.019611332565546036,
-0.03354693949222565,
-0.007037525065243244,
-0.02377273701131344,
-0.04020080715417862,
0.003930302802473307,
0.04695817828178406,
0.0011375523172318935,
0.023949459195137024,
0.03300100192427635,
-0.01675526425242424,
-0.009152112528681755,
0.016089117154479027,
0.022245388478040695,
-0.05894612893462181,
0.0016217465745285153,
0.016581950709223747,
0.017357535660266876,
-0.017769290134310722,
-0.0029307296499609947,
0.04049212858080864,
0.013607713393867016,
0.0022365283221006393,
0.051450081169605255,
-0.014422934502363205,
-0.05049668997526169,
0.0720045417547226,
-0.0009532820549793541,
-0.02901521511375904,
0.0308515727519989,
0.008365730755031109,
0.04305310547351837,
-0.01583699882030487,
-0.03187519311904907,
0.016246814280748367,
-0.03230012580752373,
0.011927091516554356,
0.0744497999548912,
0.006751920562237501,
0.011348244734108448,
-0.025506677106022835,
-0.005829752888530493,
-0.002142262412235141,
0.007191404700279236,
-0.05868557468056679,
0.0005269012763164937,
0.006506888195872307,
-0.020159276202321053,
-0.03533635288476944,
-0.040246352553367615,
0.0064515620470047,
-0.05646545812487602,
0.05113745480775833,
0.0915704295039177,
0.043831776827573776,
-0.028339656069874763,
0.018794408068060875,
-0.0483287014067173,
-0.06501764059066772,
0.01906452886760235,
0.027251455932855606,
-0.012075996026396751,
-0.015307971276342869,
0.017278151586651802,
0.0037277243100106716,
0.012375496327877045,
0.016791854053735733,
-0.002401015255600214,
0.04817618429660797,
-0.02708372287452221,
-0.08671242743730545,
-0.026349682360887527,
0.045328132808208466,
-0.004282335750758648,
-0.02720673382282257,
-0.05869626626372337,
0.04996632784605026,
0.01599317044019699,
0.07966513186693192,
0.015250727534294128,
0.039937201887369156,
-0.011700103059411049,
0.014963433146476746,
0.0005115375388413668,
-0.028022048994898796,
0.018003910779953003,
-0.013618916273117065,
-0.01875227876007557,
0.008239825256168842,
-0.04696216434240341,
0.004599310923367739,
-0.007809983100742102,
0.028355782851576805,
-0.03511372208595276,
0.06713724881410599,
0.005812658462673426,
0.014728733338415623,
0.010777967981994152,
0.009823205880820751,
-0.02679227665066719,
0.07929294556379318,
-0.03456909954547882,
-0.006989512592554092,
0.027824895456433296,
-0.028309684246778488,
0.005206928588449955,
0.022790120914578438,
0.04604513943195343,
0.03737301751971245,
-0.005145446863025427,
-0.020244775339961052,
-0.01104938518255949,
0.008076053112745285,
-0.01935044303536415,
-0.042137403041124344,
-0.01003499235957861,
0.017350587993860245,
0.0015602929051965475,
-0.014676199294626713,
0.019264914095401764,
-0.025960490107536316,
-0.03240072354674339,
0.009805267676711082,
-0.06794388592243195,
-0.010961981490254402,
-0.05853250250220299,
0.00906515121459961,
0.03945784270763397,
0.008977721445262432,
0.04701685532927513,
0.023870376870036125,
0.030166151002049446,
-0.07648972421884537,
-0.033693112432956696,
-0.05334582179784775,
0.017812397330999374,
0.0008330000564455986,
-0.0014477934455499053,
0.011735841631889343,
0.02064962312579155,
0.03693709522485733,
-0.00840809103101492,
0.06229158490896225,
-0.019832290709018707,
-0.022746210917830467,
0.029249293729662895,
-0.026998411864042282,
0.030427124351263046,
0.02829141356050968,
0.00518572423607111,
-0.00734947994351387,
-0.0018097010906785727,
-0.03879876807332039,
0.06081822142004967,
-0.0030969895888119936,
0.06994400173425674,
0.035395797342061996,
0.014608807861804962,
-0.03285600244998932,
0.015771571546792984,
-0.020680079236626625,
-0.004108228255063295,
-0.02406219020485878,
-0.01518433727324009,
-0.04067772254347801,
-0.016521820798516273,
0.04681168124079704,
0.061779286712408066,
-0.026730291545391083,
0.02814631722867489,
0.027179814875125885,
0.017547301948070526,
0.030962584540247917,
0.042892295867204666,
-0.02236766181886196,
-0.035520944744348526,
0.020551403984427452,
0.023374758660793304,
0.003439327934756875,
0.01224625762552023,
0.01715719886124134,
0.030232097953557968,
0.013268822804093361,
-0.0007875518058426678,
-0.051014430820941925,
-0.002610116731375456,
-0.06305208802223206,
-0.02022213116288185,
0.01594594307243824,
-0.02328674867749214,
0.041331443935632706,
-0.009531119838356972,
0.03527428209781647,
0.009910114109516144,
-0.013818996958434582,
-0.0008265237556770444,
0.0015861373394727707,
-0.009854190051555634,
0.02688843384385109,
0.018466057255864143,
-0.08100840449333191,
-0.03159402310848236,
0.017386477440595627,
-0.03726328909397125,
-0.011479230597615242,
-0.016975820064544678,
-0.02859879471361637,
-0.044222258031368256,
0.006019646767526865,
0.02147877961397171,
-0.003712316043674946,
0.013956455513834953,
-0.012473830953240395,
-0.05600248649716377,
0.05649835616350174,
-0.03182455897331238,
0.007554537616670132,
0.017822999507188797,
0.008114997297525406,
0.004220378585159779,
-0.023649802431464195,
-0.03402995690703392,
0.009301985614001751,
-0.006527876015752554,
0.048331622034311295,
-0.00184731709305197,
-0.027988923713564873,
-0.027128584682941437,
0.021468956023454666,
0.03410991281270981,
0.016069890931248665,
0.0038638280238956213,
0.011013787239789963,
0.028537657111883163,
-0.003912204410880804,
-0.022873984649777412,
-0.017348509281873703,
-0.007055419497191906,
-0.04447583481669426,
-0.017173027619719505,
0.020827218890190125,
0.016084201633930206,
-0.04276180639863014,
0.06006094068288803,
0.01099430676549673,
-0.04530021548271179,
0.013928473927080631,
-0.054297711700201035,
-0.023536598309874535,
0.028781471773982048,
0.013327712193131447,
0.05553123354911804,
-0.007621606811881065,
-0.040958765894174576,
0.0708913803100586,
0.01832270249724388,
-0.03215857595205307,
-0.002710969652980566,
-0.01459740661084652,
0.0033425551373511553,
-0.0009613153524696827,
0.0001244453014805913,
0.01258119661360979,
-0.01508992351591587,
0.019638728350400925,
0.029003867879509926,
0.0466495007276535,
0.031783100217580795,
0.024313058704137802,
0.002642018487676978,
0.006101688835769892,
0.011190583929419518,
0.005654127337038517,
0.034204188734292984,
-0.016982030123472214,
-0.019820155575871468,
-0.0003306368598714471,
0.004799592774361372,
0.03588106855750084,
-0.013201314024627209,
-0.03341275081038475,
0.03521887585520744,
0.021949540823698044,
0.013016819953918457,
-0.0025357306003570557,
0.03558098524808884,
0.008751876652240753,
-0.017686014994978905,
0.019122974947094917,
0.050232499837875366,
0.016918139532208443,
-0.0023711007088422775,
-0.00022541020007338375,
-0.01419889461249113,
0.0323636569082737,
-0.04705081507563591,
-0.00771889416500926,
0.004706753883510828,
-0.024705933406949043,
0.039991531521081924,
-0.018615789711475372,
-0.0015298131620511413,
0.02266470342874527,
0.015778053551912308,
-0.00036402506520971656,
-0.009987429715692997,
-0.014882327988743782,
0.026459719985723495,
-0.051327627152204514,
0.01298834290355444,
-0.0009365737205371261,
0.03244202211499214,
0.01618620567023754,
0.00644433218985796,
0.0010212110355496407,
0.021290961652994156,
0.025854069739580154,
-0.019639410078525543,
-0.0898246020078659,
-0.02425205335021019,
-0.05402511730790138,
0.03070003166794777,
-0.019997982308268547,
-0.027762075886130333,
0.017021648585796356,
0.021631069481372833,
-0.04722782224416733,
-0.03763841465115547,
-0.010072431527078152,
-0.06746097654104233,
0.022263474762439728,
-0.027420785278081894,
-0.0045022484846413136,
-0.013488809578120708,
-0.006159636192023754,
0.05058429017663002,
-0.02298915386199951,
0.0032857689075171947,
0.030574863776564598,
-0.038266051560640335,
-0.02430029772222042,
-0.016745692119002342,
0.0438467338681221,
-0.004532477352768183,
0.035642147064208984,
0.03395869582891464,
0.02431182935833931,
-0.026169052347540855,
-0.0056606135331094265,
0.011867360211908817,
0.04891333729028702,
-0.01203132700175047,
-0.0021531125530600548,
-0.0009363552089780569,
-0.06461869925260544,
-0.002074495190754533,
-0.012406118214130402,
0.07276498526334763,
0.019170327112078667,
-0.019755307585000992,
0.0362434908747673,
-0.008483614772558212,
-0.037141915410757065,
0.042216043919324875,
0.04623808711767197,
-0.004205905366688967,
-0.04771117866039276,
-0.053041622042655945,
-0.015342723578214645,
-0.019567659124732018,
-0.0037401248700916767,
0.02950473129749298,
-0.040885087102651596,
-0.003638739697635174,
0.008595204912126064,
0.045915111899375916,
-0.013752209022641182,
-0.04887840896844864,
0.019774144515395164,
-0.036993447691202164,
-0.020707063376903534,
-0.014330164529383183,
-0.016640787944197655,
0.0012437354307621717,
0.043950196355581284,
0.03562713414430618,
0.01556712482124567,
-0.005494685843586922,
-0.06270046532154083,
0.024752119556069374,
0.051414813846349716,
0.02580282837152481,
0.014161849394440651,
0.0072021326050162315,
-0.03184422105550766,
-0.011677305214107037,
0.07162445783615112,
0.020787255838513374,
0.03191474452614784,
-0.0188875962048769,
-0.02061827853322029,
-0.0331733264029026,
0.007991575635969639,
0.019666587933897972,
-0.02114253304898739,
0.012312307953834534,
-0.002152443863451481,
-0.01267219427973032,
0.01849188096821308,
-0.010816382244229317,
0.041736386716365814,
0.001418690662831068,
0.03366595134139061,
0.06517842411994934,
0.036439795047044754,
0.007597755640745163,
0.01758785918354988,
-0.01986038312315941,
-0.04717739671468735,
0.015742385759949684,
0.007694209925830364,
-0.006129151210188866,
0.05394544452428818,
-0.02321249432861805,
-0.04656629264354706,
0.006937277037650347,
0.02364770695567131,
-0.004720785189419985,
0.00048597523709759116,
-0.046707168221473694,
0.012589708901941776,
0.011776376515626907,
-0.01367957890033722,
0.017503369599580765,
0.02814183570444584,
0.02842249535024166,
-0.0038614189252257347,
-0.01895698718726635,
0.06668157875537872,
-0.011723955161869526,
-0.004744243808090687,
0.001034439424984157,
-0.014902448281645775,
-0.010068243369460106,
0.030963463708758354,
-0.045968662947416306,
0.03233138844370842,
-0.0031964259687811136,
-0.04019513353705406,
-0.0030978627037256956,
0.02596024051308632,
0.03840035945177078,
-0.015857281163334846,
-0.004496872890740633,
-0.0020065181888639927,
0.002562898676842451,
-0.016296502202749252,
0.012027150951325893,
-0.015293799340724945,
-0.014833841472864151,
0.035652074962854385,
-0.02616100199520588,
-0.00591809069737792,
-0.04897037893533707,
0.038248494267463684,
-0.001446354202926159,
-0.04019240289926529,
0.04390314593911171,
-0.008685535751283169,
-0.003639694768935442,
-0.014574634842574596,
-0.034516554325819016,
-0.028201939538121223,
-0.02091761864721775,
-0.03139430657029152,
0.016821647062897682,
-0.03418632596731186,
0.0237259641289711,
0.01982388086616993,
0.010785864666104317,
-0.10007916390895844,
-0.059100888669490814,
-0.00989450141787529,
0.027438657358288765,
-0.032301533967256546,
-0.017974916845560074,
-0.022789930924773216,
-0.029872121289372444,
-0.0068931556306779385,
0.0013165154960006475,
0.039635445922613144,
-0.02092650905251503,
-0.017844093963503838,
0.011004336178302765,
0.049836691468954086,
0.05208704248070717,
0.0031005842611193657,
-0.03759092837572098,
0.017884425818920135,
0.001525802887044847,
-0.003203779924660921,
-0.023321062326431274,
-0.008671791292726994,
-0.007344390265643597,
0.018396027386188507,
0.01350580807775259,
-0.00809809286147356,
0.023443792015314102,
-0.067844919860363,
0.014096410945057869,
0.03230876475572586,
-0.021743878722190857,
0.03878473490476608,
-0.05705616623163223,
-0.007754041813313961,
-0.030033662915229797,
0.0049773575738072395,
-0.03589930012822151,
-0.00584038719534874,
0.005356031935662031,
-0.048829302191734314,
0.05105568841099739,
0.014697461389005184,
0.03878694027662277,
0.005330703686922789,
0.03824494034051895,
-0.003391214180737734,
-0.03145802766084671,
0.016686679795384407,
-0.05199706181883812,
-0.057946108281612396,
-0.020222142338752747,
0.028603095561265945,
0.021817492321133614,
0.02800021320581436,
-0.04278726503252983,
-0.06570600718259811,
-0.013857140205800533,
0.04239051416516304,
0.04523266479372978,
-0.026875900104641914,
0.03806367516517639,
0.02719610556960106,
-0.01969660259783268,
-0.0020055233035236597,
0.016412824392318726,
-0.019568756222724915,
0.04865832254290581,
-0.022667227312922478,
0.058577973395586014,
-0.02797326259315014,
0.009718495421111584,
0.002810698002576828,
0.04042365401983261,
-0.038269829005002975,
0.017453821375966072,
0.018653249368071556,
-0.0038770621176809072,
0.032435037195682526,
0.014839674346148968,
-0.030177148059010506,
0.08954644948244095,
-0.05673598125576973,
0.01860060542821884,
-0.0053082918748259544,
-0.03091428056359291,
0.005581325385719538,
0.0041708690114319324,
0.011285955086350441,
0.012230238877236843,
-0.028873594477772713,
-0.008942107670009136,
0.027584727853536606,
0.028706882148981094,
0.05552278086543083,
0.014271441847085953,
0.012910513207316399,
0.014028633944690228,
0.02183467149734497,
0.02582879178225994,
0.021931733936071396,
-0.047367241233587265,
-0.046738676726818085,
-0.04473070427775383,
-0.03666028380393982,
0.02893461473286152,
0.04446869716048241,
-0.02653714455664158,
-0.02686956338584423,
-0.04806353896856308,
0.020807061344385147,
0.012253508903086185,
0.039507631212472916,
-0.005629457999020815,
0.04151370748877525,
-0.008417152799665928,
0.03952214866876602,
-0.0008016157662495971,
0.028017446398735046,
0.08981901407241821,
0.10055815428495407,
-0.011989587917923927,
-0.11647635698318481,
0.02178926020860672,
-0.008626176975667477,
0.016391698271036148,
-0.07644922286272049,
0.0184396430850029,
-0.025821685791015625,
0.01972982846200466,
-0.009007738903164864,
0.09833217412233353,
0.003561648540198803,
0.005925952456891537,
0.04852481931447983,
-0.02944544143974781,
-0.034418001770973206,
-0.0037217282224446535,
0.022321786731481552,
-0.02948238141834736,
-0.011281943880021572,
-0.038650624454021454,
0.04107958450913429,
0.01434432715177536,
0.005187155678868294,
-0.03000144474208355,
0.01260385476052761,
0.01420489139854908,
0.02155689150094986,
-0.04928518459200859,
-0.04238563030958176,
0.0060709682293236256,
-0.015627659857273102,
-0.010661914013326168,
-0.015906300395727158,
-0.00020626875630114228,
0.02103404887020588,
0.020002814009785652,
0.039782822132110596,
0.004614789038896561,
-0.00009676624176790938,
-0.003402263857424259,
0.05810549855232239,
-0.008589605800807476,
-0.03183645382523537,
-0.010205235332250595,
0.018679074943065643,
-0.030606452375650406,
0.02352590300142765,
0.018410280346870422,
0.018673621118068695,
0.0037224539555609226,
-0.0178298931568861,
0.009233498945832253,
-0.028622595593333244,
0.04043025150895119,
-0.023978393524885178,
-0.019627436995506287,
0.0082316305488348,
0.036799006164073944,
-0.029061883687973022,
0.024486089125275612,
-0.031266216188669205,
-0.042350832372903824,
-0.013401562348008156,
-0.03488573059439659,
-0.020993590354919434,
-0.010112976655364037,
-0.053195320069789886,
-0.04115724563598633,
0.029040265828371048,
-0.020050058141350746,
-0.040550850331783295,
-0.0074496944434940815,
0.030076801776885986,
0.057047005742788315,
0.024020133540034294,
-0.05094357207417488,
0.010910911485552788,
-0.01889737881720066,
-0.015318023972213268,
-0.026374608278274536,
0.00702910590916872,
-0.0010539722861722112,
-0.0013845264911651611,
0.0018896128749474883,
0.027496524155139923,
-0.016981512308120728,
0.0009390199556946754,
-0.05059810355305672,
0.024237846955657005,
0.02714839205145836,
-0.01949438638985157,
0.004696658346801996,
0.006399837322533131,
-0.06481615453958511,
0.009563646279275417,
-0.0153775904327631,
0.01793004758656025,
0.020789042115211487,
-0.006500604096800089,
0.037467941641807556,
0.02948041819036007,
-0.021886203438043594,
-0.00621039466932416,
0.03237354755401611,
-0.029658673331141472,
0.031399816274642944,
0.012082228437066078,
0.0034629160072654486,
-0.01924973912537098,
-0.06736016273498535,
-0.027105750516057014,
-0.0064116064459085464,
0.005768948700278997,
0.026854032650589943,
0.008534194901585579,
-0.0014664538903161883,
-0.010560628958046436,
-0.005631952080875635,
-0.030059481039643288,
-0.054707761853933334,
-0.03927665576338768,
0.0011792397126555443,
0.004594952333718538,
0.0034490746911615133,
-0.0019078694749623537,
0.021933142095804214,
-0.007272007409483194,
-0.046529341489076614,
-0.009942886419594288,
0.03872246667742729,
-0.05435923859477043,
0.003326872130855918,
-0.005255920812487602,
0.026237817481160164,
0.0190195944160223,
-0.025808144360780716,
-0.055361345410346985,
0.046521078795194626,
-0.029959749430418015,
-0.06678695976734161,
0.00671800272539258,
-0.005428520031273365,
0.008184483274817467,
0.05111394822597504,
-0.014234169386327267,
-0.055733323097229004,
0.058233682066202164,
-0.018564371392130852,
0.0007008183165453374,
-0.003683897666633129,
0.0035283127799630165,
-0.037306852638721466,
0.00019757624249905348,
0.0015714935725554824,
-0.018068941310048103,
0.012781867757439613,
-0.018236856907606125,
0.022762851789593697,
0.018735535442829132,
-0.04255590960383415,
0.007394193205982447,
-0.030033722519874573,
0.029131293296813965,
0.035655491054058075,
0.028075825423002243,
0.003560183336958289,
0.06603606045246124,
-0.014166491106152534,
0.014862908981740475,
0.011892192997038364,
0.00014699366874992847,
-0.11842901259660721,
0.004425723105669022,
0.006226217839866877,
0.008716663345694542,
0.027316490188241005,
-0.07787885516881943,
0.01758887618780136,
0.044127169996500015,
-0.084483802318573,
0.01936507597565651,
-0.03675437718629837,
-0.05708303302526474,
-0.061833564192056656,
-0.014712626114487648,
0.016779756173491478,
0.0604836642742157,
0.05611685663461685,
0.04527433216571808,
-0.00014473489136435091,
0.010267075151205063,
-0.032866135239601135,
0.004404175095260143,
0.01191173680126667,
0.019824281334877014,
0.007494960445910692,
-0.021525733172893524,
0.018941791728138924,
-0.0054512848146259785,
-0.010566511191427708,
0.016804978251457214,
0.003122575581073761,
-0.018024152144789696,
0.01471557468175888,
0.027903368696570396,
0.0045409612357616425,
0.023521631956100464,
0.030798211693763733,
-0.017942670732736588,
0.011908963322639465,
0.004728316329419613,
0.01908302865922451,
0.005025856196880341,
-0.04208450764417648,
0.019223693758249283,
0.03986644372344017,
-0.028586750850081444,
-0.013281493447721004,
0.04718281328678131,
-0.016115635633468628,
-0.0009196826140396297,
-0.02478558011353016,
-0.027428464964032173,
0.04058653861284256,
-0.03486322984099388,
0.04694550484418869,
-0.0333373062312603,
-0.01470582652837038,
0.028122445568442345,
0.004049502778798342,
-0.012247670441865921,
0.048640813678503036,
-0.0006044432520866394,
-0.01758456788957119,
0.011521008796989918,
0.01695815660059452,
0.017097393050789833,
-0.047886013984680176,
0.0011346270330250263,
-0.03126123547554016,
0.01055692695081234,
0.005339100956916809,
-0.05086104944348335,
-0.04224991798400879,
0.0240959320217371,
0.018016817048192024,
0.03592965379357338,
-0.004202218726277351,
-0.02757355011999607,
-0.015010462142527103,
-0.07561933249235153,
0.023639004677534103,
-0.002408338710665703,
0.006997192744165659,
-0.012973170727491379,
0.001903059659525752,
0.008931075222790241,
0.0015717874048277736,
0.07258982956409454,
-0.005474230274558067,
0.016950059682130814,
-0.0014593340456485748,
0.04331796243786812,
0.0012421350693330169,
-0.017638392746448517,
-0.04495533928275108,
-0.0027172034606337547,
-0.036979541182518005,
-0.014892899431288242,
-0.014386673457920551,
-0.013011286966502666,
0.024720899760723114,
0.027672799304127693,
0.021926671266555786,
-0.0019445389043539762,
0.029336437582969666,
-0.07214470952749252,
0.05574340000748634,
-0.0004082986561115831,
-0.016749626025557518,
0.0754951760172844,
-0.03278220072388649,
-0.005864702630788088,
0.01273395400494337,
-0.0014149030903354287,
-0.006736752111464739,
0.048427172005176544,
-0.02852284163236618,
0.015827691182494164,
-0.029090018942952156,
0.010034793987870216,
-0.0006984503124840558,
0.005011494737118483,
0.017432987689971924,
0.06664478033781052,
-0.05519407242536545,
0.0033587238285690546,
0.03468460962176323,
0.007319023832678795,
0.017886346206068993,
-0.0041096326895058155,
-0.025185899809002876,
0.023646196350455284,
0.038295991718769073,
0.03964197263121605,
0.02917851321399212,
0.0386359840631485,
0.012763825245201588,
0.011241951026022434,
0.024422537535429,
-0.033186618238687515,
-0.0015564864734187722,
-0.01030457392334938,
0.0475042499601841,
-0.03290894255042076,
-0.027744250372052193,
0.0008173323003575206,
-0.028533991426229477,
0.020677244290709496,
0.061445727944374084,
-0.03909650817513466,
0.07590772956609726,
-0.046053696423769,
0.009406305849552155,
-0.013735797256231308,
-0.014986282214522362,
-0.015160389244556427,
0.024957720190286636,
-0.006201192736625671,
0.044829439371824265,
-0.01310653891414404,
0.01492856815457344,
0.0034133854787796736,
-0.013847306370735168,
0.014031580649316311,
-0.035862602293491364,
0.02387421205639839,
-0.008716416545212269,
0.026087159290909767,
-0.006295148283243179,
-0.019255083054304123,
-0.0250766072422266,
0.004436502233147621,
0.024047933518886566,
0.029713669791817665,
0.03972038999199867,
-0.0044479514472186565,
-0.02143274061381817,
-0.014762519858777523,
0.035557668656110764,
-0.049571167677640915,
-0.00978930201381445,
-0.04151222109794617,
-0.005088134668767452,
-0.008789504878222942,
0.014088627882301807
] |
<p>I am working on the Dirac equation on curved spacetime. A Foldy-Wouthuysen transformation was applied to obtain the semiclassical limit of the equation to study the dynamics of the spin of the electron in curved spacetime. </p>
<p>In the semiclassical limit up to order $\hbar$ the Hamiltonian then takes a familiar form: </p>
<p>$H =\; ... \,+\, \hbar \, \Sigma \cdot \, \Omega^{(1)}$,</p>
<p>where $\Sigma$ is the spin vector and $\Omega$ is the precession frequency due to gravitational effects. If I look closer to $\Omega$, I find that it contains the metric $g_{\mu \nu}(x)$ and its first derivatives $\partial_\lambda g_{\mu\nu}$. </p>
<p>As far as I understand, one can always find an appropriate coordinate system in which the first derivatives of the metric can be made vanish at a certain point $x$ (so called normal coordinates). To my knowledge, this is actually good because the principle of equivalence states that gravitational effects (in this case the spin precession of the electron) must be able to be set zero at <em>one point</em>. </p>
<p><strong>Q1</strong>: The Dirac equation is certainly a local theory. Therefore, should gravitational effects only appear as fictitious forces? (Should they only contain first derivatives of the metric)?</p>
<p>Now I calculated the semiclassical limit to an higher order $\hbar^2$ (I did this by evaluating the commutators in $\Omega^{(1)}$ to a higher precision.). The Hamiltonain looks like this:</p>
<p>$H =\; ... \,+\, \hbar \, \Sigma \cdot \, \Omega^{(1)} \; + \hbar^2 \, \Sigma \cdot \, \Omega^{(2)}$</p>
<p>Looking at $\Omega^{(2)}$, I find <strong><em>second derivatives of the metric</em>.</strong> This is a bit more confusing to me, since the Riemann curvature tensor is made of second derivatives and since curvature is the "objective ingredient" in general relativity, there exists no coordinate system in which curvature effects can be "gauged away". </p>
<p><strong>Q2</strong>: Is the appearance of these second derivative terms problematic in any way? Do they mean that the principle of equivalence could be violated here (even if only at the order $\hbar^2$)?</p>
<p>This is my ongoing research so any input would be very welcome.</p>
<p><em>This is my first post. Please excuse me, if my question is not asked optimally.</em></p>
| 8,867 |
[
-0.029343880712985992,
-0.012878035195171833,
0.03983993083238602,
-0.03505390137434006,
0.022330498322844505,
0.020923903211951256,
-0.057994212955236435,
-0.04026801884174347,
0.014585111290216446,
-0.06295808404684067,
0.008443141356110573,
0.008886747993528843,
0.06627602875232697,
0.019655756652355194,
0.032389990985393524,
0.005112724378705025,
-0.009142938069999218,
0.01066136360168457,
-0.027068577706813812,
-0.005974086467176676,
0.004356329794973135,
0.015214541926980019,
-0.003243654267862439,
-0.010068586096167564,
0.015164528973400593,
-0.03443019837141037,
-0.015083779580891132,
-0.01517335046082735,
-0.019508924335241318,
0.04847463592886925,
-0.026069939136505127,
-0.023329492658376694,
0.0011595163960009813,
0.03077060915529728,
0.024641970172524452,
0.0323992557823658,
-0.019384846091270447,
-0.04018926993012428,
0.03270595148205757,
-0.000694472691975534,
-0.0610668808221817,
-0.021362705156207085,
-0.008428467437624931,
0.06198194995522499,
-0.013445510528981686,
0.022918175905942917,
0.013079190626740456,
0.0093400739133358,
0.06191219761967659,
-0.022376174107193947,
0.058119311928749084,
0.012965565547347069,
0.01063639484345913,
0.020507557317614555,
-0.04510404169559479,
-0.02646210417151451,
0.06072019785642624,
0.0324484184384346,
-0.017935536801815033,
-0.041365042328834534,
-0.017637070268392563,
-0.023391757160425186,
-0.012267425656318665,
-0.025757860392332077,
-0.021305402740836143,
0.05703815817832947,
0.033999912440776825,
-0.038920413702726364,
0.016038205474615097,
-0.017091069370508194,
0.008137224242091179,
-0.018283125013113022,
-0.014420273713767529,
-0.04209624230861664,
0.01162609551101923,
-0.011799909174442291,
-0.00231484929099679,
-0.010690669529139996,
0.029193978756666183,
0.005021073389798403,
-0.011227395385503769,
0.024349123239517212,
0.03680920600891113,
0.02582242712378502,
-0.01082681491971016,
-0.01408278476446867,
0.0505540668964386,
0.01888032630085945,
0.024207640439271927,
0.06166709586977959,
0.001146450056694448,
0.02490035444498062,
0.04034338518977165,
-0.06180013716220856,
-0.028081580996513367,
0.07818978279829025,
0.00695990351960063,
0.047937531024217606,
-0.019733358174562454,
-0.020603064447641373,
-0.01976434513926506,
-0.07050661742687225,
0.004586820024996996,
0.07127750664949417,
0.025071490556001663,
-0.01787923462688923,
-0.023623555898666382,
0.023741351440548897,
-0.03987659141421318,
-0.028192143887281418,
-0.01830524019896984,
-0.004982947837561369,
-0.032979682087898254,
-0.020334575325250626,
-0.002265969756990671,
-0.026882274076342583,
0.005795592442154884,
-0.030579103156924248,
0.0277969092130661,
0.05592328682541847,
0.02863771840929985,
-0.032599326223134995,
-0.009253173135221004,
-0.05289063602685928,
-0.049224141985177994,
0.01639690436422825,
0.06526777893304825,
-0.0016541306395083666,
-0.03166159242391586,
-0.02841073088347912,
0.04629382863640785,
0.0013411695836111903,
0.014500146731734276,
0.03811277076601982,
-0.0011325201485306025,
-0.0068979221396148205,
-0.10202119499444962,
-0.03685213625431061,
0.017199184745550156,
0.020105818286538124,
0.033965397626161575,
-0.07622246444225311,
0.010722333565354347,
0.03833133354783058,
0.07473954558372498,
0.0042401463724672794,
0.03141295164823532,
-0.013244323432445526,
0.022206993773579597,
0.013403156772255898,
-0.00874422024935484,
-0.04338238388299942,
0.015449524857103825,
-0.03603803738951683,
-0.04811396822333336,
-0.05293988436460495,
0.004127426538616419,
0.0016911932034417987,
0.05291958898305893,
-0.017025025561451912,
0.09707436710596085,
-0.0324351042509079,
0.0003732879413291812,
-0.02107243239879608,
0.008702383376657963,
-0.050933338701725006,
0.043610505759716034,
0.014997252263128757,
-0.006985859479755163,
0.028615551069378853,
-0.01664457470178604,
0.03171146661043167,
-0.00964948907494545,
0.004893816541880369,
0.02238285355269909,
-0.05803920701146126,
-0.015515981242060661,
-0.020635385066270828,
-0.018882937729358673,
0.001467373687773943,
-0.02906186506152153,
-0.02258596196770668,
-0.021971577778458595,
0.013397837989032269,
-0.004887067247182131,
0.023027699440717697,
0.0013380651362240314,
0.01639721915125847,
-0.009028037078678608,
-0.04088449850678444,
0.017941487953066826,
-0.07828269153833389,
-0.01125408336520195,
-0.019244875758886337,
-0.019509512931108475,
0.018337475135922432,
0.01171966828405857,
-0.001957574160769582,
-0.012466155923902988,
-0.03866882622241974,
0.0006382873398251832,
0.04437794163823128,
0.009242163971066475,
-0.016640467569231987,
0.014377380721271038,
0.036797404289245605,
0.03203081339597702,
0.03432634100317955,
0.029626255854964256,
0.013019314967095852,
-0.055163413286209106,
0.03271159529685974,
-0.007341420743614435,
0.034991174936294556,
0.0016334456158801913,
0.028698602691292763,
-0.002986991312354803,
-0.041486695408821106,
-0.010545398108661175,
0.01560984831303358,
-0.0611824169754982,
0.07027831673622131,
0.042109258472919464,
-0.04311518371105194,
0.039834242314100266,
0.04865650087594986,
0.012798327021300793,
0.016341369599103928,
0.023625683039426804,
-0.0239737406373024,
-0.04323452338576317,
0.009203171357512474,
0.04410254582762718,
0.059585750102996826,
-0.03429243713617325,
0.004026501905173063,
0.0028219767846167088,
0.04222869500517845,
0.039762429893016815,
0.009154760278761387,
-0.01775873638689518,
-0.041844096034765244,
0.04226384684443474,
-0.011793860234320164,
0.018235862255096436,
0.03975032642483711,
0.051625918596982956,
0.01903548464179039,
0.011296257376670837,
0.005586031824350357,
-0.02500099688768387,
0.05368943512439728,
-0.04168581962585449,
0.012594633735716343,
0.00460489746183157,
-0.02688102424144745,
0.08050035685300827,
-0.00035632913932204247,
0.027232427150011063,
0.02830819971859455,
-0.02785804681479931,
-0.0024834838695824146,
-0.032396625727415085,
0.007274634204804897,
0.017519991844892502,
0.0033912102226167917,
-0.012364455498754978,
-0.02923586405813694,
0.004599380772560835,
-0.07317734509706497,
-0.009272945113480091,
-0.05285801365971565,
-0.022635001689195633,
0.02198188006877899,
0.012051678262650967,
0.01652275212109089,
0.06046466901898384,
0.029381681233644485,
-0.0015791233163326979,
-0.04204380139708519,
0.020405201241374016,
-0.01757899299263954,
0.00323860882781446,
0.04796953499317169,
-0.04998764768242836,
-0.0005360086797736585,
-0.06402556598186493,
-0.014415662735700607,
0.056909650564193726,
0.01225894782692194,
0.03907521069049835,
0.016270894557237625,
-0.02066938206553459,
-0.030528170987963676,
-0.04355070739984512,
-0.03255729004740715,
0.00725689297541976,
-0.03740585595369339,
-0.0044990768656134605,
0.04813888296484947,
0.030397167429327965,
-0.0027448241598904133,
0.016261642798781395,
0.019975721836090088,
-0.05796787887811661,
0.011628315784037113,
-0.005030267406255007,
-0.008232830092310905,
-0.022042283788323402,
0.015691764652729034,
0.025635847821831703,
-0.020100140944123268,
-0.02033112198114395,
-0.04368670657277107,
-0.0376862995326519,
0.041747983545064926,
-0.028973402455449104,
0.029931431636214256,
-0.027522217482328415,
-0.034003838896751404,
0.0901753380894661,
0.005072855390608311,
0.016395358368754387,
-0.025531133636832237,
0.015782222151756287,
0.010780712589621544,
-0.019215067848563194,
-0.025120116770267487,
-0.013288265094161034,
0.026975927874445915,
0.019398726522922516,
0.04908617213368416,
0.015905875712633133,
0.01792393997311592,
-0.0010702150175347924,
-0.024870678782463074,
0.027194593101739883,
-0.0049676839262247086,
-0.00215497356839478,
0.0640612319111824,
0.027946362271904945,
-0.007004172075539827,
0.007859764620661736,
0.006785213947296143,
0.015417193993926048,
0.012295931577682495,
-0.03784317895770073,
0.04331964626908302,
-0.008610264398157597,
-0.002236553467810154,
0.013967310078442097,
0.03579289838671684,
-0.0011084210127592087,
-0.04956940934062004,
-0.016074111685156822,
-0.010739079676568508,
0.04068145528435707,
-0.0017657881835475564,
0.0051295398734509945,
0.0333019495010376,
0.03921707719564438,
-0.0373145155608654,
0.01037496980279684,
0.020962143316864967,
-0.015235094353556633,
0.03460980951786041,
-0.032947830855846405,
-0.011461432091891766,
0.0031904762145131826,
0.05865562707185745,
0.04376101866364479,
-0.01779666543006897,
-0.03472791239619255,
-0.01581592485308647,
-0.044701602309942245,
0.02832801267504692,
0.009917289018630981,
0.05648956447839737,
0.0010457946918904781,
0.041682034730911255,
0.034332603216171265,
0.0391109324991703,
-0.005123469978570938,
-0.019054947420954704,
-0.06205548346042633,
0.0063558011315763,
-0.02835659310221672,
-0.026561973616480827,
0.0040477872826159,
-0.008807666599750519,
-0.0076447720639407635,
-0.01892027072608471,
-0.013024663552641869,
-0.040364716202020645,
-0.015387511812150478,
-0.03596553951501846,
0.023764198645949364,
-0.07670184224843979,
-0.04436706006526947,
-0.03681971877813339,
0.05194411799311638,
0.03598038852214813,
0.013612997718155384,
-0.01400796603411436,
0.018977664411067963,
-0.03702571988105774,
0.009556830860674381,
-0.03911025822162628,
0.00982517097145319,
0.016033044084906578,
0.014618889428675175,
0.04187396168708801,
0.004544041585177183,
-0.012971717864274979,
-0.00796786230057478,
0.056168846786022186,
0.08114250004291534,
0.03581785410642624,
-0.01609455980360508,
0.0015184214571490884,
-0.03746470436453819,
-0.004909837152808905,
-0.0018942274618893862,
0.08980128169059753,
0.007645795587450266,
0.008362768217921257,
0.021841637790203094,
-0.003734247526153922,
0.0035626604221761227,
0.019818376749753952,
0.038469668477773666,
0.0051041399128735065,
-0.05815228819847107,
-0.05166994407773018,
-0.022036563605070114,
-0.020831095054745674,
0.031173953786492348,
-0.015242824330925941,
-0.024055443704128265,
-0.046972133219242096,
-0.0023568065371364355,
0.015573174692690372,
0.0603625550866127,
-0.02795686572790146,
0.019597753882408142,
-0.018729127943515778,
0.023270491510629654,
0.007780053652822971,
0.013407712802290916,
-0.016086390241980553,
0.050014253705739975,
0.06736965477466583,
-0.04830147698521614,
0.021812699735164642,
-0.06762019544839859,
0.000183646465302445,
0.02620949037373066,
0.03260710462927818,
0.020976802334189415,
-0.021156173199415207,
-0.059958141297101974,
0.026106545701622963,
0.015390640124678612,
-0.005104436539113522,
0.030199723318219185,
0.030566440895199776,
0.01046655885875225,
-0.018099689856171608,
-0.04632485285401344,
-0.053782135248184204,
0.02703166753053665,
-0.020625468343496323,
0.0056811184622347355,
-0.056008901447057724,
0.027952365577220917,
-0.04556555300951004,
0.01852334663271904,
-0.0019545787945389748,
0.03994695469737053,
0.03442369028925896,
-0.0006637206533923745,
0.004023249261081219,
0.004142774734646082,
-0.01757633313536644,
-0.09360825270414352,
-0.01797354593873024,
0.02337602898478508,
-0.022212181240320206,
0.07073211669921875,
-0.016235049813985825,
-0.04328186810016632,
0.0469447560608387,
0.008257094770669937,
0.018266865983605385,
0.03284386917948723,
-0.0251736082136631,
0.042638737708330154,
0.026532869786024094,
-0.004144804086536169,
0.013784117996692657,
-0.0018189367838203907,
-0.01868230476975441,
-0.008133389055728912,
-0.011775159277021885,
-0.005952891428023577,
-0.046331316232681274,
-0.000001050647711053898,
-0.050434280186891556,
0.0004529769066721201,
-0.030729560181498528,
0.017277374863624573,
-0.008923336863517761,
0.02819802425801754,
0.0017059979727491736,
-0.06412848085165024,
0.008456327952444553,
0.04427134990692139,
-0.0010488501284271479,
-0.014787958934903145,
-0.02381995879113674,
0.03751571103930473,
0.00258763344027102,
-0.016830671578645706,
-0.023661047220230103,
-0.0067114620469510555,
-0.007009880151599646,
0.04882837459445,
-0.019922610372304916,
0.0330670103430748,
0.023975273594260216,
-0.0023691346868872643,
0.015236894600093365,
-0.03568748012185097,
0.029901187866926193,
-0.0018535368144512177,
-0.031614094972610474,
0.04592214897274971,
-0.019676970317959785,
-0.0072578685358166695,
0.045289404690265656,
-0.01123370137065649,
-0.04154667630791664,
-0.02625420317053795,
-0.02362913265824318,
0.0623207725584507,
0.032920192927122116,
-0.07480188459157944,
-0.028675135225057602,
0.014463226310908794,
-0.01459334883838892,
-0.025245051831007004,
0.007633826695382595,
0.02158556692302227,
-0.0483706071972847,
-0.018291858956217766,
0.035759493708610535,
0.022752458229660988,
-0.020667895674705505,
-0.000050205162551719695,
0.007471426390111446,
0.030430004000663757,
0.03559907153248787,
-0.01653498038649559,
-0.019337117671966553,
0.01420511119067669,
-0.02471141144633293,
0.005553046241402626,
0.015573389828205109,
0.04743525758385658,
-0.01242558192461729,
-0.02109728381037712,
-0.01879318617284298,
-0.01059570163488388,
0.01854475401341915,
0.00992249883711338,
-0.034592099487781525,
0.05251529440283775,
0.026121344417333603,
-0.03465742990374565,
-0.02868027426302433,
-0.02007540687918663,
-0.021938355639576912,
0.02785305678844452,
-0.01276212278753519,
0.02269021049141884,
-0.03215020149946213,
-0.04291148856282234,
0.02032654546201229,
0.01148481946438551,
-0.009919432923197746,
0.014254209585487843,
0.06259607523679733,
0.007043639663606882,
-0.029967542737722397,
0.017333613708615303,
-0.026156237348914146,
0.007490057498216629,
0.01948126032948494,
-0.010870249941945076,
0.03316287696361542,
-0.015687929466366768,
-0.005762143060564995,
-0.04647905007004738,
-0.03046170249581337,
0.019423771649599075,
0.09194936603307724,
0.024177847430109978,
0.00531709985807538,
0.018284253776073456,
0.012646403163671494,
-0.04003230854868889,
-0.008559138514101505,
-0.015227623283863068,
0.019826699048280716,
0.0024886990431696177,
0.03235736861824989,
-0.03655815124511719,
-0.008526488207280636,
0.014814473688602448,
0.04219095781445503,
-0.04231177270412445,
-0.024546844884753227,
0.03064415231347084,
0.0012946900678798556,
0.015322111546993256,
-0.04438523203134537,
-0.03917964920401573,
0.03922281786799431,
-0.005474492441862822,
0.06599921733140945,
0.010542190633714199,
-0.003285870887339115,
0.006883201189339161,
0.04375592991709709,
0.030891280621290207,
-0.00036943837767466903,
-0.05497876927256584,
-0.008209673687815666,
0.018149474635720253,
0.013838286511600018,
-0.006580059416592121,
0.006106155458837748,
0.00832576584070921,
0.0729125589132309,
0.0039209104143083096,
0.049825072288513184,
-0.009593946859240532,
-0.05276155471801758,
0.028756041079759598,
-0.05608976632356644,
-0.05448368564248085,
0.08416339755058289,
-0.0055391849018633366,
-0.03500709682703018,
0.01273051556199789,
-0.021852338686585426,
0.03669692575931549,
0.03186418116092682,
0.010915112681686878,
0.002671321388334036,
0.07078718394041061,
-0.03439226746559143,
-0.03553403913974762,
-0.0021752179600298405,
-0.03349187225103378,
0.12178084254264832,
0.04102925956249237,
-0.00507744774222374,
-0.02802400104701519,
0.006633333396166563,
0.03992544114589691,
0.017834629863500595,
0.0003425847680773586,
0.01818900555372238,
-0.0031239348463714123,
-0.019330067560076714,
0.0010163479018956423,
0.020438814535737038,
-0.01262902282178402,
-0.01232591550797224,
0.04379385709762573,
-0.05837852135300636,
-0.02599312923848629,
-0.006895088590681553,
0.003169294912368059,
0.002074990887194872,
-0.00790698267519474,
-0.02067887783050537,
0.03571595624089241,
-0.03196876868605614,
0.025535758584737778,
-0.03237729147076607,
-0.006051453296095133,
-0.003842093050479889,
-0.040372271090745926,
-0.06564749032258987,
0.0067335935309529305,
-0.02589385211467743,
-0.036615774035453796,
-0.024406174197793007,
0.0016782756429165602,
0.03449985757470131,
-0.01220235787332058,
0.04751613736152649,
0.019743388518691063,
-0.03865181654691696,
0.016851162537932396,
0.019703004509210587,
0.07305669784545898,
-0.0318894200026989,
0.005777581594884396,
-0.0076897237449884415,
0.06812186539173126,
0.0019356601405888796,
-0.016285426914691925,
0.02973007783293724,
-0.031055256724357605,
0.022517094388604164,
-0.025217801332473755,
0.019566690549254417,
-0.035017210990190506,
-0.0007670574705116451,
0.016954950988292694,
-0.01619177870452404,
-0.03317113593220711,
0.0478338822722435,
0.041927520185709,
-0.018351620063185692,
-0.018361426889896393,
-0.009869040921330452,
0.0021143658086657524,
-0.032408881932497025,
0.020569751039147377,
0.008383989334106445,
-0.01266036368906498,
-0.00793788768351078,
-0.028619399294257164,
-0.03571150079369545,
-0.016001109033823013,
0.009203186258673668,
0.0010004909709095955,
0.04815126210451126,
0.0040344176813960075,
0.0015829249750822783,
-0.037270743399858475,
-0.07942087948322296,
0.020367076620459557,
-0.011600087396800518,
-0.02072134241461754,
-0.01845099963247776,
-0.007021468132734299,
0.0027563348412513733,
0.04054337739944458,
0.0022918658796697855,
-0.013697023503482342,
0.030140770599246025,
0.006677580531686544,
0.0061162724159657955,
0.003888485487550497,
-0.05040746182203293,
0.005589816253632307,
-0.025168361142277718,
0.0056428853422403336,
-0.0029820576310157776,
0.007417927961796522,
0.005688846111297607,
0.014789831824600697,
0.02127416990697384,
0.024696514010429382,
-0.017595380544662476,
-0.011722446419298649,
0.06214561313390732,
-0.04005406051874161,
0.01486942358314991,
0.012937083840370178,
-0.0010049858829006553,
-0.04684950411319733,
0.00797212589532137,
-0.012289809063076973,
0.009495371021330357,
-0.0008604310569353402,
0.04659935086965561,
-0.016671903431415558,
0.05161207541823387,
-0.027919620275497437,
0.018663715571165085,
-0.02549094893038273,
0.0064522516913712025,
-0.04376447573304176,
0.04536674916744232,
0.013711431063711643,
-0.0321870781481266,
-0.01982969604432583,
0.051057133823633194,
0.021654672920703888,
-0.06668460369110107,
-0.0009749667369760573,
0.041935477405786514,
-0.04747442528605461,
0.01711871102452278,
0.030615977942943573,
0.008861219510436058,
0.014243820682168007,
0.018747569993138313,
-0.03646751865744591,
-0.029415618628263474,
-0.04239479824900627,
-0.025944454595446587,
0.03957455977797508,
-0.005997886881232262,
0.008754937909543514,
0.02790086343884468,
-0.03407569229602814,
0.007962056435644627,
0.044188451021909714,
-0.008003529161214828,
0.011132637970149517,
0.007997228763997555,
-0.03118000365793705,
-0.012201938778162003,
-0.020473096519708633,
0.04913216084241867,
-0.030736327171325684,
0.02066875621676445,
0.010737007483839989,
-0.005659154150635004,
-0.039790671318769455,
-0.016051415354013443,
0.016988826915621758,
-0.03793995454907417,
-0.008230566047132015,
0.0001624981960048899,
-0.012667995877563953,
0.01544822659343481,
0.05820765718817711,
-0.061463743448257446,
0.020309017971158028,
0.00696701230481267,
0.004156019072979689,
-0.11609268933534622,
-0.009153121151030064,
0.01397229265421629,
0.01621580868959427,
0.05901998654007912,
-0.001941407099366188,
0.0022778199054300785,
-0.008401144295930862,
-0.05393669754266739,
0.01813500188291073,
-0.0034333462826907635,
0.0020319228060543537,
-0.031184246763586998,
-0.004711539018899202,
-0.02537382021546364,
0.04938288778066635,
0.0356343574821949,
0.05042875558137894,
0.007212171796709299,
0.018941977992653847,
0.002870383206754923,
-0.042942535132169724,
-0.0038582475390285254,
0.024005062878131866,
0.022122390568256378,
-0.02942524664103985,
0.05858328193426132,
-0.0291601475328207,
-0.02856465056538582,
0.018212607130408287,
0.012179047800600529,
-0.013888003304600716,
-0.04123656824231148,
0.005512258503586054,
0.004707781132310629,
0.02379085309803486,
0.06453955173492432,
-0.021597763523459435,
-0.006846730597317219,
-0.004617021884769201,
-0.004514783620834351,
0.053163543343544006,
-0.015764320269227028,
-0.005173888523131609,
0.0005971773061901331,
-0.0415252260863781,
-0.028248876333236694,
-0.0004630603070836514,
0.0016121690860018134,
-0.025520237162709236,
0.00018236525647807866,
0.00625862181186676,
-0.024312658235430717,
0.00042519139242358506,
0.017280083149671555,
-0.018994314596056938,
0.008066399954259396,
0.03340567275881767,
-0.00506809214130044,
0.015491699799895287,
0.06563868373632431,
-0.03709421306848526,
-0.014049019664525986,
0.021112488582730293,
0.003494380274787545,
-0.00934096984565258,
-0.06539057940244675,
-0.005512925796210766,
-0.007794140838086605,
0.010714558884501457,
-0.00538981007412076,
-0.0009347801678813994,
-0.012384900823235512,
0.03486357629299164,
-0.004020975902676582,
-0.015197383239865303,
-0.06433958560228348,
-0.013298246078193188,
0.013665402308106422,
-0.0687408596277237,
-0.002358549740165472,
0.008164707571268082,
0.010078620165586472,
0.011281047947704792,
-0.040148332715034485,
-0.003520864760503173,
0.026965362951159477,
0.05760897323489189,
0.0030077409464865923,
-0.03123888187110424,
0.02626141719520092,
-0.007990383543074131,
0.004301256034523249,
-0.05124242231249809,
-0.026290956884622574,
-0.002801140071824193,
0.0011288890382274985,
0.0011703085619956255,
0.001211059163324535,
-0.033409539610147476,
0.029644960537552834,
0.019443301483988762,
0.006624871399253607,
0.03141532838344574,
0.017414383590221405,
-0.020653635263442993,
0.03578638285398483,
0.009675995446741581,
-0.017609616741538048,
0.05703524872660637,
0.032573625445365906,
0.01261793915182352,
0.07158417254686356,
-0.03742331266403198,
-0.05325227603316307,
0.0023050119634717703,
0.016004744917154312,
-0.013942745514214039,
-0.02849133126437664,
-0.018694180995225906,
0.01477887574583292,
-0.02173500880599022,
0.005553672090172768,
0.04005306214094162,
-0.04235893860459328,
-0.028552426025271416,
0.03727829083800316,
-0.0069258371368050575,
0.011778908781707287,
0.04836788401007652,
0.006621400825679302,
0.01180325448513031,
0.004490622319281101,
0.05077701434493065,
0.0485914908349514,
0.0043432749807834625,
0.01987154223024845,
-0.008089554496109486,
0.029825642704963684,
-0.023452317342162132,
-0.01021307148039341,
0.02054346166551113,
0.017942167818546295,
-0.05248182639479637,
-0.0031078734900802374,
0.030313516035676003,
-0.03421267122030258,
-0.0008749242406338453,
0.006651479750871658,
-0.025692109018564224,
0.06313146650791168,
-0.012337923981249332,
0.023018596693873405,
-0.02163820154964924,
-0.00048446751316078007,
-0.013300053775310516,
0.015243979170918465,
-0.02019694447517395,
0.06224862113595009,
0.01364009827375412,
-0.0008359552011825144,
-0.03417709842324257,
-0.01210980024188757,
-0.018498264253139496,
-0.036551583558321,
0.016006549820303917,
0.049812596291303635,
0.00008833379251882434,
0.01360322069376707,
-0.014794625341892242,
-0.0097401337698102,
-0.029355205595493317,
0.011266607791185379,
0.012395537458360195,
0.0341840498149395,
-0.04685364291071892,
0.019931839779019356,
-0.028012901544570923,
0.012229620479047298,
-0.04415004327893257,
-0.016965709626674652,
0.014811473898589611,
0.016707422211766243,
-0.03844750300049782,
-0.018840337172150612
] |
<p>In his classical mechanics lecture, Prof Susskind gives a short exercise, which I "feel" is very simple, but don't know where to start with. The question is:</p>
<blockquote>
<p>"There is a coordinate system $(x,y)$, which is stationary. Another system, $(X,Y)$ with origin common to the previous one is rotating with a uniform velocity, through an angle $\omega{t}$. The trajectories are(ignoring masses and $t$):</p>
<p>$$\ddot{X} = {\omega^2}x - \omega\dot{y}$$</p>
<p>$$\ddot{Y} = \omega^2{y} + \omega \dot{x}$$</p>
<p>Prove that one of the trajectories is circular."</p>
</blockquote>
<p>However, both the terms will equal to $0$ because the velocity is constant, and hence the acceleration is zero. Now, what should I do with these? Should I prove $\ddot{x}$ = $\ddot{y}$= $0$, or something else? Please explain.</p>
| 8,868 |
[
-0.01476004347205162,
-0.012498529627919197,
-0.009133622981607914,
-0.009906270541250706,
0.010545927099883556,
-0.03391898423433304,
-0.02877524308860302,
-0.01813727244734764,
0.004854951519519091,
0.013080194592475891,
-0.006640399340540171,
0.03758415952324867,
0.03871355205774307,
0.00789891742169857,
0.029780123382806778,
-0.005931328050792217,
-0.0246869008988142,
-0.01617240160703659,
-0.013230057433247566,
-0.023648954927921295,
0.006819820497184992,
-0.032384492456912994,
-0.0033790641464293003,
-0.01723477430641651,
-0.005706601310521364,
0.021813780069351196,
0.018531834706664085,
-0.020952844992280006,
0.0213424451649189,
0.04799240455031395,
-0.03802485018968582,
0.02066800557076931,
-0.013258352875709534,
0.027263255789875984,
0.028835637494921684,
0.020616501569747925,
-0.03545735031366348,
0.0009594385628588498,
0.03258420526981354,
0.014452610164880753,
-0.03554873913526535,
-0.01223243772983551,
0.0066656628623604774,
0.07652705162763596,
-0.002777276560664177,
0.021231839433312416,
0.01969059742987156,
0.024248814210295677,
0.08533644676208496,
-0.016992943361401558,
0.06820835173130035,
-0.01464549545198679,
0.028439423069357872,
0.032886359840631485,
0.0023358233738690615,
-0.00007555691263405606,
0.05344491824507713,
0.017504680901765823,
-0.024198340252041817,
-0.007686330005526543,
-0.022226426750421524,
-0.03879760205745697,
0.012230356223881245,
-0.038691092282533646,
-0.020238390192389488,
0.017601465806365013,
0.015352750197052956,
-0.003946436569094658,
0.002755494089797139,
-0.014096889644861221,
0.006589009426534176,
0.04338593780994415,
0.03155829757452011,
-0.04022975265979767,
-0.008211134001612663,
-0.03453580290079117,
0.023638922721147537,
0.020391687750816345,
0.0026450094301253557,
0.002695525763556361,
-0.007194069214165211,
0.020367834717035294,
0.03601294755935669,
0.053114648908376694,
-0.0073509011417627335,
-0.01628771424293518,
0.04060623049736023,
0.016613904386758804,
0.02311943843960762,
0.04372489079833031,
0.034331951290369034,
0.00022003817139193416,
-0.00295047415420413,
-0.015831705182790756,
0.008280999958515167,
0.05786488205194473,
0.006089428439736366,
0.05181073769927025,
0.043533604592084885,
-0.02358979359269142,
0.002928245346993208,
-0.06486819684505463,
0.023110415786504745,
0.0537286177277565,
0.028888439759612083,
0.01244497299194336,
-0.028213467448949814,
0.030339257791638374,
-0.03094036877155304,
-0.034223105758428574,
-0.07565723359584808,
0.011153528466820717,
-0.000991049688309431,
0.022599762305617332,
-0.005466757342219353,
-0.00375942955724895,
-0.0129415113478899,
-0.01047238614410162,
0.042020443826913834,
0.03856445848941803,
0.07149853557348251,
-0.013506164774298668,
0.0033235126174986362,
-0.024319112300872803,
-0.07010554522275925,
-0.018978551030158997,
0.02357463538646698,
-0.006742605473846197,
-0.031046541407704353,
0.031645242124795914,
-0.003356048371642828,
-0.009921167977154255,
-0.029921960085630417,
-0.0019723125733435154,
0.028647374361753464,
-0.015404680743813515,
-0.11643817275762558,
-0.06450550258159637,
0.031223852187395096,
0.015577908605337143,
-0.036227237433195114,
-0.05611658841371536,
-0.005461177788674831,
0.03145614266395569,
0.06617533415555954,
-0.03916597738862038,
-0.031593576073646545,
0.011838399805128574,
0.03241162747144699,
-0.00887347012758255,
-0.019315820187330246,
-0.05892116576433182,
-0.0012752095935866237,
-0.04651492089033127,
0.02104378677904606,
-0.04133092612028122,
0.001865108497440815,
0.03473828732967377,
-0.0007031945860944688,
-0.01699380949139595,
0.05892777070403099,
-0.040367309004068375,
0.008400890044867992,
0.03314896300435066,
0.008267705328762531,
-0.039549440145492554,
0.0790264755487442,
0.020990075543522835,
-0.020036747679114342,
0.0551232174038887,
0.015457067638635635,
0.08776979893445969,
-0.017422419041395187,
0.0005956577369943261,
0.053371209651231766,
-0.04348624125123024,
-0.019118916243314743,
-0.004041766747832298,
-0.022949766367673874,
0.016948143020272255,
-0.03155626356601715,
-0.05409477651119232,
-0.01290816254913807,
-0.013917862437665462,
-0.014413798227906227,
0.07923417538404465,
0.002030079485848546,
0.05655960366129875,
0.010783165693283081,
-0.037917956709861755,
0.001771301031112671,
-0.06453800946474075,
0.03558291867375374,
-0.0038838947657495737,
-0.014373230747878551,
0.012196516618132591,
0.042006414383649826,
0.0019641448743641376,
-0.02114979922771454,
-0.003953142557293177,
-0.0037956195883452892,
0.04668410122394562,
0.021011006087064743,
-0.03291011601686478,
0.02455553226172924,
0.03299294039607048,
0.021151019260287285,
0.006203044205904007,
0.004278925247490406,
-0.03039736859500408,
0.023034371435642242,
0.00574655132368207,
0.017612677067518234,
0.00017567869508638978,
0.020861899480223656,
0.015458934009075165,
-0.01130607258528471,
-0.02326984517276287,
-0.010892047546803951,
0.03616032004356384,
-0.05785742774605751,
0.07850169390439987,
0.0513756237924099,
-0.01788678765296936,
0.019552649930119514,
0.045096542686223984,
0.040086448192596436,
0.022894341498613358,
0.008350095711648464,
-0.007548706140369177,
-0.036989908665418625,
-0.013499963097274303,
0.033626459538936615,
0.046811189502477646,
-0.05827726796269417,
0.025117632001638412,
0.048562485724687576,
0.0553094707429409,
-0.0071871317923069,
0.0122220478951931,
0.001356575870886445,
-0.027540380135178566,
0.020971225574612617,
0.012868132442235947,
-0.008034766651690006,
0.051616013050079346,
0.047882724553346634,
0.010517903603613377,
0.006119321566075087,
0.024789130315184593,
-0.035144079476594925,
0.03438740596175194,
0.006368160247802734,
0.0016263823490589857,
0.04336502030491829,
-0.0010445343796163797,
0.03566248342394829,
0.009989292360842228,
0.03026340715587139,
0.010926073417067528,
-0.0166078619658947,
-0.007137611508369446,
-0.010847765021026134,
0.02935674972832203,
-0.016581688076257706,
-0.0006042227614670992,
-0.026820775121450424,
-0.025687649846076965,
0.04354752227663994,
-0.06307592242956161,
-0.03930818289518356,
-0.01075058151036501,
-0.060596223920583725,
-0.007775402162224054,
-0.009613091126084328,
0.03994409739971161,
0.033813200891017914,
0.02966206520795822,
-0.020623715594410896,
-0.04789919778704643,
-0.011062408797442913,
-0.014841635711491108,
-0.005432591773569584,
0.056252509355545044,
-0.04192864149808884,
0.016036583110690117,
-0.05152410641312599,
-0.021320102736353874,
0.06562899053096771,
0.0005393780884332955,
0.00739657087251544,
0.03895983099937439,
0.008976447395980358,
-0.055781301110982895,
-0.036760490387678146,
-0.025090964511036873,
0.018384752795100212,
-0.0572815015912056,
-0.01004362665116787,
0.05802934244275093,
-0.0034985574893653393,
-0.033954400569200516,
0.02133457362651825,
-0.04315224289894104,
-0.042682599276304245,
-0.015174795873463154,
-0.00837190542370081,
0.04656205698847771,
-0.022057313472032547,
0.027112141251564026,
-0.007381759583950043,
0.002525512594729662,
0.005882376804947853,
-0.05462709441781044,
-0.03149867802858353,
0.012645880691707134,
-0.023788832128047943,
0.0567084401845932,
-0.0001362089824397117,
-0.021114081144332886,
0.08801281452178955,
0.026655850932002068,
-0.017050214111804962,
-0.010373368859291077,
0.003476263489574194,
-0.005597895476967096,
-0.03429820388555527,
-0.03999665379524231,
0.010040642693638802,
0.0013247301103547215,
0.013307110406458378,
0.035521261394023895,
-0.0022002749610692263,
0.004687660839408636,
-0.0027836940716952085,
0.02075347676873207,
-0.010317220352590084,
-0.0009549136739224195,
0.005132197868078947,
0.05003004148602486,
0.0349416583776474,
-0.013135675340890884,
0.01184406504034996,
0.0007715830579400063,
0.04144107922911644,
-0.005285574123263359,
-0.06510834395885468,
0.027723198756575584,
0.014655033126473427,
-0.011257798410952091,
0.029215674847364426,
0.029739240184426308,
0.001492143259383738,
-0.010234781540930271,
-0.010485400445759296,
-0.002507674740627408,
0.03477952256798744,
0.001122121000662446,
-0.006864652503281832,
0.029116373509168625,
0.016782762482762337,
-0.02253863587975502,
-0.009891682304441929,
-0.008352669887244701,
-0.014641458168625832,
0.057490263134241104,
-0.04953373223543167,
-0.001807200605981052,
0.03126084432005882,
-0.003464349312707782,
-0.009019852615892887,
-0.01757550798356533,
-0.0513874813914299,
-0.005889595486223698,
-0.0776580274105072,
0.023021064698696136,
-0.01925506629049778,
0.043522872030735016,
0.013476362451910973,
0.05927580967545509,
0.003951787482947111,
-0.00943818036466837,
0.03473547101020813,
-0.005222102627158165,
-0.04848688840866089,
0.04550297558307648,
-0.03442714735865593,
-0.02129022590816021,
0.012268700636923313,
0.04511005058884621,
0.02104664407670498,
-0.027664532884955406,
-0.010032578371465206,
-0.03068004734814167,
-0.02982032299041748,
-0.023274531587958336,
0.024870671331882477,
-0.055756427347660065,
-0.06415704637765884,
-0.03261835128068924,
0.00571758858859539,
0.03842037171125412,
-0.012974639423191547,
-0.004955420736223459,
0.038084447383880615,
-0.04555228352546692,
0.020233210176229477,
-0.05622952803969383,
-0.003951394930481911,
0.017178183421492577,
-0.019024157896637917,
0.020421834662556648,
0.036024872213602066,
0.01282475609332323,
-0.001686431118287146,
-0.019923370331525803,
0.0357334204018116,
-0.0052391402423381805,
-0.03237844631075859,
-0.027770191431045532,
-0.03815141320228577,
-0.006122667342424393,
-0.013248133473098278,
0.08535826951265335,
0.007751891389489174,
-0.005452537909150124,
0.03258626535534859,
0.026875989511609077,
0.03655052185058594,
0.03390652313828468,
0.04430215805768967,
0.019844790920615196,
0.003583600977435708,
-0.03191094100475311,
-0.02496001310646534,
-0.05217645689845085,
-0.009619088843464851,
0.010249612852931023,
-0.02762313187122345,
-0.008777453564107418,
-0.022590750828385353,
0.024453220888972282,
0.04135388880968094,
0.02420935034751892,
0.015766583383083344,
-0.025434136390686035,
0.04252256453037262,
-0.025153666734695435,
-0.019105665385723114,
0.04397130385041237,
0.012778494507074356,
0.032592032104730606,
0.008203878067433834,
-0.006472960580140352,
-0.0521472804248333,
-0.009639758616685867,
0.024554740637540817,
0.034931547939777374,
0.014369767159223557,
-0.00702291913330555,
-0.04088805988430977,
-0.01786588504910469,
0.05463689938187599,
-0.041641879826784134,
0.04624447226524353,
-0.004048381466418505,
-0.00903751514852047,
-0.020461149513721466,
-0.030659999698400497,
-0.051679737865924835,
0.0028003568295389414,
-0.001240900019183755,
0.028598293662071228,
-0.008505246601998806,
-0.02805008739233017,
-0.02909182198345661,
-0.005647105630487204,
0.02187368832528591,
0.027287639677524567,
0.015108340419828892,
-0.05848849192261696,
-0.0007186802686192095,
0.03209054097533226,
-0.003903475357219577,
-0.0652281790971756,
-0.02334856055676937,
0.023155294358730316,
-0.030026301741600037,
0.04964257404208183,
-0.025708014145493507,
-0.04023143649101257,
0.029643326997756958,
-0.018091710284352303,
-0.03048098087310791,
0.03940969705581665,
-0.04217180609703064,
0.008067496120929718,
0.03909292817115784,
0.02673269622027874,
0.0032397026661783457,
0.018996980041265488,
0.005461488850414753,
-0.006690556183457375,
-0.02151879109442234,
-0.007749862503260374,
-0.015468914993107319,
0.007759087719023228,
-0.03981108218431473,
0.025318676605820656,
-0.011671134270727634,
0.006605783011764288,
0.004841936752200127,
0.01871049404144287,
-0.026585375890135765,
-0.057408999651670456,
0.021592823788523674,
0.051921796053647995,
0.008539962582290173,
-0.003251041518524289,
0.006550968624651432,
0.02791089005768299,
0.0036080044228583574,
-0.040624141693115234,
-0.004497127141803503,
0.0010654703946784139,
0.006533839274197817,
0.028969326987862587,
-0.0011909978929907084,
0.022984862327575684,
-0.022016629576683044,
-0.02503504976630211,
-0.013020842336118221,
-0.07020142674446106,
0.035574670881032944,
-0.004856572952121496,
-0.006329410243779421,
0.03459710255265236,
-0.04517684504389763,
-0.04670951887965202,
-0.008359911851584911,
0.028350073844194412,
-0.018450237810611725,
-0.06152782216668129,
-0.005679139401763678,
0.037136420607566833,
0.0036990330554544926,
-0.05936318635940552,
-0.09986982494592667,
0.009052248671650887,
0.011204379610717297,
0.0013197913067415357,
-0.017372289672493935,
0.01828671433031559,
-0.020883752033114433,
-0.01671048067510128,
-0.011449490673840046,
0.017063938081264496,
-0.0007375411805696785,
-0.03312026336789131,
0.02602030150592327,
0.020679429173469543,
0.056730203330516815,
-0.023090526461601257,
-0.03650565817952156,
0.002124403603374958,
-0.012522910721600056,
-0.006983469240367413,
-0.00778958760201931,
0.07057863473892212,
-0.035471051931381226,
-0.07226067036390305,
-0.014758327044546604,
0.02662157639861107,
0.02313077636063099,
-0.02203751914203167,
-0.02354172058403492,
0.052793726325035095,
0.013782167807221413,
-0.017224926501512527,
-0.023847106844186783,
0.027653589844703674,
-0.004802087787538767,
-0.01838006265461445,
0.030353263020515442,
0.03670286387205124,
0.020707039162516594,
-0.04904213175177574,
0.015395848080515862,
-0.005206654313951731,
-0.006781725212931633,
-0.015659866854548454,
0.07123088836669922,
-0.0008670836105011404,
0.0010938601335510612,
0.00144382833968848,
0.006793228909373283,
0.023726170882582664,
0.03623778373003006,
-0.031545478850603104,
-0.011954008601605892,
-0.030168920755386353,
-0.030866552144289017,
-0.03585294634103775,
-0.04004155471920967,
0.032260626554489136,
0.0870218500494957,
0.002147071994841099,
0.09259141981601715,
0.03486046940088272,
0.04373978078365326,
-0.021913329139351845,
0.02283310331404209,
-0.01150407362729311,
-0.04095303639769554,
0.0022130594588816166,
0.028455445542931557,
-0.03142055124044418,
-0.022850006818771362,
0.023488687351346016,
0.05005275830626488,
0.01284480094909668,
-0.016076458618044853,
0.04014032334089279,
-0.028352562338113785,
0.008009793236851692,
0.00015524119953624904,
-0.0419766940176487,
0.013429604470729828,
-0.013819942250847816,
0.09237440675497055,
-0.014005030505359173,
-0.03420373424887657,
0.04366662725806236,
0.023631708696484566,
0.015615016222000122,
-0.014881239272654057,
-0.009621074423193932,
-0.04028636962175369,
0.009471300058066845,
0.004652844276279211,
0.011630953289568424,
-0.017531221732497215,
-0.0005000544479116797,
0.035471558570861816,
0.017873534932732582,
0.03958562761545181,
-0.033134575933218,
-0.04835933446884155,
-0.0018526572966948152,
-0.016646722331643105,
-0.02323269098997116,
0.023908773437142372,
0.008218985982239246,
-0.019150160253047943,
0.023540237918496132,
-0.03221989423036575,
-0.023340245708823204,
0.02764272876083851,
0.04105061665177345,
-0.03629370033740997,
0.061761800199747086,
-0.027041273191571236,
-0.005582287907600403,
-0.0174033734947443,
-0.0063234190456569195,
0.08802495151758194,
0.027184288948774338,
0.004565207287669182,
-0.042729541659355164,
0.01187718752771616,
-0.0020469033624976873,
0.017267923802137375,
-0.037949059158563614,
0.02733798511326313,
-0.004158508963882923,
0.02680380642414093,
0.008643177337944508,
0.005959814880043268,
0.017382236197590828,
0.015361220575869083,
0.027973152697086334,
-0.047860562801361084,
-0.021774275228381157,
-0.05421898886561394,
0.007179563399404287,
0.007945366203784943,
0.02306300960481167,
0.008168421685695648,
0.034893494099378586,
-0.052309099584817886,
-0.00956382229924202,
-0.025244850665330887,
-0.05494637042284012,
0.05366545170545578,
0.0025813733227550983,
-0.03755350783467293,
0.03975667059421539,
0.02023746445775032,
-0.04373019561171532,
-0.043434903025627136,
0.024412788450717926,
0.020218828693032265,
0.007925959303975105,
0.059167973697185516,
0.030284054577350616,
0.019267136231064796,
-0.0255979485809803,
0.04410521686077118,
0.02155347540974617,
-0.021666044369339943,
-0.006700512487441301,
-0.04666746035218239,
0.08980962634086609,
-0.013279695995151997,
0.01158556155860424,
-0.00938301533460617,
-0.0006599470507353544,
-0.01616682857275009,
-0.0643673837184906,
-0.014229009859263897,
-0.00418873829767108,
0.02885548770427704,
-0.01944376341998577,
0.006876751314848661,
-0.0691440999507904,
0.018313441425561905,
0.026867538690567017,
0.0012747998116537929,
0.01341861579567194,
-0.010327469557523727,
-0.0050842659547924995,
0.0219577644020319,
0.04182367026805878,
-0.011346505023539066,
-0.02836422249674797,
-0.035391535609960556,
-0.004528504330664873,
-0.013398651964962482,
0.0184371005743742,
0.002377438358962536,
0.004026162903755903,
0.05353106930851936,
0.020495934411883354,
-0.02292991615831852,
-0.013035060837864876,
-0.05466409772634506,
0.0024786624126136303,
0.0009726884309202433,
-0.02985326014459133,
-0.009703699499368668,
-0.010173117741942406,
0.03174456208944321,
0.043806370347738266,
-0.028985440731048584,
0.009243623353540897,
0.035489264875650406,
0.05165307968854904,
0.023942360654473305,
0.012562993913888931,
-0.035651687532663345,
0.03846167027950287,
-0.016214599832892418,
0.009371733292937279,
-0.047301553189754486,
0.029897352680563927,
0.050733670592308044,
0.03259103000164032,
0.009341595694422722,
0.006028070580214262,
0.011573447845876217,
0.023501573130488396,
0.04589195176959038,
-0.058552298694849014,
-0.009991719387471676,
0.03573188930749893,
0.015012088231742382,
-0.05073835328221321,
-0.011061880737543106,
-0.025375517085194588,
0.0005484203575178981,
-0.011016692034900188,
0.029092729091644287,
-0.02540118806064129,
0.04987510293722153,
-0.051435910165309906,
0.033732254058122635,
-0.07729408144950867,
0.0048902747221291065,
-0.026333903893828392,
0.0033840546384453773,
0.0346742644906044,
-0.01366911269724369,
-0.027438269928097725,
0.03761543706059456,
0.01904180645942688,
-0.015437550842761993,
-0.002662505954504013,
0.030148876830935478,
-0.004991181194782257,
-0.019325239583849907,
0.02432086132466793,
0.013616400770843029,
0.04577653482556343,
-0.03162485361099243,
-0.016493558883666992,
-0.005253140348941088,
-0.012593329884111881,
-0.003604263300076127,
0.0057026054710149765,
0.0034806355834007263,
0.011599669232964516,
-0.0003037074056919664,
-0.05405125394463539,
-0.010520578362047672,
0.06397192925214767,
-0.0376269668340683,
-0.020718608051538467,
-0.01301109790802002,
-0.031202930957078934,
-0.03325635567307472,
0.023024434223771095,
0.03321247547864914,
-0.005460688844323158,
0.013727093115448952,
0.02145388349890709,
0.02914397418498993,
-0.017669059336185455,
0.005117707885801792,
-0.011200989596545696,
0.019316263496875763,
-0.007079071365296841,
0.0008961560670286417,
0.023677486926317215,
0.023586733266711235,
0.04238859564065933,
-0.036503978073596954,
0.00759305153042078,
0.011614518240094185,
0.009559358470141888,
-0.07929563522338867,
0.00857518520206213,
0.004674961324781179,
0.010243122465908527,
0.03955547511577606,
-0.020802374929189682,
-0.01986667327582836,
0.07673535495996475,
-0.058889538049697876,
0.0013233543140813708,
-0.044464316219091415,
-0.0031948680989444256,
-0.027391348034143448,
-0.04157523438334465,
0.02815576270222664,
0.04199504852294922,
0.03774634748697281,
0.048541612923145294,
-0.010706159286201,
0.030031265690922737,
-0.009275006130337715,
-0.008690599352121353,
0.021606096997857094,
0.017169829457998276,
-0.015155491419136524,
-0.01035693846642971,
0.05934963747859001,
-0.030435901135206223,
-0.057791274040937424,
0.03773680329322815,
-0.018272260203957558,
-0.007114604115486145,
-0.01764652132987976,
0.03356565907597542,
-0.015489669516682625,
0.012669132091104984,
0.01967059075832367,
0.024078136309981346,
-0.04043784737586975,
-0.010166818276047707,
0.04163694009184837,
0.03852121904492378,
-0.04811263084411621,
-0.04902103543281555,
0.013543027453124523,
-0.035856541246175766,
-0.06969179958105087,
0.01858552172780037,
0.0034624310210347176,
0.024717574939131737,
0.024436015635728836,
-0.0002783499367069453,
0.009887764230370522,
-0.0004531221929937601,
0.008244363591074944,
-0.01662830077111721,
0.003739678068086505,
0.005927323829382658,
-0.020494142547249794,
0.004790995270013809,
-0.005625060759484768,
-0.01789180375635624,
-0.01592135801911354,
0.007465577684342861,
-0.02848144806921482,
-0.0077945152297616005,
-0.07130254060029984,
-0.020141201093792915,
0.0023570742923766375,
0.013828222639858723,
-0.016032636165618896,
-0.06231802701950073,
-0.020962204784154892,
0.03648342192173004,
0.03204444423317909,
-0.010876402258872986,
-0.007561734411865473,
-0.018683159723877907,
-0.021927904337644577,
-0.045744389295578,
0.012254261411726475,
0.034855954349040985,
-0.020153967663645744,
-0.0357741042971611,
-0.031118303537368774,
-0.04711494967341423,
0.015033628791570663,
0.03196391090750694,
-0.011882727965712547,
-0.023053085431456566,
0.01756814308464527,
-0.017945757135748863,
-0.0028885439969599247,
-0.0664459839463234,
0.01077877264469862,
-0.019044814631342888,
-0.020704567432403564,
0.023964786902070045,
-0.005395771469920874,
-0.020812271162867546,
0.004364602267742157,
0.06670481711626053,
-0.01281543169170618,
0.04335647448897362,
0.005074490327388048,
-0.03948671743273735,
0.01023565698415041,
-0.012436126358807087,
0.023915421217679977,
0.05712756887078285,
0.02461620420217514,
0.012497776187956333,
0.037805020809173584,
-0.05365345999598503,
-0.05358155444264412,
0.040561456233263016,
-0.06780777871608734,
-0.0035906743723899126,
-0.03463640436530113,
-0.027247613295912743,
0.016003545373678207,
-0.0453728623688221,
0.009188137948513031,
0.053463831543922424,
0.0017388801788911223,
-0.028010673820972443,
0.0023895727936178446,
0.028128763660788536,
0.03857267275452614,
-0.019533410668373108,
-0.0072021703235805035,
0.03915492817759514,
-0.035298772156238556,
0.0244721882045269,
0.007218944374471903,
0.028446251526474953,
0.0034083027858287096,
0.005344943143427372,
0.03793754801154137,
-0.023318924009799957,
0.038430195301771164,
-0.01725291647017002,
0.029688406735658646,
-0.01782607100903988,
-0.0045394292101264,
-0.011432498693466187,
-0.017199993133544922,
-0.009505334310233593,
0.03502558916807175,
0.009395081549882889,
0.03962286189198494,
-0.02394997328519821,
0.000274985795840621,
0.01031848881393671,
-0.02228369191288948,
-0.047133587300777435,
-0.018230261281132698,
-0.02910558693110943,
0.014302076771855354,
-0.008470705710351467,
0.018999388441443443,
-0.015126311220228672,
-0.04449624568223953,
0.038993846625089645,
-0.005639074370265007,
0.003681264817714691,
0.015574191696941853,
-0.000023673977921134792,
0.014569733291864395,
-0.01723944954574108,
0.003493412397801876,
-0.012568407692015171,
0.06823789328336716,
0.04363337904214859,
0.018926186487078667,
-0.03339856490492821,
0.002398752374574542,
-0.03485250473022461,
0.03852362930774689,
-0.09026357531547546,
-0.0281523447483778,
-0.011923675425350666,
0.03091547265648842,
0.030353326350450516,
-0.024189310148358345
] |
<p>I'm searching for basic literature or papers introducing the action of polarizing beam splitters with single photons. Unfortunately the most books and papers only focus on usual beam splitters.</p>
<p>The only paper I found is <a href="http://vcq.quantum.at/fileadmin/Publications/2001-13.pdf" rel="nofollow">this one</a> (Zeilinger - Photon statistics
at beam splitters) but even there is just a little section about polarizing beam splitters. Above all it is full of typos.</p>
| 8,869 |
[
-0.011788514442741871,
-0.014351436868309975,
-0.0065840184688568115,
-0.03063521906733513,
0.057559702545404434,
0.013298518024384975,
-0.011005462147295475,
-0.034671712666749954,
0.013877695426344872,
-0.0445735864341259,
0.065720334649086,
0.03505260497331619,
0.047573551535606384,
0.04588860273361206,
0.005349558312445879,
0.0072210063226521015,
0.00605274410918355,
-0.018546482548117638,
-0.007009296678006649,
-0.009084025397896767,
-0.024843309074640274,
0.02772657573223114,
-0.03665933012962341,
0.030169231817126274,
-0.025385018438100815,
0.01866920106112957,
-0.014058697037398815,
-0.0027868396136909723,
0.01603635400533676,
0.0408552810549736,
-0.03899101912975311,
-0.020937204360961914,
-0.007895653136074543,
0.03611256182193756,
-0.019190702587366104,
-0.040421150624752045,
-0.0023966124281287193,
-0.07021254301071167,
0.004610960837453604,
0.021003076806664467,
-0.023849377408623695,
0.014376200735569,
-0.04557216539978981,
0.007258112076669931,
-0.043299105018377304,
0.014925673604011536,
-0.016033628955483437,
-0.030238622799515724,
0.0619705431163311,
-0.08151143044233322,
0.030832018703222275,
-0.013454326428472996,
0.0300142765045166,
0.01967853493988514,
-0.019461791962385178,
0.049212004989385605,
0.0673883780837059,
0.05266216769814491,
0.016055792570114136,
-0.03866258263587952,
-0.018694357946515083,
-0.000291564705548808,
-0.007060470525175333,
-0.022112833335995674,
-0.061485692858695984,
0.006141951307654381,
0.004052983596920967,
-0.05558859929442406,
0.044135164469480515,
-0.01811080239713192,
0.016108395531773567,
-0.010651756078004837,
0.03924653306603432,
-0.025800807401537895,
-0.02230788953602314,
-0.020909296348690987,
0.008874990046024323,
0.025750773027539253,
0.03358089551329613,
0.012190536595880985,
0.028083790093660355,
0.0020663731265813112,
-0.0031017432920634747,
0.026307232677936554,
-0.040279489010572433,
-0.02167670615017414,
0.09050416946411133,
-0.04565441980957985,
-0.008479660376906395,
0.011292153038084507,
-0.008719081990420818,
0.02213856391608715,
0.029088685289025307,
0.050681374967098236,
-0.05877526476979256,
0.02343265898525715,
0.006825448013842106,
0.07315272092819214,
-0.013785903342068195,
-0.006695193704217672,
0.012435578741133213,
-0.02087809517979622,
-0.003479019505903125,
0.05824652686715126,
-0.017823833972215652,
-0.0361875556409359,
-0.0023931751493364573,
0.04974867403507233,
-0.0271165631711483,
-0.015598515048623085,
-0.03530699014663696,
0.014852800406515598,
0.00810165423899889,
-0.003268725238740444,
0.0007050798740237951,
-0.03225318342447281,
-0.00004045692185172811,
-0.011200688779354095,
0.06186562404036522,
0.08517178893089294,
0.016441157087683678,
-0.023425303399562836,
0.02870236709713936,
-0.048546358942985535,
-0.05497454106807709,
0.0071083190850913525,
0.049940481781959534,
-0.002418444026261568,
-0.06021663174033165,
0.029225436970591545,
0.02061021886765957,
-0.027544692158699036,
0.03606906533241272,
-0.007661221083253622,
-0.010199490003287792,
-0.03443843498826027,
-0.09155769646167755,
-0.03450345993041992,
0.037955913692712784,
-0.021918265148997307,
0.0033984463661909103,
-0.04577038064599037,
0.0059932684525847435,
0.018202127888798714,
0.0851966068148613,
-0.011473513208329678,
0.0403311513364315,
-0.031448304653167725,
0.03403297811746597,
0.019683927297592163,
-0.028583137318491936,
0.007403091993182898,
0.013598106801509857,
-0.008142607286572456,
-0.002015313133597374,
-0.0574883371591568,
0.029605278745293617,
0.04624418541789055,
-0.01718633808195591,
-0.016501393169164658,
0.03641324117779732,
0.0024015314411371946,
0.015947844833135605,
0.005650766659528017,
-0.03252682834863663,
-0.04753519967198372,
0.09843632578849792,
0.023630034178495407,
0.007497194688767195,
0.015247257426381111,
-0.038089510053396225,
0.0001358708250336349,
-0.0018076259875670075,
0.014160677790641785,
-0.007322084624320269,
-0.04391830787062645,
-0.0013788224896416068,
0.03104955330491066,
0.009374423883855343,
-0.008188292384147644,
-0.016737613826990128,
-0.009802361950278282,
-0.023082980886101723,
0.022664839401841164,
-0.031074127182364464,
0.03879917412996292,
-0.008437616750597954,
0.007737375795841217,
0.005568527616560459,
-0.06564968079328537,
0.01829046569764614,
-0.02701902762055397,
0.02705872431397438,
0.0055254073813557625,
-0.023264780640602112,
0.05268489569425583,
0.022864213213324547,
0.04061196371912956,
-0.013764539733529091,
-0.06274816393852234,
-0.035231392830610275,
-0.01236571092158556,
0.00975729338824749,
0.007793889846652746,
0.04357340186834335,
0.027517251670360565,
0.026326047256588936,
0.005417163949459791,
0.04352691024541855,
-0.024487873539328575,
-0.02136629819869995,
0.01730991154909134,
-0.009609944187104702,
0.037081919610500336,
0.007488653063774109,
-0.0026541620027273893,
-0.015442767180502415,
0.0016632170882076025,
0.008361122570931911,
-0.016635863110423088,
-0.023857634514570236,
0.04329850152134895,
0.04920316860079765,
0.04134998098015785,
-0.0116353090852499,
0.022739864885807037,
0.037178885191679,
-0.008048268035054207,
-0.00040180329233407974,
-0.03658274561166763,
-0.017378024756908417,
0.031363703310489655,
0.05514594912528992,
0.02262471802532673,
-0.057382382452487946,
0.03299221023917198,
0.035755448043346405,
0.02401883155107498,
0.003964608069509268,
0.01652964949607849,
-0.056512098759412766,
-0.0400099977850914,
0.040481723845005035,
0.032516397535800934,
0.025204230099916458,
-0.0020832987502217293,
0.003081758739426732,
-0.019184613600373268,
0.0062008993700146675,
0.025805214419960976,
-0.01717301458120346,
0.012086179107427597,
-0.010603954084217548,
0.018774792551994324,
0.020011182874441147,
-0.04565034061670303,
0.040244895964860916,
-0.05036665499210358,
0.006788306869566441,
0.014431159012019634,
-0.001583578297868371,
0.02059684321284294,
-0.03460513800382614,
-0.035328809171915054,
-0.012792245484888554,
-0.00017980085976887494,
-0.02084008790552616,
-0.008800970390439034,
0.007736443541944027,
-0.011937005445361137,
0.024815469980239868,
-0.016840064898133278,
0.008741728961467743,
-0.020778387784957886,
-0.02241753414273262,
-0.004003739915788174,
0.026473429054021835,
0.022915232926607132,
-0.025643782690167427,
-0.02850642241537571,
0.007317504845559597,
-0.01675700955092907,
0.03256741911172867,
-0.026878148317337036,
-0.03308933600783348,
0.013586091808974743,
-0.04730704054236412,
-0.02075032889842987,
0.023621270433068275,
-0.0258841160684824,
-0.01061190478503704,
-0.029344143345952034,
-0.006821710150688887,
-0.0462590791285038,
-0.017254985868930817,
-0.007411139085888863,
-0.018981507048010826,
-0.04963645339012146,
-0.00042227355879731476,
-0.003803762374445796,
-0.00226612389087677,
-0.011242314241826534,
-0.027978364378213882,
-0.00982925109565258,
-0.027681803330779076,
-0.0033317457418888807,
-0.018218476325273514,
0.018618760630488396,
-0.05858679488301277,
0.01302450243383646,
0.04309511557221413,
-0.03258790820837021,
0.003505305154249072,
-0.046912867575883865,
-0.03694316744804382,
0.005070842802524567,
0.02166721597313881,
0.0009810562478378415,
-0.014492261223495007,
-0.01842915266752243,
0.07931032031774521,
-0.015357059426605701,
-0.05244758725166321,
-0.036144908517599106,
0.01620071567595005,
-0.012263866141438484,
-0.000068535482569132,
0.018294211477041245,
0.009778209030628204,
-0.0025393166579306126,
0.02443772740662098,
0.02284884825348854,
0.005858386401087046,
0.030636504292488098,
0.029696838930249214,
-0.007762388326227665,
-0.013232870027422905,
-0.00465627433732152,
-0.02206598035991192,
0.019300267100334167,
0.033089250326156616,
-0.0531766414642334,
-0.00834711268544197,
0.006665327120572329,
-0.0017463674303144217,
0.00944044440984726,
-0.055324871093034744,
0.026570042595267296,
0.01581321470439434,
0.0018052465748041868,
-0.012596373446285725,
0.014271433465182781,
0.013986439444124699,
-0.026628803461790085,
0.042680006474256516,
0.03965425118803978,
0.031828854233026505,
-0.019028548151254654,
0.005866263527423143,
0.025739073753356934,
0.035090088844299316,
0.00911623239517212,
-0.023541392758488655,
-0.017093563452363014,
-0.027950599789619446,
0.025652233511209488,
-0.02575736865401268,
-0.037611279636621475,
0.05947526916861534,
0.03167807683348656,
0.01818888634443283,
-0.011212482117116451,
0.001089518889784813,
0.006566781550645828,
-0.04385289177298546,
0.03806620463728905,
-0.0020011274609714746,
0.021950889378786087,
-0.003064874093979597,
0.05582780763506889,
0.0063646696507930756,
0.02272866480052471,
0.0239555761218071,
-0.0032951151952147484,
-0.07572779804468155,
0.031159184873104095,
-0.03720548003911972,
-0.005624887999147177,
0.012615038082003593,
0.015553495846688747,
-0.020801659673452377,
-0.023510843515396118,
-0.046974606812000275,
-0.04482319578528404,
-0.0053315069526433945,
-0.04603590443730354,
0.011428002268075943,
-0.016145041212439537,
-0.04193488135933876,
-0.017173608765006065,
0.024005696177482605,
0.0004765049961861223,
-0.033914513885974884,
-0.014940298162400723,
0.005692487116903067,
-0.04224925488233566,
0.019844770431518555,
0.005737394094467163,
0.038080669939517975,
0.02266163006424904,
0.028462303802371025,
0.05434511601924896,
0.0032184403389692307,
-0.02176402136683464,
0.028754327446222305,
-0.006056466139853001,
0.02246505208313465,
-0.00432891771197319,
-0.028174947947263718,
0.021765684708952904,
0.010425898246467113,
0.01677573285996914,
-0.04252837225794792,
0.047270920127630234,
0.0139198312535882,
-0.009709460660815239,
0.02191583625972271,
0.018910618498921394,
-0.023061515763401985,
0.019548164680600166,
0.08216720074415207,
0.017668407410383224,
0.01127935852855444,
-0.02042568475008011,
-0.01867075078189373,
0.004700744524598122,
0.0022209854796528816,
-0.000042126081098103896,
-0.002042223932221532,
0.007885407656431198,
0.012038325890898705,
0.023396287113428116,
0.03635627403855324,
-0.0012271166779100895,
-0.0024403338320553303,
0.003716501407325268,
-0.013884947635233402,
-0.01971268467605114,
-0.01380830630660057,
0.007380318827927113,
0.038000497967004776,
0.028434334322810173,
0.02923623099923134,
-0.005142272915691137,
-0.06807707995176315,
0.007913568057119846,
0.05357871577143669,
0.028360625728964806,
-0.017578309401869774,
0.0049742115661501884,
0.013795256614685059,
0.006157157011330128,
0.05801190808415413,
-0.017990978434681892,
0.03324158862233162,
-0.012349299155175686,
-0.027081886306405067,
-0.0035061929374933243,
0.017479591071605682,
-0.004353993106633425,
0.004045642446726561,
0.01994721032679081,
0.017585333436727524,
0.002940213307738304,
-0.025266926735639572,
0.008650877512991428,
0.0026371886488050222,
0.017825650051236153,
0.04893889278173447,
0.0035014143213629723,
0.016691425815224648,
0.0016054960433393717,
0.07583005726337433,
-0.025664128363132477,
-0.10569621622562408,
0.0388609953224659,
-0.015984605997800827,
-0.026777921244502068,
0.06675373017787933,
-0.03318168595433235,
-0.015788903459906578,
0.04551934823393822,
0.0274245273321867,
-0.019104884937405586,
-0.015248311683535576,
-0.023285889998078346,
-0.008150146342813969,
0.020383195951581,
0.0008250059327110648,
0.09248767048120499,
0.059961527585983276,
-0.034414276480674744,
-0.01668696478009224,
-0.007377600762993097,
0.07706744968891144,
-0.012047645635902882,
0.0011499058455228806,
-0.007276616059243679,
0.025450021028518677,
-0.022895511239767075,
0.06715196371078491,
-0.07593686878681183,
0.007699071429669857,
-0.010696996934711933,
-0.02553083933889866,
-0.0039051214698702097,
0.024609578773379326,
-0.030391093343496323,
-0.005856059025973082,
-0.012886421754956245,
0.03348183631896973,
-0.0039216335862874985,
-0.01452049519866705,
-0.005600825883448124,
-0.0033577417489141226,
0.013299582526087761,
-0.0008586923941038549,
0.011832225136458874,
0.004965005908161402,
-0.04594844952225685,
-0.03983360156416893,
0.03699198737740517,
-0.05220504850149155,
0.04469988867640495,
0.005040081683546305,
0.02918267995119095,
0.03994161635637283,
-0.05815327540040016,
-0.05734742805361748,
0.013684787787497044,
-0.0054280199110507965,
0.03731879964470863,
-0.07401083409786224,
-0.008469756692647934,
-0.024828918278217316,
-0.004738194867968559,
-0.05743652582168579,
-0.055313535034656525,
0.0370800718665123,
-0.010084879584610462,
-0.02386600337922573,
-0.035744376480579376,
0.035829972475767136,
0.0029950030148029327,
-0.03556203097105026,
-0.024400673806667328,
0.023604124784469604,
-0.03685443475842476,
-0.004999201279133558,
-0.008137105964124203,
0.013280104845762253,
0.010120516642928123,
-0.023287193849682808,
-0.03574616089463234,
-0.016952404752373695,
0.005754134152084589,
-0.013246561400592327,
0.004104228224605322,
0.013026491738855839,
-0.015684256330132484,
-0.08617035299539566,
-0.015841690823435783,
0.01816585473716259,
0.03774121776223183,
-0.03924822434782982,
0.027715273201465607,
0.014771129004657269,
0.03900907188653946,
0.013241911306977272,
0.005325966514647007,
0.0046621509827673435,
-0.0007143035181798041,
0.05738910287618637,
-0.000631193513981998,
-0.003775289049372077,
-0.025160860270261765,
-0.044711753726005554,
0.032500091940164566,
-0.031196970492601395,
-0.0257103331387043,
0.00770373223349452,
0.07587922364473343,
0.010036329738795757,
-0.0017397052142769098,
0.01425201166421175,
-0.0351376049220562,
-0.026819439604878426,
-0.019923048093914986,
-0.0027568629011511803,
0.010667312890291214,
-0.001510642352513969,
0.012287062592804432,
-0.054924823343753815,
-0.005112739745527506,
0.013924187049269676,
0.07251011580228806,
0.02088257297873497,
0.013942095451056957,
0.03510017693042755,
-0.03293290734291077,
-0.013372752815485,
-0.048513974994421005,
-0.02055441588163376,
-0.003176551777869463,
0.028767749667167664,
0.04907536134123802,
-0.02223317325115204,
0.03058936446905136,
0.008926632814109325,
0.10089611262083054,
-0.010264546610414982,
0.036197904497385025,
0.026876667514443398,
0.03968963399529457,
0.03564629703760147,
-0.021244486793875694,
-0.053152117878198624,
0.05099314823746681,
-0.0793556421995163,
0.018713071942329407,
0.004738219082355499,
0.011848081834614277,
0.027577592059969902,
-0.004341511987149715,
0.02739647589623928,
-0.050909627228975296,
-0.018998658284544945,
-0.05710257589817047,
0.018895067274570465,
-0.013494289480149746,
-0.029739126563072205,
0.012363365851342678,
0.011945391073822975,
0.03272537887096405,
0.012502660974860191,
0.021588167175650597,
-0.01758779026567936,
-0.04011254385113716,
-0.07462204992771149,
-0.04406397044658661,
-0.04031508043408394,
0.05941259115934372,
-0.024964626878499985,
-0.0039041030686348677,
0.015285705216228962,
-0.036199554800987244,
0.07436410337686539,
0.025708278641104698,
0.056056272238492966,
0.017647486180067062,
0.027645930647850037,
-0.014496459625661373,
0.025761578232049942,
0.017686793580651283,
-0.029633307829499245,
0.12124853581190109,
0.019822105765342712,
0.027354253455996513,
-0.07446525245904922,
0.009419729001820087,
-0.017324484884738922,
0.028768209740519524,
-0.018124328926205635,
0.001640651491470635,
-0.02797563560307026,
0.012173114344477654,
-0.0049282158724963665,
0.06878191232681274,
0.009458848275244236,
-0.037693072110414505,
0.030541321262717247,
-0.05042216181755066,
-0.029868395999073982,
0.02727569453418255,
0.03328441455960274,
-0.012140616774559021,
-0.014508431777358055,
-0.051125895231962204,
-0.004749388433992863,
-0.02117733284831047,
-0.008929279632866383,
-0.02559938281774521,
-0.01692122593522072,
0.01700485311448574,
-0.0015745433047413826,
0.001242934144102037,
-0.026320938020944595,
-0.004780448041856289,
-0.030639516189694405,
-0.008149372413754463,
0.0029747486114501953,
0.034120503813028336,
-0.021408842876553535,
0.031057488173246384,
0.016868041828274727,
0.0183832086622715,
-0.01184556819498539,
0.0588337779045105,
-0.0016160033410415053,
-0.058170218020677567,
-0.002044357592239976,
0.020003153011202812,
0.03496884927153587,
-0.025782326236367226,
0.02323601022362709,
-0.017237907275557518,
-0.04342138394713402,
0.017557697370648384,
-0.009874244220554829,
-0.03403494134545326,
-0.014692126773297787,
-0.0018334980122745037,
-0.039401791989803314,
0.023076998069882393,
0.014194040559232235,
0.007744546048343182,
-0.01321964617818594,
0.010511927306652069,
-0.023287829011678696,
-0.0021287596318870783,
-0.019549725577235222,
-0.02593012899160385,
0.004848314914852381,
-0.01589193381369114,
-0.022314034402370453,
-0.019657734781503677,
0.008179651573300362,
-0.021615726873278618,
-0.03516044095158577,
0.03198903053998947,
0.024101296439766884,
0.03755691275000572,
-0.007762002758681774,
-0.026593614369630814,
0.016283297911286354,
-0.05738787725567818,
-0.0029289531521499157,
-0.01238499116152525,
-0.04974920302629471,
0.028315605595707893,
0.03431537374854088,
0.0670180693268776,
0.023999657481908798,
0.018634673207998276,
-0.0036134696565568447,
-0.011724184267222881,
-0.01146494597196579,
0.05160071700811386,
-0.018114250153303146,
-0.011114520952105522,
0.017079370096325874,
0.007695135660469532,
-0.03000064007937908,
-0.051554154604673386,
0.005674134939908981,
0.019077355042099953,
-0.017560578882694244,
0.021848367527127266,
0.018636135384440422,
-0.016774268820881844,
-0.019360825419425964,
0.03573419153690338,
-0.04456203058362007,
0.0067758020013570786,
0.020473670214414597,
0.043012529611587524,
-0.04841550439596176,
-0.017646417021751404,
0.006963496096432209,
-0.013934929855167866,
0.016794508323073387,
0.019678940996527672,
-0.029643379151821136,
-0.014824924990534782,
-0.015814144164323807,
-0.0029989657923579216,
-0.015263919718563557,
-0.027569426223635674,
-0.012033875100314617,
0.013274133205413818,
-0.0005216854042373598,
0.049408044666051865,
-0.04919381067156792,
0.04033700376749039,
0.02228425070643425,
-0.03462379798293114,
0.030690431594848633,
0.04549350589513779,
-0.007256187964230776,
0.02612403966486454,
0.04929332807660103,
0.024910522624850273,
0.04634401574730873,
0.000923001382034272,
-0.01235469151288271,
0.044532183557748795,
-0.029950225725769997,
-0.059640057384967804,
0.053082916885614395,
-0.010138935409486294,
0.005531547125428915,
0.03981644660234451,
-0.026298759505152702,
-0.010169152170419693,
0.018976369872689247,
0.014001688919961452,
-0.012576773762702942,
-0.02805047482252121,
-0.0057950993068516254,
0.019298328086733818,
-0.0005657058209180832,
0.004316580947488546,
-0.006495361216366291,
-0.043000489473342896,
0.02317182347178459,
0.005008616950362921,
0.0028862806502729654,
0.013157485984265804,
-0.025480758398771286,
0.0152853112667799,
0.012862655334174633,
-0.014938785694539547,
-0.01834219880402088,
0.02545330300927162,
0.0726553201675415,
-0.021231895312666893,
0.022518951445817947,
-0.002511948812752962,
0.043502043932676315,
-0.12156499922275543,
-0.007933741435408592,
-0.015763811767101288,
0.07002677768468857,
0.03298185020685196,
-0.043050337582826614,
0.0315297469496727,
0.03712718188762665,
-0.0901351347565651,
0.019222186878323555,
0.0002510295598767698,
-0.053052715957164764,
-0.043742381036281586,
0.01730252616107464,
-0.03839283436536789,
0.07181881368160248,
-0.025509139522910118,
0.03109150379896164,
0.03994842246174812,
0.03622566536068916,
-0.0318518728017807,
-0.03667724132537842,
-0.03488941490650177,
0.006466779392212629,
0.021161461248993874,
0.011577443219721317,
0.09337270259857178,
-0.016832388937473297,
-0.05295320600271225,
0.0616883859038353,
-0.015283524058759212,
-0.025909028947353363,
0.011685451492667198,
0.0051650251261889935,
-0.007116620894521475,
0.042588237673044205,
0.017283158376812935,
0.007565197069197893,
0.01966490037739277,
-0.008703150786459446,
0.031859900802373886,
0.01891184039413929,
0.0024997990112751722,
0.023629827424883842,
0.045473258942365646,
-0.028011854737997055,
-0.016295524314045906,
0.020176662132143974,
-0.0043796636164188385,
-0.030958330258727074,
-0.0003955813590437174,
-0.000026803152650245465,
0.04079275578260422,
-0.02192559465765953,
0.05600107088685036,
-0.05942326411604881,
-0.018572816625237465,
-0.02093576081097126,
-0.008182133547961712,
0.030434921383857727,
0.03599303588271141,
-0.019540047273039818,
-0.05258792266249657,
0.033573757857084274,
-0.01925637200474739,
0.02426963672041893,
-0.033304598182439804,
-0.019216910004615784,
0.011589517816901207,
-0.018182413652539253,
0.0122008565813303,
-0.030925776809453964,
-0.040088217705488205,
0.0055228341370821,
-0.04811375215649605,
0.01275669876486063,
-0.0016171184834092855,
-0.008823415264487267,
-0.0071017141453921795,
-0.04863341525197029,
0.022977188229560852,
0.016790783032774925,
0.000945836422033608,
-0.002408559899777174,
-0.0026839429046958685,
-0.03139639273285866,
0.044998180121183395,
0.03451446816325188,
-0.03553011640906334,
-0.001166128320619464,
-0.004104688297957182,
0.003369503188878298,
0.03063776344060898,
-0.04735317453742027,
0.0217021182179451,
0.00013312502414919436,
-0.02399258129298687,
-0.01763398014008999,
-0.00999910943210125,
-0.004091293551027775,
-0.017687154933810234,
0.009921763092279434,
0.03176803141832352,
-0.021575208753347397,
-0.011343704536557198,
-0.028770560398697853,
0.05954563245177269,
0.030479678884148598,
0.013468376360833645,
0.044906508177518845,
-0.020452110096812248,
0.041108839213848114,
0.025590596720576286,
-0.03235546872019768,
-0.0392061322927475,
-0.03519756346940994,
-0.05910491570830345,
0.016571832820773125,
-0.01674181967973709,
0.00856228731572628,
0.04258294031023979,
-0.04305342957377434,
0.004455056507140398,
-0.0000023885208975116257,
-0.043582670390605927,
0.01742994599044323,
0.03883808106184006,
0.004324349574744701,
0.004930729512125254,
-0.0058477651327848434,
0.03176423907279968,
0.01874624192714691,
0.0025621000677347183,
-0.013612482696771622,
0.037609171122312546,
-0.009439891204237938,
0.05668091028928757,
0.05867307633161545,
0.02630649134516716,
-0.015939861536026,
0.06552810221910477,
0.022418972104787827,
0.025047067552804947,
0.013812383636832237,
-0.007360836956650019,
0.010248207487165928,
0.014168757013976574,
-0.006897223647683859,
0.035792335867881775,
-0.02305096946656704,
0.0498872846364975,
-0.01528302300721407,
0.011454022489488125,
-0.04396037384867668,
-0.009961169213056564,
0.021130962297320366,
-0.019339581951498985,
0.0049650599248707294,
0.05006559565663338,
-0.025998398661613464,
-0.002184930257499218,
-0.028785834088921547,
0.0013160562375560403,
0.031842462718486786,
-0.047106411308050156,
0.01702098548412323,
-0.031148608773946762,
-0.005843255668878555,
0.015515460632741451,
-0.04602876678109169,
0.01568196527659893,
-0.022766249254345894,
-0.010555233806371689,
0.028593285009264946,
0.014592032879590988,
0.018147099763154984,
-0.029074691236019135,
-0.012873898260295391,
0.07175207138061523,
-0.03062584064900875,
0.003538800636306405,
-0.025985345244407654,
0.0010945919202640653,
-0.024389460682868958,
0.02037891559302807
] |
<p>For one particle angular momentum eigenket, we can represent it in position space, such as</p>
<p>$\langle\theta,\phi|l,m\rangle=Y_{lm}$</p>
<p>where $Y_{lm}$ means spherical harmonics. </p>
<p>But if we have we have two particle with angular momentum $\frac{1}{2}$(of course no angular momentum $\frac{1}{2}$ particle, but for simplicity) , the total angular momentum state $|10\rangle$ can be represented by sum of each angular momentum, </p>
<p>$|10\rangle$=$\frac{1}{\sqrt{2}}(|\frac{1}{2},\frac{1}{2}\rangle)+|\frac{1}{2},\frac{1}{2}\rangle$</p>
<p>At this stage, what is $\langle\theta,\phi|1,1\rangle$, when the added angular momentum represened in position space??</p>
<p>First I thought that it was </p>
<p>$\langle\theta,\phi|10\rangle$ $= \frac{1}{\sqrt{2}}(\langle\theta,\phi|\frac{1}{2},\frac{1}{2}\rangle)+\langle\theta,\phi|\frac{1}{2},\frac{1}{2}\rangle)\\=\frac{1}{\sqrt{2}}(Y_{\frac{1}{2},\frac{1}{2}}(\theta,\phi)Y_{\frac{1}{2},\frac{1}{2}}(\theta,\phi)+Y_{\frac{1}{2},\frac{1}{2}}(\theta,\phi)Y_{\frac{1}{2},\frac{1}{2}}(\theta,\phi))$</p>
<p>$\langle\theta,\phi|10\rangle$ $= Y_{1,0}(\theta, \phi)$</p>
<p>thus </p>
<p>$ Y_{1,0}(\theta, \phi) = \langle\theta,\phi|10\rangle = \frac{1}{\sqrt{2}}(Y_{\frac{1}{2},\frac{1}{2}}(\theta,\phi)Y_{\frac{1}{2},\frac{1}{2}}(\theta,\phi)+Y_{\frac{1}{2},\frac{1}{2}}(\theta,\phi)Y_{\frac{1}{2},\frac{1}{2}}(\theta,\phi))$</p>
<p>but if we think the bra operator, $\langle\theta,\phi|$ acts on total angular momentum state, it cannot acts on each particle's hilbert space, I think the right side of last equation cannot be hold. </p>
<p>so I thought that I have to find the corresponding operator of $\langle\theta,\phi|$, which acts on total angular momentum hilbert space, to each particle's space, but I'm not sure about this idea.</p>
<p>Is this right? if then, what is that operator?</p>
| 8,870 |
[
0.0014621552545577288,
0.005083183757960796,
0.010627984069287777,
-0.0468711294233799,
0.061789076775312424,
-0.009118027053773403,
-0.019751325249671936,
-0.03410134091973305,
0.0049896580167114735,
-0.05591800436377525,
0.06032571196556091,
0.01476997509598732,
0.05919217690825462,
0.021263137459754944,
0.005284911021590233,
0.01109656784683466,
-0.026451123878359795,
-0.003906483296304941,
-0.028262032195925713,
-0.023708797991275787,
-0.008484816178679466,
0.029154237359762192,
-0.013096392154693604,
-0.01642814837396145,
-0.03195509687066078,
0.058332256972789764,
0.049569547176361084,
0.0038286284543573856,
0.006216074805706739,
0.058808282017707825,
-0.007947949692606926,
-0.03651917353272438,
0.03347041830420494,
0.028665468096733093,
0.007823070511221886,
-0.017947951331734657,
-0.025983907282352448,
-0.018855491653084755,
0.0030092932283878326,
0.033647675067186356,
-0.06321927160024643,
-0.02325834520161152,
-0.05698784440755844,
0.03722294792532921,
-0.022684171795845032,
-0.004060028586536646,
-0.021560024470090866,
0.010497496463358402,
0.05301472917199135,
-0.04000839218497276,
0.0660487562417984,
0.015230372548103333,
-0.010556511580944061,
-0.020509446039795876,
-0.0006789302569814026,
-0.015789566561579704,
0.05940952152013779,
0.08889561146497726,
0.027186376973986626,
-0.060635559260845184,
-0.013062283396720886,
-0.029497819021344185,
-0.013646024279296398,
0.0011508024763315916,
-0.003244052641093731,
0.003862725803628564,
0.026696419343352318,
-0.011054719798266888,
-0.02058945596218109,
-0.006288065575063229,
0.03186060115695,
-0.014834534376859665,
0.04327530413866043,
-0.05756711959838867,
0.014843435026705265,
0.007416907697916031,
0.010522786527872086,
0.013758525252342224,
-0.003954730927944183,
0.006247989367693663,
0.0013165349373593926,
0.012454843148589134,
0.044029250741004944,
0.013610226102173328,
-0.01006785687059164,
0.007034861017018557,
0.06375784426927567,
0.007012057583779097,
0.00846331287175417,
0.050910670310258865,
0.024932458996772766,
0.038132794201374054,
0.04469684511423111,
-0.008310402743518353,
-0.02733341045677662,
0.02185206674039364,
-0.020637257024645805,
0.01604515314102173,
-0.00048494053771719337,
-0.00942264311015606,
0.0017116577364504337,
-0.0386754535138607,
0.010273917578160763,
0.07535044103860855,
-0.05164838582277298,
0.01271884050220251,
-0.03461736813187599,
-0.010374607518315315,
-0.038370851427316666,
-0.005649146158248186,
-0.02453857660293579,
0.04734351858496666,
-0.02031940594315529,
0.030059542506933212,
-0.013692252337932587,
-0.011362328194081783,
0.00029872075538150966,
0.016405029222369194,
0.0707043930888176,
0.04918067529797554,
0.01994057558476925,
-0.027405451983213425,
-0.020233020186424255,
-0.008973021060228348,
-0.05392327532172203,
0.012539965100586414,
0.029004521667957306,
-0.017664941027760506,
-0.07503116130828857,
0.009777870960533619,
0.03499993681907654,
0.01261024922132492,
0.028432652354240417,
0.021662939339876175,
0.019893920049071312,
-0.03281364217400551,
-0.10553790628910065,
-0.03051138110458851,
0.04492770880460739,
-0.041744839400053024,
0.010910981334745884,
-0.04587164148688316,
0.03744541108608246,
0.030702752992510796,
0.06182209029793739,
-0.012175423093140125,
0.02384655363857746,
0.02178623527288437,
0.043405599892139435,
0.0027805983554571867,
-0.006325509399175644,
-0.013521965593099594,
-0.012936732731759548,
-0.045028261840343475,
0.013746671378612518,
-0.03405407816171646,
0.03084532544016838,
0.06098530441522598,
-0.00017217290587723255,
0.0212742667645216,
0.01845180056989193,
-0.005048494320362806,
0.015795063227415085,
0.025875095278024673,
0.002181372605264187,
-0.010333039797842503,
0.05280175432562828,
0.022089971229434013,
0.0055865016765892506,
0.05740983784198761,
-0.02668403834104538,
-0.0025523195508867502,
-0.02957693673670292,
0.02535439096391201,
0.0388789065182209,
-0.03333538398146629,
-0.029695598408579826,
-0.08165950328111649,
-0.01719871535897255,
-0.007636963855475187,
-0.031418778002262115,
-0.0527426078915596,
-0.0196501687169075,
0.04546723514795303,
0.023511134088039398,
0.019606543704867363,
0.02737518586218357,
-0.009918116964399815,
-0.029255526140332222,
-0.04438187927007675,
-0.02040177956223488,
-0.04572421684861183,
0.009570960886776447,
-0.00943557359278202,
-0.0336422361433506,
0.05729855224490166,
-0.002621348248794675,
0.032501302659511566,
-0.006557088810950518,
-0.0309961698949337,
-0.03564564138650894,
0.028196383267641068,
-0.0007509741117246449,
-0.0098413722589612,
0.0302606001496315,
0.06850384920835495,
0.036991968750953674,
0.032080646604299545,
0.02338378317654133,
-0.0024123697075992823,
-0.010150063782930374,
-0.022897908464074135,
0.013326878659427166,
0.05452585592865944,
0.044139452278614044,
-0.008921751752495766,
-0.01552918367087841,
0.012096614576876163,
-0.0660257413983345,
0.029818806797266006,
-0.051170237362384796,
0.0686001256108284,
0.06906601041555405,
-0.039344340562820435,
0.005950483493506908,
0.016099339351058006,
0.008541149087250233,
0.013576150871813297,
0.01580682024359703,
-0.01054169237613678,
-0.037041861563920975,
0.0009037105483002961,
0.039152711629867554,
0.04433826357126236,
-0.042725224047899246,
0.0035078919027000666,
0.05245833471417427,
0.05685225874185562,
0.00511762173846364,
-0.0013050641864538193,
-0.03580203652381897,
-0.062403567135334015,
0.02949507161974907,
0.017604611814022064,
-0.017895327880978584,
-0.012071616016328335,
0.029161274433135986,
-0.02508310042321682,
0.0036259705666452646,
0.026359472423791885,
-0.040173087269067764,
0.038778580725193024,
-0.01116629596799612,
-0.01834682933986187,
-0.0033465418964624405,
-0.027430284768342972,
0.03760066628456116,
-0.021496225148439407,
0.054581381380558014,
0.025428008288145065,
-0.026587357744574547,
-0.035701289772987366,
-0.018162235617637634,
-0.003373189130797982,
-0.020122654736042023,
-0.01466780249029398,
-0.01730772852897644,
-0.0056281015276908875,
0.020931106060743332,
-0.03259049355983734,
-0.014015302993357182,
0.008800927549600601,
-0.02671697735786438,
-0.00017389905406162143,
-0.013974830508232117,
0.04893200471997261,
0.01620287261903286,
0.010659022256731987,
-0.032789766788482666,
-0.02118372917175293,
0.015232324600219727,
0.0077335103414952755,
0.026476314291357994,
0.0032519884407520294,
-0.07187921553850174,
-0.0023664585314691067,
-0.057232875376939774,
-0.01559955533593893,
0.013107117265462875,
-0.010562928393483162,
0.0009538602316752076,
-0.022413643077015877,
-0.002488568425178528,
-0.06421031057834625,
-0.032627057284116745,
-0.011405392549932003,
-0.0017426847480237484,
-0.05617854371666908,
-0.009945586323738098,
0.029130348935723305,
0.035890307277441025,
-0.03989214450120926,
-0.024379659444093704,
-0.04975523427128792,
-0.01828770712018013,
-0.0378098338842392,
-0.001730546122416854,
0.03316822648048401,
-0.036132361739873886,
0.022921230643987656,
0.022120404988527298,
0.00764011824503541,
-0.01268229354172945,
-0.08136063069105148,
-0.03115268610417843,
0.006856104824692011,
-0.0016807711217552423,
0.04979592189192772,
-0.013688787817955017,
-0.035389576107263565,
0.08875060081481934,
0.002129931002855301,
-0.01224068645387888,
-0.01632477156817913,
0.06316908448934555,
0.025103367865085602,
-0.04126716032624245,
0.016788089647889137,
0.029586877673864365,
-0.007715528830885887,
0.026474403217434883,
-0.014117729850113392,
-0.0030693979933857918,
0.05342749506235123,
0.0009086451027542353,
0.018369341269135475,
0.02318951115012169,
0.001529511297121644,
0.013106511905789375,
0.03988755866885185,
-0.008995870128273964,
-0.012148783542215824,
-0.00357373571023345,
0.004054155200719833,
0.038469649851322174,
0.004051899071782827,
-0.06938327848911285,
0.07073566317558289,
-0.012835054658353329,
0.01732361875474453,
-0.013074933551251888,
0.05775640532374382,
0.018645262345671654,
-0.04305757209658623,
0.010103840380907059,
0.005823174491524696,
0.02888648211956024,
0.00004303549576434307,
-0.03632136806845665,
0.03089088946580887,
-0.011676311492919922,
-0.014663148671388626,
-0.0027978261932730675,
0.0070597464218735695,
0.00005140434950590134,
0.05864160135388374,
-0.03552848845720291,
-0.07389393448829651,
-0.01825680583715439,
0.04342695698142052,
0.004364908207207918,
-0.0309978649020195,
-0.039696380496025085,
0.014325656928122044,
-0.07624195516109467,
-0.013618727214634418,
-0.026369018480181694,
0.05714542418718338,
-0.005057119764387608,
0.05886370688676834,
0.0006883079768158495,
-0.0023154206573963165,
0.018245398998260498,
-0.0036687960382550955,
-0.05970015749335289,
-0.01886572688817978,
0.012013318948447704,
-0.002486132550984621,
0.021180786192417145,
-0.020798956975340843,
-0.0005383913521654904,
-0.0431637242436409,
-0.017687572166323662,
-0.03803040459752083,
-0.01540848333388567,
-0.031381264328956604,
0.03922340273857117,
-0.03647163510322571,
-0.0007331753149628639,
-0.019090617075562477,
0.058358628302812576,
0.04401731491088867,
-0.003990305587649345,
0.03692634776234627,
0.06671719998121262,
-0.05925557762384415,
0.03738177567720413,
-0.020232200622558594,
0.023311996832489967,
0.036813315004110336,
0.017263762652873993,
0.03672107309103012,
0.03402028605341911,
-0.017656894400715828,
0.008197729475796223,
-0.0208585262298584,
0.06304991990327835,
0.021876763552427292,
-0.027451861649751663,
-0.0015107080107554793,
-0.03042076900601387,
-0.0026014368049800396,
-0.009594134986400604,
0.06766802072525024,
-0.0037056917790323496,
-0.0033765709958970547,
0.029149943962693214,
0.015823092311620712,
0.005556655582040548,
0.020923899486660957,
0.026921939104795456,
-0.006777648814022541,
-0.01976553536951542,
-0.02777716889977455,
0.02508070319890976,
-0.010602067224681377,
0.007710759062319994,
0.0072082653641700745,
-0.03815707191824913,
-0.01644766330718994,
0.015392390079796314,
0.011785974726080894,
-0.0060549089685082436,
-0.011095378547906876,
0.01707964949309826,
-0.04526358097791672,
0.0000854927275213413,
-0.008393656462430954,
-0.007935169152915478,
0.005727388430386782,
0.034786611795425415,
0.01579185761511326,
0.028101257979869843,
0.018433736637234688,
-0.02245735190808773,
0.01719643734395504,
0.039753254503011703,
0.005969320889562368,
0.0013096050824970007,
0.0004180296091362834,
-0.007569729350507259,
-0.05463668704032898,
0.03049732930958271,
-0.025972094386816025,
0.04697788506746292,
-0.024459434673190117,
-0.014887736178934574,
-0.01202276162803173,
-0.0738494023680687,
-0.0563386008143425,
0.03639044985175133,
-0.02415654994547367,
0.014919997192919254,
-0.05578238144516945,
-0.006613984704017639,
-0.0205028485506773,
0.0024682623334228992,
-0.006348114926367998,
0.025234434753656387,
-0.0009461439913138747,
-0.010251088067889214,
-0.005375399719923735,
0.03322833031415939,
-0.01052931509912014,
-0.08098433911800385,
-0.0072970082983374596,
0.016539044678211212,
-0.006868075579404831,
-0.0013492174912244081,
-0.06664985418319702,
-0.09007270634174347,
0.0211039986461401,
0.020817510783672333,
0.037333350628614426,
0.014529166743159294,
-0.015592671930789948,
0.10045553743839264,
0.06792907416820526,
-0.023891596123576164,
0.039674147963523865,
-0.00961803738027811,
-0.005256451666355133,
0.00569009967148304,
-0.03361278399825096,
-0.0002291442797286436,
-0.03205670043826103,
0.015774482861161232,
-0.04771224409341812,
0.03296240046620369,
-0.023573623970150948,
0.062438007444143295,
-0.03818150982260704,
0.02633884735405445,
-0.013747072778642178,
-0.03384044021368027,
-0.021876566112041473,
0.006115759257227182,
-0.016492074355483055,
-0.013868552632629871,
-0.018732262775301933,
0.019398700445890427,
0.03498586267232895,
0.012530714273452759,
0.0034577997867017984,
-0.01653112657368183,
0.002280560787767172,
0.032376933842897415,
0.028224652633070946,
0.003249078057706356,
-0.03459759056568146,
-0.0031757690012454987,
0.02088833972811699,
-0.0470748133957386,
0.08004133403301239,
-0.0333971306681633,
0.016765600070357323,
0.023808443918824196,
-0.05186047405004501,
-0.07784699648618698,
0.024596191942691803,
-0.015392491593956947,
0.022809453308582306,
-0.01850922591984272,
-0.03380868211388588,
0.010536911897361279,
-0.0018984812777489424,
-0.03609204664826393,
0.005224146414548159,
0.026577332988381386,
-0.010910695418715477,
-0.02010100707411766,
-0.005836766678839922,
0.005884949117898941,
-0.01735665835440159,
-0.05808384343981743,
-0.002107667736709118,
0.0454016849398613,
-0.040713630616664886,
-0.011669371277093887,
0.01715320162475109,
0.024351242929697037,
0.0322502925992012,
-0.0065147168934345245,
-0.01747734844684601,
0.013728998601436615,
-0.020080912858247757,
0.024095162749290466,
-0.001138194464147091,
0.050220150500535965,
-0.032475050538778305,
-0.039377402514219284,
-0.03711323440074921,
-0.009638005867600441,
0.027342025190591812,
-0.018898023292422295,
-0.025681793689727783,
0.020361125469207764,
-0.0137527696788311,
0.030488530173897743,
0.006227971985936165,
-0.011513004079461098,
-0.023262623697519302,
0.0381070151925087,
-0.014893320389091969,
-0.02599257044494152,
-0.016247069463133812,
-0.043721701949834824,
0.02658952958881855,
0.014441502280533314,
-0.014072805643081665,
0.0008311084238812327,
0.05638570338487625,
-0.013278397731482983,
-0.002315996680408716,
0.03138922154903412,
0.009012307971715927,
-0.0082057174295187,
-0.04241974279284477,
0.026889050379395485,
0.006994281429797411,
0.03868424892425537,
-0.03995400667190552,
-0.000175102410139516,
-0.02071501314640045,
0.021906189620494843,
0.05013656988739967,
0.005781747400760651,
0.032602157443761826,
0.03319921717047691,
0.0020456144120544195,
-0.03738513961434364,
-0.04720558226108551,
-0.02350189909338951,
-0.0033840034157037735,
-0.009760548360645771,
0.061941567808389664,
-0.05224253609776497,
0.00016720961139071733,
0.05363992229104042,
0.0670989453792572,
-0.03837432339787483,
0.008554530330002308,
0.033723846077919006,
-0.025946980342268944,
0.013419130817055702,
0.004822047892957926,
-0.049926742911338806,
0.026899216696619987,
-0.03579292073845863,
0.0313069224357605,
-0.00026393879670649767,
-0.008718172088265419,
0.028307611122727394,
0.046765945851802826,
0.045164018869400024,
-0.02051626518368721,
-0.003425795817747712,
-0.04357966408133507,
0.01331313420087099,
0.0198300089687109,
-0.02793213538825512,
-0.01810320094227791,
0.023126570507884026,
0.039135754108428955,
0.014120052568614483,
-0.0032822275534272194,
-0.0054465788416564465,
-0.05185956507921219,
-0.05444341525435448,
-0.006156697869300842,
-0.044584181159734726,
-0.003219736972823739,
-0.027837520465254784,
-0.0031399866566061974,
0.00538914930075407,
-0.008170569315552711,
0.02443401888012886,
0.01802455075085163,
0.03485042601823807,
-0.039672594517469406,
0.054430123418569565,
0.035054486244916916,
0.023293670266866684,
-0.01242055743932724,
0.013132580555975437,
0.1386217325925827,
0.029005806893110275,
0.03372037410736084,
-0.022245708853006363,
-0.0110018914565444,
0.014643966220319271,
0.018711119890213013,
-0.016564002260565758,
0.02283308282494545,
0.012045219540596008,
0.01100964192301035,
-0.021814383566379547,
0.06400015205144882,
-0.01641147956252098,
-0.005750499200075865,
0.007947749458253384,
-0.024884391576051712,
-0.05119357630610466,
-0.009244225919246674,
-0.001121455803513527,
-0.028927244246006012,
0.007704474963247776,
-0.028384795412421227,
0.014901572838425636,
-0.03388860821723938,
0.01966269314289093,
-0.03494742140173912,
-0.0256139375269413,
-0.006806182209402323,
-0.00232556089758873,
-0.05417345464229584,
0.009688153862953186,
-0.003181574633345008,
0.00839647464454174,
-0.015861403197050095,
0.03460302948951721,
-0.000380576413590461,
-0.019775310531258583,
0.02623489312827587,
0.04008691757917404,
-0.01605299860239029,
0.008284386247396469,
0.0037712352350354195,
-0.02633586898446083,
-0.03106665425002575,
-0.004701065365225077,
-0.02409416064620018,
0.11064625531435013,
-0.021312886849045753,
-0.018210722133517265,
-0.02143741026520729,
-0.02093026414513588,
0.015035506337881088,
-0.028934767469763756,
0.013991013169288635,
0.011346209794282913,
0.037228092551231384,
0.0045671770349144936,
0.02754390612244606,
-0.007867390289902687,
-0.012022127397358418,
0.020184136927127838,
0.029466910287737846,
-0.025035226717591286,
0.006445829290896654,
0.015552274882793427,
0.024906130507588387,
0.026148464530706406,
0.026377802714705467,
-0.002789626829326153,
-0.032000914216041565,
0.015196174383163452,
-0.043720558285713196,
-0.04197780415415764,
0.037997134029865265,
0.0043111806735396385,
0.04418468847870827,
0.017953356727957726,
-0.013244901783764362,
-0.017963021993637085,
-0.06282413005828857,
-0.00835429783910513,
0.0026116780936717987,
-0.03665319085121155,
0.02335619367659092,
0.002298203995451331,
-0.00658238772302866,
0.07657992094755173,
-0.03957538679242134,
-0.0385427325963974,
-0.008265269920229912,
0.04206943139433861,
0.02305571176111698,
-0.004261336755007505,
-0.0379384383559227,
0.030928246676921844,
-0.015132701955735683,
0.0005871180328540504,
-0.02061258628964424,
0.006543514784425497,
0.012041894719004631,
0.033999595791101456,
0.0009740522364154458,
0.03504485264420509,
-0.009036610834300518,
-0.031153157353401184,
0.01595563441514969,
-0.026276271790266037,
-0.017719607800245285,
0.06154487654566765,
0.024630313739180565,
-0.025641869753599167,
0.008992262184619904,
0.020124904811382294,
-0.025304503738880157,
0.018173998221755028,
-0.006464891601353884,
-0.011316658928990364,
-0.016864977777004242,
-0.02165578305721283,
0.0030522760935127735,
0.03155605494976044,
0.027835650369524956,
-0.025388916954398155,
0.023244792595505714,
-0.0028530703857541084,
-0.014277053065598011,
-0.015492280013859272,
0.024020923301577568,
0.004760881885886192,
0.010456583462655544,
0.05359142646193504,
0.027324100956320763,
-0.021294154226779938,
-0.01478249579668045,
0.022836249321699142,
0.004521896131336689,
0.05276673287153244,
-0.016993362456560135,
-0.018026527017354965,
0.00027071929071098566,
-0.016025541350245476,
-0.019647734239697456,
0.04514913260936737,
0.003785546403378248,
0.07496396452188492,
0.06350796669721603,
0.01159648597240448,
-0.032071370631456375,
0.009252785705029964,
-0.014058723114430904,
-0.012284628115594387,
0.002194794127717614,
-0.012324056588113308,
0.02433839440345764,
-0.02936992049217224,
0.046216584742069244,
-0.022273555397987366,
0.006999898701906204,
0.029228903353214264,
-0.010635544545948505,
-0.03873300179839134,
-0.016417404636740685,
0.0008163159945979714,
0.008258407935500145,
0.046593859791755676,
0.029956797137856483,
-0.012713697738945484,
0.0000487886973132845,
0.005164583679288626,
-0.022324729710817337,
0.03093559667468071,
0.03814913332462311,
0.004059997852891684,
-0.0758344903588295,
-0.044661253690719604,
0.017346523702144623,
0.003465218935161829,
0.039557427167892456,
-0.038127973675727844,
0.0038907951675355434,
0.03183766454458237,
-0.1009010374546051,
0.010517550632357597,
-0.0025344211608171463,
0.0016689205076545477,
-0.02423327974975109,
-0.0038459133356809616,
-0.02696201764047146,
0.05848798155784607,
0.016865819692611694,
0.05380721762776375,
-0.0016397014260292053,
-0.0032445478718727827,
-0.02027704007923603,
-0.019663924351334572,
-0.021037641912698746,
0.013795733451843262,
-0.027095036581158638,
0.00038840132765471935,
0.07983873784542084,
-0.03575906157493591,
-0.006982461549341679,
0.02962625026702881,
-0.015891894698143005,
-0.02421541139483452,
-0.040091343224048615,
0.02764352411031723,
-0.0007602123660035431,
0.041071925312280655,
-0.028791317716240883,
0.003919821698218584,
0.010807144455611706,
0.010320383124053478,
0.0340033657848835,
0.00048443861305713654,
-0.010360915213823318,
-0.014970464631915092,
-0.001508733257651329,
-0.03295410796999931,
-0.04062812775373459,
0.032231055200099945,
0.009919489733874798,
0.004808036144822836,
0.04204275831580162,
0.018859658390283585,
-0.005864395294338465,
-0.024493366479873657,
0.03105223923921585,
-0.026644935831427574,
-0.005358767230063677,
-0.02872016653418541,
0.009332157671451569,
-0.013927798718214035,
-0.003914299886673689,
-0.005732527002692223,
-0.027509454637765884,
0.014870768412947655,
0.01964925229549408,
-0.0272284634411335,
-0.02863728441298008,
-0.02175811305642128,
0.036876071244478226,
-0.0014550263294950128,
0.02435723878443241,
-0.00907925982028246,
-0.058854714035987854,
0.009156470187008381,
-0.025851771235466003,
0.023604845628142357,
0.0033873997163027525,
-0.012029466219246387,
-0.009510030969977379,
-0.09448082000017166,
0.0022183707915246487,
0.06092485040426254,
-0.006832135375589132,
-0.008026177994906902,
-0.000642565602902323,
-0.005837616976350546,
0.02634105272591114,
0.08017805963754654,
0.03297595679759979,
-0.003983908332884312,
0.010452961549162865,
-0.022909928113222122,
0.03221607953310013,
-0.04523133113980293,
0.0043215323239564896,
-0.030230827629566193,
-0.012771183624863625,
0.0008323285146616399,
-0.01285697054117918,
-0.017392735928297043,
0.0087727140635252,
0.0489785373210907,
-0.027932045981287956,
-0.037337273359298706,
-0.010054667480289936,
-0.01010313630104065,
0.06576710194349289,
0.0034730923362076283,
0.023664768785238266,
0.04590637609362602,
0.008341182954609394,
0.002223114250227809,
0.023579660803079605,
-0.03230847418308258,
-0.031480107456445694,
-0.027644997462630272,
-0.052377745509147644,
-0.017180614173412323,
-0.04783078283071518,
0.0013105174293741584,
0.04615028575062752,
-0.025261301547288895,
-0.023655150085687637,
0.06346932798624039,
-0.00866745412349701,
-0.026547791436314583,
0.05307125300168991,
0.0010945468675345182,
0.05320913717150688,
0.037030357867479324,
0.04324527084827423,
0.0015573346754536033,
-0.007642850279808044,
0.02214701659977436,
0.03235336020588875,
0.01707335375249386,
0.021452028304338455,
-0.027356218546628952,
-0.0037682922556996346,
-0.01683424785733223,
0.00897649209946394,
-0.02369622327387333,
0.030039852485060692,
-0.010114775039255619,
0.0142776845023036,
0.015130576677620411,
-0.03857378661632538,
-0.011436023749411106,
0.00762648181989789,
-0.01780388318002224,
0.08902358263731003,
-0.06344841420650482,
-0.008794649504125118,
-0.02967437356710434,
0.011284957639873028,
-0.006506870500743389,
0.0056882258504629135,
0.0277105700224638,
0.03798551857471466,
-0.0003563418867997825,
-0.03882696479558945,
-0.025515591725707054,
-0.0028197094798088074,
0.028574343770742416,
-0.03850775212049484,
0.005907578859478235,
0.024937734007835388,
-0.005067640449851751,
-0.0045507983304560184,
-0.04955555871129036,
-0.016067011281847954,
-0.038672272115945816,
0.036620885133743286,
-0.00005087434692541137,
0.03247060254216194,
0.00011463953705970198,
-0.03281829133629799,
-0.009571447968482971,
0.02545740455389023,
-0.013437364250421524,
-0.031575482338666916,
-0.010857650078833103,
0.0095263896510005,
0.0002626504865474999,
-0.01990424282848835
] |
<p>Isolated system will preserve its entropy unchanged (for fully reversible system) or it will increase its entropy (for system with irreversible processes).</p>
<p>For a closed system, it can receive energy in form of heat. Does this always imply, that its entropy will be below maximum? Is it possible to add heat in such a way, that entropy will remain unchanged and maximum?</p>
| 8,871 |
[
-0.027141310274600983,
-0.016598008573055267,
-0.011399741284549236,
0.030292034149169922,
0.028832044452428818,
0.004079964943230152,
-0.03844832628965378,
-0.01889158971607685,
-0.0018596956506371498,
-0.04949651286005974,
0.04213081672787666,
0.018220840021967888,
-0.0039468929171562195,
0.02331165410578251,
0.013673023320734501,
0.0037548579275608063,
-0.001777512370608747,
-0.015972930938005447,
0.0006003457820042968,
0.002971808658912778,
-0.047511592507362366,
0.06408220529556274,
0.007722936570644379,
-0.0011538538383319974,
-0.04787560924887657,
0.052258215844631195,
0.002256114035844803,
-0.008135012350976467,
0.027731256559491158,
0.04342188313603401,
0.0010500091593712568,
-0.02834230102598667,
0.002342983614653349,
0.03415564447641373,
0.039359889924526215,
-0.031892865896224976,
-0.037091709673404694,
-0.012148468755185604,
0.003760523861274123,
-0.02188008278608322,
-0.03456699848175049,
-0.02162259817123413,
-0.002261933172121644,
0.021640244871377945,
-0.032983966171741486,
0.01517440378665924,
-0.003292651381343603,
-0.010396210476756096,
0.030553732067346573,
-0.0576062873005867,
0.03333719074726105,
-0.008062997832894325,
0.0277035441249609,
0.012531694024801254,
0.015184342861175537,
0.01851338893175125,
0.0639115497469902,
0.044662706553936005,
-0.007145647890865803,
-0.03668423742055893,
-0.0022121684160083532,
-0.005589216481894255,
-0.02109706960618496,
-0.01696399413049221,
-0.0037836285773664713,
0.017443235963582993,
-0.0002718734322115779,
-0.0038871399592608213,
0.05834608152508736,
0.030867429450154305,
-0.007109890691936016,
0.015823885798454285,
0.038879331201314926,
-0.011756490916013718,
0.04447081685066223,
-0.03202585503458977,
0.010891709476709366,
0.0017431421438232064,
0.025065889582037926,
0.03861010819673538,
0.04342425614595413,
0.015000791288912296,
0.041904598474502563,
0.04334161430597305,
0.013857612386345863,
-0.019603142514824867,
0.08138773590326309,
0.0055406647734344006,
0.0589560866355896,
0.04175421968102455,
0.01494589727371931,
0.008579973131418228,
0.025756334885954857,
-0.025154095143079758,
-0.023065900430083275,
0.002379724755883217,
-0.00802722480148077,
0.04199051856994629,
-0.021593213081359863,
-0.0036417930386960506,
-0.002556134480983019,
-0.0021037303376942873,
0.037246063351631165,
0.04327193647623062,
0.04268549755215645,
-0.009779520332813263,
-0.0649132952094078,
-0.008328376337885857,
0.01800469309091568,
-0.003990810830146074,
-0.03877723589539528,
0.014396724291145802,
0.004090867005288601,
-0.01413078885525465,
-0.0036801823880523443,
-0.029246265068650246,
-0.012177199125289917,
-0.04978637024760246,
0.055559054017066956,
0.04689024016261101,
0.037719544023275375,
-0.00727339182049036,
0.006072881165891886,
-0.01839148811995983,
-0.059386175125837326,
0.03507659584283829,
0.030201848596334457,
0.012623925693333149,
-0.06683013588190079,
0.027755964547395706,
-0.015376978553831577,
0.008794751949608326,
-0.010986021719872952,
-0.004841730464249849,
0.04052380844950676,
-0.026578862220048904,
-0.11154123395681381,
-0.057688452303409576,
0.03941589966416359,
-0.01031486876308918,
-0.015974631533026695,
-0.07098904997110367,
0.019927728921175003,
0.06521249562501907,
0.07561321556568146,
-0.008835979737341404,
-0.014858306385576725,
0.012949123047292233,
0.011670771054923534,
0.02297356352210045,
-0.002229209989309311,
-0.02966502122581005,
0.00378816737793386,
-0.03271786868572235,
-0.012910011224448681,
-0.06505230069160461,
0.05428534001111984,
0.062282439321279526,
-0.015925105661153793,
0.01214694045484066,
0.007553896866738796,
-0.06418032199144363,
-0.009410985745489597,
-0.0015507773496210575,
-0.018355054780840874,
-0.03645181655883789,
0.09311804920434952,
-0.02282196469604969,
0.04979630932211876,
0.01735359989106655,
0.032990261912345886,
0.026065735146403313,
-0.030962111428380013,
0.016214028000831604,
0.020596785470843315,
-0.007043326739221811,
-0.022134676575660706,
-0.03344903513789177,
0.0009310362511314452,
0.04555334523320198,
-0.02661493979394436,
-0.013046984560787678,
-0.029865402728319168,
0.0023559879045933485,
0.0037478727754205465,
0.010380642488598824,
0.02619681879878044,
0.0061998614110052586,
0.010791962966322899,
-0.04593050107359886,
-0.018412137404084206,
-0.08612638711929321,
0.016812827438116074,
0.02329687587916851,
-0.000051465747674228624,
0.02069465070962906,
0.03927991911768913,
0.05400014668703079,
-0.036576204001903534,
0.013558659702539444,
-0.004280945286154747,
0.0019022490596398711,
-0.00629016337916255,
-0.02007879689335823,
0.027090786024928093,
0.06879419088363647,
0.04570140689611435,
0.025628121569752693,
0.025810368359088898,
-0.0072866203263401985,
-0.05808272585272789,
0.004488414153456688,
-0.029961219057440758,
0.007544322870671749,
0.004236111417412758,
-0.013151400722563267,
0.019442055374383926,
0.011578505858778954,
-0.009093600325286388,
-0.008600770495831966,
-0.0088282385841012,
0.08984927833080292,
0.02933124452829361,
0.013962497003376484,
0.005404789466410875,
0.0341484397649765,
0.03528645262122154,
0.014979899860918522,
-0.033365026116371155,
-0.04300738126039505,
-0.07222037762403488,
0.001270257169380784,
0.012415756471455097,
0.05607719346880913,
-0.08631501346826553,
0.012667085975408554,
0.01522124744951725,
-0.01771957240998745,
0.027511749416589737,
-0.00008719202742213383,
-0.01818706840276718,
-0.03198962286114693,
0.06528214365243912,
0.004225459415465593,
0.025381984189152718,
0.020328950136899948,
0.01985609158873558,
-0.018729673698544502,
0.024806665256619453,
-0.0027363707777112722,
0.025395628064870834,
0.009088329039514065,
0.014742476865649223,
0.022102905437350273,
-0.018184524029493332,
-0.025281373411417007,
-0.002016387414187193,
-0.017202289775013924,
0.010016737505793571,
-0.021806349977850914,
-0.00047631870256736875,
0.025850581005215645,
-0.032634004950523376,
0.0024925912730395794,
-0.032314181327819824,
-0.0095901470631361,
-0.025043772533535957,
-0.025555701926350594,
0.0220490675419569,
-0.03426183760166168,
0.00034854179830290377,
-0.018609801307320595,
0.03341780975461006,
-0.01770775206387043,
-0.015114795416593552,
0.03534070774912834,
-0.019259445369243622,
0.015264409594237804,
-0.06229352578520775,
-0.008532747626304626,
-0.024626364931464195,
-0.030124055221676826,
-0.008688134141266346,
0.012188711203634739,
-0.03127218782901764,
0.02155068702995777,
-0.024898992851376534,
-0.040313392877578735,
0.01564178615808487,
-0.042639341205358505,
0.023363327607512474,
0.010618493892252445,
-0.01366406586021185,
-0.054188646376132965,
-0.005258253775537014,
0.00011359374911990017,
0.0138466227799654,
-0.01997266337275505,
-0.013799083419144154,
0.08066415786743164,
-0.006084000691771507,
-0.03153713420033455,
-0.008511463180184364,
-0.06322764605283737,
-0.04354472458362579,
0.009524640627205372,
-0.02307695895433426,
0.011101661249995232,
-0.009905916638672352,
0.0353386253118515,
0.04800941422581673,
-0.03120909444987774,
-0.029402349144220352,
-0.05013309046626091,
-0.06520893424749374,
0.016245681792497635,
-0.030853265896439552,
0.027290167286992073,
-0.011709620244801044,
-0.01539812982082367,
0.047690097242593765,
0.0295967198908329,
-0.038305968046188354,
0.000011195297702215612,
-0.031185930594801903,
-0.006547409575432539,
-0.005057317204773426,
-0.03596552461385727,
0.007563904859125614,
0.006976848468184471,
0.028456436470150948,
0.04619666188955307,
0.022880546748638153,
0.007007851265370846,
-0.0020520836114883423,
-0.05172297731041908,
0.04089115187525749,
0.024025840684771538,
0.03458835184574127,
0.05227036401629448,
-0.0021964870393276215,
-0.009724144823849201,
0.019687945023179054,
0.020179636776447296,
0.051779936999082565,
0.00526922382414341,
-0.029854875057935715,
0.06321293115615845,
0.03549899160861969,
0.037124983966350555,
-0.048491220921278,
0.06449012458324432,
-0.028576437383890152,
0.027512725442647934,
0.008888776414096355,
0.011043621227145195,
0.04022219404578209,
-0.008321723900735378,
-0.0060498351231217384,
-0.019686944782733917,
0.08242013305425644,
-0.01857512630522251,
-0.0281970277428627,
0.01139412634074688,
0.005563104059547186,
0.03517244756221771,
0.030800506472587585,
0.007560451980680227,
0.03440757095813751,
0.021903418004512787,
0.02342662401497364,
0.011538764461874962,
-0.004097743891179562,
0.0035925854463130236,
-0.08025073260068893,
0.004786646459251642,
-0.018661243841052055,
0.038536347448825836,
0.018443135544657707,
0.030448995530605316,
0.011492251418530941,
0.016910986974835396,
0.03840356320142746,
-0.0031229460146278143,
-0.07232930511236191,
0.06258946657180786,
-0.01618661917746067,
-0.002396723022684455,
0.01767062582075596,
0.010365825146436691,
0.010706974193453789,
-0.031228190287947655,
-0.043329183012247086,
-0.012203224003314972,
-0.010765546932816505,
-0.058985307812690735,
-0.031156523153185844,
-0.04019707813858986,
-0.048236116766929626,
0.003178561804816127,
0.013006902299821377,
0.02033223584294319,
-0.05790017545223236,
0.012205383740365505,
0.0243705902248621,
-0.013667639344930649,
0.036320850253105164,
0.009456927888095379,
0.01438132580369711,
0.02941366285085678,
0.02251146361231804,
0.040638573467731476,
0.029153097420930862,
0.014055524952709675,
0.023763185366988182,
0.011369380168616772,
0.007398029789328575,
0.007997531443834305,
-0.01844954490661621,
-0.03217354044318199,
-0.043326910585165024,
-0.004266728181391954,
-0.021504780277609825,
0.00579815125092864,
-0.001121880137361586,
0.04491741955280304,
-0.013170335441827774,
-0.01749342307448387,
-0.05043327063322067,
-0.0054597738198935986,
0.03649502992630005,
0.007020034361630678,
-0.05734776705503464,
-0.010872268117964268,
-0.03598443791270256,
-0.020310260355472565,
0.00499777402728796,
0.004610902164131403,
-0.008066157810389996,
-0.03412998095154762,
0.030284836888313293,
-0.028121044859290123,
0.028527509421110153,
-0.019440701231360435,
-0.020958513021469116,
0.026290439069271088,
0.04523976147174835,
0.016443202272057533,
0.003855467773973942,
0.026220958679914474,
0.0064133224077522755,
0.0024371277540922165,
-0.00843642558902502,
-0.011971360072493553,
-0.05551857501268387,
-0.009341645054519176,
0.060759786516427994,
0.05437161400914192,
-0.008105847053229809,
-0.011767827905714512,
-0.042354557663202286,
-0.0024615819565951824,
0.030856763944029808,
0.018078533932566643,
0.04126369208097458,
-0.010641809552907944,
-0.027535753324627876,
-0.0073247808031737804,
-0.03337571769952774,
-0.020819131284952164,
0.015342500992119312,
0.00047285176697187126,
0.02191445603966713,
0.004225325770676136,
-0.018651774153113365,
-0.004034674260765314,
-0.0028221486136317253,
-0.021857667714357376,
0.03455359861254692,
-0.03699497878551483,
0.019117912277579308,
0.002554526785388589,
0.0055254483595490456,
-0.00510694133117795,
-0.08170358836650848,
0.018266594037413597,
0.0021703499369323254,
-0.05784375220537186,
0.004303427413105965,
-0.031383201479911804,
-0.023879293352365494,
0.027737030759453773,
0.012540689669549465,
-0.030250413343310356,
-0.01551478449255228,
-0.013719187118113041,
0.07735894620418549,
0.01815580017864704,
-0.01822158508002758,
0.0570446141064167,
0.07498142868280411,
-0.010994752869009972,
-0.012972919270396233,
-0.019596081227064133,
0.043835561722517014,
-0.054667118936777115,
0.0022945969831198454,
-0.060494743287563324,
0.029871707782149315,
-0.030647465959191322,
0.058432482182979584,
-0.001281566685065627,
0.01840408332645893,
-0.010066445916891098,
-0.03614019975066185,
-0.006938515231013298,
0.02844676375389099,
0.011131458915770054,
0.006832202896475792,
-0.04124319180846214,
0.046166643500328064,
-0.008061632513999939,
-0.0112082464620471,
-0.009004522114992142,
0.004529224708676338,
0.014204702340066433,
0.03314876928925514,
-0.0416361503303051,
0.04480277746915817,
-0.004350793547928333,
-0.03374801576137543,
-0.007894960232079029,
-0.026367366313934326,
0.07098013907670975,
-0.026260802522301674,
0.005244184751063585,
0.03932665288448334,
-0.04197009652853012,
0.03052699938416481,
0.003927257377654314,
-0.0005787689588032663,
-0.03696504607796669,
-0.05190321430563927,
0.0762847363948822,
0.002886377042159438,
0.0013732347870245576,
-0.07261032611131668,
-0.03526512160897255,
0.033270105719566345,
-0.0037483784835785627,
-0.02818690612912178,
-0.06408140808343887,
-0.011887794360518456,
-0.03564111888408661,
-0.037630729377269745,
-0.015052475966513157,
0.0020290911197662354,
0.011671233922243118,
0.004475714638829231,
0.025931065902113914,
0.026471290737390518,
0.006964913569390774,
-0.00036225392250344157,
-0.022233864292502403,
0.03601018339395523,
-0.007153225131332874,
-0.007195570040494204,
-0.004929371643811464,
0.02985997311770916,
-0.024530477821826935,
-0.019412437453866005,
0.02231312356889248,
0.025459611788392067,
0.04469875246286392,
0.017598319798707962,
-0.02798345498740673,
0.03955073282122612,
-0.0004715957911685109,
-0.019156204536557198,
-0.011248105205595493,
0.006141797173768282,
0.018537823110818863,
0.01813557557761669,
0.011922371573746204,
-0.01039173174649477,
0.00776972621679306,
-0.07272765785455704,
0.0036914879456162453,
0.010434204712510109,
-0.02225426957011223,
-0.004721674136817455,
0.07213979959487915,
0.014170300215482712,
-0.01943635754287243,
-0.017649509012699127,
-0.012492428533732891,
0.033760521560907364,
-0.011341202072799206,
0.002971622394397855,
0.0023925190325826406,
-0.01606881618499756,
-0.03983191400766373,
-0.0268261656165123,
-0.05164024233818054,
-0.02623157948255539,
0.040082938969135284,
-0.022126104682683945,
0.03943614661693573,
0.01351637952029705,
0.0005267930100671947,
-0.006900896783918142,
-0.015853695571422577,
-0.0015161932678893209,
0.00821762066334486,
-0.004422501195222139,
0.05536511540412903,
-0.008222224190831184,
-0.01801995560526848,
0.028863972052931786,
0.051799844950437546,
-0.049087461084127426,
0.024014677852392197,
0.03361675888299942,
0.012413138523697853,
0.0008467757143080235,
-0.06718143820762634,
-0.019868887960910797,
0.013613234274089336,
-0.03946009278297424,
0.04154546558856964,
0.023276325315237045,
-0.02244764007627964,
0.016007335856556892,
-0.001604159246198833,
0.025498392060399055,
-0.07160406559705734,
-0.002028693212196231,
-0.03639393299818039,
0.01417194027453661,
0.003023459343239665,
0.014390164986252785,
0.022480765357613564,
-0.018683332949876785,
0.0009021700243465602,
0.004648555535823107,
-0.005720216315239668,
0.0022272078786045313,
-0.06920604407787323,
-0.006129665300250053,
-0.019607001915574074,
-0.06538505852222443,
0.032315969467163086,
0.022133858874440193,
-0.01948556676506996,
0.03577763959765434,
0.010227677412331104,
0.01520648691803217,
0.02159799449145794,
0.038820017129182816,
0.033553991466760635,
0.0700523853302002,
0.026848582550883293,
0.021180374547839165,
-0.008202270604670048,
0.0482664629817009,
0.10769283771514893,
0.06302381306886673,
-0.009218314662575722,
-0.060551390051841736,
0.013363460078835487,
0.00260405195876956,
0.027598902583122253,
-0.00458029517903924,
0.027716852724552155,
-0.00025136847398243845,
0.011435342021286488,
0.02019212767481804,
0.03324945643544197,
-0.014122233726084232,
-0.0002287762617925182,
0.03651890531182289,
-0.07988283783197403,
-0.03151312842965126,
0.022174278274178505,
0.013707386329770088,
-0.011370712891221046,
0.019574053585529327,
-0.03045525774359703,
-0.03479093685746193,
0.005347197409719229,
0.020894311368465424,
-0.029508160427212715,
-0.060767047107219696,
0.0325411893427372,
0.005528355948626995,
-0.009912814944982529,
-0.014851081185042858,
0.0055452617816627026,
-0.00043186379480175674,
-0.02400711551308632,
0.018352629616856575,
0.026165608316659927,
0.019259115681052208,
-0.017503824084997177,
0.025437192991375923,
0.017665840685367584,
0.004376170225441456,
0.03833702206611633,
-0.000016848403902258724,
-0.04892797768115997,
-0.00030243402579799294,
0.010617844760417938,
0.027014965191483498,
-0.0018690157448872924,
0.017059653997421265,
-0.0197235606610775,
0.020108332857489586,
0.013887896202504635,
-0.007204533088952303,
-0.03616446256637573,
0.010458935052156448,
0.014335617423057556,
-0.0066874208860099316,
-0.07070717215538025,
-0.0344497449696064,
0.020809227600693703,
0.006601868662983179,
0.020497262477874756,
-0.012477184645831585,
-0.013042849488556385,
0.0367911122739315,
-0.004364890046417713,
0.03053647093474865,
-0.012708621099591255,
0.008626922965049744,
-0.030166521668434143,
-0.009414366446435452,
-0.03332383558154106,
-0.03064795210957527,
-0.010568523779511452,
-0.0072640967555344105,
0.026386288926005363,
0.013578717596828938,
0.010426542721688747,
-0.04423838108778,
-0.028446119278669357,
0.02534748986363411,
0.00962748471647501,
0.0009036567062139511,
-0.03195365145802498,
0.04340755194425583,
-0.008423357270658016,
0.07016203552484512,
0.010587954893708229,
-0.031597696244716644,
0.04192410781979561,
0.0036992253735661507,
0.03782946243882179,
0.011441195383667946,
-0.006833096034824848,
0.006546077784150839,
-0.0643087700009346,
-0.001065606134943664,
0.009891464374959469,
0.037565506994724274,
0.017474446445703506,
-0.012555544264614582,
-0.017126474529504776,
0.013196439482271671,
-0.012183714658021927,
0.011403837241232395,
0.007130077574402094,
-0.009953368455171585,
-0.038632478564977646,
0.019329210743308067,
-0.028487449511885643,
0.0016660853289067745,
-0.05755005404353142,
0.0016388403018936515,
-0.012556612491607666,
-0.011202591471374035,
0.03618251159787178,
-0.016827302053570747,
0.009197432547807693,
-0.054060015827417374,
0.05030207708477974,
-0.0287557952105999,
-0.05459693819284439,
-0.028232919052243233,
-0.023762468248605728,
0.05772039666771889,
0.02809133008122444,
-0.026631807908415794,
0.026103777810931206,
0.008335591293871403,
-0.026101576164364815,
0.013086069375276566,
0.02804471366107464,
-0.019327757880091667,
-0.058419179171323776,
-0.0080306027084589,
-0.0034147833939641714,
0.06925293058156967,
-0.04355645924806595,
-0.046911731362342834,
0.04466009885072708,
-0.041380614042282104,
-0.009300917387008667,
-0.012671747244894505,
0.011639614589512348,
0.04302581027150154,
0.022352414205670357,
-0.007837126031517982,
-0.020214024931192398,
0.04122363403439522,
-0.006931610871106386,
-0.03574855253100395,
-0.0046754442155361176,
-0.02580001950263977,
-0.019750339910387993,
0.00628003990277648,
0.015828074887394905,
-0.009455365128815174,
-0.024271173402667046,
0.046737801283597946,
0.025375613942742348,
0.005383376032114029,
-0.02870659902691841,
0.006254046689718962,
-0.010193792171776295,
0.011597353965044022,
0.03327573463320732,
-0.026001056656241417,
0.04069312661886215,
0.04011531546711922,
-0.009376012720167637,
0.017700614407658577,
0.027046872302889824,
-0.017558882012963295,
-0.07466443628072739,
0.007743676193058491,
0.013078221119940281,
-0.050915032625198364,
0.030366715043783188,
-0.012917550280690193,
0.03304281458258629,
0.012734610587358475,
-0.07166397571563721,
-0.0012588207609951496,
-0.02474108338356018,
-0.009032226167619228,
-0.02506062388420105,
0.03600336238741875,
-0.04409117251634598,
0.05320017784833908,
0.05316898226737976,
0.03720751404762268,
-0.008431799709796906,
0.017221270129084587,
-0.023899178951978683,
-0.015272494405508041,
-0.039231881499290466,
0.024540819227695465,
0.005625521764159203,
-0.011002494022250175,
0.06615112721920013,
-0.03383772820234299,
-0.048763811588287354,
-0.007948728278279305,
-0.02191643789410591,
-0.01094505749642849,
0.007299474440515041,
0.017252499237656593,
-0.005468911956995726,
0.046172793954610825,
0.005259987432509661,
-0.015725012868642807,
-0.007881208322942257,
0.026068059727549553,
0.017446108162403107,
0.045738574117422104,
-0.021294645965099335,
-0.03146681934595108,
-0.0022484860382974148,
-0.005340685602277517,
-0.02061287686228752,
0.046001359820365906,
-0.0478179007768631,
-0.020927669480443,
0.005848734639585018,
0.020326482132077217,
-0.014657830819487572,
0.007572765927761793,
0.012191093526780605,
-0.018503470346331596,
-0.009732921607792377,
0.017912693321704865,
0.0021366893779486418,
-0.01183810830116272,
-0.010241203010082245,
0.00991870928555727,
0.006415024399757385,
0.030453376471996307,
-0.00008905723370844498,
-0.015196857042610645,
-0.05990944802761078,
0.00492334458976984,
0.008242164738476276,
0.0017734321299940348,
-0.0387740433216095,
-0.036577824503183365,
-0.05759492143988609,
0.03031003847718239,
0.03185327723622322,
0.0066040996462106705,
-0.009518659673631191,
-0.07627325505018234,
-0.043556224554777145,
-0.05457127094268799,
0.02651747316122055,
-0.03363171964883804,
-0.014195934869349003,
-0.0922437459230423,
-0.03138326480984688,
-0.01914135366678238,
0.02779824659228325,
0.08577079325914383,
0.006607129704207182,
-0.03266548365354538,
0.005307111889123917,
0.03021002747118473,
0.06955625861883163,
-0.01636071875691414,
0.01541899424046278,
-0.031914155930280685,
-0.007227664347738028,
0.012230892665684223,
-0.0194889884442091,
-0.025536837056279182,
0.02689974755048752,
0.037213996052742004,
-0.05200304463505745,
0.009663524106144905,
0.006850642617791891,
-0.012900281697511673,
0.054373599588871,
0.012639660388231277,
-0.02468230575323105,
0.07051597535610199,
-0.03763469681143761,
0.05545908585190773,
0.016347995027899742,
-0.016420697793364525,
-0.033670295029878616,
0.02586377039551735,
-0.03496352210640907,
-0.0036659755278378725,
-0.01075572520494461,
-0.04527345299720764,
0.02423964813351631,
-0.01840657740831375,
0.008266844786703587,
0.050831444561481476,
-0.06722775846719742,
0.013000337406992912,
0.03369322791695595,
0.01607643812894821,
0.042111095041036606,
-0.007615142501890659,
0.047875821590423584,
-0.0017708060331642628,
0.025249488651752472,
-0.028312431648373604,
0.07502671331167221,
0.04089682549238205,
-0.024326158687472343,
0.005420253612101078,
0.016112321987748146,
-0.03515568748116493,
0.01537388376891613,
0.024190202355384827,
-0.009291889145970345,
-0.0492631196975708,
-0.02558014541864395,
0.02066882699728012,
0.005722470581531525,
0.025854170322418213,
0.005302604753524065,
0.003255430143326521,
0.03527605161070824,
0.006029846146702766,
0.027257610112428665,
-0.05541771650314331,
-0.027568191289901733,
-0.03839779645204544,
-0.037189047783613205,
0.038271207362413406,
0.04178448021411896,
-0.007977879606187344,
-0.001626181765459478,
-0.02145833894610405,
-0.010140462778508663,
0.01643267087638378,
-0.04737579822540283,
0.04831579700112343,
0.0075071766041219234,
0.022507522255182266,
-0.021844029426574707,
-0.009003435261547565,
-0.030898762866854668,
-0.0133206220343709,
0.04039394110441208,
0.03986871615052223,
0.03307241573929787,
0.0298592709004879,
-0.05264296010136604,
0.013470619916915894,
0.06289935857057571,
-0.02716696448624134,
0.006335797253996134,
-0.015621362254023552,
0.03849465772509575,
-0.01222414430230856,
-0.00799991749227047
] |
<p>I am wondering if the mass density profile $\rho(\vec{r})$ has been characterized for atomic particles such as quarks and electrons. I am currently taking an intro class in quantum mechanics, and I have run this question by several professors. It is my understanding from the viewpoint of quantum physics a particle's position is given by a probability density function $\Psi(\vec{r},t)$. I also understand that when books quote the "radius" of an electron they are typically referring to some approximate range into which an electron is "likely" to fall, say, one standard deviation from the expectation value of its position or maybe $10^{-15}$ meters.</p>
<p>However it is my impression that, in this viewpoint, wherever the particle "is" or even whether or not the particle "had" any position to begin with (via the Bell Inequalities), it is assumed that if it were (somehow) found, it <em>would</em> be a <em>point</em> mass. This has been verified by my professors and GSIs. I am wondering if its really true.</p>
<p>If the particle was truly a <em>point</em> mass then <em>wherever</em> it <em>is</em>, it would presumably have an <em>infinite</em> mass density. Wouldn't that make electrons and quarks indistinguishable from very tiny black holes? Is there any practical difference between saying that subatomic particles are black holes and that they are point masses? I am aware of such problems as Hawking Radiation although at the scales of the Schwarchild radius of an electron (back of the envelope calculation yields $\tilde{}10^{-57}$ meters), would it really make any more sense to use quantum mechanics as opposed to general relativity?</p>
<p>If anyone knows of an upper bound on the volume over which an electron/quark/gluon/anything else is distributed I would be interested to know. A quick Google Search has yielded nothing but the "classical" electron radius, which is not what I am referring to.</p>
<p>Thanks in advance; look forward to the responses.</p>
| 329 |
[
-0.0076634702272713184,
-0.02068285271525383,
0.051544103771448135,
-0.06426503509283066,
0.02294374629855156,
-0.0035193294752389193,
-0.02628733403980732,
-0.031096946448087692,
-0.02822493389248848,
-0.016298145055770874,
0.031117185950279236,
0.016283825039863586,
0.08731433749198914,
-0.008052337914705276,
0.0056554884649813175,
0.0067094312980771065,
-0.011722111143171787,
-0.009719177149236202,
-0.0196924339979887,
-0.0672188475728035,
0.04611854627728462,
0.061471760272979736,
0.027630506083369255,
-0.02809794433414936,
-0.023332078009843826,
0.03390058875083923,
-0.008530618622899055,
0.008245752193033695,
0.02520267479121685,
0.04312560707330704,
-0.005491183139383793,
-0.02234690822660923,
0.023379793390631676,
0.01284692995250225,
0.026502391323447227,
-0.024309298023581505,
-0.01593131758272648,
-0.03098280541598797,
-0.03326211869716644,
0.003364273114129901,
-0.07599375396966934,
-0.03134339302778244,
-0.01719658449292183,
0.039526987820863724,
-0.018432293087244034,
0.007341400254517794,
0.037211596965789795,
-0.052686478942632675,
0.04069133475422859,
-0.08049267530441284,
0.04652814194560051,
0.04875053092837334,
0.036597516387701035,
0.008875977247953415,
0.006385039538145065,
-0.015066426247358322,
0.08296284079551697,
0.06043844297528267,
-0.029693644493818283,
-0.05820492282509804,
-0.02778017893433571,
-0.03273550048470497,
0.005909780506044626,
0.0003180139174219221,
-0.016337377950549126,
0.02676180563867092,
-0.028210479766130447,
-0.007715368643403053,
-0.008123454637825489,
-0.039379436522722244,
0.035949088633060455,
0.03837746009230614,
-0.003624225500971079,
0.004117004107683897,
0.0348006971180439,
-0.028918474912643433,
0.02419915422797203,
-0.00909446831792593,
0.01329073403030634,
0.02858775667846203,
-0.02529243566095829,
0.02431529387831688,
0.04920753836631775,
0.0049272747710347176,
0.01570357196033001,
-0.030291838571429253,
0.05001266673207283,
-0.010978647507727146,
-0.0032911121379584074,
0.0654601901769638,
-0.04453546181321144,
-0.002914117882028222,
0.034555476158857346,
-0.02140013501048088,
-0.04123280942440033,
0.012136011384427547,
-0.01844804361462593,
0.04555715620517731,
-0.016844678670167923,
-0.027245497331023216,
0.03024298883974552,
-0.022364052012562752,
0.027516303583979607,
0.0817374512553215,
-0.0019447641680017114,
-0.016693735495209694,
-0.05310387164354324,
-0.0009277188801206648,
-0.0019472732674330473,
-0.012726129032671452,
-0.04241832718253136,
0.023750653490424156,
-0.007934740744531155,
-0.0059188674204051495,
0.03905992582440376,
-0.03328010067343712,
0.012113776989281178,
-0.011867174878716469,
0.06937328726053238,
0.07038953900337219,
0.025667842477560043,
-0.007251611910760403,
0.0007037906325422227,
-0.05028896406292915,
-0.039516810327768326,
0.00848336424678564,
0.057250019162893295,
0.009756114333868027,
-0.037780117243528366,
0.00479475874453783,
0.011184667237102985,
0.0467090904712677,
0.03847239539027214,
-0.020912084728479385,
0.048058923333883286,
-0.0482378713786602,
-0.08083393424749374,
-0.04779784753918648,
0.05112893879413605,
0.013612661510705948,
-0.03843459114432335,
-0.03728417307138443,
-0.00469942344352603,
0.02915680781006813,
0.052652906626462936,
0.016076164320111275,
0.030770473182201385,
-0.025659242644906044,
0.04472968354821205,
0.01164082158356905,
-0.010059378109872341,
0.009816691279411316,
-0.009671716019511223,
-0.026562830433249474,
0.03009234182536602,
-0.05054377391934395,
0.027291972190141678,
0.008582167327404022,
0.01038755290210247,
-0.049855787307024,
0.06720693409442902,
-0.012893036007881165,
0.004743661731481552,
0.02850557491183281,
-0.007866505533456802,
-0.030947495251893997,
0.061529286205768585,
0.025232745334506035,
-0.005421236623078585,
0.04116123169660568,
0.015404018573462963,
0.032892558723688126,
0.044712912291288376,
0.004618839826434851,
0.040629711002111435,
-0.05208514630794525,
-0.023165397346019745,
-0.0388462170958519,
0.031145868822932243,
0.03472113609313965,
-0.05751807242631912,
-0.02396867610514164,
0.006108805071562529,
-0.012068101204931736,
0.018444396555423737,
0.01515871286392212,
-0.03915141150355339,
-0.017000645399093628,
-0.012583357281982899,
-0.056103046983480453,
0.009456770494580269,
-0.05846831575036049,
0.01860271394252777,
0.01019358355551958,
0.012249109335243702,
0.05273500084877014,
0.015401051379740238,
0.012059809640049934,
-0.04973535239696503,
-0.038236383348703384,
-0.004284936934709549,
0.046920839697122574,
-0.003689901437610388,
-0.01877438649535179,
0.009761548601090908,
0.02444409392774105,
0.015550662763416767,
-0.015165593475103378,
-0.01436841581016779,
0.0007997216307558119,
-0.0447784923017025,
-0.007028724066913128,
-0.012829138897359371,
0.03141222521662712,
0.014138257130980492,
0.0008730686968192458,
-0.0016073898877948523,
-0.00587864127010107,
-0.01588946208357811,
0.05390116944909096,
0.003136073937639594,
0.0699806958436966,
-0.006303693167865276,
0.019058028236031532,
-0.021411076188087463,
0.02313663251698017,
0.048146821558475494,
-0.0002521424030419439,
0.00003351253690198064,
-0.020224934443831444,
-0.03481649234890938,
-0.0052098301239311695,
0.011401657946407795,
0.03530697897076607,
-0.03731333836913109,
0.020063310861587524,
0.03163391351699829,
0.03203704208135605,
0.03303197771310806,
0.01707278937101364,
-0.02920011803507805,
-0.0310652032494545,
0.016020089387893677,
-0.00044304985203780234,
0.015176902525126934,
0.018205178901553154,
0.048190731555223465,
-0.004212751518934965,
0.011783905327320099,
-0.014441663399338722,
-0.015984173864126205,
0.041465312242507935,
-0.02029712125658989,
-0.0010433000279590487,
-0.023160886019468307,
-0.02214738354086876,
0.023170780390501022,
-0.03775981441140175,
0.01771182008087635,
0.02106996811926365,
-0.05563129484653473,
-0.020030561834573746,
-0.035258032381534576,
-0.014243220910429955,
0.011995011009275913,
0.03405783325433731,
-0.04682165011763573,
-0.007570653688162565,
0.003540022298693657,
-0.05975107476115227,
-0.011510676704347134,
-0.037407781928777695,
-0.007810063194483519,
-0.023487521335482597,
0.036416105926036835,
0.042529039084911346,
0.00898047722876072,
0.011933576315641403,
-0.01663048565387726,
-0.036422211676836014,
-0.0002103118458762765,
-0.01673266664147377,
-0.0006922109751030803,
0.03324200585484505,
-0.051985953003168106,
0.013267610222101212,
-0.06800195574760437,
-0.05821915343403816,
0.03254290297627449,
-0.03862471133470535,
0.018577758222818375,
-0.005411216523498297,
-0.046186983585357666,
-0.030667435377836227,
0.008120938204228878,
-0.010763389989733696,
-0.003926022909581661,
-0.024644287303090096,
0.028574900701642036,
0.05416448414325714,
-0.03650180995464325,
-0.013887460343539715,
0.01719701662659645,
-0.03248438984155655,
-0.052557677030563354,
-0.013318226672708988,
0.014369193464517593,
0.025578921660780907,
-0.02685192972421646,
0.016135316342115402,
0.03942861780524254,
-0.04114622250199318,
-0.007922720164060593,
-0.041142407804727554,
-0.06215827539563179,
0.032236263155937195,
-0.009202666580677032,
0.028319071978330612,
0.025304971262812614,
-0.02297114208340645,
0.07183358818292618,
0.01869422383606434,
-0.027332808822393417,
-0.014405529014766216,
0.001011448446661234,
-0.0028820582665503025,
0.02985178492963314,
-0.029142994433641434,
0.023703277111053467,
0.024751199409365654,
-0.023179903626441956,
0.034455157816410065,
0.05311938002705574,
-0.0206313319504261,
0.008299014531075954,
-0.02849559672176838,
-0.009449648670852184,
-0.017133736982941628,
0.001150736352428794,
0.04718584939837456,
-0.006596309132874012,
-0.0116531727835536,
-0.015235207043588161,
-0.003876953851431608,
0.037320028990507126,
-0.0034203198738396168,
-0.052994344383478165,
0.023961300030350685,
0.01862243004143238,
0.028600353747606277,
0.009156474843621254,
0.001556467730551958,
-0.01182313822209835,
-0.021137677133083344,
0.01900673843920231,
0.012090211734175682,
0.05013742670416832,
-0.0019626030698418617,
-0.021936429664492607,
0.015128841623663902,
0.05758463963866234,
-0.049260109663009644,
-0.02926170639693737,
0.005173720885068178,
-0.007514480967074633,
0.02652478776872158,
-0.030370330438017845,
-0.03419642895460129,
0.04692075401544571,
0.018074940890073776,
0.046337779611349106,
-0.03600428253412247,
-0.04086592048406601,
0.0005811373703181744,
-0.05583038926124573,
-0.003981000278145075,
0.010969097726047039,
0.048343393951654434,
0.012837680988013744,
0.00774609437212348,
0.047719474881887436,
-0.010596266947686672,
0.0011053753551095724,
-0.0047317673452198505,
-0.059670042246580124,
-0.024279724806547165,
-0.05393113195896149,
-0.008498855866491795,
-0.019899161532521248,
-0.01931970752775669,
-0.011222949251532555,
-0.0043251775205135345,
-0.00783972442150116,
-0.002385367639362812,
0.01964910700917244,
-0.0511358343064785,
0.025014646351337433,
-0.05739939585328102,
-0.034467410296201706,
-0.029635585844516754,
0.05308423936367035,
0.0004964175750501454,
-0.02069074660539627,
0.033916883170604706,
0.02136693336069584,
-0.03778227046132088,
-0.022031642496585846,
0.008629352785646915,
0.0346648283302784,
0.001856318674981594,
0.04467738792300224,
0.04905795305967331,
0.009630168788135052,
-0.028887001797556877,
0.02186731994152069,
0.03334248811006546,
0.07010436803102493,
-0.015527607873082161,
-0.014655005186796188,
-0.011383995413780212,
-0.022313421592116356,
-0.03593968227505684,
0.0005481782136484981,
0.058574479073286057,
-0.013131512328982353,
-0.0227658674120903,
0.03255033120512962,
-0.0042442819103598595,
-0.004987260792404413,
0.02862899750471115,
0.04797440394759178,
0.03093375451862812,
-0.03851817175745964,
-0.034703273326158524,
-0.011005477979779243,
-0.027101876214146614,
0.01814926043152809,
0.006970100570470095,
-0.013334106653928757,
-0.011997588910162449,
-0.008774462155997753,
0.000174752451130189,
0.0020896780770272017,
-0.06382782012224197,
-0.016529735177755356,
-0.02717224322259426,
0.020935291424393654,
-0.041960399597883224,
0.000421929988078773,
0.0036665964871644974,
-0.004772070795297623,
0.042822860181331635,
0.01246874313801527,
0.019196495413780212,
-0.05029429867863655,
-0.011129037477076054,
0.027249019593000412,
0.03618047386407852,
0.029816007241606712,
0.0025785930920392275,
-0.06155306100845337,
0.015187850221991539,
0.059087708592414856,
-0.006686579901725054,
0.01759866438806057,
-0.03669346496462822,
-0.014304140582680702,
-0.00005481266271090135,
-0.009502587839961052,
0.024011962115764618,
0.013071611523628235,
-0.015785865485668182,
-0.012277655303478241,
-0.06141849234700203,
0.010737369768321514,
-0.027011670172214508,
0.02614864520728588,
0.04645208641886711,
0.0691576674580574,
0.03404088318347931,
0.014305115677416325,
0.015153128653764725,
0.001685330062173307,
0.015476856380701065,
-0.08752498030662537,
-0.01566711999475956,
0.014246230944991112,
-0.015746895223855972,
0.04903672635555267,
-0.028756795451045036,
-0.05341096967458725,
0.027828902006149292,
-0.004576538223773241,
-0.012809080071747303,
0.012255048379302025,
-0.040953416377305984,
0.056938815861940384,
0.005674203857779503,
-0.016895359382033348,
0.03113558702170849,
-0.012268628925085068,
0.01308892760425806,
-0.006213041953742504,
-0.03076747991144657,
0.03995952010154724,
-0.03393601253628731,
-0.016189586371183395,
-0.030102187767624855,
0.02035338617861271,
-0.03496100753545761,
0.04328567907214165,
0.019156737253069878,
0.01019340381026268,
-0.011239010840654373,
-0.052118994295597076,
0.0035897649358958006,
-0.00021148165978956968,
-0.005205996800214052,
0.028500881046056747,
0.0007775008562020957,
0.022229857742786407,
0.010444211773574352,
-0.018842222169041634,
-0.006064055021852255,
0.013955420814454556,
0.005109773017466068,
0.052704110741615295,
-0.02046053670346737,
0.05799006298184395,
-0.021037127822637558,
-0.012843401171267033,
0.04925702512264252,
-0.0309530608355999,
0.06465815752744675,
-0.009024865925312042,
-0.03656480088829994,
0.007276976015418768,
-0.04676657170057297,
-0.04045133665204048,
-0.006942675914615393,
0.008509410545229912,
0.04944298788905144,
-0.05643237754702568,
0.022194094955921173,
0.0376734621822834,
0.03306013345718384,
-0.08914206176996231,
-0.014935413375496864,
-0.0009954969864338636,
0.02211272157728672,
0.0014697168953716755,
-0.005726526025682688,
0.04496598243713379,
-0.06017997860908508,
0.01283076498657465,
-0.0016282708384096622,
0.021907707676291466,
-0.04009156674146652,
-0.03102349303662777,
-0.010157606564462185,
0.021316571161150932,
0.04097168520092964,
-0.014639102853834629,
-0.01873686909675598,
-0.0022185062989592552,
0.04232069104909897,
0.031194603070616722,
0.007176070008426905,
0.043578244745731354,
-0.01982417330145836,
-0.03973940387368202,
-0.03742292523384094,
-0.00947126466780901,
0.015927854925394058,
-0.032600853592157364,
-0.011240559630095959,
0.03654622659087181,
0.025975417345762253,
0.016522374004125595,
0.01468721590936184,
0.021685998886823654,
-0.040705591440200806,
0.00009189621778205037,
0.005924129858613014,
-0.016219479963183403,
-0.0029056882485747337,
-0.02681383490562439,
0.05224738270044327,
-0.029339615255594254,
0.013045852072536945,
0.019254030659794807,
0.04415997117757797,
0.015552239492535591,
-0.021362842991948128,
0.01648774743080139,
-0.05123630911111832,
0.04090093448758125,
-0.014243625104427338,
-0.006136033684015274,
0.03252392262220383,
0.014255438931286335,
0.013625374995172024,
-0.03807127848267555,
-0.04045895114541054,
0.00779310055077076,
0.04280196875333786,
0.03561267629265785,
0.028598418459296227,
0.010880568064749241,
-0.0063028945587575436,
0.0031195185147225857,
-0.039612721651792526,
0.0013703443109989166,
0.009580856189131737,
0.010399947874248028,
0.034233883023262024,
-0.02804235741496086,
-0.01888708397746086,
0.03216824680566788,
0.042863164097070694,
-0.04384203627705574,
0.04602140188217163,
0.02696150913834572,
0.04187079891562462,
-0.008256793953478336,
-0.0019219680689275265,
-0.02268701232969761,
0.025215117260813713,
-0.036952387541532516,
0.006866517011076212,
0.002583176363259554,
-0.0035390069242566824,
-0.006701215635985136,
0.004074405413120985,
0.03202517703175545,
0.013290410861372948,
-0.055730316787958145,
-0.04590454325079918,
0.04681804031133652,
0.0167495459318161,
0.025986891239881516,
-0.04514877498149872,
0.020725160837173462,
0.0020383603405207396,
0.016220401972532272,
0.013832634314894676,
0.014988192357122898,
-0.04305006191134453,
-0.027523763477802277,
-0.059786465018987656,
-0.07291703671216965,
0.024013273417949677,
-0.008228922262787819,
-0.02764972858130932,
0.01857302337884903,
-0.04383070021867752,
0.011929991655051708,
0.041344381868839264,
0.03281668201088905,
-0.029999252408742905,
0.07315406948328018,
0.005227081477642059,
0.019015347585082054,
-0.015325305052101612,
0.012683674693107605,
0.10361751168966293,
0.05996493250131607,
0.014623685739934444,
-0.024916203692555428,
0.00897099170833826,
-0.005095453932881355,
0.04783479496836662,
-0.019733812659978867,
0.02221604622900486,
-0.0067545631900429726,
-0.0032828859984874725,
0.01197087112814188,
0.054840754717588425,
0.019719112664461136,
-0.020604176446795464,
0.07059711962938309,
-0.021093398332595825,
-0.040563926100730896,
-0.00039984655450098217,
0.0476180799305439,
0.011935739777982235,
0.028300898149609566,
-0.035826072096824646,
0.030201051384210587,
-0.01338818296790123,
0.024296680465340614,
-0.04698465019464493,
0.003535460913553834,
-0.005135343410074711,
-0.01134360022842884,
-0.07186584174633026,
-0.005782341118901968,
0.020066600292921066,
-0.013609484769403934,
-0.022381851449608803,
0.009275608696043491,
0.01156948134303093,
-0.014272928237915039,
0.018953990191221237,
0.051697738468647,
-0.0007302824524231255,
0.017080852761864662,
0.019688835367560387,
0.03339880332350731,
-0.031665902584791183,
-0.0397794172167778,
0.0036750310100615025,
0.034269750118255615,
-0.06595353037118912,
-0.011946631595492363,
-0.001732849981635809,
0.024043645709753036,
0.004192515276372433,
-0.06150427460670471,
-0.030643628910183907,
-0.03534991294145584,
0.0195815060287714,
0.013135518878698349,
-0.01784307137131691,
-0.02758409082889557,
0.04940824955701828,
-0.017654310911893845,
0.03318812698125839,
0.00019589309522416443,
-0.0021901153959333897,
0.013278506696224213,
-0.008785052224993706,
0.04240502417087555,
-0.017738888040184975,
-0.012463151477277279,
-0.04669175669550896,
-0.026981493458151817,
-0.06099088490009308,
-0.02697770670056343,
0.024216650053858757,
0.016312794759869576,
0.046049319207668304,
0.031254954636096954,
0.01261303573846817,
0.0326349101960659,
-0.06921648234128952,
0.020035535097122192,
-0.032182421535253525,
-0.017086248844861984,
-0.016994351521134377,
-0.013353957794606686,
0.005819200072437525,
0.04094070941209793,
-0.04355582967400551,
-0.0127113563939929,
-0.010760978795588017,
0.022408366203308105,
-0.005420221947133541,
-0.03781683370471001,
0.007022396195679903,
0.017404446378350258,
-0.038648348301649094,
0.01190340518951416,
-0.0390663780272007,
-0.007359521929174662,
0.02957993745803833,
0.004664380569010973,
-0.007968557067215443,
0.04138544574379921,
-0.005650731734931469,
0.005306773819029331,
0.0151207922026515,
-0.00023731424880679697,
0.01620335876941681,
0.04225568473339081,
0.03248792886734009,
-0.035371940582990646,
-0.023389412090182304,
-0.034587547183036804,
-0.008878645487129688,
-0.034015025943517685,
0.015457226894795895,
0.018122708424925804,
0.009119111113250256,
0.003386711934581399,
-0.02263748086988926,
-0.015625832602381706,
0.03436283767223358,
-0.02851545438170433,
0.03907870873808861,
0.02820897474884987,
-0.013417589478194714,
-0.029101036489009857,
0.023837247863411903,
-0.014186589047312737,
-0.04306681826710701,
-0.003912596497684717,
0.020314689725637436,
-0.06610611826181412,
0.016769593581557274,
0.024431200698018074,
0.009492236189544201,
0.054113004356622696,
-0.015272385440766811,
-0.007507194299250841,
0.03848380595445633,
-0.049841899424791336,
-0.05039571225643158,
0.04291176423430443,
-0.02715425007045269,
0.008355970494449139,
0.033167995512485504,
0.02238011546432972,
-0.0032174631487578154,
0.0798702985048294,
0.0009945339988917112,
-0.007484490051865578,
0.0038270694203674793,
-0.019411377608776093,
-0.03245379403233528,
-0.00276170764118433,
0.022225935012102127,
-0.019464390352368355,
-0.01023784652352333,
0.023626241832971573,
0.03480672091245651,
-0.03349645063281059,
-0.0008132871007546782,
0.02722996287047863,
-0.012116081081330776,
0.010144971311092377,
0.009938755072653294,
0.00692554609850049,
-0.0030938268173485994,
0.041869111359119415,
-0.06827768683433533,
0.055920545011758804,
0.03156454488635063,
0.03193081170320511,
-0.1102074533700943,
-0.015332182869315147,
0.039172474294900894,
-0.009642674587666988,
0.03701600059866905,
-0.023032641038298607,
-0.027054496109485626,
0.02062203362584114,
-0.07883846759796143,
0.035783298313617706,
-0.027637086808681488,
-0.018730076029896736,
-0.02180381305515766,
-0.013729901984333992,
-0.03014557436108589,
0.043345991522073746,
0.030808694660663605,
0.06659035384654999,
0.0030480073764920235,
0.013425711542367935,
-0.01575641706585884,
-0.04804489389061928,
-0.032366588711738586,
0.04058925807476044,
-0.008599013090133667,
-0.023562630638480186,
0.08582555502653122,
-0.03631798177957535,
0.013928945176303387,
0.04218191280961037,
0.013725361786782742,
-0.009934970177710056,
-0.011488392017781734,
-0.005628129001706839,
0.008583622984588146,
0.025977645069360733,
0.03201277181506157,
0.0018032186198979616,
-0.00510449381545186,
0.014879745431244373,
0.023478355258703232,
0.009936361573636532,
-0.004915454890578985,
0.01613098382949829,
0.008130884729325771,
-0.027567468583583832,
0.0008850701269693673,
0.050603337585926056,
-0.011707217432558537,
-0.011810354888439178,
0.006452449131757021,
0.020630396902561188,
-0.004885970614850521,
-0.027291180565953255,
0.0025098195765167475,
-0.05617252364754677,
0.0006063093896955252,
0.011505230329930782,
0.030260559171438217,
-0.004128710832446814,
0.0162334181368351,
-0.006283044349402189,
-0.024257177487015724,
0.011214683763682842,
-0.0010352513054385781,
-0.02929331362247467,
-0.06077679991722107,
0.0012861927971243858,
-0.019820282235741615,
0.03771340101957321,
0.036251313984394073,
-0.0708124116063118,
-0.027699390426278114,
0.042749080806970596,
-0.0012130170362070203,
0.03295382857322693,
-0.00848484504967928,
0.00817328505218029,
-0.020478684455156326,
-0.07231463491916656,
0.005139547400176525,
-0.006041174754500389,
0.026288995519280434,
-0.03999026119709015,
-0.035313889384269714,
0.003707227064296603,
-0.002588746603578329,
0.03211747854948044,
0.023829106241464615,
-0.003218887373805046,
0.02427545376121998,
-0.008039752021431923,
0.00014704403292853385,
-0.042036350816488266,
-0.018207507207989693,
-0.006022212561219931,
-0.053733497858047485,
-0.003915837500244379,
0.0031881779432296753,
-0.01629572920501232,
0.03031071648001671,
0.049621134996414185,
0.013524425216019154,
0.010068850591778755,
0.00704196235165,
-0.05170727148652077,
0.08377774059772491,
0.030006900429725647,
0.02749137207865715,
0.031698957085609436,
0.015865694731473923,
0.016715826466679573,
0.019548555836081505,
-0.0213045384734869,
-0.021504372358322144,
0.013653249479830265,
-0.013114357367157936,
-0.01730986312031746,
0.010311782360076904,
0.03618646413087845,
0.005849213805049658,
-0.035112541168928146,
-0.01728837750852108,
0.04284949228167534,
-0.015617127530276775,
-0.04274542257189751,
0.04420812427997589,
0.014298886060714722,
0.06380214542150497,
-0.017374247312545776,
-0.026030398905277252,
0.02882423996925354,
-0.011873658746480942,
-0.02926787920296192,
0.029883436858654022,
0.04874420538544655,
0.007787683047354221,
0.017533013597130775,
0.05498894304037094,
0.0055178445763885975,
0.017394930124282837,
-0.0006855034735053778,
0.04127197712659836,
-0.01798051781952381,
-0.015021514147520065,
0.02356908656656742,
-0.022863062098622322,
0.0029897931963205338,
0.009810930117964745,
-0.029815515503287315,
0.08674875646829605,
0.021845504641532898,
-0.003120905952528119,
-0.0312338937073946,
-0.00880682747811079,
-0.02062126435339451,
0.02507048286497593,
-0.010428793728351593,
0.052223410457372665,
-0.0017474412452429533,
-0.013164732605218887,
-0.012448403052985668,
-0.0010784000623971224,
0.028626874089241028,
-0.04014184698462486,
0.002873177407309413,
-0.008433974348008633,
0.006473922170698643,
-0.039064761251211166,
-0.00894967745989561,
0.018278207629919052,
0.012072155252099037,
0.014555483125150204,
0.012719335034489632,
0.02797362022101879,
0.0029966491274535656,
-0.025099754333496094,
-0.024558434262871742,
0.050974760204553604,
-0.06114954873919487,
-0.013424701057374477,
-0.032785434275865555,
0.02504851296544075,
-0.046709854155778885,
-0.017822016030550003
] |
<p>In answer to <a href="http://physics.stackexchange.com/questions/843/maxwells-demon-constant-information-energy-equivalence">Maxwell's Demon Constant (Information-Energy equivalence)</a> there is stated that one bit of information allows to perform $kT \cdot \ln2$ Joules of work. Which paper supports the thesis? (there are many publications on Maxwell daemon, Szilard engine, Landauer's principle).</p>
| 8,872 |
[
-0.026531130075454712,
0.016873737797141075,
-0.02299589291214943,
-0.03716922923922539,
0.021770592778921127,
0.02519932948052883,
-0.03861139342188835,
-0.02025916427373886,
-0.04247390851378441,
0.007065217010676861,
0.05682074651122093,
0.05532674863934517,
0.042039696127176285,
0.06232333183288574,
-0.013869710266590118,
0.022940868511795998,
-0.020834192633628845,
0.000009424211384612136,
0.006269508507102728,
-0.05615749582648277,
0.011805174872279167,
0.002972763031721115,
-0.03009563870728016,
0.011536667123436928,
-0.03784980997443199,
0.035829562693834305,
-0.03258158266544342,
0.001923073548823595,
-0.005035535432398319,
0.014318142086267471,
-0.03896193206310272,
-0.02319297194480896,
-0.0022665446158498526,
0.026636501774191856,
-0.023543251678347588,
-0.0181895662099123,
-0.04892166703939438,
-0.057967912405729294,
0.03425348550081253,
0.006209132727235556,
-0.02740478329360485,
0.00014386232942342758,
0.014116681180894375,
0.030664116144180298,
-0.00979700032621622,
0.044131774455308914,
-0.00738659268245101,
-0.03555123507976532,
0.03735066205263138,
-0.05288102850317955,
0.044007446616888046,
0.009929514490067959,
0.010503287427127361,
0.027502261102199554,
0.012626632116734982,
0.016976576298475266,
0.06830330938100815,
0.07816864550113678,
0.006733974441885948,
-0.02647797018289566,
-0.04374444857239723,
-0.03658493608236313,
-0.001353084691800177,
-0.022309711202979088,
-0.01683094911277294,
0.06243429705500603,
0.007178350351750851,
-0.025416068732738495,
0.026849381625652313,
0.01364499144256115,
0.006925791036337614,
-0.018287859857082367,
0.0333421491086483,
0.014153867028653622,
0.042987074702978134,
-0.0037880365271121264,
-0.0044260332360863686,
0.007229223381727934,
0.02463310956954956,
0.06866644322872162,
-0.01661239191889763,
-0.022670477628707886,
0.03760584816336632,
0.05196134001016617,
0.023130115121603012,
0.012245958670973778,
0.06729283928871155,
-0.009564313106238842,
0.013853331096470356,
0.04526912793517113,
-0.00428240979090333,
0.014273976907134056,
0.039285238832235336,
-0.020368501543998718,
0.014766648411750793,
0.013148223049938679,
0.002455600304529071,
0.025011060759425163,
-0.018319904804229736,
-0.05031538009643555,
0.01059560477733612,
-0.031373538076877594,
0.02504129894077778,
0.06671644747257233,
0.017732225358486176,
0.004376956261694431,
0.011673616245388985,
0.031997427344322205,
-0.028495868667960167,
0.01649797149002552,
-0.024421213194727898,
0.0006957535515539348,
0.026365036144852638,
0.008246248587965965,
-0.009151584468781948,
-0.009173397906124592,
0.010361275635659695,
0.00006403120642062277,
0.08892274647951126,
0.03453705087304115,
0.013131068088114262,
-0.01794855110347271,
0.021989285945892334,
-0.05813925340771675,
-0.06136457622051239,
0.06077020615339279,
0.027073388919234276,
-0.03219860792160034,
-0.04704095423221588,
0.032649584114551544,
0.001053527696058154,
-0.037446919828653336,
0.02042912319302559,
0.02791682258248329,
0.020228717476129532,
-0.024656642228364944,
-0.061297111213207245,
-0.046749796718358994,
0.04913981258869171,
-0.002375867450609803,
-0.02506871148943901,
-0.03946391120553017,
0.007387253455817699,
0.014836447313427925,
0.0807606503367424,
-0.009137235581874847,
0.030544033274054527,
-0.043967343866825104,
0.04240180552005768,
0.03596257418394089,
0.007386191748082638,
-0.02619110234081745,
0.02468794956803322,
0.005088981706649065,
0.02506672590970993,
-0.055021487176418304,
0.04566789045929909,
0.03701965883374214,
-0.023934412747621536,
-0.014502978883683681,
0.06354872137308121,
-0.025718634948134422,
-0.01918673887848854,
0.0013243407011032104,
0.014752194285392761,
-0.034081775695085526,
0.10448406636714935,
-0.013563613407313824,
0.027028590440750122,
-0.029229728505015373,
0.005538483615964651,
0.023153778165578842,
0.007519062142819166,
0.013869084417819977,
0.013684067875146866,
-0.065425805747509,
-0.02526032365858555,
-0.030977020040154457,
-0.004939301870763302,
-0.025971876457333565,
-0.02536630630493164,
-0.03966682031750679,
0.012666636146605015,
-0.0014428563881665468,
0.0064442772418260574,
0.014816958457231522,
-0.04255598410964012,
0.0071289800107479095,
0.012914545834064484,
-0.03163976967334747,
-0.00531344348564744,
-0.019630229100584984,
0.04569017514586449,
-0.020539049059152603,
-0.03664413467049599,
0.040281232446432114,
-0.030421290546655655,
0.027025457471609116,
-0.031780898571014404,
-0.018312297761440277,
0.02072075754404068,
0.018030241131782532,
0.02303462103009224,
0.012247253209352493,
-0.009298562072217464,
0.0508827306330204,
0.01775580830872059,
-0.0003220700309611857,
0.014136720448732376,
-0.023773331195116043,
-0.05580681934952736,
0.028032245114445686,
-0.011389266699552536,
0.014732125215232372,
-0.024125350639224052,
-0.0032435476314276457,
0.040160369127988815,
0.02925317920744419,
-0.01381219457834959,
0.01902688480913639,
-0.02514326386153698,
0.027334626764059067,
0.03692923113703728,
0.021207746118307114,
-0.011352433823049068,
0.027948515489697456,
-0.019247474148869514,
0.03396487608551979,
0.009855872020125389,
-0.047379713505506516,
-0.04673171415925026,
-0.014427710324525833,
0.04185732081532478,
0.029528042301535606,
-0.03447336331009865,
0.03476450592279434,
0.05604928731918335,
0.004534488543868065,
0.005354073364287615,
0.024098997935652733,
-0.04400061070919037,
-0.044834695756435394,
0.02139285020530224,
0.0014515951042994857,
-0.007811793591827154,
0.012870511040091515,
0.05740141123533249,
-0.01380312442779541,
-0.013522385619580746,
0.03634410351514816,
-0.012538247741758823,
0.023600459098815918,
-0.02122482843697071,
0.018050996586680412,
-0.01850360445678234,
-0.0478878915309906,
0.04174116253852844,
-0.03313995897769928,
0.03562595695257187,
0.03263749182224274,
0.01680707558989525,
0.020227016881108284,
0.02599881961941719,
-0.05587346851825714,
-0.03608876094222069,
-0.05069335177540779,
-0.006786954589188099,
-0.011374250054359436,
0.01800418272614479,
-0.028418730944395065,
0.016384471207857132,
0.04756632819771767,
-0.016676565632224083,
-0.01051633246243,
0.0019626591820269823,
0.0011736470041796565,
-0.004912788514047861,
-0.0002997053670696914,
-0.041837867349386215,
-0.0031043062917888165,
-0.015574843622744083,
-0.016019493341445923,
-0.002858443185687065,
0.018140383064746857,
-0.05321134254336357,
0.0063907913863658905,
0.009875571355223656,
-0.04701758921146393,
0.07089351117610931,
-0.03495390713214874,
0.03830162435770035,
0.020206399261951447,
-0.02037760242819786,
-0.03649573773145676,
0.03188283368945122,
0.0010062488727271557,
0.006212582811713219,
-0.04030395671725273,
0.010091986507177353,
0.00867487397044897,
-0.004862069617956877,
-0.052558783441782,
-0.02329590916633606,
-0.014584416523575783,
-0.053981706500053406,
-0.02034149318933487,
-0.01722608134150505,
0.0008161431178450584,
-0.004565846174955368,
0.04248557984828949,
0.0506724938750267,
-0.030731480568647385,
-0.01866486296057701,
-0.06784433126449585,
-0.0821976363658905,
0.02517140656709671,
-0.03719806298613548,
0.06145120784640312,
-0.03362565115094185,
-0.04037940874695778,
0.07044009119272232,
0.018582221120595932,
-0.019427252933382988,
-0.02049555443227291,
-0.033401958644390106,
0.02165388874709606,
-0.029389020055532455,
-0.028897888958454132,
0.01569114439189434,
-0.0015318599762395024,
0.017870793119072914,
0.005485800560563803,
0.01061157789081335,
0.025813892483711243,
-0.00048642075853422284,
-0.014340338297188282,
0.024641377851366997,
-0.00495093734934926,
-0.023059727624058723,
0.020481504499912262,
0.03084186464548111,
-0.037272680550813675,
0.039514731615781784,
-0.002942088758572936,
-0.005042066797614098,
0.02059299871325493,
-0.04935290664434433,
0.04213881865143776,
0.02390936389565468,
0.011086201295256615,
-0.008307201787829399,
0.014653285034000874,
0.00466925511136651,
-0.05910244956612587,
0.003357390873134136,
0.03455762937664986,
0.011335443705320358,
-0.0003951603430323303,
-0.004134003538638353,
0.0096964156255126,
0.01844577118754387,
0.005533176474273205,
-0.02772519737482071,
-0.03640531748533249,
0.019574303179979324,
0.012927360832691193,
-0.013018808327615261,
-0.00964622013270855,
0.00029760136385448277,
0.004001073073595762,
0.03133067116141319,
-0.012398958206176758,
-0.02028314210474491,
-0.0013635841896757483,
-0.04801518842577934,
-0.012354923412203789,
-0.039723966270685196,
0.02803349308669567,
-0.01156116183847189,
0.029078364372253418,
-0.0012281580129638314,
0.02546849474310875,
0.02482570707798004,
-0.018846120685338974,
-0.08135183900594711,
0.02368667535483837,
-0.07181168347597122,
-0.010673481039702892,
0.043553050607442856,
0.002075460273772478,
0.003116188570857048,
-0.02279140055179596,
-0.04458771273493767,
-0.0029291058890521526,
0.0398818664252758,
-0.06133587658405304,
0.028252435848116875,
-0.03291185945272446,
-0.06021856144070625,
-0.008447956293821335,
0.023952500894665718,
0.041557468473911285,
-0.026847777888178825,
0.0011179180582985282,
0.017230546101927757,
-0.02277478761970997,
0.024434823542833328,
0.010436104610562325,
-0.0012270455481484532,
0.008787729777395725,
0.012133208103477955,
0.0004229092155583203,
-0.018936164677143097,
0.009135042317211628,
0.017090454697608948,
0.004568763077259064,
0.03535958006978035,
-0.010097532533109188,
-0.05204883962869644,
-0.04695191979408264,
-0.01694813370704651,
0.018764013424515724,
-0.029336396604776382,
0.08563260734081268,
0.009029649198055267,
0.054098814725875854,
-0.004744467791169882,
0.04840477555990219,
-0.01167238224297762,
0.009833146817982197,
0.05327707529067993,
-0.015723764896392822,
-0.024626851081848145,
-0.027566850185394287,
-0.002424099249765277,
0.005263408645987511,
-0.02149781957268715,
0.040897004306316376,
0.005482800304889679,
0.017036063596606255,
-0.00039576811832375824,
-0.008197945542633533,
0.025756187736988068,
-0.006171977613121271,
-0.02181435376405716,
0.016426797956228256,
-0.007917648181319237,
-0.010173674672842026,
-0.007372800726443529,
0.006502402480691671,
0.012193205766379833,
0.019718928262591362,
-0.011731690727174282,
-0.03794533386826515,
-0.07093477249145508,
0.001034035929478705,
0.010587135329842567,
0.05753230303525925,
-0.0176362544298172,
0.026850169524550438,
-0.027688445523381233,
0.014188648201525211,
0.0216438677161932,
-0.02484440617263317,
0.0459970086812973,
-0.008725988678634167,
0.019892556592822075,
-0.005438212305307388,
0.0014369483105838299,
-0.003054618602618575,
0.011561119928956032,
0.03008965402841568,
0.02112586237490177,
0.011314313858747482,
-0.021466879174113274,
0.037418242543935776,
0.005443691276013851,
0.011712849140167236,
0.04219993203878403,
-0.03085440956056118,
0.02312486618757248,
-0.00688904756680131,
0.04257192835211754,
-0.05018911510705948,
-0.07946211099624634,
0.01763314940035343,
-0.029748499393463135,
-0.004460890311747789,
0.0031504337675869465,
-0.06927362084388733,
-0.06603437662124634,
0.026459092274308205,
0.012333093211054802,
-0.04853297024965286,
-0.021261418238282204,
-0.042886681854724884,
0.05134475231170654,
0.07266939431428909,
0.013602483086287975,
0.05190172418951988,
0.03712433576583862,
-0.027178552001714706,
0.04670300707221031,
-0.006854222156107426,
0.02553616650402546,
-0.034323953092098236,
0.017637137323617935,
-0.022353708744049072,
0.038257747888565063,
-0.06352438032627106,
0.04478299617767334,
0.009571202099323273,
0.024754976853728294,
0.003959030844271183,
0.0035511029418557882,
-0.05862772837281227,
0.003422957845032215,
0.01578247919678688,
-0.016073811799287796,
-0.0167514830827713,
0.027479706332087517,
-0.011154429987072945,
-0.019517766311764717,
0.008459166623651981,
-0.0011745248921215534,
0.016530558466911316,
0.022853314876556396,
0.016352150589227676,
0.02183660864830017,
-0.05560962110757828,
-0.018491335213184357,
0.05174291133880615,
-0.020730772987008095,
0.05209179222583771,
-0.007799170911312103,
0.012633901089429855,
0.00572036299854517,
-0.02702918089926243,
-0.04373013228178024,
-0.004213050473481417,
0.005161148961633444,
0.011532487347722054,
-0.06752675026655197,
0.04927987977862358,
-0.019268404692411423,
-0.0019842132460325956,
-0.056612614542245865,
0.004041087813675404,
0.027060043066740036,
-0.046114757657051086,
-0.014564179815351963,
-0.0373576283454895,
0.023815732449293137,
-0.05104595050215721,
-0.0275608878582716,
-0.012317047454416752,
0.035679206252098083,
0.0036144815385341644,
0.0006664031534455717,
0.021495968103408813,
0.016680831089615822,
-0.0048676589503884315,
0.023988261818885803,
-0.07277477532625198,
-0.003824422135949135,
0.007692850660532713,
0.008098263293504715,
0.0024514738470315933,
-0.0395335778594017,
-0.0022534537129104137,
0.01609339751303196,
0.005859647877514362,
0.01782134547829628,
0.03176550939679146,
-0.007889991626143456,
-0.0007406665245071054,
0.050944745540618896,
0.026228317990899086,
-0.020423026755452156,
-0.05079729110002518,
0.0021353948395699263,
0.015644999220967293,
0.05952712520956993,
-0.0006520036258734763,
-0.015563184395432472,
-0.059942781925201416,
-0.009175213053822517,
0.00644720671698451,
-0.013060002587735653,
-0.020834721624851227,
-0.008096549659967422,
0.10314618796110153,
0.009385614655911922,
-0.018527306616306305,
0.021713221445679665,
-0.022443952038884163,
0.0011535686207935214,
-0.025791317224502563,
0.04447970539331436,
-0.026638489216566086,
-0.006669908761978149,
-0.03229830041527748,
-0.046336278319358826,
-0.020196586847305298,
0.010973471216857433,
0.0662093535065651,
-0.0020042099058628082,
0.06397967785596848,
0.01729961484670639,
-0.018471794202923775,
0.03217380493879318,
-0.021887894719839096,
-0.014729929156601429,
0.001158777391538024,
0.01365140825510025,
0.01646556332707405,
0.00355498306453228,
-0.007956900633871555,
0.04225754737854004,
0.01846299134194851,
-0.04088078439235687,
-0.011063843965530396,
0.01082214992493391,
0.03698950260877609,
0.015536308288574219,
-0.05912011116743088,
-0.035161618143320084,
0.07060272991657257,
-0.04201483726501465,
0.03685780614614487,
0.0091017447412014,
0.023646261543035507,
0.047379568219184875,
-0.01015527918934822,
0.019957637414336205,
-0.057854000478982925,
-0.014325764961540699,
-0.0470704585313797,
0.036464873701334,
0.0004152109322603792,
0.005017524119466543,
0.027028275653719902,
-0.014284415170550346,
-0.0014109985204413533,
0.0011964930454269052,
-0.005542562808841467,
-0.0044584316201508045,
-0.04403691738843918,
-0.01880066655576229,
-0.0336795412003994,
-0.03407209366559982,
0.016706721857190132,
0.022007282823324203,
-0.021481258794665337,
0.06338579207658768,
-0.05667758733034134,
0.0568242110311985,
0.02477230131626129,
0.02991430088877678,
0.018934065476059914,
0.08281393349170685,
-0.05275494232773781,
0.042878489941358566,
-0.028070032596588135,
0.010000246576964855,
0.12130720168352127,
0.046129260212183,
0.024151310324668884,
-0.08013521879911423,
0.0455131009221077,
-0.014283305034041405,
0.03135789930820465,
-0.007733703125268221,
0.0180906243622303,
-0.014615176245570183,
-0.014572595246136189,
0.03611345216631889,
0.05138933286070824,
-0.022650618106126785,
-0.02048191800713539,
-0.03454936668276787,
-0.026995647698640823,
-0.006454861722886562,
0.049136318266391754,
0.01675591804087162,
0.013024215586483479,
-0.015552849508821964,
-0.0004916687612421811,
-0.007511510979384184,
-0.007614025846123695,
-0.025252236053347588,
-0.007514133583754301,
-0.03193984553217888,
-0.0002079247060464695,
-0.003049798309803009,
-0.05458404868841171,
-0.03362523391842842,
0.01270974986255169,
-0.011132147163152695,
0.004207845311611891,
-0.01154622808098793,
-0.008028040640056133,
0.05016830936074257,
-0.017700346186757088,
0.06663743406534195,
0.028143303468823433,
-0.020644186064600945,
0.04540977254509926,
0.005267861299216747,
-0.050382111221551895,
0.013779076747596264,
-0.041629642248153687,
0.008444052189588547,
-0.03187844157218933,
0.055927056819200516,
0.029286935925483704,
-0.01867026276886463,
-0.005566408392041922,
-0.032960813492536545,
-0.037382084876298904,
0.0215834341943264,
0.01277144718915224,
-0.023941030725836754,
0.0029545321594923735,
-0.03512418642640114,
-0.005675820168107748,
-0.023100294172763824,
0.01692214421927929,
-0.013723055832087994,
-0.028714269399642944,
0.009827434085309505,
0.04406202211976051,
0.04819941148161888,
-0.012406387366354465,
-0.03518608212471008,
-0.02431180328130722,
-0.028398703783750534,
-0.05329008027911186,
-0.015328281559050083,
-0.010408143512904644,
-0.011957489885389805,
0.0071541983634233475,
0.015809781849384308,
-0.029576383531093597,
-0.023153534159064293,
-0.04207250103354454,
0.02332189865410328,
0.021866168826818466,
0.00523902103304863,
-0.011310454457998276,
0.00029361373162828386,
0.027091819792985916,
0.018570082262158394,
0.004750716499984264,
0.029581692069768906,
0.04508005082607269,
0.022605089470744133,
0.016967132687568665,
-0.023510247468948364,
0.019409162923693657,
-0.0196857787668705,
-0.06306827813386917,
0.01081918366253376,
-0.014503562822937965,
0.01753002405166626,
0.00253195408731699,
-0.00018380003166384995,
0.008345001377165318,
0.020615341141819954,
-0.018929582089185715,
0.0016618059016764164,
0.0090263020247221,
-0.0008272975101135671,
-0.014075212180614471,
0.03536900877952576,
-0.0005469844327308238,
-0.015367948450148106,
-0.006154734641313553,
-0.025171557441353798,
0.026041319593787193,
-0.030903959646821022,
0.0011424407130107284,
-0.029185529798269272,
0.0013358797878026962,
-0.02492985874414444,
0.01419751439243555,
-0.016719775274395943,
-0.014204747043550014,
-0.005663417745381594,
-0.02882228046655655,
0.013550911098718643,
0.050719328224658966,
-0.0017095118528231978,
0.05467796325683594,
0.016317425295710564,
0.013717638328671455,
0.02238200604915619,
0.020763762295246124,
-0.03977905586361885,
0.008639496751129627,
-0.0011597167467698455,
0.01130807213485241,
0.04630650207400322,
-0.044731415808200836,
-0.043892040848731995,
0.025418730452656746,
-0.039447326213121414,
-0.04092695936560631,
0.07214591652154922,
-0.039876680821180344,
-0.04316785931587219,
0.00557857658714056,
-0.014992060139775276,
-0.021739168092608452,
0.07271964102983475,
-0.02506924420595169,
-0.0009016283438540995,
0.009622049517929554,
-0.022386614233255386,
-0.017917368561029434,
-0.0019446649821475148,
-0.0036300020292401314,
0.019274022430181503,
-0.011091584339737892,
0.03065723180770874,
0.024226360023021698,
-0.019556306302547455,
-0.003473317250609398,
0.003020367817953229,
0.0057243481278419495,
0.029830697923898697,
0.01024327427148819,
-0.014360020868480206,
0.05382482334971428,
0.054262425750494,
-0.014307452365756035,
0.03424113616347313,
-0.0185659471899271,
-0.014993864111602306,
-0.11682870239019394,
0.017666200175881386,
-0.004396287724375725,
0.0352693647146225,
0.027253320440649986,
-0.0619981624186039,
0.04964335262775421,
0.00434458302333951,
-0.09086208790540695,
0.00681170541793108,
-0.010355539619922638,
-0.025027573108673096,
-0.01901869848370552,
0.0015481029404327273,
-0.028876109048724174,
0.012667002156376839,
0.002058233367279172,
0.009442390874028206,
0.026691311970353127,
0.02530200406908989,
-0.036264169961214066,
-0.03340687230229378,
-0.019533202052116394,
0.02953457273542881,
-0.012887950986623764,
-0.0019418983720242977,
0.06292381882667542,
-0.005672793369740248,
-0.04332298785448074,
0.05149412900209427,
-0.033987291157245636,
-0.010441368445754051,
-0.03445630893111229,
0.03634026646614075,
0.013833721168339252,
0.041904326528310776,
0.052508559077978134,
-0.0080641470849514,
0.016008561477065086,
-0.013811721466481686,
-0.008754245936870575,
0.020771529525518417,
0.018344219774007797,
0.0045401654206216335,
-0.006664121523499489,
0.019964871928095818,
0.010141854174435139,
0.040980689227581024,
-0.0496785007417202,
-0.02616783045232296,
0.01788179948925972,
0.005987534299492836,
0.010306000709533691,
-0.020488232374191284,
0.0037247424479573965,
-0.07120499759912491,
-0.024480057880282402,
0.026253603398799896,
0.02832726389169693,
0.0012203545775264502,
0.006988647393882275,
-0.0206704493612051,
-0.03498280793428421,
0.03460793197154999,
0.023088591173291206,
-0.02413264289498329,
-0.04945167154073715,
-0.017037054523825645,
-0.005161632783710957,
0.041928116232156754,
-0.01634293794631958,
-0.058665815740823746,
-0.05489624664187431,
0.036344755440950394,
0.004207308404147625,
0.02945273369550705,
0.008576232008635998,
-0.017853470519185066,
0.02219681441783905,
-0.06154756620526314,
0.04198496416211128,
0.0036029452458024025,
0.0120740020647645,
0.0026353660505264997,
-0.034706152975559235,
0.026952669024467468,
-0.006258042063564062,
0.060992151498794556,
-0.0036095103714615107,
-0.030027592554688454,
0.02725386619567871,
-0.040680523961782455,
0.05042140930891037,
-0.031149649992585182,
0.00816085934638977,
-0.05871964618563652,
-0.009937542490661144,
-0.005302468780428171,
0.002480121562257409,
-0.014727659523487091,
-0.0007982694660313427,
0.03538208082318306,
0.05257589742541313,
-0.02254028245806694,
-0.028237778693437576,
-0.03476019948720932,
0.03928767144680023,
0.015130178071558475,
-0.0015432750806212425,
0.029243510216474533,
0.01776837930083275,
0.06189746409654617,
-0.010007862001657486,
0.026307953521609306,
-0.042644817382097244,
0.02346801944077015,
-0.02736971713602543,
0.022450901567935944,
-0.010699084028601646,
0.025310417637228966,
0.04772745072841644,
-0.06384127587080002,
-0.020462455227971077,
0.0408342182636261,
0.011419977061450481,
-0.019826781004667282,
0.04569214954972267,
-0.002795165404677391,
0.026433246210217476,
0.026357732713222504,
0.04037110134959221,
0.0023611956275999546,
-0.018182378262281418,
-0.02178329974412918,
0.04212797060608864,
0.01349947415292263,
-0.000006308204774541082,
0.012242061085999012,
0.03640148043632507,
-0.05772258713841438,
0.03493614122271538,
0.014715022407472134,
-0.006369683425873518,
-0.017701810225844383,
-0.04341227188706398,
0.011551938951015472,
0.01104098092764616,
-0.01096118800342083,
0.04901105910539627,
-0.008562342263758183,
0.052088476717472076,
-0.02495584450662136,
0.010402134619653225,
-0.036029960960149765,
-0.013556042686104774,
-0.0005762228392995894,
-0.02758403867483139,
0.012261043302714825,
0.05566713213920593,
0.0009836136596277356,
-0.008119354955852032,
0.015585127286612988,
-0.024443957954645157,
-0.008607495576143265,
-0.05348615348339081,
-0.0018112927209585905,
0.0003856810217257589,
-0.011038417927920818,
-0.03686502203345299,
-0.004254004452377558,
-0.019499581307172775,
-0.024583159014582634,
0.012282558716833591,
0.05436133220791817,
-0.008137455210089684,
0.01850314810872078,
-0.02033911645412445,
-0.0016231415793299675,
0.07020089775323868,
-0.01619480922818184,
-0.017068492248654366,
-0.008450387045741081,
0.019813407212495804,
0.012828894890844822,
0.013045488856732845
] |
<p>The 1D delta potential well $V(x) = -A\delta(x - a)$ always has exactly one bound state. The same is true for the 3D delta potential well $V(\vec{r}) = -A\delta(\vec{r}-\vec{a})$. I can show this for $l = 0$, I don't know how to do the calculations otherwise.</p>
<p>So two questions,</p>
<ol>
<li><p>Can I conclude that there is only one bound state for the 3D potential well for $l \not = 0$? I've seen that the energies of the eigenstates for the hydrogen atom depend only on $n$, but I am wondering whether this is an instance of a more general result?</p></li>
<li><p>When $\vec{a} = 0$ and $l=0$, there are no normalizable eigenstates. For $l \not = 0$, the effective potential in the radial equation becomes large at the origin, can I use this to conclude that there are no bound states when $\vec{a}=0$?</p></li>
</ol>
| 8,873 |
[
-0.0348326675593853,
0.008533145301043987,
-0.01671767048537731,
0.006947639398276806,
0.05990581214427948,
-0.032701458781957626,
-0.05383112281560898,
-0.07707810401916504,
0.022080715745687485,
-0.03839075192809105,
0.016790958121418953,
0.008903773501515388,
0.05632885918021202,
0.03182780742645264,
0.04056316614151001,
0.02974037453532219,
-0.013946151360869408,
-0.03769739717245102,
0.0067506833001971245,
-0.01660883240401745,
0.008126125670969486,
0.011440304107964039,
0.038422275334596634,
0.0013595556374639273,
-0.04171421378850937,
0.017010590061545372,
-0.004289044067263603,
-0.014918354339897633,
0.01641048677265644,
0.061911992728710175,
-0.02142699807882309,
0.005957202520221472,
0.005952185019850731,
0.0746942088007927,
0.011733976192772388,
0.0274218637496233,
-0.024200676009058952,
-0.01060748752206564,
-0.04108094424009323,
0.05132842808961868,
-0.03216320276260376,
-0.033643096685409546,
0.030707968398928642,
0.07722488045692444,
-0.0017327717505395412,
-0.018481919541954994,
0.001352913910523057,
-0.019535157829523087,
0.06601756811141968,
-0.023860732093453407,
0.045086126774549484,
-0.03659427538514137,
0.043227799236774445,
0.008168081752955914,
-0.005490004550665617,
-0.02830950729548931,
0.0570126473903656,
0.07002103328704834,
0.034175947308540344,
-0.03436192497611046,
-0.04297091066837311,
-0.017257412895560265,
-0.02870766632258892,
0.023560309782624245,
-0.011999079026281834,
-0.002453648019582033,
-0.0023803601507097483,
-0.033467989414930344,
-0.00392674095928669,
-0.04494669288396835,
0.004085600841790438,
0.020850446075201035,
-0.00865109171718359,
-0.021688228473067284,
0.029214568436145782,
-0.005216273479163647,
-0.004215853288769722,
0.01951606571674347,
0.013986200094223022,
0.014202045276761055,
-0.011295423842966557,
0.0281077828258276,
0.03310210630297661,
0.034082815051078796,
-0.018452920019626617,
-0.025793811306357384,
0.05495757237076759,
-0.004177842289209366,
-0.008637274615466595,
0.03583504632115364,
0.007586309220641851,
0.020036978647112846,
0.02460024319589138,
-0.026907019317150116,
-0.02268012799322605,
0.022902214899659157,
0.014071537181735039,
0.027549326419830322,
0.005687055177986622,
-0.028554746881127357,
-0.03832971677184105,
-0.052860941737890244,
0.013230516575276852,
0.06984028220176697,
0.01395421102643013,
0.0010446843225508928,
-0.012906749732792377,
0.025886794552206993,
-0.015309622511267662,
-0.027756763622164726,
-0.02913413941860199,
0.030850637704133987,
0.02790200337767601,
-0.012929377146065235,
-0.02209697663784027,
-0.00997652392834425,
-0.031991247087717056,
-0.048022571951150894,
0.007711541373282671,
0.06635890156030655,
0.02707582339644432,
-0.02268991991877556,
0.021327419206500053,
-0.024446282535791397,
-0.04941626265645027,
0.011057937517762184,
0.032932206988334656,
0.01072661578655243,
-0.0210332702845335,
0.027246640995144844,
0.015906494110822678,
0.014668062329292297,
-0.0036803707480430603,
-0.008597690612077713,
0.05293678119778633,
-0.010720721445977688,
-0.12218774855136871,
-0.06464667618274689,
0.021408719941973686,
-0.02747672237455845,
-0.005100958980619907,
-0.021830474957823753,
-0.026775741949677467,
0.040239330381155014,
0.07019199430942535,
-0.0008692831615917385,
-0.006341111846268177,
0.010659962892532349,
0.02978014200925827,
0.021225787699222565,
-0.004819690249860287,
-0.019375205039978027,
-0.015919920057058334,
-0.05057567358016968,
-0.026811765506863594,
-0.05156192183494568,
0.06584389507770538,
0.015013260766863823,
0.033752862364053726,
-0.007935859262943268,
0.0916038379073143,
-0.011888569220900536,
0.023697415366768837,
0.010185974650084972,
0.011550107039511204,
-0.017451602965593338,
0.057554516941308975,
0.023258626461029053,
-0.006507091224193573,
0.03535710275173187,
-0.01904664747416973,
0.043480806052684784,
-0.027897430583834648,
0.03788412734866142,
0.03531031683087349,
-0.05418935790657997,
-0.01019946951419115,
-0.06971282511949539,
0.01474844105541706,
0.019882863387465477,
-0.03748451918363571,
-0.0016700613778084517,
-0.001239341334439814,
0.019709741696715355,
0.016219571232795715,
0.08595693111419678,
-0.006460476201027632,
-0.0029784853104501963,
0.0022529377602040768,
-0.03235052153468132,
0.03171868994832039,
-0.03501526266336441,
0.03359469026327133,
0.03151451796293259,
-0.020309746265411377,
0.04540388286113739,
0.027827268466353416,
0.009086216799914837,
-0.020405584946274757,
-0.02445734292268753,
-0.009851234965026379,
0.030992647632956505,
-0.020735369995236397,
-0.023625487461686134,
0.06092805042862892,
0.04633112624287605,
0.04077940061688423,
-0.014097482897341251,
0.052960291504859924,
-0.02591790072619915,
-0.011509225703775883,
-0.00972540769726038,
-0.041651081293821335,
0.04024728015065193,
0.03876085206866264,
0.0188831128180027,
-0.029654012992978096,
-0.013597957789897919,
0.01198736671358347,
0.039312392473220825,
-0.08667447417974472,
0.04667667672038078,
0.025810828432440758,
-0.03338674083352089,
-0.00811751652508974,
0.0583699569106102,
0.0014055301435291767,
0.02284916490316391,
0.0054024215787649155,
-0.049524884670972824,
-0.04184270277619362,
-0.008851099759340286,
0.04425257071852684,
0.02649587206542492,
-0.047787144780159,
0.014869996346533298,
0.03037904016673565,
0.01979440078139305,
0.049113016575574875,
0.01748010516166687,
-0.049889788031578064,
-0.04720625281333923,
0.017948342487215996,
0.015825655311346054,
-0.016766708344221115,
0.030031342059373856,
0.038452547043561935,
0.00787551049143076,
0.03951294720172882,
-0.0007056380854919553,
-0.017909575253725052,
0.0416104793548584,
-0.029059994965791702,
0.023897845298051834,
0.020735617727041245,
-0.044232115149497986,
0.04111518710851669,
-0.00883455853909254,
0.02411758340895176,
0.010850447230041027,
-0.03175593167543411,
-0.006158354692161083,
-0.01508665643632412,
0.005008598789572716,
0.0436682254076004,
-0.012947573326528072,
-0.013559728860855103,
0.01651577837765217,
0.013726415112614632,
-0.009774064645171165,
0.008695158176124096,
-0.04203478619456291,
0.009135214611887932,
-0.016217723488807678,
0.013414708897471428,
0.03756421059370041,
-0.004290204960852861,
0.011257107369601727,
-0.027118775993585587,
-0.020896490663290024,
-0.00409065093845129,
-0.02414107136428356,
-0.006429555360227823,
0.039800334721803665,
-0.019984908401966095,
-0.006376122590154409,
-0.03005312941968441,
-0.009365150704979897,
0.023222189396619797,
-0.011634026654064655,
-0.0023966305889189243,
-0.002915232675150037,
-0.04040788859128952,
-0.03373295068740845,
-0.02516775391995907,
-0.004324898589402437,
0.003092395607382059,
-0.020965827628970146,
0.01029166765511036,
0.03194083645939827,
0.034600913524627686,
-0.03132646530866623,
0.030927540734410286,
-0.01713522896170616,
-0.006959510035812855,
-0.0441669225692749,
-0.004657610785216093,
0.03341689705848694,
-0.025292115285992622,
0.06248093023896217,
0.044085897505283356,
-0.04584719240665436,
-0.004735925234854221,
-0.03886539861559868,
-0.006383151281625032,
0.015891456976532936,
-0.014172122813761234,
0.03510061278939247,
-0.014017864130437374,
0.008403746411204338,
0.08582846075296402,
0.010755629278719425,
0.0021240930072963238,
-0.015485990792512894,
-0.01703210547566414,
-0.020417796447873116,
0.0014762296341359615,
0.02416837029159069,
0.03917153552174568,
-0.012658416293561459,
0.029627984389662743,
-0.01562807895243168,
0.07063549757003784,
0.0028521232306957245,
0.000983329606242478,
0.004793207161128521,
0.02621825411915779,
0.04889731854200363,
0.01872565597295761,
0.05057201161980629,
0.014485188759863377,
0.005558690521866083,
-0.02083093486726284,
-0.0071771638467907906,
0.032981205731630325,
0.03946756571531296,
-0.045387789607048035,
0.044448576867580414,
-0.027298703789711,
0.039131101220846176,
-0.013423578813672066,
0.03752796724438667,
0.03251497447490692,
-0.004030262120068073,
-0.01806226745247841,
0.006465919781476259,
0.052426960319280624,
-0.030969960615038872,
-0.009999782778322697,
0.04313374683260918,
-0.01716281846165657,
-0.0009159077308140695,
-0.0051368484273552895,
0.007420288398861885,
0.009083233773708344,
0.032384518533945084,
-0.02977149188518524,
-0.03592230752110481,
0.026034122332930565,
0.0434957854449749,
0.014401943422853947,
-0.03729582577943802,
-0.039438359439373016,
0.017500875517725945,
-0.04959755390882492,
-0.02964409440755844,
-0.03145584464073181,
0.0463612899184227,
-0.005034293979406357,
0.03338819742202759,
0.02447364665567875,
0.00827399455010891,
0.010904181748628616,
-0.02355758659541607,
-0.029246436432003975,
-0.048325810581445694,
-0.030316440388560295,
-0.012362375855445862,
-0.016586938872933388,
0.005688246339559555,
-0.026143783703446388,
-0.01079594250768423,
-0.012351864948868752,
0.01032839436084032,
-0.03589192032814026,
-0.05667724087834358,
-0.020505718886852264,
-0.02131514810025692,
-0.03244386613368988,
-0.03722740709781647,
0.03030060976743698,
0.025301232933998108,
-0.0036733299493789673,
0.023749694228172302,
0.02896912209689617,
-0.07140165567398071,
-0.025027645751833916,
-0.023828741163015366,
-0.0006247902638278902,
0.01321386732161045,
0.05285884067416191,
0.04741993919014931,
0.04206369072198868,
0.00887095183134079,
-0.04614204913377762,
0.006527867168188095,
0.028852174058556557,
0.006760905496776104,
-0.008426684886217117,
0.029977990314364433,
-0.02927470952272415,
0.00022901943884789944,
0.0007639918476343155,
0.06938079744577408,
-0.02089187502861023,
0.055824194103479385,
0.019763078540563583,
-0.01059777196496725,
-0.008264409378170967,
0.025029463693499565,
0.03878213092684746,
0.006982205435633659,
-0.001526557025499642,
-0.046952985227108,
0.0495133139193058,
-0.028812436386942863,
0.020656246691942215,
-0.017445966601371765,
-0.036525942385196686,
-0.02066660299897194,
0.00712154246866703,
0.010455673560500145,
0.045084398239851,
-0.0037928633391857147,
-0.025709178298711777,
-0.015565510839223862,
0.03196330741047859,
-0.032229822129011154,
0.012238112278282642,
0.02046108804643154,
-0.0023461838718503714,
0.028775671496987343,
-0.005179034546017647,
0.010091380216181278,
-0.06708315014839172,
-0.024158883839845657,
0.01318043190985918,
0.02893521636724472,
0.009746180847287178,
-0.001907764351926744,
-0.02430799975991249,
-0.044591065496206284,
0.04704912751913071,
-0.04199131205677986,
0.012301878072321415,
-0.032583557069301605,
-0.008846085518598557,
-0.005097421817481518,
-0.051972635090351105,
-0.02770007960498333,
-0.026680326089262962,
0.012565081007778645,
0.01725138910114765,
-0.030371811240911484,
-0.006034624297171831,
-0.038469891995191574,
0.006915531121194363,
-0.01395213883370161,
0.04421209543943405,
0.027792269363999367,
-0.02786264754831791,
-0.014039969071745872,
0.03505530580878258,
-0.03371065482497215,
-0.101102814078331,
0.002915556076914072,
0.04595246911048889,
0.03345514461398125,
0.0565243661403656,
-0.039386965334415436,
-0.04304105043411255,
0.059439629316329956,
0.01275375485420227,
-0.034538209438323975,
0.005258218385279179,
-0.021858850494027138,
0.031721338629722595,
0.020334675908088684,
-0.014065270312130451,
0.043631412088871,
0.02715384215116501,
0.02384624257683754,
-0.006948831956833601,
-0.026985693722963333,
-0.006052407901734114,
-0.020997097715735435,
0.010489162988960743,
-0.041817158460617065,
0.019218068569898605,
0.012592924758791924,
0.03228534758090973,
-0.008254142478108406,
0.009826397523283958,
0.02169659547507763,
-0.021885693073272705,
-0.001670937635935843,
0.015334846451878548,
-0.00022877924493514001,
0.007327314466238022,
-0.0022773442324250937,
-0.00877550058066845,
0.015280038118362427,
-0.0319470651447773,
-0.02462385594844818,
0.0023639334831386805,
0.01518707163631916,
0.03895673155784607,
0.0040658446960151196,
0.010094674304127693,
-0.007903724908828735,
-0.01566273719072342,
0.021319787949323654,
-0.09326045215129852,
0.03804211691021919,
-0.0014752800343558192,
0.02190290577709675,
-0.009841915220022202,
-0.04274865984916687,
-0.023647960275411606,
0.03310824930667877,
-0.02810625359416008,
0.007390294689685106,
-0.0044886404648423195,
0.018494505435228348,
-0.0185367651283741,
0.0002547724870964885,
-0.07223197817802429,
0.020161619409918785,
-0.01588032767176628,
0.004054711200296879,
-0.016479412093758583,
-0.027587149292230606,
-0.008886510506272316,
-0.021591994911432266,
0.004381643608212471,
-0.025140829384326935,
0.021633120253682137,
-0.02202882617712021,
0.002469498198479414,
0.02831094339489937,
0.03691291809082031,
0.0870412066578865,
-0.018024519085884094,
-0.005306307692080736,
-0.026056483387947083,
-0.022903449833393097,
-0.010236884467303753,
0.027135875076055527,
0.04173882678151131,
-0.038097552955150604,
-0.036750245839357376,
-0.010712314397096634,
-0.01876888982951641,
0.0281317587941885,
-0.012141442857682705,
-0.03921578451991081,
0.013390450738370419,
-0.02195020020008087,
0.00497805792838335,
-0.0012241785880178213,
-0.012035266496241093,
-0.02393498830497265,
0.011619549244642258,
0.011660882271826267,
0.007939613424241543,
-0.0379829928278923,
-0.02958102524280548,
0.007771816570311785,
-0.01841774210333824,
-0.027149435132741928,
0.002156532369554043,
0.07323980331420898,
0.01749151572585106,
0.01594986580312252,
-0.0075556132942438126,
0.008140899240970612,
0.01850634068250656,
-0.017129559069871902,
-0.008773538284003735,
0.010741496458649635,
0.012268341146409512,
-0.01812094636261463,
-0.09049287438392639,
-0.04502718895673752,
0.06286025792360306,
0.025804264470934868,
0.012315542437136173,
0.04389231279492378,
0.0015763785922899842,
0.036202363669872284,
-0.04885992407798767,
-0.05175304412841797,
-0.0411306694149971,
0.007922163233160973,
-0.025922341272234917,
0.04744776710867882,
-0.04497537761926651,
0.0018178770551458001,
0.012416134588420391,
0.05593635514378548,
-0.006887807045131922,
-0.02068128064274788,
0.024240607395768166,
-0.01664392091333866,
0.004581142216920853,
-0.0206162016838789,
-0.01586904190480709,
0.0554569847881794,
-0.003075757995247841,
0.00037299413816072047,
0.024973822757601738,
-0.03129657357931137,
0.05437810346484184,
0.0017630222719162703,
0.04650446027517319,
-0.08796634525060654,
-0.032247211784124374,
-0.009850299917161465,
0.027057837694883347,
0.01425536721944809,
0.017485614866018295,
0.008681305684149265,
0.007537463679909706,
0.03424638509750366,
0.015683069825172424,
0.01612231135368347,
-0.021001996472477913,
-0.04911511763930321,
-0.03872565180063248,
0.006965793669223785,
-0.01884596049785614,
0.030150938779115677,
-0.02189435064792633,
-0.04780910909175873,
0.017283307388424873,
-0.045476604253053665,
0.03414549678564072,
0.006822861731052399,
0.02354724332690239,
-0.016590312123298645,
0.055974651128053665,
0.005899533163756132,
0.014503481797873974,
0.009693106636404991,
0.014263367280364037,
0.12396847456693649,
0.07906315475702286,
0.039553988724946976,
-0.06175319850444794,
0.004937293939292431,
0.023964110761880875,
0.005521039944142103,
-0.017065593972802162,
-0.005790284834802151,
-0.013016370125114918,
-0.03372384235262871,
-0.04307933524250984,
0.053354524075984955,
-0.033869143575429916,
0.015777550637722015,
0.044703852385282516,
-0.02759159356355667,
-0.03731730580329895,
0.004643663763999939,
0.009892554953694344,
0.011926009319722652,
0.006216419395059347,
-0.023860907182097435,
0.05862930044531822,
-0.031338244676589966,
0.021283358335494995,
-0.047076571732759476,
-0.01190071552991867,
0.042769018560647964,
-0.038325998932123184,
-0.03716449812054634,
-0.01079088356345892,
-0.016723105683922768,
-0.0022980868816375732,
-0.022484978660941124,
0.01705928146839142,
0.010879839770495892,
-0.011979764327406883,
0.026230286806821823,
0.04227215051651001,
-0.041610706597566605,
0.022859275341033936,
0.005734442267566919,
0.01987176202237606,
-0.043176133185625076,
-0.01766040548682213,
-0.0013621437828987837,
0.03718942403793335,
-0.011466732248663902,
0.005866654217243195,
-0.007453167345374823,
0.003695884020999074,
-0.0049237338826060295,
-0.04920155927538872,
-0.0074395383708179,
-0.00936391856521368,
0.025708762928843498,
0.00293157109990716,
-0.01652875356376171,
-0.004612141288816929,
0.0016949500422924757,
0.027474435046315193,
-0.0013353759422898293,
-0.03503333404660225,
0.014385920949280262,
0.0568525604903698,
-0.026197081431746483,
0.07167302072048187,
0.017307667061686516,
0.0063440739177167416,
0.005236084572970867,
-0.0022619643714278936,
-0.022936522960662842,
-0.01053702924400568,
0.021752407774329185,
-0.0020233949180692434,
0.06424348056316376,
0.03771234676241875,
0.011736029759049416,
-0.010822467505931854,
-0.13669128715991974,
0.011454734019935131,
-0.015581083483994007,
-0.019801829010248184,
0.010834349319338799,
-0.006485118065029383,
0.016674812883138657,
0.04720289632678032,
-0.003181988140568137,
0.008824318647384644,
0.010561389848589897,
0.04411995783448219,
0.004149173852056265,
-0.02564808540046215,
-0.043604232370853424,
0.004498641937971115,
-0.08960597217082977,
0.027741940692067146,
-0.031235333532094955,
-0.01364967506378889,
0.006538904272019863,
0.03403497114777565,
-0.004021625965833664,
0.06580966711044312,
-0.04207067936658859,
-0.033711548894643784,
-0.020885784178972244,
-0.033909108489751816,
0.02107059955596924,
0.006158940959721804,
0.04308653622865677,
-0.03679252415895462,
-0.05491860955953598,
-0.01985572837293148,
-0.03261985629796982,
0.005615511909127235,
-0.043058935552835464,
-0.021385405212640762,
0.03452811762690544,
-0.039713677018880844,
-0.020017055794596672,
-0.05893664062023163,
-0.02610800601541996,
-0.03327949717640877,
0.015374916605651379,
0.004693559370934963,
0.0047583431005477905,
-0.021467333659529686,
-0.009940538555383682,
-0.005329762119799852,
-0.00985542219132185,
0.019702373072504997,
0.02621510997414589,
-0.018592555075883865,
0.006016293074935675,
0.022572988644242287,
0.0064658490009605885,
0.03309962525963783,
0.0026122834533452988,
-0.012662293389439583,
0.03488290682435036,
-0.05691896006464958,
-0.03311431035399437,
0.021587325260043144,
-0.01037357747554779,
0.04060542955994606,
0.02871677465736866,
-0.0192643404006958,
-0.02500213496387005,
0.036085449159145355,
-0.007796117104589939,
0.011829948052763939,
0.004006639122962952,
-0.015053266659379005,
0.026141561567783356,
0.011335968039929867,
0.01087094284594059,
-0.009940600022673607,
-0.007380682975053787,
0.007151153404265642,
0.011653188616037369,
-0.03082459792494774,
-0.0006211933796294034,
0.019162507727742195,
0.018239935860037804,
0.018351418897509575,
0.02597561851143837,
-0.0263510849326849,
0.02923555113375187,
0.03573876991868019,
-0.018029777333140373,
0.05816841125488281,
0.05617000162601471,
0.044024303555488586,
-0.11176976561546326,
-0.008594905026257038,
-0.03384117782115936,
0.02575075253844261,
0.010123289190232754,
-0.06845279037952423,
0.008200742304325104,
0.03586867079138756,
-0.08809066563844681,
0.01811487041413784,
0.03251172602176666,
0.018697073683142662,
-0.04180600494146347,
-0.0020488868467509747,
-0.04233677685260773,
0.013237320818006992,
0.01789313368499279,
0.035442713648080826,
-0.006372243631631136,
0.01675024814903736,
-0.031360093504190445,
-0.03544112294912338,
-0.009911785833537579,
0.04620775207877159,
0.0012973848497495055,
-0.022458158433437347,
0.04216165840625763,
-0.019182180985808372,
-0.04404999688267708,
-0.000982751022092998,
-0.043772660195827484,
-0.019241774454712868,
-0.004494013264775276,
0.009515682235360146,
-0.007588849402964115,
0.04090883955359459,
0.04031609743833542,
0.024834344163537025,
-0.0019386813510209322,
0.0406096912920475,
-0.013101344928145409,
0.00825525727123022,
0.0022059695329517126,
-0.018307635560631752,
0.03506912291049957,
-0.037305209785699844,
-0.04818825051188469,
0.04438638687133789,
-0.008172399364411831,
0.021820399910211563,
-0.0013253232464194298,
0.001478561433032155,
-0.0029852502048015594,
-0.010265925899147987,
-0.017170758917927742,
-0.012581233866512775,
0.011218798346817493,
0.014564196579158306,
0.042827703058719635,
0.0019840719178318977,
0.015200125053524971,
-0.009955509565770626,
-0.0541151724755764,
0.04191269353032112,
-0.00782692153006792,
-0.047499075531959534,
-0.045809827744960785,
-0.004868910647928715,
0.0063873520120978355,
-0.0019673791248351336,
-0.04801064357161522,
0.01554202102124691,
-0.06116516515612602,
0.019620802253484726,
-0.021984295919537544,
0.013343972153961658,
-0.022294389083981514,
-0.04035349190235138,
-0.026983430609107018,
-0.06119468808174133,
0.02507980726659298,
0.030394306406378746,
0.005605168640613556,
-0.026812057942152023,
0.0022840495221316814,
0.0010699137346819043,
0.028022751212120056,
0.04712386056780815,
-0.019306859001517296,
-0.03908924013376236,
0.04490906000137329,
-0.02232048287987709,
0.017150934785604477,
-0.018754860386252403,
-0.01520462241023779,
-0.005885460413992405,
-0.02402501553297043,
-0.0019249692559242249,
-0.011505304835736752,
-0.012828287668526173,
0.03356948122382164,
-0.010251935571432114,
0.0030133535619825125,
-0.03286496922373772,
-0.010369541123509407,
-0.016962828114628792,
0.06380606442689896,
0.011995433829724789,
-0.00514351949095726,
0.06662715971469879,
0.028701871633529663,
-0.005754775367677212,
0.008416724391281605,
-0.030235378071665764,
-0.036089807748794556,
0.011307625100016594,
-0.04524241387844086,
-0.027360323816537857,
-0.0033815845381468534,
0.003674672916531563,
0.005929131060838699,
0.007578793913125992,
-0.00898914784193039,
0.056542620062828064,
0.001704118913039565,
-0.01949690841138363,
0.03858635574579239,
0.016042543575167656,
0.05130208283662796,
-0.00254445499740541,
0.009787578135728836,
0.040176164358854294,
0.025322318077087402,
0.024843597784638405,
0.01468963734805584,
0.03119831345975399,
0.027756081894040108,
0.004131163004785776,
0.004933033604174852,
-0.018272675573825836,
0.0071382420137524605,
-0.002403893042355776,
0.009345831349492073,
-0.025726698338985443,
0.026636265218257904,
0.04365304484963417,
0.00833524763584137,
-0.02100524865090847,
-0.022887835279107094,
0.000722608354408294,
0.055812202394008636,
-0.030651727691292763,
0.01903587579727173,
-0.05295579507946968,
-0.0063113621436059475,
0.024852018803358078,
0.04106273129582405,
0.005369758699089289,
0.04908754304051399,
-0.03683653101325035,
-0.030850406736135483,
-0.02925964631140232,
0.010123015381395817,
0.04433892294764519,
-0.04824524745345116,
-0.0007881778292357922,
-0.0017533852951601148,
-0.021532947197556496,
-0.046634823083877563,
0.00863100029528141,
-0.02988903410732746,
0.007808992639183998,
0.014110930263996124,
0.05021512135863304,
0.031010720878839493,
-0.0052720061503350735,
0.005672155879437923,
0.008943294174969196,
0.0493498221039772,
-0.04621175676584244,
-0.06139767915010452,
0.0020416758488863707,
0.022403687238693237,
0.00013557588681578636,
0.00150341319385916
] |
<p>I am having trouble with a physics problem. The problem is as follows:</p>
<p>A car is traveling at 54.0 mi/h on a horizontal highway.</p>
<p>A) If the coefficient of static friction between road and tires on a rainy day is 0.103, what is the minimum distance in which the car will stop?</p>
<p>B) What is the stopping distance when the surface is dry and µs = 0.595?</p>
<p>This is what I have so far for A)</p>
<pre><code>fs = µs * Fn
Fn = Mg
fs = Ma
Ma = µs * Mg
a = µs * g
V = 54 - a * t
0 = 54 - a * t
t = 53.497 seconds
dist = 54*t - (a/2)*t^2
= 1444.42243 miles
= 2324572.57 meters
</code></pre>
<p>This is not the correct answer. Any help would me much appreciated.</p>
| 8,874 |
[
-0.0031796488910913467,
-0.04276163876056671,
-0.04216547682881355,
0.04152316600084305,
0.014461032114923,
0.004312565550208092,
-0.00448448583483696,
-0.027711372822523117,
-0.011842695064842701,
0.02994379587471485,
0.03698878362774849,
0.06528404355049133,
0.012645971029996872,
0.037697721272706985,
0.05007782578468323,
-0.009021512232720852,
0.016455868259072304,
-0.030102035030722618,
0.02463354356586933,
0.0024885882157832384,
-0.012817628681659698,
-0.01632184349000454,
0.01701684296131134,
-0.0023237215355038643,
-0.003758540842682123,
0.027391616255044937,
0.02770232781767845,
-0.007666981779038906,
-0.021899867802858353,
0.025452954694628716,
-0.030070554465055466,
-0.06851781904697418,
-0.03497379645705223,
-0.0032950635068118572,
0.02800215780735016,
0.0562901608645916,
-0.05015062168240547,
0.008332131430506706,
-0.04873606190085411,
-0.0008975458331406116,
0.022990508005023003,
0.04535051807761192,
-0.04339053854346275,
0.06886026263237,
-0.01960078254342079,
0.03351728245615959,
0.027735531330108643,
0.00898635946214199,
0.023858260363340378,
-0.02318699099123478,
0.07396527379751205,
0.004390666261315346,
0.032060738652944565,
0.0016780877485871315,
-0.004294860642403364,
0.01959211379289627,
0.03912796080112457,
0.06902018934488297,
-0.02919411100447178,
-0.07409229874610901,
-0.0033104277681559324,
-0.008568890392780304,
0.0020938338711857796,
-0.03174932301044464,
-0.009756849147379398,
-0.0010783378966152668,
-0.04729098826646805,
-0.05065889656543732,
0.03881077468395233,
0.0138684818521142,
-0.005854391027241945,
0.0038218949921429157,
0.016849299892783165,
-0.030216138809919357,
0.03137778490781784,
-0.02832571230828762,
0.023335283622145653,
-0.0060283467173576355,
0.012112362310290337,
0.027098121121525764,
0.004527349956333637,
0.008561402559280396,
0.011436580680310726,
0.06267699599266052,
0.030418599024415016,
-0.019440792500972748,
0.0759897530078888,
-0.0007498061168007553,
0.013737439177930355,
0.05556381121277809,
0.000829044496640563,
0.0034380543511360884,
0.019829286262392998,
0.03011586330831051,
0.013170614838600159,
0.02481990121304989,
0.008859770372509956,
0.03932825103402138,
-0.0035675957333296537,
-0.003208259353414178,
-0.004873058758676052,
-0.013671896420419216,
0.05579429492354393,
0.010510561987757683,
-0.017979584634304047,
-0.0036341797094792128,
-0.02798391319811344,
0.00838539656251669,
0.00907902792096138,
0.031761348247528076,
-0.048055898398160934,
0.02139313519001007,
-0.010258241556584835,
0.029800591990351677,
0.0016603994881734252,
-0.057385582476854324,
0.024948567152023315,
-0.005885722115635872,
0.00830872729420662,
0.03139925003051758,
0.034979447722435,
-0.043328944593667984,
0.025484314188361168,
-0.004149806685745716,
-0.012592731975018978,
-0.012434066273272038,
0.008497288450598717,
0.007146400399506092,
-0.028998561203479767,
0.00027379649691283703,
-0.016035763546824455,
0.0037739905528724194,
0.02202667109668255,
-0.008467256091535091,
0.02822422981262207,
-0.03714315593242645,
-0.04604319483041763,
-0.07003630697727203,
0.011862832121551037,
0.0008819684735499322,
0.007232428528368473,
-0.024626880884170532,
0.006339939311146736,
0.015801766887307167,
0.03065217100083828,
-0.009214531630277634,
0.04067050665616989,
-0.016413889825344086,
0.03353332355618477,
-0.012010248377919197,
-0.005980459973216057,
-0.031730130314826965,
-0.007232105825096369,
-0.018600143492221832,
0.02693663351237774,
-0.058545637875795364,
0.016069035977125168,
0.011407126672565937,
0.015448818914592266,
-0.03277411684393883,
0.026603369042277336,
0.005206940695643425,
0.004156547598540783,
-0.01430070772767067,
-0.01519731618463993,
-0.03321830555796623,
0.0610915869474411,
-0.00435646204277873,
0.012223316356539726,
0.004776765592396259,
0.014068381860852242,
0.013468718156218529,
-0.02481933683156967,
0.01536906510591507,
0.06634123623371124,
-0.030165474861860275,
-0.026610974222421646,
-0.019270634278655052,
0.02982417307794094,
0.006723934784531593,
-0.028202034533023834,
-0.048882607370615005,
0.00642181932926178,
0.01005503535270691,
-0.00012394088844303042,
0.043072961270809174,
0.022969925776124,
0.0334307923913002,
0.012003563344478607,
-0.009916531853377819,
-0.01783568039536476,
-0.02622813545167446,
0.019771385937929153,
0.018382888287305832,
-0.004445698112249374,
-0.02102970890700817,
-0.022667517885565758,
0.013840335421264172,
-0.059684962034225464,
-0.023413576185703278,
0.009053539484739304,
0.01767721213400364,
-0.023608272895216942,
-0.022078929468989372,
0.026268480345606804,
0.06207830086350441,
0.06383979320526123,
-0.03220352903008461,
0.0026322188787162304,
-0.03010980598628521,
0.02059214748442173,
-0.01448735874146223,
-0.03142722696065903,
0.0002798131317831576,
0.016882050782442093,
0.02186988666653633,
0.016336090862751007,
0.00817321427166462,
0.016692182049155235,
-0.015664666891098022,
-0.035062409937381744,
0.10733817517757416,
0.07709676772356033,
0.018813015893101692,
-0.004555060062557459,
-0.003579395357519388,
-0.016684848815202713,
0.030164454132318497,
-0.011195666156709194,
0.013861333020031452,
-0.05604391172528267,
-0.012285832315683365,
0.03056255914270878,
0.010742515325546265,
-0.0303680207580328,
-0.0019247723976150155,
0.024993594735860825,
-0.038606878370046616,
0.04953243210911751,
0.03190966695547104,
0.006827293895184994,
-0.035294320434331894,
0.023418975993990898,
0.011872490867972374,
0.0021364304702728987,
0.022544756531715393,
0.02546902559697628,
0.050601501017808914,
-0.003196908626705408,
-0.06895130127668381,
-0.000623000378254801,
0.044131096452474594,
0.028689604252576828,
0.03782968968153,
0.0021100498270243406,
-0.04027392342686653,
0.05778410658240318,
-0.025515440851449966,
-0.00741689745336771,
0.061602480709552765,
0.02362741157412529,
-0.0021697981283068657,
-0.029799455776810646,
-0.04742608219385147,
0.03160363808274269,
0.027728132903575897,
-0.002477220958098769,
-0.021989939734339714,
0.042669981718063354,
-0.04868960380554199,
-0.0018070428632199764,
-0.01465339120477438,
0.004509431775659323,
-0.007080127485096455,
0.018282560631632805,
0.07669778168201447,
0.013706990517675877,
0.06885093450546265,
-0.017412099987268448,
0.002542143454775214,
0.0019596947822719812,
-0.0882282480597496,
-0.007029110565781593,
-0.004501239862293005,
-0.018251584842801094,
-0.014399792067706585,
-0.00962828192859888,
-0.02604513429105282,
0.020726196467876434,
0.004632206633687019,
-0.04230005294084549,
0.029103444889187813,
-0.0048578595742583275,
-0.017045587301254272,
-0.03791007772088051,
-0.012104182504117489,
0.008235806599259377,
-0.024308448657393456,
0.006671604700386524,
0.043574053794145584,
0.007633780129253864,
-0.025541603565216064,
-0.005142980255186558,
-0.03927774727344513,
-0.015034048818051815,
-0.0578194186091423,
-0.03681723400950432,
0.0025688374880701303,
-0.002873428398743272,
0.02702522836625576,
0.007960502989590168,
-0.017827505245804787,
0.02903198078274727,
-0.06665598601102829,
-0.057982735335826874,
0.012748033739626408,
-0.005436873994767666,
0.065618596971035,
-0.021870100870728493,
-0.02002301998436451,
0.07101229578256607,
0.020808031782507896,
-0.02021034248173237,
0.024922823533415794,
-0.03677240386605263,
-0.01793004386126995,
-0.03605741634964943,
-0.009058399125933647,
0.016728593036532402,
-0.030394062399864197,
0.026112578809261322,
0.011000823229551315,
0.053224626928567886,
0.03362052142620087,
0.0042835865169763565,
0.001865147496573627,
-0.03769776225090027,
0.0183302853256464,
-0.0016366324853152037,
0.05447522550821304,
0.022569846361875534,
-0.021182818338274956,
0.054599579423666,
-0.04213905707001686,
0.055665723979473114,
-0.005360369570553303,
-0.05418749898672104,
0.03023797646164894,
-0.004689900670200586,
0.014512144029140472,
-0.02643236331641674,
0.024427028372883797,
0.003293960588052869,
-0.023133769631385803,
0.002284737303853035,
0.01343516819179058,
0.05695478990674019,
-0.012840026058256626,
-0.028996579349040985,
0.028900757431983948,
0.05066802725195885,
-0.015476456843316555,
-0.012086774222552776,
-0.0017325634835287929,
0.007757039275020361,
0.0005396845517680049,
-0.039521217346191406,
-0.026126665994524956,
0.03852086514234543,
0.04301554709672928,
0.06305897980928421,
0.04126502573490143,
-0.0596700981259346,
-0.0199133213609457,
-0.056108325719833374,
-0.02789957821369171,
0.00617845868691802,
0.08382318168878555,
-0.007594947703182697,
0.016300737857818604,
0.03209780156612396,
0.02184024453163147,
-0.008706727996468544,
0.011457898654043674,
-0.10221601277589798,
0.06129995733499527,
-0.013567152433097363,
-0.06554683297872543,
0.02089102193713188,
-0.019906852394342422,
0.02264787070453167,
-0.03887145221233368,
0.00044891281868331134,
0.052720971405506134,
0.045816369354724884,
-0.06778296828269958,
-0.013284724205732346,
-0.03045693226158619,
-0.03522687777876854,
-0.033397696912288666,
0.00503389211371541,
0.028507430106401443,
-0.02361094392836094,
0.001593718072399497,
0.06521744281053543,
-0.049763139337301254,
-0.026529647409915924,
0.0038863669615238905,
0.03517697751522064,
0.004079361911863089,
0.05182180926203728,
0.015342002734541893,
0.037310510873794556,
0.019209444522857666,
-0.01596761681139469,
0.00003684168041218072,
0.0216879453510046,
0.007137408014386892,
0.009741219691932201,
-0.06756214052438736,
-0.05769059434533119,
-0.027747711166739464,
-0.00578062841668725,
0.027407018467783928,
-0.013856087811291218,
0.01879226602613926,
0.002562233479693532,
0.00447433115914464,
-0.012799706310033798,
0.06014038622379303,
0.0649876594543457,
-0.018461933359503746,
-0.006915700156241655,
-0.03750266134738922,
-0.035381853580474854,
-0.04413162171840668,
0.016098717227578163,
0.023823298513889313,
0.010242880322039127,
-0.012197501957416534,
-0.04321862757205963,
0.00037057927693240345,
-0.0014807697152718902,
0.004007088951766491,
0.031539883464574814,
-0.023333827033638954,
0.029979052022099495,
0.008844331838190556,
-0.0038657572586089373,
0.0011062421835958958,
0.01684914529323578,
0.04638228565454483,
-0.0023167983163148165,
-0.0024710437282919884,
-0.11099051684141159,
-0.054340776056051254,
0.006520342081785202,
0.05232025682926178,
-0.005402395036071539,
-0.055249664932489395,
-0.059992678463459015,
0.0018516933778300881,
0.06389612704515457,
-0.05326220765709877,
0.03946962580084801,
0.012857555411756039,
0.024872053414583206,
-0.029922042042016983,
-0.0175949577242136,
-0.033384013921022415,
0.03561985492706299,
0.016717255115509033,
0.017265474423766136,
0.018826544284820557,
-0.05287715792655945,
-0.0371907502412796,
-0.036262739449739456,
0.00998733751475811,
0.0239104051142931,
-0.01255597360432148,
-0.03355220705270767,
-0.012048949487507343,
-0.004007565323263407,
-0.03964894264936447,
-0.05611066147685051,
0.003195504192262888,
-0.007122690323740244,
-0.007202365901321173,
0.02250419184565544,
-0.00033182738116011024,
0.012782445177435875,
0.04713919758796692,
0.03589707985520363,
-0.017790822312235832,
-0.02039898745715618,
-0.01735854335129261,
0.007211272604763508,
0.03255375847220421,
-0.016496526077389717,
-0.004036273341625929,
-0.01877598837018013,
0.019399451091885567,
0.02192394994199276,
-0.020248014479875565,
-0.002255016239359975,
0.03222501650452614,
-0.016746602952480316,
-0.033732928335666656,
-0.014430910348892212,
-0.03654928132891655,
0.035093776881694794,
-0.014507395215332508,
0.029425593093037605,
-0.03825097158551216,
-0.042883217334747314,
-0.0014684329507872462,
0.01459407340735197,
-0.0052534593269228935,
0.004349204711616039,
0.03503298759460449,
-0.02602698840200901,
-0.02838093228638172,
-0.03911617770791054,
-0.0007390010287053883,
-0.02350430190563202,
-0.002082763472571969,
0.011800895445048809,
-0.006785156205296516,
0.017457686364650726,
0.005871485453099012,
-0.054368533194065094,
0.03105427324771881,
-0.0631013885140419,
0.007849878631532192,
-0.00488996971398592,
0.008814595639705658,
0.03682461380958557,
-0.04132244735956192,
-0.011026942171156406,
0.04951450973749161,
-0.0017671049572527409,
-0.0040582576766610146,
-0.048967909067869186,
0.06942293047904968,
0.04781835898756981,
0.0032420395873486996,
-0.03811540827155113,
-0.03357179835438728,
0.01659303344786167,
0.025402767583727837,
-0.026742221787571907,
-0.0548749715089798,
-0.01702856831252575,
-0.05294018238782883,
-0.03930184245109558,
-0.01027070265263319,
0.03262297809123993,
-0.0393405482172966,
0.012848295271396637,
0.029862836003303528,
0.02239234931766987,
0.06335638463497162,
-0.011015400290489197,
0.04199829325079918,
0.013051251880824566,
-0.009705745615065098,
-0.025921160355210304,
0.00007740699220448732,
0.04507521539926529,
-0.022029705345630646,
-0.040079087018966675,
0.02168508991599083,
0.008565813302993774,
0.0641167014837265,
0.011892079375684261,
0.00617616530507803,
0.02268577739596367,
0.02170410193502903,
-0.0024272433947771788,
-0.04105430841445923,
0.017378423362970352,
-0.0017222879687324166,
-0.004577524960041046,
-0.04827184975147247,
-0.001974149839952588,
-0.0006949126836843789,
0.02946246974170208,
-0.01202405896037817,
-0.02051590383052826,
0.005574509501457214,
-0.01871372200548649,
0.0680791437625885,
-0.03596576675772667,
0.02080557495355606,
0.04337829723954201,
-0.016318295150995255,
0.02714875340461731,
0.0034722548443824053,
-0.0249759741127491,
0.017137683928012848,
-0.013433371670544147,
-0.004178396426141262,
-0.020159969106316566,
-0.03318120166659355,
0.007803572807461023,
0.04012010246515274,
0.01876506581902504,
0.05386435613036156,
0.038778066635131836,
0.012394190765917301,
0.009501347318291664,
0.006353067699819803,
-0.04438447952270508,
0.021330852061510086,
0.027319516986608505,
0.0347447395324707,
-0.014044106006622314,
-0.01148710772395134,
0.013863126747310162,
-0.016433972865343094,
0.0463721789419651,
-0.007394530810415745,
0.002834178740158677,
0.0011151761282235384,
0.016452563926577568,
-0.0405094139277935,
-0.00681232800707221,
0.0064527252689003944,
0.0023733212146908045,
0.0280220415443182,
0.02307962253689766,
-0.006853263359516859,
0.06411150842905045,
0.012437921017408371,
0.00877538975328207,
-0.007397707551717758,
0.011035270057618618,
-0.03215069696307182,
0.01890549249947071,
-0.0061016869731247425,
-0.0046800910495221615,
0.009088017977774143,
-0.0009497108985669911,
0.025481533259153366,
-0.00009346587467007339,
0.06645859777927399,
-0.05017288774251938,
-0.019812002778053284,
0.003415595041587949,
-0.039083462208509445,
-0.06072496622800827,
0.08133262395858765,
-0.010622519068419933,
-0.03663275018334389,
0.04708964005112648,
-0.06482593715190887,
0.04229866340756416,
0.008054045960307121,
-0.0019247089512646198,
0.014285843819379807,
0.06846804171800613,
0.001406695693731308,
0.05614420771598816,
-0.017194533720612526,
-0.013079998083412647,
0.12600335478782654,
0.056897055357694626,
0.01403909269720316,
0.0035270294174551964,
0.01343629602342844,
-0.01904996857047081,
0.007020378950983286,
-0.048802729696035385,
-0.014964652247726917,
0.005453590769320726,
0.02596389688551426,
0.05095057189464569,
0.006511650048196316,
0.008540756069123745,
0.023075025528669357,
0.02097071148455143,
-0.003606965532526374,
-0.03601965308189392,
0.0061653489246964455,
-0.006246449891477823,
-0.016293633729219437,
0.001222174265421927,
-0.04093090072274208,
0.021520210430026054,
0.01350439339876175,
-0.021192405372858047,
-0.027980687096714973,
-0.01878812164068222,
0.021029895171523094,
-0.006181729957461357,
-0.04766273871064186,
0.05299222096800804,
0.030801577493548393,
-0.014747655019164085,
-0.03190259262919426,
0.027795100584626198,
0.04970235005021095,
0.018403414636850357,
-0.009688911959528923,
0.04001583531498909,
0.020696358755230904,
-0.018706003203988075,
0.01824132539331913,
0.0069853756576776505,
-0.04932994395494461,
0.009358706884086132,
-0.037561286240816116,
0.030243337154388428,
0.004410690627992153,
0.0014569772174581885,
0.011424032971262932,
0.017186051234602928,
0.016168761998414993,
-0.03473840653896332,
-0.002004201989620924,
0.0206451453268528,
0.04031962901353836,
-0.03300485759973526,
-0.03651727735996246,
-0.034284740686416626,
0.019493917003273964,
0.008296950720250607,
-0.014891103841364384,
0.015325481072068214,
-0.007115263491868973,
-0.031164390966296196,
-0.004637726116925478,
0.043493468314409256,
-0.030289197340607643,
-0.023466337472200394,
0.0025948963593691587,
0.00554707320407033,
-0.0061798193491995335,
-0.050246261060237885,
0.00040368756162934005,
0.01908656395971775,
0.0019009693060070276,
0.009911688975989819,
0.01433731708675623,
-0.01676151342689991,
-0.008420918136835098,
0.019150348380208015,
0.00038812292041257024,
-0.010338559746742249,
-0.006669498980045319,
-0.026736116036772728,
-0.010860104113817215,
0.023870203644037247,
-0.031715065240859985,
0.008361016400158405,
0.013561168685555458,
0.03749667853116989,
0.020950859412550926,
-0.0212978795170784,
-0.02926291525363922,
0.005578291602432728,
-0.04832644760608673,
0.05421219766139984,
0.009195241145789623,
0.0466189906001091,
0.010118698701262474,
0.013865616172552109,
0.013162294402718544,
0.017226772382855415,
-0.039284367114305496,
0.0007252064533531666,
0.01853870041668415,
-0.04514570161700249,
-0.03187848627567291,
0.06177294999361038,
-0.026373805478215218,
-0.047173671424388885,
0.0287559162825346,
-0.018968546763062477,
0.004531760700047016,
-0.0037652382161468267,
-0.003945242613554001,
-0.02815849520266056,
0.04545412212610245,
-0.03266787528991699,
-0.01343229878693819,
0.004289731848984957,
-0.004161051474511623,
-0.010166585445404053,
-0.035826608538627625,
-0.03324137628078461,
0.0040742759592831135,
-0.0330684594810009,
0.020488698035478592,
-0.011445392854511738,
0.014965751208364964,
0.009499605745077133,
0.01837199553847313,
0.0382707342505455,
0.023960433900356293,
0.015910707414150238,
0.024243224412202835,
0.06715712696313858,
-0.028105709701776505,
-0.01645294763147831,
0.01892937533557415,
-0.018695425242185593,
0.009314441122114658,
0.0036498066037893295,
0.0012555683497339487,
0.037323810160160065,
-0.00476363580673933,
-0.019255205988883972,
0.028131801635026932,
0.11517895013093948,
-0.029820838943123817,
0.026522284373641014,
-0.014771242626011372,
-0.0545857809484005,
0.018072985112667084,
-0.04194062203168869,
-0.013771596364676952,
-0.010359032079577446,
-0.0175750944763422,
0.009986086748540401,
0.03652011975646019,
-0.011021054349839687,
-0.005912850145250559,
0.017028121277689934,
-0.02031562104821205,
-0.03355381637811661,
0.010233253240585327,
0.027687806636095047,
0.0007939840434119105,
0.02611037716269493,
-0.02313271537423134,
0.01413201168179512,
-0.0242731012403965,
0.02379535883665085,
-0.06610408425331116,
0.0047420295886695385,
0.012623959220945835,
0.01824248768389225,
0.06969547271728516,
-0.04306824505329132,
-0.0026897976640611887,
0.0252219270914793,
-0.0354849137365818,
-0.03667619451880455,
-0.024687930941581726,
-0.020624546334147453,
-0.03664955496788025,
-0.013071348890662193,
0.02242574281990528,
0.015520409680902958,
0.01816665753722191,
0.01230992004275322,
0.04694044589996338,
0.028114235028624535,
-0.01737779937684536,
-0.03033490478992462,
0.0007612358313053846,
0.047170862555503845,
0.0019579636864364147,
-0.006107137072831392,
0.038580022752285004,
-0.04187333583831787,
0.0075859627686440945,
0.019374970346689224,
-0.07080838829278946,
0.023580556735396385,
-0.02142169699072838,
-0.008357362821698189,
0.006358605809509754,
0.03487425297498703,
0.03046325407922268,
0.008604542352259159,
-0.007086846511811018,
0.0019743589218705893,
-0.03634295240044594,
-0.0067690047435462475,
-0.013118078000843525,
0.026585189625620842,
0.06466693431138992,
-0.025590937584638596,
-0.044347308576107025,
0.017691466957330704,
-0.014211399480700493,
0.01825757697224617,
0.006734065245836973,
0.037078119814395905,
0.012124532833695412,
-0.09262219816446304,
-0.08527679741382599,
-0.016529444605112076,
0.010307499207556248,
0.07023508101701736,
0.010571030899882317,
-0.007272363640367985,
0.015383412130177021,
-0.00027546912315301597,
-0.06541910767555237,
0.005418823100626469,
-0.03271687775850296,
-0.05390672758221626,
-0.05395200476050377,
-0.014743122272193432,
-0.004921754356473684,
-0.014600194059312344,
-0.0022254164796322584,
0.002140830736607313,
-0.0003589545958675444,
0.035617273300886154,
0.021309802308678627,
-0.041925519704818726,
0.0064133694395422935,
0.0018219606718048453,
0.04049113020300865,
-0.06639363616704941,
-0.03041802905499935,
-0.02865436114370823,
-0.04373961314558983,
-0.029354263097047806,
-0.04542074352502823,
-0.02404014579951763,
0.004589434247463942,
0.047451503574848175,
-0.001614782609976828,
0.010765432380139828,
-0.0072447373531758785,
-0.03463955968618393,
0.022594403475522995,
-0.026274658739566803,
0.02958493120968342,
-0.010864881798624992,
-0.039520759135484695,
-0.015075341798365116,
-0.005780528299510479,
0.010261094197630882,
-0.02794524095952511,
-0.02157432958483696,
0.011706667020916939,
0.015596040524542332,
-0.005768176168203354,
-0.014212642796337605,
-0.0014398543862625957,
0.0006009968346916139,
-0.015433941036462784,
0.06469560414552689,
-0.02574087679386139,
0.01861926168203354,
0.03716079518198967,
-0.04103653132915497,
-0.0408228375017643,
0.015340093523263931,
-0.05162176489830017,
0.0034167105332016945,
-0.001990756718441844,
-0.0359371192753315,
0.052345309406518936,
-0.06379029899835587,
0.0325266532599926,
0.010569483041763306,
-0.0058546969667077065,
-0.02582688257098198,
0.02973507158458233,
0.04593593254685402,
0.04824015125632286,
-0.02543645165860653,
0.041588589549064636,
0.008340179920196533,
-0.050645072013139725,
0.008692842908203602,
0.04354668781161308,
0.019404523074626923,
-0.01618344523012638,
-0.0031722087878733873,
0.011564374901354313,
-0.022823406383395195,
0.03789876028895378,
-0.019468611106276512,
0.007933302782475948,
0.02168773114681244,
-0.016566315665841103,
0.0224143136292696,
0.004482665564864874,
-0.007370783481746912,
0.03883742913603783,
0.02172067202627659,
0.00816453155130148,
-0.04645925387740135,
0.0076347156427800655,
-0.013142291456460953,
0.0005062508280389011,
-0.04043223708868027,
0.013201553374528885,
0.0004970316658727825,
-0.026246123015880585,
-0.006324750371277332,
-0.020807169377803802,
0.028021978214383125,
0.022717462852597237,
0.022280504927039146,
0.00035739137092605233,
0.024409731850028038,
-0.013694830238819122,
-0.027458999305963516,
-0.003496733261272311,
-0.027529461309313774,
-0.016293656080961227,
-0.004981018137186766,
0.06151878461241722,
0.07459190487861633,
-0.05459832400083542,
-0.057686131447553635,
-0.01988142728805542,
0.012351498939096928,
0.06610827147960663,
-0.05314796417951584,
-0.0427679717540741,
-0.03859509900212288,
0.020212627947330475,
-0.016533557325601578,
-0.04653874784708023
] |
<p>I have approximately 10 papers that claim that, from the equation for shape energy:
$$ F = \frac{1}{2}k_c \int (c_1+c_2-c_0)^2 dA + \Delta p \int dV + \lambda \int dA$$
one can use "methods of variational calculus" to derive the following:
$$\Delta p - 2\lambda H + k(2H+c_0)(2H^2-2K-c_0H)+2k\nabla^2H=0$$
But I'm having a lot of trouble tracking down the original derivation. The guy who did it first was Helfrich, and here's his and Ou-yang's paper deriving it:
<a href="http://prl.aps.org/abstract/PRL/v59/i21/p2486_1" rel="nofollow">http://prl.aps.org/abstract/PRL/v59/i21/p2486_1</a> . However, they don't show an actual derivation, instead saying "the derivation will appear in a full paper by the authors" or something like that. Yet everybody cites the paper I just linked for a derivation. Does anybody know a source that can derive this, or can give me some hints to figure it out myself? To be honest I can't even figure out how to find the first variation.</p>
<p>Edit: So, after some careful thought and hours and hours of work and learning, I realized that the answer that got the bounty was wrong. The author stopped replying to my messages after I gave him bounty.... thanks guys. That said, I've almost got it all figured out (in intense detail) and will post a pdf of my own notes once I'm done!</p>
| 8,875 |
[
-0.04509580135345459,
-0.015000765211880207,
0.057637814432382584,
-0.013059037737548351,
0.02273419313132763,
0.011896124109625816,
-0.04553208500146866,
-0.04411190003156662,
0.011127852834761143,
-0.0659324899315834,
-0.0014393707970157266,
0.02982739545404911,
0.07901892066001892,
0.03492974117398262,
0.02046741358935833,
0.005917614325881004,
0.006582745350897312,
-0.00229763169772923,
-0.005671001970767975,
-0.0657591000199318,
0.0389765165746212,
-0.012071046978235245,
-0.02155977487564087,
-0.0007833800045773387,
-0.030789397656917572,
0.01967214047908783,
-0.003923372365534306,
-0.013868950307369232,
-0.00540037639439106,
0.07645723968744278,
-0.05248637869954109,
-0.03411164879798889,
0.009288878180086613,
0.00737356673926115,
-0.027255704626441002,
0.025457657873630524,
-0.016278643161058426,
-0.0203816257417202,
-0.05272040516138077,
0.04134707525372505,
-0.02561154030263424,
0.0005325261736288667,
0.02434627339243889,
0.05227299779653549,
0.010693072341382504,
0.005380065646022558,
0.002285577356815338,
-0.07697142660617828,
0.0705568939447403,
-0.07179738581180573,
0.0938660055398941,
-0.004970441106706858,
0.02389955334365368,
0.005492747761309147,
-0.01600693352520466,
-0.024339953437447548,
0.043229468166828156,
0.05957801267504692,
0.01866944134235382,
-0.05847427248954773,
-0.03699604049324989,
0.007112167309969664,
0.00820071529597044,
-0.014866459183394909,
-0.028871553018689156,
0.011017466895282269,
-0.022910380735993385,
-0.02587391994893551,
0.05779349431395531,
-0.027239585295319557,
0.01967427507042885,
-0.023642243817448616,
0.046256572008132935,
0.00940436776727438,
0.00522803096100688,
0.005737574305385351,
-0.009877706877887249,
0.013106061145663261,
0.020149774849414825,
0.03547733649611473,
-0.032382529228925705,
-0.000370414782082662,
0.03681525960564613,
0.04024186730384827,
-0.009650344029068947,
0.0027845147997140884,
0.07392802834510803,
0.014292263425886631,
0.022000720724463463,
0.02355225197970867,
0.005743820685893297,
0.003489510854706168,
0.0396370030939579,
-0.006550053600221872,
0.0017749198013916612,
0.02095053158700466,
0.03383157402276993,
0.04397222772240639,
-0.023715553805232048,
-0.021020615473389626,
-0.023797037079930305,
-0.03850236535072327,
-0.027248088270425797,
0.06881594657897949,
0.029492968693375587,
-0.018762696534395218,
0.0011352652218192816,
0.026411058381199837,
-0.040317051112651825,
-0.0023413023445755243,
-0.022405581548810005,
0.018441351130604744,
-0.015072590671479702,
-0.03747735545039177,
-0.0397113673388958,
-0.03022131323814392,
-0.034107524901628494,
0.001485693035647273,
0.04864118620753288,
0.021546954289078712,
0.05593414977192879,
0.006425380241125822,
0.03626434877514839,
-0.0516446977853775,
-0.05551496893167496,
0.015677323564887047,
0.06779565662145615,
-0.02375408448278904,
-0.010917207226157188,
0.010386963374912739,
-0.012475467287003994,
-0.014876647852361202,
-0.004567472264170647,
0.019655965268611908,
-0.03001105971634388,
0.0038741366006433964,
-0.08200078457593918,
-0.06024526432156563,
0.016559261828660965,
-0.012212379835546017,
-0.001265557250007987,
-0.04379258677363396,
-0.0002133164380211383,
0.05902570113539696,
0.08190213143825531,
-0.005756292957812548,
-0.0302909966558218,
-0.01496855542063713,
0.008161455392837524,
-0.011661608703434467,
-0.011169261299073696,
-0.04561354219913483,
0.0070425886660814285,
-0.016347616910934448,
-0.025659022852778435,
-0.05345068499445915,
0.011271548457443714,
0.005887641571462154,
0.00938689336180687,
-0.013525323010981083,
0.11315248906612396,
0.008684500120580196,
-0.015945376828312874,
0.007819476537406445,
0.03403264284133911,
-0.030186858028173447,
0.07157298922538757,
0.0285785049200058,
-0.025048812851309776,
0.00021072951494716108,
0.033580802381038666,
-0.015994058921933174,
-0.01739882491528988,
0.03233583644032478,
0.041832391172647476,
-0.040338899940252304,
-0.013881510123610497,
-0.03633224964141846,
-0.0081786485388875,
0.020545735955238342,
-0.024405043572187424,
-0.037652093917131424,
-0.015386156737804413,
0.004925218410789967,
-0.008793485350906849,
0.040528010576963425,
-0.026548538357019424,
0.008327660150825977,
-0.0038085749838501215,
-0.010692344978451729,
0.007224197965115309,
-0.049277085810899734,
0.030500037595629692,
0.017474455758929253,
-0.011030755937099457,
0.03891367092728615,
-0.0061798435635864735,
0.004192110616713762,
0.0020027856808155775,
-0.03757288306951523,
-0.0014027954312041402,
-0.0018387518357485533,
0.035232145339250565,
0.004915853962302208,
0.004976090043783188,
0.05222581326961517,
0.04458446055650711,
0.008476242423057556,
0.05040019005537033,
0.0012742695398628712,
-0.0021286739502102137,
0.012248788960278034,
-0.022066529840230942,
0.0010646560695022345,
-0.03162650018930435,
0.017450105398893356,
-0.012339443899691105,
-0.0064703975804150105,
0.03038557805120945,
0.012947369366884232,
-0.06147674843668938,
0.06806524097919464,
0.03869518265128136,
0.06726992875337601,
0.0027278068009763956,
0.04688525199890137,
-0.018686678260564804,
0.02732909843325615,
-0.01655501313507557,
-0.042905937880277634,
-0.004484149161726236,
-0.021463235840201378,
0.03969337418675423,
0.01939661242067814,
-0.028928084298968315,
-0.015170569531619549,
0.01064196228981018,
0.008502645418047905,
0.0479302816092968,
0.006157820113003254,
0.004745244514197111,
-0.01782674342393875,
0.03074713796377182,
-0.004406321793794632,
-0.006268112920224667,
-0.011753849685192108,
0.029294567182660103,
0.019276726990938187,
0.03901217505335808,
0.038287077099084854,
-0.04252943769097328,
0.012644380331039429,
0.009975304827094078,
0.023179462179541588,
-0.02654922753572464,
0.02363676391541958,
0.0782952755689621,
-0.017026744782924652,
0.0223896075040102,
0.0731496512889862,
-0.02891184575855732,
-0.0046712132170796394,
-0.0190506000071764,
-0.021345270797610283,
0.019049471244215965,
-0.005323752760887146,
-0.014169959351420403,
-0.011773223988711834,
0.002568894997239113,
-0.014038942754268646,
0.022833047434687614,
-0.012015747837722301,
-0.04596734046936035,
0.010384240187704563,
0.012706346809864044,
-0.023736676201224327,
0.03720291331410408,
-0.0009424760355614126,
-0.008611207827925682,
-0.017694896087050438,
0.013580209575593472,
0.009321648627519608,
0.016746772453188896,
0.032171644270420074,
-0.027460258454084396,
0.020328132435679436,
-0.02748720347881317,
-0.00802015420049429,
0.05590677261352539,
-0.007983400486409664,
0.0017652753740549088,
0.0214279405772686,
-0.002610814291983843,
-0.05976923555135727,
0.0013430856633931398,
-0.01760990172624588,
0.010783713310956955,
-0.020873257890343666,
0.0274570994079113,
-0.001964462222531438,
0.016673726961016655,
-0.022425858303904533,
0.05494864284992218,
0.001081092283129692,
-0.038820672780275345,
-0.022553496062755585,
0.005563585553318262,
0.017008040100336075,
-0.009517606347799301,
0.04330190271139145,
0.040286801755428314,
0.022378884255886078,
0.010907395742833614,
-0.04356105998158455,
-0.06509573012590408,
0.029170753434300423,
-0.04340268298983574,
0.01415952481329441,
-0.020902443677186966,
-0.04087613523006439,
0.09066566079854965,
0.012363200075924397,
-0.06525050848722458,
0.0028478039894253016,
0.0006073592812754214,
0.011150900274515152,
-0.011291907168924809,
0.006299248896539211,
0.015354183502495289,
-0.0042228782549500465,
0.04340643063187599,
-0.028462281450629234,
0.031144144013524055,
0.07342611253261566,
-0.017692923545837402,
-0.027815071865916252,
0.020832087844610214,
0.012224153615534306,
-0.0028951060958206654,
0.01613321527838707,
0.03608763590455055,
-0.014228210784494877,
0.025457942858338356,
0.025293458253145218,
0.019566552713513374,
0.028743278235197067,
-0.03226331248879433,
0.03854410722851753,
-0.006702218670397997,
-0.02521395869553089,
-0.038655754178762436,
0.030262209475040436,
-0.01206444762647152,
-0.0627761036157608,
0.0018563218181952834,
0.013879649341106415,
0.058892931789159775,
-0.02579003944993019,
0.0009223699453286827,
0.013387588784098625,
-0.005352999083697796,
0.007130018435418606,
-0.037642382085323334,
-0.01822572387754917,
-0.005277922376990318,
-0.0034009465016424656,
-0.002199022565037012,
-0.007441108115017414,
0.01329913642257452,
0.05456458404660225,
0.054344210773706436,
-0.0076403128914535046,
-0.05452510714530945,
0.03444982320070267,
-0.07737114280462265,
-0.00450155371800065,
-0.02329082414507866,
0.05036843568086624,
0.0017426017438992858,
0.07371002435684204,
-0.002102513099089265,
-0.005494752898812294,
0.03485385701060295,
0.010243808850646019,
-0.07493364065885544,
0.011529462411999702,
-0.024661777541041374,
-0.013871959410607815,
-0.0005962221184745431,
-0.01208554022014141,
0.04169069230556488,
-0.006714468821883202,
-0.04060474783182144,
-0.0264644343405962,
-0.015775466337800026,
-0.024006010964512825,
0.0434495247900486,
-0.025915469974279404,
-0.055673036724328995,
-0.001992929959669709,
0.005994514096528292,
0.05098460987210274,
-0.04664793983101845,
0.003787679597735405,
0.04679819568991661,
-0.01460585929453373,
0.006242632865905762,
-0.03650549426674843,
0.02513732947409153,
-0.020106026902794838,
0.028079526498913765,
-0.011503078043460846,
-0.018224267289042473,
0.038512904196977615,
0.010737077333033085,
-0.03841781988739967,
0.06143411248922348,
0.014156738296151161,
-0.0029321745969355106,
-0.00869237631559372,
-0.046144239604473114,
0.02113179862499237,
0.008313669823110104,
0.05013308301568031,
-0.013933445326983929,
0.036440808326005936,
0.008454529568552971,
0.03745679929852486,
-0.01750483363866806,
0.048352111130952835,
0.032123252749443054,
-0.002803598064929247,
-0.024997591972351074,
-0.06850028038024902,
0.02147153578698635,
-0.03032105788588524,
-0.025762848556041718,
-0.011419808492064476,
-0.012197277508676052,
-0.036711666733026505,
-0.0014126551104709506,
0.014879663474857807,
-0.012736031785607338,
0.005209594964981079,
-0.030129091814160347,
-0.01615609973669052,
0.011094671674072742,
-0.04277954250574112,
0.00014591861690860242,
0.029611149802803993,
0.038303837180137634,
0.05797373503446579,
-0.01665814220905304,
-0.0005600359872914851,
-0.0489082932472229,
-0.026864539831876755,
0.020441701635718346,
0.04813569411635399,
-0.009063124656677246,
0.0131169892847538,
-0.06941305845975876,
-0.04324902221560478,
0.03746773302555084,
-0.009152478538453579,
0.0116964690387249,
0.013633206486701965,
0.010287629440426826,
0.03745228424668312,
0.0028686432633548975,
-0.05158103629946709,
0.017321055755019188,
0.02811542898416519,
0.015215223655104637,
-0.025515470653772354,
-0.0053499238565564156,
-0.0048481072299182415,
0.042196378111839294,
0.014000997878611088,
0.03746119886636734,
0.004249176476150751,
-0.04518641531467438,
-0.009416118264198303,
0.016143761575222015,
-0.031275518238544464,
-0.07334864139556885,
-0.0017747634556144476,
-0.003388941753655672,
-0.0013703168369829655,
0.03155837208032608,
-0.037694111466407776,
-0.026241108775138855,
0.04189947620034218,
0.01720219850540161,
-0.013397363014519215,
-0.0037925438955426216,
-0.00543035427108407,
0.06401187181472778,
0.07252971827983856,
-0.0016355278203263879,
0.050737228244543076,
0.04011904075741768,
-0.04514472931623459,
-0.04981996864080429,
0.007175512611865997,
0.026382718235254288,
-0.007016720250248909,
-0.00610376289114356,
-0.05888577178120613,
0.014637812040746212,
-0.04470689594745636,
0.002361590275540948,
-0.01073585357517004,
0.027823032811284065,
-0.021734319627285004,
-0.014104455709457397,
-0.016306929290294647,
0.011414235457777977,
0.01721903681755066,
0.000056916935136541724,
0.027223246172070503,
0.015915777534246445,
0.07067503780126572,
0.022872254252433777,
-0.004402882419526577,
0.009926209226250648,
-0.01567322388291359,
0.00970522128045559,
0.016791153699159622,
0.012205862440168858,
-0.041112374514341354,
-0.0012130304239690304,
0.024355243891477585,
-0.04054312780499458,
0.02863626554608345,
-0.01184412743896246,
0.012851191684603691,
0.016490811482071877,
-0.024807307869195938,
-0.023982202634215355,
-0.03863883763551712,
-0.006893653888255358,
0.02472669631242752,
-0.03750653937458992,
0.04015462100505829,
-0.007622470147907734,
0.022403497248888016,
-0.08814879506826401,
0.0326639823615551,
0.035589296370744705,
-0.0006524635828100145,
-0.05166862532496452,
0.010696898214519024,
-0.0015319986268877983,
-0.004698152653872967,
-0.03125888854265213,
0.03030332364141941,
0.04937078431248665,
-0.015655620023608208,
0.0191133264452219,
0.002030740724876523,
0.038250360637903214,
0.009820602834224701,
0.018542081117630005,
-0.018285274505615234,
0.022184232249855995,
-0.020460277795791626,
-0.039216332137584686,
0.01287597045302391,
0.04968995973467827,
-0.004876489285379648,
0.03306810185313225,
-0.024713760241866112,
0.007848142646253109,
0.038300156593322754,
-0.028293924406170845,
0.0019473058637231588,
0.036259252578020096,
0.036661189049482346,
-0.011855844408273697,
-0.018471084535121918,
-0.004141062032431364,
-0.02088562585413456,
0.02192918211221695,
0.005489450879395008,
-0.008304831571877003,
-0.022662989795207977,
-0.01590368151664734,
0.025131138041615486,
-0.01877974346280098,
0.010175948962569237,
-0.03906808793544769,
0.0652780756354332,
-0.0314510352909565,
-0.0128836240619421,
0.005480629857629538,
0.0008419914520345628,
0.020937656983733177,
0.027433177456259727,
0.01439810823649168,
0.014312139712274075,
-0.012940998189151287,
-0.055836550891399384,
-0.020984897390007973,
-0.048500411212444305,
0.06303779035806656,
0.09628845006227493,
-0.027227357029914856,
0.05334489420056343,
-0.0020166474860161543,
0.021129745990037918,
0.017097311094403267,
-0.007215394638478756,
-0.03511730954051018,
-0.030850842595100403,
-0.006949262227863073,
0.058264847844839096,
-0.04127455875277519,
-0.020895810797810555,
0.04573511332273483,
0.0243220254778862,
-0.057842519134283066,
0.021867092698812485,
-0.024860568344593048,
0.04425235837697983,
0.011945256032049656,
-0.031060481444001198,
-0.03577831760048866,
0.038655295968055725,
0.0010268911719322205,
0.03693404048681259,
0.0030512018129229546,
-0.009703035466372967,
0.02452859841287136,
-0.004366753157228231,
0.01404177863150835,
-0.017827654257416725,
-0.020679622888565063,
-0.013799149543046951,
0.0503266341984272,
0.033486783504486084,
-0.018066037446260452,
0.007576738949865103,
0.005721383262425661,
-0.007402848452329636,
-0.004040926694869995,
-0.013714981265366077,
-0.030733268707990646,
-0.046358440071344376,
-0.011133749037981033,
-0.04676249995827675,
-0.04826050251722336,
0.011239594779908657,
0.03163063898682594,
-0.01646839827299118,
0.03295917809009552,
-0.005482164211571217,
-0.002414782764390111,
0.046187203377485275,
0.016969328746199608,
0.04957813024520874,
0.09074275940656662,
-0.049952130764722824,
0.0013552152086049318,
-0.04432889446616173,
0.013625822961330414,
0.13782323896884918,
0.04106945917010307,
0.03423497825860977,
-0.07502549141645432,
0.025731196627020836,
-0.007408906240016222,
-0.0138882240280509,
-0.03717975690960884,
0.04195193201303482,
-0.014191598631441593,
-0.013957863673567772,
-0.00613924115896225,
0.0489131435751915,
0.005321361590176821,
0.018521763384342194,
0.036851994693279266,
-0.02094225026667118,
-0.0273392666131258,
0.047047875821590424,
-0.005351929925382137,
-0.02618594653904438,
-0.02560005895793438,
0.013975976034998894,
0.01563369855284691,
0.008617485873401165,
0.021183183416724205,
-0.03572496771812439,
-0.06068427115678787,
0.004307899624109268,
0.0016534959431737661,
-0.0039328583516180515,
0.004257938824594021,
-0.014775522984564304,
0.024276209995150566,
0.012852245010435581,
0.011769026517868042,
0.02463458478450775,
0.0044577172957360744,
0.023518415167927742,
0.02725859545171261,
0.0211358480155468,
0.025247620418667793,
0.027089213952422142,
0.012517730705440044,
-0.007059176452457905,
-0.04665195196866989,
-0.03846188634634018,
0.03941768780350685,
-0.059922829270362854,
0.025536177679896355,
0.013973875902593136,
-0.03006785362958908,
-0.015123902820050716,
-0.024947021156549454,
0.010570566169917583,
-0.03653515502810478,
0.016344767063856125,
-0.004281003959476948,
-0.02091320790350437,
-0.016722548753023148,
0.012540684081614017,
-0.005402670241892338,
-0.0027191853150725365,
-0.03267816826701164,
-0.00864800252020359,
-0.03142327815294266,
-0.009861752390861511,
0.05804286524653435,
-0.015094131231307983,
-0.03422442078590393,
-0.026264486834406853,
-0.03759557008743286,
-0.038549985736608505,
0.00514109106734395,
-0.039732448756694794,
0.012055820785462856,
0.04122190922498703,
-0.019457386806607246,
-0.01929333247244358,
-0.040778957307338715,
-0.04675279185175896,
-0.007783577311784029,
-0.005877525545656681,
0.001239268109202385,
-0.013483654707670212,
0.027182448655366898,
0.012007820419967175,
0.03549535945057869,
-0.033426422625780106,
0.026809874922037125,
-0.011803802102804184,
0.03102157451212406,
-0.018777815625071526,
-0.019493741914629936,
-0.025065377354621887,
-0.01525625865906477,
-0.0017947115702554584,
0.0034457631409168243,
-0.007753006182610989,
-0.0033689618576318026,
0.00174321245867759,
0.026183217763900757,
-0.00242167292162776,
0.04305168241262436,
-0.030578263103961945,
0.0004993973416276276,
0.014473550021648407,
-0.03733425959944725,
0.025578267872333527,
-0.011229191906750202,
0.000738248520065099,
-0.04807553067803383,
-0.022749541327357292,
-0.0041355411522090435,
-0.0317951925098896,
-0.01008969359099865,
0.051049839705228806,
-0.05885930731892586,
0.02537280134856701,
-0.04800443351268768,
-0.005239720921963453,
-0.04381389543414116,
0.013754123821854591,
-0.02552453614771366,
0.04487750306725502,
0.0162808857858181,
0.03279290348291397,
-0.01573081500828266,
0.04216913506388664,
-0.012531408108770847,
-0.022830598056316376,
0.030152324587106705,
-0.014152123592793941,
-0.026433873921632767,
0.018233824521303177,
0.013201743364334106,
0.024880221113562584,
0.049910470843315125,
0.028066812083125114,
-0.04619704186916351,
0.016843337565660477,
-0.040843505412340164,
-0.06226849555969238,
-0.0005972933722659945,
0.008427201770246029,
0.022436611354351044,
0.008565379306674004,
-0.025731684640049934,
-0.0011193044483661652,
0.03468802943825722,
0.007041379809379578,
-0.006318544037640095,
0.017497923225164413,
-0.022246818989515305,
-0.013121772557497025,
-0.022942345589399338,
0.016875281929969788,
-0.015192853286862373,
0.0011767440009862185,
0.04454111307859421,
-0.00810734648257494,
-0.04847504943609238,
-0.0006917726714164019,
0.00342564401216805,
-0.03684132173657417,
-0.012213402427732944,
-0.01753612421452999,
0.014601222239434719,
0.016389694064855576,
0.04041675850749016,
-0.011239803396165371,
-0.0014366747345775366,
0.010921860113739967,
-0.011831252835690975,
-0.08009485900402069,
0.027730094268918037,
-0.02688245289027691,
0.03993405029177666,
0.03331156075000763,
-0.08579637110233307,
0.06590894609689713,
0.013854799792170525,
-0.04572715237736702,
0.03879912570118904,
-0.04662328585982323,
0.01253984309732914,
0.004646642133593559,
-0.005258036777377129,
-0.0454581156373024,
0.05003524199128151,
0.02438005618751049,
0.04488655552268028,
0.05574263259768486,
0.04136013984680176,
-0.014720086939632893,
-0.014198237098753452,
0.00419479189440608,
0.022462032735347748,
0.03997486084699631,
-0.02925884537398815,
0.059925906360149384,
0.006953706033527851,
-0.028544573113322258,
0.04312608018517494,
-0.03341331332921982,
-0.027223365381360054,
-0.04720565676689148,
0.011883950792253017,
0.03603607043623924,
0.02648489736020565,
0.004320986103266478,
0.003344568656757474,
-0.019701335579156876,
-0.02285863645374775,
-0.02739359624683857,
-0.005914969835430384,
0.00614911038428545,
0.03570939227938652,
0.010035371407866478,
-0.0035898194182664156,
-0.057873018085956573,
0.0627516433596611,
-0.03515208885073662,
-0.023777863010764122,
0.0013611107133328915,
-0.05229274183511734,
0.025994781404733658,
-0.0026847906410694122,
0.029208196327090263,
-0.059107884764671326,
-0.026118576526641846,
0.01336425356566906,
-0.010878290049731731,
-0.024051355198025703,
0.02885872684419155,
-0.02893802523612976,
-0.020462961867451668,
0.040786370635032654,
0.01911783218383789,
-0.032229162752628326,
-0.0652264729142189,
0.010366122238337994,
-0.024921033531427383,
-0.0008892681798897684,
-0.0008803126984275877,
-0.05704024061560631,
-0.06107323616743088,
-0.017615454271435738,
0.007884154096245766,
0.023425566032528877,
-0.026693720370531082,
-0.046420395374298096,
0.012005348689854145,
-0.08963513374328613,
0.04706288129091263,
-0.012392263859510422,
-0.007770437281578779,
0.020855924114584923,
-0.025115754455327988,
0.006369421258568764,
0.012470239773392677,
0.021281830966472626,
-0.038592640310525894,
-0.05000637471675873,
0.002844766480848193,
-0.012590612284839153,
-0.005572576075792313,
0.0025113809388130903,
0.006127886474132538,
0.002756920177489519,
0.004714517388492823,
0.01143139973282814,
0.020476777106523514,
0.027124788612127304,
0.025994248688220978,
0.03101235069334507,
0.01933666318655014,
0.02777324616909027,
-0.00910944677889347,
-0.030750619247555733,
0.01309637725353241,
0.006452752277255058,
-0.02658078446984291,
0.0781092420220375,
-0.011100742034614086,
0.00457953242585063,
-0.006716415751725435,
0.00007891377026680857,
-0.036529865115880966,
-0.01899208314716816,
-0.015387569554150105,
-0.035216424614191055,
-0.013894997537136078,
0.0035918059293180704,
0.05490478128194809,
-0.02694304846227169,
-0.017184872180223465,
0.048649679869413376,
-0.03715365752577782,
-0.052642617374658585,
0.045380547642707825,
0.016925323754549026,
0.03180660679936409,
0.03001772239804268,
0.012130586430430412,
-0.00911342166364193,
0.022907698526978493,
-0.007179288659244776,
-0.005782181862741709,
0.03362355753779411,
0.006334753707051277,
-0.00971276592463255,
-0.013030819594860077,
-0.04184025898575783,
0.010011338628828526,
-0.007460056338459253,
0.005243777763098478,
-0.02060377597808838,
-0.04165290668606758,
0.008160633966326714,
0.026716500520706177,
-0.014602698385715485,
-0.000927476619835943,
-0.0358721949160099,
0.062474168837070465,
0.04938803240656853,
-0.0014783068327233195,
-0.022085189819335938,
-0.006231654901057482,
0.0095807621255517,
0.016738899052143097,
0.019697926938533783,
0.04080300033092499,
0.002144897123798728,
0.00325960130430758,
-0.031812217086553574,
-0.0033893994987010956,
-0.000537139130756259,
-0.03826463222503662,
0.004332190845161676,
-0.001181634608656168,
-0.009569899179041386,
-0.008135396987199783,
-0.0341317281126976,
0.01592937298119068,
-0.014033024199306965,
0.022158244624733925,
0.05355285480618477,
0.0351400151848793,
0.007270048838108778,
0.01778874360024929,
-0.002270387951284647,
0.05268586799502373,
-0.044684551656246185,
0.014588015154004097,
-0.011419332586228848,
-0.0027102683670818806,
-0.01038827933371067,
-0.016502875834703445
] |
<p>I remember asking my second year Mechanics teacher about why do the Lagrangians give the equations of motion. His answer was that there is no answer to that, it is an empirical fact, and that asking the why of the Lagrangians is the same as asking why Newton's laws hold.</p>
<p>I understood his point but I wonder if you have a better answer. Why do Hamiltonians and Lagrangians work?</p>
| 293 |
[
-0.015062857419252396,
0.019006287679076195,
-0.019736697897315025,
-0.022998906672000885,
0.02480866201221943,
-0.004947461187839508,
-0.026497598737478256,
0.015798799693584442,
0.003597840666770935,
0.008254625834524632,
-0.003887480590492487,
0.039042338728904724,
0.039141032844781876,
-0.009392528794705868,
0.036619365215301514,
0.005454095546156168,
-0.005386738572269678,
-0.020013174042105675,
-0.008299441076815128,
0.011498912237584591,
-0.019118331372737885,
0.006652158219367266,
0.014024867676198483,
-0.02025003731250763,
-0.022017378360033035,
-0.016815628856420517,
0.025801779702305794,
-0.014383574016392231,
0.02638993412256241,
0.04672718420624733,
0.009422757662832737,
0.01626688428223133,
0.030797023326158524,
0.029793983325362206,
0.01027697790414095,
0.008531116880476475,
-0.02759934403002262,
-0.01727522723376751,
0.01292856503278017,
0.018002966418862343,
-0.04231361672282219,
-0.015194281935691833,
-0.005787269212305546,
0.031122634187340736,
-0.02886461839079857,
0.04609740152955055,
0.02288106083869934,
-0.001632349449209869,
0.04195272549986839,
-0.035583361983299255,
0.0689377561211586,
0.00801553949713707,
0.01531209982931614,
0.03532712161540985,
-0.01334475539624691,
-0.0033937713596969843,
0.0705140084028244,
0.045855943113565445,
-0.022337011992931366,
-0.05083601176738739,
-0.03476349264383316,
-0.02260369434952736,
0.0007568959845229983,
-0.0108046168461442,
0.002914061304181814,
0.023725589737296104,
0.016770469024777412,
-0.03343050181865692,
0.033850543200969696,
0.0043844375759363174,
-0.007227099034935236,
-0.01481364294886589,
0.04588424041867256,
0.00402425741776824,
0.0017928421730175614,
-0.02839881367981434,
0.040606409311294556,
0.0050676180981099606,
0.015093935653567314,
0.025828629732131958,
0.004989697132259607,
0.018271788954734802,
0.04810801520943642,
0.042270369827747345,
-0.02330593205988407,
-0.008379745297133923,
0.0745939314365387,
0.031002381816506386,
0.021669328212738037,
0.017332030460238457,
-0.011538890190422535,
-0.0015161592746153474,
0.012318436056375504,
0.014954974874854088,
0.02366793155670166,
0.0009686585981398821,
0.010194475762546062,
0.07197867333889008,
0.0412159226834774,
-0.004007022362202406,
0.013289152644574642,
-0.028359010815620422,
0.005414704792201519,
0.05835718661546707,
-0.01993042603135109,
-0.027222659438848495,
-0.040859997272491455,
0.022842638194561005,
-0.03293413668870926,
0.0005850094021297991,
-0.019790800288319588,
0.029223628342151642,
0.0020513138733804226,
0.007914179936051369,
0.029482804238796234,
0.0009334547212347388,
0.022472508251667023,
-0.025340909138321877,
0.06673724204301834,
0.05297008901834488,
0.035834457725286484,
-0.039669521152973175,
0.012424740940332413,
-0.019545158371329308,
-0.016826456412672997,
-0.01718684285879135,
0.030273286625742912,
-0.013884404674172401,
-0.002508773235604167,
-0.026690466329455376,
0.003898320021107793,
-0.021486932411789894,
-0.04964835196733475,
0.011845623143017292,
0.036878801882267,
-0.02462729625403881,
-0.10295221954584122,
-0.044064465910196304,
0.04192650690674782,
0.04000214859843254,
-0.04669627174735069,
-0.08321072161197662,
-0.011465144343674183,
0.023471588268876076,
0.07108623534440994,
-0.008361022919416428,
-0.0010119389044120908,
0.03604191914200783,
0.014845333993434906,
-0.020450344309210777,
-0.007805281318724155,
-0.022677477449178696,
0.0033481409773230553,
-0.05635884776711464,
-0.0009322875994257629,
-0.09309989213943481,
0.009491797536611557,
0.0028991173021495342,
-0.01191923301666975,
-0.028511367738246918,
0.06141050532460213,
-0.024776993319392204,
0.013445084914565086,
0.01063435897231102,
0.007630731910467148,
-0.01826256327331066,
0.053839150816202164,
0.01140048447996378,
0.002401456469669938,
0.05594443902373314,
0.009258219040930271,
0.03444262966513634,
0.01973814330995083,
0.032468944787979126,
0.01960046961903572,
-0.004645884968340397,
-0.050377458333969116,
0.02448504976928234,
-0.004377240315079689,
-0.023083921521902084,
-0.02934645116329193,
-0.042691946029663086,
0.016216125339269638,
0.0013249170733615756,
-0.0368613675236702,
0.03802213445305824,
0.0346667543053627,
0.02495848760008812,
-0.031176147982478142,
-0.029320161789655685,
0.0016660508699715137,
-0.10242558270692825,
0.038097284734249115,
-0.019651275128126144,
-0.00996210053563118,
0.04116440564393997,
0.01713641919195652,
0.019687872380018234,
-0.026909852400422096,
-0.021838411688804626,
-0.03265925869345665,
0.02271490916609764,
0.0007210508338175714,
0.004007435869425535,
0.023235198110342026,
0.046203020960092545,
0.042223621159791946,
0.003344845026731491,
0.026759520173072815,
-0.010776620358228683,
-0.0383794829249382,
0.011042911559343338,
-0.0029332039412111044,
0.00994031596928835,
-0.006990555673837662,
-0.002159841824322939,
-0.013737727887928486,
-0.02112070471048355,
-0.009167474694550037,
0.038518309593200684,
-0.04611038789153099,
0.0903136283159256,
0.036331139504909515,
0.018986649811267853,
0.010118084959685802,
0.08808369189500809,
-0.027816476300358772,
0.004371188580989838,
0.015140794217586517,
-0.008561290800571442,
-0.02766033262014389,
-0.010606393218040466,
0.024751678109169006,
0.06436329334974289,
-0.04976317659020424,
-0.006731605157256126,
0.024401918053627014,
0.04210474714636803,
-0.011663900688290596,
0.03770565986633301,
-0.045455142855644226,
-0.021120145916938782,
0.048644207417964935,
0.014089248143136501,
-0.010569645091891289,
0.01607629284262657,
0.04623115062713623,
0.04117440804839134,
-0.0033636244479566813,
0.018783703446388245,
-0.04636475816369057,
0.06844957172870636,
0.007391235325485468,
0.008352586068212986,
0.04086899757385254,
-0.01747540943324566,
0.03828602284193039,
-0.009670797735452652,
0.017930420115590096,
0.02675400674343109,
0.010952233336865902,
-0.030727585777640343,
-0.03444230556488037,
-0.005677308887243271,
0.04062587022781372,
-0.01651035062968731,
-0.02997574396431446,
-0.02146204188466072,
0.027941666543483734,
-0.02951866015791893,
-0.0010647244052961469,
-0.0013149852165952325,
-0.0406089685857296,
-0.027148740366101265,
0.01672527752816677,
-0.0144419576972723,
0.015394078567624092,
0.038887470960617065,
-0.006131305359303951,
-0.033572133630514145,
-0.01095870416611433,
-0.0472412183880806,
0.022754548117518425,
0.023075556382536888,
-0.030604228377342224,
0.03466051444411278,
-0.03992509841918945,
-0.006516069173812866,
0.06383732706308365,
-0.008958488702774048,
0.021698540076613426,
0.010173836722970009,
-0.028082409873604774,
-0.03781801089644432,
-0.01038398128002882,
-0.04062401503324509,
0.002436114940792322,
-0.01808006502687931,
0.016377676278352737,
0.044911302626132965,
-0.04505738988518715,
-0.0290747731924057,
-0.004648346919566393,
-0.0517747700214386,
-0.05336988717317581,
0.009994905441999435,
-0.008909116499125957,
-0.0006862695445306599,
-0.02518206462264061,
0.010195818729698658,
0.03778477758169174,
-0.03296811506152153,
-0.002263403031975031,
-0.06317165493965149,
-0.027519037947058678,
0.015474371612071991,
0.002908281981945038,
0.01898655667901039,
-0.013489799574017525,
-0.008964617736637592,
0.06936473399400711,
0.013550989329814911,
-0.061765722930431366,
-0.0023652405943721533,
-0.02653137780725956,
-0.020257988944649696,
-0.0036915484815835953,
0.047111161053180695,
0.0439516082406044,
-0.004662626422941685,
0.027476415038108826,
0.019481567665934563,
0.003615780733525753,
0.004294741433113813,
0.0336192287504673,
0.008628795854747295,
-0.019915804266929626,
0.009762383997440338,
-0.017927315086126328,
0.016272086650133133,
0.016687599942088127,
-0.05629636347293854,
0.012260230258107185,
0.0031001432798802853,
0.030103178694844246,
-0.008861175738275051,
-0.06634432077407837,
0.06784199923276901,
0.018552128225564957,
-0.009193643927574158,
-0.02072104997932911,
0.028878729790449142,
-0.01770729199051857,
0.0007937925402075052,
-0.000014585249118681531,
0.008347327820956707,
0.0015122228069230914,
-0.015922974795103073,
0.038114048540592194,
0.02475382201373577,
0.021429158747196198,
-0.0411820188164711,
-0.020486295223236084,
0.01271278876811266,
-0.02558424510061741,
0.01141970045864582,
0.019910864531993866,
-0.03178109973669052,
0.048731036484241486,
0.010478813201189041,
0.00965400692075491,
-0.010011560283601284,
-0.05694524943828583,
-0.005291410256177187,
-0.06981115788221359,
0.009098549373447895,
0.0059616160579025745,
0.04917937144637108,
0.0029456939082592726,
0.073891282081604,
-0.0025969138368964195,
0.04064374789595604,
0.014155755750834942,
-0.0029709762893617153,
-0.07649073004722595,
0.0523180328309536,
-0.0330004021525383,
-0.03730422258377075,
-0.014614204876124859,
-0.006096171215176582,
0.03645402938127518,
-0.02649061009287834,
-0.023651456460356712,
-0.014899253845214844,
-0.009920814074575901,
-0.05837254226207733,
-0.019102657213807106,
-0.03811678662896156,
-0.06089289113879204,
-0.015224291011691093,
0.004336481913924217,
0.007068444509059191,
-0.012530284933745861,
0.012930677272379398,
0.04916705936193466,
-0.022230353206396103,
-0.024328051134943962,
-0.02228943631052971,
-0.015839843079447746,
0.03589679300785065,
-0.02499040588736534,
0.014465454034507275,
0.019475553184747696,
-0.0004943452659063041,
0.03503447771072388,
0.026937123388051987,
0.060072463005781174,
0.011384152807295322,
-0.004233344458043575,
-0.0052754683420062065,
-0.05231621488928795,
-0.006299266126006842,
0.0010040453635156155,
0.03572503849864006,
0.0072513148188591,
-0.010812473483383656,
0.02367483638226986,
0.0018535247072577477,
0.02002943865954876,
0.05204072967171669,
0.004584379959851503,
0.046701230108737946,
-0.018939701840281487,
-0.05768382176756859,
0.0035331055987626314,
-0.049983762204647064,
-0.012131593190133572,
0.026661936193704605,
-0.037575528025627136,
-0.00630058953538537,
0.011600540950894356,
0.010219933465123177,
-0.00246980506926775,
-0.007240986451506615,
-0.013987286947667599,
-0.004872895777225494,
0.05945299193263054,
0.015342445112764835,
0.0067074657417833805,
0.020003821700811386,
0.06327994912862778,
0.026688259094953537,
-0.012592295184731483,
-0.006166068837046623,
-0.0741618275642395,
-0.01421807985752821,
0.019459716975688934,
0.006134853698313236,
-0.04483383521437645,
-0.013075527735054493,
-0.022190852090716362,
-0.056252334266901016,
0.055929724127054214,
-0.041351884603500366,
0.021204546093940735,
-0.009227707982063293,
0.012458155862987041,
-0.03559653088450432,
-0.03057205118238926,
-0.0231859739869833,
0.01196993887424469,
-0.009348319843411446,
0.02346578612923622,
-0.02885592170059681,
0.0037382845766842365,
-0.029638072475790977,
0.02263731136918068,
0.03811453655362129,
0.06081710383296013,
0.01952151581645012,
-0.00020014717301819474,
-0.029404543340206146,
0.019956622272729874,
-0.03088933788239956,
-0.09285130351781845,
-0.03387012705206871,
0.001169700059108436,
-0.0012385101290419698,
0.02105376310646534,
-0.03699985891580582,
-0.05785132572054863,
0.010598821565508842,
-0.03190147131681442,
-0.009212560951709747,
-0.016420718282461166,
-0.04025758057832718,
-0.010458520613610744,
0.03140723332762718,
0.014897190034389496,
0.0305379256606102,
0.028593292459845543,
-0.02361600659787655,
-0.031381599605083466,
-0.021275218576192856,
0.0025023361667990685,
-0.01960807479918003,
-0.03185626491904259,
-0.03884438797831535,
-0.0065204366110265255,
-0.024201223626732826,
0.0551823191344738,
0.007532399147748947,
0.005577948410063982,
-0.04665512591600418,
-0.03892652690410614,
-0.043572764843702316,
0.05828169360756874,
0.030436091125011444,
-0.03063621185719967,
-0.015466363169252872,
0.026471612975001335,
0.03510478511452675,
-0.06613334268331528,
0.020697884261608124,
0.004607871174812317,
-0.020133772864937782,
0.04869266226887703,
-0.00013584275438915938,
0.03234236687421799,
-0.011813180521130562,
-0.016832970082759857,
0.01600015163421631,
-0.042246945202350616,
0.031883008778095245,
0.0036373890470713377,
-0.0023651281371712685,
0.024010352790355682,
-0.038423098623752594,
-0.06592722237110138,
-0.013710304163396358,
0.0032941389363259077,
0.028668656945228577,
-0.01668325439095497,
0.0036598474252969027,
0.014824889600276947,
-0.01104365661740303,
-0.07059311121702194,
-0.05240888148546219,
-0.0013149440055713058,
0.010046001523733139,
-0.01979939267039299,
-0.008959675207734108,
0.04523864760994911,
-0.029512211680412292,
-0.03122112713754177,
0.038321543484926224,
0.05363011732697487,
-0.01689322292804718,
-0.012767747975885868,
0.026946302503347397,
-0.011992412619292736,
0.013036512769758701,
-0.03398299217224121,
-0.017160989344120026,
0.004426227416843176,
-0.0468926876783371,
0.004038920160382986,
-0.009943191893398762,
0.057362355291843414,
-0.0047459108754992485,
-0.011308579705655575,
-0.003977753221988678,
0.004279083572328091,
0.05047252029180527,
-0.000189511789358221,
0.01776648871600628,
0.051445405930280685,
0.01914610154926777,
-0.00954529270529747,
-0.059303928166627884,
0.016632232815027237,
-0.00415175361558795,
0.021147627383470535,
0.018059134483337402,
0.027800196781754494,
-0.031099921092391014,
-0.015428664162755013,
0.027054650709033012,
-0.01845606230199337,
0.0009827452013269067,
0.013063988648355007,
0.03689970076084137,
-0.022216467186808586,
0.022671181708574295,
0.02426101826131344,
0.03287515416741371,
0.025971846655011177,
-0.003966778516769409,
-0.007545402739197016,
0.021652938798069954,
0.031332071870565414,
-0.012573370710015297,
-0.029564520344138145,
-0.019779393449425697,
0.04692323878407478,
0.08723534643650055,
-0.008675300516188145,
0.06283256411552429,
0.01652809977531433,
0.018539834767580032,
0.003163082292303443,
0.004625929053872824,
-0.012283742427825928,
-0.017801180481910706,
0.0030022659339010715,
0.013403776101768017,
-0.044591981917619705,
0.003815376665443182,
0.04377303272485733,
0.009163692593574524,
-0.033385634422302246,
-0.03390813618898392,
0.028399767354130745,
0.032563839107751846,
-0.025159748271107674,
0.02469397895038128,
-0.038505569100379944,
0.02287251129746437,
-0.03723325952887535,
0.05107775703072548,
0.009125426411628723,
-0.0516863577067852,
0.043661441653966904,
-0.03133541718125343,
-0.002291441196575761,
-0.03145405650138855,
0.003301682649180293,
-0.024322472512722015,
0.035072702914476395,
0.019224055111408234,
0.034635916352272034,
0.01436521578580141,
0.021518776193261147,
0.023778259754180908,
0.004844041541218758,
0.016624456271529198,
0.016233159229159355,
-0.06810832768678665,
-0.03133724257349968,
-0.036628883332014084,
-0.0625397339463234,
0.024008046835660934,
0.01619207113981247,
-0.01976502314209938,
0.00905061699450016,
-0.032344501465559006,
-0.003918870817869902,
-0.0021135234273970127,
0.04696984961628914,
-0.046971071511507034,
0.07326465845108032,
0.012276451103389263,
-0.006616820581257343,
-0.006730849388986826,
-0.001167411683127284,
0.10088258236646652,
0.03142848610877991,
-0.005106563679873943,
-0.0787203311920166,
0.00784657709300518,
0.012814142741262913,
-0.0031157606281340122,
-0.02325197122991085,
0.037760525941848755,
0.03806409239768982,
0.02639254368841648,
-0.018096327781677246,
0.04947734624147415,
-0.013105799444019794,
-0.001112067955546081,
0.08802980184555054,
-0.035723112523555756,
-0.040110498666763306,
-0.009079859592020512,
0.006705444771796465,
0.002275706734508276,
0.021826688200235367,
-0.017482124269008636,
0.01448144018650055,
-0.04167551547288895,
-0.012996184639632702,
0.003922322299331427,
-0.0445529967546463,
0.021460026502609253,
0.007193987723439932,
-0.05248149484395981,
0.014987890608608723,
0.032271284610033035,
-0.026114512234926224,
-0.060923460870981216,
0.0005007226718589664,
0.01152186281979084,
0.0010061924112960696,
0.048128392547369,
0.013700843788683414,
-0.010791776701807976,
0.014043779112398624,
-0.003197557758539915,
0.006330475676804781,
-0.038434214890003204,
-0.005330417305231094,
-0.05020659789443016,
0.05736866965889931,
-0.008258633315563202,
0.020894845947623253,
-0.0020135114900767803,
-0.024369852617383003,
-0.038368865847587585,
-0.04758431762456894,
-0.03707640990614891,
-0.01696857064962387,
0.03625575825572014,
-0.03841600939631462,
-0.029560217633843422,
-0.05780458822846413,
-0.022536054253578186,
-0.03416355699300766,
0.03204815462231636,
0.0062635596841573715,
0.021915489807724953,
-0.01185930147767067,
0.014368720352649689,
0.030020015314221382,
-0.0348445400595665,
-0.01447542104870081,
-0.05131354182958603,
-0.025023285299539566,
-0.054032161831855774,
-0.005895927082747221,
0.01604434661567211,
0.04694689065217972,
0.00454722298309207,
-0.0030894603114575148,
-0.01169490348547697,
-0.008104355074465275,
-0.07127571105957031,
0.01398528553545475,
0.007776725105941296,
-0.019656457006931305,
-0.0067737409844994545,
-0.007283085025846958,
0.014907347038388252,
0.0483376607298851,
-0.0070610567927360535,
-0.008018161170184612,
0.011495884507894516,
-0.03493913635611534,
0.02251664362847805,
-0.020725484937429428,
-0.026121612638235092,
0.04967663064599037,
-0.03987027332186699,
0.007760961540043354,
-0.00410005496814847,
0.014260567724704742,
0.014454483985900879,
0.02337246760725975,
0.010459262877702713,
0.02899717539548874,
-0.01678904891014099,
-0.001562131685204804,
0.028522051870822906,
-0.006655614823102951,
0.013289476744830608,
0.019469300284981728,
0.04140828922390938,
-0.05014602839946747,
-0.03422423452138901,
-0.030988546088337898,
0.009587431326508522,
0.009497041814029217,
0.025924496352672577,
-0.011838200502097607,
0.00428385566920042,
-0.015041141770780087,
0.0350644625723362,
-0.05325054004788399,
0.024822071194648743,
-0.07823025435209274,
0.038132186979055405,
-0.018481507897377014,
-0.03937592729926109,
-0.052492983639240265,
0.038669150322675705,
-0.006048735696822405,
-0.03126262500882149,
0.03208369389176369,
0.05888015404343605,
-0.010876578278839588,
-0.022469663992524147,
0.007102121599018574,
-0.039240624755620956,
0.04849964380264282,
0.010773491114377975,
-0.025955501943826675,
0.02047627791762352,
-0.03238275647163391,
-0.04338930547237396,
0.003433170262724161,
-0.023038702085614204,
0.024540802463889122,
0.03780461475253105,
-0.03143860772252083,
0.005467370618134737,
0.029640773311257362,
-0.025585446506738663,
0.0015299911610782146,
-0.005301700439304113,
-0.018884645774960518,
-0.0411822646856308,
-0.015727726742625237,
0.012355429120361805,
-0.02048318274319172,
-0.0026426492258906364,
0.012789356522262096,
0.02936703711748123,
0.00790159311145544,
0.007199532352387905,
0.01990661583840847,
0.006829043384641409,
0.012708842754364014,
0.005655879154801369,
0.01863141357898712,
0.005566842388361692,
0.06072905659675598,
-0.029514355584979057,
0.044277265667915344,
0.00812703836709261,
0.03162636235356331,
-0.06793899834156036,
0.0075057814829051495,
-0.012276044115424156,
-0.016568128019571304,
0.06757257133722305,
-0.019472133368253708,
0.027180777862668037,
0.025591908022761345,
-0.08064577728509903,
0.0068161399103701115,
-0.06310518085956573,
-0.004429406486451626,
0.003908849786967039,
0.002230033278465271,
-0.0007494787569157779,
0.058020077645778656,
0.03912511095404625,
0.031996019184589386,
0.00823129341006279,
-0.004574332851916552,
0.02065729908645153,
0.013134362176060677,
-0.0043741026893258095,
0.03922054544091225,
-0.026289669796824455,
0.04520494490861893,
0.06051277741789818,
-0.0021020714193582535,
-0.035964399576187134,
0.014543120749294758,
-0.009607994928956032,
-0.0028031556867063046,
-0.006516864523291588,
0.002755691297352314,
-0.021578676998615265,
0.01826975680887699,
0.012714564800262451,
-0.031652748584747314,
-0.020893333479762077,
0.010444199666380882,
0.0018024655291810632,
0.041565656661987305,
-0.011379779316484928,
-0.014490263536572456,
0.04000250995159149,
-0.04743925854563713,
-0.04786204546689987,
0.022248903289437294,
0.018640127032995224,
0.01753644086420536,
0.029025783762335777,
0.025408297777175903,
0.0026083614211529493,
-0.025201622396707535,
0.014058849774301052,
-0.043413225561380386,
-0.01220268290489912,
0.01637268252670765,
0.03710869699716568,
0.0003282120742369443,
0.03649371489882469,
-0.0016563661629334092,
0.0072164456360042095,
0.00023039380903355777,
0.018335659056901932,
0.003179116640239954,
-0.08406153321266174,
0.013620293699204922,
0.029607728123664856,
-0.01230689324438572,
-0.035779889672994614,
-0.04902307689189911,
-0.024760691449046135,
0.04758646711707115,
0.023376788944005966,
0.02428554929792881,
-0.030334603041410446,
-0.04685963690280914,
-0.018692918121814728,
-0.04166646674275398,
0.054824404418468475,
0.01973503828048706,
0.005028815474361181,
-0.0601760596036911,
-0.033612288534641266,
0.00964476726949215,
0.022906091064214706,
0.024038465693593025,
-0.010806598700582981,
-0.0009111787076108158,
0.01232124399393797,
0.0073148575611412525,
0.010889512486755848,
-0.0013511769939213991,
0.013251367025077343,
-0.031804800033569336,
-0.003515084972605109,
-0.01433182880282402,
-0.02006329968571663,
-0.034921325743198395,
0.03783561661839485,
0.031685907393693924,
-0.02652413584291935,
0.07117445766925812,
-0.0023230749648064375,
-0.05294080451130867,
0.05221204459667206,
0.027443159371614456,
0.010985600762069225,
0.0728701651096344,
0.002797282999381423,
0.01837127096951008,
0.038902852684259415,
-0.054197851568460464,
-0.020051447674632072,
0.049819789826869965,
-0.041362520307302475,
-0.0000346812121279072,
-0.012338203378021717,
-0.020994272083044052,
0.017103342339396477,
-0.03689124435186386,
0.011296861805021763,
0.041130878031253815,
-0.023471031337976456,
-0.031059470027685165,
0.03165952488780022,
0.0136383892968297,
0.023348107933998108,
-0.004322063643485308,
0.02569461427628994,
0.03819870203733444,
0.007140967063605785,
-0.000946482818108052,
0.05807584151625633,
0.060989804565906525,
-0.01197304017841816,
0.010762485675513744,
0.049392275512218475,
-0.001716564642265439,
0.04467090219259262,
0.009646340273320675,
0.057237911969423294,
-0.05298502370715141,
-0.03234865516424179,
0.0011787820840254426,
-0.019708387553691864,
0.02618168294429779,
0.026665540412068367,
-0.029268071055412292,
0.07856413722038269,
-0.051708441227674484,
-0.0038280992303043604,
-0.00009046291233971715,
-0.0021042576991021633,
-0.02118886634707451,
-0.0338873565196991,
0.01113472692668438,
0.032938383519649506,
0.0036706249229609966,
0.014726117253303528,
-0.027988096699118614,
0.0015913320239633322,
0.03727158159017563,
0.00297488272190094,
0.006030113436281681,
0.016748566180467606,
-0.015600071288645267,
-0.0009885260369628668,
-0.0065797800198197365,
-0.04977039992809296,
-0.01876271516084671,
0.033715587109327316,
0.047057319432497025,
0.005655514542013407,
-0.017089368775486946,
-0.028639139607548714,
-0.06273338943719864,
0.07637742161750793,
-0.08108611404895782,
-0.041042670607566833,
-0.017545364797115326,
0.004473079927265644,
-0.026819931343197823,
-0.016603494063019753
] |
<p>For my homework in engineering, I was given a question like this: There is an axle attached to a gear, which is meshed with another gear, which has an axle attached to it. I am given the diameter of both gears, and the torque on the input axle. How would I go about finding the torque on the output axle? I'm ommitting the specific numbers, because I would like to know how to solve such a problem in general. What is the relation between thetorque of the wheel and the torque of the axle? Is this even solveable without axle diameters? We went over the problem in class, but I can't for the life of me remember what we did. Thanks</p>
| 8,876 |
[
-0.013340644538402557,
-0.023668667301535606,
-0.01493153627961874,
0.011897685006260872,
0.0037396603729575872,
0.018029237166047096,
-0.03239920735359192,
0.0065061915665864944,
0.022441234439611435,
0.0020958585664629936,
0.0034414471592754126,
0.03088381513953209,
0.0504218153655529,
0.018619151785969734,
0.032946161925792694,
0.015694161877036095,
-0.015492924489080906,
-0.00844467245042324,
0.021248547360301018,
-0.016890008002519608,
0.004014259669929743,
-0.00408309418708086,
0.023345010355114937,
-0.014727560803294182,
-0.01264226995408535,
0.013572235591709614,
0.04005373269319534,
-0.04576648026704788,
0.02997560054063797,
0.046471744775772095,
0.027486039325594902,
-0.02821509726345539,
0.019600940868258476,
0.017524627968668938,
-0.0015643083024770021,
0.00433484697714448,
-0.05058381333947182,
0.009562162682414055,
-0.004307967610657215,
0.049612004309892654,
-0.049188125878572464,
-0.005096327979117632,
0.014543460682034492,
0.06430455297231674,
0.0021961466409265995,
0.04909227788448334,
-0.013925859704613686,
-0.01790083758533001,
0.014048476703464985,
-0.08378683775663376,
0.0831523984670639,
0.01060496922582388,
0.03796510025858879,
0.04215697571635246,
-0.0018848222680389881,
0.009890674613416195,
0.0904972106218338,
0.06260934472084045,
-0.01671692728996277,
-0.049418702721595764,
-0.04844088479876518,
-0.000525173731148243,
-0.02359706349670887,
-0.017549294978380203,
-0.036394357681274414,
0.023404812440276146,
-0.018395252525806427,
-0.017538711428642273,
0.06242040917277336,
-0.02170511707663536,
0.013449196703732014,
0.05740601196885109,
0.07795947045087814,
-0.017275791615247726,
0.0004921815707348287,
-0.046386078000068665,
0.03098251111805439,
0.018648557364940643,
0.03435560315847397,
0.03695850446820259,
-0.02987738698720932,
0.02198275923728943,
0.052995260804891586,
0.07802682369947433,
-0.002159666270017624,
-0.026408907026052475,
0.043893877416849136,
0.0022889473475515842,
-0.0015385543229058385,
0.02280440554022789,
-0.0052450429648160934,
-0.001595162320882082,
0.043218374252319336,
-0.03715192899107933,
0.01717197149991989,
0.030070459470152855,
-0.019786043092608452,
0.04434773325920105,
0.005846890155225992,
-0.03882759064435959,
0.03217329829931259,
-0.016263509169220924,
-0.023709582164883614,
0.058238688856363297,
-0.00402494752779603,
0.010659661144018173,
0.036838918924331665,
0.020668886601924896,
-0.006426965817809105,
-0.014395251870155334,
-0.03789615258574486,
0.019381968304514885,
-0.003766244975849986,
0.01171713974326849,
0.007336327340453863,
-0.018231935799121857,
-0.020893674343824387,
0.0027121787425130606,
0.042964912950992584,
0.061454061418771744,
0.02642960660159588,
-0.03315074369311333,
0.010165801271796227,
-0.02693859115242958,
-0.03094935044646263,
0.02425883151590824,
0.00949685089290142,
-0.01840038038790226,
-0.010616091080009937,
0.039232898503541946,
0.010807768441736698,
-0.04866490140557289,
0.0077943033538758755,
-0.004421453457325697,
0.029875770211219788,
-0.05068786069750786,
-0.045601893216371536,
-0.07589752972126007,
0.025569116696715355,
-0.0030538972932845354,
-0.026541974395513535,
-0.07142936438322067,
0.04191598668694496,
0.040276724845170975,
0.06107781454920769,
0.03134579211473465,
0.045772939920425415,
0.025145839899778366,
0.0348481684923172,
-0.02103401906788349,
-0.0036466442979872227,
-0.04117928817868233,
0.007138699293136597,
-0.013632782734930515,
0.05001930147409439,
-0.04444879665970802,
0.011055609211325645,
0.014014224521815777,
0.0058778803795576096,
-0.06825528293848038,
0.051765285432338715,
0.011008243076503277,
-0.018842998892068863,
0.07506807148456573,
0.018213903531432152,
-0.029479019343852997,
0.05490768328309059,
0.013812835328280926,
-0.026632754132151604,
0.012746483087539673,
0.0118632223457098,
0.0035618271213024855,
-0.00036676079616881907,
0.0332963652908802,
0.036139726638793945,
-0.01562484074383974,
-0.019106769934296608,
-0.04445871710777283,
0.010051465593278408,
0.021276457235217094,
-0.007289429660886526,
-0.06817769259214401,
0.017877858132123947,
0.014239171519875526,
-0.015634993091225624,
0.040319278836250305,
0.009798580780625343,
0.0011768199037760496,
0.03561634570360184,
-0.01112503744661808,
0.004662673454731703,
-0.03486126288771629,
-0.015706390142440796,
-0.016652697697281837,
0.0013265962479636073,
0.01007882785052061,
0.002557821338996291,
0.043892379850149155,
-0.04749053344130516,
0.011762293986976147,
0.02243546023964882,
0.004808527417480946,
-0.004842577036470175,
-0.013819294050335884,
0.023380756378173828,
0.047030895948410034,
0.0812113955616951,
-0.0245968047529459,
0.03266563266515732,
0.0018608738901093602,
-0.008602422662079334,
0.009302102029323578,
-0.023254260420799255,
0.02181037701666355,
-0.011910210363566875,
-0.0075742099434137344,
-0.0022867994848638773,
0.0011947494931519032,
0.0002923370630014688,
0.03503191098570824,
-0.024413209408521652,
0.09947434812784195,
0.06056865304708481,
0.026918401941657066,
-0.003017154987901449,
0.03419318422675133,
0.019232863560318947,
0.020976347848773003,
-0.020482273772358894,
-0.030642211437225342,
-0.0365874245762825,
-0.003913268446922302,
0.026890259236097336,
0.016485819593071938,
-0.04961070045828819,
0.003593244357034564,
0.060161344707012177,
0.02676365152001381,
0.009216202422976494,
0.045359984040260315,
-0.04355423152446747,
0.007930855266749859,
0.015298542566597462,
0.032772693783044815,
0.018778512254357338,
0.03483662009239197,
-0.011974488385021687,
0.061048537492752075,
0.0076093547977507114,
0.013626272790133953,
-0.026634402573108673,
0.05520045757293701,
0.01650031842291355,
0.00877467729151249,
0.021649492904543877,
0.010451553389430046,
0.04359310120344162,
-0.0232470091432333,
0.007545181084424257,
0.028602417558431625,
0.032465994358062744,
0.009133538231253624,
0.011458861641585827,
0.009008741937577724,
0.03436891362071037,
0.00440418254584074,
0.004520116373896599,
0.00038581539411097765,
0.0060947248712182045,
-0.023815888911485672,
-0.006809982471168041,
0.022323068231344223,
0.0014757990138605237,
-0.02293790504336357,
0.007514464668929577,
-0.002604052424430847,
-0.007522685453295708,
0.019643006846308708,
0.015750259160995483,
-0.02922440506517887,
-0.006374946795403957,
-0.013124199584126472,
-0.006286644842475653,
0.01351890992373228,
-0.05033684894442558,
0.029550453647971153,
-0.007781109772622585,
-0.023858601227402687,
0.05851446092128754,
-0.01065016444772482,
0.030880339443683624,
0.014333980157971382,
-0.022134864702820778,
-0.04012284427881241,
-0.023446189239621162,
-0.0039826747961342335,
0.021790143102407455,
-0.02143518626689911,
0.05123456194996834,
0.03573993965983391,
-0.01685497537255287,
-0.04938401281833649,
-0.005853002425283194,
-0.0750361829996109,
-0.04931141808629036,
-0.04009494185447693,
-0.0069141448475420475,
0.023748619481921196,
-0.005949010141193867,
0.011941158212721348,
-0.011784380301833153,
-0.0478295236825943,
-0.0014046760043129325,
-0.05750804767012596,
-0.03138138726353645,
0.00828417669981718,
0.01826408877968788,
0.04229066148400307,
0.010111342184245586,
-0.04361480101943016,
0.041199903935194016,
-0.02995884045958519,
-0.05949913337826729,
-0.030591899529099464,
0.005883776117116213,
0.0049527171067893505,
-0.024842532351613045,
0.00308133359067142,
0.04282889887690544,
-0.0066396272741258144,
0.022718898952007294,
0.0338328592479229,
0.025775551795959473,
0.062367260456085205,
0.04583282396197319,
-0.0030696929898113012,
-0.01927952840924263,
0.015437746420502663,
-0.02806233987212181,
0.030282098799943924,
0.03520524874329567,
-0.025523865595459938,
0.03033274970948696,
-0.005522858817130327,
0.012479263357818127,
-0.0008081234991550446,
-0.0595916323363781,
-0.007175263017416,
-0.01310574822127819,
-0.0013205973664298654,
-0.004515941720455885,
0.022933298721909523,
0.007374088745564222,
0.020531797781586647,
0.012336019426584244,
0.036298029124736786,
0.03449805825948715,
-0.042680516839027405,
-0.04017861559987068,
0.04154971241950989,
0.0022497945465147495,
-0.019657332450151443,
-0.05037934333086014,
-0.01886308565735817,
-0.021264981478452682,
0.01831069216132164,
-0.03498675301671028,
-0.03007105365395546,
0.017379343509674072,
0.02364981174468994,
0.017218805849552155,
0.01282587368041277,
-0.03542158007621765,
0.046925947070121765,
-0.07206332683563232,
-0.030754469335079193,
-0.010753944516181946,
0.06555528938770294,
-0.010535681620240211,
0.02552594058215618,
0.049623388797044754,
0.026262566447257996,
0.00011981972784269601,
-0.014717236161231995,
-0.06969135254621506,
0.05784139409661293,
-0.03451411798596382,
-0.05361263081431389,
0.011516982689499855,
0.013337944634258747,
-0.0077850669622421265,
-0.04992270469665527,
-0.03464889153838158,
-0.0012697657803073525,
-0.0004261010035406798,
-0.057135410606861115,
0.0014124596491456032,
-0.013572619296610355,
-0.04888511821627617,
-0.0239623561501503,
0.019342053681612015,
0.03696270287036896,
-0.02525477483868599,
0.0468587763607502,
0.05933147668838501,
-0.03418784216046333,
0.0018511137459427118,
-0.0467425212264061,
0.006320876069366932,
0.0057064080610871315,
0.03285893052816391,
0.028833581134676933,
0.053695954382419586,
-0.02452647127211094,
0.014237315393984318,
0.010945862159132957,
0.06625996530056,
0.014938922598958015,
-0.0406421460211277,
-0.03551154583692551,
-0.03572383150458336,
0.006815237458795309,
-0.017868131399154663,
0.047420576214790344,
-0.0677742213010788,
0.005633687600493431,
0.07400961965322495,
0.0002886188740376383,
-0.0205138698220253,
0.037941861897706985,
0.057460345327854156,
0.02496224455535412,
-0.03803170844912529,
-0.045709557831287384,
-0.012023485265672207,
-0.03081561252474785,
-0.00503816083073616,
0.0336635522544384,
-0.007358561269938946,
0.01889561116695404,
-0.026641707867383957,
0.023573890328407288,
-0.009488518349826336,
-0.010406697168946266,
0.018031327053904533,
-0.015241917222738266,
0.06056665629148483,
0.0037564486265182495,
-0.022046096622943878,
0.008482103236019611,
0.013957297429442406,
0.040621791034936905,
-0.006416183430701494,
0.009122749790549278,
-0.08031518012285233,
-0.0006526194629259408,
0.031123748049139977,
0.01846269704401493,
-0.029642319306731224,
-0.004827512428164482,
-0.0023857741616666317,
0.0050107501447200775,
0.06217016652226448,
-0.026647495105862617,
0.05876757577061653,
-0.044144049286842346,
0.005575692281126976,
-0.0044503225944936275,
0.003780412022024393,
-0.009716098196804523,
0.03266996517777443,
0.0057273609563708305,
0.008719276636838913,
-0.031204242259263992,
-0.01749870553612709,
-0.02499169111251831,
0.0331883579492569,
0.026033129543066025,
0.020116766914725304,
0.031065477058291435,
-0.025032084435224533,
0.017537211999297142,
0.06211737170815468,
-0.007971365936100483,
-0.06156683713197708,
-0.013610455207526684,
-0.005870737135410309,
-0.012505165301263332,
0.02241925336420536,
-0.05314623564481735,
-0.009804273955523968,
0.0305696502327919,
-0.03234589844942093,
0.004337396938353777,
0.01630515046417713,
-0.026448681950569153,
0.001543113961815834,
0.029133465141057968,
0.01174661610275507,
0.048132069408893585,
0.03559323400259018,
-0.0012300899252295494,
-0.04072796180844307,
-0.03488534316420555,
0.0343279205262661,
0.009729238227009773,
-0.020117146894335747,
0.00270855613052845,
0.04419383034110069,
-0.03009665757417679,
0.048347026109695435,
-0.003199757542461157,
0.05131782591342926,
-0.06821224838495255,
-0.022924907505512238,
-0.007285973057150841,
0.027888575568795204,
0.010006565600633621,
-0.0101724648848176,
0.02332332916557789,
-0.022666361182928085,
0.010734530165791512,
-0.050423141568899155,
0.0029119562823325396,
-0.0004574929771479219,
0.011982625350356102,
-0.0068261148408055305,
-0.0110888397321105,
0.009083237498998642,
-0.027422552928328514,
-0.03571518138051033,
0.018376776948571205,
-0.023949526250362396,
0.0636037215590477,
-0.011001951061189175,
-0.0020608073100447655,
0.04408674314618111,
-0.056587688624858856,
-0.03849843889474869,
0.027651242911815643,
0.0016628799494355917,
0.05225289985537529,
-0.038372017443180084,
0.013048315420746803,
0.010588164441287518,
-0.03976680710911751,
-0.014029288664460182,
-0.0529613122344017,
0.01235002838075161,
-0.018785085529088974,
0.01594836451113224,
-0.005755712278187275,
0.009989255107939243,
-0.008846416138112545,
-0.04846193268895149,
-0.014437367208302021,
0.05169670656323433,
-0.03270341455936432,
0.014664226211607456,
-0.019721874967217445,
-0.023213520646095276,
0.04189496487379074,
0.012693328782916069,
-0.0007942431839182973,
0.012377574108541012,
-0.014354352839291096,
-0.016758156940340996,
0.03458424285054207,
0.038352467119693756,
-0.026201501488685608,
-0.023861322551965714,
-0.010226981714367867,
0.008387897163629532,
0.04706580191850662,
-0.006141985766589642,
0.002643799176439643,
0.021141551434993744,
0.03151504695415497,
-0.01578664965927601,
-0.0003897699061781168,
0.038722310215234756,
0.010344806127250195,
0.020858781412243843,
-0.019647780805826187,
-0.006407841108739376,
-0.02548844739794731,
-0.003158204723149538,
0.004570243414491415,
-0.01508270762860775,
0.0068089826963841915,
-0.02084456756711006,
0.041192252188920975,
-0.006814541760832071,
0.018319150432944298,
0.005985674913972616,
-0.017754366621375084,
0.023886412382125854,
-0.016970094293355942,
0.0073327901773154736,
-0.010702583007514477,
-0.0025503826327621937,
-0.03684372082352638,
-0.05219617486000061,
-0.017991719767451286,
-0.034982047975063324,
0.09085199236869812,
-0.055044326931238174,
0.06549578160047531,
0.0562179833650589,
-0.004805711098015308,
0.018458060920238495,
-0.00014627761265728623,
-0.016364827752113342,
0.002089553978294134,
0.005769799463450909,
0.04583915323019028,
-0.008317452855408192,
0.007535972632467747,
0.015285620465874672,
-0.00039821950485929847,
-0.014076960273087025,
-0.02512432634830475,
-0.002514350926503539,
0.03791775926947594,
0.0020073384512215853,
0.014909463934600353,
-0.03231080248951912,
-0.0064112236723303795,
0.022286219522356987,
0.04302374646067619,
-0.03628372400999069,
0.016428088769316673,
0.07843813300132751,
0.01594526879489422,
0.02494845539331436,
-0.026675062254071236,
-0.027025677263736725,
-0.029603760689496994,
0.011324786581099033,
0.03415107727050781,
-0.027026677504181862,
0.00156433938536793,
0.04762909561395645,
0.024221045896410942,
-0.020214185118675232,
0.01908785104751587,
-0.05994544178247452,
-0.02769668586552143,
-0.012676948681473732,
-0.04834328591823578,
-0.046189114451408386,
0.017764180898666382,
0.018758045509457588,
-0.05067126080393791,
0.04325133189558983,
-0.043846096843481064,
0.005340545438230038,
0.02382599376142025,
0.028863105922937393,
-0.04399961605668068,
0.08056989312171936,
-0.023544272407889366,
0.02376701310276985,
-0.006317556370049715,
-0.0049915616400539875,
0.07452625781297684,
0.02270946465432644,
0.030975159257650375,
-0.06874947249889374,
0.006824465002864599,
-0.03619445115327835,
-0.044749170541763306,
-0.07404818385839462,
0.052494533360004425,
-0.014178350567817688,
-0.004874922800809145,
0.049770720303058624,
0.0009721453534439206,
-0.01172904297709465,
-0.021439095959067345,
0.05784592032432556,
-0.016069872304797173,
-0.0511137917637825,
-0.016909277066588402,
0.03880982846021652,
-0.005836696829646826,
0.005884238984435797,
-0.0491163395345211,
0.01616055518388748,
-0.06311378628015518,
-0.015425939112901688,
-0.028156232088804245,
-0.03340490907430649,
0.028441838920116425,
0.014175954274833202,
-0.05333971232175827,
0.040294099599123,
0.031791917979717255,
-0.026823103427886963,
0.0008966578170657158,
0.007072424981743097,
0.0349896103143692,
0.01327371783554554,
-0.006686326581984758,
0.00021565979113802314,
0.004531520418822765,
0.020768344402313232,
-0.004680831916630268,
-0.013566035777330399,
-0.06147993355989456,
-0.010174057446420193,
-0.015346248634159565,
0.03429900109767914,
0.03158603608608246,
0.02809874340891838,
0.026095636188983917,
0.022095875814557076,
-0.000798823602963239,
-0.05542852729558945,
-0.03475692868232727,
-0.009242989122867584,
0.023856664076447487,
-0.06737816333770752,
-0.010149084031581879,
-0.011219064705073833,
0.051649369299411774,
-0.015014895237982273,
0.02024794928729534,
0.006458931602537632,
-0.01845703087747097,
0.011888151988387108,
-0.031727347522974014,
0.03684382140636444,
-0.011385462246835232,
-0.050610922276973724,
-0.017209742218255997,
-0.012296754866838455,
0.014267336577177048,
0.02718278579413891,
0.029742809012532234,
-0.005072918254882097,
0.006214391905814409,
-0.026576003059744835,
-0.031215718016028404,
0.0032379692420363426,
-0.06103897839784622,
-0.00016869115643203259,
-0.003073431784287095,
-0.0035361764021217823,
-0.05836944654583931,
0.025062205269932747,
0.019166963174939156,
0.024590708315372467,
-0.03927364945411682,
-0.01446685940027237,
0.010139845311641693,
-0.01415414921939373,
0.041015155613422394,
-0.02400345169007778,
-0.006257875356823206,
0.04010813683271408,
-0.03401404246687889,
-0.02363739162683487,
-0.00416371738538146,
0.05670858174562454,
0.03182750195264816,
0.015726590529084206,
-0.018327103927731514,
0.032268088310956955,
0.02292965166270733,
0.046993400901556015,
0.022969305515289307,
-0.0014777281321585178,
-0.013360274024307728,
0.029733406379818916,
0.0029264092445373535,
-0.08339022845029831,
-0.009193054400384426,
-0.024686940014362335,
-0.041094325482845306,
-0.003888251492753625,
-0.004940250888466835,
-0.06186651065945625,
-0.010942526161670685,
-0.03930417820811272,
0.02970585972070694,
-0.058420855551958084,
0.005553444381803274,
-0.004146012477576733,
-0.01973751001060009,
0.02846069075167179,
0.007349954452365637,
-0.007584641687572002,
0.02675694227218628,
0.008365209214389324,
-0.0220125000923872,
0.006794284097850323,
-0.0021054409444332123,
0.00977211445569992,
-0.03036712296307087,
0.0033455779775977135,
-0.013024663552641869,
0.05649099498987198,
-0.05146945267915726,
-0.021189354360103607,
0.0855366438627243,
-0.0392998568713665,
0.04883931949734688,
0.03681167960166931,
-0.004065686836838722,
0.018526524305343628,
0.00972133781760931,
-0.016147762537002563,
-0.025753915309906006,
0.05164378136396408,
-0.023954803124070168,
0.0009288210421800613,
0.0001057444023899734,
-0.02358444221317768,
-0.02121446654200554,
0.01873842254281044,
-0.008904512040317059,
-0.03724651038646698,
-0.0022638849914073944,
0.0065884701907634735,
0.04519134387373924,
-0.005396487191319466,
-0.011347044259309769,
0.04392267391085625,
0.04589959979057312,
0.016710633412003517,
0.03188050910830498,
-0.013991624116897583,
-0.0014369204873219132,
0.05357629433274269,
-0.017683986574411392,
0.03002135269343853,
0.03251935541629791,
0.0031805625185370445,
-0.06752718240022659,
-0.0027628664392977953,
-0.00853362213820219,
-0.007955176755785942,
0.044151272624731064,
-0.03128887340426445,
-0.02158140018582344,
0.014082945883274078,
-0.05627995729446411,
-0.019887281581759453,
-0.008677538484334946,
-0.05198802053928375,
-0.028392136096954346,
-0.029714878648519516,
0.043475501239299774,
0.025420211255550385,
0.040129758417606354,
0.059633519500494,
0.03713519498705864,
-0.004768370650708675,
-0.050387702882289886,
-0.04446521773934364,
0.019496766850352287,
0.024836746975779533,
-0.0035469275899231434,
0.011519544757902622,
0.02525756135582924,
-0.030917171388864517,
-0.03392387181520462,
0.024017490446567535,
-0.008932586759328842,
0.01645972765982151,
-0.005753375124186277,
-0.0002637371653690934,
-0.009920564480125904,
0.04460502415895462,
0.015039266087114811,
-0.005807071458548307,
-0.027754705399274826,
0.017383957281708717,
-0.005965223535895348,
0.0016087110852822661,
-0.05952564999461174,
-0.0013793774414807558,
0.03845309838652611,
-0.03761015832424164,
-0.030005451291799545,
0.021782957017421722,
-0.028713775798678398,
-0.021980110555887222,
0.0021028255578130484,
-0.013801748864352703,
-0.027950668707489967,
-0.039076514542102814,
-0.017757058143615723,
-0.03283946216106415,
-0.021590210497379303,
0.0166291706264019,
-0.009140901267528534,
-0.009297522716224194,
0.01428365707397461,
-0.026878058910369873,
-0.017561160027980804,
-0.0008531154599040747,
-0.006567835342139006,
-0.02711569331586361,
-0.05650007352232933,
-0.022330841049551964,
0.01532216276973486,
-0.037375304847955704,
0.0019773899111896753,
-0.05354677885770798,
-0.0100031066685915,
0.048141006380319595,
0.009069815278053284,
-0.0001437464525224641,
0.027442390099167824,
-0.002651180373504758,
-0.033347237855196,
-0.039452243596315384,
0.0020400488283485174,
0.03454626351594925,
-0.03291229531168938,
-0.020842017605900764,
0.0027242384385317564,
-0.0036188524682074785,
0.009977520443499088,
0.006140478886663914,
-0.0033464550506323576,
-0.022429196164011955,
-0.0043829334899783134,
-0.024105383083224297,
-0.004497182089835405,
-0.018607666715979576,
0.004326756577938795,
-0.022696513682603836,
-0.01550983265042305,
-0.007011898327618837,
-0.03412628918886185,
-0.037731509655714035,
-0.014100323431193829,
0.008070157840847969,
-0.017344996333122253,
0.03328654170036316,
0.003705761395394802,
-0.008422927930951118,
0.022216565907001495,
-0.0025680416729301214,
0.017283568158745766,
0.08760961890220642,
-0.008884843438863754,
0.015078435651957989,
0.006460828240960836,
0.028588341549038887,
-0.05642786622047424,
0.04546076059341431,
-0.05288826301693916,
0.02634236216545105,
-0.016827519983053207,
0.0057632047683000565,
0.061326559633016586,
-0.04862424358725548,
0.0016190898604691029,
0.042431000620126724,
-0.031759634613990784,
-0.009587237611413002,
0.01496224943548441,
0.02851305902004242,
0.009458811953663826,
-0.05572409927845001,
0.009818519465625286,
0.0060793147422373295,
-0.04214994236826897,
0.019034061580896378,
0.01936875656247139,
0.026132483035326004,
0.02189275436103344,
-0.01156748179346323,
0.051895227283239365,
-0.02354523167014122,
0.014606703072786331,
-0.029277153313159943,
0.016145959496498108,
-0.026448048651218414,
-0.056174494326114655,
-0.050749536603689194,
-0.05512600019574165,
0.029366690665483475,
0.01941879279911518,
-0.02017960138618946,
0.06716881692409515,
-0.031141644343733788,
0.0038133361376821995,
0.00480789877474308,
0.018354902043938637,
-0.035137832164764404,
-0.028721924871206284,
-0.02136848121881485,
0.016424007713794708,
-0.04453016445040703,
-0.022574812173843384,
0.011773239821195602,
-0.014813299290835857,
0.07056896388530731,
0.011507597751915455,
-0.0001257276308024302,
-0.014231226406991482,
-0.0024341619573533535,
-0.022606702521443367,
-0.018459655344486237,
-0.03940531238913536,
-0.030419470742344856,
0.048022475093603134,
0.04497871175408363,
-0.0013058598851785064,
-0.011034119874238968,
-0.01789463497698307,
-0.026482433080673218,
0.06148519366979599,
-0.08059398829936981,
-0.018020201474428177,
-0.014130035415291786,
-0.0014506937004625797,
-0.020045962184667587,
-0.011324184015393257
] |
<p>Can someone please explain what the <a href="http://en.wikipedia.org/wiki/Event_horizon" rel="nofollow">event horizon</a> of a black hole is? I mean is it the actual surface of the black hole or is it the point of no return where light can no longer escape?</p>
| 294 |
[
-0.018634123727679253,
-0.059312380850315094,
0.011829751543700695,
-0.04459000006318092,
0.021015409380197525,
0.013761949725449085,
-0.02116050384938717,
-0.04673220217227936,
-0.04843900352716446,
-0.01162736490368843,
0.023641737177968025,
0.041732463985681534,
0.032715678215026855,
0.004314260091632605,
-0.013635121285915375,
0.023926906287670135,
0.002293080324307084,
-0.00009312824113294482,
-0.016990775242447853,
-0.04388376325368881,
0.0013774874387308955,
-0.008510529063642025,
-0.0018062368035316467,
0.010152217000722885,
-0.03644634410738945,
0.0011142196599394083,
0.037543971091508865,
0.012662583030760288,
0.02923322096467018,
0.05034642666578293,
-0.019283529371023178,
-0.04582134261727333,
-0.01660044677555561,
0.0015151993138715625,
-0.010945607908070087,
-0.000820312590803951,
0.0018553368281573057,
-0.021064063534140587,
-0.03363887593150139,
-0.006189070176333189,
-0.018861010670661926,
-0.012889151461422443,
0.014571947045624256,
0.056106746196746826,
-0.045509763062000275,
-0.030024413019418716,
-0.005338470451533794,
-0.02969709038734436,
0.011148858815431595,
-0.06170537322759628,
0.05083223059773445,
-0.021605635061860085,
0.03152951970696449,
-0.012137707322835922,
0.023733487352728844,
0.02860078774392605,
0.0799831822514534,
0.06188381835818291,
-0.03803849592804909,
-0.05065636336803436,
-0.024346398189663887,
0.015511794947087765,
-0.0018630103440955281,
-0.015320216305553913,
-0.010113807395100594,
0.04252913221716881,
-0.005874574650079012,
-0.03222474455833435,
0.04808713123202324,
0.01107013039290905,
-0.009034689515829086,
0.024536987766623497,
-0.010022359900176525,
-0.015743011608719826,
0.02023984119296074,
-0.07019513845443726,
0.021356893703341484,
-0.00903026107698679,
0.012487857602536678,
0.0513310581445694,
0.0043916660360991955,
0.001196772325783968,
0.05300989747047424,
0.008522911928594112,
0.023849865421652794,
0.02269376441836357,
0.10484504699707031,
-0.0021353154443204403,
0.011593339964747429,
0.014940434135496616,
-0.0217708982527256,
0.010606939904391766,
-0.00405158894136548,
-0.036496859043836594,
-0.0302958432585001,
0.024138854816555977,
0.007306779734790325,
0.0693696066737175,
-0.018572784960269928,
-0.03861222043633461,
0.00504085561260581,
0.037012193351984024,
0.008226705715060234,
0.05215790495276451,
0.015103806741535664,
-0.018369290977716446,
-0.08306079357862473,
0.036188848316669464,
-0.01316873449832201,
-0.010855474509298801,
-0.04370104894042015,
0.028573960065841675,
-0.007184233516454697,
0.0015165217919275165,
0.04607555642724037,
-0.04736219719052315,
0.025755921378731728,
0.009307701140642166,
0.029364416375756264,
0.06902514398097992,
0.032148513942956924,
-0.04079090431332588,
0.013361502438783646,
0.002772097708657384,
-0.05670034512877464,
0.018725086003541946,
0.07145031541585922,
-0.011819693259894848,
-0.03492055833339691,
0.006231747567653656,
-0.023697229102253914,
0.0011277281446382403,
0.03906826674938202,
0.010604679584503174,
0.041747063398361206,
-0.03406751528382301,
-0.08857857435941696,
-0.07777715474367142,
0.03875183314085007,
-0.012128837406635284,
-0.028811195865273476,
-0.04190836474299431,
0.018420087173581123,
0.023912403732538223,
0.06481374800205231,
0.013120867311954498,
-0.001979852793738246,
0.008896560408174992,
0.02346125617623329,
-0.011713135987520218,
-0.01192715484648943,
0.021270209923386574,
-0.002768965670838952,
-0.033299416303634644,
0.010543815791606903,
-0.07153013348579407,
0.00642945384606719,
0.045238226652145386,
-0.0006712276954203844,
-0.07876252382993698,
0.07917112112045288,
-0.013095078058540821,
-0.009198177605867386,
0.04206548258662224,
-0.03703823313117027,
-0.012589067220687866,
0.10363814979791641,
0.027448659762740135,
-0.009914309717714787,
0.06911149621009827,
0.03447726368904114,
0.04488582909107208,
0.022363455966114998,
0.03146691992878914,
0.014063824899494648,
-0.030506707727909088,
-0.018774788826704025,
-0.038875628262758255,
0.02305499091744423,
0.01286192424595356,
-0.04320666939020157,
-0.030068671330809593,
0.015325004234910011,
0.001213724142871797,
0.0014009315054863691,
0.04334316775202751,
-0.028646880760788918,
-0.04932183399796486,
-0.0006069012451916933,
-0.03762926161289215,
-0.022467855364084244,
-0.044644374400377274,
0.0242602676153183,
-0.00823219958692789,
0.023699000477790833,
0.0034135624300688505,
0.009437449276447296,
0.020080236718058586,
-0.05833211541175842,
-0.003737970720976591,
0.008705716580152512,
0.056586332619190216,
0.0023262668401002884,
-0.026054540649056435,
-0.0034475177526474,
0.04502548649907112,
0.02451535128057003,
-0.012212254106998444,
-0.005406638607382774,
-0.01454771775752306,
0.0009420436108484864,
-0.015059306286275387,
0.00492193503305316,
0.01638437621295452,
-0.021759791299700737,
-0.008203528821468353,
0.006549646612256765,
0.02441595122218132,
0.03464346379041672,
0.01316151861101389,
-0.03264852985739708,
0.07316029071807861,
0.015857912600040436,
0.026236627250909805,
-0.013937772251665592,
0.0026082384865731,
-0.0019329411443322897,
0.0010562615934759378,
-0.007554561831057072,
0.011932438239455223,
-0.022457560524344444,
0.02140599675476551,
0.046868372708559036,
-0.008345192298293114,
-0.03411218523979187,
0.012819597497582436,
0.02201073430478573,
0.03306558355689049,
0.03985213860869408,
0.06451551616191864,
-0.0221580620855093,
0.012016398832201958,
0.009763614274561405,
-0.013114716857671738,
0.013454803265631199,
0.023386839777231216,
0.039329156279563904,
0.013396311551332474,
0.00641742255538702,
-0.02662445604801178,
-0.004383091814815998,
0.06691550463438034,
-0.04514509439468384,
-0.015247572213411331,
-0.008390574716031551,
-0.014600739814341068,
0.01984226517379284,
-0.03601383790373802,
0.02001439407467842,
-0.00024490265059284866,
-0.008444778621196747,
-0.015736380591988564,
-0.05852622911334038,
-0.009113255888223648,
0.01629473641514778,
0.024006124585866928,
-0.01630515046417713,
-0.0020631286315619946,
0.02852453850209713,
-0.03301331028342247,
0.04120079055428505,
-0.02897373028099537,
-0.014416824094951153,
-0.051639311015605927,
-0.00041027090628631413,
0.0210953988134861,
-0.007159873377531767,
0.02512737363576889,
0.0028903509955853224,
-0.06513378769159317,
0.007696875371038914,
-0.05208347365260124,
-0.017072472721338272,
0.013714528642594814,
-0.050178129225969315,
0.03525381535291672,
-0.03345765918493271,
-0.0339273065328598,
0.058399248868227005,
0.009407677687704563,
0.005271129310131073,
0.014448178000748158,
-0.04170446842908859,
-0.025496911257505417,
0.010541019029915333,
-0.024301445111632347,
0.007384369615465403,
-0.025054780766367912,
-0.004210713319480419,
0.04858697950839996,
-0.03633253276348114,
-0.007904679514467716,
0.03307896852493286,
-0.014845415018498898,
-0.05854596570134163,
-0.013331632129848003,
-0.003258558688685298,
0.026830194517970085,
-0.014402671717107296,
0.009912743233144283,
0.03758348524570465,
-0.07114340364933014,
0.033587370067834854,
-0.026056088507175446,
-0.04751558229327202,
0.03541380912065506,
-0.030191460624337196,
-0.020239844918251038,
-0.016725249588489532,
-0.02061687596142292,
0.05888931825757027,
0.02336246334016323,
-0.03549279645085335,
0.00642017787322402,
0.0001899568160297349,
-0.01780284382402897,
-0.026922008022665977,
-0.013813331723213196,
0.023605188354849815,
0.006936374586075544,
0.003357168985530734,
-0.0022941825445741415,
0.03307413309812546,
0.020748088136315346,
0.01353900320827961,
0.006543971598148346,
-0.029264375567436218,
-0.005268944893032312,
-0.006127360742539167,
0.04478750005364418,
0.01419429387897253,
-0.050448279827833176,
0.034552715718746185,
-0.012087083421647549,
0.046884361654520035,
0.008258908055722713,
-0.027612347155809402,
0.034586403518915176,
-0.018747512251138687,
0.01472336333245039,
-0.0029566192533820868,
0.007149376906454563,
-0.02165639027953148,
-0.0017755463486537337,
0.010481852106750011,
-0.011296944692730904,
0.043595653027296066,
-0.0033151654060930014,
-0.022612059488892555,
0.02455167844891548,
0.027250029146671295,
-0.06381383538246155,
-0.013327301479876041,
0.00014316278975456953,
-0.02155167981982231,
0.002566928043961525,
0.008160913363099098,
-0.033723101019859314,
0.0624757744371891,
0.024496624246239662,
0.02820255607366562,
0.012089096941053867,
-0.021234983578324318,
-0.012716029770672321,
-0.08521789312362671,
0.012391192838549614,
0.027570106089115143,
0.01573348045349121,
-0.011623579077422619,
0.04766538739204407,
0.016287196427583694,
0.02894158847630024,
0.027026280760765076,
0.0017548731993883848,
-0.10467525571584702,
-0.015657510608434677,
-0.06771308928728104,
-0.032152287662029266,
-0.038990043103694916,
-0.019864628091454506,
0.004906500224024057,
-0.005670187994837761,
-0.03418126702308655,
0.018921367824077606,
0.00986848957836628,
-0.06976954638957977,
0.01738274097442627,
-0.033626314252614975,
0.020466802641749382,
-0.016004180535674095,
0.024155382066965103,
0.04339947551488876,
0.04241478443145752,
-0.010460826568305492,
0.04604396969079971,
-0.009314673021435738,
-0.013820870779454708,
0.05150626599788666,
-0.00771612161770463,
-0.0007441072375513613,
0.04093252867460251,
0.043258361518383026,
-0.005322298966348171,
-0.013757710345089436,
0.012528539635241032,
0.01635458692908287,
0.02913231961429119,
-0.005599480587989092,
-0.02144680917263031,
-0.03209756314754486,
-0.046997763216495514,
-0.018700461834669113,
-0.033432427793741226,
0.0542539544403553,
-0.0267688799649477,
0.017216945067048073,
0.029385019093751907,
0.0004086907720193267,
0.0013302918523550034,
0.03567183017730713,
0.03442557156085968,
0.0037288435269147158,
-0.030930854380130768,
-0.06153285875916481,
-0.04615218564867973,
-0.029915107414126396,
0.01235941518098116,
0.022484153509140015,
0.01566452905535698,
-0.05088282376527786,
0.007002272177487612,
0.014577039517462254,
-0.015107394196093082,
-0.027411725372076035,
-0.02866406925022602,
0.010419092141091824,
0.009693778119981289,
-0.022446535527706146,
0.017037158831954002,
0.029519297182559967,
0.04089081659913063,
0.04028156399726868,
0.011760535649955273,
-0.005820774007588625,
-0.07893449068069458,
-0.020615380257368088,
0.03964018449187279,
0.0291209165006876,
0.010878344066441059,
-0.03477602079510689,
-0.08406494557857513,
0.01153225265443325,
0.033384185284376144,
-0.025282828137278557,
0.011363394558429718,
-0.010198215022683144,
0.028486082330346107,
0.001924695330671966,
0.014151366427540779,
0.03185195103287697,
0.033071160316467285,
-0.020501570776104927,
0.01615212857723236,
-0.01636260189116001,
0.029620982706546783,
-0.019424935802817345,
0.014352052472531796,
0.008431008085608482,
0.06472942233085632,
0.02340417355298996,
0.009410331025719643,
0.026952147483825684,
0.022739708423614502,
-0.018534112721681595,
-0.08573052287101746,
-0.03678790479898453,
0.03412092104554176,
-0.04789430648088455,
0.021037502214312553,
-0.0362015925347805,
-0.010649411007761955,
0.01285516656935215,
0.01705440692603588,
-0.01031431183218956,
0.024822214618325233,
-0.044805802404880524,
-0.007462589535862207,
0.03074820153415203,
-0.0169548150151968,
0.04193407669663429,
-0.004841956309974194,
0.014622826129198074,
-0.007984529249370098,
-0.039877865463495255,
0.048802074044942856,
-0.06302165240049362,
-0.008139612153172493,
-0.01119035854935646,
-0.014093498699367046,
-0.05095241963863373,
0.05990957096219063,
-0.006483366712927818,
0.006420780438929796,
-0.016416046768426895,
-0.027301285415887833,
-0.041963640600442886,
0.014616146683692932,
0.000036595185520127416,
0.004372903145849705,
0.0014587456826120615,
-0.0059827216900885105,
0.004831103608012199,
-0.04167044535279274,
0.0047735064290463924,
0.011611776426434517,
0.002593793673440814,
0.031407132744789124,
-0.0013747586635872722,
0.022730005905032158,
-0.00914287194609642,
-0.038529172539711,
0.053592998534440994,
-0.04311244189739227,
0.05219741538167,
-0.024580543860793114,
0.0022113528102636337,
0.027571948245167732,
-0.058350324630737305,
-0.031513605266809464,
-0.036083023995161057,
0.003118540858849883,
0.04143333435058594,
-0.06893257051706314,
0.059403736144304276,
0.05510041490197182,
0.030302276834845543,
-0.08760303258895874,
-0.04803425818681717,
0.06080992519855499,
0.013701102696359158,
-0.028514094650745392,
0.007877028547227383,
0.020179644227027893,
-0.05557537078857422,
-0.03077969327569008,
-0.026899399235844612,
0.016687683761119843,
-0.027076618745923042,
0.0046479287557303905,
0.010549464263021946,
-0.01245886366814375,
0.022087909281253815,
0.031889330595731735,
-0.03448281064629555,
0.017436837777495384,
0.018789056688547134,
0.016677187755703926,
-0.0218204315751791,
0.06831835210323334,
-0.010714243166148663,
-0.009479643777012825,
-0.037622272968292236,
-0.001786146778613329,
0.03438772261142731,
-0.006896907929331064,
0.06772923469543457,
0.029166195541620255,
0.04509810358285904,
-0.00516929617151618,
-0.030085595324635506,
0.010747869499027729,
-0.032593630254268646,
0.03291668742895126,
-0.007476435508579016,
-0.00448607187718153,
0.013228096067905426,
-0.04018722102046013,
0.04281649366021156,
0.008148233406245708,
0.016162611544132233,
0.00016994948964565992,
0.05720793455839157,
0.007061235141009092,
-0.0028426831122487783,
-0.04230072721838951,
-0.0452231764793396,
0.002410757588222623,
0.005213210359215736,
0.03338963910937309,
0.03577350080013275,
0.024390170350670815,
-0.01297987811267376,
-0.02192504331469536,
-0.032685622572898865,
0.009881487116217613,
0.06488701701164246,
-0.024471912533044815,
0.023451874032616615,
0.02660411037504673,
0.007663307245820761,
0.0017325124936178327,
-0.03676673397421837,
0.006701763719320297,
0.016807150095701218,
0.0023569867480546236,
0.002549919066950679,
-0.005114346276968718,
0.0006765026482753456,
0.014595739543437958,
0.0516909658908844,
-0.005153534468263388,
0.04338613525032997,
0.02231679856777191,
0.03742654621601105,
-0.0011255528079345822,
0.03799804672598839,
-0.03732796385884285,
0.01652248203754425,
-0.014956262893974781,
0.04577051103115082,
0.000018562821423984133,
0.012341496534645557,
0.040201544761657715,
-0.020518433302640915,
0.03443686664104462,
-0.03193645179271698,
-0.02675662189722061,
-0.042502228170633316,
0.018823988735675812,
-0.006529503036290407,
0.0031236784998327494,
-0.032802462577819824,
0.0009172173449769616,
-0.0036508573684841394,
-0.00847235880792141,
0.006735708564519882,
0.009894931688904762,
-0.058643046766519547,
-0.04618939384818077,
-0.03836233168840408,
-0.047399815171957016,
0.028218956664204597,
0.01998072676360607,
-0.02005705237388611,
0.012942757457494736,
-0.048847831785678864,
-0.02188718132674694,
0.012225055135786533,
0.06027941778302193,
-0.026116400957107544,
0.0728917270898819,
0.005017534364014864,
0.006666013039648533,
-0.01544143632054329,
-0.006192000117152929,
0.1013539656996727,
0.05988982319831848,
0.005747650749981403,
-0.08716559410095215,
-0.0031561492942273617,
-0.042546965181827545,
0.014620914123952389,
-0.03674190491437912,
0.023428743705153465,
-0.020246947184205055,
0.0268072709441185,
0.04673577845096588,
0.03823535889387131,
0.028522321954369545,
-0.0029255885165184736,
0.026581963524222374,
-0.020785626024007797,
-0.028839001432061195,
0.01921834982931614,
0.02764483354985714,
-0.025876590982079506,
0.037855569273233414,
-0.0419812873005867,
0.011272385716438293,
-0.015006914734840393,
0.001337630208581686,
-0.029049068689346313,
-0.017685580998659134,
0.03562050685286522,
0.0067757596261799335,
-0.033437635749578476,
-0.011248000897467136,
-0.0015545678324997425,
-0.00966634787619114,
-0.005593923851847649,
0.03831442818045616,
0.017842132598161697,
-0.0011143067386001348,
0.008565443567931652,
0.007389840669929981,
0.026478687301278114,
-0.014018691144883633,
-0.0034908377565443516,
0.010244827717542648,
-0.049034904688596725,
-0.004367067478597164,
-0.002978761214762926,
0.0254687387496233,
-0.016236118972301483,
0.028981029987335205,
-0.02381904423236847,
0.003540890524163842,
0.005467293318361044,
-0.04500789940357208,
-0.009754229336977005,
-0.016255615279078484,
-0.007301639765501022,
0.02034696191549301,
-0.04939408600330353,
-0.03882342204451561,
0.021074295043945312,
-0.010759055614471436,
0.041422199457883835,
0.003683989867568016,
0.029655134305357933,
0.022711647674441338,
-0.03126576170325279,
0.024471905082464218,
-0.02571079134941101,
-0.020177653059363365,
-0.005681296344846487,
-0.005904794670641422,
-0.06341080367565155,
0.004183492157608271,
0.006367370020598173,
0.021486181765794754,
0.0020970322657376528,
0.03733425214886665,
0.019882861524820328,
-0.00403827428817749,
-0.04267359897494316,
0.030572153627872467,
-0.025243233889341354,
-0.0692397877573967,
-0.024159887805581093,
0.00936655793339014,
0.037381626665592194,
0.014112919569015503,
0.002201396506279707,
0.006955923046916723,
-0.014876418747007847,
-0.002073985990136862,
-0.006575465202331543,
-0.0012520160526037216,
0.006235270295292139,
0.03329011797904968,
-0.014084074646234512,
-0.00572898518294096,
-0.016378303989768028,
0.04506286606192589,
0.034551266580820084,
-0.0019896633457392454,
0.009072241373360157,
0.004769023973494768,
-0.04343787208199501,
-0.0020272901747375727,
0.0164343174546957,
-0.021545108407735825,
-0.0016415577847510576,
0.014163942076265812,
0.02344266138970852,
-0.05440480262041092,
-0.02589823491871357,
-0.02704421989619732,
-0.004737894516438246,
-0.005477815866470337,
0.05403808504343033,
-0.017726244404911995,
0.009018348529934883,
0.01894502341747284,
0.02524675242602825,
-0.060788918286561966,
-0.016598178073763847,
-0.0545019693672657,
0.03544813022017479,
0.03957730531692505,
-0.013137087225914001,
-0.006136356852948666,
-0.007660885341465473,
0.005103139206767082,
-0.015223955735564232,
0.0007106791599653661,
0.029070641845464706,
-0.03184204548597336,
0.028562378138303757,
0.02020205371081829,
-0.019138101488351822,
0.04906989634037018,
0.005496603902429342,
-0.014222259633243084,
0.03082636184990406,
-0.05889493599534035,
-0.04621347412467003,
0.0462389811873436,
0.017863614484667778,
0.054109327495098114,
0.02441377565264702,
-0.025170715525746346,
-0.011339451186358929,
0.06678564846515656,
-0.02505192719399929,
-0.03666234388947487,
-0.01739451289176941,
-0.047072798013687134,
-0.031071297824382782,
0.018462488427758217,
0.018466616049408913,
-0.02341236174106598,
-0.008733482100069523,
0.022334357723593712,
-0.005612892564386129,
-0.02854008972644806,
-0.0042868065647780895,
0.0029101581312716007,
-0.010933882556855679,
0.009298502467572689,
-0.001548665575683117,
-0.00438795005902648,
0.02775276079773903,
0.0675063356757164,
-0.03116312064230442,
0.043155886232852936,
0.05577712133526802,
0.012041916139423847,
-0.06513788551092148,
-0.016345670446753502,
0.007910768501460552,
0.009347738698124886,
0.042278166860342026,
-0.044855549931526184,
0.047996941953897476,
0.04059695452451706,
-0.035534098744392395,
0.024373535066843033,
-0.02461368776857853,
-0.037951063364744186,
-0.03354334831237793,
0.010653739795088768,
0.012535595335066319,
0.05594458431005478,
0.053625836968421936,
0.04124138504266739,
-0.0030508225318044424,
-0.007032869849354029,
-0.01199528481811285,
-0.02926844172179699,
-0.003961178474128246,
0.04740474373102188,
-0.0278546754270792,
-0.02281620167195797,
0.0800027847290039,
0.010909387841820717,
-0.02135169692337513,
0.03346443548798561,
0.013560914434492588,
0.006171367131173611,
0.02481207437813282,
-0.007058780174702406,
0.009657085873186588,
-0.020470378920435905,
0.015499560162425041,
-0.030064014717936516,
-0.04134717211127281,
0.024095334112644196,
0.03074253536760807,
0.02445293217897415,
0.006808212958276272,
-0.005191893316805363,
0.00007407965313177556,
-0.045021239668130875,
-0.01917252689599991,
0.007779117673635483,
-0.011843672953546047,
-0.027904365211725235,
-0.027475997805595398,
0.0037347329780459404,
0.01508423313498497,
-0.04650190845131874,
-0.011837666854262352,
-0.06414160132408142,
-0.00850052759051323,
0.02611795999109745,
-0.0034180579241365194,
0.016914397478103638,
0.028582951053977013,
0.004100150428712368,
-0.0471784844994545,
0.011105257086455822,
-0.029054194688796997,
0.005978958681225777,
-0.037482429295778275,
0.02380886673927307,
0.012867826968431473,
-0.02815077267587185,
0.03441152349114418,
-0.017953718081116676,
-0.010213065892457962,
0.00266124214977026,
0.015102210454642773,
0.00539424316957593,
-0.0060090599581599236,
-0.06850862503051758,
-0.030949791893363,
-0.05619587376713753,
0.015459012240171432,
-0.009431367740035057,
-0.007848667912185192,
-0.04286036267876625,
-0.01612005941569805,
0.003906567115336657,
0.017056046053767204,
0.037014443427324295,
-0.03919098526239395,
0.0028599391225725412,
0.006948689930140972,
0.006176447961479425,
0.0016774064861238003,
-0.030134428292512894,
-0.014132720418274403,
-0.0032819483894854784,
-0.05526316538453102,
-0.007690662983804941,
0.0055247084237635136,
-0.03213021159172058,
0.03963033854961395,
0.05921582132577896,
0.012210789136588573,
0.08318206667900085,
-0.038941506296396255,
0.009851041249930859,
0.044763386249542236,
0.031971074640750885,
0.002630281262099743,
0.04603472352027893,
-0.025884481146931648,
0.013181558810174465,
0.0392228402197361,
-0.016561908647418022,
0.00931441131979227,
0.03030647151172161,
-0.009478873573243618,
0.00013785991177428514,
0.00849170982837677,
-0.0046703871339559555,
0.03789234161376953,
-0.058406710624694824,
-0.003377240151166916,
0.033277858048677444,
-0.026574531570076942,
-0.027061983942985535,
0.08696220815181732,
0.021454639732837677,
0.03624961897730827,
-0.03610353171825409,
-0.008910800330340862,
-0.007106378208845854,
0.0026360386982560158,
-0.00254814769141376,
0.04693090170621872,
0.0472722165286541,
-0.0115275289863348,
0.02573695220053196,
-0.005682724062353373,
-0.04379277676343918,
0.01978473924100399,
-0.023740608245134354,
0.05830444395542145,
-0.026437858119606972,
-0.04727967455983162,
-0.0022820441517978907,
-0.02885977178812027,
0.029476510360836983,
0.03387734293937683,
-0.022721052169799805,
0.0766654759645462,
-0.02352471463382244,
0.02087930589914322,
0.014906060881912708,
0.002998380921781063,
-0.03482910618185997,
0.02623331919312477,
0.02092205546796322,
0.05550793930888176,
0.029103824868798256,
-0.02254626527428627,
0.0026989516336470842,
0.015596263110637665,
0.042734574526548386,
-0.009555385448038578,
0.03187919780611992,
-0.012720598839223385,
-0.011442524380981922,
-0.01044014934450388,
-0.0097560565918684,
0.0060882861725986,
-0.022030120715498924,
-0.0030675216112285852,
0.013191931881010532,
0.0013042502105236053,
0.02492421492934227,
0.0019654352217912674,
-0.02159649319946766,
0.028869561851024628,
-0.06121331453323364,
0.013010374270379543,
-0.0034244582056999207,
0.04516657441854477,
-0.030533334240317345,
0.0057101682759821415
] |
<p>Consider a quantum system described by a <a href="http://physics.stackexchange.com/questions/4930/what-does-it-mean-for-a-hamiltonian-or-system-to-be-gapped-or-gapless"><em>gapped</em> Hamiltonian</a> $H_0$ with <em>degenerate</em> ground states (GS), adding a perturbation term $V$ to $H_0$, then the low-energy physics can be described by an <em>effective Hamiltonian</em> $H_{eff}$ acting within the GS subspace of $H_0$, where $H_{eff}$ can be calculated from <strong>degenerate perturbation theory</strong>.</p>
<p>What if the GS degeneracy of $H_0$ is a <strong>topological degeneracy</strong> ? </p>
<p>I learned that <a href="http://physics.stackexchange.com/questions/70728/reconciling-topological-insulators-and-topological-order/72241#72241">the topological degeneracy is robust against ANY local perturbations</a>. Does this imply that: if the above $H_0$ describes a topologically ordered system defined on a torus with a topological GS degeneracy, and $V$ represents ANY local perturbations, then would the resulting <em>effective Hamiltonian</em> $H_{eff}$ be always trivial (i.e., $H_{eff}=$constant number) ??</p>
<p>And in the opposite case, if we find $H_{eff}$ (corresponding to ANY local perturbations $V$) is a constant number <em>at any finite order</em> from a degenerate perturbation theory calculation, then does this imply that $H_0$ describes a topologically ordered system??</p>
<p>Of course, for a finite system, $H_{eff}$ is usually NOT a constant number. All the above we talk about is in the thermodynamic limit.</p>
<p>Thanks a lot.</p>
| 8,877 |
[
-0.03523387759923935,
-0.00032835773890838027,
0.03379951789975166,
-0.023028908297419548,
0.0501900315284729,
0.019019480794668198,
-0.015610847622156143,
-0.03256138041615486,
0.050011470913887024,
-0.05333761125802994,
0.004534304141998291,
-0.0002123576559824869,
0.016960011795163155,
0.02961888536810875,
0.0004884679219685495,
0.024608202278614044,
-0.006778568960726261,
-0.0450722873210907,
-0.03223256394267082,
0.000012870857062807772,
0.017496995627880096,
0.03186524659395218,
0.02066834643483162,
0.005351726897060871,
-0.02719019167125225,
-0.008982373401522636,
0.006053929682821035,
0.017742842435836792,
-0.001944505493156612,
0.0753386989235878,
-0.03398548439145088,
0.002593999495729804,
0.007929493673145771,
0.008787817321717739,
-0.014750955626368523,
0.026155108585953712,
-0.008854140527546406,
-0.032284483313560486,
0.008116668090224266,
-0.010006616823375225,
-0.025664987042546272,
-0.017492976039648056,
-0.021708138287067413,
0.06670770794153214,
-0.003657386638224125,
-0.009984221309423447,
-0.0022616207133978605,
-0.010973349213600159,
0.04651021212339401,
-0.03551234304904938,
0.007585042621940374,
-0.020123660564422607,
0.006089657545089722,
0.03558005020022392,
0.0022984512615948915,
-0.023729506880044937,
0.06660318374633789,
0.09151826798915863,
-0.013459236361086369,
-0.055969640612602234,
-0.01824369840323925,
-0.05279438942670822,
-0.012021609582006931,
-0.01990063302218914,
-0.016415338963270187,
0.03297913819551468,
0.03437253087759018,
-0.023370010778307915,
0.02948114089667797,
-0.006296596955507994,
-0.008999628946185112,
-0.03465430811047554,
-0.0026418063789606094,
-0.04273615777492523,
0.05010836198925972,
-0.01187984086573124,
-0.004959898069500923,
0.0123444814234972,
-0.0023657451383769512,
0.05940813198685646,
-0.017945097759366035,
-0.006224374752491713,
0.02442314475774765,
0.02498004585504532,
0.005574362352490425,
0.001326366444118321,
0.057309046387672424,
-0.03624876216053963,
-0.021866047754883766,
0.04097440838813782,
-0.009951964020729065,
-0.01035603228956461,
0.019081061705946922,
-0.0363931730389595,
0.009948979131877422,
0.030499210581183434,
0.02957487292587757,
0.03924364596605301,
-0.04148995503783226,
0.020402692258358,
-0.0054328530095517635,
-0.0333351269364357,
0.02917727828025818,
0.06592737883329391,
0.009220600128173828,
-0.015594546683132648,
-0.0308523029088974,
0.023398717865347862,
-0.04161553084850311,
-0.035168904811143875,
-0.0436563715338707,
0.025292135775089264,
-0.004002574365586042,
-0.011777551844716072,
-0.04702134430408478,
-0.008149074390530586,
-0.0002703143109101802,
-0.03671066090464592,
0.052696485072374344,
0.07410372793674469,
0.04372493177652359,
0.01369976531714201,
0.025386808440089226,
-0.04911641404032707,
-0.06804303079843521,
-0.015207049436867237,
0.056804608553647995,
0.014198455959558487,
-0.029812145978212357,
0.01417907327413559,
0.012683950364589691,
-0.007664847653359175,
0.002733405213803053,
-0.003178900107741356,
0.03825003653764725,
-0.0012431934010237455,
-0.11478403210639954,
-0.020036838948726654,
0.04634242132306099,
-0.0039675249718129635,
-0.030114343389868736,
-0.03806068003177643,
-0.004778008442372084,
0.012515897862613201,
0.031001295894384384,
0.0012884250609204173,
0.0009834266966208816,
0.024687331169843674,
0.05904091149568558,
0.035796865820884705,
-0.01725919358432293,
-0.013582982122898102,
0.008893970400094986,
-0.07155381888151169,
-0.009910685010254383,
-0.03900103643536568,
0.0497492216527462,
0.0425029881298542,
-0.004245373420417309,
0.008589229546487331,
0.07403001189231873,
0.010129746049642563,
0.004172984044998884,
-0.0016559972427785397,
0.013754809275269508,
0.011858731508255005,
0.07031478732824326,
-0.016264183446764946,
0.03753882274031639,
0.043218739330768585,
-0.022799232974648476,
-0.009389909915626049,
-0.012343330308794975,
0.007168085314333439,
0.018863024190068245,
-0.009144559502601624,
-0.004013579338788986,
-0.05568399652838707,
-0.025480277836322784,
0.0052694459445774555,
-0.04953029751777649,
-0.018973704427480698,
-0.016660017892718315,
0.018798546865582466,
-0.0025246040895581245,
0.035458147525787354,
0.004852702375501394,
-0.0005823064129799604,
0.0018460816936567426,
-0.04821090027689934,
-0.042554259300231934,
-0.05917910486459732,
-0.0037551438435912132,
0.008371841162443161,
0.02290862612426281,
0.06722117215394974,
0.013331159017980099,
-0.02794252336025238,
-0.01834147423505783,
-0.0336247980594635,
-0.010905473493039608,
0.0311583299189806,
0.010679611004889011,
-0.016468597576022148,
0.062226761132478714,
0.02063244767487049,
0.04552081972360611,
-0.0029914071783423424,
0.052589572966098785,
-0.01135182473808527,
-0.059924669563770294,
0.01907975599169731,
-0.0304851233959198,
0.06026170775294304,
-0.007023207377642393,
0.007056800648570061,
0.0029374577570706606,
-0.007509590592235327,
-0.025623980909585953,
0.014910407364368439,
-0.04607345163822174,
0.028658641502261162,
0.03196125105023384,
0.022241489961743355,
0.019912559539079666,
0.04501435533165932,
-0.018062900751829147,
0.02002820000052452,
-0.011366498656570911,
-0.004406900145113468,
-0.08142215013504028,
-0.004806641023606062,
0.0639360249042511,
0.054065216332674026,
-0.022761408239603043,
-0.0024256559554487467,
0.007300292607396841,
0.026600077748298645,
0.022212913259863853,
0.017481792718172073,
-0.03381752967834473,
-0.009543697349727154,
0.044753532856702805,
0.006038768216967583,
0.005313012283295393,
0.01352159958332777,
-0.01839827373623848,
0.015400334261357784,
0.019918857142329216,
0.020366176962852478,
0.03250419721007347,
0.05522652342915535,
-0.01699753850698471,
-0.027472257614135742,
-0.023624997586011887,
-0.02094540186226368,
0.021117093041539192,
-0.012976027093827724,
0.043628305196762085,
0.010281214490532875,
-0.03173793479800224,
0.037211183458566666,
-0.0376136340200901,
-0.03225028142333031,
0.02027955837547779,
-0.024714050814509392,
-0.05406427010893822,
0.003925090190023184,
0.02563835121691227,
-0.026975730434060097,
-0.00045363596291281283,
-0.065558522939682,
0.0182487815618515,
-0.01993715576827526,
-0.0007329885265789926,
0.03635202348232269,
0.005263668019324541,
0.01962924748659134,
-0.0452510230243206,
-0.005669709295034409,
0.045985449105501175,
-0.029755515977740288,
0.036551397293806076,
0.03429218381643295,
-0.020660288631916046,
-0.0029907559510320425,
-0.044219862669706345,
-0.02093060314655304,
0.03655709698796272,
-0.0029253121465444565,
-0.008102786727249622,
0.034776974469423294,
0.014605852775275707,
-0.04848220944404602,
-0.015451502054929733,
-0.01278426218777895,
0.02338004857301712,
-0.05532391369342804,
0.0013053352013230324,
0.04498182237148285,
0.015086537227034569,
-0.04967271909117699,
0.0026948186568915844,
0.020181328058242798,
-0.031426142901182175,
0.02446388266980648,
-0.03485571965575218,
0.009887471795082092,
-0.01971827819943428,
0.02062816172838211,
0.014541459269821644,
-0.009469292126595974,
-0.010046633891761303,
-0.07474147528409958,
-0.0445566289126873,
-0.005399277899414301,
-0.03342705965042114,
0.050197772681713104,
-0.013841094449162483,
-0.03362376242876053,
0.11238346993923187,
0.004364667925983667,
-0.024125857278704643,
0.006624577566981316,
-0.053400371223688126,
0.01585477963089943,
-0.0043945289216935635,
0.012745533138513565,
0.022753391414880753,
0.04373674839735031,
0.024158481508493423,
0.03253461420536041,
0.05687950178980827,
0.019962908700108528,
0.007599321659654379,
-0.002859157044440508,
-0.007237977348268032,
0.03465520963072777,
-0.01892249472439289,
0.06320595741271973,
-0.007903496734797955,
0.0033286018297076225,
-0.000373661721823737,
-0.019368384033441544,
0.04001639783382416,
0.038888201117515564,
-0.06022445484995842,
0.06034974753856659,
-0.007585577666759491,
0.020031537860631943,
0.011509587988257408,
0.054605524986982346,
0.036143336445093155,
-0.035509511828422546,
-0.013036790303885937,
0.00707283103838563,
0.029018187895417213,
0.00047355209244415164,
-0.00512665044516325,
0.05553530156612396,
0.036457743495702744,
-0.013061094097793102,
0.00174229615367949,
0.024530110880732536,
0.023852499201893806,
0.006277117878198624,
-0.035866864025592804,
-0.020314248278737068,
0.03339188173413277,
0.05408533290028572,
0.0018525334307923913,
-0.01699964329600334,
-0.04906207323074341,
0.005002783611416817,
-0.055474281311035156,
-0.012154740281403065,
-0.02128734067082405,
0.04094785824418068,
-0.017168764024972916,
0.020358579233288765,
0.016068337485194206,
-0.014655934646725655,
-0.03574669361114502,
-0.001043720287270844,
-0.060322921723127365,
-0.006402919534593821,
-0.021664194762706757,
-0.014813799411058426,
0.014347298070788383,
-0.002697427524253726,
0.022810861468315125,
0.019258039072155952,
-0.04130358248949051,
-0.039310477674007416,
0.01740245334804058,
-0.02513822354376316,
0.016857752576470375,
-0.03207823261618614,
-0.06642880290746689,
-0.03337571769952774,
0.026969250291585922,
0.06233665347099304,
-0.024312932044267654,
0.006930684205144644,
-0.010671346448361874,
-0.03435315936803818,
0.012193671427667141,
-0.028175080195069313,
0.014516700990498066,
0.024813221767544746,
0.04090673103928566,
0.012717895209789276,
0.05340835452079773,
0.02188766747713089,
-0.037824999541044235,
0.03080034628510475,
0.07389380037784576,
0.0020860417280346155,
-0.016899222508072853,
0.026513205841183662,
-0.018850503489375114,
-0.022234462201595306,
0.007110809441655874,
0.0877685546875,
-0.010725856758654118,
0.01747368648648262,
0.0170570220798254,
0.020177410915493965,
-0.047457415610551834,
0.04998099431395531,
0.002409726846963167,
0.030878892168402672,
-0.015478518791496754,
-0.0473778173327446,
-0.008004862815141678,
-0.025478631258010864,
0.006433908361941576,
-0.012938699685037136,
-0.025451701134443283,
-0.015387646853923798,
0.023645350709557533,
-0.002137481002137065,
0.03154275566339493,
-0.021108156070113182,
-0.005972495302557945,
0.0022727451287209988,
0.004443100653588772,
-0.011973568238317966,
0.006158896721899509,
-0.018214108422398567,
0.025582335889339447,
0.044961486011743546,
-0.0021298364736139774,
0.02755994163453579,
-0.09843237698078156,
-0.05648010969161987,
0.0669608935713768,
0.022463202476501465,
0.023630410432815552,
-0.03684904798865318,
-0.07959767431020737,
-0.011441566981375217,
0.05529080703854561,
-0.000518582935910672,
0.05180706828832626,
-0.009184008464217186,
-0.04216925799846649,
-0.037154216319322586,
-0.06758719682693481,
-0.007616536691784859,
0.01950857788324356,
0.01969980262219906,
0.025361210107803345,
-0.008539293892681599,
0.008660526014864445,
-0.017585091292858124,
-0.009891591966152191,
0.014471360482275486,
0.05706433206796646,
-0.007575491908937693,
0.004879498854279518,
0.011638653464615345,
0.0006444592727348208,
-0.014713253825902939,
-0.08192668110132217,
0.03959756717085838,
0.04230600595474243,
0.024632586166262627,
0.03152449429035187,
-0.0373523011803627,
-0.03048081509768963,
0.02080421708524227,
0.018266398459672928,
-0.0024589679669588804,
0.02147950604557991,
0.0011964284349232912,
0.11886990070343018,
0.04507432505488396,
-0.007117054425179958,
0.0437781922519207,
0.0499156154692173,
-0.007565855514258146,
-0.004765793215483427,
-0.010115020908415318,
0.005620007868856192,
-0.05218740180134773,
0.016044609248638153,
-0.03015044517815113,
-0.003035825677216053,
-0.052124544978141785,
0.040946755558252335,
-0.01882822997868061,
0.006819094531238079,
0.022367270663380623,
-0.014709094539284706,
-0.002620257204398513,
0.009723298251628876,
-0.008104302920401096,
-0.031227029860019684,
0.015902884304523468,
0.022786619141697884,
0.038164734840393066,
0.0007556352065876126,
0.04548044875264168,
-0.0032219081185758114,
0.029085125774145126,
0.050281450152397156,
-0.02328174002468586,
0.013010954484343529,
-0.054188322275877,
-0.0282040573656559,
-0.008795059286057949,
-0.06278932094573975,
0.06706984341144562,
-0.004419646225869656,
-0.01245367992669344,
-0.007461416535079479,
-0.016035547479987144,
-0.046248048543930054,
0.004194329492747784,
-0.004203487187623978,
-0.03293447569012642,
-0.01447545550763607,
0.02089976705610752,
0.03706759214401245,
-0.02477281540632248,
-0.08088074624538422,
-0.009023706428706646,
0.024413641542196274,
0.022593751549720764,
-0.013799021020531654,
-0.02944895438849926,
-0.016908923164010048,
0.002441828139126301,
-0.005857410375028849,
0.009304305538535118,
0.02173231914639473,
-0.06760917603969574,
0.03259732574224472,
0.03914804384112358,
0.023340348154306412,
0.04532061517238617,
0.011589684523642063,
-0.015124416910111904,
0.01202593557536602,
-0.03245222941040993,
0.028776779770851135,
0.023870643228292465,
0.031794484704732895,
-0.03020874783396721,
-0.004954703617841005,
-0.01601756364107132,
-0.006358637940138578,
0.017575019970536232,
0.009858079254627228,
-0.04169643297791481,
0.036408837884664536,
-0.01155107282102108,
0.015216859988868237,
-0.022102896124124527,
-0.009882311336696148,
-0.01890958473086357,
0.015134752728044987,
0.031783584505319595,
-0.009188003838062286,
-0.026028623804450035,
-0.03609863296151161,
-0.00017005061090458184,
0.0002893292985390872,
-0.04578235372900963,
-0.0016477491008117795,
0.06317342817783356,
-0.018188759684562683,
-0.00216104369610548,
0.03150874003767967,
-0.06138048321008682,
-0.0014377408660948277,
-0.026715565472841263,
0.0068922690115869045,
0.004039177671074867,
0.006782872136682272,
-0.03657425194978714,
-0.05598585307598114,
-0.05452945455908775,
0.008597072213888168,
0.021592585369944572,
0.012822483666241169,
-0.0008713084971532226,
0.006721986457705498,
-0.01982245407998562,
-0.01885136030614376,
-0.013898087665438652,
-0.01298531610518694,
-0.004147620406001806,
-0.0026962116826325655,
-0.007896317169070244,
-0.03351152315735817,
-0.02076430432498455,
0.042269375175237656,
0.06778296828269958,
-0.0844266265630722,
0.020888153463602066,
0.06616917252540588,
0.0028876131400465965,
0.012337340973317623,
-0.023409459739923477,
-0.04488109052181244,
0.055045776069164276,
-0.06310002505779266,
0.03651777282357216,
0.02032649517059326,
-0.026313820853829384,
0.023725826293230057,
0.03262149542570114,
0.02724645473062992,
-0.034842126071453094,
-0.02410423383116722,
-0.03521421179175377,
0.0654594749212265,
-0.026304416358470917,
0.009133124724030495,
0.009744997136294842,
-0.003503331681713462,
0.011490796692669392,
-0.024132896214723587,
0.0022037713788449764,
-0.022774826735258102,
-0.03455124795436859,
-0.008521458134055138,
-0.026807738468050957,
-0.03875137120485306,
0.016247371211647987,
0.010180259123444557,
-0.043588120490312576,
0.027296366170048714,
-0.04736055061221123,
0.024268804118037224,
0.001034087035804987,
0.021039526909589767,
-0.031601570546627045,
0.05077584087848663,
-0.0025310262572020292,
0.032412439584732056,
0.02409992553293705,
-0.026884272694587708,
0.1371106505393982,
0.06378588825464249,
0.013594693504273891,
-0.06506554782390594,
0.0027250282000750303,
0.03278012201189995,
0.034427039325237274,
-0.017182670533657074,
-0.012785482220351696,
0.017768897116184235,
0.008224829100072384,
-0.017959432676434517,
0.04503704607486725,
-0.0021183642093092203,
0.0014869788428768516,
0.05073675885796547,
-0.03164685145020485,
-0.015174764208495617,
-0.014529111795127392,
0.01750859059393406,
0.013125615194439888,
0.01581401750445366,
0.005700630135834217,
-0.00830476637929678,
0.004309145268052816,
0.03048781491816044,
-0.02951335534453392,
-0.008989755995571613,
0.024281220510601997,
0.015308091416954994,
-0.05860916152596474,
-0.0005281149642542005,
-0.02045396715402603,
-0.008424784056842327,
-0.033632002770900726,
-0.014879168011248112,
0.020263414829969406,
0.02196931652724743,
0.0374513603746891,
0.03304346650838852,
-0.040178246796131134,
-0.010130095295608044,
0.01241085771471262,
-0.0034977481700479984,
-0.05309699848294258,
0.004092888906598091,
-0.024331187829375267,
0.034076109528541565,
-0.000812308513559401,
0.012249630875885487,
-0.005722350440919399,
-0.026999814435839653,
0.004112095572054386,
-0.018154187127947807,
0.00318583520129323,
-0.009630491025745869,
0.039871376007795334,
-0.02410603128373623,
-0.049854543060064316,
-0.005433870013803244,
0.01969338022172451,
-0.025072304531931877,
0.0033908244222402573,
-0.02945532649755478,
-0.03125743940472603,
0.006815943401306868,
-0.011001567356288433,
0.019957374781370163,
0.020043358206748962,
0.0021471905056387186,
-0.005413935519754887,
-0.0212184339761734,
-0.045507531613111496,
-0.04060376435518265,
-0.006579789333045483,
0.007657148875296116,
0.05326823517680168,
0.011896317824721336,
0.0008425607811659575,
0.0013354670954868197,
-0.0552397146821022,
0.01909615471959114,
-0.011730099096894264,
-0.025090577080845833,
-0.011753324419260025,
0.00236335676163435,
0.007158010732382536,
0.06366972625255585,
-0.029971042647957802,
-0.0017676298739388585,
0.03346364200115204,
0.03285544365644455,
0.018453016877174377,
0.004099072422832251,
-0.005619090050458908,
0.010006570257246494,
-0.040376804769039154,
-0.003975168336182833,
0.009598401375114918,
-0.001548893516883254,
0.01381266862154007,
-0.009325622580945492,
-0.012136123143136501,
0.03032843768596649,
0.029161684215068817,
-0.009149442426860332,
0.026356322690844536,
-0.03718288242816925,
0.023994997143745422,
0.04065564274787903,
0.03915620595216751,
-0.03496429696679115,
-0.04252012446522713,
-0.0004100600490346551,
-0.03445705771446228,
0.009254580363631248,
0.0222941767424345,
-0.030894232913851738,
0.0034750078339129686,
-0.0080989059060812,
0.03318480774760246,
-0.05750695988535881,
-0.031861305236816406,
-0.01921505481004715,
0.011246021836996078,
0.0018591092666611075,
-0.0017652151873335242,
0.0459403470158577,
0.04431388899683952,
-0.0015248009003698826,
-0.02809549681842327,
0.05882015451788902,
0.04708528518676758,
-0.01420240756124258,
0.01459843572229147,
0.012493561953306198,
-0.003700830275192857,
0.030653730034828186,
0.01589600183069706,
-0.04504614323377609,
0.020552026107907295,
-0.033177781850099564,
-0.03341732919216156,
0.001202594954520464,
0.007095897104591131,
0.004613679368048906,
0.023956406861543655,
-0.033776577562093735,
-0.013523426838219166,
0.0061991396360099316,
-0.015160231851041317,
-0.006923339329659939,
-0.014541386626660824,
-0.0021959873847663403,
-0.028005434200167656,
-0.03639984503388405,
0.024140024557709694,
0.018253814429044724,
0.017607027664780617,
0.00032759501482360065,
0.015780983492732048,
-0.0141123216599226,
-0.01751674711704254,
-0.020811500027775764,
-0.022368373349308968,
0.017076412215828896,
-0.009297453798353672,
0.007685989141464233,
-0.033400628715753555,
0.0462973527610302,
-0.02643032930791378,
0.03043641522526741,
0.005619246978312731,
0.0332823246717453,
-0.10209601372480392,
-0.004626536276191473,
0.004418333526700735,
0.02270195633172989,
0.035513896495103836,
-0.003293431829661131,
0.03178659453988075,
0.029559576883912086,
-0.06723230332136154,
0.05657139793038368,
0.0013040369376540184,
0.03776402026414871,
-0.037116069346666336,
-0.007882455363869667,
-0.04658817872405052,
0.03379087895154953,
0.027108967304229736,
0.0346858911216259,
0.007615933660417795,
0.01928742043673992,
-0.04504384845495224,
-0.017614590004086494,
0.0016022479394450784,
0.023038841784000397,
-0.024386359378695488,
-0.03835576772689819,
0.039754416793584824,
-0.01770373247563839,
-0.029181165620684624,
-0.018935656175017357,
0.003972571808844805,
-0.027448434382677078,
-0.011338064447045326,
0.012392275035381317,
0.010569654405117035,
0.004659050144255161,
0.0033489542547613382,
0.012785197235643864,
-0.022940881550312042,
0.007897001691162586,
-0.010164286941289902,
0.05935870110988617,
-0.015220577828586102,
0.0026652002707123756,
0.035578999668359756,
-0.02503989264369011,
-0.035959642380476,
0.05294468626379967,
-0.031748369336128235,
0.0028589440044015646,
0.00043107796227559447,
0.01445885468274355,
0.006389454938471317,
-0.020212559029459953,
-0.0034110078122466803,
-0.03085382841527462,
-0.02754686400294304,
0.008540569804608822,
0.019166672602295876,
-0.0003313079650979489,
0.02337999828159809,
-0.007250661961734295,
-0.02415144257247448,
0.042332518845796585,
-0.006138728465884924,
0.001588407438248396,
-0.05326542258262634,
-0.04203280434012413,
-0.018251517787575722,
0.05201185122132301,
-0.024178607389330864,
-0.033101558685302734,
-0.032695915549993515,
0.033139292150735855,
-0.00794006884098053,
0.023318715393543243,
-0.06330636888742447,
-0.05061175301671028,
-0.016124052926898003,
-0.03476954251527786,
0.0008424990228377283,
0.006285684183239937,
0.008940300904214382,
-0.026221035048365593,
0.0011465552961453795,
0.0035051030572503805,
0.00904170423746109,
0.015696801245212555,
0.02333194948732853,
-0.021128440275788307,
0.048996806144714355,
0.004261550959199667,
0.03725947439670563,
-0.013193546794354916,
0.006748195271939039,
-0.006669093854725361,
0.007875535637140274,
0.018688395619392395,
-0.0055037918500602245,
-0.05737122893333435,
0.03503106161952019,
0.03173847496509552,
0.017085490748286247,
0.009532010182738304,
-0.007534099277108908,
-0.03833308070898056,
0.0780852660536766,
-0.0038497091736644506,
0.011401706375181675,
0.08581902086734772,
0.015717733651399612,
0.014978932216763496,
0.010576358996331692,
-0.008069485425949097,
-0.0035257411655038595,
-0.012172657996416092,
-0.06614881753921509,
-0.043567072600126266,
0.00018850098422262818,
-0.014147832989692688,
0.021221568807959557,
-0.04147476702928543,
0.015649668872356415,
0.04395418241620064,
-0.012630607932806015,
-0.024573635309934616,
0.04387625679373741,
0.010658820159733295,
0.040964946150779724,
0.010976774618029594,
-0.0014858286594972014,
0.013679695315659046,
-0.02121989242732525,
-0.002006819238886237,
0.05610183626413345,
0.02580736018717289,
-0.0014919992536306381,
0.02319382131099701,
0.007513365242630243,
0.005779937840998173,
0.03672739490866661,
-0.005325289908796549,
-0.0006604744121432304,
-0.01565917208790779,
-0.015042698942124844,
0.0606410875916481,
-0.0021728784777224064,
-0.015758590772747993,
0.045281268656253815,
-0.022523468360304832,
0.07278335094451904,
0.01576230488717556,
-0.024351539090275764,
-0.03847258910536766,
0.0006922525353729725,
0.0048061260022223,
-0.0008076793747022748,
0.0009731237078085542,
0.04090511053800583,
-0.019741619005799294,
0.01534304954111576,
-0.023268135264515877,
0.028741100803017616,
-0.008870052173733711,
-0.051748547703027725,
0.02320808731019497,
0.04400353133678436,
0.005347453057765961,
-0.008917710743844509,
-0.021296784281730652,
-0.027713172137737274,
0.0030525922775268555,
0.0025430587120354176,
0.022320514544844627,
-0.015582907013595104,
-0.0182885080575943,
-0.043569017201662064,
-0.06215737387537956,
0.07173184305429459,
-0.025289354845881462,
0.010357571765780449,
-0.043136514723300934,
-0.03274556249380112,
-0.03124193288385868,
-0.04466189444065094
] |
<p>I understand mass and energy are the same, but in this question I will be talking about mass being turned into usable energy (electricity/heat/etc). We can make our energy through chemical reactions like burning coal. We can also make energy from nuclear decay (and soon the fusion) of atoms. </p>
<p>But is there any know way to take subnuclear particles and turn them into energy? How about quarks and other particles that make up protons/neutrons/electrons? </p>
<p>More specifically, I have heard (and know little) about Quantum Field Theory. Do we know any way to take the energy form an excited field of, lets say a quark and transfer it into the electron field?</p>
<p>I hope this is not a silly question and thanks.</p>
| 8,878 |
[
0.021206827834248543,
-0.03610729053616524,
0.004211668390780687,
-0.04196999594569206,
0.00619869027286768,
-0.01191689446568489,
-0.037870585918426514,
-0.05114316940307617,
0.027604326605796814,
-0.03397111967206001,
0.011862090788781643,
0.014071948826313019,
0.03888988867402077,
-0.017154905945062637,
-0.00013122070231474936,
0.03157668188214302,
-0.015492905862629414,
-0.01912764087319374,
-0.006587068550288677,
-0.03164457157254219,
0.015567847527563572,
0.012542267329990864,
-0.011722024530172348,
0.020991872996091843,
-0.001961696660146117,
0.03667037934064865,
0.03754555433988571,
0.027907371520996094,
0.0050683654844760895,
0.07210026681423187,
0.0440940335392952,
-0.05550775304436684,
0.026996390894055367,
0.027959413826465607,
0.009134408086538315,
-0.000707563478499651,
-0.031488724052906036,
-0.05242009088397026,
0.020551420748233795,
0.0019342016894370317,
-0.03909742832183838,
-0.034359924495220184,
-0.0035668215714395046,
0.048553742468357086,
-0.008489741012454033,
0.0011765013914555311,
-0.0000341302584274672,
-0.026843538507819176,
0.05374808609485626,
-0.0659787729382515,
0.05836832523345947,
0.031791187822818756,
0.024765480309724808,
0.0018290858715772629,
-0.009049441665410995,
-0.013382451608777046,
0.07628148794174194,
0.061548300087451935,
-0.0012319523375481367,
-0.027827132493257523,
-0.034283172339200974,
0.0053116437047719955,
-0.006276071537286043,
-0.02831881307065487,
-0.039593640714883804,
0.018933895975351334,
-0.03559501841664314,
0.009378633461892605,
0.03011349029839039,
-0.007234151475131512,
0.026509970426559448,
0.02307283878326416,
0.04739437252283096,
0.025471040979027748,
-0.006074096076190472,
-0.0153119508177042,
0.03555069863796234,
-0.02482031285762787,
0.0469922199845314,
0.05594290792942047,
-0.02979530207812786,
0.013577111065387726,
0.026045624166727066,
0.03240513801574707,
0.015674853697419167,
-0.003046876285225153,
0.035472482442855835,
-0.040670786052942276,
0.02373352088034153,
0.028506359085440636,
-0.01939430832862854,
-0.003679674118757248,
0.045336734503507614,
0.008889197371900082,
-0.04067574813961983,
0.029598699882626534,
0.023768188431859016,
0.028440486639738083,
0.020373128354549408,
-0.028534146025776863,
0.06326770037412643,
0.03756604716181755,
0.040628716349601746,
0.06267973780632019,
0.019079342484474182,
-0.03633778914809227,
-0.037692949175834656,
0.0086665078997612,
0.01042028795927763,
-0.004420004319399595,
-0.03934256732463837,
-0.008868486620485783,
-0.007041627075523138,
-0.01639985665678978,
0.028073901310563087,
-0.047685738652944565,
-0.016156762838363647,
-0.02471761219203472,
0.07335713505744934,
0.07284132391214371,
0.0402812696993351,
-0.0375368557870388,
0.030054796487092972,
-0.030513131991028786,
-0.06941363215446472,
-0.020123913884162903,
0.006533404346555471,
0.016045676544308662,
-0.029085014015436172,
0.015805421397089958,
-0.01081984955817461,
-0.028658276423811913,
0.01054721511900425,
-0.012738844379782677,
0.036170247942209244,
-0.02442345768213272,
-0.09425020217895508,
-0.04432368278503418,
0.03716539219021797,
-0.03375585377216339,
-0.017364978790283203,
-0.06097746640443802,
0.006343120709061623,
0.032230548560619354,
0.06365468353033066,
0.03396504744887352,
-0.021168749779462814,
-0.025009483098983765,
0.033456988632678986,
0.014791230671107769,
0.01403484120965004,
-0.045755937695503235,
-0.002354299882426858,
-0.018069909885525703,
0.04680073261260986,
-0.03195485100150108,
0.036348871886730194,
0.008599641732871532,
-0.018996091559529305,
-0.0010405248031020164,
0.08042825013399124,
-0.002611779607832432,
0.01019030436873436,
0.01138077862560749,
-0.011013946495950222,
-0.029921477660536766,
0.06846756488084793,
0.02954498864710331,
-0.026974191889166832,
0.025812147185206413,
0.02743639051914215,
0.02041785791516304,
0.03270738571882248,
0.04125311225652695,
0.029203077778220177,
-0.04566974565386772,
-0.03952641040086746,
-0.028812313452363014,
0.043691858649253845,
-0.009567239321768284,
-0.05252295732498169,
-0.01740729622542858,
0.0010483532678335905,
-0.013473322615027428,
0.009780880995094776,
0.03736241161823273,
-0.009879372082650661,
-0.04266345873475075,
-0.005085476208478212,
-0.04726412519812584,
-0.006719066761434078,
-0.06132655218243599,
0.02526058256626129,
-0.00003423101588850841,
0.020888928323984146,
0.0059659723192453384,
0.016870392486453056,
0.018456704914569855,
-0.05430125445127487,
-0.04584779962897301,
-0.023564409464597702,
0.047062210738658905,
-0.013057676143944263,
-0.0049316175282001495,
0.011969400569796562,
0.033657852560281754,
0.030027057975530624,
0.001397627405822277,
0.0188163872808218,
0.012264248915016651,
-0.032746218144893646,
-0.0045515066012740135,
-0.03160785511136055,
0.007261682767421007,
0.0035809786058962345,
-0.007527029607445002,
0.008061242289841175,
-0.009213991463184357,
-0.017195748165249825,
0.039981357753276825,
-0.01844950020313263,
0.09301222860813141,
-0.0015542551409453154,
0.03078291565179825,
-0.010443758219480515,
0.0443563237786293,
0.03195369988679886,
0.04193710908293724,
-0.00456640450283885,
-0.057903729379177094,
-0.05585121363401413,
0.0020415291655808687,
0.04302056506276131,
-0.00665595568716526,
-0.05065068602561951,
0.019035374745726585,
0.02172880433499813,
0.021406009793281555,
0.03054400160908699,
0.023768452927470207,
-0.043594010174274445,
-0.005060740280896425,
0.0071428571827709675,
0.019037310034036636,
0.0006996218580752611,
0.019050998613238335,
0.025832094252109528,
0.009479432366788387,
-0.010530726984143257,
0.019927270710468292,
-0.010921956971287727,
0.03820141404867172,
-0.040529556572437286,
-0.007330934517085552,
0.011869559064507484,
-0.06832942366600037,
0.031653616577386856,
-0.048017892986536026,
0.02532058209180832,
-0.008692624978721142,
-0.027466077357530594,
0.009335536509752274,
0.008947357535362244,
-0.01698170229792595,
0.0011677754810079932,
0.016378700733184814,
-0.0317864827811718,
-0.0020709154196083546,
0.011528031900525093,
-0.025735463947057724,
0.011138370260596275,
-0.015473154373466969,
0.006433349102735519,
-0.04285408928990364,
0.01226824801415205,
0.03283987566828728,
-0.0012472117086872458,
0.028923967853188515,
-0.019704680889844894,
-0.04255276173353195,
0.004450738895684481,
-0.06610842049121857,
0.009572310373187065,
0.05187379568815231,
-0.048472046852111816,
0.013489475473761559,
-0.07205981016159058,
-0.0569281168282032,
0.05201834440231323,
-0.02502896636724472,
0.02119547501206398,
0.013736387714743614,
-0.015099035575985909,
-0.04151853173971176,
0.028948219493031502,
-0.02445664070546627,
-0.006944000255316496,
0.01587565429508686,
0.017271174117922783,
0.04311562702059746,
0.005536133889108896,
-0.03760215640068054,
-0.01053287461400032,
-0.018219443038105965,
-0.03429292514920235,
-0.015271997079253197,
0.025102335959672928,
0.028089020401239395,
-0.010384769178926945,
0.0902363732457161,
0.01850072480738163,
-0.060085196048021317,
0.011853678151965141,
-0.051668982952833176,
-0.0205357875674963,
0.005763756576925516,
0.01718313805758953,
0.014881053939461708,
0.012187585234642029,
-0.020104309543967247,
0.04247307777404785,
0.019014989957213402,
-0.07636214792728424,
0.010088629089295864,
-0.023079896345734596,
0.003639342961832881,
-0.019172964617609978,
0.0015410518972203135,
0.0165302362293005,
0.01380076166242361,
0.010805033147335052,
0.024844679981470108,
0.04298008233308792,
-0.0029730882961302996,
0.016448117792606354,
-0.05365646257996559,
0.01781296543776989,
0.012274281121790409,
0.01839621551334858,
0.028059110045433044,
-0.02753567323088646,
-0.07488089799880981,
0.032248735427856445,
0.020726624876260757,
0.002979676006361842,
-0.006993669085204601,
-0.006372862961143255,
0.04714197665452957,
0.04277404770255089,
0.007874783128499985,
-0.05012987181544304,
0.02991839312016964,
-0.009390557184815407,
0.00012866970791947097,
0.06732001900672913,
0.03345508128404617,
0.042730726301670074,
0.01719428226351738,
0.02193760871887207,
0.00023469398729503155,
0.05303499102592468,
-0.029435228556394577,
-0.0315232053399086,
-0.009887727908790112,
-0.01138359121978283,
0.015787020325660706,
0.001469478360377252,
-0.006626534275710583,
0.029694808647036552,
0.05191323906183243,
0.04997752234339714,
0.0002042173146037385,
0.0011332588037475944,
0.01793048158288002,
-0.06756334006786346,
-0.004310566000640392,
0.0003866232291329652,
0.0718548372387886,
0.0149301178753376,
0.05422411859035492,
0.046922218054533005,
0.009726123884320259,
0.03262249380350113,
-0.01666022464632988,
-0.06882418692111969,
0.0394398532807827,
-0.03090362250804901,
0.024433361366391182,
-0.025440026074647903,
-0.004731971304863691,
-0.013988274149596691,
0.0008312538848258555,
-0.048935387283563614,
-0.04014646261930466,
-0.005224924068897963,
-0.016653839498758316,
0.011445868760347366,
-0.058018799871206284,
-0.0439649298787117,
-0.039509035646915436,
0.022088127210736275,
0.05965117737650871,
-0.049908027052879333,
-0.028104165568947792,
0.012953146360814571,
-0.05040726065635681,
-0.006479926407337189,
0.0027064818423241377,
0.00590871088206768,
-0.0048399618826806545,
0.048410892486572266,
0.042496323585510254,
0.025840459391474724,
-0.06263308972120285,
0.01046074740588665,
0.024136913940310478,
0.04479406774044037,
-0.008663707412779331,
-0.02001144178211689,
-0.016030531376600266,
-0.033040229231119156,
-0.005708598531782627,
0.0011196964187547565,
0.03486521914601326,
0.008890790864825249,
0.003998364321887493,
0.017868248745799065,
0.0031589744612574577,
-0.04433256760239601,
0.052727364003658295,
0.07228513807058334,
-0.0036098784767091274,
-0.02673560008406639,
-0.04945757985115051,
0.0007659337134100497,
-0.02066725678741932,
-0.011604538187384605,
0.03452644497156143,
-0.005633218213915825,
-0.025276271626353264,
0.007097798399627209,
0.02227197214961052,
0.03653327375650406,
-0.035747673362493515,
0.0033560888841748238,
-0.014909557066857815,
0.03645816817879677,
-0.0007094118627719581,
-0.033896032720804214,
-0.010157107375562191,
0.014684490859508514,
0.03814401477575302,
0.0006523755728267133,
0.013940545730292797,
-0.09229416400194168,
0.024513032287359238,
0.03889590874314308,
0.047609493136405945,
-0.016154900193214417,
-0.0001423098292434588,
-0.057481549680233,
-0.004818609915673733,
0.047765884548425674,
-0.03317951038479805,
0.021424610167741776,
-0.02252248115837574,
-0.010406363755464554,
-0.00019369287474546582,
-0.015583624131977558,
0.01789969392120838,
0.02682928740978241,
-0.025307103991508484,
-0.008205512538552284,
-0.02885870635509491,
-0.028852123767137527,
-0.010297863744199276,
0.04505614563822746,
0.031113680452108383,
0.054099190980196,
0.0224809180945158,
0.00786646269261837,
0.009272207506000996,
0.014646708033978939,
0.0026447188574820757,
-0.10199293494224548,
-0.01941726543009281,
-0.0016946059186011553,
-0.030254552140831947,
0.031194401904940605,
-0.039038725197315216,
-0.0760587826371193,
0.003484042128548026,
-0.0003689657023642212,
-0.0028939549811184406,
-0.04039528965950012,
-0.07800010591745377,
0.020618990063667297,
0.0340229794383049,
0.02844204194843769,
0.058322492986917496,
0.04449155554175377,
-0.05091357231140137,
-0.006946203764528036,
-0.024061646312475204,
0.009018048644065857,
-0.02794634737074375,
-0.0006434240494854748,
-0.005594524554908276,
0.013556660152971745,
0.0069564515724778175,
0.03524640202522278,
-0.015020106919109821,
0.00476732337847352,
-0.006744366604834795,
-0.05756956338882446,
-0.03827166184782982,
0.012219611555337906,
-0.01660970225930214,
-0.022314319387078285,
-0.0031940594781190157,
0.022169534116983414,
-0.006407000124454498,
-0.03050285205245018,
0.00803481787443161,
0.012744962237775326,
-0.00926967989653349,
0.002379542449489236,
-0.03814959153532982,
0.022818664088845253,
-0.03582201153039932,
-0.0011511341435834765,
0.03311625495553017,
-0.041586194187402725,
0.041393522173166275,
-0.036057259887456894,
0.01315588504076004,
-0.006505152676254511,
-0.08743998408317566,
-0.03647058084607124,
-0.00981574784964323,
0.003409232245758176,
0.008254718035459518,
-0.01200941763818264,
0.044493887573480606,
0.004771865904331207,
0.01912774331867695,
-0.08273676037788391,
-0.059966929256916046,
0.0024122309405356646,
-0.0023903348483145237,
0.015634896233677864,
-0.03703958913683891,
0.0016420752508565784,
-0.05701453238725662,
-0.025430956855416298,
0.010309776291251183,
0.031936001032590866,
-0.06859812140464783,
0.01886880211532116,
0.01615026406943798,
0.005831154063344002,
0.036980096250772476,
0.0014281405601650476,
-0.017972225323319435,
0.031356167048215866,
0.027933908626437187,
-0.0044537875801324844,
-0.005795337725430727,
0.049540795385837555,
-0.026507165282964706,
-0.03699498623609543,
-0.0048735779710114,
0.002855647588148713,
0.029020333662629128,
-0.015482841990888119,
-0.006763124838471413,
0.07698691636323929,
0.05048380047082901,
-0.006827505771070719,
-0.02121419832110405,
0.05744953453540802,
0.02854713797569275,
0.007079100236296654,
-0.013649743050336838,
0.021939795464277267,
-0.021104848012328148,
-0.008531490340828896,
0.03539404645562172,
-0.01611235737800598,
0.0339834988117218,
0.008634260855615139,
0.030418915674090385,
0.0009176129242405295,
-0.013448904268443584,
0.029701927676796913,
-0.01762019284069538,
0.012629596516489983,
-0.010512428358197212,
0.028187617659568787,
-0.0029524764977395535,
0.01500402856618166,
0.004342755302786827,
-0.032584048807621,
-0.015428703278303146,
-0.038993801921606064,
0.037287257611751556,
-0.004048312548547983,
0.04671019688248634,
0.02671521157026291,
0.0008967799949459732,
-0.019630245864391327,
-0.0221543051302433,
0.004031708929687738,
0.020474355667829514,
-0.0007590231252834201,
0.025222133845090866,
0.01914011687040329,
-0.0080335084348917,
0.03015807829797268,
0.02253549173474312,
-0.017529495060443878,
0.06143856793642044,
0.010504094883799553,
0.06198641285300255,
0.00440087728202343,
-0.014038462191820145,
-0.062470942735672,
0.011498312465846539,
-0.028216319158673286,
0.009519577026367188,
-0.017796657979488373,
-0.03203863650560379,
0.015555378049612045,
0.005303644575178623,
0.013430091552436352,
0.01641686074435711,
-0.019584117457270622,
-0.03858055919408798,
0.03813348338007927,
-0.007765091490000486,
-0.010126587003469467,
-0.02751101925969124,
0.03776223585009575,
0.0171511210501194,
0.024632692337036133,
0.015904726460576057,
0.036194927990436554,
-0.08182473480701447,
-0.035065148025751114,
-0.06662425398826599,
-0.061193231493234634,
0.03533198684453964,
-0.0059541394002735615,
-0.021227581426501274,
0.010545449331402779,
-0.0005291374982334673,
-0.0010501100914552808,
-0.016101891174912453,
0.03585915267467499,
-0.018098006024956703,
0.04653410241007805,
-0.008589684031903744,
0.01844455860555172,
-0.0033730289433151484,
0.0309248398989439,
0.09460634738206863,
0.03984920307993889,
-0.008138426579535007,
-0.053749118000268936,
0.02018026076257229,
-0.06156068667769432,
0.021037612110376358,
-0.01994585432112217,
0.020874403417110443,
-0.023835403844714165,
0.008354609832167625,
-0.022440625354647636,
0.06165362149477005,
0.011086506769061089,
0.011218228377401829,
0.08287975192070007,
-0.013935941271483898,
-0.03501541540026665,
0.0037665136624127626,
0.02463296428322792,
-0.02845810353755951,
0.021289248019456863,
-0.059213921427726746,
0.0033054503146559,
-0.031934235244989395,
0.00427169119939208,
-0.0070194159634411335,
-0.03019881621003151,
0.02282816730439663,
0.003267749212682247,
-0.0416811928153038,
-0.02521255798637867,
-0.014925806783139706,
-0.007733788341283798,
-0.015074143186211586,
0.0058131348341703415,
0.026397524401545525,
-0.010434108786284924,
0.004508469253778458,
0.037306882441043854,
0.05796827748417854,
-0.00060689338715747,
-0.03068065643310547,
0.021409159526228905,
-0.026044638827443123,
-0.016525156795978546,
-0.03480720892548561,
0.021052811294794083,
-0.03005046769976616,
-0.011235336773097515,
0.01873701438307762,
0.0136039350181818,
0.02238592877984047,
-0.013395040296018124,
-0.01213687565177679,
-0.03301326557993889,
0.026990119367837906,
-0.0009065591148100793,
0.005105070304125547,
-0.03838827461004257,
0.039427172392606735,
-0.03992897644639015,
0.014904963783919811,
0.00414090184494853,
-0.0010944767855107784,
0.01673685759305954,
-0.007071101572364569,
0.0016502360813319683,
-0.010219024494290352,
-0.015067925676703453,
-0.024754829704761505,
-0.02326040156185627,
-0.02028932422399521,
-0.016480423510074615,
0.030599333345890045,
0.04012376815080643,
0.0227859728038311,
0.008747565560042858,
-0.005768293980509043,
-0.005144667811691761,
-0.039471227675676346,
0.050684455782175064,
0.001420250628143549,
-0.0026234593242406845,
-0.01914874091744423,
0.015230692923069,
0.01749309152364731,
0.063790462911129,
-0.03825341537594795,
-0.010098445229232311,
-0.008207830600440502,
-0.03593594208359718,
0.023775646463036537,
-0.045492514967918396,
-0.01912480778992176,
-0.001162480446510017,
0.0006034470279701054,
-0.013529128395020962,
-0.030092529952526093,
0.01033895555883646,
0.03520781546831131,
-0.022087398916482925,
-0.009899457916617393,
0.034863729029893875,
-0.009192312136292458,
0.010975852608680725,
0.0281069315969944,
-0.003909918013960123,
-0.0006067302892915905,
-0.015765901654958725,
0.01602204144001007,
-0.009436426684260368,
-0.024637820199131966,
-0.018316006287932396,
0.023586155846714973,
-0.015007673762738705,
0.028693173080682755,
-0.03287511318922043,
0.017562152817845345,
-0.032794252038002014,
0.025182554498314857,
-0.022718878462910652,
0.01821861043572426,
-0.07048382610082626,
-0.0032243465539067984,
0.022703466936945915,
-0.024661872535943985,
-0.04461877420544624,
0.023176277056336403,
-0.012818699702620506,
0.00011973922664765269,
0.03558671846985817,
0.02654159627854824,
-0.049379412084817886,
0.0023120648693293333,
0.03198099881410599,
0.014739889651536942,
0.04845786094665527,
-0.020176468417048454,
0.004097058903425932,
0.039023276418447495,
-0.05717970058321953,
-0.0198613703250885,
0.0002928311878349632,
-0.03992140293121338,
0.02955002896487713,
0.042084913700819016,
-0.013768286444246769,
-0.02492988295853138,
0.07552849501371384,
0.009809165261685848,
-0.0001669849589234218,
0.035647619515657425,
-0.028835386037826538,
-0.03648075833916664,
0.0193948857486248,
0.0051231710240244865,
-0.013530419208109379,
-0.042620617896318436,
0.04784137383103371,
0.017449548467993736,
0.00986243411898613,
-0.02160480059683323,
-0.017429780215024948,
-0.012697615660727024,
0.021800126880407333,
0.044830288738012314,
-0.01350605022162199,
0.003454166231676936,
0.04293062537908554,
-0.04627592861652374,
0.004987944848835468,
-0.008178227581083775,
0.01617041975259781,
-0.0972197875380516,
-0.037292346358299255,
0.0031625491101294756,
-0.04150543361902237,
0.032424699515104294,
-0.030996648594737053,
0.020672883838415146,
0.014267053455114365,
-0.06167256087064743,
0.026930302381515503,
-0.029203832149505615,
-0.02564985677599907,
-0.0039281342178583145,
0.014688859693706036,
-0.02828325517475605,
0.040705859661102295,
0.03401092067360878,
0.06343109160661697,
-0.00006229392602108419,
0.022529996931552887,
0.01984819583594799,
0.013325446285307407,
-0.031021034345030785,
0.025451626628637314,
0.01793447509407997,
-0.008060737513005733,
0.0859135240316391,
-0.06266840547323227,
-0.01719888672232628,
0.024689454585313797,
0.008720163255929947,
0.010525871999561787,
-0.022272931411862373,
-0.01330185029655695,
-0.01928807981312275,
0.04523388668894768,
0.00988154485821724,
-0.001384527189657092,
0.031567610800266266,
0.034826602786779404,
0.018856070935726166,
-0.0032501595560461283,
-0.010328027419745922,
0.019778510555624962,
0.012859154492616653,
-0.013091417960822582,
-0.02168714627623558,
0.055585410445928574,
-0.0264967642724514,
-0.03257707133889198,
-0.0016180288512259722,
0.012160327285528183,
0.02179640531539917,
-0.010932879522442818,
-0.022312534973025322,
-0.04944233223795891,
-0.017986321821808815,
-0.00850849412381649,
-0.028300529345870018,
0.0065449741668999195,
0.01785540021955967,
0.000546266557648778,
0.0020866277627646923,
0.012251794338226318,
0.02224510908126831,
-0.02095085196197033,
-0.03818831220269203,
0.032247960567474365,
0.03986062854528427,
0.04329795762896538,
0.004268655553460121,
-0.09141257405281067,
-0.04233605042099953,
0.03195745125412941,
-0.007180537562817335,
0.04794587194919586,
-0.020593615248799324,
-0.0010067721595987678,
-0.019858885556459427,
-0.03889084607362747,
0.0064577748998999596,
0.0032279144506901503,
0.01517733559012413,
-0.027842264622449875,
-0.031333573162555695,
0.030408669263124466,
-0.015909608453512192,
0.03936465457081795,
-0.036434683948755264,
-0.01649906486272812,
0.02005635015666485,
-0.017006151378154755,
0.013563510030508041,
-0.026292316615581512,
-0.0099762799218297,
-0.031184714287519455,
-0.04881836846470833,
-0.02026824839413166,
0.018509939312934875,
-0.031765565276145935,
0.040156323462724686,
0.03749007359147072,
0.0018128890078514814,
-0.007552732713520527,
-0.011631554923951626,
-0.02421288937330246,
0.040822263807058334,
-0.01907038688659668,
0.010959355160593987,
0.041595760732889175,
-0.030463311821222305,
0.02331341989338398,
0.009371169842779636,
-0.025737566873431206,
-0.008807539939880371,
0.03160747140645981,
-0.05640245974063873,
0.022999068722128868,
-0.02370857447385788,
-0.0182771235704422,
0.029242923483252525,
-0.02938971482217312,
0.022328732535243034,
0.03663909435272217,
-0.04368482902646065,
0.016290627419948578,
0.05442700907588005,
0.03859677165746689,
0.036925897002220154,
0.021459193900227547,
-0.001960939494892955,
-0.002284861169755459,
0.033266276121139526,
0.015328461304306984,
0.07170186191797256,
0.04409893974661827,
-0.01575055532157421,
0.024143073707818985,
0.023526480421423912,
0.010176686570048332,
-0.007546487729996443,
0.01613396219909191,
0.0035479264333844185,
-0.04014664143323898,
-0.000488153425976634,
0.015508287586271763,
-0.02822502702474594,
0.025646543130278587,
0.0334940105676651,
-0.054912783205509186,
0.07008174806833267,
-0.01008238922804594,
-0.0013528141425922513,
-0.012072906829416752,
0.0027545688208192587,
-0.010865719057619572,
0.016680657863616943,
-0.03286284580826759,
0.06346992403268814,
0.004545188508927822,
-0.0031153575982898474,
-0.007891619578003883,
0.00652420474216342,
0.0087696248665452,
-0.041212987154722214,
0.029030105099081993,
0.0008349303971044719,
-0.00439520413056016,
-0.028520919382572174,
-0.007932559587061405,
-0.005241076927632093,
-0.04248529672622681,
0.006880355998873711,
0.058026354759931564,
0.038111474364995956,
0.012597146444022655,
-0.03293098136782646,
-0.0008882492547854781,
0.059038180857896805,
-0.03296196833252907,
-0.0021296737249940634,
-0.023553261533379555,
0.008089984767138958,
-0.034282464534044266,
-0.0014174309326335788
] |
<p>Is there any way to find the pressure of a liquid inside a closed container without making contact with it? </p>
<p>You can make any assumptions, like transparent container or anything, only rule, the sensing device shouldn't make contact with the liquid.</p>
| 8,879 |
[
-0.016555780544877052,
-0.013231056742370129,
-0.021385187283158302,
-0.036298420280218124,
0.02137712575495243,
-0.031101340427994728,
-0.046321671456098557,
-0.00010694051889004186,
0.024872146546840668,
0.0068480996415019035,
0.06341329216957092,
0.025807255879044533,
0.025461172685027122,
-0.020537199452519417,
0.00501511013135314,
0.003872702829539776,
-0.003895921865478158,
0.006392756011337042,
0.02800891548395157,
-0.05961039662361145,
-0.020954832434654236,
0.025406455621123314,
0.0022083609364926815,
-0.011266130954027176,
-0.017436804249882698,
0.006504240911453962,
0.020355209708213806,
-0.04100961610674858,
0.021390771493315697,
0.043940648436546326,
-0.03216467425227165,
-0.032992321997880936,
-0.00710161030292511,
0.006379209458827972,
0.037126634269952774,
-0.027043502777814865,
-0.045500967651605606,
-0.01987460069358349,
-0.038920726627111435,
0.0032820631749927998,
-0.01563650369644165,
0.0214398093521595,
0.03283485770225525,
0.0386488251388073,
-0.0030074615497142076,
0.03884408622980118,
0.003874425310641527,
-0.025576025247573853,
0.027380866929888725,
-0.06639141589403152,
0.018112853169441223,
-0.01881091110408306,
0.04908893257379532,
0.05982222408056259,
-0.008962982334196568,
0.01410914957523346,
0.06299027800559998,
0.0670311450958252,
-0.029260503128170967,
-0.03202414512634277,
0.02072119154036045,
0.013524260371923447,
-0.007782059721648693,
-0.020280424505472183,
-0.03856930509209633,
-0.02890654094517231,
-0.013681577518582344,
-0.013216511346399784,
0.015547242015600204,
-0.0022210022434592247,
-0.019137926399707794,
-0.0053942203521728516,
0.022372161969542503,
0.0035513469483703375,
0.017949966713786125,
-0.030087951570749283,
-0.005657401401549578,
0.045029282569885254,
0.023528823629021645,
0.05758228898048401,
0.0022138776257634163,
-0.0034658492077142,
0.022725040093064308,
0.026896996423602104,
0.012835182249546051,
-0.07072018831968307,
0.05214247107505798,
0.010296604596078396,
-0.026179369539022446,
0.05644151568412781,
-0.03683752566576004,
0.008874536491930485,
0.023039821535348892,
0.0052412343211472034,
-0.014682293869554996,
-0.01133615244179964,
-0.031805865466594696,
0.06556692719459534,
0.0034076061565428972,
-0.08937887102365494,
0.027167346328496933,
0.015120316296815872,
0.010235495865345001,
0.10888790339231491,
-0.0036726314574480057,
-0.04714474454522133,
0.006967585533857346,
0.007148614153265953,
0.03736892342567444,
0.03393598273396492,
-0.021693794056773186,
-0.042958542704582214,
-0.011504673399031162,
-0.020960163325071335,
0.000346305372659117,
-0.009642618708312511,
-0.03786396607756615,
-0.019433477893471718,
0.019383328035473824,
0.05186723545193672,
0.028068970888853073,
-0.015288731083273888,
0.0023773086722940207,
-0.04043826833367348,
-0.050647132098674774,
0.036893799901008606,
0.006493562366813421,
-0.004293063655495644,
-0.03609918802976608,
-0.00436985120177269,
-0.015375022776424885,
0.005781353916972876,
0.02629018947482109,
0.001796654425561428,
0.05819077044725418,
-0.03128569945693016,
-0.077315554022789,
-0.07885035127401352,
0.0630556046962738,
0.002110792323946953,
-0.034940384328365326,
-0.06706193834543228,
0.03133844956755638,
0.038651928305625916,
0.05290645733475685,
0.022686295211315155,
-0.006225827150046825,
-0.01545779313892126,
0.008593859151005745,
-0.016891274601221085,
-0.018191851675510406,
-0.01229070220142603,
0.0037593888118863106,
-0.009914614260196686,
-0.004424841608852148,
-0.0560389906167984,
0.018687916919589043,
0.025949640199542046,
-0.010783440433442593,
-0.01896097883582115,
0.046808596700429916,
-0.04280630499124527,
-0.0072204070165753365,
0.01641673594713211,
0.010836000554263592,
-0.07528109103441238,
0.05064981058239937,
-0.024688100442290306,
0.021189533174037933,
0.01572163589298725,
0.029167944565415382,
0.039396416395902634,
-0.011426328681409359,
-0.02533084712922573,
0.049990084022283554,
-0.006888207979500294,
-0.03138319030404091,
-0.009892215952277184,
0.061823055148124695,
0.0021606320515275,
-0.03011908382177353,
-0.01684032566845417,
-0.003134248312562704,
0.0221556443721056,
0.012458894401788712,
-0.010834489949047565,
0.00897345133125782,
-0.03953868895769119,
-0.0007556686759926379,
-0.0344063863158226,
0.021603645756840706,
-0.04893072694540024,
0.026504309847950935,
0.017795048654079437,
0.03947269916534424,
0.03573356941342354,
0.021073410287499428,
0.027251439169049263,
-0.05874044448137283,
-0.0556328110396862,
-0.019216636195778847,
0.01210213452577591,
0.028807383030653,
-0.02438320219516754,
-0.008143887855112553,
0.015308622270822525,
0.043188825249671936,
-0.008612398989498615,
-0.01933370530605316,
-0.024438712745904922,
-0.01825127564370632,
-0.0047461166977882385,
-0.05324601009488106,
-0.017482314258813858,
-0.00791716668754816,
-0.01556394249200821,
0.04513416439294815,
0.03579450398683548,
0.007130384910851717,
0.02045741304755211,
-0.004091787151992321,
0.0682767704129219,
0.06803499907255173,
0.00796425435692072,
0.039805807173252106,
-0.05117719992995262,
0.010732471942901611,
0.006659790873527527,
0.0186319462954998,
-0.006296693347394466,
-0.0912645235657692,
-0.049352433532476425,
0.0024143510963767767,
0.01099042035639286,
-0.020720455795526505,
0.008080631494522095,
0.033634502440690994,
-0.00012282541138119996,
0.029819292947649956,
0.0015374469803646207,
-0.02376798540353775,
-0.00264710932970047,
0.010421250015497208,
0.06799271702766418,
0.012659754604101181,
0.009527070447802544,
0.023876657709479332,
0.06355088949203491,
0.062110744416713715,
-0.01726992428302765,
0.013639562763273716,
-0.010391258634626865,
-0.011760314926505089,
0.02483562007546425,
0.013865244574844837,
0.011338037438690662,
-0.0014190325746312737,
-0.018515776842832565,
0.023566288873553276,
-0.0040558879263699055,
0.005153900012373924,
-0.0025984200183302164,
-0.02713162451982498,
0.0026951879262924194,
0.008034998551011086,
0.003033759305253625,
-0.06370604783296585,
-0.013898284174501896,
0.03477645292878151,
-0.039691612124443054,
-0.0017967664171010256,
-0.014988863840699196,
0.028830228373408318,
-0.027606667950749397,
0.012256243266165257,
0.02831113152205944,
-0.007361248601227999,
0.0290761049836874,
-0.049144189804792404,
-0.020462142303586006,
0.00723413098603487,
-0.019152909517288208,
-0.02487538941204548,
0.005631687119603157,
-0.03573239967226982,
-0.009103689342737198,
-0.03635933995246887,
-0.0189948920160532,
0.0139803197234869,
-0.01157362014055252,
0.007007016334682703,
0.0007355349371209741,
0.025410937145352364,
-0.054284535348415375,
-0.002101542428135872,
-0.008901138789951801,
-0.008935559540987015,
-0.004942618776112795,
0.029742209240794182,
0.003318881383165717,
0.027385417371988297,
-0.03754710406064987,
0.01349484734237194,
-0.03484214097261429,
-0.04242014139890671,
-0.03542982414364815,
-0.020810773596167564,
0.005598837044090033,
-0.046473391354084015,
0.013524611480534077,
0.028349371626973152,
-0.060206372290849686,
-0.01301614474505186,
-0.041245993226766586,
-0.03862314671278,
0.01594996638596058,
0.01088753156363964,
0.028534146025776863,
0.020758388563990593,
-0.010041702538728714,
0.03754320740699768,
-0.04107936471700668,
-0.07099475711584091,
-0.010080147534608841,
-0.039127543568611145,
-0.026026539504528046,
-0.03272642195224762,
-0.038726579397916794,
0.028066834434866905,
-0.0196772962808609,
-0.005374213680624962,
0.015219674445688725,
0.029439808800816536,
0.04706650972366333,
0.0508621521294117,
0.016277391463518143,
-0.027958489954471588,
0.04906878620386124,
0.0013794329715892673,
0.05253526568412781,
0.025716403499245644,
0.016244100406765938,
0.02235918492078781,
0.00515721132978797,
0.042725056409835815,
0.04925408959388733,
-0.04609687626361847,
0.029044492170214653,
0.030334187671542168,
0.0011054304195567966,
-0.025936434045433998,
0.007442673202604055,
-0.0005358898779377341,
0.012328309006989002,
0.0033279419876635075,
0.06104179471731186,
0.031938862055540085,
-0.0027320371009409428,
-0.04121514782309532,
0.04511246457695961,
0.052616726607084274,
-0.019186748191714287,
-0.06956811994314194,
0.034424278885126114,
-0.018250783905386925,
0.04927657172083855,
-0.003710385411977768,
-0.01059249322861433,
0.04790816828608513,
0.028293754905462265,
0.03844475373625755,
-0.002283260924741626,
-0.00355402915738523,
0.006671955343335867,
-0.05642905458807945,
-0.02170819230377674,
0.011670894920825958,
0.03050253726541996,
0.014551586471498013,
0.0472838468849659,
0.04274171218276024,
0.025517454370856285,
0.045288410037755966,
0.019071074202656746,
-0.0822298675775528,
0.018881503492593765,
-0.013721040450036526,
0.0045005460269749165,
-0.021482978016138077,
-0.00024269730783998966,
-0.02136554941534996,
-0.05925625562667847,
-0.0013229030882939696,
-0.0012889537028968334,
0.04045724868774414,
-0.06325580924749374,
-0.005628239829093218,
0.007457857485860586,
0.008591822348535061,
-0.029767753556370735,
0.020918892696499825,
0.018172265961766243,
-0.008452455513179302,
0.04153905808925629,
0.030596861615777016,
0.013055321760475636,
-0.012821546755731106,
0.007912841625511646,
-0.009003357030451298,
0.0009177104802802205,
0.06732381135225296,
0.027622677385807037,
0.00992646161466837,
-0.019701136276125908,
-0.01696033962070942,
0.01174366008490324,
0.045741718262434006,
-0.027771087363362312,
-0.012055045925080776,
-0.025957191362977028,
-0.04611882194876671,
0.00024069665232673287,
0.030082788318395615,
0.00445726839825511,
-0.04423613101243973,
0.03812997788190842,
-0.0005554644158110023,
-0.03561417758464813,
-0.02927204966545105,
0.031629741191864014,
0.06871502101421356,
0.019043462350964546,
-0.033156462013721466,
-0.0386335663497448,
0.004162372089922428,
-0.053643081337213516,
0.0033967362251132727,
0.00988778192549944,
0.019005684182047844,
0.016398988664150238,
0.003466598456725478,
0.011802945286035538,
0.02963121607899666,
-0.03938094899058342,
0.01295378990471363,
0.0095716817304492,
0.0017286844085901976,
-0.036014582961797714,
0.014097180217504501,
0.068320132791996,
0.03834853321313858,
0.025331441313028336,
-0.012022356502711773,
-0.03767690435051918,
-0.09916996210813522,
-0.008202318102121353,
0.041058581322431564,
0.023243442177772522,
0.01763315685093403,
0.015667688101530075,
-0.0459127351641655,
-0.05898497998714447,
0.04358474910259247,
-0.015782684087753296,
-0.01827089861035347,
-0.031514186412096024,
0.00848336797207594,
-0.04944516718387604,
-0.03446570783853531,
-0.016992097720503807,
-0.006429268978536129,
-0.036508165299892426,
-0.019072335213422775,
-0.00901926402002573,
-0.03075547143816948,
-0.003999174572527409,
0.009612415917217731,
-0.009554170072078705,
0.049497850239276886,
0.018481487408280373,
0.021461153402924538,
-0.025722801685333252,
0.014209209010004997,
-0.055890437215566635,
-0.069795623421669,
0.0019813976250588894,
-0.015471185557544231,
0.005687742028385401,
0.02747740037739277,
0.00816585123538971,
-0.08033299446105957,
0.06311725825071335,
-0.03333258256316185,
-0.02296254225075245,
0.0011786381946876645,
-0.02699211612343788,
0.03622681275010109,
0.04570716619491577,
0.0021646509412676096,
0.023107729852199554,
0.029306504875421524,
0.017382556572556496,
-0.028847286477684975,
-0.032470084726810455,
0.01830012910068035,
-0.02453736588358879,
-0.03192298486828804,
-0.005926813930273056,
0.01163673959672451,
-0.04105808585882187,
0.04139076545834541,
0.009431663900613785,
0.020821990445256233,
-0.0015192535938695073,
-0.028567448258399963,
-0.0045017157681286335,
0.03631113842129707,
0.005158369429409504,
-0.00379116996191442,
0.00961864460259676,
0.009234602563083172,
0.006151426117867231,
-0.030140351504087448,
0.00555564695969224,
-0.00611872598528862,
0.030829880386590958,
0.015577632933855057,
-0.03649891912937164,
0.02370677888393402,
-0.025352394208312035,
0.003480705199763179,
0.03219430148601532,
-0.029754098504781723,
0.055462706834077835,
-0.01393970474600792,
0.023243360221385956,
0.020281057804822922,
0.00028592569287866354,
0.002917972393333912,
0.02939785085618496,
-0.021079687401652336,
0.03197610750794411,
-0.06803565472364426,
0.050603222101926804,
0.012300891801714897,
0.011110817082226276,
-0.05857846140861511,
-0.004173490684479475,
0.032822512090206146,
-0.0018192235147580504,
-0.0026073548942804337,
-0.03532106801867485,
-0.009214676916599274,
-0.0261872336268425,
-0.013171215541660786,
-0.021290002390742302,
-0.0005454225465655327,
-0.023021744564175606,
-0.02696036733686924,
0.00907556340098381,
-0.01905117556452751,
0.031429167836904526,
0.0006699864170514047,
-0.022712701931595802,
-0.005484698340296745,
-0.013184785842895508,
-0.0026681125164031982,
0.01663200557231903,
0.010680933482944965,
-0.031918011605739594,
-0.019519813358783722,
-0.025774359703063965,
-0.02579365484416485,
0.04913561791181564,
-0.019800985231995583,
0.038674890995025635,
0.013761245645582676,
0.01175994798541069,
-0.0322130061686039,
-0.0027930326759815216,
0.007197811268270016,
0.01473280694335699,
0.019480982795357704,
0.01064544077962637,
-0.02518574334681034,
-0.015878336504101753,
-0.0009194258018396795,
-0.006830213125795126,
-0.0332697257399559,
-0.03669821470975876,
-0.024348346516489983,
0.07597251236438751,
0.009017065167427063,
0.007768719457089901,
-0.0019910389091819525,
-0.04088381677865982,
0.0021890788339078426,
-0.01341195497661829,
-0.032108452171087265,
-0.007186441216617823,
0.031863659620285034,
-0.045659810304641724,
-0.06345092505216599,
-0.03636607527732849,
-0.016348781064152718,
0.049289703369140625,
-0.02490081824362278,
0.07354457676410675,
0.014835267327725887,
0.015266897156834602,
-0.0071424879133701324,
0.0401604063808918,
0.007813465781509876,
0.01536655705422163,
-0.020139295607805252,
0.08006196469068527,
0.0030910789500921965,
-0.0017496254295110703,
0.020020687952637672,
0.034165412187576294,
-0.04498498886823654,
-0.016780905425548553,
0.05681754648685455,
0.033347103744745255,
0.02789381332695484,
-0.04412173479795456,
-0.017004501074552536,
0.022415289655327797,
-0.0428926944732666,
-0.00023132414207793772,
0.015725258737802505,
-0.0325695239007473,
0.004239027388393879,
-0.006574053317308426,
0.0072887493297457695,
-0.010586065240204334,
0.009808795526623726,
-0.03231042996048927,
0.046168986707925797,
0.028425337746739388,
0.021726053208112717,
0.0001579358649905771,
0.015723930671811104,
0.005464395508170128,
0.004148270469158888,
-0.031108764931559563,
-0.0011264736531302333,
-0.05439149588346481,
-0.021622877568006516,
-0.03258247673511505,
-0.005675087682902813,
0.025123534724116325,
0.005196461454033852,
-0.018424704670906067,
0.029917070642113686,
-0.020439177751541138,
0.04561464488506317,
0.020449424162507057,
0.04703541472554207,
-0.0032122544944286346,
0.059479113668203354,
-0.02683202363550663,
0.018633926287293434,
-0.020182404667139053,
0.03827041760087013,
0.11947078257799149,
0.020917829126119614,
0.03476795554161072,
-0.07866527885198593,
-0.0051810238510370255,
-0.019419008865952492,
-0.004102228209376335,
-0.019030045717954636,
0.02666877582669258,
-0.01649237610399723,
0.012888950295746326,
-0.015688247978687286,
0.058219775557518005,
-0.012140663340687752,
0.01674612984061241,
0.0515260249376297,
-0.05220628157258034,
-0.01650792919099331,
0.0004466682730708271,
0.011613843962550163,
-0.052857883274555206,
-0.0029857719782739878,
-0.008634394034743309,
0.04661976918578148,
-0.03822563588619232,
-0.0426161102950573,
-0.03121037967503071,
-0.02488476224243641,
0.03334223851561546,
0.002841145033016801,
-0.0712338462471962,
0.01939832977950573,
0.018444200977683067,
-0.011326774023473263,
-0.05614430829882622,
0.039594948291778564,
0.016096919775009155,
0.009395843371748924,
-0.0026625075843185186,
-0.0034418923314660788,
0.03338341787457466,
-0.01658356375992298,
-0.007094621658325195,
0.000009370147381559946,
-0.0103181516751647,
-0.0032092079054564238,
0.020248234272003174,
0.042461998760700226,
0.020212600007653236,
-0.03052976168692112,
0.011575392447412014,
-0.01957625523209572,
-0.013488979078829288,
-0.044564299285411835,
-0.03745308890938759,
0.027318386361002922,
0.032887887209653854,
-0.005185949150472879,
-0.03543149679899216,
-0.00903872400522232,
0.04535578191280365,
-0.028715994209051132,
-0.008067065849900246,
-0.022363366559147835,
0.030023135244846344,
0.010814514942467213,
0.026354676112532616,
0.0476563423871994,
-0.009136971086263657,
-0.0018184789223596454,
-0.03382853418588638,
-0.008420591242611408,
-0.0479864738881588,
-0.007141841575503349,
-0.005801205523312092,
0.011896469630300999,
0.024833260104060173,
-0.004925860092043877,
0.028545964509248734,
-0.0015651981811970472,
-0.08042187243700027,
0.06828273832798004,
-0.055298369377851486,
0.022024694830179214,
-0.029936837032437325,
0.000381190562620759,
0.026909885928034782,
0.0701989158987999,
-0.006238848902285099,
-0.04584692046046257,
0.032015398144721985,
0.03980204463005066,
0.058087289333343506,
-0.017110848799347878,
-0.06071283295750618,
0.0014837299240753055,
-0.009769214317202568,
0.04109329730272293,
0.01428729947656393,
0.026174385100603104,
0.022501129657030106,
0.019279561936855316,
-0.01039622537791729,
-0.02720710076391697,
-0.0662730485200882,
0.009153877384960651,
-0.01787460595369339,
-0.013157477602362633,
-0.024508178234100342,
-0.035062097012996674,
0.03463057056069374,
-0.02646373026072979,
-0.03723086044192314,
-0.039336998015642166,
-0.02810162492096424,
0.006172871682792902,
0.027646545320749283,
-0.0026187824551016092,
0.004463049117475748,
0.009327620267868042,
0.012844961136579514,
-0.010549764148890972,
0.01115808542817831,
-0.027171680703759193,
-0.08491236716508865,
0.010233861394226551,
-0.014576454646885395,
-0.011568413116037846,
0.016634322702884674,
-0.03992093726992607,
0.008709756657481194,
0.02597283385694027,
0.01749476231634617,
0.029250450432300568,
0.007531765382736921,
0.06889505684375763,
-0.016376148909330368,
-0.00018153846031054854,
-0.05403602123260498,
-0.0382860004901886,
0.04962707310914993,
-0.0221425611525774,
-0.021188557147979736,
0.0007349242805503309,
-0.013693077489733696,
0.034000054001808167,
0.04400370270013809,
-0.008158893324434757,
-0.01601150818169117,
0.02848278358578682,
-0.009829742833971977,
0.014855096116662025,
-0.0034635683987289667,
-0.029128262773156166,
0.012537349946796894,
0.012118189595639706,
0.04586341977119446,
-0.0059341914020478725,
-0.0058007738552987576,
0.03618881478905678,
0.026241503655910492,
0.0643312931060791,
0.010390372015535831,
0.04459850862622261,
0.028430799022316933,
0.030164971947669983,
0.047127559781074524,
-0.020527513697743416,
0.009219389408826828,
0.030391259118914604,
-0.014063152484595776,
0.025804879143834114,
0.0076229688711464405,
0.0001654990774113685,
-0.11686430126428604,
0.018458379432559013,
-0.028180072084069252,
0.030502023175358772,
0.0619051456451416,
-0.04990316927433014,
-0.003448504488915205,
0.02321409247815609,
-0.0582510381937027,
-0.017168235033750534,
-0.02182929962873459,
-0.04504561424255371,
-0.011344332247972488,
0.04185685142874718,
-0.02001265250146389,
0.043820884078741074,
0.011817854829132557,
0.010979166254401207,
0.02053081803023815,
0.03355637565255165,
0.018990209326148033,
-0.022949034348130226,
0.003289257874712348,
0.045284319669008255,
-0.006896568927913904,
-0.016269316896796227,
0.016171416267752647,
-0.0248776376247406,
0.0004864715738222003,
0.00553941959515214,
-0.01193113625049591,
0.011668362654745579,
-0.02539946883916855,
0.014470404013991356,
-0.0210348479449749,
0.04372955113649368,
0.010382615029811859,
0.01784074306488037,
-0.019935131072998047,
0.05171656236052513,
-0.007202549371868372,
0.02945687621831894,
0.009368867613375187,
0.011509192176163197,
0.011190351098775864,
-0.01935150846838951,
-0.015061181038618088,
0.01701798476278782,
-0.0375913605093956,
-0.006495406851172447,
0.041692741215229034,
-0.00902131199836731,
-0.0004465880920179188,
-0.021785173565149307,
-0.023677954450249672,
-0.031574539840221405,
0.03634707257151604,
0.022664442658424377,
0.04189169779419899,
-0.06354336440563202,
-0.0009380907285958529,
-0.004857858642935753,
-0.045200325548648834,
0.024974213913083076,
0.008589041419327259,
-0.04656660929322243,
-0.04887302592396736,
0.002720616990700364,
-0.004440219607204199,
-0.02288886159658432,
0.01804831624031067,
-0.020106764510273933,
-0.018075985834002495,
0.02202504873275757,
0.01655462011694908,
0.009409659542143345,
0.06724537163972855,
-0.0037260781973600388,
-0.029460901394486427,
-0.07442714273929596,
0.06828155368566513,
-0.012990677729249,
0.009840360842645168,
-0.0019675397779792547,
-0.011563008651137352,
-0.019716687500476837,
0.007450483739376068,
0.048970215022563934,
-0.0037966580130159855,
0.0025294984225183725,
-0.024692820385098457,
0.010693679563701153,
-0.011943488381803036,
-0.007140215020626783,
0.005783450324088335,
-0.014901449903845787,
-0.028573080897331238,
0.015029780566692352,
-0.025105684995651245,
0.002360475482419133,
-0.0013632506597787142,
0.03932473808526993,
0.003378494642674923,
-0.007975498214364052,
0.021947070956230164,
-0.028218097984790802,
0.03790302202105522,
0.020041972398757935,
0.017498670145869255,
0.08003132045269012,
-0.0076032038778066635,
0.008237643167376518,
-0.0016899361507967114,
0.002410556422546506,
-0.04072950780391693,
0.03598850592970848,
-0.03229278698563576,
-0.0011080298572778702,
-0.025559525936841965,
-0.0027309360448271036,
-0.013950176537036896,
-0.02932029590010643,
-0.0009815789526328444,
0.01095432136207819,
-0.04835650697350502,
-0.017527690157294273,
0.06986036151647568,
0.009607383981347084,
0.037707678973674774,
-0.016909372061491013,
0.03582755848765373,
0.03996308147907257,
0.03459089994430542,
0.007572573143988848,
0.054597318172454834,
0.08612001687288284,
0.0021065545734018087,
-0.00007171999459387735,
0.046711262315511703,
0.01178064662963152,
0.002599448896944523,
0.01955953799188137,
0.021562086418271065,
0.011741179041564465,
-0.044686611741781235,
-0.010851404629647732,
-0.018105490133166313,
0.024201640859246254,
-0.007405191659927368,
0.01653987169265747,
0.07608368247747421,
-0.0332845114171505,
0.008982785046100616,
-0.06326809525489807,
0.009604345075786114,
0.0022611066233366728,
0.021888209506869316,
0.03900078311562538,
0.02504611387848854,
-0.02320917695760727,
-0.005890049040317535,
-0.0008555068052373827,
-0.009357571601867676,
0.0133202588185668,
-0.004325205460190773,
0.027195211499929428,
0.000273990910500288,
0.01406938023865223,
-0.029285253956913948,
-0.05544697865843773,
-0.026556063443422318,
-0.04049098119139671,
0.02325737290084362,
0.0163839440792799,
0.040170565247535706,
0.0302351675927639,
-0.01057831384241581,
-0.02422531694173813,
0.0548701137304306,
-0.06467374414205551,
0.010787482373416424,
-0.0018745830748230219,
0.023218587040901184,
0.022347237914800644,
-0.022046728059649467
] |
<p>There is an object moving in circle, with this law: </p>
<p>$$ \alpha = -k^2 \theta $$</p>
<p>With $ \alpha = \frac{ d \omega }{dt} $, and $ \omega= \frac{d \theta}{dt} $, $\theta$ = angle, $k$ positive constant. </p>
<p>I need to compute $ \theta $ in function of time. My attempt: </p>
<p>$$ \frac{d^2 \theta}{dt^2} = -k \theta $$
$$ \frac{d^2 \theta}{\theta} = -k^2 dt^2 $$
$$ \int_{\theta_0}^{\theta} {\frac{d^2 \theta}{\theta}} = - \int{k^2 dt^2} $$
$$ \ln\Big(\frac{\theta}{\theta_0}\Big) d\theta = -k^2 t \cdot dt$$</p>
<p>So I try to get the solution computing: </p>
<p>$$ \int_{\theta_0}^{\theta} \ln\Big(\frac{\theta}{\theta_0}\Big) d\theta = -\int k^2 t \cdot dt $$</p>
<p>But it's wrong, the solution is $\theta = \theta_0 \sin \big( kt + \phi \big) $.</p>
| 8,880 |
[
-0.016893161460757256,
-0.023977069184184074,
-0.00956808216869831,
0.004788713529706001,
0.016336515545845032,
-0.03074929118156433,
-0.04239101707935333,
-0.02434862032532692,
-0.004920163657516241,
-0.011310175992548466,
0.016900256276130676,
0.029728440567851067,
0.04826893284916878,
0.05889416113495827,
0.026966184377670288,
-0.014127198606729507,
-0.03542592003941536,
-0.02014179714024067,
-0.0001989880547625944,
-0.05974102392792702,
0.019424939528107643,
0.017443064600229263,
0.01182576548308134,
-0.04261833429336548,
-0.025123368948698044,
0.010728063061833382,
0.049799516797065735,
-0.013866475783288479,
-0.014543486759066582,
0.045187000185251236,
-0.038024917244911194,
0.0015248168492689729,
0.015476725064218044,
0.039930444210767746,
-0.004388946574181318,
0.03173871710896492,
-0.04819922149181366,
-0.012276307679712772,
-0.01381151657551527,
0.04212423041462898,
-0.010960240848362446,
-0.02599991299211979,
0.013177253305912018,
0.0626303032040596,
-0.013415283523499966,
0.012100397609174252,
-0.008848315104842186,
-0.02096790261566639,
0.046212777495384216,
-0.046924810856580734,
0.08237513154745102,
-0.025765307247638702,
0.04042269289493561,
0.03569231554865837,
-0.011075238697230816,
-0.021794747561216354,
0.03127855062484741,
0.0797489657998085,
-0.010692691430449486,
-0.046619608998298645,
-0.036039624363183975,
-0.027056243270635605,
-0.0024285458493977785,
0.013790411874651909,
0.020037909969687462,
-0.013861138373613358,
-0.01067245751619339,
-0.000420018972363323,
-0.009176262654364109,
0.007315997965633869,
0.03558552637696266,
0.01734028570353985,
0.05244847387075424,
0.01421282161027193,
0.004719650372862816,
-0.03229503333568573,
0.01475280337035656,
0.024461226537823677,
0.0028890492394566536,
0.044119928032159805,
-0.01610608771443367,
0.003375569125637412,
0.02670552209019661,
0.026693493127822876,
0.016431139782071114,
0.008377330377697945,
0.06056039407849312,
0.0069914949126541615,
-0.02212090976536274,
0.05432266369462013,
-0.0032258513383567333,
0.06535305827856064,
0.0023510155733674765,
-0.03191734105348587,
0.011861483566462994,
0.03690112382173538,
0.006783816963434219,
0.04144230857491493,
0.007728660944849253,
-0.014938239939510822,
0.007165322545915842,
-0.053399283438920975,
0.00936234649270773,
0.06713163107633591,
0.018388712778687477,
-0.0030097358394414186,
-0.03886019438505173,
-0.008175204508006573,
-0.00030536047415807843,
-0.02895941585302353,
-0.011499298736453056,
0.020163841545581818,
0.008415091782808304,
0.010920201428234577,
-0.020306628197431564,
-0.006386168301105499,
-0.04862239584326744,
0.006677737459540367,
0.037321820855140686,
0.03616239130496979,
0.04565603286027908,
-0.018434850499033928,
0.030421661213040352,
-0.005685840267688036,
-0.07122116535902023,
0.04029234126210213,
0.015003511682152748,
-0.009156216867268085,
-0.02378871478140354,
0.040163010358810425,
-0.0020604324527084827,
-0.01497900765389204,
0.009483502246439457,
0.020176894962787628,
0.057624656707048416,
-0.013092467561364174,
-0.04752325639128685,
-0.07120603322982788,
0.004497942980378866,
-0.004180183634161949,
-0.0025956497993320227,
-0.04648613929748535,
0.03244117274880409,
0.028407396748661995,
0.06963962316513062,
0.030088232830166817,
-0.032754234969615936,
0.03834778442978859,
0.032896459102630615,
-0.0050977496430277824,
-0.03156265616416931,
0.0035486703272908926,
0.006025461945682764,
0.011136534623801708,
0.0048753065057098866,
-0.05723073333501816,
0.020980261266231537,
0.028698720037937164,
-0.010676363483071327,
-0.0047065578401088715,
0.057723984122276306,
-0.02388901822268963,
0.016974247992038727,
0.019268667325377464,
-0.0030266062822192907,
-0.0342852845788002,
0.09031155705451965,
0.03626699000597,
0.008916081860661507,
0.003743440844118595,
0.03289615362882614,
0.011056221090257168,
-0.05020173266530037,
-0.016150223091244698,
0.05668766424059868,
-0.013653241097927094,
-0.004190783482044935,
-0.022084278985857964,
0.010018255561590195,
-0.0023764939978718758,
-0.005236894823610783,
-0.04924056679010391,
-0.01695861481130123,
0.002932762261480093,
0.008870577439665794,
0.06877892464399338,
-0.006582614965736866,
0.041695427149534225,
-0.0005699046305380762,
-0.01753109134733677,
-0.019154805690050125,
-0.0305035263299942,
0.04229069873690605,
-0.021580126136541367,
-0.010665389709174633,
0.03150273859500885,
-0.012013248167932034,
0.017833128571510315,
-0.004641311708837748,
-0.026781544089317322,
0.005019919481128454,
0.0007916893810033798,
0.0012914759572595358,
-0.037441421300172806,
0.042667802423238754,
0.06716491281986237,
0.02892909198999405,
-0.019672608003020287,
0.01452875416725874,
-0.03034324198961258,
0.05517169460654259,
-0.013438304886221886,
0.0038753061089664698,
0.01632079668343067,
0.01977534033358097,
0.0017998941475525498,
0.0061416104435920715,
-0.007642772048711777,
0.033403754234313965,
0.03200924023985863,
-0.040586214512586594,
0.08053837716579437,
0.07608572393655777,
0.00860811211168766,
0.015898702666163445,
0.030546819791197777,
0.0026330987457185984,
-0.0018458088161423802,
0.01785949058830738,
-0.05165756493806839,
-0.05030657723546028,
0.008043627254664898,
0.04538466036319733,
-0.004628336057066917,
-0.044460050761699677,
0.0013804719783365726,
0.04549850523471832,
0.0361899808049202,
0.03313803672790527,
-0.00470545282587409,
-0.026026682928204536,
-0.014204035513103008,
0.0024444484151899815,
0.007802704349160194,
-0.028085047379136086,
-0.004929710645228624,
0.014226778410375118,
0.003195311641320586,
0.01185651682317257,
-0.011306109838187695,
-0.02431986667215824,
0.02980503812432289,
0.010770309716463089,
0.015939464792609215,
0.022481046617031097,
-0.007217084988951683,
0.0497286282479763,
0.005953093059360981,
0.03118632733821869,
0.05690472945570946,
-0.013148673810064793,
0.00962959323078394,
-0.011027175933122635,
0.0044000474736094475,
0.017933949828147888,
0.025512302294373512,
-0.023539738729596138,
-0.021171672269701958,
0.01870993711054325,
-0.014551416039466858,
-0.027639446780085564,
-0.002764894161373377,
-0.03272220492362976,
-0.00710176071152091,
0.007813955657184124,
0.019834274426102638,
0.03278307616710663,
-0.01407909207046032,
0.008551543578505516,
-0.006422401871532202,
-0.024374794214963913,
0.00852357316762209,
-0.005765852052718401,
0.07240977138280869,
-0.07962970435619354,
0.009182712994515896,
0.014608237892389297,
-0.04566328600049019,
0.04140298068523407,
0.028874138370156288,
0.0180683396756649,
0.020840927958488464,
-0.04754549637436867,
-0.06406205892562866,
-0.022759897634387016,
-0.018442993983626366,
0.027043595910072327,
-0.05578815937042236,
0.042876217514276505,
0.036601174622774124,
0.026454929262399673,
0.0013625582214444876,
-0.006679776590317488,
-0.055097710341215134,
-0.047872405499219894,
-0.051485441625118256,
-0.0015522576868534088,
0.032598115503787994,
-0.005231485236436129,
0.004032206255942583,
-0.014332856051623821,
-0.04414379596710205,
-0.004445030819624662,
-0.06906414777040482,
-0.01203532237559557,
0.0170117300003767,
-0.0009269571746699512,
0.027172725647687912,
-0.0015021131839603186,
-0.01661601848900318,
0.0907311737537384,
0.012331590987741947,
-0.016001129522919655,
-0.025610508397221565,
0.0034483345225453377,
-0.018023895099759102,
-0.07872451096773148,
-0.02475237287580967,
0.03103337436914444,
-0.05447565019130707,
0.03684190660715103,
-0.000724197190720588,
0.015437188558280468,
0.03413677215576172,
0.025933939963579178,
-0.011875574477016926,
0.030508359894156456,
0.011991703882813454,
-0.003036276437342167,
0.04559360444545746,
0.034574732184410095,
0.0004143448604736477,
0.017205823212862015,
0.0031757927499711514,
0.053801022469997406,
0.03419701009988785,
-0.047247711569070816,
0.016472624614834785,
-0.01923120953142643,
-0.03258296474814415,
0.014109998941421509,
0.030220234766602516,
-0.015342648141086102,
-0.023005684837698936,
-0.032971616834402084,
0.0383569709956646,
0.05904029309749603,
-0.006750624161213636,
-0.004993298556655645,
0.04254811257123947,
0.0013708750484511256,
-0.012322569265961647,
-0.023362822830677032,
-0.055399563163518906,
-0.00908149778842926,
0.023452676832675934,
-0.04225418344140053,
-0.0051935818046331406,
-0.0016669550677761436,
0.026099076494574547,
0.010652176104485989,
0.0002837635111063719,
-0.046924296766519547,
0.02173730917274952,
-0.05513707920908928,
-0.028616901487112045,
-0.0375431552529335,
0.052781011909246445,
0.00008211947715608403,
0.04538804665207863,
0.037419434636831284,
-0.005321643780916929,
0.05356742814183235,
0.023839810863137245,
-0.09228362888097763,
0.06529302895069122,
-0.042310841381549835,
-0.028393009677529335,
0.01010051742196083,
0.010109922848641872,
0.006129777058959007,
-0.028975099325180054,
0.01175670139491558,
0.00710301473736763,
-0.01707901619374752,
-0.044331323355436325,
0.01847878284752369,
0.0007832985138520598,
-0.011358783580362797,
-0.029910413548350334,
0.05171855911612511,
0.043379202485084534,
-0.037039052695035934,
0.022366419434547424,
0.05926019698381424,
-0.0011255976278334856,
0.03575117513537407,
-0.06686771661043167,
-0.005221950821578503,
0.0003373648796696216,
0.05064655840396881,
0.0014999824343249202,
-0.020470477640628815,
0.0018180670449510217,
0.008595620281994343,
-0.019404416903853416,
0.06094034016132355,
0.028644762933254242,
-0.006820335518568754,
-0.04365862160921097,
-0.05275106057524681,
0.012710903771221638,
-0.0322534404695034,
0.07804832607507706,
0.00020158421830274165,
0.0038315702695399523,
0.056716181337833405,
-0.01270373072475195,
0.024529920890927315,
0.007450951263308525,
0.04375931993126869,
-0.03331349045038223,
-0.025117285549640656,
-0.019578538835048676,
-0.012843961827456951,
-0.014933661557734013,
-0.016899196431040764,
0.021950189024209976,
-0.017105603590607643,
0.010669860057532787,
0.004194736015051603,
0.005839100107550621,
0.018404703587293625,
0.03483153507113457,
0.01100668404251337,
-0.0021160768810659647,
0.019798332825303078,
-0.012211117893457413,
-0.02233966626226902,
0.04078971594572067,
0.04040471464395523,
0.02580316737294197,
0.0006242500967346132,
0.014507230371236801,
-0.08202285319566727,
-0.0357026532292366,
0.010194973088800907,
0.022764913737773895,
0.003951362334191799,
-0.003224617103114724,
-0.07105100154876709,
-0.043291497975587845,
0.05492337793111801,
-0.04995298758149147,
0.07086767256259918,
-0.03174619376659393,
0.0053956094197928905,
0.00041168538155034184,
-0.04972630366683006,
-0.01534888707101345,
0.024582820013165474,
-0.028960397467017174,
0.006878800690174103,
-0.056978292763233185,
0.0025607419665902853,
0.02808557264506817,
0.003300193464383483,
0.010362963192164898,
0.04012797400355339,
0.02305341139435768,
-0.058197371661663055,
0.005086906254291534,
-0.007432427257299423,
-0.0348481684923172,
-0.03462468087673187,
0.01507754996418953,
0.0058201695792376995,
-0.006266055628657341,
-0.004489017650485039,
-0.040141623467206955,
-0.02855231612920761,
0.03331926092505455,
-0.009647699072957039,
-0.013046554289758205,
-0.010677549056708813,
-0.050923582166433334,
0.013883372768759727,
0.04523009434342384,
0.012929701246321201,
0.042877376079559326,
0.02091206982731819,
-0.0008781807264313102,
-0.00995979830622673,
-0.011413819156587124,
0.006830874364823103,
0.01503633614629507,
0.0015794752398505807,
-0.009530540555715561,
-0.01969865709543228,
-0.03367399796843529,
0.03936062753200531,
-0.005792457610368729,
0.017171913757920265,
-0.025855351239442825,
0.0226607546210289,
-0.020030777901411057,
0.04133303090929985,
0.005687096156179905,
-0.001597365946508944,
0.05415968969464302,
-0.0006201639189384878,
0.040016211569309235,
-0.03166820481419563,
0.00863740872591734,
-0.03373173624277115,
-0.014201981015503407,
0.04289235919713974,
-0.004662798717617989,
-0.02071060985326767,
-0.030334392562508583,
-0.06551295518875122,
-0.013276468962430954,
-0.044912662357091904,
0.015450561419129372,
-0.02549775503575802,
0.000028344753445708193,
0.05195552483201027,
-0.05813290551304817,
-0.05753270536661148,
-0.019296884536743164,
0.006112040486186743,
0.044377557933330536,
-0.056207288056612015,
0.008945265784859657,
0.030190136283636093,
0.02172139286994934,
-0.05195213854312897,
-0.0364624485373497,
0.005339046008884907,
-0.0019759065471589565,
-0.005180272273719311,
0.001273792120628059,
-0.02681909129023552,
0.00030579225858673453,
-0.056213319301605225,
0.015496673062443733,
0.04293004423379898,
-0.005146421026438475,
-0.004243054892867804,
-0.019215524196624756,
0.030870964750647545,
0.055499367415905,
0.0094321109354496,
0.011306673288345337,
0.030465751886367798,
-0.024279821664094925,
-0.043470337986946106,
0.018340829759836197,
0.06814120709896088,
-0.030902402475476265,
-0.020512785762548447,
0.0036534746177494526,
0.03253459185361862,
0.03200790286064148,
0.036288678646087646,
-0.039802078157663345,
0.02580292895436287,
0.019665470346808434,
0.013823091052472591,
-0.030085664242506027,
0.013702726922929287,
0.02635323815047741,
0.029519934207201004,
-0.02392089180648327,
-0.011297847144305706,
-0.06116236001253128,
-0.03245628997683525,
-0.005447088275104761,
-0.01952727511525154,
0.03686343878507614,
-0.036168210208415985,
0.0437588132917881,
-0.04786599799990654,
0.0034873036202043295,
0.007855124771595001,
0.019605081528425217,
0.024978358298540115,
-0.015433046966791153,
0.002147231949493289,
0.023440465331077576,
0.0001287817140109837,
-0.04638435319066048,
-0.020245786756277084,
-0.012470650486648083,
-0.01878678798675537,
0.07719176262617111,
-0.01789131760597229,
0.04722948744893074,
-0.01584828644990921,
0.022217752411961555,
0.001956996973603964,
-0.023649035021662712,
-0.04551507160067558,
-0.008099626749753952,
-0.008085082285106182,
0.027282387018203735,
-0.013268939219415188,
0.02978956140577793,
0.01418439019471407,
0.043419212102890015,
-0.02616087719798088,
-0.009419784881174564,
-0.005254816263914108,
0.002263852162286639,
-0.026141135022044182,
0.017061231657862663,
-0.015105674974620342,
0.013779891654849052,
-0.03241151571273804,
0.0648232027888298,
-0.0432259626686573,
-0.005880863405764103,
0.05848025903105736,
0.003987578209489584,
0.01561239454895258,
-0.01653781346976757,
0.006117843557149172,
-0.018515734001994133,
0.0032283358741551638,
0.011274031363427639,
-0.022260941565036774,
-0.016529174521565437,
0.022402778267860413,
0.021258186548948288,
0.015331199392676353,
0.0014928270829841495,
-0.029319701716303825,
-0.050223637372255325,
-0.03234373405575752,
-0.061868343502283096,
-0.05932977423071861,
0.0441819429397583,
0.008051831275224686,
0.00031830224907025695,
0.03265710920095444,
-0.015602605417370796,
0.0149585772305727,
0.04601980000734329,
0.012505530379712582,
-0.03335190564393997,
0.13009802997112274,
-0.007715485990047455,
0.03182075917720795,
-0.019938964396715164,
0.0021012471988797188,
0.11035258322954178,
0.01542419008910656,
-0.039661094546318054,
-0.04440709203481674,
0.020862886682152748,
-0.029016641899943352,
0.013775077648460865,
-0.06195029243826866,
0.02706747129559517,
-0.02765827067196369,
-0.02887079492211342,
0.022623121738433838,
0.03213522955775261,
-0.00018378124514129013,
-0.009802194312214851,
0.011764241382479668,
-0.027970727533102036,
-0.04265189915895462,
-0.007485055364668369,
-0.0063089788891375065,
-0.00401590159162879,
0.028034206479787827,
0.006856195628643036,
0.046635888516902924,
-0.056960590183734894,
0.001701732398942113,
-0.037407536059617996,
-0.0407060906291008,
0.04061391204595566,
-0.0135716013610363,
-0.06870456039905548,
0.04562898725271225,
0.033027831465005875,
-0.044033147394657135,
-0.01368272490799427,
0.0292756799608469,
0.028481656685471535,
0.008165350183844566,
0.047984812408685684,
0.06623613089323044,
0.011960494332015514,
0.025613322854042053,
-0.004212514963001013,
0.009985359385609627,
-0.002657527569681406,
0.013410769402980804,
-0.047310542315244675,
0.06201065331697464,
-0.00426585553213954,
0.027131397277116776,
0.0025290322955697775,
0.013800226151943207,
-0.022735413163900375,
-0.06321178376674652,
-0.002503198804333806,
0.007122385315597057,
0.010801575146615505,
-0.03426181524991989,
0.0013510846765711904,
0.010495669208467007,
0.024618910625576973,
0.027587847784161568,
0.04496905952692032,
-0.026103582233190536,
0.01593692973256111,
0.011559741571545601,
0.0008926254231482744,
0.03874529153108597,
-0.012272721156477928,
-0.026537278667092323,
-0.0003071447426918894,
-0.003349343314766884,
-0.03199967369437218,
0.04734594747424126,
-0.003474969184026122,
-0.0027439105324447155,
0.016894398257136345,
-0.020033543929457664,
-0.0196713674813509,
-0.07938698679208755,
-0.05845300480723381,
0.004527013283222914,
0.021690284833312035,
-0.03711725026369095,
-0.040803346782922745,
-0.003498931648209691,
0.01776876114308834,
0.037235792726278305,
-0.013731160201132298,
-0.009489205665886402,
0.008329708129167557,
0.047772277146577835,
0.0232120081782341,
-0.027875427156686783,
-0.0486539788544178,
-0.0006743118283338845,
-0.013021267019212246,
0.04660285636782646,
-0.04876327142119408,
0.047695841640233994,
0.016833966597914696,
0.0022120028734207153,
0.006904793903231621,
0.04686877876520157,
-0.023898376151919365,
0.031762685626745224,
-0.013227017596364021,
-0.007349010556936264,
-0.0057748607359826565,
0.012348146177828312,
0.012983957305550575,
-0.02137637510895729,
0.0043435837142169476,
-0.0329698845744133,
0.01895594783127308,
-0.004594648256897926,
-0.010709045454859734,
-0.02384589985013008,
0.034596800804138184,
-0.04947664961218834,
-0.003758074948564172,
-0.029835298657417297,
0.047678690403699875,
-0.007177612278610468,
0.00703497463837266,
-0.02790161967277527,
0.004974828101694584,
-0.03371564298868179,
0.06176816299557686,
-0.002543681301176548,
-0.021847596392035484,
0.02108723670244217,
0.03623737022280693,
-0.0008653795230202377,
-0.02171389013528824,
0.012326550669968128,
-0.024348801001906395,
0.02673395164310932,
-0.031168250367045403,
-0.012978849932551384,
0.0263776034116745,
0.0023885711561888456,
-0.02337033674120903,
0.032266952097415924,
0.005044146906584501,
0.017634117975831032,
-0.00648388359695673,
-0.017455384135246277,
-0.0013827400980517268,
0.04829717054963112,
-0.02119077928364277,
-0.011535871773958206,
0.006419154349714518,
-0.07524512708187103,
-0.015404310077428818,
-0.02241283282637596,
0.026412060484290123,
-0.0061752949841320515,
0.019212132319808006,
0.02058415673673153,
0.017291665077209473,
-0.008171469904482365,
-0.006546003744006157,
-0.007032312918454409,
0.03531847149133682,
0.02119140513241291,
0.05445185303688049,
-0.0012807053280994296,
0.07903878390789032,
0.014642538502812386,
0.012045677751302719,
0.01508550625294447,
-0.0038700182922184467,
-0.01818511076271534,
-0.08469066023826599,
0.01738477125763893,
0.0004728780477307737,
0.030712077394127846,
0.08360113948583603,
-0.07278022170066833,
-0.0070049394853413105,
0.02991570346057415,
-0.05748704448342323,
0.031373538076877594,
-0.041432932019233704,
0.015649549663066864,
-0.0122142992913723,
-0.035668134689331055,
0.005383811891078949,
0.029604481533169746,
0.0371045283973217,
0.04887108504772186,
0.009037632495164871,
-0.005407595541328192,
0.035191673785448074,
-0.03429708257317543,
0.0008342084474861622,
0.034970205277204514,
0.024595215916633606,
-0.0023708848748356104,
0.05893804132938385,
-0.06082930788397789,
-0.010968543589115143,
-0.0005095181404612958,
-0.02054656483232975,
0.037036411464214325,
-0.0027947956696152687,
0.018785251304507256,
0.009934201836585999,
0.05241408944129944,
0.0009762568515725434,
0.02766549214720726,
-0.019031107425689697,
0.004701151046901941,
0.018846092745661736,
-0.010720289312303066,
-0.03650462627410889,
-0.03615657985210419,
-0.00590115413069725,
-0.0489959754049778,
-0.06412380933761597,
0.03725242242217064,
0.0064312429167330265,
-0.007851202972233295,
-0.01602911576628685,
-0.03826776146888733,
0.03167469799518585,
-0.03111954778432846,
-0.023347098380327225,
-0.006374383345246315,
-0.017288723960518837,
0.026576481759548187,
-0.0350269116461277,
0.0006769716856069863,
-0.03707211837172508,
-0.03053283877670765,
-0.05486851558089256,
0.019213782623410225,
-0.010054653510451317,
-0.0006796530797146261,
-0.03527525067329407,
-0.03388122841715813,
-0.005292847752571106,
-0.005329653155058622,
0.024128902703523636,
-0.018055938184261322,
-0.025510570034384727,
0.011844159103929996,
-0.0031585583928972483,
0.01834886148571968,
0.0038455750327557325,
-0.007109140045940876,
-0.03077208623290062,
-0.05668662488460541,
0.023916058242321014,
-0.011732976883649826,
-0.029175132513046265,
-0.02188485488295555,
-0.015490338206291199,
-0.013767390511929989,
0.025232017040252686,
0.008118782192468643,
-0.009597433730959892,
0.0025915796868503094,
0.00595753313973546,
-0.05076708644628525,
0.0031480237375944853,
-0.06020071357488632,
-0.0005224841297604144,
-0.004380805417895317,
-0.008807569742202759,
0.017519600689411163,
0.01588873751461506,
-0.005884681362658739,
0.00825041625648737,
-0.007398458197712898,
0.012009001336991787,
0.028315018862485886,
0.0007918200572021306,
-0.030178643763065338,
0.014687183313071728,
-0.010492568835616112,
0.013570738956332207,
0.059922732412815094,
-0.0033662118948996067,
0.029510630294680595,
0.03403894230723381,
-0.01927664875984192,
-0.02989468351006508,
0.038519758731126785,
-0.09979917854070663,
-0.03767208755016327,
-0.04524751380085945,
0.000612532370723784,
0.015269880183041096,
-0.04830295965075493,
-0.019760344177484512,
0.05283764749765396,
-0.014198042452335358,
-0.019017096608877182,
0.020559636875987053,
-0.022743459790945053,
0.07330963015556335,
-0.010522796772420406,
0.02038498967885971,
0.03848994895815849,
0.013257197104394436,
0.015482006594538689,
-0.0012710279552266002,
-0.0004549245350062847,
-0.022242126986384392,
-0.02205345220863819,
0.026955416426062584,
0.004136589355766773,
0.008699066005647182,
-0.027515480294823647,
0.03291430324316025,
-0.00838951114565134,
-0.00201628846116364,
-0.010783586651086807,
-0.03587764874100685,
-0.011787546798586845,
0.02870907261967659,
-0.01991465501487255,
0.03298354521393776,
-0.014648038893938065,
0.032987434417009354,
0.0013630015309900045,
-0.04304410144686699,
-0.006499958224594593,
0.03932276368141174,
0.031378280371427536,
0.017170041799545288,
-0.022823231294751167,
-0.022725887596607208,
0.008069186471402645,
-0.013007399626076221,
-0.0015317527577280998,
-0.03613846376538277,
0.0030152429826557636,
-0.010127788409590721,
-0.021902766078710556,
-0.015547245740890503,
-0.04828750714659691,
-0.03309934213757515,
-0.058570876717567444,
0.026380397379398346,
0.031228454783558846,
0.01718834973871708,
-0.02443283423781395,
-0.013415456749498844,
-0.02090749889612198,
0.05182352662086487,
-0.048399727791547775,
0.02226170338690281,
-0.004434507805854082,
0.00517094973474741,
0.04083935543894768,
-0.040859855711460114
] |
<p>In a turning plane, will the vector of combined centrifugal plus gravity force experienced by passengers be perpendicular to the floor? In other words, will the passengers experience the feeling of inclination without looking into windows?</p>
<p>I think that the reaction of air is perpendicular to the wings and as such, there will be no feeling of inclination. Am I right?</p>
| 8,881 |
[
-0.050508979707956314,
-0.02458358369767666,
-0.03062869794666767,
0.020005889236927032,
0.025694668292999268,
0.021811984479427338,
-0.03694538772106171,
-0.0026946316938847303,
0.007113482337445021,
-0.03862109035253525,
-0.007674282416701317,
0.052939724177122116,
0.027109481394290924,
0.0345529243350029,
-0.020667755976319313,
-0.022844647988677025,
-0.035210974514484406,
0.018701404333114624,
0.01410158071666956,
-0.03195786103606224,
-0.012940759770572186,
-0.008557479828596115,
0.012428625486791134,
-0.021224211901426315,
-0.035525787621736526,
0.023254644125699997,
0.035381995141506195,
-0.06512385606765747,
-0.010345163755118847,
0.011271119117736816,
-0.027949098497629166,
0.02663043513894081,
0.014040578156709671,
0.025385741144418716,
0.021335739642381668,
-0.007359660696238279,
-0.025612540543079376,
0.03967665508389473,
-0.018969062715768814,
0.0067771500907838345,
-0.011418286710977554,
0.011848850175738335,
-0.013432326726615429,
0.06455758213996887,
-0.0045898412354290485,
0.01588955521583557,
-0.01908729411661625,
0.022886866703629494,
0.04775526002049446,
-0.1121353954076767,
0.05051174759864807,
-0.016020970419049263,
-0.018897639587521553,
-0.00022913895372767001,
0.04332143813371658,
-0.01719372719526291,
0.04546085745096207,
0.07469744235277176,
0.005506948102265596,
-0.033910129219293594,
0.013765459880232811,
-0.02592318132519722,
-0.028186971321702003,
-0.05241602659225464,
-0.03950846567749977,
0.00754171796143055,
-0.010191414505243301,
-0.03472083434462547,
0.03524717688560486,
-0.015195941552519798,
-0.010794617235660553,
0.052627597004175186,
0.017758863046765327,
-0.011671280488371849,
-0.0037450126837939024,
-0.04194328933954239,
0.0504576601088047,
0.018261659890413284,
0.01259259507060051,
0.020775286480784416,
0.00458476971834898,
0.003014023182913661,
0.04307171702384949,
0.06880487501621246,
0.027483496814966202,
0.005420860834419727,
0.05774766206741333,
-0.005973484832793474,
0.01616164669394493,
0.06777959316968918,
0.028635350987315178,
-0.010300575755536556,
0.010057549923658371,
-0.010528321377933025,
-0.03769075125455856,
0.005728369113057852,
-0.0036094048991799355,
0.05092950537800789,
0.03040187805891037,
-0.024079620838165283,
-0.03582502529025078,
0.03202735260128975,
-0.018200568854808807,
0.06863951683044434,
0.008805929683148861,
-0.0027402241248637438,
-0.016827575862407684,
0.0013764818431809545,
-0.011812360025942326,
-0.018337426707148552,
-0.06545376777648926,
0.027584265917539597,
-0.0327436588704586,
-0.026093270629644394,
0.026523420587182045,
0.017929857596755028,
-0.00761565612629056,
-0.009249670431017876,
0.029550470411777496,
0.0896158292889595,
0.05672416090965271,
-0.0293265450745821,
-0.013254756107926369,
-0.03356020525097847,
-0.048737991601228714,
0.015319406986236572,
0.03650921583175659,
-0.0333695188164711,
-0.03402397036552429,
-0.02333303540945053,
0.022726040333509445,
-0.04313238337635994,
0.01286290306597948,
0.008947386406362057,
0.028192689642310143,
-0.0024142831098288298,
-0.08598353713750839,
-0.07084602862596512,
0.05560647323727608,
0.010720153339207172,
-0.004428906366229057,
-0.09279198199510574,
-0.013275213539600372,
0.055613983422517776,
0.03336351737380028,
0.00900763738900423,
0.02391868084669113,
0.007976476103067398,
0.009906195104122162,
0.03941529244184494,
-0.029562892392277718,
0.04391852393746376,
-0.021358195692300797,
-0.03888211399316788,
-0.03986061364412308,
-0.030840296298265457,
0.0023550952319055796,
0.02583690546452999,
0.011336029507219791,
-0.06530807912349701,
0.016160020604729652,
-0.02685079537332058,
0.014467095956206322,
-0.020016279071569443,
-0.012968149967491627,
-0.03232565522193909,
0.06023550033569336,
0.01927921548485756,
-0.004544040188193321,
-0.015418220311403275,
0.008157585747539997,
0.025704244151711464,
-0.014205771498382092,
0.021849462762475014,
0.05453607067465782,
-0.015720553696155548,
-0.004203231539577246,
-0.025051791220903397,
0.04970468208193779,
-0.006557693239301443,
-0.0316949337720871,
-0.0346699096262455,
-0.038858432322740555,
0.01588554121553898,
-0.02211133949458599,
0.053491346538066864,
-0.012312985956668854,
-0.02772095799446106,
-0.004277296829968691,
-0.04044615104794502,
0.010856613516807556,
-0.04860970377922058,
0.01929214969277382,
-0.014965545386075974,
-0.02253614366054535,
0.022340673953294754,
0.002638360485434532,
0.02194971591234207,
-0.060715608298778534,
-0.002739453222602606,
-0.03616771847009659,
-0.0030670599080622196,
0.02299937978386879,
-0.013079410418868065,
-0.00690494803711772,
0.03024696372449398,
0.04016377404332161,
-0.008309519849717617,
-0.013264261186122894,
-0.027758127078413963,
-0.006678481586277485,
-0.00519372895359993,
-0.03474321961402893,
0.0047718980349600315,
0.014073239639401436,
0.025146877393126488,
0.023028245195746422,
0.03415132313966751,
0.020328551530838013,
0.05184480547904968,
-0.05543963983654976,
0.03955438360571861,
0.059644605964422226,
0.004585710354149342,
0.06876273453235626,
0.031276147812604904,
0.0070794387720525265,
-0.008073038421571255,
0.033908944576978683,
-0.016054024919867516,
-0.04329262301325798,
-0.011773481965065002,
0.051474813371896744,
-0.012918633408844471,
-0.015305344946682453,
0.011277172714471817,
0.010966692119836807,
0.05656469613313675,
-0.007957094348967075,
0.027357375249266624,
0.011691223829984665,
-0.029571084305644035,
0.01133810542523861,
0.018884696066379547,
0.03323255479335785,
0.0066620768047869205,
0.022182069718837738,
0.018592413514852524,
-0.005979288835078478,
0.016471274197101593,
-0.018416710197925568,
0.01700466498732567,
0.022254351526498795,
0.04684360325336456,
-0.02054467983543873,
0.004360198974609375,
0.051261913031339645,
0.007720226887613535,
-0.018587520346045494,
0.017866455018520355,
-0.016154667362570763,
-0.03632460534572601,
0.015063882805407047,
-0.02036409266293049,
-0.01212041825056076,
0.016855616122484207,
-0.0031466269865632057,
-0.0005273200804367661,
0.06165105104446411,
-0.047869157046079636,
0.023188726976513863,
-0.002046089619398117,
-0.007746712304651737,
0.02769404649734497,
-0.01090914849191904,
0.01987312361598015,
0.010924667119979858,
0.032950591295957565,
0.010686111636459827,
-0.00317693455144763,
0.03308689594268799,
-0.05269484221935272,
-0.014053567312657833,
-0.0015350168105214834,
-0.0627693384885788,
0.034848809242248535,
-0.05736992508172989,
-0.03806055709719658,
-0.0017639138968661427,
0.022773906588554382,
0.005611453205347061,
0.03087921068072319,
-0.011942926794290543,
-0.0795627310872078,
0.005232042632997036,
-0.04301249608397484,
-0.020834553986787796,
-0.027057182043790817,
-0.0026668047066777945,
0.020012540742754936,
0.019564658403396606,
-0.00812368281185627,
0.008049468509852886,
-0.06529567390680313,
-0.07012157887220383,
-0.0005688443197868764,
-0.005442917812615633,
0.014216450043022633,
-0.025881439447402954,
0.01991410180926323,
0.039951715618371964,
-0.03414774686098099,
-0.00795767828822136,
-0.0675189197063446,
-0.030463239178061485,
0.019855253398418427,
-0.015209262259304523,
0.03362460806965828,
0.031488340348005295,
-0.019020743668079376,
0.05850853770971298,
-0.0020318995229899883,
-0.03644251450896263,
-0.03483588993549347,
-0.03102821484208107,
-0.006078158039599657,
-0.006375259719789028,
0.019545769318938255,
0.04305323213338852,
0.014505906030535698,
0.025823084637522697,
-0.00017495351494289935,
0.010443358682096004,
-0.023318488150835037,
0.0321408286690712,
-0.028043271973729134,
-0.0015182718634605408,
-0.0002633118419907987,
0.035561107099056244,
0.00826045498251915,
0.020012982189655304,
0.012967806309461594,
-0.012884861789643764,
0.025077318772673607,
0.029662657529115677,
0.05080537497997284,
-0.025480637326836586,
0.07592810690402985,
-0.011899364180862904,
0.00412824796512723,
-0.001381841953843832,
0.03203414008021355,
-0.012724445201456547,
0.006541573908179998,
-0.017641182988882065,
0.012941259890794754,
0.03359871357679367,
-0.03117278777062893,
-0.0203845277428627,
0.052076030522584915,
0.016798842698335648,
-0.025718320161104202,
-0.030432460829615593,
0.03436506539583206,
0.027172543108463287,
0.040572457015514374,
-0.043998122215270996,
-0.012708909809589386,
0.018072854727506638,
0.05353134498000145,
0.02135622687637806,
0.07587121427059174,
-0.061311978846788406,
0.03760942816734314,
-0.05142124369740486,
0.022099997848272324,
0.0008473917259834707,
0.024960676208138466,
-0.02700735256075859,
0.02784738317131996,
0.0015293019823729992,
0.02065933868288994,
0.01787165179848671,
0.006088115740567446,
-0.0815245658159256,
-0.0007786394562572241,
-0.03178737685084343,
-0.0018826964078471065,
-0.013991902582347393,
-0.01812283881008625,
-0.021136511117219925,
-0.056241344660520554,
-0.03277016803622246,
-0.017179688438773155,
-0.027331549674272537,
-0.048291150480508804,
0.007679292932152748,
-0.011407631449401379,
-0.01447245478630066,
-0.004808653611689806,
0.03841889649629593,
0.01513983216136694,
-0.03902117535471916,
0.06440918147563934,
0.0548827238380909,
-0.028892982751131058,
-0.0023835645988583565,
-0.008197573013603687,
0.02947179600596428,
-0.0336298830807209,
0.044076792895793915,
0.021231040358543396,
-0.013783568516373634,
-0.03931191936135292,
0.004923991393297911,
-0.015237126499414444,
0.002719329437240958,
-0.003449462354183197,
0.013686652295291424,
-0.03223260119557381,
-0.04588291049003601,
-0.028050938621163368,
0.0036163548938930035,
-0.004087961744517088,
0.011899508535861969,
0.0034706539008766413,
0.02522265538573265,
0.013945959508419037,
-0.0026856805197894573,
0.007345820777118206,
0.03258905187249184,
0.025886595249176025,
-0.0011097188107669353,
-0.02988830767571926,
0.029366010800004005,
-0.014263518154621124,
-0.03440466895699501,
0.02523268386721611,
0.0055609773844480515,
-0.05504435673356056,
-0.04329357668757439,
0.030945738777518272,
0.005457958206534386,
-0.004172696731984615,
0.04240097478032112,
-0.03153963014483452,
0.00787951797246933,
0.012767951935529709,
0.014818094670772552,
-0.030483661219477654,
0.044883403927087784,
0.039167314767837524,
0.018325388431549072,
-0.02043541520833969,
-0.08414984494447708,
0.00969455111771822,
0.031686894595623016,
0.014690518379211426,
-0.037342239171266556,
0.003207618836313486,
-0.02989237569272518,
-0.027605222538113594,
0.026042895391583443,
-0.01015747245401144,
-0.01969987340271473,
-0.07293969392776489,
-0.013072569854557514,
-0.03750796243548393,
-0.021932311356067657,
-0.03650589659810066,
0.03057594783604145,
-0.013641090132296085,
-0.012710311450064182,
-0.007364316843450069,
0.0068890745751559734,
0.0014072696212679148,
0.001971559366211295,
0.029930537566542625,
-0.0052308510057628155,
0.04401341453194618,
0.004566107876598835,
-0.01472145039588213,
0.012647772207856178,
-0.07507994771003723,
-0.06972861289978027,
0.000014635527804784942,
0.03525364026427269,
-0.005186738912016153,
0.02517746388912201,
0.0015581197803840041,
-0.027492215856909752,
0.002740177558735013,
-0.004058435093611479,
0.024578573182225227,
0.01207774505019188,
-0.02902832441031933,
0.021490072831511497,
0.024573488160967827,
0.007277814205735922,
0.01903519220650196,
0.01668855920433998,
-0.0308001060038805,
-0.013108021579682827,
0.029773568734526634,
0.036167025566101074,
-0.02456299588084221,
-0.01839189976453781,
0.005837556440383196,
0.006992005743086338,
-0.03617733716964722,
0.028484150767326355,
-0.009054269641637802,
0.039953410625457764,
-0.03884274140000343,
-0.02300390601158142,
-0.05286404490470886,
0.048782020807266235,
0.04889471083879471,
0.02538995072245598,
-0.0264881681650877,
-0.006705599371343851,
-0.013484434224665165,
-0.0312202125787735,
-0.019144892692565918,
-0.028725478798151016,
-0.004368605557829142,
0.04615680128335953,
-0.006894224788993597,
-0.012013216502964497,
-0.024186117574572563,
-0.0041183531284332275,
-0.014261264353990555,
-0.07221569865942001,
0.06656978279352188,
-0.025510137900710106,
0.0037416620180010796,
0.084291473031044,
-0.029268354177474976,
0.009984554722905159,
0.05915141478180885,
0.00034892436815425754,
0.009604530408978462,
-0.017579583451151848,
0.02249082922935486,
0.01900048553943634,
0.029977193102240562,
-0.01928292028605938,
-0.027371855452656746,
0.04164956137537956,
0.021912364289164543,
-0.030060652643442154,
-0.06997070461511612,
-0.03245319053530693,
-0.042126208543777466,
-0.04010479152202606,
0.002553296275436878,
0.019624361768364906,
-0.03795996308326721,
0.02491101808845997,
0.02616620436310768,
-0.027626069262623787,
0.06475493311882019,
-0.00048033864004537463,
-0.031629856675863266,
0.01648164540529251,
-0.008996432647109032,
-0.008766277693212032,
-0.02317913807928562,
0.03984224051237106,
-0.011734838597476482,
-0.03582942858338356,
-0.016549883410334587,
-0.03238243982195854,
0.037570029497146606,
-0.00479808310046792,
0.03916154429316521,
-0.0005822755629196763,
-0.02293027937412262,
-0.023876605555415154,
-0.01896173506975174,
-0.005572301801294088,
-0.016055885702371597,
0.017159486189484596,
-0.013537335209548473,
0.011057980358600616,
0.03450293838977814,
-0.008202149532735348,
0.03848540782928467,
0.05300787463784218,
-0.01517405454069376,
0.009817849844694138,
0.10455552488565445,
0.005606763064861298,
-0.02560187689960003,
-0.021270325407385826,
0.00179813161958009,
0.050002600997686386,
-0.001895016641356051,
-0.009980452246963978,
0.0075370073318481445,
-0.006032806821167469,
-0.0026701067108660936,
-0.02886008657515049,
-0.03505038842558861,
0.012543074786663055,
0.05291089788079262,
-0.007691347040235996,
0.06842329353094101,
-0.014341268688440323,
0.036074068397283554,
-0.021404391154646873,
0.005105034448206425,
0.0006750420434400439,
-0.026405729353427887,
-0.012598421424627304,
0.018959911540150642,
-0.013875914737582207,
-0.02450312115252018,
0.00030721514485776424,
0.06060964986681938,
-0.005544567480683327,
-0.047626011073589325,
0.02902209386229515,
0.009036927483975887,
0.04384368658065796,
0.005710497964173555,
-0.03516744077205658,
0.02855966053903103,
-0.04048269987106323,
0.06016933545470238,
-0.03431582450866699,
-0.014993254095315933,
0.020518656820058823,
0.00972903985530138,
0.04877025634050369,
-0.04406021535396576,
0.006856394000351429,
-0.010171196423470974,
0.01490762084722519,
0.006823510397225618,
0.005451140459626913,
-0.05887391045689583,
0.033637989312410355,
0.06834974139928818,
-0.015131121501326561,
-0.029204878956079483,
0.01494558434933424,
-0.06825011223554611,
-0.01746193878352642,
-0.03739751875400543,
0.005137366242706776,
0.035880621522665024,
0.0047531998716294765,
-0.02462773025035858,
0.019999047741293907,
-0.0035502142272889614,
0.025589633733034134,
0.009762796573340893,
0.01618640124797821,
0.02893364615738392,
0.04848651960492134,
-0.023690544068813324,
0.03413912653923035,
-0.03303202986717224,
0.00811775866895914,
0.14510424435138702,
-0.0073320153169333935,
-0.013678190298378468,
-0.024548443034291267,
-0.008203173987567425,
-0.00872165709733963,
-0.014550683088600636,
0.00850395206362009,
0.02669125236570835,
0.027967818081378937,
0.006074842531234026,
0.0305488184094429,
0.051288507878780365,
-0.011940325610339642,
-0.03798045217990875,
0.01813710853457451,
-0.03272875398397446,
-0.04742920771241188,
-0.025898737832903862,
0.020607981830835342,
-0.04366590082645416,
0.00032678540446795523,
-0.01948157139122486,
0.0345383882522583,
-0.035341501235961914,
0.04320602864027023,
0.0045632957480847836,
-0.04081231728196144,
0.016264185309410095,
-0.0016047828830778599,
-0.0621771365404129,
-0.006986746098846197,
0.04170951992273331,
-0.014559103175997734,
-0.0710776224732399,
-0.005541744641959667,
-0.020580649375915527,
-0.012918589636683464,
0.04160786792635918,
0.01990831457078457,
0.004883196670562029,
0.020536955446004868,
0.02105151303112507,
0.01824796572327614,
-0.05214851349592209,
-0.023709386587142944,
-0.017670487985014915,
0.01456416118890047,
-0.01113721914589405,
0.010258167050778866,
-0.006800300907343626,
0.022469988092780113,
-0.006139938719570637,
-0.08621449768543243,
0.020332539454102516,
-0.016443002969026566,
0.000558425032068044,
-0.01603785529732704,
-0.026896538212895393,
-0.00628439337015152,
0.03424462303519249,
0.05572928860783577,
-0.023562708869576454,
-0.054301731288433075,
-0.00870914850383997,
0.0030358112417161465,
0.009169408120214939,
0.07784916460514069,
-0.03816010802984238,
-0.02609742060303688,
-0.05033542215824127,
-0.02720627561211586,
-0.04916616156697273,
0.004420806188136339,
0.01952698640525341,
0.03071034885942936,
0.008450795896351337,
-0.014584449119865894,
-0.0111031923443079,
-0.030485181137919426,
-0.008178955875337124,
0.03541973978281021,
0.004215097986161709,
-0.011165686883032322,
0.025338398292660713,
0.003527470864355564,
0.013659408316016197,
0.058634646236896515,
-0.03104175254702568,
-0.005360908340662718,
0.028840385377407074,
0.0180429145693779,
-0.005567307583987713,
-0.006132057402282953,
-0.03701994940638542,
0.021515605971217155,
-0.02297295443713665,
-0.0018456368707120419,
-0.010884136892855167,
0.06344838440418243,
0.01013589184731245,
-0.006300540640950203,
-0.03123611770570278,
0.02151048555970192,
0.004735778551548719,
0.02546553686261177,
0.036200571805238724,
-0.024428268894553185,
0.010782100260257721,
0.015311664901673794,
0.0324304923415184,
-0.0758228674530983,
-0.02250736393034458,
-0.03975469246506691,
-0.011026670224964619,
-0.0564589686691761,
0.017625682055950165,
0.023624075576663017,
0.02129058539867401,
-0.0007489346899092197,
0.050981659442186356,
-0.030963392928242683,
-0.04774774610996246,
-0.04884399473667145,
0.03731358423829079,
0.01258133351802826,
0.018108339980244637,
-0.01314337458461523,
0.002965290565043688,
-0.029485251754522324,
-0.01670941896736622,
0.00335509586147964,
0.02848169580101967,
-0.005746453069150448,
-0.007306046783924103,
0.02372782863676548,
-0.029968155547976494,
0.02240271493792534,
-0.025008227676153183,
0.003939558286219835,
0.03380356729030609,
-0.007027973420917988,
-0.04936110973358154,
0.00771057466045022,
0.009589109569787979,
0.03579937666654587,
0.03033457323908806,
-0.017499472945928574,
0.016511663794517517,
0.029013963416218758,
0.014807458035647869,
-0.0012439573183655739,
-0.021866483613848686,
-0.000042971852963091806,
-0.0011283130152150989,
-0.05421324446797371,
0.004441836848855019,
-0.041234586387872696,
-0.018381040543317795,
0.039957594126462936,
0.020913230255246162,
-0.03482099249958992,
0.014143886044621468,
-0.025876013562083244,
-0.034235794097185135,
-0.014836551621556282,
-0.014155378565192223,
-0.0017484904965385795,
0.0075889695435762405,
0.016120439395308495,
-0.04732038080692291,
0.040361955761909485,
0.019500277936458588,
0.015208541415631771,
-0.08882487565279007,
-0.04270157963037491,
0.05958127975463867,
-0.00902213342487812,
0.03240912780165672,
-0.05293138325214386,
0.013156069442629814,
0.04852304235100746,
-0.10008519887924194,
0.019163843244314194,
-0.0031396676786243916,
-0.02061712183058262,
-0.017617089673876762,
0.019521206617355347,
0.03265390917658806,
0.021344419568777084,
0.0012443925952538848,
-0.007295837160199881,
0.010043750517070293,
0.025017596781253815,
-0.009425715543329716,
-0.0179987084120512,
0.03320058435201645,
0.017877519130706787,
-0.02632077969610691,
-0.011797084473073483,
0.03817981854081154,
-0.040037889033555984,
-0.03633015602827072,
0.029954321682453156,
0.023186324164271355,
0.028277309611439705,
-0.021292582154273987,
-0.00006740986282238737,
0.012445023283362389,
0.022770261391997337,
0.020466219633817673,
-0.0067123956978321075,
-0.04094213247299194,
0.06341835856437683,
-0.002794896252453327,
0.03471281751990318,
-0.024218259379267693,
-0.004293710459023714,
0.006673714611679316,
0.006082166451960802,
-0.01494431309401989,
0.036236945539712906,
-0.052073393017053604,
-0.050773050636053085,
-0.029528414830565453,
0.01616290584206581,
-0.02473665215075016,
-0.024150189012289047,
0.018624674528837204,
-0.049262672662734985,
0.0055579231120646,
0.006950185168534517,
-0.02363615296781063,
-0.0006002838490530849,
0.040174562484025955,
0.02044137567281723,
0.000147162500070408,
0.018398160114884377,
-0.013337492942810059,
-0.021713681519031525,
-0.022375956177711487,
-0.00716687086969614,
-0.00816776417195797,
-0.008326854556798935,
0.009562862105667591,
-0.036989446729421616,
0.0048666964285075665,
0.010923908092081547,
0.0323868989944458,
0.006177155766636133,
0.009503946639597416,
-0.03616219758987427,
-0.028519589453935623,
-0.025484975427389145,
0.03821542486548424,
0.024520203471183777,
-0.01138216070830822,
-0.006144245155155659,
-0.030243748798966408,
-0.00878135021775961,
-0.006995291914790869,
0.0577022060751915,
0.03148627281188965,
-0.0012803233694285154,
0.026589076966047287,
0.005758955609053373,
0.02461177110671997,
-0.003350436920300126,
0.008919863030314445,
0.0077218483202159405,
-0.05117994174361229,
0.0006796392844989896,
-0.016001371666789055,
-0.004174821078777313,
-0.015328184701502323,
0.03133251145482063,
-0.025561045855283737,
0.04931638389825821,
0.004361512139439583,
-0.05760226026177406,
0.061216387897729874,
0.06409980356693268,
0.03906072676181793,
0.07930808514356613,
-0.0159754641354084,
-0.0017306860536336899,
-0.0013461108319461346,
-0.011172697879374027,
-0.016656257212162018,
0.024940716102719307,
-0.004543596878647804,
0.00147177220787853,
-0.028208281844854355,
0.010120813734829426,
0.038719892501831055,
-0.005188443697988987,
-0.02176045998930931,
0.03493043780326843,
-0.059121761471033096,
0.016810912638902664,
0.03824697434902191,
0.02967103384435177,
0.017879163846373558,
0.0008695016149431467,
0.030541175976395607,
0.027912916615605354,
-0.02877001091837883,
0.05557266250252724,
0.038444437086582184,
0.023842711001634598,
0.025899363681674004,
-0.011735010892152786,
0.04959472268819809,
-0.018782243132591248,
0.03411064296960831,
0.03320518881082535,
0.038848984986543655,
-0.009025011211633682,
0.00811352301388979,
0.01935664564371109,
0.028862109407782555,
-0.00807434692978859,
0.021232791244983673,
-0.007197066210210323,
0.08475311845541,
-0.007883391343057156,
0.014037049375474453,
-0.03448987752199173,
-0.01161263883113861,
-0.006709608249366283,
0.006243105046451092,
0.055413950234651566,
0.0450226329267025,
0.03947832062840462,
-0.017165498808026314,
-0.006302429363131523,
0.006077517755329609,
-0.008183912374079227,
-0.016569338738918304,
0.03349610045552254,
-0.019028544425964355,
0.005940075032413006,
0.0004949425929225981,
-0.048208028078079224,
-0.020014232024550438,
-0.016699092462658882,
0.008111299015581608,
0.03086983971297741,
0.07943814247846603,
-0.021973220631480217,
-0.005345671903342009,
-0.03777474910020828,
0.03707025572657585,
-0.05668721720576286,
-0.04345839098095894,
0.013832049444317818,
0.014336446300148964,
0.010075787082314491,
0.005516114179044962
] |
<p>For the combination of the resistors, shown in the figure. Calculate the equivalent resistance between A and B, please help me to find the answer of this complicated question this is a question from an easy part but, I don't know how to solve this. </p>
<p><img src="http://I.stack.imgur.com/3wsWo.jpg" alt="For the combination of the resistors, shown in the figure. Calculate the equivalent resistance between A and B, please help me to find the answer of this complicated question this is a question from an easy part but, I don't KNOW TO SOLVE THIS"></p>
| 8,882 |
[
-0.018725544214248657,
0.0014054245548322797,
-0.009235876612365246,
0.006140169221907854,
0.043849196285009384,
0.004436087794601917,
-0.004614168778061867,
-0.00992665160447359,
0.011618332006037235,
-0.0063886381685733795,
0.0563502237200737,
0.028131846338510513,
0.015492258593440056,
0.019365007057785988,
0.01836586184799671,
0.0038055144250392914,
-0.013669123873114586,
0.02096485160291195,
0.01896011084318161,
-0.014615753665566444,
0.010158025659620762,
0.012027203105390072,
0.02300921082496643,
0.00452775601297617,
-0.028233323246240616,
0.03446837514638901,
0.06320647895336151,
-0.017409294843673706,
0.0016224856954067945,
0.06042635440826416,
-0.01835840754210949,
-0.05092225223779678,
0.03868849575519562,
0.034074608236551285,
0.0037828513886779547,
0.020285725593566895,
-0.029146185144782066,
-0.020496223121881485,
-0.0335417278110981,
0.028599128127098083,
-0.0031191192101687193,
-0.015242560766637325,
0.005222400184720755,
0.04831381514668465,
-0.019123831763863564,
-0.005143717397004366,
0.003471666481345892,
0.0034668734297156334,
-0.012530284933745861,
-0.07180781662464142,
0.07452011853456497,
-0.004010747652500868,
0.0680195540189743,
0.04017264023423195,
-0.013417966663837433,
-0.01306968741118908,
0.0772629976272583,
0.0707123801112175,
-0.00004504979369812645,
-0.036302004009485245,
0.014891445636749268,
-0.01376219093799591,
0.004818587563931942,
-0.04718202352523804,
-0.030390193685889244,
0.027432553470134735,
-0.02015046775341034,
0.02450461871922016,
0.000987126142717898,
0.012060646899044514,
0.037022121250629425,
-0.00228808238171041,
0.01667121611535549,
-0.021425098180770874,
0.01621495559811592,
-0.039077889174222946,
0.0024580610916018486,
0.01441709790378809,
0.03610524535179138,
0.04122467339038849,
-0.03610525652766228,
0.03076210804283619,
0.048975732177495956,
0.022475715726614,
0.015595568343997002,
-0.04854649677872658,
0.04227927699685097,
-0.002591637196019292,
0.008433779701590538,
-0.037648770958185196,
0.008784286677837372,
0.04733733460307121,
0.03726192191243172,
0.025705959647893906,
-0.038628462702035904,
0.013934209011495113,
-0.019901318475604057,
0.03795823082327843,
0.0005252924747765064,
-0.03616303578019142,
0.03759070858359337,
-0.022251926362514496,
0.015360898338258266,
0.0997580885887146,
0.021952370181679726,
0.01692545786499977,
-0.022860422730445862,
-0.0004900165949948132,
0.02238873951137066,
-0.022541923448443413,
-0.04376845434308052,
0.06870435178279877,
-0.012879805639386177,
0.010848239064216614,
-0.015869390219449997,
-0.03924970328807831,
-0.017984680831432343,
-0.02676587551832199,
0.01960335671901703,
0.01870003156363964,
0.017313841730356216,
-0.031603049486875534,
0.028270501643419266,
0.004346601199358702,
-0.052624259144067764,
-0.006445702631026506,
-0.021846652030944824,
-0.012954366393387318,
-0.016477173194289207,
0.05956827849149704,
-0.013838853687047958,
-0.04621759429574013,
-0.00998520478606224,
0.019349701702594757,
0.042611442506313324,
-0.028079135343432426,
-0.06637156009674072,
-0.0961718037724495,
0.0012877944391220808,
-0.04432804509997368,
-0.0065352534875273705,
-0.07591526955366135,
0.046505313366651535,
0.033687200397253036,
0.049222495406866074,
-0.000503097428008914,
0.009308122098445892,
0.04518179967999458,
0.030217045918107033,
0.018926018849015236,
0.010564206168055534,
-0.02987539954483509,
-0.00993921048939228,
-0.0004943784442730248,
0.04241356998682022,
-0.07615829259157181,
-0.006658964324742556,
0.026806943118572235,
-0.0011877913493663073,
-0.03156688064336777,
0.0181535966694355,
-0.0001006742604658939,
-0.017444735392928123,
0.026020223274827003,
0.007795470301061869,
-0.011172305792570114,
0.050687357783317566,
-0.02171630598604679,
-0.016218777745962143,
0.029406310990452766,
-0.02497534081339836,
0.010327273979783058,
-0.0021082600578665733,
0.004346674773842096,
0.04399661347270012,
-0.023476770147681236,
-0.023221006616950035,
-0.023395808413624763,
-0.0014117263490334153,
0.027655476704239845,
-0.048988841474056244,
-0.08034927397966385,
0.007277351804077625,
0.025981931015849113,
0.0351155623793602,
0.04522765427827835,
0.008219807408750057,
-0.03796863928437233,
-0.0172771904617548,
-0.005828438326716423,
-0.02349730394780636,
-0.07398447394371033,
-0.009790059179067612,
0.002210371196269989,
-0.025922397151589394,
-0.00765911303460598,
0.005067538935691118,
0.021939421072602272,
-0.028875302523374557,
0.006468103267252445,
-0.007098261266946793,
-0.006909358315169811,
-0.010111137293279171,
0.01721096597611904,
0.009063041768968105,
0.04183885082602501,
0.06966354697942734,
-0.03225455805659294,
0.0456320159137249,
-0.024778122082352638,
0.012986785732209682,
0.003411683486774564,
-0.02166604995727539,
0.007962088100612164,
-0.011721065267920494,
-0.03058314323425293,
0.008005397394299507,
0.03699922561645508,
0.023949291557073593,
0.029155081138014793,
-0.031352248042821884,
0.047221604734659195,
0.02277173474431038,
0.0343879833817482,
-0.022084644064307213,
0.022278476506471634,
0.03524920344352722,
0.0375555045902729,
-0.028560005128383636,
-0.0017999660922214389,
-0.06421150267124176,
0.016592293977737427,
0.04987095668911934,
0.011909017339348793,
-0.05074186623096466,
0.024933207780122757,
0.027790509164333344,
0.01799619011580944,
0.03536280617117882,
0.07719120383262634,
-0.013045516796410084,
0.014949571341276169,
0.0006018839194439352,
0.024888725951313972,
0.005267658270895481,
0.024843819439411163,
-0.022923219949007034,
0.023478936403989792,
0.016297776252031326,
-0.012215828523039818,
-0.03375967592000961,
0.056270428001880646,
0.021020639687776566,
0.04973836615681648,
-0.0036226678639650345,
-0.01119658350944519,
0.0024876731913536787,
-0.025284042581915855,
0.04215765371918678,
-0.0015956436982378364,
0.02833286114037037,
0.030538396909832954,
0.02486099675297737,
0.00020418154599610716,
0.005502536427229643,
-0.0028702770359814167,
-0.010292771272361279,
-0.045820724219083786,
0.01347453985363245,
-0.01519087702035904,
0.03797909989953041,
-0.020098604261875153,
0.00036674345028586686,
-0.0360768660902977,
-0.009739316068589687,
0.03504026308655739,
0.0012070398079231381,
0.05016934871673584,
-0.06004539132118225,
-0.029924167320132256,
-0.005480702500790358,
-0.03295837715268135,
-0.016450168564915657,
-0.007515421137213707,
-0.04092039912939072,
0.017012450844049454,
-0.008298982866108418,
-0.04330272600054741,
0.044325605034828186,
0.017548270523548126,
-0.03012487106025219,
0.01815394125878811,
-0.006475802045315504,
-0.05864359065890312,
-0.0049258042126894,
-0.0013812780380249023,
0.03515896573662758,
-0.03378821909427643,
0.007383779622614384,
0.06574419885873795,
-0.009750140830874443,
-0.014886199496686459,
0.004689973313361406,
-0.04219522699713707,
-0.04175298288464546,
0.017635181546211243,
-0.022122163325548172,
-0.00044412395800463855,
-0.010923531837761402,
0.02010585181415081,
0.001435958780348301,
-0.003529560286551714,
-0.019345104694366455,
-0.0424751378595829,
-0.041473716497421265,
0.014268811792135239,
0.0051390728913247585,
0.03180014342069626,
-0.008074811659753323,
-0.047700244933366776,
0.07340220361948013,
-0.005786293186247349,
-0.013966257683932781,
-0.010871414095163345,
-0.04529912769794464,
0.015941165387630463,
-0.004684672690927982,
-0.011080625467002392,
0.08546382933855057,
-0.023874390870332718,
0.02651735581457615,
0.027004661038517952,
0.018338218331336975,
0.07571329176425934,
-0.007473023142665625,
0.03657699376344681,
0.00514479773119092,
0.03717433661222458,
-0.004945510067045689,
0.07311462610960007,
-0.017050381749868393,
-0.004900486208498478,
0.031679246574640274,
0.00919319037348032,
0.020145835354924202,
0.022930100560188293,
-0.023112962022423744,
0.02039850316941738,
-0.03627145662903786,
0.025662647560238838,
-0.05382327362895012,
0.03162533789873123,
0.018201379105448723,
0.006651617120951414,
-0.006084437482059002,
0.022330081090331078,
0.053875282406806946,
-0.030307579785585403,
-0.01124412752687931,
0.05583014711737633,
0.0412936732172966,
-0.029204195365309715,
-0.06380419433116913,
0.008306398056447506,
-0.012481174431741238,
0.029365163296461105,
-0.0031110020354390144,
-0.040573276579380035,
0.006095728371292353,
0.027445130050182343,
-0.009567353874444962,
0.03251103311777115,
-0.032508283853530884,
0.02518823742866516,
-0.06756460666656494,
-0.022193972021341324,
-0.037821151316165924,
0.06589353084564209,
-0.01019553653895855,
0.061146531254053116,
-0.0028968462720513344,
0.0004328083887230605,
0.009481503628194332,
0.007451534271240234,
-0.0503496453166008,
0.029110413044691086,
0.003694347105920315,
-0.03368891403079033,
-0.007133748847991228,
-0.031264834105968475,
0.000966397114098072,
-0.021858852356672287,
-0.039918262511491776,
-0.013328994624316692,
0.010166778229176998,
-0.03832779824733734,
0.01597922295331955,
-0.00033375064958818257,
-0.005874612834304571,
-0.03558053821325302,
0.03664384409785271,
-0.0018479840364307165,
-0.03193322569131851,
0.02992522157728672,
0.0167897529900074,
-0.024039020761847496,
-0.018525568768382072,
-0.0220805611461401,
-0.002743714489042759,
-0.0036611019168049097,
0.03401849791407585,
0.016103148460388184,
0.04307057708501816,
-0.007213350851088762,
-0.03887556493282318,
0.021822107955813408,
0.06851454824209213,
0.015869243070483208,
-0.07086638361215591,
-0.04418878257274628,
-0.0328703336417675,
-0.015301150269806385,
-0.0353548526763916,
0.0538504384458065,
-0.02333126589655876,
0.02741354890167713,
0.02748788334429264,
0.020462896674871445,
-0.050070103257894516,
0.015192416496574879,
0.03442901372909546,
0.014145199209451675,
-0.006842839531600475,
-0.023163888603448868,
-0.034052833914756775,
-0.0588349811732769,
0.01800537295639515,
0.0509774386882782,
-0.0006776534137316048,
-0.04352423548698425,
-0.018757831305265427,
0.07342680543661118,
0.043546441942453384,
-0.013014906086027622,
0.03156215697526932,
0.002252215752378106,
0.012805591337382793,
0.02967214211821556,
-0.019487634301185608,
-0.009820743463933468,
0.018607167527079582,
0.039991557598114014,
-0.016979973763227463,
-0.03249913454055786,
-0.06479258835315704,
-0.020433977246284485,
0.025847451761364937,
0.029640337452292442,
-0.04433023929595947,
0.0016174266347661614,
-0.03468406945466995,
0.019551090896129608,
0.04197610542178154,
-0.05391914024949074,
0.003233675379306078,
0.0009368907194584608,
0.006925503257662058,
-0.02327178604900837,
-0.05287213623523712,
-0.008362451568245888,
0.03092852793633938,
-0.004031081683933735,
-0.0015908341156318784,
0.00016768358182162046,
-0.017165569588541985,
0.03219461813569069,
-0.03374854102730751,
0.07201547920703888,
0.06992479413747787,
-0.020545778796076775,
0.022251274436712265,
0.024484550580382347,
0.03400450199842453,
-0.03868040069937706,
-0.04242076352238655,
0.0374581441283226,
-0.030106810852885246,
-0.020033394917845726,
0.04987391456961632,
-0.038135431706905365,
-0.03260234370827675,
0.06117488071322441,
-0.024233125150203705,
0.051426105201244354,
-0.01339185144752264,
-0.02175847254693508,
0.04992786422371864,
0.07419023662805557,
-0.03076590783894062,
0.0749504342675209,
-0.011245152913033962,
-0.02927742712199688,
0.002555161016061902,
-0.01754358783364296,
-0.012576226145029068,
-0.043524887412786484,
-0.010919674299657345,
0.0010551323648542166,
0.007670097053050995,
-0.024518392980098724,
0.06026512756943703,
-0.030701681971549988,
0.02780350297689438,
-0.028581472113728523,
-0.015396172180771828,
0.006648675072938204,
-0.018040640279650688,
-0.006468822248280048,
0.011716240085661411,
0.006321909837424755,
0.03477419167757034,
0.030480382964015007,
-0.07414208352565765,
0.007767465431243181,
-0.007662658579647541,
0.025201601907610893,
0.005770510528236628,
-0.033521540462970734,
0.03328268975019455,
-0.055723149329423904,
-0.00821665208786726,
-0.03643490746617317,
-0.043560050427913666,
0.05434130132198334,
0.005287220235913992,
0.006443343590945005,
0.021310340613126755,
-0.03200448676943779,
-0.053834330290555954,
0.027063095942139626,
0.021776249632239342,
-0.004167323466390371,
-0.06722629815340042,
0.05171738192439079,
0.029481228440999985,
0.0010679392144083977,
-0.04746618494391441,
-0.04069569706916809,
0.034978821873664856,
0.027459589764475822,
0.01826261170208454,
-0.026705604046583176,
-0.019036157056689262,
0.008300529792904854,
-0.03720030188560486,
-0.005286617670208216,
0.03991912677884102,
-0.029294945299625397,
-0.01719575747847557,
-0.013936576433479786,
0.011177289299666882,
0.06866983324289322,
0.016074288636446,
0.025285230949521065,
0.012309500947594643,
-0.06752079725265503,
-0.03415614739060402,
-0.01230541244149208,
0.03646968677639961,
-0.009041287936270237,
-0.04210374876856804,
0.02277667447924614,
0.006429041735827923,
0.07414712756872177,
-0.0017616159748286009,
0.0011798753403127193,
0.018610142171382904,
0.04058868810534477,
-0.027139820158481598,
-0.011943473480641842,
0.013485913164913654,
0.03347225859761238,
0.02628684788942337,
-0.003884117351844907,
0.010367180220782757,
-0.06740031391382217,
-0.04101280868053436,
0.0075033074244856834,
-0.007296514231711626,
-0.049164995551109314,
-0.03953186422586441,
0.11069312691688538,
-0.02527489885687828,
0.015213266015052795,
0.009127601981163025,
-0.021782075986266136,
0.030261944979429245,
0.0011501985136419535,
0.005573958158493042,
0.03770841285586357,
-0.012607197277247906,
-0.0341726690530777,
-0.032581884413957596,
-0.05805600807070732,
-0.009769217111170292,
0.05131692439317703,
-0.0056825317442417145,
0.05594900622963905,
0.04159148037433624,
0.008956434205174446,
0.034210532903671265,
0.009557556360960007,
-0.017077775672078133,
0.012502077966928482,
0.006977458484470844,
0.026415055617690086,
-0.01142493449151516,
-0.02089039236307144,
0.04506398364901543,
0.007014481350779533,
0.003059557406231761,
-0.006816357374191284,
0.009896141476929188,
-0.008740518242120743,
-0.02990846522152424,
0.042481742799282074,
0.008791952393949032,
0.015505567193031311,
-0.014200507663190365,
0.021968688815832138,
0.0077821603044867516,
-0.02994907833635807,
0.0594625398516655,
-0.01058954931795597,
-0.007398353423923254,
-0.0048108333721756935,
-0.021235009655356407,
-0.01371739897876978,
-0.0027847366873174906,
0.02444768138229847,
0.01924707554280758,
0.004181215073913336,
0.041699908673763275,
0.00818405020982027,
-0.0064733983017504215,
0.036106422543525696,
-0.031701598316431046,
-0.06670258939266205,
0.007183201145380735,
-0.020365092903375626,
-0.03981805220246315,
0.028591103851795197,
-0.015989430248737335,
-0.02656916342675686,
0.03160757198929787,
-0.01764528825879097,
0.008204640820622444,
-0.010603330098092556,
0.04178756847977638,
-0.03375032916665077,
0.09786025434732437,
0.009658942930400372,
0.07974104583263397,
0.0044098468497395515,
0.0056687770411372185,
0.07722049206495285,
0.03963583707809448,
0.028798600658774376,
-0.07319540530443192,
0.023380639031529427,
-0.0013167611323297024,
-0.013709555380046368,
-0.037754058837890625,
0.011301844380795956,
-0.008600426837801933,
0.005555764771997929,
-0.0006890555960126221,
-0.023390622809529305,
-0.005421641748398542,
-0.004184248391538858,
0.018436362966895103,
-0.01744159124791622,
-0.04784702509641647,
-0.015126309357583523,
0.04324544593691826,
-0.005008071660995483,
-0.008600274100899696,
-0.038414668291807175,
0.02487480826675892,
-0.04934929311275482,
-0.02608492411673069,
-0.047097448259592056,
-0.012550316751003265,
0.04131961241364479,
-0.030617613345384598,
-0.02464267611503601,
0.028558868914842606,
0.030782528221607208,
-0.03334227204322815,
-0.048272810876369476,
0.0648583397269249,
0.028362497687339783,
-0.004078795667737722,
-0.003025240730494261,
0.021074991673231125,
0.026972323656082153,
-0.014444566331803799,
0.01076886709779501,
-0.002287826035171747,
-0.05275449529290199,
-0.004139837343245745,
-0.030257944017648697,
0.009066195227205753,
0.019151750952005386,
0.024953115731477737,
0.007796957157552242,
0.038115620613098145,
-0.020056702196598053,
-0.05404166877269745,
0.005636017769575119,
-0.005934305489063263,
0.00591219263151288,
-0.020157689228653908,
-0.03613317385315895,
-0.03955887630581856,
0.015026837587356567,
-0.03735824301838875,
0.009983642026782036,
-0.0038346857763826847,
-0.011466477066278458,
0.006809056270867586,
-0.002734661800786853,
0.031160712242126465,
-0.03220865875482559,
0.0031651982571929693,
-0.046769510954618454,
0.003865768201649189,
-0.007682131137698889,
-0.017108017578721046,
0.010927081108093262,
0.01693122461438179,
0.015839045867323875,
0.007592987734824419,
-0.006676058284938335,
-0.024055715650320053,
-0.07942306250333786,
0.0137768080458045,
0.005003398284316063,
0.016892051324248314,
-0.03593365475535393,
-0.03002418577671051,
0.03788965195417404,
0.03446560353040695,
-0.009492670185863972,
0.002853165380656719,
0.02041391283273697,
0.007648563478142023,
0.04889489337801933,
-0.019346604123711586,
-0.010564202442765236,
0.012112801894545555,
-0.06359124183654785,
0.021326130256056786,
0.023621713742613792,
0.055068839341402054,
0.008235311135649681,
0.04390166699886322,
0.0031789022032171488,
0.0175835732370615,
-0.02371382527053356,
-0.009609846398234367,
-0.031138719990849495,
-0.01085975393652916,
0.011354113928973675,
0.028793590143322945,
0.019009489566087723,
0.002477051690220833,
0.009563539177179337,
-0.0037538374308496714,
-0.011469228193163872,
0.04760971665382385,
0.0025446948129683733,
-0.01694738306105137,
-0.022506387904286385,
-0.030513104051351547,
0.002907840069383383,
-0.047383714467287064,
0.002414589747786522,
-0.011426216922700405,
-0.05076240748167038,
0.018405765295028687,
0.015083801932632923,
-0.035517074167728424,
0.03211706876754761,
0.026699421927332878,
0.019729411229491234,
0.033762410283088684,
0.020509373396635056,
-0.0006739908712916076,
-0.033774878829717636,
0.013877619989216328,
0.011256827041506767,
0.044169966131448746,
-0.039252497255802155,
-0.04704861715435982,
0.05777530372142792,
-0.03569423407316208,
0.03000527434051037,
0.014887021854519844,
0.03190361708402634,
0.03367965668439865,
-0.0006195104215294123,
-0.03671640530228615,
-0.020453093573451042,
0.06656593829393387,
-0.016126973554491997,
0.005917594768106937,
-0.002895976649597287,
-0.03356071934103966,
0.015566395595669746,
-0.0038799538742750883,
-0.0168630238622427,
0.02146017551422119,
0.018233032897114754,
0.0329316109418869,
0.04212895408272743,
-0.009740445762872696,
-0.005499718245118856,
0.051674824208021164,
0.026243889704346657,
0.03297104313969612,
0.00045320705976337194,
0.008417505770921707,
0.006045612972229719,
0.0034560314379632473,
-0.006529271136969328,
0.03686022013425827,
-0.01801607571542263,
-0.028823209926486015,
-0.06915387511253357,
0.007777072489261627,
0.009342808276414871,
-0.02419198304414749,
0.04257446154952049,
-0.04857306927442551,
-0.011063199490308762,
0.02314639464020729,
-0.05327191948890686,
-0.030504396185278893,
-0.0075556375086307526,
-0.0015644747763872147,
-0.021624939516186714,
-0.025754984468221664,
-0.010510902851819992,
0.03895334154367447,
-0.006422617007046938,
0.04384684935212135,
0.019228270277380943,
-0.003138383850455284,
-0.018402082845568657,
-0.04792274534702301,
0.01216951571404934,
0.022559747099876404,
-0.010076723992824554,
-0.02302589826285839,
0.013031586073338985,
-0.003826889907941222,
0.010494883172214031,
0.03704814240336418,
-0.008518128655850887,
-0.0007613644702360034,
-0.00720924511551857,
0.030484916642308235,
0.021695762872695923,
0.04719427600502968,
-0.013010268099606037,
-0.005544663406908512,
-0.04502878710627556,
-0.016490668058395386,
0.01358308456838131,
-0.0014109545154497027,
-0.014561319723725319,
-0.005038220901042223,
0.00933558214455843,
-0.023022394627332687,
-0.04471082612872124,
-0.0058186789974570274,
-0.033007845282554626,
-0.032452292740345,
-0.00978864450007677,
-0.0319308377802372,
0.004709956701844931,
-0.05018959566950798,
-0.011025892570614815,
-0.023855220526456833,
0.011614476330578327,
0.05779707059264183,
-0.012753760442137718,
-0.006459715310484171,
0.016605820506811142,
-0.02397666871547699,
-0.012519778683781624,
0.004445546772330999,
0.020895615220069885,
-0.014438807964324951,
-0.03253792226314545,
-0.01482428889721632,
0.01971524767577648,
0.0011016291100531816,
0.011032713577151299,
-0.04825073853135109,
-0.04782992973923683,
0.0008848338620737195,
-0.01441232580691576,
0.004102576058357954,
0.003215931123122573,
-0.04545241594314575,
-0.04439927265048027,
-0.008882487192749977,
0.046626411378383636,
0.013660370372235775,
-0.07415062189102173,
-0.0422881618142128,
-0.03126407414674759,
-0.008578550070524216,
0.023965628817677498,
0.06319770961999893,
0.013175353407859802,
-0.03824557736515999,
-0.0021630132105201483,
0.006894679740071297,
0.06499125808477402,
-0.06994587182998657,
0.011238896287977695,
0.024788884446024895,
-0.02603677287697792,
-0.0005872870096936822,
-0.0069869514554739,
0.013605701737105846,
0.024439794942736626,
-0.02956288494169712,
-0.011706724762916565,
-0.024641195312142372,
0.03047160990536213,
0.00686218123883009,
-0.010873094201087952,
-0.012412725016474724,
0.0050972639583051205,
0.07106917351484299,
-0.014618352055549622,
0.01863594353199005,
0.003970595076680183,
-0.0023379563353955746,
-0.03243353217840195,
0.03310063108801842,
-0.0169315654784441,
0.013406651094555855,
-0.0004538167268037796,
0.005939595866948366,
0.02581515721976757,
-0.09971875697374344,
-0.040451448410749435,
0.01375534012913704,
-0.049730539321899414,
-0.010885358788073063,
0.08163102716207504,
-0.010739498771727085,
0.0368475615978241,
-0.037827860563993454,
0.03870215266942978,
-0.050467174500226974,
-0.030266985297203064,
0.01239654328674078,
-0.0054772719740867615,
-0.001421999535523355,
-0.023815682157874107,
-0.0040989466942846775,
0.03735214099287987,
-0.008436386473476887,
0.019658364355564117,
0.009857308119535446,
-0.019801558926701546,
-0.017814969643950462,
0.01601593755185604,
0.02200471982359886,
-0.038454797118902206,
0.012786312960088253,
0.049508728086948395,
-0.020949099212884903,
0.09199879318475723,
-0.046216461807489395,
0.01717790588736534,
0.0036771255545318127,
0.004375701770186424,
-0.019732091575860977,
0.0037616852205246687,
0.02468637190759182,
-0.011288792826235294,
0.0015753012849017978,
-0.025179976597428322,
-0.0020813527517020702,
-0.01282336376607418,
0.0062944660894572735,
-0.023656457662582397,
0.025706076994538307,
-0.014574127271771431,
-0.04209843650460243,
-0.019328223541378975,
0.0008956425008364022,
-0.036537423729896545,
-0.026722010225057602,
0.028935866430401802,
0.03126763552427292,
-0.014231635257601738,
0.011422017589211464,
-0.009813893586397171,
0.0038696788251399994,
0.04649900645017624,
-0.02632102556526661,
-0.01425372064113617,
-0.027078578248620033,
-0.0009996496373787522,
0.029801614582538605,
-0.014849611558020115
] |
<p>Why do stars flicker and planets don't? At least this is what I've read online and seen on the night sky. I've heard that it has to do something with the fact that stars emit light and planets reflect it. But I don't get it, isn't this light, just "light"? What happens to the reflected light that it doesn't flicker anymore?</p>
<p>I was thinking that it has to do something with Earth's atmosphere, different temperatures or something (if this has any role at all).</p>
| 261 |
[
-0.04008922725915909,
-0.0012298696674406528,
0.0010844651842489839,
-0.02680610865354538,
0.041733268648386,
0.016595229506492615,
-0.03861796483397484,
-0.02578757517039776,
-0.00007065891259117052,
-0.0068682157434523106,
0.017031230032444,
0.052049826830625534,
0.019832000136375427,
0.05552105978131294,
0.014634368009865284,
-0.013292312622070312,
0.005996848456561565,
-0.024378133937716484,
-0.035814788192510605,
-0.012407947331666946,
-0.049642082303762436,
-0.026977960020303726,
0.021524976938962936,
0.009171729907393456,
-0.054448794573545456,
0.03819884732365608,
0.03296765685081482,
0.006463910918682814,
0.014443731866776943,
0.06546540558338165,
0.009266084991395473,
0.002466467209160328,
0.00034428067738190293,
0.032311324030160904,
0.016019506379961967,
0.0410059355199337,
-0.023270385339856148,
0.005985135678201914,
-0.0020571816712617874,
0.0348622128367424,
-0.01307503692805767,
0.0047757187858223915,
-0.027952851727604866,
0.008436736650764942,
-0.002183265285566449,
-0.015474274754524231,
0.02464727871119976,
0.018509261310100555,
0.053595319390296936,
-0.05069611221551895,
0.033472172915935516,
-0.05041370540857315,
-0.0022976738400757313,
0.03310481086373329,
-0.006766189355403185,
0.03956000134348869,
0.11578580737113953,
0.07906187325716019,
0.005786837078630924,
-0.03329231217503548,
-0.010232812725007534,
-0.027403205633163452,
-0.031922608613967896,
-0.02182680182158947,
-0.008865369483828545,
0.009808444418013096,
0.014575432986021042,
-0.05387255549430847,
0.036724016070365906,
0.05812089517712593,
0.023283686488866806,
-0.022251131013035774,
0.025701286271214485,
-0.025277763605117798,
-0.0343041718006134,
-0.037544045597314835,
0.05427118018269539,
0.006039314437657595,
0.06061025708913803,
0.05410335958003998,
0.007594345137476921,
-0.014959118328988552,
0.009559535421431065,
-0.026175329461693764,
-0.011236585676670074,
0.02070457488298416,
0.10480310022830963,
0.014528629370033741,
0.00621055206283927,
-0.004103187005966902,
0.0011017576325684786,
0.022853000089526176,
0.0349116250872612,
0.02250419557094574,
-0.01025929395109415,
0.015723349526524544,
-0.0011573212686926126,
0.03135964274406433,
-0.0014206897467374802,
-0.022776102647185326,
-0.028000615537166595,
0.008613747544586658,
0.05133828520774841,
0.05129329115152359,
-0.0034427521750330925,
-0.015958212316036224,
-0.03693261370062828,
-0.006310651544481516,
-0.011554833501577377,
-0.001696505001746118,
-0.0445655956864357,
0.03272750973701477,
-0.003993625286966562,
0.02956332452595234,
0.006235620938241482,
-0.02971636690199375,
0.01037111971527338,
0.0010662185959517956,
0.04602934792637825,
0.09426811337471008,
-0.024806194007396698,
-0.016167117282748222,
-0.009352833963930607,
-0.017426909878849983,
-0.04459109157323837,
0.02672829106450081,
0.014553912915289402,
-0.010224963538348675,
-0.018342016264796257,
0.00747557682916522,
-0.012509558349847794,
-0.03981335088610649,
0.03775511682033539,
-0.02253323420882225,
0.014357472769916058,
0.005810455419123173,
-0.09760037809610367,
-0.0054224454797804356,
0.032397981733083725,
-0.020705988630652428,
-0.03102351352572441,
-0.0395723320543766,
0.03744745999574661,
-0.0032207530457526445,
0.08535972237586975,
0.010669022798538208,
-0.04570041596889496,
-0.010762738063931465,
0.036334577947854996,
0.013118316419422626,
-0.07019660621881485,
-0.019176878035068512,
0.008846740238368511,
-0.06938796490430832,
0.018244093284010887,
-0.034685809165239334,
0.021496720612049103,
0.012980306521058083,
-0.010388089343905449,
0.0000974764334387146,
0.03492305800318718,
-0.024851130321621895,
0.0034038033336400986,
0.018240785226225853,
0.007195313926786184,
-0.061090026050806046,
0.09166346490383148,
0.02039266750216484,
0.00810382328927517,
0.02354767546057701,
-0.015118488110601902,
-0.004551006481051445,
-0.000021534175175474957,
0.050292328000068665,
0.0217814389616251,
-0.024302663281559944,
-0.04046595096588135,
0.014845803380012512,
0.0016527606640011072,
-0.009189021773636341,
-0.048228442668914795,
-0.012302576564252377,
0.02022506482899189,
-0.0030851128976792097,
0.02444094978272915,
0.06056777015328407,
0.024259822443127632,
0.017203334718942642,
0.019141068682074547,
-0.036619074642658234,
-0.001223196741193533,
-0.036261677742004395,
-0.01744369976222515,
-0.043498024344444275,
-0.034254588186740875,
-0.019221799448132515,
0.038808487355709076,
0.0021860571578145027,
-0.016809219494462013,
-0.014738709665834904,
0.015385981649160385,
0.05861598998308182,
-0.00830408651381731,
-0.028127608820796013,
0.019709249958395958,
0.07558272033929825,
0.024917203933000565,
0.026963280513882637,
0.008823325857520103,
-0.029756352305412292,
-0.03197649121284485,
-0.008727150969207287,
-0.016959453001618385,
0.04408528283238411,
-0.017354579642415047,
-0.023178787901997566,
0.06337199360132217,
0.034442879259586334,
-0.03551501780748367,
-0.02015027031302452,
-0.029146691784262657,
0.05503446236252785,
0.026099586859345436,
-0.008076753467321396,
0.004379375372081995,
0.039203934371471405,
-0.0003374700900167227,
0.009520210325717926,
-0.004107986111193895,
-0.017518602311611176,
-0.05178680643439293,
0.02177872322499752,
0.05425756797194481,
0.003548984881490469,
0.0038270559161901474,
0.016742700710892677,
0.010867839679121971,
0.03296033665537834,
0.008428125642240047,
0.012406017631292343,
-0.029086116701364517,
-0.02597581222653389,
-0.00710385711863637,
-0.01699359156191349,
0.02488616108894348,
0.032489605247974396,
0.03121745027601719,
0.006574562750756741,
0.019107026979327202,
-0.02411576360464096,
-0.05348606035113335,
0.008315306156873703,
-0.0013370311353355646,
0.030604224652051926,
-0.014540319330990314,
-0.002675452269613743,
0.03417465090751648,
-0.02612215280532837,
-0.003883291268721223,
0.009234894998371601,
0.01692708395421505,
0.04273275285959244,
-0.026564616709947586,
-0.03187843784689903,
0.01994377002120018,
0.01662365160882473,
-0.05983930453658104,
-0.009755116887390614,
0.02048979513347149,
0.0030386107973754406,
0.03370178863406181,
0.012762856669723988,
-0.0004910113639198244,
-0.04876706004142761,
-0.014486871659755707,
0.0006542587070725858,
0.006561847869306803,
0.024964846670627594,
-0.03756917640566826,
-0.001305106678046286,
0.007369102444499731,
-0.01892825774848461,
-0.011724318377673626,
-0.015137288719415665,
-0.0530785471200943,
0.02264351025223732,
0.0040003452450037,
-0.043913520872592926,
0.040781665593385696,
0.0015741422539576888,
-0.003820926882326603,
-0.0006882645539008081,
0.009889849461615086,
-0.07680011540651321,
0.04083803668618202,
-0.01904563419520855,
0.004533915780484676,
-0.03988444805145264,
0.018736114725470543,
0.04198350012302399,
-0.016521260142326355,
-0.04375473037362099,
-0.0055661508813500404,
-0.05998970568180084,
-0.033578433096408844,
-0.016378803178668022,
-0.025335727259516716,
0.028348062187433243,
-0.06014402583241463,
0.001488202135078609,
0.031680282205343246,
-0.05042099952697754,
0.013757641427218914,
-0.009668184444308281,
-0.027046699076890945,
-0.033042434602975845,
-0.036394841969013214,
0.022520868107676506,
-0.022410284727811813,
-0.023755747824907303,
0.024450836703181267,
0.04743563011288643,
0.021812893450260162,
-0.020133502781391144,
0.0008455736096948385,
-0.012338882312178612,
-0.04228685423731804,
0.03298358619213104,
0.047448381781578064,
0.024724220857024193,
-0.004092778079211712,
-0.02176072634756565,
0.001939991139806807,
0.019417589530348778,
0.014174090698361397,
-0.023622624576091766,
0.003608606057241559,
-0.03181885555386543,
0.0008109277114272118,
0.025165574625134468,
0.028157446533441544,
-0.031100478023290634,
0.015995638445019722,
-0.014609419740736485,
0.030218586325645447,
0.023738795891404152,
-0.03705050051212311,
0.03187389299273491,
-0.05038408190011978,
-0.004578884690999985,
-0.03515022248029709,
0.021592218428850174,
0.022742846980690956,
0.034217964857816696,
-0.005813348572701216,
0.007181407883763313,
0.048836078494787216,
0.016775714233517647,
-0.008833938278257847,
0.03995112329721451,
0.01800171472132206,
0.0016604074044153094,
-0.019244033843278885,
0.0009489755611866713,
-0.014244641177356243,
0.018329482525587082,
-0.024726182222366333,
-0.008410949259996414,
0.07688243687152863,
0.031318873167037964,
0.01742153987288475,
-0.0013160869712010026,
-0.02022278495132923,
-0.04085133969783783,
-0.0226741973310709,
0.016697648912668228,
-0.02511110156774521,
0.04698793962597847,
-0.0018231588182970881,
0.06143608316779137,
0.013315485790371895,
0.027865612879395485,
0.006104476749897003,
-0.011540225706994534,
-0.09655815362930298,
0.02314302697777748,
-0.0022124534007161856,
-0.02185276336967945,
-0.0365176796913147,
0.013194164261221886,
-0.017728960141539574,
-0.03877889737486839,
-0.01097948756068945,
-0.06418798118829727,
-0.02161254920065403,
-0.029972227290272713,
-0.010103107430040836,
0.013111425563693047,
-0.04338366910815239,
-0.03315013274550438,
0.023473339155316353,
0.03106546215713024,
0.0008537964895367622,
0.056341398507356644,
0.01438082568347454,
-0.04138413071632385,
0.01213117502629757,
-0.006072596181184053,
-0.01853916607797146,
0.03822646290063858,
0.0021555807907134295,
0.03453023359179497,
0.008945581503212452,
-0.05007333308458328,
-0.001795401331037283,
0.025895122438669205,
0.01623479835689068,
0.01939890906214714,
-0.02686757594347,
0.0083025973290205,
-0.02932198904454708,
-0.019007110968232155,
0.026973247528076172,
0.06506208330392838,
-0.06717181205749512,
-0.006958408746868372,
0.02520320750772953,
-0.026300987228751183,
0.0015590644907206297,
0.02795606106519699,
-0.019733034074306488,
-0.003011181019246578,
-0.013655479997396469,
-0.021686730906367302,
-0.009254148229956627,
-0.031437527388334274,
0.01723313517868519,
0.010551052168011665,
0.029464205726981163,
-0.008696912787854671,
-0.037495993077754974,
0.007543980143964291,
-0.01417553797364235,
0.02498364821076393,
-0.03546582907438278,
-0.013392377644777298,
-0.0000337681412929669,
-0.03461921215057373,
0.007961224764585495,
0.02424168772995472,
0.03658853843808174,
0.014411652460694313,
-0.0011388023849576712,
-0.0021055566612631083,
-0.05561896041035652,
-0.038767699152231216,
0.032496288418769836,
0.003907621372491121,
-0.015721196308732033,
-0.020210327580571175,
-0.07577098160982132,
-0.02463807538151741,
-0.0024997994769364595,
-0.039943765848875046,
0.028034448623657227,
-0.009036079049110413,
-0.028776729479432106,
-0.02173285372555256,
-0.03929639235138893,
0.042282331734895706,
0.02622360549867153,
0.011225673370063305,
0.05513085424900055,
-0.0006512671243399382,
-0.02688475139439106,
-0.012372535653412342,
0.0004121108795516193,
-0.008912096731364727,
0.042721670120954514,
-0.03289082273840904,
-0.011350198648869991,
-0.012456629425287247,
-0.003918448928743601,
-0.02876408025622368,
-0.0600244365632534,
-0.016617240384221077,
-0.019305076450109482,
-0.0029356481973081827,
0.04158962890505791,
-0.015243533998727798,
-0.07293032854795456,
0.007367347367107868,
-0.008671650663018227,
-0.008247223682701588,
-0.005360591225326061,
-0.009047307074069977,
0.01825823076069355,
0.013512791134417057,
0.028067855164408684,
0.0763828381896019,
0.08019193261861801,
-0.03449487313628197,
-0.020321644842624664,
0.020367002114653587,
0.03387415409088135,
-0.06687934696674347,
-0.032187625765800476,
0.01017875224351883,
-0.0330299474298954,
-0.029061440378427505,
0.060744550079107285,
-0.002716908697038889,
-0.0010632062330842018,
0.012310163117945194,
-0.04157597944140434,
-0.003147508017718792,
0.04078897461295128,
0.013923916965723038,
0.005896892864257097,
-0.009497026912868023,
0.022416137158870697,
0.01932283118367195,
0.022520024329423904,
0.032384082674980164,
-0.016173535957932472,
-0.030457736924290657,
0.01847405545413494,
0.008993890136480331,
-0.012122252956032753,
-0.06252659112215042,
0.017227094620466232,
-0.00442223297432065,
-0.01809607818722725,
0.04120592772960663,
0.030953189358115196,
0.030747275799512863,
0.05070030689239502,
-0.05266788601875305,
-0.02594936639070511,
-0.020573608577251434,
-0.03463798016309738,
0.05760836973786354,
-0.048802755773067474,
0.016574570909142494,
-0.034043505787849426,
-0.020197365432977676,
-0.07619860768318176,
-0.028351975604891777,
0.04028661921620369,
0.03287576884031296,
-0.05749299004673958,
-0.010496007278561592,
-0.00042358273640275,
-0.0015892282826825976,
-0.048413753509521484,
0.023703327402472496,
0.008044937625527382,
-0.039573099464178085,
0.017616907134652138,
0.013649647124111652,
0.01003370899707079,
0.040971968322992325,
0.011534906923770905,
-0.006560096517205238,
-0.0033127255737781525,
-0.03954136371612549,
0.009727787226438522,
-0.053916823118925095,
0.052779972553253174,
-0.000472348794573918,
-0.05434233322739601,
-0.0011171725345775485,
-0.010323320515453815,
-0.025722205638885498,
-0.024379782378673553,
-0.014511428773403168,
0.047055069357156754,
-0.00634261267259717,
0.00993612315505743,
-0.048642583191394806,
0.028170965611934662,
0.024713853374123573,
0.015740811824798584,
-0.0025710049085319042,
-0.00196277629584074,
0.003001730889081955,
-0.02677016146481037,
0.0044027771800756454,
-0.006236998364329338,
0.025122055783867836,
0.005782253108918667,
0.061979155987501144,
-0.027682162821292877,
-0.020125646144151688,
0.030302951112389565,
0.005850606597959995,
0.02085561491549015,
0.00010495386959519237,
0.015642976388335228,
0.017043406143784523,
-0.01566925272345543,
-0.025108395144343376,
-0.02383081056177616,
-0.014102756045758724,
-0.030150746926665306,
0.05110025405883789,
-0.016155695542693138,
0.018664522096514702,
0.003928642254322767,
0.02249375358223915,
0.006848996039479971,
-0.04409682750701904,
-0.016952576115727425,
0.015375777147710323,
-0.011613201349973679,
0.002587518421933055,
-0.052074600011110306,
0.025856677442789078,
0.07014347612857819,
0.02999824471771717,
-0.004989944398403168,
0.06498180329799652,
0.018652383238077164,
0.03218461573123932,
-0.014423565939068794,
0.03523331135511398,
-0.033783819526433945,
-0.013048067688941956,
-0.009438339620828629,
0.039752472192049026,
0.026993615552783012,
-0.007097301073372364,
0.058720264583826065,
0.0024740376975387335,
0.020778069272637367,
-0.06152704358100891,
0.007668050937354565,
-0.052761711180210114,
-0.013779627159237862,
0.03946460410952568,
-0.0008284950745292008,
0.035400379449129105,
-0.007029107306152582,
0.017872998490929604,
0.012924980372190475,
-0.02403172478079796,
-0.02585476078093052,
-0.05533650144934654,
-0.05163354426622391,
-0.007523098960518837,
-0.05652902275323868,
0.05073240026831627,
-0.0006948474328964949,
-0.05732937157154083,
0.009695813059806824,
0.00014220816956367344,
-0.000791289028711617,
-0.022922053933143616,
0.028652867302298546,
-0.0373968705534935,
0.03691429644823074,
-0.016937093809247017,
-0.011243653483688831,
-0.012881724163889885,
0.01943916454911232,
0.11589944362640381,
-0.02306285873055458,
0.042329058051109314,
-0.02248484268784523,
-0.007772613782435656,
-0.02275681123137474,
0.03805306926369667,
-0.0028945282101631165,
0.003304174402728677,
-0.011782421730458736,
0.02710403874516487,
0.01578790321946144,
0.040223028510808945,
0.06158549338579178,
-0.04607588052749634,
0.02110779657959938,
-0.021190613508224487,
0.024184536188840866,
-0.0020842677913606167,
0.005551480688154697,
-0.011133703403174877,
0.049143508076667786,
-0.035244401544332504,
0.026049785315990448,
-0.00551488297060132,
0.009887730702757835,
-0.011940649710595608,
-0.010410783812403679,
-0.011876345612108707,
0.0403306819498539,
-0.06317441910505295,
0.005692017264664173,
0.044924404472112656,
-0.04109380021691322,
-0.007957189343869686,
0.02029578574001789,
0.035790879279375076,
-0.048036493360996246,
0.02566729299724102,
0.030665354803204536,
-0.008363387547433376,
0.004587013740092516,
0.01623338833451271,
0.0033912742510437965,
-0.02824191190302372,
-0.036409419029951096,
-0.054982397705316544,
0.0471617765724659,
0.014127149246633053,
0.020217977464199066,
0.0019782024901360273,
-0.0004942878149449825,
0.00650567514821887,
-0.02826147899031639,
0.04275964945554733,
-0.03360810875892639,
-0.017639292404055595,
-0.049936454743146896,
-0.06759795546531677,
0.0027880368288606405,
0.02409578114748001,
-0.02645290270447731,
0.043279942125082016,
-0.02859959937632084,
-0.0026389521081000566,
-0.032417070120573044,
-0.00671321852132678,
-0.006235533393919468,
-0.003065815195441246,
0.00797304417937994,
-0.02446410246193409,
0.02384292706847191,
-0.023928698152303696,
-0.054174862802028656,
0.03210919722914696,
0.04284508526325226,
-0.017597723752260208,
0.01952194981276989,
-0.027701226994395256,
-0.04972285032272339,
-0.02526763826608658,
0.025881022214889526,
0.0020528065506368876,
-0.03720587119460106,
-0.0014020742382854223,
-0.015401884913444519,
0.0510576032102108,
0.006295435596257448,
-0.03952282294631004,
0.011372586712241173,
-0.005333533510565758,
0.05138315260410309,
0.046256814152002335,
-0.023194575682282448,
-0.015693332999944687,
0.02382049709558487,
0.017650529742240906,
-0.019712401553988457,
-0.01122474018484354,
0.03613724932074547,
0.05848061665892601,
0.007585014682263136,
0.035409364849328995,
0.01124085858464241,
-0.03946557268500328,
-0.005613318178802729,
-0.003949565347284079,
-0.01125488430261612,
0.009140374138951302,
0.0041276151314377785,
0.012141430750489235,
0.03032609261572361,
-0.04541458934545517,
-0.006651957519352436,
-0.013373025692999363,
-0.01700730249285698,
0.0074956584721803665,
-0.00738078448921442,
0.02427888661623001,
-0.028466783463954926,
0.021195976063609123,
-0.019912436604499817,
0.0003718881926033646,
-0.07611619681119919,
0.019779443740844727,
0.028520971536636353,
-0.024009045213460922,
-0.014746368862688541,
0.011879676021635532,
-0.013771924190223217,
-0.007748628035187721,
0.0423809252679348,
0.002009218791499734,
0.021285811439156532,
0.003199384780600667,
0.053553249686956406,
-0.05128413811326027,
0.023092132061719894,
-0.005905233323574066,
-0.032244667410850525,
0.04590515047311783,
-0.026075046509504318,
-0.08088983595371246,
0.035377804189920425,
-0.019697679206728935,
0.04102643206715584,
0.025054767727851868,
0.010822169482707977,
0.0062347594648599625,
0.07097404450178146,
-0.012667512521147728,
-0.0185413658618927,
0.005712913349270821,
0.0427340529859066,
0.0039052115753293037,
0.038644373416900635,
0.03588215634226799,
-0.048785608261823654,
-0.008489071391522884,
0.05285120755434036,
0.01591446064412594,
-0.042675092816352844,
0.014473779127001762,
-0.010894695296883583,
-0.050464991480112076,
0.01588185876607895,
0.002729895059019327,
0.02166455239057541,
0.021131079643964767,
-0.02647501789033413,
0.01270952820777893,
0.06920494139194489,
0.010326923802495003,
-0.007405246142297983,
-0.09058235585689545,
0.03676337003707886,
-0.0223587304353714,
0.002635199809446931,
0.0071882568299770355,
-0.04543151333928108,
-0.004050155635923147,
0.03854689002037048,
-0.0931737869977951,
0.018159279599785805,
-0.0008802904048934579,
-0.02561674825847149,
-0.020272044464945793,
0.0037697714287787676,
-0.0046823411248624325,
0.027881890535354614,
0.008396046236157417,
0.002306569367647171,
0.022857125848531723,
0.039688460528850555,
-0.025510122999548912,
-0.005295027047395706,
-0.0032040898222476244,
0.039877090603113174,
-0.020199820399284363,
0.017808621749281883,
0.05636494234204292,
-0.023661183193325996,
-0.00704546133056283,
0.0357358492910862,
0.03592421114444733,
0.05281589925289154,
-0.029180854558944702,
0.003764884313568473,
-0.017594236880540848,
0.020147962495684624,
-0.012323910370469093,
-0.023240379989147186,
0.02220085635781288,
0.010730566456913948,
0.01573532447218895,
0.009099697694182396,
-0.012946147471666336,
-0.0013189089950174093,
0.04476083070039749,
-0.06832490116357803,
-0.01323928963392973,
-0.033522311598062515,
0.009535597637295723,
0.015003612264990807,
0.023596718907356262,
0.03226698189973831,
0.0164951104670763,
-0.00494418665766716,
-0.01651507243514061,
-0.072812519967556,
-0.005375557113438845,
0.016925757750868797,
0.008817721158266068,
0.0023095044307410717,
0.012211989611387253,
-0.011104286648333073,
-0.030402960255742073,
0.008177352137863636,
0.013328968547284603,
-0.02798105776309967,
0.015620973892509937,
-0.0006298478110693395,
0.008159243501722813,
-0.0028479339089244604,
-0.009399756789207458,
0.012866743840277195,
-0.042213212698698044,
-0.006753170397132635,
0.0349775031208992,
0.03061816468834877,
-0.04916207864880562,
-0.0701175108551979,
-0.03240320459008217,
-0.03223692998290062,
0.02229197882115841,
0.0005620644660666585,
-0.005876154638826847,
-0.05777070298790932,
-0.02828793227672577,
-0.03579099848866463,
0.047874365001916885,
0.031995583325624466,
0.003857731819152832,
-0.0012942042667418718,
0.014846928417682648,
-0.0031110690906643867,
0.03731303662061691,
-0.06032003462314606,
0.04423881322145462,
0.015340819954872131,
-0.028044871985912323,
0.02213149704039097,
-0.015240401029586792,
0.00011578258272493258,
0.013375841081142426,
0.046174369752407074,
-0.03302140161395073,
0.048049937933683395,
0.018938207998871803,
-0.04026872664690018,
0.0655498206615448,
0.032583098858594894,
-0.0023394650779664516,
0.051820941269397736,
-0.020127031952142715,
-0.026493126526474953,
0.03226086497306824,
-0.014671583659946918,
-0.0455470010638237,
0.01546064019203186,
-0.014639027416706085,
-0.012527735903859138,
-0.00132809451315552,
-0.033689554780721664,
-0.00015734770568087697,
-0.025729766115546227,
0.014234345406293869,
0.06070641428232193,
0.009630111977458,
-0.023985818028450012,
0.07794757187366486,
-0.0077473777346313,
0.03206527978181839,
0.023812459781765938,
0.03305470943450928,
-0.03031822293996811,
0.018620850518345833,
-0.021587727591395378,
0.03898414969444275,
-0.006614228710532188,
0.014967727474868298,
0.038676127791404724,
0.009713472798466682,
0.03496507927775383,
0.03866738826036453,
-0.024549107998609543,
0.04990958422422409,
-0.036675844341516495,
0.009178662672638893,
0.019814131781458855,
0.010188018903136253,
-0.018931059166789055,
0.06782441586256027,
-0.0063032303005456924,
0.09500222653150558,
-0.03179631754755974,
0.014244139194488525,
0.018593061715364456,
-0.005296529270708561,
-0.025723185390233994,
-0.01902001164853573,
0.03968051075935364,
-0.0003812262148130685,
-0.0006940673338249326,
-0.0077360766008496284,
0.009288717992603779,
0.024583004415035248,
0.028716884553432465,
-0.05792269483208656,
0.03143206611275673,
0.007409850601106882,
0.007738395128399134,
0.0027238992042839527,
0.02919507771730423,
-0.014303425326943398,
-0.03322077915072441,
0.005209891125559807,
-0.002068765228614211,
0.00930020771920681,
0.0015763470437377691,
-0.024394331499934196,
-0.02717493288218975,
0.037710003554821014,
-0.08153872936964035,
-0.025718702003359795,
0.007535230368375778,
0.06845298409461975,
-0.0008593035163357854,
-0.028925154358148575
] |
<p>In a <a href="http://physics.stackexchange.com/q/72308/8563">recent question</a>, Ben Crowell raised an observation which really puzzled me. I obtained a partial answer by looking in the literature, but I would like to know if it's on the right track, and a fuller explanation for it.</p>
<p>It is a well-known fact in atomic and molecular physics that electronic eigenstates of inversion-symmetric molecules never have electronic dipole moments. This is because the electromagnetic hamiltonian that governs molecular physics is parity invariant: under a reflection the eigenstates must map to themselves, but nonzero vector quantities - like dipole moments - must switch signs.</p>
<p>However, it was a fairly big news item earlier this year (see e.g. the <a href="http://www.york.ac.uk/news-and-events/news/2013/research/pear-shaped/" rel="nofollow">University of York press release</a> or the piece in <a href="http://dx.doi.org/10.1038/nature.2013.12952" rel="nofollow"><em>Nature News</em>, 8 May 2013</a>) that atomic nuclei can be 'pear-shaped'. This was predicted in the fifties, such as e.g.</p>
<blockquote>
<p>Stability of Pear-Shaped Nuclear Deformations. K. Lee and D. R. Inglis. <a href="http://dx.doi.org/10.1103/PhysRev.108.774" rel="nofollow"><em>Phys. Rev.</em> <strong>108</strong> no. 3, pp. 774-778 (1957)</a></p>
</blockquote>
<p>and was experimentally confirmed this year in</p>
<blockquote>
<p>Studies of pear-shaped nuclei using accelerated radioactive beams. L. P. Gaffney, P. A. Butler et al. <a href="http://dx.doi.org/10.1038/nature12073" rel="nofollow"><em>Nature</em> <strong>497</strong>, 199–204 (09 May 2013)</a>. <a href="http://ns.ph.liv.ac.uk/~lg/papers/StudiesOfNuclearPearShapesUsingAcceleratedRadioactiveBeams_Archive.pdf" rel="nofollow">E-print on L.P. Gaffney's L.U. page</a>.</p>
</blockquote>
<p>A pear-shaped nucleus is one that has a nonzero electric octupolar moment. The pear shape arises from the added contributions of quadrupole and octupole perturbations on a spherical shape, winding up with something like this:</p>
<p><img src="http://i.stack.imgur.com/8Qp3z.gif" alt="enter image description here"></p>
<p>However, this poses an immense problem, because octupole moments have odd parity. If you reflect a pear-shaped nucleus (as opposed to a rugby-ball-shaped quadrupolar one), you get a pear pointing the other way. Having such a nucleus requires a mixing of parity-even and -odd contributions to an energy eigenstate, and this is not allowed for eigenstates of the parity-conserving electromagnetic and strong interactions that (presumably) shape atomic nuclei.</p>
<p>To put this another way, having a pear-shaped nucleus requires a way to tell which way the pear will point. The nuclear angular momentum can break isotropy and provide a special axis, but the 'pear' is a vector (pointing from the base to the stem) and one needs parity-violating machinery to turn a pseudovector angular momentum into a vector quantity.</p>
<p>Another way to phrase this is by saying that if such an eigenstate were possible for a parity-conserving hamiltonian, then the reflected version should also be a degenerate, inseparable eigenstate. Having a unique such ground state means having a way to lift that degeneracy.</p>
<p>I can then pose my question: <strong>why are pear-shaped nuclei possible?</strong> Is my reasoning incorrect? That is, can parity-conserving hamiltonians lead to such parity-mixed eigenstates? Or are there in fact parity-violating interactions that decisively lift the degeneracies and shape these nuclei? If so, what are they?</p>
| 8,883 |
[
-0.06766234338283539,
-0.018414553254842758,
0.03478959947824478,
-0.06363357603549957,
0.06867396831512451,
0.038888026028871536,
-0.019009489566087723,
0.000191157465451397,
0.027329115197062492,
-0.05634881556034088,
0.06674256920814514,
0.03723350539803505,
0.03866969421505928,
0.014205028302967548,
-0.0005152918747626245,
0.02144767716526985,
0.04196828603744507,
-0.014222504571080208,
-0.02624945528805256,
-0.009434504434466362,
0.0348699577152729,
-0.0022661504335701466,
-0.013938069343566895,
-0.02008700557053089,
0.002294883830472827,
0.036655280739068985,
0.03397023677825928,
-0.0009900520090013742,
0.009560205042362213,
0.07085538655519485,
0.0009570274851284921,
-0.002891354961320758,
0.045881904661655426,
-0.05571739375591278,
0.03804897144436836,
-0.004634070675820112,
0.034352850168943405,
-0.015153051353991032,
0.009123648516833782,
0.04285724461078644,
-0.0062454212456941605,
0.013558396138250828,
-0.016202716156840324,
0.05471545830368996,
-0.02332083135843277,
0.030413558706641197,
-0.024637266993522644,
0.0019247372401878238,
0.06137551739811897,
-0.020538149401545525,
0.05984262749552727,
-0.031521108001470566,
0.03458194062113762,
0.009004109539091587,
-0.00418897345662117,
-0.023129794746637344,
0.0642329677939415,
0.03972391411662102,
-0.02053697779774666,
-0.058397822082042694,
0.001913106651045382,
-0.017544271424412727,
-0.01739249750971794,
0.009737594984471798,
-0.03950504958629608,
0.01367392111569643,
-0.014987376518547535,
-0.039773598313331604,
-0.00586646469309926,
0.009531144984066486,
0.020641932263970375,
0.014017059467732906,
0.02646951749920845,
-0.020533621311187744,
0.042168524116277695,
-0.030918600037693977,
0.044160906225442886,
-0.0007637387607246637,
0.027138441801071167,
0.018533043563365936,
0.0012726287823170424,
0.015818774700164795,
0.011343581601977348,
-0.009501354768872261,
0.008734667673707008,
-0.012207096442580223,
0.04959484189748764,
-0.041885219514369965,
-0.011472780257463455,
0.05388902500271797,
0.024474618956446648,
0.006822546944022179,
0.024817107245326042,
-0.013926610350608826,
-0.019186971709132195,
0.0322037898004055,
0.02024664171040058,
0.04576496779918671,
-0.03665393963456154,
0.0028798719868063927,
-0.013037644326686859,
-0.020983582362532616,
0.017673086374998093,
0.11445283889770508,
-0.012039701454341412,
-0.03710048273205757,
-0.017709877341985703,
0.02047986164689064,
-0.05081619694828987,
0.008451460860669613,
-0.0013896743766963482,
-0.01041562668979168,
-0.002392970724031329,
-0.016865521669387817,
0.006902235560119152,
-0.01947857066988945,
0.004158645868301392,
-0.011639720760285854,
0.03885403275489807,
0.053256019949913025,
0.009652242064476013,
-0.041009820997714996,
0.005717057269066572,
-0.05820372700691223,
-0.08500578254461288,
-0.03554496169090271,
0.06517478078603745,
0.012382782064378262,
-0.06218700483441353,
0.007085635792464018,
0.02717583067715168,
-0.0010665175504982471,
0.03325735777616501,
-0.027652468532323837,
0.019660422578454018,
0.030877523124217987,
-0.11457213014364243,
-0.05230536684393883,
0.029801854863762856,
0.02518654614686966,
-0.033590734004974365,
-0.092178113758564,
-0.027587326243519783,
0.05010032653808594,
0.07097487896680832,
-0.020850805565714836,
-0.010402549989521503,
0.021975982934236526,
0.08048027753829956,
0.012863075360655785,
0.01863296888768673,
0.0061375792138278484,
0.034105464816093445,
-0.02939210832118988,
-0.019611073657870293,
-0.06664710491895676,
0.05486161261796951,
0.009122202172875404,
0.008025353774428368,
0.010768692940473557,
0.04878302291035652,
-0.0293581485748291,
-0.006141695659607649,
-0.024745158851146698,
-0.02040879987180233,
-0.002477755304425955,
0.07411643117666245,
0.0409182533621788,
-0.04311319813132286,
0.06316189467906952,
-0.025936689227819443,
0.028529565781354904,
-0.04339327663183212,
0.023568280041217804,
0.019332511350512505,
-0.07511258870363235,
-0.0036731224972754717,
-0.021366799250245094,
-0.030255567282438278,
0.003475980134680867,
-0.021573903039097786,
-0.01037830114364624,
-0.02475949004292488,
0.016808802261948586,
0.010398373007774353,
0.04912446066737175,
0.0025974998716264963,
0.04035390913486481,
0.03970520943403244,
-0.08003522455692291,
-0.01156698539853096,
-0.01897505298256874,
0.009590299800038338,
-0.029976315796375275,
-0.04057346656918526,
0.029703855514526367,
-0.01983431726694107,
-0.014794567599892616,
0.007989705540239811,
-0.042396996170282364,
-0.005934675224125385,
0.03230671212077141,
0.03881711885333061,
-0.021680012345314026,
0.024092525243759155,
0.038515765219926834,
0.018244771286845207,
-0.03402290865778923,
0.03055725246667862,
-0.04506012052297592,
-0.016277102753520012,
0.0033850781619548798,
0.0021146503277122974,
0.0048690009862184525,
0.028541777282953262,
-0.007412002421915531,
-0.009018858894705772,
-0.003960076719522476,
0.017108449712395668,
0.005087122321128845,
-0.007989313453435898,
0.014300589449703693,
0.0028560918290168047,
0.022968143224716187,
0.049728721380233765,
0.07589980959892273,
0.06993100792169571,
0.059329185634851456,
0.012970393523573875,
-0.05007297918200493,
-0.07697956264019012,
-0.04034441336989403,
0.028428295627236366,
0.03747900202870369,
-0.04028952494263649,
0.023487748578190804,
-0.010405990295112133,
0.0352395661175251,
0.012541655451059341,
0.026591740548610687,
-0.036843203008174896,
-0.055552106350660324,
0.009952476248145103,
0.0013628549640998244,
-0.0009622584329918027,
0.03678666427731514,
0.02289889007806778,
0.006083879619836807,
0.04122665151953697,
0.0029101416002959013,
0.007549073547124863,
-0.03237452358007431,
0.010473345406353474,
-0.03877144679427147,
0.0012686951085925102,
-0.05028267204761505,
0.04563937336206436,
-0.01843981072306633,
0.003933771979063749,
0.013921141624450684,
-0.03151151165366173,
-0.01062443945556879,
-0.042561694979667664,
-0.015860838815569878,
-0.03105601854622364,
0.01913304254412651,
-0.026397008448839188,
-0.03406171873211861,
0.023176243528723717,
-0.025278853252530098,
-0.0028851244132965803,
-0.03454964980483055,
-0.020103508606553078,
0.012129382230341434,
-0.019902579486370087,
0.03178667649626732,
0.02909703366458416,
-0.02809041552245617,
-0.024861251935362816,
-0.0026082005351781845,
-0.017474662512540817,
-0.008801314979791641,
-0.0019665402360260487,
0.010036386549472809,
-0.024766329675912857,
0.03029024787247181,
-0.030951978638768196,
0.014184718020260334,
0.030552620068192482,
-0.011746373027563095,
-0.007954786531627178,
-0.004298941697925329,
0.007198951207101345,
-0.04506620764732361,
-0.03424838185310364,
-0.013031191192567348,
0.00912629533559084,
-0.04388599470257759,
-0.008999716490507126,
0.06700799614191055,
-0.009163710288703442,
-0.01900087483227253,
0.01837986707687378,
-0.016045717522501945,
-0.0059625981375575066,
-0.02423771657049656,
-0.019761206582188606,
0.0058251540176570415,
0.0079196747392416,
-0.0005151453660801053,
0.03911938518285751,
-0.00730817811563611,
-0.007679598871618509,
-0.07218493521213531,
-0.05877764895558357,
-0.005452866666018963,
-0.020218290388584137,
0.07219325006008148,
-0.00198844145052135,
0.013515714555978775,
0.08680766075849533,
-0.007112011779099703,
-0.040067095309495926,
-0.010722419247031212,
0.002204440999776125,
-0.015794582664966583,
-0.03174547106027603,
0.03060046397149563,
0.041702400892972946,
0.02617451548576355,
0.010343160480260849,
-0.007631127722561359,
0.034173134714365005,
-0.01451917365193367,
-0.004711437970399857,
-0.037343692034482956,
0.027710553258657455,
-0.007090185768902302,
-0.0192723385989666,
-0.000151880070916377,
0.020509039983153343,
-0.013902385719120502,
0.006730102933943272,
-0.01657778210937977,
0.008199293166399002,
0.013378585688769817,
-0.08854702860116959,
0.06259194016456604,
0.000710018677636981,
0.04338138923048973,
0.01000932976603508,
0.04652539640665054,
-0.006830691359937191,
-0.0037820779252797365,
-0.003805766347795725,
0.028397182002663612,
0.07017967104911804,
-0.0020908231381326914,
0.01603027805685997,
0.0457487590610981,
0.03496548905968666,
0.06552352756261826,
-0.0081191910430789,
0.018599320203065872,
-0.03182933107018471,
0.012833664193749428,
-0.04534753039479256,
-0.029777880758047104,
0.056822773069143295,
0.02435683272778988,
0.0205560140311718,
0.013055444695055485,
-0.009798103012144566,
0.019720980897545815,
-0.021782590076327324,
-0.0031768721528351307,
0.0058828252367675304,
0.046070899814367294,
0.007851708680391312,
0.055060625076293945,
0.007176071405410767,
0.03128247335553169,
-0.015276342630386353,
-0.032622531056404114,
-0.07123055309057236,
0.011318022385239601,
-0.03217361867427826,
-0.0005663306801579893,
-0.031620923429727554,
0.011265622451901436,
-0.013182154856622219,
0.008201014250516891,
-0.043668895959854126,
-0.023950956761837006,
-0.013909993693232536,
-0.02323482558131218,
0.0169166699051857,
-0.046877358108758926,
-0.04529566690325737,
0.0071860020980238914,
0.045896030962467194,
0.08975479006767273,
-0.06660816073417664,
0.0519077405333519,
-0.0013637004885822535,
-0.04994267597794533,
-0.007857069373130798,
-0.03760531544685364,
0.0552496500313282,
0.02207251451909542,
0.04374264180660248,
-0.0010731666116043925,
0.015566560439765453,
-0.04073626175522804,
0.003242162521928549,
0.03596818447113037,
0.013781845569610596,
0.016035636886954308,
-0.04588155820965767,
0.0016442445339635015,
-0.027047473937273026,
0.009778324514627457,
0.0011648987419903278,
0.041412144899368286,
-0.002850748598575592,
0.05518727004528046,
-0.018644027411937714,
-0.00744624063372612,
-0.008895938284695148,
0.03965268284082413,
0.003982515539973974,
0.021993307396769524,
0.005857235752046108,
-0.049177564680576324,
-0.0051169628277421,
0.010943875648081303,
0.0052369022741913795,
-0.006174406502395868,
-0.005022514145821333,
-0.01339447870850563,
0.00923157762736082,
0.03825455158948898,
0.039969176054000854,
-0.010978014208376408,
-0.017298255115747452,
-0.029965339228510857,
-0.020915502682328224,
-0.04602934792637825,
0.013586378656327724,
0.012279855087399483,
0.02607189118862152,
0.050225384533405304,
0.032109037041664124,
-0.02592930942773819,
-0.06834726780653,
-0.008140390738844872,
0.032365500926971436,
0.05383264645934105,
-0.020520811900496483,
-0.01816708780825138,
-0.03553786873817444,
-0.010475036688148975,
0.06700246036052704,
-0.02996727079153061,
0.043857213109731674,
-0.039238959550857544,
0.00196000374853611,
-0.007091146893799305,
-0.03803242743015289,
-0.038159653544425964,
-0.002100809942930937,
-0.0021446244791150093,
-0.0061844727024436,
-0.009666274301707745,
-0.03973158448934555,
0.01861307956278324,
0.014029082842171192,
-0.0027892873622477055,
0.017663413658738136,
-0.001889595529064536,
0.006682055536657572,
-0.006683622486889362,
-0.00609086686745286,
-0.025979619473218918,
-0.068825364112854,
0.025110159069299698,
-0.00007635884685441852,
0.006605055183172226,
0.03715962544083595,
-0.041514456272125244,
-0.06341838836669922,
0.0043217879720032215,
-0.039199985563755035,
-0.01724403351545334,
0.010508468374609947,
-0.018791353330016136,
0.048923056572675705,
0.04258110374212265,
-0.04328175261616707,
0.06274152547121048,
0.09670941531658173,
-0.021693523973226547,
-0.0291715320199728,
-0.024770744144916534,
0.0038331151008605957,
-0.027197062969207764,
0.009792768396437168,
-0.029985502362251282,
0.057098038494586945,
-0.034014634788036346,
0.044642847031354904,
-0.007122431416064501,
0.029650133103132248,
0.03575332462787628,
-0.033647529780864716,
-0.002058167476207018,
0.006680041551589966,
-0.02019372209906578,
-0.026587381958961487,
0.004539285786449909,
-0.0202953964471817,
0.008929088711738586,
0.002592942211776972,
0.025171268731355667,
-0.031609173864126205,
-0.00042138007120229304,
0.05350557714700699,
-0.018812712281942368,
0.0011485564755275846,
-0.051936075091362,
-0.028922351077198982,
-0.0022500092163681984,
-0.03649349883198738,
0.01293431967496872,
-0.037033047527074814,
0.0003955777210649103,
0.045665666460990906,
-0.04166129231452942,
0.007101112045347691,
0.043719321489334106,
-0.020814964547753334,
-0.026639273390173912,
-0.007748918607831001,
-0.018442794680595398,
-0.02744843065738678,
0.018215695396065712,
-0.03394642844796181,
-0.02106967568397522,
0.03192169964313507,
0.016181377694010735,
-0.06816602498292923,
-0.02600782923400402,
-0.011181674897670746,
0.01421415340155363,
-0.0012265696423128247,
-0.01352152694016695,
0.01099703460931778,
-0.07100967317819595,
0.005384455900639296,
0.030711503699421883,
0.03472559526562691,
0.05898964777588844,
0.013041745871305466,
-0.017330117523670197,
-0.007553277537226677,
0.012860866263508797,
0.027591699734330177,
-0.0058140987530350685,
0.013666938059031963,
-0.0036667892709374428,
-0.05160612612962723,
-0.0005076066008768976,
0.002554735168814659,
0.02187291905283928,
0.002411113353446126,
0.006613240577280521,
0.03908465802669525,
-0.04616186395287514,
-0.024406174197793007,
-0.0059404331259429455,
0.003865402191877365,
-0.010472746565937996,
0.03407617285847664,
0.0053900484926998615,
0.014528188854455948,
0.007141010835766792,
-0.06532641500234604,
0.0027868254110217094,
0.025801554322242737,
0.015411746688187122,
0.01976173371076584,
0.028172537684440613,
0.0034070343244820833,
-0.005905698053538799,
0.007881108671426773,
-0.04175228998064995,
0.04103465750813484,
0.0007052635191939771,
0.0009108408121392131,
-0.04102133959531784,
0.0016622011316940188,
-0.021581582725048065,
-0.028750518336892128,
-0.031161053106188774,
0.0381842702627182,
0.04010762646794319,
0.020037807524204254,
0.030726956203579903,
-0.014948923140764236,
-0.0002554792445152998,
-0.03041965141892433,
-0.048271022737026215,
0.01766630820930004,
-0.004427039530128241,
-0.005850421730428934,
0.05482293665409088,
-0.03497498854994774,
-0.002367636188864708,
0.03615916520357132,
0.08120608329772949,
-0.03394857794046402,
0.025317227467894554,
0.024280551820993423,
-0.01085046399384737,
0.006207997445017099,
-0.02754761092364788,
-0.00939745083451271,
0.06701327860355377,
-0.028853299096226692,
0.018958693370223045,
0.01848776452243328,
-0.00952943880110979,
-0.01704873889684677,
-0.008898994885385036,
0.03672606498003006,
-0.041742775589227676,
-0.02862618677318096,
-0.020778799429535866,
0.025339659303426743,
0.014409895054996014,
-0.038751278072595596,
-0.054472699761390686,
-0.01859879679977894,
0.03521542251110077,
-0.001874470617622137,
0.00386940804310143,
-0.030211275443434715,
-0.027481909841299057,
0.021101614460349083,
-0.012266534380614758,
-0.042474258691072464,
0.032653387635946274,
-0.02406563051044941,
0.0006143744685687125,
0.02602415904402733,
0.0009539073216728866,
0.0058120847679674625,
0.02156941220164299,
0.024457313120365143,
-0.005041967146098614,
0.05915552005171776,
-0.023850634694099426,
-0.020859351381659508,
-0.03458467498421669,
-0.03713453561067581,
0.165795236825943,
0.011872736737132072,
0.028030874207615852,
-0.0024437811225652695,
0.03889927640557289,
0.028156111016869545,
0.04525412991642952,
0.006648579612374306,
-0.031844280660152435,
-0.014147152192890644,
0.01892128959298134,
-0.01000380702316761,
0.0366368293762207,
0.034264300018548965,
0.018940825015306473,
0.006290521007031202,
-0.029002079740166664,
-0.00562237249687314,
-0.029427852481603622,
0.022919505834579468,
0.013484672643244267,
-0.005038588307797909,
-0.05495008826255798,
0.014516321942210197,
-0.02494553104043007,
0.0017965820152312517,
-0.05793023109436035,
0.011507298797369003,
0.02772325836122036,
0.029177388176321983,
-0.02100919559597969,
-0.02211408130824566,
0.018922260031104088,
-0.006683497689664364,
-0.02301619201898575,
0.029811620712280273,
0.009197081439197063,
0.018675245344638824,
0.03988967090845108,
0.03369041904807091,
-0.0007333771209232509,
-0.020190704613924026,
0.01729370839893818,
-0.0017582094296813011,
-0.05175335332751274,
-0.013683627359569073,
-0.0364166721701622,
0.023823002353310585,
-0.04482463002204895,
0.0069188205525279045,
-0.012131107039749622,
-0.025927675887942314,
0.03286350890994072,
-0.04683176055550575,
-0.008393391966819763,
0.01796526275575161,
-0.019581880420446396,
-0.013509082607924938,
-0.008909237571060658,
0.026288600638508797,
-0.008394432254135609,
0.007091164588928223,
0.020495373755693436,
0.0023127964232116938,
-0.026330504566431046,
0.006672097370028496,
-0.02866370789706707,
0.042999349534511566,
0.010988093912601471,
-0.010379637591540813,
-0.058300841599702835,
0.01775999180972576,
-0.03842055797576904,
-0.009682292118668556,
0.011466970667243004,
-0.0046689980663359165,
0.05305427685379982,
0.018526820465922356,
-0.00897920411080122,
-0.025024769827723503,
-0.045345488935709,
0.05801241099834442,
0.022335905581712723,
-0.000688500760588795,
0.006349966861307621,
0.004959587473422289,
0.017145052552223206,
0.007637055590748787,
-0.040890756994485855,
0.0383363775908947,
-0.022432850673794746,
0.037681423127651215,
-0.008246050216257572,
-0.01426702830940485,
-0.012590363621711731,
0.028417449444532394,
-0.012554123066365719,
-0.003396687563508749,
-0.01816437765955925,
0.019324688240885735,
0.039867956191301346,
0.017325224354863167,
-0.010610134340822697,
0.003382149152457714,
-0.01997074857354164,
-0.028121396899223328,
0.06334716081619263,
-0.039545994251966476,
-0.00007370259118033573,
-0.0210624597966671,
0.013976380228996277,
-0.055384561419487,
-0.056197576224803925,
0.00098902708850801,
-0.04534073546528816,
0.010111294686794281,
0.018223309889435768,
0.008905638940632343,
0.0005143054877407849,
-0.08637941628694534,
0.017956797033548355,
-0.025431407615542412,
-0.03145507350564003,
-0.05306169390678406,
-0.01674288883805275,
-0.015061755664646626,
0.03937043622136116,
-0.013819371350109577,
0.010862820781767368,
0.006721953861415386,
-0.008466646075248718,
0.059622623026371,
0.02930821105837822,
0.004231225699186325,
0.015521818771958351,
0.007509144023060799,
0.037214212119579315,
0.02323460765182972,
0.023969603702425957,
-0.034488651901483536,
0.025206971913576126,
-0.03376411646604538,
-0.06174356862902641,
0.031937479972839355,
-0.019713304936885834,
-0.010651477612555027,
0.000901536550372839,
0.00463695265352726,
0.027612851932644844,
0.021908048540353775,
-0.030635783448815346,
-0.015214487910270691,
0.013476509600877762,
0.039737824350595474,
0.00590470340102911,
0.0000618423437117599,
0.009951302781701088,
-0.0028876864816993475,
0.004179705865681171,
0.038393791764974594,
0.014077477157115936,
0.0010534783359616995,
-0.014369343407452106,
-0.029352465644478798,
-0.03679416701197624,
-0.015734564512968063,
-0.016652202233672142,
0.03622708097100258,
0.016684578731656075,
0.012109932489693165,
-0.035422828048467636,
0.04578157514333725,
0.031018059700727463,
0.01743265427649021,
-0.07159920781850815,
-0.011745224706828594,
0.03273942694067955,
0.00976879894733429,
0.04067283123731613,
-0.018331404775381088,
0.026443421840667725,
0.014406029134988785,
-0.08287704735994339,
0.019472692161798477,
-0.0011419315123930573,
-0.009156596846878529,
-0.00189704739023,
-0.004319406114518642,
-0.0602564662694931,
0.028716227039694786,
0.004564675036817789,
0.03588235750794411,
0.031809400767087936,
0.03468365967273712,
-0.026236752048134804,
-0.02899010293185711,
-0.017102783545851707,
0.01751212775707245,
-0.01205714512616396,
-0.007833580486476421,
0.0678291916847229,
-0.014295399188995361,
-0.006238535977900028,
0.02780613675713539,
-0.05193857103586197,
0.002516841981559992,
-0.0481766052544117,
-0.014374240301549435,
0.01564490608870983,
0.013503369875252247,
0.002907798858359456,
-0.0028815881814807653,
-0.02436501905322075,
-0.02754652500152588,
-0.017209548503160477,
0.026087692007422447,
0.034152690321207047,
-0.002179350471124053,
-0.027393564581871033,
-0.03376546874642372,
-0.030683044344186783,
0.0027895637322217226,
-0.005270838737487793,
0.008538218215107918,
0.0035839169286191463,
0.013503088615834713,
0.01074301265180111,
0.010414013639092445,
0.040428124368190765,
-0.039124730974435806,
0.016788965091109276,
-0.018470196053385735,
0.014078480191528797,
0.008922742679715157,
0.05142899602651596,
0.006582571193575859,
-0.0007397179142571986,
0.012491476722061634,
0.007252424024045467,
-0.04010425880551338,
-0.031064990907907486,
0.01894926093518734,
0.023343557491898537,
0.029276246204972267,
-0.01974593661725521,
-0.025290532037615776,
-0.08806172013282776,
0.025558922439813614,
0.033134251832962036,
0.013637823984026909,
-0.01840507984161377,
-0.024513086304068565,
-0.025441190227866173,
-0.06517758220434189,
0.03040514700114727,
-0.007609215565025806,
0.010092673823237419,
-0.015835292637348175,
-0.002611458534374833,
0.009743747301399708,
0.020101767033338547,
0.06371304392814636,
0.017262768000364304,
-0.004264311399310827,
0.019307555630803108,
-0.046998582780361176,
0.019378896802663803,
-0.018435733392834663,
-0.015319164842367172,
0.02751949429512024,
0.009091631509363651,
0.025692859664559364,
-0.013156581670045853,
-0.007644818164408207,
0.013752886094152927,
0.015996620059013367,
-0.0073786149732768536,
-0.013279847800731659,
0.019093211740255356,
-0.038844652473926544,
0.058971066027879715,
0.025379857048392296,
-0.02529541589319706,
0.044549718499183655,
-0.002380669815465808,
0.005272206384688616,
-0.010517016053199768,
-0.04023154824972153,
-0.03450583294034004,
-0.00011034174531232566,
-0.041899990290403366,
-0.02203022874891758,
-0.030781323090195656,
-0.04027619585394859,
0.01976034976541996,
-0.03422922641038895,
0.012384620495140553,
0.04556354880332947,
-0.0361202210187912,
-0.015116247348487377,
0.019295211881399155,
-0.002787025412544608,
0.029356282204389572,
0.01642206683754921,
0.02668512612581253,
0.041935551911592484,
-0.027170803397893906,
0.022262243553996086,
0.012419753707945347,
0.017933698371052742,
0.02323794551193714,
0.003727310337126255,
0.03177694231271744,
-0.0012117379810661077,
0.018375426530838013,
0.021945107728242874,
-0.0330873541533947,
-0.009883873164653778,
0.006510062608867884,
0.06110638380050659,
-0.0074332416988909245,
-0.029129019007086754,
0.004664439242333174,
-0.013308213092386723,
0.07121418416500092,
0.031993377953767776,
-0.012982912361621857,
-0.024799514561891556,
-0.011030897498130798,
0.011158956214785576,
0.015129624865949154,
0.010590665973722935,
-0.006564262788742781,
0.0008924886933527887,
-0.017944473773241043,
-0.014232359826564789,
-0.0013118763454258442,
0.013259452767670155,
-0.03842592239379883,
0.0010534696048125625,
0.00610736571252346,
0.02405051328241825,
0.01943320594727993,
0.0019397292053326964,
-0.03754318132996559,
-0.00953642837703228,
-0.00995312724262476,
0.02266794815659523,
0.02971569634974003,
0.013316218741238117,
0.0003694528713822365,
0.00460390280932188,
0.07153364270925522,
-0.05858159810304642,
-0.03264107182621956,
-0.013150415383279324,
0.02974453940987587,
-0.006942909210920334,
0.006061805412173271
] |
<p>Is it possible to build a water tower that will provide enough pressure to run an electricity generator? A water pump can be used to send water up to the tower. The water pump can be powered by solar panels. Alternatively the water pump could also be powered by the electricity produced from the generator.</p>
<p>The water tower can hold 20,000 to 30,000 gallons of water. Could this have enough pressure to send the water down a pipe and pass it through an electric generator where it will cause a turbine to rotate and produce electricity? </p>
<p>Once the water passes through the generator it can be redirected back to the water pump. The water will then be pumped back to the water tower making it a water circulation system. I would like to find out if it is physically possible to produce more power from the pressure stored in the water tower than it is required to pump it up. If solar panels are used to power the water pump, is it theoretically possible to produce more electric power using this method?</p>
<p>I am not familiar with any similar projects but I am looking to see if this setup will have the capacity to produce enough electricity to make it a feasible project.</p>
| 8,884 |
[
-0.047547563910484314,
-0.027521595358848572,
-0.022496148943901062,
-0.017651384696364403,
0.036687400192022324,
-0.046374257653951645,
-0.04387141391634941,
-0.03730091080069542,
0.03008122928440571,
-0.03906834125518799,
0.02594844438135624,
0.02278870902955532,
0.02800566703081131,
-0.017320388928055763,
-0.004024000372737646,
0.016589896753430367,
0.0014969641342759132,
0.0007168199517764151,
0.022995339706540108,
-0.016377650201320648,
-0.06170900538563728,
0.012560670264065266,
-0.03166445344686508,
0.015810294076800346,
-0.005924039985984564,
-0.003193875774741173,
0.03226088732481003,
0.018338460475206375,
-0.042484428733587265,
0.03552262485027313,
0.01648690365254879,
-0.0423537939786911,
-0.004841693677008152,
0.07077893614768982,
0.028971439227461815,
0.022498296573758125,
-0.01372360996901989,
-0.046304840594530106,
-0.01332500483840704,
0.011225531809031963,
0.013609376735985279,
0.022655578330159187,
0.03245886042714119,
0.0014591756043955684,
-0.03027793951332569,
0.05167991667985916,
-0.0005291847046464682,
-0.046559542417526245,
0.007310591638088226,
-0.061893437057733536,
0.03995279595255852,
0.03773614391684532,
0.03352823480963707,
0.0297178216278553,
-0.013941345736384392,
0.0033512823283672333,
0.06722418963909149,
0.08339454978704453,
-0.014270339161157608,
-0.014792356640100479,
-0.00962982140481472,
0.024974113330245018,
-0.014743131585419178,
-0.04159102588891983,
-0.04419209808111191,
-0.007118615321815014,
0.010058977641165257,
0.0010627760784700513,
0.012052108533680439,
-0.040285203605890274,
0.04206084832549095,
-0.009428650140762329,
0.03053581528365612,
0.028653694316744804,
0.005863334517925978,
-0.020059969276189804,
-0.016859760507941246,
0.004662278573960066,
0.006233036518096924,
0.026215581223368645,
-0.013261144980788231,
0.0387720949947834,
-0.006643925327807665,
0.05434111878275871,
0.0301422830671072,
0.00518651632592082,
0.03894814848899841,
-0.02850184217095375,
0.031730279326438904,
-0.007052955683320761,
-0.007060467265546322,
-0.01165207289159298,
0.009195653721690178,
0.0037732955534011126,
-0.013228616677224636,
0.0019432466942816973,
-0.025031011551618576,
0.036152370274066925,
0.013376583345234394,
-0.02481086552143097,
0.03221561387181282,
-0.009979881346225739,
0.013963272795081139,
0.06643174588680267,
0.03482090309262276,
-0.047945890575647354,
0.006440028548240662,
0.0022792620584368706,
-0.010318312793970108,
0.026468578726053238,
-0.039234708994627,
-0.006031003315001726,
-0.009956829249858856,
-0.05410904064774513,
0.010026606731116772,
0.004165035206824541,
0.015818903222680092,
-0.004879992920905352,
0.054058391600847244,
0.026375826448202133,
0.03829878568649292,
-0.015290576964616776,
0.0410761795938015,
-0.03471360728144646,
-0.037847645580768585,
0.008992413058876991,
-0.0009759526001289487,
-0.021379364654421806,
-0.0755537748336792,
0.06583576649427414,
0.014904899522662163,
0.0329587459564209,
0.001858818344771862,
-0.017859485000371933,
0.07111622393131256,
-0.022694870829582214,
-0.0848059430718422,
-0.04866109415888786,
0.04121360182762146,
0.005628630518913269,
0.012239696457982063,
-0.06271017342805862,
0.04212002083659172,
0.011562866158783436,
0.0650707483291626,
-0.0005425265990197659,
-0.008259991183876991,
0.0075363037176430225,
0.06033580005168915,
0.007690845988690853,
-0.02557915821671486,
0.018217869102954865,
0.03295174241065979,
-0.011121333576738834,
-0.002518352819606662,
-0.08047989010810852,
0.034230466932058334,
0.039190441370010376,
0.01963299699127674,
-0.008178035728633404,
0.018681401386857033,
0.003144051879644394,
0.010287102311849594,
-0.002409858163446188,
-0.04361674189567566,
-0.0036930835340172052,
0.026945404708385468,
-0.004623920191079378,
-0.03179850056767464,
-0.0045884354040026665,
0.04624876379966736,
0.061680812388658524,
0.03629397973418236,
0.009524847380816936,
0.042514920234680176,
-0.04240455850958824,
0.015966087579727173,
-0.051700543612241745,
0.04868942126631737,
0.012608351185917854,
0.0047286152839660645,
-0.020568083971738815,
-0.03201876953244209,
0.019130729138851166,
0.05081675201654434,
0.010465252213180065,
-0.00816216878592968,
-0.026516590267419815,
-0.01403807569295168,
-0.042003754526376724,
-0.010554366745054722,
-0.043670352548360825,
0.006194619927555323,
-0.013123112730681896,
0.024098055437207222,
-0.0319739393889904,
0.02286737971007824,
0.034092728048563004,
-0.05299181491136551,
-0.009057537652552128,
0.01971755176782608,
0.03600616380572319,
-0.0005999125423841178,
0.04495106264948845,
0.019817637279629707,
0.06242126226425171,
0.05402093753218651,
-0.012929720804095268,
-0.01415499672293663,
-0.023733071982860565,
-0.05745484307408333,
-0.026156160980463028,
-0.02468426153063774,
-0.0017473468324169517,
0.014811058528721333,
0.027057217434048653,
0.04552387073636055,
0.026428965851664543,
0.020217258483171463,
0.010361588560044765,
-0.00028772393125109375,
0.07965584099292755,
0.06335445493459702,
-0.0038638031110167503,
0.02212405949831009,
0.021410629153251648,
0.022252729162573814,
-0.005349104292690754,
-0.01260464172810316,
-0.02466164343059063,
-0.07451377809047699,
0.018807129934430122,
0.012031368911266327,
0.000952466856688261,
-0.038034699857234955,
0.04327520728111267,
0.028338000178337097,
0.008917597122490406,
0.02175268717110157,
0.04623396694660187,
-0.011609381064772606,
0.051299650222063065,
0.015914790332317352,
0.04556465893983841,
0.004242621827870607,
0.023856045678257942,
0.02052481286227703,
0.053564269095659256,
-0.0013385285856202245,
-0.06318511068820953,
0.02162163145840168,
0.04175001382827759,
-0.02859383448958397,
0.015089328400790691,
-0.01667420007288456,
-0.03886878862977028,
0.02707086317241192,
-0.06897828727960587,
-0.0012089157244190574,
-0.03013509325683117,
0.007460832130163908,
0.024546930566430092,
-0.02477584034204483,
-0.03743169829249382,
-0.0045991139486432076,
0.024487512186169624,
0.0046512167900800705,
-0.01563730277121067,
0.037213195115327835,
-0.051210738718509674,
0.04156968370079994,
-0.041960760951042175,
0.00637825345620513,
-0.04806996136903763,
0.004887937568128109,
0.028634514659643173,
-0.022413352504372597,
0.032635971903800964,
-0.036477189511060715,
-0.032112088054418564,
-0.008971258997917175,
-0.022031588479876518,
-0.021809987723827362,
-0.004527153912931681,
-0.04104474186897278,
-0.03187473490834236,
-0.0020964047871530056,
-0.042000025510787964,
0.029125094413757324,
0.02697599120438099,
-0.008714261464774609,
0.013649586588144302,
0.012217639945447445,
-0.029493624344468117,
0.019877659156918526,
-0.04798460006713867,
0.011777249164879322,
-0.011692089959979057,
-0.041586656123399734,
0.0365012027323246,
-0.0111542958766222,
-0.020513342693448067,
0.011777362786233425,
-0.04212301969528198,
-0.00418940931558609,
0.012996971607208252,
0.008771163411438465,
-0.01286282204091549,
-0.033826883882284164,
0.046169403940439224,
0.01268222089856863,
-0.07067734748125076,
0.007407804951071739,
-0.056708503514528275,
-0.05496165528893471,
0.012530958279967308,
-0.004031486809253693,
0.07392678409814835,
0.03851088881492615,
-0.049171559512615204,
0.06643848866224289,
-0.002857258776202798,
-0.034918081015348434,
-0.018200460821390152,
-0.026031890884041786,
0.01863216981291771,
-0.02727959305047989,
-0.023787640035152435,
0.05231865867972374,
-0.0449729785323143,
-0.008707398548722267,
0.0313866063952446,
-0.0020238624420017004,
0.022182323038578033,
-0.011114589869976044,
0.005469262599945068,
-0.022921497002243996,
0.0025573191232979298,
0.03534415736794472,
0.03155195340514183,
-0.030217954888939857,
-0.03403284028172493,
-0.026515522971749306,
-0.028086798265576363,
0.016763245686888695,
0.0025366852059960365,
-0.026283372193574905,
0.03544546663761139,
0.016835251823067665,
0.025935696437954903,
-0.07736551761627197,
0.0494132824242115,
0.0008137811673805118,
-0.00039809520239941776,
0.003640989540144801,
0.028149046003818512,
0.0897238478064537,
0.023931438103318214,
-0.024135814979672432,
0.03519618511199951,
0.07890969514846802,
-0.017564883455634117,
-0.06473400443792343,
-0.008973408490419388,
-0.016739701852202415,
0.005700042005628347,
0.0017368184635415673,
-0.01953596994280815,
0.04673481360077858,
-0.019056620076298714,
0.0162278413772583,
0.04552505165338516,
0.011679008603096008,
0.02253274992108345,
-0.059776272624731064,
0.01908552274107933,
-0.03285716474056244,
0.04001152515411377,
-0.0068796174600720406,
0.04621247947216034,
0.028558379039168358,
-0.020221807062625885,
0.024185068905353546,
-0.01922227442264557,
-0.04933738335967064,
0.0011659367009997368,
-0.03635992109775543,
0.014468293637037277,
0.001958173932507634,
-0.0025235647335648537,
-0.028717955574393272,
-0.0034600698854774237,
-0.028900058940052986,
-0.011045604012906551,
-0.004409073852002621,
-0.03447246178984642,
0.003703122027218342,
-0.005490942858159542,
-0.006384143140166998,
0.012266511097550392,
-0.01511266641318798,
0.035427335649728775,
-0.036133334040641785,
0.059142567217350006,
-0.0040978058241307735,
-0.03668675944209099,
0.0032256043050438166,
0.021302586421370506,
0.007417330052703619,
-0.0032203993760049343,
0.004605834372341633,
0.04379896819591522,
0.03275366872549057,
0.010099503211677074,
-0.03652001917362213,
-0.01685279607772827,
0.0341847762465477,
0.002011303324252367,
-0.01656137779355049,
-0.03244880214333534,
-0.02762526459991932,
0.0022958354093134403,
0.05045014247298241,
0.0135072385892272,
0.01860964111983776,
0.012297891080379486,
-0.0038594899233430624,
-0.036713629961013794,
-0.013745971024036407,
0.031659360975027084,
0.0631573423743248,
-0.007916335016489029,
-0.019661586731672287,
-0.05190371721982956,
-0.00864344835281372,
-0.020597772672772408,
-0.009218328632414341,
0.006701536942273378,
0.014663157053291798,
-0.03821692243218422,
0.009653251618146896,
0.03202773630619049,
0.01575937122106552,
-0.02245272509753704,
0.04298711568117142,
0.01680588163435459,
0.04984511062502861,
-0.00291703874245286,
0.007933801971375942,
0.03059196285903454,
0.02118627354502678,
0.007605339866131544,
-0.0043206894770264626,
-0.015119699761271477,
-0.10438347607851028,
-0.025908544659614563,
0.05274752527475357,
0.04153012856841087,
-0.0037707912269979715,
0.013203563168644905,
-0.0518396720290184,
-0.03667578473687172,
0.03587068244814873,
-0.024549884721636772,
0.013205614872276783,
-0.008857648819684982,
-0.02239292487502098,
-0.020645013079047203,
-0.03916146606206894,
0.014943817630410194,
-0.014020477421581745,
-0.06858514994382858,
0.032783493399620056,
-0.0023659521248191595,
-0.019356274977326393,
0.017649324610829353,
0.017495576292276382,
0.06730832904577255,
0.01400790922343731,
0.002850964665412903,
-0.00007911030115792528,
-0.03714042529463768,
0.031895238906145096,
-0.028699930757284164,
-0.08199742436408997,
0.0036647235974669456,
-0.040209751576185226,
-0.03179541602730751,
0.033552128821611404,
-0.01962323486804962,
-0.036073241382837296,
0.04969416558742523,
-0.013051378540694714,
-0.029021117836236954,
-0.019921230152249336,
-0.04893472045660019,
-0.0033450410701334476,
0.041661884635686874,
0.024580152705311775,
0.03675534203648567,
0.055200424045324326,
-0.03410230204463005,
0.012652648612856865,
-0.02349589392542839,
0.014208816923201084,
-0.019533738493919373,
-0.017334289848804474,
-0.029900697991251945,
0.01755484938621521,
-0.0024400223046541214,
0.0006911937380209565,
-0.023524215444922447,
0.03616531565785408,
-0.0012108645169064403,
0.00786314345896244,
0.007474333513528109,
0.024651478976011276,
0.010262967087328434,
-0.024996202439069748,
-0.054418567568063736,
0.04181578755378723,
0.02735668234527111,
-0.028109503909945488,
-0.00824811216443777,
-0.010417556390166283,
0.051681555807590485,
0.0029537288937717676,
-0.032160937786102295,
-0.0040395730175077915,
-0.0143278231844306,
-0.0019457852467894554,
0.04169720038771629,
-0.032884374260902405,
0.06852632015943527,
-0.016974298283457756,
0.023859620094299316,
0.03400605544447899,
-0.054098695516586304,
-0.015336900018155575,
0.034623727202415466,
-0.009156810119748116,
-0.005957870744168758,
-0.02823546901345253,
0.04123007878661156,
0.01734991744160652,
-0.0003700116358231753,
-0.015715880319476128,
-0.033517684787511826,
0.048232149332761765,
0.03225608170032501,
0.0034023660700768232,
-0.028721028938889503,
-0.01630542054772377,
-0.01819692738354206,
-0.03531007468700409,
-0.011515091173350811,
0.006276209373027086,
-0.032820168882608414,
0.006319317501038313,
0.013785798102617264,
-0.015253517776727676,
0.08840662240982056,
-0.01636338047683239,
-0.01462552510201931,
0.028769738972187042,
-0.010676886886358261,
-0.023996097967028618,
-0.05198410525918007,
0.022940032184123993,
-0.049953244626522064,
-0.017015576362609863,
-0.007565376348793507,
0.017150061205029488,
0.04372560977935791,
-0.026381971314549446,
0.02650379203259945,
0.035489290952682495,
0.03726454824209213,
-0.005152300000190735,
0.009236724115908146,
0.040123458951711655,
0.008835002779960632,
0.042174387723207474,
-0.029720868915319443,
-0.014257919043302536,
-0.03907836228609085,
-0.020717715844511986,
-0.007232642732560635,
0.013912218622863293,
-0.026729442179203033,
-0.01497711893171072,
0.09143701940774918,
-0.010678114369511604,
0.0026480872184038162,
-0.010846800170838833,
-0.022171838209033012,
0.0022281832061707973,
0.009381274692714214,
-0.008413444273173809,
-0.034360144287347794,
0.01059014443308115,
-0.01730775088071823,
-0.04259894788265228,
-0.016441840678453445,
-0.032061606645584106,
0.05804269015789032,
0.005903203040361404,
0.056040208786726,
0.020954465493559837,
-0.0029546453151851892,
0.01331943180412054,
-0.041484590619802475,
-0.019176175817847252,
0.016801387071609497,
-0.0043907128274440765,
0.01843622326850891,
0.0008920583059079945,
-0.0040619028732180595,
0.03386411815881729,
0.024583017453551292,
0.005153127480298281,
0.0065153115428984165,
0.065916508436203,
0.015752265229821205,
-0.0004255686071701348,
-0.04714801535010338,
-0.04543667659163475,
0.01911243051290512,
-0.054666075855493546,
0.023240951821208,
-0.020349755883216858,
-0.013188241049647331,
0.019357377663254738,
-0.008725271560251713,
-0.043469641357660294,
-0.030277416110038757,
-0.008458368480205536,
-0.055607035756111145,
0.009467319585382938,
-0.005077768117189407,
0.0323663204908371,
-0.014444599859416485,
0.024074481800198555,
0.005097327288240194,
0.015910554677248,
0.0024731282610446215,
-0.007333059329539537,
-0.04415486380457878,
-0.04221304506063461,
-0.04417920485138893,
-0.046962931752204895,
0.04373033344745636,
0.019850455224514008,
-0.002105261432006955,
0.010094471275806427,
0.0014835902256891131,
-0.0010625956347212195,
-0.024760767817497253,
0.04016238823533058,
-0.020635612308979034,
0.07411938160657883,
-0.02686869166791439,
0.04217249155044556,
0.02556920051574707,
0.03393059968948364,
0.11295536160469055,
0.02914109267294407,
0.021876676008105278,
-0.04809262603521347,
0.034746475517749786,
-0.0025034837890416384,
-0.0011651460081338882,
-0.026829635724425316,
0.013171768747270107,
-0.00501742959022522,
0.024001387879252434,
-0.0023974739015102386,
0.006214803084731102,
-0.030925819650292397,
0.01668577641248703,
0.08606109023094177,
-0.016914047300815582,
-0.018497111275792122,
0.02999681793153286,
0.024243127554655075,
-0.0435250960290432,
0.02163049578666687,
-0.03200353682041168,
0.044194333255290985,
-0.04242829605937004,
-0.022434119135141373,
-0.007674296386539936,
-0.01972845010459423,
0.028412431478500366,
-0.023434767499566078,
-0.027116306126117706,
-0.023086540400981903,
-0.005251596681773663,
-0.03170588240027428,
-0.03545265644788742,
0.04913919419050217,
-0.023127872496843338,
0.008882798254489899,
-0.0209161639213562,
0.06221902370452881,
0.019411537796258926,
-0.006814087275415659,
-0.02530745044350624,
0.02989790588617325,
-0.07185927033424377,
0.04150037094950676,
-0.014845157042145729,
-0.03682144358754158,
0.0037228395231068134,
-0.016003014519810677,
-0.010900725610554218,
-0.01640750840306282,
0.04620132967829704,
-0.019637146964669228,
-0.03570852056145668,
-0.0022038740571588278,
0.040569715201854706,
-0.016291750594973564,
-0.0442487858235836,
-0.033109672367572784,
-0.0005534352967515588,
-0.039670415222644806,
0.010433858260512352,
-0.009703761897981167,
-0.007329966872930527,
0.021357350051403046,
0.01627584919333458,
0.021950645372271538,
0.004382426850497723,
-0.04560743272304535,
-0.023940283805131912,
0.030247462913393974,
-0.028278086334466934,
0.009141194634139538,
0.0056579820811748505,
0.027388615533709526,
0.01558382622897625,
0.044281210750341415,
-0.005860806908458471,
-0.012874020263552666,
-0.0369250662624836,
0.03514552116394043,
-0.03223080933094025,
-0.024099009111523628,
-0.02493388019502163,
0.011438625864684582,
0.007253988180309534,
0.06324181705713272,
0.0030791808385401964,
-0.026279330253601074,
-0.0031797217670828104,
0.029287615790963173,
0.05899632349610329,
-0.0489441454410553,
-0.04886676371097565,
-0.00014936132356524467,
-0.022726912051439285,
-0.013946964405477047,
-0.0036296804901212454,
0.03632615879178047,
0.018490027636289597,
0.014819802716374397,
-0.017978418618440628,
-0.013521287590265274,
-0.03706999868154526,
-0.009448087774217129,
0.039188042283058167,
-0.0076971049420535564,
-0.0073172952979803085,
-0.03455287218093872,
0.02682313695549965,
0.0038233473896980286,
0.0016283716540783644,
0.00990740954875946,
-0.023705068975687027,
0.009486031718552113,
-0.005565584637224674,
-0.033358681946992874,
-0.010551214218139648,
-0.047164637595415115,
0.031306736171245575,
-0.04259658604860306,
0.002045135712251067,
-0.0584406778216362,
-0.059606052935123444,
-0.005404026247560978,
-0.01355485338717699,
-0.01593697816133499,
0.04906013607978821,
-0.034434057772159576,
0.0003537804295774549,
0.03478192910552025,
0.021000105887651443,
-0.020927708595991135,
0.0134060587733984,
0.0408906564116478,
-0.004895198158919811,
0.06442258507013321,
-0.04523315653204918,
-0.01102373842149973,
0.07340601831674576,
0.012992708012461662,
-0.0035354874562472105,
0.005256324540823698,
-0.027474654838442802,
0.017525209113955498,
0.03880748152732849,
-0.05105166882276535,
-0.012691058218479156,
0.047098513692617416,
-0.0007005922961980104,
0.01638975739479065,
-0.007160074543207884,
-0.014704426750540733,
0.013774801045656204,
0.03396689146757126,
0.018522849306464195,
-0.04354831203818321,
-0.004920909181237221,
0.01275718118995428,
0.03440246358513832,
0.01507695484906435,
-0.02836727350950241,
0.009745263494551182,
-0.0016546983970329165,
0.006485661491751671,
0.04723045229911804,
-0.013620533980429173,
0.016427956521511078,
0.01807580702006817,
-0.03319941461086273,
0.02100251242518425,
0.00721457414329052,
-0.013020893558859825,
-0.053675491362810135,
-0.0031556205358356237,
-0.014825064688920975,
-0.010561118833720684,
0.007967379875481129,
-0.025219954550266266,
0.008823076263070107,
-0.013049240224063396,
-0.07058531790971756,
-0.003230147762224078,
-0.012493976391851902,
-0.01738041639328003,
-0.02956092357635498,
0.019419683143496513,
0.008139885030686855,
0.030615339055657387,
0.032000984996557236,
0.052470602095127106,
-0.025794805958867073,
0.021013842895627022,
0.025515656918287277,
0.004178311210125685,
-0.004436732269823551,
0.018399421125650406,
0.0337534099817276,
0.009790838696062565,
0.046719640493392944,
-0.05308898538351059,
-0.020521506667137146,
0.016151489689946175,
-0.015034438110888004,
0.025320010259747505,
0.00718958443030715,
0.018858565017580986,
0.008073088712990284,
0.07764837890863419,
0.04199528321623802,
0.008183581754565239,
-0.03878934308886528,
0.016502179205417633,
0.043738026171922684,
0.005464770831167698,
-0.014029666781425476,
-0.001178366830572486,
0.04286067187786102,
-0.011942609213292599,
-0.002040829276666045,
0.01746763288974762,
-0.031088823452591896,
-0.010224786587059498,
0.020179487764835358,
-0.02260253019630909,
0.008578963577747345,
0.027385184541344643,
0.013927032239735126,
-0.02955557033419609,
-0.006218691822141409,
0.03267079219222069,
-0.013166713528335094,
0.011124121025204659,
0.007375327870249748,
0.010537560097873211,
-0.031633008271455765,
0.026544706895947456,
-0.024295324459671974,
-0.04958498477935791,
-0.05019170045852661,
0.02267535775899887,
0.018979886546730995,
-0.006495701614767313,
-0.016335923224687576,
-0.022793445736169815,
0.006244329269975424,
0.044384993612766266,
0.0282838586717844,
0.031088566407561302,
0.06009327247738838,
-0.022712096571922302,
0.014667971059679985,
-0.0559149794280529,
0.05284256488084793,
-0.0036581626627594233,
0.040367525070905685,
0.0014034589985385537,
-0.02498530223965645,
-0.0006786012672819197,
0.001159590668976307,
0.03314697742462158,
-0.03638368472456932,
-0.00980232935398817,
0.0267962533980608,
-0.007581752724945545,
0.03488052263855934,
-0.04108390957117081,
0.015557822771370411,
0.021331720054149628,
-0.06558019667863846,
0.03361993283033371,
-0.036367375403642654,
-0.0131119005382061,
-0.001761067658662796,
0.05845535546541214,
-0.004014006350189447,
-0.025438589975237846,
-0.0047094617038965225,
0.016964763402938843,
0.04247036948800087,
0.03663589432835579,
0.00198243441991508,
0.07035990804433823,
-0.03476664796471596,
0.017443187534809113,
-0.004260391928255558,
-0.008862396702170372,
-0.02416665479540825,
0.03307393565773964,
-0.06475696712732315,
0.03242413327097893,
-0.02074209228157997,
-0.0737488642334938,
0.01762143149971962,
-0.060113683342933655,
-0.018557678908109665,
0.02059953659772873,
-0.01718434877693653,
-0.018028652295470238,
0.09076301008462906,
-0.0012486112536862493,
0.017002929002046585,
-0.059550460427999496,
-0.018155034631490707,
0.004033468663692474,
-0.008983397856354713,
-0.01879444532096386,
0.03160852938890457,
0.041745495051145554,
-0.007515785750001669,
0.005351108033210039,
0.056293752044439316,
0.044770024716854095,
0.01778649166226387,
0.03298395127058029,
0.01884174346923828,
-0.016561469063162804,
-0.0801522508263588,
0.00931368675082922,
0.0031464581843465567,
0.028846705332398415,
0.02032424323260784,
-0.03171014413237572,
0.05597029626369476,
0.02939438261091709,
-0.006769509986042976,
-0.04375295341014862,
-0.004281993024051189,
0.028551911935210228,
0.0043296064250171185,
-0.023701053112745285,
0.0494716502726078,
0.005909557919949293,
0.009145889431238174,
-0.025073714554309845,
0.01304110512137413,
-0.02162470854818821,
-0.030018744990229607,
0.028641173616051674,
-0.02194124646484852,
-0.008564994670450687,
-0.03005131334066391,
-0.0344466008245945,
-0.047002196311950684,
-0.041522275656461716,
-0.0033142955508083105,
0.02518627978861332,
-0.006298436783254147,
0.0230756513774395,
-0.0290059931576252,
-0.0029971664771437645,
0.03902038186788559,
-0.034326814115047455,
-0.006196914240717888,
0.001644542091526091,
-0.03265892714262009,
0.02373805083334446,
-0.02802295610308647
] |
<p>Consider free energy of sharp interface $\Gamma$
$$ \int_\Gamma \sigma\;\mathrm{d}S $$
or also free energy of diffuse interface of characteristic width $\epsilon$ given by Cahn-Hilliard/Allen-Cahn functional of phase-field $c\in [0,1]$
$$ \int_\Omega \left[ 12\frac{\sigma}{\epsilon}c^2(1-c)^2 + \frac{3}{4}\sigma\epsilon|\nabla c|^2 \right]\;\mathrm{d}V .$$</p>
<ol>
<li>Is there some reasoning to conclusively deduce if these are Gibbs energies or Helmholtz energies?</li>
<li>Or would such a conclusion be equivalent to definition of circumstances under which surface tension/energy $\sigma$ is measured?</li>
<li>If latter holds what are these conditions for either Gibbs or Helmholtz energy and which are of practical significance and being typically measured?</li>
</ol>
| 8,885 |
[
-0.001948104822076857,
-0.0013829604722559452,
0.012691441923379898,
-0.021237041801214218,
0.0184658020734787,
0.006005819886922836,
-0.03719135746359825,
-0.027685537934303284,
0.013276386074721813,
0.002213891828432679,
0.05687206983566284,
-0.018315665423870087,
0.03608148545026779,
0.024673767387866974,
0.028858892619609833,
-0.002509174169972539,
-0.0340263731777668,
-0.00683469045907259,
-0.02210487611591816,
-0.007670823484659195,
0.00588739849627018,
0.04251789301633835,
0.003632876556366682,
-0.009736578911542892,
-0.012752966955304146,
0.0043687280267477036,
-0.017844712361693382,
-0.03434198722243309,
-0.024515504017472267,
0.042913634330034256,
-0.01939171738922596,
-0.04487442597746849,
0.028756288811564445,
-0.032735150307416916,
-0.029142772778868675,
-0.01761520840227604,
-0.012556669302284718,
-0.02683315798640251,
-0.04759938269853592,
0.041419606655836105,
-0.06253723055124283,
0.014241314493119717,
-0.010562947019934654,
0.03398825600743294,
-0.009242210537195206,
-0.025064269080758095,
-0.03047243133187294,
-0.046030040830373764,
-0.0189511738717556,
-0.05653289705514908,
-0.01229176577180624,
-0.008107369765639305,
0.046233125030994415,
0.021521978080272675,
0.021077677607536316,
-0.021165326237678528,
0.0065099578350782394,
0.0672805905342102,
0.002187789883464575,
-0.036176647990942,
-0.020499546080827713,
0.02113093063235283,
0.009822259657084942,
-0.021114131435751915,
-0.021340901032090187,
0.0295714158564806,
0.01885364018380642,
-0.02880803868174553,
0.030226200819015503,
-0.015337579883635044,
-0.017342081293463707,
-0.017210908234119415,
0.026672163978219032,
0.016100965440273285,
0.03597117215394974,
0.0349770151078701,
-0.009976791217923164,
0.032937221229076385,
0.030985098332166672,
0.04612019658088684,
0.032703932374715805,
0.008933923207223415,
0.03348659351468086,
0.016979200765490532,
-0.005543403793126345,
0.013032174669206142,
0.07326573133468628,
-0.004812650382518768,
0.0026273392140865326,
0.01079455204308033,
0.026918772608041763,
0.007149324286729097,
0.0038136036600917578,
-0.04308760538697243,
-0.02765515260398388,
-0.008222312666475773,
-0.010625166818499565,
0.000669945206027478,
-0.005671385210007429,
-0.0340137779712677,
-0.02344338968396187,
-0.047482311725616455,
0.004619101993739605,
0.09352206438779831,
0.008401717059314251,
-0.02024931088089943,
-0.047307875007390976,
0.0227216687053442,
-0.03845715895295143,
-0.023284992203116417,
-0.04648272693157196,
-0.01616716757416725,
-0.022599460557103157,
-0.0030945981852710247,
-0.011648310348391533,
0.027771111577749252,
0.016055608168244362,
-0.030694758519530296,
0.042989276349544525,
0.08118529617786407,
0.042425334453582764,
-0.028486033901572227,
-0.02504447102546692,
0.03329981118440628,
-0.13333161175251007,
0.03420253470540047,
0.0373457707464695,
-0.017458941787481308,
-0.042678918689489365,
0.014614936895668507,
-0.011472663842141628,
0.02208130434155464,
0.008295807056128979,
0.02755749225616455,
-0.005181095562875271,
0.015818463638424873,
-0.07421226799488068,
-0.05159957706928253,
0.06336064636707306,
-0.03738383203744888,
-0.03107512928545475,
-0.069448322057724,
-0.0014014535117894411,
0.027009041979908943,
0.05750488489866257,
-0.014756791293621063,
0.013206113129854202,
-0.030538078397512436,
0.025305936112999916,
-0.021575821563601494,
-0.019652606919407845,
-0.021156851202249527,
0.004201431758701801,
-0.03410857915878296,
-0.031045448035001755,
-0.022607605904340744,
0.013186795637011528,
0.03247770667076111,
-0.009912333451211452,
-0.006488214246928692,
0.0592569001019001,
0.0025883736088871956,
0.01502155140042305,
0.022687407210469246,
-0.006903188303112984,
-0.03633997589349747,
0.04103245958685875,
0.002201411873102188,
0.05240097641944885,
0.029429832473397255,
0.019463464617729187,
-0.0014593268278986216,
-0.0076673696748912334,
0.03442830592393875,
0.035150837153196335,
-0.008469052612781525,
-0.02634023129940033,
0.006396391894668341,
0.01738492213189602,
0.002986849984154105,
-0.028307944536209106,
-0.008022153750061989,
-0.038999252021312714,
0.005947649013251066,
0.011864076368510723,
0.04647429659962654,
-0.0032295596320182085,
-0.04372255876660347,
0.00009433546802029014,
-0.03865601122379303,
-0.019746307283639908,
-0.042407821863889694,
0.04849077761173248,
-0.006831514183431864,
-0.02978993020951748,
0.05976008623838425,
-0.02117263711988926,
-0.021072980016469955,
-0.05145531892776489,
-0.019258292391896248,
-0.013976204209029675,
0.04859866946935654,
0.021338103339076042,
-0.009697794914245605,
0.06342202425003052,
0.028164217248558998,
0.061436016112565994,
-0.0048913415521383286,
0.04195037856698036,
-0.0032967666629701853,
-0.04242437332868576,
0.002444671466946602,
-0.040033239871263504,
0.03910326212644577,
0.007625641766935587,
-0.03747973218560219,
-0.0008439703960902989,
0.00955763179808855,
-0.016143109649419785,
0.03058217652142048,
-0.041752565652132034,
0.038334231823682785,
0.045487988740205765,
0.030638841912150383,
0.01572440192103386,
0.05229378491640091,
0.017400246113538742,
0.019908269867300987,
-0.0004530451260507107,
-0.002464056946337223,
-0.053149815648794174,
-0.000906419416423887,
0.06387125700712204,
0.09002607315778732,
-0.01622729003429413,
0.0027321556117385626,
0.04319516941905022,
-0.002399342367425561,
0.04675974324345589,
0.01169346459209919,
0.021893536671996117,
-0.060089342296123505,
0.032194387167692184,
0.021241476759314537,
0.011264256201684475,
-0.0013218882959336042,
0.005351454019546509,
0.031968917697668076,
0.05095912516117096,
-0.023880554363131523,
0.00896548107266426,
0.010116077959537506,
0.009932714514434338,
-0.00855240784585476,
-0.017766645178198814,
0.0005143609014339745,
0.0216988418251276,
-0.03993290290236473,
0.017954792827367783,
0.01983671821653843,
0.012020684778690338,
0.018579961732029915,
-0.02200610563158989,
-0.014569424092769623,
0.047729697078466415,
0.02763882838189602,
0.003526527900248766,
-0.022840214893221855,
0.017865825444459915,
-0.030516106635332108,
0.005727565381675959,
-0.0023549979086965322,
-0.011648681946098804,
-0.0008562124567106366,
-0.031989820301532745,
0.029358241707086563,
-0.01870695687830448,
-0.018482038751244545,
-0.04063178971409798,
-0.019046980887651443,
0.0034797536209225655,
-0.006649709306657314,
0.005822543054819107,
0.054953042417764664,
-0.03098808228969574,
-0.025848999619483948,
-0.01870129071176052,
-0.03156007453799248,
0.03506442904472351,
-0.01395487505942583,
0.007321343291550875,
0.0357062891125679,
-0.007087389938533306,
-0.026594003662467003,
-0.014102110639214516,
0.0011241950560361147,
0.0248034056276083,
-0.026690011844038963,
-0.00617087772116065,
0.02401166968047619,
-0.03725063428282738,
-0.04900120943784714,
0.022386815398931503,
0.003441005013883114,
-0.0998963788151741,
-0.008063334040343761,
-0.010679111815989017,
0.0548742301762104,
0.000986916129477322,
0.04245792701840401,
0.06204474717378616,
-0.05063452199101448,
-0.047220874577760696,
-0.04779711365699768,
-0.0688566192984581,
0.04589858278632164,
-0.08062557876110077,
-0.0010682034771889448,
-0.006720223464071751,
-0.04300564527511597,
0.08077014237642288,
0.0022739851847290993,
-0.040152497589588165,
0.017474951222538948,
-0.02223474718630314,
-0.038471024483442307,
-0.0010629439493641257,
0.0006774098728783429,
0.010050988756120205,
-0.01598445139825344,
0.04894010350108147,
-0.03968104347586632,
0.05754762142896652,
0.02950839325785637,
0.017374884337186813,
-0.006560026668012142,
0.04865633696317673,
-0.012390290386974812,
-0.006248574238270521,
0.04886377602815628,
0.003994364757090807,
0.021869005635380745,
-0.01178652048110962,
0.006759782787412405,
0.02378123439848423,
0.05181024223566055,
-0.06421534717082977,
0.03935058414936066,
-0.002191009232774377,
0.00026470745797269046,
-0.03777046874165535,
0.014908418990671635,
0.009399764239788055,
-0.03008248843252659,
0.007599642965942621,
0.02618998847901821,
0.05396835878491402,
-0.03463445231318474,
-0.014013086445629597,
0.03261737525463104,
0.017989542335271835,
-0.021329866722226143,
-0.021443840116262436,
0.0003930101520381868,
-0.04137185961008072,
0.043664079159498215,
-0.022882435470819473,
-0.022781437262892723,
0.05279230326414108,
0.04282630980014801,
0.04239990562200546,
0.018423814326524734,
-0.03726329281926155,
-0.021902691572904587,
-0.047194093465805054,
0.023191416636109352,
0.004064667038619518,
0.06362885236740112,
0.024780068546533585,
0.059812091290950775,
0.017200050875544548,
0.012821811251342297,
0.010729096829891205,
-0.007599392905831337,
-0.05458106845617294,
-0.016374995931982994,
0.012088319286704063,
0.019594848155975342,
-0.008140712976455688,
-0.042112790048122406,
0.046323493123054504,
-0.02507888525724411,
-0.018723158165812492,
-0.029025860130786896,
0.05925765261054039,
-0.0583612360060215,
0.033553242683410645,
-0.03461316600441933,
-0.05854596942663193,
-0.024647749960422516,
0.05037475377321243,
0.00058483995962888,
-0.0516095869243145,
0.006861131172627211,
0.03799344599246979,
-0.008968244306743145,
0.01175590418279171,
-0.006412634160369635,
-0.010090646333992481,
-0.015497656539082527,
0.03297896310687065,
0.002789345569908619,
-0.00012628594413399696,
0.018426869064569473,
-0.004897431004792452,
0.037076063454151154,
0.05124436691403389,
-0.014086751267313957,
0.005905942991375923,
-0.041883278638124466,
-0.07098852843046188,
0.012376480735838413,
0.005645119119435549,
0.0801708921790123,
0.013038461096584797,
-0.010976508259773254,
0.022553928196430206,
-0.02818998694419861,
-0.020361313596367836,
0.0951487198472023,
0.04317798465490341,
0.0028608799912035465,
-0.011319814249873161,
-0.02332264930009842,
-0.02647652104496956,
-0.03700149059295654,
-0.02013259381055832,
0.048922598361968994,
0.017582738772034645,
-0.0398862287402153,
-0.013612519949674606,
0.009364930912852287,
0.00016535917529836297,
-0.017186960205435753,
0.011690466664731503,
0.053664445877075195,
0.016388850286602974,
-0.0030608016531914473,
-0.036259185522794724,
0.0017673696856945753,
0.012239202857017517,
0.039373986423015594,
-0.005895005073398352,
0.0037547117099165916,
-0.05335183069109917,
-0.030547449365258217,
0.05008840933442116,
0.032376714050769806,
0.009524859488010406,
0.007104846183210611,
-0.040423810482025146,
-0.023178517818450928,
0.021902531385421753,
-0.02940761111676693,
0.013817205093801022,
-0.020694559440016747,
0.017026809975504875,
-0.03233706206083298,
-0.022793838754296303,
-0.01991199515759945,
0.016175519675016403,
0.039924584329128265,
-0.004619317129254341,
-0.05585123226046562,
-0.02605457417666912,
0.03688770905137062,
0.023595603182911873,
-0.019266188144683838,
0.04703577980399132,
-0.012333674356341362,
-0.019243093207478523,
0.01874433271586895,
0.01350872777402401,
-0.04552169889211655,
-0.06732124835252762,
0.006451226770877838,
0.004649659618735313,
0.04484331235289574,
0.03940597176551819,
0.002840538276359439,
-0.0764179676771164,
0.052391890436410904,
0.004165161866694689,
-0.006799375172704458,
0.026324918493628502,
0.03153393790125847,
0.08659295737743378,
0.04318384453654289,
0.020765909925103188,
0.05449830740690231,
0.007587464526295662,
-0.035415925085544586,
-0.03576568141579628,
-0.03813694790005684,
0.036488860845565796,
-0.05184515565633774,
-0.02105994150042534,
-0.05487145110964775,
-0.03231515362858772,
0.01129051111638546,
0.01783590391278267,
-0.015242544002830982,
0.02964935079216957,
-0.01228051446378231,
-0.06839203089475632,
-0.022015787661075592,
-0.02662644535303116,
0.045519933104515076,
-0.01656471937894821,
0.013438645750284195,
-0.010497071780264378,
0.020868882536888123,
0.00804443284869194,
0.012344174087047577,
-0.003792953910306096,
0.018272262066602707,
0.024122096598148346,
-0.00034084965591318905,
-0.017682554200291634,
-0.047850143164396286,
0.004872367717325687,
-0.0038629467599093914,
-0.01771341823041439,
0.04763992130756378,
0.001423808396793902,
0.05189654603600502,
-0.009140326641499996,
-0.03110247105360031,
0.010092847980558872,
0.005145511124283075,
0.00891705323010683,
0.017945194616913795,
-0.04040411487221718,
0.055391374975442886,
0.016733037307858467,
0.00790015235543251,
-0.05923084914684296,
0.001799569115974009,
-0.0018070705700665712,
0.022299304604530334,
-0.019745735451579094,
-0.03962310031056404,
0.03550286963582039,
-0.02606860175728798,
-0.0280702356249094,
0.042577821761369705,
-0.002247231313958764,
-0.03948812931776047,
-0.012602854520082474,
0.0145943658426404,
0.04649115353822708,
0.05809854343533516,
0.0022824411280453205,
-0.03504448011517525,
0.026847677305340767,
-0.004336360841989517,
-0.008483280427753925,
-0.001371516496874392,
0.022872423753142357,
0.0018526155035942793,
-0.00009903984755510464,
0.003344892058521509,
-0.02698163315653801,
0.038047827780246735,
-0.027561143040657043,
-0.010160814970731735,
0.01984785497188568,
-0.00044592737685889006,
-0.027934715151786804,
-0.007735942490398884,
-0.01366405375301838,
-0.012162206694483757,
0.046891119331121445,
0.004265571478754282,
0.014366306364536285,
-0.03414896875619888,
-0.01051619928330183,
-0.00444769999012351,
-0.01686619594693184,
-0.028601793572306633,
-0.03538011759519577,
0.049793388694524765,
0.00028308562468737364,
0.004448698367923498,
0.02718639373779297,
-0.015570825897157192,
0.06026636064052582,
-0.006225272547453642,
0.01852986216545105,
0.01895240694284439,
0.02689734473824501,
-0.035140588879585266,
-0.04475758597254753,
-0.06520387530326843,
0.032443515956401825,
0.06731177121400833,
-0.004806219134479761,
0.03444785624742508,
0.03473480045795441,
-0.04772079363465309,
0.007289340253919363,
-0.05266231298446655,
0.004337461199611425,
0.00487168924883008,
-0.052509572356939316,
0.021528109908103943,
-0.004031455144286156,
-0.026231154799461365,
0.029772711917757988,
-0.005222086329013109,
-0.08820744603872299,
0.021373340860009193,
0.005599549040198326,
0.05568180978298187,
0.022960789501667023,
-0.04354016110301018,
-0.043808139860630035,
0.08764944970607758,
-0.058897584676742554,
0.01741349883377552,
0.002938710618764162,
-0.00856046937406063,
0.030299849808216095,
0.045863863080739975,
0.028426073491573334,
-0.04524015262722969,
0.013158687390387058,
-0.0003342734416946769,
0.020975733175873756,
0.024943364784121513,
-0.023090383037924767,
-0.009093571454286575,
-0.006760999094694853,
0.020667487755417824,
-0.01037648692727089,
-0.0108909010887146,
0.020042316988110542,
-0.05653031915426254,
0.02089715376496315,
-0.014348359778523445,
-0.02171177975833416,
0.01806456223130226,
0.006274636369198561,
-0.006339431740343571,
0.007383854128420353,
-0.05220361799001694,
-0.005813006777316332,
0.04190623015165329,
0.007243141997605562,
-0.01961331255733967,
0.05934504047036171,
-0.014357022941112518,
0.0333082340657711,
0.018582480028271675,
0.02454582042992115,
0.13772547245025635,
0.053543973714113235,
0.014349053613841534,
-0.0354696661233902,
0.012960778549313545,
-0.0008760724449530244,
0.029587898403406143,
-0.016232039779424667,
-0.0047054230235517025,
0.003982202615588903,
-0.016499580815434456,
-0.0032683187164366245,
0.04300159588456154,
0.0013087905244901776,
0.018155906349420547,
0.010245837271213531,
-0.04215248301625252,
-0.016466472297906876,
0.02657300792634487,
0.015148656442761421,
-0.04203306883573532,
0.019008202478289604,
-0.020346395671367645,
-0.022336766123771667,
-0.008618386462330818,
-0.016554158180952072,
0.012855623848736286,
-0.03697694092988968,
0.04880787804722786,
0.013315903022885323,
-0.03678962588310242,
-0.00906843226402998,
0.00973288994282484,
0.021433904767036438,
-0.024645792320370674,
-0.018802674487233162,
0.004497539717704058,
-0.01442344207316637,
-0.01017945446074009,
0.02946440875530243,
0.013758189976215363,
-0.015916042029857635,
-0.0016623431583866477,
0.025803063064813614,
-0.03683913126587868,
-0.018968727439641953,
-0.021406851708889008,
0.04935509338974953,
-0.03754175826907158,
-0.018228841945528984,
-0.01888115331530571,
-0.01502251997590065,
0.031725265085697174,
-0.019868003204464912,
-0.024448683485388756,
-0.04600976034998894,
0.02467532642185688,
-0.0049108038656413555,
-0.006758634001016617,
-0.022145770490169525,
0.02463095635175705,
-0.02645694650709629,
0.01747663877904415,
-0.014351632446050644,
-0.03241245448589325,
-0.0030795696657150984,
-0.017148537561297417,
0.038043610751628876,
0.002637240570038557,
-0.0014499409589916468,
-0.004454913083463907,
0.004145138431340456,
-0.04875022545456886,
-0.012848369777202606,
-0.026338627561926842,
-0.00781088974326849,
0.034816935658454895,
0.03761599212884903,
-0.011094845831394196,
-0.00774941174313426,
-0.10270389914512634,
0.03999700769782066,
-0.03643063083291054,
-0.00435129227116704,
-0.04372178763151169,
0.0174553319811821,
0.017460716888308525,
0.033729422837495804,
0.023939207196235657,
-0.00025054274010472,
0.016666309908032417,
0.03983239457011223,
0.011108114384114742,
0.003163909772410989,
-0.06234230846166611,
-0.014164416119456291,
0.002490463200956583,
0.020033925771713257,
0.01974179595708847,
0.0177678894251585,
0.015467103570699692,
0.04960332438349724,
0.0163736529648304,
0.031421057879924774,
-0.024012815207242966,
0.021470453590154648,
-0.010978290811181068,
0.031800057739019394,
-0.0039788479916751385,
0.029226912185549736,
0.018602818250656128,
0.010863806121051311,
-0.0245506651699543,
-0.02424859069287777,
0.026071978732943535,
-0.018923666328191757,
0.006965307518839836,
-0.014661160297691822,
0.011197412386536598,
0.0009309800807386637,
0.02146456018090248,
-0.07414150983095169,
-0.0623355358839035,
-0.02890763245522976,
-0.02008052170276642,
0.009088004939258099,
0.04030764847993851,
-0.005598943214863539,
0.04187969118356705,
-0.028642810881137848,
-0.04893521964550018,
0.011136222630739212,
0.04121152684092522,
-0.02991815283894539,
-0.006520871538668871,
0.040600646287202835,
0.01882481761276722,
0.03432321175932884,
-0.013053524307906628,
-0.016995709389448166,
0.03995921090245247,
-0.025947868824005127,
-0.07934390753507614,
-0.006632213015109301,
-0.002351333387196064,
0.042554304003715515,
0.043509356677532196,
0.01039101555943489,
-0.027334097772836685,
0.02751382812857628,
-0.010858187451958656,
0.038876257836818695,
-0.02229994162917137,
-0.028267277404665947,
-0.03633488714694977,
-0.02728460170328617,
0.0551501102745533,
0.017958814278244972,
0.000552468525711447,
0.03901540860533714,
-0.028106769546866417,
-0.013445153832435608,
-0.009002060629427433,
0.04246510937809944,
-0.03291889652609825,
-0.0035498093347996473,
0.027520732954144478,
-0.015710970386862755,
0.04785105586051941,
0.005917302332818508,
-0.003623517695814371,
0.04031826928257942,
0.011226339265704155,
-0.025173736736178398,
-0.08796334266662598,
-0.04108502343297005,
0.010619817301630974,
0.06517568975687027,
0.04336710646748543,
-0.0402359664440155,
0.028028948232531548,
-0.012007283978164196,
-0.03942396864295006,
0.007373814471065998,
-0.022387629374861717,
-0.00034525603405199945,
-0.028973296284675598,
-0.0030098347924649715,
-0.026043714955449104,
0.05164555087685585,
-0.0023275986313819885,
0.025092940777540207,
0.03605823218822479,
0.057571154087781906,
-0.02782048098742962,
-0.02896818146109581,
-0.006756098475307226,
0.021008983254432678,
-0.012918404303491116,
-0.04207347705960274,
0.061959393322467804,
-0.02478095516562462,
-0.018662214279174805,
-0.00018139617168344557,
0.01421315222978592,
-0.009128506295382977,
0.01527597475796938,
-0.014717851765453815,
-0.022472811862826347,
0.031484153121709824,
0.026350896805524826,
-0.010905836708843708,
-0.006741645745933056,
-0.021027740091085434,
-0.014511858113110065,
0.010948755778372288,
0.025435004383325577,
-0.019721386954188347,
-0.0067299106158316135,
-0.005726453848183155,
-0.04694993793964386,
0.06212992966175079,
-0.049053702503442764,
-0.03492535650730133,
-0.0022546378895640373,
-0.0029367513488978148,
0.046716876327991486,
-0.014921395108103752,
0.03455536067485809,
-0.029773930087685585,
-0.03220130130648613,
0.012394056655466557,
0.026900483295321465,
-0.0004637045494746417,
0.029183225706219673,
0.029087457805871964,
-0.015253208577632904,
0.029966650530695915,
0.023096175864338875,
-0.04043962061405182,
-0.04287043213844299,
-0.032873351126909256,
-0.03311523422598839,
-0.003969721030443907,
-0.009442394599318504,
-0.02400495670735836,
-0.05419403687119484,
0.038224026560783386,
0.02447003312408924,
0.03757442161440849,
-0.014391237869858742,
-0.027725305408239365,
-0.01566336303949356,
-0.0551023930311203,
-0.012761831283569336,
-0.014192421920597553,
0.00020140194101259112,
-0.027161473408341408,
-0.025369655340909958,
-0.0012510837987065315,
-0.03457427769899368,
0.04099443554878235,
0.030150791630148888,
-0.008898483589291573,
-0.00819450430572033,
0.01183583028614521,
0.022243689745664597,
-0.028641942888498306,
-0.020601049065589905,
-0.035395484417676926,
-0.014197967015206814,
0.016943728551268578,
-0.011449635960161686,
0.012047698721289635,
0.009039218537509441,
0.050582271069288254,
-0.01502140425145626,
0.03100966103374958,
0.020291367545723915,
-0.006923979613929987,
0.04168229177594185,
0.01209643017500639,
0.006849219556897879,
0.04405022785067558,
-0.028579654172062874,
0.030701134353876114,
0.002747579710558057,
-0.04307689145207405,
-0.027404578402638435,
0.008692142553627491,
-0.003412418533116579,
-0.031036173924803734,
-0.024976124987006187,
-0.0013246348826214671,
0.024692954495549202,
-0.0015688627026975155,
-0.02811640501022339,
0.022239254787564278,
-0.01195115502923727,
0.006103875115513802,
0.06086170673370361,
0.012909038923680782,
0.011703645810484886,
-0.0024734281469136477,
0.022842127829790115,
0.00871643889695406,
0.0039220587350428104,
-0.005109746940433979,
0.030503928661346436,
0.0548296682536602,
-0.014362911693751812,
-0.011563761159777641,
0.02918580360710621,
-0.031128089874982834,
-0.03900448977947235,
0.027432406321167946,
-0.01102008018642664,
0.008541585877537727,
-0.04006046801805496,
0.022621219977736473,
0.01999029889702797,
0.017546750605106354,
0.015450319275259972,
0.0035441815853118896,
0.07907263934612274,
0.01295294240117073,
-0.01627393253147602,
-0.023188641294836998,
-0.006626754067838192,
-0.024861859157681465,
0.02188853733241558,
0.022498490288853645,
0.051213812083005905,
-0.013564643450081348,
-0.0020770085975527763,
-0.013058532029390335,
-0.00214107776992023,
0.0034451335668563843,
-0.035598691552877426,
0.01626894623041153,
0.005365700460970402,
0.03558312729001045,
-0.007392063271254301,
0.009372018277645111,
-0.02431120164692402,
-0.038108546286821365,
0.03661990165710449,
0.0464031882584095,
0.014719957485795021,
0.03846605494618416,
-0.024082399904727936,
-0.03169256076216698,
0.02511535957455635,
-0.014638074673712254,
-0.014510913752019405,
0.0028273172210901976,
0.014946863986551762,
0.021509848535060883,
0.00123131787404418
] |
<p>The <a href="http://en.wikipedia.org/wiki/Positive_energy_theorem" rel="nofollow">positive mass conjecture</a> was proved by <a href="http://www.doctoryau.com/papers/PositiveMassConjecture.pdf" rel="nofollow">Schoen and Yau</a> and later reproved by <a href="http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.cmp/1103919981" rel="nofollow">Witten</a>. Total mass in a gravitating system must be positive except in the case of flat Minkowski space, where energy is zero. Since QG is intended to be a theory of interaction with force particles called gravitons, one may begin to wonder if the interactions are in fact the important defining features of the space in question. So does a theory with interactions also require that space be curved?</p>
| 8,886 |
[
-0.023124922066926956,
-0.0323474295437336,
0.012053139507770538,
-0.03580798953771591,
0.03941714018583298,
0.019897839054465294,
-0.046823084354400635,
-0.0023072469048202038,
0.020629409700632095,
-0.043206699192523956,
0.01752365753054619,
-0.020273897796869278,
0.05005503073334694,
0.0270062442868948,
-0.008654026314616203,
-0.0004859838809352368,
0.0063555315136909485,
-0.019473275169730186,
-0.025084329769015312,
-0.06012018769979477,
-0.010201909579336643,
0.03271109238266945,
0.014405389316380024,
0.03283074125647545,
0.011975577101111412,
-0.02599547803401947,
0.03486436977982521,
-0.007618136238306761,
-0.018973946571350098,
0.06757783144712448,
-0.030446209013462067,
0.026027703657746315,
-0.0036987634375691414,
0.025275684893131256,
0.02784091979265213,
-0.02422449178993702,
-0.043044764548540115,
0.002044971799477935,
0.02178877219557762,
0.024016933515667915,
-0.024259988218545914,
-0.0179993137717247,
0.0009435941465198994,
0.047758281230926514,
-0.029503583908081055,
0.039019085466861725,
0.014484035782516003,
-0.026558594778180122,
0.06099853664636612,
-0.0632910281419754,
0.044619131833314896,
0.033157672733068466,
0.034394074231386185,
-0.001866693957708776,
-0.016392938792705536,
-0.005744675640016794,
0.0347471609711647,
0.06534413248300552,
0.0171552412211895,
-0.06401127576828003,
-0.025195151567459106,
-0.010322664864361286,
0.018352994695305824,
-0.014081805013120174,
-0.054115843027830124,
0.04024125263094902,
-0.006909750401973724,
-0.02092849463224411,
0.04310239106416702,
0.006061939988285303,
0.0034456783905625343,
0.03233068808913231,
0.02867995761334896,
0.028548261150717735,
0.00820971094071865,
-0.019757967442274094,
0.015330949798226357,
0.010254367254674435,
0.03053167462348938,
0.01849951036274433,
-0.007052773144096136,
-0.004984179511666298,
0.021237919107079506,
0.02526342310011387,
-0.0008835668559186161,
-0.027927547693252563,
0.03827305883169174,
0.02708934061229229,
-0.00002622055762913078,
0.03717535734176636,
-0.01250146422535181,
-0.006528601050376892,
0.03377959504723549,
-0.0487556979060173,
-0.025615349411964417,
0.029547223821282387,
-0.015203925780951977,
0.026134725660085678,
-0.0007112904568202794,
-0.015897322446107864,
-0.022792693227529526,
0.0027370965108275414,
0.006344188936054707,
0.05571898818016052,
0.03014417551457882,
-0.05724377930164337,
-0.05136052519083023,
0.014937016181647778,
-0.01946008764207363,
0.0028486449737101793,
-0.03111325576901436,
-0.030447620898485184,
-0.013646837323904037,
0.0009180952911265194,
0.018598807975649834,
-0.03526628017425537,
0.007931613363325596,
-0.040932778269052505,
0.04250338673591614,
0.05365266278386116,
0.059780895709991455,
-0.016001256182789803,
0.015146800316870213,
-0.04153958708047867,
-0.04603166505694389,
-0.013292841613292694,
0.07502017170190811,
-0.015182727947831154,
-0.03189065679907799,
0.035012613981962204,
0.05406394973397255,
0.01281038485467434,
-0.0021834978833794594,
0.0194193534553051,
0.05971959978342056,
-0.0057584731839597225,
-0.07910676300525665,
-0.050178978592157364,
0.03800119832158089,
0.014930813573300838,
-0.006123797502368689,
-0.04337525740265846,
-0.014721640385687351,
0.03793858736753464,
0.10558214038610458,
-0.004615917336195707,
-0.005928027909249067,
-0.0026373998261988163,
0.08103418350219727,
0.031056009232997894,
-0.0317886583507061,
0.0017020524246618152,
-0.026222648099064827,
-0.03416558355093002,
-0.026876438409090042,
-0.07622925192117691,
0.0006397875840775669,
0.004713304340839386,
0.008424103260040283,
-0.04605785012245178,
0.09855403006076813,
-0.03617541491985321,
0.03301461786031723,
0.006964582484215498,
-0.03692839294672012,
0.008524933829903603,
0.06358155608177185,
0.030972689390182495,
-0.02617707848548889,
0.05746285989880562,
0.025894150137901306,
0.04773009940981865,
0.01834794506430626,
0.024204233661293983,
0.03370664641261101,
-0.05836896598339081,
-0.017174823209643364,
-0.05200548097491264,
0.040981829166412354,
-0.006322057452052832,
-0.04027482867240906,
-0.025638265535235405,
-0.05655793473124504,
0.004375999793410301,
0.001154811936430633,
0.04829760640859604,
-0.001666362746618688,
0.0103890560567379,
0.03287617489695549,
0.012824952602386475,
-0.0012143375352025032,
-0.0644412636756897,
0.02489316277205944,
0.015727311372756958,
0.005702705588191748,
0.010732106864452362,
0.027276931330561638,
-0.0004438169999048114,
-0.04867883399128914,
-0.010883194394409657,
0.006593624595552683,
0.05109264701604843,
-0.01271015964448452,
-0.0014074062928557396,
0.02031633071601391,
0.054671160876750946,
0.027793683111667633,
-0.022765642032027245,
-0.010931100696325302,
-0.005748342722654343,
-0.03429015725851059,
0.060721926391124725,
0.010838844813406467,
0.03166546672582626,
-0.00887705571949482,
0.004353886935859919,
0.0003905450867023319,
-0.01794014312326908,
-0.008659538812935352,
0.04512188211083412,
-0.04792466759681702,
0.030712176114320755,
0.04474359005689621,
-0.023708080872893333,
0.026799270883202553,
0.0484720878303051,
0.005988260731101036,
0.02453591860830784,
-0.003029549727216363,
-0.010932821780443192,
-0.026476383209228516,
-0.021815752610564232,
0.036883316934108734,
0.024358130991458893,
-0.030363822355866432,
0.008093181997537613,
0.03511013463139534,
0.03528566658496857,
-0.01357297133654356,
-0.0030902682337909937,
-0.023248206824064255,
-0.02934621460735798,
0.061220042407512665,
0.006103822961449623,
0.014131211675703526,
0.014658414758741856,
0.0235375314950943,
0.02881011553108692,
-0.008085832931101322,
-0.011580690741539001,
-0.03570418059825897,
-0.008809727616608143,
0.0027458956465125084,
0.02393380180001259,
0.002020845655351877,
-0.0013678750256076455,
0.030255455523729324,
-0.04252239689230919,
0.026164770126342773,
0.020252855494618416,
-0.011781563982367516,
-0.01769966259598732,
-0.03408879414200783,
-0.033030916005373,
-0.007483609952032566,
0.013950005173683167,
-0.017831286415457726,
-0.03440780192613602,
0.002093699760735035,
-0.07604026049375534,
-0.002801374299451709,
-0.0109479371458292,
-0.048129722476005554,
0.006925488822162151,
0.024716617539525032,
0.028235023841261864,
0.017957545816898346,
0.02628205716609955,
-0.021772313863039017,
0.0033586930949240923,
0.011657978408038616,
-0.0011936093214899302,
-0.02414196915924549,
0.06374158710241318,
-0.052563972771167755,
-0.02134685218334198,
-0.06942594796419144,
-0.043276622891426086,
0.01787356100976467,
-0.02247489243745804,
0.018937820568680763,
0.003557457821443677,
-0.019073093309998512,
-0.013528702780604362,
-0.038235682994127274,
-0.0777486190199852,
0.008908378891646862,
-0.008445942774415016,
-0.0020416220650076866,
0.01569449156522751,
-0.007232040632516146,
-0.03791989013552666,
0.04087681323289871,
-0.032142333686351776,
-0.03021467663347721,
-0.06021841987967491,
-0.015681924298405647,
0.05178013816475868,
-0.03093338944017887,
0.04513045400381088,
0.026833269745111465,
-0.03196975588798523,
-0.01227109506726265,
-0.05603905767202377,
-0.04263675957918167,
0.04736883193254471,
-0.021136131137609482,
0.04119183123111725,
-0.0023162630386650562,
-0.0307951420545578,
0.05105925351381302,
0.03272552043199539,
-0.009588122367858887,
0.00026236576377414167,
-0.0026084526907652617,
-0.01689833588898182,
0.006669894326478243,
0.014893488958477974,
-0.016356708481907845,
0.019414022564888,
0.0412820428609848,
0.02680451236665249,
0.028147436678409576,
-0.011457518674433231,
-0.001069384627044201,
-0.0329316072165966,
-0.013562038540840149,
-0.01966238021850586,
0.02477206476032734,
0.04518108442425728,
0.048872966319322586,
0.0060699209570884705,
0.00011735019506886601,
0.018453313037753105,
0.024522636085748672,
0.006102654617279768,
-0.030037494376301765,
0.05104492977261543,
0.0072590941563248634,
0.05039161816239357,
-0.016896933317184448,
0.022156478837132454,
-0.029437342658638954,
-0.01955808885395527,
0.038874607533216476,
0.03203253448009491,
0.03052384965121746,
-0.004773127846419811,
-0.01521366462111473,
-0.011943249963223934,
0.048236407339572906,
-0.023565316572785378,
-0.018441952764987946,
0.00966851320117712,
-0.0192535649985075,
0.03997690975666046,
-0.005301588214933872,
0.01685369201004505,
0.034732673317193985,
0.019247865304350853,
0.014217850752174854,
0.018196286633610725,
-0.019125251099467278,
-0.013025660067796707,
-0.07652409374713898,
0.0008283393108285964,
0.01700429432094097,
0.011265492998063564,
-0.006141739431768656,
0.026019198819994926,
0.025381162762641907,
0.002857307204976678,
-0.02077002078294754,
-0.016767002642154694,
-0.09168358892202377,
0.013250194489955902,
-0.05847814306616783,
0.013717638328671455,
0.007958264090120792,
-0.008391192182898521,
-0.01565289869904518,
-0.0257163867354393,
-0.013078639283776283,
-0.051977548748254776,
-0.0015535092679783702,
-0.08416647464036942,
0.016068266704678535,
-0.05231233313679695,
-0.05190124735236168,
0.02379629574716091,
0.013353497721254826,
0.042859405279159546,
-0.05247468128800392,
0.003168716561049223,
0.05859106034040451,
-0.05265307426452637,
-0.035900749266147614,
-0.0028758225962519646,
0.02242491953074932,
0.01354635413736105,
0.019271107390522957,
0.01564684696495533,
0.03278595954179764,
-0.0029054826591163874,
0.000619721133261919,
0.003922596108168364,
0.04232648387551308,
-0.005941122770309448,
-0.029382003471255302,
-0.014345240779221058,
-0.03534891828894615,
-0.009403498843312263,
0.005254107527434826,
0.060470182448625565,
0.006904762703925371,
-0.0007949043647386134,
0.03984837234020233,
-0.008493143133819103,
-0.01571163907647133,
0.04266137629747391,
0.08223199099302292,
0.023761650547385216,
-0.02678913250565529,
-0.033768195658922195,
-0.017402011901140213,
-0.021720627322793007,
-0.028410615399479866,
0.014201120473444462,
0.001248445245437324,
-0.013947594910860062,
0.030904699116945267,
0.012377887964248657,
0.0032093615736812353,
-0.057043422013521194,
0.006430542096495628,
-0.005524003878235817,
0.01472237054258585,
-0.04477721452713013,
0.010829959996044636,
0.03736855462193489,
-0.004431676585227251,
0.04256725683808327,
-0.037348609417676926,
-0.020896591246128082,
-0.0805947408080101,
0.0013487631222233176,
0.03765808790922165,
0.046694107353687286,
0.025264061987400055,
-0.013139722868800163,
-0.05453808978199959,
-0.01604633778333664,
0.00015703137614764273,
-0.030270082876086235,
0.015356795862317085,
-0.024257594719529152,
0.009488385170698166,
-0.01898850128054619,
-0.017531417310237885,
0.0011695033172145486,
0.015426683239638805,
0.023135187104344368,
-0.008740974590182304,
-0.012967620976269245,
0.004791169427335262,
-0.011316980235278606,
0.01940951496362686,
0.014628973789513111,
0.03694717213511467,
0.0352688729763031,
0.015464585274457932,
0.0034995689056813717,
0.0016706573078408837,
-0.030443862080574036,
-0.08219248056411743,
-0.010706627741456032,
0.02266698330640793,
-0.0379551537334919,
0.07904185354709625,
0.002270500874146819,
-0.03456909582018852,
-0.0009240468498319387,
-0.02819048799574375,
-0.0033682817593216896,
-0.01640387810766697,
-0.056433841586112976,
0.031029341742396355,
0.03888741508126259,
-0.011579640209674835,
0.026540953665971756,
0.017321400344371796,
-0.055073510855436325,
-0.03857114538550377,
-0.02314276620745659,
0.016504794359207153,
-0.010421724990010262,
-0.006106795743107796,
-0.02998538501560688,
0.0019121968653053045,
-0.046967800706624985,
0.006064882967621088,
-0.006678702775388956,
-0.03340501710772514,
-0.01667545922100544,
-0.03856213390827179,
0.0009431560756638646,
-0.0020009370055049658,
0.013744729571044445,
0.019970988854765892,
-0.007574141025543213,
0.024183211848139763,
-0.00570597592741251,
-0.014237035065889359,
0.018826089799404144,
0.03450688347220421,
-0.029984304681420326,
0.03605974093079567,
0.024940403178334236,
0.004232699517160654,
-0.013521246612071991,
-0.02325008064508438,
-0.0176532082259655,
-0.03237871080636978,
0.039139002561569214,
0.030205506831407547,
-0.009100052528083324,
0.01959233731031418,
-0.03383370488882065,
-0.01341293565928936,
-0.02756558731198311,
-0.008129323832690716,
-0.015532705001533031,
0.015344226732850075,
0.030861126258969307,
0.03437160700559616,
0.03455081209540367,
-0.07527525722980499,
-0.02944706752896309,
-0.04352155700325966,
0.022000083699822426,
0.0014142186846584082,
-0.024416550993919373,
-0.007754376623779535,
-0.05665111541748047,
-0.004775893408805132,
-0.012751065194606781,
0.03114931471645832,
-0.05966074764728546,
-0.0004434621660038829,
0.011913546361029148,
0.04329568147659302,
0.03265766054391861,
0.011717605404555798,
0.01363271102309227,
0.04633410647511482,
0.024477815255522728,
-0.009975796565413475,
0.0067971330136060715,
0.03659490495920181,
-0.0047507812269032,
-0.04506771266460419,
-0.03263981640338898,
0.002177154179662466,
-0.004985030274838209,
-0.019925536587834358,
-0.011646074242889881,
0.04733748361468315,
0.015814650803804398,
-0.02186988852918148,
-0.00470049399882555,
0.03638983145356178,
-0.05798087269067764,
0.003898149123415351,
-0.005291546229273081,
0.02681765891611576,
0.006962560582906008,
-0.029817037284374237,
0.05192602425813675,
-0.030795399099588394,
-0.03883884474635124,
-0.009646711871027946,
0.04593360424041748,
0.021303502842783928,
-0.03222311660647392,
-0.009012834168970585,
-0.007981269620358944,
0.007153537590056658,
-0.03032793290913105,
0.010208306834101677,
-0.02464105188846588,
-0.013623652048408985,
-0.021745316684246063,
-0.05804651230573654,
-0.02499876730144024,
-0.00029886438278481364,
0.06045754626393318,
0.014658541418612003,
0.06554453819990158,
-0.011195744387805462,
-0.03938192129135132,
-0.01041631493717432,
-0.025837304070591927,
0.02282875031232834,
-0.006875044200569391,
0.015601269900798798,
0.029672915115952492,
-0.033317796885967255,
0.004534690175205469,
0.009231354109942913,
0.041055768728256226,
-0.03150367736816406,
0.004238455090671778,
0.03978428989648819,
0.034142304211854935,
0.04276804253458977,
-0.027561301365494728,
-0.06326613575220108,
0.049321021884679794,
-0.03748561441898346,
0.0353589691221714,
0.007284500636160374,
-0.0020622641313821077,
0.00508591765537858,
0.017203766852617264,
0.0203343965113163,
0.01060918252915144,
-0.04364529624581337,
-0.03182771056890488,
0.046116989105939865,
-0.001244798069819808,
-0.014810447581112385,
-0.020163264125585556,
-0.010963878594338894,
-0.006863929331302643,
0.016970733180642128,
0.03138341009616852,
0.012115134857594967,
-0.07531733065843582,
-0.012502158991992474,
-0.036764707416296005,
-0.026742922142148018,
0.04078691825270653,
-0.0027446940075606108,
-0.04957817122340202,
0.007541123311966658,
-0.03145409747958183,
0.02125459723174572,
0.01528424397110939,
0.021445604041218758,
-0.028528515249490738,
0.05887589603662491,
-0.028691664338111877,
0.011345825158059597,
-0.017125427722930908,
-0.03468916192650795,
0.14697706699371338,
0.046768900007009506,
0.0026220357976853848,
-0.06784407049417496,
0.019636528566479683,
-0.005727695766836405,
-0.02215946838259697,
-0.01643506810069084,
0.004472880158573389,
-0.026752332225441933,
-0.016140619292855263,
-0.0059072053991258144,
0.060261473059654236,
0.025066548958420753,
0.0020128097385168076,
0.059778403490781784,
-0.021170444786548615,
-0.06034987419843674,
0.002762360731139779,
0.020363636314868927,
-0.027369119226932526,
0.03699969872832298,
-0.025397250428795815,
0.006242334842681885,
-0.03319799154996872,
0.04488849639892578,
-0.013469928875565529,
0.00021296084742061794,
0.017367638647556305,
0.05807141959667206,
-0.04504893720149994,
-0.007089698221534491,
0.003429209580644965,
-0.03313221409916878,
-0.03800014406442642,
-0.0035266904160380363,
-0.005402900744229555,
0.001238928991369903,
0.008034485392272472,
0.03223472461104393,
-0.03820158168673515,
0.007068467792123556,
0.0076633114367723465,
0.03831513598561287,
-0.06516338884830475,
0.0007597855292260647,
0.025416644290089607,
0.04571681469678879,
-0.03141336143016815,
0.01635676808655262,
0.031865108758211136,
-0.047288812696933746,
0.01416305173188448,
-0.04166989400982857,
-0.02781662717461586,
-0.016871297731995583,
0.025385988876223564,
-0.04162609204649925,
0.03308752551674843,
-0.020215263590216637,
0.044467151165008545,
0.010952522978186607,
0.025505289435386658,
0.011012114584445953,
-0.023872507736086845,
0.03235170990228653,
-0.01597706787288189,
0.02707405760884285,
-0.009907886385917664,
-0.0201796256005764,
-0.015454947017133236,
-0.04489600285887718,
-0.028590979054570198,
-0.003784443251788616,
-0.00841725803911686,
0.04947802424430847,
0.042176708579063416,
0.009740364737808704,
0.026940738782286644,
-0.01152307353913784,
-0.019896937534213066,
0.02402498386800289,
-0.03224688395857811,
-0.015511293895542622,
-0.02784205600619316,
-0.0009972534608095884,
-0.007488757371902466,
0.0574309267103672,
-0.060064591467380524,
-0.022349856793880463,
-0.0260997973382473,
0.013488314114511013,
-0.018967505544424057,
-0.00031162778032012284,
-0.018776483833789825,
0.005961560644209385,
-0.03049139305949211,
-0.003906412050127983,
-0.031139038503170013,
0.01013018749654293,
-0.011963902972638607,
0.01064745057374239,
0.017113788053393364,
0.02846216782927513,
-0.009241374209523201,
-0.005267736501991749,
0.01535050943493843,
0.008622904308140278,
0.015941796824336052,
0.012819930911064148,
-0.01055176742374897,
-0.054364223033189774,
-0.030719222500920296,
0.002327075693756342,
0.02389252744615078,
0.0006819465779699385,
0.05181603133678436,
-0.03424929082393646,
0.03310825675725937,
-0.007579208351671696,
-0.0010185259161517024,
-0.06388352066278458,
-0.026705104857683182,
-0.06831899285316467,
0.023403780534863472,
-0.0024752868339419365,
-0.004950464703142643,
-0.000731078558601439,
0.011277170851826668,
-0.0284488033503294,
-0.022247079759836197,
0.00376465218141675,
0.020426224917173386,
-0.04047283157706261,
-0.004870583303272724,
0.0338079109787941,
-0.009126960299909115,
0.03345870599150658,
-0.014216387644410133,
-0.024633899331092834,
0.03004693239927292,
-0.06707241386175156,
-0.06666065007448196,
-0.02108021453022957,
-0.01524399220943451,
0.017680741846561432,
0.019151518121361732,
-0.02271660417318344,
0.00238803424872458,
0.02700117789208889,
-0.016837868839502335,
0.030761994421482086,
0.012519617564976215,
-0.05124779790639877,
-0.021092785522341728,
-0.005414626561105251,
0.007973810657858849,
-0.011235324665904045,
0.006435627583414316,
0.013891159556806087,
0.01872595213353634,
-0.02671867422759533,
-0.026093659922480583,
-0.00036802521208301187,
-0.023003393784165382,
0.051118142902851105,
0.01758555695414543,
0.026417529210448265,
-0.010800201445817947,
0.0509224459528923,
-0.056087903678417206,
-0.011675916612148285,
0.04350857064127922,
0.0009562605991959572,
-0.0776413083076477,
-0.03141423314809799,
0.01201129611581564,
0.024041054770350456,
0.0424758605659008,
-0.05095943063497543,
0.06654714047908783,
-0.010888943448662758,
-0.053517989814281464,
0.04297676309943199,
-0.017046332359313965,
0.02198907732963562,
-0.04957869276404381,
-0.01728379726409912,
-0.02244664914906025,
0.011616850271821022,
0.03867935761809349,
0.06303555518388748,
0.009059226140379906,
0.018752139061689377,
-0.0007771188975311816,
0.00972733460366726,
0.0029360465705394745,
0.016728149726986885,
-0.003961256239563227,
0.00041100173257291317,
0.0907844752073288,
-0.030737701803445816,
-0.036472856998443604,
0.02776496112346649,
-0.010825198143720627,
-0.029063045978546143,
0.014314739964902401,
-0.007852249778807163,
0.0035589439794421196,
0.038337040692567825,
0.07008709758520126,
-0.01868160255253315,
-0.01165848970413208,
-0.007204115856438875,
0.028816062957048416,
0.028914621099829674,
0.019659927114844322,
0.019690467044711113,
-0.0003794473013840616,
-0.023182030767202377,
-0.01779276132583618,
0.0156625397503376,
0.0009888744680210948,
0.01238248310983181,
-0.009251096285879612,
-0.013507317751646042,
0.001995571656152606,
0.027272913604974747,
0.02366487868130207,
-0.0468486063182354,
0.009264697320759296,
0.012248042039573193,
0.00689695356413722,
-0.0025269011966884136,
0.0225302055478096,
-0.00012467408669181168,
0.011167960241436958,
0.006530135869979858,
0.0018785533029586077,
0.0006070072413422167,
-0.057945072650909424,
0.004919418133795261,
-0.0017635866533964872,
0.0414438396692276,
-0.0023653365205973387,
-0.043843988329172134,
-0.016114449128508568,
0.04418241232633591,
0.019506605342030525,
0.04727382957935333,
-0.029471661895513535,
0.012982328422367573,
0.02026764675974846,
-0.05971476435661316,
0.023364795371890068,
0.016747502610087395,
0.01625514030456543,
-0.0059792171232402325,
0.008387353271245956,
-0.013941735029220581,
-0.02091841585934162,
0.030911190435290337,
-0.048413291573524475,
-0.055441711097955704,
0.007551339454948902,
-0.012890557758510113,
-0.015251843258738518,
0.006621075794100761,
0.010344634763896465,
-0.0007239888072945178,
-0.02730715088546276,
0.03494300693273544,
0.01004250068217516,
-0.0027697014156728983,
0.040879685431718826,
0.04550774022936821,
-0.024890821427106857,
0.0028780754655599594,
0.02416430413722992,
-0.02173556759953499,
0.0947326049208641,
0.0024207921233028173,
0.016348570585250854,
0.07479497045278549,
0.004213863052427769,
0.04398709908127785,
0.04670502245426178,
-0.027936581522226334,
-0.0025406484492123127,
0.005264477804303169,
-0.013112257234752178,
-0.04895402863621712,
-0.014801377430558205,
0.0003719991073012352,
0.02702152356505394,
-0.015787646174430847,
-0.02728985622525215,
0.08453473448753357,
-0.021477824077010155,
-0.03698813170194626,
0.011514934711158276,
0.022762902081012726,
0.05594330281019211,
0.0057161059230566025,
-0.009263023734092712,
0.01786315068602562,
0.017043963074684143,
0.00654361117631197,
0.0689210444688797,
0.03563351556658745,
0.018331343308091164,
-0.010226080194115639,
0.054203007370233536,
0.002634868724271655,
0.012846474535763264,
0.038610540330410004,
0.026168962940573692,
-0.036773018538951874,
0.007085410878062248,
-0.009739959612488747,
-0.01063127163797617,
0.046070195734500885,
0.004462915472686291,
-0.015157625079154968,
0.059327661991119385,
-0.008520505391061306,
0.016374120488762856,
-0.022052578628063202,
0.0010151962051168084,
-0.01042973343282938,
0.038934703916311264,
0.011638516560196877,
0.03895476087927818,
0.038727786391973495,
-0.015258773230016232,
-0.030853811651468277,
-0.022014278918504715,
-0.010040453635156155,
-0.024647396057844162,
0.010743633843958378,
0.010367081500589848,
0.009094269014894962,
0.031096067279577255,
-0.0005428319564089179,
0.0017573758959770203,
-0.0008032783516682684,
0.02307402715086937,
0.04700382426381111,
0.03685835376381874,
-0.04864120110869408,
0.033135462552309036,
-0.05086533725261688,
0.056567080318927765,
-0.066949762403965,
-0.0035664078313857317,
-0.009111832827329636,
-0.028556467965245247,
0.015575110912322998,
-0.008208672516047955
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.