question stringlengths 37 38.8k | group_id stringlengths 2 6 | sentence_embeddings listlengths 768 768 |
|---|---|---|
<p>This question is motivated by <a href="http://physics.stackexchange.com/questions/98067/does-natural-unit-of-information-and-entropy-nat-play-special-role-in-the-free">this one</a>.</p>
<p>Suppose $l$ is the minimum measurable unit of length. What is entropy of a spinless particle contained in this interval?</p>
<p>We know that entropy of a two-level system depends on the probabilities of the respective levels, if the probability of the state 0 is $p_0$, then the entropy (in <a href="http://en.wikipedia.org/wiki/Nat_%28information%29" rel="nofollow">natural units</a>) is:</p>
<p>$$S= -\sum_{i=0}^1 p_i \ln p_i = -p_0 \ln p_0 - (1 - p_0) \ln (1 - p_0)$$</p>
<p>So if $p_0=1/2$ then $S=\ln 2\: \mathrm{nat}$, equal to $1\: \mathrm{bit}$. A particle which has the maximum in the middle has entropy of $1\: \mathrm{bit}$ (it is equally likely to be measured to the right and to the left of the middle).</p>
<p>Since we cannot measure intervals smaller than $l$, we cannot make guesses about where the maximum of the probability for the particle is located. As such, if we assume that the particle is equally likely have the maximum of the probability in any point on the interval $x\in[0,l]$, the total entropy becomes
$$S=\int_0^l \frac{-(1-\frac xl) \ln (1- \frac xl)-\frac xl \ln (\frac xl)}{l} \, dx=\int_0^1 -(1-x) \ln (1-x)-x \ln (x) \, dx=\frac12$$</p>
<p>An entropy of a similar particle contained in a square area with side $l$ will be twice more, that is $1\: \mathrm{nat}$.</p>
<p>Now if we assume that $l=2l_p$ where $l_p$ is the Planck length, we arrive that such spinless particle has entropy of $1\: \mathrm{nat}$ per 4 square Planck length or $1/4\: \mathrm{nat}$ for one square Planck length.</p>
<p>Thus from the only assumption that double Planck length is the minimum measurable interval, and double Planck length squared is expected to contain 1 particle on average we arrive at the standard value of the Black Hole entropy in nats:</p>
<p>$$S=\frac{A}{4l_p^2}=\frac14 A_p$$</p>
<p>Where $A_p$ is the area in Planck units.</p>
<p>Sometimes I encountered a claim that the fundamental unit of information is 1 bit. From the above considerations it follows that possibly the fundamental unit is 1/2 (or 1 or 1/4) nat.</p>
<p><strong>UPDATE</strong></p>
<p>Note that the distance of $2l_p$ between two particles is natural if we assume that the particles are <a href="http://en.wikipedia.org/wiki/Planck_particle" rel="nofollow">planckons</a>, whose radius is Planck length $l_p$. Thus densely packed planckons will have average distance exactly $2l_p$.As such, the Black Hole can be viewed as a spherical shell consisting of one layer of planckons.</p> | g6565 | [
-0.011858668178319931,
-0.0014222076861187816,
-0.0028681261464953423,
-0.04275841638445854,
-0.003935459069907665,
0.02606487274169922,
-0.016299856826663017,
0.008725139312446117,
-0.038787197321653366,
-0.0040414100512862206,
-0.002452622167766094,
0.013704751618206501,
-0.0103661073371768,
-0.05522371828556061,
-0.03265705704689026,
0.025138545781373978,
0.03518754243850708,
-0.00945589691400528,
0.04735264182090759,
0.007192669436335564,
-0.018213722854852676,
-0.00334173534065485,
0.0026201556902378798,
-0.06582849472761154,
-0.0434139110147953,
-0.04816526919603348,
0.04864729940891266,
0.013881961815059185,
-0.10194630175828934,
-0.0027941609732806683,
0.014686131849884987,
-0.027985313907265663,
0.04526232182979584,
-0.06703536957502365,
-0.09296846389770508,
-0.011958976276218891,
0.01951402612030506,
0.03841664269566536,
0.010345221497118473,
0.015293908305466175,
0.0294228196144104,
-0.07276539504528046,
-0.03650683909654617,
-0.04164859652519226,
0.006060644052922726,
0.058359287679195404,
0.03910638019442558,
0.046082232147455215,
0.04508737102150917,
-0.030442673712968826,
-0.014710544608533382,
0.04707849770784378,
0.03306059539318085,
0.05969756096601486,
0.04373937100172043,
0.07807303965091705,
-0.0002037632220890373,
-0.009639575146138668,
0.03532995656132698,
0.06090272217988968,
0.057194922119379044,
0.0015069935470819473,
-0.016264930367469788,
-0.010293823666870594,
0.02605968527495861,
0.06829704344272614,
-0.018438559025526047,
0.021077267825603485,
-0.050529297441244125,
-0.013740459457039833,
-0.018256034702062607,
-0.04117431119084358,
-0.023786943405866623,
-0.02518763393163681,
0.026058819144964218,
0.05157959833741188,
0.026380440220236778,
0.06575015932321548,
-0.0007793005206622183,
0.030395468696951866,
-0.022885886952280998,
0.0068789091892540455,
0.03344487398862839,
-0.004398750606924295,
0.011459867469966412,
0.03935881331562996,
-0.024477114900946617,
-0.07230806350708008,
-0.008055314421653748,
0.1130194291472435,
-0.023416059091687202,
-0.027357010170817375,
0.046060338616371155,
-0.013577102683484554,
0.022899838164448738,
0.03928167000412941,
-0.006123116705566645,
-0.027940990403294563,
-0.036425888538360596,
0.04852830618619919,
-0.037371039390563965,
0.016637898981571198,
0.020205961540341377,
-0.005800474435091019,
0.006803634576499462,
-0.04128248617053032,
-0.016078626736998558,
-0.0016929993871599436,
-0.0033522541634738445,
-0.008540884591639042,
0.031292591243982315,
-0.006244249176234007,
0.00939192809164524,
0.018876265734434128,
-0.025561954826116562,
0.04630356281995773,
0.09806008636951447,
-0.010785105638206005,
-0.026793746277689934,
0.044923946261405945,
-0.016682930290699005,
0.013801192864775658,
0.05657515302300453,
0.03911972418427467,
0.009605852887034416,
-0.0128095131367445,
0.0030675700400024652,
0.009341158904135227,
-0.01770937629044056,
-0.01778976432979107,
-0.005578458309173584,
-0.0064979963935911655,
-0.07187063246965408,
0.029295623302459717,
-0.08616185933351517,
0.06264159083366394,
-0.02359975315630436,
0.023268606513738632,
-0.006414102390408516,
-0.03268524259328842,
-0.09929715096950531,
-0.028603777289390564,
0.008090279065072536,
-0.017660092562437057,
0.01597593165934086,
0.003141143824905157,
0.02369781583547592,
-0.06922277063131332,
-0.014998511411249638,
-0.005200703162699938,
-0.043954506516456604,
0.0658428743481636,
0.0019412634428590536,
0.0032602425199002028,
-0.01815389283001423,
0.007565522566437721,
0.03955067694187164,
0.04296700656414032,
-0.008688663132488728,
0.022485116496682167,
0.020517772063612938,
-0.0027599330060184,
0.03913901373744011,
0.021381739526987076,
-0.05268188193440437,
0.02904214896261692,
0.00924746785312891,
-0.08217833936214447,
0.008642347529530525,
-0.06192900985479355,
0.004712130408734083,
-0.00031088016112335026,
-0.025212302803993225,
0.04126311093568802,
-0.04771164432168007,
-0.025427859276533127,
0.004104644525796175,
0.03717970848083496,
0.013431292958557606,
0.006670188624411821,
-0.027392162010073662,
0.018950950354337692,
0.060688409954309464,
-0.009029447101056576,
-0.026090282946825027,
-0.018397610634565353,
0.014097540639340878,
0.05440215766429901,
0.007898946292698383,
-0.016138916835188866,
-0.04307026043534279,
-0.004535543732345104,
0.0020997896790504456,
0.07634086906909943,
0.026279401034116745,
0.008278550580143929,
-0.008293595165014267,
-0.082283154129982,
0.0010019518667832017,
-0.033110298216342926,
0.0005877829389646649,
-0.013115971349179745,
0.02683858573436737,
-0.021096179261803627,
0.05142426863312721,
0.007585369981825352,
0.012648534961044788,
0.023415911942720413,
-0.0115473298355937,
0.023425687104463577,
0.028545532375574112,
-0.052609678357839584,
-0.023330802097916603,
0.03357481211423874,
0.014618116430938244,
-0.05923113599419594,
-0.030739396810531616,
0.00188696407712996,
0.020537573844194412,
-0.05734798684716225,
-0.012902704067528248,
0.01294776052236557,
0.04068166762590408,
-0.05306531861424446,
0.021786946803331375,
0.006703777238726616,
-0.005418781656771898,
-0.025692179799079895,
-0.026980435475707054,
0.0838041752576828,
-0.07997819781303406,
-0.0054773292504251,
-0.003922746516764164,
0.02871236391365528,
0.0059804669581353664,
0.09632179141044617,
-0.004060904961079359,
-0.006629770155996084,
0.03166813775897026,
-0.020927421748638153,
0.05399823188781738,
-0.005062735173851252,
-0.06315925717353821,
0.027911853045225143,
-0.02095547877252102,
-0.01311118621379137,
-0.04974130541086197,
-0.022983184084296227,
-0.035411641001701355,
0.03851597383618355,
-0.029949843883514404,
-0.010562059469521046,
0.026231395080685616,
-0.0022154455073177814,
0.02703595720231533,
0.010300857946276665,
0.03604473918676376,
-0.0022348451893776655,
-0.06707386672496796,
-0.04480336606502533,
0.027246788144111633,
-0.007275603245943785,
-0.00456221541389823,
0.02510124444961548,
-0.001376084634102881,
-0.006296003703027964,
-0.081956647336483,
0.06888855248689651,
0.008973555639386177,
0.04092627763748169,
0.06832544505596161,
0.07416900992393494,
-0.025011330842971802,
-0.005778636317700148,
0.05327889323234558,
0.04722107574343681,
0.023153213784098625,
0.03328639641404152,
0.003690491896122694,
-0.028714120388031006,
-0.03795921057462692,
0.04153755307197571,
-0.049417462199926376,
0.009960254654288292,
0.05534054711461067,
-0.0612611249089241,
0.012529222294688225,
0.03405183181166649,
0.023806855082511902,
0.04126688838005066,
0.005034979898482561,
0.027097104117274284,
0.043531857430934906,
0.03158773481845856,
0.031500525772571564,
0.006110654678195715,
0.00934686977416277,
-0.0031717075034976006,
0.02288566343486309,
0.008429980836808681,
-0.034796807914972305,
-0.02824118360877037,
-0.0205227080732584,
-0.04046808183193207,
0.0031330811325460672,
0.0005987787735648453,
-0.06081083416938782,
-0.012451929040253162,
-0.001593979075551033,
0.008658180944621563,
-0.0018640446942299604,
0.06883527338504791,
0.04616697132587433,
0.013120457530021667,
-0.046236325055360794,
0.00042236148146912456,
-0.004536725580692291,
0.020241694524884224,
-0.024189677089452744,
-0.022226419299840927,
0.07389941066503525,
-0.043126869946718216,
0.012251167558133602,
-0.0003568998072296381,
0.02041204273700714,
-0.05573341250419617,
-0.04445192217826843,
-0.008946914225816727,
-0.08893009275197983,
0.026384981349110603,
0.028522146865725517,
-0.07121642678976059,
0.019485756754875183,
0.011176343075931072,
-0.041849009692668915,
-0.06729700416326523,
-0.03262168541550636,
-0.007135828025639057,
0.02312019281089306,
0.01171866711229086,
0.04389715939760208,
-0.014002731069922447,
-0.06025322899222374,
0.00029411897412501276,
-0.033744312822818756,
0.004825463984161615,
-0.030409662052989006,
-0.05950203537940979,
-0.017407342791557312,
0.003039150033146143,
0.01713440753519535,
0.01838439330458641,
0.010051227174699306,
-0.035409070551395416,
0.019740818068385124,
0.023136749863624573,
0.03336469456553459,
0.0003833149094134569,
0.056873153895139694,
-0.02134694717824459,
0.02730228193104267,
-0.054347991943359375,
0.03318333625793457,
-0.04147109016776085,
-0.04619598388671875,
-0.02057727612555027,
0.020605018362402916,
-0.004718819633126259,
0.0646333396434784,
-0.009193725883960724,
-0.047947466373443604,
-0.044939860701560974,
0.0018187311943620443,
0.010182752273976803,
-0.020763486623764038,
-0.02614372968673706,
-0.013173405081033707,
0.026957383379340172,
-0.06965377181768417,
0.005428624805063009,
-0.004572340287268162,
-0.034850042313337326,
-0.0066488939337432384,
-0.01869058795273304,
0.024832557886838913,
-0.013426225632429123,
-0.022752180695533752,
-0.02801818959414959,
0.003443499095737934,
-0.05085885897278786,
-0.03273897245526314,
-0.009195287711918354,
-0.020175524055957794,
0.01528182066977024,
-0.015373039059340954,
-0.027150385081768036,
0.0743941217660904,
0.012688015587627888,
0.038241997361183167,
0.04933120310306549,
0.041765280067920685,
-0.02400200068950653,
-0.004276009742170572,
-0.023998672142624855,
0.008828701451420784,
-0.05303068459033966,
-0.009433025494217873,
-0.014325018972158432,
0.0025312199722975492,
0.0033925045281648636,
0.00767078110948205,
0.03403586149215698,
0.034055713564157486,
-0.019484588876366615,
-0.004417638760060072,
0.01404076348990202,
-0.05163261294364929,
-0.05713082104921341,
-0.0028001489117741585,
0.023562263697385788,
-0.006279383320361376,
-0.01862100139260292,
0.03640659525990486,
-0.004718286916613579,
-0.07190325111150742,
-0.03351288661360741,
0.0623859241604805,
0.048748794943094254,
-0.03595514968037605,
-0.011432983912527561,
0.03136969357728958,
0.02855500392615795,
0.015504168346524239,
0.056420426815748215,
-0.040832847356796265,
0.05171717703342438,
-0.047285690903663635,
0.0015629385598003864,
-0.021793285384774208,
0.011810222640633583,
0.01888442598283291,
-0.006919222883880138,
0.005941588897258043,
-0.02933209203183651,
0.013620859012007713,
-0.008961980231106281,
0.03450607508420944,
0.0006655663019046187,
-0.009236695244908333,
-0.016783546656370163,
0.07191547751426697,
-0.014773346483707428,
-0.008050914853811264,
-0.08410331606864929,
0.031021542847156525,
0.0041891722939908504,
-0.05826304107904434,
0.06337659806013107,
0.02505607157945633,
-0.011984258890151978,
-0.008367902599275112,
0.02353844605386257,
-0.020079972222447395,
0.019048746675252914,
-0.015202442184090614,
-0.06324344873428345,
-0.09114973992109299,
0.03041655756533146,
-0.026802003383636475,
-0.010379606857895851,
0.0409385971724987,
-0.002878789324313402,
0.025996487587690353,
0.00937292817980051,
0.00802966021001339,
0.029130304232239723,
-0.027382193133234978,
-0.018921544775366783,
-0.04357144981622696,
0.0036287622060626745,
-0.030766645446419716,
-0.025423331186175346,
-0.004950425121933222,
0.05609649792313576,
0.028275737538933754,
0.021851086989045143,
-0.013142186217010021,
0.011069719679653645,
0.018659083172678947,
0.013699712231755257,
0.02478046528995037,
-0.008860534988343716,
0.07541979104280472,
0.015327566303312778,
-0.062108322978019714,
-0.051382604986429214,
0.0022463351488113403,
-0.046599652618169785,
0.05256780982017517,
0.012567860074341297,
-0.07074207812547684,
0.03617525100708008,
0.04954718053340912,
0.040459733456373215,
-0.03994916379451752,
-0.01727192848920822,
-0.016238370910286903,
0.024399390444159508,
-0.038262706249952316,
0.03845643624663353,
0.0533330924808979,
-0.011003549210727215,
-0.04392634332180023,
-0.03010956197977066,
-0.025842277333140373,
-0.05135975033044815,
0.05257172882556915,
0.03981932997703552,
-0.03574632480740547,
0.00124175357632339,
0.0020814130548387766,
-0.01713935099542141,
0.07305597513914108,
-0.03327358886599541,
0.06028631702065468,
-0.021071286872029305,
-0.06489615142345428,
-0.003541037905961275,
0.017977431416511536,
0.04757220298051834,
0.00000863529112393735,
0.0024938685819506645,
-0.012734230607748032,
-0.016085278242826462,
0.0037449286319315434,
-0.0018208591500297189,
-0.004471481777727604,
0.01624923199415207,
0.054840248078107834,
-0.02376575581729412,
0.0041801659390330315,
-0.10316065698862076,
-0.018609749153256416,
0.04733826965093613,
-0.022233132272958755,
-0.03217475861310959,
-0.03781387582421303,
-0.017738500609993935,
-0.000319356273394078,
0.00480313366279006,
0.016451874747872353,
-0.008422750048339367,
-0.009540288709104061,
-0.021094240248203278,
0.01516502071171999,
-0.02483137883245945,
0.023563917726278305,
0.03312384709715843,
-0.0036999424919486046,
0.0019762986339628696,
-0.00512703275308013,
-0.00943891890347004,
0.010909494943916798,
0.09553182125091553,
0.010355539619922638,
-0.03429582715034485,
-0.00411548838019371,
-0.05451171100139618,
0.02716781012713909,
0.0649794340133667,
-0.05441029369831085,
0.0443757101893425,
-0.011948484927415848,
0.012226374819874763,
0.047670137137174606,
-0.016093267127871513,
-0.005568249151110649,
-0.04461686685681343,
-0.04000527039170265,
-0.0012842795113101602,
-0.05674025043845177,
-0.00876103900372982,
0.002419519703835249,
-0.029436083510518074,
0.005831521935760975,
0.05919766053557396,
0.00681036151945591,
0.006632767617702484,
-0.02272629365324974,
0.028875743970274925,
-0.0030262276995927095,
-0.034148335456848145,
-0.01668969914317131,
0.0025909419637173414,
-0.0006133628776296973,
-0.04441693425178528,
-0.01525577437132597,
-0.12133537232875824,
-0.012097170576453209,
0.010302537120878696,
-0.055584315210580826,
-0.03780830651521683,
0.021136190742254257,
-0.026292361319065094,
0.0003525822830852121,
0.07689078897237778,
-0.05881835147738457,
0.02897033840417862,
-0.0005710230907425284,
0.06334683299064636,
-0.013571702875196934,
0.011105185374617577,
-0.031018568202853203,
0.009042423218488693,
-0.03027765452861786,
-0.03218860924243927,
-0.021918704733252525,
-0.03537939116358757,
-0.04566404968500137,
0.045187029987573624,
0.03703200817108154,
0.05244065076112747,
-0.05465736240148544,
-0.07436849921941757,
0.02196367084980011,
0.05238987132906914,
0.027149902656674385,
0.02780393324792385,
0.034562744200229645,
0.04875054210424423,
0.04122721403837204,
0.038423892110586166,
-0.004215418826788664,
0.07933186739683151,
0.0005685377400368452,
-0.015699025243520737,
-0.048747722059488297,
0.016100311651825905,
0.03826144337654114,
0.04718773812055588,
0.022611483931541443,
-0.06707990914583206,
0.035845011472702026,
0.043486036360263824,
-0.013014407828450203,
-0.01861993782222271,
0.060275282710790634,
0.07189495861530304,
-0.050075337290763855,
0.03170715644955635,
0.0015755569329485297,
0.0033572607208043337,
0.018025292083621025,
-0.020814675837755203,
-0.023801391944289207,
0.022332051768898964,
0.01432125922292471,
0.012192814610898495,
0.02838299423456192,
0.0006884678150527179,
0.008444092236459255,
-0.062499821186065674,
0.015364366583526134,
-0.013744755648076534,
-0.003450754564255476,
0.04239944368600845,
0.028754184022545815,
-0.035240188241004944,
0.001299117924645543,
-0.11406167596578598,
0.0024344732519239187,
-0.03435933589935303,
-0.02040942758321762,
-0.0011022157268598676,
-0.03674808144569397,
-0.0129244988784194,
-0.001483555999584496,
0.03880936652421951,
-0.01402655802667141,
0.001355677959509194,
0.06424587219953537,
0.017906518653035164,
0.021538199856877327,
-0.04980235546827316,
-0.04638631269335747,
0.057917892932891846,
-0.07046423852443695,
0.03780409321188927,
0.07152534276247025,
0.006026605609804392,
0.01153072901070118,
0.0161600299179554,
0.024679729714989662,
-0.014437411911785603,
-0.062009863555431366,
0.016340527683496475,
0.05510659143328667,
0.0495266355574131,
0.033602531999349594,
-0.07048390060663223,
0.018663454800844193,
-0.034437019377946854,
-0.039197541773319244,
-0.03383539617061615,
0.0487167164683342,
0.042398788034915924,
0.0362812876701355,
0.0217746552079916,
-0.04045707359910011,
-0.0025085394736379385,
0.014310565777122974,
-0.018450845032930374,
0.011498533189296722,
0.022397682070732117,
-0.025639716535806656,
-0.0039162361063063145,
0.02568363957107067,
0.03600830212235451,
-0.003215576522052288,
-0.022862644866108894,
-0.019550936296582222,
-0.040379978716373444,
-0.07485463470220566,
-0.010716989636421204,
-0.018073532730340958,
-0.04453106224536896,
0.00010039014887297526,
0.00314456969499588,
-0.010084313340485096,
0.012804213911294937,
0.03517606854438782,
-0.027502533048391342,
-0.027442896738648415,
-0.02856305055320263,
-0.034497860819101334,
0.0278177373111248,
0.006788068450987339,
0.06075335666537285,
-0.018217001110315323,
0.01855297200381756,
-0.006047092378139496,
-0.033451687544584274,
0.05459240823984146,
-0.029517341405153275,
-0.05658860504627228,
-0.028248364105820656,
-0.04302415996789932,
0.04829858988523483,
0.02031630091369152,
-0.038872841745615005,
-0.03500497713685036,
-0.029005147516727448,
0.04190312325954437,
0.051222652196884155,
0.04250243306159973,
-0.05504221096634865,
0.013799615204334259,
-0.018919698894023895,
-0.022662773728370667,
0.029698872938752174,
0.002849409356713295,
-0.012306595221161842,
0.036472927778959274,
0.035609010607004166,
0.04533863067626953,
0.007321142591536045,
0.04130443185567856,
0.054543398320674896
] |
<p>Let's say you are in the air 500 meters above flat land and you have no parachute. Which pose - forming a sphere or spreading all extremities to make yourself as wide as possible or other - is the most appropriate to cause the highest likelihood of survival?</p>
<ol>
<li>in the air</li>
<li>right before impact</li>
</ol>
<p>In other words: which body position causes the least amount of negative acceleration in this context?</p>
<p>PS: As a side-question: Which body position enables you to control the direction of flight to control your angle of impact and make it as flat as possible?</p>
<p>My take: In the air make yourself as wide as possible and control direction by weight displacement. Right before impact, form a sphere when having a flat angle of impact and let rolling take care of the change of kinetic energy into heat and potential energy.</p> | g6566 | [
0.0497555173933506,
-0.0018036181572824717,
0.01416975911706686,
0.07240008562803268,
-0.02619618922472,
0.10251514613628387,
0.05637890100479126,
0.030891869217157364,
-0.007037334144115448,
-0.026965707540512085,
0.046179529279470444,
-0.08559069782495499,
0.007867990992963314,
0.004873002879321575,
0.014859163202345371,
0.02048773132264614,
0.05022422596812248,
-0.07712813466787338,
0.026353955268859863,
-0.011842545121908188,
-0.01879754103720188,
-0.08314163982868195,
-0.05102413520216942,
0.012978178448975086,
-0.03553874045610428,
-0.01499680895358324,
-0.015996068716049194,
0.0116707319393754,
-0.05667022243142128,
-0.0102401003241539,
0.06458411365747452,
0.03121383860707283,
0.02819884940981865,
-0.02353961206972599,
-0.036071039736270905,
-0.04116901382803917,
-0.00463457964360714,
0.04854073002934456,
-0.04006224498152733,
-0.05281394347548485,
-0.022511381655931473,
-0.07866515219211578,
-0.013567001558840275,
0.031027117744088173,
-0.019734608009457588,
-0.00955598708242178,
0.021545622497797012,
0.007974423468112946,
0.0200418122112751,
-0.027454650029540062,
-0.014804370701313019,
0.005832915659993887,
-0.037711285054683685,
-0.08273112028837204,
0.04754967242479324,
0.02066756971180439,
0.01980455033481121,
-0.021458689123392105,
-0.031249037012457848,
-0.026382312178611755,
-0.03160214424133301,
0.0025340321008116007,
-0.05457454174757004,
-0.0016749161295592785,
0.04965348541736603,
0.004855522885918617,
-0.08180177211761475,
0.024648290127515793,
0.024758797138929367,
-0.02081371657550335,
0.039338838309049606,
-0.03936779499053955,
-0.07708004862070084,
-0.010130831971764565,
-0.024778539314866066,
0.01716822199523449,
-0.030261943116784096,
0.003519985591992736,
0.05603263899683952,
0.008894788101315498,
0.005429134238511324,
0.02188737690448761,
0.030645495280623436,
-0.057559046894311905,
0.07511170953512192,
-0.013407249934971333,
0.016325538977980614,
-0.042733434587717056,
0.006320504005998373,
0.025755304843187332,
0.07122421264648438,
0.049600787460803986,
0.06730025261640549,
0.01938120648264885,
-0.05862103030085564,
0.06589538604021072,
-0.005883593577891588,
0.08707049489021301,
-0.012139949016273022,
0.02363751269876957,
0.003223268548026681,
-0.024173587560653687,
-0.026454372331500053,
0.012336667627096176,
-0.02371259778738022,
-0.011033237911760807,
0.047536760568618774,
-0.05279838666319847,
0.04775596410036087,
-0.025681478902697563,
-0.024823034182190895,
0.026289278641343117,
-0.06525079160928726,
-0.028635133057832718,
-0.0608515702188015,
-0.0534968301653862,
0.03925898298621178,
0.017552601173520088,
0.007482349872589111,
0.07733135670423508,
-0.04316744580864906,
0.036454953253269196,
0.031853508204221725,
0.01823415420949459,
-0.03849301487207413,
-0.037784330546855927,
-0.04469578340649605,
0.011076529510319233,
0.03324378281831741,
-0.0043521481566131115,
-0.010267007164657116,
-0.015101022087037563,
-0.08081478625535965,
0.008503710851073265,
-0.03287177532911301,
0.04178466647863388,
-0.058411385864019394,
-0.0019499931950122118,
0.025414060801267624,
-0.007339110132306814,
0.0032534198835492134,
0.015068951062858105,
0.03433430567383766,
-0.051824480295181274,
-0.030307533219456673,
0.009798090904951096,
0.022861281409859657,
0.01311176735907793,
-0.016329053789377213,
0.06807571649551392,
-0.007847004570066929,
0.021217070519924164,
-0.011904717423021793,
-0.060799822211265564,
0.012830480933189392,
0.023394348099827766,
-0.0009300698875449598,
0.03374503180384636,
0.027099426835775375,
-0.0071009378880262375,
0.06935392320156097,
0.00986646767705679,
-0.016193941235542297,
0.018602728843688965,
-0.03154849261045456,
-0.012936060316860676,
-0.052490897476673126,
-0.048979662358760834,
-0.0016678994288668036,
-0.0029323820490390062,
-0.06020757183432579,
-0.08913038671016693,
0.02864409051835537,
0.02001042291522026,
0.006173871457576752,
-0.01313643716275692,
0.016893256455659866,
-0.06592638790607452,
0.011442870832979679,
0.00995752215385437,
0.04166325181722641,
-0.010966497473418713,
0.013322198763489723,
0.019624020904302597,
-0.003991350531578064,
-0.029433341696858406,
0.06624647974967957,
0.06250591576099396,
-0.08646345883607864,
-0.023694217205047607,
0.013360850512981415,
-0.04504769295454025,
-0.03290442004799843,
-0.038247641175985336,
-0.060084667056798935,
-0.02421826869249344,
0.11414328962564468,
0.01861577294766903,
-0.059236329048871994,
0.05357429012656212,
0.022987043485045433,
0.024969059973955154,
0.020434390753507614,
-0.009053121320903301,
-0.07360437512397766,
0.0473954975605011,
0.049995556473731995,
-0.008703419007360935,
0.03790508210659027,
-0.009262384846806526,
0.05441468209028244,
-0.008801141753792763,
0.04245665296912193,
-0.019774217158555984,
0.04189961403608322,
0.06354058533906937,
-0.025106878951191902,
-0.0041849189437925816,
-0.018612664192914963,
-0.026754125952720642,
-0.003467220114544034,
0.02770380675792694,
-0.025089653208851814,
-0.030174585059285164,
-0.02745445817708969,
0.03901992738246918,
-0.023589633405208588,
-0.04524599015712738,
0.047769784927368164,
-0.05262349545955658,
-0.0562048964202404,
0.017870478332042694,
0.024540521204471588,
-0.03827456384897232,
0.023973889648914337,
0.014331940561532974,
0.03963720425963402,
0.0874953344464302,
0.013666260056197643,
-0.017438651993870735,
0.021950991824269295,
-0.0006787439342588186,
-0.03738872706890106,
-0.02374553307890892,
0.04103376343846321,
-0.006830888334661722,
-0.013889681547880173,
-0.005461995955556631,
-0.0032346865627914667,
0.03950680047273636,
-0.012188615277409554,
0.014165750704705715,
-0.061438098549842834,
-0.06578077375888824,
-0.0038610331248492002,
0.00000804746650828747,
-0.06581953912973404,
0.034606631845235825,
-0.0364118367433548,
-0.005603226367384195,
0.012950804084539413,
-0.007464236579835415,
-0.005029425956308842,
-0.014018040150403976,
-0.10557308793067932,
0.06591266393661499,
-0.06481259316205978,
0.013801285065710545,
-0.001569755026139319,
0.033434052020311356,
-0.018724914640188217,
0.009264783933758736,
-0.0751831978559494,
0.07262774556875229,
-0.015538291074335575,
-0.042824048548936844,
-0.03390584886074066,
0.0015976266004145145,
-0.04630206152796745,
0.00685438746586442,
0.032467070966959,
-0.005610711872577667,
0.0026453298050910234,
0.03580135852098465,
0.07639278471469879,
0.016823992133140564,
0.009850540198385715,
0.014205120503902435,
-0.03831211104989052,
0.02191382460296154,
-0.002261499175801873,
-0.022201556712388992,
0.052689362317323685,
0.00853849295526743,
0.015811733901500702,
0.04905523359775543,
0.017082005739212036,
-0.033761877566576004,
-0.03477559611201286,
-0.019474918022751808,
-0.01715073361992836,
-0.009179641492664814,
0.030863875523209572,
0.013783392496407032,
0.01516159251332283,
0.04969862103462219,
-0.000472394865937531,
-0.03699646517634392,
0.03445184603333473,
-0.032564349472522736,
-0.037327904254198074,
0.04794105887413025,
-0.03697612136602402,
0.04988742247223854,
-0.0543743260204792,
0.0069892518222332,
-0.06266210228204727,
-0.02625194564461708,
-0.010938312858343124,
-0.05744641274213791,
0.01586359553039074,
-0.027936888858675957,
-0.00006412260700017214,
0.015578767284750938,
0.019271450117230415,
0.053604502230882645,
-0.0005084263975732028,
0.05177387595176697,
0.03149263560771942,
-0.055297378450632095,
0.030337480828166008,
0.051251184195280075,
-0.005923244170844555,
-0.0033794818446040154,
-0.023682940751314163,
-0.04519261419773102,
-0.011939379386603832,
0.006356572266668081,
0.033727604895830154,
0.028634360060095787,
-0.004738355055451393,
-0.011431192979216576,
-0.014730623923242092,
-0.029796652495861053,
0.0466645322740078,
-0.004391322378069162,
0.034047383815050125,
0.009646713733673096,
0.004968360066413879,
0.012603608891367912,
0.04092804342508316,
-0.020659437403082848,
-0.0392388217151165,
-0.02959747053682804,
0.03297223895788193,
0.017751473933458328,
-0.011923471465706825,
0.033999841660261154,
-0.02627008780837059,
0.005288342013955116,
-0.04864876717329025,
-0.02645963616669178,
-0.01096956804394722,
-0.011946422979235649,
0.018166042864322662,
-0.021904954686760902,
-0.061918433755636215,
0.00665875943377614,
-0.0429893434047699,
0.056626856327056885,
0.011515781283378601,
-0.031022047623991966,
-0.009542997926473618,
-0.04445508122444153,
0.06165606528520584,
0.028980428352952003,
0.02369060553610325,
-0.010557967238128185,
-0.022595664486289024,
-0.011859696358442307,
0.05222320929169655,
0.0075411684811115265,
-0.011463498696684837,
0.015048238448798656,
-0.014903769828379154,
0.03268193453550339,
-0.036529168486595154,
-0.054284002631902695,
0.021900584921240807,
-0.0027484321035444736,
-0.028109116479754448,
-0.09532409906387329,
-0.007938504219055176,
0.014501462690532207,
0.051912058144807816,
0.055865559726953506,
-0.009335861541330814,
-0.002335631288588047,
-0.022570407018065453,
0.06843292713165283,
0.03398289158940315,
0.02645665965974331,
-0.0273892879486084,
0.03792779892683029,
0.0118833864107728,
0.02263486757874489,
0.029020877555012703,
-0.0011634078109636903,
-0.04154953360557556,
-0.016794215887784958,
0.12636558711528778,
0.07089893519878387,
-0.07819104194641113,
-0.0703837051987648,
0.031059397384524345,
-0.03312051668763161,
0.0027898577973246574,
0.018408460542559624,
0.04555051773786545,
0.05757305026054382,
0.03793545439839363,
0.030657704919576645,
0.0011599266435950994,
-0.03633803874254227,
0.043503958731889725,
0.007941825315356255,
0.046969857066869736,
-0.025905588641762733,
-0.016382094472646713,
0.045547932386398315,
-0.02791162207722664,
0.02032863162457943,
0.027555139735341072,
-0.01945766806602478,
-0.031090250238776207,
0.006295764818787575,
0.015843290835618973,
-0.0014961689012125134,
0.062394674867391586,
0.020084938034415245,
0.029557975009083748,
-0.0012835427187383175,
-0.00818448793143034,
-0.02719801291823387,
0.012978366576135159,
0.047676146030426025,
-0.006489206105470657,
-0.042372480034828186,
0.033226702362298965,
-0.025579269975423813,
-0.010459855198860168,
-0.0282388087362051,
0.07040190696716309,
-0.028142733499407768,
-0.08270979672670364,
-0.01728961057960987,
-0.031901683658361435,
-0.02291431836783886,
0.008392659947276115,
-0.011723607778549194,
0.020980987697839737,
0.010021926835179329,
-0.014642092399299145,
0.0020107016898691654,
0.018401790410280228,
0.04716944694519043,
-0.06314685940742493,
-0.017757542431354523,
-0.03044763021171093,
0.005448079667985439,
-0.032886307686567307,
0.023116087540984154,
0.04056005924940109,
0.02999473363161087,
-0.019092170521616936,
0.05819534510374069,
0.0013183667324483395,
-0.015941038727760315,
0.015426499769091606,
0.015471012331545353,
0.011990266852080822,
0.006365017965435982,
-0.03994673863053322,
-0.0556500218808651,
0.02598312310874462,
0.022775741294026375,
0.009513110853731632,
-0.02945847436785698,
0.0849001333117485,
-0.00633499538525939,
0.04220401123166084,
-0.01635548286139965,
-0.04631790891289711,
-0.019669268280267715,
-0.03511616960167885,
0.032231107354164124,
0.011143060401082039,
-0.0062594665214419365,
0.015357177704572678,
0.0035127277951687574,
-0.056887030601501465,
-0.031880903989076614,
0.05178460478782654,
-0.021056869998574257,
-0.07448320090770721,
-0.04262133687734604,
0.05893661081790924,
0.002821783535182476,
0.037042710930109024,
0.014765306375920773,
-0.05292825400829315,
0.03348582237958908,
-0.013666260987520218,
-0.011384449899196625,
-0.01312472578138113,
-0.012812872417271137,
-0.01256791315972805,
0.03229324519634247,
-0.025710515677928925,
0.007646930869668722,
0.04976706951856613,
-0.03893076628446579,
0.029674703255295753,
0.023003071546554565,
0.07833162695169449,
-0.022680005058646202,
-0.011423608288168907,
-0.014248576015233994,
-0.003919420298188925,
-0.005294543690979481,
0.021686693653464317,
0.016612984240055084,
-0.0008830731967464089,
-0.021632125601172447,
-0.04920700192451477,
-0.038883570581674576,
-0.025081925094127655,
0.042500026524066925,
0.011622206307947636,
-0.04146106168627739,
-0.05638968199491501,
-0.010934622026979923,
-0.0006258853827603161,
0.07524778693914413,
-0.0666854977607727,
0.0039630769751966,
-0.09620301425457001,
0.02433944307267666,
-0.009872917085886002,
-0.02255753055214882,
-0.002830059267580509,
0.050022903829813004,
-0.004822711925953627,
-0.005415199790149927,
0.018890060484409332,
0.011473697610199451,
-0.03921780735254288,
0.03234250470995903,
-0.006445617880672216,
-0.06222547963261604,
-0.010412653908133507,
0.007751794066280127,
0.047794561833143234,
0.04193281754851341,
0.018004806712269783,
-0.026224521920084953,
-0.009235826320946217,
-0.0437566302716732,
0.016774721443653107,
0.0300400722771883,
0.011696730740368366,
-0.06273724883794785,
0.06214920058846474,
0.06523896008729935,
0.01875246688723564,
-0.016785746440291405,
0.039240770041942596,
-0.00451439106836915,
-0.03490697592496872,
0.04935983568429947,
-0.040138788521289825,
-0.02339617721736431,
0.03820774704217911,
-0.05941757559776306,
-0.020927589386701584,
0.02657376043498516,
-0.02569534257054329,
0.023739686235785484,
-0.019233331084251404,
-0.04601823166012764,
-0.0032659873832017183,
0.004148463718593121,
-0.013534518890082836,
0.03035159781575203,
-0.06337036192417145,
-0.04614681750535965,
-0.026151614263653755,
-0.004655772354453802,
-0.06981692463159561,
0.012493983842432499,
0.02599053457379341,
-0.014719988219439983,
0.04017876833677292,
0.021526340395212173,
0.02076851762831211,
0.049010951071977615,
0.02707529440522194,
0.017398826777935028,
0.011199641041457653,
-0.02834368869662285,
-0.02725624106824398,
0.0508401021361351,
0.022461116313934326,
0.012338778004050255,
-0.024150267243385315,
0.016550827771425247,
0.014274394139647484,
-0.012407476082444191,
0.018881645053625107,
-0.025422286242246628,
-0.05089377984404564,
-0.02529272250831127,
0.0023896852508187294,
-0.003309190971776843,
-0.03181038796901703,
-0.03381909430027008,
-0.015826161950826645,
0.036844607442617416,
-0.03815505653619766,
0.03569662943482399,
0.010640828870236874,
0.035329148173332214,
-0.03640207648277283,
0.08702614903450012,
-0.024436337873339653,
0.02518729493021965,
0.013672985136508942,
0.0169568732380867,
0.038723599165678024,
0.02439759112894535,
0.004264723509550095,
0.03842185065150261,
-0.03858485445380211,
0.02861488237977028,
-0.039695654064416885,
0.01071926299482584,
0.012357918545603752,
-0.036303307861089706,
0.013326781801879406,
-0.001642924384213984,
-0.0017054418567568064,
-0.03095283731818199,
-0.016901925206184387,
-0.03128804266452789,
0.02913830056786537,
0.03062969073653221,
0.027561243623495102,
0.001139824278652668,
-0.013480732217431068,
-0.047572970390319824,
-0.016345690935850143,
0.0050473324954509735,
0.0019252606434747577,
0.004020992666482925,
-0.0506579615175724,
0.0015840455889701843,
0.023263420909643173,
0.013958025723695755,
-0.054387565702199936,
0.02678721956908703,
-0.009922180324792862,
-0.006909860298037529,
-0.056386351585388184,
-0.052147574722766876,
-0.00173956120852381,
-0.0026769523974508047,
0.014715556986629963,
-0.02307259663939476,
-0.007453380152583122,
0.034942418336868286,
-0.00000526266330780345,
0.013469577766954899,
-0.03348352015018463,
-0.006881410256028175,
-0.018781354650855064,
-0.01167876273393631,
0.009180127643048763,
0.02188868261873722,
0.0012178556062281132,
-0.0610269270837307,
-0.048541806638240814,
0.05284379422664642,
-0.0042076073586940765,
0.021894173696637154,
-0.04698847606778145,
0.02533811517059803,
0.03731342405080795,
0.06575693935155869,
0.0007762388559058309,
0.015098054893314838,
-0.004288969561457634,
-0.017821865156292915,
0.01214139349758625,
0.02755899168550968,
0.0299240630120039,
0.01264766976237297,
0.054955728352069855,
0.03029780089855194,
-0.008998829871416092,
0.023205213248729706,
0.0731206089258194,
0.021618904545903206,
0.037704091519117355,
0.03985300287604332,
-0.03435944765806198,
0.05336590111255646,
-0.016088295727968216,
0.03679000586271286,
0.04813642054796219,
0.04799468442797661,
0.025242604315280914,
0.005017457064241171,
-0.025556331500411034,
-0.03532963618636131,
-0.024488011375069618,
-0.0662267729640007,
-0.034318577498197556,
0.004763685632497072,
0.04222561791539192,
-0.029661621898412704,
-0.005673334002494812,
-0.04073755815625191,
-0.028519531711935997,
0.04566376656293869,
0.006036774720996618,
-0.0235440731048584,
-0.034035034477710724,
0.022699447348713875,
-0.06899145245552063,
0.028835980221629143,
-0.04896191507577896,
0.02396239899098873,
-0.02566787227988243,
-0.012461480684578419,
-0.016068266704678535,
-0.025316409766674042,
0.057749032974243164,
0.051959019154310226,
0.03763191029429436,
0.0018766530556604266,
-0.013978669419884682,
-0.039383795112371445,
-0.0515136644244194,
0.0591123029589653,
-0.01019927766174078,
0.028973327949643135,
0.008493153378367424,
0.015637481585144997,
0.022065460681915283,
0.036233119666576385,
-0.03548150882124901,
-0.023248225450515747,
0.06556595116853714,
-0.059157419949769974,
-0.03555990010499954,
0.005945480894297361,
0.014429100789129734,
0.021117478609085083
] |
<p>What is the formula we use to calculate average speed?</p> | g225 | [
0.013383958488702774,
0.02394086867570877,
0.0081877326592803,
0.0004150773456785828,
0.011494922451674938,
-0.061225321143865585,
0.03784753009676933,
0.02163785696029663,
-0.05675650015473366,
0.021979661658406258,
0.05486404895782471,
0.050048694014549255,
0.026717903092503548,
0.05141367390751839,
-0.016534505411982536,
0.0047875456511974335,
0.021847136318683624,
-0.01200187299400568,
0.025947922840714455,
0.05239279568195343,
0.004056544508785009,
-0.01690637320280075,
0.02331233210861683,
-0.04931186884641647,
0.0064070033840835094,
-0.03968777880072594,
-0.07005057483911514,
-0.04855119809508324,
-0.11007522791624069,
0.04001921787858009,
0.023093368858098984,
-0.024322573095560074,
-0.0018429899355396628,
-0.03568665683269501,
-0.03267042711377144,
0.010450809262692928,
-0.0041023315861821175,
-0.006172678433358669,
0.05358237028121948,
-0.018456164747476578,
0.0017063752748072147,
-0.048843976110219955,
-0.00097432523034513,
0.027795391157269478,
0.0003401024150662124,
-0.037250448018312454,
-0.015538719482719898,
-0.03375259414315224,
-0.050073496997356415,
0.010927430354058743,
-0.027244342491030693,
0.026313701644539833,
0.0379096195101738,
-0.02077699638903141,
-0.03778805583715439,
0.02677334100008011,
0.020457107573747635,
-0.04352853074669838,
-0.043600741773843765,
0.02740149013698101,
-0.02344386838376522,
-0.0591697134077549,
0.054825834929943085,
0.026853442192077637,
0.04542479291558266,
-0.008656993508338928,
0.03121246211230755,
-0.020285028964281082,
0.005683570634573698,
-0.046749670058488846,
-0.01355897355824709,
-0.01711667887866497,
0.02539520151913166,
-0.08406299352645874,
-0.08562904596328735,
-0.03918176889419556,
0.024010663852095604,
-0.031875260174274445,
0.03262058645486832,
0.04526832327246666,
0.059836529195308685,
-0.008101481013000011,
-0.018450895324349403,
0.004375628661364317,
-0.013391551561653614,
-0.04027547314763069,
-0.013154170475900173,
0.013238256797194481,
0.0007460188353434205,
0.00950547680258751,
-0.000582973996642977,
-0.029061926528811455,
0.033487237989902496,
-0.011758904904127121,
0.0484653040766716,
-0.05100934952497482,
-0.026186572387814522,
0.0030326307751238346,
-0.024094121530652046,
0.047914788126945496,
-0.005103901959955692,
0.003445080714300275,
0.029398545622825623,
-0.029144158586859703,
0.0052840388379991055,
0.012160147540271282,
-0.027451403439044952,
-0.013360932469367981,
-0.036072541028261185,
-0.05819833651185036,
0.014335586689412594,
-0.022295242175459862,
0.011268455535173416,
0.007756796199828386,
-0.006204981356859207,
-0.08189599215984344,
-0.012957116588950157,
-0.019547488540410995,
0.014298714697360992,
0.00907090213149786,
0.04527098685503006,
-0.005138660315424204,
-0.05645567551255226,
0.03804602846503258,
0.022477177903056145,
0.01613950915634632,
-0.016945049166679382,
-0.042557504028081894,
0.026707302778959274,
-0.012438267469406128,
0.01756337471306324,
-0.019146107137203217,
0.016404524445533752,
0.04624135419726372,
-0.05094704404473305,
0.040167711675167084,
0.0021071305964142084,
0.030290957540273666,
0.005670694634318352,
0.021368129178881645,
-0.046599894762039185,
-0.07784169912338257,
0.029321128502488136,
0.0003001310396939516,
-0.035095855593681335,
0.037153616547584534,
-0.05093363672494888,
-0.04822239279747009,
0.010459997691214085,
-0.0010315318359062076,
0.05522285774350166,
0.03498334437608719,
0.029887735843658447,
0.03424522653222084,
-0.04549955949187279,
-0.022941766306757927,
-0.012754547409713268,
0.08009764552116394,
0.008066334761679173,
0.1025889441370964,
0.05819245055317879,
-0.008274916559457779,
-0.0389106422662735,
0.03101705200970173,
-0.06947018951177597,
0.013712812215089798,
0.02544333040714264,
-0.02151036635041237,
-0.028122100979089737,
-0.039145611226558685,
0.01460432168096304,
0.003434473183006048,
0.0012218471383675933,
-0.002422741148620844,
0.005825178697705269,
-0.015985876321792603,
0.05619943141937256,
-0.013717351481318474,
-0.00602327473461628,
0.03715191408991814,
0.026593133807182312,
-0.004125933162868023,
0.06815329194068909,
-0.06659522652626038,
-0.06142869219183922,
0.012179169803857803,
-0.02638465352356434,
-0.052981678396463394,
-0.08251743018627167,
0.014669899828732014,
-0.004839309491217136,
0.015047448687255383,
0.02084164135158062,
0.03820808604359627,
-0.012491635978221893,
0.010430998168885708,
0.051768507808446884,
-0.02238016575574875,
-0.006224325392395258,
-0.006909339223057032,
0.037640128284692764,
0.03384259715676308,
-0.000024982879040180705,
-0.035343803465366364,
0.019309457391500473,
-0.019437866285443306,
-0.00966962892562151,
0.06565335392951965,
0.029078615829348564,
0.03834200277924538,
0.06464380025863647,
0.023379793390631676,
-0.012910924851894379,
0.09363473951816559,
0.010988206602633,
-0.007122314069420099,
-0.010159320197999477,
-0.018353795632719994,
-0.022464852780103683,
0.01072603464126587,
0.018291335552930832,
-0.01986943930387497,
-0.04349201172590256,
0.0220631193369627,
-0.04999315366148949,
0.006393044721335173,
0.0010217053350061178,
0.003758569248020649,
0.03839444741606712,
0.07968980073928833,
0.03192472830414772,
-0.055822085589170456,
-0.08271481841802597,
0.0015252565499395132,
-0.06047537177801132,
0.0438556931912899,
-0.007350774481892586,
0.029621321707963943,
0.014307740144431591,
0.06280237436294556,
0.057426102459430695,
-0.024832624942064285,
0.009209845215082169,
-0.0074062771163880825,
-0.031568076461553574,
-0.023274540901184082,
0.017083249986171722,
-0.043679408729076385,
-0.00007783532055327669,
0.0729622021317482,
0.011811337433755398,
-0.019884241744875908,
0.009697988629341125,
-0.0415998175740242,
0.017520109191536903,
-0.028363121673464775,
-0.023840727284550667,
0.012298977933824062,
-0.04350138455629349,
-0.036396414041519165,
-0.02576827071607113,
0.09129169583320618,
-0.005545640364289284,
-0.04291567951440811,
-0.018703756853938103,
-0.04106771573424339,
-0.006825402844697237,
-0.010255216620862484,
0.007448718883097172,
0.02894064038991928,
-0.011225789785385132,
0.02321462891995907,
0.003069587517529726,
-0.0039075687527656555,
0.013895063661038876,
-0.03900044038891792,
0.06152373179793358,
-0.06819472461938858,
0.006466931663453579,
0.0034823990426957607,
-0.028354445472359657,
-0.011123674921691418,
-0.021826425567269325,
0.024722397327423096,
-0.020168228074908257,
-0.08337585628032684,
0.09262565523386002,
0.04856390133500099,
-0.0025372931268066168,
0.04733363911509514,
-0.013726688921451569,
-0.005038089584559202,
-0.016836531460285187,
0.02733842097222805,
0.03684353828430176,
0.12670719623565674,
0.12831923365592957,
-0.05413144454360008,
0.014151771552860737,
-0.03979329392313957,
0.053827155381441116,
-0.047473181039094925,
-0.015199628658592701,
-0.002706063212826848,
-0.051315248012542725,
0.026966406032443047,
0.02317226305603981,
-0.03202660754323006,
0.005444459617137909,
0.009477010928094387,
-0.004579378291964531,
0.043495673686265945,
0.0063074384815990925,
-0.012542449869215488,
-0.05448399484157562,
0.01635020785033703,
0.024289023131132126,
-0.010153361596167088,
0.02991846390068531,
-0.00047810663818381727,
0.015438265167176723,
-0.09136443585157394,
-0.021177729591727257,
-0.009460086934268475,
-0.04349244385957718,
0.028238805010914803,
0.005461906082928181,
0.017633425071835518,
0.02391173504292965,
-0.005895324982702732,
0.018570665270090103,
0.03229617327451706,
-0.001707959221675992,
0.02610238641500473,
-0.009414716623723507,
-0.02890215441584587,
0.09723814576864243,
0.05271889269351959,
0.0008658930892124772,
0.025164375081658363,
0.005337974522262812,
-0.00023768075334373862,
-0.05678943544626236,
-0.030084628611803055,
-0.04118278622627258,
-0.03177393600344658,
0.022267233580350876,
-0.00923166237771511,
-0.0383392870426178,
0.0057729980908334255,
0.012818563729524612,
0.011760288849473,
-0.06052606552839279,
-0.06910025328397751,
0.003091973252594471,
0.017549708485603333,
-0.0023703579790890217,
-0.04291282221674919,
0.005261035170406103,
0.033635012805461884,
0.024337485432624817,
-0.0011010151356458664,
0.02387406677007675,
0.04835396632552147,
-0.01723502017557621,
-0.013538709841668606,
-0.02259240113198757,
0.0834847167134285,
-0.033044423907995224,
-0.06489215046167374,
-0.012406913563609123,
-0.0001211741182487458,
0.0330241359770298,
-0.0058664134703576565,
-0.02523639053106308,
-0.0007137671927921474,
-0.027696825563907623,
-0.01608540117740631,
-0.027730340138077736,
0.008582736365497112,
0.051527239382267,
0.011284276843070984,
-0.010020445100963116,
-0.03229020908474922,
-0.025113938376307487,
-0.0220309030264616,
-0.016098881140351295,
-0.029077356681227684,
0.013387233018875122,
-0.026903705671429634,
0.025857191532850266,
-0.018869638442993164,
0.0033107143826782703,
-0.0014028804143890738,
-0.002738351235166192,
-0.04279328137636185,
0.0007162563852034509,
0.030632518231868744,
-0.03789064288139343,
0.046729352325201035,
-0.006116969510912895,
0.01619994267821312,
-0.001034203334711492,
0.0072799972258508205,
0.004378733690828085,
-0.018054230138659477,
0.010762949474155903,
-0.049707263708114624,
0.053196512162685394,
0.008214594796299934,
-0.08661631494760513,
0.029144074767827988,
0.0438951812684536,
0.012504031881690025,
0.028681699186563492,
0.03091440163552761,
0.03819885849952698,
-0.04746512323617935,
-0.012090448290109634,
-0.02300071343779564,
-0.004674369934946299,
0.017963601276278496,
0.0365888886153698,
-0.017927637323737144,
-0.039661306887865067,
-0.017757227644324303,
0.08037368953227997,
0.011958545073866844,
-0.028511926531791687,
0.014241667464375496,
0.04861867055296898,
0.033650100231170654,
-0.02127704955637455,
0.06499998271465302,
-0.015330263413488865,
0.02797851338982582,
0.028285764157772064,
0.07516729086637497,
0.06825177371501923,
-0.0176029521971941,
-0.03238365799188614,
-0.0182783342897892,
0.05167119577527046,
0.027040764689445496,
-0.04220104217529297,
0.06141422688961029,
-0.00830119103193283,
-0.05105496570467949,
-0.053455471992492676,
-0.03917967155575752,
0.0644286721944809,
0.02251259982585907,
0.0013951155124232173,
-0.0002520674024708569,
-0.015304733999073505,
0.030704140663146973,
-0.05678083002567291,
-0.002430308610200882,
0.057178981602191925,
0.032923609018325806,
-0.07440835237503052,
-0.0018432720098644495,
0.01680757850408554,
-0.03264350816607475,
-0.030559999868273735,
0.028101196512579918,
0.010551185347139835,
0.013602393679320812,
0.013277520425617695,
0.00038195474189706147,
0.014392239972949028,
-0.0556054562330246,
-0.03149130940437317,
-0.00091694196453318,
-0.0012660971842706203,
0.02205786667764187,
-0.007196450140327215,
0.016500119119882584,
-0.05252065137028694,
-0.002195616252720356,
-0.0339675098657608,
0.002479289658367634,
0.005130671430379152,
-0.012628564611077309,
-0.024143921211361885,
0.03913261368870735,
-0.05222195014357567,
0.013742883689701557,
-0.06639352440834045,
-0.06807541847229004,
-0.03969230130314827,
0.038213539868593216,
0.022261982783675194,
-0.04707270488142967,
-0.069912850856781,
-0.02974909543991089,
-0.018409347161650658,
0.014652179554104805,
-0.013521180488169193,
0.002040452789515257,
-0.05930790305137634,
0.07128220051527023,
-0.043171994388103485,
-0.01918026991188526,
0.05319786071777344,
0.04076574742794037,
0.003071538871154189,
0.014708596281707287,
-0.00378552102483809,
0.018345890566706657,
0.1096469834446907,
0.030739393085241318,
0.05177169293165207,
-0.05493282899260521,
-0.03915682062506676,
0.00009334956848761067,
0.0052064042538404465,
-0.02828392945230007,
-0.0015032694209367037,
-0.03731634467840195,
0.05389795079827309,
0.04600919783115387,
0.04501733556389809,
0.005942398216575384,
0.02947136014699936,
0.01562205795198679,
-0.08783470839262009,
-0.00661835353821516,
0.030697956681251526,
-0.06892434507608414,
0.0015113125555217266,
-0.013850439339876175,
-0.01954212784767151,
-0.08030106872320175,
-0.016807569190859795,
0.020562445744872093,
-0.01104260329157114,
-0.056239571422338486,
0.04402713105082512,
-0.02229604870080948,
-0.07167279720306396,
0.048695966601371765,
-0.006097234319895506,
0.04337981715798378,
0.0334586426615715,
0.015308074653148651,
-0.04179731756448746,
-0.018282081931829453,
-0.018791940063238144,
-0.03389870002865791,
0.02855929359793663,
0.015013243071734905,
0.028855979442596436,
-0.04380842670798302,
-0.006213624961674213,
0.01494337897747755,
-0.013580402359366417,
0.004513212945312262,
0.004180025774985552,
-0.012181056663393974,
0.022545520216226578,
0.03681815788149834,
0.06594758480787277,
0.023906322196125984,
-0.011035001836717129,
-0.0544070303440094,
0.027836984023451805,
0.03946612402796745,
-0.006393967196345329,
-0.04319937899708748,
-0.02234504744410515,
-0.0029095113277435303,
-0.011205325834453106,
-0.0053875078447163105,
0.05907980352640152,
0.05129235237836838,
0.007672341540455818,
-0.041698358952999115,
-0.01878422684967518,
-0.02821086347103119,
0.011122873052954674,
-0.008952297270298004,
-0.04202640429139137,
-0.007974924519658089,
-0.06919367611408234,
-0.03836986795067787,
-0.0038807298988103867,
0.01025150716304779,
0.007246251683682203,
-0.023066101595759392,
0.039565131068229675,
0.030165569856762886,
-0.02395673841238022,
-0.0618165098130703,
0.02870631217956543,
0.0006917410064488649,
-0.02407040260732174,
-0.013326531276106834,
0.002310127718374133,
-0.0010197967058047652,
-0.006459190510213375,
0.014118202030658722,
0.05315211042761803,
-0.020592637360095978,
0.015112300403416157,
0.013929834589362144,
0.03881308063864708,
-0.02355811558663845,
-0.051121409982442856,
0.0041378336027264595,
-0.0035575497895479202,
0.02756873331964016,
0.03346817567944527,
0.038053013384342194,
-0.04678448662161827,
0.03660288825631142,
0.011558406054973602,
0.016711317002773285,
0.03300199657678604,
0.002547171199694276,
0.025132881477475166,
-0.021735962480306625,
-0.0023913318291306496,
-0.008886109106242657,
0.08103082329034805,
0.014165051281452179,
-0.016877852380275726,
-0.032676126807928085,
-0.007423607632517815,
-0.057546041905879974,
0.05461772531270981,
0.009519405663013458,
-0.0073838550597429276,
-0.0023831664584577084,
-0.017070699483156204,
0.02238345332443714,
-0.00894272979348898,
0.06835495680570602,
-0.0007967910496518016,
0.03262273222208023,
0.07144327461719513,
0.01964694634079933,
-0.048413168638944626,
0.022387908771634102,
-0.07227110862731934,
-0.009246873669326305,
0.015104579739272594,
0.009489098563790321,
-0.0727250948548317,
-0.015596446581184864,
0.0045323362573981285,
-0.011526322923600674,
-0.045546554028987885,
0.03235641494393349,
-0.015901468694210052,
-0.013211536221206188,
0.03889871761202812,
0.01735992357134819,
0.007947024889290333,
0.000628325913567096,
0.02037595584988594,
-0.03427581489086151,
0.04299722984433174,
0.0107674989849329,
0.0033582844771444798,
0.008176836185157299,
-0.017356490716338158,
-0.0278229471296072,
-0.024862395599484444,
-0.03987301141023636,
-0.01148177683353424,
0.0027244591619819403,
-0.039888154715299606,
0.023166198283433914,
0.021879898384213448,
0.05420719459652901,
-0.01194352563470602,
-0.015518108382821083,
-0.055577926337718964,
-0.005174046382308006,
0.00034394627436995506,
0.030080262571573257,
-0.011986196041107178,
-0.023424867540597916,
0.04721260443329811,
0.07820258289575577,
0.01007909793406725,
-0.04586892947554588,
0.014101131819188595,
0.0014074528589844704,
-0.019280146807432175,
-0.0015501993475481868,
0.04139772430062294,
-0.047566480934619904,
-0.020209848880767822,
0.018216896802186966,
-0.0551474466919899,
0.04687679931521416,
0.004939602222293615,
0.06008359417319298,
0.009943767450749874,
0.014737579971551895,
0.04215279221534729,
0.08118827641010284,
-0.05299108475446701,
-0.006039116531610489,
-0.03376639634370804,
0.013773986138403416,
-0.015482071787118912,
-0.02786131575703621,
-0.013737152330577374,
0.02395598776638508,
0.04562722519040108,
0.012194203212857246,
-0.02024735137820244,
-0.030521929264068604,
0.021921437233686447,
-0.0773252472281456,
-0.05170891806483269,
0.009818640537559986,
0.05932500958442688,
-0.0005884722340852022,
0.05236304923892021,
-0.024568727239966393,
0.011673931032419205,
-0.029710844159126282,
0.029634976759552956,
0.002708951709792018,
-0.01195584051311016,
-0.007959051057696342,
-0.03167594596743584,
0.0238477885723114,
-0.01630329340696335,
0.06765347719192505,
-0.049606092274188995,
0.023461228236556053,
0.05210268869996071,
0.012661953456699848,
-0.06541171669960022,
0.11426513642072678,
-0.03518958389759064,
0.02205200120806694,
-0.017910221591591835,
0.047355975955724716,
0.01989399828016758,
0.030473193153738976,
0.019717730581760406,
0.0347931794822216,
0.038396332412958145,
-0.05176585167646408,
0.04034624621272087,
0.03463207557797432,
-0.03588194400072098,
0.042873140424489975,
0.012820434756577015,
-0.044626712799072266,
-0.011598496697843075,
0.010906247422099113,
-0.07492166757583618,
-0.029027393087744713,
-0.009927337057888508,
-0.05125600844621658,
-0.014371342957019806,
0.03939255326986313,
0.033947188407182693,
-0.014644577167928219,
-0.06950193643569946,
-0.016745030879974365
] |
<p>In multi-electron atoms, the electronic state of the optically active "subshell" is often expressed in "term symbols" notation. I.e. $^{2S+1}L_J$. This presumes that the system of electrons has definite $L^2$, $S^2$ and $\mathbf{J}$ eigenstates.</p>
<p>In order to determine all the possible electronic states compatible with the Pauli's exclusion principle, the technique is to assign to each electron its $m_s$ and $m_l$ and to see what states can be found in terms of eigenvalues of $L^2$, $S^2$, $J^2$ and $J_z$.</p>
<p>What justifies this procedure? In other words, the assumption so far was: </p>
<ul>
<li>heavy nucleus -> the Hamiltonian is spherically symmetric -> total $\mathbf{J}$ is conserved</li>
<li>spin-orbit is negligible to some extent -> total $S^2$ and $L^2$ are conserved</li>
</ul>
<p>What justifies, apart from intuitiveness, returning to the single electron picture (assigning to every electron its spin and angular momentum) to find what states are allowed or not according to the requirement that the total wavefunction should be antisymmetric? And could be there exceptions?</p> | g6567 | [
-0.012413164600729942,
0.019566446542739868,
-0.004702460952103138,
0.00019988766871392727,
-0.021918602287769318,
-0.03029952570796013,
0.050393734127283096,
0.030706729739904404,
0.06742270290851593,
0.020123731344938278,
0.003237923141568899,
0.00989967305213213,
0.0576484315097332,
0.04162652790546417,
-0.015748372301459312,
-0.036789800971746445,
0.06546627730131149,
0.03135247901082039,
0.043299317359924316,
0.00817850325256586,
-0.005531569477170706,
0.027337754145264626,
-0.03048328496515751,
0.0002787166158668697,
0.029987910762429237,
0.043160416185855865,
-0.016283169388771057,
-0.04061300307512283,
0.009168049320578575,
0.03026629239320755,
0.01692909561097622,
-0.07485552877187729,
0.05003881826996803,
-0.06155473738908768,
0.005152648780494928,
0.016931619495153427,
0.06640204787254333,
0.031894877552986145,
-0.03072129748761654,
0.0341225266456604,
-0.03018938936293125,
-0.031554169952869415,
-0.003078949637711048,
-0.01729423739016056,
0.05148156359791756,
-0.006981147453188896,
-0.007922589778900146,
0.014361991547048092,
-0.021964790299534798,
-0.03580981120467186,
0.037506379187107086,
0.041559189558029175,
0.04425378888845444,
-0.0028582224622368813,
0.023799197748303413,
0.008282525464892387,
-0.08413054794073105,
0.014301714487373829,
0.04315713420510292,
0.010428059846162796,
0.039819445461034775,
0.008863231167197227,
-0.015191322192549706,
0.01994975470006466,
0.06012288108468056,
0.02552037686109543,
-0.048680923879146576,
0.007975230924785137,
0.010013995692133904,
-0.002756696892902255,
-0.007408331613987684,
-0.02793668396770954,
-0.0006734283524565399,
-0.01795022375881672,
0.011783045716583729,
-0.009526815265417099,
-0.04784518852829933,
0.004418468102812767,
0.06640502065420151,
0.05599469318985939,
-0.05584678426384926,
-0.0445343554019928,
0.03162422776222229,
-0.006840493064373732,
0.007122992072254419,
0.024526668712496758,
0.004862966015934944,
-0.026737140491604805,
-0.019153254106640816,
0.039571359753608704,
0.026811150833964348,
-0.010812987573444843,
0.05019393563270569,
0.003317741909995675,
0.006874911952763796,
0.013493495993316174,
0.0005643731565214694,
0.02751806192100048,
-0.06103425472974777,
-0.027379024773836136,
0.020447203889489174,
-0.009055067785084248,
-0.00454020407050848,
-0.009775251150131226,
0.011191995814442635,
0.04011033475399017,
-0.04175291955471039,
-0.002742739859968424,
0.024729620665311813,
0.04038744792342186,
-0.006621163338422775,
0.011817924678325653,
0.007381926290690899,
-0.03306112438440323,
-0.10186251252889633,
0.021166274324059486,
0.030386587604880333,
-0.04992477968335152,
-0.04653282091021538,
0.040986720472574234,
-0.009850231930613518,
0.02934304066002369,
0.05948551371693611,
0.06878189742565155,
-0.0014100164407864213,
0.001450681360438466,
-0.05966871976852417,
-0.024020493030548096,
0.03490246832370758,
-0.032866690307855606,
-0.03785349801182747,
0.004898708313703537,
0.0023488395381718874,
0.04953668266534805,
0.016801083460450172,
-0.06836449354887009,
-0.020011281594634056,
0.003837895579636097,
-0.03347243741154671,
-0.06607135385274887,
0.018698440864682198,
-0.02365252934396267,
-0.04972310736775398,
-0.033319562673568726,
-0.0002866218565031886,
-0.06683461368083954,
-0.02378065697848797,
0.0016262581339105964,
0.012025860138237476,
0.03743114694952965,
0.019389035180211067,
0.03492290526628494,
0.0358085073530674,
-0.01841925084590912,
-0.004053183831274509,
-0.04431527480483055,
0.08007615804672241,
-0.04672513157129288,
-0.02833327278494835,
0.07094281911849976,
0.013675822876393795,
-0.03848971053957939,
-0.01620429754257202,
0.039397504180669785,
-0.040716417133808136,
-0.015330706723034382,
-0.029371000826358795,
-0.04125717282295227,
0.021089956164360046,
-0.03317013010382652,
-0.06406232714653015,
-0.021501393988728523,
0.02279803156852722,
0.03352385014295578,
0.03991639241576195,
0.011077756993472576,
-0.02300410531461239,
-0.06853966414928436,
0.06876693665981293,
0.06641783565282822,
-0.00962816085666418,
0.024929244071245193,
-0.010981063358485699,
0.06259859353303909,
0.016023196280002594,
-0.011155033484101295,
-0.0203397199511528,
0.039344821125268936,
-0.04082673415541649,
0.04433855786919594,
0.09345627576112747,
0.06533724069595337,
0.020493483170866966,
-0.015471321530640125,
-0.00734071247279644,
-0.002407636260613799,
0.0047880555503070354,
-0.04851385951042175,
-0.052765969187021255,
-0.021397946402430534,
-0.0025734647642821074,
0.026623953133821487,
-0.016243180260062218,
0.004821304697543383,
0.016914531588554382,
-0.021486813202500343,
-0.005149555392563343,
0.03905562683939934,
-0.0032779956236481667,
-0.010457492433488369,
0.00684753805398941,
-0.03975694254040718,
-0.014058972708880901,
0.0037890183739364147,
0.015871644020080566,
0.009759713895618916,
0.01533741969615221,
0.019334403797984123,
-0.004276779945939779,
0.022890113294124603,
-0.01831202767789364,
-0.005520615726709366,
-0.028179533779621124,
0.04562273621559143,
0.03195633739233017,
0.03693721070885658,
-0.03848259523510933,
0.010212394408881664,
-0.037441350519657135,
0.03326762840151787,
-0.0673314705491066,
-0.023049410432577133,
-0.013186306692659855,
-0.07702802866697311,
-0.022390181198716164,
0.02286217361688614,
-0.013692038133740425,
0.009649687446653843,
0.00000828328211355256,
0.03631680831313133,
0.01428457722067833,
0.005136791616678238,
0.00315281399525702,
0.060383833944797516,
0.02801373414695263,
-0.017399029806256294,
0.011180846020579338,
0.028139661997556686,
-0.042581185698509216,
0.028242943808436394,
-0.0874740481376648,
0.010839284397661686,
-0.06675892323255539,
0.041665513068437576,
-0.008475072681903839,
-0.032566193491220474,
-0.004437358118593693,
0.005269531160593033,
-0.04441065341234207,
0.026323508471250534,
-0.0035772172268480062,
0.0038982578553259373,
-0.010778077878057957,
0.018352171406149864,
0.02249489538371563,
-0.013622022233903408,
0.01601823791861534,
-0.03707233816385269,
-0.021254612132906914,
0.009310531429946423,
-0.0566910058259964,
0.09177617728710175,
-0.03849443420767784,
0.04527563229203224,
0.015030957758426666,
0.013986064121127129,
-0.026597756892442703,
0.03693576157093048,
0.019517596811056137,
0.0340646393597126,
-0.03803720325231552,
-0.007164182607084513,
-0.03433395177125931,
0.029421882703900337,
0.015676051378250122,
-0.04171929135918617,
0.026953743770718575,
0.04213123023509979,
0.006969895213842392,
-0.034522633999586105,
-0.037693340331315994,
0.03748584911227226,
0.016786590218544006,
0.02729913219809532,
-0.0451587438583374,
-0.041826434433460236,
0.015264937654137611,
-0.05453163757920265,
-0.013677683658897877,
0.08023591339588165,
-0.018385479226708412,
0.0649842843413353,
0.04409656301140785,
-0.02509492076933384,
0.06347447633743286,
0.026743466034531593,
-0.028017939999699593,
-0.02121729776263237,
-0.02245347760617733,
-0.036132726818323135,
-0.02537587471306324,
0.05891568213701248,
0.008589007891714573,
-0.03632097691297531,
-0.038022730499506,
-0.0117775434628129,
0.01928163506090641,
0.00586710823699832,
0.04179554432630539,
-0.0281303059309721,
-0.03674774244427681,
0.07915756106376648,
0.008909267373383045,
0.0020407543051987886,
0.024156060069799423,
0.011110986582934856,
-0.0950351133942604,
-0.03847186267375946,
-0.04999812692403793,
-0.031150544062256813,
0.022265778854489326,
0.01624036207795143,
0.027107728645205498,
0.004464942496269941,
-0.023465381935238838,
0.00622692471370101,
-0.00011244529014220461,
-0.024385781958699226,
0.05908217653632164,
0.017910990864038467,
-0.019623873755335808,
-0.025907522067427635,
-0.026311257854104042,
-0.0236139465123415,
-0.007733305916190147,
-0.027345407754182816,
-0.10221249610185623,
0.014022449031472206,
-0.024134105071425438,
-0.030766300857067108,
-0.061399780213832855,
0.055129826068878174,
-0.026845060288906097,
-0.0009467697236686945,
0.024509910494089127,
0.01622614823281765,
0.003621411509811878,
0.06442053616046906,
0.0561479814350605,
0.009145105257630348,
-0.013259555213153362,
-0.03225889801979065,
-0.014322072267532349,
-0.05616750568151474,
0.03875218331813812,
-0.011581623926758766,
-0.0005166347837075591,
-0.03559845685958862,
0.0827452689409256,
-0.028520137071609497,
-0.01920432038605213,
-0.02544255182147026,
0.0003495163982734084,
-0.042683131992816925,
0.026414910331368446,
-0.03640889376401901,
-0.03751827031373978,
-0.010309714823961258,
-0.0812678411602974,
0.008002283051609993,
-0.026703137904405594,
0.00827849842607975,
0.03636297583580017,
0.04597436264157295,
0.03440452739596367,
0.03866760432720184,
-0.0358022004365921,
0.048980437219142914,
-0.01649133861064911,
0.020544685423374176,
0.03667804226279259,
-0.05515856295824051,
-0.057846564799547195,
-0.03287794068455696,
0.02603662759065628,
-0.0027430786285549402,
0.07182334363460541,
-0.10811646282672882,
0.03969070687890053,
0.02981613390147686,
-0.017611674964427948,
-0.02908637560904026,
0.024854252114892006,
-0.06742793321609497,
0.035386502742767334,
0.01980338804423809,
0.02176804468035698,
0.008794968947768211,
0.029020316898822784,
-0.01705315336585045,
-0.015525409020483494,
-0.01504511758685112,
0.02504829503595829,
0.03908495977520943,
-0.04954218119382858,
-0.02037888765335083,
0.008901149034500122,
-0.048158008605241776,
0.0008756181341595948,
-0.004733856301754713,
0.017109589651226997,
0.07147807627916336,
-0.025569353252649307,
-0.004749098792672157,
-0.03183593600988388,
0.03637157380580902,
0.006961614824831486,
-0.010673274286091328,
0.016370806843042374,
-0.014070875942707062,
0.01358267106115818,
0.0052804299630224705,
0.023934559896588326,
-0.027253199368715286,
-0.12124721705913544,
-0.021678753197193146,
-0.03623748943209648,
0.018021712079644203,
-0.0028696770314127207,
0.060285069048404694,
0.05663381144404411,
-0.029519489035010338,
-0.007770481053739786,
0.019330767914652824,
-0.021409783512353897,
-0.002843467053025961,
-0.04578579217195511,
-0.048940036445856094,
-0.0025988235138356686,
-0.04094795510172844,
-0.012686747126281261,
-0.03366777300834656,
-0.042631059885025024,
0.018558179959654808,
-0.022105911746621132,
-0.017580818384885788,
-0.043387673795223236,
0.040202200412750244,
0.0628763735294342,
0.00281257345341146,
-0.03267540782690048,
-0.01760287955403328,
-0.05982226878404617,
0.041227713227272034,
0.023662330582737923,
0.009843903593719006,
-0.028739504516124725,
0.033788662403821945,
-0.0314040333032608,
-0.0001698031701380387,
0.05972164869308472,
0.019499991089105606,
0.0817008838057518,
-0.053549304604530334,
0.010465593077242374,
-0.08052419126033783,
-0.0018651586724445224,
-0.0005992451915517449,
-0.0051642293110489845,
0.03381526470184326,
-0.0351390577852726,
0.00042572751408442855,
0.03784312307834625,
0.018812958151102066,
-0.021106474101543427,
-0.002125419909134507,
0.02134903520345688,
-0.00009002409933600575,
-0.08340390771627426,
0.0006197735783644021,
-0.006594125647097826,
0.03236480429768562,
0.0035784952342510223,
-0.015156876295804977,
0.04968030005693436,
0.031921662390232086,
0.020229872316122055,
0.01532982662320137,
-0.02620854601264,
0.03621552884578705,
-0.03397343307733536,
-0.003862446639686823,
-0.024051068350672722,
0.02844383753836155,
-0.015977224335074425,
-0.0026958677917718887,
0.12879513204097748,
-0.04983724653720856,
-0.007207841146737337,
-0.09897394478321075,
-0.007436392363160849,
-0.04110275208950043,
-0.004350803792476654,
-0.06333918869495392,
-0.002946821041405201,
-0.07727651298046112,
0.0010279755806550384,
0.0719197690486908,
-0.006709056906402111,
-0.05148611217737198,
-0.024951450526714325,
0.01015245821326971,
0.035819657146930695,
-0.033533547073602676,
-0.00948043167591095,
0.007766118738800287,
-0.004813191946595907,
0.0031072483398020267,
0.02856251783668995,
0.04440300539135933,
0.01737421751022339,
-0.015625713393092155,
0.00221317820250988,
0.02512425370514393,
0.07356687635183334,
-0.08052036911249161,
-0.04150077700614929,
0.003638993948698044,
0.0057760500349104404,
0.018064934760332108,
0.007600633893162012,
-0.050779685378074646,
-0.024861136451363564,
0.039508938789367676,
-0.03237304836511612,
0.0009080258896574378,
0.020014766603708267,
-0.0017336799064651132,
-0.03578510507941246,
-0.03793986886739731,
-0.023958252742886543,
0.09155139327049255,
-0.034172531217336655,
-0.011205889284610748,
0.029745154082775116,
0.049696072936058044,
0.003748858580365777,
0.025480376556515694,
0.014284995384514332,
0.0321427620947361,
0.04719908908009529,
0.02445109561085701,
-0.0023534749634563923,
0.03570748120546341,
0.03080133907496929,
0.011430276557803154,
-0.031670667231082916,
-0.015840677544474602,
0.019785398617386818,
0.020320812240242958,
-0.038606058806180954,
0.011754167266190052,
0.01899818517267704,
0.009622410871088505,
0.028671132400631905,
0.02113884873688221,
-0.03339387848973274,
0.022375881671905518,
-0.008543189615011215,
-0.004267449956387281,
-0.023221725597977638,
0.06520122289657593,
0.015248439274728298,
0.0003907692153006792,
-0.018796565011143684,
0.020896458998322487,
-0.009364999830722809,
-0.004495262634009123,
0.018229536712169647,
-0.03717217966914177,
-0.0013062501093372703,
0.002756651723757386,
0.00996241346001625,
0.023807143792510033,
-0.0017970692133530974,
0.03511665388941765,
-0.009576003067195415,
-0.015795202925801277,
-0.014410500414669514,
0.02052822709083557,
0.08592736721038818,
-0.014166580513119698,
0.010314310900866985,
0.015872139483690262,
0.05544324591755867,
0.0689426138997078,
-0.060155317187309265,
-0.0034349788911640644,
0.009314254857599735,
-0.041922230273485184,
-0.035335421562194824,
-0.013570453971624374,
0.028264999389648438,
0.004087997134774923,
-0.013233267702162266,
-0.032456837594509125,
-0.003278128569945693,
0.04491439089179039,
-0.06883419305086136,
0.04405330866575241,
0.052600741386413574,
0.02420695871114731,
-0.06116285175085068,
-0.008160951547324657,
0.08888398110866547,
0.0414525531232357,
-0.05644853413105011,
-0.03395611047744751,
0.06585420668125153,
0.008335371501743793,
-0.0022176438942551613,
0.024601232260465622,
0.07115208357572556,
0.008552656508982182,
0.014179768040776253,
0.04518420994281769,
-0.022441690787672997,
0.012925422750413418,
0.05841854587197304,
0.041245222091674805,
-0.04092269390821457,
0.039583541452884674,
0.13019028306007385,
0.026879018172621727,
-0.060441337525844574,
0.0118595315143466,
0.04570689797401428,
-0.03263118490576744,
-0.013396025635302067,
-0.008391241542994976,
0.012248034588992596,
-0.01135617308318615,
-0.039735082536935806,
0.0012826846214011312,
-0.01065851841121912,
-0.009065312333405018,
-0.007676706649363041,
-0.024233942851424217,
0.010262398980557919,
-0.03704920411109924,
-0.01822669990360737,
-0.025118928402662277,
-0.01492649782449007,
-0.05509450286626816,
-0.041209883987903595,
0.022983171045780182,
0.0029836134053766727,
-0.06378202885389328,
-0.023346005007624626,
-0.018656231462955475,
-0.015385616570711136,
-0.04486079514026642,
-0.07028059661388397,
0.09442953020334244,
-0.032865509390830994,
-0.037415601313114166,
-0.0026786865200847387,
-0.016023755073547363,
-0.02649463154375553,
-0.04134945943951607,
-0.0730431005358696,
0.044948309659957886,
0.018008986487984657,
0.03280860558152199,
-0.0514911413192749,
-0.018561607226729393,
-0.016451334580779076,
0.02669895812869072,
-0.019833792001008987,
0.027563344687223434,
0.03234143927693367,
-0.0028173201717436314,
0.03447882458567619,
-0.023364543914794922,
-0.007207588758319616,
-0.008729372173547745,
-0.025422269478440285,
0.04742978885769844,
0.04315967112779617,
-0.00999740231782198,
-0.014463559724390507,
0.030084554105997086,
0.01039077527821064,
0.044493403285741806,
0.044064510613679886,
0.0034077607560902834,
-0.0062059927731752396,
-0.019889142364263535,
-0.04529714956879616,
-0.013963310979306698,
0.011464020237326622,
0.008579179644584656,
-0.0034305285662412643,
0.00918319821357727,
0.026469949632883072,
-0.03908626735210419,
-0.015594919212162495,
0.015110624022781849,
0.017805451527237892,
0.006794260814785957,
0.06576491892337799,
0.02705560438334942,
-0.037454649806022644,
0.014258130453526974,
0.025435926392674446,
-0.03686673566699028,
0.005975788459181786,
0.013370185159146786,
0.025942692533135414,
-0.0077009061351418495,
-0.028338663280010223,
0.04609426110982895,
-0.043087031692266464,
-0.017216265201568604,
-0.04302549362182617,
0.019604740664362907,
-0.027314424514770508,
-0.06887504458427429,
-0.007830518297851086,
0.05265431106090546,
-0.015400685369968414,
0.0001431388227501884,
-0.0007119430229067802,
-0.027865920215845108,
-0.047127366065979004,
0.022848831489682198,
-0.04275750741362572,
-0.04688733443617821,
0.07155712693929672,
0.00643845833837986,
-0.0363425686955452,
-0.0011495979269966483,
-0.029355734586715698,
0.029261235147714615,
0.041148606687784195,
-0.021063346415758133,
0.03527715802192688,
-0.07766056805849075,
0.041997797787189484,
0.043457258492708206,
-0.03272097930312157,
0.018594367429614067,
0.010715906508266926,
0.02464233711361885,
0.0031796430703252554,
-0.10478030890226364,
-0.02071281149983406,
-0.01030667219310999
] |
<p>In an assignment I am given a random car with a random suspension system, and told that it is sufficient to test the safety of the car with regards to the suspension on three different sinusoidal roads.</p>
<p>The first road has an amplitude of 5 centimeters and a period of 20 meters, the second road has an amplitude of 2.5 centimeters and a period of 2 meters and the third road has an amplitude of 1 centimeter and a period of 20 centimeters.</p>
<p>I can't figure out why a test on these three roads would be sufficient to conclude that the car can handle any random other road, and I am given no other information.</p>
<p>Could anyone please tell me why it is sufficient to test the suspension on only these three roads?</p> | g6568 | [
0.023438220843672752,
-0.012163924053311348,
0.0035237364936619997,
-0.012373296543955803,
0.029207564890384674,
0.011089217849075794,
-0.003832547925412655,
0.00450459960848093,
-0.0009996985318139195,
-0.007900259457528591,
-0.009101956151425838,
-0.013517206534743309,
-0.019472524523735046,
-0.014508160762488842,
-0.04049130529165268,
-0.01682373508810997,
0.0368490032851696,
0.027589119970798492,
-0.007657089736312628,
0.0002899311948567629,
-0.006010350771248341,
0.008470279164612293,
-0.037877216935157776,
-0.012261773459613323,
0.05162942036986351,
-0.016104331240057945,
-0.03851993381977081,
-0.04073531553149223,
-0.06842448562383652,
-0.009400189854204655,
0.0036245952360332012,
0.011704372242093086,
-0.008230824954807758,
-0.04709380865097046,
-0.08550921082496643,
0.010334105230867863,
0.0036066893953830004,
0.000402678590035066,
0.01219392754137516,
-0.021183455362915993,
-0.020075233653187752,
0.03817523643374443,
0.05258317291736603,
0.0010114379692822695,
-0.00897213350981474,
-0.024917930364608765,
-0.05210477486252785,
0.05900659039616585,
0.011354406364262104,
-0.029550127685070038,
-0.003866892773658037,
-0.044489726424217224,
0.04300224781036377,
0.019032958894968033,
-0.019450809806585312,
-0.029178436845541,
0.03157500922679901,
-0.004672198090702295,
-0.028699912130832672,
-0.014220645651221275,
-0.021017130464315414,
-0.00785956159234047,
-0.049583759158849716,
-0.029323311522603035,
0.02511058934032917,
-0.02489824965596199,
0.028843076899647713,
0.011211110278964043,
0.04145249351859093,
0.06171485036611557,
0.049889251589775085,
0.0031411272939294577,
-0.02555970288813114,
-0.09038543701171875,
-0.06325367093086243,
-0.014621438458561897,
0.005317860748618841,
0.03416406363248825,
0.051970530301332474,
0.03922376036643982,
0.019495796412229538,
0.025575997307896614,
-0.05960257723927498,
0.024493010714650154,
0.05438341572880745,
0.04849991574883461,
0.025022093206644058,
-0.02779344655573368,
-0.025960532948374748,
-0.014865359291434288,
0.05447545647621155,
-0.025658296421170235,
0.04713164642453194,
0.1006736159324646,
-0.01670846901834011,
-0.028008898720145226,
-0.059469420462846756,
0.12173694372177124,
0.014967119321227074,
0.04207964614033699,
-0.011158297769725323,
-0.014766897074878216,
0.044735513627529144,
-0.016958750784397125,
-0.012760059908032417,
0.02505333162844181,
0.0010034285951405764,
0.00685188127681613,
0.02874002791941166,
-0.07598838210105896,
-0.035044167190790176,
0.0032538287341594696,
-0.0388091541826725,
-0.0008522348944097757,
0.012633666396141052,
-0.010901384986937046,
0.044637538492679596,
0.003365518758073449,
0.04042215272784233,
-0.0045740725472569466,
-0.009755951352417469,
-0.02417600527405739,
-0.0516388975083828,
0.028837276622653008,
-0.0724177211523056,
0.036637380719184875,
0.014644819311797619,
0.046750035136938095,
0.04558432847261429,
0.02509796805679798,
-0.039405327290296555,
0.04017798975110054,
0.010430525057017803,
-0.02316218428313732,
-0.03751299902796745,
0.04549025371670723,
0.0645022764801979,
-0.01574864238500595,
-0.03187902644276619,
0.05801060423254967,
0.04193444177508354,
0.027498366311192513,
-0.009571083821356297,
-0.010978465899825096,
-0.015209457837045193,
0.021702401340007782,
-0.03558680787682533,
-0.028624622151255608,
0.01680625230073929,
-0.009563110768795013,
-0.002196843968704343,
0.017336398363113403,
0.00469210185110569,
0.020928021520376205,
-0.00008634253026684746,
0.011250132694840431,
-0.002840863075107336,
0.0035140637774020433,
-0.020676735788583755,
0.00673649599775672,
0.040551550686359406,
-0.02727636508643627,
0.009691892191767693,
0.008837809786200523,
-0.06932148337364197,
0.016629572957754135,
-0.01115996204316616,
-0.01787339709699154,
0.02309487573802471,
-0.005780291743576527,
-0.016008008271455765,
-0.018329612910747528,
0.051424019038677216,
0.025501331314444542,
0.025923997163772583,
0.014861403033137321,
0.07108688354492188,
-0.03829606622457504,
0.07541199773550034,
-0.031003009527921677,
-0.020888466387987137,
-0.007062000222504139,
-0.022548027336597443,
-0.014674662612378597,
-0.006210770923644304,
0.0074135069735348225,
0.027031991630792618,
0.04567746818065643,
-0.08456891775131226,
0.016534995287656784,
0.05729222297668457,
-0.0446314811706543,
-0.0002865309070330113,
-0.04068463668227196,
0.010946414433419704,
-0.044473059475421906,
0.008163073100149632,
0.030337370932102203,
0.011417154222726822,
-0.0000230627538257977,
0.08765128254890442,
0.020444322377443314,
-0.023863602429628372,
-0.004803232848644257,
0.009830369614064693,
-0.016141895204782486,
-0.02389586716890335,
0.014832894317805767,
0.011697923764586449,
0.0032034062314778566,
0.049463845789432526,
-0.009628566913306713,
0.022106217220425606,
0.03535441681742668,
0.017640039324760437,
-0.08026380091905594,
0.0585256926715374,
-0.02666878141462803,
0.022429270669817924,
0.034837864339351654,
0.07297708839178085,
-0.06777555495500565,
0.03691926971077919,
-0.05618009716272354,
-0.05895215645432472,
0.05393066629767418,
-0.04809858277440071,
-0.03206151723861694,
0.07087598741054535,
0.018957536667585373,
-0.015269758179783821,
-0.06451360136270523,
0.019884025678038597,
0.008280253037810326,
-0.013320938684046268,
0.06006990373134613,
0.06041407957673073,
-0.08117309957742691,
0.0066640242002904415,
0.011332777328789234,
-0.0006507021025754511,
0.011323499493300915,
0.025860192254185677,
-0.04018465429544449,
0.027038756757974625,
-0.011713237501680851,
0.0067230165004730225,
-0.01742442324757576,
0.03055816888809204,
0.02417844906449318,
-0.01112006139010191,
0.0183438491076231,
-0.03903541341423988,
-0.01014508493244648,
0.006807531695812941,
-0.03409966453909874,
0.02953837439417839,
-0.002512900857254863,
-0.02727331779897213,
-0.012424930930137634,
-0.03610480576753616,
-0.02151728980243206,
0.01313172746449709,
0.017547650262713432,
-0.05957421287894249,
0.0037917292211204767,
-0.0006800027331337333,
-0.012389319948852062,
-0.018963418900966644,
-0.021914945915341377,
0.03538809344172478,
0.03087705746293068,
0.05830937251448631,
0.09697233140468597,
-0.02540862374007702,
0.008672562427818775,
-0.03301257640123367,
0.0087087107822299,
-0.020985350012779236,
0.03556825593113899,
-0.022679707035422325,
-0.03406323865056038,
-0.010496360249817371,
-0.0078034899197518826,
0.0053347195498645306,
-0.031741898506879807,
0.05052595213055611,
-0.0032365384977310896,
-0.04737015813589096,
0.05134700983762741,
-0.05836349353194237,
0.01839667744934559,
0.05973105877637863,
0.01586439646780491,
0.009585860185325146,
0.046107176691293716,
-0.05549049749970436,
-0.013922330923378468,
0.006693973205983639,
0.03414082154631615,
-0.03139390051364899,
-0.017460322007536888,
0.016354426741600037,
0.007572532631456852,
0.00870600063353777,
0.031344398856163025,
-0.0026686463970690966,
-0.016281848773360252,
0.03882724791765213,
0.04380633682012558,
-0.05448715016245842,
0.059796009212732315,
-0.029423633590340614,
-0.02248096466064453,
-0.05487292259931564,
0.020886393263936043,
-0.012590042315423489,
0.03231706842780113,
-0.0011867424473166466,
0.06327219307422638,
-0.028763337060809135,
-0.020515581592917442,
-0.0116273183375597,
-0.021114742383360863,
0.023538118228316307,
0.03444366157054901,
-0.007136196829378605,
0.03118634968996048,
-0.044081948697566986,
-0.05542197450995445,
0.047054391354322433,
0.03546072170138359,
-0.002452599350363016,
-0.06960075348615646,
0.02230563759803772,
-0.07341630011796951,
0.03296696022152901,
0.004143367521464825,
0.010279926471412182,
-0.022669265046715736,
0.03625987470149994,
-0.06297893822193146,
-0.03146691620349884,
-0.06485868245363235,
-0.010614856146275997,
0.05724183842539787,
0.05521921068429947,
0.012582892552018166,
0.03526350483298302,
-0.026850169524550438,
-0.015239644795656204,
-0.030982695519924164,
-0.04373016580939293,
-0.023353667929768562,
0.002880070125684142,
0.0429256334900856,
-0.05708081275224686,
0.00787604134529829,
-0.026449108496308327,
0.024645576253533363,
-0.00956374779343605,
-0.06658836454153061,
-0.001182679319754243,
0.003662645583972335,
0.04995555430650711,
0.002398346085101366,
-0.02239323779940605,
0.0685354545712471,
-0.014878958463668823,
0.011835486628115177,
-0.0020404017996042967,
-0.02005501091480255,
-0.011630058288574219,
0.0190893542021513,
0.08037558943033218,
0.009343051351606846,
0.02127944678068161,
0.03314583748579025,
-0.06714050471782684,
0.029855582863092422,
0.027429768815636635,
-0.04671400785446167,
0.007370856124907732,
-0.012126438319683075,
-0.005985885858535767,
0.014037109911441803,
-0.02229299396276474,
0.025338703766465187,
-0.02114519104361534,
-0.04936888813972473,
0.014342359267175198,
-0.09680798649787903,
-0.038066864013671875,
-0.018490560352802277,
0.09205380082130432,
-0.03188551962375641,
0.01811598241329193,
-0.006556481588631868,
0.030579542741179466,
0.030942797660827637,
0.026705065742135048,
-0.0200902558863163,
-0.00003726888098753989,
0.008210928179323673,
-0.058911681175231934,
0.030948393046855927,
-0.0009532980620861053,
0.01476317085325718,
-0.048429764807224274,
0.015691889449954033,
0.011682250536978245,
-0.017107531428337097,
-0.009591441601514816,
-0.06634889543056488,
0.01890423335134983,
0.03708023950457573,
-0.003834000090137124,
-0.0005771465366706252,
0.0015325330896303058,
0.06353065371513367,
0.008925551548600197,
0.004197848029434681,
0.016867363825440407,
-0.05156839266419411,
0.021023986861109734,
0.013070526532828808,
0.032792828977108,
0.0011200587032362819,
-0.030050083994865417,
0.010452990420162678,
0.02966098114848137,
0.0018063567113131285,
-0.04459988325834274,
0.03466496616601944,
-0.05931621044874191,
0.014334961771965027,
-0.016872458159923553,
0.0645148977637291,
-0.011414424516260624,
-0.008319977670907974,
-0.045804064720869064,
0.02358029969036579,
-0.01661214977502823,
-0.014680825173854828,
-0.029722148552536964,
-0.018810538575053215,
-0.02116634137928486,
-0.05659704655408859,
-0.0173236895352602,
0.03573661297559738,
-0.01674085110425949,
-0.0030259699560701847,
0.013534809462726116,
-0.030128968879580498,
0.010252625681459904,
-0.005317772272974253,
0.002964949468150735,
0.01695900596678257,
0.028897756710648537,
0.045735329389572144,
-0.021032849326729774,
-0.012312310747802258,
0.025089770555496216,
0.042839862406253815,
-0.019260285422205925,
-0.006773791741579771,
-0.002170907100662589,
-0.020479707047343254,
0.0002650087990332395,
-0.01849290542304516,
-0.018565744161605835,
-0.0403573103249073,
0.04589100182056427,
-0.005318159237504005,
-0.016867078840732574,
-0.026665804907679558,
0.026925332844257355,
0.04070743918418884,
-0.03209788352251053,
-0.01752655953168869,
0.015200880356132984,
-0.05389532074332237,
-0.00124835385940969,
0.02248658798635006,
0.03223457187414169,
-0.003572891466319561,
0.024542443454265594,
-0.04665495082736015,
0.04473835602402687,
0.016745280474424362,
0.02641575038433075,
0.038734372705221176,
0.012871935963630676,
0.016130436211824417,
0.014795779250562191,
-0.07943140715360641,
0.025597356259822845,
-0.04595581814646721,
-0.09335815161466599,
-0.08193018287420273,
-0.05261368304491043,
0.0037614803295582533,
0.052836839109659195,
0.01419773604720831,
-0.0718793123960495,
-0.001996503444388509,
0.06845318526029587,
-0.08293513208627701,
-0.043214961886405945,
0.07896407693624496,
0.0017464306438341737,
0.0024326287675648928,
0.0735035240650177,
0.0006210546707734466,
-0.04764507710933685,
0.006612853612750769,
-0.03489522263407707,
0.030375586822628975,
-0.013244282454252243,
-0.01508945133537054,
0.025670653209090233,
0.0028000890742987394,
0.015306863002479076,
-0.07010096311569214,
-0.052403662353754044,
-0.02324841357767582,
-0.007787630893290043,
-0.07682547718286514,
0.014492194168269634,
-0.04698333516716957,
0.02613442949950695,
0.03498649597167969,
-0.016393957659602165,
-0.003988018725067377,
-0.011609384790062904,
-0.05514250323176384,
-0.011069218628108501,
0.029736872762441635,
-0.03937757387757301,
-0.03667638450860977,
-0.0541921891272068,
-0.01724208891391754,
0.03799806162714958,
0.07299905270338058,
-0.012654478661715984,
-0.028518397361040115,
-0.01568957418203354,
-0.04958772286772728,
0.02180277556180954,
-0.10230516642332077,
-0.017277777194976807,
0.06363936513662338,
-0.06841500848531723,
0.025377916172146797,
-0.028007688000798225,
0.0657537505030632,
-0.013409595005214214,
-0.00407666340470314,
-0.038719210773706436,
-0.045318908989429474,
0.05920136719942093,
-0.039528943598270416,
0.005192157346755266,
0.034984178841114044,
-0.021439079195261,
-0.015137530863285065,
-0.07166390120983124,
0.0544247180223465,
0.03809786215424538,
0.0841502994298935,
0.031816206872463226,
-0.013425461947917938,
0.023284612223505974,
0.06130404397845268,
0.055920351296663284,
0.0022819754667580128,
-0.030230941250920296,
0.03579891100525856,
0.03676474466919899,
-0.0003487145877443254,
-0.01360544003546238,
-0.0053533450700342655,
0.0819956362247467,
-0.019530709832906723,
0.00003328627281007357,
0.022410923615098,
-0.024772288277745247,
-0.03331835940480232,
-0.0057357302866876125,
-0.06421694159507751,
-0.050377484411001205,
-0.012921947985887527,
0.019152823835611343,
-0.056756533682346344,
0.016268989071249962,
-0.05121582746505737,
-0.02797596901655197,
0.04283009469509125,
-0.01377957221120596,
0.052395034581422806,
0.025090346112847328,
-0.021752897650003433,
0.04634303227066994,
-0.02682468481361866,
-0.03975287824869156,
0.046176403760910034,
0.05085325986146927,
-0.027455169707536697,
-0.022648749873042107,
-0.04435070604085922,
0.004665103275328875,
0.07583677768707275,
0.019863186404109,
0.06867839395999908,
-0.06015189737081528,
0.026552237570285797,
-0.05758526921272278,
-0.039468914270401,
-0.0016275022644549608,
-0.04226420447230339,
0.05147561803460121,
0.07264448702335358,
0.023572245612740517,
-0.004356497433036566,
-0.030798308551311493,
0.008494354784488678,
-0.025887586176395416,
-0.039783068001270294,
0.032541804015636444,
0.018499230965971947,
0.0034578940831124783,
0.007395591586828232,
0.011839783750474453,
0.0352621003985405,
-0.07481110095977783,
0.05098453164100647,
-0.04261591657996178,
0.028330123052001,
0.07988397032022476,
0.0015584098873659968,
0.017044946551322937,
0.035889092832803726,
-0.02288241684436798,
0.008277778513729572,
0.045540712773799896,
-0.025184156373143196,
0.05780210718512535,
0.05592651292681694,
0.01655416563153267,
0.03893636539578438,
-0.01897512376308441,
-0.031205369159579277,
0.003035220317542553,
0.020973823964595795,
-0.006435881834477186,
-0.02833876945078373,
0.02992810681462288,
0.03711910545825958,
0.031695302575826645,
-0.06472014635801315,
-0.009238671511411667,
0.02121848240494728,
-0.015300802886486053,
-0.02007276937365532,
0.005136366002261639,
0.037140727043151855,
-0.0012520650634542108,
-0.07519017159938812,
-0.007003500126302242,
-0.0030838095117360353,
0.03815969079732895,
-0.021083854138851166,
-0.03529893979430199,
0.0026695383712649345,
0.046106018126010895,
-0.03158444166183472,
0.019628779962658882,
0.06354747712612152,
0.03254212439060211,
0.030299661681056023,
0.04342612251639366,
-0.02883199229836464,
0.015468847937881947,
-0.02564670331776142,
0.032231055200099945,
0.00943584181368351,
0.051983319222927094,
-0.02956179343163967,
0.021900108084082603,
-0.05359555780887604,
0.011279860511422157,
-0.008591839112341404,
0.01121910847723484,
-0.04811371490359306,
-0.0036736978217959404,
-0.010382497683167458,
0.013673428446054459,
0.032156817615032196,
-0.009493584744632244,
-0.026995597407221794,
0.006516920868307352,
0.02537436969578266,
0.0806364119052887,
0.059104982763528824,
0.03125740960240364,
-0.04103934392333031,
0.017901942133903503,
-0.014414179138839245,
-0.05482035130262375,
0.005537064746022224,
-0.019481783732771873,
-0.01392716821283102,
-0.020149290561676025,
0.06048443913459778,
-0.07870051264762878,
-0.015541192144155502,
0.044504314661026,
0.013177724555134773,
-0.01604313775897026,
-0.00926461722701788,
-0.005763491149991751,
-0.018121950328350067,
0.05043414235115051,
-0.051224760711193085,
-0.00644946051761508,
-0.03673572838306427,
0.0275176502764225,
0.009074431844055653,
0.06477104127407074,
-0.047497257590293884,
-0.03264482691884041,
0.032815657556056976,
-0.031984128057956696,
-0.009976457804441452,
-0.026002487167716026,
0.05441876873373985,
-0.012275608256459236,
0.031155196949839592,
-0.020993547514081,
0.004451128654181957,
0.01076949667185545,
0.013166623190045357,
0.03910611569881439,
-0.024679673835635185,
0.006950167007744312,
-0.03408220410346985,
-0.007178972940891981,
0.042979370802640915,
0.02789105474948883,
-0.09604252129793167,
-0.024373440071940422,
0.002343422034755349,
-0.010502421297132969,
0.028833504766225815,
-0.011224653571844101,
-0.01435071136802435,
-0.022592952474951744,
-0.05444156751036644,
0.03815348818898201,
-0.009362446144223213,
0.01033091451972723,
0.025001203641295433,
-0.027760455384850502,
-0.03116687759757042,
-0.031373053789138794,
-0.08708056807518005,
-0.02171645127236843,
0.019812798127532005
] |
<p>Say there was some situation where you have a lot of subatomic particles interacting with each other and decided to draw (say, by joining Feynmann diagrams) those interactions- so that you got some sort of (?directed) graph... what kind of network would you obtain? Would it be scale-free? Would it be a complex network similar to a social network? What properties would it have?</p> | g6569 | [
0.02969035506248474,
0.04982119798660278,
0.009786328300833702,
-0.006358083803206682,
0.0316331572830677,
-0.021228333935141563,
-0.032109931111335754,
-0.01976359263062477,
0.017715992406010628,
-0.07028331607580185,
-0.03515097126364708,
-0.0006400957936421037,
0.028444718569517136,
-0.012860927730798721,
-0.036379922181367874,
0.0224596057087183,
-0.03842819482088089,
-0.0057470486499369144,
-0.03945701941847801,
0.027152813971042633,
-0.033460911363363266,
-0.004399317782372236,
0.04762564226984978,
0.0071921623311936855,
0.00438748300075531,
-0.04125721752643585,
0.024927394464612007,
-0.033054761588573456,
-0.08058673143386841,
-0.02778194099664688,
-0.010267367586493492,
0.004853860940784216,
0.018853381276130676,
-0.002148962579667568,
-0.07452169805765152,
-0.019444918259978294,
-0.004288159776479006,
-0.003410921199247241,
0.021170800551772118,
0.024297425523400307,
-0.0062628332525491714,
0.014144696295261383,
-0.05432172492146492,
-0.05981040000915527,
0.016369745135307312,
0.032314151525497437,
0.004170180764049292,
0.012772906571626663,
0.01519610732793808,
-0.0067805633880198,
-0.018376590684056282,
0.03572748601436615,
-0.0418611541390419,
0.00590594531968236,
0.04178513586521149,
0.03740887716412544,
0.04459337145090103,
-0.022874346002936363,
0.08022750169038773,
-0.0061287228018045425,
-0.0013879064936190844,
0.028794733807444572,
0.013189352117478848,
0.02114207297563553,
0.00927624199539423,
-0.0005636424757540226,
-0.04529261216521263,
0.02169969491660595,
0.04498347267508507,
-0.001990425633266568,
-0.02558276616036892,
-0.02928442694246769,
0.029026314616203308,
0.005839634221047163,
0.012289067730307579,
0.0957384929060936,
-0.04678531736135483,
0.01389317400753498,
0.05576309189200401,
0.003170617623254657,
-0.0728176087141037,
-0.0661589577794075,
0.010541828349232674,
-0.053208883851766586,
0.08879387378692627,
-0.03609253093600273,
-0.030938617885112762,
-0.07355161011219025,
-0.01794935017824173,
0.044652149081230164,
0.029140006750822067,
-0.0176534503698349,
0.004525542259216309,
-0.043772775679826736,
0.0047423336654901505,
-0.023261241614818573,
-0.0019087506225332618,
-0.008921023458242416,
-0.03781111538410187,
-0.033483535051345825,
-0.0031411596573889256,
-0.04007092863321304,
0.010951090604066849,
0.0014491553883999586,
-0.05472494661808014,
-0.021167397499084473,
-0.013498782180249691,
-0.0051437984220683575,
0.057553283870220184,
0.02961985021829605,
-0.01863054931163788,
-0.06553268432617188,
-0.01006556861102581,
0.04198969900608063,
0.046340636909008026,
-0.053394243121147156,
0.007724445778876543,
-0.014601116068661213,
0.040158793330192566,
0.05316254869103432,
0.028528261929750443,
-0.06273971498012543,
0.02082126960158348,
-0.03772474452853203,
-0.0321480818092823,
0.04124665632843971,
0.02044462040066719,
0.043159618973731995,
-0.05257760360836983,
-0.0655963122844696,
0.03864806890487671,
-0.049824308604002,
-0.043909523636102676,
0.0633111521601677,
-0.06879076361656189,
0.02355099469423294,
-0.06772365421056747,
-0.07096344977617264,
-0.019020307809114456,
-0.07393700629472733,
0.019459368661046028,
-0.025060992687940598,
-0.0679885596036911,
-0.014325950294733047,
-0.0075776828452944756,
-0.05123463273048401,
-0.00011296235607005656,
-0.029234305024147034,
0.023570777848362923,
0.01975219137966633,
-0.00895534548908472,
0.02333763800561428,
-0.038142550736665726,
-0.044616151601076126,
0.02533400058746338,
-0.010416368022561073,
0.05638314411044121,
-0.011786905117332935,
0.023519521579146385,
-0.04696166142821312,
0.007754728198051453,
-0.021564988419413567,
0.0010702447034418583,
-0.004480043426156044,
-0.03532704338431358,
-0.03922557085752487,
0.06688801199197769,
-0.03789447247982025,
0.005048059858381748,
0.015812944620847702,
-0.04243079945445061,
0.0054666101932525635,
-0.027305148541927338,
0.04598834738135338,
-0.004224847536534071,
0.020739290863275528,
-0.047653768211603165,
0.043325286358594894,
0.08724453300237656,
0.03549070283770561,
0.04230243340134621,
0.005520396865904331,
0.01952669769525528,
-0.04784952476620674,
0.0030165258795022964,
0.012605921365320683,
-0.0351499505341053,
-0.0022491414565593004,
0.03482716903090477,
-0.021022377535700798,
-0.008793543092906475,
-0.021851759403944016,
-0.0060089100152254105,
-0.02013608254492283,
0.029919035732746124,
-0.03975733369588852,
0.026624327525496483,
-0.06292221695184708,
0.06317489594221115,
-0.017713263630867004,
-0.008562516421079636,
0.02767295390367508,
-0.009677140973508358,
0.02523629739880562,
0.037727538496255875,
0.028254061937332153,
-0.05491023138165474,
0.018720557913184166,
0.037451185286045074,
0.014576178044080734,
0.05304818972945213,
-0.025605084374547005,
0.024556664749979973,
0.0014531641500070691,
-0.05210110917687416,
-0.05128176882863045,
-0.03318227082490921,
0.002148216590285301,
0.020911993458867073,
0.03227061778306961,
0.02057383581995964,
-0.046785496175289154,
-0.011197790503501892,
-0.015849504619836807,
0.0687074214220047,
-0.023417940363287926,
-0.030037492513656616,
0.013277456164360046,
-0.03840019926428795,
0.03396010026335716,
-0.011387021280825138,
0.022303782403469086,
-0.0039078486151993275,
-0.05293148756027222,
-0.023352256044745445,
0.013660254888236523,
-0.0013905494706705213,
-0.008142653852701187,
-0.031372200697660446,
0.01763303205370903,
0.008364636451005936,
-0.055011164397001266,
0.0025733003858476877,
-0.024117646738886833,
0.00960988737642765,
-0.011417718604207039,
0.02716776542365551,
0.059314921498298645,
-0.025852292776107788,
0.01711377687752247,
0.08030281960964203,
-0.009689935483038425,
-0.003526306012645364,
0.011663916520774364,
0.006377680692821741,
0.048111140727996826,
0.01100864913314581,
0.051899176090955734,
-0.032240789383649826,
-0.020626869052648544,
-0.027375590056180954,
-0.055350396782159805,
-0.029279449954628944,
-0.005959453992545605,
0.010713057592511177,
-0.03801656886935234,
0.047950707376003265,
-0.03683727607131004,
-0.042306553572416306,
0.001794734736904502,
-0.04839747026562691,
0.008748323656618595,
0.015836019068956375,
-0.017438329756259918,
0.03922213613986969,
0.08315488696098328,
0.03280383720993996,
0.021389897912740707,
0.01616097427904606,
0.01855836994946003,
0.021828748285770416,
0.039198171347379684,
-0.014086293056607246,
0.07336512207984924,
0.029846802353858948,
-0.037957482039928436,
0.03416081890463829,
0.00759406853467226,
-0.039168503135442734,
0.017760545015335083,
-0.00999822374433279,
-0.03363485261797905,
-0.003391875885426998,
0.007136175874620676,
0.015407437458634377,
-0.02264765463769436,
0.029663274064660072,
-0.01354192104190588,
-0.030202701687812805,
-0.014540627598762512,
-0.02478671446442604,
0.014379002153873444,
0.07742851972579956,
0.018535666167736053,
-0.023701516911387444,
-0.050443023443222046,
-0.1024903878569603,
0.010994172655045986,
0.006011987570673227,
-0.02277872897684574,
-0.02412208914756775,
0.056809648871421814,
0.01073782704770565,
0.06305301189422607,
0.03281719982624054,
0.0039467886090278625,
0.06018794700503349,
0.06090601161122322,
0.0074394200928509235,
-0.07044532150030136,
0.027690786868333817,
0.023818111047148705,
0.0542038157582283,
-0.04276398569345474,
-0.01558183878660202,
0.03547496721148491,
-0.010271388106048107,
-0.0216253362596035,
-0.021831462159752846,
-0.007732539437711239,
-0.04613494873046875,
-0.053360067307949066,
0.044911906123161316,
0.010893912054598331,
-0.06689337641000748,
-0.05124164745211601,
-0.031101463362574577,
-0.0044503784738481045,
0.04183965176343918,
0.01917162910103798,
-0.008491387590765953,
-0.03435509651899338,
-0.07825358957052231,
-0.050392378121614456,
-0.001810822170227766,
0.005152760539203882,
0.013946428894996643,
-0.034475989639759064,
0.04031635820865631,
-0.05974333733320236,
-0.014576821587979794,
-0.024368634447455406,
-0.019597945734858513,
-0.04565832391381264,
0.056406326591968536,
-0.018818864598870277,
0.0008225374040193856,
0.02058253064751625,
0.001986426068469882,
0.006796190049499273,
0.002562212757766247,
0.012978125363588333,
-0.08190401643514633,
-0.016730062663555145,
-0.013729983009397984,
0.013985197059810162,
-0.026444941759109497,
0.006432024296373129,
0.06358083337545395,
0.0071865953505039215,
0.020346205681562424,
-0.0131344273686409,
-0.020276691764593124,
0.031995370984077454,
-0.02739100530743599,
0.02509297803044319,
-0.02434675768017769,
-0.0176121536642313,
0.019623009487986565,
-0.001298298710025847,
-0.030792029574513435,
0.041210658848285675,
-0.0016353745013475418,
0.025427917018532753,
0.03615756705403328,
0.031520482152700424,
-0.04061507806181908,
0.003453219309449196,
-0.0574159175157547,
0.07426098734140396,
-0.02656649611890316,
-0.01664581336081028,
0.02383553422987461,
-0.00912350695580244,
0.02666461654007435,
-0.020675519481301308,
0.04623600095510483,
-0.025350144132971764,
0.021644432097673416,
0.021868864074349403,
0.016781941056251526,
-0.02364841103553772,
0.013944262638688087,
-0.06788572669029236,
0.04886964336037636,
-0.097396619617939,
-0.03450081869959831,
-0.009797466918826103,
0.0231170617043972,
-0.015850868076086044,
-0.00781707651913166,
-0.01414670143276453,
0.05775681883096695,
-0.004483019933104515,
-0.015129486098885536,
-0.00838763453066349,
0.0012975961435586214,
-0.04152952879667282,
-0.011254847049713135,
0.023064324632287025,
-0.023060530424118042,
0.039212170988321304,
0.006138708908110857,
0.042875535786151886,
-0.024302886798977852,
-0.020776882767677307,
-0.024928545579314232,
-0.010217363946139812,
-0.0498444028198719,
0.01331998873502016,
0.004487201105803251,
0.01780928298830986,
-0.026652971282601357,
-0.026114175096154213,
-0.05307236313819885,
-0.007520867511630058,
-0.020795810967683792,
-0.015573468990623951,
0.014567023143172264,
0.038684237748384476,
0.019139397889375687,
0.03173244744539261,
0.05132335424423218,
-0.051382094621658325,
0.03358488902449608,
0.050694629549980164,
-0.034320391714572906,
-0.03236687183380127,
-0.09945414960384369,
0.016712576150894165,
-0.01473546214401722,
0.008091912604868412,
-0.07834096252918243,
-0.029249219223856926,
-0.04251188412308693,
-0.02768237516283989,
0.0049718571826815605,
0.045503780245780945,
0.03174775093793869,
-0.02552218735218048,
-0.10245601087808609,
0.026566792279481888,
0.0059571294113993645,
0.011689314618706703,
0.018444299697875977,
-0.04203954339027405,
-0.0030092778615653515,
-0.006383346393704414,
-0.035947538912296295,
-0.03519831970334053,
0.0033870080951601267,
0.023738998919725418,
0.07088322192430496,
0.05479169264435768,
-0.043587565422058105,
-0.02901328168809414,
-0.019334867596626282,
0.03580671176314354,
0.00008944646833697334,
-0.049116410315036774,
0.027645602822303772,
0.04760603979229927,
0.006796494126319885,
-0.013435771688818932,
-0.005376358982175589,
0.01838611252605915,
-0.02075457200407982,
0.028007930144667625,
-0.03402025252580643,
-0.002662262413650751,
0.0012655967148020864,
-0.01361445989459753,
-0.02272096276283264,
0.03591984882950783,
-0.0515279658138752,
-0.08156370371580124,
-0.027060577645897865,
-0.0020604324527084827,
0.10727006942033768,
0.023818261921405792,
0.00884543638676405,
0.06996213644742966,
-0.05190012976527214,
-0.05131594091653824,
-0.015650879591703415,
0.03406229987740517,
0.06896116584539413,
-0.0688435286283493,
-0.007289917673915625,
0.009518636390566826,
-0.020133916288614273,
-0.010887481272220612,
-0.02963429130613804,
0.02526218257844448,
-0.005178574472665787,
0.030157718807458878,
-0.021136494353413582,
-0.04342789947986603,
-0.040610939264297485,
0.027680711820721626,
0.03276703506708145,
-0.01770893484354019,
0.018522292375564575,
-0.05829915776848793,
-0.03786323592066765,
0.03813653439283371,
-0.0971423089504242,
0.0347781702876091,
0.0014141469728201628,
0.08736533671617508,
0.03484395518898964,
-0.0041330005042254925,
-0.04110819473862648,
0.035848237574100494,
0.018680542707443237,
0.00043530575931072235,
0.019876163452863693,
0.05357348546385765,
0.06952835619449615,
0.013995871879160404,
0.05772017687559128,
-0.02022586762905121,
-0.009124625474214554,
0.03270183876156807,
-0.01182458084076643,
-0.05183958634734154,
0.04230153560638428,
0.0519607774913311,
0.033873606473207474,
0.03229137137532234,
-0.033403024077415466,
-0.03870571404695511,
0.004501551855355501,
0.02186592109501362,
-0.04105350002646446,
0.008142668753862381,
-0.012420975603163242,
0.030733764171600342,
0.017553122714161873,
0.06060023605823517,
0.03494172915816307,
0.0027754337061196566,
0.0049491217359900475,
-0.045989640057086945,
-0.030967118218541145,
0.007528490386903286,
-0.08591446280479431,
0.005083282478153706,
0.04240081459283829,
0.054734837263822556,
0.012557242065668106,
-0.047439396381378174,
0.024090241640806198,
0.0014036813518032432,
-0.014540920965373516,
-0.02037687599658966,
0.04391874000430107,
0.01921207830309868,
-0.003152022836729884,
0.011148049496114254,
-0.018709085881710052,
-0.013078317046165466,
0.03452443704009056,
-0.02342987433075905,
-0.005521257873624563,
0.050020381808280945,
0.0005363739328458905,
0.011993655934929848,
0.007344376761466265,
0.017107531428337097,
-0.027086863294243813,
-0.0029117166996002197,
-0.06880144774913788,
-0.042371299117803574,
0.009978278540074825,
-0.011388421058654785,
0.02533685974776745,
-0.01349837239831686,
-0.02346723899245262,
0.09362547099590302,
-0.008469093590974808,
0.03395852446556091,
-0.006931688170880079,
0.028168024495244026,
0.03107733465731144,
0.08679816126823425,
0.04157477244734764,
0.05919038876891136,
-0.01368128415197134,
-0.04090544953942299,
-0.01583193987607956,
0.048456352204084396,
0.005629997234791517,
0.001080846879631281,
0.091163270175457,
-0.04595815762877464,
0.026565980166196823,
-0.051473211497068405,
-0.029140232130885124,
-0.06098966673016548,
0.0020456735510379076,
-0.04854537174105644,
0.013052462600171566,
-0.02035132795572281,
0.015320966951549053,
0.018714824691414833,
-0.02158430777490139,
0.03234440088272095,
0.04891917109489441,
0.004919060505926609,
0.01515328511595726,
0.051890015602111816,
0.06287578493356705,
0.01747131161391735,
-0.014589107595384121,
0.031581487506628036,
-0.03729923442006111,
0.01837894879281521,
0.07851143181324005,
0.019544975832104683,
-0.012167045846581459,
0.02971849963068962,
0.04705655574798584,
0.006587176583707333,
0.019170138984918594,
-0.023263955488801003,
0.007593370042741299,
0.0373089499771595,
-0.025665033608675003,
0.024905670434236526,
0.02338440716266632,
-0.02032858319580555,
-0.04433785378932953,
0.0036425194703042507,
-0.009432842954993248,
-0.07820300757884979,
-0.046745967119932175,
0.04004824534058571,
0.0169199388474226,
-0.04243004694581032,
-0.08811687678098679,
0.024314220994710922,
0.009402884170413017,
-0.004222244024276733,
0.021461207419633865,
0.04536094143986702,
0.009396795183420181,
0.013847032561898232,
-0.045085374265909195,
-0.009100033901631832,
-0.039743244647979736,
-0.0335901714861393,
-0.02979285456240177,
0.05763379484415054,
-0.005777232814580202,
-0.04684546962380409,
0.02526143752038479,
0.0039047624450176954,
0.012760404497385025,
0.0062467739917337894,
0.01578621380031109,
0.02566005103290081,
0.04790323227643967,
-0.00020377534383442253,
-0.0071968683041632175,
0.04484818875789642,
-0.009210631251335144,
0.0027281413786113262,
-0.00014826850383542478,
-0.06449902802705765,
-0.0027568682562559843,
0.04020769149065018,
-0.018966350704431534,
-0.009068764746189117,
0.0053655714727938175,
0.014421059750020504,
0.008064717054367065,
0.04020882025361061,
0.04620911926031113,
0.07751858234405518,
0.04454893618822098,
0.03916657716035843,
-0.022572513669729233,
-0.005470298230648041,
0.03756635636091232,
0.030085237696766853,
0.004248512908816338,
-0.03714984282851219,
-0.006270348560065031,
-0.06591132283210754,
-0.015682943165302277,
0.08383675664663315,
0.04995174705982208,
0.08665087074041367,
-0.012909023091197014,
0.027001183480024338,
0.0013494928134605289,
-0.019397761672735214,
0.007154139690101147,
0.060700923204422,
-0.032950837165117264,
0.02391050197184086,
-0.011775730177760124,
-0.025003336369991302,
-0.0007386091747321188,
-0.008709081448614597,
-0.03522301837801933,
-0.05324818938970566,
-0.007882189005613327,
0.03318146988749504,
0.03470442816615105,
0.0011283529456704855,
-0.03883541002869606,
0.053276512771844864,
-0.015823934227228165,
-0.061505451798439026,
-0.0030602733604609966,
0.008158648386597633,
-0.0161494929343462,
-0.029681218788027763,
0.0031151073053479195,
-0.013197533786296844,
0.008635975420475006,
-0.010500233620405197,
0.059072017669677734,
-0.018793394789099693,
-0.02813107706606388,
-0.021227093413472176,
0.05579402297735214,
0.005061394069343805,
-0.035133007913827896,
-0.02111017517745495,
0.053059786558151245,
-0.022499023005366325,
0.05219433084130287,
0.0007158211665228009,
0.008721851743757725,
0.034090861678123474,
0.0030242688953876495,
0.013613516464829445,
-0.0053849839605391026,
0.023319322615861893,
-0.057525716722011566,
0.0774330347776413,
-0.06393903493881226,
0.044707462191581726,
0.0039019424002617598,
0.038173872977495193
] |
<p>Imagine a bar </p>
<p>spinning like a helicopter propeller,</p>
<p>At $\omega$ rad/s because the extremes of the bar goes at speed</p>
<p>$$V = \omega * r$$</p>
<p>then we can reach near $c$ (speed of light)
applying some <strong>finite</strong> amount of energy
just doing </p>
<p>$$\omega = V / r$$</p>
<p>The bar should be long, low density, strong to minimize the
amount of energy needed</p>
<p>For example a $2000\,\mathrm{m}$ bar</p>
<p>$$\omega = 300 000 \frac{\mathrm{rad}}{\mathrm{s}} = 2864789\,\mathrm{rpm}$$</p>
<p>(a dental drill can commonly rotate at $400000\,\mathrm{rpm}$)</p>
<p>$V$ (with dental drill) = 14% of speed of light.</p>
<p>Then I say this experiment can be really made
and bar extremes could approach $c$.</p>
<p>What do you say? </p>
<p><strong>EDIT</strong>:</p>
<p>Our planet is orbiting at sun and it's orbiting milky way, and who knows what else, then any Earth point have a speed of 500 km/s or more agains CMB.</p>
<p>I wonder if we are orbiting something at that speed then there would be detectable relativist effect in different direction of measurements, simply extending a long bar or any directional mass in different galactic directions we should measure mass change due to relativity, simply because $V = \omega * r$</p>
<p>What do you think?</p> | g121 | [
0.0002992994268424809,
0.028541600331664085,
0.0007578777731396258,
-0.0041016265749931335,
0.07042388617992401,
0.020075399428606033,
0.03450152650475502,
0.04424915090203285,
-0.03991790860891342,
-0.03205393627285957,
0.0659453496336937,
0.01647229865193367,
-0.01534285955131054,
0.0057978699915111065,
0.02775840274989605,
-0.039894621819257736,
0.02189434878528118,
-0.06931838393211365,
0.04411516338586807,
0.0723002478480339,
0.0008472837507724762,
-0.040633101016283035,
-0.0037133125588297844,
-0.0031012401450425386,
-0.01307513564825058,
0.001955146435648203,
0.03199896588921547,
-0.015100889839231968,
-0.0705094188451767,
0.04347509518265724,
-0.03881236910820007,
-0.07555165141820908,
-0.0033294076565653086,
-0.013973730616271496,
-0.014558791182935238,
-0.0988464504480362,
0.0003928857622668147,
0.05261551961302757,
0.0013661159900948405,
-0.01100179087370634,
-0.045899536460638046,
0.01231261808425188,
0.030240699648857117,
-0.030752547085285187,
0.039765723049640656,
0.00553659163415432,
0.05794022977352142,
0.00534867262467742,
0.03231725096702576,
-0.05647400766611099,
-0.0653587281703949,
-0.002243253169581294,
0.04107782989740372,
0.03535529226064682,
0.009995024651288986,
0.050946805626153946,
-0.005044497083872557,
-0.017443105578422546,
0.057843033224344254,
-0.005921129137277603,
-0.01355162262916565,
-0.036900535225868225,
0.028571726754307747,
0.004168007988482714,
-0.005949509795755148,
0.027358097955584526,
-0.012007330544292927,
-0.0007909281412139535,
0.011951749213039875,
-0.011688023805618286,
0.032921914011240005,
-0.03033122979104519,
-0.026062069460749626,
-0.015689797699451447,
-0.06324440240859985,
0.012647831812500954,
-0.00027650941046886146,
-0.009211837314069271,
-0.0009875994874164462,
-0.006177206989377737,
-0.029228709638118744,
-0.03261449933052063,
-0.03465747833251953,
-0.01683845929801464,
0.05205874145030975,
-0.024293938651680946,
0.015191926620900631,
-0.020623769611120224,
0.01650167629122734,
0.0011035919887945056,
0.09858249127864838,
-0.07572652399539948,
0.08737324923276901,
0.021135587245225906,
-0.014040360227227211,
-0.06456554681062698,
0.01653764210641384,
0.06960024684667587,
-0.06104309856891632,
-0.0014675197890028358,
0.0017436760244891047,
0.022506875917315483,
-0.01729414612054825,
0.05565608665347099,
-0.024627994745969772,
-0.02504199557006359,
0.016541337594389915,
0.012905786745250225,
0.0012203669175505638,
-0.04245106875896454,
0.0012120018946006894,
-0.05175641551613808,
0.013586342334747314,
-0.03641800954937935,
-0.043076060712337494,
-0.018478771671652794,
0.09018352627754211,
-0.016422787681221962,
-0.007023911457508802,
0.061715930700302124,
0.10009138286113739,
0.020889626815915108,
-0.026491738855838776,
0.08114492148160934,
-0.01705395244061947,
0.013162089511752129,
0.01408146321773529,
-0.0027976869605481625,
0.01787242479622364,
-0.01686706207692623,
-0.03690730035305023,
0.01518484391272068,
-0.011690070852637291,
-0.0015139690367504954,
-0.019834177568554878,
0.012944867834448814,
-0.05402743071317673,
0.020176243036985397,
-0.007094257511198521,
-0.00043036480201408267,
-0.001935489010065794,
-0.02062220312654972,
0.0078102946281433105,
0.0017760891932994127,
-0.02951357699930668,
0.025904064998030663,
-0.03238477185368538,
0.0671287477016449,
0.0719514712691307,
0.023468922823667526,
0.010227885097265244,
0.053008247166872025,
0.009868750348687172,
0.0020361703354865313,
0.012901172041893005,
0.02609942853450775,
0.02278246358036995,
0.02685609459877014,
0.021614501252770424,
0.06034237891435623,
0.019549792632460594,
0.009095821529626846,
0.003941519185900688,
-0.04365845024585724,
-0.06793203204870224,
0.026045726612210274,
-0.005100992973893881,
0.006538847927004099,
0.012987582944333553,
-0.008966140449047089,
-0.10802336037158966,
-0.02966384030878544,
0.02607836201786995,
0.006759576499462128,
0.03255942091345787,
0.023303302004933357,
0.01078443881124258,
-0.008551589213311672,
-0.021838145330548286,
0.0488961823284626,
0.002601673360913992,
-0.03933728113770485,
0.02848653309047222,
-0.031090622767806053,
0.014440045692026615,
0.032866138964891434,
0.03569864109158516,
-0.02068150043487549,
-0.033566996455192566,
-0.034495968371629715,
-0.0029629687778651714,
-0.006802330259233713,
-0.014646019786596298,
0.0074775926768779755,
-0.023781249299645424,
0.05359119549393654,
0.040912263095378876,
-0.050710201263427734,
-0.04310661181807518,
0.06888409703969955,
-0.022014833986759186,
0.052819475531578064,
0.0392954982817173,
0.020079148933291435,
-0.0033351543825119734,
-0.052316244691610336,
0.0019440988544374704,
-0.013976461254060268,
0.019064990803599358,
0.027225429192185402,
0.1351460963487625,
0.011252771131694317,
-0.030967434868216515,
0.030871855095028877,
0.010845774784684181,
0.00619771471247077,
0.018160762265324593,
0.028527431190013885,
0.027533169835805893,
0.02996770478785038,
0.017992187291383743,
0.00009110421524383128,
0.020590031519532204,
0.005347845144569874,
-0.01917342282831669,
-0.04581904783844948,
-0.058058854192495346,
-0.027352644130587578,
0.049000080674886703,
0.005571604240685701,
0.005893345922231674,
0.06829095631837845,
0.061226192861795425,
0.018141349777579308,
0.05391762778162956,
0.0005185852060094476,
-0.0017052387120202184,
0.007406826596707106,
-0.03707977011799812,
0.006376804783940315,
0.045603375881910324,
-0.04330041632056236,
-0.057014092803001404,
-0.031158005818724632,
0.0012550265528261662,
-0.06830891966819763,
0.002345590153709054,
0.03624289855360985,
0.015531770884990692,
0.023353103548288345,
0.05319053679704666,
0.016023680567741394,
-0.03288937360048294,
0.014077947475016117,
0.014793282374739647,
-0.018429651856422424,
-0.027774285525083542,
0.0683235451579094,
-0.0849895104765892,
-0.036421969532966614,
-0.04322524741292,
0.02646471932530403,
0.002700354205444455,
-0.011377821676433086,
-0.025994641706347466,
-0.006367656867951155,
-0.04010181874036789,
-0.0037415619008243084,
-0.026100153103470802,
-0.005275551695376635,
-0.041492730379104614,
-0.013478069566190243,
0.039674606174230576,
0.02725064754486084,
0.00006551970000145957,
0.016010291874408722,
0.012750626541674137,
-0.028103496879339218,
0.01679306849837303,
0.004294015001505613,
-0.010289368219673634,
0.03579523041844368,
-0.06612462550401688,
0.009778606705367565,
-0.020896630361676216,
-0.01483162585645914,
-0.0019520382629707456,
-0.001390931662172079,
-0.05612002685666084,
0.024164985865354538,
0.026255924254655838,
0.011483142152428627,
0.0357716828584671,
0.0061824265867471695,
0.056016191840171814,
0.058906059712171555,
0.07177631556987762,
0.01861124485731125,
0.008867292664945126,
0.0031223874539136887,
0.020624009892344475,
-0.03348119929432869,
-0.03593062236905098,
0.04109000787138939,
-0.04794461652636528,
0.008887328207492828,
-0.03436914458870888,
-0.02723105065524578,
0.019302986562252045,
-0.0047141555696725845,
0.030800430104136467,
0.0704769715666771,
0.02452852763235569,
0.018580658361315727,
-0.06508670747280121,
0.005331291351467371,
-0.035745732486248016,
-0.005204963032156229,
0.010667462833225727,
-0.044708892703056335,
0.052077457308769226,
-0.06698215752840042,
-0.03176213428378105,
-0.04211971163749695,
0.03493289276957512,
0.02102208137512207,
-0.0339462049305439,
-0.036936186254024506,
-0.07721304893493652,
-0.011237331666052341,
0.052708931267261505,
0.07982850074768066,
-0.007337877061218023,
0.02862791158258915,
-0.06772603839635849,
-0.016999557614326477,
0.012463272549211979,
0.05100226402282715,
0.06581282615661621,
0.06661307066679001,
-0.026762695983052254,
-0.025748198851943016,
-0.017955908551812172,
0.004059091676026583,
0.002799655543640256,
0.06913003325462341,
-0.0024615481961518526,
0.01079302653670311,
-0.023531323298811913,
-0.022009020671248436,
0.022626278921961784,
-0.04010860621929169,
-0.021522000432014465,
-0.03346201032400131,
0.06884205341339111,
0.02485618367791176,
0.05603225529193878,
0.04763428494334221,
0.06270162016153336,
-0.060418568551540375,
0.0017585947643965483,
0.03810816630721092,
0.006516410503536463,
-0.009358738549053669,
-0.031991224735975266,
0.038185153156518936,
-0.01309483777731657,
0.021191729232668877,
-0.05064387992024422,
0.008522072806954384,
0.012362692505121231,
-0.03829047456383705,
-0.0054149869829416275,
-0.008238394744694233,
0.020795775577425957,
-0.024952640756964684,
0.01732008531689644,
0.027883470058441162,
0.006593378260731697,
0.03884375840425491,
0.025655442848801613,
-0.002583123743534088,
-0.009712609462440014,
-0.03989417850971222,
-0.061982277780771255,
0.02224596217274666,
-0.024165015667676926,
-0.044273409992456436,
-0.022461825981736183,
-0.012178987264633179,
-0.0013318895362317562,
-0.03170844539999962,
0.04035612568259239,
0.022319357842206955,
-0.010704009793698788,
-0.030030632391572,
0.058003585785627365,
-0.06999482959508896,
-0.06783581525087357,
0.022173358127474785,
-0.03763915225863457,
0.015868112444877625,
0.014920924790203571,
0.007877834141254425,
-0.08768266439437866,
-0.08039690554141998,
0.034670256078243256,
-0.02031782828271389,
-0.032277967780828476,
-0.0034746380988508463,
0.02223079837858677,
-0.06422857195138931,
0.002241650829091668,
-0.0755530372262001,
0.030408009886741638,
0.031378377228975296,
-0.015710564330220222,
-0.011551854200661182,
0.04679064825177193,
0.04921776056289673,
-0.020896868780255318,
0.07326066493988037,
0.008011672645807266,
-0.011737629771232605,
0.012803700752556324,
0.06346053630113602,
-0.003575066337361932,
-0.00744610046967864,
0.048071373254060745,
-0.00833978597074747,
0.035674821585416794,
-0.011867167428135872,
-0.0340767428278923,
0.007228825706988573,
-0.009401503019034863,
0.05637926608324051,
-0.007183460518717766,
0.017834920436143875,
0.005723467096686363,
0.0022857473231852055,
-0.017042353749275208,
0.002095677424222231,
0.024219369515776634,
-0.019204633310437202,
-0.03233543410897255,
0.07914264500141144,
-0.039841584861278534,
-0.04538724943995476,
-0.010548129677772522,
-0.01164034940302372,
-0.0740981251001358,
-0.003080120775848627,
0.005208468530327082,
0.035423923283815384,
0.03911937028169632,
-0.03922354429960251,
-0.014386658556759357,
0.05794944241642952,
0.037812378257513046,
0.07596118748188019,
-0.06876068562269211,
-0.003924235701560974,
0.04718368127942085,
-0.005374398082494736,
0.010561130940914154,
-0.011468390002846718,
-0.036284469068050385,
-0.07714367657899857,
-0.03899126872420311,
-0.013572687283158302,
-0.06536322832107544,
-0.0008113232324831188,
0.02082691714167595,
0.061660055071115494,
-0.035558927804231644,
0.008065969683229923,
0.01759413816034794,
-0.02900305949151516,
-0.03192973881959915,
-0.08066631108522415,
-0.07649468630552292,
-0.0008990535861812532,
0.02730601094663143,
-0.05491974949836731,
-0.02651957981288433,
-0.00018440881103742868,
-0.13195191323757172,
-0.0071314130909740925,
-0.0312368031591177,
-0.02157871052622795,
0.006891798228025436,
0.04001326858997345,
-0.039977654814720154,
-0.06444956362247467,
0.01322374027222395,
0.01814231462776661,
-0.03615803271532059,
-0.055893536657094955,
-0.029769157990813255,
-0.02786080539226532,
-0.034045081585645676,
0.06944797188043594,
-0.0294894278049469,
-0.0017625143518671393,
-0.07079005241394043,
0.04621215537190437,
0.023346461355686188,
0.023058127611875534,
-0.04100719094276428,
0.05114399269223213,
-0.05736716836690903,
0.025559036061167717,
0.03058028593659401,
-0.017167771235108376,
-0.02064727619290352,
-0.017996633425354958,
0.053797151893377304,
0.047934696078300476,
0.0376291498541832,
-0.08512528240680695,
-0.009966994635760784,
-0.020739642903208733,
0.05371775105595589,
-0.006984005216509104,
0.003298515686765313,
0.005868976470082998,
-0.026369864121079445,
0.020827507600188255,
0.020748067647218704,
-0.02671387605369091,
0.027620848268270493,
-0.02245977334678173,
0.04382087290287018,
-0.027686510235071182,
-0.039684269577264786,
-0.006205274257808924,
0.0612478032708168,
0.009825249202549458,
-0.021283704787492752,
-0.07094036787748337,
-0.009264971129596233,
-0.016935333609580994,
0.05159727483987808,
0.06549414992332458,
0.07341060787439346,
-0.005799423437565565,
-0.06902074068784714,
-0.010095205157995224,
0.04384704306721687,
-0.0063590994104743,
0.00661240192130208,
-0.011604436673223972,
-0.027181077748537064,
0.005909981671720743,
0.0028860196471214294,
0.018681585788726807,
0.00739454198628664,
-0.08534352481365204,
-0.038621366024017334,
-0.0347316712141037,
0.016211848706007004,
0.021008174866437912,
0.03683413192629814,
0.0386626273393631,
-0.0024894087109714746,
-0.06440093368291855,
0.04145136848092079,
-0.04665485769510269,
0.054162248969078064,
0.05419488996267319,
-0.048239246010780334,
0.0039020408876240253,
-0.03846229612827301,
-0.0014847646234557033,
0.06886273622512817,
-0.000841817120090127,
0.03315965086221695,
0.008581328205764294,
-0.0070029920898377895,
-0.023931866511702538,
-0.0028756738174706697,
-0.009346887469291687,
0.015682360157370567,
0.016413329169154167,
0.014272517524659634,
-0.006390996277332306,
-0.0007311075460165739,
0.022717289626598358,
0.019276434555649757,
-0.0904567688703537,
-0.00585465831682086,
-0.017200812697410583,
0.00391924474388361,
-0.06314809620380402,
-0.07350613921880722,
-0.022604867815971375,
0.01853089965879917,
-0.08493909239768982,
-0.03004981391131878,
0.001389473327435553,
-0.023702112957835197,
-0.02075088955461979,
0.02283303439617157,
0.019613657146692276,
0.010051356628537178,
-0.025664987042546272,
-0.012658655643463135,
-0.005998016335070133,
0.054460927844047546,
-0.0029567398596554995,
-0.021360671147704124,
0.051523737609386444,
0.020334260538220406,
-0.012736907228827477,
-0.02839871309697628,
0.011768200434744358,
0.0376216396689415,
-0.014376289211213589,
0.044565796852111816,
0.02692941203713417,
0.028603380545973778,
-0.004199714865535498,
0.0040852767415344715,
-0.05071217194199562,
0.0022940081544220448,
0.03665362671017647,
-0.03861382603645325,
0.002777277957648039,
0.012265107594430447,
0.02510955184698105,
0.031104030087590218,
0.004160190932452679,
-0.0005421385867521167,
0.05192144960165024,
-0.0029659124556928873,
0.05667721480131149,
-0.0356663279235363,
0.03914313390851021,
0.031241662800312042,
0.015917649492621422,
0.04095236584544182,
-0.030562642961740494,
-0.018598543480038643,
0.03414812684059143,
-0.015609491616487503,
0.026798779144883156,
0.033235739916563034,
0.007710004225373268,
0.0022934461012482643,
-0.011673377826809883,
0.002615920966491103,
-0.07029582560062408,
-0.02599225379526615,
-0.007239774335175753,
-0.021130379289388657,
0.02800823748111725,
0.046858638525009155,
-0.007783082779496908,
-0.0061241937801241875,
-0.0718531385064125,
-0.014874027110636234,
-0.010960056446492672,
0.012753564864397049,
-0.024069031700491905,
-0.03510412201285362,
0.027065150439739227,
-0.049733966588974,
-0.02020302414894104,
-0.042843110859394073,
-0.015560219995677471,
0.004305270966142416,
-0.04757003113627434,
-0.03410516306757927,
-0.02671317756175995,
-0.008422354236245155,
0.01589563861489296,
0.011893673799932003,
-0.015818437561392784,
-0.029221132397651672,
0.011831012554466724,
0.0028131038416177034,
0.06501752138137817,
-0.03570093587040901,
0.029057595878839493,
-0.009599900804460049,
0.03815096989274025,
-0.057753756642341614,
-0.022197987884283066,
-0.00868821982294321,
-0.019900599494576454,
-0.03920108824968338,
0.06404951959848404,
-0.01979856938123703,
-0.016119014471769333,
0.0038343851920217276,
0.015245995484292507,
0.004279971122741699,
0.04524807259440422,
-0.015005511231720448,
0.011081493459641933,
-0.028925934806466103,
0.005519603844732046,
0.04183589294552803,
0.006312580779194832,
0.006536285392940044,
0.06162337586283684,
-0.012154911644756794,
-0.003293307265266776,
-0.021028924733400345,
0.013376599177718163,
0.0335390567779541,
0.08079438656568527,
0.0021784764248877764,
0.004925994668155909,
-0.004130844492465258,
0.058144401758909225,
-0.014205551706254482,
-0.005208136513829231,
0.02839469723403454,
-0.047750167548656464,
-0.028923939913511276,
0.025173531845211983,
-0.013312974944710732,
-0.028752008453011513,
-0.009772959165275097,
-0.027591003105044365,
-0.005494334269315004,
-0.037709444761276245,
-0.0060155559331178665,
-0.0322905071079731,
0.05929827317595482,
-0.010204309597611427,
-0.07391010224819183,
0.016764366999268532,
-0.057738855481147766,
0.009018098004162312,
-0.010798635892570019,
0.03666264936327934,
-0.01663106679916382,
0.05497629940509796,
0.0026831994764506817,
-0.031629811972379684,
-0.017924731597304344,
-0.01612408272922039,
0.04548553377389908,
-0.0030286095570772886,
0.006328917574137449,
0.028022149577736855,
0.036382533609867096,
0.007048426195979118,
-0.016948165372014046,
0.06202095001935959,
-0.015613996423780918,
0.035968564450740814,
0.0006882637972012162,
-0.04638595134019852,
0.02613341063261032,
-0.029338497668504715,
-0.002815962303429842,
-0.01798449456691742,
0.026411905884742737,
-0.008287535980343819,
-0.006716058123856783,
-0.037020906805992126,
0.025881994515657425,
-0.04726119339466095,
0.004592185374349356,
0.01693265326321125
] |
<p>Assume we have a conveyor scales. Which consists of scales, and motor with conveyor belt placed above, so that the boxes can be measured (weight) while moving above. What I want is to create the model of the oscillations of that scale.
The equation of the oscillations of the spring is well known for everybody.
How to include the influence of the motor, conveyor and other important effects to the system? Is there any papers (articles) about this thema?
I think that the influence of the motor in simle case can be modelled as the force:
$F(t) = A sin(\Omega t)$ Where $A$ is a constant and $\Omega$ is the parameter which depends on the motor (frequency), which is also constant (depending on the speed of the motor). How to add the ocsillations created by conveyor belt and may be some other oscillations such as box moving above can create additional vibrations?</p>
<p>EDIT 1:
I want to crate the model. I have created one for a scales, but without conveyor and motor. It seems that they do not match. The data of the model and the real data of the conveyor with scales. So there sems to be a big influence of a motor, conveyor belt etc. And what I want is to identify what has a big influence and include it inside the system. So that my model will match the real system. I don't care of some influences which do not make big difference. It is difficult to identify what makes a big influence. And It is more difficult to model for example the moving of the conveyor with or without a box above. How to do it?</p> | g226 | [
0.013434459455311298,
0.04803710803389549,
-0.01951802708208561,
-0.025821417570114136,
0.04877888038754463,
-0.000011699728929670528,
0.01948205940425396,
0.017736254259943962,
-0.046659328043460846,
-0.0300455205142498,
-0.05407201871275902,
-0.02337820455431938,
0.09697231650352478,
0.04673376306891441,
0.0063874488696455956,
0.01821398176252842,
0.04747135564684868,
-0.011425474658608437,
0.023905055597424507,
0.02371770143508911,
0.06625814735889435,
0.02862754464149475,
-0.01164040993899107,
-0.05446821078658104,
0.0076401736587285995,
0.05370175838470459,
0.0002882292028516531,
0.005051749758422375,
0.024474384263157845,
0.027419155463576317,
-0.05753457546234131,
0.0011081876000389457,
0.01273224875330925,
-0.027829105034470558,
-0.07177712768316269,
-0.03400807827711105,
0.03511100262403488,
0.0071712383069098,
-0.006774932611733675,
0.012352382764220238,
0.015938548371195793,
-0.016050605103373528,
-0.011905874125659466,
0.008865460753440857,
-0.028274191543459892,
-0.03943418711423874,
0.01741681806743145,
-0.07167254388332367,
-0.0035568480379879475,
0.06593779474496841,
-0.0253280121833086,
-0.03689100593328476,
-0.01238104235380888,
0.029333019629120827,
0.0072699617594480515,
-0.02855309471487999,
0.04854650795459747,
-0.012132961302995682,
0.05182139202952385,
0.004598659463226795,
-0.02760847844183445,
0.0019466442754492164,
0.005795123986899853,
0.03101821430027485,
0.0356023944914341,
0.012190202251076698,
0.0189713966101408,
-0.023321688175201416,
-0.012291869148612022,
-0.018399164080619812,
0.03584522753953934,
0.053309157490730286,
-0.033770881593227386,
-0.04211724177002907,
-0.02342352829873562,
0.07165779918432236,
0.00560389831662178,
0.002608490874990821,
0.01600066013634205,
0.01463763602077961,
-0.010691634379327297,
0.03313538432121277,
0.0471620112657547,
0.00898869801312685,
0.04193677380681038,
-0.0007181106484495103,
-0.05861242488026619,
0.01710180565714836,
0.03485323488712311,
-0.015190416015684605,
-0.023123260587453842,
-0.056194208562374115,
0.008764919824898243,
0.021084878593683243,
-0.008606838062405586,
-0.042856764048337936,
-0.019299954175949097,
0.08699849992990494,
0.00808300543576479,
0.022184062749147415,
0.004969313740730286,
0.003230439266189933,
-0.05465347692370415,
-0.024714548140764236,
-0.0647839680314064,
-0.0378996767103672,
0.05746999755501747,
-0.052549343556165695,
0.027118019759655,
-0.019901419058442116,
-0.026028228923678398,
-0.060074977576732635,
-0.034183867275714874,
0.012489157728850842,
-0.024815663695335388,
-0.10692588239908218,
0.0720323994755745,
0.021339301019906998,
-0.04102785140275955,
-0.010526749305427074,
0.020249031484127045,
-0.05677980184555054,
-0.03179236128926277,
0.024173520505428314,
0.006248703692108393,
-0.031834255903959274,
-0.003549744375050068,
0.01615802012383938,
-0.034085363149642944,
-0.052745115011930466,
0.05120290070772171,
-0.009865070693194866,
0.01882971078157425,
0.029269810765981674,
0.0434320792555809,
0.0788264349102974,
-0.0033521850127726793,
0.014612993225455284,
0.0014507832238450646,
0.01788058876991272,
0.0336868092417717,
0.046536192297935486,
-0.02664949931204319,
0.009414485655725002,
0.02113363705575466,
0.0543467216193676,
0.03403104096651077,
-0.013580217957496643,
0.025727326050400734,
-0.042913973331451416,
0.032792940735816956,
0.1138821616768837,
-0.08116276562213898,
-0.02991747297346592,
-0.024950796738266945,
0.002461077179759741,
-0.02044081501662731,
0.013652744702994823,
-0.021523522213101387,
-0.029932063072919846,
0.04535916820168495,
-0.03249412029981613,
0.07354287058115005,
-0.013068502768874168,
-0.03556601330637932,
-0.00070177111774683,
0.0013556889025494456,
0.0061754886992275715,
-0.002400075551122427,
0.043297480791807175,
-0.08318080753087997,
-0.028945911675691605,
0.03248574957251549,
0.004634391516447067,
0.020504888147115707,
0.03899352252483368,
0.039143625646829605,
-0.01514430157840252,
0.10841237753629684,
0.005369642283767462,
-0.007731283083558083,
-0.032891932874917984,
-0.002749269362539053,
-0.014536628499627113,
-0.06268323212862015,
0.01885266788303852,
0.056845057755708694,
0.0318174883723259,
-0.03644881024956703,
0.024096060544252396,
-0.009979658760130405,
0.002922273240983486,
0.043080687522888184,
-0.0005034629139117897,
-0.0361100435256958,
0.012072605080902576,
0.036578740924596786,
-0.047881465405225754,
-0.042008426040410995,
-0.03953888267278671,
-0.00017615326214581728,
0.02483503147959709,
0.028366457670927048,
0.023921266198158264,
0.00243886630050838,
-0.004630975890904665,
-0.02415737695991993,
-0.01018444262444973,
-0.05641007795929909,
0.02678297646343708,
-0.029485361650586128,
-0.024117834866046906,
-0.01538077276200056,
0.03846586123108864,
0.004723086953163147,
0.0031875777058303356,
0.03153296560049057,
0.006964126601815224,
0.02285092882812023,
0.04529185965657234,
-0.02055729739367962,
-0.024312438443303108,
0.07818520069122314,
0.006888386327773333,
-0.03734288737177849,
-0.018932301551103592,
0.004665964748710394,
-0.005242344923317432,
-0.021130520850419998,
0.03525373712182045,
-0.012382693588733673,
-0.033223994076251984,
0.049518004059791565,
-0.044665127992630005,
-0.006473151966929436,
-0.024352187290787697,
0.002880165819078684,
-0.019363058730959892,
0.010760754346847534,
0.015522127039730549,
0.0751725286245346,
-0.028334127739071846,
0.025627408176660538,
-0.09768117964267731,
-0.015546003356575966,
-0.009709234349429607,
0.02495047077536583,
0.03818569704890251,
-0.0057184998877346516,
0.02231273613870144,
-0.01153661124408245,
0.014297764748334885,
0.009884358383715153,
-0.027893804013729095,
0.04431592673063278,
0.013541627675294876,
-0.017193954437971115,
0.01035831868648529,
-0.01661231741309166,
-0.01239774003624916,
-0.0034743815194815397,
-0.00698263943195343,
0.015375897288322449,
0.08398527652025223,
-0.011130188591778278,
-0.05660655349493027,
0.028590282425284386,
-0.062400929629802704,
-0.03820442408323288,
-0.007519796025007963,
-0.009496418759226799,
-0.006714990362524986,
-0.0854601338505745,
-0.024515826255083084,
0.02528289705514908,
0.0062763886526227,
0.011473388411104679,
-0.052984610199928284,
-0.012633373960852623,
-0.007826854474842548,
0.03511831536889076,
-0.035534705966711044,
0.03190174326300621,
-0.026825085282325745,
0.03519807010889053,
0.008741083554923534,
0.03387074172496796,
-0.023741938173770905,
0.0236891508102417,
-0.007253178395330906,
-0.025582704693078995,
0.029217101633548737,
-0.012373500503599644,
-0.014161573722958565,
-0.05846673250198364,
0.09460830688476562,
0.022294476628303528,
-0.03854380175471306,
-0.0012883188901469111,
0.057515859603881836,
0.028628185391426086,
-0.04442385584115982,
0.03150906786322594,
0.0031194626353681087,
-0.010072973556816578,
0.012773726135492325,
-0.009737785905599594,
0.02848471887409687,
0.04755912348628044,
0.03138432279229164,
-0.06718140095472336,
-0.020068848505616188,
0.015116303227841854,
0.004510643891990185,
-0.08348531275987625,
0.014376284554600716,
-0.022128703072667122,
-0.018062110990285873,
0.005177139770239592,
-0.052538514137268066,
0.013878650031983852,
-0.09041205793619156,
0.060202740132808685,
-0.06658782809972763,
-0.015490585006773472,
0.04082173481583595,
-0.0131594929844141,
0.044509053230285645,
-0.015586293302476406,
-0.013819152489304543,
0.005254453048110008,
0.014755397103726864,
0.017970310524106026,
-0.030033092945814133,
-0.048554450273513794,
-0.057722751051187515,
-0.025728359818458557,
-0.045102789998054504,
-0.006264146417379379,
0.043159227818250656,
0.0056836348958313465,
0.01968224160373211,
0.01420801505446434,
-0.019022531807422638,
-0.06656065583229065,
-0.0018546001520007849,
-0.04154686629772186,
0.0037048719823360443,
0.03574845567345619,
-0.08566927909851074,
0.05269751697778702,
0.011937043629586697,
-0.005349012557417154,
-0.015682397410273552,
0.011499329470098019,
-0.017814503982663155,
0.0697064995765686,
0.03587448596954346,
-0.05207101255655289,
-0.004805699922144413,
0.02278839983046055,
-0.026199687272310257,
-0.010830892249941826,
0.05838998407125473,
0.04846847429871559,
-0.0037216758355498314,
-0.011944865807890892,
0.05930471792817116,
-0.02979748509824276,
-0.01461192686110735,
-0.003815804608166218,
-0.02133760415017605,
0.019456224516034126,
-0.010266979224979877,
0.074479840695858,
0.0106118842959404,
0.0879555270075798,
0.04683711752295494,
-0.034701231867074966,
0.04066312313079834,
-0.0008950908086262643,
0.03692102059721947,
-0.011429416947066784,
-0.0777733102440834,
0.06189664453268051,
-0.0321626216173172,
0.030531615018844604,
0.010591466911137104,
0.010059421882033348,
0.015544397756457329,
0.01747983507812023,
-0.07437438517808914,
-0.049432072788476944,
0.009712315164506435,
0.08200966566801071,
-0.009283754043281078,
-0.002984208520501852,
-0.041967231780290604,
-0.020991157740354538,
-0.016450101509690285,
0.0016505439998582006,
0.0013197254156693816,
0.004123111721128225,
0.06141003221273422,
0.002088327892124653,
-0.010876982472836971,
0.05187281593680382,
-0.04201919957995415,
0.02706913836300373,
0.04077264666557312,
-0.0622028224170208,
-0.03865012526512146,
0.010733568109571934,
-0.03335336595773697,
-0.021093472838401794,
0.02934947796165943,
0.07435634732246399,
0.019036412239074707,
0.008626990020275116,
0.007890770211815834,
0.013561796396970749,
0.10671577602624893,
-0.019494423642754555,
-0.008939719758927822,
-0.046565767377614975,
0.028943859040737152,
0.02412673830986023,
-0.0661705806851387,
-0.022539524361491203,
-0.05181148275732994,
-0.05933055281639099,
0.05722282454371452,
0.005164617206901312,
0.062356848269701004,
-0.038180649280548096,
0.056098707020282745,
-0.01302141323685646,
-0.009926718659698963,
-0.03327370434999466,
-0.013342170044779778,
0.0047217486426234245,
0.02870260551571846,
-0.011303463950753212,
0.01734975166618824,
-0.0614924319088459,
0.04416259750723839,
-0.042009640485048294,
-0.0023565611336380243,
-0.018919354304671288,
0.013203008100390434,
-0.01869865506887436,
0.02813216671347618,
-0.03218992054462433,
0.0031717855017632246,
0.02331455424427986,
0.02113192528486252,
0.019178632646799088,
-0.053562138229608536,
0.025408228859305382,
-0.04895811900496483,
-0.02121208794414997,
-0.032706089317798615,
-0.05676114931702614,
-0.0026057041250169277,
-0.031368594616651535,
-0.05936913192272186,
-0.037673868238925934,
-0.004315405618399382,
0.002261210698634386,
-0.020010290667414665,
0.05362243577837944,
-0.024593411013484,
0.019642844796180725,
0.06656758487224579,
0.00592674408107996,
0.010759279131889343,
-0.03611200302839279,
-0.022236881777644157,
0.002785977441817522,
0.027663517743349075,
-0.005843526218086481,
-0.012223605066537857,
0.034768689423799515,
-0.052777718752622604,
-0.03175966814160347,
-0.04949698969721794,
0.004312017001211643,
0.02575915865600109,
0.03159092366695404,
0.008396987803280354,
0.04702945053577423,
0.08355142921209335,
-0.017524464055895805,
-0.0037042247131466866,
-0.012024400755763054,
0.021029137074947357,
0.0002868907176889479,
-0.005664879456162453,
0.04014920815825462,
-0.03132639825344086,
-0.00934942252933979,
0.05216766893863678,
-0.003994010388851166,
0.020476028323173523,
-0.03972044587135315,
-0.02456211857497692,
0.023134766146540642,
0.004166718106716871,
-0.008543970994651318,
0.014475459232926369,
-0.02924646995961666,
0.08598687499761581,
-0.027757035568356514,
0.02066059224307537,
-0.0258057601749897,
-0.008831959217786789,
0.014599652960896492,
0.007027490064501762,
-0.023017704486846924,
-0.01072858925908804,
0.035453833639621735,
-0.05557192862033844,
0.07551339268684387,
-0.040231429040431976,
-0.012640737928450108,
0.0037827682681381702,
-0.03406520187854767,
-0.026331715285778046,
0.02623952180147171,
0.008020355366170406,
0.04152533411979675,
0.011049240827560425,
-0.011686979793012142,
0.02445119433104992,
0.03809855505824089,
-0.026683982461690903,
0.045507874339818954,
0.05634268373250961,
-0.016706641763448715,
-0.046019427478313446,
-0.0032577626407146454,
-0.025569168850779533,
0.04268653318285942,
0.0022351103834807873,
0.03362544625997543,
-0.04655516520142555,
0.004068159963935614,
-0.005758270155638456,
0.030348924919962883,
0.020533375442028046,
0.0034880347084254026,
0.03534119948744774,
0.019870664924383163,
0.04662982374429703,
-0.0750972256064415,
0.024945033714175224,
-0.02416139654815197,
-0.056837163865566254,
0.009985178709030151,
0.0441402830183506,
0.047789257019758224,
0.04693014547228813,
0.04637395218014717,
-0.023006107658147812,
-0.025326207280158997,
0.058924973011016846,
-0.013490238226950169,
-0.0019140439108014107,
0.07512304186820984,
0.0850561186671257,
-0.010703875683248043,
-0.0034461012110114098,
0.03843936324119568,
0.036391835659742355,
-0.010060679167509079,
0.008580626919865608,
-0.02600298821926117,
-0.051415715366601944,
-0.028053009882569313,
0.03399328887462616,
-0.03584897145628929,
0.01032119058072567,
0.011170830577611923,
-0.004917961545288563,
-0.03553199768066406,
-0.013053258880972862,
-0.058329369872808456,
-0.02808373235166073,
-0.019367484375834465,
0.0020250161178410053,
0.018229130655527115,
-0.05185270681977272,
-0.03323832526803017,
-0.010446016676723957,
0.017726842314004898,
-0.01915101893246174,
-0.037504058331251144,
0.0052345190197229385,
0.06258541345596313,
0.03349814563989639,
0.0064764912240207195,
-0.00977262295782566,
0.018383437767624855,
0.003269069129601121,
0.010164963081479073,
0.007087879814207554,
-0.059989772737026215,
-0.007535744924098253,
0.018228894099593163,
0.04690595716238022,
0.007722995709627867,
0.0397072471678257,
0.014617341570556164,
0.039590347558259964,
0.05690326169133186,
-0.003267005318775773,
0.006362693849951029,
-0.0020545595325529575,
0.01142682321369648,
-0.024393534287810326,
-0.010725441388785839,
-0.030814407393336296,
0.03956897184252739,
-0.03614581748843193,
0.02463957667350769,
-0.010670662857592106,
-0.0714835599064827,
0.04270782694220543,
0.007663855794817209,
-0.030133312568068504,
-0.03289595991373062,
0.021719425916671753,
0.0018340408569201827,
-0.013182695023715496,
-0.034946247935295105,
0.07679888606071472,
-0.012693334370851517,
0.03245265409350395,
0.01659025065600872,
0.08885859698057175,
0.00907699391245842,
0.05635546147823334,
0.0006677821511402726,
0.02482839673757553,
-0.02594674751162529,
-0.037546321749687195,
0.049046069383621216,
-0.002180988434702158,
0.0017687676008790731,
0.01349368505179882,
-0.020003369078040123,
-0.024915475398302078,
0.01245492696762085,
0.013643533922731876,
0.030029172077775,
-0.020498864352703094,
0.025035466998815536,
0.035837847739458084,
0.04561447352170944,
0.001999771688133478,
-0.05173802003264427,
-0.12541928887367249,
0.02489112690091133,
0.02249518781900406,
0.009711825288832188,
0.0619303397834301,
-0.03183335065841675,
-0.019900772720575333,
0.013483756221830845,
0.03754551336169243,
-0.02910936251282692,
-0.07000409811735153,
0.010791218839585781,
0.028405096381902695,
-0.024084394797682762,
-0.05011541768908501,
-0.021186349913477898,
0.039381224662065506,
0.019697142764925957,
-0.0596904382109642,
0.02366819605231285,
-0.033941756933927536,
-0.01772298291325569,
0.016453832387924194,
-0.004981496371328831,
0.021645216271281242,
0.017263446003198624,
-0.03553106635808945,
-0.03554524481296539,
-0.04702625423669815,
-0.007138701621443033,
-0.004331487230956554,
-0.025550736114382744,
-0.03127568960189819,
-0.06194179132580757,
0.01222231239080429,
-0.07727260887622833,
0.026266416534781456,
-0.01755281537771225,
0.002891864627599716,
0.07424767315387726,
0.02656489983201027,
-0.013691076077520847,
0.030458275228738785,
-0.024590685963630676,
0.005710768513381481,
-0.019146347418427467,
-0.06705258786678314,
-0.011549828574061394,
0.007349734660238028,
-0.06356707215309143,
0.05532441288232803,
0.016981055960059166,
-0.022822411730885506,
-0.0829603374004364,
0.08471857011318207,
-0.010616900399327278,
0.0003987882228102535,
-0.0557066909968853,
0.05928917974233627,
-0.027067838236689568,
0.04089696705341339,
-0.038911156356334686,
-0.05816544592380524,
0.021016810089349747,
-0.05280260741710663,
-0.02131720632314682,
-0.011238175444304943,
0.00827724952250719,
0.022627227008342743,
-0.020420661196112633,
-0.012209132313728333,
-0.060677025467157364,
0.038746677339076996,
-0.026601355522871017,
0.029811222106218338,
0.012471277266740799,
-0.019252382218837738,
-0.08051397651433945,
0.022807691246271133,
0.007572094444185495,
-0.07720381021499634,
-0.005429581739008427,
0.058524057269096375,
-0.0006003028829582036,
-0.022496692836284637,
-0.06116379424929619,
0.03433510661125183,
0.005446906201541424,
0.006228020414710045,
-0.0023323961067944765,
-0.022412551566958427,
-0.0003044743207283318,
-0.04276607558131218,
-0.03464294224977493,
-0.04361557215452194,
-0.035461436957120895,
0.012437529861927032,
-0.01184580847620964,
-0.003641526447609067,
-0.004149962682276964,
0.03344329819083214,
0.005549479275941849,
0.01592201739549637,
-0.03626599162817001,
-0.02873530238866806,
0.02411777712404728,
-0.01684790663421154
] |
<p>I'm reading an article about bi layered membranes which state that for the free energy function<br>
$f(\theta) = \theta \ln \theta + (1-\theta)\ln(1-\theta) + \chi \theta (1-\theta)$</p>
<p>Where $\phi_i$ is the mole fraction of certain types of lipids in layer $i$ and $\chi$ is the energy of interaction between two lipids molecules composing the layer. The article states that a critical point exist at $\chi=2$ and $\theta=0.5$. Reading in <a href="http://en.wikipedia.org/wiki/Critical_point_%28thermodynamics%29">wikipedia</a>, I concluded that removing the layers interaction part, I simply need to take the second and third derivative of the free energy of the membrane. How do I do this with the interactions? Where can I read about this?</p> | g6570 | [
0.05051669478416443,
0.020089831203222275,
-0.005519141908735037,
0.03585002198815346,
0.07117774337530136,
0.005830860696732998,
-0.019832106307148933,
-0.010800818912684917,
-0.07817307114601135,
0.017209960147738457,
-0.020771611481904984,
0.0006396261742338538,
0.017395498231053352,
-0.030565127730369568,
0.024748919531702995,
-0.05435558035969734,
0.05868852883577347,
0.01411363948136568,
0.036913011223077774,
0.021220378577709198,
-0.0841921791434288,
0.016028743237257004,
-0.0253224428743124,
-0.020973285660147667,
0.02045266702771187,
0.004740121308714151,
0.01312745176255703,
-0.008795388042926788,
-0.09229057282209396,
-0.013545714318752289,
-0.0059816353023052216,
0.011482693254947662,
0.060173630714416504,
-0.02791460044682026,
-0.04198772460222244,
-0.015653051435947418,
0.11042039096355438,
0.016202960163354874,
-0.055404625833034515,
0.02478097192943096,
0.04005766659975052,
0.03982021287083626,
0.024582937359809875,
-0.03091035969555378,
0.01591196469962597,
-0.0016615410568192601,
-0.06703870743513107,
-0.021152313798666,
-0.00734979473054409,
-0.012945274822413921,
0.04947693273425102,
0.11089855432510376,
0.03320539370179176,
-0.030911564826965332,
-0.03521541878581047,
0.050566013902425766,
-0.0032686844933778048,
-0.028068453073501587,
-0.030785921961069107,
-0.013311685062944889,
-0.005335773341357708,
-0.06618387252092361,
0.01696411892771721,
-0.009983398951590061,
0.047971226274967194,
-0.0011901521356776357,
-0.051172878593206406,
-0.02356155775487423,
-0.07557811588048935,
-0.03264980390667915,
0.020462168380618095,
-0.011425388045608997,
-0.027141163125634193,
-0.0008271026308648288,
-0.02009466104209423,
-0.029834236949682236,
-0.013698805123567581,
-0.020030340179800987,
0.002221212489530444,
0.005051566753536463,
-0.05995359644293785,
-0.007610314525663853,
0.036364901810884476,
-0.03194304183125496,
0.04172400385141373,
0.001312006264925003,
-0.020691070705652237,
-0.011462635360658169,
-0.030478620901703835,
0.06071452423930168,
-0.0012112336698919535,
-0.018972452729940414,
0.046398866921663284,
-0.037708353251218796,
0.041859425604343414,
0.006585265044122934,
0.003127293661236763,
-0.006338649429380894,
-0.0039491415955126286,
-0.004068303387612104,
-0.02062741480767727,
0.025904593989253044,
0.034057144075632095,
-0.0376339815557003,
-0.011027619242668152,
0.0024736097548156977,
0.04062887281179428,
-0.004191658925265074,
0.0020184072200208902,
0.011981935240328312,
-0.005338227842003107,
-0.04475071653723717,
-0.019743967801332474,
-0.011977939866483212,
0.08564841747283936,
-0.044735539704561234,
0.032564498484134674,
-0.027657903730869293,
-0.000963998434599489,
0.008925888687372208,
-0.03209157660603523,
-0.03806119039654732,
0.027957752346992493,
0.04104815423488617,
-0.021778246387839317,
0.011562498286366463,
-0.03007768839597702,
0.021058928221464157,
0.07088790833950043,
-0.0077305627055466175,
0.0563306100666523,
-0.023307224735617638,
0.012500566430389881,
0.020504159852862358,
0.0108175128698349,
0.03989936038851738,
-0.004764289129525423,
-0.03184546157717705,
0.035576578229665756,
-0.048599112778902054,
-0.020762907341122627,
-0.001007068669423461,
-0.0017999911215156317,
0.002997556235641241,
0.0058424584567546844,
-0.028072208166122437,
0.05089829862117767,
-0.03761684149503708,
0.03818899765610695,
-0.0051766568794846535,
0.008523168042302132,
0.07891620695590973,
-0.01105267833918333,
-0.018160639330744743,
-0.007753636222332716,
0.0316021554172039,
0.038725413382053375,
0.01234128326177597,
-0.02306945249438286,
-0.0042337095364928246,
0.03135500103235245,
-0.021613415330648422,
0.05081460624933243,
-0.009570959955453873,
-0.0013097251066938043,
0.037941064685583115,
0.009049719199538231,
-0.12488972395658493,
0.01192002184689045,
0.016652176156640053,
-0.07977300137281418,
0.02804691344499588,
-0.006973405834287405,
0.07205740362405777,
0.012504260055720806,
0.057420115917921066,
-0.07220183312892914,
-0.016389044001698494,
0.028011437505483627,
0.03418752923607826,
-0.0070069027133286,
-0.021085016429424286,
0.06389357149600983,
-0.04603249579668045,
0.023811640217900276,
0.03347114101052284,
-0.0014045698335394263,
0.035737693309783936,
-0.02638208493590355,
0.022654296830296516,
-0.04332462698221207,
0.018166614696383476,
0.034034326672554016,
-0.05894274264574051,
-0.029348311945796013,
0.10243728011846542,
0.09027567505836487,
-0.06638635694980621,
0.02480264939367771,
-0.051377855241298676,
-0.05415625870227814,
-0.019166769459843636,
0.0065926071256399155,
0.04146616533398628,
-0.022404424846172333,
0.020845947787165642,
-0.0042525362223386765,
0.00570555729791522,
-0.060970548540353775,
-0.048972513526678085,
-0.028838522732257843,
-0.029152201488614082,
-0.022319061681628227,
0.00852457620203495,
0.04083497077226639,
-0.04495806246995926,
-0.012179626151919365,
-0.016362793743610382,
0.001796314725652337,
-0.01580064371228218,
-0.025254618376493454,
0.028226014226675034,
0.08526043593883514,
-0.011137273162603378,
-0.002681405982002616,
0.01762944646179676,
-0.004897211212664843,
-0.0017039338126778603,
-0.023083290085196495,
0.03066159039735794,
-0.04632093384861946,
-0.02154902182519436,
0.0007920269854366779,
-0.013168077915906906,
-0.02323816902935505,
0.05777735263109207,
0.01821436919271946,
0.00979080144315958,
-0.021984126418828964,
0.07193302363157272,
-0.02226186729967594,
0.02183118835091591,
-0.0328826978802681,
0.06666232645511627,
-0.0662311241030693,
0.007344621699303389,
0.0007407551747746766,
0.014093661680817604,
-0.022866949439048767,
-0.01843823492527008,
0.033168673515319824,
0.005993199069052935,
0.012021456845104694,
0.06163368001580238,
-0.005416012369096279,
0.036639899015426636,
0.0011514470679685473,
0.039483264088630676,
-0.022973034530878067,
-0.008171934634447098,
0.034621890634298325,
0.0037649550940841436,
0.033273015171289444,
0.046805985271930695,
-0.016306046396493912,
-0.04096055403351784,
-0.006189555861055851,
-0.04464823380112648,
0.02498958446085453,
0.027393175289034843,
0.026830555871129036,
0.08727381378412247,
0.01768440753221512,
0.07117537409067154,
0.034221719950437546,
-0.04193461313843727,
0.04756699874997139,
-0.052776116877794266,
0.011041354387998581,
-0.027387335896492004,
-0.005126920994371176,
-0.003239445388317108,
-0.0008255737484432757,
0.00033754322794266045,
0.06775015592575073,
-0.001374706975184381,
-0.001304360805079341,
0.07357331365346909,
0.011272655799984932,
-0.0159321129322052,
0.034513041377067566,
0.030917741358280182,
-0.07571575045585632,
0.0168239064514637,
0.01674543507397175,
-0.010166381485760212,
0.0714111253619194,
-0.06345783174037933,
-0.058657556772232056,
0.01873696967959404,
-0.02000025287270546,
-0.004955913405865431,
0.01411798782646656,
0.062461450695991516,
0.030967392027378082,
-0.011637474410235882,
0.009821299463510513,
-0.01816066913306713,
0.03051810711622238,
0.004657762590795755,
-0.02349294349551201,
-0.03199002519249916,
0.017122548073530197,
-0.025031613186001778,
0.035121191293001175,
0.017162473872303963,
0.004814584273844957,
-0.01133586186915636,
0.010981643572449684,
0.0460924431681633,
-0.06207257881760597,
0.0030119773000478745,
0.041270505636930466,
0.00832596980035305,
-0.008768109604716301,
0.014827465638518333,
-0.06319304555654526,
-0.0022090962156653404,
-0.07049745321273804,
0.0009555259603075683,
0.016642704606056213,
0.01939397305250168,
0.060701366513967514,
-0.03643123060464859,
-0.04611585661768913,
-0.04566872492432594,
0.0028742942959070206,
-0.004983952268958092,
0.06701146811246872,
-0.0056746904738247395,
-0.02960432879626751,
0.03409939259290695,
0.0027730464935302734,
-0.03371337056159973,
-0.019231943413615227,
-0.04500018060207367,
-0.049085088074207306,
0.0516696535050869,
-0.026304645463824272,
-0.05824827775359154,
0.0009277068311348557,
0.010775587521493435,
-0.00870429165661335,
-0.03835858777165413,
0.04512789472937584,
0.0015603230567649007,
-0.00046444148756563663,
0.01111896988004446,
-0.001763784559443593,
0.033729247748851776,
-0.004670693539083004,
-0.08545346558094025,
0.02305976115167141,
0.04413846880197525,
-0.0061319381929934025,
-0.03052111156284809,
-0.03907664865255356,
0.04624335095286369,
0.003340639639645815,
-0.02473672665655613,
0.034007489681243896,
-0.02099960297346115,
0.039675649255514145,
0.011622177436947823,
-0.030445700511336327,
-0.008088509552180767,
-0.01868932694196701,
0.007638785056769848,
0.009918435476720333,
0.016213517636060715,
-0.014634132385253906,
-0.06989327818155289,
0.0018752001924440265,
-0.019394004717469215,
0.09927482903003693,
0.008660825900733471,
-0.06309294700622559,
-0.011349436827003956,
0.016105031594634056,
0.03706742823123932,
0.011746023781597614,
0.01062626764178276,
0.0017942471895366907,
-0.004956821445375681,
-0.041658494621515274,
-0.02057504467666149,
0.024115612730383873,
0.030992336571216583,
-0.05257680267095566,
0.058076370507478714,
0.0049268449656665325,
-0.010541887022554874,
-0.05804096907377243,
-0.005688723176717758,
0.02266056090593338,
-0.0048221563920378685,
0.027500491589307785,
-0.025318430736660957,
0.02592531591653824,
0.0172493327409029,
0.019574133679270744,
-0.018459390848875046,
-0.02396758645772934,
0.016742413863539696,
-0.05456877499818802,
-0.00989841390401125,
0.00597712816670537,
-0.055321697145700455,
0.010854406282305717,
0.004777311813086271,
-0.05375152453780174,
-0.04358348995447159,
-0.05846932902932167,
-0.027975820004940033,
-0.05283419042825699,
0.06450065970420837,
0.0673956423997879,
-0.04169332981109619,
-0.004007885232567787,
-0.05884763225913048,
0.018911829218268394,
0.011683530174195766,
-0.06232482194900513,
0.0029690961819142103,
-0.030793698504567146,
0.011553685180842876,
-0.04830237850546837,
-0.004239011090248823,
-0.010157424956560135,
0.05357006937265396,
0.0691780373454094,
-0.032552532851696014,
-0.0792064219713211,
-0.0035184163134545088,
0.008475317619740963,
0.04231597110629082,
-0.04783747345209122,
-0.07155153155326843,
0.024503855034708977,
-0.04888878017663956,
0.009860388934612274,
-0.025311410427093506,
0.02576158195734024,
0.02116505056619644,
0.0006493875989690423,
0.007221502717584372,
-0.029690319672226906,
0.012862886302173138,
-0.00009392105130245909,
-0.0047617750242352486,
0.028062501922249794,
0.005536696873605251,
0.0013680271804332733,
-0.031876444816589355,
0.019610291346907616,
-0.003151847515255213,
0.0009734997292980552,
0.025246480479836464,
-0.02105770632624626,
-0.030567742884159088,
0.0440051294863224,
0.044572390615940094,
0.045264020562171936,
-0.030666932463645935,
-0.023485740646719933,
-0.047871071845293045,
0.004806673154234886,
-0.04674213007092476,
-0.021948255598545074,
-0.06269887089729309,
0.0033208441454917192,
-0.002964848419651389,
0.024942776188254356,
0.01036891434341669,
0.010618418455123901,
-0.005344818811863661,
-0.009291710332036018,
-0.002331678057089448,
0.023980770260095596,
-0.0038580861873924732,
0.02035745419561863,
0.036186400800943375,
0.013732326216995716,
0.005601467099040747,
-0.01642792485654354,
0.011318977922201157,
0.08173906803131104,
-0.05849519371986389,
0.004211796913295984,
0.006511607673019171,
0.0059442282654345036,
0.02445819042623043,
-0.023409700021147728,
0.004361570347100496,
-0.06494738161563873,
0.029077596962451935,
0.027143357321619987,
0.007324080914258957,
0.0035891211591660976,
0.03277380019426346,
-0.022888202220201492,
-0.03894961625337601,
0.02477114461362362,
0.03231128677725792,
0.002664342988282442,
0.008926989510655403,
-0.01955362968146801,
0.014960072003304958,
-0.03805164247751236,
-0.0225202739238739,
0.028895143419504166,
-0.019333556294441223,
-0.03722313791513443,
0.0002478326787240803,
-0.007510316092520952,
-0.05252378433942795,
-0.08310168236494064,
0.0024009293410927057,
0.027414528653025627,
0.01322675496339798,
-0.033168964087963104,
-0.014526558108627796,
0.00866638496518135,
0.035555362701416016,
-0.007394739892333746,
-0.020456355065107346,
0.025734970346093178,
0.00657047051936388,
0.042405031621456146,
0.04387599229812622,
0.003143446985632181,
0.036339107900857925,
-0.004810308571904898,
0.060446131974458694,
0.007521501276642084,
0.016553277149796486,
-0.016003286466002464,
0.021149301901459694,
0.00007923152588773519,
0.029889248311519623,
-0.008794573135674,
-0.039797719568014145,
0.05075398087501526,
0.008851775899529457,
0.015994738787412643,
-0.00917279813438654,
0.029501399025321007,
-0.029283432289958,
-0.013407655991613865,
0.02744084596633911,
0.01766005903482437,
-0.08462345600128174,
0.05899907648563385,
0.024137243628501892,
0.053290605545043945,
-0.04851395636796951,
-0.04977856203913689,
0.0458298958837986,
-0.01059754192829132,
0.002014561789110303,
0.011178023181855679,
0.028379423543810844,
-0.063223697245121,
-0.016081444919109344,
0.029995394870638847,
0.05512906610965729,
-0.023393230512738228,
0.05386200174689293,
-0.036015357822179794,
-0.020996740087866783,
0.003150923876091838,
0.03290212154388428,
-0.06569091230630875,
-0.07303263247013092,
-0.03683742135763168,
0.0160222165286541,
0.005786137655377388,
-0.08345326036214828,
-0.0013762257294729352,
0.012761084362864494,
0.009161775931715965,
-0.027923762798309326,
-0.03742217645049095,
-0.001423132955096662,
0.0640600249171257,
-0.08142798393964767,
-0.018933165818452835,
0.00270907673984766,
0.014821763150393963,
0.07857734709978104,
-0.012028614990413189,
-0.09181991964578629,
-0.012084604240953922,
-0.08813231438398361,
0.021932777017354965,
0.01947050727903843,
0.009105860255658627,
0.033238623291254044,
-0.043235018849372864,
0.03335920721292496,
-0.05276546999812126,
-0.019442832097411156,
-0.022277947515249252,
-0.008333628997206688,
0.007294355425983667,
-0.03443749621510506,
-0.031095048412680626,
0.03170420601963997,
-0.02425539307296276,
0.030117617920041084,
0.022960616275668144,
0.017503395676612854,
0.045951616019010544,
-0.08335895091295242,
0.03913024812936783,
0.024951322004199028,
-0.031023968011140823,
0.020907344296574593,
0.02068442292511463,
0.01822344958782196,
0.014337451197206974,
0.037777189165353775,
-0.024984823539853096,
0.08155712485313416,
-0.041895851492881775,
-0.0011377246119081974,
-0.05682477355003357,
-0.03955201059579849,
-0.031492434442043304,
0.02635384164750576,
-0.008038169704377651,
0.0762326642870903,
0.07881256192922592,
0.05210389196872711,
-0.006683995481580496,
-0.019124669954180717,
0.02337075024843216,
-0.036585595458745956,
-0.007029227912425995,
0.08710303157567978,
0.020219234749674797,
-0.03120519407093525,
0.0008571798680350184,
0.011006539687514305,
-0.014554186724126339,
0.017226535826921463,
-0.030063770711421967,
-0.03920995816588402,
-0.0004258455301169306,
0.03692902252078056,
-0.03712554648518562,
-0.07010964304208755,
0.03308115527033806,
0.018927128985524178,
-0.0008983596926555037,
0.03466242924332619,
0.04492262005805969,
0.00528449472039938,
0.05520899221301079,
-0.02522731013596058,
-0.052585355937480927,
-0.06902854144573212,
-0.05305848643183708,
0.06494107097387314,
0.0005283015198074281,
-0.025490766391158104,
0.04400346055626869,
0.007708023302257061,
0.002368926303461194,
-0.005625192541629076,
0.022738277912139893,
-0.02907579019665718,
0.01944308914244175,
-0.0598750039935112,
-0.023424532264471054,
0.04828445240855217,
0.04359894245862961,
0.04397990182042122,
0.03354969248175621,
0.051325682550668716,
-0.010362828150391579,
0.007592993322759867,
-0.02275221422314644,
-0.025276795029640198,
0.006884975358843803,
-0.01125276554375887,
0.07531452924013138,
0.06501331180334091,
0.07291269302368164,
0.0156722292304039,
0.02253808081150055,
-0.050685763359069824,
-0.07346709817647934,
-0.002625284483656287,
-0.06165188178420067,
0.05384232476353645,
-0.02726844698190689,
-0.0713016539812088,
0.02166133187711239,
-0.01450895145535469,
0.01111105177551508,
-0.014970499090850353,
0.007811803370714188,
-0.019914045929908752,
0.01736077107489109,
-0.007676968351006508,
-0.02571156620979309,
0.0539020411670208,
-0.0008931212360039353,
0.0057455627247691154,
0.015729503706097603,
0.019805189222097397,
-0.049650292843580246,
-0.04356873035430908,
-0.04275383800268173,
-0.0317903608083725,
-0.05817346274852753,
0.02774500846862793,
0.014690070413053036,
0.04463775083422661,
-0.008748557418584824,
-0.037415213882923126,
-0.018113935366272926,
0.02532004378736019,
0.0029471025336533785,
0.0019154422916471958,
0.014165140688419342,
-0.006882614456117153,
0.032999224960803986,
-0.036403000354766846,
-0.0027161072939634323,
-0.03852219879627228,
0.03197230026125908,
-0.005088191945105791,
-0.0285810474306345,
0.01971534825861454,
-0.030526340007781982,
0.0432957261800766,
0.03429621458053589,
0.06218736246228218,
-0.05466799810528755,
0.01994028314948082,
-0.015149836428463459,
-0.018399015069007874,
0.0310023482888937,
-0.07211039215326309,
-0.057172395288944244,
-0.033352918922901154,
-0.006703896913677454,
-0.01637096330523491,
0.0033951394725590944,
-0.029846325516700745,
0.007668276783078909,
0.04039231315255165,
0.03239843621850014,
-0.010036250576376915,
0.024996617808938026,
0.02573036216199398
] |
<p>Argument: Buckling is an engineering concept that can only be applied to <strong>thin columns</strong> with <strong>compressive</strong> loading.</p>
<p>(Is it possible to) Prove the above sentence right or wrong with mathematical formulation. Emphasis on cellular and solid materials that have no concept of "thin". </p>
<p>Also, why can you use buckling to describe crack growth experiments in thin sheets:
out-of-plane deformation of sheets = buckling? => deformation in perpendicular direction respect to force is buckling? => 3D solids can experience buckling ? => example of this kind of material is...</p>
<p>Good references, rigorous treatment and mathematical approach are more than welcome.</p>
<p><strong>edit:</strong> In other words, what is the mathematical definition for buckling?</p>
<p><strong>edit2:</strong> So, buckling is the bifurcation of static equilibrium (see annav's comment below). And thus:</p>
<blockquote>
<p>More technically, consider the continuous dynamical system described
by the ODE</p>
<p>$\dot x=f(x,\lambda)\quad
> f:\mathbb{R}^n\times\mathbb{R}\rightarrow\mathbb{R}^n.$</p>
<p>A local bifurcation occurs at $(x0,λ0)$ if the Jacobian matrix
$\textrm{d}f_{x_0,\lambda_0}$ has an eigenvalue with zero real part.</p>
</blockquote>
<p>This also happens to coincide with ASTM E-9 standard, section 3.2.1 that says: </p>
<blockquote>
<p>bucklig -- (3) a local instability, either elastic or inelastic, over
a small portion of the gage length</p>
</blockquote> | g6571 | [
0.09006167948246002,
0.029595721513032913,
0.007846135646104813,
-0.003586195409297943,
0.018649013713002205,
-0.02125529572367668,
-0.01733989454805851,
-0.0373685359954834,
-0.02874850668013096,
-0.015928246080875397,
0.010246890597045422,
-0.013335769064724445,
0.04162163287401199,
-0.026139624416828156,
-0.01568739116191864,
0.02097567357122898,
0.06748486310243607,
0.000402721983846277,
0.026927383616566658,
0.07966773211956024,
-0.08557967096567154,
0.003925126511603594,
0.03016643226146698,
-0.013890921138226986,
-0.022656457498669624,
0.09343893080949783,
0.01165943406522274,
-0.009302069433033466,
-0.02106785587966442,
0.02094537764787674,
0.0330163836479187,
-0.04665033891797066,
0.011659041978418827,
-0.03677072003483772,
-0.0423133559525013,
-0.05502932146191597,
0.0032794957514852285,
0.01746300421655178,
0.04599646478891373,
-0.006955099757760763,
0.009893779642879963,
-0.006946830544620752,
0.04113495349884033,
-0.012183927930891514,
-0.005567200016230345,
0.018922103568911552,
-0.04995707795023918,
0.016087118536233902,
-0.026813799515366554,
0.016533469781279564,
-0.02301173284649849,
-0.020671267062425613,
0.014610487036406994,
-0.03254313766956329,
-0.02848070114850998,
0.0040389723144471645,
0.0016150830779224634,
0.02412150800228119,
-0.0062093427404761314,
-0.040018320083618164,
-0.022657515481114388,
0.0036569051444530487,
0.020410750061273575,
-0.025668714195489883,
0.05324612185359001,
0.008608122356235981,
-0.07784003019332886,
-0.034246619790792465,
0.030969152227044106,
0.03873702138662338,
0.004797772504389286,
-0.07170242071151733,
-0.04020163416862488,
-0.01817033812403679,
-0.026360852643847466,
0.02331848070025444,
0.007927614264190197,
-0.023303808644413948,
0.0010457973694428802,
0.028208313509821892,
-0.05283142253756523,
0.049353957176208496,
-0.032323215156793594,
0.0027766944840550423,
0.04233613982796669,
0.006438424810767174,
0.003438996383920312,
0.006752041168510914,
-0.05743866413831711,
-0.0019537077751010656,
-0.01628877967596054,
0.04333164170384407,
-0.031210867688059807,
-0.003261853940784931,
-0.03233020380139351,
-0.0035081878304481506,
0.009905497543513775,
-0.013611414469778538,
-0.012698042206466198,
0.008374543860554695,
-0.010739565826952457,
-0.008186534978449345,
-0.07107289135456085,
-0.030175313353538513,
-0.03919209912419319,
0.033379364758729935,
0.027535149827599525,
0.016498131677508354,
-0.025797422975301743,
-0.054676882922649384,
0.0007739372085779905,
0.03969874978065491,
-0.04668871685862541,
-0.022975550964474678,
-0.008049090392887592,
0.014198506250977516,
0.07225292921066284,
0.012449253350496292,
0.03080103173851967,
0.046712327748537064,
0.06626608222723007,
0.02462754026055336,
0.07986404746770859,
0.07202745974063873,
0.01344294659793377,
-0.012050282210111618,
0.0013192424084991217,
0.045989517122507095,
-0.008953627198934555,
-0.034079063683748245,
0.020375633612275124,
0.00022291566710919142,
-0.058669157326221466,
-0.05045899748802185,
0.0697968527674675,
0.04399097338318825,
-0.044814035296440125,
-0.03474769741296768,
-0.018965518102049828,
0.011047341860830784,
-0.08732988685369492,
0.04005847126245499,
0.007462004665285349,
0.03963656723499298,
0.04325004667043686,
-0.014043929055333138,
0.022955236956477165,
0.04296557977795601,
0.05585572496056557,
0.034335907548666,
-0.03232013061642647,
0.08901078253984451,
-0.02078625187277794,
-0.06447925418615341,
0.022104522213339806,
0.050221849232912064,
0.04805998504161835,
0.024698739871382713,
0.019517607986927032,
0.024612827226519585,
0.03113749995827675,
-0.030650164932012558,
-0.08778131753206253,
0.022146016359329224,
-0.0636085793375969,
0.026096753776073456,
-0.05537129566073418,
0.045990340411663055,
-0.005915550515055656,
-0.008868111297488213,
-0.0722324401140213,
0.015854867175221443,
0.04665099456906319,
-0.008321834728121758,
0.020608408376574516,
0.004789191298186779,
0.0274192001670599,
-0.07790857553482056,
0.011236274614930153,
-0.0814133733510971,
-0.05916009098291397,
0.02956255152821541,
-0.00656057707965374,
0.022294210270047188,
-0.015579178929328918,
0.020067257806658745,
0.018556736409664154,
-0.022328974679112434,
-0.04376577213406563,
0.004692459478974342,
-0.03523581847548485,
0.03196464106440544,
-0.008140873163938522,
0.07039320468902588,
-0.06728336215019226,
-0.07270985096693039,
0.030296163633465767,
-0.02169656939804554,
0.05828636512160301,
-0.048757441341876984,
0.04536847025156021,
0.010196128860116005,
0.043588124215602875,
0.009173767641186714,
-0.04990822821855545,
-0.012968008406460285,
-0.04707582667469978,
-0.026009734719991684,
-0.05641395226120949,
-0.0020334478467702866,
0.025201596319675446,
-0.03386584296822548,
-0.03141750767827034,
0.08399853110313416,
0.05016057565808296,
-0.047738637775182724,
0.04253910854458809,
-0.02475777640938759,
-0.004588230047374964,
-0.015211212448775768,
0.03057693876326084,
-0.03658777475357056,
-0.07325000315904617,
-0.012090550735592842,
0.021713657304644585,
-0.08861644566059113,
-0.028607599437236786,
0.030034787952899933,
0.07379968464374542,
-0.045998651534318924,
-0.10816490650177002,
-0.007578771561384201,
-0.0207515936344862,
-0.0038735661655664444,
0.04797656834125519,
0.0614752322435379,
-0.02266640216112137,
0.034875597804784775,
0.02112979255616665,
0.05206650495529175,
0.009671715088188648,
-0.04760707542300224,
-0.06485056132078171,
-0.043392982333898544,
-0.0016837635776028037,
-0.04469790309667587,
0.03136899322271347,
-0.05378865823149681,
0.060348521918058395,
-0.003453016048297286,
0.041882917284965515,
0.0011597692500799894,
-0.0035510442685335875,
0.041014887392520905,
-0.00575975188985467,
-0.1000688374042511,
0.01411119382828474,
0.02943808026611805,
-0.006375114433467388,
0.015042691491544247,
0.017229698598384857,
0.031649235635995865,
0.020948121324181557,
-0.013853399083018303,
-0.029980702325701714,
0.004736434202641249,
-0.05591317266225815,
-0.0007372472900897264,
-0.033382728695869446,
0.014124041423201561,
-0.027460068464279175,
0.027780376374721527,
0.006307507865130901,
0.03854713216423988,
-0.011771759949624538,
-0.03960788622498512,
-0.0293284859508276,
0.004423163831233978,
0.0016676790546625853,
-0.02174498699605465,
0.03536113351583481,
0.00772827910259366,
0.009384009055793285,
0.018185772001743317,
0.0057589709758758545,
0.01738658733665943,
0.013384477235376835,
-0.020373422652482986,
-0.010048405267298222,
0.039266131818294525,
-0.031528305262327194,
0.019994042813777924,
-0.025825152173638344,
-0.04634625092148781,
-0.021535828709602356,
0.04489722102880478,
-0.010520781390368938,
-0.05586480349302292,
-0.050311874598264694,
0.028233980759978294,
-0.012684418819844723,
-0.03060333989560604,
0.0060221953317523,
-0.045801617205142975,
0.06581699848175049,
0.03492734953761101,
-0.0005924152210354805,
-0.04938807338476181,
-0.006323610432446003,
0.012240410782396793,
0.006362610962241888,
-0.010633653961122036,
0.02065328136086464,
0.026727372780442238,
-0.054597917944192886,
-0.01615672931075096,
0.005481787957251072,
-0.023888057097792625,
-0.020059308037161827,
-0.08905484527349472,
-0.019651005044579506,
-0.028733111917972565,
-0.014453992247581482,
-0.0031596289481967688,
-0.002692698035389185,
0.012009979225695133,
-0.037284720689058304,
0.017172709107398987,
-0.043589700013399124,
0.00046847425983287394,
-0.011366813443601131,
-0.05173371732234955,
0.0508933886885643,
-0.054281629621982574,
-0.02427799254655838,
-0.06879433244466782,
-0.0383157953619957,
-0.037312112748622894,
0.04747316241264343,
-0.004463305696845055,
-0.02085810713469982,
-0.0027462285943329334,
0.018330927938222885,
-0.010428288951516151,
-0.04040033742785454,
-0.001835308619774878,
0.006731320638209581,
0.015476562082767487,
-0.0038649586495012045,
0.005157671868801117,
0.016851911321282387,
0.024944018572568893,
0.02220275066792965,
-0.055161233991384506,
-0.019125424325466156,
-0.018413526937365532,
0.015623992308974266,
0.01611156016588211,
-0.002804376883432269,
0.016992824152112007,
0.012305028736591339,
0.005852467380464077,
0.00644118944182992,
-0.034857116639614105,
-0.03638157993555069,
0.07644578814506531,
0.026517895981669426,
0.06769217550754547,
0.02178957685828209,
-0.04169240966439247,
0.0229826457798481,
-0.008575852029025555,
-0.000059575824707280844,
-0.010025198571383953,
0.0531439334154129,
-0.04660044610500336,
0.014042890630662441,
-0.008848726749420166,
0.020243311300873756,
0.035982366651296616,
0.037170473486185074,
0.024521050974726677,
0.06240633502602577,
0.05468503013253212,
-0.02575332671403885,
-0.012797446921467781,
-0.015878677368164062,
0.00036601649480871856,
-0.03614591062068939,
0.010125267319381237,
0.0188637375831604,
-0.009184412658214569,
0.008450737223029137,
0.04125083610415459,
-0.00689326599240303,
0.026216760277748108,
-0.015229561366140842,
0.02091190591454506,
-0.0522596538066864,
-0.024602429941296577,
0.01927892118692398,
0.004976904019713402,
0.00978156365454197,
0.008922496810555458,
0.034069936722517014,
-0.021125299856066704,
-0.029742509126663208,
-0.022015796974301338,
-0.02605176903307438,
-0.029855065047740936,
0.022093890234827995,
-0.042262911796569824,
-0.003819890320301056,
-0.046325113624334335,
0.05567408725619316,
0.009129464626312256,
0.050905171781778336,
0.01123499684035778,
0.012558531947433949,
-0.0479448139667511,
0.03347382694482803,
0.016050342470407486,
-0.08495263755321503,
0.07368595153093338,
0.03811490535736084,
0.06256791204214096,
-0.0037387493066489697,
-0.00808453094214201,
0.03826270252466202,
-0.04336391016840935,
-0.031850289553403854,
-0.0003513327974360436,
0.00037764135049656034,
0.018920499831438065,
-0.010368085466325283,
-0.0160811934620142,
-0.016956225037574768,
0.04991491511464119,
-0.012889647856354713,
0.06088823825120926,
0.007194452919065952,
0.009776855818927288,
0.06174195185303688,
0.027604995295405388,
0.00549941323697567,
0.01617557927966118,
-0.007248309440910816,
-0.015173596329987049,
-0.03337903320789337,
-0.03698023036122322,
-0.03251506760716438,
0.02469923533499241,
0.04130588099360466,
-0.018140718340873718,
0.03172903507947922,
-0.026456398889422417,
-0.010604385286569595,
0.040664780884981155,
0.0254985261708498,
0.04415528103709221,
0.07411710917949677,
-0.02878609672188759,
0.059765614569187164,
-0.037432242184877396,
0.01749832183122635,
0.015302474610507488,
0.022625427693128586,
-0.02311701513826847,
0.02074344828724861,
0.022838063538074493,
-0.06467252224683762,
-0.006254655309021473,
-0.023466847836971283,
0.0016658386448398232,
-0.006567826494574547,
-0.006806531921029091,
-0.002309518400579691,
0.037888530641794205,
0.027254972606897354,
-0.019214453175663948,
0.03650212660431862,
0.004312892910093069,
-0.010118595324456692,
-0.025097619742155075,
0.04221345856785774,
-0.00175258528906852,
-0.018306467682123184,
0.021665459498763084,
-0.02392706274986267,
-0.0558699294924736,
0.028247186914086342,
-0.07074327766895294,
-0.019464777782559395,
0.04866287112236023,
-0.020422620698809624,
-0.022035811096429825,
0.021076926961541176,
0.0019105775281786919,
-0.07315465062856674,
-0.03124925121665001,
-0.03421648219227791,
0.04368971288204193,
0.0003319217066746205,
0.012901526875793934,
0.044189173728227615,
-0.01760721206665039,
0.06794121116399765,
0.007975664921104908,
0.01660974882543087,
0.01563064381480217,
0.020555883646011353,
0.01145944930613041,
0.024381939321756363,
0.03743284195661545,
0.04862619936466217,
-0.015047072432935238,
-0.030320320278406143,
0.008113500662147999,
-0.0318463072180748,
-0.0713793933391571,
0.026234135031700134,
-0.01478341594338417,
-0.0509190708398819,
-0.0642646849155426,
0.005468578543514013,
0.002000272972509265,
-0.07751423120498657,
0.00414951192215085,
-0.004208797588944435,
0.01582648791372776,
-0.007982924580574036,
-0.014973328448832035,
0.043980710208415985,
-0.01670120283961296,
-0.07602810859680176,
0.041926734149456024,
0.007954609580338001,
-0.0171236339956522,
-0.032288745045661926,
-0.013698535971343517,
-0.012380889616906643,
-0.058850690722465515,
0.03494356572628021,
0.061124589294195175,
0.015448831021785736,
0.026183409616351128,
-0.06040528044104576,
-0.022774826735258102,
0.08745313435792923,
-0.011058798059821129,
-0.02594088204205036,
0.035684991627931595,
-0.015957355499267578,
0.02002321183681488,
-0.00937441922724247,
-0.004489421378821135,
0.00036495944368653,
-0.038610536605119705,
-0.011371945962309837,
-0.03007889725267887,
-0.05107768625020981,
0.04641388729214668,
-0.023607343435287476,
0.013860655948519707,
0.0346585251390934,
0.05078200623393059,
-0.04156472161412239,
0.004594780970364809,
0.0022292551584541798,
0.033989451825618744,
0.0019502145005390048,
0.033722393214702606,
0.07305490225553513,
0.0700758546590805,
-0.03344012796878815,
0.029603131115436554,
-0.022659242153167725,
0.009451530873775482,
-0.010484355501830578,
-0.03811420500278473,
-0.026847368106245995,
-0.014931600540876389,
0.03919801488518715,
0.036344293504953384,
-0.004496022593230009,
0.027291852980852127,
0.016070576384663582,
-0.034734923392534256,
0.016347579658031464,
-0.0703003853559494,
0.02894650027155876,
0.02240198664367199,
-0.0007819041493348777,
0.0671011283993721,
-0.021136993542313576,
0.015966763719916344,
0.015265467576682568,
0.04257408156991005,
0.0176747664809227,
0.0011524915462359786,
0.0006015414255671203,
0.10169943422079086,
0.017141245305538177,
-0.028118563815951347,
-0.029950760304927826,
0.004679379519075155,
0.01648048497736454,
0.010969304479658604,
0.0022100305650383234,
0.01715751178562641,
-0.005586148239672184,
0.03180898725986481,
0.002055997960269451,
-0.02610507793724537,
0.02342064306139946,
-0.08709239214658737,
0.019979232922196388,
-0.04838966578245163,
0.033796243369579315,
-0.03305898606777191,
0.01683514006435871,
-0.026313889771699905,
0.015100200660526752,
-0.037760522216558456,
0.03979480639100075,
0.03314151614904404,
-0.06428402662277222,
0.023722337558865547,
0.08461742103099823,
-0.004074188880622387,
-0.006774734705686569,
-0.020247498527169228,
-0.05490685626864433,
0.05013361573219299,
-0.025095466524362564,
0.03602921590209007,
-0.02489999681711197,
0.03388350084424019,
0.09827479720115662,
-0.009084586054086685,
-0.041623394936323166,
0.029085326939821243,
0.007760871667414904,
-0.003764933440834284,
-0.03630385547876358,
0.011860929429531097,
0.01816960796713829,
-0.003053422784432769,
-0.029234804213047028,
0.02975730411708355,
0.06471778452396393,
0.002651428570970893,
-0.0851776972413063,
-0.048527684062719345,
-0.057384081184864044,
0.028690798208117485,
0.01399245299398899,
-0.03747046738862991,
0.037385858595371246,
-0.005994066130369902,
-0.026133019477128983,
0.029818011447787285,
0.03334144130349159,
-0.059773508459329605,
0.0048473249189555645,
0.04749695584177971,
0.009042318910360336,
-0.0005391029408201575,
-0.07218094915151596,
0.005956146866083145,
0.06543352454900742,
-0.00017348438268527389,
0.01980145089328289,
0.029075413942337036,
-0.004350031726062298,
-0.0063201431185007095,
0.008891931734979153,
0.00826702918857336,
0.06660722196102142,
-0.026620473712682724,
0.09923776239156723,
0.03203915059566498,
0.025899749249219894,
0.020346052944660187,
0.012030367739498615,
-0.009164768271148205,
0.0008268831297755241,
0.011063924059271812,
0.021689726039767265,
-0.018584661185741425,
0.021506698802113533,
-0.00035798302269540727,
-0.03915565833449364,
-0.001765647903084755,
-0.028057033196091652,
-0.007842516526579857,
0.04007963463664055,
0.010604757815599442,
0.0008232088875956833,
-0.025724681094288826,
-0.0394972488284111,
-0.019599221646785736,
-0.048165518790483475,
-0.016524294391274452,
-0.00939274113625288,
0.020791996270418167,
-0.023189226165413857,
-0.06755329668521881,
-0.06937237828969955,
-0.021276047453284264,
0.012242448516190052,
0.024434616789221764,
-0.008235936053097248,
-0.0361379012465477,
0.07636544853448868,
0.007169906049966812,
0.02447720430791378,
-0.028936238959431648,
-0.0051871794275939465,
0.010922406800091267,
-0.036868348717689514,
-0.027875931933522224,
-0.022521324455738068,
-0.056334421038627625,
-0.006143075414001942,
0.05298560857772827,
0.031207319349050522,
-0.05352594330906868,
-0.06728214025497437,
0.05910840630531311,
-0.038345206528902054,
-0.02046877145767212,
0.011870386078953743,
0.02499786764383316,
-0.04076485335826874,
0.015037769451737404,
0.032776083797216415,
0.006516317371279001,
-0.052984513342380524,
0.041798438876867294,
0.014834749512374401,
0.027440594509243965,
-0.10232598334550858,
-0.01707090251147747,
0.03657448664307594,
0.006091282702982426,
-0.024017488583922386,
0.10648252069950104,
0.019771652296185493,
0.005144563969224691,
0.0019966228865087032,
0.057083092629909515,
0.024291951209306717,
0.035431552678346634,
-0.004303460009396076,
0.026759056374430656,
0.009580668993294239,
-0.056198086589574814,
0.00039652801933698356,
-0.015049558132886887,
0.015152201056480408,
0.0394413098692894,
0.009962179698050022,
-0.07425892353057861,
-0.025506800040602684,
-0.006996172945946455,
0.007564646191895008,
0.022455740720033646
] |
<p>When Einstein started to think about gravitation, he completely created a new theory that no experiment supported. He based his reasoning, as he explained it later, on small thought experiments (Gedankenexperiment) that led him to formulate the equivalence principle. From this equivalence principle, he used the principles of physics and understood that a new space-time geometry was necessary and after years of effort he obtained the Einstein's equation. It is only when he used this equation to compute the anomalous perihelion advance of the planet Mercury that he knew his theory had something to do with the real world (but one could not call this a prediction). Since then, many predictions of General Relativity have been successfully checked experimentally.</p>
<p><strong>Edited question</strong></p>
<p>A thought experiment is an experiment that has not been realized, but that was imagined. The results of such experiment are based on well established physical principles but have never been observed physically. A second example of a thought experiment considers a frictionless movement of a vehicle on a road (see Einstein and Infeld, <em><a href="http://en.wikipedia.org/wiki/The_Evolution_of_Physics" rel="nofollow">The Evolution of Physics: The Growth of Ideas From Early Concepts to Relativity and Quanta</a></em>, chapter 1 on the Galilean relativity). Another example in particle physcis is described in <a href="http://physics.stackexchange.com/questions/93839/are-there-correct-physical-predictions-made-only-from-thought-experiments-other?noredirect=1#comment192225_93839">one of the above comments</a>. Thought experiments only draw conclusions from physical considerations, not from mathematical derivations, and can therefore be used as illustrations destined to non-physicists.</p>
<p>Does anyone think of other thought experiments which results have been proved relevant later by physical experiments, either because the thought experiment has been realized or because its results had physically testable consequences ?</p> | g6572 | [
0.026950174942612648,
0.04419548809528351,
0.020184464752674103,
-0.016858655959367752,
0.05156389996409416,
0.034882284700870514,
0.023654844611883163,
-0.0038652990479022264,
-0.015229510143399239,
-0.040455903857946396,
0.010602855123579502,
-0.04278085008263588,
0.014478391967713833,
0.02897852472960949,
0.006953712087124586,
0.027669565752148628,
0.09396309405565262,
-0.03960799798369408,
0.015428130514919758,
0.015770098194479942,
0.047706522047519684,
0.03145967423915863,
-0.019251838326454163,
-0.03949899971485138,
-0.022214500233530998,
-0.028656786307692528,
-0.011590427719056606,
0.004752908367663622,
-0.04587848111987114,
0.022514089941978455,
0.025937562808394432,
-0.06331978738307953,
0.027671294286847115,
-0.04157821461558342,
-0.038078512996435165,
-0.06338152289390564,
0.0286547988653183,
0.021983740851283073,
0.01656249538064003,
-0.042171280831098557,
0.008805414661765099,
-0.01789514347910881,
-0.03920700028538704,
0.01030648685991764,
0.06297057121992111,
-0.010928047820925713,
0.016837116330862045,
-0.005316533613950014,
0.0659509152173996,
0.019291801378130913,
-0.016107218340039253,
0.07985436171293259,
0.0799141675233841,
0.01075772475451231,
0.012616814114153385,
0.04468298703432083,
0.05533021315932274,
-0.03489098697900772,
0.04399457201361656,
-0.007170704193413258,
-0.024205338209867477,
0.020948171615600586,
0.06281556189060211,
0.0019532558508217335,
0.0030801782850176096,
-0.016449373215436935,
-0.04334346950054169,
0.013867486268281937,
0.0366896353662014,
0.015125127509236336,
0.057578638195991516,
-0.042555585503578186,
-0.01957392878830433,
0.022264374420046806,
0.008287073113024235,
0.03007517009973526,
0.02900274656713009,
-0.005564785562455654,
0.05238024890422821,
0.027740396559238434,
-0.02160874754190445,
-0.04763154685497284,
-0.046794384717941284,
-0.013383815996348858,
0.06276446580886841,
-0.05353305861353874,
-0.000671661866363138,
0.025814490392804146,
0.02414948306977749,
0.03769214078783989,
0.005343342665582895,
-0.016623064875602722,
0.037789829075336456,
0.009570637717843056,
-0.06136653572320938,
-0.017258532345294952,
0.006754120346158743,
0.06520942598581314,
0.029577787965536118,
0.0320066399872303,
-0.05646289512515068,
-0.004914718680083752,
0.019763128831982613,
0.013589155860245228,
0.04889610409736633,
-0.05104855075478554,
0.03059304691851139,
0.054069600999355316,
-0.004799556918442249,
0.014167383313179016,
-0.01468503475189209,
-0.013926548883318901,
-0.019382953643798828,
-0.05129791796207428,
-0.018162650987505913,
-0.05403996631503105,
0.01588529720902443,
-0.007311275694519281,
0.05879039689898491,
0.021093500778079033,
0.015534089878201485,
0.05713783949613571,
-0.014975789934396744,
0.024181747809052467,
-0.030121169984340668,
-0.002775617642328143,
-0.005377931986004114,
-0.008497537113726139,
-0.02377491258084774,
-0.055252913385629654,
-0.020684555172920227,
0.03002765029668808,
0.026164116337895393,
0.053347762674093246,
-0.019342942163348198,
0.024381985887885094,
0.03130711615085602,
-0.029357392340898514,
0.007854052819311619,
-0.009569298475980759,
0.032018907368183136,
0.014679639600217342,
-0.013582748360931873,
0.02816912531852722,
0.02235102467238903,
-0.021762914955615997,
-0.008637715131044388,
0.006648258771747351,
-0.004275094252079725,
0.05621038004755974,
-0.06110948696732521,
0.03296016901731491,
0.016823099926114082,
-0.045053575187921524,
-0.0033068282064050436,
0.0066811442375183105,
-0.02901710383594036,
-0.002621142193675041,
0.016494952142238617,
0.011443023569881916,
-0.0006743648555129766,
-0.030253322795033455,
0.010639662854373455,
0.009715517051517963,
-0.046131111681461334,
0.024495311081409454,
0.012401679530739784,
-0.0446244478225708,
0.05480792000889778,
-0.026192456483840942,
-0.06627225130796432,
-0.050269149243831635,
0.014124253764748573,
0.062208618968725204,
-0.002455807290971279,
0.013924003578722477,
0.04986812546849251,
-0.04287657141685486,
-0.036224886775016785,
0.011617254465818405,
-0.0183545108884573,
-0.05577898770570755,
-0.013600400649011135,
-0.02298225276172161,
-0.060359690338373184,
-0.009402750059962273,
0.0004238057299517095,
-0.025675136595964432,
-0.08142611384391785,
-0.0050626457668840885,
-0.020412232726812363,
0.0026938815135508776,
-0.02380385249853134,
-0.007266039494425058,
-0.027838559821248055,
0.01869114302098751,
0.0050244806334376335,
-0.057341933250427246,
0.0024679088965058327,
0.07139270752668381,
0.0035232773516327143,
0.09313111007213593,
-0.015981247648596764,
0.005585000850260258,
0.0029757157899439335,
-0.017226815223693848,
-0.008536674082279205,
-0.04252907261252403,
0.03006865829229355,
0.005993886385113001,
0.09627198427915573,
0.04494147747755051,
0.010433266870677471,
0.010089673101902008,
-0.03910595923662186,
0.019616596400737762,
-0.006165114231407642,
-0.01905670389533043,
0.022976242005825043,
0.0324685238301754,
0.04409131407737732,
-0.00834602676331997,
0.004946459084749222,
-0.00029993581119924784,
-0.0016330546932294965,
-0.019426817074418068,
-0.03499121218919754,
-0.038794759660959244,
-0.043583061546087265,
-0.010793522000312805,
-0.004633517470210791,
0.006089816335588694,
-0.016932133585214615,
-0.010205410420894623,
0.042480405420064926,
-0.009127955883741379,
-0.03912772610783577,
-0.02886330895125866,
0.07468575239181519,
0.05697781220078468,
0.012551278807222843,
0.014351408928632736,
-0.04451579973101616,
-0.012147440575063229,
-0.014110444113612175,
-0.12109851837158203,
-0.013011603616178036,
-0.0313444547355175,
0.02885720133781433,
0.03576317057013512,
0.027624167501926422,
0.024332614615559578,
0.005673192907124758,
-0.005994471721351147,
0.00046396811376325786,
0.05900430306792259,
0.0010735314572229981,
0.029596280306577682,
-0.023987453430891037,
-0.0767044648528099,
-0.02270142175257206,
-0.023068010807037354,
0.01827785186469555,
0.05315348133444786,
-0.018512070178985596,
-0.0038525033742189407,
-0.07690182328224182,
0.00684903422370553,
-0.016329487785696983,
-0.0072357309982180595,
-0.03372611105442047,
0.01779487542808056,
-0.08026355504989624,
0.012161992490291595,
-0.03663955628871918,
0.03419486805796623,
0.00576937897130847,
-0.010548108257353306,
0.04653395712375641,
0.02831524796783924,
0.0027329125441610813,
0.017227528616786003,
-0.07761819660663605,
0.03636913374066353,
0.029650863260030746,
-0.058595433831214905,
0.0685005933046341,
0.010874742642045021,
0.007913758978247643,
-0.0356326550245285,
-0.022765101864933968,
0.014398055151104927,
0.10471633076667786,
0.0039302571676671505,
-0.02111101523041725,
0.06784522533416748,
-0.0202791765332222,
-0.01888161711394787,
-0.009226884692907333,
-0.026263214647769928,
0.0075012557208538055,
-0.01570802368223667,
0.008248437196016312,
0.06977467983961105,
0.026160920038819313,
0.005848484113812447,
-0.024637987837195396,
-0.04602024704217911,
-0.006168600171804428,
-0.046271927654743195,
0.004904943984001875,
0.07258552312850952,
0.014645473100244999,
0.004988654516637325,
-0.07906395941972733,
-0.011653978377580643,
-0.007531526032835245,
0.024859998375177383,
0.03474295884370804,
0.0037895238492637873,
0.059614744037389755,
-0.03200807422399521,
-0.00845089927315712,
-0.0373753197491169,
0.07222606241703033,
0.03691273182630539,
-0.0008035717764869332,
0.003325382247567177,
0.05088840797543526,
-0.023187175393104553,
-0.0169830285012722,
0.0652962252497673,
-0.04667969048023224,
-0.013238095678389072,
-0.008236457593739033,
-0.08354955166578293,
-0.023853382095694542,
0.03058694861829281,
0.008689001202583313,
0.03442750871181488,
0.010297819040715694,
-0.032564472407102585,
-0.027550019323825836,
0.011181269772350788,
-0.017838796600699425,
0.010784420184791088,
0.05268114432692528,
0.012418614700436592,
-0.0033807121217250824,
0.04235880449414253,
0.05101119726896286,
0.0025084340013563633,
-0.006954395677894354,
-0.013147610239684582,
-0.001867939135991037,
0.009551565162837505,
0.04631373658776283,
0.06508862972259521,
0.052183039486408234,
-0.01070516649633646,
0.012787330895662308,
0.06193600222468376,
0.008175215683877468,
-0.010959621518850327,
0.052485011518001556,
-0.011285156011581421,
-0.0078089237213134766,
-0.042603008449077606,
0.03990963473916054,
-0.026166461408138275,
-0.00042855142964981496,
0.003335464047268033,
0.03256284445524216,
0.007535910699516535,
0.06684665381908417,
0.0051168352365493774,
0.07203724980354309,
0.022163866087794304,
-0.023027818650007248,
0.00038242500158958137,
0.05701213330030441,
0.02877589873969555,
-0.0016735513927415013,
0.001368736382573843,
0.03327357769012451,
-0.030014662072062492,
-0.041677720844745636,
0.009686620905995369,
0.007482679560780525,
0.02401389554142952,
-0.011162093840539455,
0.04677166789770126,
-0.014507448300719261,
-0.017146870493888855,
-0.015635481104254723,
0.03164598345756531,
0.005367659963667393,
-0.06309835612773895,
0.05133533850312233,
-0.025738274678587914,
-0.0010845344513654709,
0.021850209683179855,
0.014092961326241493,
0.044140011072158813,
-0.0718126893043518,
-0.06612107157707214,
0.034866999834775925,
-0.03878233581781387,
-0.04221640154719353,
-0.011942800134420395,
0.025669202208518982,
0.013962408527731895,
-0.06552011519670486,
-0.09662697464227676,
-0.018690118566155434,
0.009005237370729446,
-0.03433060273528099,
-0.02944543957710266,
-0.0035082364920526743,
0.045058391988277435,
0.016905194148421288,
0.05026743933558464,
0.004753964487463236,
0.012169485911726952,
0.03559623286128044,
0.023931404575705528,
0.00006084247797844,
-0.00810088962316513,
-0.013073445297777653,
-0.06585052609443665,
0.028392750769853592,
-0.0728306844830513,
-0.02580622211098671,
0.009936423972249031,
-0.045372750610113144,
0.026832588016986847,
-0.0033260693307965994,
0.07117903977632523,
-0.029193896800279617,
-0.02368207462131977,
0.06615278869867325,
0.051124680787324905,
0.03059336543083191,
0.0043037827126681805,
0.02623007632791996,
0.04573670029640198,
0.010835529305040836,
0.004866550676524639,
-0.005076881498098373,
-0.01383029855787754,
-0.04722397029399872,
-0.012100079096853733,
-0.015205875039100647,
0.0356236957013607,
-0.00741803040727973,
-0.02852252684533596,
-0.05408415570855141,
-0.010267166420817375,
-0.021361859515309334,
0.07159947603940964,
-0.03602144122123718,
-0.02176217921078205,
0.027030998840928078,
0.0898403748869896,
-0.0075602163560688496,
-0.0009246909758076072,
-0.06853381544351578,
-0.08285042643547058,
-0.04253961145877838,
-0.04017822444438934,
-0.0918385311961174,
0.014568298123776913,
0.06228514015674591,
-0.04792993515729904,
-0.04012017324566841,
-0.01749015785753727,
-0.014235823415219784,
0.0039654881693422794,
0.022263145074248314,
-0.0002135753456968814,
-0.04905589297413826,
-0.01380863692611456,
0.03745598718523979,
-0.039071232080459595,
0.018793726339936256,
-0.008958247490227222,
-0.0756685882806778,
0.030186600983142853,
-0.020960820838809013,
-0.07659769803285599,
0.010103992186486721,
-0.04392078146338463,
-0.0009148617973551154,
-0.032827556133270264,
-0.0233760979026556,
-0.01983686164021492,
-0.058339376002550125,
-0.02152004837989807,
-0.017173532396554947,
-0.012066496536135674,
-0.017248693853616714,
0.06067588925361633,
0.041794367134571075,
-0.004125470295548439,
0.051797542721033096,
-0.026234392076730728,
-0.03400363400578499,
-0.047378357499837875,
-0.04859887808561325,
0.021351104602217674,
0.003220686223357916,
0.022928446531295776,
-0.044830113649368286,
0.012386597692966461,
0.013368690386414528,
0.0614817813038826,
0.014804600737988949,
-0.03158017247915268,
0.04404253512620926,
-0.05240526795387268,
-0.0032242964953184128,
-0.01456521637737751,
0.025106048211455345,
0.01213478296995163,
0.0388878770172596,
0.01766916923224926,
0.0022710824850946665,
-0.0015896279364824295,
0.025972994044423103,
0.037806231528520584,
0.007724449969828129,
-0.0208926759660244,
0.07009655982255936,
0.017143558710813522,
-0.026172325015068054,
-0.020997118204832077,
0.0024401978589594364,
0.008999696001410484,
0.04109863564372063,
-0.057329654693603516,
-0.06603144854307175,
0.011658516712486744,
0.04225577786564827,
0.04150107502937317,
-0.0326712392270565,
0.043228231370449066,
-0.08875805139541626,
0.036925747990608215,
0.078678198158741,
-0.08930879831314087,
-0.08739204704761505,
-0.009468487463891506,
-0.056898318231105804,
0.054238539189100266,
-0.012133413925766945,
0.0356031097471714,
-0.06756357103586197,
-0.0825028195977211,
0.008455067873001099,
0.009193360805511475,
0.0480843260884285,
0.01666259951889515,
0.02828473597764969,
0.009719552472233772,
-0.04381236433982849,
-0.05934663861989975,
0.028552645817399025,
-0.0357392244040966,
0.02809012308716774,
0.03129751235246658,
0.006366440560668707,
0.018995001912117004,
0.005061908159404993,
-0.0009071712847799063,
0.007508223410695791,
-0.07564090937376022,
0.013449274934828281,
0.01197322178632021,
-0.03156815096735954,
0.004716922994703054,
-0.002042626030743122,
0.010836053639650345,
0.08337370306253433,
-0.04267244040966034,
-0.07229085266590118,
0.025023307651281357,
-0.023913588374853134,
-0.021214256063103676,
0.03278638795018196,
-0.04659032076597214,
-0.02328890934586525,
-0.0037871727254241705,
-0.05570468306541443,
-0.06518732756376266,
-0.015830934047698975,
-0.055366937071084976,
0.04767175018787384,
-0.018402740359306335,
-0.06123947352170944,
0.032047394663095474,
-0.04851287975907326,
-0.039961960166692734,
0.04378284141421318,
0.05528867989778519,
-0.016868513077497482,
0.01220239419490099,
-0.07205351442098618,
0.0009028373751789331,
0.013933701440691948,
-0.03259367123246193,
-0.006732569541782141,
0.04220949485898018,
0.014578314498066902,
0.016870485618710518,
-0.038048312067985535,
-0.004576726816594601,
0.058210670948028564,
-0.018102552741765976,
0.03163626790046692,
-0.051784418523311615,
0.028317028656601906,
0.005471627693623304,
0.045311134308576584,
-0.041852548718452454,
-0.028340892866253853,
0.030823051929473877,
-0.005209535825997591,
-0.012965190224349499,
0.08729749917984009,
0.012812788598239422,
-0.05382310971617699,
-0.014928426593542099,
0.011670826934278011,
0.01699446514248848,
-0.0249584149569273,
-0.015479876659810543,
0.02496226504445076,
0.004146326333284378,
0.06277381628751755,
-0.03839666023850441,
-0.05839630216360092,
-0.03457994759082794,
0.0006951337563805282,
-0.013181701302528381,
-0.03772277757525444,
0.014642673544585705,
0.007028114981949329,
0.035951919853687286,
-0.0189813319593668,
0.0013592365430667996,
0.006024416536092758,
-0.0481409952044487,
0.011224930174648762,
-0.01792071759700775,
-0.01068960689008236,
0.0332522876560688,
0.001861683209426701,
0.041361719369888306,
0.03758816793560982,
-0.047909028828144073,
-0.02625439316034317,
0.012006466276943684,
-0.03925231471657753,
0.01709604635834694,
-0.054154641926288605,
0.030946336686611176,
0.03723163530230522,
-0.06194406747817993,
-0.032142411917448044,
0.02506262995302677,
0.04410499334335327,
0.0033291580621153116,
-0.02712676115334034,
0.015734445303678513,
-0.014288670383393764,
-0.023379074409604073,
-0.012069860473275185,
-0.03003867156803608,
0.011736821383237839,
-0.028930671513080597,
-0.039836227893829346,
0.07924462109804153,
0.030425995588302612,
0.06048615649342537,
-0.01607895828783512,
0.011776753701269627,
0.016677655279636383,
0.01561934594064951,
-0.08594194054603577,
-0.02488849125802517,
-0.013690021820366383,
-0.0039721038192510605,
0.031248340383172035,
-0.016438400372862816,
0.030649682506918907,
-0.0010934742167592049,
0.024450203403830528,
0.03481404110789299,
0.02455933392047882,
-0.03847662732005119,
-0.02254350483417511,
0.021054290235042572,
-0.017251959070563316,
-0.008973286487162113,
-0.021089108660817146,
0.001546447747386992,
0.012760807760059834,
0.002947325585409999,
-0.08347446471452713,
0.023504020646214485,
0.0032071885652840137,
0.0048187836073338985,
0.05080258473753929,
0.0689782127737999,
-0.0243010725826025,
-0.00351891596801579,
-0.01260900218039751,
-0.020779449492692947,
0.03408943861722946,
0.004772915504872799,
-0.009302081540226936,
-0.0018691254081204534,
-0.033183880150318146,
-0.07378020137548447,
-0.03779562935233116,
0.02663460373878479,
0.007259268779307604,
-0.009021610021591187,
0.03351834416389465,
-0.0520978644490242,
0.01129246037453413,
-0.017862126231193542,
-0.023036684840917587,
0.042381033301353455,
-0.01612195000052452,
0.014674023725092411,
0.02753343991935253,
-0.04644634574651718,
-0.014571765437722206,
-0.0001173433629446663,
0.0018582979682832956,
0.011422947980463505,
0.056396156549453735,
0.001483882311731577,
-0.009810845367610455,
-0.03583173453807831,
-0.019388264045119286,
0.07754217088222504,
0.008185542188584805,
-0.03604476526379585,
-0.02977432683110237,
0.029316511005163193,
0.002553895115852356,
0.045821525156497955,
0.028050974011421204,
-0.028456462547183037,
-0.029673896729946136,
0.021374668926000595,
0.04162367433309555,
0.010942933149635792,
-0.0014294888824224472,
-0.023042619228363037,
0.019195526838302612,
-0.02945557050406933,
-0.025110097602009773,
-0.018948525190353394,
0.05423297360539436,
-0.001348225399851799
] |
<p>In the literature (<a href="http://openlibrary.org/books/OL6927036M/Vorlesungen_u%CC%88ber_mechanik" rel="nofollow">Kirchhoff G. - Mechanic (1897), Lecture 18</a> or Lamb, H. - Hydrodynamics (1879)) one can find the following analytical closed form expression for the gravitational potential of homogeneous ellipsoid of unit density, whose surface is given by
\begin{equation}
\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1 \;.
\end{equation}
Gravitational point for internal points is
\begin{equation}
\Omega=\pi abc\int_0^\infty\left(1-\frac{x^2}{a^2+\lambda}-\frac{y^2}{b^2+\lambda}-\frac{z^2}{c^2+\lambda}\right)\frac{d\lambda}{\Delta}
\end{equation}
and for external points
\begin{equation}
\Omega=\pi abc\int_u^\infty\left(1-\frac{x^2}{a^2+\lambda}-\frac{y^2}{b^2+\lambda}-\frac{z^2}{c^2+\lambda}\right)\frac{d\lambda}{\Delta} \;,
\end{equation}
where
\begin{equation}
\Delta=\sqrt{(a^2+\lambda)(b^2+\lambda)(c^2+\lambda)}
\end{equation}
and $u$ is the positive root of equation
\begin{equation}
\frac{x^2}{a^2+u}+\frac{y^2}{b^2+u}+\frac{z^2}{c^2+u}=1 \;.
\end{equation}</p>
<p>The expressions in these formulas appear similar to <a href="http://mathworld.wolfram.com/ConfocalEllipsoidalCoordinates.html" rel="nofollow">confocal ellipsoidal coordinates</a>.</p>
<p>How can these formulas be derived? (perhaps something more readable than the <a href="http://openlibrary.org/books/OL6952302M/Ueber_die_anziehung_homogener_ellipsoide." rel="nofollow">original papers</a>)
Can they be derived in terms of <a href="http://mathworld.wolfram.com/LaplaceEquationConfocalEllipsoidalCoordinates.html" rel="nofollow">ellipsoidal harmonics</a>?</p> | g6573 | [
0.042557038366794586,
0.035522349178791046,
-0.015028037130832672,
-0.024253742769360542,
0.03452381491661072,
0.037793781608343124,
0.022845236584544182,
-0.061416301876306534,
-0.05327397957444191,
0.021560458466410637,
0.018584594130516052,
0.03260326385498047,
0.07134950160980225,
0.015038974583148956,
0.025553356856107712,
-0.015484994277358055,
0.05801551789045334,
0.030769139528274536,
0.03843650966882706,
-0.040471069514751434,
-0.003473428310826421,
0.023090805858373642,
-0.006921695079654455,
-0.020139455795288086,
-0.03953097388148308,
0.018421147018671036,
0.04851767048239708,
-0.024481812492012978,
-0.07841941714286804,
-0.013157976791262627,
-0.005350418854504824,
0.02186237834393978,
0.06761769205331802,
0.02500317618250847,
-0.006178947165608406,
0.03153872489929199,
-0.005606548860669136,
0.020918425172567368,
-0.02903793565928936,
0.012455587275326252,
0.03543452173471451,
-0.05133315175771713,
0.015237321145832539,
0.005466166418045759,
0.02714652381837368,
-0.048697330057621,
-0.03107236698269844,
0.004243185743689537,
0.01919490098953247,
-0.015419846400618553,
0.059131424874067307,
0.09518702328205109,
0.061236169189214706,
-0.08122656494379044,
-0.022022275254130363,
0.05289580672979355,
0.05772167444229126,
-0.02537604421377182,
0.01240737084299326,
0.03173885866999626,
-0.016161086037755013,
-0.03557167947292328,
-0.03443094342947006,
-0.009768303483724594,
0.05239449068903923,
-0.04402394965291023,
-0.008435402996838093,
-0.011465365998446941,
-0.05147682875394821,
0.011275745928287506,
-0.008609791286289692,
-0.0343589149415493,
0.029189234599471092,
-0.03964218124747276,
-0.07451644539833069,
0.02031407132744789,
0.01640385203063488,
0.023683488368988037,
0.03405166417360306,
-0.021262014284729958,
-0.003701700596138835,
-0.003286602906882763,
0.017334887757897377,
-0.0062261042185127735,
0.01018788293004036,
-0.034063518047332764,
0.025233877822756767,
-0.0003864778554998338,
-0.01157678198069334,
-0.008732583373785019,
-0.007062449119985104,
0.0332508310675621,
-0.006227915640920401,
-0.013399974443018436,
-0.03273775056004524,
-0.007914459332823753,
0.014375276863574982,
0.025787316262722015,
-0.02196933701634407,
-0.03432220220565796,
0.017117559909820557,
0.024100402370095253,
0.0034603646490722895,
0.014615206979215145,
0.06414902955293655,
-0.015285343863070011,
0.005565348081290722,
0.00936006847769022,
-0.034808121621608734,
0.0013042677892372012,
0.002303309040144086,
-0.014328432269394398,
0.04469791799783707,
-0.0352032370865345,
-0.037456754595041275,
-0.012846048921346664,
0.048951201140880585,
-0.03833615034818649,
-0.0020941016264259815,
0.05601631477475166,
-0.03418170288205147,
0.01095541100949049,
0.02773878537118435,
0.040762413293123245,
-0.004367210902273655,
0.01961192861199379,
-0.0161968432366848,
0.02005278505384922,
0.01679353415966034,
0.008512228727340698,
0.03158750757575035,
0.01910896599292755,
0.002008315408602357,
0.02474481426179409,
0.014138730242848396,
-0.04385687783360481,
-0.012956787832081318,
0.023638496175408363,
-0.0038518542423844337,
0.0315605066716671,
0.021938001736998558,
-0.04279514029622078,
-0.02758212946355343,
-0.054225288331508636,
-0.03408753499388695,
0.034959930926561356,
-0.022733597084879875,
-0.028936421498656273,
0.01980273239314556,
-0.030228234827518463,
-0.02690754644572735,
0.06221930682659149,
0.017743295058608055,
-0.013508875854313374,
-0.05524333566427231,
0.011255907826125622,
-0.03585340827703476,
0.04512405022978783,
0.0015913051320239902,
0.05671766772866249,
0.037381239235401154,
0.02259579487144947,
0.017001910135149956,
0.010346907190978527,
0.0006419421988539398,
0.07968421280384064,
-0.05136539041996002,
-0.07818837463855743,
0.04096650704741478,
0.002214419422671199,
-0.035275571048259735,
0.007226529065519571,
-0.016203707084059715,
0.061345841735601425,
0.038854509592056274,
0.011972618289291859,
0.03271155059337616,
-0.03684232756495476,
0.01200651004910469,
0.012025158852338791,
-0.04101531207561493,
-0.003861948847770691,
0.025307873263955116,
0.01716911420226097,
0.013743268325924873,
-0.005313829518854618,
0.047861188650131226,
-0.00039856377406977117,
-0.02268644981086254,
0.033501457422971725,
-0.016819093376398087,
0.016082560643553734,
-0.021554039791226387,
0.02312304824590683,
0.029224922880530357,
0.08751252293586731,
0.10650873929262161,
-0.054225292056798935,
-0.036318544298410416,
0.022140292450785637,
0.008607222698628902,
0.04389220103621483,
0.07284847646951675,
0.0013274706434458494,
0.006081757135689259,
-0.014186029322445393,
0.003902987577021122,
0.0005754039739258587,
-0.01378896925598383,
-0.00638212775811553,
-0.062158625572919846,
-0.03151775151491165,
0.031076909974217415,
0.015679648146033287,
0.023040171712636948,
-0.03130696341395378,
-0.04962123557925224,
0.0005265483632683754,
-0.018706096336245537,
0.02293206937611103,
-0.046141367405653,
0.02320367656648159,
0.027285438030958176,
0.006429221481084824,
0.024996161460876465,
0.005440897773951292,
0.016607314348220825,
-0.005701630376279354,
0.033608391880989075,
0.023297283798456192,
-0.0014939616667106748,
-0.02684733271598816,
0.06876366585493088,
-0.021168125793337822,
-0.026218654587864876,
-0.033215612173080444,
-0.05220286548137665,
-0.0031217620708048344,
-0.00709177553653717,
0.07178286463022232,
0.008339574560523033,
-0.034953102469444275,
-0.01275426521897316,
-0.03333291783928871,
0.00517745316028595,
-0.011072156019508839,
0.058484602719545364,
-0.02270805463194847,
0.05903610959649086,
0.03132228925824165,
0.06047193333506584,
-0.035491712391376495,
-0.019325552508234978,
-0.0003190095885656774,
0.029764549806714058,
-0.0052624912932515144,
-0.015892354771494865,
0.024656614288687706,
-0.03616245836019516,
-0.02928698994219303,
-0.0315043181180954,
0.012823488563299179,
0.008373627439141273,
0.009768039919435978,
-0.03983977437019348,
0.004009349271655083,
-0.011571182869374752,
-0.05531525984406471,
0.08249099552631378,
0.04023535177111626,
0.03776354342699051,
0.06539640575647354,
0.02462593838572502,
0.09712561964988708,
-0.05910702422261238,
0.027171403169631958,
-0.04678971320390701,
-0.002752843778580427,
0.03945017233490944,
-0.0070110284723341465,
0.03692523017525673,
-0.02263045683503151,
0.017116989940404892,
0.09825066477060318,
0.017661958932876587,
-0.05202069878578186,
-0.02744963765144348,
0.0544222816824913,
-0.006067551672458649,
-0.01680339127779007,
0.024936674162745476,
0.038720715790987015,
-0.011495479382574558,
0.036319565027952194,
-0.004112835507839918,
0.01755496859550476,
-0.03086676076054573,
-0.04201135411858559,
-0.0009951877873390913,
0.024307332932949066,
-0.007456671912223101,
0.012188843451440334,
0.0016590867890045047,
0.03464221581816673,
-0.06236379221081734,
0.047488100826740265,
-0.0222503449767828,
-0.09867455065250397,
-0.009949634782969952,
-0.0008177110576070845,
0.009853813797235489,
0.007997829467058182,
0.037518758326768875,
-0.029087422415614128,
-0.04307204857468605,
0.031957563012838364,
0.011709545738995075,
-0.024128703400492668,
-0.004009965807199478,
0.013648513704538345,
-0.01126839779317379,
-0.022514741867780685,
-0.04473760724067688,
-0.00045290644629858434,
0.020497633144259453,
0.05622844398021698,
-0.07558711618185043,
0.020771468058228493,
-0.02530517615377903,
-0.08525948971509933,
-0.012406804598867893,
-0.0032368870452046394,
0.025678323581814766,
0.03829718753695488,
-0.008696937002241611,
-0.056972723454236984,
-0.017235418781638145,
-0.038024142384529114,
0.11012901365756989,
0.003596837632358074,
-0.042133934795856476,
-0.03034878522157669,
-0.03247824311256409,
0.003128340467810631,
-0.08773637562990189,
-0.023956935852766037,
-0.006424643099308014,
0.03518807142972946,
-0.03590601682662964,
-0.009460918605327606,
-0.02385544776916504,
-0.026744011789560318,
0.062385957688093185,
-0.02910003811120987,
0.03630106896162033,
-0.0271262489259243,
0.033507756888866425,
0.024604570120573044,
0.009766749106347561,
0.03537527099251747,
-0.02847641333937645,
-0.05532517284154892,
-0.0022607017308473587,
0.00796367134898901,
0.04719232767820358,
-0.04524439945816994,
-0.0024688332341611385,
0.05765926092863083,
-0.0642499253153801,
-0.04159150272607803,
0.026896532624959946,
-0.014011593535542488,
0.06287617981433868,
0.04135917127132416,
0.019804714247584343,
-0.06640004366636276,
-0.015587523579597473,
-0.01021390501409769,
-0.038506682962179184,
0.0028501173947006464,
0.03444881737232208,
-0.004874701611697674,
-0.007676585577428341,
0.02581433765590191,
0.01808331534266472,
-0.009529286995530128,
0.006717979907989502,
-0.011193984188139439,
0.09670637547969818,
-0.051897428929805756,
0.0457271933555603,
-0.05667967349290848,
0.0015942053869366646,
-0.07350461184978485,
0.0014039510861039162,
0.00017313691205345094,
0.007568967062979937,
0.0005241600447334349,
-0.02430001087486744,
0.03701173886656761,
0.026463506743311882,
0.003487205831333995,
-0.0342070572078228,
0.044393643736839294,
-0.020266037434339523,
-0.0707952007651329,
0.0011154352687299252,
-0.061781641095876694,
0.07603266835212708,
-0.006143977399915457,
0.08800448477268219,
-0.08187315613031387,
0.07280265539884567,
-0.004149580840021372,
0.01909693330526352,
-0.03620462864637375,
0.01350974477827549,
-0.04628918692469597,
-0.028758985921740532,
0.019809311255812645,
0.0070358868688344955,
0.03905660659074783,
0.001956566469743848,
-0.050560176372528076,
-0.021779514849185944,
0.02119160257279873,
0.08612824976444244,
0.0016194655327126384,
-0.03515496850013733,
0.023900138214230537,
-0.006404037121683359,
0.02261575683951378,
0.007335019763559103,
0.0013824617490172386,
-0.08793468028306961,
0.020834892988204956,
-0.042105380445718765,
0.01962912082672119,
0.024271508678793907,
-0.012725342996418476,
-0.0308252964168787,
0.0176957119256258,
-0.023473113775253296,
-0.027544667944312096,
0.023689571768045425,
0.08367470651865005,
0.006721155717968941,
-0.102203868329525,
0.0056195990182459354,
-0.04210818186402321,
-0.038609445095062256,
-0.036818064749240875,
0.05284292995929718,
-0.01153101772069931,
-0.02454329840838909,
0.004975898191332817,
0.013365644961595535,
0.007421882823109627,
-0.005966047756373882,
-0.013125530444085598,
0.00937120895832777,
-0.029289525002241135,
0.006429802160710096,
-0.011947916820645332,
0.05888557806611061,
-0.03631674870848656,
-0.06567125767469406,
-0.0004794802807737142,
-0.010134917683899403,
-0.06081179529428482,
-0.011264286004006863,
0.05964532122015953,
0.07919491082429886,
-0.021859843283891678,
-0.016326572746038437,
0.03101619891822338,
0.03083769977092743,
-0.008991003036499023,
-0.05212940648198128,
-0.02447644993662834,
-0.04516783356666565,
-0.021965501829981804,
-0.015964161604642868,
0.030007384717464447,
-0.0033163283951580524,
0.018709935247898102,
-0.03822929039597511,
0.027073245495557785,
-0.03020540624856949,
0.08320252597332001,
0.025587737560272217,
-0.04549175873398781,
0.02656388096511364,
0.009095334447920322,
0.010528180748224258,
-0.038545623421669006,
0.006776050664484501,
-0.08308762311935425,
-0.0014267772203311324,
0.0035875802859663963,
-0.022704128175973892,
0.034722354263067245,
-0.03560568019747734,
0.0262464452534914,
0.026896527037024498,
0.046574272215366364,
0.05861768499016762,
0.015245126560330391,
0.057481799274683,
0.07206528633832932,
0.01336903590708971,
-0.015719566494226456,
0.02482740208506584,
0.009152435697615147,
0.02171524241566658,
-0.01655469834804535,
-0.03476041927933693,
0.0383724682033062,
-0.038412243127822876,
-0.05059150978922844,
0.08121972531080246,
0.031746357679367065,
-0.03204121068120003,
-0.01758907362818718,
0.041783589869737625,
0.026087505742907524,
-0.048713602125644684,
-0.029975516721606255,
0.022132793441414833,
0.02286713942885399,
-0.0700317770242691,
0.01956687495112419,
-0.006632818374782801,
-0.04850315302610397,
0.037174757570028305,
-0.03424800559878349,
-0.016712909564375877,
-0.006031332537531853,
0.0036465704906731844,
-0.049237728118896484,
-0.03693253919482231,
-0.014068212360143661,
-0.04772296920418739,
0.03598306328058243,
-0.07466618716716766,
0.009349916130304337,
0.0039125122129917145,
-0.015223291702568531,
0.018063796684145927,
-0.059082161635160446,
0.024657057598233223,
-0.017643846571445465,
0.023888563737273216,
0.02367020584642887,
-0.10013128072023392,
0.02590135671198368,
0.03468445688486099,
-0.013285776600241661,
-0.06617914140224457,
-0.05769432336091995,
0.002791515551507473,
-0.014502977021038532,
0.01228337362408638,
0.00797687005251646,
-0.012463872320950031,
-0.055698782205581665,
-0.02649306133389473,
-0.01901007443666458,
0.06718247383832932,
0.0052510411478579044,
-0.011713709682226181,
0.0289307851344347,
0.015285608358681202,
-0.003114393213763833,
0.016678765416145325,
0.052505768835544586,
-0.022286225110292435,
-0.020335298031568527,
-0.023304414004087448,
0.019071005284786224,
-0.05491122603416443,
-0.006857677828520536,
0.030424755066633224,
0.02083093300461769,
-0.08323235809803009,
0.006735426839441061,
-0.03432682901620865,
-0.0076843067072331905,
-0.00803086906671524,
-0.01915847696363926,
0.022566406056284904,
0.0013414955465123057,
-0.013630762696266174,
-0.0008022502297535539,
-0.025938354432582855,
0.029981983825564384,
0.009864553809165955,
0.04605339840054512,
0.01342396903783083,
-0.027892546728253365,
-0.02430075593292713,
0.0096576027572155,
0.0263298898935318,
0.030323123559355736,
0.04187972843647003,
-0.025449322536587715,
0.010950370691716671,
-0.02847403660416603,
-0.047886673361063004,
-0.05416380241513252,
-0.03375253081321716,
0.052262842655181885,
-0.005743547808378935,
-0.07557924836874008,
0.006191322114318609,
-0.022642625495791435,
0.005017886403948069,
0.046670712530612946,
-0.029036449268460274,
-0.030136656016111374,
0.026062652468681335,
0.031837522983551025,
-0.0020359402988106012,
-0.035948414355516434,
-0.02121994085609913,
-0.009029198437929153,
-0.06449110060930252,
0.005106502678245306,
0.05505462735891342,
0.00523093668743968,
0.04021459445357323,
0.016331229358911514,
-0.020410189405083656,
0.00859772227704525,
-0.043909016996622086,
0.013298294506967068,
-0.03166032209992409,
0.04073479399085045,
0.04925457015633583,
0.027308324351906776,
0.02319939248263836,
0.038222841918468475,
0.011593655683100224,
0.02973596379160881,
-0.08697421103715897,
-0.004295167047530413,
0.011870496906340122,
-0.0022476124577224255,
-0.09969388693571091,
0.01912088878452778,
0.0315682478249073,
-0.07929705828428268,
-0.011081523261964321,
0.06718264520168304,
-0.013998396694660187,
0.034446414560079575,
0.009367965161800385,
0.0291513092815876,
0.009058979339897633,
-0.047964662313461304,
-0.008401299826800823,
0.031505145132541656,
0.06912077218294144,
0.015914762392640114,
-0.08166918158531189,
0.02260546386241913,
0.016221076250076294,
0.004206295590847731,
-0.02164752222597599,
0.008116694167256355,
0.026119420304894447,
0.04073775187134743,
-0.04896889999508858,
-0.0028692870400846004,
-0.009782940149307251,
0.010059910826385021,
0.054559387266635895,
-0.017262520268559456,
0.011533813551068306,
-0.005273547023534775,
-0.0022742722649127245,
0.0012367900926619768,
-0.050093211233615875,
-0.01237014215439558,
-0.03354455158114433,
-0.0307332593947649,
-0.03167986497282982,
-0.06359613686800003,
0.022430557757616043,
0.0908908024430275,
-0.028657162562012672,
0.0669635757803917,
-0.05898388847708702,
-0.0033380610402673483,
-0.04614504799246788,
-0.021705610677599907,
0.0006812464562244713,
0.05171733349561691,
0.013179360888898373,
-0.02270471304655075,
0.019754603505134583,
-0.026490911841392517,
0.011123874224722385,
-0.009396479465067387,
-0.029700294137001038,
-0.026721591129899025,
-0.00914725661277771,
0.01045162696391344,
0.005605868995189667,
0.05386153236031532,
0.024924226105213165,
-0.0034083849750459194,
-0.02564767375588417,
-0.0032136342488229275,
0.03772735968232155,
0.004135371185839176,
-0.015971586108207703,
0.017014121636748314,
-0.0330268032848835,
-0.018874401226639748,
0.01830758899450302,
-0.029264995828270912,
0.028994139283895493,
-0.038399871438741684,
-0.05340220034122467,
-0.010607065632939339,
0.003305416088551283,
-0.03102855756878853,
0.02212494984269142,
-0.028463779017329216,
-0.029929643496870995,
0.02380797453224659,
0.05582175776362419,
-0.03934267535805702,
-0.005755474790930748,
-0.03849878907203674,
-0.06410443782806396,
-0.038284510374069214,
0.006374233402311802,
-0.004095894284546375,
-0.011490244418382645,
-0.08378524333238602,
0.06586502492427826,
-0.008622712455689907,
0.013917187228798866,
0.0067073586396873,
-0.05844888091087341,
0.0737089216709137,
0.03580080345273018,
0.0444539338350296,
0.008316787891089916,
0.009007885120809078,
-0.0010020711924880743,
0.014718472957611084,
0.02586212009191513,
-0.08594806492328644,
0.017451878637075424,
0.02079496532678604,
-0.017936116084456444,
-0.0008590372744947672,
-0.03213103115558624,
-0.016469256952404976,
-0.004126711282879114,
0.0035876540932804346,
0.005383525975048542,
-0.028034312650561333,
0.0074552991427481174,
0.017515255138278008
] |
<p>I am reading a physiology book chapter (<a href="http://rads.stackoverflow.com/amzn/click/0387983813" rel="nofollow">Mathematical Physiology, by Keener</a> --Respiration chapter) about the gas exchange between capillaries and alveoli. It seems that this gas exchange can be modeled after some simple physical relationships. Since I am not usually studying physics, I do not fully understand some concepts that the author uses to derive a conservation law and I would appreciate any help. </p>
<p>I do admit, however, that this question may be off-topic since it could be a mathematical lapsus rather than a physics question. </p>
<p><strong>Preliminaries</strong></p>
<p>First, the author indicates that if a gas with partial pressure $P_g$ is in contact with a liquid, the steady-state concentration $U$ of gas is given by:
$$
U = \sigma P_s
$$</p>
<p>where $\sigma$ is the solubility of the gas in the liquid. I assume that this is a particular version of Henry's Law.</p>
<p>Then, it explains if there is a difference between the partial pressure of the gas ($P_g$) and the partial pressure on the fluid ($\frac{U}{\sigma}$), then there should be some flux between the gas and the fluid and the simplest model would be to assume that this flux is linearly proportional to the pressure difference:
$$
q = D_s \left(P_g - \frac{U}{\sigma}\right)
$$</p>
<p><strong>Problem</strong></p>
<p>The author then considers a segment of a capillary (a cylindrical tube) of length $L$, constant cross-sectional area $A$ and perimeter $p$, that is in contact with a gas with partial pressure $P_g$. The fluid moves through the tube with a velocity $v(x)$. Finally, they say that since mass is conserved:
$$
\frac{d}{dt} \left( A \int_{0}^{L} U(x,t) dt \right) = v(0)AU(0,t) - v(L)AU(L,t) + p \int_{0}^{L} q(x,t) dx
$$</p>
<p><strong>Question</strong></p>
<p>How is the relationship below derived? </p>
<p>I understand that $A \int_{0}^{L} U(x,t) dt$ is in fact the total amount of the dissolved gas in the tube at a given time. I also understand how $\int_{0}^{L} q(x,t) dx$ represents the total flux of gas across the whole capillary wall. However, I fail to see what the two first elements of the right-hand represent and why is the left-side derived with respect to $t$.</p> | g6574 | [
0.031538382172584534,
-0.03473477438092232,
-0.026905618607997894,
0.01767124980688095,
0.026747042313218117,
0.04392443969845772,
0.032073404639959335,
-0.007909945212304592,
-0.02337176539003849,
-0.022864244878292084,
-0.01170521043241024,
-0.037634897977113724,
0.031534016132354736,
-0.004945085849612951,
0.04637526348233223,
0.041776515543460846,
0.08866894245147705,
-0.02790941298007965,
-0.026275739073753357,
0.040856096893548965,
-0.05117519572377205,
0.008718014694750309,
-0.04089599847793579,
-0.03583965077996254,
-0.028093229979276657,
-0.0361478254199028,
0.021860944107174873,
0.021847432479262352,
-0.04872841015458107,
-0.008143520914018154,
0.00845571979880333,
-0.0007797349244356155,
0.00813263189047575,
0.007284419611096382,
0.0030500260181725025,
-0.02279844880104065,
0.0006410925416275859,
-0.03405510634183884,
0.01150581892579794,
-0.010540158487856388,
0.08210521191358566,
0.04591146484017372,
0.022523118183016777,
0.05680358037352562,
0.007705196272581816,
-0.032670166343450546,
-0.07627484202384949,
-0.08798757195472717,
-0.031115639954805374,
-0.009121750481426716,
0.027601152658462524,
0.03968126326799393,
-0.039477329701185226,
0.007527273613959551,
0.0054757255129516125,
0.021763205528259277,
0.048566170036792755,
-0.019992846995592117,
0.03650369867682457,
0.016483750194311142,
0.053008146584033966,
0.006816757842898369,
-0.0009161695488728583,
0.008689134381711483,
0.013636481948196888,
-0.00815454963594675,
-0.01896531693637371,
-0.018219808116555214,
0.03153345733880997,
0.03726882115006447,
-0.008041433990001678,
-0.04081328958272934,
0.04629940167069435,
0.009634474292397499,
-0.01571040228009224,
0.005484872963279486,
-0.025751782581210136,
-0.02692534029483795,
0.05117008090019226,
-0.059027113020420074,
-0.06882871687412262,
0.0020898582879453897,
0.014298921450972557,
0.0022207258734852076,
-0.0011241293977946043,
0.012937945313751698,
-0.06391517072916031,
-0.026367420330643654,
-0.0421878919005394,
0.03476996347308159,
-0.011703051626682281,
-0.0032757422886788845,
0.10279589891433716,
0.00923913437873125,
0.008755997754633427,
-0.024368949234485626,
-0.002087398897856474,
0.03476627916097641,
-0.016794417053461075,
-0.02145547792315483,
-0.02339962311089039,
0.0072219474241137505,
-0.01709282584488392,
0.05192367359995842,
0.014904535375535488,
0.01213326770812273,
0.016416028141975403,
0.0697578638792038,
-0.05315117910504341,
0.026605285704135895,
0.020171621814370155,
0.02287389151751995,
-0.05130920931696892,
0.028982631862163544,
0.024159099906682968,
-0.048182472586631775,
0.04522974416613579,
0.04532323777675629,
0.053811557590961456,
0.04227659851312637,
0.010416427627205849,
0.03270058333873749,
0.038536448031663895,
-0.003725349670276046,
-0.0185126680880785,
-0.0005088060279376805,
0.03347228094935417,
-0.025416439399123192,
0.034277934581041336,
0.06331606954336166,
0.024627894163131714,
-0.03702721744775772,
-0.044099073857069016,
0.021926579996943474,
0.04565594717860222,
-0.06599116325378418,
-0.03105333261191845,
0.05074993893504143,
-0.012285522185266018,
-0.02198735810816288,
0.013527036644518375,
-0.0032416190952062607,
-0.009726757183670998,
0.05847498029470444,
-0.01669059880077839,
0.011069945991039276,
-0.04132890701293945,
-0.0587218813598156,
0.03946755453944206,
-0.04070384427905083,
-0.007299968972802162,
0.0872240886092186,
-0.010387439280748367,
-0.007225238252431154,
0.03147851303219795,
-0.024955814704298973,
0.0343804769217968,
-0.027433929964900017,
-0.004414298105984926,
0.019983261823654175,
0.03796563670039177,
-0.026489879935979843,
0.049209706485271454,
-0.017248554155230522,
-0.051436204463243484,
-0.0005239172605797648,
0.021831106394529343,
-0.06903977692127228,
0.04974980279803276,
-0.030644703656435013,
-0.013336348347365856,
-0.03367931768298149,
-0.0019016540609300137,
0.050202518701553345,
0.004425038583576679,
0.06827910989522934,
0.04764468967914581,
0.01691446825861931,
-0.02487139403820038,
-0.05569411441683769,
0.022591743618249893,
-0.02530663087964058,
-0.0061450013890862465,
-0.024968216195702553,
0.03168254345655441,
0.047267984598875046,
0.02376352809369564,
-0.024933552369475365,
-0.09835193306207657,
-0.04888265207409859,
-0.02135295979678631,
0.0010792278917506337,
0.019441382959485054,
0.032269399613142014,
-0.01007307879626751,
0.05482998862862587,
0.02748505026102066,
-0.10851673781871796,
-0.0422249436378479,
0.058610208332538605,
-0.032885145395994186,
-0.0043283808045089245,
0.04977298155426979,
0.05899260938167572,
0.025311030447483063,
0.024108057841658592,
-0.015180977061390877,
0.02348167821764946,
-0.03811204433441162,
0.017281483858823776,
-0.020516930148005486,
-0.02655602991580963,
-0.001559731550514698,
-0.010807426646351814,
-0.03101038560271263,
-0.05729532986879349,
0.0012698157224804163,
0.09609415382146835,
-0.0015209652483463287,
0.009784235619008541,
-0.006693142931908369,
-0.034160301089286804,
-0.06539081782102585,
0.0020795250311493874,
-0.01651274971663952,
-0.02369195781648159,
0.0335894338786602,
0.032830238342285156,
-0.07424686849117279,
0.04140323027968407,
-0.030803585425019264,
0.022798504680395126,
0.0005345228710211813,
-0.007016555406153202,
0.018147818744182587,
-0.001149367424659431,
-0.002617995487526059,
0.019740987569093704,
-0.015763534232974052,
0.019180821254849434,
0.012492619454860687,
-0.0439918227493763,
-0.037901632487773895,
0.030053624883294106,
0.01786772720515728,
0.06577979773283005,
0.01864134706556797,
-0.04083793982863426,
0.0039435201324522495,
0.007640042807906866,
-0.004619338549673557,
-0.0016900378977879882,
0.048464108258485794,
-0.013731387443840504,
0.01912432350218296,
-0.018046218901872635,
-0.019268354400992393,
0.013630906119942665,
-0.00905346404761076,
-0.039815641939640045,
-0.013220430351793766,
-0.026994019746780396,
0.0072180163115262985,
0.042297590523958206,
-0.05756200850009918,
0.001523266197182238,
-0.0037950787227600813,
0.06591258198022842,
0.030947821214795113,
-0.03512877598404884,
-0.01201965007930994,
0.04948430880904198,
-0.016391145065426826,
0.03974707052111626,
0.060505229979753494,
0.014142281375825405,
0.057581283152103424,
-0.059291742742061615,
-0.019699491560459137,
-0.013804316520690918,
0.025688763707876205,
0.017493804916739464,
-0.022433804348111153,
0.03600035235285759,
0.05774049833416939,
-0.052608273923397064,
0.06294148415327072,
0.022631961852312088,
0.021245509386062622,
0.04262600466609001,
-0.015877196565270424,
0.0003648875863291323,
-0.04425550624728203,
0.021019885316491127,
0.048202816396951675,
0.07627926766872406,
0.02153731696307659,
-0.03590850159525871,
-0.011225945316255093,
-0.011994016356766224,
0.0076703839004039764,
0.023304276168346405,
-0.04245857521891594,
-0.010275417938828468,
0.05548392981290817,
0.021718207746744156,
-0.05462133139371872,
-0.07135415822267532,
0.020173950120806694,
0.010622464120388031,
-0.016469085589051247,
0.00018536460993345827,
-0.0054133255034685135,
-0.048305682837963104,
-0.008445678278803825,
0.015757838264107704,
0.007450162433087826,
-0.05650408938527107,
-0.012576553039252758,
-0.007092200219631195,
-0.0023072813637554646,
-0.061496756970882416,
-0.008100039325654507,
-0.02487361617386341,
-0.022279612720012665,
-0.029578404501080513,
-0.09593810886144638,
-0.026200179010629654,
-0.027766143903136253,
-0.004688483662903309,
-0.020624961704015732,
0.04434870928525925,
0.011347657069563866,
-0.03290681168437004,
-0.01857398822903633,
0.0014303779462352395,
-0.03202709183096886,
0.04900296404957771,
0.054448727518320084,
-0.021892903372645378,
-0.014564023353159428,
-0.04298827424645424,
-0.029850486665964127,
-0.026311788707971573,
-0.01033800933510065,
-0.03093905746936798,
0.023448793217539787,
0.05486535280942917,
0.023226242512464523,
-0.014486047439277172,
0.06272639334201813,
0.02243000641465187,
0.039001401513814926,
-0.02170737087726593,
-0.030780086293816566,
0.005608965177088976,
0.03049303963780403,
0.034786392003297806,
0.027433348819613457,
0.004434157162904739,
0.04199106991291046,
-0.05056564882397652,
-0.050044894218444824,
0.043190788477659225,
-0.009194454178214073,
-0.02263428084552288,
0.022297734394669533,
0.01458706334233284,
0.020159870386123657,
-0.05708235129714012,
-0.019377680495381355,
-0.027914701029658318,
-0.04570090025663376,
0.03100305050611496,
0.0028727527242153883,
-0.07202014327049255,
-0.02262764424085617,
-0.028408074751496315,
-0.03654814139008522,
0.05925993248820305,
0.04806125909090042,
0.03793150186538696,
-0.006212908774614334,
0.027405058965086937,
0.03757771849632263,
-0.010955232195556164,
-0.022281063720583916,
0.06148912012577057,
-0.0001772452815202996,
-0.018529975786805153,
-0.010742833837866783,
-0.02594411000609398,
-0.03438572585582733,
-0.05741129443049431,
0.055829260498285294,
0.011409763246774673,
0.027973709627985954,
0.01344357617199421,
-0.056236933916807175,
0.0004957172786816955,
-0.01698186993598938,
-0.018944844603538513,
0.013057133182883263,
0.01830989494919777,
-0.018664009869098663,
0.011350701563060284,
0.01287422887980938,
-0.05809086561203003,
-0.009296591393649578,
-0.00832806620746851,
0.021814627572894096,
-0.01821785233914852,
-0.030800415202975273,
-0.03221065178513527,
-0.003968206699937582,
0.026811283081769943,
-0.04765578731894493,
-0.004418055061250925,
0.038250140845775604,
-0.002679763827472925,
0.03168487176299095,
-0.023642396554350853,
-0.051935672760009766,
0.009691022336483002,
0.015018676407635212,
0.03001890890300274,
0.04750742390751839,
-0.019602470099925995,
-0.008927970193326473,
-0.07725460827350616,
-0.007722207345068455,
0.019244413822889328,
-0.003555840579792857,
0.028295297175645828,
-0.08768238127231598,
0.051557280123233795,
-0.11451470106840134,
-0.02613764815032482,
0.0028398658614605665,
0.06627701967954636,
0.07636670023202896,
-0.011664588935673237,
0.02072356827557087,
-0.009603126905858517,
0.010050581768155098,
0.004601768217980862,
0.012132402509450912,
-0.023710135370492935,
0.014909793622791767,
-0.05326300859451294,
-0.03604598715901375,
0.0402592197060585,
-0.02748052217066288,
-0.046973153948783875,
-0.027217062190175056,
0.01788908988237381,
-0.011604896746575832,
0.006486954633146524,
0.009434129111468792,
0.030376140028238297,
-0.030514584854245186,
0.09067673981189728,
0.05384700000286102,
-0.002405930310487747,
0.0032744240015745163,
-0.06460519134998322,
-0.03945066034793854,
0.03265862539410591,
-0.023502210155129433,
-0.03631288558244705,
0.008789192885160446,
0.009637159295380116,
0.018203379586338997,
-0.00746064493432641,
0.02773429825901985,
0.01823386736214161,
-0.02149365469813347,
0.020841699093580246,
-0.005932179279625416,
-0.07033468782901764,
0.001336956862360239,
0.07290443778038025,
0.011949848383665085,
0.05941108241677284,
-0.01325205061584711,
-0.016953444108366966,
-0.03710675239562988,
-0.026683997362852097,
-0.04302014037966728,
0.03672894462943077,
-0.050442226231098175,
0.03205793723464012,
0.037597913295030594,
0.027038123458623886,
-0.006966376211494207,
-0.08625459671020508,
0.0716649740934372,
-0.01983542926609516,
-0.006661387626081705,
-0.010395081713795662,
-0.08040348440408707,
-0.009950941428542137,
-0.02329900860786438,
0.007005347404628992,
-0.009957476519048214,
0.039656512439250946,
0.027496227994561195,
-0.005943520460277796,
-0.006717389449477196,
0.013461577706038952,
0.02536764368414879,
-0.01855594851076603,
-0.030200913548469543,
0.01170048862695694,
0.0019673677161335945,
0.03997673839330673,
-0.0195926483720541,
0.02804482914507389,
0.0025099674239754677,
0.010969490744173527,
0.07813534140586853,
0.02621486783027649,
0.043544869869947433,
0.029067624360322952,
-0.05512554198503494,
0.010937805287539959,
-0.020108124241232872,
-0.01440866943448782,
-0.008499770425260067,
0.0023957283701747656,
-0.012935399077832699,
-0.006108046043664217,
-0.04039427265524864,
0.044919922947883606,
-0.08193952590227127,
-0.017867088317871094,
-0.04340539127588272,
0.029046058654785156,
0.06320608407258987,
-0.020098725333809853,
-0.0476456917822361,
-0.022649407386779785,
0.004815629217773676,
0.06901554763317108,
0.04590146243572235,
0.005096133798360825,
-0.007077929098159075,
0.003079736605286598,
-0.00796765647828579,
0.041970450431108475,
-0.013207499869167805,
-0.05539441108703613,
-0.015993472188711166,
0.0077723171561956406,
0.06288227438926697,
-0.07423693686723709,
0.05705695599317551,
-0.04465482011437416,
0.02827916294336319,
-0.01988554745912552,
0.020641516894102097,
0.05803722143173218,
0.008634177036583424,
0.024217460304498672,
-0.018086591735482216,
-0.044857919216156006,
-0.06466761231422424,
-0.008114947006106377,
0.07573812454938889,
0.020754337310791016,
0.04198296368122101,
-0.01803544908761978,
-0.010958579368889332,
-0.008610200136899948,
-0.02872498147189617,
0.015213722363114357,
-0.07918228209018707,
0.0013257171958684921,
-0.03562719747424126,
0.05721157789230347,
-0.015376562252640724,
-0.05188268423080444,
-0.0263733621686697,
-0.03554104268550873,
-0.015963032841682434,
-0.002229256322607398,
0.023791471496224403,
-0.019512230530381203,
0.07601544260978699,
0.03284601494669914,
0.026722708716988564,
-0.021515149623155594,
-0.010866221971809864,
-0.07781405746936798,
0.003577356692403555,
-0.04936410114169121,
0.040299613028764725,
-0.027632979676127434,
0.0061674402095377445,
0.022777801379561424,
-0.01432175561785698,
0.05219244211912155,
-0.039629414677619934,
-0.06693252921104431,
0.04119951277971268,
-0.04020658880472183,
0.014990351162850857,
0.010848220437765121,
-0.029264530166983604,
0.01261059008538723,
0.005666145123541355,
0.004178863484412432,
-0.004637617617845535,
-0.04401462897658348,
-0.006135294679552317,
-0.0766671821475029,
-0.0011842453386634588,
0.055312175303697586,
-0.012988242320716381,
0.009128852747380733,
0.002995977643877268,
0.021534034982323647,
0.024240748956799507,
0.009582791477441788,
0.054903898388147354,
0.029337747022509575,
-0.053807832300662994,
0.02816285938024521,
0.03783372417092323,
0.01743912696838379,
0.010023079812526703,
0.024572711437940598,
-0.007262185215950012,
-0.01171056553721428,
0.0011442219838500023,
0.024736616760492325,
-0.05693832039833069,
-0.014799734577536583,
0.06457622349262238,
0.0667419359087944,
0.022577939555048943,
-0.01584157533943653,
0.030415942892432213,
0.03752629831433296,
-0.012432990595698357,
-0.025761688128113747,
0.04352346435189247,
0.017948433756828308,
-0.0644386038184166,
0.01825844496488571,
-0.03160453587770462,
-0.02484748698771,
-0.08503897488117218,
-0.012789889238774776,
0.004624335560947657,
0.02221091277897358,
-0.00921938568353653,
-0.002367408247664571,
0.016632109880447388,
-0.07803727686405182,
-0.029322240501642227,
-0.030707692727446556,
0.008860084228217602,
0.022945381700992584,
0.026547059416770935,
0.06521084904670715,
0.035883840173482895,
-0.03493354097008705,
0.0501968190073967,
-0.06973342597484589,
-0.0017758420435711741,
-0.011798759922385216,
-0.03519747406244278,
0.028056945651769638,
0.014364054426550865,
0.014302943833172321,
0.04661043360829353,
0.013471043668687344,
-0.038107067346572876,
0.0009744542767293751,
-0.0350586473941803,
0.0061145019717514515,
0.015045366249978542,
-0.048033375293016434,
-0.046393100172281265,
-0.010225724428892136,
0.030745191499590874,
-0.01229157019406557,
0.0023398015182465315,
0.04310702905058861,
-0.018321257084608078,
0.0073589240200817585,
0.057849105447530746,
0.04620242863893509,
-0.03533530235290527,
0.02306024357676506,
0.020678315311670303,
0.041305843740701675,
-0.021253198385238647,
0.02643398754298687,
0.05862737074494362,
-0.015261487103998661,
-0.060040269047021866,
0.04158475622534752,
0.021631237119436264,
-0.018280651420354843,
-0.02666211687028408,
-0.025533566251397133,
-0.02651044726371765,
-0.027690982446074486,
0.03500273451209068,
-0.030636638402938843,
0.04170703515410423,
0.036706361919641495,
0.06482850015163422,
-0.019713085144758224,
-0.021911129355430603,
0.042009081691503525,
-0.006418786942958832,
-0.010167524218559265,
-0.009135210886597633,
-0.09151039272546768,
-0.030162600800395012,
-0.0998106524348259,
-0.058922573924064636,
-0.008944498375058174,
0.011931369081139565,
-0.0029341315384954214,
-0.06940818578004837,
0.019769975915551186,
-0.022503945976495743,
0.013108866289258003,
-0.00964468065649271,
-0.0017974844668060541,
0.048935454338788986,
0.001048786798492074,
0.07651029527187347,
-0.020854325965046883,
0.010846887715160847,
-0.001916264882311225,
-0.008969509974122047,
-0.06924761086702347,
0.04123400151729584,
-0.03554986044764519,
-0.018282614648342133,
-0.016030875965952873,
0.02369537577033043,
0.04724150523543358,
0.031108278781175613,
-0.031987834721803665,
0.06247568503022194,
0.023312261328101158,
0.06202958896756172,
0.020470311865210533,
-0.017100702971220016,
-0.08406957983970642,
0.003737777005881071,
0.053265687078237534,
-0.00881640799343586,
-0.002476373454555869,
-0.04153349995613098,
-0.0015339611563831568,
-0.019789444282650948,
-0.01608593948185444,
0.046250272542238235,
-0.01994568295776844,
-0.03798219561576843,
-0.013197867199778557
] |
<p>Or would it be acceleration voltage? Acceleration sounds like it makes more sense, but my paper says accelerating.</p>
<p>What are possible ways you could go about calculating it?</p> | g6575 | [
0.08312352001667023,
0.07586808502674103,
0.003520793514326215,
0.018161654472351074,
0.04966525733470917,
-0.02562534809112549,
-0.00884028896689415,
0.04868462681770325,
-0.04427643120288849,
-0.022103141993284225,
-0.014603449031710625,
0.03883613273501396,
0.025874964892864227,
0.045944590121507645,
0.02504066377878189,
-0.020035864785313606,
0.05197307839989662,
-0.04386107996106148,
0.022333770990371704,
0.020611319690942764,
0.011283754371106625,
-0.030745036900043488,
-0.036214109510183334,
-0.046131428331136703,
-0.04430576041340828,
0.017629817128181458,
-0.07736609131097794,
0.03398270905017853,
-0.0609356127679348,
-0.020885879173874855,
0.0331958644092083,
-0.056317511945962906,
0.0247451551258564,
-0.004236434120684862,
-0.051705170422792435,
0.022365324199199677,
0.01114683784544468,
0.061053093522787094,
0.03072216920554638,
0.012462745420634747,
0.007796390913426876,
-0.04538142308592796,
0.012042010203003883,
0.01859598606824875,
0.007914526388049126,
-0.007204902358353138,
0.006837520748376846,
-0.0345076359808445,
-0.027407215908169746,
-0.07310790568590164,
-0.05503880977630615,
0.0047226278111338615,
0.020131122320890427,
0.039281755685806274,
0.006597784347832203,
0.0352359302341938,
-0.01570502296090126,
-0.01386663131415844,
0.041809502989053726,
0.02714565210044384,
-0.0341222770512104,
-0.007141744717955589,
0.0713164433836937,
-0.015099719166755676,
0.04806673526763916,
0.005028239917010069,
-0.03154435008764267,
-0.010866648517549038,
0.02178400196135044,
-0.01092199981212616,
0.041439592838287354,
-0.0664236843585968,
-0.0379791259765625,
-0.028038235381245613,
-0.021477244794368744,
-0.00016237549425568432,
-0.022856855764985085,
0.023658260703086853,
0.04906119406223297,
0.03463392332196236,
0.005164827685803175,
0.0098949009552598,
0.012122954241931438,
-0.024340493604540825,
0.06299091875553131,
-0.0008857258362695575,
0.020083259791135788,
0.0393117256462574,
0.011463146656751633,
-0.012959221377968788,
0.03361315280199051,
0.03625912219285965,
0.07507487386465073,
-0.03844369202852249,
-0.022316675633192062,
-0.041471317410469055,
-0.0009991422994062304,
0.06752986460924149,
0.03868381306529045,
0.004391206428408623,
-0.024462426081299782,
-0.03840528428554535,
0.019594553858041763,
-0.036434710025787354,
-0.005493507720530033,
0.01840486191213131,
0.015449589118361473,
-0.08549649268388748,
0.0021345734130591154,
-0.05912619084119797,
-0.021719738841056824,
-0.08673683553934097,
0.006417754106223583,
-0.049709826707839966,
-0.008271901868283749,
-0.01631115935742855,
0.09639058262109756,
0.030418824404478073,
-0.023183723911643028,
0.04597758874297142,
-0.0011725217336788774,
0.04486526921391487,
-0.06309153884649277,
0.06536660343408585,
0.0029976472724229097,
0.026353823021054268,
0.0018340586684644222,
-0.02757728099822998,
-0.0726034939289093,
0.026309316977858543,
0.03907742723822594,
-0.013730425387620926,
0.014536052010953426,
-0.021555878221988678,
0.02061929926276207,
0.05697578936815262,
-0.02757989801466465,
-0.03214557468891144,
-0.03260311111807823,
-0.002951467875391245,
0.013930260203778744,
-0.04995105043053627,
-0.02542201802134514,
0.002593432320281863,
-0.002225978299975395,
0.02255822904407978,
-0.05721055343747139,
0.02365647815167904,
0.029642030596733093,
0.04565419629216194,
0.03295271098613739,
0.042715877294540405,
0.011705070734024048,
-0.06213047727942467,
0.07305353134870529,
-0.03979937732219696,
0.02284446731209755,
0.008850077167153358,
-0.022124743089079857,
0.05581885948777199,
0.044581931084394455,
-0.04230217635631561,
-0.0053471908904612064,
-0.017253560945391655,
-0.04896944761276245,
-0.038710396736860275,
0.01694977656006813,
0.00940730981528759,
-0.0111912302672863,
-0.020043883472681046,
0.0010281672002747655,
-0.020282356068491936,
0.052500780671834946,
0.005769724026322365,
0.03394772857427597,
0.07741506397724152,
0.04200877994298935,
-0.017216864973306656,
0.012671815231442451,
0.042930666357278824,
0.04610591009259224,
-0.018891459330916405,
0.04879295080900192,
-0.038590386509895325,
-0.017031662166118622,
-0.06195122003555298,
-0.008606916293501854,
-0.004574233200401068,
-0.04164888337254524,
0.03499467670917511,
-0.05053282901644707,
-0.03876442462205887,
0.02143014781177044,
0.006910448893904686,
-0.08297678083181381,
-0.033692918717861176,
0.010512237437069416,
-0.02860347554087639,
-0.027264272794127464,
0.02442937158048153,
0.030985957011580467,
0.061951570212841034,
-0.021997176110744476,
0.024021010845899582,
0.0449247881770134,
0.01317611988633871,
-0.05864064767956734,
-0.015418730676174164,
0.049710728228092194,
-0.001535050687380135,
0.04444735869765282,
0.062280308455228806,
0.025797851383686066,
0.07503051310777664,
-0.0011622171150520444,
0.021388648077845573,
-0.018059322610497475,
-0.022670766338706017,
-0.01384411659091711,
0.02194673754274845,
-0.03036726824939251,
-0.006596057675778866,
0.018278667703270912,
0.06427882611751556,
-0.07487871497869492,
0.0021678698249161243,
0.014018547721207142,
-0.040411874651908875,
-0.00012940255692228675,
-0.02893451787531376,
-0.06844020634889603,
-0.014718789607286453,
-0.06313464790582657,
-0.04066174104809761,
0.05835074931383133,
0.05505993217229843,
-0.02884839102625847,
0.04106606915593147,
0.008488403633236885,
0.024920610710978508,
0.07480603456497192,
-0.03388404846191406,
0.04540006443858147,
-0.008463808335363865,
-0.059115614742040634,
-0.015051404014229774,
0.059035804122686386,
-0.0068791769444942474,
-0.016984669491648674,
-0.017458822578191757,
-0.0010117135243490338,
-0.019554542377591133,
0.004524937830865383,
0.003022510791197419,
-0.016484778374433517,
-0.014852216467261314,
-0.04267209768295288,
0.016588497906923294,
-0.024444229900836945,
0.022886302322149277,
0.03095126710832119,
0.025654545053839684,
0.016374044120311737,
-0.0221685990691185,
-0.036426689475774765,
-0.0031535436864942312,
-0.00890342891216278,
-0.036048829555511475,
-0.017941923812031746,
0.01468741986900568,
-0.023075029253959656,
0.05538554862141609,
-0.05742647126317024,
-0.03668023645877838,
0.009006783366203308,
-0.01599934883415699,
0.03800357133150101,
-0.03359355032444,
0.06405218690633774,
-0.023083878681063652,
-0.028569204732775688,
-0.03980293869972229,
-0.022058118134737015,
0.04472650960087776,
-0.02768443338572979,
-0.05944301187992096,
0.06591864675283432,
-0.014695868827402592,
-0.0075406236574053764,
-0.018675466999411583,
-0.04143723472952843,
-0.035906970500946045,
0.00010380589083069935,
-0.022754989564418793,
0.02628600224852562,
0.07840969413518906,
0.06573318690061569,
-0.023580176755785942,
0.04165540635585785,
0.004474836867302656,
0.02944384515285492,
-0.037970442324876785,
0.01217510923743248,
-0.019070535898208618,
-0.03267363831400871,
0.013789801858365536,
0.005275433417409658,
0.0008633994730189443,
0.02857280522584915,
-0.0004528953577391803,
-0.055786147713661194,
-0.023192204535007477,
0.035288337618112564,
0.015720536932349205,
-0.054670609533786774,
-0.05427590757608414,
0.029452906921505928,
0.010832513682544231,
0.050086647272109985,
0.009267196990549564,
-0.03609525412321091,
-0.1072101816534996,
0.01504883635789156,
0.033330533653497696,
-0.027886107563972473,
0.03147008270025253,
0.01366005465388298,
0.04568743705749512,
0.010616575367748737,
-0.06394858658313751,
0.003797959303483367,
0.02893810160458088,
-0.05925142019987106,
0.009381106123328209,
0.004078459460288286,
-0.06468340754508972,
0.009515990503132343,
0.04473486915230751,
0.028578339144587517,
0.06717280298471451,
-0.0247934702783823,
-0.012211591005325317,
-0.018739541992545128,
-0.01784070022404194,
-0.03451225161552429,
-0.025166338309645653,
0.020015673711895943,
-0.029460780322551727,
0.04441942274570465,
-0.05118095874786377,
0.04727949574589729,
-0.04243141785264015,
-0.04760821536183357,
0.0076490226201713085,
-0.0357002429664135,
0.0028930041007697582,
-0.0025440091267228127,
0.016659000888466835,
-0.06319781392812729,
0.06861173361539841,
-0.027426423504948616,
-0.00463671050965786,
0.021100953221321106,
0.027369176968932152,
-0.008813831023871899,
0.005615539848804474,
-0.05583709850907326,
0.10277027636766434,
-0.058850664645433426,
-0.03644724562764168,
-0.023266062140464783,
-0.0030498241540044546,
0.005312875844538212,
0.028147518634796143,
0.014754759147763252,
-0.013160457834601402,
-0.028360456228256226,
-0.023561229929327965,
-0.02747553028166294,
0.04643372818827629,
0.040173474699258804,
0.018415695056319237,
-0.01658269576728344,
-0.04029523953795433,
-0.036964450031518936,
-0.05881480500102043,
-0.07273874431848526,
-0.0024975696578621864,
0.021152786910533905,
-0.061939988285303116,
0.014039142988622189,
0.033108144998550415,
-0.06140226125717163,
-0.0010457250755280256,
-0.0180658008903265,
-0.04375716298818588,
0.018241818994283676,
-0.005200703162699938,
0.017620280385017395,
0.036044660955667496,
0.020259397104382515,
0.005499522667378187,
0.04999352991580963,
0.04077931120991707,
0.001606610370799899,
0.01384669542312622,
0.07441424578428268,
-0.0281885527074337,
0.03128376603126526,
0.021784014999866486,
-0.009966625832021236,
0.020818933844566345,
0.03704157471656799,
-0.019396524876356125,
-0.005620097275823355,
0.01067596860229969,
0.048823028802871704,
0.011016073636710644,
-0.022425781935453415,
0.051034074276685715,
0.02657560631632805,
-0.04891494661569595,
0.005563313141465187,
-0.009058145806193352,
-0.018491804599761963,
0.02396627888083458,
0.04451605677604675,
-0.00992532353848219,
-0.009556401520967484,
-0.01236709300428629,
0.007804341148585081,
0.01625685952603817,
-0.019473085179924965,
0.037160180509090424,
-0.02462361380457878,
0.06818358600139618,
0.023803023621439934,
0.09866756945848465,
0.035164251923561096,
0.03757981210947037,
0.0556168258190155,
0.02400130033493042,
0.011896164156496525,
-0.0033617489971220493,
-0.006270457990467548,
0.08158902823925018,
-0.011497248895466328,
-0.01511712558567524,
-0.005449100397527218,
-0.0021284918766468763,
-0.05293022841215134,
0.011216485872864723,
-0.025851253420114517,
0.003288229228928685,
0.04293932765722275,
0.010577648878097534,
-0.038306817412376404,
-0.00965980626642704,
0.017143327742815018,
0.02546955831348896,
-0.08689998835325241,
-0.014117423444986343,
-0.002708221785724163,
-0.0037732829805463552,
0.018766120076179504,
-0.01100658718496561,
-0.012621069326996803,
-0.04646407067775726,
-0.046097174286842346,
-0.0010208318708464503,
-0.020558323711156845,
-0.03797663003206253,
-0.01978059485554695,
0.043706949800252914,
0.052417442202568054,
0.01431905385106802,
-0.01054714247584343,
0.01575600542128086,
-0.01806538924574852,
-0.04948204383254051,
-0.06975040584802628,
0.01009384635835886,
0.0033764089457690716,
-0.06419317424297333,
-0.03697214648127556,
0.027106601744890213,
-0.04100007191300392,
0.03128467872738838,
0.0103920204564929,
-0.06275017559528351,
-0.016387108713388443,
0.09185057878494263,
-0.02325679548084736,
-0.03654802218079567,
-0.026119079440832138,
0.0233360156416893,
0.017887912690639496,
-0.029732992872595787,
-0.015321335755288601,
0.004257090389728546,
-0.07005613297224045,
0.008166374638676643,
-0.00855030957609415,
-0.028119483962655067,
0.022199947386980057,
0.04474245384335518,
0.050711825489997864,
-0.0071438951417803764,
0.03181428834795952,
0.036624111235141754,
0.03928328678011894,
0.04719002917408943,
0.047406647354364395,
0.02474052831530571,
0.01814875192940235,
-0.015577769838273525,
-0.024848490953445435,
0.00839330442249775,
-0.053386036306619644,
-0.03173264488577843,
0.07063647359609604,
-0.04998335242271423,
0.03741277754306793,
0.013904373161494732,
-0.013726507313549519,
0.03848773241043091,
-0.02462049573659897,
-0.05136298015713692,
0.03216679021716118,
-0.04848584905266762,
-0.005221216939389706,
-0.014505031518638134,
-0.02011864259839058,
-0.03931504115462303,
-0.011191192083060741,
0.0014736105222254992,
0.02114374190568924,
0.01849663443863392,
0.015469267033040524,
-0.0045997328124940395,
-0.11129798740148544,
0.03011167421936989,
0.01099663507193327,
0.0651155337691307,
0.011907592415809631,
-0.03982016071677208,
-0.05677480250597,
0.04965100437402725,
0.01584993116557598,
-0.10350517183542252,
-0.014274763874709606,
0.009494234807789326,
0.0460883267223835,
0.0005685591022484004,
0.020395828410983086,
0.020122753456234932,
0.05923420935869217,
-0.001716346014291048,
-0.022055979818105698,
-0.0039519318379461765,
0.017244568094611168,
0.012330417521297932,
0.03479117527604103,
-0.01760290190577507,
0.008204145357012749,
-0.00862148404121399,
0.01753261126577854,
0.0045440602116286755,
0.01609700918197632,
-0.009040364995598793,
0.012482874095439911,
-0.02650354616343975,
0.009857218712568283,
-0.007549420464783907,
0.009282306768000126,
-0.000880672421772033,
0.02888191118836403,
0.029963839799165726,
-0.012258621864020824,
-0.026243245229125023,
-0.04959086701273918,
0.02175678126513958,
0.023133767768740654,
-0.009701701812446117,
-0.0024483243469148874,
-0.012019481509923935,
-0.038609396666288376,
0.025456087663769722,
0.030773911625146866,
-0.010829395614564419,
-0.012482719495892525,
0.004989843815565109,
0.009685619734227657,
-0.05738387256860733,
-0.06038364768028259,
-0.002440653508529067,
-0.007104741409420967,
0.018788928166031837,
0.0001927912817336619,
-0.006755605805665255,
0.045967407524585724,
0.03342851251363754,
-0.01345669012516737,
-0.014963576570153236,
0.07969596982002258,
-0.03205021470785141,
-0.004210816230624914,
0.01837988756597042,
-0.04741857200860977,
-0.08858553320169449,
-0.07916107028722763,
-0.010376034304499626,
0.016681058332324028,
-0.0035998851526528597,
-0.0170135535299778,
0.026335490867495537,
-0.009865961968898773,
0.0004121095989830792,
0.07069811224937439,
0.040603309869766235,
0.019191015511751175,
-0.005712856072932482,
0.009244708344340324,
-0.025878973305225372,
0.03795064613223076,
0.04305991157889366,
-0.011369305662810802,
-0.005034351721405983,
0.02510623261332512,
-0.07532735168933868,
-0.020947884768247604,
0.02042127214372158,
0.04933040216565132,
0.03831695020198822,
0.05596239119768143,
0.0564911924302578,
0.04037243872880936,
-0.011675081215798855,
-0.022033430635929108,
0.00844177883118391,
0.060244474560022354,
0.030881093814969063,
-0.03511856496334076,
0.0212364811450243,
-0.03792097792029381,
0.030002549290657043,
-0.01367929670959711,
-0.004968306981027126,
0.016275741159915924,
-0.025650305673480034,
0.025944367051124573,
-0.03214862570166588,
-0.04161607474088669,
0.023236600682139397,
-0.019442787393927574,
0.037562720477581024,
0.03526366129517555,
0.020990785211324692,
0.01285583432763815,
-0.012850304134190083,
0.0002654818817973137,
-0.05020242556929588,
0.05342990159988403,
0.01516477670520544,
0.002197759225964546,
-0.006647124886512756,
-0.04159862920641899,
-0.031192675232887268,
0.007548993919044733,
-0.0014291692059487104,
-0.012943018227815628,
-0.0636194571852684,
-0.024454033002257347,
-0.018635785207152367,
0.012609932571649551,
-0.024047287181019783,
-0.059831973165273666,
-0.021259548142552376,
-0.03980114310979843,
0.017800524830818176,
-0.05783030018210411,
0.0429890938103199,
-0.02544987201690674,
-0.007374364882707596,
-0.018163228407502174,
0.023418905213475227,
-0.052133459597826004,
0.03418974578380585,
0.0030445908196270466,
-0.0022352717351168394,
-0.035772573202848434,
-0.0037698259111493826,
0.03271213546395302,
-0.02558060549199581,
-0.006723483558744192,
0.023940423503518105,
-0.06190699338912964,
0.014602044597268105,
0.0012083109468221664,
0.018185120075941086,
0.027839070186018944,
0.034569498151540756,
0.06227676197886467,
0.011515537276864052,
-0.040283359587192535,
0.014918091706931591,
-0.009409038349986076,
-0.013867455534636974,
-0.0373428538441658,
0.01593494787812233,
0.027564629912376404,
0.015165411867201328,
0.026007231324911118,
0.040416695177555084,
-0.006887386552989483,
0.051854927092790604,
0.014206266961991787,
-0.01576300896704197,
-0.030279753729701042,
0.06229158490896225,
-0.014635463245213032,
0.03056304156780243,
0.044074419885873795,
-0.0293947234749794,
0.0653848797082901,
-0.05269275978207588,
-0.028678564354777336,
0.029417311772704124,
-0.0042121228761971,
0.00015353957132901996,
-0.019871627911925316,
-0.03697923943400383,
0.06371676176786423,
0.07423168420791626,
-0.05890284851193428,
0.0075377607718110085,
0.012185480445623398,
0.024512605741620064,
0.01321076788008213,
0.0577094629406929,
-0.019278429448604584,
-0.016754809767007828,
-0.05355650559067726,
-0.032284483313560486,
0.003780402708798647,
-0.031651224941015244,
-0.017188800498843193,
0.06353773921728134,
0.09110760688781738,
-0.04316724091768265,
0.0164344385266304,
-0.019045332446694374,
-0.06847719103097916,
-0.027053024619817734,
0.017995420843362808,
-0.02410256303846836,
-0.06927314400672913,
0.015356834977865219,
-0.030840519815683365,
0.02481798268854618,
-0.0035855239257216454,
0.008678426034748554,
-0.014409729279577732,
-0.02189043164253235,
0.029060950502753258,
-0.07467590272426605,
-0.04969805106520653,
-0.0753168985247612
] |
<p>My question is vague, so I'm hoping the answers will help me ask more concrete questions and maybe produce some interesting discussion.</p>
<p>In mean field theory, say for the Ising model, we treat the magnetization $m$ as a parameter and derive the equation
$$
\langle\sigma_i\rangle = \tanh (\beta J dm),
$$
where $J$ is the neighbor coupling, $\beta$ is the inverse temperature, and $d$ is the spatial dimension. Self-consistency requires
$$
\langle\sigma_i \rangle = m,
$$
from which can be derived all the ordinary mean field theory conclusions.</p>
<p>However, we don't have to impose this equation by hand if instead we minimize the mean field free energy with respect to $m$.</p>
<p>In string theory something superficially similar happens. Consistency conditions on the world-sheet theory are equivalent to equations of motion of the target-space theory. I have always wondered why this is the case, and it would be interesting to see a correspondence like mean field consistency $\simeq$ world-sheet consistency, mean field equilibrium for liberated $m$ $\simeq$ target-space vacuum.</p>
<p>An observation: mean field theory maps a physical system with site-to-site interactions to a single site problem, where the other sites are treated as creating the background magnetization $m$.</p>
<p>An analogous observation for the string: to derive Einstein's equations, we consider a string propagating in a background metric (which would be emergent from a sea of strings) and show that the background metric gets renormalized according to the Einstein-Hilbert action.</p>
<p>${}{}$</p> | g6576 | [
0.010173088870942593,
0.034907229244709015,
-0.02265014685690403,
-0.05047597363591194,
0.04073931276798248,
0.03360029309988022,
-0.0021636986639350653,
-0.019708767533302307,
-0.0015539274318143725,
0.010498413816094398,
-0.025381052866578102,
0.04127069190144539,
-0.011450055055320263,
0.007409428246319294,
-0.019006825983524323,
-0.006518706679344177,
0.058108508586883545,
-0.04679601639509201,
0.006528032943606377,
-0.04538968205451965,
-0.003033860120922327,
-0.011875473894178867,
0.0677657350897789,
-0.039792656898498535,
0.0166776105761528,
0.05398952588438988,
0.04043315351009369,
-0.03875606134533882,
-0.00513051450252533,
-0.001622181385755539,
0.002967291511595249,
0.034433335065841675,
0.05575960502028465,
-0.05671403557062149,
-0.054382145404815674,
-0.015208160504698753,
0.015799565240740776,
0.0013299769489094615,
0.026669740676879883,
-0.017702709883451462,
0.034220658242702484,
-0.04702475666999817,
0.07668010145425797,
0.00951131246984005,
0.016300257295370102,
-0.029141690582036972,
-0.06223279610276222,
-0.009973580949008465,
0.03682117536664009,
0.021022632718086243,
-0.021760832518339157,
0.05345587059855461,
0.05176422372460365,
0.04597502201795578,
0.018675820901989937,
0.0207669660449028,
0.016595885157585144,
-0.020954420790076256,
0.0371454581618309,
0.03031911887228489,
-0.0017862694803625345,
0.022461652755737305,
-0.03795742988586426,
0.05179723724722862,
0.022368470206856728,
0.022772183641791344,
-0.09496141970157623,
0.02742248959839344,
0.02504635788500309,
-0.012518513947725296,
0.04160188511013985,
0.03173620253801346,
-0.04014037549495697,
0.002067986875772476,
-0.06871763616800308,
0.011128995567560196,
0.03662164881825447,
-0.01204666867852211,
-0.04106765612959862,
0.03555968776345253,
-0.05846378579735756,
-0.05571003630757332,
0.0077639068476855755,
-0.03450184687972069,
0.08352441340684891,
-0.0753985345363617,
0.027852270752191544,
0.021023903042078018,
-0.06760833412408829,
-0.015575150959193707,
0.031095949932932854,
0.034067265689373016,
0.032479289919137955,
-0.030603215098381042,
0.044331107288599014,
-0.027340887114405632,
0.002546862931922078,
0.0616036057472229,
-0.013332153670489788,
-0.011413058266043663,
-0.026367997750639915,
-0.019695736467838287,
0.0018878686241805553,
0.048664506524801254,
-0.025663210079073906,
0.017379945144057274,
0.056422628462314606,
0.06440010666847229,
0.034664321690797806,
0.01999969221651554,
-0.05041025951504707,
-0.02328147366642952,
-0.050235144793987274,
-0.012937883846461773,
-0.05990558862686157,
-0.06107816472649574,
0.020797723904252052,
0.030409622937440872,
0.006094298325479031,
0.04382672533392906,
-0.01805407926440239,
-0.024990618228912354,
-0.010462393052875996,
0.0228461641818285,
-0.018810193985700607,
-0.029140116646885872,
-0.021460115909576416,
-0.02563682198524475,
0.01270729023963213,
-0.021367983892560005,
0.01973516121506691,
-0.05100386589765549,
-0.017513060942292213,
0.042158160358667374,
-0.026612896472215652,
-0.0020972394850105047,
-0.0529632493853569,
0.0318533293902874,
0.004903474822640419,
0.018108971416950226,
-0.04376526549458504,
-0.041829224675893784,
-0.026493171229958534,
-0.024596111848950386,
0.01673927903175354,
0.01506061851978302,
0.048771932721138,
-0.054982054978609085,
0.030412254855036736,
0.06897170096635818,
0.031233686953783035,
0.08317515254020691,
-0.00280958553776145,
-0.004830458667129278,
-0.030590355396270752,
0.02102215215563774,
-0.006104433909058571,
-0.05409161001443863,
0.015281214378774166,
-0.05454960837960243,
0.08063941448926926,
-0.04161151126027107,
0.06067148596048355,
0.01638975366950035,
-0.010001718997955322,
-0.008839568123221397,
0.03499490022659302,
0.021893780678510666,
-0.0380975604057312,
-0.060579415410757065,
-0.043530452996492386,
0.02065606229007244,
0.05112998187541962,
0.0691923126578331,
-0.07081004232168198,
0.039797622710466385,
-0.0243911761790514,
-0.006232003215700388,
-0.0021215130109339952,
0.06290163844823837,
0.019304446876049042,
-0.030226565897464752,
0.05100451409816742,
-0.08113761246204376,
0.029064809903502464,
-0.015549244359135628,
-0.05991438031196594,
-0.003555067116394639,
-0.04117352142930031,
-0.021584678441286087,
-0.005535989534109831,
0.01834297366440296,
-0.03213271498680115,
0.07068291306495667,
0.0037885101046413183,
-0.010910050012171268,
0.008107814937829971,
-0.05019168555736542,
0.00281452271156013,
-0.027586864307522774,
0.005282917059957981,
0.03805416822433472,
0.016039889305830002,
-0.015325489453971386,
-0.05718521028757095,
0.028285814449191093,
0.001194977667182684,
-0.0050125024281442165,
0.054834429174661636,
0.0012629620032384992,
0.00026575845549814403,
-0.032856784760951996,
-0.06875239312648773,
0.02761387638747692,
-0.022479671984910965,
0.012337823398411274,
0.014546833001077175,
0.01718094013631344,
-0.03742649406194687,
0.06991404294967651,
-0.006943055894225836,
-0.03457888960838318,
0.05910732224583626,
0.007931728847324848,
-0.015151286497712135,
0.01959924027323723,
-0.046287622302770615,
0.038452956825494766,
0.031395237892866135,
0.022413158789277077,
-0.0958942174911499,
-0.006068274844437838,
0.026368027552962303,
0.009341459721326828,
0.07053247839212418,
0.034336306154727936,
0.031872350722551346,
-0.0347767136991024,
0.05971227586269379,
0.03830961510539055,
-0.005137916654348373,
0.004095211625099182,
-0.06603618711233139,
0.07927487045526505,
0.026241160929203033,
0.0638636127114296,
0.026165729388594627,
0.013233615085482597,
0.0033600616734474897,
0.030799292027950287,
-0.010475254617631435,
-0.012834385968744755,
-0.010510919615626335,
-0.04087469354271889,
-0.013639691285789013,
-0.012487733736634254,
0.013326497748494148,
0.03239813074469566,
-0.02539222314953804,
-0.03127158805727959,
-0.026725081726908684,
-0.054672278463840485,
0.053407955914735794,
0.02152198553085327,
-0.003383311443030834,
-0.0005185516201891005,
0.026082530617713928,
0.0016504416707903147,
-0.037983763962984085,
-0.009962807409465313,
0.01437303051352501,
0.03710893541574478,
-0.02467290684580803,
0.06740867346525192,
0.014158249832689762,
0.01699615828692913,
0.003252448746934533,
0.03391145169734955,
0.03262191265821457,
0.003393335733562708,
-0.015122411772608757,
-0.02188807539641857,
-0.044371347874403,
-0.06373230367898941,
-0.003966116812080145,
-0.028191465884447098,
0.007216553669422865,
-0.04265029355883598,
-0.006777294911444187,
0.02274082414805889,
0.02294543944299221,
0.00489850714802742,
0.014062532223761082,
0.009777329862117767,
0.004537660162895918,
0.09660505503416061,
0.03136540204286575,
-0.05430562049150467,
0.033799268305301666,
0.06755190342664719,
-0.013898246921598911,
0.004822871182113886,
-0.0340944342315197,
-0.006741393357515335,
-0.0008867821888998151,
-0.014877832494676113,
-0.05187244340777397,
-0.08133575320243835,
-0.0004855665611103177,
-0.026200352236628532,
0.004685362800955772,
0.004559529013931751,
0.050350483506917953,
-0.014134066179394722,
-0.02389434166252613,
0.0565154105424881,
-0.022109944373369217,
-0.013496029190719128,
0.0426798090338707,
-0.04955441504716873,
-0.030160874128341675,
-0.010604471899569035,
0.04329974949359894,
-0.030760018154978752,
0.00026789927505888045,
-0.0004188329912722111,
-0.05359567701816559,
0.0014827405102550983,
-0.024227380752563477,
0.05873044952750206,
0.031642526388168335,
0.018700899556279182,
0.05279020220041275,
-0.00344640645198524,
-0.01750830188393593,
-0.07283902168273926,
-0.037285733968019485,
0.037013884633779526,
0.017557388171553612,
0.032047901302576065,
-0.034831129014492035,
-0.030783386901021004,
0.023513032123446465,
-0.006612321361899376,
0.002600275445729494,
0.07524054497480392,
0.013911006040871143,
0.020777186378836632,
0.029306450858712196,
-0.02079007588326931,
0.004254303406924009,
0.002833411330357194,
0.0324910506606102,
0.010742684826254845,
-0.026773763820528984,
0.06393744796514511,
0.06514947861433029,
0.04530856013298035,
0.016323700547218323,
-0.03234678879380226,
0.021744944155216217,
-0.007577267475426197,
-0.08361810445785522,
-0.04225383698940277,
-0.012247140519320965,
-0.040773943066596985,
-0.05166604742407799,
0.009613045491278172,
-0.012813812121748924,
-0.03678835928440094,
0.013457055203616619,
0.032927725464105606,
0.001728429109789431,
0.005088122561573982,
0.06361209601163864,
-0.009188092313706875,
-0.00854340847581625,
0.022796137258410454,
-0.02338981069624424,
0.011214671656489372,
0.0452309213578701,
-0.029105691239237785,
-0.06352244317531586,
0.006363939959555864,
0.006325829774141312,
-0.017594577744603157,
-0.05099725350737572,
0.02232428453862667,
-0.05209843069314957,
0.012438423000276089,
-0.02287493832409382,
-0.03395980969071388,
0.03166668489575386,
-0.03391420096158981,
0.05603098124265671,
0.05577509105205536,
0.02600555121898651,
0.03225245699286461,
0.06226612254977226,
0.016405874863266945,
0.03552626818418503,
0.01953967660665512,
0.03114723414182663,
-0.013319652527570724,
-0.04865414649248123,
-0.03704284504055977,
-0.007943777367472649,
-0.041323453187942505,
-0.01896740309894085,
-0.030263351276516914,
0.02335219271481037,
0.00732451630756259,
-0.04160790145397186,
-0.04806169494986534,
0.060508303344249725,
-0.05849551409482956,
0.02556261233985424,
0.007187924347817898,
-0.015097180381417274,
-0.029889365658164024,
0.008402674458920956,
0.023036999627947807,
0.014746959321200848,
-0.07765234261751175,
-0.028834905475378036,
0.057610783725976944,
-0.01133554708212614,
0.03739500045776367,
-0.004120917525142431,
-0.061547160148620605,
0.03578316420316696,
-0.006320647429674864,
-0.002918641082942486,
0.003546625142917037,
-0.1030815988779068,
0.0171516090631485,
-0.0438305027782917,
0.009759708307683468,
-0.0003427494375500828,
0.026547525078058243,
0.013651436194777489,
0.002021417487412691,
0.0436810702085495,
-0.00015820603584870696,
-0.07023508101701736,
0.04411546140909195,
-0.07391444593667984,
-0.02772458642721176,
-0.0324549600481987,
-0.023509345948696136,
-0.06081419065594673,
0.003079945920035243,
0.002532703336328268,
-0.026135429739952087,
0.029120134189724922,
-0.04090554639697075,
-0.0006987857050262392,
0.11916670203208923,
0.03883691132068634,
-0.012626565992832184,
0.009753577411174774,
0.007549398113042116,
0.04025714844465256,
0.08282248675823212,
-0.03643788397312164,
-0.04584791511297226,
0.0009083243203349411,
0.009881829842925072,
-0.02407318912446499,
0.06717793643474579,
0.045291151851415634,
0.03707873076200485,
0.021120188757777214,
-0.05422739312052727,
-0.032425545156002045,
0.047662124037742615,
-0.042889658361673355,
-0.027471765875816345,
-0.0033222862984985113,
-0.0617554672062397,
-0.041117437183856964,
0.00727068493142724,
0.04866723343729973,
0.05531351640820503,
0.01082220021635294,
0.033865123987197876,
0.0022948840633034706,
0.0018405186710879207,
-0.017138030380010605,
-0.010222804732620716,
-0.04005028307437897,
-0.026731841266155243,
-0.01008270587772131,
-0.018686454743146896,
-0.02763303741812706,
-0.0012079993030056357,
-0.01826571114361286,
-0.0044809021055698395,
-0.024706970900297165,
-0.016798846423625946,
-0.010912950150668621,
-0.0034951220732182264,
0.06098653003573418,
0.049409154802560806,
-0.050084732472896576,
0.051839251071214676,
0.022412816062569618,
0.006662821397185326,
0.008015258237719536,
0.04538780823349953,
-0.030533017590641975,
0.05207419395446777,
0.020032119005918503,
0.02608432248234749,
0.035424306988716125,
-0.04090399295091629,
0.012111629359424114,
0.01492692157626152,
0.02353927679359913,
-0.03292921558022499,
0.001239575445652008,
0.008752121590077877,
0.09062977880239487,
0.02250230871140957,
-0.005483532790094614,
0.03126869723200798,
-0.012641707435250282,
-0.03597995266318321,
0.049048762768507004,
0.020270511507987976,
-0.015503079630434513,
-0.001806997461244464,
0.027050349861383438,
0.014430869370698929,
0.021684957668185234,
-0.04015275090932846,
0.0072276354767382145,
0.03812248632311821,
0.020092718303203583,
-0.013961805030703545,
0.023792069405317307,
-0.0416470430791378,
0.038621265441179276,
0.01463458314538002,
0.010001109912991524,
0.011259431950747967,
0.007539375219494104,
-0.01901005022227764,
0.04657546803355217,
-0.05063037574291229,
-0.08901481330394745,
-0.050691816955804825,
-0.04497167840600014,
-0.0028827576898038387,
-0.02298501506447792,
0.013829934410750866,
-0.022624753415584564,
-0.01738562062382698,
-0.02621503546833992,
-0.0462784618139267,
0.0383455827832222,
0.013162887655198574,
-0.007249750662595034,
0.028172006830573082,
-0.0030258619226515293,
-0.014811648055911064,
0.027290375903248787,
-0.045381199568510056,
0.04583239182829857,
0.012595795094966888,
0.009099955670535564,
0.04610641673207283,
0.013474171981215477,
0.012844111770391464,
-0.034695837646722794,
-0.04161439090967178,
0.014218381606042385,
-0.0518222339451313,
-0.022226056084036827,
-0.007124772761017084,
0.02432994917035103,
-0.000808246317319572,
0.034928400069475174,
-0.06798706948757172,
-0.014359109103679657,
-0.017032528296113014,
-0.03758041188120842,
-0.016831764951348305,
0.06806767731904984,
-0.003470849012956023,
-0.012162244878709316,
0.010232582688331604,
0.027837883681058884,
-0.016796845942735672,
-0.019444644451141357,
-0.015066082589328289,
-0.030226804316043854,
-0.0442354716360569,
-0.05555247887969017,
0.0023483806289732456,
0.012585646472871304,
0.015609031543135643,
0.044927459210157394,
-0.03245256096124649,
0.024940140545368195,
0.06819736212491989,
-0.016761500388383865,
-0.004758759401738644,
-0.03493933379650116,
0.036514490842819214,
-0.01467833761125803,
0.04943036288022995,
-0.037869494408369064,
0.08691226691007614,
-0.0013345280895009637,
-0.025824440643191338,
0.0347621776163578,
0.06803935766220093,
-0.020068829879164696,
0.005949892103672028,
0.007909958250820637,
-0.013681214302778244,
0.04380553588271141,
-0.04053469002246857,
-0.005098335910588503,
0.01428101398050785,
0.005628674756735563,
0.005213357042521238,
0.042861469089984894,
0.00020094432693440467,
-0.057409849017858505,
0.04948711767792702,
-0.05880684405565262,
0.042073093354701996,
-0.054760608822107315,
0.044856809079647064,
0.007641986012458801,
-0.03717256709933281,
-0.06831793487071991,
0.050018325448036194,
-0.03348036855459213,
0.05494704470038414,
0.05441766232252121,
-0.006014949642121792,
-0.05775890499353409,
0.038055263459682465,
0.07069939374923706,
-0.0036519828718155622,
-0.07709964364767075,
0.04182852432131767,
0.0047773392871022224,
0.023986902087926865,
0.003401273163035512,
-0.04085054621100426,
-0.03622141852974892,
-0.010353189893066883,
-0.050843801349401474,
-0.023337997496128082,
0.014046943746507168,
-0.034223005175590515,
-0.09494291245937347,
0.0062322416342794895,
-0.03231261670589447,
-0.03358587622642517,
0.006134706549346447,
0.007159034255892038,
0.02088400535285473,
-0.0146658169105649,
0.016165003180503845,
-0.009740590117871761,
0.0073189083486795425,
-0.014830158092081547,
-0.005299555137753487,
0.0302005372941494,
-0.011459394358098507,
-0.022011058405041695,
-0.004261312540620565,
0.04121537506580353,
-0.06297926604747772,
-0.017113616690039635,
0.04068534076213837,
-0.010431595146656036,
0.02808176912367344,
-0.0019840553868561983,
-0.020011339336633682,
0.027480661869049072,
0.01647963374853134,
0.015575251542031765,
-0.030713196843862534,
0.043298833072185516,
0.002725944621488452,
0.02608606219291687,
0.030695786699652672,
-0.014662778936326504,
0.049699507653713226,
0.010829535312950611,
-0.01290857046842575,
0.03286752477288246,
0.04815151169896126,
0.00775713799521327,
0.011741326190531254,
-0.00572493951767683,
0.00009474121179664508,
-0.02621370367705822,
0.0538175068795681,
-0.04449103772640228,
-0.023293238133192062,
0.0016917428001761436,
-0.07880297303199768,
-0.052712082862854004,
-0.03888145461678505,
-0.025107095018029213,
-0.007222750224173069,
0.05166289582848549,
0.00913704838603735,
-0.036610569804906845,
-0.08694478869438171,
-0.02392367646098137,
0.03898659348487854,
0.01805708557367325,
-0.020049020648002625,
0.0351986400783062,
-0.018117139115929604,
-0.022375833243131638,
0.004225337877869606,
-0.032867077738046646,
-0.01886594481766224,
-0.07743814587593079,
0.04981503635644913,
-0.01686459220945835,
-0.045071423053741455,
-0.03406182676553726,
-0.0022357774432748556,
0.0492430180311203,
-0.009398353286087513,
0.04336366802453995,
-0.019160736352205276,
-0.037829384207725525,
0.037511423230171204,
-0.05566791072487831,
0.030545786023139954,
-0.04996839910745621,
0.025114933028817177,
-0.03150911256670952,
-0.026274895295500755,
0.03494274243712425,
0.00253501208499074,
0.019229257479310036,
0.013924185186624527,
-0.005541750229895115,
0.017240002751350403,
0.01053714845329523,
-0.03496697172522545,
0.014792349189519882,
-0.011426453478634357,
-0.030913271009922028,
0.0016258612740784883,
0.05062325671315193,
0.04253171384334564,
0.027565250173211098,
-0.03410595655441284,
-0.09572281688451767,
-0.0366562083363533,
0.024396661669015884,
-0.015432585962116718,
-0.01621687225997448,
-0.029749102890491486,
0.043535299599170685
] |
<p>If you "disobey" the constraints of the <a href="http://en.wikipedia.org/wiki/Kramers%E2%80%93Kronig_relations" rel="nofollow">Kramers-Kronig relations</a>, what happens? Do you get non-physical results?</p>
<p>I am simulating reflection and transmission off/through a slab of material. I specify the complex index of refraction $n = n_r + i n_i$ of the material, assume it has vacuum on either side, and then use the transfer-matrix method to find the reflection and transmission for some given wavelength range.</p>
<p>As I was messing around, adjusting $n_r$ and $n_i$ to see what happens, I found that with certain combinations of $n_r$ and $n_i$ I could get seemingly impossible results -- e.g., reflection going above 1 (which represents more power coming reflecting off of the material than went into it!).</p>
<p>But I was pretty arbitrarily choosing my $n$'s, and I realized that in real life one of $n_r$ or $n_i$ determines the other, from the Kramers-Kronig relations. So was I getting these bizarre results as a result of (probably) "disobeying" the K-K relations, is it more likely my simulation is broken?</p> | g6577 | [
-0.015696024522185326,
0.01552160270512104,
0.0064264689572155476,
-0.007655658759176731,
0.004401165526360273,
-0.015921222046017647,
-0.009882722981274128,
-0.021137775853276253,
-0.0009819457773119211,
0.02800900861620903,
0.001570848049595952,
-0.006115473806858063,
-0.016164829954504967,
0.04882459342479706,
-0.0398201048374176,
-0.004358558915555477,
0.0810391753911972,
0.020815817639231682,
0.012354793958365917,
0.01265977043658495,
-0.04479345306754112,
-0.005012670997530222,
-0.05090869590640068,
-0.061765752732753754,
0.029536813497543335,
-0.02337535470724106,
0.00022098032059147954,
-0.039279792457818985,
-0.06573116034269333,
0.020929455757141113,
0.027832841500639915,
-0.016728932037949562,
0.06111372634768486,
-0.045212578028440475,
-0.039562273770570755,
0.02012316696345806,
0.05564476177096367,
0.015095576643943787,
0.021860195323824883,
-0.016255544498562813,
-0.03327571600675583,
0.014090158976614475,
-0.022037245333194733,
0.0525050088763237,
-0.04634673893451691,
-0.020686592906713486,
0.010551978833973408,
0.04367828741669655,
0.01188150979578495,
-0.03408573195338249,
-0.017202233895659447,
0.02731173112988472,
0.036351919174194336,
0.05869909003376961,
0.0011752513237297535,
-0.0011396154295653105,
0.01679246313869953,
0.01311586145311594,
0.10236044973134995,
-0.014156010933220387,
0.009164267219603062,
0.01617841050028801,
-0.00922069326043129,
0.06184417009353638,
0.06175192445516586,
0.02915904112160206,
-0.04120476916432381,
0.04614284634590149,
-0.029673609882593155,
-0.05331934988498688,
-0.016023222357034683,
0.00619139289483428,
-0.008873945102095604,
-0.0431048758327961,
-0.025858283042907715,
0.020571323111653328,
0.025039199739694595,
-0.006745143793523312,
0.015281518921256065,
0.038938239216804504,
-0.010182345286011696,
-0.015454531647264957,
-0.006768539547920227,
0.010802377946674824,
0.032611921429634094,
0.05224141478538513,
0.015971628949046135,
0.02506948634982109,
0.012420200742781162,
0.026025203987956047,
0.019379815086722374,
-0.011377369984984398,
0.015103340148925781,
0.01862165704369545,
0.04513391852378845,
0.043354395776987076,
-0.031864043325185776,
0.03323330730199814,
0.007702548988163471,
0.000007123489922378212,
-0.007485812995582819,
0.07259875535964966,
0.03080027736723423,
-0.03343070670962334,
-0.06776545196771622,
0.004786740988492966,
0.08741740882396698,
0.005954217631369829,
-0.0005982012953609228,
-0.003316677175462246,
-0.055190447717905045,
-0.04025960713624954,
-0.07216980308294296,
-0.0870320126414299,
0.0016918940236791968,
-0.040934935212135315,
-0.01139912661164999,
0.019190488383173943,
0.03366556018590927,
0.009835740551352501,
0.0021588511299341917,
-0.0459582544863224,
0.0298834927380085,
0.07658294588327408,
-0.054495878517627716,
0.0062682898715138435,
0.02789456956088543,
0.013177050277590752,
0.09071490168571472,
-0.0058160205371677876,
-0.050255320966243744,
-0.025910409167408943,
-0.031821779906749725,
0.07490414381027222,
0.025073735043406487,
-0.030696576461195946,
0.04141295328736305,
0.04540017619729042,
0.005577871110290289,
-0.0290281493216753,
-0.010354510508477688,
-0.04138471931219101,
-0.06259491294622421,
-0.07157852500677109,
-0.05660814046859741,
-0.02715274505317211,
-0.003937785979360342,
-0.01158884633332491,
0.05356413498520851,
-0.06056287884712219,
-0.003638551337644458,
0.024659907445311546,
-0.028245480731129646,
-0.025846706703305244,
-0.012285999953746796,
-0.005093881860375404,
0.022987598553299904,
-0.05276012793183327,
-0.005417116917669773,
-0.058957748115062714,
0.030648162588477135,
-0.01348450593650341,
-0.005521183367818594,
-0.00543221877887845,
0.020532798022031784,
-0.06106505170464516,
0.011441051959991455,
-0.02343887835741043,
0.028323115780949593,
-0.07481665164232254,
-0.07274738699197769,
0.0028449823148548603,
-0.024930315092206,
0.01468656025826931,
0.033586543053388596,
0.11164442449808121,
0.0372641496360302,
0.02603471651673317,
-0.009426706470549107,
0.04065932705998421,
-0.02226904220879078,
-0.0006473507964983582,
-0.019227150827646255,
-0.030376141890883446,
0.0007034321315586567,
-0.02858932688832283,
0.022726375609636307,
-0.006519107148051262,
-0.03931957110762596,
-0.01453795749694109,
-0.04059087112545967,
-0.018584247678518295,
-0.0248020701110363,
-0.04456012696027756,
-0.00607258640229702,
-0.008350912481546402,
0.0007862875354476273,
0.028660066425800323,
-0.01542751770466566,
0.049355894327163696,
0.014143268577754498,
0.07774677127599716,
0.07081638276576996,
-0.0013041142374277115,
0.008726773783564568,
0.014782106503844261,
-0.038888826966285706,
-0.015940062701702118,
0.006043786648660898,
-0.04806314408779144,
0.00863572582602501,
0.028119230642914772,
0.03941628709435463,
-0.040841035544872284,
0.008228522725403309,
-0.03875771164894104,
-0.009150811471045017,
-0.0060887085273861885,
0.012034831568598747,
0.02776232734322548,
-0.01728527992963791,
-0.015467224642634392,
0.05515698343515396,
0.011798383668065071,
-0.027200981974601746,
-0.0231382604688406,
0.017029769718647003,
-0.025033319368958473,
-0.023389024659991264,
-0.022313592955470085,
-0.04359200969338417,
-0.060919713228940964,
-0.001789547735825181,
-0.027055907994508743,
0.021343978121876717,
0.012979439459741116,
-0.02597193978726864,
-0.010156791657209396,
0.02135809138417244,
0.00950607843697071,
0.024967018514871597,
-0.048609256744384766,
-0.08789677172899246,
0.04154261574149132,
-0.012672921642661095,
0.004056576639413834,
0.06312555819749832,
-0.0009549760725349188,
-0.02561694011092186,
-0.007481640670448542,
-0.008431264199316502,
0.029784800484776497,
-0.01293590385466814,
-0.004660158883780241,
-0.01772811822593212,
-0.007382503245025873,
-0.03986537083983421,
0.028841108083724976,
-0.01825825124979019,
-0.0004178847884759307,
0.015984365716576576,
-0.041116319596767426,
0.02736126258969307,
0.042878128588199615,
-0.05189010500907898,
0.005786094814538956,
0.0011848877184092999,
0.05950473994016647,
0.03262120112776756,
0.03621845692396164,
-0.038045331835746765,
0.05687418580055237,
0.0591319240629673,
0.035826317965984344,
0.016787713393568993,
0.02313576079905033,
0.0019619751255959272,
-0.09405592828989029,
0.019718296825885773,
-0.0022158429492264986,
-0.08622550964355469,
0.012445461004972458,
-0.007910959422588348,
0.0008755928720347583,
0.011018648743629456,
-0.06649117171764374,
-0.038506485521793365,
0.014184903353452682,
-0.00598240876570344,
0.006122750695794821,
-0.07375641167163849,
0.012350056320428848,
-0.0011106951860710979,
0.011246833950281143,
-0.04485892876982689,
0.014531121589243412,
-0.000031024261261336505,
-0.04331095889210701,
0.05283269286155701,
0.05766410380601883,
0.06462465226650238,
-0.01158076524734497,
-0.050871457904577255,
0.01600344106554985,
-0.04112381860613823,
0.01736965775489807,
-0.032816026359796524,
-0.05252045765519142,
0.030484884977340698,
0.009769673459231853,
0.014243727549910545,
0.019678223878145218,
0.03644941747188568,
0.0029721709433943033,
0.05283532291650772,
0.01992490515112877,
0.011358886025846004,
0.004236854612827301,
0.007652051746845245,
0.011889678426086903,
-0.03731248900294304,
0.018917664885520935,
-0.001209814683534205,
-0.01842326670885086,
0.009775633923709393,
0.0431019626557827,
-0.08948913216590881,
0.026415841653943062,
0.005188366398215294,
0.02549688145518303,
0.0012001052964478731,
-0.009918482042849064,
0.03391525521874428,
-0.02569000795483589,
-0.07052718102931976,
-0.02278873324394226,
-0.0545150488615036,
0.02126263827085495,
0.006447277497500181,
-0.0009944657795131207,
-0.02116943895816803,
-0.020601360127329826,
-0.0268112700432539,
0.01842733472585678,
0.030985910445451736,
0.05145270377397537,
-0.008566740900278091,
0.0218210406601429,
-0.020351437851786613,
0.023144157603383064,
0.003324603894725442,
0.04657144844532013,
0.07145155966281891,
-0.01773216389119625,
-0.02667670138180256,
0.013021543622016907,
-0.01050442922860384,
0.06102953106164932,
0.00345044769346714,
0.001376091269776225,
-0.0035223416052758694,
0.031212694942951202,
-0.01068421732634306,
-0.06200419366359711,
0.021215898916125298,
0.018650276586413383,
0.06721410900354385,
0.07131814956665039,
0.004968529101461172,
-0.006559787318110466,
-0.014011741615831852,
-0.015489163808524609,
0.01687527447938919,
0.006358254700899124,
0.011322644539177418,
0.0031856365967541933,
-0.03987729549407959,
-0.027794308960437775,
0.022414935752749443,
0.06727477163076401,
0.009235083125531673,
0.05092184245586395,
0.04203731566667557,
0.002618037164211273,
0.0003588491235859692,
0.02307855896651745,
0.011858365498483181,
-0.005110225640237331,
-0.07381759583950043,
-0.039242275059223175,
-0.011683431454002857,
-0.011181283742189407,
-0.03364211320877075,
0.004346136935055256,
0.022552642971277237,
-0.05260429158806801,
-0.015528866089880466,
-0.015602398663759232,
-0.016740601509809494,
0.003460012376308441,
0.05879056826233864,
0.04276061803102493,
-0.04731304571032524,
0.0025418910663574934,
0.019783426076173782,
-0.014094183221459389,
0.011134862899780273,
0.06435791403055191,
-0.016948077827692032,
0.00638591917231679,
-0.05613255128264427,
-0.038003481924533844,
-0.04832424223423004,
-0.1531052142381668,
0.007493241224437952,
-0.012483678758144379,
-0.0378463938832283,
0.017601005733013153,
-0.008928965777158737,
0.011620710603892803,
-0.02039322443306446,
0.015019009821116924,
0.0005887102452106774,
0.001862254342995584,
0.04520094022154808,
-0.026610931381583214,
0.009967929683625698,
-0.034368403255939484,
-0.03188629820942879,
-0.03635545074939728,
-0.008270585909485817,
0.004192478489130735,
-0.01332056149840355,
0.011977393180131912,
0.01701866090297699,
0.03258409723639488,
-0.015044420957565308,
-0.01875450648367405,
0.030921027064323425,
0.06193634122610092,
0.025609508156776428,
-0.020901627838611603,
0.05509326979517937,
-0.0457393042743206,
0.028861455619335175,
0.054562199860811234,
-0.07611187547445297,
-0.0026699528098106384,
-0.0210937038064003,
-0.014278889633715153,
-0.06554675102233887,
-0.027247561141848564,
-0.0052248090505599976,
-0.042726896703243256,
-0.008284118957817554,
-0.07022131234407425,
-0.0018531865207478404,
0.03203968703746796,
0.055179037153720856,
0.02203674055635929,
-0.033165086060762405,
-0.0010881911730393767,
-0.010385447181761265,
-0.031088801100850105,
0.024240532889962196,
0.01668507792055607,
-0.020772850140929222,
0.018355896696448326,
-0.03694663941860199,
-0.014121098443865776,
0.023021353408694267,
0.03351863846182823,
0.04465930536389351,
0.02038026787340641,
0.051936496049165726,
0.008239729329943657,
-0.05440690740942955,
0.04950135946273804,
-0.0991920605301857,
-0.005668092984706163,
0.01865692436695099,
0.04529336467385292,
0.0781116634607315,
0.0017209949437528849,
-0.0394071601331234,
0.034008972346782684,
-0.030028708279132843,
0.006777280941605568,
0.030390113592147827,
0.027233991771936417,
0.05975586920976639,
-0.0996265560388565,
-0.019870050251483917,
-0.021431926637887955,
-0.032457541674375534,
0.05280613526701927,
0.04637398198246956,
-0.0034515431616455317,
-0.013450747355818748,
0.006242303643375635,
-0.020890535786747932,
0.01964268647134304,
0.054233256727457047,
-0.008310372941195965,
-0.016625896096229553,
-0.019004955887794495,
0.093548983335495,
-0.010265134274959564,
0.018755435943603516,
0.0189205352216959,
0.04746882617473602,
0.022082572802901268,
0.021505756303668022,
-0.03164822980761528,
0.0014255965361371636,
-0.010993588715791702,
-0.1044652983546257,
-0.038067858666181564,
-0.09059060364961624,
-0.06808421015739441,
0.023092731833457947,
0.020660074427723885,
0.006777756381779909,
-0.03651467710733414,
-0.034567732363939285,
0.01035014446824789,
-0.003329691244289279,
-0.046028003096580505,
-0.018940627574920654,
0.0044112359173595905,
0.027281764894723892,
0.04008139297366142,
-0.006387550383806229,
0.01613840088248253,
0.016450321301817894,
-0.035286370664834976,
0.032736457884311676,
-0.015964914113283157,
0.01175468135625124,
-0.029781989753246307,
-0.007615883368998766,
0.031015513464808464,
0.04519803449511528,
0.04380015283823013,
-0.009625179693102837,
-0.004837778862565756,
0.026277555152773857,
0.025500616058707237,
0.07605350017547607,
0.031954213976860046,
-0.03314538300037384,
-0.02430502325296402,
0.00038656333344988525,
0.009409029968082905,
0.06559757888317108,
-0.011089172214269638,
-0.04865139722824097,
-0.01540480274707079,
-0.04796447604894638,
0.02621070295572281,
0.027910158038139343,
0.04033636301755905,
0.025584755465388298,
-0.0262944046407938,
-0.005338301882147789,
-0.022270159795880318,
-0.06020384281873703,
0.02240125648677349,
-0.003968897741287947,
0.02064157836139202,
0.010970943607389927,
0.004641290754079819,
-0.012745627202093601,
-0.007215610705316067,
-0.02748410776257515,
0.04765268787741661,
-0.0777248963713646,
-0.00926687940955162,
0.00816656555980444,
0.0030287669505923986,
-0.014489846304059029,
-0.011974407359957695,
0.003922305069863796,
0.013997540809214115,
-0.04636315256357193,
0.010100656189024448,
-0.03258964419364929,
0.02121458388864994,
0.033703237771987915,
-0.012671257369220257,
-0.07394133508205414,
-0.05763683840632439,
0.022591607645154,
-0.008034856989979744,
0.00827581062912941,
-0.04669126123189926,
0.06527083367109299,
0.019468359649181366,
-0.07840809971094131,
0.060801081359386444,
0.04099594056606293,
-0.014271978288888931,
0.05474872514605522,
-0.05763353407382965,
-0.03605321794748306,
0.0032981305848807096,
-0.02776396833360195,
0.05186520516872406,
-0.0037003145553171635,
0.04324818029999733,
-0.002161042531952262,
0.03860645741224289,
0.004494958091527224,
0.07888525724411011,
0.02438405156135559,
-0.03559683635830879,
0.048551853746175766,
0.004523520823568106,
-0.030156167224049568,
-0.07542648911476135,
0.004545248579233885,
-0.018992388620972633,
0.02031593769788742,
-0.0012218509800732136,
-0.025290435180068016,
0.021854732185602188,
-0.03419529274106026,
-0.03113805316388607,
0.03697784245014191,
0.0679866150021553,
0.03307359293103218,
-0.004797845613211393,
-0.0036650330293923616,
0.007697194814682007,
0.04692227393388748,
0.03947928175330162,
-0.07128588110208511,
0.060056932270526886,
0.04111180081963539,
0.06437631696462631,
0.026505379006266594,
-0.029058918356895447,
-0.00471285218372941,
-0.022337203845381737,
-0.02112491987645626,
-0.0030001113191246986,
-0.006363665219396353,
0.03273678943514824,
-0.101420097053051,
0.01764546148478985,
0.04476818069815636,
0.01692206785082817,
-0.07017658650875092,
0.031151970848441124,
-0.034402377903461456,
-0.009576728567481041,
0.008298911154270172,
0.04661678522825241,
0.042866308242082596,
-0.03194563835859299,
-0.039681658148765564,
-0.05254419147968292,
-0.06181006506085396,
-0.021104419603943825,
-0.032518163323402405,
0.05635500326752663,
0.001207655412144959,
-0.0029299636371433735,
0.016688281670212746,
-0.012652367353439331,
-0.01680893637239933,
-0.050253551453351974,
0.009784120135009289,
0.003300287527963519,
-0.007867974229156971,
-0.03132157027721405,
0.007545876316726208,
-0.003989256918430328,
-0.0031851676758378744,
0.04631773382425308,
-0.019677216187119484,
0.04338742792606354,
0.10339906811714172,
0.009313974529504776,
0.002042449079453945,
-0.006187102757394314,
-0.05636012554168701,
-0.01368620339781046,
-0.0524333156645298,
-0.010377734899520874,
0.028685079887509346,
0.0161648727953434,
0.02898762933909893,
0.037348248064517975,
-0.0049566118977963924,
0.01863144151866436,
0.0015928245848044753,
0.05252440273761749,
0.06967169791460037,
0.02656722441315651,
0.03193136304616928,
0.01396562997251749,
-0.039828523993492126,
0.019807113334536552,
-0.0011160579742863774,
-0.008377013728022575,
-0.0050507509149611,
-0.0609278567135334,
0.03865654394030571,
0.005418757908046246,
0.009256059303879738,
-0.029347075149416924,
-0.04369135946035385,
0.05194719880819321,
-0.007675164379179478,
0.014748210087418556,
-0.013711130246520042,
0.022157752886414528,
0.004630960989743471,
-0.0002945796004496515,
-0.017927175387740135,
-0.010721219703555107,
0.025658462196588516,
-0.04428306221961975,
-0.006110028363764286,
-0.03701403737068176,
-0.01377097237855196,
-0.0065255905501544476,
-0.031209168955683708,
0.07975748926401138,
-0.010462390258908272,
-0.005989184603095055,
-0.09205880016088486,
-0.007529995404183865,
0.02661370299756527,
-0.0026419535279273987,
0.000946665822993964,
0.003063560463488102,
0.017192894592881203,
-0.014253204688429832,
-0.03615299239754677,
0.006974040996283293,
0.01512689609080553,
0.032761432230472565,
-0.02873833291232586,
-0.03150000423192978,
-0.011703256517648697,
-0.01596466451883316,
-0.004824760835617781,
0.038565706461668015,
-0.11183497309684753,
0.04007527604699135,
0.025560587644577026,
-0.008240739814937115,
0.049753714352846146,
-0.0630267933011055,
-0.0221550352871418,
-0.005001187790185213,
0.08072056621313095,
0.0006163498037494719,
-0.008478773757815361,
-0.031135106459259987,
-0.08896517008543015,
0.025058286264538765,
-0.008804705925285816,
-0.03240872547030449,
0.0034361511934548616,
0.015237122774124146
] |
<p>My question is mainly an engineering question. Assume I have a turbine in which I adiabatically expand compressed air. The air cools down and does work to its surroundings, which is captured by the blades of the turbine and then is transformed into rotational energy/electricity. </p>
<p>When instead I let the compressed air flow through a nozzle into open space (no vacuum) and it expands adiabatically, it also cools down. But where is the internal energy of the air going? It does work to its surroundings, but where does this work end up? Does the surrounding heat up? Does it produce wind, i.e. kinetic energy in the surrounding air?</p>
<p>Feel free to replace adiabatic with polytropic. Whenever the gas cools down, I ask: Where does the energy end up, when I do not capture it with a turbine?</p> | g6578 | [
0.061623621731996536,
-0.010412434116005898,
0.004794434178620577,
0.011611656285822392,
-0.017456531524658203,
0.02256583236157894,
0.04380417987704277,
0.0749259814620018,
-0.06594952940940857,
-0.03118615224957466,
0.005461734253913164,
0.019661976024508476,
-0.00646259356290102,
-0.03355398774147034,
-0.0067309243604540825,
-0.010884417220950127,
0.02070443332195282,
-0.0102454898878932,
0.0649595782160759,
-0.018877245485782623,
-0.027082189917564392,
-0.025945603847503662,
0.034371353685855865,
-0.018064098432660103,
-0.028272895142436028,
-0.03777746483683586,
0.060531336814165115,
0.007552393712103367,
-0.04690364748239517,
-0.05365980789065361,
0.01964251510798931,
0.03745640814304352,
0.016380082815885544,
-0.00269304309040308,
0.0034854609984904528,
0.007644281722605228,
0.08655400574207306,
0.010121005587279797,
0.007335303351283073,
-0.0229914803057909,
0.0289164986461401,
-0.01025356538593769,
-0.041758447885513306,
0.0028881921898573637,
-0.0006639094790443778,
0.04813988879323006,
-0.0565338097512722,
-0.03127510845661163,
-0.030444899573922157,
-0.018409838899970055,
-0.0017911643953993917,
0.030559008941054344,
-0.01512439176440239,
-0.04497339576482773,
0.08183950185775757,
0.005057789850980043,
-0.004551198799163103,
-0.04800425469875336,
0.06175011768937111,
0.009725513868033886,
0.026439303532242775,
0.018340907990932465,
0.02648922987282276,
0.013266810216009617,
0.03062756359577179,
-0.04209362715482712,
-0.04236844554543495,
-0.042600445449352264,
-0.006884442642331123,
-0.0523647703230381,
-0.017464440315961838,
-0.03443487361073494,
0.020623762160539627,
-0.04180346056818962,
0.013964328914880753,
-0.0035377084277570248,
-0.012373902834951878,
-0.05691228061914444,
0.01252166647464037,
0.013777771033346653,
-0.02900833822786808,
0.026568682864308357,
0.045809246599674225,
-0.06399929523468018,
0.09649206697940826,
0.015564663335680962,
-0.0034890351817011833,
0.017733493819832802,
-0.017913365736603737,
0.00045503859291784465,
0.05119337514042854,
0.020284151658415794,
0.06641972064971924,
0.00043877778807654977,
-0.06373763829469681,
0.009858539327979088,
-0.015495478175580502,
0.0636143609881401,
-0.02033267542719841,
-0.03320019692182541,
-0.010955382138490677,
-0.027746587991714478,
-0.019481953233480453,
-0.020559778437018394,
0.0308699831366539,
-0.010833573527634144,
0.0008002262911759317,
-0.039462070912122726,
-0.02351466938853264,
0.03194951266050339,
-0.0019741072319447994,
-0.0337817445397377,
-0.03826117888092995,
-0.013885931111872196,
-0.035054344683885574,
-0.0191290695220232,
0.022911574691534042,
-0.009870599955320358,
0.011566290631890297,
0.06932432949542999,
0.042708870023489,
0.09352006763219833,
-0.019933650270104408,
-0.052282534539699554,
-0.0029114224016666412,
0.0307115837931633,
-0.008748305030167103,
-0.006065690889954567,
-0.007412731181830168,
0.0008897251100279391,
0.019283916801214218,
-0.02926507033407688,
-0.018296506255865097,
0.04080692678689957,
-0.01280851662158966,
-0.0075319730676710606,
-0.052207741886377335,
-0.022197769954800606,
0.02160477824509144,
0.052915431559085846,
-0.001024887664243579,
-0.046215832233428955,
0.005343100521713495,
0.020528854802250862,
0.00426856055855751,
-0.03391297161579132,
-0.007202452979981899,
-0.04762694984674454,
0.02753201685845852,
0.009065191261470318,
0.028370041400194168,
0.051168959587812424,
0.03394528850913048,
-0.07754643261432648,
0.09087719768285751,
0.017581529915332794,
0.0438418909907341,
-0.014243231154978275,
0.04051830619573593,
0.0024353312328457832,
0.037484101951122284,
-0.04975549131631851,
0.09299786388874054,
-0.0003990176192019135,
-0.1041039526462555,
-0.030496792867779732,
-0.017022965475916862,
-0.024963321164250374,
0.05338295176625252,
-0.019884862005710602,
-0.027596471831202507,
-0.0452633872628212,
-0.008375375531613827,
-0.06154103949666023,
0.017760328948497772,
0.06918667256832123,
0.059388428926467896,
0.03664514049887657,
0.007681766990572214,
-0.06926796585321426,
-0.015377034433186054,
0.02468317374587059,
0.03896511346101761,
-0.060447171330451965,
0.02468195930123329,
0.07208514213562012,
-0.04480654373764992,
0.009008508175611496,
-0.031527675688266754,
-0.018752165138721466,
0.042694661766290665,
-0.010515800677239895,
-0.0039532482624053955,
0.022822674363851547,
-0.0449100024998188,
0.0025984670501202345,
-0.009124896489083767,
-0.08843231201171875,
-0.03795600309967995,
-0.020660217851400375,
0.04475770518183708,
-0.0006339658284559846,
0.04282941669225693,
-0.011401503346860409,
0.06175002455711365,
0.006129124667495489,
-0.0006767931045033038,
0.03712383657693863,
0.03181977942585945,
-0.011944065801799297,
0.019160175696015358,
-0.019306227564811707,
-0.0059601906687021255,
0.020145343616604805,
0.01377046201378107,
0.006599002052098513,
-0.03873562067747116,
0.0019142975797876716,
-0.0025154869072139263,
0.0052889673970639706,
0.00842262338846922,
0.0007585504208691418,
-0.0049287197180092335,
0.008010494522750378,
-0.03521527349948883,
-0.009002694860100746,
-0.027054494246840477,
-0.04304680973291397,
-0.049553874880075455,
0.07939734309911728,
-0.07294832915067673,
0.02350161410868168,
-0.002691142028197646,
-0.04953515902161598,
0.054771970957517624,
0.024548407644033432,
-0.035595204681158066,
0.082123763859272,
0.030129898339509964,
-0.04495370760560036,
-0.0390535332262516,
-0.02055629901587963,
-0.03551905229687691,
0.03621405363082886,
-0.0059510208666324615,
0.0404183603823185,
0.012175141833722591,
-0.030020548030734062,
0.007778569590300322,
-0.004110404755920172,
0.03435502201318741,
0.028523487970232964,
0.00525198457762599,
0.03318867087364197,
-0.03799370676279068,
-0.03833429515361786,
-0.011698437854647636,
0.008608781732618809,
-0.00852054450660944,
-0.07851248234510422,
-0.007766427472233772,
0.028250543400645256,
-0.026340806856751442,
0.003316075075417757,
-0.07346194982528687,
0.0717601552605629,
0.0037820509169250727,
-0.03849433735013008,
-0.0007177958614192903,
-0.0006029534270055592,
-0.011464809067547321,
0.05101713910698891,
0.03415921702980995,
0.010629972442984581,
0.011387807317078114,
-0.056227345019578934,
0.021377524361014366,
0.04155903682112694,
0.0009862225269898772,
-0.054797928780317307,
0.029620826244354248,
-0.004435217007994652,
-0.02030193619430065,
0.03216259926557541,
0.00021116543211974204,
-0.05401916056871414,
-0.046416040509939194,
0.017790447920560837,
-0.02168472483754158,
-0.049094151705503464,
0.002101314254105091,
-0.026665285229682922,
0.028033550828695297,
0.014575961045920849,
-0.002721106167882681,
0.013109209947288036,
0.029797730967402458,
0.003912588581442833,
0.020675521343946457,
0.060007244348526,
-0.0371931791305542,
-0.060437291860580444,
-0.014531725086271763,
0.046161822974681854,
0.027282504364848137,
0.037805311381816864,
-0.08079570531845093,
-0.03213692083954811,
-0.014183697290718555,
0.04904686659574509,
-0.02130873128771782,
-0.014272388070821762,
0.0023735954891890287,
-0.002538080094382167,
-0.07254377007484436,
-0.042642224580049515,
-0.028173059225082397,
-0.06672494858503342,
0.025214774534106255,
-0.005255452822893858,
-0.0005251484108157456,
-0.0009263076935894787,
0.029426569119095802,
-0.004840816371142864,
-0.02997254580259323,
-0.002885912312194705,
0.02037387527525425,
0.017184102907776833,
0.037333399057388306,
-0.09146004170179367,
-0.07438597083091736,
-0.013545859605073929,
0.007979330606758595,
-0.04896704480051994,
-0.033790457993745804,
-0.05431516095995903,
-0.03934961557388306,
0.013718552887439728,
0.03834338113665581,
0.023722464218735695,
0.0256902314722538,
0.005321042612195015,
0.010587798431515694,
-0.020331019535660744,
-0.027529750019311905,
0.008602412417531013,
-0.02895236946642399,
0.010331066325306892,
-0.01604718156158924,
0.016214804723858833,
0.029059862717986107,
-0.000996702816337347,
-0.03927187994122505,
-0.0008066085283644497,
-0.024491164833307266,
-0.007947765290737152,
0.007269664201885462,
0.01945476420223713,
-0.018229087814688683,
0.023623980581760406,
0.022935915738344193,
-0.04365238919854164,
-0.03765002638101578,
-0.01604464277625084,
-0.05481305345892906,
0.006226459518074989,
-0.019395584240555763,
-0.020755412057042122,
-0.020546065643429756,
0.014150429517030716,
0.047119125723838806,
-0.017835335806012154,
-0.01723785512149334,
0.0373883992433548,
0.020749015733599663,
-0.00767970085144043,
0.06943177431821823,
0.04724988713860512,
-0.0016235532239079475,
-0.00453165965154767,
0.02523169480264187,
0.013106225989758968,
0.004961308091878891,
-0.011336457915604115,
-0.0026624056044965982,
0.06331410259008408,
-0.04447890445590019,
0.04944716393947601,
-0.016889329999685287,
0.0017486168071627617,
-0.0018385413568466902,
-0.004305812995880842,
-0.009079615585505962,
-0.0017583172302693129,
-0.03133952245116234,
-0.006044727750122547,
0.012435614131391048,
-0.025523411110043526,
-0.035372018814086914,
0.031697239726781845,
0.026515046134591103,
0.048402998596429825,
-0.027622083202004433,
-0.020072927698493004,
0.01941123977303505,
-0.009133235551416874,
0.06274145096540451,
0.003527237568050623,
0.02333349920809269,
-0.03442025184631348,
0.019285431131720543,
-0.021655874326825142,
-0.021240022033452988,
-0.06096572428941727,
0.05698959901928902,
-0.07441934198141098,
-0.012122705578804016,
-0.05567023903131485,
0.018632248044013977,
0.024928301572799683,
-0.004715499002486467,
0.0032178775873035192,
-0.015147424302995205,
0.07524435222148895,
-0.026905344799160957,
0.09241020679473877,
0.016855603083968163,
-0.06121935695409775,
-0.04697265848517418,
0.008356884121894836,
-0.01655997708439827,
-0.029387883841991425,
0.031045911833643913,
-0.040493715554475784,
-0.019317811354994774,
0.003944756463170052,
-0.02829737775027752,
0.030892329290509224,
0.024833418428897858,
0.07351791113615036,
0.05542437732219696,
-0.003149476135149598,
-0.023947065696120262,
-0.042050715535879135,
0.009590637870132923,
0.07785166054964066,
-0.00339504424482584,
0.01963069848716259,
0.01858297921717167,
-0.03556743636727333,
-0.10058072209358215,
0.016512632369995117,
-0.021529333665966988,
-0.015908975154161453,
0.012722598388791084,
0.030098704621195793,
-0.055751919746398926,
-0.012700967490673065,
-0.001959883840754628,
-0.02988000027835369,
-0.023494716733694077,
-0.022431930527091026,
-0.04377507045865059,
0.010203163139522076,
-0.01696978323161602,
-0.031354717910289764,
-0.013060892932116985,
0.02158297225832939,
-0.013252097181975842,
-0.032185543328523636,
0.040739238262176514,
0.05813039094209671,
-0.038311585783958435,
0.06285865604877472,
0.025558726862072945,
0.05995184928178787,
0.05080212280154228,
-0.05682158097624779,
0.06306636333465576,
0.005108429118990898,
0.04132000356912613,
0.026728136464953423,
0.02398662269115448,
0.05298834294080734,
0.027197854593396187,
0.02225862443447113,
-0.046640794724226,
0.0062825605273246765,
0.0448065809905529,
0.0073064467869699,
0.01552899181842804,
0.07031179964542389,
0.00290070497430861,
-0.024774041026830673,
-0.04179194197058678,
0.036620501428842545,
-0.02015877701342106,
-0.0621672198176384,
-0.038946352899074554,
-0.024641379714012146,
-0.006973712705075741,
0.009272444061934948,
-0.010588761419057846,
0.050603531301021576,
0.011231598444283009,
0.05795593187212944,
0.051097121089696884,
-0.007894513197243214,
-0.014796852134168148,
0.03208315744996071,
0.0021149511449038982,
0.02631375938653946,
-0.08006516844034195,
0.03861305117607117,
0.048944950103759766,
-0.018312763422727585,
-0.002865443006157875,
-0.009116999804973602,
-0.039050932973623276,
-0.04620780423283577,
0.009430448524653912,
0.021466614678502083,
0.013900676742196083,
-0.010860253125429153,
0.03638673946261406,
0.06302720308303833,
-0.03763625770807266,
0.0011885914718732238,
0.022872474044561386,
0.05805147439241409,
-0.014397300779819489,
0.02320065163075924,
0.03348832577466965,
-0.007254436612129211,
0.0018102674512192607,
0.03369094058871269,
-0.04336404427886009,
0.00004101670492673293,
0.0694664716720581,
0.005703895818442106,
0.025325370952486992,
-0.01817086525261402,
-0.04324699565768242,
-0.037199705839157104,
0.008976278826594353,
0.02103857882320881,
-0.024039139971137047,
0.01896224543452263,
0.06259587407112122,
-0.024335147812962532,
0.00165007752366364,
-0.008840956725180149,
0.035713329911231995,
-0.022159863263368607,
0.009002314880490303,
-0.04225857928395271,
0.03805537894368172,
0.009829061105847359,
-0.015446278266608715,
-0.051574643701314926,
0.028061673045158386,
0.021650003269314766,
0.025460410863161087,
0.004606453701853752,
0.049742624163627625,
-0.021750161424279213,
0.016040291637182236,
-0.003633447689935565,
0.04030429199337959,
0.012541820295155048,
0.052241384983062744,
-0.019235720857977867,
0.04024500399827957,
-0.024563567712903023,
0.044803738594055176,
0.02494139038026333,
-0.030900437384843826,
-0.016104716807603836,
-0.013699733652174473,
-0.011728369630873203,
0.025902245193719864,
0.0016821569297462702,
0.07840292155742645,
-0.009402369149029255,
0.05585789307951927,
0.03228876367211342,
-0.015845179557800293,
-0.00009007899643620476,
0.0203426294028759,
0.032530222088098526,
0.00023980916012078524,
-0.04345325753092766,
-0.012916356325149536,
0.020347246900200844,
-0.04468525946140289,
-0.012083305045962334,
0.007951066829264164,
-0.015667514875531197,
0.029166873544454575,
-0.007281908765435219,
-0.0009884422179311514,
0.04742284119129181,
0.09725520014762878,
-0.08414620161056519,
0.026820166036486626,
0.0027105165645480156,
0.015471279621124268,
0.032422635704278946,
-0.011517036706209183,
0.006747863255441189,
-0.06709864735603333,
0.013241380453109741,
0.08209264278411865,
-0.05705152824521065,
0.01621122844517231,
0.03399164229631424,
0.017712855711579323,
-0.014814099296927452,
0.02765948884189129,
-0.029106872156262398,
0.022603396326303482,
-0.03456268087029457,
0.041722141206264496,
-0.06017359346151352,
0.04657687991857529,
-0.0094713494181633,
-0.06345528364181519,
0.03760775551199913,
0.03718877583742142,
0.01944436877965927,
0.007096685003489256,
0.07951223850250244,
-0.05053330212831497,
0.0555572509765625,
-0.004782584495842457,
0.00570676289498806,
0.03306936100125313,
0.037424035370349884,
0.12643325328826904,
0.025382300838828087,
-0.047994814813137054,
0.07170765846967697,
-0.04077250137925148,
0.031055361032485962,
-0.04899534210562706,
-0.015477231703698635,
0.017880888655781746,
-0.03578261658549309,
-0.02789725735783577,
-0.0568537637591362,
-0.06535666435956955,
-0.07468870282173157,
-0.025820646435022354,
-0.02385745942592621,
-0.031850337982177734,
0.045197129249572754,
-0.026874518021941185,
-0.04908398911356926,
0.012202574871480465,
-0.05617673322558403,
0.021119818091392517,
-0.038110073655843735,
-0.01786116324365139,
0.06352998316287994,
0.00008523005089955404,
0.06343652307987213,
0.03669746220111847,
0.03266722708940506,
0.0024842810817062855,
-0.05827626585960388,
-0.024882325902581215,
-0.03874925896525383,
-0.09845282882452011,
0.012700066901743412,
-0.04815790429711342,
-0.019051259383559227,
0.018820617347955704,
0.05451745167374611,
0.009487008675932884,
-0.06332070380449295,
0.01233984250575304,
-0.024531038478016853,
-0.015482209622859955,
-0.02299511805176735,
-0.007555734366178513,
0.04497746750712395,
-0.038744814693927765,
0.0018448042683303356,
0.0008875495987012982,
-0.041664596647024155,
-0.043525584042072296,
0.041803181171417236,
0.059202294796705246,
-0.05479775369167328,
-0.04778023809194565,
-0.000028234609999344684,
0.0674644187092781,
-0.0028831560630351305,
-0.05210726335644722,
-0.01001149695366621,
0.025845075026154518,
0.006429537199437618,
0.0366542674601078,
0.0031580361537635326,
0.015549368225038052,
0.024107690900564194,
0.021294642239809036,
-0.021904276683926582,
-0.020219553261995316,
0.022670526057481766,
-0.006349681410938501,
-0.020640287548303604,
0.012554855085909367,
-0.01671730913221836,
0.02929452806711197,
-0.04108230024576187,
-0.0353938527405262,
-0.005694572348147631,
0.005081715993583202,
-0.00035952465259470046,
-0.007237532641738653,
0.013852463103830814,
-0.05627519264817238,
-0.02009008452296257,
-0.008400814607739449,
-0.006841882597655058,
-0.009182993322610855,
0.023896871134638786,
-0.008947350084781647,
-0.05631539970636368,
-0.04890647530555725,
0.04455868527293205,
0.03543831780552864,
0.01040992047637701,
-0.003838442964479327,
-0.03527214750647545,
0.08242682367563248,
-0.03264651447534561,
0.01841486245393753,
-0.013135822489857674,
-0.005162617191672325,
-0.010514858178794384,
0.04557517543435097,
-0.019024141132831573,
-0.03943385183811188,
-0.046581897884607315,
0.01637694612145424,
0.033544961363077164,
0.06873361021280289,
-0.0488564558327198,
0.033388569951057434,
-0.021969804540276527,
0.0033493584487587214,
-0.019862517714500427,
0.04571396857500076,
-0.01893359050154686,
-0.000436562520917505,
0.03549524024128914,
0.016526462510228157,
0.013262614607810974,
-0.021533189341425896,
-0.019266122952103615,
-0.07820186018943787,
-0.02234053611755371,
-0.019480695948004723,
-0.04377078637480736,
0.0026855976320803165,
0.03775258734822273
] |
<p>We know about some events that happen very quickly. For example, the <a href="https://en.wikipedia.org/wiki/Dielectric" rel="nofollow">dielectric</a> relaxation time is about $10^{-14}\, \mathrm{seconds}$. </p>
<p>I'm interested in other processes that switch extremely fast or or could be use as a very short tick in a clock.</p> | g446 | [
0.08531714975833893,
0.11450067162513733,
-0.01223441120237112,
0.02276592329144478,
0.030333567410707474,
-0.0856628492474556,
0.04256599396467209,
-0.0014258509036153555,
0.011310376226902008,
-0.010883700102567673,
-0.03831776976585388,
0.04154496267437935,
0.012255126610398293,
-0.02639545127749443,
-0.010765668004751205,
-0.03853035718202591,
0.08984121680259705,
0.04736895486712456,
0.01222744956612587,
0.050907202064991,
0.04222724586725235,
0.004503138363361359,
-0.009277822449803352,
-0.0358438715338707,
-0.011664189398288727,
0.04412750154733658,
0.008913656696677208,
-0.019586531445384026,
-0.018440209329128265,
-0.021479949355125427,
-0.0577966570854187,
-0.07821834087371826,
0.014793520793318748,
0.023034369572997093,
0.0003536113945301622,
-0.04630029574036598,
0.023059871047735214,
0.001755294855684042,
0.017093362286686897,
0.04761206731200218,
-0.019369572401046753,
-0.01991846226155758,
0.05854921042919159,
-0.045577485114336014,
0.03083389438688755,
0.019125232473015785,
0.0002716532035265118,
0.047879960387945175,
-0.020844893530011177,
-0.0972490906715393,
0.0165880024433136,
-0.012978387996554375,
0.01759333722293377,
0.048387058079242706,
-0.01676914282143116,
-0.016869455575942993,
0.012621378526091576,
0.03566285967826843,
0.047750119119882584,
-0.0037650037556886673,
-0.028336942195892334,
-0.02128918282687664,
0.03061506524682045,
-0.022917214781045914,
0.029426973313093185,
0.056260716170072556,
0.005294932052493095,
-0.033142250031232834,
0.07718367874622345,
0.043436966836452484,
-0.018645919859409332,
0.01674220710992813,
-0.09394068270921707,
-0.04502641037106514,
0.016896026208996773,
0.015788156539201736,
0.0037529405672103167,
-0.07620880752801895,
0.013674120418727398,
0.017626117914915085,
-0.10637305676937103,
-0.03190544992685318,
-0.014790824614465237,
-0.00022448629897553474,
-0.020871836692094803,
0.0202696081250906,
0.015493441373109818,
0.020349718630313873,
0.023521745577454567,
-0.018777115270495415,
0.025087354704737663,
-0.034441493451595306,
-0.0053357696160674095,
-0.01902124658226967,
-0.08417557179927826,
0.06355457752943039,
0.025025377050042152,
0.06346531957387924,
0.03728659451007843,
-0.0051352097652852535,
-0.03008500300347805,
-0.014724752865731716,
-0.03362765908241272,
-0.030148055404424667,
-0.010302646085619926,
-0.041729044169187546,
-0.017806226387619972,
-0.02538369596004486,
-0.01795101724565029,
0.013942747376859188,
0.009318932890892029,
-0.03370894864201546,
-0.02365785650908947,
0.041268590837717056,
0.01971859112381935,
0.02510673925280571,
-0.06612648069858551,
-0.013046725653111935,
-0.03039190173149109,
0.001339695299975574,
0.04326274245977402,
-0.014045637100934982,
-0.008762108162045479,
0.0026963178534060717,
0.005084407981485128,
0.010447611100971699,
0.011099312454462051,
0.026468615978956223,
-0.015476525761187077,
0.012395470403134823,
0.010637607425451279,
0.012400698848068714,
-0.02735385298728943,
0.018055779859423637,
-0.05732666328549385,
0.011984465643763542,
0.05965184047818184,
-0.027203034609556198,
0.004682060331106186,
-0.009684722870588303,
0.035263970494270325,
-0.039621323347091675,
0.0022674829233437777,
0.012525662779808044,
-0.04230593889951706,
0.029778247699141502,
-0.014314291067421436,
0.06469611078500748,
0.004563762340694666,
0.024097196757793427,
-0.014619091525673866,
-0.017054585739970207,
0.04473661258816719,
-0.007645230740308762,
0.018310459330677986,
0.019456731155514717,
0.02676706202328205,
-0.004677358083426952,
-0.004359246231615543,
0.04989789426326752,
0.04423701763153076,
-0.022676590830087662,
-0.050534892827272415,
0.036383647471666336,
-0.012724039144814014,
-0.021113449707627296,
0.04017610102891922,
0.044472597539424896,
0.009695095010101795,
-0.010790206491947174,
-0.047698214650154114,
-0.03550664708018303,
-0.010561060160398483,
0.04760206863284111,
-0.006673354189842939,
-0.017298543825745583,
0.03925999253988266,
-0.036589786410331726,
-0.0515623465180397,
-0.05162402614951134,
-0.011169960722327232,
-0.058746904134750366,
-0.039112918078899384,
-0.043721769005060196,
0.05185360088944435,
0.027298131957650185,
0.03810109198093414,
0.0051887063309550285,
-0.0819086953997612,
0.028658898547291756,
-0.05647192522883415,
-0.05271218344569206,
0.009679696522653103,
0.06971586495637894,
-0.045358385890722275,
-0.03567182272672653,
0.01355158630758524,
-0.012673440389335155,
-0.025047248229384422,
-0.01653359830379486,
-0.013956387527287006,
0.008043861947953701,
0.025317111983895302,
0.0502525195479393,
0.05537185072898865,
0.018060391768813133,
0.0020526284351944923,
-0.029948022216558456,
-0.018470872193574905,
-0.018007148057222366,
0.0995471253991127,
0.062183741480112076,
-0.013661164790391922,
-0.018335672095417976,
-0.01486970204859972,
0.00011056770745199174,
-0.026563135907053947,
-0.035067152231931686,
0.06761600077152252,
0.023336561396718025,
0.03936083987355232,
-0.005092599429190159,
0.057838618755340576,
-0.024452121928334236,
0.04758709296584129,
-0.03453952446579933,
0.017980651929974556,
0.015332183800637722,
0.04484574869275093,
0.03544393181800842,
-0.059713754802942276,
0.07918217778205872,
-0.05443930998444557,
-0.011700214818120003,
-0.04282725602388382,
0.024291282519698143,
0.025939946994185448,
-0.0038444786332547665,
0.05259772390127182,
0.032318051904439926,
0.014909323304891586,
0.004003805108368397,
-0.009758836589753628,
0.0442030131816864,
-0.1061808317899704,
-0.09725172072649002,
0.03651959076523781,
-0.014822723343968391,
0.031622715294361115,
0.009102987125515938,
0.004083867184817791,
-0.062287233769893646,
-0.022965876385569572,
-0.01719062402844429,
-0.007448424119502306,
-0.03567184880375862,
0.020645514130592346,
0.06576014310121536,
-0.03020966798067093,
-0.0012093795230612159,
-0.018473103642463684,
0.04364164546132088,
0.042916785925626755,
-0.016735753044486046,
0.059811487793922424,
-0.053549349308013916,
0.013486579060554504,
0.0030879578553140163,
-0.07140132039785385,
0.009171445854008198,
-0.04554268345236778,
-0.02499288320541382,
-0.04127030447125435,
0.020532675087451935,
-0.02458605170249939,
-0.030546020716428757,
0.05456358566880226,
-0.031391825526952744,
0.022090774029493332,
0.007852278649806976,
0.0022167041897773743,
-0.06491045653820038,
-0.021594176068902016,
-0.01023748517036438,
-0.012541541829705238,
-0.03527623042464256,
0.010524359531700611,
0.07655834406614304,
-0.055173151195049286,
0.028715098276734352,
-0.04851473867893219,
0.0227933619171381,
0.03600768744945526,
0.005266750697046518,
-0.022228403016924858,
0.03445101156830788,
0.014252612367272377,
-0.05499676614999771,
-0.0010572790633887053,
0.028138555586338043,
0.05259772390127182,
-0.039823371917009354,
-0.017640024423599243,
0.03609409183263779,
0.017384136095643044,
-0.01444191299378872,
-0.024829501286149025,
0.0004950236179865897,
0.0510588176548481,
0.0019713793881237507,
0.06421273946762085,
0.05650806799530983,
-0.02187248319387436,
-0.0126735744997859,
-0.10113579779863358,
-0.05308052524924278,
0.010036657564342022,
0.05833790823817253,
0.042426954954862595,
-0.07359541952610016,
0.030430397018790245,
-0.039051227271556854,
0.018250735476613045,
-0.052050210535526276,
0.03311493620276451,
0.027054313570261,
0.00887592975050211,
-0.030605599284172058,
-0.07365044951438904,
0.023593850433826447,
-0.028453320264816284,
0.004380454774945974,
-0.057939562946558,
-0.008388551883399487,
-0.07837652415037155,
-0.03602044656872749,
0.004889106377959251,
0.04504648968577385,
0.025146545842289925,
-0.0012848960468545556,
-0.03161842003464699,
0.009761413559317589,
-0.06317918747663498,
0.018629206344485283,
0.0417557992041111,
-0.009137449786067009,
0.04602901637554169,
-0.0449245423078537,
0.028622668236494064,
-0.022931387647986412,
0.010860886424779892,
-0.012996232137084007,
0.0006718204822391272,
-0.057333361357450485,
0.006063619628548622,
0.006114196497946978,
0.013079129159450531,
0.027288461104035378,
0.02654164656996727,
-0.037372130900621414,
-0.008629762567579746,
0.006266619544476271,
-0.007133049424737692,
0.006564771756529808,
-0.035312455147504807,
0.014136639423668385,
-0.03391815721988678,
0.06536012142896652,
0.023744111880660057,
-0.033518239855766296,
0.004368824418634176,
0.05029630661010742,
0.01873105764389038,
-0.0030131489038467407,
0.037286028265953064,
0.029287060722708702,
0.0003748646704480052,
0.04444904252886772,
-0.005914631765335798,
0.011289644986391068,
-0.0691886693239212,
-0.003890435677021742,
0.05094846338033676,
-0.04524426534771919,
-0.0066618421114981174,
-0.025276441127061844,
-0.038123082369565964,
-0.05747741088271141,
-0.05204825475811958,
-0.060120511800050735,
0.028410617262125015,
0.02211242914199829,
0.004116309806704521,
-0.01817028596997261,
-0.05126805603504181,
-0.06038030609488487,
0.05645499750971794,
-0.04046859219670296,
0.045823678374290466,
-0.01211391668766737,
-0.03392823040485382,
-0.05148295685648918,
-0.027378803119063377,
0.014294996857643127,
0.030089106410741806,
0.07288791984319687,
-0.03654789552092552,
-0.025793569162487984,
-0.014211238361895084,
-0.013202146627008915,
-0.0288158617913723,
-0.024087030440568924,
-0.029988979920744896,
0.01965123414993286,
0.03132723644375801,
0.00020558277901727706,
0.011837726458907127,
-0.00863326620310545,
0.006162825506180525,
-0.010863453149795532,
0.004826245363801718,
0.056008946150541306,
-0.017302362248301506,
0.016672467812895775,
0.028114458546042442,
-0.02370651438832283,
0.00936331506818533,
0.02373742125928402,
0.017087846994400024,
-0.014178927056491375,
0.03150596097111702,
0.004677711986005306,
-0.01782594993710518,
-0.019320335239171982,
0.020392322912812233,
0.013958669267594814,
0.02700851857662201,
0.026941834017634392,
-0.013693428598344326,
0.05732415243983269,
0.043892115354537964,
0.009591205976903439,
0.0009711651946417987,
0.03814958408474922,
-0.002568187890574336,
0.0697198361158371,
-0.009516437537968159,
-0.057174202054739,
-0.03087964653968811,
-0.06413447111845016,
-0.014773400500416756,
0.07461004704236984,
-0.05052197352051735,
-0.02168937399983406,
0.06615940481424332,
-0.03827968239784241,
-0.007954219356179237,
0.0844862163066864,
0.00463843671604991,
0.03804289922118187,
-0.04977121576666832,
-0.009029681794345379,
0.03538992628455162,
0.0065717133693397045,
-0.02975638210773468,
0.023623842746019363,
-0.011348334141075611,
-0.020019682124257088,
-0.030526814982295036,
-0.016521355137228966,
-0.04400939121842384,
0.003464161418378353,
0.014598031528294086,
0.05737990885972977,
0.00007987180288182572,
0.01554278563708067,
0.008443883620202541,
0.020812679082155228,
0.004453857429325581,
-0.016788823530077934,
-0.008036864921450615,
0.003468351671472192,
0.006802343763411045,
0.055170003324747086,
-0.010422047227621078,
-0.006041122134774923,
-0.06186359003186226,
-0.00713277468457818,
0.028226371854543686,
-0.06418769806623459,
0.021709993481636047,
0.05425911024212837,
0.04541122913360596,
0.024455539882183075,
0.028220953419804573,
-0.033567409962415695,
0.03891303762793541,
0.00995061919093132,
-0.05314178764820099,
-0.018651988357305527,
-0.04464280977845192,
-0.036500561982393265,
-0.05682489648461342,
-0.032621972262859344,
-0.02395722083747387,
0.026305411010980606,
-0.03088042326271534,
-0.004678364377468824,
-0.0060307420790195465,
0.05164346471428871,
-0.06764821708202362,
0.02327709086239338,
-0.005793333053588867,
-0.015184889547526836,
-0.010751527734100819,
-0.014670838601887226,
0.0010931615252047777,
-0.04526204988360405,
-0.013137424364686012,
-0.03275910019874573,
0.04109515994787216,
-0.048593468964099884,
0.03906726837158203,
0.030618268996477127,
-0.004889687988907099,
-0.008433288894593716,
-0.017296791076660156,
0.020212050527334213,
-0.011568740010261536,
0.014431378804147243,
0.04453390836715698,
-0.07622021436691284,
-0.038197197020053864,
0.010686831548810005,
-0.014841063879430294,
0.04603715240955353,
0.043088413774967194,
0.021606944501399994,
-0.03698762133717537,
0.011195655912160873,
-0.04248516261577606,
0.027445709332823753,
-0.001886896905489266,
0.029527688398957253,
-0.04075887054204941,
-0.047854192554950714,
0.04753607511520386,
0.02844763547182083,
0.011191110126674175,
0.012721633538603783,
0.003446308895945549,
-0.012226561084389687,
0.09820115566253662,
-0.027395449578762054,
0.013038372620940208,
0.027482187375426292,
0.031190726906061172,
0.019844409078359604,
0.0036791865713894367,
-0.013385873287916183,
0.03908613696694374,
0.04858611524105072,
0.045657072216272354,
-0.046427611261606216,
0.0018012885702773929,
-0.08156874030828476,
-0.02041066810488701,
0.01649278774857521,
0.04852902516722679,
0.009556757286190987,
0.053076643496751785,
-0.021912207826972008,
-0.045457687228918076,
-0.020650478079915047,
-0.005070019979029894,
-0.014589780941605568,
0.02765362150967121,
-0.0011186763877049088,
-0.027833038941025734,
-0.0057098958641290665,
-0.09483447670936584,
0.007762421388179064,
0.015667840838432312,
0.0204391498118639,
-0.013781684450805187,
0.0045722550712525845,
0.005752136930823326,
0.03644672781229019,
0.007585691288113594,
0.008997784927487373,
0.006527959369122982,
-0.025004863739013672,
-0.03501095622777939,
-0.05759362876415253,
0.04246202111244202,
-0.05216048285365105,
-0.05744481459259987,
-0.025983477011322975,
-0.006302226800471544,
0.02857566624879837,
-0.033398717641830444,
0.014277481473982334,
0.015355060808360577,
-0.007515694014728069,
-0.03304494917392731,
0.04806109145283699,
-0.03784450516104698,
0.03847724571824074,
0.026669787243008614,
0.03566841408610344,
0.032392747700214386,
-0.01763482205569744,
-0.014325650408864021,
-0.0242022555321455,
-0.09520366042852402,
-0.04265958443284035,
0.03484393283724785,
-0.01782369613647461,
0.02351124957203865,
-0.011694026179611683,
0.03156809136271477,
-0.014856262132525444,
0.04739024490118027,
0.017957115545868874,
-0.05815804377198219,
0.01669500768184662,
-0.02692844159901142,
0.0010372960241511464,
0.00826603639870882,
-0.03524315729737282,
0.06513199210166931,
-0.012973612174391747,
-0.05322369560599327,
0.04962769150733948,
0.020461969077587128,
-0.0029310043901205063,
-0.06164860352873802,
-0.00628711236640811,
0.010315482504665852,
-0.0036417909432202578,
0.03476228937506676,
0.038137808442115784,
-0.003291175002232194,
0.051557984203100204,
0.06114324554800987,
0.03099464252591133,
0.018729589879512787,
0.02966918610036373,
0.03102293238043785,
0.004355794750154018,
-0.0066996426321566105,
0.010388446040451527,
-0.05731569230556488,
0.01803695783019066,
0.002319538267329335,
-0.029820268973708153,
0.017870934680104256,
0.012101373635232449,
0.016572609543800354,
-0.017620468512177467,
0.03153970465064049,
0.02008572593331337,
-0.024314405396580696,
-0.020892944186925888,
0.05275391414761543,
0.04481392726302147,
-0.023781850934028625,
-0.061986979097127914,
0.015505781397223473,
-0.02848917990922928,
0.017673742026090622,
0.02025686390697956,
-0.010108957067131996,
-0.03018888644874096,
-0.0018842470599338412,
0.03706720098853111,
0.008135582320392132,
-0.004136796575039625,
0.03333442658185959,
-0.009185482747852802,
-0.02254917100071907,
0.004685916472226381,
-0.021923797205090523,
-0.029268821701407433,
-0.011681273579597473,
0.08878051489591599,
-0.03248351067304611,
0.0539642870426178,
0.02721530944108963,
0.027848517522215843,
-0.002064825501292944,
0.06338030844926834,
-0.0015184372896328568,
0.0000245088212977862,
0.03819460794329643,
-0.02139320783317089,
-0.03225696086883545,
-0.0613752119243145,
0.031184924766421318,
-0.009044822305440903,
-0.0021521649323403835,
0.01596393622457981,
0.009765098802745342,
0.02782313898205757,
0.006811357103288174,
0.02199053391814232,
-0.028417205438017845,
-0.10883498936891556,
0.00977280456572771,
0.02777389995753765,
0.035615161061286926,
0.08320752531290054,
-0.01267116330564022,
-0.05147752910852432,
0.048496078699827194,
-0.017976999282836914,
-0.02667645737528801,
-0.0667266994714737,
0.03001600131392479,
0.04764473810791969,
-0.006267293822020292,
-0.02977943606674671,
-0.03737910836935043,
-0.0017482878174632788,
0.029209323227405548,
0.002934244927018881,
-0.007349549327045679,
-0.03170383721590042,
0.03418511524796486,
-0.007654885295778513,
0.004247074946761131,
-0.03432595729827881,
0.038593992590904236,
0.02109498716890812,
-0.053473737090826035,
-0.013262786902487278,
-0.0027114313561469316,
0.055319011211395264,
-0.04885030910372734,
0.02746504172682762,
0.027260305359959602,
-0.05450353026390076,
-0.05601036548614502,
-0.001075198408216238,
0.01403652224689722,
-0.034170962870121,
0.018971681594848633,
0.016130821779370308,
0.0024856855161488056,
-0.02130265347659588,
-0.044839855283498764,
0.0174087006598711,
-0.09248214215040207,
0.019147630780935287,
-0.010152310132980347,
0.07288636267185211,
0.05699336528778076,
0.006413599941879511,
0.018001623451709747,
-0.05404350534081459,
-0.03199239820241928,
0.0008909534080885351,
-0.007917935028672218,
0.014234335161745548,
-0.006553058046847582,
-0.007701497990638018,
0.035014793276786804,
0.024450793862342834
] |
<p>Immediately prior to becoming a supernova the core of some types of stars may suffer gravitational collapse. </p>
<ul>
<li><p>What happens to any planets in orbit around the star at the instant the mass is fully collapsed? </p></li>
<li><p>Assuming this sudden change would cause some perturbation ; how large/distant would a planet in the system have to be to be relatively immune to such perturbation?</p></li>
<li><p>Could unexplained perturbation serve as an indicator of a historic supernova in the vicinity?</p></li>
</ul> | g6579 | [
-0.005586423445492983,
0.02392144314944744,
-0.002572149969637394,
-0.062489643692970276,
-0.020998874679207802,
0.06475048512220383,
-0.044010698795318604,
0.03420893847942352,
0.02239595539867878,
-0.03535595163702965,
-0.02618591859936714,
0.06529921293258667,
0.03914172202348709,
0.014199009165167809,
0.054807886481285095,
-0.011270553804934025,
0.04922419786453247,
-0.0076565914787352085,
0.04555821791291237,
-0.0008554566302336752,
-0.06340406835079193,
0.014809953980147839,
-0.022867148742079735,
0.03910839185118675,
-0.06480348855257034,
0.014310097321867943,
0.05528847500681877,
-0.020691579207777977,
0.013072989881038666,
0.008134129457175732,
0.008095284923911095,
-0.005798127967864275,
0.024949420243501663,
-0.09617521613836288,
-0.005010969936847687,
-0.002657234435901046,
0.028840357437729836,
-0.018487459048628807,
0.026957742869853973,
-0.033537380397319794,
-0.01140940748155117,
-0.030901754274964333,
0.04212716594338417,
-0.02522788941860199,
0.009092788212001324,
0.01017378456890583,
-0.008770765736699104,
-0.03454887494444847,
-0.0002788531419355422,
0.016787448897957802,
-0.03417378291487694,
0.008961054496467113,
0.015415675938129425,
-0.025982176885008812,
-0.04426874965429306,
0.04078185185790062,
0.04872584342956543,
-0.024541279301047325,
0.015626737847924232,
0.0004990178858861327,
-0.014993730932474136,
-0.0376252606511116,
0.02468132972717285,
-0.07661996781826019,
0.01350801158696413,
-0.04978100582957268,
-0.03365541994571686,
0.06707163155078888,
0.033248286694288254,
-0.01668827049434185,
-0.024467524141073227,
0.025431623682379723,
-0.05887865275144577,
-0.0518459789454937,
-0.05166803300380707,
0.06602192670106888,
-0.04937615245580673,
0.020993059501051903,
-0.0518011674284935,
0.07580756396055222,
-0.011375287547707558,
-0.012374188750982285,
0.023862887173891068,
0.03311456739902496,
0.04085099697113037,
-0.0244117621332407,
-0.042798060923814774,
0.023473192006349564,
-0.010857421904802322,
0.04011405631899834,
0.03562740236520767,
0.0032369785476475954,
-0.002340930514037609,
-0.060802362859249115,
0.017215309664607048,
-0.0006634413148276508,
-0.018729886040091515,
0.004873010795563459,
-0.02291710302233696,
-0.013643303886055946,
0.012010060250759125,
-0.0005057426169514656,
-0.035840947180986404,
-0.04722623899579048,
0.017882058396935463,
-0.003790547838434577,
0.06675659120082855,
0.02083919569849968,
0.05229936167597771,
-0.040057674050331116,
0.013068096712231636,
-0.014111682772636414,
0.05635342001914978,
-0.021569373086094856,
-0.0436827577650547,
-0.03782579302787781,
0.0873049646615982,
-0.023300593718886375,
0.04324658587574959,
0.08145508170127869,
-0.03146618232131004,
0.010941630229353905,
-0.03820732980966568,
0.0027761326637119055,
-0.04903465509414673,
-0.019894011318683624,
-0.00886070542037487,
0.044596925377845764,
0.06568650901317596,
0.034555286169052124,
-0.010765576735138893,
0.00945889949798584,
-0.07992509752511978,
0.0029010141734033823,
0.053188830614089966,
0.045207541435956955,
-0.026320768520236015,
0.01706179603934288,
-0.05231478810310364,
-0.030884113162755966,
0.049419376999139786,
0.007489361334592104,
0.05052296072244644,
0.031782038509845734,
-0.022137336432933807,
-0.004515503998845816,
0.019368896260857582,
0.037265971302986145,
-0.00889609381556511,
0.005146272014826536,
-0.043871212750673294,
-0.016847994178533554,
0.04199784994125366,
-0.08586513996124268,
0.0031637728679925203,
0.018147213384509087,
-0.042497094720602036,
-0.005707982461899519,
-0.030890870839357376,
-0.025688381865620613,
-0.007331362925469875,
-0.023783141747117043,
0.04019975662231445,
-0.0010999083751812577,
-0.05608357861638069,
0.04434635862708092,
-0.01613769307732582,
-0.018633294850587845,
0.025814561173319817,
0.05269557982683182,
-0.008129783906042576,
-0.016511771827936172,
0.0042179846204817295,
0.06541488319635391,
0.0156811885535717,
-0.015955770388245583,
0.043573688715696335,
-0.06460150331258774,
0.05909840762615204,
0.01335031259804964,
0.06583527475595474,
-0.017429564148187637,
-0.020569398999214172,
-0.02230479009449482,
0.01623440720140934,
-0.05588868632912636,
-0.017878280952572823,
0.024486789479851723,
-0.016329549252986908,
0.011259111575782299,
-0.04773489385843277,
-0.03515486791729927,
0.051077138632535934,
0.015485509298741817,
-0.009415335021913052,
-0.020788149908185005,
0.0073258844204247,
0.0080774687230587,
-0.0343877449631691,
0.03051071986556053,
-0.025008494034409523,
0.00024126139760483056,
-0.006238862406462431,
0.0022243966814130545,
-0.042146988213062286,
0.014699084684252739,
-0.04465911537408829,
0.07700672000646591,
0.006107192952185869,
-0.028170714154839516,
-0.002610619179904461,
-0.020269643515348434,
0.02352229505777359,
-0.04781219735741615,
-0.0658346638083458,
0.057037174701690674,
-0.04288458079099655,
0.05811592936515808,
0.007206331472843885,
0.053150009363889694,
0.013936040922999382,
0.018607616424560547,
0.02462943084537983,
-0.035609468817710876,
0.01333602610975504,
-0.017754297703504562,
0.006903411820530891,
0.010164856910705566,
0.05379926785826683,
0.003243481507524848,
-0.04509600251913071,
-0.03307414427399635,
0.020193930715322495,
0.020383726805448532,
-0.01355964969843626,
-0.0067687202244997025,
0.023374972864985466,
-0.06227043271064758,
-0.0030524032190442085,
-0.015591811388731003,
0.01736345887184143,
-0.005083179101347923,
-0.011375194415450096,
-0.01458190567791462,
0.04713161662220955,
-0.04973798617720604,
0.010033316910266876,
-0.01682543009519577,
-0.04048168659210205,
-0.025906801223754883,
0.003943447954952717,
0.020891573280096054,
-0.041843440383672714,
-0.011244041845202446,
-0.00979316234588623,
-0.02265302650630474,
0.008209689520299435,
0.05308333784341812,
-0.0585901215672493,
-0.00008237109432229772,
0.05961417034268379,
0.0025879405438899994,
0.03423378989100456,
-0.0017123532015830278,
0.03250138461589813,
0.022743619978427887,
0.029816193506121635,
-0.021679818630218506,
-0.005560975521802902,
0.0023195601534098387,
-0.002833685837686062,
-0.007126105483621359,
0.0057717603631317616,
0.05916045606136322,
-0.0054339137859642506,
0.03438960388302803,
-0.05597047135233879,
0.0001227568427566439,
-0.023227965459227562,
-0.04335398226976395,
0.006368870381265879,
0.005735617130994797,
-0.06962136179208755,
0.0057584443129599094,
0.006396409124135971,
-0.056339070200920105,
0.034580111503601074,
0.0371856726706028,
0.053478457033634186,
-0.03673795238137245,
0.03373505547642708,
0.011601405218243599,
0.0020848007407039404,
0.07748132199048996,
-0.03385721892118454,
0.027211174368858337,
0.017305750399827957,
0.07880078256130219,
0.012455574236810207,
0.02398686856031418,
0.07530488818883896,
-0.0612216480076313,
0.00013401880278252065,
0.02087230421602726,
0.01528436504304409,
0.020399654284119606,
-0.05607662349939346,
0.019166823476552963,
-0.01773025654256344,
-0.020679766312241554,
-0.041666384786367416,
0.021153831854462624,
0.015590311028063297,
0.031900182366371155,
-0.043217387050390244,
0.03297388181090355,
0.01685311645269394,
-0.028514716774225235,
-0.0006557847955264151,
0.016825992614030838,
-0.02769431285560131,
-0.022391097620129585,
-0.020003408193588257,
-0.020062513649463654,
-0.0001311901432927698,
-0.026053672656416893,
0.011605207808315754,
0.035420943051576614,
-0.02301119454205036,
-0.014474268071353436,
-0.024035420268774033,
-0.04804569482803345,
0.00019229169993195683,
-0.013422740623354912,
-0.033198099583387375,
0.05704909563064575,
-0.022246740758419037,
0.03353824093937874,
0.032405052334070206,
0.0843908041715622,
0.021718012169003487,
0.011479372158646584,
-0.001997201004996896,
-0.010901045985519886,
0.018270162865519524,
0.027445577085018158,
0.006483693607151508,
-0.06821632385253906,
0.02113283984363079,
-0.0844784751534462,
0.0440627746284008,
-0.04299374297261238,
0.053526561707258224,
-0.012799456715583801,
0.014339915476739407,
0.03347943350672722,
0.0011771975550800562,
-0.0040126461535692215,
-0.008657712489366531,
0.02464277297258377,
-0.009153158403933048,
-0.08160442858934402,
0.01556939072906971,
0.03178298473358154,
0.03485636040568352,
0.03874567151069641,
-0.007615853566676378,
-0.04652322083711624,
0.041068971157073975,
0.016917143017053604,
0.028577154502272606,
-0.002276557730510831,
-0.02553117647767067,
-0.026456428691744804,
0.07577801495790482,
-0.008940696716308594,
0.06301935762166977,
0.026834117248654366,
-0.058325767517089844,
0.049313805997371674,
0.061625588685274124,
-0.0031529392581433058,
0.019760409370064735,
-0.021594038233160973,
0.021731259301304817,
-0.016830937936902046,
0.024863023310899734,
-0.05721615254878998,
0.015529908239841461,
-0.01267373375594616,
0.010772807523608208,
-0.11610253900289536,
0.02631286159157753,
-0.017705721780657768,
0.03082490712404251,
-0.004263490904122591,
0.021024061366915703,
0.0065133520402014256,
0.0709131732583046,
0.041073933243751526,
-0.013752499595284462,
0.03445878252387047,
0.012018260546028614,
-0.02337862364947796,
0.0340372659265995,
-0.021449461579322815,
-0.011831790208816528,
-0.016356848180294037,
-0.029482537880539894,
-0.023416806012392044,
0.06370589882135391,
0.024303007870912552,
-0.011504911817610264,
-0.013910630717873573,
0.009297076612710953,
-0.02250085212290287,
0.04977786913514137,
0.014626847580075264,
0.015449938364326954,
0.011010554619133472,
-0.04995069280266762,
0.03519473597407341,
0.006418060977011919,
0.0176805779337883,
0.006282609887421131,
-0.011686666868627071,
0.037594616413116455,
-0.07312779873609543,
-0.0026485382113605738,
0.037955570966005325,
0.04595795273780823,
0.060239341109991074,
0.03859521448612213,
0.002807595767080784,
-0.01747819036245346,
0.0029092589393258095,
-0.05678093060851097,
0.035323936492204666,
-0.024312803521752357,
0.048290081322193146,
-0.0011262207990512252,
-0.023389000445604324,
-0.014928659424185753,
0.03697705268859863,
-0.013764054514467716,
0.04571625217795372,
0.003892205422744155,
0.0013289999915286899,
0.029893523082137108,
-0.040970578789711,
-0.02979971654713154,
-0.018944354727864265,
0.009939438663423061,
0.01206583995372057,
-0.07364542037248611,
-0.022313611581921577,
0.017615295946598053,
0.03308727592229843,
-0.01942664198577404,
0.013052788563072681,
0.03035418502986431,
-0.011509710922837257,
-0.008642969653010368,
0.026408633217215538,
0.042846791446208954,
-0.031156647950410843,
-0.011157270520925522,
-0.03546960651874542,
-0.04768881946802139,
-0.0048016998916864395,
-0.03927511349320412,
0.019493423402309418,
0.03616722673177719,
-0.012667592614889145,
-0.021913858130574226,
0.026671554893255234,
0.0011391291627660394,
-0.0372375026345253,
0.0770794078707695,
-0.03734959289431572,
0.002985157771036029,
0.010035205632448196,
0.012950032949447632,
-0.017024721950292587,
0.02452346310019493,
0.03992068022489548,
0.012428459711372852,
0.003045338671654463,
0.01435043103992939,
0.005609280429780483,
-0.06318376213312149,
-0.04074345529079437,
0.0388464480638504,
0.027821453288197517,
0.03138795867562294,
-0.04320158064365387,
-0.00167303835041821,
-0.026006020605564117,
-0.011595753021538258,
0.017682578414678574,
-0.059984926134347916,
0.029733141884207726,
0.037945568561553955,
0.039404384791851044,
-0.0021969787776470184,
0.016148952767252922,
-0.009680473245680332,
-0.04244383051991463,
0.08313698321580887,
-0.035437971353530884,
-0.06014833226799965,
0.08857110887765884,
0.02156440168619156,
0.015739675611257553,
-0.02984802797436714,
-0.038856714963912964,
-0.031789593398571014,
0.025375816971063614,
0.00048053296632133424,
-0.006037972401827574,
-0.08904964476823807,
-0.037571173161268234,
-0.01713567227125168,
0.018244652077555656,
0.06776849925518036,
0.03052649274468422,
0.01086705457419157,
-0.004383925814181566,
-0.018110383301973343,
0.01798287220299244,
0.015817051753401756,
-0.05324006453156471,
0.00002713135108933784,
-0.06765585392713547,
-0.012192144058644772,
0.018602382391691208,
-0.011976214125752449,
0.018625104799866676,
0.025325950235128403,
-0.005584512371569872,
-0.0564328208565712,
-0.0005556983524002135,
-0.026423783972859383,
-0.007900934666395187,
-0.02068292163312435,
-0.02303742617368698,
-0.031112032011151314,
0.07278741896152496,
0.00968257337808609,
-0.073561891913414,
0.016405612230300903,
0.047738268971443176,
0.014203299768269062,
0.019907524809241295,
-0.010133324190974236,
0.050203390419483185,
0.06365440040826797,
0.0018572048284113407,
0.012019838206470013,
-0.06036890298128128,
-0.029472975060343742,
-0.03153258189558983,
0.029831979423761368,
0.031360942870378494,
0.023348884657025337,
-0.005570085719227791,
-0.030232183635234833,
-0.05321407690644264,
0.07535547763109207,
0.031128084287047386,
0.03480365127325058,
-0.021861791610717773,
-0.0017479535890743136,
-0.035899825394153595,
0.03067304939031601,
-0.023713983595371246,
-0.031762681901454926,
0.003859153715893626,
0.029982034116983414,
-0.03581880405545235,
0.008246771059930325,
-0.0635589137673378,
0.021856945008039474,
-0.01617855578660965,
-0.03813076391816139,
-0.024023331701755524,
0.024073341861367226,
0.03781425207853317,
0.03320188820362091,
-0.035319600254297256,
-0.003824115265160799,
-0.04134654998779297,
0.02245859056711197,
0.01827944628894329,
-0.02300330065190792,
0.06305055320262909,
-0.07955478876829147,
0.008618790656328201,
-0.04310857877135277,
0.021486753597855568,
0.00258435751311481,
0.019663579761981964,
0.06896845996379852,
-0.00738554960116744,
-0.011213165707886219,
-0.01371072232723236,
-0.03051607497036457,
0.025185376405715942,
0.03888043016195297,
0.017664464190602303,
0.0670352652668953,
0.029974542558193207,
0.06767528504133224,
-0.008347115479409695,
-0.039960190653800964,
-0.07585731893777847,
-0.01222789566963911,
0.01690208911895752,
-0.0610346794128418,
0.017815766856074333,
-0.002577724400907755,
-0.043794117867946625,
-0.00827301386743784,
-0.034777525812387466,
-0.039448872208595276,
0.0048840767703950405,
0.017309382557868958,
-0.019796423614025116,
0.028724808245897293,
0.035359013825654984,
0.006371597293764353,
-0.006614660378545523,
-0.006578484084457159,
0.010384893976151943,
0.01970617100596428,
0.0402848981320858,
-0.014543372206389904,
-0.008541380055248737,
0.05360814929008484,
-0.03577805683016777,
0.05972171574831009,
-0.05247323960065842,
-0.033778853714466095,
-0.018111594021320343,
-0.00812971405684948,
0.044078726321458817,
0.008768060244619846,
0.005361384246498346,
0.003699489636346698,
0.004081502556800842,
-0.019335176795721054,
-0.054180510342121124,
0.042176902294158936,
-0.017312252894043922,
-0.046044789254665375,
0.030479205772280693,
-0.020411944016814232,
0.018385326489806175,
-0.044485025107860565,
-0.09666328132152557,
-0.02178988978266716,
-0.01758101023733616,
-0.003208023961633444,
-0.04470747709274292,
0.016847878694534302,
0.03737820312380791,
0.08769294619560242,
-0.086935855448246,
-0.020545924082398415,
0.016186032444238663,
0.025506913661956787,
0.02009548619389534,
-0.026909302920103073,
-0.03159782290458679,
0.005506154615432024,
0.00008277992310468107,
-0.024168670177459717,
-0.0646461471915245,
0.08087585866451263,
0.0023666219785809517,
-0.004220024682581425,
0.02180037461221218,
-0.015434532426297665,
-0.02202111855149269,
0.00900763738900423,
0.028504109010100365,
-0.017267981544137,
0.03456209972500801,
0.007022926118224859,
0.011666664853692055,
-0.023421533405780792,
0.05189821124076843,
0.0004838530730921775,
-0.04550694301724434,
0.04040408134460449,
-0.031483761966228485,
-0.00358560960739851,
0.03769347071647644,
0.030115028843283653,
-0.09570276737213135,
-0.06353241205215454,
0.04680998995900154,
0.009828920476138592,
-0.08945102244615555,
0.013302451930940151,
0.05758418142795563,
-0.051843274384737015,
0.003150927135720849,
-0.08196520060300827,
0.046152353286743164,
0.09574131667613983,
0.045642610639333725,
0.0034562726505100727,
-0.05599097162485123,
0.019663184881210327,
0.005300425924360752,
0.018693963065743446,
-0.027036193758249283,
-0.03147196024656296,
0.02984173223376274,
-0.048251740634441376,
-0.012774022296071053,
0.01826355792582035,
-0.058414410799741745,
0.02189134992659092,
-0.022373801097273827,
-0.008265956304967403,
0.04387936368584633,
-0.02255559153854847,
-0.05999750643968582,
-0.005797962192445993,
-0.0031891369726508856,
-0.012946025468409061,
-0.019779011607170105,
-0.050116851925849915,
-0.04530811682343483,
-0.03040500357747078,
-0.022602766752243042,
-0.06352026015520096,
-0.013211056590080261,
-0.0761125311255455,
-0.06879501044750214,
0.016437459737062454,
0.021650774404406548,
0.021899042651057243,
0.020199432969093323,
0.014767864719033241,
0.00522764353081584,
-0.018520276993513107,
-0.032664161175489426,
-0.01617259532213211,
0.027326025068759918,
-0.000446371384896338,
0.057703517377376556,
-0.010074523277580738,
0.05730099231004715,
-0.11287732422351837,
-0.0390237495303154,
-0.08532599359750748,
-0.004534638021141291,
0.03347840532660484,
0.05148380249738693,
0.042360857129096985,
-0.017769837751984596,
0.048200253397226334,
-0.008618162013590336,
0.0006775012006983161,
0.0297402236610651
] |
<p><strong>(1)</strong> As we know, we have theories of second quantization for both bosons and fermions. That is, let $W_N$ be the $N$ identical particle Hilbert space of bosons or fermions, then the "many particle" Hilbert space $V$ would be $V=W_0\oplus W_1\oplus W_2\oplus W_3\oplus...$ , and further we can define creation and annihilation operators which satisfy commutation(anticommutation) relations for bonsons(fermions).</p>
<p>So my first question is, do we also have a "second quantization theory" for anyons like bosons and fermions?</p>
<p><strong>(2)</strong> Generally speaking, anyons can only happen in 2D. Is this conclusion based on the assumption that the particles are <strong>point-like</strong>? </p>
<p>In <a href="http://arxiv.org/abs/quant-ph/9707021" rel="nofollow">Kitaev's toric code model</a>, the quasiparticles are <strong>point-like</strong> due to the <strong>local operators</strong> in the Hamiltonian. My question is, in 3D case, whether there exists a simple model whose Hamiltonian contains <strong>local operators</strong> and <strong>spatially extended operators</strong>, so that it has both poit-like quasiparticles(say, $\mathbf{e}$) and knot-like quasiparticles(say, $\mathbf{m}$), then the $\mathbf{e}$ and $\mathbf{m}$ particles have nontrivial mutual statistics in 3D? </p> | g6580 | [
0.0528068020939827,
-0.0502823106944561,
-0.0018710375297814608,
-0.02767742983996868,
0.09196498990058899,
0.0014383132802322507,
-0.005766712594777346,
0.014326744712889194,
-0.019564326852560043,
0.04161969572305679,
-0.04980182647705078,
0.024954406544566154,
-0.004539568442851305,
0.015290427021682262,
-0.05032730475068092,
0.06862588226795197,
0.005869294982403517,
0.05258601903915405,
0.046018559485673904,
-0.049430180341005325,
-0.0018886232282966375,
0.029895542189478874,
0.038124069571495056,
-0.05414668098092079,
0.011111175641417503,
0.006838109809905291,
0.03209102898836136,
-0.0353972464799881,
-0.02244722470641136,
-0.00277273659594357,
0.03766664117574692,
-0.021782856434583664,
0.040729038417339325,
-0.07907447963953018,
0.004594548139721155,
-0.05759483203291893,
0.05606662109494209,
-0.01132145244628191,
-0.03620946407318115,
-0.0020729701500386,
0.0043871658854186535,
-0.026431595906615257,
0.0386711023747921,
-0.017819149419665337,
-0.05918026342988014,
0.006826526951044798,
-0.030090337619185448,
0.05397110432386398,
-0.02203632891178131,
-0.012883752584457397,
0.009668594226241112,
0.027200879529118538,
0.04543488472700119,
-0.008381915278732777,
0.03164944797754288,
0.06980995088815689,
-0.012881629168987274,
-0.047632355242967606,
0.057129427790641785,
0.04893006011843681,
-0.06454724818468094,
0.05423124507069588,
0.026645345613360405,
0.01627219095826149,
0.03604944795370102,
0.03247877582907677,
-0.04284649342298508,
0.015998367220163345,
-0.011706497520208359,
-0.021282335743308067,
0.03599083051085472,
-0.04832154139876366,
-0.025350192561745644,
-0.02723662368953228,
0.044367026537656784,
0.015352390706539154,
-0.05566725507378578,
-0.008942910470068455,
-0.0010661593405529857,
-0.011858334764838219,
-0.09337622672319412,
-0.03234463930130005,
-0.05217637121677399,
-0.004154758062213659,
0.027314525097608566,
-0.06543169170618057,
0.026986828073859215,
0.0006897829589433968,
-0.00886615552008152,
0.06039923056960106,
-0.012293596751987934,
0.021593784913420677,
0.032873429358005524,
0.07218960672616959,
-0.02094271034002304,
-0.022280028089880943,
0.015972478315234184,
0.059348106384277344,
-0.05329916998744011,
0.003179145511239767,
-0.039344560354948044,
-0.02152267098426819,
0.008375106379389763,
0.000812324695289135,
0.005816531367599964,
-0.010516745038330555,
0.08602479100227356,
-0.027908146381378174,
0.02768883854150772,
0.0371275320649147,
-0.03354199603199959,
0.0232804324477911,
-0.015895342454314232,
0.018105648458003998,
-0.030254153534770012,
0.0009267835994251072,
0.021692322567105293,
-0.04915696009993553,
0.005857250653207302,
0.039716292172670364,
0.048900969326496124,
-0.028395984321832657,
0.013130910694599152,
0.03728809580206871,
0.026988042518496513,
0.020894216373562813,
-0.03338715806603432,
0.05763835087418556,
0.0029486690182238817,
0.034234121441841125,
0.003999633248895407,
-0.031490158289670944,
0.01839623972773552,
0.05332595854997635,
-0.030012622475624084,
0.03901778906583786,
-0.023027092218399048,
0.035089366137981415,
0.03631686046719551,
0.015371190384030342,
-0.04276855289936066,
-0.042707331478595734,
-0.002303903689607978,
0.035440512001514435,
-0.04577719420194626,
-0.0179179385304451,
0.0734415054321289,
-0.06376157701015472,
-0.023363959044218063,
0.05355063080787659,
0.02757817879319191,
0.025717727839946747,
0.06699047237634659,
0.016158945858478546,
-0.0427795834839344,
0.041620977222919464,
-0.02665424905717373,
0.0408596433699131,
0.03357294946908951,
-0.011214430443942547,
0.03003094159066677,
-0.0029867354314774275,
0.004041335545480251,
0.012302111834287643,
0.011657842434942722,
-0.00475567439571023,
0.03844987973570824,
-0.029589107260107994,
-0.016836632043123245,
0.0034116851165890694,
-0.031968750059604645,
0.03159255161881447,
-0.018909407779574394,
-0.0255553238093853,
0.009203118272125721,
-0.025952642783522606,
-0.10405376553535461,
-0.025357253849506378,
0.008094225078821182,
0.02241324447095394,
-0.016707533970475197,
0.018654711544513702,
-0.015166682191193104,
-0.023280339315533638,
-0.006974908523261547,
0.046556130051612854,
-0.037647999823093414,
0.05289299413561821,
0.04549162834882736,
-0.004721580073237419,
-0.010261249728500843,
-0.05147667974233627,
-0.008640809915959835,
0.022560318931937218,
-0.04219776391983032,
0.009142219088971615,
0.07260344922542572,
-0.045137736946344376,
-0.003910883795469999,
-0.04043043777346611,
0.014207988977432251,
0.04707111418247223,
0.024610809981822968,
-0.004090983886271715,
0.042485155165195465,
-0.007810595445334911,
0.001910748309455812,
0.01761069893836975,
-0.020356692373752594,
0.0350005105137825,
0.007642305921763182,
-0.018199920654296875,
0.029142383486032486,
0.03917965665459633,
-0.019245073199272156,
-0.030153660103678703,
-0.036712877452373505,
0.01223313994705677,
-0.01303203497081995,
-0.048342540860176086,
-0.02692681923508644,
-0.05042438954114914,
0.05150075629353523,
-0.05582362040877342,
-0.01708565279841423,
-0.002916263649240136,
0.004744963254779577,
-0.010661023668944836,
-0.006114338990300894,
0.04770383983850479,
-0.006165248341858387,
-0.03436208888888359,
-0.03373955190181732,
-0.08501887321472168,
0.026719313114881516,
0.054358962923288345,
-0.06811916083097458,
0.0018535535782575607,
0.05352901294827461,
0.01594904623925686,
0.0507732592523098,
-0.04105474427342415,
-0.017235923558473587,
-0.014236507937312126,
0.07085279375314713,
0.01117442175745964,
0.030060477554798126,
0.04446626082062721,
0.003951619379222393,
0.023435527458786964,
-0.01913696527481079,
-0.00650747399777174,
-0.07105281203985214,
-0.03003557398915291,
0.056428488343954086,
0.0017346178647130728,
0.07362471520900726,
0.02913324162364006,
-0.055407699197530746,
-0.08423791825771332,
0.03470413759350777,
-0.012723465450108051,
-0.005239300429821014,
0.039311379194259644,
-0.008381490595638752,
0.03232976049184799,
-0.007424998562783003,
0.02963836118578911,
-0.03384556248784065,
0.01605299673974514,
-0.06097769737243652,
0.03568962588906288,
-0.00422561913728714,
0.036009397357702255,
-0.010803939774632454,
0.0013548779534175992,
-0.039811424911022186,
-0.008606908842921257,
0.0005226177163422108,
-0.05572188273072243,
-0.045016027987003326,
0.0858834981918335,
-0.011855518445372581,
0.03553394228219986,
0.04323199391365051,
-0.0144947599619627,
-0.016578778624534607,
0.00126233184710145,
-0.007115177810192108,
0.010979892686009407,
0.03537899628281593,
0.014474027790129185,
0.020342005416750908,
0.07350799441337585,
-0.0354975163936615,
0.012441621161997318,
-0.07120673358440399,
-0.005086539778858423,
0.009001091122627258,
0.09549959748983383,
0.03083779476583004,
-0.017666680738329887,
-0.005360154435038567,
0.04329733923077583,
0.09906166046857834,
-0.03697646036744118,
-0.07303962856531143,
-0.006127683911472559,
-0.02409345470368862,
0.004376789089292288,
-0.0026395125314593315,
0.07928616553544998,
-0.01802751049399376,
-0.012022935785353184,
0.024670369923114777,
0.023313134908676147,
-0.03388192132115364,
-0.00575476698577404,
0.005891406908631325,
-0.05629400163888931,
-0.04481199383735657,
-0.02351294457912445,
0.03220504894852638,
-0.04090510308742523,
0.0619596503674984,
0.05399744585156441,
-0.060291729867458344,
-0.002842833986505866,
-0.045850902795791626,
-0.009121468290686607,
-0.06029640510678291,
-0.008451634086668491,
0.02456900104880333,
0.00734728155657649,
-0.082762710750103,
-0.06172408163547516,
-0.04041662812232971,
-0.02665962278842926,
0.0467216894030571,
-0.009724834002554417,
0.04072397202253342,
-0.002213822677731514,
-0.026054343208670616,
-0.0035706418566405773,
-0.03462125360965729,
0.019209349527955055,
0.022676846012473106,
0.005319913383573294,
0.03704327344894409,
-0.030927404761314392,
0.040453121066093445,
-0.023778684437274933,
0.06547758728265762,
0.0036531828809529543,
0.00159541517496109,
-0.01943110302090645,
0.0526619628071785,
0.011027294211089611,
0.014960735104978085,
-0.06869592517614365,
0.025372400879859924,
-0.02644363045692444,
0.05101696774363518,
0.039383526891469955,
-0.03398017957806587,
-0.006682130042463541,
0.03564294055104256,
-0.05078911781311035,
0.025950370356440544,
-0.01613619737327099,
0.036714281886816025,
0.01510525681078434,
0.00242284475825727,
-0.014278599061071873,
0.04223966598510742,
0.027944929897785187,
0.03130671754479408,
-0.022566750645637512,
-0.02914530411362648,
0.00032163705327548087,
0.029722733423113823,
0.025153985247015953,
0.013992682099342346,
0.0283205546438694,
0.01957094669342041,
0.024779409170150757,
0.010669419541954994,
-0.0059255738742649555,
-0.04263798147439957,
-0.09480219334363937,
0.008584752678871155,
-0.033521510660648346,
-0.009954027831554413,
-0.054470181465148926,
0.04208681359887123,
-0.04516755789518356,
0.030603528022766113,
-0.057870324701070786,
-0.006081853061914444,
0.07844351977109909,
-0.09553972631692886,
-0.025566279888153076,
-0.005469188559800386,
-0.09071867167949677,
-0.01801937073469162,
-0.038086846470832825,
-0.01295663882046938,
0.03432416170835495,
-0.014979242347180843,
-0.005739630199968815,
-0.0037993756122887135,
-0.011140751652419567,
0.041567232459783554,
-0.06784628331661224,
-0.012856101617217064,
-0.03672480210661888,
-0.03169915825128555,
0.008541163988411427,
-0.03638797998428345,
-0.06685846298933029,
0.012271355837583542,
0.06181276589632034,
0.04299052432179451,
0.010334833525121212,
0.018148895353078842,
0.0121536273509264,
0.026181243360042572,
-0.002654451411217451,
-0.024730943143367767,
-0.0028123159427195787,
0.013653802685439587,
-0.025760382413864136,
0.05728624388575554,
0.035192862153053284,
-0.04192452132701874,
-0.019613491371273994,
-0.02373712696135044,
0.04866097867488861,
0.016607701778411865,
-0.014123224653303623,
0.04115784168243408,
0.0017724602948874235,
0.014490297064185143,
-0.01879454404115677,
0.06722474098205566,
0.006713820621371269,
-0.028867879882454872,
0.007065534591674805,
-0.020354025065898895,
-0.007445822935551405,
0.0023962168488651514,
0.0805596336722374,
-0.010947898961603642,
0.007497512269765139,
-0.0007362193427979946,
0.011391565203666687,
-0.0032351503614336252,
-0.006259342189878225,
-0.007605934049934149,
-0.02683192677795887,
-0.055003587156534195,
0.0016461279010400176,
0.01864040456712246,
0.021455436944961548,
-0.013499340042471886,
0.009547163732349873,
-0.09545852243900299,
0.015755292028188705,
0.0004428368993103504,
-0.02196689136326313,
-0.017285970970988274,
0.007654609624296427,
0.00805321242660284,
-0.048235878348350525,
0.021878743544220924,
0.011001348495483398,
0.07306796312332153,
-0.06110590323805809,
0.03683369606733322,
-0.02655351534485817,
0.012777375057339668,
-0.030484192073345184,
0.05829994007945061,
-0.01021953672170639,
0.02125636115670204,
0.01833302155137062,
0.01568176969885826,
0.009885133244097233,
-0.04693594574928284,
0.025149665772914886,
-0.025245551019906998,
-0.030087580904364586,
-0.017763826996088028,
0.013668734580278397,
0.018636735156178474,
-0.0020862221717834473,
0.01982978545129299,
-0.0428142324090004,
-0.0005320098134689033,
0.018172144889831543,
-0.016162235289812088,
-0.04904031381011009,
0.04950100556015968,
0.01582503505051136,
-0.006155699025839567,
0.025442304089665413,
0.06973063200712204,
-0.030804399400949478,
-0.002245450159534812,
-0.01316223107278347,
-0.017808761447668076,
-0.01471426710486412,
-0.055557731539011,
-0.02223396673798561,
-0.00808016862720251,
0.05937010422348976,
-0.021700944751501083,
0.04530685022473335,
-0.04454478621482849,
-0.06166614592075348,
0.007389379199594259,
-0.020404893904924393,
0.03316577896475792,
-0.02143370546400547,
0.0265154130756855,
0.027563678100705147,
-0.04402906075119972,
-0.042980875819921494,
0.06730704009532928,
0.06375683844089508,
-0.033761028200387955,
0.007889718748629093,
-0.05313611030578613,
0.022329261526465416,
-0.020850755274295807,
-0.009751185774803162,
-0.013719722628593445,
0.03505644574761391,
0.018687231466174126,
0.03571734577417374,
0.020801428705453873,
-0.007883032783865929,
-0.007359296549111605,
0.02224412001669407,
-0.059893928468227386,
-0.013898788020014763,
-0.057734500616788864,
-0.026844169944524765,
0.027095559984445572,
-0.025552082806825638,
-0.03604893013834953,
-0.04088333249092102,
-0.024149084463715553,
-0.018573397770524025,
0.022677641361951828,
-0.0007680606795474887,
-0.04163332283496857,
-0.0009937190916389227,
0.03228442370891571,
0.001151547534391284,
-0.04466498643159866,
-0.006330200005322695,
0.04251499101519585,
-0.027683980762958527,
0.024179620668292046,
-0.004355873912572861,
0.0266374833881855,
0.03428186476230621,
-0.0029326293151825666,
0.08575577288866043,
0.03849506005644798,
0.0693599134683609,
0.04043559357523918,
0.009490713477134705,
0.013621876016259193,
-0.025587016716599464,
0.001084522227756679,
-0.025507552549242973,
-0.04428090527653694,
-0.016117190942168236,
-0.004430512432008982,
0.07745683938264847,
-0.01973721943795681,
-0.022592933848500252,
-0.03860074281692505,
0.053874656558036804,
0.06061503291130066,
-0.046866193413734436,
-0.0038888822309672832,
0.040532056242227554,
-0.037797681987285614,
0.016869906336069107,
-0.06268555670976639,
-0.059196606278419495,
-0.005219012498855591,
0.04585372284054756,
0.015407618135213852,
-0.05768216773867607,
-0.020369043573737144,
0.05230638384819031,
0.007888128980994225,
-0.00737781124189496,
-0.0005272867274470627,
0.01954078860580921,
-0.019488265737891197,
0.06762650609016418,
-0.04254058003425598,
0.0031061593908816576,
-0.03401857614517212,
0.02825629524886608,
0.01151486486196518,
-0.030405715107917786,
-0.00845465436577797,
0.039658237248659134,
0.030624207109212875,
-0.06486841291189194,
-0.004252720158547163,
-0.03670703247189522,
-0.03500554338097572,
-0.03865961730480194,
0.043199166655540466,
-0.01225090678781271,
-0.031183188781142235,
-0.04105258360505104,
0.023194357752799988,
0.03362499922513962,
0.01402206439524889,
-0.029205312952399254,
0.054284948855638504,
0.03229086846113205,
-0.031056595966219902,
-0.004800854716449976,
0.014662906527519226,
0.04442109912633896,
-0.06511277705430984,
-0.011837984435260296,
-0.05560068041086197,
-0.03904149681329727,
-0.008653373457491398,
-0.008411509916186333,
-0.04313550516963005,
0.018242210149765015,
0.021998198702931404,
-0.019868042320013046,
-0.04380311071872711,
0.008801739662885666,
0.017278719693422318,
0.005135833285748959,
-0.026506787165999413,
0.041922662407159805,
0.02803752012550831,
0.024028820917010307,
-0.012895511463284492,
-0.01783101260662079,
0.02528850920498371,
0.013340701349079609,
0.05929693952202797,
0.03990591689944267,
-0.015618531033396721,
-0.02048923447728157,
-0.05870413780212402,
0.013436910696327686,
-0.03306446224451065,
-0.04957133159041405,
0.04038819298148155,
0.044254958629608154,
0.015438609756529331,
-0.023897213861346245,
-0.061620891094207764,
0.0015102154575288296,
-0.005588478874415159,
-0.02487059310078621,
-0.07272160798311234,
-0.019695498049259186,
-0.013506448827683926,
0.00230098026804626,
0.003664798103272915,
0.07460509240627289,
-0.003223059233278036,
-0.05036509409546852,
0.07332243770360947,
0.024877876043319702,
0.03736631199717522,
-0.003395270323380828,
0.00018763002299237996,
0.05367874354124069,
0.02591828629374504,
-0.011899196542799473,
-0.040438782423734665,
0.03125672787427902,
0.06306740641593933,
-0.048659827560186386,
0.011942584998905659,
-0.02943238988518715,
-0.030397724360227585,
0.032119400799274445,
-0.0078529492020607,
0.01692529208958149,
0.04527390003204346,
0.040825095027685165,
0.02266487292945385,
-0.03340144827961922,
-0.09649140387773514,
-0.026880817487835884,
-0.00045403692638501525,
-0.04842853173613548,
0.015661442652344704,
-0.010040104389190674,
-0.03975632041692734,
-0.008557675406336784,
0.04974065348505974,
0.0008498408715240657,
0.03665170818567276,
0.041150741279125214,
0.015832284465432167,
-0.026121219620108604,
-0.011173347942531109,
-0.008868779987096786,
0.015440770424902439,
-0.045091841369867325,
-0.024043874815106392,
-0.047716591507196426,
-0.08195144683122635,
0.006750635337084532,
0.04068927466869354,
-0.020792772993445396,
0.021787766367197037,
0.0027822228148579597,
0.02494320273399353,
0.02096117101609707,
0.0035364776849746704,
0.020063018426299095,
-0.02818186767399311,
0.038364093750715256,
-0.04664254188537598,
0.00004855584484175779,
0.000026930580133921467,
0.003631108207628131,
-0.01321004144847393,
-0.05447506532073021,
-0.01405660156160593,
-0.010995603166520596,
0.06096608191728592,
0.005236882716417313,
-0.006222437135875225,
0.06452939659357071,
-0.023737970739603043,
-0.007150312419980764,
-0.015995033085346222,
-0.056864261627197266,
0.01145636010915041,
0.01366292592138052,
0.03760270029306412,
0.006471589207649231,
0.04111926630139351,
-0.02953076921403408,
0.04611169546842575,
0.009059176780283451,
-0.014006827026605606,
-0.036529961973428726,
-0.058615148067474365,
0.01306310947984457,
-0.01359749585390091,
-0.0385100357234478,
0.03818687051534653,
-0.034235529601573944,
-0.024503644555807114,
0.1008099690079689
] |
<p>I read some where that there are three types of UV and infrared rays namely UV-A, UV-B, UV-C and near infrared, mid infrared and far infrared. Which is the most abundant among the the three in Ultraviolet and infrared radiation from sun? I mean there is a total of 1000 W per unit area illumination by sun among which more than 500 watts is infrared, around 450 watts in visible and the rest part is ultraviolet so in the infrared rays which are the most abundant means which contribute to most of the 500 watts?
Also, what are the sources of infrared at night and what is the power density of infrared rays at night!.</p> | g6581 | [
0.028891783207654953,
0.003967556171119213,
0.0021887419279664755,
0.04500006139278412,
-0.0014976972015574574,
-0.009781653061509132,
0.023109134286642075,
-0.006072668358683586,
0.006931287236511707,
0.020038118585944176,
0.04662308841943741,
-0.008350252173841,
-0.035702768713235855,
0.03152136132121086,
0.012281632982194424,
-0.02152952179312706,
0.020958617329597473,
-0.01698433980345726,
0.04396593198180199,
0.07505825161933899,
-0.04842761531472206,
-0.06972357630729675,
0.030799657106399536,
-0.006567468401044607,
-0.057936813682317734,
0.01693783514201641,
0.0011839563958346844,
0.006294427439570427,
0.020992698147892952,
-0.05789243429899216,
0.08930163085460663,
-0.014080245979130268,
0.07031665742397308,
0.0032849072013050318,
0.016809815540909767,
-0.010224059224128723,
0.020256230607628822,
0.00086393509991467,
-0.02119310572743416,
0.04853815585374832,
0.0036122368182986975,
0.057437390089035034,
0.09714752435684204,
0.026020528748631477,
-0.0021980253513902426,
0.011563373729586601,
-0.0505225732922554,
0.003051827661693096,
0.006998872384428978,
-0.03763238713145256,
0.008908971212804317,
-0.020902149379253387,
0.020064083859324455,
0.023891819640994072,
0.06298930197954178,
-0.01984519511461258,
0.010203723795711994,
-0.040521297603845596,
0.018709806725382805,
0.039624977856874466,
0.060750532895326614,
0.007303065620362759,
-0.06153760105371475,
0.012347204610705376,
0.013035465031862259,
-0.01879323087632656,
-0.016264697536826134,
0.023915698751807213,
0.00759910698980093,
0.008223211392760277,
0.005404338240623474,
-0.04501350224018097,
-0.005607289262115955,
-0.024109970778226852,
-0.01755368709564209,
-0.06264527142047882,
0.022993996739387512,
-0.013783507980406284,
-0.03825550898909569,
0.08730047196149826,
0.040539927780628204,
-0.0565233938395977,
0.006360616069287062,
-0.01414358802139759,
0.025249015539884567,
-0.034210242331027985,
-0.032380856573581696,
0.008024247363209724,
-0.013448696583509445,
-0.00876326858997345,
0.036666616797447205,
0.04978323355317116,
0.08080065995454788,
-0.0021582962945103645,
-0.004460417199879885,
0.06587006896734238,
0.04084803909063339,
0.05276545509696007,
0.008440268225967884,
-0.0116217490285635,
-0.005560798570513725,
-0.049349162727594376,
0.051072850823402405,
-0.02524595893919468,
0.015555677935481071,
0.01796294003725052,
-0.06463269144296646,
-0.05811981484293938,
-0.05429358407855034,
0.06945338100194931,
-0.09604004770517349,
-0.02572539448738098,
0.001670177443884313,
-0.00945077370852232,
-0.04168607294559479,
-0.0311651099473238,
0.02384740486741066,
0.014312757179141045,
0.06457668542861938,
0.06602460145950317,
0.009577910415828228,
0.05844642221927643,
-0.035988207906484604,
-0.026211077347397804,
0.0031733724754303694,
-0.02469734475016594,
0.009830544702708721,
-0.014394067227840424,
-0.049931589514017105,
-0.022260956466197968,
0.04016035795211792,
0.0063290526159107685,
-0.008740602992475033,
0.00827329233288765,
0.07331523299217224,
0.0020803455263376236,
0.019789662212133408,
0.026479285210371017,
0.05714835971593857,
0.0426117368042469,
0.017444586381316185,
-0.011716398410499096,
0.014507546089589596,
-0.052260857075452805,
-0.05082903057336807,
0.0450759157538414,
-0.05148711055517197,
-0.008482703007757664,
-0.027632124722003937,
-0.021007327362895012,
0.05929876118898392,
0.029698660597205162,
0.02499781921505928,
-0.08660714328289032,
-0.03614182025194168,
-0.04844851419329643,
-0.026904884725809097,
-0.02914714440703392,
-0.015676377341151237,
0.00556125957518816,
-0.021626312285661697,
-0.04060238599777222,
0.014557857066392899,
-0.0141390860080719,
0.007196180988103151,
-0.07162538170814514,
-0.031019598245620728,
-0.06895367056131363,
-0.005304066929966211,
0.012774428352713585,
-0.009827664121985435,
-0.02889048121869564,
-0.003983114380389452,
-0.02417862042784691,
0.022967146709561348,
0.005912026856094599,
0.10574644804000854,
-0.03212481737136841,
-0.0020853218156844378,
0.03975362330675125,
-0.031193992123007774,
-0.026806188747286797,
-0.0382392555475235,
-0.0513923317193985,
0.01876229979097843,
0.018828783184289932,
-0.001986418617889285,
-0.041146036237478256,
-0.002637645462527871,
0.04920833930373192,
-0.03081025741994381,
-0.05418672040104866,
0.045363083481788635,
-0.029379921033978462,
-0.02799365669488907,
0.025339201092720032,
0.02326769381761551,
0.004115338437259197,
0.004348006099462509,
0.0254324022680521,
0.04489276930689812,
-0.030671613290905952,
-0.05451390892267227,
-0.011573264375329018,
0.001145035377703607,
0.09546029567718506,
-0.020744556561112404,
0.01991851069033146,
-0.025803927332162857,
0.028989415615797043,
0.012009687721729279,
-0.05968927592039108,
0.03816543519496918,
0.02152005024254322,
-0.022202765569090843,
-0.001991105265915394,
-0.09728366136550903,
0.0007770433439873159,
0.023416614159941673,
-0.02971290983259678,
-0.021586524322628975,
0.06112151965498924,
0.05986279994249344,
0.04217394068837166,
-0.008132608607411385,
0.08930568397045135,
-0.009809937328100204,
-0.0216762013733387,
0.06145511567592621,
0.052385684102773666,
-0.06671664863824844,
-0.037177857011556625,
0.017539961263537407,
0.007138374727219343,
-0.01506110280752182,
0.005884545389562845,
-0.002860970562323928,
-0.01110292598605156,
0.03726089000701904,
-0.02926841378211975,
0.01357960794121027,
0.01181902177631855,
0.037574704736471176,
-0.005118224769830704,
0.0009521216270513833,
0.028101224452257156,
-0.05294415354728699,
-0.03969668596982956,
0.04455392435193062,
0.009649597108364105,
-0.012494265101850033,
0.02300289459526539,
0.029136380180716515,
0.005091829691082239,
-0.03246660158038139,
-0.02524959109723568,
-0.030765902251005173,
0.027892153710126877,
-0.020977463573217392,
-0.019887294620275497,
-0.015057902783155441,
-0.08552476018667221,
-0.0019713877700269222,
0.013719961047172546,
0.00756352161988616,
0.06587395071983337,
0.002331503899767995,
-0.019641714170575142,
0.014566087163984776,
0.009822841733694077,
-0.02755439281463623,
0.027508869767189026,
-0.020327679812908173,
0.012402014806866646,
0.053150273859500885,
-0.00807050708681345,
-0.02296685427427292,
-0.015473665669560432,
-0.017014222219586372,
-0.058400873094797134,
0.01071256771683693,
0.041344333440065384,
0.0035570913460105658,
0.009085958823561668,
0.030995037406682968,
-0.0314081571996212,
0.0058379871770739555,
-0.024379488080739975,
0.019439272582530975,
-0.019821153953671455,
-0.0175736453384161,
-0.0371355377137661,
0.04792671278119087,
0.003669996978715062,
-0.08723133057355881,
0.0034192504826933146,
0.030883129686117172,
0.007318161893635988,
-0.019511085003614426,
0.0173451267182827,
0.03564607724547386,
-0.03218653053045273,
-0.0036620122846215963,
0.00836970005184412,
0.0046699875965714455,
0.01405410561710596,
-0.054208166897296906,
-0.05954475700855255,
0.007173449266701937,
0.029106134548783302,
-0.043490804731845856,
-0.029849620535969734,
-0.012676018290221691,
0.010064046829938889,
0.007366410456597805,
-0.025694912299513817,
0.006065101828426123,
-0.0333876870572567,
-0.0013976522022858262,
-0.016144737601280212,
-0.049893300980329514,
0.009490897879004478,
0.02206805720925331,
-0.0015785638242959976,
-0.01074032112956047,
0.067805215716362,
0.020244311541318893,
-0.00977670680731535,
0.03557681664824486,
-0.022878559306263924,
-0.06114928051829338,
0.03451898321509361,
-0.01726246066391468,
-0.015144458040595055,
-0.02622477151453495,
0.012289253994822502,
-0.05360812693834305,
0.02080647088587284,
0.036958225071430206,
0.009459459222853184,
0.07029641419649124,
0.0427965484559536,
-0.0330970399081707,
-0.030118504539132118,
0.027276579290628433,
0.01902010478079319,
-0.03334454447031021,
-0.06740313768386841,
-0.053545933216810226,
0.051599372178316116,
0.00674652773886919,
-0.04366801679134369,
-0.01390642486512661,
-0.037657756358385086,
-0.044758960604667664,
0.04610135033726692,
-0.053976934403181076,
0.025510618463158607,
0.04829537495970726,
-0.06366289407014847,
-0.004268038552254438,
-0.03157102316617966,
0.08668147772550583,
-0.00991761963814497,
-0.0440426804125309,
-0.008047726936638355,
0.048790689557790756,
-0.008473854511976242,
0.03784625977277756,
0.02824402041733265,
0.012441765516996384,
-0.05611405149102211,
-0.0182938314974308,
-0.07477676868438721,
-0.009435949847102165,
0.00130229361820966,
0.0032333997078239918,
-0.01162632741034031,
0.01535496674478054,
0.08652549982070923,
0.03626858443021774,
0.0117697948589921,
0.06747094541788101,
0.023248644545674324,
0.022531632333993912,
0.0798342376947403,
-0.03221922740340233,
-0.02274513617157936,
0.009521696716547012,
-0.050310175865888596,
0.0353647917509079,
-0.07142500579357147,
-0.07043295353651047,
0.010062461718916893,
-0.006676340475678444,
-0.037977445870637894,
0.04687226936221123,
0.013939907774329185,
0.03243718296289444,
0.03609731048345566,
0.056622374802827835,
0.02131587453186512,
-0.00566117512062192,
-0.017125219106674194,
0.0013068313710391521,
0.06970098614692688,
0.02899998612701893,
-0.04146292805671692,
0.04239808768033981,
-0.011167958378791809,
0.0019295410020276904,
0.0072970520704984665,
0.033437520265579224,
-0.05499225854873657,
0.009692042134702206,
0.006785614416003227,
-0.008958457037806511,
-0.07296605408191681,
0.029394373297691345,
0.061281777918338776,
-0.0057698325254023075,
-0.039005834609270096,
-0.07627086341381073,
-0.03216635808348656,
0.021467359736561775,
0.024123981595039368,
0.08993301540613174,
-0.009396863169968128,
-0.02225586026906967,
0.02773129940032959,
-0.005215417128056288,
-0.0002371437003603205,
0.026983004063367844,
0.02027306891977787,
0.03272489085793495,
0.006416491232812405,
0.010314815677702427,
-0.022688990458846092,
-0.002187626203522086,
0.01743181049823761,
0.05853550508618355,
0.011599181219935417,
0.005239877384155989,
0.0037384245079010725,
-0.005802284926176071,
0.05743725970387459,
0.019416794180870056,
-0.021361395716667175,
-0.016760535538196564,
-0.002445598365738988,
0.02179396152496338,
0.028384016826748848,
-0.06588060408830643,
-0.03377524018287659,
0.024058358743786812,
0.03086034581065178,
-0.07423330843448639,
-0.017791522666811943,
0.030703186988830566,
0.0006557962042279541,
-0.028404464945197105,
-0.002729842672124505,
0.02335580252110958,
0.008435637690126896,
0.06481096148490906,
-0.06927284598350525,
-0.06977306306362152,
0.03484366834163666,
-0.04396071657538414,
-0.053316038101911545,
0.019236864522099495,
0.03988940641283989,
0.05592542886734009,
0.005933335050940514,
0.013334057293832302,
-0.043035078793764114,
-0.006532604340463877,
-0.027605973184108734,
-0.027375858277082443,
0.031581807881593704,
-0.019290737807750702,
-0.0027584980707615614,
-0.021664584055542946,
0.09842534363269806,
-0.040859196335077286,
-0.009703725576400757,
0.04426521435379982,
-0.010588012635707855,
-0.013180040754377842,
-0.011216673068702221,
-0.039629556238651276,
0.033184632658958435,
0.026638837531208992,
0.033569417893886566,
0.006156009156256914,
0.026416463777422905,
0.0005453931516967714,
-0.05356783792376518,
0.007388490252196789,
0.028106754645705223,
0.0314304381608963,
-0.00857177097350359,
-0.038279131054878235,
-0.039921700954437256,
0.004481506999582052,
0.013267025351524353,
0.05337280035018921,
-0.024138033390045166,
0.04251304641366005,
0.058392543345689774,
-0.023505304008722305,
-0.05261276289820671,
-0.028524044901132584,
0.019952712580561638,
0.03667039796710014,
-0.027410931885242462,
-0.007806121371686459,
0.05125710740685463,
0.02060038596391678,
0.0032124132849276066,
0.05420798808336258,
0.013611135073006153,
0.029569078236818314,
0.061262860894203186,
0.0777137354016304,
-0.01947302743792534,
0.00909974705427885,
0.012501087971031666,
0.07165166735649109,
-0.04120771586894989,
-0.0209331251680851,
0.050149668008089066,
-0.023022880777716637,
-0.05284975841641426,
-0.0030244970694184303,
-0.010055704042315483,
0.0335027351975441,
0.02890598215162754,
0.003160636406391859,
0.034000881016254425,
-0.02211686782538891,
-0.005678575485944748,
0.009373165667057037,
0.037402357906103134,
0.055422600358724594,
-0.0396871492266655,
-0.01396102737635374,
-0.00913776271045208,
-0.00254680123180151,
0.08967345207929611,
0.024379797279834747,
0.018257806077599525,
0.02556290104985237,
-0.034812796860933304,
-0.027359794825315475,
-0.05769027769565582,
-0.013891370967030525,
0.058285921812057495,
0.023659957572817802,
-0.0001873015280580148,
0.0051072994247078896,
0.01714491657912731,
-0.00026380084455013275,
-0.029801703989505768,
-0.003774876007810235,
-0.04322991147637367,
-0.02504865825176239,
-0.04837068170309067,
0.013902021571993828,
0.017078742384910583,
0.028540756553411484,
0.02855609357357025,
0.036356523633003235,
0.007265803869813681,
0.08091868460178375,
0.003844183636829257,
0.05000922083854675,
-0.015562159940600395,
-0.048937682062387466,
-0.018120432272553444,
0.046792320907115936,
-0.02116113156080246,
-0.04176465794444084,
0.029985329136252403,
-0.031434040516614914,
0.028613422065973282,
0.034011971205472946,
-0.017330193892121315,
-0.05354594439268112,
-0.0485294945538044,
0.007670056074857712,
-0.029281655326485634,
-0.014927461743354797,
-0.007108445279300213,
-0.08869369328022003,
-0.010756198316812515,
0.005113560706377029,
-0.02539980039000511,
-0.010716189630329609,
-0.041876036673784256,
-0.021224848926067352,
0.008000336587429047,
0.027605053037405014,
-0.01308869943022728,
0.0326649434864521,
-0.028566505759954453,
0.02387366071343422,
-0.029652411118149757,
-0.017977962270379066,
0.01768648624420166,
-0.023091351613402367,
0.009543215855956078,
-0.05768486484885216,
0.016683226451277733,
-0.02683672122657299,
0.003975837957113981,
-0.0917849987745285,
-0.03961410000920296,
0.011055815033614635,
-0.05159001424908638,
0.01466258056461811,
-0.05711763724684715,
0.024625802412629128,
-0.03794386237859726,
0.05096502974629402,
0.06462489068508148,
-0.005874257069081068,
0.02525760978460312,
0.0679461881518364,
-0.006165405735373497,
0.020202914252877235,
-0.04044165089726448,
0.005773183424025774,
0.04222673177719116,
0.016305075958371162,
0.009099258109927177,
-0.02230083756148815,
-0.004340708255767822,
0.004849930759519339,
0.018063686788082123,
-0.032064829021692276,
-0.030755367130041122,
0.016665443778038025,
0.023584820330142975,
0.02537505514919758,
-0.032140351831912994,
-0.03709150478243828,
-0.07990811765193939,
-0.00032707321224734187,
-0.004287940450012684,
-0.04104763641953468,
-0.010939284227788448,
0.0302871260792017,
-0.030731841921806335,
0.007143238093703985,
0.07969261705875397,
-0.011039718985557556,
0.029180858284235,
0.011741884052753448,
-0.08158031105995178,
0.005235849879682064,
0.03736167028546333,
0.028891224414110184,
0.0683562308549881,
0.00393274798989296,
0.0737856924533844,
-0.019828401505947113,
0.002949075773358345,
-0.08436475694179535,
0.009300075471401215,
-0.001919066533446312,
0.022991018369793892,
-0.03828166052699089,
-0.050967488437891006,
-0.027760177850723267,
0.015685394406318665,
-0.03424542024731636,
0.0038379637990146875,
0.00991041399538517,
-0.058170076459646225,
-0.03513167425990105,
0.007746147457510233,
-0.005935216322541237,
-0.009341328404843807,
0.059407129883766174,
-0.01079520769417286,
-0.007319224998354912,
-0.07930337637662888,
0.051565635949373245,
-0.03757309913635254,
-0.07281100749969482,
0.01403468381613493,
0.02563760243356228,
-0.07079549133777618,
0.0053105829283595085,
-0.022548697888851166,
-0.05780736356973648,
-0.023280492052435875,
0.009922536090016365,
0.021132728084921837,
0.023130465298891068,
0.001240454032085836,
0.06400161981582642,
-0.023867303505539894,
-0.033040281385183334,
0.015547716058790684,
0.014220635406672955,
0.05414758250117302,
-0.004956705030053854,
-0.005525466986000538,
0.024455847218632698,
-0.005966633092612028,
0.043816082179546356,
0.040478892624378204,
0.00866164080798626,
-0.02294664829969406,
-0.06942200660705566,
0.02779434248805046,
-0.07701233774423599,
0.020113859325647354,
0.008697619661688805,
0.010462021455168724,
0.02519640326499939,
-0.005950466264039278,
-0.01934252679347992,
-0.041305091232061386,
0.02043369971215725,
-0.03365641087293625,
0.018352588638663292,
0.011464051902294159,
-0.02900252677500248,
-0.036584705114364624,
-0.031111514195799828,
-0.028798971325159073,
-0.030788876116275787,
0.027569295838475227,
-0.0040842462331056595,
0.0022873871494084597,
0.010788668878376484,
-0.010562011040747166,
0.0008668160880915821,
-0.004696596413850784,
0.003974294289946556,
-0.0324297659099102,
-0.03288232907652855,
-0.034471042454242706,
-0.027614735066890717,
0.03199081867933273,
0.0378604419529438,
0.0067084054462611675,
-0.04592977836728096,
0.05729741230607033,
0.032858338207006454,
0.012048216536641121,
0.041929204016923904,
-0.018764693289995193,
0.03362242132425308,
0.006413248833268881,
-0.04614710435271263,
0.018802877515554428,
0.005358763039112091,
-0.02956034615635872,
-0.03489246219396591,
-0.00991032924503088,
-0.004729528445750475,
-0.010270433500409126,
0.01497382577508688,
-0.07982191443443298
] |
<p>In spherical coordinates the flat space-time metric takes:</p>
<p>$$ds^2=-c^2dt^2+dr^2+r^2d\Omega^2$$</p>
<p>where $r^2d\Omega^2$ come from when the signature of metric $g_{\mu\nu}$ is (-,+,+,+)?</p>
<p>what is signature of spherical metric?</p>
<hr>
<p>this is signature of spherical coordinates:
$(1,r^2,r^2\sin^2\theta$)</p>
<hr>
<p>let me ask in this way,
Isn't it metric of spherical coordinates?</p>
<p>$$g_{\mu\nu}= (-1,+1,+r^2,+r^2\sin^2\theta)$$</p> | g6582 | [
-0.012167312204837799,
-0.045424334704875946,
-0.0347411185503006,
-0.04430847987532616,
0.025127438828349113,
0.03492085263133049,
0.05373704433441162,
-0.01595453917980194,
-0.0446530282497406,
0.0015015468234196305,
0.007105104625225067,
0.03329943120479584,
0.06101603806018829,
-0.052665844559669495,
0.012060528621077538,
-0.07026774436235428,
0.040906332433223724,
-0.021199412643909454,
-0.023665066808462143,
0.009996558539569378,
0.03380053490400314,
-0.0207451730966568,
0.057811517268419266,
-0.018481392413377762,
0.013154418207705021,
-0.01242462731897831,
0.09322681277990341,
-0.01767260953783989,
-0.030334003269672394,
0.00521545996889472,
0.0498577319085598,
-0.01584804616868496,
0.06447311490774155,
-0.007731106597930193,
-0.01149113941937685,
0.02558699995279312,
0.0350334495306015,
0.005024509970098734,
0.04609830677509308,
0.004889247473329306,
0.004405197221785784,
0.0044886283576488495,
0.04922294616699219,
0.07271233946084976,
-0.01671934872865677,
-0.01631840132176876,
-0.008977862074971199,
0.08670233935117722,
-0.015655869618058205,
-0.005433632060885429,
-0.014160321094095707,
0.04120345786213875,
0.005419918801635504,
-0.03755376487970352,
-0.026448369026184082,
0.05074281245470047,
0.061998721212148666,
-0.038423001766204834,
0.02526193857192993,
0.07139629870653152,
-0.00938293244689703,
-0.02667543850839138,
-0.011371536180377007,
0.02853451669216156,
0.033364612609148026,
-0.010202920064330101,
-0.025120999664068222,
0.008658728562295437,
0.021987570449709892,
-0.006449831183999777,
0.04804782569408417,
-0.03524995595216751,
0.00768832815811038,
-0.019573872908949852,
-0.028916971758008003,
0.026205074042081833,
0.050917863845825195,
0.0005501075647771358,
0.0074672456830739975,
-0.05382511392235756,
0.01459322776645422,
0.010928120464086533,
0.052359819412231445,
0.029613004997372627,
0.04916641116142273,
0.004569311626255512,
-0.0037415693514049053,
-0.012289502657949924,
-0.05385644733905792,
0.035123735666275024,
0.05568055063486099,
-0.031898900866508484,
0.010650763288140297,
-0.03444793075323105,
-0.036622025072574615,
0.007548109162598848,
0.02493566833436489,
0.0026966375298798084,
-0.026163192465901375,
-0.03066595084965229,
-0.005609840154647827,
-0.009852172806859016,
0.03284090384840965,
0.02139478363096714,
0.020991187542676926,
0.018118631094694138,
0.00316826393827796,
0.04925540089607239,
0.03779299184679985,
-0.02367166243493557,
-0.015546618029475212,
0.030835511162877083,
-0.006860376801341772,
0.002970899688079953,
-0.04126807302236557,
-0.04353605955839157,
0.002877400955185294,
-0.0508246049284935,
0.0023880042135715485,
0.07114318758249283,
-0.02222629450261593,
0.0003260797820985317,
0.005840909201651812,
0.05879437178373337,
-0.019837496802210808,
-0.018627995625138283,
-0.015189806930720806,
0.019400587305426598,
0.06466022878885269,
0.00783709716051817,
0.0610683374106884,
0.05593820661306381,
-0.01671677641570568,
0.02332093007862568,
-0.08061189204454422,
0.045807525515556335,
-0.02771739847958088,
-0.03700273111462593,
-0.04025774449110031,
-0.04400012269616127,
-0.08919144421815872,
0.005280603654682636,
0.049857284873723984,
-0.030169546604156494,
-0.012275930494070053,
0.035740066319704056,
0.04043881595134735,
-0.023123249411582947,
0.003186275949701667,
0.02792365290224552,
0.04205481708049774,
0.0786171704530716,
0.010860508307814598,
0.027723316103219986,
-0.001409780466929078,
0.0049919066950678825,
-0.028408875688910484,
-0.037304870784282684,
0.0044404021464288235,
0.03658190369606018,
0.0694720521569252,
0.0203082375228405,
0.024988709017634392,
0.002535163890570402,
-0.020047882571816444,
0.04109622538089752,
-0.022833028808236122,
0.008488564752042294,
-0.03842775523662567,
-0.06223207712173462,
-0.022905269637703896,
0.03287327289581299,
0.003932851832360029,
0.011351343244314194,
-0.027075836434960365,
-0.03310026600956917,
-0.06517081707715988,
0.018630437552928925,
0.05066739022731781,
0.02242462895810604,
-0.004110876936465502,
-0.07158815860748291,
0.004178662318736315,
-0.012516611255705357,
0.0023204113822430372,
0.014056740328669548,
0.05436650291085243,
-0.04455438628792763,
-0.014899848029017448,
0.07029033452272415,
0.01311887800693512,
-0.017632266506552696,
0.020064054057002068,
0.11242315173149109,
0.05589814856648445,
0.05911383777856827,
0.045924942940473557,
-0.009587723761796951,
-0.018309947103261948,
0.11499421298503876,
-0.023964090272784233,
-0.0009540461469441652,
0.022731073200702667,
0.01783519610762596,
-0.03972483426332474,
-0.000968019652646035,
0.022288497537374496,
-0.017808083444833755,
0.02417898364365101,
0.016516810283064842,
0.004499125760048628,
-0.028000639751553535,
-0.005561384372413158,
-0.04966185986995697,
-0.05543957278132439,
-0.0012620709603652358,
-0.030994614586234093,
-0.005110634490847588,
-0.03401642665266991,
-0.015231413766741753,
-0.03731813654303551,
0.009675192646682262,
0.03297002613544464,
0.008397798053920269,
0.01656309701502323,
0.026478547602891922,
-0.060784220695495605,
0.0013009549584239721,
0.0387175977230072,
-0.01834626868367195,
-0.021051539108157158,
-0.029615670442581177,
0.04673974961042404,
-0.0018661852227523923,
0.03747225180268288,
0.02489333599805832,
-0.017159802839159966,
-0.0344422422349453,
0.022444937378168106,
0.0032363433856517076,
-0.009544415399432182,
-0.018308034166693687,
0.015035037882626057,
-0.00013046838284935802,
0.028479427099227905,
-0.03470330312848091,
0.08586503565311432,
0.057768888771533966,
0.013612275943160057,
-0.022812997922301292,
0.019794490188360214,
-0.021856257691979408,
0.004841468762606382,
-0.05802103504538536,
0.03705942630767822,
0.008235428482294083,
-0.037596695125103,
0.014377587474882603,
-0.10649331659078598,
-0.020259728655219078,
-0.0073617552407085896,
-0.05618711933493614,
-0.00614597974345088,
-0.009054954163730145,
-0.015023448504507542,
-0.003167307935655117,
-0.011985656805336475,
0.07267768681049347,
0.025695394724607468,
-0.02307758294045925,
-0.006663811858743429,
0.02868458814918995,
-0.008420374244451523,
0.041274260729551315,
-0.06049063056707382,
-0.03429848700761795,
-0.004250767175108194,
-0.020012248307466507,
-0.011328711174428463,
0.02574535831809044,
-0.005930417217314243,
0.0019994108006358147,
-0.04723420739173889,
-0.0006049263756722212,
-0.006664992310106754,
-0.05342370271682739,
-0.038019079715013504,
0.0719425231218338,
-0.041572585701942444,
0.019637756049633026,
0.025311900302767754,
0.002840132685378194,
-0.018530555069446564,
-0.06691917032003403,
0.03457268700003624,
0.0530090406537056,
-0.00425896979868412,
0.016007382422685623,
0.002518033841624856,
0.038561660796403885,
0.014213637448847294,
-0.030018368735909462,
-0.005607211031019688,
-0.016283869743347168,
0.03708991780877113,
-0.03988421708345413,
-0.021845363080501556,
-0.046762678772211075,
-0.037215299904346466,
0.0007853148854337633,
0.06479938328266144,
0.040834277868270874,
0.006762644741684198,
0.0019902714993804693,
0.0021056761033833027,
-0.004370332229882479,
-0.04027393460273743,
-0.024000057950615883,
-0.05858416482806206,
0.017597313970327377,
-0.04514928162097931,
-0.03423736244440079,
-0.03649994730949402,
0.0035151084885001183,
0.024734685197472572,
0.016086827963590622,
-0.029561610892415047,
-0.02677314169704914,
-0.010424138978123665,
-0.03270387277007103,
0.009789608418941498,
-0.015710508450865746,
-0.04178996384143829,
0.03701817989349365,
-0.0797220766544342,
-0.005623235367238522,
0.006772554945200682,
0.06523112952709198,
0.049110930413007736,
0.05262713134288788,
0.0060319239273667336,
0.0037797903642058372,
0.019951017573475838,
0.004684880375862122,
0.016106057912111282,
0.0094031086191535,
0.034395549446344376,
0.001209935755468905,
0.00003941056638723239,
-0.019166184589266777,
-0.01731231063604355,
-0.036319468170404434,
0.016366468742489815,
-0.023077212274074554,
0.0020169727504253387,
0.07168084383010864,
0.04898548126220703,
0.042303666472435,
0.003268265165388584,
-0.05633840337395668,
0.01734456606209278,
0.014861078932881355,
-0.0004597792576532811,
-0.02644539438188076,
0.033032115548849106,
-0.06675540655851364,
0.04766907915472984,
-0.0215065386146307,
-0.02627323567867279,
-0.040156301110982895,
0.07871343940496445,
0.01177684124559164,
0.020871145650744438,
0.06503360718488693,
0.07168681174516678,
-0.026377132162451744,
-0.05370750650763512,
-0.0004720472206827253,
0.02767430990934372,
0.02314605377614498,
0.018691979348659515,
-0.03061254322528839,
-0.012734153307974339,
0.025920173153281212,
0.0020645102486014366,
-0.0026095034554600716,
-0.044012799859046936,
0.001082223141565919,
0.0192987322807312,
-0.041017111390829086,
-0.01575533114373684,
-0.02126844972372055,
0.011112230829894543,
-0.05880586430430412,
-0.001439798972569406,
-0.06743735820055008,
0.03380109369754791,
0.05337516590952873,
0.016074372455477715,
0.028763869777321815,
-0.0417022779583931,
0.020344316959381104,
0.04288741201162338,
-0.02509048953652382,
-0.02780120261013508,
0.016182636842131615,
-0.015190299600362778,
-0.003709604265168309,
0.015156276524066925,
0.009270030073821545,
0.013269643299281597,
0.0020580990239977837,
0.07549794763326645,
-0.06015334278345108,
0.05197127163410187,
0.022182336077094078,
0.006476698908954859,
-0.006762336939573288,
-0.04179174825549126,
0.010642160661518574,
-0.06171856448054314,
0.07693617790937424,
0.0685276985168457,
-0.00031824701000005007,
0.02060624025762081,
-0.01563580334186554,
0.11955160647630692,
0.031119080260396004,
-0.0372774638235569,
-0.011809805408120155,
0.04457145184278488,
-0.027867766097187996,
0.018366100266575813,
0.025379963219165802,
-0.10574495792388916,
0.02514270506799221,
0.02186410129070282,
-0.007490312680602074,
-0.04212513566017151,
-0.010000539012253284,
0.04475865140557289,
-0.005564325023442507,
0.04121779277920723,
-0.014595436863601208,
-0.03532715141773224,
-0.00014720481703989208,
-0.0003364482254255563,
-0.060778453946113586,
-0.03021899424493313,
0.03449182212352753,
-0.038589611649513245,
-0.00034886522917076945,
0.06998257339000702,
-0.05943448841571808,
0.016870707273483276,
0.027546031400561333,
-0.040611643344163895,
0.03658450022339821,
-0.03869721293449402,
0.004512218292802572,
-0.039418675005435944,
0.009626250714063644,
-0.0002562451409175992,
0.00857622642070055,
0.06751293689012527,
-0.008721180260181427,
-0.08322588354349136,
0.009170225821435452,
-0.008893647231161594,
0.008161251433193684,
-0.024573130533099174,
0.08423888683319092,
-0.009913007728755474,
-0.01963868737220764,
-0.017955338582396507,
0.06472539156675339,
-0.03312668949365616,
-0.04353856295347214,
0.011797454208135605,
-0.05755553022027016,
-0.019943488761782646,
0.015227168798446655,
-0.015986206009984016,
0.00046477679279632866,
-0.009886176325380802,
0.015334966592490673,
0.010483196005225182,
-0.008355656638741493,
0.06103594973683357,
0.03843044117093086,
0.02078826166689396,
-0.021844707429409027,
-0.01613408513367176,
0.02082470804452896,
0.01510979887098074,
0.06828081607818604,
0.0032777516171336174,
-0.07917602360248566,
-0.02522468753159046,
-0.031765494495630264,
-0.08236068487167358,
0.017963098362088203,
0.04377854987978935,
0.009542305022478104,
-0.003935448359698057,
0.02071741595864296,
0.07190876454114914,
0.01299829687923193,
0.025202052667737007,
0.023134872317314148,
-0.00398127268999815,
0.023843564093112946,
-0.006039397791028023,
-0.004053386393934488,
0.0027946506161242723,
-0.04423588886857033,
-0.019143102690577507,
-0.014522404409945011,
-0.0061340960673987865,
0.022589927539229393,
0.021787744015455246,
-0.012818614952266216,
0.016032177954912186,
-0.019356276839971542,
0.05430404096841812,
0.03979693353176117,
-0.01823994144797325,
-0.027010321617126465,
0.0923917293548584,
0.014383182860910892,
0.019117245450615883,
-0.07661660760641098,
-0.03170445188879967,
-0.0034909809473901987,
0.06161697953939438,
-0.049057815223932266,
-0.009710568003356457,
0.016755161806941032,
0.04846487194299698,
-0.0276927687227726,
-0.036348093301057816,
-0.04668540135025978,
0.019197901710867882,
0.037854548543691635,
-0.06311293691396713,
-0.018804408609867096,
0.020849592983722687,
0.0026704242918640375,
-0.03697237744927406,
-0.0009375950321555138,
-0.05607413500547409,
-0.006537226028740406,
-0.01665845327079296,
-0.018183346837759018,
-0.033031266182661057,
0.008073488250374794,
0.04933329299092293,
-0.0006291537429206073,
-0.05784890800714493,
-0.015020608901977539,
0.0017565523739904165,
-0.004321312066167593,
-0.00965783279389143,
0.025699090212583542,
0.024554358795285225,
-0.07306495308876038,
-0.03595384955406189,
-0.023528024554252625,
0.06933020800352097,
-0.013748765923082829,
-0.026179896667599678,
0.012179948389530182,
0.034927111119031906,
-0.02651131898164749,
0.03443251922726631,
0.0483664907515049,
0.04117974266409874,
0.050061412155628204,
-0.023253707215189934,
-0.012920055538415909,
0.00408955616876483,
0.04637804254889488,
0.012930824421346188,
-0.06564486771821976,
-0.014064432121813297,
0.007399255875498056,
-0.007008225191384554,
-0.010307015851140022,
-0.00777836749330163,
0.004871999379247427,
0.023544086143374443,
0.005721554160118103,
-0.0305216945707798,
0.014592486433684826,
-0.041112374514341354,
-0.02917477674782276,
0.0018466809997335076,
0.059681251645088196,
-0.020477846264839172,
-0.043720781803131104,
-0.0025248646270483732,
0.02091181091964245,
0.06352987140417099,
-0.019054003059864044,
-0.01644759438931942,
-0.046843841671943665,
-0.06421268731355667,
-0.03429989889264107,
-0.0013643933925777674,
0.008660067804157734,
0.0015493989922106266,
0.06387845426797867,
-0.028094276785850525,
0.04701569303870201,
-0.01748736947774887,
-0.0759870782494545,
-0.005911803338676691,
0.022517168894410133,
-0.053395625203847885,
-0.06257403641939163,
0.05202415958046913,
0.053961243480443954,
-0.026593152433633804,
-0.03192802891135216,
0.015381982550024986,
-0.04336396977305412,
0.002227026503533125,
0.022885538637638092,
-0.023686213418841362,
-0.013445853255689144,
-0.01395901758223772,
0.0018729210132732987,
-0.04072012007236481,
-0.0064112721011042595,
-0.018023882061243057,
-0.03086833842098713,
0.007311539258807898,
0.040893785655498505,
0.004013238474726677,
0.0223478265106678,
0.028591956943273544,
0.006786329671740532,
0.06112497299909592,
-0.04849390685558319,
-0.05168827250599861,
-0.010996183380484581,
0.04362430423498154,
0.017689689993858337,
-0.07722826302051544,
0.05357758700847626,
0.02589554339647293,
-0.07209151238203049,
0.008869225159287453,
0.06752994656562805,
-0.0477571003139019,
-0.01487258356064558,
-0.014484983868896961,
0.01720578595995903,
-0.033432118594646454,
-0.044388871639966965,
-0.012086771428585052,
-0.023943621665239334,
-0.015298890881240368,
0.023968612775206566,
-0.05315176397562027,
-0.0041564879938960075,
0.026905503123998642,
-0.08653125166893005,
0.04999830573797226,
-0.043329767882823944,
0.00599466310814023,
0.030071474611759186,
0.015013720840215683,
-0.006655002478510141,
-0.00756326038390398,
0.028936391696333885,
-0.022319592535495758,
0.015022458508610725,
-0.031341928988695145,
-0.01517731137573719,
0.03412187099456787,
0.0017922719707712531,
-0.050077784806489944,
0.004609694238752127,
-0.044823020696640015,
0.02253510057926178,
0.01777646131813526,
-0.045047007501125336,
-0.021610738709568977,
0.00782767217606306,
-0.0410001277923584,
0.02967134676873684,
-0.0713215321302414,
0.0186845101416111,
0.047316163778305054,
-0.011132634244859219,
0.062293194234371185,
0.0354730486869812,
-0.02520439587533474,
-0.030535535886883736,
-0.00007710303907515481,
-0.042006056755781174,
-0.027986805886030197,
0.02863726019859314,
-0.007208629976958036,
0.0010910766432061791,
0.02368469536304474,
-0.010345847345888615,
0.03224176540970802,
0.009865186177194118,
0.055286943912506104,
-0.05869944021105766,
-0.014669010415673256,
-0.005290613509714603,
-0.02768174558877945,
-0.00034702804987318814,
-0.05051688849925995,
0.02198018878698349,
0.009012707509100437,
-0.060371607542037964,
-0.06495349109172821,
-0.0204685777425766,
0.018593452870845795,
-0.0542900413274765,
0.0028293493669480085,
0.002898227656260133,
-0.0194113589823246,
-0.025032633915543556,
0.05189719796180725,
-0.005490683019161224,
-0.019117342308163643,
-0.010329247452318668,
-0.0363796167075634,
0.04436488449573517,
-0.018294643610715866,
0.02823208086192608,
-0.05689064785838127,
-0.01581244170665741,
0.008276265114545822,
-0.0514582060277462,
0.017667297273874283,
-0.06754432618618011,
0.004514387343078852,
-0.024239003658294678,
-0.03937076777219772,
-0.07567689567804337,
-0.021026011556386948,
0.024745333939790726,
0.06402725726366043,
-0.02717428468167782,
0.06332855671644211,
0.06992585211992264,
0.016259435564279556,
-0.014341460540890694,
-0.04378647357225418,
-0.091269850730896,
0.03901039436459541,
-0.015145154669880867,
0.048747844994068146,
-0.03266278654336929,
0.03167383000254631,
-0.020327527076005936,
-0.026730572804808617,
0.035166021436452866,
0.023764200508594513,
-0.033708807080984116,
-0.00802330207079649,
0.05645553767681122
] |
<p>If light is passed through two polarizing filters before arriving at a target, and both of the filters are oriented at 90° to each other, then no light will be received at the target. If a third filter is added between the first two, oriented at a 45° angle (as shown below), light will reach the target.</p>
<p>Why is this the case? As I understand it, a polarized filter does nothing except filter out light--it does not alter the light passing through in any way. If two filters exist that will eliminate all of the light, why does the presence of a third, which should serve only to filter out additional light, actually act to allow light through?</p>
<p><img src="http://i.stack.imgur.com/OogSm.png" alt="Image of three polarizers, target is at the right"></p> | g6583 | [
-0.03202067315578461,
-0.0010736524127423763,
0.017778214067220688,
0.017590653151273727,
0.08807948976755142,
-0.0017391013680025935,
-0.009568680077791214,
0.03222019970417023,
-0.04093464836478233,
-0.015689998865127563,
-0.008096510544419289,
-0.007033980451524258,
-0.013344691134989262,
-0.017484959214925766,
-0.019092261791229248,
0.03245333209633827,
0.09441471844911575,
0.01879155822098255,
0.01685846596956253,
0.017545942217111588,
-0.032408397644758224,
0.008160709403455257,
-0.016858192160725594,
-0.089814692735672,
0.0015027563786134124,
0.011003736406564713,
0.0015781255206093192,
-0.05717150866985321,
-0.005594028625637293,
0.022664563730359077,
0.024598486721515656,
0.022130297496914864,
-0.027544785290956497,
-0.046324945986270905,
-0.02058248408138752,
-0.025088531896471977,
0.06308111548423767,
0.032543182373046875,
-0.022790098562836647,
-0.011876503936946392,
-0.00456807017326355,
0.07594312727451324,
0.02878395840525627,
-0.07524330914020538,
0.013554173521697521,
-0.039532776921987534,
-0.019697468727827072,
0.029966268688440323,
0.024488013237714767,
0.01400682982057333,
0.00046317846863530576,
-0.005078107118606567,
-0.002606568858027458,
0.01920880563557148,
0.04837658256292343,
0.03710043430328369,
-0.003773421049118042,
-0.009051920846104622,
0.02912413328886032,
0.07353520393371582,
0.001624877448193729,
0.010181061923503876,
0.00036726819234900177,
0.023042939603328705,
-0.026727192103862762,
-0.028735000640153885,
-0.012425433844327927,
-0.04034608229994774,
0.05593123286962509,
0.08203516155481339,
-0.018396509811282158,
0.013710048981010914,
-0.0027985135093331337,
-0.08341055363416672,
0.01110432855784893,
0.0040235500782728195,
-0.0034545946400612593,
0.018720466643571854,
0.00425856513902545,
0.026388395577669144,
0.043051641434431076,
-0.010700222104787827,
-0.020954987034201622,
0.010161780752241611,
-0.0008090741466730833,
0.04051695391535759,
0.027305487543344498,
-0.037231821566820145,
-0.035859014838933945,
-0.06813759356737137,
0.003655478125438094,
0.04553093761205673,
0.06831619888544083,
0.006382593419402838,
-0.06833876669406891,
0.016098398715257645,
-0.012275326997041702,
0.032835837453603745,
-0.0014367433032020926,
0.08812680095434189,
0.009035248309373856,
0.04069966822862625,
0.019374655559659004,
0.04691991209983826,
0.01685268059372902,
-0.027328915894031525,
0.07295721769332886,
0.06755488365888596,
-0.025117116048932076,
-0.011438644491136074,
-0.12888412177562714,
-0.05964692682027817,
-0.034134671092033386,
-0.06674425303936005,
-0.01609882153570652,
-0.021392444148659706,
0.0759972408413887,
-0.01313976850360632,
0.047374527901411057,
0.026069222018122673,
0.04552105814218521,
0.03264695778489113,
-0.025838594883680344,
0.05491048842668533,
-0.014884404838085175,
0.042485032230615616,
0.006510129664093256,
0.03500930592417717,
0.020394861698150635,
-0.04575642943382263,
0.024883706122636795,
0.0033824427518993616,
0.02018149569630623,
0.006110809743404388,
-0.0005908161401748657,
-0.016486214473843575,
0.029485531151294708,
-0.002951580099761486,
0.018675215542316437,
0.008977443911135197,
-0.0188438780605793,
-0.03979356586933136,
0.020473452284932137,
-0.017285026609897614,
-0.006548983510583639,
-0.022500021383166313,
-0.033699098974466324,
0.01233657356351614,
0.04156794026494026,
-0.012279174290597439,
0.010668763890862465,
0.04661067575216293,
0.025499707087874413,
0.03747869282960892,
-0.01889972947537899,
-0.03329962491989136,
0.010374765843153,
-0.06266535073518753,
-0.024741115048527718,
0.026297608390450478,
0.036245621740818024,
0.007058354094624519,
-0.017886629328131676,
-0.0025807868223637342,
-0.04005569964647293,
0.028877006843686104,
0.02886176109313965,
-0.10511956363916397,
-0.07813961803913116,
-0.03362162783741951,
-0.055761225521564484,
0.022827187553048134,
0.007836145348846912,
0.02886858955025673,
0.026322398334741592,
0.09786497056484222,
0.07427051663398743,
0.03929579257965088,
0.03066994808614254,
0.02407342940568924,
-0.10460884869098663,
0.0025635017082095146,
-0.029595838859677315,
0.0047342199832201,
-0.04730673134326935,
-0.04410131648182869,
0.02119598537683487,
0.040819328278303146,
-0.10131464153528214,
0.03074253909289837,
0.03225603699684143,
-0.008898735046386719,
-0.004071117378771305,
-0.025166047737002373,
-0.06060073524713516,
-0.01671488955616951,
-0.03516687452793121,
0.009441091679036617,
0.0036812967155128717,
0.017341306433081627,
-0.02079438418149948,
0.004135375376790762,
0.003026006743311882,
-0.005150658078491688,
0.010452084243297577,
0.012404045090079308,
-0.0043199323117733,
-0.005108298268169165,
0.005326586775481701,
-0.017483768984675407,
-0.054819975048303604,
-0.020160051062703133,
0.01573871076107025,
-0.013743235729634762,
-0.018643036484718323,
0.005715053994208574,
0.01807309500873089,
0.07111147791147232,
-0.006504247896373272,
0.01669352315366268,
-0.009616188704967499,
-0.009622708894312382,
-0.037657514214515686,
-0.02358412742614746,
-0.04729562625288963,
0.0025972339790314436,
-0.10868419706821442,
-0.013526177033782005,
-0.007969801314175129,
0.05258709564805031,
-0.027423016726970673,
-0.03808823227882385,
0.06281120330095291,
0.01031265314668417,
0.01796269789338112,
0.03542167320847511,
-0.028230316936969757,
-0.01135723665356636,
0.036077167838811874,
0.04210929200053215,
-0.022746330127120018,
0.02678575925529003,
0.008314736187458038,
0.011076080612838268,
0.10952479392290115,
-0.02737601101398468,
0.002247368451207876,
-0.012316202744841576,
-0.026647189632058144,
0.04274040460586548,
0.009504285641014576,
0.04151419177651405,
-0.01067599467933178,
-0.006140417885035276,
-0.022499702870845795,
-0.025881126523017883,
0.018629761412739754,
-0.01202907133847475,
-0.027015693485736847,
-0.007185790687799454,
-0.008036229759454727,
-0.03996742144227028,
0.04521820694208145,
-0.025173768401145935,
-0.03585169464349747,
-0.00805110763758421,
0.024213101714849472,
0.0047830319963395596,
0.028776124119758606,
-0.021893998607993126,
-0.06676089018583298,
0.058623261749744415,
0.09097515791654587,
0.016125572845339775,
-0.003153839847072959,
0.0192821454256773,
-0.058085035532712936,
0.0046019055880606174,
-0.0256936214864254,
0.04766148701310158,
-0.029027795419096947,
0.07794138044118881,
-0.023677712306380272,
-0.03477051481604576,
0.03716906160116196,
-0.023550011217594147,
0.06293033808469772,
0.02263837866485119,
-0.008676688186824322,
0.0031866307836025953,
-0.0603913851082325,
0.027212055400013924,
0.014780297875404358,
-0.04335935413837433,
0.029019670560956,
-0.02106723003089428,
-0.0030911772046238184,
-0.07574585825204849,
-0.033379435539245605,
0.04600749537348747,
-0.03874976933002472,
0.0669005736708641,
0.02738007716834545,
-0.0766172781586647,
0.04731295257806778,
-0.031574368476867676,
-0.02850533276796341,
-0.03130071237683296,
-0.02588716335594654,
0.052694570273160934,
0.007579620461910963,
0.02677055448293686,
-0.05595669522881508,
0.036631010472774506,
0.06489913910627365,
-0.022168194875121117,
-0.0524454191327095,
-0.011802375316619873,
-0.01709534227848053,
0.06676021963357925,
0.02976178005337715,
0.06895116716623306,
-0.0405004546046257,
-0.0037878609728068113,
0.04643300175666809,
-0.029273543506860733,
0.0035450970754027367,
0.03922618553042412,
0.0008633218239992857,
0.000030079101634328254,
0.04893273860216141,
-0.01828519068658352,
-0.0052499230951070786,
-0.003998869098722935,
-0.01878809742629528,
0.021220125257968903,
-0.017662011086940765,
0.044498004019260406,
0.026390932500362396,
-0.04079693928360939,
0.03266468271613121,
0.02353418804705143,
-0.08058568090200424,
-0.027251802384853363,
-0.015730304643511772,
-0.014648281037807465,
0.012137805111706257,
-0.016208622604608536,
-0.012244662269949913,
-0.012940682470798492,
0.012790591455996037,
-0.0008427775464951992,
0.007796700112521648,
0.012787094339728355,
-0.07455999404191971,
-0.0030262910295277834,
-0.03611773997545242,
0.05519925057888031,
0.02567135915160179,
0.013708369806408882,
-0.00909832026809454,
0.013014396652579308,
-0.027073821052908897,
-0.0301798265427351,
-0.0024440379347652197,
0.03081323206424713,
-0.0074468450620770454,
-0.044403284788131714,
-0.017248978838324547,
0.0007631256012246013,
0.03625231236219406,
-0.0431511364877224,
-0.021458959206938744,
-0.024979954585433006,
0.03097505494952202,
-0.0449836365878582,
0.030619055032730103,
0.06414392590522766,
-0.0732269138097763,
0.027577005326747894,
0.033137720078229904,
-0.0009195134625770152,
0.02506467141211033,
0.005113024264574051,
0.042026761919260025,
0.018306035548448563,
-0.026074828580021858,
-0.025724364444613457,
-0.03879544138908386,
-0.01725197024643421,
-0.06479725241661072,
0.04662354663014412,
-0.012254052795469761,
0.018231788650155067,
0.027237365022301674,
-0.020540930330753326,
0.00017144769662991166,
-0.09285492449998856,
0.02171834371984005,
0.013262302614748478,
0.038917675614356995,
0.005625923629850149,
-0.0375852957367897,
-0.014133147895336151,
-0.03435933217406273,
-0.01624627225100994,
0.01347880344837904,
0.03573628515005112,
-0.003950466401875019,
0.02763945981860161,
-0.025344787165522575,
0.029828164726495743,
-0.021638276055455208,
-0.03024166449904442,
0.04880741611123085,
-0.014521608129143715,
-0.021484142169356346,
0.0270891971886158,
0.00508761964738369,
-0.015577390789985657,
0.03501678258180618,
0.009847724810242653,
0.00343122985213995,
0.009966486133635044,
-0.01617642305791378,
0.04808942601084709,
0.018802395090460777,
-0.06437516957521439,
0.021036293357610703,
-0.01522828172892332,
0.0012274787295609713,
-0.0038658634293824434,
0.001645055366680026,
0.04956641420722008,
0.02104853466153145,
-0.0133796576410532,
-0.07437959313392639,
0.04617821052670479,
0.008428406901657581,
0.058131635189056396,
0.009202282875776291,
0.007584648206830025,
-0.05016111955046654,
-0.04205423966050148,
0.013683075085282326,
-0.03588670864701271,
0.020547427237033844,
0.02276655286550522,
0.021582579240202904,
-0.013581421226263046,
-0.00859206635504961,
-0.027389897033572197,
-0.0625913217663765,
0.0035783243365585804,
-0.08374475687742233,
0.025107301771640778,
0.006987367756664753,
0.038244180381298065,
0.011394551955163479,
0.04147128760814667,
-0.050773441791534424,
-0.008192368783056736,
-0.0541035458445549,
-0.050695061683654785,
0.036325789988040924,
0.0037809412460774183,
0.033203113824129105,
-0.03050416335463524,
-0.05783737078309059,
0.052271559834480286,
-0.015692727640271187,
0.041800107806921005,
-0.035410717129707336,
0.10179702937602997,
-0.021122848615050316,
-0.003326397156342864,
-0.013058739714324474,
-0.00978909619152546,
-0.008739463984966278,
-0.0329003781080246,
0.0036254138685762882,
-0.08234874904155731,
0.024468209594488144,
-0.021787257865071297,
-0.02081567607820034,
-0.0009451598743908107,
0.0022027373779565096,
0.054538749158382416,
-0.02878035046160221,
-0.0260469950735569,
0.03897792100906372,
0.0069771017879247665,
-0.05408599600195885,
-0.01565662771463394,
0.0009214418823830783,
0.07393443584442139,
0.0521780289709568,
0.025340542197227478,
0.03900112584233284,
-0.03086494840681553,
-0.032116908580064774,
0.0009706640266813338,
-0.016676755622029305,
-0.036511585116386414,
-0.011494298465549946,
0.006581638008356094,
0.032312795519828796,
-0.07289359718561172,
0.01860528066754341,
0.038837533444166183,
0.007095443084836006,
-0.07693009078502655,
0.00922754779458046,
0.041812341660261154,
0.004967654123902321,
-0.007485082373023033,
0.0009540639584884048,
-0.00502515584230423,
-0.0030909166671335697,
0.020335352048277855,
-0.0219432283192873,
-0.01727948896586895,
-0.06556545197963715,
-0.019142035394906998,
0.030855907127261162,
0.010814446024596691,
-0.05810016766190529,
-0.003726388094946742,
0.029958514496684074,
0.019158661365509033,
-0.024665629491209984,
0.019915824756026268,
0.045243557542562485,
0.025702983140945435,
0.03872260823845863,
-0.06133303418755531,
0.02116984874010086,
-0.003280806588009,
0.0407274030148983,
0.016234060749411583,
-0.03658850118517876,
-0.04101845249533653,
0.023073920980095863,
0.11750004440546036,
-0.0010273945517838001,
-0.0012793850619345903,
0.010468901135027409,
-0.015105259604752064,
0.0020794998854398727,
-0.01726572960615158,
-0.006796419154852629,
0.016075175255537033,
-0.05081366002559662,
-0.007926898077130318,
0.028778310865163803,
0.02330077812075615,
-0.02435361221432686,
-0.013948989100754261,
0.025262154638767242,
-0.0964018926024437,
0.013592571020126343,
0.00525549054145813,
-0.01865537278354168,
-0.007895291782915592,
-0.006917324382811785,
-0.007723918650299311,
-0.04404442012310028,
0.048771705478429794,
-0.00328428135253489,
0.019297588616609573,
-0.007441623602062464,
-0.07672692835330963,
-0.002235199324786663,
0.07994353771209717,
0.04799140617251396,
0.040322646498680115,
-0.03775038942694664,
-0.02859368547797203,
-0.01761782169342041,
0.029521482065320015,
0.043326485902071,
0.003154108300805092,
0.015280956402420998,
-0.03090638481080532,
0.033761538565158844,
0.027519335970282555,
-0.0694003701210022,
-0.0064330995082855225,
0.06754039973020554,
-0.056322015821933746,
-0.03485669568181038,
-0.030305545777082443,
-0.03375235199928284,
-0.05035412684082985,
-0.01443751435726881,
-0.05235118791460991,
0.030890677124261856,
0.083740234375,
-0.019475718960165977,
-0.020018165931105614,
0.028848355636000633,
-0.02246670238673687,
0.08820945769548416,
-0.041429873555898666,
0.015572085976600647,
0.0320608913898468,
-0.0337502546608448,
-0.07164692133665085,
0.029167452827095985,
-0.009849650785326958,
0.00759643642231822,
0.031635843217372894,
-0.04319683089852333,
0.04132001847028732,
-0.019977521151304245,
-0.023341916501522064,
-0.0914246067404747,
-0.038865357637405396,
0.009362264536321163,
0.014681205153465271,
-0.013286317698657513,
-0.020718542858958244,
-0.019054453819990158,
-0.05346974730491638,
-0.026980258524417877,
0.013034126721322536,
0.016215255483984947,
-0.014134182594716549,
0.005649021826684475,
0.120200514793396,
-0.005246151238679886,
-0.022284507751464844,
0.030526455491781235,
-0.008127888664603233,
0.03368135541677475,
-0.03769414871931076,
-0.023683026432991028,
0.00007162900146795437,
0.050118789076805115,
0.07752304524183273,
0.009750042110681534,
0.024503760039806366,
0.012175064533948898,
0.0404454804956913,
0.006774649024009705,
0.04114411771297455,
0.008522739633917809,
-0.055423300713300705,
-0.04941935837268829,
-0.0028586327098309994,
-0.044968657195568085,
-0.02889472432434559,
0.024166682735085487,
0.03743675351142883,
-0.022475924342870712,
0.010448027402162552,
0.0086162518709898,
-0.0046869744546711445,
0.0022485924419015646,
-0.0024679882917553186,
-0.029131503775715828,
-0.049967266619205475,
-0.05507904291152954,
0.004818239714950323,
-0.011035428382456303,
0.023584552109241486,
0.037767443805933,
-0.03689638152718544,
-0.0023017856292426586,
-0.013763200491666794,
-0.05282408744096756,
-0.015313232317566872,
0.0442197322845459,
0.02030845358967781,
-0.019877981394529343,
-0.006427417974919081,
0.007070643827319145,
-0.004146489314734936,
0.027449050918221474,
-0.008389889262616634,
0.013608194887638092,
0.03561357036232948,
0.00948470737785101,
-0.07560398429632187,
-0.03839613124728203,
-0.0015680656069889665,
0.027424613013863564,
-0.023917822167277336,
-0.02792816422879696,
-0.009688870050013065,
0.008593020029366016,
0.024902474135160446,
0.009743094444274902,
-0.022736040875315666,
-0.018080895766615868,
0.04098622128367424,
0.02758045494556427,
0.017312079668045044,
0.004470366053283215,
0.015125890262424946,
-0.0026106408331543207,
-0.025358740240335464,
-0.0006476356065832078,
-0.06623109430074692,
0.09063615649938583,
0.016564397141337395,
0.028358280658721924,
-0.005786707624793053,
0.031758200377225876,
0.009872794151306152,
-0.02839970961213112,
0.02025659941136837,
0.00449306471273303,
0.02101605013012886,
-0.04830249771475792,
-0.014259838499128819,
-0.02136390469968319,
0.012398716993629932,
-0.03204081580042839,
-0.059533629566431046,
0.014154651202261448,
0.052150968462228775,
-0.029107704758644104,
-0.014405970461666584,
-0.003318456467241049,
0.03752496838569641,
0.039066132158041,
0.0013008808018639684,
0.04084799438714981,
0.020401325076818466,
0.03004729188978672,
0.011265840381383896,
-0.05979152023792267,
0.034459326416254044,
-0.02642683871090412,
0.0344865657389164,
-0.001436946913599968,
-0.02744612656533718,
0.027870582416653633,
-0.002313298173248768,
0.04269513115286827,
0.01666162721812725,
0.003759864019230008,
-0.04846983402967453,
0.0437048077583313,
0.007052361499518156,
0.010207908228039742,
-0.0055846781469881535,
0.025910470634698868,
-0.020820695906877518,
0.0016390822129324079,
0.06198393926024437,
-0.009729060344398022,
0.027907559648156166,
0.03297897055745125,
-0.06350208073854446,
-0.009582752361893654,
-0.04392353445291519,
0.018580876290798187,
-0.033521875739097595,
-0.0015034552197903395,
-0.052412454038858414,
-0.04209546744823456,
-0.05359162017703056,
-0.006185754202306271,
0.006869847886264324,
-0.0560750812292099,
0.015081445686519146
] |
<p>New question: In string theory and QFT, do particles travel back in time? Not related to antimatter: Do they travel back and forth in time in reality or are these just interpretations of mathematical formulas used to make sense of calculations?</p>
<p>This is a different question (<a href="http://physics.stackexchange.com/q/58101">from this one</a>) as it concerns strings and not antimatter...</p> | g6584 | [
0.03232550248503685,
0.018125416710972786,
0.016499638557434082,
-0.028390252962708473,
0.06159447506070137,
-0.0010901890927925706,
0.01088036224246025,
-0.016569875180721283,
-0.061708223074674606,
0.015111149288713932,
-0.031813450157642365,
0.07800659537315369,
0.000313769793137908,
-0.031871993094682693,
-0.09399478882551193,
-0.010130876675248146,
0.04834650456905365,
0.07438062131404877,
0.00968827772885561,
0.002380777383223176,
0.042696792632341385,
0.043025095015764236,
-0.01685248129069805,
-0.03532063215970993,
-0.0017409124411642551,
0.0025259831454604864,
-0.022133756428956985,
-0.020217543467879295,
-0.04395756497979164,
-0.03788205236196518,
0.08084375411272049,
-0.011205049231648445,
0.02488800883293152,
-0.08593685925006866,
-0.004879650194197893,
-0.0776553526520729,
0.02154652029275894,
-0.020153488963842392,
0.04209912195801735,
0.0214996375143528,
0.022957446053624153,
-0.015512321144342422,
0.01041177473962307,
0.0331227071583271,
0.03925139829516411,
0.06381373107433319,
-0.03336697444319725,
-0.004326525144279003,
-0.04847900569438934,
-0.03251517936587334,
-0.04637710005044937,
0.016904130578041077,
0.025743573904037476,
0.04937836900353432,
-0.050344645977020264,
-0.004889822565019131,
0.055293720215559006,
-0.04443893954157829,
0.10833708941936493,
0.04683145508170128,
-0.05183190852403641,
0.025160223245620728,
-0.007201285567134619,
-0.0016532668378204107,
0.04763864725828171,
-0.02065367065370083,
-0.042524971067905426,
-0.009764374233782291,
-0.018490782007575035,
0.021939804777503014,
0.06531179696321487,
-0.023859767243266106,
-0.032770898193120956,
-0.0016323502641171217,
0.002695264294743538,
0.0712980106472969,
0.018343856558203697,
-0.02931852638721466,
-0.006846440490335226,
0.011277146637439728,
-0.045563437044620514,
-0.032067690044641495,
-0.0081308763474226,
0.035106390714645386,
0.05961991101503372,
-0.07729015499353409,
-0.0007465613889507949,
0.04637933149933815,
0.01134431641548872,
0.008915397338569164,
-0.04589015245437622,
-0.03228899836540222,
0.042000364512205124,
0.007079167291522026,
0.002646791748702526,
-0.03218691051006317,
-0.016765553504228592,
0.013029307126998901,
-0.03917495906352997,
0.0037329557817429304,
-0.035092953592538834,
0.0454256646335125,
0.012326422147452831,
0.03387042507529259,
0.0269948560744524,
-0.04425881430506706,
0.08073204755783081,
-0.02688690461218357,
0.016698792576789856,
0.03421584144234657,
-0.053378090262413025,
0.005015412345528603,
-0.01619771681725979,
-0.0028479639440774918,
-0.06223239377140999,
0.02146480232477188,
0.004838034976273775,
-0.033613622188568115,
-0.004943307489156723,
0.04150589555501938,
-0.001955469837412238,
-0.00443502701818943,
0.053135477006435394,
-0.00359880062751472,
-0.037092722952365875,
0.0029029008001089096,
-0.04758213460445404,
-0.021034888923168182,
-0.03574804961681366,
0.008798415772616863,
-0.041618239134550095,
0.00800230260938406,
0.024396883323788643,
0.06095755472779274,
-0.022953666746616364,
0.0324675589799881,
0.009161673486232758,
-0.007155550643801689,
-0.009541441686451435,
0.0027067784685641527,
0.05526379495859146,
-0.06461121886968613,
-0.015607181005179882,
-0.04355017468333244,
-0.05300241336226463,
0.02046443149447441,
-0.020776713266968727,
-0.040520742535591125,
-0.01830214448273182,
0.06185508146882057,
0.035687413066625595,
0.07780791074037552,
-0.016487352550029755,
0.018030576407909393,
0.07207409292459488,
0.002767964033409953,
0.00369880348443985,
0.009572216309607029,
-0.04037339240312576,
-0.011126545257866383,
0.06012320891022682,
0.015554476529359818,
0.004653473384678364,
-0.011306868866086006,
-0.01471518911421299,
0.006225180812180042,
-0.010009914636611938,
-0.054112497717142105,
0.02668723836541176,
-0.08399256318807602,
-0.03155079483985901,
0.011215227656066418,
0.020798737183213234,
0.018999837338924408,
-0.003747506532818079,
0.004274776671081781,
-0.015168128535151482,
-0.010744315572082996,
-0.05860263481736183,
-0.0626324936747551,
-0.017556585371494293,
0.027912890538573265,
0.008414579555392265,
-0.014562513679265976,
-0.03592728450894356,
0.0067555406130850315,
-0.041876453906297684,
0.007333222310990095,
-0.05538373813033104,
-0.004262452945113182,
-0.0169571153819561,
0.008285598829388618,
-0.023642031475901604,
-0.0028707184828817844,
0.02476818673312664,
-0.058200158178806305,
-0.028533831238746643,
0.01564967818558216,
-0.009083042852580547,
0.029974669218063354,
0.04774293303489685,
0.039037615060806274,
0.05656060948967934,
-0.062680684030056,
0.0944567397236824,
0.004882461857050657,
-0.02069181017577648,
-0.04315652698278427,
0.03765251487493515,
-0.04218214377760887,
0.0352090559899807,
0.06618255376815796,
0.021345172077417374,
0.0414634570479393,
-0.059311773627996445,
-0.02075325697660446,
-0.017624307423830032,
-0.012667698785662651,
0.009150892496109009,
0.031716130673885345,
-0.011448201723396778,
-0.014877397567033768,
0.07485964894294739,
-0.03462522104382515,
-0.03500733897089958,
0.01262167189270258,
-0.01945316232740879,
-0.03794889524579048,
-0.05004607513546944,
0.024659786373376846,
-0.0835610181093216,
0.009022909216582775,
-0.07484923303127289,
-0.030971288681030273,
0.06317997723817825,
-0.018436497077345848,
-0.015179549343883991,
-0.0320354662835598,
0.10344698280096054,
0.023172251880168915,
0.013377571478486061,
0.02827501855790615,
-0.043590594083070755,
0.015894228592514992,
0.05470583215355873,
-0.05143172666430473,
0.012631281279027462,
0.014519707299768925,
-0.025549722835421562,
0.03453551232814789,
0.057091400027275085,
-0.024609943851828575,
-0.06642945855855942,
0.04659538343548775,
0.0030259164050221443,
-0.02036353014409542,
0.024141700938344002,
0.0009422620059922338,
-0.06681139767169952,
-0.02831445448100567,
0.013896043412387371,
0.007632025517523289,
-0.008202475495636463,
-0.017731573432683945,
-0.009173099882900715,
-0.023905325680971146,
-0.019211841747164726,
0.030561214312911034,
-0.025437450036406517,
-0.009579450823366642,
-0.05264133960008621,
0.016184240579605103,
0.08582786470651627,
-0.00711653009057045,
0.018705707043409348,
-0.002737760543823242,
0.018313193693757057,
0.011521325446665287,
0.01987796276807785,
-0.013545658439397812,
-0.0218159519135952,
-0.034213948994874954,
-0.021031208336353302,
-0.022938279435038567,
-0.024039631709456444,
-0.07457900047302246,
0.02577180415391922,
-0.027078360319137573,
-0.012934621423482895,
0.011399712413549423,
0.004763553384691477,
-0.0019393105758354068,
0.04057300463318825,
0.016317907720804214,
-0.033758580684661865,
0.09187429398298264,
0.06582800298929214,
-0.04984511435031891,
-0.00529449200257659,
0.06260417401790619,
-0.043664950877428055,
-0.0026863468810915947,
0.020923813804984093,
0.01801038347184658,
0.05488079786300659,
0.03051762655377388,
-0.0644611194729805,
-0.040865518152713776,
-0.027240412309765816,
-0.026744194328784943,
-0.012683108448982239,
0.07432693243026733,
0.005911257583647966,
0.022342924028635025,
0.018995223566889763,
0.02246589958667755,
-0.026855096220970154,
0.03577449172735214,
0.03452933207154274,
-0.007600064855068922,
-0.04058035835623741,
-0.025815390050411224,
0.026233430951833725,
-0.023904332891106606,
0.006052239332348108,
-0.028100168332457542,
-0.03927147760987282,
0.007085402030497789,
-0.07768891006708145,
-0.06321434676647186,
-0.022083571180701256,
-0.051935747265815735,
0.012300034984946251,
-0.019596407189965248,
-0.03557204827666283,
-0.016577066853642464,
0.025897441431879997,
0.02906757965683937,
-0.032641030848026276,
0.03323689475655556,
-0.034946903586387634,
-0.0302407406270504,
0.05352426692843437,
0.0340367816388607,
0.031024154275655746,
0.0659521222114563,
0.023747704923152924,
0.04549597576260567,
0.02592972107231617,
0.025932548567652702,
0.013462251052260399,
0.049977850168943405,
0.037733294069767,
0.052184395492076874,
-0.009108527563512325,
0.02432766556739807,
0.007348527666181326,
0.05807816982269287,
0.052203137427568436,
-0.02295246347784996,
-0.030349571257829666,
0.0016815396957099438,
-0.013173308223485947,
0.02350199595093727,
0.014917825348675251,
-0.03778557851910591,
0.03718053922057152,
0.00697097834199667,
0.05007900297641754,
-0.017340868711471558,
0.04461243748664856,
0.031288694590330124,
-0.012750416062772274,
0.038908541202545166,
-0.01381445862352848,
0.000246381969191134,
0.03974620997905731,
0.0017636765260249376,
-0.019137367606163025,
0.008064817637205124,
0.04116182401776314,
0.044066257774829865,
0.030649492517113686,
-0.008001811802387238,
0.04441126435995102,
0.019350165501236916,
-0.050172194838523865,
-0.034855931997299194,
-0.04065237194299698,
-0.025243759155273438,
-0.00036127661587670445,
0.03433024138212204,
-0.010444367304444313,
-0.06081990897655487,
-0.019964663311839104,
-0.013052061200141907,
0.01497588586062193,
-0.031681716442108154,
0.011715472675859928,
-0.044489942491054535,
0.016059666872024536,
0.0437246598303318,
-0.054570939391851425,
-0.019144607707858086,
-0.02924489974975586,
0.003822166472673416,
0.03410536050796509,
-0.091905377805233,
-0.011365171521902084,
-0.017676690593361855,
-0.05147438123822212,
-0.02779368869960308,
-0.027002127841114998,
-0.04084360599517822,
0.020332850515842438,
0.0030583341140300035,
-0.0008235645364038646,
0.0072411224246025085,
-0.02385244145989418,
-0.02860374189913273,
0.03877278044819832,
-0.005111176986247301,
0.02030286192893982,
-0.005259215831756592,
-0.04006824642419815,
0.042959436774253845,
0.02875468321144581,
-0.011409019120037556,
-0.03172827512025833,
-0.027816995978355408,
0.017234530299901962,
0.028002025559544563,
-0.00023332001001108438,
0.01891382597386837,
-0.03664378449320793,
0.04718629643321037,
0.004131538327783346,
0.04764394834637642,
0.09190391004085541,
-0.04643063619732857,
0.059025608003139496,
0.018069138750433922,
0.03180953860282898,
-0.034143611788749695,
-0.060104597359895706,
0.027380140498280525,
-0.0669708102941513,
-0.02703959308564663,
-0.005355767905712128,
-0.021011337637901306,
-0.05996573343873024,
0.06709816306829453,
-0.032842013984918594,
0.005699990317225456,
-0.0383792370557785,
-0.015061002224683762,
0.008147945627570152,
-0.03865651413798332,
0.02438521757721901,
0.03795117512345314,
-0.07076562196016312,
0.009744148701429367,
0.04275577515363693,
0.03373191878199577,
-0.03563600778579712,
-0.014217069372534752,
-0.01362567488104105,
-0.010960518382489681,
-0.030055364593863487,
0.028996312990784645,
-0.03302304074168205,
0.024279115721583366,
0.004602787550538778,
-0.03875213861465454,
-0.012973520904779434,
-0.05740069970488548,
0.019686704501509666,
0.014161596074700356,
-0.021290022879838943,
-0.024405086413025856,
-0.011691352352499962,
0.018060453236103058,
0.03996714577078819,
-0.024671262130141258,
-0.02262779138982296,
0.07292650640010834,
-0.018876569345593452,
0.05071742460131645,
-0.003617999842390418,
-0.053965747356414795,
-0.017642883583903313,
-0.04960327968001366,
0.04801426827907562,
-0.025304557755589485,
-0.006653327960520983,
-0.017305493354797363,
0.006305979564785957,
0.03348150849342346,
-0.05142996087670326,
-0.02194107137620449,
0.007178933825343847,
0.014173083007335663,
0.0044848499819636345,
0.027142930775880814,
-0.003809899790212512,
0.060365431010723114,
0.01808318682014942,
-0.004993983078747988,
-0.05980550870299339,
-0.04320771247148514,
0.08596935123205185,
0.03019486926496029,
-0.07478242367506027,
0.005034642294049263,
0.04780273139476776,
0.025054361671209335,
-0.014134403318166733,
0.012118443846702576,
0.04875437542796135,
-0.02477641962468624,
-0.05998751521110535,
0.08321073651313782,
0.03464927524328232,
-0.029125597327947617,
0.013521343469619751,
0.0010365619091317058,
-0.047725629061460495,
-0.03172783926129341,
-0.005133185535669327,
0.03455251827836037,
-0.009698480367660522,
-0.010863934643566608,
0.0413636639714241,
-0.0021250310819596052,
-0.01386045478284359,
0.014127437956631184,
-0.008160443976521492,
-0.039918649941682816,
0.030916182324290276,
0.013309984467923641,
-0.06728676706552505,
0.03152167424559593,
-0.0063920048996806145,
0.058074090629816055,
-0.0496797040104866,
0.0042479862459003925,
0.007258185185492039,
-0.01625203527510166,
0.0901484340429306,
-0.07602567970752716,
-0.004014444537460804,
0.03893623873591423,
-0.045430149883031845,
-0.020391590893268585,
0.017504844814538956,
0.05104372650384903,
-0.004357509780675173,
-0.02099669724702835,
-0.003432691562920809,
0.012327861040830612,
-0.02206871472299099,
0.004284500144422054,
0.029087817296385765,
0.012518943287432194,
0.004784118849784136,
-0.049113284796476364,
0.01430068351328373,
-0.03997717425227165,
0.048755161464214325,
-0.0017709247767925262,
0.07426875084638596,
0.0021046698093414307,
-0.02026510052382946,
0.006611540447920561,
0.023657970130443573,
0.004997038748115301,
-0.03356567770242691,
-0.11226103454828262,
-0.05192827805876732,
-0.033454880118370056,
0.024435151368379593,
0.028780415654182434,
0.0183233805000782,
-0.007692779880017042,
-0.03144630417227745,
0.028742456808686256,
-0.04428728669881821,
0.010543645359575748,
0.04284549877047539,
-0.0071279797703027725,
-0.04604529216885567,
-0.021920382976531982,
-0.05899947136640549,
-0.007639020681381226,
-0.04040544107556343,
0.0233190655708313,
-0.0009542744373902678,
0.01670968346297741,
-0.04641501605510712,
0.003927720710635185,
0.00811306107789278,
0.017543036490678787,
0.05482454225420952,
-0.004193010739982128,
0.04438190162181854,
0.026474222540855408,
0.037377916276454926,
0.043125398457050323,
0.010253079235553741,
-0.02071889489889145,
0.04277632012963295,
-0.00953148864209652,
0.023282092064619064,
0.07861621677875519,
0.004755530506372452,
0.00007554960757261142,
-0.022008728235960007,
0.030465340241789818,
-0.03641090914607048,
0.008486158214509487,
0.038467828184366226,
-0.029205026105046272,
-0.027087567374110222,
-0.03863700479269028,
0.01727239042520523,
0.04201420396566391,
-0.00523833092302084,
0.07188203930854797,
0.03868177533149719,
-0.015880778431892395,
-0.0036842881236225367,
0.012039946392178535,
0.008056564256548882,
0.01711130701005459,
-0.0030772630125284195,
-0.03316401317715645,
-0.024245573207736015,
0.01392071321606636,
-0.10772956162691116,
0.06583203375339508,
-0.0312657356262207,
0.011379888281226158,
0.013287961483001709,
-0.012824641540646553,
-0.04734192043542862,
-0.0031827103812247515,
0.08533012121915817,
-0.018932541832327843,
-0.01875750906765461,
-0.009816843084990978,
0.056383807212114334,
-0.030077839270234108,
-0.061844728887081146,
0.017715804278850555,
-0.003914537839591503,
-0.05374681577086449,
-0.01439586840569973,
0.07993202656507492,
0.040406234562397,
-0.034251999109983444,
-0.043335165828466415,
-0.026793472468852997,
-0.03387352079153061,
0.030658196657896042,
0.011695384979248047,
0.015085576102137566,
0.03617268055677414,
-0.051702823489904404,
0.032151319086551666,
0.006550149526447058,
-0.018502259626984596,
0.007591296918690205,
0.005012595560401678,
-0.0006566442316398025,
0.0035936045460402966,
-0.026509564369916916,
-0.024783268570899963,
0.041328754276037216,
-0.007247419562190771,
0.07015857100486755,
0.0645742192864418,
0.00017230572120752186,
0.009864318184554577,
0.012297584675252438,
0.0016854205168783665,
0.05902687460184097,
-0.040029700845479965,
-0.00542595935985446,
-0.03494489565491676,
-0.009191387332975864,
0.05208232253789902,
0.006297444924712181,
-0.007332090754061937,
-0.014980358071625233,
0.03570808470249176,
0.0042333160527050495,
0.06991709768772125,
0.023899821564555168,
0.0467386357486248,
-0.01956842839717865,
-0.03794366866350174,
0.011387629434466362,
0.025463350117206573,
-0.00374310789629817,
0.03364250808954239,
-0.06179841235280037,
0.02247067540884018,
-0.009466414339840412,
-0.10433345288038254,
-0.0004427618405316025,
-0.05143946781754494,
0.04837079718708992,
0.035796258598566055,
0.052209705114364624,
0.053261611610651016,
0.008442521095275879,
0.007746166083961725,
-0.013337569311261177,
0.0017458279617130756,
-0.029649905860424042,
-0.001289824489504099,
0.004906284622848034,
-0.02638496272265911,
-0.021272476762533188,
-0.03307964280247688,
-0.02977137453854084,
-0.008780624717473984,
-0.03477668762207031,
0.017520546913146973,
-0.012387154623866081,
0.007684207521378994,
0.011765697039663792,
-0.07401508837938309,
0.0349087193608284,
-0.011603530496358871,
0.030045967549085617,
-0.017328040674328804,
-0.030363032594323158,
-0.011571964249014854,
-0.002162604359909892,
0.034825604408979416,
-0.023282095789909363,
0.004764963407069445,
-0.0008865197887644172,
-0.06632903963327408,
-0.0408199280500412,
-0.037170302122831345,
0.010156027041375637,
0.019828785210847855,
-0.0232185497879982,
0.04021086171269417,
0.02473880909383297,
-0.007294406183063984,
0.057278361171483994,
0.041665468364953995,
-0.017392799258232117,
0.0077545843087136745,
0.025928597897291183,
-0.0021011261269450188,
-0.0015503756003454328,
-0.0052724299021065235,
-0.04098298028111458,
0.01795957237482071,
0.0023067607544362545,
-0.0023280559107661247,
0.013331451453268528,
-0.03174000605940819,
0.01489815954118967
] |
<p>The first <a href="http://en.wikipedia.org/wiki/Chern_class" rel="nofollow">Chern number</a> $\cal C$ is known to be related to various physical objects.</p>
<ol>
<li><p>Gauge fields are known as connections of some principle bundles. In particular, principle $U(1)$ bundle is said to be classified by first Chern number. In terms of electromagnetic field, ${\cal C} \neq 0$ is equivalent to the existence of monopoles. </p></li>
<li><p>In the case of integer quantum Hall states, Chern number is simply the Hall conductance up to a constant.</p></li>
</ol>
<p>In both physical problems, Chern number is related to vorticity -- a quantized value (first case, Dirac's string argument and second, vortices in magnetic Brillouin zone).</p>
<p>Then my questions:</p>
<ol>
<li><p>What was the "physical" picture in Chern's mind when he originally "dreamed up" the theory? (Maybe knots, but how?)</p></li>
<li><p>If I want to learn how Chern classified $U(1)$ bundles using integers (first Chern number), which books or papers should I refer to?</p></li>
</ol>
<p>Notes: </p>
<p>My point is that mathematical theorems are not God-given but arose from concrete problems. I was asking what was <em>the original problem</em> that Chern solved, from which he codified the general theorems? And Chern number seems related to vorticity and then what are the corresponding vortices in his problem?</p> | g6585 | [
0.05678887665271759,
0.013434289954602718,
-0.0025749702472239733,
-0.019769055768847466,
0.07207512855529785,
-0.004494502674788237,
0.08271199464797974,
0.004560495261102915,
-0.023972725495696068,
0.004535512533038855,
-0.07762087136507034,
0.01647045463323593,
-0.021957064047455788,
0.03285503759980202,
0.050452426075935364,
-0.05986406281590462,
-0.025011809542775154,
-0.01584644615650177,
0.011693336069583893,
-0.1005064994096756,
0.009723718278110027,
0.04690247401595116,
0.019838847219944,
-0.053260933607816696,
0.025313004851341248,
0.0005347535479813814,
0.011699646711349487,
0.002815099898725748,
0.005251309368759394,
-0.08031211793422699,
0.03130040690302849,
-0.036885689944028854,
0.07454397529363632,
-0.030455240979790688,
0.001933006220497191,
-0.00041817306191660464,
-0.03929329290986061,
0.04006937891244888,
0.026524346321821213,
0.008033168502151966,
0.06348554790019989,
-0.03615283593535423,
0.026801293715834618,
-0.017102224752306938,
-0.0712657943367958,
0.07771449536085129,
-0.05252835899591446,
-0.007261856459081173,
0.0022691229823976755,
0.0752742737531662,
0.038719791918992996,
0.03285714611411095,
0.08277377486228943,
-0.005899546667933464,
0.009658641181886196,
-0.026496822014451027,
0.0257741566747427,
-0.06288721412420273,
0.08191855996847153,
0.031664274632930756,
0.042184632271528244,
0.05799539387226105,
0.014934564009308815,
0.01952183060348034,
0.036375727504491806,
0.04091813042759895,
0.0003858518903143704,
0.013045091181993484,
0.014879693277180195,
0.0261407271027565,
-0.049672242254018784,
-0.063619464635849,
0.009002613835036755,
0.03154880926012993,
-0.022034484893083572,
0.004806593991816044,
0.06393857300281525,
-0.023148350417613983,
0.042207982391119,
0.01077025756239891,
-0.008324901573359966,
0.006828338373452425,
-0.04501199349761009,
-0.047703638672828674,
0.10725627839565277,
0.011768141761422157,
-0.031957171857357025,
-0.04556867107748985,
-0.0010224998695775867,
0.015423876233398914,
-0.001152081647887826,
-0.007739644031971693,
-0.012678813189268112,
0.026983780786395073,
0.037337325513362885,
0.007642632350325584,
0.030878134071826935,
0.020501872524619102,
-0.044154513627290726,
0.014955303631722927,
-0.0042307451367378235,
-0.054697733372449875,
0.025976572185754776,
-0.023488929495215416,
-0.025888321921229362,
0.020907439291477203,
0.016210703179240227,
-0.01920202001929283,
0.03627517446875572,
0.060127176344394684,
-0.09962646663188934,
0.03172704204916954,
-0.040330931544303894,
-0.011854037642478943,
-0.010983272455632687,
0.03341292962431908,
0.055998798459768295,
0.0007551646558567882,
-0.023630820214748383,
0.022063111886382103,
0.008264929987490177,
-0.010991298593580723,
0.050318535417318344,
0.017556514590978622,
-0.0034122453071177006,
0.001353909494355321,
-0.03869209811091423,
-0.01438671350479126,
0.03080434538424015,
-0.03414541855454445,
0.037548862397670746,
-0.029898017644882202,
0.04547969996929169,
-0.008899211883544922,
-0.04556771367788315,
0.02354544959962368,
-0.04128424823284149,
-0.007612321991473436,
0.04012675583362579,
0.04769667983055115,
-0.02027294412255287,
-0.09315798431634903,
-0.021730909124016762,
0.009625027887523174,
-0.006085988134145737,
0.03433915972709656,
-0.012602212838828564,
-0.03848181292414665,
0.03632301837205887,
0.023270118981599808,
0.005376399029046297,
0.07800135016441345,
0.009356998838484287,
-0.040093738585710526,
-0.01507426705211401,
0.01404061820358038,
0.038776665925979614,
0.007118513807654381,
-0.013540071435272694,
0.01315738633275032,
0.029567517340183258,
-0.015250761061906815,
0.023838603869080544,
0.015736643224954605,
-0.02564876154065132,
-0.06592091172933578,
-0.017453204840421677,
-0.00520097091794014,
0.008827411569654942,
-0.047126512974500656,
-0.032203901559114456,
0.07704329490661621,
0.022375456988811493,
0.043833039700984955,
0.04267825186252594,
-0.004599407780915499,
-0.02392691560089588,
0.003501317696645856,
-0.009716354310512543,
0.008447323925793171,
-0.06007402762770653,
-0.04655671492218971,
0.03299179673194885,
-0.012342861853539944,
-0.022460812702775,
0.040377065539360046,
-0.018804850056767464,
0.029191887006163597,
0.005252989940345287,
-0.04536106809973717,
-0.024611538276076317,
-0.04262511059641838,
-0.028199659660458565,
0.07885829359292984,
-0.032880932092666626,
0.005916595458984375,
0.0076262629590928555,
-0.02294185385107994,
-0.04433280602097511,
0.01499977707862854,
0.0055218590423464775,
0.04742561653256416,
0.0375942587852478,
-0.007111117243766785,
0.017933644354343414,
0.038625914603471756,
-0.02830244041979313,
-0.03550047054886818,
0.02801128849387169,
-0.04064387455582619,
0.054504938423633575,
-0.045774538069963455,
0.006801493000239134,
0.0066374521702528,
-0.08829917758703232,
-0.05701187252998352,
0.00738948117941618,
-0.03078894130885601,
-0.02946224808692932,
-0.02910366840660572,
-0.015548628754913807,
-0.017815470695495605,
0.11860191076993942,
0.0582779161632061,
-0.008800891228020191,
0.016608688980340958,
-0.03993624821305275,
-0.0011722227791324258,
-0.007850398309528828,
-0.023528456687927246,
-0.02096276730298996,
0.01070212759077549,
0.05202800780534744,
-0.01724664866924286,
0.028838561847805977,
0.007771058939397335,
-0.06484339386224747,
-0.004983628634363413,
-0.016247626394033432,
0.04421703517436981,
0.013544603250920773,
-0.0102405846118927,
0.02961733192205429,
-0.017792189493775368,
0.025749605149030685,
-0.016719097271561623,
0.00506016006693244,
-0.03378716856241226,
-0.03914450854063034,
0.05122274160385132,
0.009107221849262714,
0.003142676781862974,
-0.011812310665845871,
0.09450362622737885,
-0.005761115346103907,
0.03402726724743843,
0.020592335611581802,
-0.013557828962802887,
0.03139545023441315,
-0.02513989619910717,
0.0171932615339756,
-0.06480664014816284,
0.005295435898005962,
-0.0060010747984051704,
-0.08887121826410294,
0.001982102170586586,
-0.037223462015390396,
0.05360418185591698,
-0.028975283727049828,
-0.015311118215322495,
0.0008645085617899895,
0.03512270748615265,
0.015533702448010445,
-0.07844940572977066,
0.02617645636200905,
-0.05389022082090378,
0.01572307199239731,
0.044818948954343796,
-0.04776773974299431,
-0.049822572618722916,
-0.014386800117790699,
0.017267100512981415,
-0.010119989514350891,
0.014260980300605297,
-0.0003406688047107309,
-0.020995480939745903,
-0.00978225376456976,
0.012245962396264076,
0.009926515631377697,
0.028718017041683197,
0.020983600988984108,
-0.01699857786297798,
0.03857004642486572,
0.02692556194961071,
-0.004075948614627123,
-0.04069091007113457,
0.034664586186409,
0.02330344170331955,
-0.0362466461956501,
0.01911154016852379,
0.07798337191343307,
-0.02283686213195324,
-0.03296838700771332,
0.06564062833786011,
0.021102281287312508,
-0.0018448729533702135,
-0.03927623853087425,
-0.00016586680430918932,
-0.04230561852455139,
-0.017521407455205917,
-0.010531401261687279,
0.012955998070538044,
0.04005124047398567,
-0.03667355701327324,
-0.013913407921791077,
0.046635568141937256,
0.024455150589346886,
0.02391001209616661,
0.04703744128346443,
-0.008310183882713318,
-0.040990449488162994,
-0.011625927872955799,
0.05013260245323181,
-0.04952249675989151,
0.07134516537189484,
0.039866749197244644,
0.015217028558254242,
0.04669269919395447,
0.0028536468744277954,
-0.060843851417303085,
-0.010808774270117283,
-0.02720586583018303,
-0.020981868728995323,
-0.025234023109078407,
-0.05054900050163269,
-0.06227520853281021,
-0.04373480752110481,
-0.045720282942056656,
0.05431205779314041,
0.01114435400813818,
-0.00497267534956336,
0.01500646211206913,
-0.053750425577163696,
-0.04502397030591965,
0.01228480227291584,
0.03518044948577881,
-0.010352320969104767,
0.012383819557726383,
-0.03290770202875137,
0.009812301956117153,
-0.0038135030772536993,
-0.02311115153133869,
0.003731862176209688,
0.06686427444219589,
-0.016646625474095345,
0.044485904276371,
0.0098198177292943,
0.02234625443816185,
0.004865927621722221,
0.001998532796278596,
-0.0017604263266548514,
0.030130578204989433,
0.0035299919545650482,
0.010640190914273262,
-0.0004965760745108128,
-0.05496225878596306,
-0.01258775219321251,
0.01301647536456585,
0.034721001982688904,
0.03398988023400307,
-0.036495331674814224,
0.005196418147534132,
0.014785699546337128,
-0.0030671514105051756,
0.007587578147649765,
-0.012076118029654026,
-0.03244810178875923,
-0.007025144528597593,
-0.03745640441775322,
-0.012751122936606407,
0.03406551480293274,
-0.00926847755908966,
0.07196266204118729,
0.05661461502313614,
-0.037721820175647736,
0.02868000790476799,
-0.016681984066963196,
0.025025513023138046,
0.029066070914268494,
-0.0527203232049942,
0.020818213000893593,
-0.025465399026870728,
-0.0334063358604908,
-0.031247667968273163,
-0.0024918154813349247,
0.028485920280218124,
0.0030288128182291985,
0.016609735786914825,
-0.002101879334077239,
0.005581494886428118,
0.00539338868111372,
-0.07805664837360382,
0.004825810436159372,
0.0013935355236753821,
-0.0262829028069973,
0.03686594218015671,
0.058849040418863297,
-0.013495845720171928,
0.020740967243909836,
-0.045147888362407684,
0.01534830592572689,
-0.021708279848098755,
0.01446141954511404,
-0.12135735154151917,
0.019350187852978706,
-0.042488303035497665,
-0.007311221212148666,
-0.04480089992284775,
0.03992000222206116,
-0.006124116014689207,
-0.009777328930795193,
0.0340302512049675,
0.02262009121477604,
-0.028422093018889427,
-0.05104715749621391,
0.0424310527741909,
0.058279380202293396,
-0.013993040658533573,
-0.06322470307350159,
-0.005696263629943132,
-0.02391923777759075,
0.010112577117979527,
0.006117671728134155,
0.02211078256368637,
-0.013355477713048458,
0.00807153433561325,
0.020138880237936974,
-0.015566186979413033,
-0.032511185854673386,
0.020536532625555992,
0.049329936504364014,
-0.022349338978528976,
0.005688941106200218,
-0.012762967497110367,
0.007036953698843718,
-0.03524832800030708,
-0.08876627683639526,
-0.007561299949884415,
-0.020735453814268112,
0.001914060558192432,
0.02655315399169922,
-0.008773584850132465,
-0.02438504993915558,
-0.04609574005007744,
0.009919164702296257,
-0.05161236599087715,
0.031578145921230316,
-0.03888389840722084,
0.032011013478040695,
0.012279183603823185,
-0.01741643436253071,
0.013426669873297215,
-0.04088500887155533,
-0.06425518542528152,
0.05736035481095314,
0.027150163426995277,
-0.009410037659108639,
-0.023240327835083008,
-0.0749594047665596,
-0.01022657286375761,
-0.004088382702320814,
-0.014458730816841125,
0.020351191982626915,
-0.029325995594263077,
0.04058384522795677,
-0.024219684302806854,
0.06288672983646393,
-0.023733248934149742,
0.002999118994921446,
-0.031584516167640686,
0.010879524052143097,
-0.009977308101952076,
-0.01839473471045494,
0.022906925529241562,
-0.016335874795913696,
-0.08321511000394821,
-0.03346332535147667,
0.016339696943759918,
-0.07190342992544174,
0.029697235673666,
-0.02092178352177143,
-0.04112682864069939,
0.023353807628154755,
0.02097027190029621,
-0.006882896181195974,
-0.07102503627538681,
-0.035150665789842606,
-0.014257856644690037,
-0.014710103161633015,
0.021939216181635857,
0.0026918768417090178,
-0.016443783417344093,
-0.04122445732355118,
0.021236933767795563,
-0.006303663365542889,
-0.042944446206092834,
0.015496551990509033,
-0.04741528257727623,
-0.0011722907656803727,
-0.0029701769817620516,
-0.021075014024972916,
0.019374938681721687,
-0.0225786492228508,
0.0010179773671552539,
0.009685707278549671,
0.01079775020480156,
-0.0626625344157219,
-0.006638344377279282,
0.03469451144337654,
-0.013300803489983082,
0.0006440069410018623,
0.018736079335212708,
0.06342088431119919,
-0.0014060616958886385,
-0.07281524688005447,
-0.0004607343871612102,
-0.044694382697343826,
-0.07096952199935913,
0.03786972910165787,
0.05114373564720154,
-0.00410221004858613,
-0.02068929560482502,
0.020505236461758614,
-0.011658051051199436,
-0.04858782887458801,
0.054524023085832596,
0.011727104894816875,
-0.07037080824375153,
0.021321430802345276,
0.024871474131941795,
-0.03662750869989395,
-0.006139500066637993,
-0.004773684311658144,
-0.044881872832775116,
0.005218599457293749,
-0.020884960889816284,
-0.007748846895992756,
0.01595824956893921,
0.042565230280160904,
-0.021399326622486115,
-0.02596556767821312,
-0.016790946945548058,
0.01776609569787979,
-0.019649915397167206,
-0.023790720850229263,
-0.00846931803971529,
0.010533971711993217,
-0.01264224573969841,
-0.01092891301959753,
0.020431242883205414,
0.05780407041311264,
-0.019884949550032616,
-0.03396999090909958,
0.012075339443981647,
-0.00324167194776237,
0.04870638996362686,
0.023538757115602493,
-0.014274584129452705,
0.06086260452866554,
0.07003383338451385,
-0.026186460629105568,
0.02866525948047638,
0.00004756341513711959,
0.016555285081267357,
0.04748331010341644,
0.007796330843120813,
-0.036125801503658295,
-0.1389123946428299,
-0.019686106592416763,
-0.028898071497678757,
-0.0029351150151342154,
0.07264793664216995,
0.05646555498242378,
-0.0776028111577034,
-0.02136511355638504,
0.028997913002967834,
-0.03693744167685509,
-0.017430076375603676,
0.009864959865808487,
-0.013973996043205261,
-0.006826858967542648,
0.06627143919467926,
-0.00952181313186884,
-0.033394500613212585,
-0.02914498746395111,
0.029559528455138206,
0.07391074299812317,
-0.038468021899461746,
-0.0803777277469635,
-0.019000336527824402,
0.03995385393500328,
0.008267111144959927,
-0.014612207189202309,
0.007296867202967405,
-0.010899410583078861,
0.0037128841504454613,
0.019757894799113274,
-0.0612671859562397,
0.057930756360292435,
0.02233961783349514,
0.01876026578247547,
-0.007839564234018326,
-0.03229020535945892,
0.014705779030919075,
-0.0038343549240380526,
-0.043554771691560745,
0.02816813252866268,
-0.0226972047239542,
0.02303791232407093,
-0.020409876480698586,
0.04800277575850487,
-0.00043936551082879305,
0.040112271904945374,
0.028038864955306053,
0.06064959987998009,
0.05263422057032585,
-0.004728393163532019,
-0.009048223495483398,
0.06500830501317978,
-0.0018266375409439206,
-0.05376606434583664,
0.0227361973375082,
0.03613417595624924,
0.024429339915513992,
0.018528979271650314,
-0.004562056623399258,
-0.019455481320619583,
-0.011389256455004215,
0.07921535521745682,
0.023135626688599586,
-0.022592181339859962,
0.024296090006828308,
0.05372907593846321,
0.0054270317777991295,
0.0528605654835701,
-0.07500145584344864,
-0.002957899821922183,
-0.01215155515819788,
-0.01832432486116886,
0.001192177296616137,
-0.030604559928178787,
0.00950841885060072,
0.032395802438259125,
-0.021119773387908936,
-0.031717509031295776,
-0.020000912249088287,
0.015076684765517712,
-0.002161179669201374,
0.0009473928948864341,
0.01971357688307762,
-0.038383953273296356,
0.047553807497024536,
0.009476256556808949,
-0.0032140780240297318,
-0.03634747862815857,
0.05437376722693443,
-0.0013687311438843608,
-0.04039328545331955,
0.03728840872645378,
-0.07284248620271683,
0.03283826634287834,
-0.006762397941201925,
-0.05418936535716057,
-0.0064582242630422115,
-0.025790715590119362,
-0.007222886197268963,
-0.022185105830430984,
0.015184154734015465,
0.020527642220258713,
0.008345097303390503,
-0.025122638791799545,
0.08139774948358536,
0.048123735934495926,
-0.030377138406038284,
-0.014253669418394566,
0.007452758029103279,
-0.05967054143548012,
0.03992687538266182,
0.03447844460606575,
-0.03522754833102226,
0.05919535085558891,
-0.09420664608478546,
0.04842760041356087,
-0.025893332436680794,
-0.010785805061459541,
-0.07577142864465714,
-0.005315009038895369,
0.0003420890716370195,
0.02320965565741062,
-0.011395629495382309,
0.05606817826628685,
0.0275543462485075,
-0.021938784047961235,
-0.016149643808603287,
0.010423165746033192,
-0.018854966387152672,
-0.022318286821246147,
0.0032901111990213394,
-0.0524868369102478,
0.06438837200403214,
0.0007947597769089043,
0.012846332043409348,
0.03753582388162613,
0.049722012132406235,
0.004229605197906494,
0.04845305532217026,
0.01965063251554966,
-0.011280979961156845,
-0.03943689540028572,
0.033101074397563934,
0.01102572400122881,
0.005104450974613428,
-0.00595824932679534,
0.04849783331155777,
-0.006997233256697655,
0.022518770769238472,
0.021102972328662872,
0.049220211803913116,
-0.08302246034145355,
0.060565825551748276,
0.02715364284813404,
-0.03278141841292381,
-0.014025909826159477,
0.008043764159083366,
-0.04496011510491371,
0.03209143877029419,
-0.014719770289957523,
0.022091306746006012,
0.07762710005044937,
-0.0424642451107502,
-0.023306388407945633,
0.014728553593158722,
0.034456636756658554,
0.010713843628764153,
-0.04006141796708107,
-0.018569063395261765,
-0.07841546833515167,
0.07379075884819031,
-0.012394480407238007,
0.005136347375810146,
-0.03723221644759178,
0.018732070922851562,
0.020166220143437386,
0.0017136590322479606,
-0.0005519799306057394,
-0.026862112805247307,
0.037435248494148254,
0.02586153708398342,
0.072880819439888,
-0.009952676482498646,
0.006000293884426355,
-0.05828598886728287,
0.05840599909424782,
0.04390842095017433,
-0.012226912193000317,
-0.003153088968247175,
0.005382114555686712,
-0.0034195499029010534
] |
<p>In the special relativistic action for a massive point particle, </p>
<p>$$\int_{t_i}^{t_f}\mathcal {L}dt,$$</p>
<p>why is the Lagrangian </p>
<p>$$\mathcal {L}=-E_o\gamma^{-1}$$</p>
<p>a negative number?</p> | g924 | [
0.046468187123537064,
0.004954833071678877,
-0.00999225303530693,
-0.010082785971462727,
0.08119145035743713,
0.03897746652364731,
0.05002502351999283,
0.08178254961967468,
-0.0625106617808342,
0.016274048015475273,
0.010088116861879826,
0.09472397714853287,
0.07463593035936356,
0.019569775089621544,
-0.007284273859113455,
-0.03202680125832558,
0.06143118813633919,
-0.010031064040958881,
-0.007108647376298904,
-0.0024669438134878874,
-0.012059717439115047,
0.02886885032057762,
0.034822653979063034,
-0.01650572381913662,
0.08970247209072113,
0.017507662996649742,
0.03951188921928406,
-0.01850476674735546,
-0.025987181812524796,
-0.020503826439380646,
0.05584414303302765,
-0.010365508496761322,
-0.011813472956418991,
-0.012685640715062618,
-0.00481451116502285,
-0.019967136904597282,
0.0484808012843132,
0.057195622473955154,
0.02614033967256546,
0.008144914172589779,
-0.028807831928133965,
0.009193104691803455,
0.04336455464363098,
-0.018378864973783493,
0.005892622750252485,
-0.003278665244579315,
-0.001273885602131486,
0.014024841599166393,
-0.038984984159469604,
0.02147219143807888,
0.014188370667397976,
-0.004946411587297916,
-0.02821868471801281,
-0.04661225527524948,
0.037763047963380814,
0.01627577841281891,
-0.088103286921978,
-0.015914244577288628,
-0.0083674481138587,
0.06174740567803383,
0.014175817370414734,
-0.08042359352111816,
0.03224971517920494,
0.021480463445186615,
0.0707118809223175,
0.004277451429516077,
-0.04082164540886879,
-0.0025525721721351147,
-0.011728867888450623,
0.0019776765257120132,
-0.01148829236626625,
-0.04169883951544762,
0.03816895931959152,
-0.03496880456805229,
-0.009514173492789268,
0.02914021536707878,
-0.04379966855049133,
0.041289426386356354,
-0.04499760642647743,
-0.03114735148847103,
-0.054645292460918427,
-0.0506473109126091,
0.037044961005449295,
-0.01972222328186035,
0.06074604392051697,
-0.01386341918259859,
0.04997061938047409,
0.0018521830206736922,
-0.015537112019956112,
-0.004441019147634506,
0.05950629338622093,
0.0003137093153782189,
0.0598357692360878,
0.019178949296474457,
-0.008109827525913715,
-0.003711472963914275,
0.019400199875235558,
0.04374226927757263,
-0.0711730420589447,
-0.0007197092054411769,
0.05969276279211044,
0.05225256830453873,
-0.03250415623188019,
0.018930256366729736,
-0.028461625799536705,
0.023196442052721977,
-0.007000997196882963,
-0.004313994664698839,
0.022071871906518936,
-0.002285528229549527,
0.012857083231210709,
-0.025759505107998848,
0.0288515817373991,
-0.07584653794765472,
-0.041883938014507294,
0.05330805107951164,
0.012710703536868095,
-0.07020498812198639,
-0.03905992582440376,
0.06256852298974991,
0.027030980214476585,
-0.003615399356931448,
-0.03887647017836571,
0.08342340588569641,
-0.02255685068666935,
-0.03561577573418617,
0.018888967111706734,
0.03279945254325867,
-0.0025798450224101543,
0.015240466222167015,
-0.027581816539168358,
0.04934476688504219,
-0.05133955180644989,
-0.011782822199165821,
0.005203134845942259,
0.0338902473449707,
0.014168581925332546,
0.0037720552645623684,
0.015682030469179153,
-0.027112731710076332,
-0.012974551878869534,
-0.00591657031327486,
0.052508749067783356,
-0.05430132523179054,
-0.036187924444675446,
-0.001629104372113943,
0.013031542301177979,
-0.03282495215535164,
0.013312743045389652,
0.008666562847793102,
0.008336572907865047,
0.01655616983771324,
0.04093093425035477,
0.003105851821601391,
0.055974286049604416,
-0.009248553775250912,
0.035056259483098984,
0.052547477185726166,
-0.062293555587530136,
-0.0007020107004791498,
0.03783326968550682,
0.008998909965157509,
-0.006056061014533043,
0.014675967395305634,
-0.018363477662205696,
0.04102044552564621,
-0.017261609435081482,
-0.039833612740039825,
-0.02254456840455532,
-0.033615175634622574,
-0.05807854235172272,
-0.005134407430887222,
0.03015976957976818,
-0.029948916286230087,
-0.002515227533876896,
0.0046981158666312695,
-0.0451401025056839,
-0.03679141774773598,
-0.0040960353799164295,
0.019952256232500076,
-0.040057241916656494,
-0.09582854062318802,
-0.012676743790507317,
-0.021416913717985153,
-0.014329936355352402,
-0.030234910547733307,
-0.03022611513733864,
0.07697559148073196,
-0.023758942261338234,
0.02138322778046131,
0.011969813145697117,
0.030288629233837128,
-0.013151987455785275,
0.0004837496380787343,
-0.00851515308022499,
0.022365424782037735,
0.0036355452612042427,
-0.06406227499246597,
-0.047382425516843796,
0.004942307248711586,
-0.008769659325480461,
0.029061919078230858,
0.045335542410612106,
0.006612266413867474,
-0.021052192896604538,
-0.08746486157178879,
-0.038911689072847366,
0.02573486790060997,
0.013805347494781017,
0.03476175665855408,
0.045497726649045944,
-0.05183227360248566,
0.016378527507185936,
-0.036834586411714554,
-0.013202269561588764,
-0.07233009487390518,
0.00025187883875332773,
0.030260799452662468,
-0.024568134918808937,
0.031222522258758545,
-0.09568153321743011,
0.024407053366303444,
0.0641804188489914,
-0.012302078306674957,
0.022221963852643967,
0.018583869561553,
-0.022545896470546722,
-0.05913770943880081,
0.03511864319443703,
-0.015202331356704235,
-0.07476110011339188,
0.029324855655431747,
-0.03428027778863907,
0.02178545668721199,
0.01782606728374958,
-0.026774372905492783,
-0.02554558776319027,
-0.02071371115744114,
0.01763441227376461,
0.016325633972883224,
0.023825479671359062,
-0.05425351485610008,
-0.01944665051996708,
-0.015321392565965652,
0.01920759305357933,
0.037990156561136246,
0.00227244570851326,
0.016576426103711128,
-0.07296890020370483,
-0.009208548814058304,
-0.025710338726639748,
-0.04267805442214012,
0.004227522294968367,
0.039177026599645615,
0.050922807306051254,
-0.017545729875564575,
-0.01560160331428051,
-0.013778147287666798,
-0.010874171741306782,
0.013991598971188068,
-0.01338632870465517,
0.0008224121993407607,
-0.017499417066574097,
0.039110247045755386,
-0.007700162939727306,
0.02179144136607647,
-0.03787917271256447,
0.008622881956398487,
0.04239848628640175,
-0.024787841364741325,
0.033308133482933044,
0.07146790623664856,
0.04562096670269966,
0.03798641636967659,
-0.03223466873168945,
-0.013539387844502926,
-0.04527553543448448,
-0.020175715908408165,
0.0497698076069355,
-0.04237285628914833,
-0.006365381181240082,
0.038937412202358246,
-0.0016767926281318069,
-0.010746504180133343,
0.03167222440242767,
-0.07878625392913818,
-0.029950110241770744,
-0.027126440778374672,
-0.07186941057443619,
-0.028073403984308243,
0.049252700060606,
0.015585961751639843,
-0.018080607056617737,
-0.05521908402442932,
0.06686478853225708,
-0.00564027251675725,
-0.04963589087128639,
-0.04980166256427765,
-0.013522605411708355,
0.04941965639591217,
0.02515660785138607,
-0.02298431470990181,
-0.05760752409696579,
-0.03502891585230827,
-0.03799842298030853,
0.0002020534739131108,
0.018333619460463524,
-0.013608538545668125,
-0.06367602199316025,
0.006221472285687923,
-0.00005766237518400885,
0.06964660435914993,
0.031958285719156265,
-0.03835468739271164,
-0.013234560377895832,
0.027167947962880135,
-0.024815913289785385,
-0.024271825328469276,
0.03899705410003662,
0.007162135560065508,
-0.03722488135099411,
-0.02906252071261406,
-0.009671386331319809,
0.031931813806295395,
0.03847803920507431,
0.03082849085330963,
-0.035086214542388916,
0.020751409232616425,
0.005736039485782385,
0.0048965164460241795,
-0.015229655429720879,
-0.061204466968774796,
0.01904241554439068,
0.05397353693842888,
0.0002434759953757748,
0.04565637931227684,
-0.032946567982435226,
-0.010096017271280289,
0.06891672313213348,
0.004361840896308422,
-0.07684553414583206,
-0.0318014919757843,
-0.03942802920937538,
0.052173737436532974,
0.056956563144922256,
-0.035146839916706085,
0.035688165575265884,
0.018418896943330765,
0.06472845375537872,
0.05105159431695938,
-0.035542234778404236,
-0.041241392493247986,
0.009882723912596703,
-0.014827689155936241,
0.003342370269820094,
-0.04034290462732315,
-0.004712849855422974,
0.03625516965985298,
-0.0007914568413980305,
-0.0016812487738206983,
-0.01137989666312933,
0.0057737757451832294,
-0.0454353429377079,
0.06568595767021179,
0.013547186739742756,
0.06430669128894806,
-0.07005412876605988,
-0.046787139028310776,
0.012213281355798244,
-0.003607789985835552,
0.03827112913131714,
-0.01227217260748148,
0.01741013117134571,
0.01799091510474682,
0.00950087234377861,
-0.006157125346362591,
-0.03159452602267265,
-0.041476644575595856,
-0.027673983946442604,
-0.01866704411804676,
0.06697266548871994,
-0.04338999092578888,
-0.0502176508307457,
-0.0031042650807648897,
0.0495903454720974,
0.019655883312225342,
-0.03516727313399315,
-0.01328116562217474,
0.0026409043930470943,
-0.083128921687603,
0.0077676912769675255,
-0.03017103485763073,
-0.016045669093728065,
-0.020237909629940987,
0.06996641308069229,
0.01454926561564207,
0.02756614238023758,
0.0026108117308467627,
0.01664823107421398,
0.010832186788320541,
-0.019400781020522118,
0.05334259942173958,
0.06054170802235603,
-0.006605428643524647,
0.014027637429535389,
-0.003964525647461414,
0.04674398899078369,
0.02667953260242939,
0.03240378573536873,
-0.047842785716056824,
-0.023228999227285385,
-0.027836909517645836,
-0.02287636511027813,
-0.0539250448346138,
0.014512256719172001,
-0.05793292820453644,
0.007439110893756151,
-0.01994205266237259,
0.0030586959328502417,
-0.01927359215915203,
0.050679925829172134,
0.008455678820610046,
0.057869378477334976,
-0.01711444742977619,
0.03274614363908768,
0.06544094532728195,
0.012282542884349823,
0.05938666686415672,
-0.06680236011743546,
-0.03664682060480118,
-0.00760111678391695,
0.02253473736345768,
0.02878810465335846,
0.004993750713765621,
-0.025194676592946053,
0.08789379894733429,
-0.036932364106178284,
0.0659312903881073,
0.08770614862442017,
0.08502525836229324,
0.01896306872367859,
-0.03278527036309242,
-0.0000573372672079131,
-0.03958052024245262,
0.059661779552698135,
0.010510549880564213,
-0.026408344507217407,
-0.034738924354314804,
-0.05437927320599556,
-0.0173827912658453,
0.03585698828101158,
-0.005362912081182003,
-0.053539641201496124,
-0.021121330559253693,
0.060172684490680695,
0.019661208614706993,
-0.01595928519964218,
0.03747010976076126,
-0.024849239736795425,
0.0351824089884758,
-0.06657847762107849,
-0.04446142911911011,
0.02400350570678711,
0.05051524564623833,
0.039182212203741074,
-0.001453834818676114,
-0.035443615168333054,
0.024534311145544052,
-0.057040028274059296,
-0.01640056073665619,
-0.03379043564200401,
-0.008410348556935787,
0.04037413373589516,
0.001794622396118939,
-0.050883565098047256,
-0.007518924307078123,
-0.047715768218040466,
-0.004772009328007698,
-0.040443580597639084,
-0.010501495562493801,
0.01915684901177883,
-0.04294269531965256,
0.009666290134191513,
-0.016448592767119408,
-0.010946789756417274,
0.033491648733615875,
-0.051159631460905075,
-0.0005047821905463934,
0.022281382232904434,
0.0016363827744498849,
0.01022567879408598,
-0.04930809885263443,
0.014541937969624996,
0.0567314513027668,
0.027426334097981453,
-0.015232186764478683,
-0.012702085077762604,
0.024399030953645706,
0.008426915854215622,
-0.0005004220292903483,
-0.07648120075464249,
-0.0212390199303627,
-0.025118490681052208,
-0.012014668434858322,
0.008499755524098873,
0.03359675779938698,
0.04047222062945366,
-0.017694413661956787,
-0.005714032333344221,
-0.017033850774168968,
-0.006153667811304331,
-0.01089944876730442,
0.06078687682747841,
-0.02065088227391243,
0.02214094251394272,
-0.02733801305294037,
0.03323535993695259,
-0.015497070737183094,
-0.0030142900068312883,
-0.020754743367433548,
-0.002632983261719346,
0.0008039687527343631,
-0.01925673335790634,
-0.04963560774922371,
-0.03976992145180702,
-0.021366653963923454,
-0.03723924234509468,
-0.022956684231758118,
-0.009610663168132305,
0.0016986698610708117,
0.0035233167000114918,
0.0024693834129720926,
0.04562832787632942,
0.008364011533558369,
-0.033289842307567596,
0.007244229782372713,
0.013826362788677216,
-0.025056151673197746,
0.015335863456130028,
-0.0119162043556571,
0.07098786532878876,
-0.05293610319495201,
-0.02305018901824951,
0.03219708800315857,
-0.012905510142445564,
0.03463884815573692,
-0.028972934931516647,
-0.003997943829745054,
-0.029973994940519333,
-0.06095794588327408,
-0.009187808260321617,
0.024934325367212296,
0.007668003905564547,
-0.030283231288194656,
-0.019531162455677986,
-0.038817133754491806,
0.02473967708647251,
0.029574960470199585,
0.019531480967998505,
-0.027389707043766975,
-0.03280113264918327,
-0.04289734736084938,
0.052992768585681915,
0.02439582534134388,
0.03472818806767464,
-0.028455164283514023,
0.01361755933612585,
-0.05733013153076172,
0.003950695041567087,
-0.03554881364107132,
-0.032789941877126694,
0.08067486435174942,
-0.029053278267383575,
0.02013815939426422,
0.061339668929576874,
0.0207725390791893,
-0.01232538465410471,
0.006772496737539768,
-0.050488509237766266,
0.01845477893948555,
-0.011431321501731873,
0.06188800558447838,
0.04603232815861702,
-0.08650919049978256,
0.004646850284188986,
-0.03219367563724518,
-0.031495265662670135,
-0.011038639582693577,
-0.02406294085085392,
0.09829758107662201,
0.05410382151603699,
-0.011310167610645294,
-0.07333683967590332,
-0.0012394055956974626,
-0.014245540834963322,
0.03144649416208267,
-0.03038044087588787,
-0.05056501924991608,
-0.015625251457095146,
-0.028488878160715103,
0.06284738332033157,
0.07103342562913895,
-0.009290416724979877,
-0.0020092756021767855,
-0.010473256930708885,
-0.01773298718035221,
-0.03971739113330841,
0.01758350245654583,
0.00975062046200037,
0.033204175531864166,
0.04899553954601288,
0.017063047736883163,
-0.02877083420753479,
0.0034763189032673836,
0.047002799808979034,
-0.039055224508047104,
0.040839783847332,
0.06042828410863876,
-0.037241172045469284,
-0.009268458001315594,
0.03441265597939491,
-0.02933138608932495,
-0.02131805755198002,
0.01171466987580061,
0.021742239594459534,
0.012305183336138725,
-0.05509074404835701,
0.027859259396791458,
-0.044128235429525375,
0.01087180059403181,
0.008579535409808159,
0.024534370750188828,
-0.04104965180158615,
0.047116994857788086,
0.02056266926229,
-0.0028512815479189157,
-0.06687182933092117,
0.031041467562317848,
0.03317917138338089,
0.014082865789532661,
-0.030698109418153763,
0.046844806522130966,
0.015657784417271614,
-0.08748294413089752,
-0.08154579252004623,
0.0744851678609848,
-0.024802858009934425,
-0.006676732562482357,
-0.05752980336546898,
-0.00515405461192131,
-0.004547080956399441,
0.021633459255099297,
-0.032938361167907715,
-0.00828213058412075,
-0.013122105039656162,
-0.05305684357881546,
0.01993580162525177,
0.0152584882453084,
-0.011192132718861103,
-0.005204800050705671,
-0.02981720305979252,
0.0016953758895397186,
0.02940700389444828,
0.0007234264630824327,
0.04828167334198952,
0.02905617095530033,
0.0018750748131424189,
-0.022416621446609497,
0.04358404502272606,
-0.007010217290371656,
-0.005954534746706486,
0.010213596746325493,
-0.08316381275653839,
0.01160676870495081,
-0.007635663729161024,
0.010162550956010818,
0.03999403491616249,
0.01884741336107254,
-0.06585212796926498,
0.024080902338027954,
0.0067297047935426235,
0.04755116626620293,
0.0034427312202751637,
-0.028156772255897522,
-0.058055274188518524,
-0.023274380713701248,
-0.01034490205347538,
0.0018936077831313014,
-0.03499898687005043,
0.02391636371612549,
0.007160719484090805,
0.04266347736120224,
0.021856067702174187,
0.04798951372504234,
0.029071157798171043,
-0.009233402088284492,
-0.0077202110551297665,
0.03849255293607712,
-0.006751930341124535,
0.02715756744146347,
0.023037048056721687,
-0.03291377052664757,
-0.05896869674324989,
0.016341406852006912,
0.03273316100239754,
0.050575271248817444,
0.032439690083265305,
-0.029964309185743332,
0.004382514860481024,
0.045349251478910446,
-0.020513301715254784,
-0.003888673847541213,
-0.020372623577713966,
0.028197254985570908,
0.053564369678497314,
0.016729604452848434,
-0.005715752951800823,
-0.009567190892994404,
0.05487639456987381,
-0.08053798973560333,
0.03779499977827072,
0.010674028657376766,
-0.024294275790452957,
-0.10080166906118393,
-0.00550226541236043,
-0.07200811803340912,
0.017253244295716286,
0.0078110406175255775,
0.05604548752307892,
0.03505973145365715,
-0.04808203876018524,
0.0191426370292902,
-0.06922154873609543,
0.06487781554460526,
-0.020583199337124825,
-0.004810502752661705,
-0.011272542178630829,
-0.042605362832546234,
0.025298278778791428,
0.027006488293409348,
-0.01421018224209547,
-0.04028366133570671,
0.034882768988609314,
0.06614560633897781,
-0.006803236436098814,
-0.026282068341970444,
0.008886681869626045,
0.012981181964278221,
0.025561967864632607,
0.0013333054957911372,
0.022690091282129288,
0.007775927893817425,
-0.02564620040357113,
0.07204524427652359,
0.04037339612841606,
-0.022533193230628967,
0.02718091942369938,
-0.05316254496574402,
0.015931427478790283,
-0.011503005400300026,
0.010480719618499279,
-0.019475147128105164,
0.01817593351006508,
-0.015218866057693958,
-0.0011303339852020144,
-0.03157426789402962,
-0.018906254321336746,
-0.0046256594359874725
] |
<p>The question concerns <a href="http://www.theepochtimes.com/n3/739183-former-nasa-physicist-disputes-einsteins-relativity-theory/?photo=2" rel="nofollow">this video</a>: </p>
<p>It says that the <a href="http://en.wikipedia.org/wiki/Gravitational_lens" rel="nofollow">Gravitational Lens</a> effect is an illusion, meaning it's not caused by gravity but by change in density of a plasma atmosphere. It claims further that this gravitational lens effect is not present with other massive objects that aren't made of, or surrounded by, plasma. </p>
<p>Does this mean general relativity is invalid, somewhat invalid, or still luckily valid? What is the merit of claim that bending could be caused by plasma and not by gravity? </p> | g6586 | [
0.05109719932079315,
0.05374550819396973,
-0.006303379312157631,
0.025435419753193855,
0.03775712847709656,
0.08981435745954514,
0.021699924021959305,
0.042428139597177505,
-0.03802398964762688,
0.006056707352399826,
0.11071151494979858,
0.014029637910425663,
0.01794295758008957,
0.006350921932607889,
-0.03797084838151932,
0.008942478336393833,
0.07670196145772934,
-0.04681920260190964,
-0.045551687479019165,
0.0534210242331028,
0.0036104086320847273,
-0.042979370802640915,
-0.010363724082708359,
-0.040465347468853,
-0.005067428108304739,
0.006098110694438219,
0.004264557734131813,
0.005572807975113392,
3.3740306548679655e-7,
-0.04957106336951256,
0.0031226284336298704,
0.0002164506004191935,
-0.012668532319366932,
-0.058407094329595566,
-0.017748981714248657,
-0.03355727717280388,
0.0030053574591875076,
0.04124743118882179,
0.047840602695941925,
-0.035044871270656586,
-0.08002911508083344,
-0.034289587289094925,
0.019226398319005966,
-0.006528572179377079,
0.018273891881108284,
0.031787388026714325,
0.005695946980267763,
0.025888707488775253,
0.03145148605108261,
-0.02630171924829483,
-0.025366313755512238,
0.03267326205968857,
-0.01942729763686657,
0.0103065837174654,
-0.031432028859853745,
0.0329597070813179,
-0.01751767098903656,
0.05791749060153961,
0.05863439291715622,
-0.043463729321956635,
0.02615080587565899,
0.05156498774886131,
0.06018202751874924,
0.020761026069521904,
-0.02679581195116043,
-0.018304578959941864,
-0.07556326687335968,
-0.0371856652200222,
0.04146096110343933,
-0.024759631603956223,
0.03293266519904137,
-0.0034413887187838554,
-0.05054464936256409,
0.009877519682049751,
-0.027581915259361267,
0.08727717399597168,
-0.03386550396680832,
0.04906164109706879,
0.004764451179653406,
0.0017256621504202485,
-0.001973050180822611,
0.04643521457910538,
-0.010119129903614521,
0.006430738605558872,
0.07953034341335297,
0.005038639530539513,
0.00858076848089695,
-0.005144604481756687,
0.012610943987965584,
0.05325046926736832,
0.010910801589488983,
-0.02494608238339424,
0.01634805276989937,
0.02835514210164547,
0.010559567250311375,
-0.00831087026745081,
-0.05689338594675064,
0.08884195238351822,
-0.025331348180770874,
0.0443570651113987,
-0.08747386187314987,
0.03216022625565529,
-0.007371979765594006,
0.018591666594147682,
0.02731952629983425,
-0.00011357830953784287,
0.0070240795612335205,
0.03204500302672386,
0.03756445273756981,
-0.04511414095759392,
-0.027350516989827156,
0.007121516391634941,
0.03940621018409729,
-0.03259087726473808,
-0.057316701859235764,
-0.08317141979932785,
0.02861977554857731,
0.008245138451457024,
0.00036993317189626396,
0.02951817959547043,
-0.036857739090919495,
0.05830778554081917,
0.021127309650182724,
0.09486696124076843,
-0.034877125173807144,
-0.07374906539916992,
0.05689289793372154,
-0.023816067725419998,
0.004578570369631052,
-0.056214358657598495,
0.010994506999850273,
-0.04828150197863579,
0.0138876186683774,
-0.0011924655409529805,
0.02687462419271469,
0.019205242395401,
0.036836087703704834,
-0.003206339431926608,
-0.06791898608207703,
0.032877255231142044,
0.01997993141412735,
0.014157332479953766,
0.06791707128286362,
-0.027140352874994278,
-0.02232675440609455,
0.03044426627457142,
-0.022922664880752563,
0.03904583305120468,
0.08288951218128204,
0.0054028709419071674,
-0.02081882394850254,
0.05208313837647438,
0.0036813600454479456,
-0.05018451437354088,
-0.03403155505657196,
-0.004993955139070749,
-0.03901759535074234,
-0.012773948721587658,
0.015908395871520042,
0.011188275180757046,
0.048267364501953125,
-0.04028305783867836,
0.007232171017676592,
-0.008455443195998669,
-0.0263719130307436,
0.014466739259660244,
-0.0033034931402653456,
0.010411220602691174,
-0.02118789590895176,
-0.08278748393058777,
-0.04998045414686203,
-0.005368180572986603,
0.032899510115385056,
0.029427744448184967,
0.006286915857344866,
0.03540416806936264,
0.001305512385442853,
-0.022879421710968018,
-0.009012958034873009,
-0.018840214237570763,
-0.027188243344426155,
-0.02617044188082218,
-0.043782033026218414,
-0.033974941819906235,
-0.0011326073436066508,
-0.032352689653635025,
0.017517615109682083,
0.007676182314753532,
-0.02028295211493969,
0.03755369037389755,
-0.02807316742837429,
-0.020138463005423546,
0.021085703745484352,
-0.013564192689955235,
0.00309967459179461,
-0.01916029118001461,
0.051595401018857956,
-0.013411012478172779,
-0.009923925623297691,
0.061503030359745026,
-0.047190021723508835,
0.014392107725143433,
0.003732130164280534,
-0.03812985494732857,
0.033995162695646286,
-0.002833713311702013,
-0.010566080920398235,
-0.05517652630805969,
0.021373501047492027,
0.0027566913049668074,
0.027333129197359085,
-0.028239373117685318,
0.05484064668416977,
-0.022509630769491196,
-0.014269682578742504,
0.039298027753829956,
-0.02955908514559269,
0.06277335435152054,
-0.003319470677524805,
0.00010986928100464866,
-0.02679448574781418,
0.06160538271069527,
0.0005698034656234086,
0.0026621390134096146,
0.022308552637696266,
-0.03749886155128479,
0.005053118336945772,
-0.013197467662394047,
-0.012600709684193134,
-0.04599059000611305,
-0.02072044461965561,
0.003117810469120741,
-0.06580547243356705,
-0.04061855375766754,
0.06110777705907822,
0.02034156769514084,
-0.01064672414213419,
-0.0022790555376559496,
0.028533661738038063,
0.012863507494330406,
-0.008270928636193275,
-0.04435261711478233,
-0.04451543092727661,
-0.09685344249010086,
0.03892437368631363,
-0.042737528681755066,
0.01820494793355465,
-0.032394956797361374,
0.015731986612081528,
0.014010298997163773,
-0.0033772194292396307,
-0.021296454593539238,
-0.00878901407122612,
0.009623564779758453,
0.037152212113142014,
0.03218486160039902,
-0.025292810052633286,
0.04368830844759941,
-0.05949721112847328,
0.029456747695803642,
0.043765779584646225,
-0.04516075924038887,
-0.006874363403767347,
-0.02312353439629078,
-0.11414387822151184,
0.00030132074607536197,
-0.03305056318640709,
0.01579768769443035,
-0.002322218846529722,
0.0664956122636795,
0.007963521406054497,
0.0015108886873349547,
-0.04406973719596863,
0.035482507199048996,
0.014078152365982533,
0.05643121525645256,
-0.0193665511906147,
0.009536408819258213,
0.01394833717495203,
-0.00592922605574131,
-0.013451635837554932,
0.007905449718236923,
-0.05219311639666557,
0.02270904742181301,
0.03288192301988602,
-0.009449396282434464,
-0.0563543327152729,
-0.007307770662009716,
0.05489911139011383,
0.03424687311053276,
0.02568303421139717,
0.05321120098233223,
-0.00035968341398984194,
0.030836325138807297,
-0.057051654905080795,
0.04937516525387764,
-0.021903494372963905,
0.0112984050065279,
-0.07058673352003098,
-0.03787614777684212,
-0.013822361826896667,
-0.005877099931240082,
-0.012990441173315048,
0.019392071291804314,
0.015078304335474968,
0.01893981359899044,
-0.04602859914302826,
-0.03847721591591835,
0.005254718475043774,
-0.03563506156206131,
-0.002642436185851693,
0.03206782042980194,
0.021481305360794067,
0.06194703280925751,
-0.0014601777074858546,
0.003424190217629075,
-0.05015392601490021,
-0.007018817588686943,
-0.029842032119631767,
-0.0012856352841481566,
0.0021971482783555984,
-0.04665188118815422,
-0.03612159565091133,
-0.07274463027715683,
0.028642402961850166,
0.00777642335742712,
0.01530439779162407,
-0.03199372440576553,
0.0342586413025856,
0.01904672011733055,
0.03244100883603096,
-0.04674827307462692,
-0.02052456885576248,
-0.023337705060839653,
-0.011714405380189419,
-0.02727038972079754,
0.018146507441997528,
0.02848881110548973,
0.07854443043470383,
0.05336827412247658,
-0.01737445779144764,
-0.025425080209970474,
-0.04900701716542244,
-0.0027317178901284933,
-0.011874699033796787,
0.056154247373342514,
-0.0005674256826750934,
-0.011303871870040894,
-0.0042403643019497395,
0.018785113468766212,
0.052186042070388794,
0.03232540562748909,
0.01044592633843422,
-0.011485239490866661,
-0.0035995144862681627,
-0.035569678992033005,
0.030139604583382607,
0.015341523103415966,
0.020589543506503105,
-0.04724125191569328,
0.05802909657359123,
-0.04685916006565094,
-0.005969110876321793,
-0.022851966321468353,
0.006927612237632275,
0.0007601648103445768,
-0.008559033274650574,
-0.009997921995818615,
0.01781197264790535,
-0.03720828890800476,
-0.027035096660256386,
-0.024395283311605453,
-0.023599592968821526,
0.05453203245997429,
0.058906182646751404,
0.01811417192220688,
0.0757240280508995,
0.04669559374451637,
-0.034489527344703674,
0.02882687747478485,
0.06132030859589577,
0.07484006881713867,
0.048012133687734604,
0.03370434045791626,
0.010301340371370316,
-0.06281029433012009,
-0.03473654389381409,
-0.015981078147888184,
0.029080970212817192,
-0.07391957938671112,
-0.026710789650678635,
0.0045709991827607155,
-0.0019814951810985804,
-0.016161026433110237,
0.018099555745720863,
-0.010054265148937702,
0.007889586500823498,
-0.012635807506740093,
0.02391061559319496,
-0.002107033971697092,
0.05771755427122116,
0.05438685417175293,
0.04597112536430359,
0.004358366131782532,
0.01031374093145132,
-0.04046730697154999,
0.030554696917533875,
0.027159687131643295,
-0.04549012333154678,
0.0038247264456003904,
0.013250963762402534,
0.030280327424407005,
-0.052204351872205734,
-0.07101819664239883,
0.0699755996465683,
0.040441058576107025,
-0.013305003754794598,
0.024709267541766167,
0.05064617469906807,
-0.007905601523816586,
-0.010424329899251461,
0.06525391340255737,
-0.0004937824560329318,
-0.022056270390748978,
-0.02139388397336006,
0.06932852417230606,
0.029241960495710373,
-0.013325683772563934,
0.0005870108725503087,
-0.008739611133933067,
0.034476812928915024,
0.007439879700541496,
-0.03822655230760574,
-0.010503475554287434,
-0.030851436778903008,
0.048633042722940445,
-0.06870122998952866,
0.09204099327325821,
0.012288101948797703,
0.027335451915860176,
0.03550463914871216,
-0.012661157175898552,
0.04554987698793411,
-0.016367701813578606,
0.011895934119820595,
0.028991490602493286,
-0.052971649914979935,
-0.016420254483819008,
-0.03907957300543785,
0.015366937965154648,
-0.06902828812599182,
-0.03964094817638397,
0.039184290915727615,
0.00433386443182826,
-0.017096633091568947,
0.009171588346362114,
-0.01111749280244112,
0.020261183381080627,
-0.0033145546913146973,
0.019842028617858887,
-0.03436773270368576,
0.005550254136323929,
0.04890366643667221,
0.05207354202866554,
0.06198178976774216,
-0.038080260157585144,
-0.00048452839837409556,
-0.03905105963349342,
-0.012310420162975788,
-0.05579875409603119,
-0.037636034190654755,
0.017842121422290802,
-0.003796911332756281,
0.015933267772197723,
0.024620652198791504,
-0.008405040018260479,
-0.022109171375632286,
-0.001964071299880743,
-0.006827606353908777,
-0.03539403900504112,
-0.0031697305385023355,
0.00683778990060091,
0.08449158817529678,
-0.05323546752333641,
0.053688593208789825,
0.06649290770292282,
-0.02747734636068344,
0.027921538800001144,
-0.001990617485716939,
-0.02786753512918949,
0.02772459387779236,
-0.05713605508208275,
-0.018736543133854866,
-0.02023281902074814,
0.0001998642401304096,
-0.017926933243870735,
-0.04026210308074951,
-0.011663248762488365,
0.02873757854104042,
0.0028389585204422474,
0.0010862211929634213,
0.04233625903725624,
0.03840359300374985,
-0.04448150470852852,
-0.022717135027050972,
0.013049089349806309,
0.0092237563803792,
-0.019739581272006035,
-0.013636262156069279,
0.05249052867293358,
-0.031331632286310196,
-0.0531708262860775,
-0.007527328096330166,
0.018289750441908836,
0.03860502690076828,
-0.015506639145314693,
-0.05951879546046257,
-0.007662098854780197,
0.024931741878390312,
-0.020700762048363686,
0.03193829581141472,
-0.05537435784935951,
0.038736555725336075,
0.00788290798664093,
0.026145294308662415,
-0.005658573471009731,
0.04125012829899788,
-0.0004998506628908217,
0.02502700872719288,
0.03940562903881073,
-0.002708313288167119,
-0.019165895879268646,
0.07220330089330673,
0.023014165461063385,
0.035124167799949646,
-0.016259677708148956,
-0.009327350184321404,
0.025711167603731155,
0.01942369155585766,
-0.0357515774667263,
0.009393572807312012,
0.01597471348941326,
0.04792502149939537,
0.0336708165705204,
-0.059816379100084305,
0.04253033921122551,
-0.03930797427892685,
0.014347170479595661,
0.06211704760789871,
-0.06831031292676926,
0.005989694967865944,
0.02100924402475357,
0.010437056422233582,
0.012400384061038494,
0.05775134265422821,
-0.012780227698385715,
-0.023338207975029945,
-0.07447603344917297,
0.023255130276083946,
-0.0409211739897728,
0.024753695353865623,
-0.009068076498806477,
-0.008129854686558247,
-0.03854329511523247,
0.017244650050997734,
-0.017064062878489494,
-0.02833283692598343,
-0.017605304718017578,
0.0688529834151268,
-0.000837702420540154,
-0.03878027945756912,
0.03096989542245865,
-0.07429008185863495,
-0.018789280205965042,
0.014074623584747314,
-0.008427909575402737,
-0.003375788452103734,
0.012298651039600372,
-0.05654645711183548,
0.022169409319758415,
0.021651681512594223,
-0.02837255969643593,
0.031305477023124695,
-0.06290381401777267,
-0.06196040287613869,
-0.044859156012535095,
-0.05409945547580719,
0.008495970629155636,
0.0663597583770752,
-0.009482086636126041,
-0.030452562496066093,
-0.06421446055173874,
-0.045098982751369476,
-0.030378324910998344,
-0.08126496523618698,
-0.08353953808546066,
-0.0011134058004245162,
-0.015772156417369843,
-0.012319773435592651,
0.032946065068244934,
-0.01334356889128685,
0.02264709211885929,
-0.02033611200749874,
0.04679544270038605,
0.016663067042827606,
-0.051606640219688416,
-0.041780438274145126,
0.01755773462355137,
0.017408831045031548,
0.006735354661941528,
0.005637560971081257,
0.035147614777088165,
0.008723518811166286,
-0.030292028561234474,
0.002286694711074233,
-0.04669128730893135,
-0.06497014313936234,
-0.008926469832658768,
-0.03030877746641636,
-0.04289156198501587,
-0.01263093389570713,
-0.048577211797237396,
0.03016774170100689,
0.032725073397159576,
0.012429475784301758,
0.01682185009121895,
-0.029728181660175323,
-0.004741219338029623,
0.046319447457790375,
0.0293128602206707,
-0.05031147226691246,
-0.02828684076666832,
-0.03766762092709541,
0.006644985172897577,
0.04423316568136215,
0.047845788300037384,
-0.002155663911253214,
0.017058173194527626,
0.046875134110450745,
-0.010239298455417156,
-0.03270033001899719,
-0.07302167266607285,
0.06358447670936584,
-0.028843270614743233,
-0.07717935740947723,
-0.01953037641942501,
-0.013401820324361324,
-0.011272643692791462,
-0.07538039982318878,
-0.02596745267510414,
-0.05005784332752228,
-0.02700292319059372,
0.014284641481935978,
0.03217776119709015,
-0.030335601419210434,
0.04334395378828049,
-0.032510075718164444,
-0.005717157851904631,
0.03209870308637619,
-0.06362743675708771,
-0.026240544393658638,
-0.03198375180363655,
0.05023134872317314,
0.027315637096762657,
-0.005478191189467907,
0.018796497955918312,
0.002375070471316576,
-0.059436436742544174,
-0.04418575018644333,
0.07699413597583771,
0.015359025448560715,
0.005209146533161402,
0.02893848717212677,
0.01625099591910839,
0.02606535702943802,
-0.020352136343717575,
-0.019324054941534996,
-0.03534863889217377,
0.033762190490961075,
0.023538287729024887,
-0.0003173074219375849,
0.0858716294169426,
0.07612770050764084,
0.040706343948841095,
-0.09869807213544846,
-0.011278173886239529,
0.03008023463189602,
0.04668937623500824,
-0.03862325847148895,
-0.04835142567753792,
0.00645364448428154,
0.042081013321876526,
-0.02292102575302124,
0.01580825448036194,
-0.025718890130519867,
0.007702885661274195,
0.023743843659758568,
0.020998116582632065,
0.01204688474535942,
-0.005006643012166023,
-0.03575905039906502,
-0.02011300064623356,
-0.06495970487594604,
-0.02579401433467865,
0.061887819319963455,
0.07144569605588913,
-0.04040933772921562,
-0.0026244528125971556,
-0.001839194679632783,
-0.024401241913437843,
0.07676707953214645,
-0.043748144060373306,
0.02151934616267681,
0.016633406281471252,
0.0039029577746987343,
-0.053857408463954926,
0.018513191491365433,
-0.00801768433302641,
-0.015146031975746155,
-0.04926697537302971,
-0.038685284554958344,
-0.012647240422666073,
0.006150440312922001,
-0.057075537741184235,
-0.014305016957223415,
0.03541182726621628,
0.03587302565574646,
-0.05840679258108139,
-0.01866711862385273,
-0.029496965929865837,
-0.03251603990793228,
0.030412260442972183,
-0.01374126598238945,
-0.04137662425637245,
0.00010691873467294499,
0.018982021138072014,
0.03248301520943642,
-0.08119885623455048,
0.00831284373998642,
0.0009359270334243774,
0.015296345576643944,
0.01179675292223692,
0.0008467300212942064,
-0.015229244716465473,
0.028906388208270073,
0.012508399784564972,
-0.013595866039395332,
0.015265936963260174,
0.01173819974064827,
-0.002904215594753623,
0.004220382776111364,
0.03841106593608856,
0.01996086910367012,
0.010583868250250816,
0.05251654237508774,
0.0028214631602168083,
-0.0269475057721138,
0.014053630642592907,
-0.007374660577625036,
-0.005314664915204048,
-0.016952963545918465,
-0.024330759420990944,
0.0813649594783783,
-0.050502926111221313,
-0.02711564488708973,
0.009296668693423271,
0.00039482078864239156,
-0.0009950976818799973
] |
<p>I have a ball of metal about an inch in diameter and a concave disc of another metal (which is magnetic) around the ring of the disc (about $12 {\rm mm}$ in diameter). I don't know which metals they are. The ball is not magnetic on its own. That is <a href="http://en.wikipedia.org/wiki/Paramagnetism" rel="nofollow">paramagnetism</a>, right?</p>
<p>The magnetic ring is strongly attracted to the surface of the ball, '<em>sticking</em>' to it. However, I can stick a paperclip on the opposite side of the ball as if it has become magnetic itself, until I remove the magnetic ring from the ball.</p>
<p>When I wave the paperclip the same distance from only the ring itself, I feel no force at that distance.</p>
<p>Has the strong magnetic field of the ring caused a temporary magnetic alignment through the metal of the ball, allowing the paperclip to be attracted to it while the ring remains?</p> | g6587 | [
0.03692144155502319,
0.025103392079472542,
0.0011465313145890832,
-0.03461776301264763,
0.030818326398730278,
0.04548158496618271,
0.00299593573436141,
0.0029520464595407248,
-0.024123430252075195,
0.02813657559454441,
-0.034041665494441986,
0.019061582162976265,
-0.03590889275074005,
-0.05560741946101189,
0.04262659326195717,
0.0639176294207573,
0.0507766492664814,
-0.00012502142635639757,
0.058033622801303864,
0.020216476172208786,
-0.0007755852420814335,
0.011775842867791653,
-0.0005243950290605426,
-0.01688043586909771,
-0.009879075922071934,
-0.018457552418112755,
0.03371284902095795,
-0.05948369577527046,
0.0020810554269701242,
-0.026145093142986298,
-0.04178245738148689,
0.0012336965883150697,
0.03518061339855194,
-0.02385829947888851,
-0.012193763628602028,
-0.032968904823064804,
0.03410285711288452,
0.008698280900716782,
-0.033141300082206726,
0.008888554759323597,
-0.012591938488185406,
0.03551386296749115,
0.022843271493911743,
-0.022882090881466866,
0.05387376621365547,
-0.014530861750245094,
-0.03424769639968872,
0.027308164164423943,
-0.0007185937138274312,
-0.026203207671642303,
-0.05846618115901947,
-0.013181873597204685,
0.012229823507368565,
0.007935593836009502,
-0.006030015181750059,
0.054594364017248154,
0.03674490377306938,
-0.0005537964752875268,
0.08420507609844208,
0.0410238653421402,
-0.034638650715351105,
0.033084768801927567,
0.0017546742456033826,
-0.013036728836596012,
-0.0010199033422395587,
-0.03425829857587814,
-0.035782281309366226,
0.005786255467683077,
-0.023196976631879807,
0.0007560916128568351,
0.00028485379880294204,
0.013556791469454765,
0.00013277989637572318,
-0.028195083141326904,
-0.004646096844226122,
0.025320233777165413,
0.018052199855446815,
-0.05486784502863884,
-0.0023743899073451757,
-0.03500426560640335,
-0.01799905113875866,
0.00901147723197937,
-0.011051388457417488,
0.025706252083182335,
0.03218957036733627,
0.003978334367275238,
-0.035036008805036545,
-0.05026581510901451,
-0.04063836485147476,
0.01047312468290329,
0.04149326682090759,
0.02062976360321045,
0.04343418404459953,
0.05923895165324211,
-0.016177043318748474,
-0.025810612365603447,
-0.013897031545639038,
0.0930207297205925,
-0.036753345280885696,
0.01848713867366314,
-0.016610389575362206,
-0.0009953394765034318,
0.029374057427048683,
0.02861584909260273,
-0.003025333397090435,
0.0242906641215086,
0.004671940580010414,
0.009786639362573624,
0.026445403695106506,
0.03109508752822876,
-0.031694065779447556,
-0.021257856860756874,
-0.03512644022703171,
-0.006076105870306492,
0.018229562789201736,
0.027441008016467094,
0.003883386729285121,
-0.021514873951673508,
-0.043220389634370804,
0.05709866061806679,
0.03055078536272049,
-0.035089362412691116,
-0.018678242340683937,
0.08794524520635605,
-0.051624130457639694,
-0.031284768134355545,
0.026121782138943672,
-0.011665640398859978,
0.011753063648939133,
0.014222131110727787,
0.01146454643458128,
0.002837307518348098,
0.07349233329296112,
0.002231878461316228,
-0.010801161639392376,
-0.015455895103514194,
0.027286415919661522,
-0.0035513904877007008,
-0.03329949826002121,
-0.010779025964438915,
0.026346828788518906,
-0.06202111393213272,
0.025618689134716988,
-0.0302745271474123,
-0.05131993442773819,
0.0631553903222084,
-0.03499811887741089,
0.022630520164966583,
0.042068298906087875,
0.0549568310379982,
0.03758380934596062,
0.018152955919504166,
-0.04654017090797424,
-0.09213663637638092,
0.01049137208610773,
0.017499012872576714,
0.030545314773917198,
-0.006862793583422899,
0.028802301734685898,
-0.05607645958662033,
0.08147686719894409,
-0.027279721572995186,
0.05117415636777878,
-0.02032218873500824,
-0.06751325726509094,
0.03483233228325844,
0.0571514330804348,
0.017106838524341583,
-0.05487266555428505,
0.020774129778146744,
-0.021733814850449562,
-0.003199539612978697,
0.009717699140310287,
0.019056418910622597,
0.017855500802397728,
-0.009596371091902256,
0.04113825783133507,
-0.043507643043994904,
0.047796353697776794,
-0.01568719558417797,
0.028581924736499786,
-0.007060387171804905,
0.039311185479164124,
0.0057241846807301044,
0.004052747040987015,
-0.02706262655556202,
-0.02420920319855213,
0.06732890009880066,
-0.04413596913218498,
-0.026946542784571648,
-0.027871238067746162,
-0.032758887857198715,
-0.05605781823396683,
0.05759276822209358,
0.0019017403246834874,
-0.04976608604192734,
-0.0023562083952128887,
-0.006083856802433729,
-0.0307136420160532,
-0.06736612319946289,
-0.014781276695430279,
0.00410078139975667,
-0.02538030408322811,
0.0029359287582337856,
-0.04635471850633621,
-0.04162023589015007,
0.027124473825097084,
0.014278692193329334,
0.04986806958913803,
0.04417511448264122,
0.022689376026391983,
0.04674554243683815,
-0.03224649280309677,
-0.02783304639160633,
-0.026294942945241928,
0.036074962466955185,
0.017778394743800163,
0.043316442519426346,
-0.044529989361763,
0.04893854260444641,
-0.005217030178755522,
0.05740271508693695,
0.030680730938911438,
0.0069482596591115,
-0.04446377977728844,
-0.01210738904774189,
-0.01909492537379265,
0.05012313276529312,
-0.03396596759557724,
0.02823585271835327,
-0.027514902874827385,
-0.014928160235285759,
0.011341020464897156,
0.0159600917249918,
0.037992212921381,
0.060517214238643646,
0.01896398514509201,
-0.021284397691488266,
-0.005329051520675421,
-0.05478363484144211,
0.009348873980343342,
-0.04405529424548149,
-0.031393278390169144,
0.008012971840798855,
-0.01774398423731327,
-0.06146939843893051,
0.08240298181772232,
-0.0030453710351139307,
0.01679251343011856,
0.018710976466536522,
0.08140454441308975,
-0.06802093982696533,
-0.03160296380519867,
0.04824614152312279,
-0.01751134730875492,
-0.008877313695847988,
-0.07000323385000229,
0.02636561542749405,
-0.07217497378587723,
-0.023295249789953232,
-0.01899554207921028,
-0.05051940307021141,
0.047360144555568695,
0.028622416779398918,
-0.038804635405540466,
-0.0168932992964983,
-0.04711253196001053,
0.023993544280529022,
-0.0018162393243983388,
0.004121345467865467,
-0.02359597012400627,
0.022588007152080536,
0.024941440671682358,
0.01707569696009159,
-0.010059261694550514,
0.027145523577928543,
0.007205306086689234,
-0.01654120348393917,
0.01780278980731964,
0.007463124115020037,
0.026546664535999298,
0.06838411837816238,
-0.05625529959797859,
-0.04750009998679161,
0.0019289868650957942,
-0.04297777637839317,
-0.03305933624505997,
-0.011196671053767204,
0.011954241432249546,
-0.016156839206814766,
-0.0045044333674013615,
0.03248467296361923,
0.07268765568733215,
-0.0038740357849746943,
0.012708194553852081,
0.06342573463916779,
-0.017267026007175446,
0.056126341223716736,
-0.008852707222104073,
0.03115733154118061,
0.04008333012461662,
0.0026347592938691378,
-0.05932259187102318,
-0.016140228137373924,
0.011346024461090565,
0.03698473051190376,
-0.0247616246342659,
-0.048449065536260605,
0.024542871862649918,
0.008244228549301624,
0.015919292345643044,
0.07218638062477112,
0.04003328084945679,
-0.015081828460097313,
-0.026638254523277283,
-0.006482255179435015,
-0.0028440358582884073,
0.057503875344991684,
-0.022088421508669853,
0.040806882083415985,
-0.021757962182164192,
-0.032481346279382706,
0.0008360220235772431,
-0.06029884144663811,
0.07875537127256393,
-0.015663672238588333,
-0.022673550993204117,
-0.0448203943669796,
-0.007296077441424131,
-0.05002112314105034,
-0.005179882515221834,
-0.02415790967643261,
-0.026394004002213478,
-0.019895188510417938,
-0.08993441611528397,
-0.01581450365483761,
0.017317213118076324,
0.06266158819198608,
-0.003902384778484702,
0.032910704612731934,
0.04744825139641762,
-0.025902211666107178,
-0.045619651675224304,
-0.052084870636463165,
0.0012659651692956686,
0.13035134971141815,
0.020264092832803726,
-0.018924390897154808,
0.008725553750991821,
0.03673544153571129,
0.037493620067834854,
-0.0131293386220932,
0.026174260303378105,
-0.014579796232283115,
0.0385521724820137,
0.023140860721468925,
0.012142695486545563,
-0.0033648579847067595,
-0.020018933340907097,
-0.028788762167096138,
-0.05602153763175011,
0.00303275347687304,
0.010804105550050735,
-0.03142159432172775,
-0.0018514130497351289,
0.07790662348270416,
-0.020695021376013756,
-0.021792760118842125,
-0.0030329502187669277,
0.0073209828697144985,
-0.02008109912276268,
-0.037213146686553955,
-0.024631017819046974,
0.02788158878684044,
0.030773142352700233,
0.006698577664792538,
0.03792586177587509,
0.00998701248317957,
-0.04545975849032402,
0.0007414089632220566,
-0.012142634019255638,
0.07701746374368668,
-0.0041181957349181175,
0.08548260480165482,
0.0044907438568770885,
0.015705440193414688,
-0.029839955270290375,
-0.028783757239580154,
0.015625756233930588,
-0.02771672047674656,
-0.011385416612029076,
0.04375739395618439,
0.022647248581051826,
0.011556282639503479,
-0.020760448649525642,
0.0054674213752150536,
-0.024955660104751587,
0.002199916634708643,
0.06242235004901886,
-0.0250912643969059,
0.031809739768505096,
-0.02190621942281723,
-0.04307467117905617,
-0.010373548604547977,
0.009316092357039452,
-0.012566745281219482,
0.008151350542902946,
-0.009691053070127964,
-0.03176431357860565,
-0.04406863823533058,
0.021786915138363838,
-0.0347265750169754,
-0.07544134557247162,
-0.02022973634302616,
0.006847619544714689,
-0.025527264922857285,
0.013883458450436592,
0.09313055127859116,
-0.03148309886455536,
-0.049001529812812805,
-0.028018005192279816,
0.05572604387998581,
0.06595567613840103,
-0.011922233738005161,
-0.030632086098194122,
0.04487212002277374,
0.008858982473611832,
0.014394540339708328,
0.030053628608584404,
0.0028023580089211464,
-0.003093858016654849,
0.05828898400068283,
-0.014440711587667465,
-0.01074123289436102,
-0.039112139493227005,
0.0338410846889019,
-0.06007308512926102,
0.018285445868968964,
0.06401824206113815,
0.02609724923968315,
0.034089431166648865,
-0.003962664864957333,
0.028209567070007324,
-0.0165163055062294,
-0.047245923429727554,
0.025312941521406174,
-0.0490708127617836,
0.020908912643790245,
-0.06948694586753845,
-0.07367121428251266,
-0.04115037992596626,
0.007206680253148079,
-0.013146133162081242,
-0.014222783036530018,
-0.026544621214270592,
-0.04476900026202202,
-0.041455939412117004,
-0.012503430247306824,
-0.024037925526499748,
-0.02165050059556961,
0.0019108694978058338,
-0.004597934428602457,
-0.019909143447875977,
-0.004297045525163412,
-0.0024270506110042334,
-0.03096582368016243,
0.021920597180724144,
-0.08160953223705292,
-0.011727133765816689,
-0.01981988362967968,
0.03921334818005562,
0.0501200295984745,
0.016607780009508133,
0.0504494309425354,
0.06551085412502289,
0.0056473431177437305,
0.03176547959446907,
-0.008186962455511093,
0.048999492079019547,
-0.08071821928024292,
-0.025914251804351807,
0.06005005165934563,
0.038499586284160614,
-0.01869136095046997,
0.01967395469546318,
0.0009556571021676064,
0.0020599872805178165,
0.05572545900940895,
0.016844259575009346,
0.018309764564037323,
0.02491423860192299,
-0.05519270524382591,
0.010385067202150822,
-0.01764829456806183,
-0.024292806163430214,
-0.053787678480148315,
-0.002778131514787674,
0.008064168505370617,
-0.012967171147465706,
-0.047909125685691833,
-0.026660311967134476,
-0.018361808732151985,
0.050554659217596054,
0.05389280617237091,
-0.042675647884607315,
0.01792929694056511,
-0.039866797626018524,
0.01239620428532362,
0.05264142155647278,
0.06441754847764969,
-0.06176646053791046,
0.03415495902299881,
0.055114198476076126,
0.019098496064543724,
-0.015715479850769043,
0.04401364177465439,
-0.003963907714933157,
0.032667338848114014,
0.0020122244022786617,
0.026530781760811806,
-0.004480946343392134,
-0.0024841148406267166,
0.01036131288856268,
-0.06725350767374039,
-0.0024914254900068045,
-0.014726036228239536,
-0.061933208256959915,
0.0005406903219409287,
0.033411409705877304,
0.06416438519954681,
0.010387484915554523,
0.0010864785872399807,
0.06848261505365372,
0.025941992178559303,
0.0013584726257249713,
-0.09418772161006927,
0.05985833704471588,
-0.05447366088628769,
-0.024462958797812462,
0.028559856116771698,
0.0482398122549057,
-0.07807941734790802,
0.06303681433200836,
0.03902518376708031,
-0.01377834565937519,
-0.02317437343299389,
-0.0015652661677449942,
-0.014067670330405235,
0.06051948666572571,
-0.054251957684755325,
0.031989045441150665,
0.0306496974080801,
-0.0122990682721138,
0.0536583811044693,
0.029505152255296707,
0.044970933347940445,
-0.02728482522070408,
-0.025189721956849098,
0.033403173089027405,
-0.046103883534669876,
0.08911502361297607,
-0.03709835186600685,
-0.04201849177479744,
0.05006725713610649,
-0.01009353157132864,
0.03305501118302345,
-0.032437145709991455,
-0.03308236226439476,
0.025483878329396248,
-0.041670847684144974,
0.01544458419084549,
-0.011033573187887669,
-0.011639268137514591,
0.02530369721353054,
0.009904708713293076,
0.048855025321245193,
-0.05956908315420151,
-0.008270522579550743,
-0.02633809670805931,
0.020054703578352928,
0.03682927414774895,
0.019379625096917152,
0.02676919661462307,
-0.0562637597322464,
0.02274448052048683,
-0.03156491741538048,
-0.06742110103368759,
0.013779500499367714,
0.04360686242580414,
-0.09621560573577881,
-0.08568891137838364,
-0.0006961653125472367,
-0.025284240022301674,
-0.024950018152594566,
-0.03915154188871384,
0.04608386754989624,
-0.061449334025382996,
0.01697038672864437,
-0.048713624477386475,
0.07888789474964142,
-0.007510421331971884,
-0.042287636548280716,
0.04929894581437111,
0.01817444898188114,
0.006312188226729631,
0.008607493713498116,
-0.017531635239720345,
-0.003946642857044935,
0.012043580412864685,
0.005722071509808302,
-0.042285069823265076,
0.024826252833008766,
-0.016363495960831642,
0.016662759706377983,
-0.02878587134182453,
0.0019488285761326551,
0.029673688113689423,
0.008597059175372124,
-0.035495925694704056,
-0.07174772024154663,
-0.06848156452178955,
-0.016232388094067574,
-0.03401826694607735,
-0.01707763411104679,
-0.05528450757265091,
-0.03843478485941887,
-0.056939709931612015,
-0.02427617274224758,
-0.037993479520082474,
0.022993169724941254,
-0.00623592734336853,
0.05675707384943962,
-0.025169167667627335,
0.016746671870350838,
-0.04525865614414215,
0.0316523052752018,
0.04100074991583824,
-0.01184061449021101,
0.028575818985700607,
-0.006686044856905937,
-0.011938600800931454,
0.03304572403430939,
-0.007553990930318832,
0.0028076092712581158,
0.021165527403354645,
-0.006958220154047012,
-0.00834857951849699,
0.008466922678053379,
-0.03263549879193306,
0.029558954760432243,
-0.010126409120857716,
0.012635152786970139,
-0.049524251371622086,
0.031086640432476997,
-0.029865264892578125,
0.06883622705936432,
-0.03918161615729332,
-0.007619543932378292,
-0.011232568882405758,
0.029487883672118187,
-0.028759071603417397,
-0.03111204132437706,
-0.0482669435441494,
-0.08020544052124023,
-0.009663550183176994,
0.019628215581178665,
0.01227578241378069,
-0.06294813007116318,
-0.027337532490491867,
-0.046865276992321014,
0.03418926149606705,
-0.051158055663108826,
0.029600581154227257,
0.026612311601638794,
-0.0003009685024153441,
0.03008207306265831,
0.012648154981434345,
-0.015813278034329414,
0.046829815953969955,
0.01647244021296501,
-0.062248747795820236,
0.0406726635992527,
0.0010552876628935337,
-0.021368199959397316,
-0.029822053387761116,
0.016201982274651527,
-0.018210727721452713,
0.06315738707780838,
0.03018942102789879,
-0.014915470033884048,
0.02562570571899414,
0.00813624169677496,
0.05187491327524185,
0.08545195311307907,
-0.005583273712545633,
-0.009384174831211567,
0.03753073513507843,
0.021463682875037193,
0.04259888455271721,
-0.009618350304663181,
-0.004703226033598185,
0.04776636138558388,
0.007624538615345955,
-0.027979237958788872,
0.05730896443128586,
0.033214736729860306,
-0.062385547906160355,
0.04052329063415527,
-0.035934653133153915,
0.016149289906024933,
0.008094711229205132,
0.03800322115421295,
0.00540993083268404,
-0.027365580201148987,
-0.010988363064825535,
0.040156081318855286,
-0.02720165066421032,
-0.00885473657399416,
0.02517656609416008,
-0.020448539406061172,
-0.03439514711499214,
0.038619644939899445,
-0.009916462004184723,
-0.07105923444032669,
-0.01112326793372631,
-0.048422638326883316,
0.0058197928592562675,
-0.010103910230100155,
0.029188914224505424,
0.045719780027866364,
0.003667447017505765,
-0.05856750160455704,
-0.0633266493678093,
-0.04676501452922821,
-0.030574919655919075,
-0.04299839958548546,
-0.00956995040178299,
0.010925550945103168,
0.025312993675470352,
-0.02242811769247055,
-0.0026298542506992817,
-0.045168187469244,
-0.017427176237106323,
-0.015067809261381626,
-0.005702604539692402,
0.006428082473576069,
-0.05465012043714523,
0.07953248918056488,
0.003330900566652417,
0.0023938787635415792,
-0.012245086953043938,
-0.012947923503816128,
-0.045550744980573654,
0.034826721996068954,
0.028130266815423965,
-0.0396198034286499,
-0.050771184265613556,
0.02644849568605423,
0.04527800530195236,
-0.01630144752562046,
-0.03051183931529522,
-0.051081784069538116,
0.006501575466245413,
-0.012944387272000313,
0.06284426152706146,
0.045925382524728775,
-0.043198153376579285,
0.01911282166838646
] |
<p>If we are travelling with the speed of light, can we see whats behind us(like if we are moving away from earth can we able see the earth)? And how we see the things that we are approaching with speed of light? Does the things look like fast forwarding because we are moving and the source also sending photons with the same light speed.</p> | g6588 | [
-0.012285040691494942,
0.04067358002066612,
0.029355963692069054,
0.031156688928604126,
-0.0017793932929635048,
-0.027856187894940376,
0.023242518305778503,
-0.019602537155151367,
-0.03855299949645996,
-0.04179483652114868,
0.08516459912061691,
0.05295531079173088,
0.0786375030875206,
0.02897612750530243,
-0.010602188296616077,
-0.04554101079702377,
0.07140840590000153,
-0.04288717359304428,
-0.013964757323265076,
0.007041282951831818,
0.03536636754870415,
0.059680961072444916,
-0.00863899476826191,
-0.012018438428640366,
-0.05584866926074028,
0.015687022358179092,
-0.001767896581441164,
-0.03887966647744179,
-0.006441799458116293,
-0.028078902512788773,
0.06012842804193497,
-0.05652111396193504,
0.005963693372905254,
-0.010414081625640392,
0.04831840470433235,
-0.010070300661027431,
0.039161890745162964,
0.016433099284768105,
-0.012905195355415344,
-0.013245471753180027,
-0.015031064860522747,
-0.031825412064790726,
0.014948002994060516,
-0.02176687680184841,
0.05819685012102127,
0.016652746126055717,
0.0291554294526577,
-0.027995986863970757,
0.0012728993315249681,
0.022642605006694794,
-0.06197275593876839,
0.007225325331091881,
-0.0674145519733429,
0.01991814747452736,
0.038637205958366394,
-0.01241739746183157,
0.008417101576924324,
-0.04849022626876831,
0.1303674727678299,
-0.007259661797434092,
-0.03553728386759758,
0.011148101650178432,
0.053765907883644104,
0.004601227585226297,
0.07297828793525696,
-0.02952631749212742,
-0.04831709712743759,
-0.022428762167692184,
-0.006338817998766899,
-0.032097477465867996,
0.04992257058620453,
0.017656248062849045,
-0.09946601837873459,
-0.04526375234127045,
0.03560436889529228,
0.004425080493092537,
0.08426359295845032,
-0.016360990703105927,
0.0027237723115831614,
0.05421783775091171,
-0.03184293210506439,
-0.05287795141339302,
-0.027351537719368935,
-0.02740531601011753,
0.0047792838886380196,
0.017761731520295143,
-0.0046697803772985935,
0.027945782989263535,
-0.009143326431512833,
-0.0031356588006019592,
0.02320760488510132,
-0.025460444390773773,
0.07144983857870102,
0.07396145910024643,
-0.01996760629117489,
0.008889994584023952,
-0.027136685326695442,
0.03453851863741875,
0.009564907290041447,
-0.012410181574523449,
-0.031823981553316116,
0.02197258174419403,
0.031071862205863,
0.04980718716979027,
0.015431070700287819,
-0.013241381384432316,
-0.009244147688150406,
-0.02057424560189247,
-0.020545605570077896,
-0.02304702438414097,
-0.024533463642001152,
-0.09491664171218872,
-0.011664101853966713,
0.013270615600049496,
-0.054788194596767426,
-0.05443701520562172,
0.04893052205443382,
0.03935234248638153,
0.032393112778663635,
0.07135750353336334,
0.045718833804130554,
0.033260688185691833,
-0.006264411378651857,
-0.015865091234445572,
0.01248987764120102,
0.0015102742472663522,
-0.01776111125946045,
-0.031193574890494347,
-0.010175452567636967,
0.0089912423864007,
-0.0035911868326365948,
0.04728803038597107,
-0.007132594473659992,
0.06651359051465988,
-0.02482665702700615,
-0.016568053513765335,
0.03329624608159065,
0.022359531372785568,
0.017237527295947075,
0.04762709513306618,
0.05030104145407677,
-0.04733458161354065,
0.0030493757221847773,
-0.012064739130437374,
-0.023623518645763397,
-0.015635935589671135,
0.006591421086341143,
0.022346507757902145,
-0.009090017527341843,
0.02685554139316082,
-0.007854419760406017,
0.05251915752887726,
0.036171428859233856,
0.021273745223879814,
0.012536856345832348,
-0.04586155340075493,
0.001411834149621427,
0.004937308374792337,
-0.04315274581313133,
-0.010521998628973961,
0.030519889667630196,
-0.013247201219201088,
-0.0014411439187824726,
-0.017148597165942192,
-0.022807307541370392,
0.0018496281700208783,
0.006081173662096262,
-0.010365014895796776,
0.01810392737388611,
0.03366706147789955,
-0.0016712922370061278,
0.04746844246983528,
0.041825685650110245,
0.03151679411530495,
0.028654729947447777,
-0.03455433249473572,
0.03427693620324135,
-0.017038777470588684,
-0.07021289318799973,
0.026696182787418365,
-0.03458913043141365,
-0.03309257701039314,
-0.023483218625187874,
-0.017371580004692078,
-0.026705820113420486,
-0.03257083520293236,
-0.04798080027103424,
-0.0019200325477868319,
-0.028779612854123116,
-0.002793902298435569,
0.02531610243022442,
-0.0735231339931488,
-0.04628543183207512,
0.04072962701320648,
0.004450054373592138,
-0.06129210442304611,
0.008980697952210903,
-0.003992633894085884,
0.02518785558640957,
-0.02701638452708721,
-0.022879712283611298,
0.08193893730640411,
-0.005117734428495169,
-0.006240833085030317,
0.013749190606176853,
-0.022058574482798576,
0.028717225417494774,
0.018483884632587433,
0.01216850895434618,
-0.026055369526147842,
0.08576103299856186,
-0.033303793519735336,
0.047091465443372726,
0.027790671214461327,
0.005275862757116556,
0.006043160334229469,
-0.044016387313604355,
0.007271622773259878,
0.0003956771979574114,
0.011117535643279552,
-0.00507009495049715,
-0.018400663509964943,
-0.03132976219058037,
-0.06009695306420326,
-0.0521194227039814,
-0.0030604039784520864,
-0.052111320197582245,
-0.017092833295464516,
0.05007033050060272,
0.09123250842094421,
-0.002294837264344096,
0.012292914092540741,
0.02928834967315197,
0.005725450348109007,
0.022282637655735016,
-0.017931414768099785,
-0.0328756682574749,
0.015036288648843765,
0.003526190761476755,
0.0007774839177727699,
0.006480307783931494,
-0.038552526384592056,
-0.056821558624506,
-0.003450824413448572,
0.02456493116915226,
-0.02904278039932251,
0.03129177540540695,
0.0005270089022815228,
0.009745562449097633,
0.038729384541511536,
0.041852034628391266,
-0.004738413263112307,
-0.031906336545944214,
0.06808366626501083,
0.0036961750593036413,
-0.0335061252117157,
-0.01925780437886715,
0.052529796957969666,
-0.056476518511772156,
-0.038647208362817764,
-0.04061693325638771,
0.010545175522565842,
-0.07240945845842361,
0.013628785498440266,
-0.01035362295806408,
-0.006654858123511076,
0.022368017584085464,
0.020986326038837433,
-0.03571388125419617,
0.000410825276048854,
-0.02747369557619095,
0.003161634784191847,
0.013419361785054207,
-0.017760751768946648,
-0.021538304165005684,
0.012554951943457127,
0.04667016491293907,
-0.006343667861074209,
-0.02127741277217865,
0.001717985956929624,
-0.018774772062897682,
-0.01841661147773266,
-0.027126068249344826,
-0.02479317970573902,
-0.005150859244167805,
-0.06366457790136337,
0.01906689815223217,
0.005437843967229128,
0.003929647151380777,
0.008639970794320107,
-0.056658945977687836,
0.0032934544142335653,
0.07707080245018005,
-0.01708160527050495,
-0.020669834688305855,
0.03794189915060997,
0.06994213908910751,
-0.030835436657071114,
-0.006522257346659899,
-0.016278861090540886,
0.04017498344182968,
-0.02920745126903057,
-0.029509849846363068,
-0.010372117161750793,
0.023092785850167274,
0.0037664971314370632,
-0.08065153658390045,
-0.005342874210327864,
0.02900576964020729,
-0.04371245577931404,
0.03121849335730076,
0.0430995337665081,
-0.04818115383386612,
0.010302691720426083,
0.041368186473846436,
-0.01408932451158762,
0.008177360519766808,
0.03035467490553856,
-0.007905964739620686,
0.043557751923799515,
0.03370962664484978,
-0.0032194643281400204,
-0.03607671707868576,
-0.02019345387816429,
0.018149491399526596,
0.02652653679251671,
0.019761912524700165,
-0.014758937060832977,
-0.06425957381725311,
-0.023751629516482353,
0.03807096928358078,
-0.01935851387679577,
-0.05342184752225876,
0.021458759903907776,
-0.03931109979748726,
0.021341722458600998,
0.02830173447728157,
0.028050197288393974,
0.06733126193284988,
-0.011214902624487877,
0.06547737866640091,
-0.00032687425846233964,
-0.06816688925027847,
0.034258026629686356,
0.007087079808115959,
-0.015222005546092987,
-0.027716081589460373,
0.0009914010297507048,
-0.05805884301662445,
0.00526256812736392,
0.05674009770154953,
0.016525860875844955,
-0.03600076213479042,
-0.05736859515309334,
0.014610526151955128,
0.050255708396434784,
0.0026194588281214237,
0.006060214713215828,
0.04840279370546341,
-0.057529017329216,
-0.05356854945421219,
-0.004546351730823517,
0.07025640457868576,
0.0032054136972874403,
0.00531936576589942,
-0.03610546514391899,
-0.0048678722232580185,
-0.004117776174098253,
0.02939561940729618,
0.02092379331588745,
0.0003982564085163176,
-0.008073625154793262,
-0.0544930025935173,
0.02881624363362789,
-0.013995240442454815,
-0.025488050654530525,
0.018011249601840973,
-0.029726166278123856,
-0.04475896432995796,
0.012176153250038624,
0.014733826741576195,
0.032027438282966614,
0.053600478917360306,
-0.015799539163708687,
0.023613426834344864,
0.025053951889276505,
0.012371263466775417,
-0.09106585383415222,
-0.0018866588361561298,
-0.010120929218828678,
0.02683156728744507,
-0.05891024321317673,
0.019710272550582886,
-0.027038438245654106,
-0.02499150112271309,
0.03093571960926056,
0.03441610187292099,
0.020931299775838852,
-0.02789740450680256,
0.023945624008774757,
0.004357184749096632,
0.04286065697669983,
0.005109160207211971,
0.019726285710930824,
-0.04169850051403046,
-0.029624955728650093,
-0.026241393759846687,
-0.05710857734084129,
-0.014690914191305637,
-0.01087888889014721,
-0.05518596991896629,
-0.011978456750512123,
-0.05077749863266945,
0.017005708068609238,
-0.018483934924006462,
0.047153666615486145,
0.006534029729664326,
-0.011031586676836014,
0.039975348860025406,
-0.0046016378328204155,
-0.0041807303205132484,
0.0473051518201828,
0.034966208040714264,
-0.019025351852178574,
-0.07518620789051056,
0.07647128403186798,
0.11721419543027878,
-0.05454917997121811,
-0.09123428165912628,
0.02028415910899639,
-0.00848984532058239,
-0.0034050841350108385,
0.03441484272480011,
0.0805530846118927,
0.013623770326375961,
0.041838452219963074,
-0.002585437847301364,
-0.0062179905362427235,
0.0381755493581295,
-0.001275973510928452,
0.027915898710489273,
0.036604996770620346,
0.05656077340245247,
0.005693537648767233,
-0.04756706953048706,
0.06765095144510269,
0.005459097679704428,
-0.009681252762675285,
-0.0023973770439624786,
-0.028232432901859283,
-0.029244186356663704,
0.018872149288654327,
-0.0551571361720562,
-0.013616696000099182,
-0.0008265720680356026,
0.03375519439578056,
-0.05369437485933304,
-0.003876336384564638,
0.006674467585980892,
-0.009247205220162868,
0.01817507855594158,
0.03295516595244408,
0.08870721608400345,
-0.014233045279979706,
-0.03382306173443794,
0.015520645305514336,
-0.07248193025588989,
-0.010486937128007412,
-0.02801709808409214,
0.024082111194729805,
-0.03402046859264374,
-0.004226159304380417,
-0.02121591381728649,
0.006333599332720041,
-0.015195953659713268,
-0.00911630131304264,
-0.05192386358976364,
0.016701029613614082,
-0.036420345306396484,
-0.016208922490477562,
0.014972888864576817,
0.012002835050225258,
0.02448786050081253,
-0.06437740474939346,
-0.047492533922195435,
0.0008402220555581152,
-0.011645056307315826,
0.04428471624851227,
-0.02250005304813385,
-0.06586232036352158,
-0.022639410570263863,
-0.020095737650990486,
0.004475120455026627,
-0.024826541543006897,
-0.0815131664276123,
0.051656849682331085,
0.05438646674156189,
0.04323386773467064,
-0.028406359255313873,
0.017340730875730515,
-0.008957906626164913,
0.0028310560155659914,
0.007378982845693827,
0.010452077724039555,
0.047330040484666824,
0.03658280521631241,
0.06088459864258766,
-0.034195464104413986,
-0.02282072976231575,
0.06956484913825989,
-0.048783078789711,
0.03628457710146904,
-0.05428819730877876,
-0.03951997682452202,
-0.03175745904445648,
-0.0692441388964653,
-0.021529357880353928,
-0.000857968523632735,
0.038296494632959366,
-0.0326862633228302,
-0.020073311403393745,
0.015736306086182594,
0.05531809851527214,
-0.004638642072677612,
0.0386575311422348,
-0.04655630141496658,
-0.046282727271318436,
0.030127841979265213,
0.015741335228085518,
0.03448997437953949,
0.025774966925382614,
0.03514646366238594,
0.048396941274404526,
-0.015329889953136444,
0.0014323493232950568,
-0.002278665080666542,
0.056854456663131714,
-0.03293124586343765,
0.05846940726041794,
0.018430141732096672,
-0.03578818589448929,
-0.049282256513834,
-0.01755456253886223,
0.11150939762592316,
0.06701788306236267,
-0.010393110103905201,
0.01145014725625515,
0.040003444999456406,
0.0049598850309848785,
-0.00963100790977478,
0.009078187867999077,
0.030284453183412552,
-0.06541819870471954,
0.026086119934916496,
-0.053407084196805954,
0.046160388737916946,
-0.015952181071043015,
-0.010184647515416145,
0.029758905991911888,
-0.022112932056188583,
0.07509081065654755,
0.03226284310221672,
-0.014557542279362679,
-0.02675897441804409,
0.0019749486818909645,
-0.04053213447332382,
0.04204796627163887,
0.010416451841592789,
0.004353253170847893,
0.012951959855854511,
0.006196352653205395,
-0.037892892956733704,
-0.07929538935422897,
0.005423767492175102,
-0.007316926494240761,
-0.05920364707708359,
0.031791575253009796,
-0.005086127202957869,
-0.04890992119908333,
-0.020614221692085266,
-0.0007076209876686335,
0.03208574280142784,
0.017296943813562393,
-0.032649725675582886,
0.039395030587911606,
0.0013839148450642824,
-0.04456045478582382,
0.04753312095999718,
0.04017646238207817,
-0.027507435530424118,
-0.01711255870759487,
0.023551171645522118,
-0.01992644928395748,
-0.0875166654586792,
-0.006006163079291582,
-0.04531973600387573,
-0.028738288208842278,
0.03188757225871086,
-0.018962044268846512,
0.0896364226937294,
0.005443571601063013,
-0.030798736959695816,
0.018919382244348526,
-0.03849086910486221,
0.032741729170084,
0.033160626888275146,
0.009582209400832653,
-0.007947751320898533,
0.05322524905204773,
-0.022388946264982224,
0.027160365134477615,
-0.030792614445090294,
0.003936026245355606,
-0.019312776625156403,
-0.018316740170121193,
-0.05266759172081947,
-0.04370886832475662,
-0.038559965789318085,
0.0650390163064003,
-0.012572248466312885,
0.03206226974725723,
-0.022027743980288506,
0.004960769321769476,
0.022356940433382988,
-0.010506706312298775,
0.028446724638342857,
0.0003585795930121094,
0.04229481518268585,
-0.02352386899292469,
0.019009647890925407,
0.05436857044696808,
0.03077583760023117,
-0.00809005182236433,
0.011403585784137249,
0.049648918211460114,
0.004311806056648493,
0.015703916549682617,
0.031824953854084015,
-0.00769465696066618,
0.015399607829749584,
0.05734589323401451,
-0.024415047839283943,
-0.052056118845939636,
0.0009134754654951394,
-0.0037847179919481277,
0.012618173845112324,
0.018653227016329765,
-0.05145527422428131,
-0.00934400875121355,
-0.01075008139014244,
-0.02313767746090889,
-0.0298378374427557,
0.00860891118645668,
0.024404501542448997,
0.0241836030036211,
-0.00011285533400950953,
0.011155766434967518,
0.0573880560696125,
-0.05637693777680397,
-0.06938745081424713,
-0.014332865364849567,
-0.02756698615849018,
-0.08095795661211014,
-0.020865540951490402,
-0.0017364909872412682,
0.04709503427147865,
0.025550274178385735,
-0.048111893236637115,
-0.07513324171304703,
0.025762805715203285,
0.016445182263851166,
-0.0443105585873127,
-0.025891108438372612,
0.011417543515563011,
-0.01956045813858509,
0.031752120703458786,
-0.04256579652428627,
0.024248367175459862,
0.00554411206394434,
-0.020425990223884583,
0.03469522297382355,
0.0766686499118805,
0.015993690118193626,
0.08460530638694763,
-0.010430512018501759,
0.044400595128536224,
0.020730149000883102,
-0.0749545469880104,
-0.01979687251150608,
-0.07397475838661194,
0.041028622537851334,
-0.03673885762691498,
-0.041271667927503586,
-0.040132589638233185,
-0.0009545269422233105,
-0.05163881927728653,
-0.004494749009609222,
-0.00003479627048363909,
-0.029308246448636055,
0.004090501926839352,
-0.03645210340619087,
0.02996785379946232,
0.05644042789936066,
-0.0029760529287159443,
-0.012866753153502941,
-0.0519971139729023,
0.02518421597778797,
-0.002063415478914976,
-0.01082608476281166,
0.020865175873041153,
0.03351890668272972,
0.04194242134690285,
-0.05263390392065048,
0.045192163437604904,
-0.027595676481723785,
0.025422481819987297,
0.02225865237414837,
0.029118617996573448,
-0.0004823433409910649,
-0.005423855967819691,
-0.060140788555145264,
0.019138233736157417,
-0.04737627133727074,
-0.016137229278683662,
-0.02890915796160698,
0.04790123179554939,
0.07112587243318558,
0.028345255181193352,
-0.0514029897749424,
-0.02584460750222206,
0.03703102469444275,
0.050478216260671616,
-0.03285612910985947,
-0.004812208004295826,
-0.053361259400844574,
0.04163794219493866,
0.00875002145767212,
-0.05754515528678894,
0.008716141805052757,
0.0062765153124928474,
-0.008081015199422836,
-0.04155287519097328,
0.012829973362386227,
-0.022235393524169922,
0.00883356761187315,
-0.01819583959877491,
0.06750054657459259,
-0.00560802360996604,
-0.0032211083453148603,
-0.004994101822376251,
0.014831430278718472,
0.050957534462213516,
-0.04342106729745865,
0.0607757642865181,
0.02087508887052536,
0.006225146818906069,
-0.0162355937063694,
-0.04060759022831917,
-0.05469762906432152,
0.002214177278801799,
0.013174035586416721,
-0.05147543549537659,
-0.021921692416071892,
-0.036308448761701584,
0.032129738479852676,
-0.03503020107746124,
-0.05333622172474861,
-0.019689219072461128
] |
<p>Pioneer <a href="http://en.wikipedia.org/wiki/Pioneer_10">10</a> & <a href="http://en.wikipedia.org/wiki/Pioneer_11">11</a> are robotic space probes launched by the NASA in the early 1970's. After leaving our solar system, an <strong>unusual deceleration</strong> of both spacecrafts has been measured to be approximately $$\ddot{r}_p = -(8.74±1.33)×10^{−10} \frac{m}{s^2}$$ with respect to our solar system.</p>
<p><a href="http://en.wikipedia.org/wiki/Pioneer_anomaly#Proposed_explanations">Several attempts</a> were made to <strong>explain this tiny effect</strong>, called the <a href="http://en.wikipedia.org/wiki/Pioneer_anomaly">Pioneer anomaly</a>, but none was fully accepted in the scientific community so far.</p>
<p>Two months ago, <a href="http://arxiv.org/abs/1103.5222v1">Frederico Francisco et al</a> have proposed another solution to the problem. They assume, roughly speaking, that the <strong>thermal radiation</strong> of the spacecraft caused by plutonium on board along with the actual structure of the probes is responsible for this mystery of modern physics.</p>
<p>Here an image of Pioneer 10 taken from Wikipedia along with a sketch of the <strong>radiation model</strong> employed in the paper:
<img src="http://i.stack.imgur.com/Ukwcx.png" alt="Pioneer 10 and heat model"></p>
<p>Hence my question:</p>
<blockquote>
<h3>Is the Pioneer anomaly finally explained?</h3>
</blockquote>
<p>Sincerely</p> | g6589 | [
0.04467477276921272,
0.03822809085249901,
-0.006741278804838657,
0.010660102590918541,
0.031068574637174606,
0.06099915876984596,
0.021337486803531647,
0.03757094964385033,
-0.013800038956105709,
-0.03655068576335907,
0.04675523564219475,
0.04366208240389824,
0.0107832420617342,
0.003176160389557481,
0.041707903146743774,
-0.0005685732467100024,
0.1149914488196373,
-0.028405535966157913,
0.03095848485827446,
0.051292624324560165,
0.0016949304845184088,
-0.012015328742563725,
-0.021197181195020676,
-0.04363378509879112,
-0.014237308874726295,
-0.017275772988796234,
0.0016009206883609295,
-0.00036394078051671386,
0.028646867722272873,
-0.018187379464507103,
0.026902280747890472,
-0.029980000108480453,
0.04543839767575264,
-0.050265032798051834,
-0.02513173781335354,
-0.04183175042271614,
0.003204566426575184,
0.019825320690870285,
-0.016337554901838303,
-0.01837889663875103,
-0.010127132758498192,
-0.03550155833363533,
-0.015410416759550571,
0.035770248621702194,
-0.013790409080684185,
0.0015924766194075346,
-0.014391599223017693,
-0.006592751946300268,
0.010162007063627243,
0.01896176114678383,
-0.008265921846032143,
-0.0067578330636024475,
0.043189603835344315,
0.013667126186192036,
-0.009884919039905071,
-0.013806089758872986,
0.010470835492014885,
-0.007520495913922787,
0.08125483989715576,
-0.0034592892043292522,
0.007515565492212772,
0.04175497964024544,
0.0277733001857996,
-0.020364809781312943,
0.013804304413497448,
-0.029172856360673904,
0.043210871517658234,
0.038860876113176346,
0.0023302689660340548,
-0.05786912515759468,
0.045359134674072266,
-0.02977462112903595,
-0.07949670404195786,
0.02683880366384983,
-0.03245819732546806,
0.024695225059986115,
-0.013595047406852245,
0.003263480495661497,
0.027416156604886055,
-0.013667350634932518,
-0.029268953949213028,
0.03815058618783951,
-0.032360199838876724,
0.02461862564086914,
0.05016491562128067,
-0.025229569524526596,
-0.040148116648197174,
0.0613635890185833,
-0.009542637504637241,
-0.04200351983308792,
0.002264154376462102,
-0.021267149597406387,
0.015002747997641563,
-0.022208694368600845,
0.015554710291326046,
0.021535301581025124,
-0.010450977832078934,
0.032060761004686356,
-0.04477090761065483,
-0.022286782041192055,
0.008473112247884274,
0.03957822546362877,
-0.0073185754008591175,
0.04226372018456459,
0.018123526126146317,
-0.007839679718017578,
0.04191482812166214,
0.050051528960466385,
-0.006003027781844139,
-0.027758734300732613,
-0.0023295702412724495,
-0.024925801903009415,
-0.0032922071404755116,
-0.030729323625564575,
0.04687431454658508,
-0.03898920863866806,
0.04593045637011528,
-0.03332816809415817,
-0.022681402042508125,
0.012036807835102081,
-0.015354366041719913,
0.0009667720878496766,
-0.05214032530784607,
0.1287270337343216,
-0.07263890653848648,
0.02526354044675827,
0.014503571204841137,
-0.07424923032522202,
0.0100754639133811,
0.03140825405716896,
-0.017708254978060722,
0.07117627561092377,
-0.02725127711892128,
0.04656938463449478,
0.06590433418750763,
-0.0062889703549444675,
-0.02730628103017807,
0.034153781831264496,
0.015186455100774765,
0.00435596564784646,
-0.009718560613691807,
-0.019699102267622948,
0.009092976339161396,
-0.0030413768254220486,
-0.03917532414197922,
-0.01172536052763462,
-0.055276162922382355,
0.06760801374912262,
0.036036472767591476,
0.058779578655958176,
0.04846939072012901,
0.0590861514210701,
-0.03760877624154091,
-0.05106798931956291,
-0.04953734576702118,
0.012392477132380009,
-0.030336571857333183,
0.04000452533364296,
-0.03157515451312065,
0.009046096354722977,
0.04352610930800438,
0.02957826852798462,
0.010565636679530144,
0.034812089055776596,
-0.055859457701444626,
0.04107538238167763,
-0.01896081678569317,
-0.09138715267181396,
-0.009280601516366005,
-0.016530726104974747,
-0.051825471222400665,
-0.02809717506170273,
0.01633230596780777,
0.0571211613714695,
-0.030881624668836594,
0.030158663168549538,
0.05973758548498154,
-0.06117677316069603,
0.026016484946012497,
-0.013525057584047318,
-0.029202697798609734,
-0.009838400408625603,
0.026897627860307693,
-0.009948167949914932,
-0.002117140917107463,
-0.022059712558984756,
0.04299111291766167,
0.0002904379216488451,
-0.03391503542661667,
-0.023490682244300842,
-0.008903245441615582,
-0.0022439302410930395,
0.011350132524967194,
-0.050411660224199295,
0.036859165877103806,
-0.0547117181122303,
-0.0367155522108078,
-0.011417812667787075,
-0.060043442994356155,
0.06293685734272003,
0.012931426987051964,
0.002486970741301775,
-0.0008974633528850973,
-0.003364148549735546,
0.013419325463473797,
-0.04248031601309776,
-0.022371310740709305,
-0.009361154399812222,
0.040386561304330826,
-0.03878762573003769,
-0.002629198832437396,
-0.03235762193799019,
-0.01384944561868906,
0.020625052973628044,
-0.03403745964169502,
-0.03160259872674942,
0.001419686945155263,
-0.014749608933925629,
0.02458549290895462,
-0.050104040652513504,
-0.04496603459119797,
0.020050644874572754,
-0.0002521157148294151,
0.021521510556340218,
0.0028163676615804434,
0.024234047159552574,
0.0024931312073022127,
-0.07214297354221344,
-0.07974006235599518,
-0.002395347459241748,
-0.05837910249829292,
0.03176932409405708,
-0.055082377046346664,
0.004989129025489092,
0.07915613800287247,
-0.0017645321786403656,
-0.002705375896766782,
-0.027359161525964737,
-0.04678206890821457,
0.01753423735499382,
-0.010191832669079304,
-0.0012257221387699246,
-0.08491714298725128,
0.017237624153494835,
0.04563876986503601,
-0.08580716699361801,
0.02770817093551159,
-0.0011220488231629133,
-0.024619504809379578,
-0.07423501461744308,
0.03882065787911415,
-0.02739223651587963,
-0.03428034856915474,
-0.00688380841165781,
0.003084181807935238,
0.016725091263651848,
-0.030548658221960068,
0.11084581166505814,
-0.07534772902727127,
-0.0637068971991539,
0.0004512182786129415,
0.013752717524766922,
0.0056925383396446705,
0.04507024586200714,
-0.0031678678933531046,
-0.001730473362840712,
-0.029804401099681854,
-0.03946845605969429,
-0.06090002506971359,
-0.04930412024259567,
-0.011189567856490612,
0.05134693533182144,
0.03633740544319153,
0.05050532519817352,
-0.014187050983309746,
0.06237952038645744,
0.0032660174183547497,
-0.013835594989359379,
0.05458005145192146,
-0.0214068666100502,
-0.016530949622392654,
0.025700725615024567,
-0.03328057751059532,
-0.022856857627630234,
-0.019718537107110023,
-0.006051003001630306,
-0.05984698235988617,
0.025421610102057457,
0.014603899791836739,
-0.006309355143457651,
0.027186112478375435,
-0.05975564569234848,
0.07324787229299545,
-0.02227829396724701,
0.006579773500561714,
0.016560573130846024,
0.05616099014878273,
0.03427625447511673,
-0.03630279004573822,
-0.0036327929701656103,
0.14396175742149353,
-0.06418770551681519,
0.009281319566071033,
0.007890294305980206,
-0.028372520580887794,
-0.0027649474795907736,
-0.010142115876078606,
-0.012988636270165443,
-0.061053723096847534,
-0.008153234608471394,
-0.000450570514658466,
0.005828408524394035,
-0.04957917705178261,
0.060651931911706924,
0.0017023467225953937,
0.007327771745622158,
-0.08725100010633469,
0.01650347374379635,
0.011389090679585934,
0.04202466830611229,
-0.039981529116630554,
-0.06382973492145538,
-0.0524136945605278,
-0.01714632287621498,
0.06649723649024963,
0.025339968502521515,
-0.020671363919973373,
-0.04299895465373993,
-0.04173393175005913,
-0.0033451735507696867,
0.016639279201626778,
-0.029646549373865128,
-0.0444822832942009,
-0.041451383382081985,
-0.04706163331866264,
0.009026695042848587,
-0.037334371358156204,
0.13037265837192535,
0.03608493134379387,
0.05627095699310303,
-0.04114430770277977,
0.018352201208472252,
-0.00956082995980978,
-0.04123459756374359,
0.0343233123421669,
0.04403409734368324,
0.009050973691046238,
-0.02765241637825966,
-0.0429697148501873,
0.03353928029537201,
0.06697044521570206,
0.04423646628856659,
-0.014387106522917747,
-0.023799527436494827,
-0.020930247381329536,
0.04408249258995056,
-0.04338209703564644,
-0.033620819449424744,
0.005831332877278328,
-0.006108261179178953,
-0.021725375205278397,
0.009648906998336315,
0.0074976845644414425,
-0.004178995732218027,
0.03370196372270584,
0.01561951544135809,
0.025698954239487648,
0.07585613429546356,
0.0018268678104504943,
-0.0632731169462204,
-0.0522194504737854,
0.005371200852096081,
-0.05111362412571907,
-0.05171767249703407,
0.06637467443943024,
-0.05286816507577896,
0.0477992482483387,
-0.0009352501947432756,
-0.04818720743060112,
0.08854671567678452,
0.012739741243422031,
0.008737107738852501,
0.03674367815256119,
0.01306641660630703,
0.08286638557910919,
0.014295476488769054,
-0.01224333606660366,
-0.03196367248892784,
-0.013448868878185749,
-0.07777844369411469,
-0.05064082518219948,
-0.0027455405797809362,
-0.01696030981838703,
0.0054077403619885445,
-0.005792719312012196,
-0.03288224712014198,
0.02401665784418583,
0.022609643638134003,
-0.005464139860123396,
0.007020073942840099,
0.040556617081165314,
0.028356177732348442,
0.014115473255515099,
0.008791796863079071,
-0.016237657517194748,
-0.023398103192448616,
-0.019025396555662155,
0.004894690588116646,
-0.041552044451236725,
0.02126564458012581,
-0.0024622189812362194,
0.03689255565404892,
-0.03240400552749634,
-0.07582506537437439,
0.01602686010301113,
0.002609929069876671,
0.02290245145559311,
0.03609829768538475,
0.03724599629640579,
0.027157146483659744,
-0.04035870358347893,
0.058650314807891846,
-0.010419242084026337,
0.00729345390573144,
0.0742197334766388,
0.08135762810707092,
-0.026135733351111412,
0.023660095408558846,
0.04980163648724556,
-0.05330018699169159,
0.007628762628883123,
0.002934535499662161,
-0.06549650430679321,
0.00892788264900446,
0.001699336338788271,
0.03414135426282883,
0.005366784054785967,
0.043582115322351456,
-0.0385989286005497,
0.08298205584287643,
0.02317485213279724,
-0.01048363372683525,
0.007664084900170565,
0.061077892780303955,
0.014112777076661587,
0.07938569784164429,
0.04288563132286072,
-0.04794080927968025,
0.006966016720980406,
-0.022717371582984924,
-0.05491907149553299,
-0.05007736757397652,
0.02294609695672989,
0.050605371594429016,
-0.032577913254499435,
-0.0019100378267467022,
0.033976390957832336,
-0.028349921107292175,
0.0010350275551900268,
0.029664386063814163,
-0.04542529210448265,
0.000632766867056489,
0.013487935066223145,
0.016559304669499397,
0.06736715883016586,
-0.025848450139164925,
-0.0649803876876831,
-0.035186827182769775,
-0.015857331454753876,
-0.04744787886738777,
-0.03844078630208969,
-0.014326377771794796,
0.016827117651700974,
0.028351452201604843,
-0.03151506930589676,
0.012737547047436237,
0.003431545803323388,
-0.04083043336868286,
0.04737650975584984,
0.021860776469111443,
0.01580232009291649,
0.017533382400870323,
-0.0009759516105987132,
-0.011613588780164719,
-0.011515372432768345,
-0.016670869663357735,
-0.08795545995235443,
0.03488455340266228,
0.04924863204360008,
-0.039658792316913605,
-0.013431561179459095,
-0.029621699824929237,
0.016370898112654686,
-0.038563307374715805,
-0.001583582954481244,
0.007650061510503292,
0.004791914019733667,
0.024747787043452263,
0.0017163037555292249,
0.004937126301229,
0.02602192386984825,
-0.0031111263670027256,
0.002316811354830861,
0.007120154798030853,
0.0004948535934090614,
-0.013847715221345425,
0.049505386501550674,
0.024474959820508957,
0.03626023977994919,
-0.03328273072838783,
-0.06466308981180191,
0.08430163562297821,
0.02737765945494175,
-0.02178339846432209,
0.01595202647149563,
-0.018322058022022247,
0.016988787800073624,
-0.02959807775914669,
-0.013409052044153214,
-0.052330534905195236,
-0.01245749182999134,
-0.06170196831226349,
0.05200094357132912,
0.018615558743476868,
0.0037611655425280333,
0.01885635033249855,
-0.019992884248495102,
0.024966832250356674,
0.023955373093485832,
0.07362727075815201,
-0.011366859078407288,
0.03510059043765068,
0.06391757726669312,
0.053864844143390656,
-0.0007227638852782547,
-0.015295553021132946,
0.03481706604361534,
0.018694749101996422,
0.02622709609568119,
-0.04989676550030708,
-0.02076706476509571,
0.034722745418548584,
0.0494181253015995,
0.026894686743617058,
0.010353172197937965,
0.03318752720952034,
-0.00546224694699049,
-0.007015787530690432,
0.04560986906290054,
-0.05166131630539894,
-0.01978037878870964,
-0.009424016810953617,
0.02306295745074749,
0.034087199717760086,
-0.01899082399904728,
-0.012477309443056583,
0.002333076437935233,
-0.03412895277142525,
-0.09360809624195099,
-0.07359456270933151,
-0.019035344943404198,
0.004145079292356968,
0.05499870702624321,
0.01195363700389862,
0.046330541372299194,
0.022972585633397102,
-0.011912324465811253,
-0.07857000082731247,
0.027616873383522034,
-0.04979385435581207,
0.013536886312067509,
0.0004221491690259427,
0.026249989867210388,
0.04179058596491814,
0.04341121390461922,
0.0050831944681704044,
-0.026099350303411484,
0.03847047686576843,
-0.0494048111140728,
0.0060886540450155735,
-0.016254588961601257,
0.01204146258533001,
0.04929083213210106,
-0.0053923907689750195,
-0.03166890889406204,
0.010851801373064518,
-0.07223497331142426,
0.042555589228868484,
0.055384814739227295,
0.0024286131374537945,
-0.006575684063136578,
-0.025086089968681335,
-0.02610926888883114,
0.0018082682508975267,
-0.06451234966516495,
-0.01656956970691681,
-0.0030165580101311207,
0.006746067199856043,
-0.06250043213367462,
0.03188200667500496,
-0.0179317407310009,
0.0036361890379339457,
0.08474859595298767,
0.0527835413813591,
0.049531057476997375,
-0.02563786320388317,
0.0375385619699955,
0.029833456501364708,
0.039266493171453476,
0.025168973952531815,
-0.023674989119172096,
0.03653091564774513,
0.010461068712174892,
-0.019156642258167267,
0.003054145025089383,
-0.028635764494538307,
0.004431078210473061,
0.009941104799509048,
-0.024736452847719193,
0.04522118717432022,
-0.0049680545926094055,
0.00663678627461195,
-0.05085664615035057,
-0.04017174243927002,
-0.03756006434559822,
0.008757427334785461,
0.001997791463509202,
-0.018695874139666557,
0.04390568658709526,
0.017016064375638962,
-0.015371285378932953,
0.019157569855451584,
0.04439177364110947,
0.002383744576945901,
-0.002669582376256585,
-0.02543620578944683,
0.025694098323583603,
0.03733421117067337,
-0.0070540872402489185,
-0.013612029142677784,
-0.003911205101758242,
-0.031383540481328964,
-0.042493440210819244,
-0.02738087996840477,
-0.0255419984459877,
0.04766193777322769,
-0.008844261057674885,
0.04678463935852051,
-0.02655521221458912,
-0.01678466983139515,
0.021788237616419792,
-0.049951229244470596,
0.029340701177716255,
0.004976864904165268,
0.041003815829753876,
0.011859075166285038,
-0.013550754636526108,
0.02846408262848854,
0.031590815633535385,
-0.049148477613925934,
0.04954100772738457,
-0.033173929899930954,
-0.0028603796381503344,
0.028537895530462265,
-0.004639578051865101,
0.025204479694366455,
-0.02157391980290413,
-0.03416113182902336,
-0.007163711823523045,
-0.04305250197649002,
0.009004318155348301,
-0.027191806584596634,
-0.05558498576283455,
-0.030217070132493973,
-0.017329471185803413,
0.0003955381107516587,
0.044280149042606354,
-0.08883191645145416,
0.045550718903541565,
0.0403391569852829,
0.033377375453710556,
0.030645029619336128,
-0.009741870686411858,
0.007810833863914013,
0.011212361045181751,
-0.02351253665983677,
-0.04864173382520676,
-0.03259638696908951,
0.0030789526645094156,
0.02843182347714901,
-0.03831249475479126,
0.07983686774969101,
0.005820383317768574,
0.0286076832562685,
0.007517938502132893,
0.0077714333310723305,
-0.04968574270606041,
0.018611261621117592,
0.007629890460520983,
-0.026095733046531677,
0.00009497747669229284,
0.005466827191412449,
0.001018086331896484,
0.01545793004333973,
-0.01982320286333561,
0.02472909912467003,
0.004938162863254547,
-0.034428250044584274,
-0.047696229070425034,
-0.035338375717401505,
-0.00017851525626610965,
0.000024857554308255203,
0.04048008471727371,
-0.0122058792039752,
-0.013491296209394932,
-0.012947656214237213,
-0.04389705881476402,
-0.0028248934540897608,
-0.017632586881518364,
-0.07148458063602448,
0.009671145118772984,
-0.024718977510929108,
-0.01026144064962864,
-0.017672181129455566,
-0.002674684626981616,
-0.04587386175990105,
-0.009216527454555035,
-0.049506593495607376,
0.08147114515304565,
-0.017426444217562675,
0.063985675573349,
0.004926247056573629,
-0.04822354391217232,
-0.05802629515528679,
-0.008267905563116074,
0.0032906709238886833,
0.009491545148193836,
0.01722658984363079,
-0.008804243057966232,
0.006271899212151766,
-0.004161179531365633,
0.013648295775055885,
0.01698707789182663,
-0.0015380835393443704,
-0.011837652884423733,
-0.039441999047994614,
-0.03018021211028099,
0.008483230136334896,
-0.005736296996474266,
-0.05492902174592018,
0.028886687010526657,
-0.008795088157057762,
-0.018181417137384415,
-0.014177033677697182,
0.03787938877940178,
0.011544245295226574,
-0.008267516270279884,
0.00616971030831337,
-0.03351529315114021,
-0.034537456929683685,
-0.006074877921491861,
-0.04199138656258583,
-0.036580972373485565,
-0.0113069461658597,
0.03468097746372223,
-0.005812950897961855,
0.034606918692588806,
-0.007165140938013792
] |
<p>In all the literature I've seen the turbulent energy spectrum described as $E(k)$ instead of $E(L)$, i.e. as a function of a wave number not eddy size. The connection via $k=2\pi/\lambda$ is clear, but exactly what wave process is meant here. Is the idea that turbulent flow can be viewed as a superposition of waves? Waves of what? Or is this just a common notation used for energy spectra? </p> | g6590 | [
0.03238056227564812,
0.010899857617914677,
-0.021482186391949654,
-0.07465516030788422,
0.0642060860991478,
0.001849031075835228,
0.026266565546393394,
0.03290135785937309,
-0.049710340797901154,
-0.05582597106695175,
0.0011052655754610896,
0.0029009422287344933,
0.06168070062994957,
0.02789091132581234,
-0.03263407200574875,
-0.06724507361650467,
0.045572105795145035,
0.023664768785238266,
0.002383053069934249,
-0.012587243691086769,
-0.04157876595854759,
-0.019635921344161034,
0.015421269461512566,
0.009710684418678284,
0.020291442051529884,
0.01164928823709488,
0.0004475924069993198,
-0.06359931826591492,
-0.006876041181385517,
-0.09089388698339462,
0.030004026368260384,
0.01339141745120287,
0.06252789497375488,
-0.014606423676013947,
-0.057617466896772385,
0.013091315515339375,
0.031191499903798103,
0.028346389532089233,
0.05762388929724693,
-0.033015064895153046,
0.025327473878860474,
0.046156931668519974,
-0.012427463196218014,
-0.02388056181371212,
-0.03355002403259277,
0.022130748257040977,
-0.014219972304999828,
0.025488723069429398,
-0.05224502831697464,
-0.0005980503046885133,
0.027346234768629074,
0.013733350671827793,
0.034456394612789154,
0.03368910402059555,
-0.0041748839430511,
0.04264319688081741,
0.008598832413554192,
-0.015734681859612465,
0.06507930159568787,
0.06077918782830238,
0.04873872920870781,
-0.033559102565050125,
-0.025393541902303696,
0.014993644319474697,
0.07795043289661407,
0.03569083288311958,
-0.0006570327095687389,
-0.014448782429099083,
0.011105936020612717,
-0.010310330428183079,
0.0372086800634861,
-0.05778002738952637,
0.01305108331143856,
-0.0528779961168766,
-0.03184572979807854,
-0.018276220187544823,
0.001514639938250184,
-0.02441444806754589,
0.005853371229022741,
0.037089891731739044,
0.0300027746707201,
-0.028387682512402534,
-0.006233301945030689,
0.007951396517455578,
0.04258578270673752,
0.03729492798447609,
-0.0021552590187639,
0.03414056450128555,
-0.03218212351202965,
-0.013634804636240005,
0.010146104730665684,
-0.03758378326892853,
0.027483955025672913,
0.01008957251906395,
0.0027961761225014925,
-0.008590265177190304,
-0.022794876247644424,
0.02744905836880207,
-0.018872173503041267,
-0.004645128268748522,
-0.036612268537282944,
-0.003908858168870211,
-0.021228281781077385,
-0.031090129166841507,
0.01500796526670456,
-0.0031616257037967443,
-0.023494591936469078,
-0.017794650048017502,
0.04090099409222603,
-0.05782347172498703,
-0.032206859439611435,
0.04386426508426666,
-0.012708812020719051,
0.021177086979150772,
-0.04623705521225929,
-0.021675074473023415,
0.05202888324856758,
-0.0017241941532120109,
-0.0077407872304320335,
0.016124321147799492,
0.08612853288650513,
-0.005285619292408228,
0.05053624510765076,
0.0524657778441906,
0.04701429605484009,
0.05335255712270737,
0.0014245754573494196,
0.001437856932170689,
0.04443035274744034,
-0.018949048593640327,
0.08446085453033447,
-0.030615847557783127,
0.007055081892758608,
-0.027474287897348404,
0.06193482503294945,
0.043596863746643066,
-0.018246466293931007,
0.015379219315946102,
-0.03180426359176636,
-0.014197265729308128,
0.024150392040610313,
-0.042775657027959824,
0.021792039275169373,
-0.0780111774802208,
-0.04414668306708336,
0.003941608592867851,
-0.0017733763670548797,
-0.054844729602336884,
0.008480066433548927,
0.015678461641073227,
-0.007610830012708902,
0.0181365255266428,
-0.036748263984918594,
-0.02648354135453701,
0.004320213105529547,
0.04067401587963104,
0.04486844316124916,
-0.010732868686318398,
0.005013422109186649,
0.06094706803560257,
0.044552985578775406,
0.05361035838723183,
0.04175122454762459,
-0.0033549948129802942,
-0.05958952009677887,
-0.01190652884542942,
0.028509659692645073,
-0.005940414499491453,
-0.015453144907951355,
0.0022367555648088455,
0.017960140481591225,
-0.0033808471634984016,
-0.010811546817421913,
0.012863623909652233,
0.02394629642367363,
0.06011735275387764,
0.06022229790687561,
-0.028178608044981956,
0.027458421885967255,
0.0014713824493810534,
-0.023813461884856224,
0.02285304293036461,
0.02479320950806141,
-0.0418759286403656,
0.03484348952770233,
0.022776499390602112,
-0.026241974905133247,
0.005029050167649984,
0.012106179259717464,
0.003805700223892927,
0.042211104184389114,
-0.011532154865562916,
0.004739836789667606,
0.023594755679368973,
-0.012682387605309486,
0.01992294192314148,
-0.06345012784004211,
-0.03336789831519127,
-0.07893934100866318,
-0.008941666223108768,
0.04086219519376755,
0.03028860315680504,
0.030629457905888557,
0.005266000051051378,
0.0530729778110981,
0.08921550959348679,
-0.03326396644115448,
-0.018761642277240753,
-0.04236539825797081,
0.026320436969399452,
-0.009998484514653683,
-0.03308471664786339,
-0.05800324305891991,
-0.025634832680225372,
0.010132716037333012,
-0.016356203705072403,
0.0012284638360142708,
-0.007143043912947178,
0.0037902905605733395,
0.016574760898947716,
-0.10074502974748611,
-0.043213069438934326,
0.026145314797759056,
0.00831602979451418,
0.010986545123159885,
0.06370040029287338,
-0.036042969673871994,
-0.025496939197182655,
0.030827121809124947,
-0.04133192449808121,
-0.07361428439617157,
0.018776603043079376,
-0.002015262609347701,
-0.017013316974043846,
-0.022808199748396873,
0.007625809404999018,
0.03448978066444397,
0.035039253532886505,
-0.011752638034522533,
0.003931306768208742,
0.01693066395819187,
0.0026002556551247835,
-0.01148796733468771,
0.028795016929507256,
0.027683183550834656,
0.031232925131917,
0.044039834290742874,
0.022906150668859482,
-0.044446252286434174,
-0.014740705490112305,
-0.0020808163098990917,
-0.08030498027801514,
-0.011587067507207394,
0.031215714290738106,
0.0038851804565638304,
-0.032242316752672195,
0.03605534881353378,
0.0928601399064064,
-0.007151533383876085,
0.06442943960428238,
0.02234363555908203,
0.08614064007997513,
-0.0096599031239748,
-0.040116772055625916,
-0.029717888683080673,
-0.030399205163121223,
0.0063009317964315414,
0.058601390570402145,
-0.024408288300037384,
-0.04914039000868797,
-0.01893213763833046,
0.04402470961213112,
0.02966003492474556,
-0.023749981075525284,
0.013114863075315952,
-0.08934071660041809,
-0.019580118358135223,
-0.042753178626298904,
0.05076117068529129,
-0.023612169548869133,
-0.002429133513942361,
-0.0551106296479702,
0.001647536177188158,
0.03619001805782318,
-0.019203217700123787,
-0.10159607231616974,
0.0402352437376976,
0.07133793830871582,
0.04234479367733002,
0.010717657394707203,
0.03551674634218216,
-0.01690262369811535,
-0.04264359921216965,
-0.0018633484141901135,
-0.010774174705147743,
0.018221823498606682,
0.04789027199149132,
-0.0033000160474330187,
0.010182141326367855,
-0.02294432371854782,
0.009913516230881214,
-0.013585301116108894,
0.0020113149657845497,
-0.025941360741853714,
0.021554891020059586,
0.02547190897166729,
-0.07181473076343536,
-0.04461615905165672,
-0.06978510320186615,
-0.04459354281425476,
-0.017269570380449295,
0.038053516298532486,
-0.005157188978046179,
0.08534635603427887,
-0.04363783076405525,
0.0408170148730278,
-0.05932280048727989,
-0.015911925584077835,
-0.028496112674474716,
0.0015681536169722676,
-0.06681860238313675,
-0.04358678683638573,
0.07198918610811234,
-0.027305949479341507,
-0.003627309575676918,
-0.012648563832044601,
-0.018277032300829887,
-0.03405731916427612,
-0.019022513180971146,
-0.011808712035417557,
-0.03910953551530838,
-0.007295097224414349,
-0.008603820577263832,
-0.002924505388364196,
0.0037011553067713976,
0.009053271263837814,
-0.05449230968952179,
-0.05675683170557022,
-0.00003900512456311844,
0.06766274571418762,
-0.02423730492591858,
0.011508227325975895,
0.003770829178392887,
0.00040933815762400627,
0.009745500981807709,
0.02989303134381771,
-0.06373842060565948,
-0.011362342163920403,
-0.006998477037996054,
-0.04022343084216118,
-0.02284148894250393,
0.034949418157339096,
0.025782525539398193,
-0.030159367248415947,
0.013910427689552307,
-0.0004492116568144411,
0.002402079291641712,
-0.015631597489118576,
0.010072100907564163,
0.02111697942018509,
0.04095911234617233,
-0.020025528967380524,
-0.00153327826410532,
-0.05348922312259674,
-0.006794368382543325,
-0.028057172894477844,
0.01606765016913414,
-0.013435843400657177,
-0.013205927796661854,
-0.019266707822680473,
0.0025704647414386272,
-0.04072211682796478,
0.012297545559704304,
-0.049820467829704285,
0.035297494381666183,
-0.015073481947183609,
0.029692742973566055,
0.06553857028484344,
0.04517515376210213,
0.03029550425708294,
0.03581543639302254,
-0.030913617461919785,
0.0003103629860561341,
0.0014783047372475266,
-0.014480949379503727,
-0.020141921937465668,
-0.03878668323159218,
0.0697011724114418,
-0.027286818251013756,
-0.022050537168979645,
0.02467302791774273,
-0.0552506148815155,
-0.015190016478300095,
-0.0006664275424554944,
-0.008094307035207748,
0.020280862227082253,
0.05156874284148216,
0.004631091374903917,
-0.05200580134987831,
0.09611905366182327,
0.023606088012456894,
0.0037313071079552174,
-0.049433182924985886,
0.003826807253062725,
-0.006903561297804117,
0.07245337218046188,
0.10026922821998596,
-0.026767147704958916,
0.008226540870964527,
-0.03237507492303848,
0.041799381375312805,
0.02572524920105934,
-0.0026249580550938845,
-0.07509100437164307,
-0.025212349370121956,
-0.003754626726731658,
-0.0021561940666288137,
-0.06238026171922684,
0.0028727243188768625,
0.05859587341547012,
0.03170308843255043,
-0.012599656358361244,
0.012816774658858776,
0.034596461802721024,
-0.014160407707095146,
0.05392925813794136,
0.057805050164461136,
0.04683560132980347,
-0.05717672407627106,
-0.03179767727851868,
0.014104647561907768,
0.016365397721529007,
-0.0330190472304821,
0.009237709455192089,
-0.05535687506198883,
-0.017396366223692894,
0.03820229694247246,
0.008396207354962826,
-0.03209308162331581,
0.04283241182565689,
-0.02183702029287815,
-0.007634578738361597,
-0.006579239387065172,
0.03685050830245018,
0.04630570858716965,
0.008061015978455544,
0.01614106073975563,
-0.039134733378887177,
-0.07447054982185364,
-0.012835709378123283,
-0.0248730406165123,
0.03658114746212959,
-0.012765821069478989,
0.03296402096748352,
0.005613344721496105,
-0.03392259404063225,
-0.01279398426413536,
0.013060765340924263,
0.008173766545951366,
-0.021627355366945267,
-0.031604792922735214,
-0.00457055913284421,
0.005153751000761986,
0.015333755873143673,
0.037128549069166183,
-0.005546177737414837,
-0.04177282005548477,
0.010372134856879711,
-0.043220240622758865,
0.008588007651269436,
0.05593160539865494,
-0.02395637333393097,
-0.024330472573637962,
-0.033663831651210785,
0.027078619226813316,
0.0017011970048770308,
-0.001029417384415865,
-0.004756213165819645,
0.02063479647040367,
-0.04116623476147652,
0.05103002116084099,
-0.009532567113637924,
-0.009995323605835438,
-0.015458510257303715,
-0.0014705018838867545,
0.028605980798602104,
-0.011485552415251732,
-0.005892092362046242,
0.003608781611546874,
0.040632884949445724,
-0.005236157216131687,
0.030443474650382996,
-0.025622989982366562,
0.012330672703683376,
0.06278979778289795,
0.0158621184527874,
0.05328725278377533,
-0.07625216245651245,
0.010363411158323288,
-0.0067604039795696735,
0.009300552308559418,
-0.0367051362991333,
-0.0223544929176569,
0.006033889017999172,
0.031141329556703568,
0.022043170407414436,
0.09999532997608185,
0.00996062345802784,
-0.018360061571002007,
0.024753618985414505,
-0.03766322508454323,
-0.028614310547709465,
-0.05406660586595535,
0.021773342043161392,
-0.02769429050385952,
-0.03230108693242073,
-0.028663119301199913,
-0.0011506957234814763,
0.020003652200102806,
0.05119581148028374,
0.022935887798666954,
0.028810661286115646,
-0.05105871334671974,
0.00036684845690615475,
-0.021517569199204445,
0.00562741793692112,
-0.04930693283677101,
0.014882453717291355,
0.029441144317388535,
0.00718957232311368,
-0.008870325982570648,
0.0005229124799370766,
0.024766813963651657,
0.031302858144044876,
0.035352922976017,
-0.013329978100955486,
-0.012165883556008339,
0.02110757865011692,
0.0070887235924601555,
0.08894039690494537,
0.0256876852363348,
-0.011929620988667011,
-0.05445703864097595,
0.03622222691774368,
-0.012058015912771225,
0.058853160589933395,
0.05335189774632454,
0.05832403898239136,
0.007659986615180969,
-0.061349838972091675,
0.024715041741728783,
-0.017118215560913086,
0.05350010097026825,
-0.0216688085347414,
-0.038014039397239685,
0.030312100425362587,
0.07533294707536697,
-0.055288683623075485,
-0.033231209963560104,
0.006736378185451031,
-0.004600585903972387,
0.03815418854355812,
-0.010388991795480251,
-0.03388197347521782,
0.05447046831250191,
-0.03883439302444458,
-0.0033784459810703993,
-0.0353863388299942,
-0.027239760383963585,
0.07361675798892975,
-0.03841729089617729,
-0.04083092883229256,
0.004048763308674097,
-0.020126767456531525,
0.007499843370169401,
-0.04893280938267708,
0.04910324513912201,
-0.010650784708559513,
-0.037714023143053055,
-0.05174323916435242,
-0.016501300036907196,
0.004322633612900972,
0.021435948088765144,
-0.006178976967930794,
-0.02920941263437271,
0.0035375047009438276,
-0.026894763112068176,
-0.02969697117805481,
0.013317473232746124,
0.09823352098464966,
-0.05507037416100502,
-0.02839406207203865,
-0.05019513890147209,
0.03793894127011299,
-0.004667174071073532,
0.0021955559495836496,
-0.044568099081516266,
0.009752485901117325,
-0.005726858042180538,
0.030030515044927597,
-0.01644434593617916,
-0.005827899556607008,
0.00910852663218975,
-0.04434556886553764,
-0.03899846598505974,
-0.009692265652120113,
-0.010677757672965527,
0.011350424028933048,
-0.09738675504922867,
0.06222911179065704,
0.008980498649179935,
-0.0410614013671875,
0.050776999443769455,
-0.03991391509771347,
-0.018035950139164925,
-0.0032219775021076202,
-0.03501972556114197,
0.0103067671880126,
0.025297371670603752,
-0.02040587179362774,
0.060715336352586746,
-0.09190087765455246,
0.021254975348711014,
-0.005515276920050383,
0.027529872953891754,
0.022078702226281166,
-0.03389057144522667,
0.006613498087972403,
0.036287419497966766,
0.0375661738216877,
0.018958481028676033,
-0.023019710555672646,
-0.015131721273064613,
0.08917304128408432,
-0.06045408919453621,
-0.042374808341264725,
-0.072117879986763,
0.006378886289894581,
0.04614591225981712,
0.06241916865110397,
-0.016843272373080254,
0.0722222849726677,
-0.00040671046008355916,
0.016632627695798874,
-0.03073466196656227,
-0.007945533841848373,
-0.002909601666033268,
-0.0168886911123991,
-0.0939290001988411,
-0.06259950250387192,
-0.05388255789875984,
-0.016712570562958717,
-0.039627157151699066,
-0.01453428529202938,
-0.032849691808223724,
-0.0018122972687706351,
-0.019962307065725327,
0.004419853910803795,
0.02682790532708168,
-0.04204852133989334,
0.05262867361307144,
0.04283875226974487,
-0.046848151832818985,
-0.0011596539989113808,
0.00582239031791687,
0.03745613619685173,
0.04738198593258858,
-0.0318470261991024,
0.014192719012498856,
-0.027623847126960754,
0.02875443361699581,
-0.03422679752111435,
-0.025345327332615852,
-0.02702196128666401,
-0.0783182829618454,
0.013118548318743706,
-0.04134448245167732,
-0.031493596732616425,
0.001455236691981554,
-0.011545930989086628,
-0.03255990147590637,
0.048774830996990204,
0.06699298322200775,
-0.02032516710460186,
0.001180444029159844,
0.05180588737130165,
-0.0689137876033783,
-0.010506372898817062,
-0.04085899516940117,
-0.03788688778877258,
-0.024628277868032455,
0.06992509216070175,
0.028910253196954727,
-0.038840629160404205,
-0.02709045633673668,
0.01280828658491373,
0.010063611902296543,
-0.0171981081366539,
-0.006609957665205002,
0.08608782291412354,
0.07895243167877197,
-0.010883253999054432,
-0.032987579703330994,
0.003054662374779582,
-0.010644768364727497,
0.0057115196250379086,
0.033529218286275864,
-0.041448891162872314,
-0.02258848212659359,
-0.024034937843680382,
-0.01328308880329132,
-0.020765356719493866,
0.007967617362737656,
0.014868906699120998,
-0.006706956773996353,
0.006477889139205217,
0.02002861350774765,
0.010950176976621151,
-0.06894790381193161,
0.01219885516911745,
0.041942380368709564,
0.043807461857795715,
-0.003389347344636917,
-0.030177682638168335,
0.036853305995464325,
0.017304029315710068,
0.008845822885632515,
0.02583261765539646,
-0.018146498128771782,
-0.017403898760676384,
-0.06965664774179459,
0.019458899274468422,
-0.03190182149410248,
-0.01770656183362007,
-0.03231046721339226,
-0.024559833109378815,
0.026371261104941368,
0.011159011162817478,
0.05655292049050331,
-0.025109564885497093,
0.02743157185614109,
-0.0016753999516367912,
-0.004561095964163542,
0.009533054195344448,
-0.014581744559109211,
-0.07058613747358322,
-0.037132952362298965,
-0.045159343630075455,
-0.03222426399588585,
-0.029798895120620728,
0.012375496327877045,
0.0937652513384819,
0.03536777198314667,
0.0648854523897171,
0.07193063199520111,
-0.031828902661800385,
0.027234068140387535,
0.025412501767277718,
-0.02532496489584446,
-0.005101833026856184,
-0.019559772685170174,
0.02538994699716568,
-0.006432163063436747,
-0.008421595208346844,
-0.0428907684981823,
-0.03943416476249695,
0.03532668203115463,
0.06902986019849777
] |
<p>I've seen many science popularisation documentaries and read few books (obviously not being scientist myself). I am able to <em>process and understand</em> basic ideas behind most of these. However for general relativity there is this one illustration, which is being used over and over (image from Wikipedia):</p>
<p><img src="http://upload.wikimedia.org/wikipedia/commons/2/22/Spacetime_curvature.png" alt="Spacetime curvature (from Wikipedia)"></p>
<p>I always thought that general relativity gives another way how you can describe gravity. However for this illustration to work, there needs to be another force, pulling the object down (referring to a direction in the attached image). If I put two non-moving objects in the image, what force will pull them together?</p>
<p>So where is my understanding incorrect? Or is general relativity not about explaining gravity and just describes how heavy objects bends spacetime (in that case the analogy is being used not correctly in my opinion)?</p>
<hr>
<p><strong>UPDATE</strong> Thank you for the answers and comments. Namely the XKCD comics is a spot on. I understand that the analogy with bent sheet of fabric pretty bad, but it seems that it can be fixed if you don't bent the fabric, but just distort the drawn grid. </p>
<p>Would you be so kind and answer the second part of the question as well - whether general relativity is explaining gravitational force. To me it seems that it is not (bending of spacetime simply can not affect two non-moving objects). However most of the time it is being presented that it does.</p> | g6591 | [
-0.0013714126544073224,
0.04203972965478897,
-0.006108108442276716,
-0.035402197390794754,
0.05835016071796417,
0.055400069802999496,
0.023938069120049477,
0.03278118371963501,
-0.04997308924794197,
-0.04558849707245827,
0.06654645502567291,
-0.04016200825572014,
0.02848927490413189,
0.007631178945302963,
0.011557251214981079,
0.03000451996922493,
0.05538209527730942,
-0.03417014330625534,
0.05739828571677208,
0.03362196311354637,
-0.005935992579907179,
0.01820109598338604,
0.03790230304002762,
-0.037690553814172745,
-0.09768330305814743,
-0.025568939745426178,
0.01215091161429882,
-0.015005337074398994,
-0.07977322489023209,
-0.027171725407242775,
0.042491041123867035,
0.023709522560238838,
0.009864523075520992,
-0.0936572402715683,
-0.009221384301781654,
-0.020321927964687347,
0.016554392874240875,
-0.0047256615944206715,
0.004829114302992821,
0.04231639578938484,
-0.05081091821193695,
0.02670496702194214,
0.007175246253609657,
-0.02149515226483345,
0.02326935902237892,
-0.024495046585798264,
-0.037628207355737686,
-0.012001658789813519,
0.053722865879535675,
-0.062357667833566666,
0.0027006797026842833,
0.060473088175058365,
0.054606202989816666,
0.00016934171435423195,
0.022612743079662323,
-0.014508817344903946,
0.02022925205528736,
0.0017744738142937422,
0.09756752103567123,
-0.0006749521708115935,
-0.03163984790444374,
0.03982889652252197,
0.051193393766880035,
-0.0025387019850313663,
0.016918214038014412,
0.036212753504514694,
-0.02368265576660633,
-0.032565563917160034,
0.04364977777004242,
-0.007912012748420238,
0.020895374938845634,
0.00836536567658186,
0.010230359621345997,
-0.016726532950997353,
-0.052051663398742676,
0.02600260265171528,
-0.0031233348418027163,
-0.00019453854474704713,
-0.0021932567469775677,
0.004028958734124899,
-0.0022340151481330395,
0.029400497674942017,
0.021035615354776382,
0.05712456256151199,
0.12837262451648712,
-0.010568302124738693,
-0.04764656722545624,
0.019460899755358696,
0.019433805719017982,
0.03288619592785835,
0.04103581979870796,
-0.027491845190525055,
0.029014529660344124,
0.05245751142501831,
-0.02424478903412819,
-0.03631909191608429,
-0.03301330655813217,
0.05211319029331207,
-0.00945034809410572,
0.03263475000858307,
-0.04378027841448784,
-0.013518721796572208,
0.006748302839696407,
0.022043952718377113,
-0.019872920587658882,
0.03545636311173439,
0.023957088589668274,
0.059362176805734634,
0.01643696241080761,
-0.056814588606357574,
-0.09060391783714294,
-0.005935553926974535,
0.009412314742803574,
-0.03400832414627075,
0.005838474724441767,
-0.04728156700730324,
0.07909274846315384,
-0.02748933620750904,
-0.0004432254354469478,
0.00651837233453989,
-0.0205093827098608,
0.05728312209248543,
0.027681227773427963,
0.05459143593907356,
-0.026058310642838478,
-0.06103525310754776,
0.03333663195371628,
-0.009431895799934864,
-0.012610949575901031,
-0.027143210172653198,
0.022140424698591232,
-0.029104266315698624,
0.09377864748239517,
0.01621861197054386,
-0.01610550656914711,
0.033807478845119476,
-0.0016315019456669688,
-0.02569710835814476,
-0.03019420988857746,
0.020018495619297028,
0.01047398429363966,
-0.044636402279138565,
0.032190367579460144,
-0.030630039051175117,
0.006109080743044615,
0.023585733026266098,
-0.03291090205311775,
0.038399625569581985,
0.04491722211241722,
-0.006971017457544804,
0.01679827645421028,
0.09449280053377151,
0.0005112834624014795,
-0.08651123195886612,
0.05640575662255287,
-0.006150154862552881,
0.009782345965504646,
0.007215464953333139,
0.04996167868375778,
0.03151295706629753,
0.07766395807266235,
-0.0165127944201231,
-0.03757091984152794,
0.005207208916544914,
-0.03953249379992485,
0.031152695417404175,
-0.020938411355018616,
-0.047349948436021805,
0.0051259673200547695,
-0.022548632696270943,
-0.054962169378995895,
-0.025815965607762337,
0.013125689700245857,
0.04441973939538002,
-0.022063642740249634,
0.026976242661476135,
0.03940301388502121,
-0.04955127462744713,
-0.024856112897396088,
-0.019504424184560776,
-0.013904400169849396,
-0.05075123906135559,
0.0014373688027262688,
-0.04176754876971245,
-0.017587043344974518,
-0.02114252559840679,
-0.02610079012811184,
0.044966667890548706,
-0.012327715754508972,
0.04140409082174301,
-0.03230055794119835,
-0.02189958468079567,
0.006951907183974981,
0.011975256726145744,
-0.03721485286951065,
0.0034433691762387753,
0.03152594715356827,
-0.01112257968634367,
-0.010579322464764118,
0.03321400657296181,
0.010592318139970303,
-0.022727129980921745,
0.026486678048968315,
0.011164953000843525,
0.02734263800084591,
0.027646157890558243,
-0.0773925930261612,
0.013710280880331993,
0.05744519457221031,
-0.029439281672239304,
0.05869726464152336,
-0.034964483231306076,
0.04157854616641998,
-0.0397205613553524,
-0.034106913954019547,
0.005391085520386696,
-0.028116052970290184,
0.005856386385858059,
-0.07478906959295273,
0.02518322877585888,
0.002508427482098341,
-0.015841461718082428,
0.047302402555942535,
-0.02451738528907299,
0.010398544371128082,
0.009062395431101322,
-0.006262979470193386,
-0.043765198439359665,
0.01055071596056223,
-0.012115697376430035,
-0.07208926230669022,
-0.025987902656197548,
-0.0185543242841959,
0.0033500988502055407,
0.05027076601982117,
-0.00011391934822313488,
0.011963450349867344,
0.00653028255328536,
0.006761581636965275,
-0.01192293781787157,
0.014305510558187962,
-0.0242319293320179,
0.002759090391919017,
-0.040074847638607025,
0.034783508628606796,
-0.0009436547989025712,
0.03824354335665703,
-0.07177522778511047,
0.03477449715137482,
0.05494282767176628,
0.028239676728844643,
-0.050133924931287766,
-0.06481423228979111,
0.010324389673769474,
0.036964014172554016,
0.006093522533774376,
-0.004727625288069248,
0.051895368844270706,
-0.10824386030435562,
-0.015215196646749973,
0.04476133733987808,
-0.06069966405630112,
-0.010877726599574089,
0.04269018769264221,
-0.09310977160930634,
-0.026295993477106094,
0.011148640885949135,
-0.000014391909644473344,
-0.0031101806089282036,
0.019624236971139908,
-0.04567587748169899,
0.014281011186540127,
-0.03937060758471489,
-0.04010637104511261,
-0.04476715996861458,
0.021224496886134148,
-0.029313543811440468,
-0.011631857603788376,
-0.059308044612407684,
-0.045705635100603104,
0.02514311857521534,
-0.004857910796999931,
-0.036261770874261856,
-0.04165465384721756,
0.05590938404202461,
-0.010885666124522686,
-0.05209878832101822,
-0.024882258847355843,
0.02860523760318756,
0.03803865984082222,
-0.010481790639460087,
0.03695716708898544,
0.016679657623171806,
-0.042756058275699615,
-0.037710417062044144,
0.004898746497929096,
-0.018193764612078667,
0.02249377965927124,
-0.02755124680697918,
-0.012365230359137058,
-0.010589266195893288,
0.020764127373695374,
0.052692245692014694,
0.047071002423763275,
-0.0008561841677874327,
-0.031503960490226746,
-0.003774663433432579,
-0.08377397805452347,
-0.018023351207375526,
-0.037237800657749176,
0.012021545320749283,
0.013413730077445507,
0.023573031648993492,
0.04501769691705704,
-0.012606765143573284,
-0.02541940100491047,
0.004721478093415499,
0.002338364953175187,
0.001981790643185377,
0.016281235963106155,
0.02318362146615982,
0.010840246453881264,
0.00046559583279304206,
-0.002436634385958314,
-0.028234755620360374,
0.031148051843047142,
-0.003915541339665651,
-0.024550046771764755,
0.0017784514930099249,
-0.017131300643086433,
0.03626324608922005,
-0.03637063503265381,
-0.022245323285460472,
-0.015122965909540653,
-0.05652960389852524,
0.02864951640367508,
0.020208995789289474,
-0.043158259242773056,
0.047798626124858856,
-0.011799132451415062,
0.028308497741818428,
-0.05385415628552437,
-0.06292290985584259,
0.018583746626973152,
0.021536463871598244,
0.03959503024816513,
0.02930956706404686,
0.010655113495886326,
-0.042995162308216095,
-0.017577655613422394,
0.018815219402313232,
-0.025268882513046265,
0.0009640646167099476,
-0.01679879054427147,
-0.01793310046195984,
-0.0010067842667922378,
0.0018662252696231008,
0.010985169559717178,
-0.031210357323288918,
-0.035918839275836945,
0.03247386962175369,
0.0022928775288164616,
-0.029715469107031822,
0.03713798150420189,
-0.00666958000510931,
0.011794941499829292,
0.030115025117993355,
0.0008982883882708848,
-0.028223687782883644,
-0.008920402266085148,
0.0422656312584877,
0.0029277605935931206,
-0.02507011592388153,
0.004627312067896128,
0.05714207515120506,
-0.0360071063041687,
0.06194378808140755,
0.014355646446347237,
-0.03102528676390648,
0.035434894263744354,
0.06271526962518692,
0.04108421504497528,
0.02310749888420105,
0.028679724782705307,
0.057432305067777634,
-0.015776360407471657,
-0.032523225992918015,
-0.0011330818524584174,
0.017179634422063828,
-0.021974436938762665,
-0.01852395012974739,
0.002093240153044462,
-0.017873290926218033,
-0.02717244252562523,
-0.0196518674492836,
-0.010623489506542683,
0.02116706408560276,
0.06123194098472595,
0.016154548153281212,
-0.004234398249536753,
-0.03557037189602852,
0.036722827702760696,
-0.011743729934096336,
0.014388902112841606,
-0.033626489341259,
-0.0031771643552929163,
0.029613640159368515,
-0.05229893699288368,
-0.02419177256524563,
-0.042553700506687164,
0.036657389253377914,
0.05638866499066353,
-0.013543600216507912,
-0.07442457228899002,
0.07089309394359589,
-0.011023523285984993,
0.013626959174871445,
0.03125912696123123,
0.0030970140360295773,
0.03375724330544472,
0.013981607742607594,
0.08147779852151871,
-0.02829822525382042,
-0.018903808668255806,
-0.017338449135422707,
0.12241879105567932,
-0.0034772781655192375,
-0.002075537573546171,
0.04963389411568642,
-0.03138578310608864,
-0.0007160084205679595,
0.003566908184438944,
0.016172192990779877,
0.014350274577736855,
-0.05919702723622322,
0.0721946656703949,
0.017646070569753647,
0.08459599316120148,
0.01739196479320526,
-0.0016557929338887334,
0.08842184394598007,
0.026365945115685463,
0.0216655470430851,
-0.005015740171074867,
-0.01886332966387272,
0.02031417191028595,
-0.04016847535967827,
-0.005673930048942566,
-0.02755492925643921,
-0.024300720542669296,
-0.06402313709259033,
0.012624640017747879,
0.011164073832333088,
-0.012782271951436996,
-0.00928895641118288,
0.02916758321225643,
0.025591937825083733,
-0.0026827254332602024,
-0.04053883999586105,
0.003555733012035489,
-0.05242815241217613,
-0.004245483782142401,
0.02156616374850273,
0.004130193963646889,
0.013335301540791988,
-0.021053584292531013,
-0.06983698904514313,
-0.03660183399915695,
-0.015486433170735836,
0.015558741986751556,
-0.030851585790514946,
-0.023514561355113983,
-0.039966341108083725,
0.0075649358332157135,
0.04606589674949646,
0.05081389099359512,
-0.023472484201192856,
0.021793808788061142,
-0.008918448351323605,
-0.0401916429400444,
-0.01870923861861229,
-0.022804664447903633,
0.04586510732769966,
-0.07466089725494385,
0.03730341047048569,
-0.030225833877921104,
0.026651857420802116,
0.044550348073244095,
0.04852162301540375,
-0.008637896738946438,
0.013458678498864174,
-0.06099095195531845,
-0.029254766181111336,
-0.007427804172039032,
-0.02612530253827572,
0.028235817328095436,
0.014181209728121758,
-0.008391055278480053,
0.0015079195145517588,
-0.04376951605081558,
0.013223768211901188,
0.07600430399179459,
0.018875865265727043,
-0.019549543038010597,
-0.02288670465350151,
0.03341077268123627,
0.053842127323150635,
-0.0651361271739006,
-0.020662184804677963,
0.13946011662483215,
-0.020338328555226326,
-0.004731704946607351,
-0.014104652218520641,
0.019446536898612976,
0.06712343543767929,
-0.01576213724911213,
0.026965485885739326,
0.014642898924648762,
0.05497186258435249,
-0.02163773775100708,
0.02843368612229824,
0.02060122601687908,
0.004333102609962225,
-0.039924997836351395,
0.012756016105413437,
-0.017494160681962967,
-0.03449182212352753,
0.04250889644026756,
0.047288332134485245,
0.04942190274596214,
0.009311329573392868,
0.02239813655614853,
0.04675109684467316,
0.032060544937849045,
0.008512676693499088,
-0.01963835395872593,
0.038632117211818695,
0.009207447059452534,
0.05429573729634285,
-0.04235612973570824,
-0.026632897555828094,
0.026949848979711533,
-0.016257567331194878,
0.060512740164995193,
-0.04209038242697716,
0.01520788948982954,
-0.022807294502854347,
-0.04165026918053627,
0.052276868373155594,
-0.01704096421599388,
-0.019236134365200996,
-0.024614594876766205,
0.03661078214645386,
0.053092870861291885,
0.023782679811120033,
0.016138922423124313,
0.019384566694498062,
-0.1122748926281929,
0.05918969213962555,
-0.009131267666816711,
0.021881498396396637,
-0.019477492198348045,
-0.00941876694560051,
-0.011897897347807884,
0.035579655319452286,
0.005025964695960283,
0.02569899894297123,
-0.020627206191420555,
0.0684601366519928,
0.037476036697626114,
-0.03418729081749916,
-0.002457710914313793,
0.0368269719183445,
0.009854163974523544,
-0.026082690805196762,
0.003580824239179492,
-0.00854029692709446,
-0.016001978889107704,
-0.06651628017425537,
-0.0045190248638391495,
0.00642057042568922,
-0.02409629337489605,
0.012044709175825119,
-0.06095598638057709,
-0.07690167427062988,
0.038656365126371384,
-0.06870532035827637,
-0.0173804834485054,
0.01583246886730194,
-0.02320421300828457,
-0.022182326763868332,
0.0025230119936168194,
0.01747826673090458,
-0.03048705868422985,
-0.04670337960124016,
-0.028782330453395844,
0.023686280474066734,
0.010753883048892021,
-0.014758842065930367,
-0.0019828344229608774,
-0.06648369878530502,
0.023948246613144875,
0.01722114160656929,
0.017581192776560783,
0.03104531019926071,
-0.01220212783664465,
-0.02870986983180046,
-0.020575828850269318,
0.03315671160817146,
-0.03728009760379791,
-0.06135222688317299,
0.02158760093152523,
-0.009749425575137138,
0.032672587782144547,
-0.010831682942807674,
-0.04784129932522774,
-0.032016728073358536,
-0.008173485286533833,
0.0108613520860672,
-0.04749177396297455,
-0.012601288966834545,
0.006891594734042883,
0.05077109485864639,
0.007725810166448355,
0.01924699731171131,
0.023547999560832977,
-0.05314926430583,
0.031294457614421844,
0.020243456587195396,
0.013427932746708393,
-0.05624040216207504,
-0.0343073345720768,
-0.023529592901468277,
0.011321654543280602,
0.004544752184301615,
0.08630490303039551,
-0.023559747263789177,
0.05107930675148964,
0.039429280906915665,
0.03677217289805412,
-0.050034575164318085,
-0.025759803131222725,
0.028557121753692627,
-0.02025335468351841,
-0.021027792245149612,
-0.0394350104033947,
0.00190089107491076,
0.018404880538582802,
-0.06622442603111267,
0.008376999758183956,
0.0035311563406139612,
-0.05038808658719063,
-0.03727766126394272,
0.05754871293902397,
-0.06955661624670029,
0.0537978932261467,
-0.04085041210055351,
-0.029312219470739365,
0.03442807123064995,
-0.0782160684466362,
-0.03462231904268265,
-0.06495174020528793,
-0.00964075792580843,
0.025443563237786293,
-0.07834853231906891,
0.06216299161314964,
0.007647899445146322,
0.0030271040741354227,
-0.03369494527578354,
0.04755546525120735,
-0.017508849501609802,
-0.036198582500219345,
0.02879444882273674,
-0.011186014860868454,
0.004386442247778177,
-0.05652263015508652,
-0.027721388265490532,
-0.027699511498212814,
0.025304442271590233,
-0.029708806425333023,
-0.0003705692943185568,
0.04530810937285423,
0.07548598945140839,
0.032129913568496704,
-0.0855739489197731,
0.03217308595776558,
0.0490909218788147,
0.046016354113817215,
-0.030792236328125,
-0.011477455496788025,
0.01579505391418934,
0.019303087145090103,
-0.043218791484832764,
0.05426618456840515,
0.017999904230237007,
0.008729091845452785,
-0.015715816989541054,
0.03559226542711258,
0.004683414474129677,
-0.005627559032291174,
-0.007577045354992151,
0.010255248285830021,
-0.09708943963050842,
-0.0225451048463583,
0.028135456144809723,
0.02100159414112568,
-0.041661009192466736,
-0.04721987619996071,
-0.0012412536889314651,
-0.06829575449228287,
0.024364639073610306,
-0.0019871126860380173,
0.011968866921961308,
-0.02085880935192108,
0.01691335439682007,
0.008844506926834583,
-0.010199743323028088,
0.009159054607152939,
0.0021446587052196264,
-0.008069436997175217,
0.007757487241178751,
0.010300930589437485,
-0.0031261707190424204,
-0.07355687767267227,
-0.011528853327035904,
0.03058384731411934,
0.017030833289027214,
-0.04037737846374512,
-0.0548495315015316,
0.01902814209461212,
-0.04827040806412697,
0.004285420756787062,
-0.01970960572361946,
0.035660166293382645,
0.012463611550629139,
0.07029269635677338,
0.009952671825885773,
-0.060792285948991776,
-0.002168310107663274,
0.0029911426827311516,
-0.017221059650182724,
-0.001773921656422317,
-0.01045915950089693,
0.02359909750521183,
0.010151972062885761,
-0.012482190504670143,
-0.017963282763957977,
0.016429640352725983,
0.02989022061228752,
0.008016573265194893,
0.008763590827584267,
0.038083259016275406,
-0.011093423701822758,
-0.025941526517271996,
0.06908733397722244,
-0.0657690241932869,
-0.04501817747950554,
-0.002109968103468418,
0.0205158069729805,
-0.013672241941094398,
-0.027563052251935005,
-0.003589056432247162,
-0.010797983035445213,
-0.03960710018873215,
0.010291323997080326,
-0.0031569297425448895,
-0.05941060557961464,
0.03053232841193676
] |
<p>On a quantum scale the smallest unit is the <a href="http://en.wikipedia.org/wiki/Planck_scale">Planck scale</a>, which is a discrete measure.</p>
<p>There several question that come to mind:</p>
<ol>
<li>Does that mean that particles can only live in a discrete grid-like structure, i.e. have to "magically" jump from one pocket to the next? But where are they in between? Does that even give rise to the old paradox that movement as such is impossible (e.g. <a href="http://en.wikipedia.org/wiki/Zeno%27s_paradoxes">Zeno's paradox</a>)?</li>
<li>Does the same hold true for time (i.e. that it is discrete) - with all the ensuing paradoxes?</li>
<li>Mathematically does it mean that you have to use difference equations instead of differential equations? (And sums instead of integrals?)</li>
<li>From the point of view of the space metric do you have to use a discrete metric (e.g. the <a href="http://en.wikipedia.org/wiki/Manhattan_metric">Manhattan metric</a>) instead of good old Pythagoras?</li>
</ol>
<p>Thank you for giving me some answers and/or references where I can turn to.</p>
<p><strong>Update:</strong> I just saw this call for papers - it seems to be quite a topic after all: <em>Is Reality Digital or Analog?</em> FQXi Essay Contest, 2011. <a href="http://web.archive.org/web/20110504051348/http://www.fqxi.org/community/essay">Call for papers (at Wayback Machine)</a>, <a href="http://www.fqxi.org/community/forum/category/31417">All essays</a>, <a href="http://www.fqxi.org/community/essay/winners/2011.1">Winners</a>. One can find some pretty amazing papers over there.</p> | g114 | [
-0.021113045513629913,
0.05783569812774658,
-0.03293889760971069,
-0.04252725467085838,
0.029836516827344894,
-0.019628873094916344,
-0.017933689057826996,
-0.03056729957461357,
-0.030221864581108093,
-0.05608903244137764,
-0.01311683189123869,
-0.02301853708922863,
0.04420856013894081,
-0.050379566848278046,
-0.03058904968202114,
-0.014333384111523628,
0.036595698446035385,
-0.028214989230036736,
0.021284697577357292,
0.006704210769385099,
0.0073579587042331696,
0.021992510184645653,
0.04205647110939026,
-0.047380976378917694,
0.0027047989424318075,
-0.007487150840461254,
0.021833227947354317,
-0.05190129950642586,
-0.05748995020985603,
0.015445858240127563,
0.017793864011764526,
-0.017714355140924454,
0.05608263239264488,
-0.049605898559093475,
-0.03239826485514641,
0.02608911320567131,
0.031253814697265625,
0.020230820402503014,
0.017661703750491142,
0.03109726868569851,
0.03231106325984001,
-0.05574716627597809,
-0.02259954996407032,
-0.04128847271203995,
0.021990425884723663,
0.013665485195815563,
-0.018024099990725517,
-0.006298081949353218,
0.06052042171359062,
0.021853948011994362,
-0.02317408286035061,
0.046354979276657104,
0.037430644035339355,
0.05099979043006897,
-0.0040925052016973495,
0.03481274098157883,
0.03764259070158005,
0.019960502162575722,
0.07915555685758591,
0.03047674521803856,
0.011334378272294998,
-0.0014112613862380385,
-0.011733708903193474,
-0.005724471062421799,
0.04946675896644592,
0.020340217277407646,
-0.03335995227098465,
0.0014946602750569582,
-0.014464088715612888,
-0.0020476849749684334,
-0.02596367336809635,
-0.09204470366239548,
0.012364200316369534,
-0.03210679441690445,
-0.008130662143230438,
0.0580856017768383,
0.01619337871670723,
-0.0036284560337662697,
0.019430335611104965,
-0.016236700117588043,
-0.057270266115665436,
0.002274345140904188,
0.06770068407058716,
-0.025115681812167168,
0.05546381697058678,
0.019465824589133263,
-0.02336157113313675,
-0.0323144868016243,
-0.0019863254856318235,
0.053821660578250885,
-0.0264095701277256,
-0.032116346061229706,
0.029029902070760727,
-0.01295134425163269,
-0.021378835663199425,
-0.01525262650102377,
0.0032372171990573406,
0.058510828763246536,
-0.030128294602036476,
0.004288858734071255,
-0.01792292483150959,
0.03034001961350441,
-0.01706286333501339,
-0.011963761411607265,
-0.0030297618359327316,
-0.004434634931385517,
-0.009158546105027199,
0.021555522456765175,
0.046328410506248474,
-0.0222783200442791,
-0.0347665399312973,
-0.030709179118275642,
-0.045543648302555084,
-0.018944894894957542,
-0.009006193839013577,
0.022588687017560005,
0.04088369756937027,
-0.03594322130084038,
0.019963592290878296,
0.009141186252236366,
0.015976784750819206,
0.0016307382611557841,
0.03447731211781502,
0.04645892605185509,
-0.0548158623278141,
0.0066582560539245605,
0.032810043543577194,
-0.0006936104036867619,
-0.003735274076461792,
-0.0251489095389843,
0.08611159771680832,
0.05837657302618027,
-0.1266648918390274,
0.0073494501411914825,
-0.005920860450714827,
0.016577303409576416,
0.012547865509986877,
-0.002094508847221732,
-0.011281139217317104,
0.024245796725153923,
0.009031448513269424,
-0.014474159106612206,
-0.008349878713488579,
-0.021616609767079353,
0.0046793739311397076,
-0.05620001628994942,
-0.04357200115919113,
-0.03809523582458496,
-0.015580354258418083,
-0.015110773034393787,
0.01074674166738987,
0.07581451535224915,
0.005787139758467674,
0.006155964452773333,
-0.017387155443429947,
0.0037920998875051737,
0.04613516479730606,
0.08327771723270416,
-0.028717156499624252,
-0.07930057495832443,
0.028105467557907104,
-0.019750701263546944,
0.005407852120697498,
0.03550292178988457,
-0.004933449439704418,
0.007537674158811569,
0.02929556556046009,
-0.0021905661560595036,
0.017472494393587112,
-0.07148914039134979,
-0.015788909047842026,
-0.04457521811127663,
0.004730308428406715,
0.06324609369039536,
0.004893437027931213,
0.0823102742433548,
0.00407790020108223,
0.0058997017331421375,
-0.05263336002826691,
-0.06886432319879532,
0.022079892456531525,
-0.015724483877420425,
0.021766886115074158,
-0.07589229196310043,
-0.00240722787566483,
-0.01974872499704361,
-0.010332458652555943,
0.016296997666358948,
0.0212232768535614,
-0.020461419597268105,
-0.012057819403707981,
-0.013811353594064713,
0.03336530551314354,
-0.00807074923068285,
-0.008586050942540169,
-0.0354686863720417,
0.0033225619699805975,
-0.05039522796869278,
-0.012953071855008602,
-0.061669740825891495,
0.03727814927697182,
0.03895178437232971,
0.04269963875412941,
-0.025276560336351395,
0.0440659262239933,
0.004641581326723099,
-0.025169573724269867,
-0.01102154515683651,
-0.0012878800043836236,
-0.03117361105978489,
0.044923335313797,
-0.050357356667518616,
-0.06343047320842743,
-0.0017011644085869193,
-0.07347372174263,
-0.00042693899013102055,
0.0452047623693943,
-0.01871407963335514,
0.03456622734665871,
0.005772132892161608,
-0.01461631990969181,
-0.052412211894989014,
0.01416336465626955,
0.0030630528926849365,
0.010325891897082329,
-0.014423687011003494,
0.011335897259414196,
-0.017293881624937057,
0.027480699121952057,
0.09296128898859024,
-0.10042156279087067,
-0.024069329723715782,
0.03545572981238365,
-0.037676770240068436,
0.02932312712073326,
0.060882363468408585,
-0.031709618866443634,
0.006808754056692123,
0.04934021830558777,
0.02369317226111889,
0.09524029493331909,
-0.030410628765821457,
-0.06555736064910889,
0.03138143569231033,
0.0488252155482769,
-0.028711935505270958,
-0.008178988471627235,
0.029605761170387268,
-0.023268382996320724,
-0.013173110783100128,
0.02352004311978817,
-0.07206793129444122,
-0.008996336720883846,
-0.027384338900446892,
0.014345240779221058,
0.02592521160840988,
0.03562714159488678,
-0.009395239874720573,
-0.0796516165137291,
0.01964503899216652,
0.03508720546960831,
0.0061069088988006115,
-0.018869874998927116,
0.017196865752339363,
0.012822747230529785,
-0.053791988641023636,
-0.01184232346713543,
0.01788174733519554,
-0.020770469680428505,
-0.04111410304903984,
0.028224695473909378,
0.05723598599433899,
-0.006591208279132843,
0.04820384085178375,
-0.00015004570013843477,
-0.012052974663674831,
0.023618066683411598,
-0.036787163466215134,
0.07135031372308731,
-0.015768706798553467,
-0.023749511688947678,
-0.014871814288198948,
-0.07417083531618118,
-0.023045703768730164,
0.047594111412763596,
-0.07632362097501755,
0.006240821443498135,
-0.014027854427695274,
-0.05405097454786301,
0.06205077841877937,
-0.05231766402721405,
0.0066029466688632965,
0.006251027807593346,
0.013273532502353191,
-0.06696658581495285,
0.06907927244901657,
-0.03969482704997063,
-0.08103674650192261,
-0.009184815920889378,
-0.020147211849689484,
0.023121410980820656,
-0.02914074994623661,
-0.005885285325348377,
0.01210821233689785,
0.05991242453455925,
0.030537156388163567,
-0.0363042876124382,
-0.0030737982597202063,
-0.0015151238767430186,
-0.02800092287361622,
0.023030655458569527,
0.06199873983860016,
-0.018160812556743622,
-0.0015144773060455918,
0.013316217809915543,
-0.052872657775878906,
0.0046772221103310585,
0.0666351392865181,
0.022180944681167603,
-0.021246155723929405,
0.05692048370838165,
-0.066700279712677,
-0.019269615411758423,
-0.049699146300554276,
0.04014292731881142,
-0.002022203989326954,
-0.07009910047054291,
0.009435981512069702,
0.042572446167469025,
0.05181014537811279,
0.032357193529605865,
-0.01005614548921585,
0.03955696523189545,
0.005106070078909397,
-0.060222920030355453,
-0.06436877697706223,
-0.06900139153003693,
0.02049669250845909,
0.0309771541506052,
-0.026795674115419388,
-0.09293236583471298,
-0.023074427619576454,
-0.07843407988548279,
0.021540408954024315,
0.023567093536257744,
0.01705927960574627,
0.06883560866117477,
0.012870276346802711,
0.002271730452775955,
0.006647209171205759,
-0.004663792904466391,
-0.036571647971868515,
-0.016419721767306328,
-0.023254672065377235,
0.0013114848406985402,
0.008294404484331608,
0.03861217200756073,
0.027798805385828018,
0.04817112907767296,
-0.013854799792170525,
-0.013091146014630795,
-0.04748545587062836,
0.04728398844599724,
-0.023362236097455025,
0.00457774056121707,
0.005147410556674004,
-0.04019201919436455,
0.05811179801821709,
-0.00009944922203430906,
-0.008244194090366364,
-0.0569739043712616,
0.04942336305975914,
-0.011661220341920853,
0.059934746474027634,
0.03056037425994873,
-0.06272444128990173,
-0.0038102935068309307,
-0.004266858566552401,
-0.01217786967754364,
-0.0022311904467642307,
-0.022932130843400955,
0.05155980587005615,
0.03804156929254532,
-0.03249098360538483,
0.047928765416145325,
-0.009108217433094978,
-0.06993475556373596,
-0.06270750612020493,
-0.025768114253878593,
-0.025519290938973427,
-0.036000948399305344,
-0.005167943891137838,
-0.04412340745329857,
0.01840483769774437,
0.00007815023127477616,
0.011421432718634605,
0.02756619080901146,
0.00670229597017169,
0.00153428188059479,
0.05961557850241661,
0.017068857327103615,
0.005941160023212433,
-0.039910443127155304,
0.013240842148661613,
0.030741561204195023,
-0.018756529316306114,
0.0023157603573054075,
0.029724983498454094,
-0.02925924025475979,
-0.022679494693875313,
0.028175055980682373,
0.0467570461332798,
-0.0014146714238449931,
-0.07014010101556778,
0.01104028895497322,
0.012814879417419434,
-0.010983120650053024,
-0.04186372831463814,
0.0016745913308113813,
0.04263424500823021,
-0.011212408542633057,
0.04197269678115845,
-0.022421684116125107,
0.016955828294157982,
-0.06682819128036499,
0.034253790974617004,
0.030505092814564705,
0.06317532807588577,
-0.04973902553319931,
-0.005845985375344753,
0.01902167685329914,
0.05134420096874237,
0.023351747542619705,
0.07947880774736404,
0.022197403013706207,
0.02174600213766098,
-0.02213873900473118,
0.028251852840185165,
-0.01757943630218506,
-0.037579361349344254,
0.09366156905889511,
0.0251337718218565,
0.02730187401175499,
0.015582563355565071,
-0.011140605434775352,
0.04358807951211929,
-0.06409953534603119,
-0.016838891431689262,
-0.02934155985713005,
0.017906764522194862,
0.06090903654694557,
0.05174194276332855,
-0.018482059240341187,
-0.0851905420422554,
-0.00410812720656395,
-0.036461472511291504,
-0.015307503752410412,
0.0417531318962574,
0.0394725576043129,
0.021516991779208183,
-0.05737268924713135,
-0.02569904737174511,
-0.03305448964238167,
0.0624794103205204,
0.009956504218280315,
-0.003947888035327196,
-0.07777784019708633,
0.03872030973434448,
-0.07712741941213608,
-0.06788236647844315,
0.04205229505896568,
0.0313347689807415,
-0.014835448004305363,
0.03820497542619705,
-0.0133860157802701,
-0.0015847340691834688,
-0.011659976094961166,
0.053118105977773666,
-0.02630995400249958,
-0.03263939544558525,
-0.030330315232276917,
0.0056077707558870316,
0.0228680782020092,
0.025532709434628487,
-0.0028478242456912994,
0.0073586441576480865,
-0.018860027194023132,
-0.03736364096403122,
-0.0030913595110177994,
0.02357790432870388,
0.009816291742026806,
-0.011586627922952175,
0.04548513516783714,
0.008709684014320374,
-0.017414255067706108,
-0.005144156981259584,
-0.0008506266749463975,
-0.006879482883960009,
-0.000906929955817759,
-0.006277817767113447,
-0.03735596314072609,
0.05876779556274414,
0.005626121070235968,
-0.045309919863939285,
0.0203507412225008,
0.028568312525749207,
0.06272930651903152,
0.011404024437069893,
0.014662348665297031,
-0.003922945354133844,
0.006712069734930992,
-0.002014382276684046,
-0.03503958880901337,
0.013858169317245483,
0.0013655547518283129,
-0.05234552174806595,
-0.024631522595882416,
-0.017245126888155937,
0.012386039830744267,
-0.0062626018188893795,
-0.00913599319756031,
-0.025649486109614372,
0.04711200296878815,
-0.02479998767375946,
-0.005972364451736212,
0.00907896552234888,
-0.07167749851942062,
-0.02687181904911995,
0.01078897062689066,
0.06748814880847931,
0.04374523460865021,
0.031095100566744804,
0.0015441944124177098,
0.03514213114976883,
-0.04009681195020676,
0.04296620190143585,
0.018720930442214012,
0.0727330818772316,
0.03639136999845505,
0.012936851009726524,
-0.05466447398066521,
-0.05585193261504173,
0.03460685536265373,
0.04494671896100044,
0.008860362693667412,
-0.016860662028193474,
0.01052530761808157,
0.03980754315853119,
0.03650574013590813,
-0.012505083344876766,
-0.028647636994719505,
0.031122203916311264,
-0.004587452858686447,
0.02443588525056839,
-0.05979794263839722,
-0.022278498858213425,
0.02545068971812725,
-0.029583202674984932,
-0.029472067952156067,
-0.003339156974107027,
0.056229718029499054,
0.012535354122519493,
0.026601087301969528,
-0.0476175881922245,
0.015669111162424088,
-0.0629369392991066,
0.015995318070054054,
0.025629451498389244,
0.04376114904880524,
0.010824006050825119,
0.018437689170241356,
0.01486106775701046,
0.06891633570194244,
0.024919504299759865,
-0.030826259404420853,
-0.02075168676674366,
-0.011513995006680489,
-0.019498975947499275,
-0.09652230888605118,
-0.002021797001361847,
0.006013771519064903,
0.06560904532670975,
-0.00324985827319324,
-0.003932297229766846,
-0.012510203756392002,
0.08181431889533997,
-0.020594576373696327,
-0.0011355846654623747,
-0.010289584286510944,
0.007040291093289852,
0.009622901678085327,
-0.021335087716579437,
-0.010675748810172081,
-0.025404522195458412,
-0.0666084811091423,
-0.022901320829987526,
0.03635339438915253,
-0.03728485852479935,
-0.062449969351291656,
0.026387440040707588,
-0.012881564907729626,
-0.05156715214252472,
-0.019411396235227585,
-0.043134164065122604,
-0.021194813773036003,
0.03462300822138786,
-0.049445778131484985,
0.023407526314258575,
-0.007295394781976938,
0.04430433735251427,
-0.009764962829649448,
0.0482364185154438,
0.047622960060834885,
0.010668785311281681,
-0.0011584748281165957,
-0.04618224501609802,
0.010504207573831081,
-0.00566817307844758,
-0.03819042816758156,
0.023121148347854614,
0.01093333587050438,
-0.024373870342969894,
0.0007293378002941608,
-0.02166740968823433,
-0.0032254441175609827,
0.023462004959583282,
0.003426349489018321,
0.03430412709712982,
0.023097367957234383,
0.031166648492217064,
-0.02781020477414131,
-0.011149419471621513,
0.03734854981303215,
0.0719885379076004,
-0.036945097148418427,
0.004049388226121664,
-0.038481444120407104,
-0.012046081945300102,
0.05751020461320877,
-0.018581829965114594,
0.06967899948358536,
-0.005668574012815952,
0.044429533183574677,
-0.02847525291144848,
-0.004820193164050579,
0.03336312994360924,
0.02166653238236904,
0.06589151173830032,
-0.037033289670944214,
-0.012231276370584965,
0.05708542838692665,
-0.014942435547709465,
-0.03368464484810829,
-0.0052869608625769615,
-0.02094407193362713,
0.04088549315929413,
-0.004974795505404472,
-0.0018963725306093693,
0.035033442080020905,
-0.070368193089962,
-0.012302028946578503,
-0.05827614292502403,
0.05114607512950897,
-0.010170998051762581,
0.011106613092124462,
0.05986184999346733,
0.01453208178281784,
-0.004624950233846903,
0.015356281772255898,
-0.0471891388297081,
0.0050420877523720264,
-0.03169967979192734,
-0.020753197371959686,
0.024812869727611542,
0.0697166919708252,
-0.03556056693196297,
-0.020395897328853607,
0.05745338648557663,
0.014457453973591328,
-0.015135404653847218,
0.08398118615150452,
-0.0010426427470520139,
-0.0035682751331478357,
-0.07499948143959045,
-0.06330257654190063,
0.022719355300068855,
-0.03625526651740074,
0.012324963696300983,
0.03527236357331276,
-0.06229615956544876,
0.011918038129806519,
-0.024381855502724648,
0.048828091472387314,
0.02183344028890133,
-0.04601620137691498,
0.023441456258296967,
0.03304865211248398,
0.04687659814953804,
0.012379568070173264,
-0.023797187954187393,
0.01007272582501173,
-0.005905137863010168,
-0.040092721581459045,
-0.016428930684924126,
0.03779705613851547,
0.0247286856174469,
0.01922684721648693,
-0.02647837996482849,
-0.0557115413248539,
-0.03888905420899391,
-0.030642755329608917,
0.014208982698619366,
0.0063581448048353195,
-0.02593996934592724,
0.05533442273736,
-0.012945613823831081,
-0.016485445201396942,
-0.012436078861355782,
0.04645712673664093,
-0.01888926699757576,
0.0327799916267395,
-0.03380201384425163,
-0.02089816704392433,
-0.044411033391952515,
-0.00230580591596663,
-0.05121176317334175,
0.003073351690545678,
-0.04364446923136711,
0.014238913543522358,
-0.007057052105665207,
-0.02356744557619095,
-0.009826664812862873,
-0.027600273489952087,
-0.008785133250057697,
-0.03166496381163597,
0.06069674715399742,
0.026162849739193916,
0.008582258597016335,
0.056595973670482635,
-0.023752018809318542,
-0.020776040852069855,
-0.0033655830193310976,
0.0479043647646904,
0.06189798191189766,
-0.024021806195378304,
-0.028976762667298317,
-0.05597704276442528,
0.029613545164465904,
0.03473828732967377,
0.008826171047985554,
-0.010944955982267857,
0.032392144203186035,
-0.04124996066093445,
0.016284417361021042,
0.03605448827147484,
-0.05387106165289879,
0.04033023118972778,
0.029118964448571205,
0.009531068615615368,
-0.031972505152225494,
0.02408929541707039,
-0.016568100079894066,
0.009069704450666904,
0.042695123702287674,
-0.09182360023260117,
-0.0408053882420063,
0.0030628438107669353,
0.015633419156074524
] |
<p>If a vibrating atom can produce light why can't an alternating current of electrons do the same?</p>
<p>EDIT: When I use the term "light" I mean all EMR</p> | g6592 | [
0.0034606794361025095,
0.04430529475212097,
-0.020377254113554955,
-0.004711575340479612,
0.04867260903120041,
0.02484283037483692,
-0.009254640899598598,
-0.017696639522910118,
0.03445707634091377,
-0.018714040517807007,
0.013359001837670803,
0.010703656822443008,
-0.01641271635890007,
0.04086234048008919,
-0.03531922399997711,
0.006238244473934174,
0.01041880901902914,
-0.00860905647277832,
0.0314834900200367,
0.03927377983927727,
0.02838473580777645,
0.007051759399473667,
-0.005882509518414736,
-0.06896575540304184,
0.021423783153295517,
0.0442538820207119,
0.006059881299734116,
-0.07540085166692734,
-0.052815668284893036,
0.0118508730083704,
0.009197523817420006,
-0.01210889220237732,
0.031971536576747894,
0.030296318233013153,
-0.005493782460689545,
-0.0889723151922226,
-0.00858596246689558,
0.03752966970205307,
0.032469578087329865,
0.01954011060297489,
-0.007769724354147911,
0.046001136302948,
0.004946845583617687,
0.02507718652486801,
0.023205721750855446,
-0.03363058716058731,
0.031242741271853447,
0.04875510185956955,
-0.05017823353409767,
-0.03568852320313454,
0.018708059564232826,
-0.014034471474587917,
0.0394185446202755,
-0.012888114899396896,
0.07365334033966064,
-0.039987608790397644,
-0.06805887818336487,
-0.008147361688315868,
0.04441451653838158,
0.028176797553896904,
-0.026884453371167183,
-0.024775054305791855,
0.008411203511059284,
0.07355333864688873,
0.028942536562681198,
-0.04009687155485153,
-0.021232526749372482,
-0.0464041605591774,
0.07892384380102158,
0.039300426840782166,
0.03629833087325096,
-0.046582844108343124,
-0.04271789640188217,
-0.0005671380204148591,
0.027127781882882118,
0.01308590266853571,
0.0048628877848386765,
0.02277078665792942,
0.03734898194670677,
-0.004311039112508297,
-0.05073340982198715,
-0.012569126673042774,
-0.011599966324865818,
-0.017485758289694786,
0.07609105855226517,
-0.03101233020424843,
-0.016584297642111778,
-0.055324189364910126,
0.025853216648101807,
0.011570494621992111,
0.053433191031217575,
-0.07247567176818848,
0.09278363734483719,
-0.005662302020937204,
-0.01671767793595791,
-0.060132887214422226,
-0.0011836568592116237,
0.019962521269917488,
0.004641325678676367,
-0.023141512647271156,
-0.04346567764878273,
-0.01044752448797226,
0.014277935959398746,
-0.006201899144798517,
0.005843273364007473,
-0.012372826226055622,
-0.010862656868994236,
-0.04683437570929527,
0.0055486420169472694,
-0.0036570345982909203,
0.027181284502148628,
-0.02626550942659378,
-0.00881007220596075,
-0.02651461958885193,
-0.028270898386836052,
-0.03774948790669441,
0.06324908137321472,
0.00628167949616909,
-0.0326242633163929,
0.06445395201444626,
0.04510544613003731,
-0.005407263990491629,
-0.015454537235200405,
-0.012306353077292442,
-0.06486162543296814,
0.006590683478862047,
0.027364294975996017,
0.036866217851638794,
0.04257998615503311,
-0.010591207072138786,
-0.006032716482877731,
0.002831703517585993,
-0.01913994550704956,
0.025256870314478874,
0.04964650049805641,
0.019081218168139458,
0.019890381023287773,
-0.054905518889427185,
0.01487743854522705,
0.006581077817827463,
0.019760655239224434,
0.004833758808672428,
-0.00521070696413517,
-0.05012214928865433,
-0.0370652973651886,
0.06533120572566986,
-0.03166627883911133,
0.009865139611065388,
0.06657417863607407,
0.0774998813867569,
-0.007759366650134325,
0.06347203999757767,
0.028533432632684708,
-0.021272679790854454,
0.01237223856151104,
-0.04148384928703308,
0.08853504061698914,
0.00017616500554140657,
-0.058748211711645126,
0.024083660915493965,
0.03646405041217804,
0.021054985001683235,
-0.014599976129829884,
-0.016897905617952347,
0.021191515028476715,
0.02929154969751835,
0.0005276998854242265,
-0.00559118902310729,
-0.0020340988412499428,
-0.04087882488965988,
-0.06293386220932007,
0.025471186265349388,
0.01741519756615162,
0.06566011160612106,
0.07728048413991928,
0.06680025905370712,
0.027888210490345955,
-0.034654777497053146,
0.030995696783065796,
-0.01688356325030327,
-0.061544474214315414,
-0.022443080320954323,
0.014513005502521992,
-0.02172563597559929,
-0.030769232660531998,
0.013422672636806965,
-0.0314721018075943,
-0.0114925941452384,
-0.04604853689670563,
-0.007716867607086897,
0.0034686883445829153,
-0.006350671872496605,
-0.03390709310770035,
0.02364478074014187,
-0.03826502338051796,
-0.05966203659772873,
-0.02429346553981304,
-0.019241267815232277,
0.010956265963613987,
0.0004960533697158098,
0.022962119430303574,
0.053439293056726456,
0.02191925421357155,
-0.026209834963083267,
0.03208170086145401,
0.0061239684000611305,
-0.07352600246667862,
-0.039741531014442444,
0.06698223203420639,
0.00268610124476254,
0.0638648197054863,
0.025173719972372055,
0.024446262046694756,
0.039992913603782654,
-0.030344009399414062,
-0.05942365527153015,
0.0019074816955253482,
-0.0218514371663332,
-0.03335711732506752,
0.015052501112222672,
0.0017150462372228503,
-0.0293436199426651,
-0.01902439445257187,
-0.011801849119365215,
-0.047499023377895355,
0.008940275758504868,
-0.04394186660647392,
-0.004847244825214148,
-0.012564443051815033,
-0.025383520871400833,
-0.026785636320710182,
0.03476087376475334,
0.0030854165088385344,
0.012539823539555073,
0.007277538999915123,
0.037249352782964706,
0.023923030123114586,
0.018896836787462234,
-0.036181170493364334,
-0.01966704986989498,
-0.008184169419109821,
0.00233672303147614,
0.007598775904625654,
-0.004695674870163202,
-0.01935633458197117,
0.00845867395401001,
0.013009504415094852,
0.03395363315939903,
0.0033289180137217045,
-0.01468556746840477,
0.06524157524108887,
-0.0022572814486920834,
-0.04850362613797188,
0.02611248940229416,
-0.003022415330633521,
-0.0949372872710228,
0.04696227237582207,
0.06378597766160965,
-0.003804869018495083,
-0.010763661935925484,
-0.02135160192847252,
-0.027641436085104942,
0.020583562552928925,
0.00010269979975419119,
-0.026325415819883347,
-0.010713430121541023,
0.024027371779084206,
-0.03505970910191536,
-0.00015433640510309488,
0.01924361102283001,
-0.08558066934347153,
0.055925190448760986,
-0.03617381677031517,
0.014263476245105267,
-0.03121844492852688,
-0.0015780928079038858,
0.015363934449851513,
-0.013297487050294876,
0.05104482173919678,
-0.05179613456130028,
-0.00571436807513237,
0.018593385815620422,
-0.01086153369396925,
-0.043730609118938446,
0.01951824314892292,
-0.03394196182489395,
0.009374299086630344,
-0.00810438022017479,
-0.004916445817798376,
0.015089524909853935,
-0.01914910599589348,
-0.008474466390907764,
0.03213552385568619,
0.00252866861410439,
-0.07241133600473404,
0.010141081176698208,
0.01578083075582981,
-0.004070318304002285,
-0.07502812147140503,
0.09501701593399048,
0.022343123331665993,
-0.0021983433980494738,
0.03230070695281029,
0.07007528096437454,
-0.012133474461734295,
-0.01631326600909233,
0.011800527572631836,
-0.029548030346632004,
0.02030366286635399,
0.05860774219036102,
-0.0015153844142332673,
0.05939728394150734,
0.0073850094340741634,
-0.0011675201822072268,
-0.04867413267493248,
0.033507440239191055,
0.0041960435919463634,
-0.009384616278111935,
0.03895636275410652,
-0.02679266408085823,
-0.023104675114154816,
-0.01729707419872284,
0.025109071284532547,
-0.03838636726140976,
-0.01715712808072567,
0.0069393590092659,
-0.007158808410167694,
0.027228694409132004,
-0.03201443701982498,
-0.009376849047839642,
0.013196459040045738,
0.0033961336594074965,
0.01947428658604622,
0.009393817745149136,
-0.012218992225825787,
-0.05857846513390541,
-0.011978867463767529,
0.057294972240924835,
-0.0024041475262492895,
0.006174761801958084,
-0.005615624599158764,
0.01638917252421379,
-0.09115473926067352,
0.019430849701166153,
-0.0110397320240736,
0.06977634876966476,
-0.07928857952356339,
-0.03814361244440079,
0.0010318689746782184,
-0.04275265708565712,
0.02508227340877056,
0.023830516263842583,
0.009903492406010628,
0.02003704197704792,
-0.044526223093271255,
0.007660157512873411,
0.04041947051882744,
0.03508981689810753,
0.00417603412643075,
-0.017229024320840836,
-0.006455893162637949,
-0.059506624937057495,
0.04892905801534653,
-0.03168861195445061,
-0.039593588560819626,
0.01564975269138813,
-0.014217756688594818,
0.041115887463092804,
0.00946786254644394,
-0.013962912373244762,
0.023945624008774757,
-0.045033734291791916,
-0.015003480948507786,
-0.03707362338900566,
0.03488056734204292,
-0.07146524637937546,
0.024348760023713112,
0.017263295128941536,
-0.06477494537830353,
0.021828066557645798,
0.013548789545893669,
-0.0014579173875972629,
0.025160333141684532,
0.013270705007016659,
0.009150492958724499,
0.016298530623316765,
-0.03689754009246826,
0.03951810672879219,
-0.07632187008857727,
-0.05217325687408447,
-0.0027494037058204412,
0.0005113171064294875,
-0.03098718449473381,
0.005565295461565256,
-0.020941883325576782,
-0.03293931111693382,
0.04256478697061539,
-0.10163447260856628,
0.05390800163149834,
0.03081156127154827,
0.03886311501264572,
0.0025710691697895527,
0.017934564501047134,
0.0032667971681803465,
-0.006435342598706484,
-0.005117734428495169,
0.03908652439713478,
-0.04438208416104317,
0.02560240961611271,
0.008344910107553005,
-0.026424888521432877,
0.01332338061183691,
-0.009444908238947392,
0.00785171240568161,
-0.02060130052268505,
-0.0011926854494959116,
0.029786041006445885,
0.016713570803403854,
0.06359703093767166,
0.027081945911049843,
-0.008915182203054428,
0.038747385144233704,
0.02560983970761299,
0.005526973865926266,
0.05059202015399933,
0.07123691588640213,
-0.01024133712053299,
-0.03254549577832222,
-0.017322154715657234,
-0.05917879566550255,
0.003713989397510886,
-0.015721069648861885,
-0.047836340963840485,
-0.04547514393925667,
-0.04885328933596611,
0.06233709305524826,
-0.019803328439593315,
0.05457310751080513,
0.07520481944084167,
0.06653058528900146,
0.100031279027462,
-0.0401359461247921,
0.025672102347016335,
0.03461337462067604,
0.010679468512535095,
0.07820526510477066,
-0.03397960588335991,
-0.030512522906064987,
-0.004720412660390139,
0.004463749006390572,
0.015156801789999008,
-0.017680682241916656,
-0.05267292633652687,
-0.013416040688753128,
-0.008765315636992455,
-0.028563790023326874,
-0.04389866441488266,
0.00754741532728076,
0.018809227272868156,
0.04679330810904503,
-0.012693973258137703,
-0.011273451149463654,
0.03380914777517319,
-0.009766694158315659,
0.02628551796078682,
0.048988427966833115,
-0.005573946516960859,
-0.015933552756905556,
-0.11546216160058975,
-0.06374641507863998,
0.012593665160238743,
0.03617051988840103,
-0.015074740163981915,
0.05568891391158104,
0.04581482708454132,
-0.023988373577594757,
0.02328023873269558,
-0.05430476367473602,
-0.04332774505019188,
-0.04847252741456032,
-0.041432417929172516,
-0.046739112585783005,
-0.04380195587873459,
0.013765440322458744,
0.0029750270769000053,
-0.017178812995553017,
-0.05044015124440193,
0.0674230083823204,
-0.018218928948044777,
-0.07403309643268585,
0.008853951469063759,
0.052378084510564804,
-0.05276074633002281,
-0.08610941469669342,
0.026089606806635857,
0.013036674819886684,
-0.009684275835752487,
0.034023966640233994,
-0.014072509482502937,
0.036880847066640854,
-0.05432910472154617,
-0.03368308022618294,
-0.022721046581864357,
-0.03932516276836395,
-0.03275827318429947,
-0.02204068936407566,
-0.01940704509615898,
0.021738411858677864,
-0.05261971056461334,
-0.0016429133247584105,
-0.02183889038860798,
-0.04673122987151146,
0.006748710758984089,
0.07355595380067825,
0.03830756992101669,
0.03599151223897934,
-0.05655992403626442,
0.008378386497497559,
-0.07057461887598038,
-0.013863539323210716,
0.01453386526554823,
-0.022679097950458527,
0.04803509637713432,
-0.06698447465896606,
-0.011584712192416191,
0.024126991629600525,
-0.0333188995718956,
-0.004197061527520418,
0.05477401241660118,
0.05476647987961769,
0.03953850269317627,
0.015121099539101124,
0.037210434675216675,
-0.0346766859292984,
0.046683188527822495,
-0.05088111758232117,
0.040487293154001236,
-0.00489776162430644,
-0.0860009640455246,
0.04104473441839218,
0.005518800113350153,
-0.02280084788799286,
0.028768673539161682,
0.04130374267697334,
0.066428042948246,
-0.009297795593738556,
0.00803056824952364,
-0.01796363666653633,
0.0026955779176205397,
0.0051063052378594875,
-0.0058434042148292065,
0.05447846278548241,
-0.026141932234168053,
0.04501276835799217,
0.00554608553647995,
0.04353060573339462,
0.0006991307018324733,
-0.021032048389315605,
-0.0288859773427248,
-0.013005321845412254,
0.04112539440393448,
0.029181433841586113,
0.03392128273844719,
-0.023785512894392014,
0.06498988717794418,
-0.0022605988197028637,
-0.008800229988992214,
0.02447662688791752,
-0.011728741228580475,
0.05675509199500084,
-0.017366081476211548,
0.03043225221335888,
0.026904461905360222,
0.005402981303632259,
0.03286616876721382,
0.013997795060276985,
-0.019454222172498703,
-0.05948634445667267,
-0.07252778112888336,
-0.0184823926538229,
0.01761826127767563,
-0.015377223491668701,
-0.011565200984477997,
-0.013360349461436272,
0.05053960159420967,
-0.013445990160107613,
-0.008795621804893017,
0.0004816224391106516,
0.08427420258522034,
-0.043952226638793945,
-0.05330239236354828,
-0.008982600644230843,
-0.016445342451334,
0.009129757061600685,
-0.03662720322608948,
-0.011955443769693375,
0.004656441044062376,
-0.0586673766374588,
0.007441935129463673,
0.03236095979809761,
0.09914354979991913,
-0.01401364617049694,
0.03736290708184242,
0.021276870742440224,
0.022332409396767616,
0.0093002300709486,
-0.06569088250398636,
-0.0033863303251564503,
0.003593232249841094,
0.02471166104078293,
-0.09530775994062424,
-0.02081092819571495,
-0.021785981953144073,
-0.0328621007502079,
-0.03300723060965538,
-0.03466823697090149,
-0.02499626763164997,
-0.0016827686922624707,
0.03753138333559036,
0.04688112810254097,
-0.04007348418235779,
0.01956264115869999,
-0.013978327624499798,
-0.029498757794499397,
0.022482778877019882,
0.03869667649269104,
-0.07616148144006729,
0.06522808969020844,
0.05235237628221512,
0.012601533904671669,
-0.00017830375873018056,
0.04032214730978012,
-0.02231569029390812,
0.06720168143510818,
0.007995732128620148,
0.03095324896275997,
-0.007900193333625793,
-0.07300455868244171,
0.04085707291960716,
-0.02093294821679592,
-0.031401798129081726,
0.08147943764925003,
0.03281267359852791,
0.05200411379337311,
-0.04244106262922287,
-0.008578506298363209,
0.07089908421039581,
-0.03621688485145569,
-0.026226110756397247,
0.01955845206975937,
-0.01703789457678795,
-0.04083618149161339,
-0.020479004830121994,
0.05103173479437828,
-0.010213389992713928,
-0.004453375469893217,
0.01608777791261673,
0.006906341761350632,
0.014111718162894249,
-0.013613319024443626,
-0.04171207174658775,
-0.007856795564293861,
0.006337231025099754,
0.00034200234222225845,
0.04003732278943062,
-0.011890954338014126,
-0.05294911935925484,
-0.10914871841669083,
0.03653401508927345,
0.0023909287992864847,
-0.02063887193799019,
-0.07098235189914703,
0.03401980549097061,
-0.0004455775488168001,
0.005880441050976515,
-0.008680339902639389,
-0.021910076960921288,
0.02027755416929722,
0.016650181263685226,
-0.014685183763504028,
-0.04822608828544617,
0.0059904553927481174,
0.04215230047702789,
-0.039391495287418365,
-0.008613336831331253,
0.006294596940279007,
-0.06826300173997879,
-0.014915753155946732,
0.03193673491477966,
-0.039694126695394516,
-0.021558508276939392,
-0.006460162345319986,
-0.009764512069523335,
-0.02216605469584465,
-0.016013525426387787,
0.04551878944039345,
-0.021055443212389946,
0.011254477314651012,
0.030843619257211685,
-0.04020179435610771,
-0.024734530597925186,
-0.023526273667812347,
0.0075972541235387325,
0.00567294005304575,
0.027068788185715675,
0.0009848895715549588,
0.03620575740933418,
0.0007859176839701831,
-0.015588963404297829,
0.013927371241152287,
-0.0037476085126399994,
0.041682031005620956,
-0.008718997240066528,
0.03893578052520752,
0.016781428828835487,
0.056490812450647354,
0.01705065742135048,
0.014463599771261215,
0.04061386361718178,
0.02771606668829918,
0.02350482903420925,
-0.004022237379103899,
-0.024999136105179787,
-0.011026393622159958,
0.026720218360424042,
-0.04861059412360191,
0.0583159439265728,
-0.020002102479338646,
0.03865937516093254,
-0.020420223474502563,
0.052179500460624695,
0.0352819487452507,
0.029240980744361877,
-0.03906041383743286,
-0.06561895459890366,
0.048307422548532486,
0.0016931791324168444,
0.031487837433815,
0.0031836729031056166,
0.005341113545000553,
-0.006674635224044323,
0.00950763002038002,
0.004335587844252586,
-0.023033244535326958,
0.007353007793426514,
-0.013693551532924175,
-0.05092192441225052,
-0.015160365961492062,
0.04079488292336464,
-0.0012278934009373188,
-0.06925854831933975,
-0.004463041666895151,
-0.046872179955244064,
-0.006327600684016943,
0.06658226251602173,
-0.043577246367931366,
0.025458291172981262,
0.03458566591143608,
-0.002898301463574171,
0.03148265182971954,
-0.0647214725613594,
0.04926391690969467,
0.005669213365763426,
-0.059883370995521545,
-0.005818923935294151,
-0.02672475576400757,
-0.05877029150724411,
-0.013888323679566383
] |
<p>consider object A with mass $m_{A}$ and positional vector $\overrightarrow{r_{A}}$</p>
<p>object B with mass $m_{B}$ and positional vector $\overrightarrow{r_{B}}$</p>
<p>object C with mass $m_{C}$ and positional vector $\overrightarrow{r_{C}}$</p>
<p>since reference frame is inertial (assumed) so</p>
<p>$m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}=\overrightarrow{F}{}_{AB}+\overrightarrow{F}{}_{AC}$</p>
<p>$\Rightarrow$$m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}=G\frac{m_{A}m_{B}}{\left|\overrightarrow{r_{B}}-\overrightarrow{r_{A}}\right|^{3}}(\overrightarrow{r_{B}}-\overrightarrow{r_{A}})+G\frac{m_{A}m_{C}}{\left|\overrightarrow{r_{C}}-\overrightarrow{r_{A}}\right|^{3}}(\overrightarrow{r_{C}}-\overrightarrow{r_{A}})$ ....[1]</p>
<p>for potential energy equation is to be integrated with a positional
vector and i am trying
hard to figure out what that vector could be, but still no success. please
help</p>
<hr>
<p>Potential energy of a object due to another object
$m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}=\overrightarrow{F_{A}}=G\frac{m_{A}m_{B}}{\left|\overrightarrow{r_{A}}-\overrightarrow{r_{B}}\right|^{3}}(\overrightarrow{r_{B}}-\overrightarrow{r_{A}})$</p>
<p>assuming $\overrightarrow{r_{0}}=\overrightarrow{r_{B}}-\overrightarrow{r_{A}}$</p>
<p>$\Rightarrow m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{0}}=-(1+\frac{m_{A}}{m_{B}})(G\frac{m_{A}m_{B}}{r_{0}^{2}}\hat{r_{0}})$</p>
<p>$\Rightarrow\intop_{\overrightarrow{r_{0i}}}^{\overrightarrow{r_{0f}}}\left(m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{0}}\right).d\overrightarrow{r_{0}}=-\intop_{\overrightarrow{r_{0i}}}^{\overrightarrow{r_{0f}}}\left((1+\frac{m_{A}}{m_{B}})(G\frac{m_{A}m_{B}}{r_{0}^{2}}\hat{r_{0}})\right).d\overrightarrow{r_{0}}$</p>
<p>$\Rightarrow\left.\frac{1}{2}m_{A}v_{0}^{2}\right|_{v_{0}(\overrightarrow{r_{0i}})}^{v_{0}(\overrightarrow{r_{0f}})}=\left.G\frac{m_{A}(m_{A}+m_{B})}{r_{0}}\right|_{\overrightarrow{r_{0i}}}^{\overrightarrow{r_{0f}}}$</p>
<p>So What positional vector should be integrated with equ [1] ?
How it is decided ? (i mean what kind of property(s) that vector should possess ?)</p>
<p>EDIT 1</p>
<p>$\int_{\overrightarrow{r_{i}}}^{\overrightarrow{r_{f}}}\left(m_{A}\frac{d^{2}}{dt^{2}}\overrightarrow{r_{A}}\right).d\overrightarrow{r}=\int_{\overrightarrow{r_{i}}}^{\overrightarrow{r_{f}}}\left(G\frac{m_{A}m_{B}}{\left|\overrightarrow{r_{B}}-\overrightarrow{r_{A}}\right|^{3}}(\overrightarrow{r_{B}}-\overrightarrow{r_{A}})+G\frac{m_{A}m_{C}}{\left|\overrightarrow{r_{C}}-\overrightarrow{r_{A}}\right|^{3}}(\overrightarrow{r_{C}}-\overrightarrow{r_{A}})\right).d\overrightarrow{r}$
.....[2]</p>
<p>questions </p>
<p>a) what is $\overrightarrow{r}$ in terms of $\overrightarrow{r_{A}}$,$\overrightarrow{r_{B}}$or
$\overrightarrow{r_{C}}$ ?</p>
<p>b) solve equ [2].</p> | g6593 | [
0.048440635204315186,
-0.01753488928079605,
-0.007684042211622,
-0.0016347687924280763,
0.03202364593744278,
-0.013481494039297104,
0.09146972000598907,
0.010207955725491047,
-0.11196908354759216,
0.00776643306016922,
0.0034349511843174696,
0.003391081700101495,
-0.022955041378736496,
-0.03760243207216263,
0.041264306753873825,
0.0001544644037494436,
0.05964552238583565,
-0.0020044627599418163,
0.006808644626289606,
0.01462635025382042,
0.011875077150762081,
0.012950753793120384,
0.01313219964504242,
0.014054146595299244,
-0.023874670267105103,
-0.03324531391263008,
0.07319588959217072,
-0.012065798044204712,
-0.05782988667488098,
-0.007183806039392948,
0.01739976555109024,
0.036544084548950195,
0.004671164322644472,
-0.06879162788391113,
-0.025510141626000404,
0.024633577093482018,
0.06005913019180298,
0.00028179812943562865,
0.006882462650537491,
0.017973363399505615,
-0.022504808381199837,
-0.03562052920460701,
0.03667382895946503,
0.003756680293008685,
0.027800174430012703,
-0.020473316311836243,
0.02681582234799862,
0.02055036835372448,
-0.012307408265769482,
-0.02471885457634926,
0.0009722517570480704,
0.06405115872621536,
0.04932146519422531,
-0.05854877457022667,
0.004984439350664616,
0.05317123979330063,
0.028368474915623665,
-0.02996613271534443,
0.01873902790248394,
0.07857111096382141,
-0.008180300705134869,
-0.0005111411446705461,
-0.055852245539426804,
0.03517060726881027,
0.05947548523545265,
-0.033291999250650406,
-0.05704835429787636,
-0.015086935833096504,
-0.03534567356109619,
-0.06186438351869583,
0.026986941695213318,
-0.010260708630084991,
0.006046928931027651,
-0.04509555175900459,
-0.032550401985645294,
-0.019836967810988426,
0.0241989828646183,
-0.010235182009637356,
0.03819149360060692,
-0.03275931999087334,
0.02110833115875721,
0.039409905672073364,
0.015348750166594982,
0.02536626346409321,
0.0691569447517395,
0.012523127719759941,
0.04341914877295494,
0.06520950794219971,
-0.04268278181552887,
-0.03702366352081299,
0.028755081817507744,
-0.030803723260760307,
0.02298308163881302,
-0.02444751188158989,
0.008450686000287533,
0.03917447105050087,
-0.029970450326800346,
0.03774533048272133,
-0.06470589339733124,
-0.04053362086415291,
-0.002235362073406577,
0.020014824345707893,
0.020281430333852768,
-0.008288934826850891,
0.04079638421535492,
-0.012666016817092896,
0.04238562658429146,
0.0361853688955307,
-0.015860017389059067,
-0.012927589006721973,
-0.006545098498463631,
0.018604978919029236,
-0.010920294560492039,
-0.03705653175711632,
-0.07263345271348953,
-0.06432898342609406,
0.0925641655921936,
0.007946508005261421,
-0.029208462685346603,
0.03419744595885277,
-0.0012445064494386315,
0.02794536016881466,
0.006707201711833477,
0.10213996469974518,
-0.022682782262563705,
0.018483739346265793,
-0.04051297530531883,
-0.03868922218680382,
0.043202925473451614,
-0.026315147057175636,
0.01803230680525303,
-0.06075694411993027,
0.03927895799279213,
-0.019100815057754517,
0.010076279751956463,
0.039017435163259506,
0.008738705888390541,
-0.00015177245950326324,
0.024132005870342255,
0.03375115245580673,
0.023317215964198112,
-0.02671724557876587,
0.005336581263691187,
0.012927843257784843,
-0.03687388822436333,
0.09571625292301178,
-0.004830976016819477,
-0.051538001745939255,
0.0382813885807991,
-0.0038784232456237078,
-0.00818661693483591,
0.08125780522823334,
-0.06004383787512779,
0.00915906485170126,
0.10650359839200974,
0.004302249755710363,
-0.029744740575551987,
-0.04074978083372116,
0.005891043692827225,
-0.021878361701965332,
0.03896038234233856,
-0.000006119085810496472,
-0.013427100144326687,
-0.014079833403229713,
-0.004869382828474045,
-0.0317106656730175,
0.022640015929937363,
-0.03884667903184891,
0.002523587318137288,
-0.07311355322599411,
-0.009081974625587463,
0.030697384849190712,
0.05283592268824577,
0.02513325773179531,
0.009607232175767422,
0.06530208885669708,
-0.02890145406126976,
-0.03855832293629646,
0.07630746811628342,
0.0044382670894265175,
0.006689518690109253,
0.00676172599196434,
0.04385966807603836,
-0.015755509957671165,
-0.02277301624417305,
0.02102062664926052,
0.04206816479563713,
0.08874346315860748,
-0.017910722643136978,
0.04113025963306427,
-0.03276137262582779,
0.03487288951873779,
0.03891361877322197,
0.05034210532903671,
-0.01004467997699976,
0.07270146906375885,
0.07699954509735107,
-0.047888532280921936,
-0.051167089492082596,
-0.012746636755764484,
-0.01202215626835823,
-0.006983260624110699,
0.039213575422763824,
0.05311637744307518,
0.04546264931559563,
0.007615297567099333,
0.04534723982214928,
0.026525292545557022,
0.01379426196217537,
0.027422651648521423,
-0.041750937700271606,
-0.009770779870450497,
-0.008833307772874832,
0.029554208740592003,
-0.015244940295815468,
-0.0454714260995388,
0.002917938632890582,
-0.02656969614326954,
-0.07323027402162552,
-0.027043035253882408,
-0.04433685541152954,
-0.022110873833298683,
0.0035389161203056574,
0.023357290774583817,
-0.07342763245105743,
0.04619895666837692,
-0.020568525418639183,
-0.012669493444263935,
0.027067048475146294,
-0.004212371073663235,
-0.0031760255806148052,
0.02708660438656807,
0.029337866231799126,
-0.020040716975927353,
0.05473698303103447,
-0.027619654312729836,
-0.017820199951529503,
-0.006852931808680296,
-0.014169305562973022,
-0.02288808301091194,
0.041395481675863266,
0.03407161682844162,
0.022800154983997345,
-0.05463072657585144,
0.052510183304548264,
0.03692613169550896,
0.05885516107082367,
0.028132231906056404,
0.03095940873026848,
0.05126551166176796,
-0.04457364231348038,
0.00940152257680893,
-0.00499179121106863,
-0.022568020969629288,
-0.0013879277976229787,
0.03433137387037277,
-0.10535881668329239,
0.020070688799023628,
-0.026891745626926422,
-0.03603174537420273,
-0.05145981162786484,
-0.020852262154221535,
-0.01747041381895542,
0.011656722985208035,
-0.08786099404096603,
0.009595859795808792,
-0.03331376612186432,
-0.017110386863350868,
0.0365535132586956,
0.013108428567647934,
0.029752440750598907,
0.06473307311534882,
0.017746569588780403,
0.041120465844869614,
-0.0013454287545755506,
0.00009043317550094798,
-0.023613303899765015,
-0.07112209498882294,
0.058039065450429916,
0.01862950623035431,
-0.006528759840875864,
-0.03892507031559944,
-0.039463479071855545,
0.054739080369472504,
0.013635575771331787,
-0.027137059718370438,
-0.05965175852179527,
0.07844197005033493,
0.006151942536234856,
-0.046523988246917725,
-0.03666960820555687,
0.034809812903404236,
0.02428394742310047,
-0.02893044613301754,
-0.00491226464509964,
-0.01811561919748783,
0.025933055207133293,
-0.05204165726900101,
0.020371589809656143,
0.018591459840536118,
-0.010645073838531971,
0.022207077592611313,
-0.018197735771536827,
-0.025882884860038757,
0.03406378626823425,
-0.052195992320775986,
-0.0329405814409256,
-0.058436259627342224,
0.03482550010085106,
0.013252549804747105,
-0.019809570163488388,
-0.008856227621436119,
-0.012987500987946987,
-0.035573069006204605,
-0.044221676886081696,
-0.01206156611442566,
-0.04723142087459564,
-0.031260982155799866,
-0.0074574328027665615,
-0.07838843017816544,
-0.013020787388086319,
0.009461412206292152,
0.04382597655057907,
0.022125929594039917,
0.004318038001656532,
0.04582324996590614,
-0.030572984367609024,
0.0009712464525364339,
-0.040802113711833954,
-0.003151229815557599,
-0.002058004727587104,
0.05344424396753311,
0.05164676159620285,
0.02478620409965515,
-0.02506774477660656,
0.015206806361675262,
0.00022088625701144338,
0.02551531419157982,
0.06776797026395798,
-0.010399620980024338,
-0.0005538127734325826,
-0.004548919387161732,
-0.0010027404641732574,
0.012661350890994072,
0.006614516489207745,
0.00919976457953453,
0.020316539332270622,
0.028111008927226067,
0.037090737372636795,
0.00849824771285057,
0.0006991047412157059,
-0.012026685290038586,
0.019144989550113678,
-0.012464920058846474,
0.0032151127234101295,
-0.00029367720708251,
0.011663621291518211,
0.0339743010699749,
-0.053867995738983154,
0.018937520682811737,
-0.009985703974962234,
-0.02576955035328865,
0.030872268602252007,
-0.014046920463442802,
0.0494084358215332,
0.00003762872802326456,
-0.06284843385219574,
-0.02112434245646,
-0.015759043395519257,
-0.03483578562736511,
0.02891785278916359,
-0.0513298362493515,
-0.07038790732622147,
-0.013992952182888985,
0.006383523810654879,
-0.06827744841575623,
-0.009451122023165226,
-0.037806689739227295,
-0.033848896622657776,
0.013012604787945747,
-0.0007458290201611817,
0.0036743837408721447,
0.0033254779409617186,
-0.000744983262848109,
0.016910362988710403,
0.05670240521430969,
-0.012524682097136974,
-0.011823846958577633,
0.05057360231876373,
-0.008607665076851845,
-0.03170052915811539,
-0.01848648115992546,
-0.06791269779205322,
-0.008951752446591854,
0.007700581103563309,
0.02780924364924431,
-0.011669408529996872,
0.007672570645809174,
-0.010010047815740108,
0.009304864332079887,
-0.035148985683918,
0.018534818664193153,
0.007776929065585136,
-0.05065857619047165,
-0.042965929955244064,
0.012231157161295414,
0.026613688096404076,
-0.0050443317741155624,
0.0012531415559351444,
-0.006448978558182716,
-0.0046485536731779575,
0.01629110425710678,
-0.039617422968149185,
-0.06171184033155441,
-0.0023853222373872995,
0.014856400899589062,
0.01231677457690239,
-0.011634459719061852,
-0.017722612246870995,
0.007445852737873793,
0.012537865899503231,
0.009795487858355045,
0.031470887362957,
-0.03271183371543884,
0.007614417467266321,
0.04802551865577698,
0.04786902666091919,
-0.03458113595843315,
-0.013909011147916317,
0.03954209014773369,
0.022404305636882782,
0.059830233454704285,
0.008574786596000195,
0.006863463204354048,
-0.027522526681423187,
0.022981375455856323,
-0.026556573808193207,
-0.012084298767149448,
0.0048176925629377365,
0.018366828560829163,
0.011348342522978783,
0.00749643798917532,
-0.009455012157559395,
-0.04504518583416939,
0.006096420809626579,
0.017010552808642387,
-0.019906895235180855,
-0.05426787585020065,
0.01857680082321167,
-0.007451838813722134,
0.06442129611968994,
0.027989527210593224,
-0.005821600556373596,
-0.022318977862596512,
-0.017266610637307167,
0.010672204196453094,
-0.060046326369047165,
-0.00005417898137238808,
-0.00517728365957737,
-0.040802888572216034,
0.007579145487397909,
-0.0562589168548584,
-0.07611171156167984,
-0.03922279551625252,
0.06199268624186516,
-0.03994210809469223,
-0.020954139530658722,
0.039500657469034195,
0.0029213791713118553,
-0.009154376573860645,
0.026832448318600655,
-0.02096857875585556,
0.011309098452329636,
0.02517325058579445,
0.0030469121411442757,
0.021201973780989647,
-0.028677422553300858,
-0.020403139293193817,
0.03804365545511246,
-0.013203191570937634,
-0.06533265113830566,
0.05646190792322159,
0.03325190395116806,
0.03829270228743553,
-0.0023529022000730038,
0.0005566392792388797,
-0.04379613697528839,
0.010824746452271938,
0.010645242407917976,
0.05215206742286682,
0.03486257418990135,
0.03655177354812622,
-0.02849668264389038,
-0.029950788244605064,
0.009843581356108189,
0.04660860449075699,
-0.0059326631017029285,
-0.01841995306313038,
0.019238494336605072,
-0.006170949432998896,
-0.033665359020233154,
0.0019546865951269865,
-0.03620738908648491,
0.0010839136084541678,
0.027607997879385948,
0.05061323195695877,
0.10400064289569855,
-0.0228524599224329,
-0.04988584294915199,
0.017443444579839706,
0.012121938169002533,
0.02026822790503502,
0.009815006516873837,
0.02643579989671707,
-0.04764970764517784,
-0.039418336004018784,
0.0004707317566499114,
0.0007361046737059951,
-0.03774126619100571,
-0.06510619074106216,
0.06352855265140533,
-0.03079737164080143,
0.030263230204582214,
-0.017257506027817726,
0.05644075945019722,
-0.002468589460477233,
0.010878950357437134,
-0.04533512890338898,
-0.019184397533535957,
0.03336622938513756,
-0.06613849103450775,
-0.01542472280561924,
-0.01590258628129959,
-0.013392770662903786,
-0.01321589108556509,
-0.04535200819373131,
-0.008629696443676949,
0.003500562161207199,
0.05816083028912544,
0.003653331659734249,
-0.008375815115869045,
-0.08048080652952194,
0.003469359828159213,
0.04122708737850189,
-0.09385047852993011,
0.017583593726158142,
0.0030977479182183743,
-0.015532318502664566,
-0.010969163849949837,
-0.04304111376404762,
-0.005264796782284975,
0.01349607016891241,
-0.01939491741359234,
-0.030324682593345642,
0.02324877306818962,
-0.02983103320002556,
0.00409654900431633,
-0.0056227645836770535,
-0.024314720183610916,
-0.012730876915156841,
0.026358062401413918,
-0.04556400701403618,
0.03808050602674484,
-0.010582170449197292,
0.027594076469540596,
-0.00037707702722400427,
0.013970297761261463,
-0.02897672727704048,
0.038096290081739426,
-0.036703165620565414,
-0.03960559517145157,
0.01043744757771492,
-0.012691976502537727,
0.016807567328214645,
0.07415974885225296,
0.029686961323022842,
-0.028183184564113617,
0.009225098416209221,
-0.006720270961523056,
-0.023915909230709076,
-0.005354858003556728,
0.033412713557481766,
0.04248794540762901,
-0.008201435208320618,
-0.029757503420114517,
0.060450684279203415,
-0.05609830468893051,
-0.06500479578971863,
-0.0038306256756186485,
-0.038213688880205154,
-0.012546377256512642,
-0.011832555755972862,
-0.02986169047653675,
-0.03835416957736015,
-0.033115603029727936,
0.026749974116683006,
-0.014839543029665947,
-0.047773830592632294,
0.015214254148304462,
0.043671999126672745,
0.037746530026197433,
0.019447453320026398,
0.02608335390686989,
-0.002468968043103814,
0.019825944676995277,
0.004875865764915943,
-0.08474339544773102,
-0.05770530551671982,
-0.0505671501159668,
0.0031632971949875355,
0.004557264968752861,
0.029012851417064667,
0.028143996372818947,
0.012206305749714375,
0.024555763229727745,
0.026200462132692337,
-0.009477350860834122,
0.05222783237695694,
0.03157762810587883,
-0.009143865667283535,
0.012690359726548195,
-0.015075751580297947,
0.016346311196684837,
-0.05178401991724968,
0.013207247480750084,
-0.006217144429683685,
-0.05413131043314934,
0.04871125891804695,
0.07399304211139679,
0.01368874404579401,
0.07576106488704681,
-0.03912772610783577,
-0.009743588976562023,
0.031856413930654526,
-0.03286467492580414,
0.004151889123022556,
-0.052734147757291794,
0.055786456912755966,
-0.003225825261324644,
0.051898978650569916,
0.01360473595559597,
0.060301609337329865,
-0.043358564376831055,
-0.016772940754890442,
-0.012482987716794014,
-0.03610539063811302,
0.047488193958997726,
-0.03858086094260216,
-0.05118778347969055,
-0.03495299443602562,
-0.017253680154681206,
0.015115532092750072,
-0.04158089682459831,
0.01469366904348135,
-0.07035937160253525,
-0.022662699222564697,
0.006216634996235371,
0.033188194036483765,
0.07568012923002243,
-0.05992810055613518,
0.0174875371158123,
-0.02896844409406185,
-0.030056390911340714,
0.036385659128427505,
0.00950490590184927,
0.06770604848861694,
0.005505161359906197,
-0.04393239691853523,
-0.0280787143856287,
-0.0424639992415905,
-0.04713543504476547,
0.00967700220644474,
-0.03164775297045708,
0.061000190675258636,
-0.0069793942384421825,
0.04445556923747063,
0.053584128618240356,
0.03487716615200043,
-0.017813777551054955,
-0.023398781195282936,
0.008274344727396965,
0.02048911526799202,
-0.02388431318104267,
0.028116801753640175,
-0.05836164951324463,
0.03697669133543968,
0.036807842552661896,
0.02334572933614254,
-0.05925777181982994,
0.02492200769484043,
-0.018430931493639946,
0.0660349503159523,
0.0686333104968071,
-0.0004778399888891727,
-0.04987427592277527,
-0.035896945744752884,
-0.04924657940864563,
0.04063626378774643,
0.04204520210623741,
0.014620156958699226,
0.028376281261444092,
-0.107726089656353,
0.01016045268625021,
0.00021456240210682154,
0.008703784085810184,
-0.03685455024242401,
0.0024593924172222614,
-0.01637871563434601,
0.02436351403594017,
0.034305352717638016,
0.031247660517692566,
-0.006985091604292393,
0.023554448038339615,
-0.0028269027825444937,
-0.0041372766718268394,
0.028774401172995567,
-0.057764749974012375,
0.07336444407701492,
0.003520530415698886,
-0.005672503728419542,
-0.027574824169278145,
0.018377143889665604,
-0.03356020897626877,
-0.0708872452378273,
-0.0037518092431128025,
-0.012752797454595566,
-0.032704953104257584,
-0.05420533940196037,
0.03819684684276581,
-0.05952455848455429,
-0.04925072565674782,
-0.033581703901290894,
-0.052238721400499344,
0.07967893779277802,
-0.01458423025906086,
0.011824091896414757,
0.029697079211473465,
-0.06985611468553543,
-0.0014342335052788258,
-0.01642208732664585,
0.004785149358212948,
-0.11153394728899002,
-0.05387839302420616,
0.01679929345846176,
0.009363432414829731,
-0.05551452562212944,
-0.028104476630687714,
0.02461203932762146,
0.06857222318649292,
-0.018973056226968765,
0.036113690584897995,
0.02668578363955021,
-0.056232750415802,
0.00660060066729784,
0.08694589138031006,
-0.03584329038858414,
0.034931764006614685,
0.03910677507519722,
-0.010686865076422691,
0.03785610944032669,
0.011594229377806187,
-0.03284219279885292,
-0.0382736474275589,
0.019149893894791603,
-0.0035747999791055918,
-0.019781621173024178,
-0.02333822473883629,
0.01766461506485939
] |
<p>I am looking at the <a href="http://en.wikipedia.org/wiki/Poincare_sphere" rel="nofollow">Poincaré sphere</a> and I am trying to compute a <a href="http://en.wikipedia.org/wiki/Jones_calculus" rel="nofollow">Jones matrix</a> for a particular rotation. Specifically, I would like it to perform the following maps:</p>
<p>$O :|H \rangle \rightarrow |R \rangle$</p>
<p>$O :|V \rangle \rightarrow |L \rangle$</p>
<p>$O :|L \rangle \rightarrow |H \rangle$</p>
<p>$O :|R \rangle \rightarrow |V \rangle$</p>
<p>where $|R \rangle$, $|L \rangle$ are right circular and left circular light. Is this possible? I should mention that I would also accept the same equations with L,R replaced by linearly polarized light $|D \rangle$, $|A \rangle$. If it is possible, what would be common plates that could do it?</p> | g6594 | [
-0.0172869935631752,
-0.03923187404870987,
-0.033427540212869644,
-0.04052900895476341,
0.0328955240547657,
-0.05959262698888779,
0.02570733241736889,
-0.04236603528261185,
0.020247487351298332,
0.03928463160991669,
0.023309189826250076,
0.03284256532788277,
0.008973267860710621,
-0.011335303075611591,
-0.004695700481534004,
0.007298095617443323,
0.07168760895729065,
0.036271460354328156,
0.022828159853816032,
-0.01142446231096983,
0.0033023206051439047,
0.011046087369322777,
0.048038020730018616,
-0.06775002181529999,
0.040711645036935806,
0.0061075701378285885,
-0.007403808645904064,
0.007465163711458445,
-0.06002764776349068,
0.01726974919438362,
-0.008141102269291878,
-0.026888178661465645,
0.03417724370956421,
-0.06675446033477783,
0.02105536498129368,
0.013652635738253593,
0.06494960188865662,
0.009886238723993301,
0.07269434630870819,
0.012543564662337303,
0.021161893382668495,
0.017580976709723473,
0.056800663471221924,
0.028907891362905502,
0.05702150613069534,
-0.05153395235538483,
0.004544421099126339,
0.037183795124292374,
-0.022430576384067535,
0.019978798925876617,
-0.03301215544342995,
0.03284844011068344,
0.029757874086499214,
-0.04709584638476372,
-0.03686407580971718,
0.0411277711391449,
-0.013403434306383133,
-0.022110555320978165,
0.050402749329805374,
0.06295847147703171,
-0.052601467818021774,
-0.04421372339129448,
-0.020717093721032143,
0.03134353458881378,
-0.010301913134753704,
0.0045580933801829815,
-0.01151890680193901,
-0.05121447518467903,
-0.04248291254043579,
0.03043191134929657,
0.01222018152475357,
-0.04284784570336342,
0.04071887210011482,
-0.03652123734354973,
-0.04852984473109245,
-0.015225067734718323,
0.03486735001206398,
-0.01085295993834734,
0.03821536898612976,
0.0008450356544926763,
-0.052268657833337784,
0.049324411898851395,
0.021565688773989677,
-0.02463698945939541,
0.030163301154971123,
0.04532104358077049,
0.053671933710575104,
0.010474625043570995,
-0.022888686507940292,
-0.004418520722538233,
0.05393296107649803,
-0.009468307718634605,
0.03341192752122879,
0.021619372069835663,
-0.012788769789040089,
-0.0007905730744823813,
-0.027575528249144554,
-0.011054075323045254,
-0.02269122004508972,
-0.015862008556723595,
-0.04235774651169777,
0.005613136570900679,
-0.03558563068509102,
-0.019602136686444283,
0.02722337283194065,
-0.024079935625195503,
0.047581613063812256,
-0.013138895854353905,
-0.0321049764752388,
-0.017261819913983345,
-0.04109952598810196,
-0.029884593561291695,
-0.052657559514045715,
-0.03243899345397949,
-0.02372862584888935,
-0.08007486164569855,
0.09485846012830734,
0.011160354129970074,
0.007803717162460089,
0.07338099926710129,
0.05508428066968918,
0.018625184893608093,
0.023591574281454086,
0.10448609292507172,
0.03868235647678375,
0.08900002390146255,
0.009571559727191925,
0.002854568650946021,
0.08959262073040009,
-0.01763305999338627,
0.00032969407038763165,
-0.005506566260010004,
0.04533259943127632,
0.028094997629523277,
-0.0081477090716362,
0.0002299377229064703,
-0.025958482176065445,
0.02476038783788681,
0.001671169069595635,
-0.039867278188467026,
0.008274097926914692,
-0.053927771747112274,
-0.005551743321120739,
0.014975707046687603,
0.012959991581737995,
0.015409840270876884,
-0.009156238287687302,
-0.07267431169748306,
0.06087252125144005,
0.07978963851928711,
-0.010240050032734871,
0.08500926196575165,
0.0027061644941568375,
0.021828457713127136,
0.010531136766076088,
0.04571753740310669,
0.0078979367390275,
-0.06962900608778,
0.002170682419091463,
-0.02436671033501625,
0.032287582755088806,
0.006871670018881559,
0.0021940264850854874,
-0.017968803644180298,
-0.051102414727211,
-0.012626090086996555,
-0.019664062187075615,
0.013124961405992508,
-0.04462243989109993,
-0.0856320858001709,
-0.02188735641539097,
-0.0014960499247536063,
0.037799280136823654,
0.00541292317211628,
0.01837790571153164,
0.04859036207199097,
-0.05738798528909683,
-0.024668419733643532,
0.05313432961702347,
-0.00006177099567139521,
-0.031177613884210587,
-0.0023467419669032097,
0.017200222238898277,
-0.026395272463560104,
0.027284665033221245,
-0.0020385736133903265,
-0.020106922835111618,
-0.0005259484169073403,
-0.10649111121892929,
-0.010506187565624714,
0.04342610388994217,
0.04605577141046524,
0.024150511249899864,
0.0037942861672490835,
-0.035336535423994064,
0.007626127451658249,
0.0013441926566883922,
-0.009090800769627094,
-0.047319650650024414,
0.08494344353675842,
0.02430848404765129,
0.0027135678101330996,
0.05111624673008919,
0.02737526409327984,
0.006157777272164822,
-0.023242225870490074,
0.004150428809225559,
-0.02142190933227539,
0.022090455517172813,
0.022920534014701843,
0.024790648370981216,
0.01412222906947136,
-0.005097163375467062,
0.0028214978519827127,
-0.04255511611700058,
-0.014124284498393536,
-0.007524763233959675,
0.019832829013466835,
-0.016367921605706215,
0.030073394998908043,
-0.043542053550481796,
0.020387420430779457,
-0.022737735882401466,
0.021890243515372276,
-0.024704966694116592,
0.02422594279050827,
-0.01733851432800293,
-0.016756050288677216,
-0.01628837361931801,
0.033656731247901917,
-0.03321973606944084,
-0.013845718465745449,
0.06119757890701294,
-0.0038789331447333097,
0.034168146550655365,
-0.008336658589541912,
-0.01993229240179062,
0.019823778420686722,
-0.01145227812230587,
0.056378502398729324,
-0.008573872968554497,
0.01813872903585434,
0.02202923782169819,
-0.01144544966518879,
-0.014602801762521267,
-0.017552871257066727,
0.04444103315472603,
0.006019267253577709,
0.04088359326124191,
0.08429557830095291,
0.0021340292878448963,
-0.015016308054327965,
-0.029216472059488297,
0.0017259134911000729,
-0.018303226679563522,
0.007703026290982962,
-0.04123156517744064,
-0.014786407351493835,
-0.026004014536738396,
-0.022092444822192192,
-0.031481657177209854,
0.0014307079836726189,
-0.044432953000068665,
0.006519770715385675,
-0.030717024579644203,
0.01612495630979538,
-0.002433744026347995,
-0.008679416961967945,
0.03241856023669243,
0.03004888817667961,
-0.04060390219092369,
0.06464163959026337,
0.09839925915002823,
0.027970410883426666,
-0.036366213113069534,
-0.06415984779596329,
-0.02691642940044403,
0.03389563784003258,
-0.04144798219203949,
0.01731906272470951,
0.01511881873011589,
-0.055345162749290466,
-0.01353750005364418,
0.05295708030462265,
-0.002899461891502142,
-0.05100110545754433,
-0.033843837678432465,
0.08063656091690063,
-0.033997517079114914,
0.043090153485536575,
-0.09323004633188248,
0.01447876263409853,
0.03204992786049843,
-0.030047737061977386,
0.00548513000831008,
-0.02578328736126423,
0.05145867541432381,
-0.038277894258499146,
0.019248098134994507,
0.0947282686829567,
0.028120601549744606,
-0.009762730449438095,
0.0046394397504627705,
0.0494270846247673,
0.05955155938863754,
-0.002171905478462577,
-0.02158202975988388,
-0.034140825271606445,
0.020942507311701775,
0.0656297579407692,
0.024101916700601578,
-0.0026416343171149492,
-0.07502120733261108,
-0.003215501783415675,
0.0020155496895313263,
-0.0268094502389431,
-0.03008350357413292,
-0.05786186829209328,
0.03484078124165535,
0.007801136001944542,
-0.05235162377357483,
-0.026493119075894356,
-0.043695565313100815,
-0.007503056898713112,
0.03037663921713829,
0.044244956225156784,
-0.035513874143362045,
-0.005723266862332821,
-0.017617229372262955,
-0.03244709596037865,
0.04533040151000023,
0.002911938587203622,
0.02135293558239937,
0.0005878473166376352,
-0.06705032289028168,
-0.025576673448085785,
-0.02272513136267662,
0.024152722209692,
0.053573139011859894,
-0.06401032954454422,
-0.041691310703754425,
-0.08141063153743744,
-0.03407278656959534,
-0.03229203075170517,
0.014809023588895798,
-0.0051718177273869514,
-0.006943970452994108,
0.0006713566835969687,
0.023938948288559914,
-0.02276776172220707,
-0.028390787541866302,
-0.039178650826215744,
0.055041905492544174,
-0.013785390183329582,
0.05750594660639763,
0.03501508757472038,
0.02958785556256771,
0.0927593782544136,
0.03642888739705086,
0.006546913646161556,
-0.02337425947189331,
-0.02972722239792347,
-0.019290871918201447,
-0.014207988046109676,
0.048787232488393784,
0.04449052736163139,
0.03804883360862732,
0.03591649979352951,
-0.022745715454220772,
0.009018690325319767,
0.03426757827401161,
0.03710661455988884,
0.007242310326546431,
-0.042473696172237396,
-0.012051839381456375,
-0.03442864492535591,
-0.00813936535269022,
0.023068683221936226,
-0.015352163463830948,
0.0011268701637163758,
-0.09305494278669357,
-0.003278787015005946,
0.04599983990192413,
0.06497867405414581,
-0.00691559910774231,
0.032509755343198776,
-0.0030606971122324467,
0.0262112058699131,
-0.0026177617255598307,
0.037433940917253494,
-0.014057538472115993,
-0.048723574727773666,
-0.021736161783337593,
-0.004548182245343924,
0.033968981355428696,
-0.03055463172495365,
-0.007095783948898315,
-0.0834561213850975,
-0.11813949793577194,
0.01346143800765276,
0.04716205596923828,
-0.026934172958135605,
0.024183468893170357,
0.0029717020224779844,
-0.03670279309153557,
-0.058336976915597916,
0.014950140379369259,
0.04557358846068382,
0.02722191996872425,
-0.008943099528551102,
-0.04769674316048622,
-0.04148232191801071,
0.04402963072061539,
-0.05563049763441086,
0.038924653083086014,
0.05745267495512962,
0.012798148207366467,
-0.00043902764446102083,
-0.003657254623249173,
0.018853219226002693,
-0.010251672007143497,
0.05511080101132393,
-0.0006236709887161851,
-0.0026235822588205338,
0.02841438166797161,
0.03320488706231117,
0.0566679984331131,
-0.05709262564778328,
0.04640670865774155,
-0.04742185398936272,
0.03296651691198349,
-0.005060412455350161,
-0.021299729123711586,
-0.032087624073028564,
-0.01405284833163023,
-0.07762525230646133,
-0.07001127302646637,
0.0378609336912632,
0.024305326864123344,
-0.016528304666280746,
-0.021446306258440018,
-0.00491828890517354,
0.03274234011769295,
-0.031937915831804276,
0.0017970665358006954,
0.02002079039812088,
-0.0008121757418848574,
-0.02550974115729332,
0.006989501882344484,
-0.013256239704787731,
0.0006883720052428544,
-0.007484181318432093,
0.021735405549407005,
-0.012498120777308941,
-0.013893870636820793,
0.01975277066230774,
-0.029074911028146744,
0.04113525524735451,
0.004808826372027397,
0.029423555359244347,
0.010655407793819904,
-0.0419374480843544,
-0.020067820325493813,
-0.06848803162574768,
0.04834406077861786,
0.012370269745588303,
-0.08188005536794662,
0.07107431441545486,
-0.05028915032744408,
-0.036545462906360626,
0.005593622103333473,
0.012145230546593666,
0.011255617253482342,
0.004356587305665016,
-0.08285707235336304,
-0.01907251589000225,
-0.05426345020532608,
-0.042860765010118484,
-0.0038577010855078697,
-0.0541033074259758,
-0.03986801952123642,
0.0032288762740790844,
0.014176007360219955,
0.004861645400524139,
-0.00385196297429502,
-0.007344874553382397,
-0.0274529866874218,
-0.030585695058107376,
-0.020713189616799355,
0.015064220875501633,
-0.020137619227170944,
0.01570044830441475,
-0.02856695093214512,
-0.012680752202868462,
0.029525641351938248,
0.016062049195170403,
0.010461515747010708,
-0.059825148433446884,
-0.064470574259758,
0.01633823662996292,
-0.010914602316915989,
0.0038472614251077175,
0.007290317676961422,
-0.04066687822341919,
-0.010374619625508785,
-0.009396331384778023,
0.04573947563767433,
0.0495821088552475,
0.021772239357233047,
0.03643450513482094,
0.005570066627115011,
-0.05668375641107559,
0.021737217903137207,
0.01965528540313244,
-0.03852070868015289,
-0.024236368015408516,
-0.07017114758491516,
-0.007585298735648394,
-0.02959025278687477,
-0.055333517491817474,
0.013516961596906185,
-0.0452093780040741,
0.007364185526967049,
0.014499434269964695,
0.039931103587150574,
0.021715950220823288,
-0.0314905047416687,
0.0030734543688595295,
0.03508736565709114,
0.015530938282608986,
-0.020561838522553444,
-0.06693550944328308,
0.025517424568533897,
0.005175312981009483,
0.007250119931995869,
-0.04952091723680496,
0.028313761577010155,
0.002782056573778391,
0.04466147720813751,
-0.014954362995922565,
-0.02805481106042862,
-0.055333126336336136,
0.07443226873874664,
0.04681135341525078,
-0.00940465647727251,
-0.0019270398188382387,
0.03731599450111389,
-0.010424328036606312,
-0.020516647025942802,
-0.018787814304232597,
-0.0574256032705307,
0.04088189825415611,
0.014870810322463512,
-0.043019816279411316,
-0.005474223755300045,
0.00991752091795206,
-0.025844698771834373,
-0.04107384383678436,
-0.005973870866000652,
0.016790466383099556,
0.08793526142835617,
-0.07200722396373749,
-0.00851472932845354,
-0.044704798609018326,
-0.012813475914299488,
0.0006069567170925438,
-0.002299162093549967,
0.012447607703506947,
0.03467289358377457,
0.08846591413021088,
-0.027414953336119652,
-0.04954831674695015,
-0.039889879524707794,
0.06862043589353561,
0.06314881891012192,
0.02182171680033207,
-0.006355399265885353,
0.020282620564103127,
-0.013736629858613014,
0.02848823554813862,
-0.006477997172623873,
0.028687410056591034,
0.011414559558033943,
0.007664796430617571,
-0.004493552725762129,
0.002588978735730052,
-0.03276070952415466,
0.04932722821831703,
0.02907421812415123,
-0.049025148153305054,
-0.00779959000647068,
-0.022555658593773842,
-0.06009658798575401,
-0.01792936399579048,
-0.01704428158700466,
-0.009118660353124142,
-0.02390768565237522,
0.05125606432557106,
0.025466540828347206,
-0.011792014352977276,
0.02062571793794632,
-0.02748621068894863,
0.028757445514202118,
-0.01134329754859209,
0.013642675243318081,
-0.022424260154366493,
-0.09900180250406265,
-0.03937637805938721,
0.022465405985713005,
0.029784642159938812,
-0.0010391224641352892,
0.02056235820055008,
0.020751696079969406,
0.04005050286650658,
-0.033293526619672775,
-0.012259217910468578,
-0.04534465819597244,
0.018931806087493896,
0.02938253805041313,
-0.016690673306584358,
0.026868531480431557,
-0.044104281812906265,
-0.04473637416958809,
-0.04301893338561058,
0.029294341802597046,
0.0017370512941852212,
-0.016095854341983795,
0.02366846427321434,
0.056723810732364655,
0.07909092307090759,
0.042061615735292435,
-0.008726336061954498,
-0.023198263719677925,
-0.010447373613715172,
0.05367652326822281,
0.0064465622417628765,
-0.08667917549610138,
0.033603355288505554,
0.048090752214193344,
0.03782997652888298,
0.004534753039479256,
0.057968590408563614,
0.027063993737101555,
0.030061904340982437,
-0.00017174531240016222,
-0.024978064000606537,
-0.012016315944492817,
-0.017297115176916122,
-0.040613945573568344,
0.07336927950382233,
0.07348380982875824,
0.03447423875331879,
-0.01008154172450304,
0.027833648025989532,
-0.0367841012775898,
-0.005742955487221479,
0.037695009261369705,
0.0029992905911058187,
0.020550215616822243,
-0.009087612852454185,
-0.0062064859084784985,
-0.014512740075588226,
-0.01924842596054077,
-0.04842599853873253,
-0.022569401189684868,
-0.018361162394285202,
-0.028928518295288086,
0.03158422186970711,
0.013851886615157127,
-0.0169130377471447,
-0.021848367527127266,
0.02136402390897274,
-0.027086080983281136,
0.04988650977611542,
0.0012769006425514817,
0.02465670369565487,
-0.005392932798713446,
0.009035322815179825,
-0.0021786238066852093,
-0.0015180400805547833,
0.03203757479786873,
-0.023796137422323227,
-0.027226174250245094,
0.04076336324214935,
0.03487154841423035,
0.0005200332961976528,
0.020544307306408882,
-0.014088073745369911,
0.030595162883400917,
-0.011910824105143547,
-0.011304154992103577,
0.02768896520137787,
0.00857853889465332,
0.04049072042107582,
-0.012921633198857307,
-0.021601708605885506,
-0.012956084683537483,
0.019505659118294716,
-0.05155500769615173,
-0.017653116956353188,
-0.01577652432024479,
-0.0025992118753492832,
-0.01828925684094429,
-0.05368618667125702,
-0.01388601679354906,
-0.04105121269822121,
-0.04218124970793724,
-0.007756254635751247,
0.02517259493470192,
0.018932925537228584,
0.0059929401613771915,
0.06404329091310501,
-0.08002833276987076,
0.022862473502755165,
0.0034623295068740845,
-0.02618437260389328,
0.0070948186330497265,
0.047166381031274796,
0.007589614484459162,
0.019197886809706688,
-0.04689444229006767,
0.0011552706127986312,
0.0008206263883039355,
-0.017512980848550797,
0.02879217080771923,
-0.024532968178391457,
-0.02312052622437477,
0.03183136135339737,
0.03182957321405411,
0.00270868930965662,
0.039915040135383606,
0.021488284692168236,
-0.05063110589981079,
0.007924034260213375,
0.02567683532834053,
0.007469770032912493,
-0.09878913313150406,
-0.0418744832277298,
0.039669640362262726,
0.02989790216088295,
0.012661561369895935,
-0.0623168908059597,
0.04498031362891197,
-0.04259975627064705,
-0.006158336065709591,
0.011548293754458427,
-0.02270166203379631,
0.013021525926887989,
0.031001050025224686,
-0.05280749127268791,
-0.047519195824861526,
0.07447737455368042,
0.01756073534488678,
-0.026033945381641388,
0.04762466251850128,
-0.0423317514359951,
-0.012803100980818272,
0.011362497694790363,
0.06558609753847122,
-0.03414522483944893,
0.005082802847027779,
-0.01677311770617962,
-0.0413515530526638,
0.039676912128925323,
0.021924201399087906,
-0.09482236951589584,
-0.031518299132585526,
0.043711207807064056
] |
<p>How are the external magnetic field intensity H, magnetisation M and the entropy related to each other? i.e. if I change the magnetic field intensity by dH what will be the change in entropy dS in terms of M. </p> | g6595 | [
-0.02490917779505253,
-0.010762154124677181,
-0.006234962027519941,
-0.06791726499795914,
0.01801198534667492,
-0.018600493669509888,
-0.020957693457603455,
0.05904553458094597,
-0.06863655149936676,
0.0010673931101337075,
-0.05751891806721687,
0.01947496086359024,
0.055071815848350525,
-0.019470777362585068,
0.030559463426470757,
0.06446710973978043,
-0.030452627688646317,
0.0140162268653512,
0.00876266323029995,
0.002611073898151517,
-0.05647386983036995,
0.008402982726693153,
0.00880889780819416,
-0.06134602054953575,
-0.02433401718735695,
-0.012363621033728123,
0.05879070982336998,
-0.03404480963945389,
-0.004310490097850561,
-0.006772888358682394,
0.010201697237789631,
0.056189779192209244,
0.023888511583209038,
-0.05032562464475632,
-0.039705559611320496,
0.01787056028842926,
0.03997034579515457,
0.07412026077508926,
0.019840577617287636,
0.01802222430706024,
0.015526998788118362,
-0.02874995768070221,
0.024099910631775856,
-0.06697297096252441,
-0.04934483766555786,
0.004011719021946192,
-0.019887983798980713,
-0.013743515126407146,
-0.0104100052267313,
0.013311157003045082,
-0.041321367025375366,
0.002106179716065526,
0.05956120043992996,
0.015732672065496445,
0.03655843436717987,
0.046255555003881454,
0.008312989957630634,
-0.06609391421079636,
0.07745519280433655,
0.022407598793506622,
0.005360024515539408,
-0.043353334069252014,
-0.07132767885923386,
0.031041843816637993,
-0.020500853657722473,
-0.019630812108516693,
0.008902309462428093,
-0.03796836733818054,
-0.016627119854092598,
0.022234024479985237,
-0.057237282395362854,
-0.04186442121863365,
-0.023501502349972725,
-0.015514099970459938,
0.010806151665747166,
0.060402531176805496,
0.09186191856861115,
-0.042298898100852966,
0.04992185905575752,
-0.008432609960436821,
-0.07471659779548645,
-0.03910357877612114,
0.042901862412691116,
-0.021125702187418938,
0.05545593798160553,
0.021159693598747253,
0.03164709359407425,
0.006236406974494457,
0.02553589455783367,
-0.0041459305211901665,
-0.02216511033475399,
-0.03322531655430794,
-0.008312786929309368,
-0.02390776202082634,
-0.03158974647521973,
0.07666417956352234,
0.028100579977035522,
0.040345121175050735,
0.012745517306029797,
0.00922498106956482,
-0.022376950830221176,
-0.04525327682495117,
0.04160987585783005,
-0.016583649441599846,
-0.03737214580178261,
0.021150454878807068,
0.015049898996949196,
-0.023370960727334023,
-0.03484847769141197,
0.062424298375844955,
-0.013569542206823826,
-0.023402323946356773,
-0.06475914269685745,
-0.004233321640640497,
-0.026133134961128235,
-0.03883854299783707,
0.06771411746740341,
-0.061599504202604294,
-0.020840050652623177,
0.00529239047318697,
0.054028239101171494,
0.005598232615739107,
-0.003006367478519678,
0.046795330941677094,
0.009205601178109646,
0.0032788256648927927,
0.0006540807080455124,
0.017199937254190445,
0.04808850586414337,
-0.08034391701221466,
0.027833690866827965,
-0.039412595331668854,
0.040781501680612564,
0.0035422968212515116,
0.018497584387660027,
0.008570290170609951,
0.027442051097750664,
0.010344869457185268,
-0.0044721998274326324,
0.030684819445014,
-0.011194082908332348,
-0.03539649397134781,
0.01361320074647665,
-0.04302085191011429,
0.003696838626638055,
0.045564960688352585,
-0.0023388650733977556,
-0.06089954078197479,
0.003451284021139145,
-0.011527356691658497,
0.060658425092697144,
-0.023750483989715576,
-0.004488751292228699,
0.029214784502983093,
-0.019155623391270638,
-0.008421206846833229,
0.013783251866698265,
0.06054707616567612,
-0.02062060311436653,
0.004514271859079599,
0.011199972592294216,
-0.04197557643055916,
0.05357843637466431,
0.01911957375705242,
-0.001066095195710659,
0.021565979346632957,
0.12057105451822281,
-0.027822021394968033,
-0.006175353657454252,
-0.005740239284932613,
-0.01605568639934063,
0.011023562401533127,
0.013725591823458672,
-0.0032380030024796724,
0.00854295864701271,
0.07648911327123642,
-0.00604406138882041,
-0.01932779885828495,
0.044703178107738495,
0.03725457936525345,
0.004632552154362202,
0.059173062443733215,
0.06058615818619728,
-0.052273672074079514,
0.016461923718452454,
0.01760871894657612,
0.010958712548017502,
0.006454050540924072,
-0.06902029365301132,
-0.001506460946984589,
-0.010916412808001041,
-0.009664329700171947,
-0.018048154190182686,
0.018020611256361008,
0.030428551137447357,
-0.01797705516219139,
-0.03872038051486015,
0.02996605820953846,
-0.02171529270708561,
-0.005801761522889137,
0.000810174155049026,
0.0487084686756134,
0.0499422587454319,
-0.01088765449821949,
0.013035813346505165,
0.05161453038454056,
0.041023124009370804,
0.02786274626851082,
0.0594031922519207,
-0.0060889278538525105,
0.00017680175369605422,
-0.05015213415026665,
-0.01036488264799118,
0.005205599591135979,
0.017108626663684845,
-0.016997890546917915,
0.014577727764844894,
0.026454269886016846,
-0.023321060463786125,
-0.0009986677905544639,
-0.010140450671315193,
0.00482543557882309,
0.04604673013091087,
0.031003693118691444,
-0.08693148195743561,
-0.01897757314145565,
-0.008351297117769718,
0.04984097182750702,
-0.004624802153557539,
-0.015755362808704376,
0.012246784754097462,
0.030736083164811134,
0.011800839565694332,
0.009553877636790276,
-0.03829643130302429,
0.04426495358347893,
0.023036640137434006,
-0.002892172895371914,
0.01852295733988285,
0.027015885338187218,
-0.002937008859589696,
0.043761271983385086,
-0.005916548892855644,
0.024022212252020836,
0.0013738127890974283,
-0.03390226140618324,
0.06584049761295319,
0.017334554344415665,
-0.050112590193748474,
0.04210558906197548,
0.02215508557856083,
0.0015688104322180152,
-0.0010041353525593877,
0.028317304328083992,
-0.018418824300169945,
0.005145195405930281,
-0.05579891800880432,
-0.004178984090685844,
-0.04767335206270218,
-0.004459851887077093,
-0.00787353329360485,
-0.007590522523969412,
0.02461835741996765,
0.04869457706809044,
-0.03962504491209984,
-0.01587320677936077,
0.0011788633419200778,
-0.022528300061821938,
0.001632483908906579,
-0.03768270090222359,
-0.006947062909603119,
0.0906025692820549,
0.013903922401368618,
0.023881591856479645,
0.021759910508990288,
0.030875010415911674,
0.004389047622680664,
0.003028523176908493,
-0.003156080609187484,
-0.08262749761343002,
0.0028049603570252657,
0.02653897926211357,
-0.06756821274757385,
-0.006225711200386286,
-0.00834314338862896,
-0.025739748030900955,
0.01762285642325878,
-0.024096187204122543,
-0.023173203691840172,
0.03150632977485657,
-0.005901811644434929,
0.0320509634912014,
0.03182457014918327,
0.000326974899508059,
0.01333870179951191,
-0.0023793026339262724,
0.030298098921775818,
-0.030181802809238434,
0.01797725446522236,
0.058048635721206665,
0.023035665974020958,
0.014180849306285381,
-0.03619660437107086,
-0.007251677103340626,
0.02065729722380638,
0.038461506366729736,
-0.09864555299282074,
-0.058142825961112976,
0.021730167791247368,
0.010291497223079205,
-0.0661853775382042,
-0.0474635548889637,
0.02531435713171959,
-0.006616774946451187,
0.02839650586247444,
0.014319594949483871,
0.03148147463798523,
-0.0007543861865997314,
0.01466740109026432,
0.010115992277860641,
0.0029829563573002815,
-0.06324102729558945,
-0.0012534352717921138,
-0.059350188821554184,
0.016094747930765152,
-0.0016262856079265475,
0.010370769537985325,
-0.05461001768708229,
-0.034139130264520645,
-0.001079629990272224,
0.031393714249134064,
-0.01612294651567936,
0.029011942446231842,
-0.025291983038187027,
-0.14780659973621368,
0.032610535621643066,
-0.026293806731700897,
-0.07717112451791763,
-0.03193661943078041,
0.047167323529720306,
0.03906488046050072,
-0.029069125652313232,
-0.08276821672916412,
0.0053392923437058926,
-0.024659665301442146,
0.0402517095208168,
-0.03732168674468994,
-0.04087534919381142,
0.0011860063532367349,
0.018930699676275253,
-0.015646647661924362,
0.0049056196585297585,
0.04670131206512451,
0.03221631795167923,
-0.0025541535578668118,
-0.037044815719127655,
0.03477882593870163,
-0.03293255716562271,
-0.03414567932486534,
0.01482013426721096,
-0.03994940593838692,
-0.05071365460753441,
-0.022138716652989388,
-0.023989172652363777,
-0.0530906580388546,
0.07960408180952072,
-0.02119513973593712,
0.021252531558275223,
-0.058304522186517715,
-0.015263054519891739,
0.002279639942571521,
-0.023348910734057426,
-0.06049366295337677,
0.014280369505286217,
0.008733022026717663,
-0.05283096432685852,
0.05846733972430229,
-0.024773288518190384,
-0.04407672584056854,
0.02790187858045101,
0.0032099029049277306,
0.03226000815629959,
-0.0027642708737403154,
0.0182019155472517,
0.053268853574991226,
-0.01342826709151268,
-0.014367693103849888,
0.06112859398126602,
0.0074203661642968655,
-0.055323608219623566,
-0.010512959212064743,
0.004993366543203592,
0.014317736960947514,
-0.0032428286504000425,
0.021754972636699677,
0.008133018389344215,
0.014571635983884335,
0.008155577816069126,
-0.012878760695457458,
0.014092502184212208,
0.008629607036709785,
0.005596514325588942,
-0.01266349758952856,
0.0421585775911808,
-0.004071332979947329,
-0.06234807148575783,
-0.0087994784116745,
0.006738944444805384,
0.041173674166202545,
-0.04624791815876961,
0.00636011827737093,
-0.03802206367254257,
0.0052290079183876514,
-0.032641202211380005,
0.014800380915403366,
0.016317078843712807,
0.04248394817113876,
-0.03200710564851761,
0.005884499289095402,
-0.011577781289815903,
0.046681031584739685,
0.013596104457974434,
-0.0164844561368227,
0.007009419146925211,
-0.0634055957198143,
0.054246559739112854,
0.06504794210195541,
-0.008119983598589897,
0.018346533179283142,
-0.03760714828968048,
-0.023910576477646828,
0.030020534992218018,
-0.0017156933899968863,
0.06611958891153336,
-0.04329586401581764,
0.07087480276823044,
-0.03157171607017517,
0.007500004023313522,
-0.026992714032530785,
-0.045977506786584854,
0.04253605753183365,
0.04605930671095848,
-0.016011472791433334,
-0.03602428734302521,
-0.038808420300483704,
0.03830049932003021,
-0.05712645873427391,
-0.007021363824605942,
0.0037979059852659702,
-0.046324700117111206,
-0.05909962207078934,
0.022025151178240776,
-0.013032699935138226,
-0.02978266403079033,
0.04624008387327194,
0.041123006492853165,
-0.02925514057278633,
0.014071165584027767,
-0.014003866352140903,
-0.05675516650080681,
-0.06866591423749924,
0.0352703332901001,
-0.04575439542531967,
-0.009496273472905159,
-0.052147235721349716,
-0.02325332909822464,
-0.04417926073074341,
0.002373156603425741,
-0.056306708604097366,
0.038520559668540955,
0.1118742823600769,
0.0053482335060834885,
0.013424361124634743,
-0.029808763414621353,
0.07440046966075897,
0.0635654479265213,
-0.0003507981891743839,
-0.04457342252135277,
0.00284782238304615,
-0.0589769072830677,
-0.007558744866400957,
0.0029671478550881147,
0.06560766696929932,
0.05045145004987717,
-0.026453720405697823,
-0.016687562689185143,
0.022516947239637375,
-0.0022074501030147076,
0.026711978018283844,
-0.028977394104003906,
-0.005096239037811756,
0.05953919142484665,
0.06090454384684563,
0.01537864375859499,
-0.03512544184923172,
0.003440834814682603,
-0.06133658066391945,
-0.04661920666694641,
-0.04237888380885124,
0.0017677515279501677,
-0.05408751219511032,
0.06228259578347206,
-0.03511878475546837,
0.009380530565977097,
-0.0066190748475492,
0.06968101114034653,
0.0729793980717659,
-0.06574343889951706,
0.039720650762319565,
0.05420353636145592,
-0.03338305652141571,
0.047361116856336594,
0.001894377637654543,
0.019291546195745468,
0.03159844130277634,
0.010597233660519123,
0.00571824423968792,
0.031711380928754807,
0.03092264011502266,
-0.06416136771440506,
0.06129811704158783,
0.00013972462329547852,
0.04845282435417175,
-0.060149844735860825,
-0.0794127881526947,
0.04753788933157921,
-0.03851178288459778,
-0.005384679883718491,
0.01657327450811863,
0.04344962164759636,
-0.007368953432887793,
0.08346813917160034,
0.010393507778644562,
0.0062704128213226795,
-0.0015590771799907088,
-0.08017189800739288,
0.02760271169245243,
0.02027897723019123,
-0.030679643154144287,
0.06958846002817154,
-0.0020761005580425262,
-0.027148300781846046,
-0.022059854120016098,
0.012384451925754547,
-0.005531241651624441,
-0.016687165945768356,
-0.0017053178744390607,
-0.056481484323740005,
-0.006482125259935856,
-0.001981921959668398,
-0.048649657517671585,
-0.012190941721200943,
0.03127104789018631,
-0.02234334498643875,
-0.05696025863289833,
-0.0070625958032906055,
0.06790313124656677,
-0.006558750756084919,
0.04514402523636818,
0.03130180388689041,
0.03885820508003235,
-0.004830216523259878,
-0.043621692806482315,
0.005491893272846937,
-0.0030795831698924303,
-0.039142657071352005,
0.056175097823143005,
0.02194112353026867,
0.05016729235649109,
0.07789406925439835,
-0.013895170763134956,
0.05475122481584549,
-0.027878403663635254,
-0.031855031847953796,
0.0269081462174654,
0.006778495851904154,
-0.019524209201335907,
-0.05299883708357811,
-0.039763227105140686,
-0.033608052879571915,
-0.03200245648622513,
0.024721721187233925,
0.047093410044908524,
-0.017221810296177864,
-0.021825328469276428,
0.026888767257332802,
-0.03369743749499321,
-0.004979812074452639,
0.02374264970421791,
-0.0008365468820556998,
-0.0391109474003315,
0.030299551784992218,
0.011981664225459099,
0.0022273364011198282,
-0.02168346382677555,
0.0035025663673877716,
-0.043176472187042236,
-0.004166341386735439,
-0.006356297992169857,
0.0059967609122395515,
-0.04223136976361275,
-0.050084929913282394,
-0.009586009196937084,
-0.038161471486091614,
0.012740924023091793,
0.028555238619446754,
-0.02322324924170971,
0.006907507311552763,
-0.07270964980125427,
0.009451249614357948,
0.013546866364777088,
-0.03710847720503807,
0.00770967174321413,
0.016696706414222717,
0.03315814957022667,
0.00699276477098465,
-0.028042646124958992,
0.03399565443396568,
0.033657561987638474,
0.02670758217573166,
-0.03025979734957218,
-0.053088873624801636,
0.029383815824985504,
-0.05641339346766472,
0.0005788997514173388,
0.0575728565454483,
-0.009483731351792812,
-0.035673588514328,
-0.05922015756368637,
0.010743086226284504,
-0.02116771601140499,
0.013216709718108177,
0.02878546714782715,
0.06264948099851608,
0.024051537737250328,
0.009087339043617249,
0.017141055315732956,
-0.008810336701571941,
0.01894461363554001,
0.0674382746219635,
0.04339759424328804,
-0.0005832695751450956,
-0.018344607204198837,
-0.04421444982290268,
0.0027717642951756716,
-0.04944053664803505,
0.006431469228118658,
-0.0325743593275547,
-0.0394684262573719,
0.017721934244036674,
-0.00574118597432971,
-0.0062489258125424385,
0.01011764258146286,
0.013230525888502598,
-0.018883254379034042,
0.08206693828105927,
-0.012838131748139858,
0.05971800535917282,
0.026342589408159256,
-0.006167392246425152,
0.011637642979621887,
0.004434054717421532,
-0.02093425765633583,
-0.0024050285574048758,
0.055643461644649506,
0.03591596335172653,
0.036024801433086395,
-0.0005034139612689614,
0.010666828602552414,
-0.0035817588213831186,
-0.013125963509082794,
-0.034197017550468445,
-0.06249286234378815,
0.009447313845157623,
-0.017616646364331245,
-0.01919189840555191,
-0.0019323609303683043,
-0.0041887108236551285,
0.01298234611749649,
0.009504633955657482,
-0.023819919675588608,
-0.0347563810646534,
0.006865601520985365,
-0.02456783689558506,
-0.025416933000087738,
0.057793084532022476,
-0.08708391338586807,
0.006297592539340258,
0.09878174960613251,
0.03148447349667549,
-0.01303150225430727,
-0.04817502945661545,
0.026933103799819946,
-0.02581625245511532,
-0.058873631060123444,
0.01879124529659748,
0.01404203474521637,
0.04304623231291771,
0.038513511419296265,
-0.068028524518013,
0.049160558730363846,
0.004765900317579508,
0.024417590349912643,
0.0030607059597969055,
0.046781737357378006,
0.022929882630705833,
-0.013575652614235878,
0.00917770341038704,
0.011877371929585934,
0.041118793189525604,
0.03726253658533096,
0.0116995545104146,
0.019386865198612213,
-0.03304577246308327,
-0.021400636062026024,
0.001878612325526774,
-0.08685143291950226,
-0.03223845362663269,
0.007959055714309216,
0.020405884832143784,
-0.010314499959349632,
0.006367061752825975,
-0.05513804405927658,
-0.004132363013923168,
-0.04013608396053314,
-0.00011969134357059374,
0.014813079498708248,
0.005873522721230984,
0.04641834273934364,
-0.010196806862950325,
-0.001090772682800889,
-0.011693420819938183,
-0.04239349439740181,
-0.03794041648507118,
-0.06930096447467804,
0.01055392250418663,
0.03286238759756088,
-0.03444157913327217,
0.04610719904303551,
-0.024340780451893806,
0.003945698495954275,
-0.040033210068941116,
0.04664521664381027,
-0.001228143461048603,
0.0007275743409991264,
-0.016484105959534645,
-0.0549432672560215,
0.048328448086977005,
0.021032141521573067,
0.007827450521290302,
0.017800575122237206,
-0.06671510636806488,
-0.05303967371582985,
-0.03596600517630577,
0.03535659983754158,
-0.04650783911347389,
-0.05478357896208763,
0.034592244774103165,
0.015545970760285854,
-0.004628709517419338,
0.04645160958170891,
-0.04283883795142174,
-0.056335512548685074,
0.04534575715661049,
-0.017959071323275566,
0.036324966698884964,
0.002096872078254819,
0.020972440019249916
] |
<p>An isolated system $A$ has entropy $S_a>0$.</p>
<p>Next, the isolation of $A$ is temporarily violated, and it has entropy reduced $$S_b ~=~ S_a - S,\space\space\space S\leq S_a.$$</p>
<p>Is it true to say: <strong>the process of lowering entropy of a system requires work and energy?</strong></p>
<p>I am not sure if energy of the system must be changed when entropy is reduced. However, energy certainly is required – changing entropy is work and uses energy?</p> | g6596 | [
-0.011030582711100578,
-0.018241597339510918,
-0.00700860982760787,
0.001014787470921874,
-0.030988316982984543,
-0.039470523595809937,
-0.023872070014476776,
0.04552027955651283,
-0.022543029859662056,
0.01824622042477131,
-0.07167244702577591,
0.026290182024240494,
-0.016512876376509666,
0.0015668855048716068,
-0.044047001749277115,
0.04908245429396629,
0.055720869451761246,
-0.02217678911983967,
-0.003859678516164422,
0.03450828418135643,
-0.051544636487960815,
-0.0020957577507942915,
0.019389402121305466,
-0.033441558480262756,
0.05748981982469559,
-0.048540566116571426,
0.07072635740041733,
-0.03469721972942352,
-0.03520456328988075,
0.01174684427678585,
0.02646426297724247,
-0.00397665286436677,
0.07428935170173645,
-0.07169755548238754,
-0.03488438203930855,
-0.014250749722123146,
0.12439098209142685,
0.04749506339430809,
0.020665345713496208,
-0.03812618926167488,
-0.02520771324634552,
-0.008320351131260395,
-0.006752932444214821,
-0.022333785891532898,
0.0035966860596090555,
-0.02725515328347683,
0.014392798766493797,
-0.001529269153252244,
-0.014132026582956314,
-0.022544942796230316,
0.040483422577381134,
0.04241032153367996,
-0.00378752825781703,
-0.011837788857519627,
0.025166409090161324,
0.013794726692140102,
-0.0032353198621422052,
-0.013302027247846127,
0.029698241502046585,
-0.00608249893411994,
0.011559275910258293,
-0.012824423611164093,
0.017002016305923462,
0.012157319113612175,
-0.0012830375926569104,
-0.01644100621342659,
0.028259340673685074,
-0.041147682815790176,
0.007895637303590775,
0.00876842811703682,
-0.010804866440594196,
0.011653166264295578,
-0.027976185083389282,
-0.027063583955168724,
0.07827119529247284,
0.0010453475406393409,
0.06013503298163414,
-0.03499908000230789,
-0.06033266335725784,
0.032417453825473785,
0.008779138326644897,
-0.0283040851354599,
0.029287973418831825,
0.012756303884088993,
0.013195101171731949,
0.01383979618549347,
0.013196810148656368,
-0.02878967486321926,
0.03208282217383385,
0.054173510521650314,
0.0028486009687185287,
-0.030161935836076736,
0.07301415503025055,
-0.00592467375099659,
-0.0010512863518670201,
0.03564705327153206,
0.002016606042161584,
0.026231015101075172,
0.023464318364858627,
0.007067080587148666,
-0.021436557173728943,
-0.10906117409467697,
-0.020733781158924103,
-0.07426844537258148,
-0.015533944591879845,
-0.005087336990982294,
0.015312213450670242,
-0.024238329380750656,
0.00676521472632885,
0.03317161649465561,
0.031008267775177956,
0.00789624359458685,
-0.04343608766794205,
-0.046866901218891144,
0.022160714492201805,
-0.009086019359529018,
0.09760892391204834,
-0.059895314276218414,
0.0011782386573031545,
0.021308770403265953,
-0.0406811460852623,
-0.007445590570569038,
0.004964787978678942,
0.08300333470106125,
-0.023202968761324883,
0.03823799639940262,
0.013861519284546375,
0.051247987896203995,
0.04705298691987991,
-0.011829319410026073,
-0.016643250361084938,
0.017342306673526764,
0.00270721479319036,
0.029584620147943497,
0.007999757304787636,
0.02103555016219616,
-0.018879439681768417,
-0.001517802127636969,
0.01304697897285223,
-0.023390693590044975,
-0.00016250192129518837,
0.0394321046769619,
-0.02283845841884613,
0.0016014935681596398,
-0.029950348660349846,
-0.030027000233530998,
-0.012858182191848755,
0.02732575312256813,
0.012680231593549252,
-0.017171192914247513,
-0.019263586029410362,
0.032650433480739594,
-0.03349485248327255,
-0.03809577599167824,
0.018436502665281296,
-0.015120603144168854,
0.038292307406663895,
0.055160973221063614,
0.05151791125535965,
-0.012651502154767513,
0.0656433254480362,
-0.028872227296233177,
0.0831085816025734,
0.010550711303949356,
-0.0602886825799942,
0.055145613849163055,
-0.004491688217967749,
-0.02255137450993061,
0.030352458357810974,
-0.030465038493275642,
-0.08538027852773666,
-0.05013900250196457,
-0.012456484138965607,
0.02909921668469906,
-0.012879917398095131,
0.05462443828582764,
0.06230565533041954,
-0.013039489276707172,
0.02085333876311779,
-0.02960118278861046,
-0.048102401196956635,
0.04362472891807556,
0.05141361802816391,
-0.03511703386902809,
0.04445505514740944,
0.038966093212366104,
-0.027317259460687637,
0.012466536834836006,
-0.08241292089223862,
0.0009199542691931129,
-0.039530251175165176,
0.013082736171782017,
0.00008865175914252177,
0.005742603447288275,
0.019500426948070526,
0.008103850297629833,
-0.039996854960918427,
-0.026477618142962456,
-0.054854996502399445,
0.01597920060157776,
0.003120782785117626,
0.015418333932757378,
0.015592612326145172,
-0.011019004508852959,
0.031237710267305374,
0.04958542063832283,
-0.0700514018535614,
0.0005314715090207756,
-0.0026795449666678905,
-0.004438475705683231,
0.043912116438150406,
-0.01806364208459854,
-0.03306581825017929,
-0.013508890755474567,
-0.019131816923618317,
-0.023700745776295662,
0.014618612825870514,
0.03210780769586563,
-0.01803646981716156,
0.02689806930720806,
-0.0448889434337616,
0.03766092658042908,
0.012972776778042316,
0.035542067140340805,
-0.017718438059091568,
0.0006304781418293715,
-0.08071764558553696,
-0.025541646406054497,
0.012996042147278786,
0.022894781082868576,
0.009419632144272327,
0.038984816521406174,
0.009457982145249844,
-0.01825682632625103,
-0.025208301842212677,
0.04399074241518974,
0.025878317654132843,
0.024578500539064407,
0.05623878911137581,
0.008486603386700153,
0.000009357890121464152,
-0.05886302515864372,
-0.012130683287978172,
0.0017614415846765041,
0.04824152961373329,
0.019900890067219734,
0.005494656506925821,
-0.024384574964642525,
-0.04563162848353386,
-0.029448602348566055,
0.013002771884202957,
-0.01274073962122202,
-0.008760635741055012,
0.011006071232259274,
-0.010676112025976181,
0.017934784293174744,
0.022478768602013588,
0.03802269697189331,
0.0036476890090852976,
-0.012796430848538876,
0.037770241498947144,
-0.027000505477190018,
0.016119597479701042,
0.03464014455676079,
-0.0036420125979930162,
-0.012601303867995739,
-0.032998550683259964,
-0.02798335812985897,
0.07233979552984238,
-0.02546512708067894,
-0.010029977187514305,
0.032305408269166946,
-0.012035503052175045,
0.004855664446949959,
0.02704937383532524,
0.002992458175867796,
-0.003504555905237794,
-0.04071709141135216,
0.014201728627085686,
0.016752704977989197,
0.010889098979532719,
0.017945919185876846,
-0.08227085322141647,
0.046852272003889084,
0.016265634447336197,
-0.02375894971191883,
-0.01777864433825016,
-0.03606077656149864,
-0.02651454135775566,
-0.02639162726700306,
-0.002090500434860587,
0.015323055908083916,
0.049745041877031326,
-0.0268817450851202,
-0.028889836743474007,
0.05303066596388817,
-0.003235690062865615,
-0.06369700282812119,
-0.028484100475907326,
0.018858639523386955,
-0.002316158963367343,
0.018514851108193398,
-0.007376343943178654,
0.04546056687831879,
0.07239479571580887,
0.0864388644695282,
-0.06318343430757523,
-0.045472390949726105,
-0.047084737569093704,
0.012078053317964077,
-0.007914076559245586,
-0.0062317089177668095,
0.02697029523551464,
0.007534630596637726,
-0.02404015138745308,
0.01477795373648405,
-0.06109238043427467,
-0.053059205412864685,
-0.00348958233371377,
-0.02978823147714138,
-0.020434074103832245,
-0.013359365053474903,
0.005791518371552229,
-0.03172794729471207,
0.001742368214763701,
0.023022213950753212,
-0.016929956153035164,
-0.02077026478946209,
-0.059244368225336075,
-0.020612725988030434,
0.00032749888487160206,
-0.02711227722465992,
0.009370180778205395,
-0.03673255071043968,
-0.08762340247631073,
0.01398450043052435,
-0.013077625073492527,
-0.04392024129629135,
0.03886299952864647,
0.027917198836803436,
0.04443517327308655,
0.04144183546304703,
-0.011402325704693794,
0.025224804878234863,
0.011235903948545456,
0.07479137182235718,
-0.024730274453759193,
-0.058467354625463486,
0.03206927701830864,
-0.0026861107908189297,
0.048058271408081055,
-0.0031611716840416193,
0.01220739632844925,
-0.014624448493123055,
-0.02788344956934452,
-0.03509436175227165,
-0.0021537693683058023,
-0.019815940409898758,
-0.02048027515411377,
-0.03899187222123146,
-0.006192104425281286,
-0.057201117277145386,
0.04398857429623604,
0.05005773901939392,
-0.04975688457489014,
0.01861836016178131,
0.02913345955312252,
-0.011536559090018272,
-0.00749804126098752,
-0.0005981244030408561,
0.033481501042842865,
-0.04293669015169144,
-0.022237971425056458,
-0.009172369726002216,
0.009884705767035484,
-0.016243528574705124,
0.036340225487947464,
0.03963970020413399,
-0.04531220346689224,
0.015026637353003025,
0.0668550506234169,
-0.040540438145399094,
-0.02119196020066738,
0.03408833593130112,
0.05384182557463646,
0.017377305775880814,
0.0038032932206988335,
0.026979411020874977,
-0.05765809863805771,
-0.02144211158156395,
-0.012809094041585922,
0.02196226827800274,
0.0012527755461633205,
-0.00930392649024725,
0.006158805452287197,
0.03430432453751564,
0.07600045204162598,
0.004107209388166666,
0.0225351732224226,
0.047479383647441864,
-0.021545615047216415,
-0.013196445070207119,
0.013201850466430187,
0.023612193763256073,
0.0076200286857783794,
-0.06721540540456772,
-0.015310386195778847,
-0.01871846243739128,
-0.03253762051463127,
0.012024992145597935,
0.013649530708789825,
-0.1420065462589264,
-0.040627412497997284,
-0.04521135985851288,
-0.047655705362558365,
-0.04689789190888405,
0.0021116507705301046,
-0.03468085080385208,
0.005868931300938129,
0.04038010165095329,
0.03430695831775665,
0.041234228760004044,
-0.014302879571914673,
0.026716746389865875,
-0.024466389790177345,
0.11851883679628372,
0.0034445140045136213,
0.04297230765223503,
0.022479338571429253,
-0.06368982046842575,
0.0008616555714979768,
0.048190969973802567,
-0.030299197882413864,
0.011800101958215237,
0.014859750866889954,
0.046377912163734436,
-0.015858402475714684,
-0.015020717866718769,
-0.01116058137267828,
0.03249272704124451,
0.01785176247358322,
0.007970201782882214,
-0.010206944309175014,
-0.03629102557897568,
0.046041302382946014,
0.0173780657351017,
-0.0034044282510876656,
-0.0031442337203770876,
-0.00834440067410469,
-0.07706049829721451,
-0.04617036506533623,
0.041239891201257706,
0.0322321280837059,
-0.031040769070386887,
0.03595593199133873,
0.004943113308399916,
-0.04609299078583717,
0.0020179091952741146,
-0.03480633720755577,
0.05255559831857681,
-0.045228078961372375,
-0.06323996186256409,
0.05586165934801102,
0.03632315248250961,
0.005574224982410669,
0.03415293991565704,
-0.06174315884709358,
0.027844907715916634,
-0.05681085214018822,
-0.02643534541130066,
0.02701578103005886,
0.010217465460300446,
-0.020129570737481117,
0.0347801148891449,
-0.03280524164438248,
-0.021135341376066208,
-0.01346189621835947,
-0.01225089281797409,
0.061597444117069244,
0.033496253192424774,
0.03355831280350685,
-0.03762039914727211,
-0.002178339520469308,
-0.0018716715276241302,
0.019156770780682564,
0.017623500898480415,
-0.03734368830919266,
-0.02800479158759117,
0.03382054716348648,
0.02261980250477791,
0.013059661723673344,
0.1079716607928276,
0.06097622588276863,
0.08550502359867096,
-0.024406973272562027,
-0.014558733440935612,
-0.009258587844669819,
-0.044425636529922485,
-0.0012770273024216294,
0.04674581065773964,
-0.05885685980319977,
-0.01394062489271164,
0.03567075356841087,
0.014443223364651203,
-0.04478474333882332,
0.0039301118813455105,
0.009391024708747864,
-0.002568522235378623,
-0.023997753858566284,
0.025759361684322357,
-0.03864533454179764,
0.040705129504203796,
0.03525643050670624,
0.012561636045575142,
-0.00590974697843194,
-0.02062184177339077,
0.0017280953470617533,
0.0018035134999081492,
-0.0397380106151104,
-0.07609187811613083,
0.042282599955797195,
-0.0001250063069164753,
0.03309341147542,
-0.04694982245564461,
0.0018344965064898133,
0.036133501678705215,
-0.09263142943382263,
0.034083664417266846,
-0.00009332373883808032,
0.028924057260155678,
-0.01191591564565897,
0.03831847757101059,
-0.05905858427286148,
0.024154160171747208,
0.034162044525146484,
-0.0406850166618824,
-0.0010833824053406715,
0.04011860489845276,
-0.02905994839966297,
0.02633294276893139,
-0.03616984933614731,
-0.07538590580224991,
-0.01999347284436226,
0.023037215694785118,
-0.04880918189883232,
-0.06974723190069199,
-0.023984156548976898,
-0.08699513971805573,
-0.013277590274810791,
-0.06332026422023773,
-0.05869678035378456,
-0.012333412654697895,
-0.015842938795685768,
0.014481334015727043,
-0.013217969797551632,
0.01995396800339222,
0.012479348108172417,
-0.017472553998231888,
0.02355150692164898,
-0.01999630406498909,
0.0477629229426384,
-0.02583606354892254,
-0.0451309010386467,
-0.012592281214892864,
0.0752839595079422,
-0.11455200612545013,
0.04927200824022293,
0.03809447959065437,
0.015289241448044777,
0.07012370973825455,
-0.0015536091523244977,
0.03767756000161171,
0.00400671036913991,
-0.010220354422926903,
0.023065928369760513,
0.00872162077575922,
-0.060740504413843155,
-0.011407852172851562,
-0.05019387975335121,
0.00933013390749693,
-0.0354762077331543,
-0.04524260014295578,
0.013233854435384274,
-0.04573215916752815,
-0.025498349219560623,
0.06155842915177345,
-0.026299240067601204,
0.033934786915779114,
0.0839768648147583,
0.044732604175806046,
0.010899556800723076,
-0.05124285817146301,
-0.02909902110695839,
0.06385783106088638,
-0.01212623342871666,
0.07099486142396927,
-0.055375900119543076,
-0.012888510711491108,
-0.02326197922229767,
0.04065423458814621,
-0.01453968696296215,
-0.07043591141700745,
0.03318342566490173,
-0.07813108712434769,
-0.041482117027044296,
0.0672077089548111,
0.020536279305815697,
0.05945573374629021,
-0.0018786241998896003,
0.012782841920852661,
-0.029051506891846657,
0.009953147731721401,
0.06270212680101395,
0.006185169331729412,
0.008308841846883297,
-0.012705888599157333,
-0.042209845036268234,
0.027875442057847977,
-0.06369028985500336,
-0.024573007598519325,
0.00012431763752829283,
-0.0038264140021055937,
0.031162379309535027,
0.002312034135684371,
-0.01949452981352806,
0.09308090060949326,
-0.0147537337616086,
-0.012829948216676712,
0.01820775493979454,
0.030583659186959267,
-0.03166293352842331,
0.056565556675195694,
-0.041105274111032486,
0.008270283229649067,
-0.05576730892062187,
-0.03768981993198395,
-0.04290714114904404,
0.05722681060433388,
0.05142301321029663,
-0.009698850102722645,
0.016122890636324883,
0.016298823058605194,
-0.010205652564764023,
0.0437447652220726,
-0.029729390516877174,
-0.005285885650664568,
0.03716568648815155,
-0.034981463104486465,
-0.00392930256202817,
-0.014050296507775784,
-0.022765491157770157,
-0.007484332658350468,
-0.06949035078287125,
-0.04162226617336273,
0.00938495434820652,
0.0735277384519577,
-0.07456263154745102,
0.02396218292415142,
-0.002012534998357296,
-0.00639402074739337,
0.049049679189920425,
-0.018733201548457146,
0.016251401975750923,
0.05642259865999222,
0.031042611226439476,
0.07320839911699295,
0.03911749646067619,
-0.05926459655165672,
-0.012352190911769867,
-0.012278018519282341,
-0.008929447270929813,
-0.027183562517166138,
-0.024876609444618225,
-0.023717178031802177,
-0.03400610014796257,
0.014261399395763874,
0.03690967708826065,
-0.020517515018582344,
0.026154858991503716,
0.014172318391501904,
-0.00861013401299715,
-0.010008147917687893,
-0.021099507808685303,
-0.03654583543539047,
0.00813776720315218,
0.07471663504838943,
-0.042730171233415604,
0.05112213268876076,
0.015820959582924843,
-0.023068256676197052,
-0.0531265027821064,
0.010223486460745335,
-0.002835928462445736,
0.03431306406855583,
-0.0022415330167859793,
-0.023066984489560127,
0.046172767877578735,
0.032180316746234894,
0.017984483391046524,
-0.08006880432367325,
-0.010991438291966915,
0.026187725365161896,
-0.012548591941595078,
0.04793258011341095,
-0.022255340591073036,
0.03301085904240608,
0.01054319180548191,
-0.06175362318754196,
0.00030796215287409723,
0.019896375015378,
-0.03044310212135315,
0.019947776570916176,
0.025300735607743263,
-0.04707135632634163,
0.021724827587604523,
-0.024686407297849655,
-0.016392936930060387,
-0.0011300782207399607,
0.01390824280679226,
-0.0385214239358902,
0.00007913702575024217,
0.011119326576590538,
-0.04895595461130142,
-0.027806010097265244,
-0.004441105294972658,
0.025819456204771996,
0.06754063814878464,
-0.03575826436281204,
0.039972346276044846,
-0.0252949558198452,
-0.019965974614024162,
-0.03829921782016754,
-0.0006160814664326608,
0.02162312902510166,
-0.0328148752450943,
0.004728307016193867,
-0.0021900353021919727,
-0.013829371891915798,
0.0010015923762694001,
0.03425073251128197,
-0.043390754610300064,
-0.0193471759557724,
0.006348470691591501,
0.024582603946328163,
0.025273317471146584,
-0.02005033940076828,
0.021792232990264893,
-0.025032659992575645,
0.057230256497859955,
-0.011480513028800488,
0.0035812114365398884,
-0.05627692490816116,
-0.014757342636585236,
-0.029912574216723442,
0.001478079124353826,
-0.025165429338812828,
-0.016287904232740402,
-0.009497856721282005,
0.004902041517198086,
0.03788866102695465,
-0.021609604358673096,
0.02999686449766159,
-0.015911400318145752,
0.03024350479245186,
0.03522047773003578,
-0.035008132457733154,
0.06651414930820465,
0.044064514338970184
] |
<p>In <a href="http://en.wikipedia.org/wiki/Metric_expansion_of_space#Understanding_the_expansion_of_Universe" rel="nofollow">this wikipedia article</a> it is described how a beam of light, with its locally constant speed, can travel "faster than light". That is to say it travels a distance, which, from a special relativistic point of view, is surprisingly big. </p>
<p>I wonder if a gravitational wave on such a curved spacetime (of which the wave is actually part of) behaves equally. </p>
<blockquote>
<p>Does a gravitational wave also ride on expanding spacetime, just as light does? Do the nonlinearities of gravitation-gravitation interaction influence the propagation of a wave (like e.g. a plasma) such that light and gravity are effectively not equally fast?</p>
<p>If I want to send a fast signal in this expanding universe scenario, in what fashion do I decide to I send it?</p>
</blockquote> | g6597 | [
0.027797801420092583,
0.10333189368247986,
0.01805698685348034,
0.03287738934159279,
0.006374250166118145,
-0.008999456651508808,
-0.033392876386642456,
-0.034305013716220856,
-0.03587166965007782,
-0.02201020158827305,
0.0527842678129673,
0.009071364998817444,
0.03693956881761551,
0.03609883785247803,
-0.016454823315143585,
-0.03092706948518753,
0.038445331156253815,
-0.048014186322689056,
0.05819973722100258,
0.023961473256349564,
-0.009265054948627949,
0.014649192802608013,
0.02001280151307583,
-0.023106055334210396,
-0.013204613700509071,
0.015073657967150211,
0.04022395610809326,
-0.06324218958616257,
-0.014598319306969643,
-0.044144827872514725,
-0.00819022860378027,
-0.012113369069993496,
0.00002037606100202538,
-0.0436830148100853,
-0.041271716356277466,
0.0440681092441082,
-0.02716347575187683,
-0.038434069603681564,
0.03680368512868881,
0.0011854944750666618,
-0.032004464417696,
-0.0005566768231801689,
-0.026808135211467743,
0.027859900146722794,
0.08666373789310455,
-0.04390449821949005,
-0.015491497702896595,
0.027291228994727135,
0.04800068959593773,
-0.025439292192459106,
-0.04244360700249672,
0.0175214521586895,
0.0002811709709931165,
0.023311229422688484,
0.05375342816114426,
0.04463154822587967,
-0.0460418239235878,
-0.0014868290163576603,
0.07596494257450104,
0.02233307622373104,
-0.038616765290498734,
-0.014497434720396996,
0.09503043442964554,
-0.0331292599439621,
0.009918522089719772,
0.021870432421565056,
-0.002920372411608696,
-0.06801608949899673,
-0.0045244270004332066,
-0.04254041239619255,
0.058686550706624985,
-0.06663313508033752,
-0.03698097914457321,
-0.09528840333223343,
-0.015779558569192886,
0.04469390586018562,
0.02620481327176094,
0.015179039910435677,
-0.028685053810477257,
0.01238612923771143,
-0.019816594198346138,
-0.02392887882888317,
-0.015919335186481476,
0.008473383262753487,
-0.03934160992503166,
-0.024158699437975883,
0.015102391131222248,
-0.0169962290674448,
-0.0009540377650409937,
-0.008419690653681755,
0.016046902164816856,
-0.02619241178035736,
0.04089973121881485,
0.04965381696820259,
-0.053898490965366364,
0.0019238500390201807,
-0.05600457265973091,
0.06294278800487518,
-0.004923139698803425,
0.016976231709122658,
-0.05431850254535675,
-0.007000850047916174,
0.010091437958180904,
0.013716825284063816,
0.020742356777191162,
-0.04079211875796318,
-0.015975724905729294,
-0.022439882159233093,
0.00617231335490942,
-0.01804623194038868,
-0.010977707803249359,
-0.07757594436407089,
0.03006451390683651,
-0.07261344790458679,
-0.09362628310918808,
-0.0313897542655468,
0.012831883504986763,
0.054202038794755936,
0.0032657801639288664,
0.012985432520508766,
-0.013870478607714176,
0.06281042098999023,
-0.038199249655008316,
0.018401311710476875,
0.009173610247671604,
-0.0041022347286343575,
-0.028907515108585358,
-0.004934650845825672,
0.0051608337089419365,
-0.005516733508557081,
-0.020725851878523827,
0.028465518727898598,
-0.03353920951485634,
0.03803505748510361,
-0.021191978827118874,
-0.0038496104534715414,
0.02062200754880905,
-0.022132061421871185,
-0.04183734208345413,
0.019878292456269264,
-0.03621054068207741,
-0.06867709010839462,
0.023743342608213425,
-0.029505625367164612,
-0.042822953313589096,
0.017397498711943626,
0.025344030931591988,
0.0013489387929439545,
0.05073395371437073,
-0.03413613513112068,
0.003954035695642233,
0.10477470606565475,
-0.024976953864097595,
-0.0471513494849205,
-0.012773988768458366,
0.03503361716866493,
0.03161092847585678,
-0.01123366691172123,
-0.027632372453808784,
0.02599162608385086,
0.04905160516500473,
-0.020600611343979836,
-0.012370549142360687,
-0.0034956675954163074,
0.008503152057528496,
0.07312782853841782,
0.0359257310628891,
-0.07371008396148682,
0.013083253987133503,
-0.019215503707528114,
-0.059123698621988297,
-0.015612782910466194,
0.0308387354016304,
0.049218785017728806,
0.04762599989771843,
0.016543567180633545,
0.00991911068558693,
-0.028399141505360603,
-0.07784318923950195,
-0.014357849955558777,
-0.08062741160392761,
-0.08007622510194778,
-0.04357752576470375,
-0.05100414529442787,
-0.019103022292256355,
-0.026533056050539017,
-0.021055134013295174,
-0.03834157437086105,
-0.03682355582714081,
-0.04096067696809769,
-0.018267948180437088,
-0.05455193296074867,
0.00483736302703619,
0.05552582070231438,
-0.009895521216094494,
-0.002689491491764784,
0.021054066717624664,
0.01722402684390545,
-0.016146225854754448,
0.015975352376699448,
-0.014005467295646667,
0.09187491983175278,
0.04641835018992424,
-0.017198221758008003,
0.0528937503695488,
0.029304251074790955,
-0.01543093379586935,
0.011264080181717873,
0.034390680491924286,
0.005401838105171919,
0.08427950739860535,
-0.03617280349135399,
0.04437343031167984,
0.0469643659889698,
0.0019228713354095817,
0.028364913538098335,
-0.02790079638361931,
0.03989311307668686,
0.0012396764941513538,
0.029967786744236946,
0.004444046877324581,
0.0923687070608139,
0.003337679896503687,
-0.041377030313014984,
-0.005104015115648508,
-0.06842759251594543,
-0.01582258567214012,
-0.02259507030248642,
0.025451403111219406,
0.027371343225240707,
-0.007270173169672489,
-0.004418381489813328,
0.010547243990004063,
-0.027921807020902634,
0.06798477470874786,
-0.012356912717223167,
-0.036259036511182785,
0.023249482735991478,
-0.034911613911390305,
-0.017163477838039398,
0.015690457075834274,
-0.002237387001514435,
0.002243436174467206,
0.01625998690724373,
-0.007739336229860783,
-0.08968903869390488,
0.008687993511557579,
-0.07942777127027512,
-0.05088482424616814,
0.008518397808074951,
0.05265885591506958,
-0.01669256202876568,
-0.011031183414161205,
0.030798694118857384,
-0.002486229408532381,
-0.02184954471886158,
-0.01642109639942646,
0.0550856776535511,
-0.12486658245325089,
-0.008681071922183037,
0.008099425584077835,
0.028635140508413315,
0.01695905812084675,
-0.018647046759724617,
-0.01751430332660675,
-0.010634158737957478,
0.019952934235334396,
0.03743236884474754,
-0.04577478766441345,
0.030813558027148247,
-0.024438567459583282,
0.01485175546258688,
-0.022677907720208168,
-0.009323269128799438,
0.004912571515887976,
-0.0007544675027020276,
0.0073337978683412075,
-0.03473857417702675,
-0.0034427877981215715,
-0.038459502160549164,
-0.007284978404641151,
-0.05706304311752319,
-0.07997411489486694,
0.0017892109462991357,
0.008319482207298279,
-0.09092516452074051,
0.02330363541841507,
0.04671734943985939,
-0.008491535671055317,
-0.0020080944523215294,
-0.007040390279144049,
0.0537201426923275,
-0.02119271457195282,
0.05383676663041115,
-0.03352556750178337,
0.059135209769010544,
-0.008378881961107254,
0.01269253809005022,
0.005616911221295595,
0.012110101990401745,
-0.03113158605992794,
-0.10040027648210526,
0.0380028635263443,
-0.02052205801010132,
-0.04311993718147278,
0.012143822386860847,
-0.07080049067735672,
-0.007862738333642483,
-0.017678631469607353,
0.03199751302599907,
0.03190555050969124,
0.0291401669383049,
0.012617697939276695,
0.028788920491933823,
-0.010425538755953312,
-0.033460672944784164,
-0.015381818637251854,
-0.01811860129237175,
0.0021405909210443497,
0.021702757105231285,
0.04511570557951927,
-0.010954250581562519,
-0.06072976812720299,
0.015778454020619392,
0.002789662452414632,
0.006940390449017286,
0.020284732803702354,
0.02564588002860546,
-0.033969130367040634,
0.02993559092283249,
0.012125765904784203,
-0.0011656449642032385,
-0.006909415125846863,
0.01262236014008522,
-0.00198871036991477,
-0.03260676935315132,
0.017465826123952866,
0.04198889061808586,
0.07210612297058105,
0.055226024240255356,
-0.024604149162769318,
0.021940642967820168,
-0.05114568769931793,
0.038371432572603226,
-0.003898952854797244,
0.02930450439453125,
0.03941144049167633,
0.007303161546587944,
-0.043695081025362015,
-0.038394179195165634,
0.01588761992752552,
-0.004155478440225124,
-0.0008557578548789024,
-0.025633040815591812,
0.0005178181454539299,
-0.015486817806959152,
-0.0058836303651332855,
-0.009810342453420162,
-0.021267037838697433,
-0.053532712161540985,
0.003405991941690445,
-0.014726808294653893,
-0.003317621536552906,
0.02585608884692192,
-0.017519265413284302,
0.00278283073566854,
0.02964758314192295,
-0.028289807960391045,
-0.0422891266644001,
-0.0015741686802357435,
0.0821816697716713,
-0.06440717726945877,
0.013099762611091137,
0.056368544697761536,
0.021271370351314545,
-0.030675986781716347,
0.027113452553749084,
-0.038158826529979706,
0.010629654861986637,
0.009869914501905441,
0.05422098562121391,
0.07945168018341064,
0.05013583227992058,
-0.010564037598669529,
0.014300736598670483,
0.029578523710370064,
-0.03501035273075104,
-0.029561586678028107,
0.05153066664934158,
-0.0398610457777977,
0.03738237917423248,
-0.05799847096204758,
0.010770807042717934,
0.008954523131251335,
-0.010514560155570507,
-0.017112746834754944,
-0.0068727112375199795,
-0.00485059292986989,
-0.004629067610949278,
0.039198264479637146,
-0.004804486408829689,
0.06162261962890625,
-0.0041756159625947475,
-0.01887207105755806,
-0.0588722750544548,
-0.0361984483897686,
0.03486546874046326,
-0.015424244105815887,
-0.0075316959992051125,
0.02755354344844818,
-0.024853892624378204,
0.037066500633955,
-0.032567333430051804,
-0.09436638653278351,
0.04299959912896156,
0.04015670716762543,
0.05238370597362518,
-0.06530115008354187,
-0.006797654088586569,
0.02383020706474781,
0.0002829880395438522,
0.009110722690820694,
0.038984380662441254,
0.004662693478167057,
-0.023480970412492752,
0.050431329756975174,
0.03308482840657234,
-0.06367585062980652,
-0.012536708265542984,
0.008246933110058308,
-0.0030623862985521555,
0.02204480767250061,
0.0017018106300383806,
0.04629185050725937,
0.003961092326790094,
0.052164167165756226,
0.0016621866961941123,
0.05356808006763458,
0.0408293642103672,
0.013065037317574024,
0.049522675573825836,
0.0048609646037220955,
-0.016141967847943306,
-0.008663836866617203,
0.019932864233851433,
0.0484168715775013,
-0.05471973121166229,
-0.025100257247686386,
0.006614204030483961,
-0.018087290227413177,
-0.05937835946679115,
0.006708793342113495,
0.04757272079586983,
-0.03351907804608345,
0.009585544466972351,
0.04812752082943916,
-0.011532590724527836,
-0.028870606794953346,
0.07715281844139099,
-0.01033970806747675,
-0.036347512155771255,
0.04542553797364235,
0.02448095753788948,
0.0005152879748493433,
-0.013653750531375408,
0.011786098591983318,
-0.03006589226424694,
-0.04543168097734451,
-0.06860329210758209,
-0.004319676663726568,
-0.01984953135251999,
-0.03070957399904728,
0.02310793660581112,
0.03307441249489784,
0.0029418650083243847,
0.024744566529989243,
-0.012008988298475742,
0.015884872525930405,
-0.02299235202372074,
-0.03457644581794739,
-0.04050774127244949,
-0.057534925639629364,
0.07231137156486511,
-0.006796649657189846,
-0.013223698362708092,
0.008010690100491047,
0.01896131969988346,
0.08158282935619354,
0.0030314745381474495,
-0.037905387580394745,
0.04407469928264618,
-0.021368995308876038,
-0.053181253373622894,
0.02512452006340027,
0.006630904972553253,
0.00008243598858825862,
0.006716051604598761,
-0.039757076650857925,
0.00993166584521532,
-0.02603743225336075,
-0.015367936342954636,
0.03860330209136009,
-0.0012906776973977685,
-0.018509522080421448,
-0.0314740426838398,
0.0978192389011383,
-0.009403797797858715,
0.03326483815908432,
-0.0967235192656517,
0.0733792781829834,
-0.015018019825220108,
0.0032740915194153786,
-0.03161870315670967,
0.008394830860197544,
0.060118041932582855,
-0.09051543474197388,
-0.017621507868170738,
0.022787485271692276,
-0.03391961380839348,
-0.02134682983160019,
-0.019858989864587784,
-0.022768300026655197,
-0.008580069988965988,
-0.03594440966844559,
0.041529469192028046,
0.031017648056149483,
-0.007606829516589642,
-0.004781357944011688,
0.021335970610380173,
-0.016090281307697296,
0.07721199095249176,
0.012072775512933731,
0.024498166516423225,
-0.005763125605881214,
0.006739715114235878,
-0.022553684189915657,
0.04572310298681259,
0.014276132918894291,
0.011156724765896797,
-0.007582645397633314,
-0.03121534362435341,
-0.012384513393044472,
-0.012026306241750717,
0.09505227208137512,
-0.0034997800830751657,
0.05715091526508331,
-0.027919841930270195,
0.010220786556601524,
0.0627906322479248,
-0.026255574077367783,
-0.04520256072282791,
-0.025646300986409187,
0.011768101714551449,
0.035002291202545166,
0.0183822363615036,
0.03831752762198448,
0.03069896623492241,
0.009599442593753338,
-0.030326563864946365,
-0.05475220829248428,
0.021938461810350418,
0.04267878830432892,
0.016464918851852417,
-0.08347187936306,
-0.008126568049192429,
-0.040645770728588104,
-0.011924432590603828,
-0.09767598658800125,
0.08577997237443924,
-0.0033590798266232014,
-0.05744335427880287,
0.002031291602179408,
-0.029721103608608246,
-0.015423126518726349,
0.017811452969908714,
-0.05498170852661133,
0.04054337739944458,
-0.022454379126429558,
-0.03798901289701462,
-0.011224191635847092,
-0.052411776036024094,
-0.0025070367846637964,
0.05790957063436508,
0.027414700016379356,
-0.009756777435541153,
0.01719929464161396,
-0.013264941982924938,
0.03182269260287285,
0.034165315330028534,
-0.044020798057317734,
-0.011117675341665745,
-0.04473740607500076,
-0.01811547391116619,
-0.022515028715133667,
-0.017924509942531586,
-0.03595384955406189,
-0.033104173839092255,
0.02867322973906994,
-0.04463114216923714,
0.02723005600273609,
-0.018970854580402374,
0.033427100628614426,
0.07271590083837509,
0.03515000641345978,
0.008633256889879704,
-0.00579168600961566,
-0.05117481201887131,
0.016512418165802956,
0.04495804384350777,
-0.008351866155862808,
0.043098561465740204,
0.030265918001532555,
0.018346965312957764,
-0.010401029139757156,
0.01780533418059349,
-0.05768322944641113,
-0.013621341437101364,
-0.04073013365268707,
0.038196008652448654,
0.05173211917281151,
0.04332466796040535,
-0.013040833175182343,
0.031164728105068207,
-0.0001744323380989954,
-0.028997745364904404,
-0.013371523469686508,
-0.016061192378401756,
-0.011577056720852852,
0.013274355791509151,
-0.02245982177555561,
0.017879320308566093,
0.028341136872768402,
-0.03743261471390724,
0.04871150478720665,
0.05154948681592941,
0.013380059972405434,
-0.020280756056308746,
0.03370724618434906,
-0.004281041212379932,
-0.0043683648109436035,
0.028344979509711266,
0.04169999435544014,
0.005613698158413172,
0.034000322222709656,
-0.0401221327483654,
0.011178302578628063,
0.020009730011224747,
-0.04598888009786606,
0.05255328491330147,
0.024393975734710693,
-0.006296004634350538,
-0.01666189916431904,
-0.02772633731365204,
-0.012649445794522762,
-0.03809738531708717,
0.005012190900743008,
-0.03506409749388695,
0.047879915684461594,
-0.011982260271906853,
-0.013215779326856136,
-0.004660752601921558,
-0.05371925234794617,
-0.0012222656514495611,
0.03255277872085571,
0.009420851245522499,
0.04936915636062622,
-0.013999185524880886,
0.013890947215259075,
-0.00022092853032518178,
0.03118227608501911,
0.01590038277208805,
0.014982511289417744,
0.043803051114082336,
0.03253595158457756,
0.0561697892844677,
-0.021764148026704788,
-0.11166650801897049,
-0.01515901181846857,
0.015207006596028805,
0.005837500095367432,
0.015451708808541298,
0.038121242076158524,
0.017501424998044968,
0.08711181581020355,
-0.009114633314311504,
0.0036218222230672836,
-0.03739264979958534,
0.025672998279333115,
-0.005960215348750353,
-0.04777652770280838,
-0.012139854952692986,
0.01409770455211401,
-0.018455203622579575,
0.0061696371994912624,
0.04503203555941582,
0.009864703752100468,
-0.034263066947460175,
0.042040981352329254,
-0.007622923702001572,
-0.014650185592472553,
-0.09348487108945847,
0.02496144361793995,
-0.03662260249257088,
-0.005138084292411804,
0.05591660365462303,
0.0034369744826108217,
-0.015451472252607346,
-0.05567624792456627,
0.0037316938396543264,
-0.011305581778287888,
0.027166247367858887,
0.04028145223855972,
-0.06933977454900742,
-0.0035465494729578495,
-0.015423959121108055,
0.009725620970129967,
0.047337114810943604,
0.0007197191007435322,
0.030122404918074608,
-0.015905585139989853,
-0.03982958197593689,
0.016852883622050285,
0.007678220979869366,
-0.04858199879527092,
0.030176633968949318,
0.003840517718344927,
-0.012636370956897736,
-0.018434325233101845,
-0.037188995629549026,
-0.021841855719685555,
0.018716394901275635,
-0.03905893862247467,
-0.049756087362766266,
-0.011687664315104485,
-0.06378571689128876,
0.05750918388366699,
-0.038904819637537,
-0.0067438893020153046,
0.022546270862221718,
0.05099720135331154,
0.003135510254651308,
-0.04008426144719124,
-0.00924169085919857,
0.037355031818151474,
0.005145061295479536,
0.042743537575006485,
-0.0001829099201131612,
-0.032312024384737015,
0.06237882375717163,
-0.026634488254785538,
0.018529657274484634,
0.06360960006713867,
0.004806123208254576,
0.03741583973169327,
0.029197312891483307,
-0.01835523545742035,
-0.03268832340836525,
-0.021400211378932,
0.023639362305402756,
-0.034001484513282776,
0.04979948699474335,
-0.008983452804386616,
0.011907447129487991,
-0.039504118263721466,
-0.0017447833670303226,
0.0026791056152433157,
0.0002467650338076055,
0.021724460646510124
] |
<blockquote>
<p><strong>Possible Duplicate:</strong><br>
<a href="http://physics.stackexchange.com/questions/759/does-quantum-physics-really-suggests-this-universe-as-a-computer-simulation">Does Quantum Physics really suggests this universe as a computer simulation?</a> </p>
</blockquote>
<p>I know the title sounds far-fetched, but the idea was first brought to my attention by a comment by Prof. Jim Gates of the University of Maryland during the <a href="http://www.youtube.com/watch?v=lYeN66CSQhg" rel="nofollow">2011 Issac Asimov Memorial Debate</a>.</p>
<p>Google lead me to <a href="http://www.bottomlayer.com/bottom/argument/Argument4.html" rel="nofollow">this essay</a> which seems to argue that the universe/reality shares many analogues to how a modern Turing machine (a computer) does what we perceive it to do. It doesn't come out and state that <em>The Matrix</em> ought to be reclassified as a documentary, but it leaves that possibility open.</p>
<p>Not being a physicist, I'm wondering just how much water these ideas might hold. Is this an avenue that we really ought to explore or are these scientists abusing an (apparently uncanny) analogy?</p> | g227 | [
-0.013364648446440697,
0.06615246087312698,
0.01315534021705389,
-0.011626778170466423,
0.03655771166086197,
-0.004406256601214409,
-0.00708294752985239,
0.02186841331422329,
0.04621616378426552,
0.01304337102919817,
0.05528358370065689,
0.02304122969508171,
0.0323367603123188,
0.057629913091659546,
-0.0343773290514946,
-0.0026459081564098597,
-0.014687267132103443,
-0.017946939915418625,
0.05225294828414917,
0.00653004739433527,
0.022438183426856995,
0.009927473030984402,
0.012086594477295876,
-0.025084590539336205,
-0.08653254061937332,
-0.042834311723709106,
0.002375394105911255,
-0.08107814937829971,
-0.005296212621033192,
0.020031394436955452,
0.027959981933236122,
-0.005874857306480408,
0.040885988622903824,
-0.05276964232325554,
-0.03307808190584183,
-0.022480763494968414,
0.003536550560966134,
0.012543200515210629,
0.03856895491480827,
-0.013833323493599892,
-0.031299736350774765,
-0.0031218561343848705,
-0.0791596993803978,
0.00230682035908103,
0.011030249297618866,
0.03284948691725731,
0.012740431353449821,
0.0018689678981900215,
0.09465014189481735,
-0.04412129521369934,
-0.0020557416137307882,
-0.02124686725437641,
0.050257910043001175,
0.060402799397706985,
0.08277150988578796,
0.010751181282103062,
-0.009972226805984974,
0.04700562357902527,
0.09727934747934341,
-0.009668882004916668,
0.04215140640735626,
0.028265515342354774,
0.04924299567937851,
0.023252271115779877,
0.005339786410331726,
0.05870361998677254,
-0.01266565453261137,
0.06028556451201439,
-0.033468883484601974,
-0.013941901735961437,
0.01626773551106453,
-0.035596542060375214,
-0.03616248071193695,
0.050141166895627975,
0.048437025398015976,
0.02558954618871212,
-0.021387245506048203,
-0.035598162561655045,
0.035159870982170105,
0.030913058668375015,
0.004101254511624575,
-0.022088168188929558,
-0.02158837392926216,
0.004975663963705301,
0.0054623279720544815,
-0.0170412827283144,
-0.056690458208322525,
0.0035832219291478395,
0.040310341864824295,
0.06827368587255478,
-0.005530419759452343,
-0.010311626829206944,
0.07239913940429688,
0.0196077823638916,
-0.01747039705514908,
-0.03388497605919838,
-0.019766483455896378,
0.02890639193356037,
-0.022943969815969467,
0.043793756514787674,
-0.06010999158024788,
0.017908284440636635,
0.06299489736557007,
-0.04740414768457413,
-0.004976749885827303,
0.044730305671691895,
0.002020113402977586,
-0.018652448430657387,
-0.0387692004442215,
0.016535121947526932,
0.007331817876547575,
-0.006473388057202101,
-0.08025894314050674,
-0.03221125155687332,
-0.057990074157714844,
-0.0016072830185294151,
0.0628262534737587,
-0.055871762335300446,
-0.016217147931456566,
0.028888670727610588,
-0.015018457546830177,
0.022889379411935806,
-0.005119533743709326,
0.029661361128091812,
0.004806250799447298,
0.019925836473703384,
0.029114142060279846,
-0.011636183597147465,
-0.0004612540069501847,
-0.0235595665872097,
-0.01858401857316494,
-0.01934412680566311,
-0.010711483657360077,
0.04237385094165802,
0.025097964331507683,
0.014218753203749657,
-0.039810240268707275,
-0.04482783377170563,
-0.02809825912117958,
0.030716603621840477,
-0.015563985332846642,
-0.027905141934752464,
-0.03656385466456413,
-0.0006270226440392435,
-0.015404517762362957,
0.03606615960597992,
-0.05883878096938133,
0.05816483497619629,
0.002062377519905567,
-0.002691072877496481,
0.05101973935961723,
0.0693235918879509,
-0.025143805891275406,
-0.07480241358280182,
0.001835322706028819,
0.025387367233633995,
0.03052138164639473,
-0.029083846136927605,
-0.00040243015973828733,
0.011346246115863323,
0.06340853869915009,
-0.02351485751569271,
0.013579362072050571,
0.0006866423063911498,
-0.030945319682359695,
0.006551351863890886,
0.04382949694991112,
-0.06496501713991165,
0.0396810844540596,
-0.021908579394221306,
-0.02248762920498848,
-0.03017042949795723,
-0.03538208454847336,
0.03141436353325844,
0.0027406299486756325,
-0.018166188150644302,
-0.02964850515127182,
-0.04765791445970535,
-0.0009670690633356571,
-0.007691313978284597,
-0.03580313175916672,
-0.000430035317549482,
-0.01340087316930294,
0.011096468195319176,
-0.014086778275668621,
-0.0242634154856205,
-0.027005964890122414,
0.07117516547441483,
-0.01803642138838768,
-0.017233915627002716,
-0.08240598440170288,
-0.03232165053486824,
-0.002408063504844904,
0.003928912803530693,
0.016487902030348778,
-0.022523008286952972,
0.008197374641895294,
0.017279813066124916,
0.013239433988928795,
-0.03983449935913086,
0.03727603331208229,
0.025874214246869087,
-0.021222220733761787,
0.013953004032373428,
-0.007604946382343769,
0.034220535308122635,
-0.009366502985358238,
-0.011585536412894726,
-0.04782663658261299,
-0.024080753326416016,
0.10803059488534927,
0.04741225019097328,
0.03144842013716698,
0.029770836234092712,
-0.013649491593241692,
0.003104293253272772,
-0.006780320778489113,
-0.050204500555992126,
-0.036047354340553284,
0.06756686419248581,
0.017249571159482002,
-0.05868569016456604,
0.038440167903900146,
0.005372491665184498,
0.020911836996674538,
-0.004999547265470028,
-0.07335972040891647,
-0.028633669018745422,
-0.029900599271059036,
0.039060212671756744,
0.02221178263425827,
0.0010188048472627997,
0.005397603381425142,
-0.005423319526016712,
0.035184696316719055,
0.020511852577328682,
-0.008856263011693954,
0.05625448748469353,
0.03347369655966759,
-0.004204313736408949,
0.005245367530733347,
-0.059585340321063995,
-0.09293141961097717,
0.03856119140982628,
0.05625751242041588,
-0.07037389278411865,
0.03401024639606476,
-0.011321940459311008,
-0.012258556671440601,
-0.03157179802656174,
0.028484350070357323,
-0.06521328538656235,
-0.0328659750521183,
-0.007443597074598074,
0.04137994721531868,
0.005273814778774977,
0.05282454192638397,
0.052057623863220215,
-0.007287149783223867,
-0.0006802004645578563,
0.06278800964355469,
-0.053642258048057556,
0.006156791467219591,
-0.003048619953915477,
0.034181732684373856,
0.03251225873827934,
-0.0350191630423069,
-0.028599945828318596,
-0.02732120081782341,
-0.004834665451198816,
0.006972192786633968,
0.012173770926892757,
0.0036415690556168556,
-0.008295570500195026,
0.005889574531465769,
0.017999397590756416,
-0.014599460177123547,
0.023837557062506676,
0.033522434532642365,
-0.03305589780211449,
-0.029067665338516235,
0.03496095538139343,
-0.043814826756715775,
0.004841433838009834,
0.06074882671236992,
-0.08115853369235992,
-0.03930066153407097,
-0.05312056094408035,
-0.03180820494890213,
-0.02909744344651699,
0.013658685609698296,
-0.01589292846620083,
-0.03302830457687378,
0.0315060093998909,
-0.0671287477016449,
-0.008008554577827454,
-0.01628910005092621,
0.016872836276888847,
-0.0038844801019877195,
0.052924744784832,
0.008925789035856724,
-0.0009043398895300925,
0.01212333608418703,
0.06818868964910507,
0.006201563403010368,
0.03445974737405777,
-0.06652788072824478,
-0.021368546411395073,
-0.028501922264695168,
-0.0750717744231224,
-0.006193873472511768,
0.06666363775730133,
-0.02244928479194641,
0.028907060623168945,
0.01691727712750435,
0.046206917613744736,
-0.023636972531676292,
0.05021645501255989,
0.001542851678095758,
-0.0052162460051476955,
-0.0008030654862523079,
0.005580533761531115,
-0.033719465136528015,
0.014123724773526192,
0.06958873569965363,
0.07810630649328232,
-0.005020315293222666,
-0.03724324703216553,
-0.03284195438027382,
-0.06179679557681084,
0.05646725744009018,
-0.08245495706796646,
-0.007604967337101698,
-0.0031111077405512333,
-0.08957754075527191,
-0.07881899178028107,
-0.00016925351519603282,
0.006607895251363516,
0.03775988519191742,
-0.031299617141485214,
-0.004331854172050953,
0.01860630139708519,
0.02561594545841217,
0.030347442254424095,
0.04409482330083847,
0.0653594583272934,
0.008333349600434303,
0.06366557627916336,
0.017359109595417976,
-0.050942469388246536,
0.020763175562024117,
0.022293565794825554,
0.032190725207328796,
0.013316445052623749,
-0.002972027752548456,
0.019208760932087898,
0.025248520076274872,
0.024482108652591705,
0.0472223199903965,
-0.012344718910753727,
-0.05834460258483887,
-0.025257442146539688,
0.007974199019372463,
-0.028611108660697937,
0.009150620549917221,
0.011071162298321724,
-0.03833824396133423,
0.04297969117760658,
-0.011311489157378674,
0.007626171689480543,
0.0028859677258878946,
-0.006544904783368111,
-0.012038715183734894,
-0.03120536357164383,
0.06917375326156616,
-0.00695806322619319,
0.03228161111474037,
-0.0027332594618201256,
0.037403758615255356,
-0.014086945913732052,
-0.01870797760784626,
0.03277972340583801,
0.03761720284819603,
-0.028699975460767746,
0.035056233406066895,
0.0013483650982379913,
-0.00967421941459179,
-0.021813414990901947,
-0.023409483954310417,
-0.0027522859163582325,
0.018679581582546234,
-0.0014829463325440884,
-0.03208804503083229,
-0.007577964104712009,
-0.001390380202792585,
0.0015357743250206113,
-0.03551905229687691,
-0.05021650716662407,
-0.03504379466176033,
-0.00912125501781702,
0.025849344208836555,
-0.026812994852662086,
0.013746754266321659,
0.06168673187494278,
-0.015099688433110714,
-0.0399041585624218,
-0.005233199801295996,
-0.04251376911997795,
-0.007661084178835154,
-0.04372464865446091,
0.02368081733584404,
0.02553427405655384,
-0.013343782164156437,
-0.04489127919077873,
0.0031325004529207945,
0.026339679956436157,
-0.04212050512433052,
-0.006536182016134262,
0.013276158832013607,
0.03598427399992943,
0.028624920174479485,
0.05022696033120155,
0.002314680954441428,
0.04650713875889778,
-0.006868888158351183,
0.002721999306231737,
-0.0021076579578220844,
0.022203927859663963,
-0.014945005998015404,
-0.026738351210951805,
0.03898469731211662,
0.025763709098100662,
0.025851497426629066,
0.047142453491687775,
0.04067034274339676,
0.035160426050424576,
-0.0000893937103683129,
0.024465961381793022,
0.02431267686188221,
0.007831382565200329,
0.04781950265169144,
-0.003942249342799187,
0.02066130004823208,
-0.0017465912969782948,
-0.012634317390620708,
0.028488267213106155,
-0.05230057239532471,
0.060778599232435226,
-0.08886778354644775,
-0.03910084068775177,
-0.03924128785729408,
0.054213810712099075,
0.020877275615930557,
-0.019734714180231094,
0.01101360097527504,
-0.024523044005036354,
0.008874297142028809,
0.0020357321482151747,
-0.0240427628159523,
0.035364676266908646,
-0.05877531319856644,
0.018345464020967484,
0.00008546934986952692,
0.059753067791461945,
0.008954161778092384,
0.04225733503699303,
-0.10132113099098206,
-0.028056368231773376,
-0.03229539841413498,
-0.05336382985115051,
0.02143976092338562,
-0.00859026238322258,
-0.006430149078369141,
0.019516512751579285,
0.03155847266316414,
-0.04848578944802284,
-0.05933573096990585,
-0.02019716426730156,
-0.008495197631418705,
0.041494857519865036,
-0.03585241734981537,
0.023845793679356575,
0.06902576982975006,
-0.037968311458826065,
0.03251147270202637,
0.03558309003710747,
-0.062187906354665756,
0.028089549392461777,
-0.05392855405807495,
-0.02308354340493679,
0.026404952630400658,
-0.022270018234848976,
0.0022388631477952003,
-0.046870265156030655,
-0.004086448345333338,
0.004305561073124409,
-0.01895790547132492,
-0.016631465405225754,
-0.01278686337172985,
0.05339960381388664,
-0.014862874522805214,
0.01329398900270462,
0.004584077745676041,
-0.019604193046689034,
-0.016300588846206665,
0.036858197301626205,
0.023985834792256355,
0.002167819067835808,
-0.023468302562832832,
0.013888985849916935,
-0.011407746002078056,
0.005156779196113348,
-0.043531060218811035,
-0.0015937946736812592,
0.045511603355407715,
-0.007083178032189608,
-0.015689415857195854,
-0.03322392702102661,
-0.026911474764347076,
-0.07147377729415894,
0.0423397496342659,
0.029011430218815804,
0.05233406648039818,
-0.0059036738239228725,
-0.0197883490473032,
-0.03008047305047512,
-0.0077194469049572945,
-0.012987615540623665,
0.01754729449748993,
0.019454337656497955,
0.05016535520553589,
0.05144784227013588,
-0.0009759434615261853,
0.006295049097388983,
-0.018515238538384438,
0.025576235726475716,
0.01701963320374489,
0.010406904853880405,
0.024985946714878082,
0.01812051609158516,
-0.02792942523956299,
0.0010976941557601094,
0.027281055226922035,
0.07325372099876404,
0.035886723548173904,
-0.0013687979662790895,
-0.005475097335875034,
0.010604253970086575,
0.05768344923853874,
-0.07715429365634918,
-0.06360035389661789,
-0.03208195045590401,
-0.04115039482712746,
0.05319220572710037,
0.06100176274776459,
0.009330123662948608,
0.00855889730155468,
-0.06467548757791519,
0.008359563536942005,
-0.01292889192700386,
-0.059258781373500824,
0.07825513184070587,
0.00225034705363214,
-0.014291837811470032,
-0.03756968677043915,
0.05504097789525986,
0.0027583432383835316,
-0.02984943985939026,
0.03141399100422859,
0.052929043769836426,
0.014558564871549606,
-0.06369157135486603,
-0.03496489301323891,
-0.05382668972015381,
-0.025839315727353096,
-0.052995748817920685,
0.021541617810726166,
-0.04804997518658638,
-0.02376343309879303,
-0.07375649362802505,
0.03525255620479584,
-0.06931270658969879,
0.05243895947933197,
-0.026199504733085632,
0.037597253918647766,
0.009960955940186977,
-0.07860975712537766,
0.05326931178569794,
-0.010472110472619534,
0.02306154929101467,
-0.04534907266497612,
-0.003997392486780882,
-0.0257446076720953,
-0.011409422382712364,
-0.023471714928746223,
-0.018359916284680367,
0.026359334588050842,
-0.02645624801516533,
-0.06560296565294266,
0.0541377067565918,
-0.03452345356345177,
-0.010832112282514572,
0.012510123662650585,
0.006875335238873959,
0.006179658230394125,
0.04321841523051262,
-0.03167075663805008,
0.025228027254343033,
0.04325559362769127,
-0.019812051206827164,
-0.04470723122358322,
0.028528384864330292,
-0.006242759060114622,
0.007056241389364004,
-0.0017580966232344508,
-0.03179826959967613,
0.010540258139371872,
-0.06898920238018036,
-0.03746160864830017,
0.001558273914270103,
0.017257314175367355,
0.005027112551033497,
0.04300137236714363,
-0.016901206225156784,
-0.007806465961039066,
0.07109244167804718,
-0.04022767022252083,
0.08059960603713989,
0.09698084741830826,
0.033930808305740356,
-0.0675218477845192,
-0.02631337009370327,
0.07543738186359406,
0.04637516289949417,
0.004693684633821249,
0.04316822066903114,
-0.05093125253915787,
-0.048536740243434906,
0.002891340758651495,
-0.01459878496825695,
-0.008965766988694668,
-0.07064149528741837,
-0.010923841968178749,
0.0001602653501322493,
-0.02270766906440258,
0.002759671537205577,
0.03759190812706947,
0.04675573110580444,
-0.018315404653549194,
-0.0023863737005740404,
0.033588703721761703,
-0.0031876773573458195,
-0.0673111230134964,
0.0017292688135057688,
-0.05987626686692238,
0.052833192050457,
0.007591985631734133,
0.004102533217519522,
0.019461167976260185,
-0.12082785367965698,
-0.02091227099299431,
-0.04792725294828415,
-0.03962969779968262,
-0.0699692964553833,
-0.04674355685710907,
0.04068921506404877,
-0.0028031161054968834,
-0.024185480549931526,
-0.028957990929484367,
-0.008674352429807186,
-0.041730012744665146,
-0.07132605463266373,
-0.005892342422157526,
-0.028796806931495667,
-0.010537853464484215,
-0.08111267536878586,
0.03978080302476883,
0.04258989915251732,
-0.047560133039951324,
0.005627715028822422,
0.003543685656040907,
0.03510870411992073,
0.06527327746152878,
0.014936723746359348,
-0.012436535209417343,
0.030585067346692085,
0.022002367302775383,
-0.03533197566866875,
-0.0659361407160759,
-0.034209202975034714,
0.02985292114317417,
-0.0347709022462368,
-0.026829028502106667,
-0.011723008938133717,
0.019884245470166206,
0.05576014518737793,
0.029695866629481316,
0.02578163892030716,
0.0373513326048851,
0.0186983160674572,
-0.04215274751186371,
0.05787190794944763,
-0.04397459328174591,
0.024861477315425873,
0.023162277415394783,
0.00554579496383667,
0.004709604661911726,
0.0364004485309124,
-0.0176108255982399,
0.0016361242160201073,
0.012356673367321491,
0.030576782301068306,
0.004766477271914482,
0.029422756284475327,
0.029341554269194603,
-0.006308628711849451,
0.03881959989666939,
-0.019331801682710648,
0.024039050564169884,
-0.026766609400510788,
0.015262394212186337,
0.008086868561804295,
-0.037356898188591,
0.021727126091718674,
-0.014094763435423374,
0.02701856568455696,
0.012692241929471493,
-0.03620307147502899,
-0.050354499369859695,
-0.007659938186407089,
0.025475990027189255,
-0.023260854184627533,
0.024222632870078087,
0.0057763950899243355,
-0.036986224353313446,
-0.011583821848034859,
-0.04105854779481888,
0.03377309814095497,
-0.02879456616938114,
-0.033979833126068115,
0.011362599208950996,
-0.016409074887633324,
0.018892524763941765,
-0.015151580795645714,
0.042758598923683167,
-0.0787099301815033,
-0.049592338502407074,
-0.0007166045252233744,
0.03962692245841026,
-0.023827308788895607,
-0.004304123111069202,
-0.047873370349407196,
-0.002784575102850795,
0.044772956520318985,
0.06616098433732986,
-0.03230663016438484,
0.027238382026553154,
0.029591994360089302,
0.0417194701731205,
-0.0018890239298343658,
-0.008727160282433033,
-0.05161318555474281,
-0.009123774245381355,
-0.014869986101984978,
-0.03858498856425285,
-0.027508080005645752,
0.004065836779773235,
0.029689880087971687
] |
<p>Say we have an expression of the form:
$$
\left<0\right|:\phi(x)^2: : \phi(y)^2:\left|0\right>,
$$
where $\phi$ is some scalar field. I have heard the claim several times, that in evaluating this expression using Wick contractions, one only has to contract terms between groups of normal ordered terms. In this example this would mean we only have to contract $\phi(x)$ with $\phi(y)$ but not $\phi(x)$ with $\phi(x)$. I have no clue how to derive this. Has anyone got an idea?</p>
<p>EDIT: And say we consider anticommuting operators, would we have:
$$
\left<:\Psi^{\dagger}(x)\Psi(x)::\Psi^{\dagger}(0)\Psi(0):\right> = (-1)^3\left<\Psi^{\dagger}(x)\Psi(0)\right>\left<\Psi^{\dagger}(x)\Psi(0)\right>,
$$
or with a plus sign?</p> | g6598 | [
-0.008683375082910061,
0.006940849125385284,
-0.022770076990127563,
0.005770787131041288,
0.042161863297224045,
-0.07214701920747757,
0.03689519688487053,
0.013714363798499107,
0.0033291017170995474,
0.000045621298340847716,
-0.0524253286421299,
0.05245552957057953,
-0.04028220474720001,
0.011641704477369785,
-0.02122470922768116,
0.0425356887280941,
0.0007421808550134301,
0.009247501380741596,
0.029935715720057487,
0.009112897329032421,
-0.09118454158306122,
0.01879810355603695,
0.0005493787466548383,
-0.0060035111382603645,
0.05397689715027809,
-0.054796867072582245,
0.0010503854136914015,
-0.006627020426094532,
-0.06040605902671814,
-0.06441919505596161,
0.03542027994990349,
0.05183527246117592,
0.0225225780159235,
-0.06125691905617714,
-0.0384543351829052,
0.014199890196323395,
0.040192168205976486,
0.020718902349472046,
0.0243571437895298,
0.01159332413226366,
-0.013768665492534637,
0.017586855217814445,
0.04081610217690468,
-0.01431540958583355,
0.009651889093220234,
-0.0288400761783123,
-0.004078164231032133,
0.055245205760002136,
-0.012947832234203815,
-0.029467923566699028,
-0.009575958363711834,
0.029643947258591652,
0.023528601974248886,
-0.04130260646343231,
-0.02498084306716919,
0.05175037682056427,
0.04994385316967964,
-0.04304192587733269,
0.028109734877943993,
0.03214219957590103,
-0.0542592853307724,
-0.037739019840955734,
0.05781180411577225,
-0.03827841952443123,
0.03736672177910805,
-0.026286588981747627,
0.016375485807657242,
0.01903710700571537,
-0.009885961189866066,
-0.028046799823641777,
0.00019666737352963537,
-0.031601909548044205,
0.047588035464286804,
-0.020749475806951523,
-0.01771746389567852,
0.004768807906657457,
-0.012058969587087631,
-0.08292493224143982,
0.05693308264017105,
0.017221948131918907,
-0.022058159112930298,
-0.07249464094638824,
0.029083723202347755,
0.06539956480264664,
0.02579759992659092,
-0.013435760512948036,
0.03505993261933327,
-0.024319607764482498,
-0.0028352902736514807,
0.06170166656374931,
0.02464643493294716,
-0.02311481349170208,
-0.001823084894567728,
0.03522660210728645,
0.008793672546744347,
0.019791383296251297,
-0.0036943405866622925,
0.02159796841442585,
-0.003123442642390728,
-0.025291476398706436,
0.0073635694570839405,
0.041738562285900116,
-0.008079896681010723,
-0.000269462849246338,
-0.020135516300797462,
0.01571287401020527,
0.02363753505051136,
0.018060021102428436,
0.00036965575418435037,
-0.01847492903470993,
-0.013055730611085892,
0.028191931545734406,
-0.04217970371246338,
-0.06312274187803268,
0.048502419143915176,
-0.0320717878639698,
0.015654325485229492,
0.02290876768529415,
-0.011723794974386692,
0.030412325635552406,
-0.00216154707595706,
-0.022200368344783783,
0.01246741134673357,
0.038289789110422134,
0.013018738478422165,
-0.023979781195521355,
0.01813102513551712,
0.042500898241996765,
-0.010665269568562508,
-0.01755543053150177,
0.06756242364645004,
-0.004932739306241274,
0.05508586764335632,
0.0883398950099945,
0.006621917709708214,
0.016913706436753273,
-0.04416254907846451,
0.01607361249625683,
0.012203359976410866,
-0.08580788969993591,
-0.035106681287288666,
0.0034111510030925274,
-0.021134184673428535,
0.003502926556393504,
-0.011363119818270206,
-0.03380467742681503,
0.04710114002227783,
-0.06548719853162766,
0.01595793105661869,
0.06923738867044449,
-0.029846783727407455,
0.0428561195731163,
-0.004351416602730751,
0.009216390550136566,
-0.02051541581749916,
0.0025205782148987055,
0.035384856164455414,
0.006977839861065149,
-0.04968244582414627,
0.00955173559486866,
0.009575355798006058,
0.03458451107144356,
0.009739510715007782,
0.023002441972494125,
-0.04912728816270828,
-0.043748222291469574,
0.026541782543063164,
-0.007292882539331913,
-0.04435453936457634,
-0.07045315951108932,
0.02128741703927517,
0.04402478039264679,
0.012978733517229557,
-0.03509124368429184,
0.023129945620894432,
0.07021643966436386,
-0.03378785029053688,
0.0041013979353010654,
0.01217783335596323,
0.027919281274080276,
-0.06307248771190643,
0.011988040991127491,
0.009077632799744606,
-0.020478732883930206,
-0.022205935791134834,
-0.039566412568092346,
-0.06377905607223511,
-0.00682164216414094,
-0.02012326754629612,
-0.010081455111503601,
0.020525634288787842,
0.02444986067712307,
0.021674413233995438,
0.0072996472008526325,
-0.01761249080300331,
-0.01767442561686039,
-0.029937468469142914,
-0.06715069711208344,
0.013575118966400623,
-0.016979819163680077,
-0.00824545044451952,
-0.021470656618475914,
-0.041902657598257065,
-0.04088762775063515,
-0.009929892607033253,
-0.0034015493001788855,
-0.020381897687911987,
0.020946595817804337,
0.035412877798080444,
-0.016620859503746033,
0.013479745015501976,
-0.09564534574747086,
0.03991072252392769,
0.028647154569625854,
-0.017303790897130966,
-0.05724814161658287,
0.006287981290370226,
-0.000821361318230629,
-0.0341525673866272,
-0.012423279695212841,
-0.016251347959041595,
-0.027364153414964676,
0.017328526824712753,
-0.0035811651032418013,
0.011077246628701687,
0.02235715091228485,
0.05072086676955223,
0.05831227824091911,
0.03378928080201149,
0.026884321123361588,
-0.09968774020671844,
0.013532670214772224,
-0.04330815002322197,
-0.06489303708076477,
-0.027492821216583252,
0.008285369724035263,
-0.034179992973804474,
0.055199459195137024,
0.011415734887123108,
0.06123138964176178,
-0.001124658272601664,
0.01801963709294796,
-0.025932246819138527,
0.030627097934484482,
0.026781843975186348,
-0.0042853872291743755,
0.03232596069574356,
0.022868888452649117,
-0.03320031613111496,
0.0511467270553112,
-0.02592909336090088,
0.004775163251906633,
-0.020084192976355553,
-0.021024171262979507,
-0.03560253605246544,
-0.04917016625404358,
-0.0034453868865966797,
-0.03889773041009903,
-0.0309413094073534,
-0.010033158585429192,
-0.016656722873449326,
0.0698876902461052,
0.03760896623134613,
0.023793190717697144,
-0.0409390926361084,
-0.02730332501232624,
0.005655887071043253,
0.035706955939531326,
0.03894959017634392,
0.008666696958243847,
-0.029740385711193085,
-0.007160705514252186,
-0.008302557282149792,
-0.005567880813032389,
-0.03211748227477074,
-0.06454598158597946,
-0.022022100165486336,
-0.030379099771380424,
0.021110927686095238,
0.04311058297753334,
0.04356799274682999,
-0.0002427185681881383,
0.005837135948240757,
0.0438874252140522,
-0.0012254409957677126,
-0.03541293367743492,
-0.0022692966740578413,
0.036940693855285645,
-0.00875131506472826,
0.01331039797514677,
-0.007989390753209591,
0.023962581530213356,
0.009870409965515137,
-0.04110700264573097,
0.002007042523473501,
-0.009316307492554188,
0.017389658838510513,
-0.00972513947635889,
0.033153995871543884,
0.03978307172656059,
-0.006649005692452192,
0.01833486557006836,
0.021839963272213936,
0.03486702963709831,
0.004713691771030426,
-0.022370781749486923,
-0.017904823645949364,
-0.07289029657840729,
-0.029784321784973145,
-0.010620190761983395,
-0.006179633550345898,
0.020566727966070175,
-0.024945087730884552,
0.0057106949388980865,
-0.05250444635748863,
-0.031976357102394104,
0.007285239174962044,
0.01444126758724451,
-0.00483803590759635,
-0.04960102215409279,
-0.00803618784993887,
-0.05999407172203064,
0.06199837848544121,
0.014155130833387375,
-0.02458271011710167,
-0.0036111194640398026,
-0.06593789905309677,
0.04386739060282707,
-0.05785032734274864,
-0.06549480557441711,
0.014071624726057053,
-0.004415589384734631,
0.03908853232860565,
0.004375236574560404,
-0.04175364226102829,
-0.06567889451980591,
-0.004644317086786032,
0.017462916672229767,
-0.010897909291088581,
0.007172957994043827,
0.0357925221323967,
-0.02160377986729145,
-0.048962801694869995,
0.0011230732779949903,
-0.020908161997795105,
-0.059118155390024185,
-0.032776545733213425,
0.06992384791374207,
0.044379014521837234,
-0.01545693352818489,
-0.03875555098056793,
-0.04935607314109802,
0.026193639263510704,
-0.05057363957166672,
-0.00891305971890688,
0.016301151365041733,
0.03384455665946007,
-0.023286595940589905,
0.0048728203400969505,
0.015911875292658806,
0.015190073288977146,
0.02399165742099285,
-0.018115980550646782,
0.015696337446570396,
0.01665438711643219,
0.041612476110458374,
0.04571260139346123,
0.08438390493392944,
0.015846749767661095,
-0.0047690668143332005,
0.00048114077071659267,
0.007195489481091499,
0.034094009548425674,
0.02107894793152809,
-0.058071717619895935,
-0.008989316411316395,
0.028791263699531555,
-0.014902645722031593,
0.06355591863393784,
-0.013965317979454994,
-0.05030420050024986,
0.0576932467520237,
0.03611749783158302,
-0.03290672227740288,
-0.056171055883169174,
-0.016211066395044327,
-0.013951919041574001,
0.037365686148405075,
-0.070856012403965,
0.011279345490038395,
-0.001362788607366383,
-0.0277694184333086,
-0.022394180297851562,
0.033189840614795685,
0.027183501049876213,
-0.035662636160850525,
0.02548261359333992,
0.021139230579137802,
-0.015631239861249924,
-0.053098127245903015,
0.0030788835138082504,
-0.03181786090135574,
0.04218921810388565,
-0.03450477868318558,
-0.01380985602736473,
-0.041709575802087784,
0.03812215104699135,
0.02085135132074356,
0.04819512367248535,
-0.06144965440034866,
-0.004700652789324522,
-0.04338402301073074,
0.00140066584572196,
0.040251120924949646,
0.01007484458386898,
-0.015508443117141724,
0.023991582915186882,
-0.008759449236094952,
-0.07118917256593704,
0.01652618683874607,
0.011614229530096054,
0.0156562477350235,
0.004245346412062645,
-0.0024363980628550053,
0.029604341834783554,
0.11509232968091965,
0.03640376776456833,
0.00548667972907424,
0.02382575161755085,
-0.005791782401502132,
-0.03747973591089249,
0.11102423071861267,
-0.016569074243307114,
0.031322773545980453,
-0.014226735569536686,
-0.010172151029109955,
-0.07297965884208679,
0.034844525158405304,
0.038080766797065735,
-0.007696504704654217,
-0.018022283911705017,
0.0016585917910560966,
-0.03591113165020943,
-0.05523828789591789,
0.0006443556630983949,
-0.019199978560209274,
-0.05183786153793335,
-0.04207243770360947,
0.007954324595630169,
-0.019926998764276505,
-0.04207240045070648,
0.05033859610557556,
0.021130435168743134,
-0.0863756462931633,
0.07017220556735992,
-0.015123828314244747,
0.0006558610475622118,
0.002995937829837203,
-0.027748532593250275,
-0.020503152161836624,
-0.01893303543329239,
-0.08008129149675369,
-0.000996079994365573,
-0.00890872161835432,
0.028075043112039566,
-0.003516435855999589,
-0.0943155363202095,
0.03171733021736145,
-0.10352399945259094,
0.03293208032846451,
0.04109774902462959,
0.05707739666104317,
0.02838762104511261,
-0.05936604365706444,
-0.02541375905275345,
-0.011645099148154259,
0.028421230614185333,
0.03360293060541153,
-0.051433272659778595,
-0.012427866458892822,
0.017578361555933952,
-0.04103896766901016,
-0.04917878285050392,
-0.0031062231864780188,
0.04891052469611168,
0.04610768333077431,
-0.0060535576194524765,
-0.018687894567847252,
0.025771884247660637,
-0.03785143792629242,
0.03209499269723892,
0.05015556886792183,
-0.007176603656262159,
-0.03557506576180458,
-0.07006745785474777,
-0.016496790573000908,
0.02319418638944626,
-0.013437294401228428,
0.02777963876724243,
-0.01588228903710842,
-0.03366997465491295,
-0.0016745703760534525,
-0.041363444179296494,
0.013525985181331635,
-0.010675672441720963,
0.06715703755617142,
0.007903724908828735,
0.03605516999959946,
0.015152105130255222,
0.03194968402385712,
0.013660396449267864,
-0.021791212260723114,
0.11699803173542023,
-0.005516068544238806,
-0.005858323071151972,
-0.0008477825904265046,
-0.014145726338028908,
-0.038991253823041916,
0.023958561941981316,
-0.06205907464027405,
0.07909557968378067,
0.030939213931560516,
-0.00873776338994503,
-0.012434417381882668,
0.06167701259255409,
0.05355384573340416,
-0.013358737342059612,
-0.060642313212156296,
-0.029078403487801552,
-0.015512467361986637,
0.008564094081521034,
0.036779094487428665,
0.005973847582936287,
-0.00990261510014534,
0.05955316126346588,
-0.06445658951997757,
-0.02562238648533821,
0.07071349769830704,
0.00925454217940569,
0.006425938569009304,
-0.0750170424580574,
-0.014185418374836445,
-0.018275456503033638,
0.0231497623026371,
-0.028712183237075806,
0.01984608732163906,
0.006424381863325834,
-0.030700433999300003,
-0.018996097147464752,
-0.03917362168431282,
0.01929834671318531,
-0.030811524018645287,
-0.03201392665505409,
-0.05692523345351219,
0.03223082795739174,
0.020029529929161072,
-0.019491324201226234,
-0.013020330108702183,
-0.009017915464937687,
-0.017290648072957993,
0.02440977469086647,
-0.013880319893360138,
0.03415345400571823,
0.03204786777496338,
0.018788082525134087,
-0.008714141324162483,
0.0050519416108727455,
0.03632862865924835,
-0.024120710790157318,
0.005257092881947756,
0.038049422204494476,
0.04699869826436043,
0.027595924213528633,
0.05886856094002724,
0.06447585672140121,
0.018841195851564407,
0.0007930745487101376,
0.025574488565325737,
-0.00045521120773628354,
0.015074447728693485,
0.004184954799711704,
-0.04135172814130783,
0.009876510128378868,
-0.059517741203308105,
-0.0668681338429451,
0.031155752018094063,
0.03804308921098709,
-0.01356141921132803,
0.05024903267621994,
0.04140685871243477,
-0.009784729219973087,
-0.0022814865224063396,
0.0035534529015421867,
0.03716026991605759,
-0.0024443070869892836,
0.05201473459601402,
0.046592820435762405,
0.04927459731698036,
0.022730102762579918,
0.007961836643517017,
0.0475940927863121,
0.054238371551036835,
0.04313089698553085,
-0.08733758330345154,
0.03861776366829872,
0.023531045764684677,
-0.043803535401821136,
0.058637555688619614,
-0.03420419245958328,
-0.020801208913326263,
-0.01456349529325962,
-0.023434074595570564,
0.011247929185628891,
0.011807537637650967,
-0.007976427674293518,
-0.015218059532344341,
0.016914552077651024,
0.09565503895282745,
-0.014102528803050518,
-0.01478409580886364,
0.03568382188677788,
0.023662764579057693,
-0.0337495282292366,
-0.01576332561671734,
0.033363357186317444,
0.03197222203016281,
0.009586869738996029,
-0.049495939165353775,
0.02987552434206009,
0.04898707941174507,
0.027911650016903877,
0.0045123049058020115,
-0.03286692500114441,
0.012092288583517075,
-0.008108843117952347,
0.0271469559520483,
-0.07226239889860153,
0.09066996723413467,
0.01579207181930542,
0.07635283470153809,
0.016423005610704422,
0.018707403913140297,
0.040562164038419724,
-0.05450283735990524,
-0.042295366525650024,
0.02710098773241043,
-0.009179319255053997,
-0.03645686060190201,
-0.047352246940135956,
-0.02690647542476654,
-0.007303909864276648,
0.004458791576325893,
-0.03606502339243889,
0.03459199145436287,
-0.023898961022496223,
0.030317677184939384,
0.039084360003471375,
0.06935964524745941,
-0.07890167832374573,
-0.05937068536877632,
0.03486493602395058,
0.014136438257992268,
0.021952098235487938,
0.07533625513315201,
-0.006262792274355888,
0.010905812494456768,
-0.004885610193014145,
0.04214812442660332,
0.038281917572021484,
0.009250017814338207,
-0.04730965197086334,
-0.023303477093577385,
-0.037810567766427994,
-0.004822698887437582,
0.008667804300785065,
-0.04894736409187317,
0.08007694780826569,
0.020292621105909348,
0.02283698506653309,
0.008715188130736351,
-0.024894487112760544,
-0.02299761213362217,
-0.012330187484622002,
-0.02861841581761837,
-0.02205895632505417,
0.09335702657699585,
0.04907328635454178,
-0.02481677755713463,
-0.022472672164440155,
0.031106367707252502,
0.05005089193582535,
-0.03084101714193821,
-0.022566506639122963,
-0.003479722421616316,
0.026982495561242104,
-0.023174798116087914,
0.009713699109852314,
0.09714967757463455,
-0.01931741274893284,
0.04289883375167847,
0.05720826983451843,
0.009816001169383526,
-0.048595622181892395,
-0.004173812922090292,
-0.004534013103693724,
0.0016579002840444446,
-0.019219661131501198,
-0.01550920307636261,
-0.024522975087165833,
-0.09375027567148209,
0.009534844197332859,
0.008575529791414738,
-0.04622757062315941,
0.0013329057255759835,
-0.014645581133663654,
-0.011700445786118507,
0.0069361599162220955,
0.009826645255088806,
0.0403306744992733,
-0.031468089669942856,
0.00527118518948555,
0.021971896290779114,
-0.014408268965780735,
-0.0636637881398201,
0.0008529140031896532,
-0.03170209378004074,
-0.06372170150279999,
0.024514392018318176,
-0.0052105276845395565,
0.05929572880268097,
0.002298185834661126,
-0.07413278520107269,
-0.03321462124586105,
0.08510705083608627,
-0.026759594678878784,
0.02746427059173584,
-0.03691716492176056,
-0.06287894397974014,
0.012277026660740376,
-0.029132425785064697,
-0.051777396351099014,
-0.013635649345815182,
-0.03292069211602211,
-0.013923515565693378,
0.04424427077174187,
-0.00871158204972744,
0.001920081558637321,
0.018340878188610077,
0.03470192477107048,
-0.009721779264509678,
-0.03505229949951172,
0.04871173948049545,
-0.02416575327515602,
0.06456688791513443,
0.03358432278037071,
-0.027281610295176506,
0.010063217021524906,
0.005233618430793285,
0.015852531418204308,
0.03799201920628548,
-0.026995470747351646,
-0.03485475108027458,
-0.06200212985277176,
0.003707433585077524,
-0.028537752106785774,
-0.03733773157000542,
0.014251073822379112,
0.004510627128183842
] |
<p>I am trying to make sense of <a href="http://arxiv.org/abs/physics/0210005" rel="nofollow">arXiv:physics/0210005</a>. I am confused with the concept of information bearing degrees of freedom of a system mentioned at the very beginning. To verify the arguments of the paper, I would like to start with a 1-D quantum simple harmonic oscillator. We know that it has two degrees of freedom, momentum and position. You can also use generalized degrees of freedom if you want. My question is which of these are the information bearing degrees of freedom?</p> | g6599 | [
0.04107074812054634,
0.0008589160861447453,
0.0005711746052838862,
-0.010933621786534786,
0.06342893838882446,
0.019851457327604294,
0.06691402196884155,
-0.03913012146949768,
-0.012217836454510689,
-0.03963780775666237,
-0.027963396161794662,
0.004797876346856356,
-0.019706567749381065,
-0.016184240579605103,
-0.010739874094724655,
-0.049710437655448914,
0.05174809694290161,
0.07369206845760345,
0.04923509433865547,
-0.028906410560011864,
0.028935370966792107,
0.026723524555563927,
-0.10036846250295639,
-0.019372571259737015,
-0.010074660181999207,
0.0045426879078149796,
0.004797816276550293,
-0.08477681130170822,
-0.01670778915286064,
-0.021056078374385834,
-0.07648012787103653,
-0.03165837749838829,
0.06637759506702423,
-0.0020911102183163166,
0.008482621051371098,
-0.02245909534394741,
0.03200451284646988,
-0.023199748247861862,
0.018234949558973312,
0.022975511848926544,
-0.049244996160268784,
-0.020571859553456306,
-0.003554019844159484,
-0.019606968387961388,
0.03441723808646202,
0.05205722898244858,
0.02977537363767624,
-0.011473199352622032,
-0.0281122587621212,
-0.020722322165966034,
0.006336433347314596,
0.02075505256652832,
0.032868023961782455,
0.06086178869009018,
0.008995294570922852,
0.0458805188536644,
0.013514801859855652,
-0.056709468364715576,
0.010558126494288445,
0.00044509072904475033,
0.014343529008328915,
0.039049554616212845,
-0.015560860745608807,
-0.015380223281681538,
0.023994045332074165,
-0.006599646992981434,
-0.0570853017270565,
-0.06195182725787163,
-0.039837297052145004,
-0.011115998961031437,
0.02213132567703724,
-0.029574038460850716,
-0.024372277781367302,
-0.017409460619091988,
0.01613754592835903,
-0.037875063717365265,
0.013728695921599865,
-0.051151104271411896,
0.0473763570189476,
-0.006671268027275801,
-0.029680540785193443,
-0.08498110622167587,
0.06974448263645172,
-0.006056411191821098,
0.09584962576627731,
0.020353153347969055,
-0.0186642874032259,
0.024999428540468216,
-0.0010765653569251299,
0.06651104986667633,
0.040779393166303635,
-0.02311772294342518,
0.025808868929743767,
0.0187305249273777,
-0.0016023799544200301,
-0.003977173939347267,
-0.06910693645477295,
0.018458079546689987,
0.018260546028614044,
0.06596130132675171,
-0.028780711814761162,
0.0004032497527077794,
0.0025067597161978483,
-0.024088658392429352,
0.016287051141262054,
-0.04333476349711418,
-0.01958184503018856,
-0.04525446146726608,
-0.012150539085268974,
0.012470996007323265,
-0.04923655092716217,
0.017674315720796585,
0.014656628482043743,
-0.06810969859361649,
-0.04758754372596741,
-0.02356557548046112,
0.10243452340364456,
-0.005840647500008345,
-0.00985982920974493,
-0.0071950736455619335,
-0.012918807566165924,
0.03721213340759277,
0.043540533632040024,
0.08844054490327835,
-0.01608852669596672,
-0.00902439747005701,
0.0031734684016555548,
-0.021672602742910385,
0.025592422112822533,
-0.03399300575256348,
-0.009734364226460457,
-0.018445344641804695,
-0.01784876547753811,
0.02236158400774002,
-0.025236139073967934,
0.0054177152924239635,
0.06375470757484436,
-0.007952549494802952,
0.008099541068077087,
0.007238483987748623,
0.04274491220712662,
-0.033928338438272476,
0.002150388201698661,
-0.07212301343679428,
0.030447019264101982,
0.0026511664036661386,
0.030268648639321327,
-0.022670656442642212,
0.060347095131874084,
0.012720725499093533,
0.012998729944229126,
0.014546727761626244,
0.0035690527874976397,
-0.0398855097591877,
-0.0003773291246034205,
-0.011065519414842129,
0.019385065883398056,
0.01841067150235176,
0.02784094028174877,
0.03512310981750488,
0.026409616693854332,
0.015157556161284447,
0.06351584941148758,
-0.02331857569515705,
-0.02410936914384365,
-0.00730983866378665,
-0.0032577018719166517,
-0.043986666947603226,
-0.005676425993442535,
-0.04770931601524353,
-0.01716420240700245,
-0.03953108191490173,
-0.03933277726173401,
0.035138364881277084,
-0.020313454791903496,
0.02159845270216465,
0.01344876829534769,
0.027188993990421295,
0.08757387846708298,
0.03317752107977867,
0.02050177752971649,
-0.00290933926589787,
-0.004503021016716957,
0.00397765077650547,
-0.026523107662796974,
0.026324691250920296,
0.0730489119887352,
0.012523902580142021,
-0.07304701209068298,
0.025220884010195732,
-0.0009958137525245547,
-0.038110166788101196,
-0.04356447979807854,
-0.006515032611787319,
-0.03986286371946335,
-0.01472749374806881,
0.02681809663772583,
-0.018046336248517036,
-0.038495734333992004,
0.0332554467022419,
-0.01771821454167366,
0.029353320598602295,
0.015073582530021667,
0.014134465716779232,
0.049055516719818115,
0.005833685398101807,
0.01460224762558937,
0.038334667682647705,
0.0011261127656325698,
0.004562817979604006,
0.0222003236413002,
-0.014445362612605095,
0.0007762510213069618,
0.031916793435811996,
0.024919137358665466,
-0.0657191202044487,
0.042832087725400925,
-0.020673613995313644,
0.014045333489775658,
-0.052490234375,
-0.00392840476706624,
0.02974826656281948,
0.06263188272714615,
-0.013905978761613369,
-0.024534817785024643,
0.05354577675461769,
-0.051289379596710205,
-0.04797779768705368,
-0.045241862535476685,
0.06864422559738159,
-0.06165344640612602,
-0.019571051001548767,
-0.007356191985309124,
-0.012543064542114735,
0.03010113537311554,
0.03957124426960945,
-0.014259048737585545,
-0.027812229469418526,
0.0516614131629467,
0.03830511495471001,
0.018190519884228706,
0.031479042023420334,
-0.03089674562215805,
-0.06508464366197586,
-0.018408790230751038,
0.028364261612296104,
0.04765506461262703,
-0.02632364258170128,
-0.037640444934368134,
0.003491588868200779,
-0.02211880125105381,
-0.06309682130813599,
0.037504907697439194,
-0.0076007298193871975,
0.005082482937723398,
0.009648626670241356,
-0.0007130596786737442,
-0.03846650570631027,
-0.027439787983894348,
-0.025715000927448273,
-0.02141367830336094,
-0.10638252645730972,
0.008263190276920795,
0.039085738360881805,
-0.04013214260339737,
0.001977285835891962,
0.009348009712994099,
-0.02890332043170929,
0.0037221082020550966,
-0.024167455732822418,
-0.0061951554380357265,
0.07912025600671768,
-0.03500485420227051,
0.07107099890708923,
-0.047123122960329056,
-0.017234330996870995,
0.01087899785488844,
-0.015399684198200703,
-0.06665041297674179,
0.0012627794640138745,
-0.01483965665102005,
0.01576375402510166,
-0.003659073496237397,
0.009236413054168224,
0.06721947342157364,
-0.049781426787376404,
-0.012755069881677628,
0.04323616996407509,
-0.004245956894010305,
0.02558271586894989,
-0.060718268156051636,
0.02758541703224182,
0.03158937767148018,
0.03646852821111679,
-0.040025826543569565,
0.07911942899227142,
0.04202998802065849,
-0.004677527118474245,
-0.03744730353355408,
0.07191213220357895,
0.013612388633191586,
0.028676485642790794,
-0.011836186982691288,
0.05273136496543884,
-0.010305024683475494,
0.00731344148516655,
-0.02220483496785164,
0.0032890629954636097,
0.016292793676257133,
0.005737054627388716,
-0.05334347113966942,
-0.022493576630949974,
0.046300116926431656,
-0.0002752933942247182,
-0.005719044245779514,
-0.0015080436132848263,
-0.05943071097135544,
0.0017955198418349028,
-0.03519770875573158,
-0.02185348980128765,
-0.0501001700758934,
-0.06602483987808228,
0.0033928826451301575,
-0.04036587104201317,
0.12836503982543945,
0.09131886810064316,
-0.041123777627944946,
0.0007338568684644997,
-0.06271959841251373,
-0.09612902998924255,
0.028008639812469482,
-0.0054965270683169365,
-0.0073160696774721146,
-0.02939663827419281,
-0.009760403074324131,
-0.034589994698762894,
-0.015479007735848427,
0.0028448079247027636,
-0.0025213644839823246,
0.021425919607281685,
0.02462012693285942,
0.011143398471176624,
0.011377585120499134,
0.022735146805644035,
-0.0005599242285825312,
-0.013201610185205936,
-0.01356351189315319,
0.011727187782526016,
-0.009263004176318645,
-0.00014908789307810366,
-0.010871986858546734,
0.03607925772666931,
-0.02287919446825981,
0.016436858102679253,
0.0056215329095721245,
0.07924339175224304,
0.00573092931881547,
0.056755151599645615,
0.02523655630648136,
-0.01713946834206581,
-0.007048197090625763,
-0.017642013728618622,
0.02088375762104988,
0.0641661211848259,
0.008057814091444016,
-0.03359299153089523,
-0.03533557802438736,
-0.0005968806799501181,
0.025224698707461357,
-0.00518212141469121,
-0.03497679904103279,
-0.09213576465845108,
0.04352077096700668,
0.00008413539035245776,
0.062108464539051056,
0.026852762326598167,
0.012687303125858307,
-0.024594932794570923,
-0.05356542766094208,
0.022177213802933693,
0.025664331391453743,
0.003951667807996273,
0.04503285884857178,
0.012650563381612301,
0.06763820350170135,
0.004480564966797829,
0.017517535015940666,
0.03891536965966225,
-0.02746128849685192,
-0.03723302483558655,
0.06714513897895813,
-0.059945814311504364,
-0.011740943416953087,
0.010977399535477161,
0.020189886912703514,
0.01999831013381481,
-0.016383569687604904,
0.005467304028570652,
-0.03674323856830597,
0.05138426646590233,
0.013661864213645458,
-0.022352103143930435,
-0.001617982517927885,
0.00332475733011961,
0.01597304455935955,
0.06116004288196564,
0.01312066800892353,
-0.022316444665193558,
0.014382684603333473,
-0.00982020515948534,
-0.043891388922929764,
0.003616266418248415,
0.01947890780866146,
-0.03951086103916168,
0.0010735706891864538,
0.09108193963766098,
0.005332698114216328,
-0.08038859069347382,
0.008489750325679779,
0.01692637801170349,
-0.03470020741224289,
0.06709686666727066,
0.02550947107374668,
-0.011964610777795315,
-0.05866082012653351,
0.00251580448821187,
0.06120818108320236,
0.0048298100009560585,
0.003322622971609235,
-0.011943865567445755,
0.012957898899912834,
-0.04952201992273331,
0.06419198215007782,
-0.0054067461751401424,
-0.06650589406490326,
0.033479414880275726,
-0.010681727901101112,
0.0038169012404978275,
-0.00657674903050065,
0.03317073732614517,
0.07458491623401642,
0.012184553779661655,
-0.026444492861628532,
-0.04506182298064232,
0.026242034509778023,
0.03136669844388962,
-0.01259202603250742,
0.015253538265824318,
0.024927327409386635,
-0.03233460336923599,
0.036758601665496826,
0.04613000154495239,
-0.061105936765670776,
-0.07838581502437592,
0.031552139669656754,
0.028480710461735725,
-0.06764592975378036,
0.004200696479529142,
0.00027931781369261444,
-0.0072687044739723206,
0.018017560243606567,
-0.017337266355752945,
-0.008113844320178032,
-0.02169082686305046,
0.024165261536836624,
-0.004877801053225994,
-0.039147645235061646,
0.011088673025369644,
-0.06983254849910736,
-0.01303123589605093,
0.05067004635930061,
-0.04581143334507942,
0.006586889270693064,
0.032911404967308044,
0.033474620431661606,
-0.0211167149245739,
0.02015136368572712,
-0.049734145402908325,
0.01878543198108673,
-0.048387736082077026,
0.02564813382923603,
-0.027599237859249115,
0.021308191120624542,
0.06319320201873779,
0.023471713066101074,
-0.05134733393788338,
0.01798298954963684,
-0.031978510320186615,
-0.008539793081581593,
-0.007763785310089588,
0.03855513408780098,
0.027896663174033165,
0.0034592917654663324,
-0.031489573419094086,
-0.010594197548925877,
-0.030477814376354218,
-0.02281070500612259,
0.008601575158536434,
-0.01086493395268917,
-0.017642658203840256,
-0.09733845293521881,
0.036919303238391876,
0.02835109457373619,
0.0306804571300745,
-0.038290999829769135,
0.03195143863558769,
0.01750892959535122,
-0.062091194093227386,
-0.011739340610802174,
0.0010632188059389591,
-0.03175760433077812,
-0.011651089414954185,
-0.009955037385225296,
0.0002300220658071339,
0.046735771000385284,
-0.06666668504476547,
-0.02100735902786255,
0.015184176154434681,
0.0034966059029102325,
0.04647460952401161,
-0.010919513180851936,
0.0340595617890358,
0.024185361340641975,
-0.05007867142558098,
-0.006541973911225796,
0.010604184120893478,
-0.06224648281931877,
-0.03716469556093216,
0.0366348959505558,
0.09305791556835175,
0.03127961978316307,
0.03709603101015091,
0.07849418371915817,
-0.023146405816078186,
-0.02139822021126747,
0.003415197366848588,
-0.027334343641996384,
-0.0588766485452652,
0.009969995357096195,
0.04166514798998833,
-0.05584628880023956,
-0.002182245720177889,
-0.0043523283675313,
0.059881649911403656,
-0.021295178681612015,
-0.060193635523319244,
0.022984571754932404,
-0.0017324598738923669,
-0.00046973853022791445,
0.030409786850214005,
-0.012401157990098,
0.02908877097070217,
-0.007702635135501623,
0.0005876514478586614,
-0.010110302828252316,
-0.009890771470963955,
0.02134726755321026,
0.012496493756771088,
0.015623887069523335,
0.021047523245215416,
0.041834499686956406,
0.028790604323148727,
0.058740999549627304,
0.023679278790950775,
0.02850295789539814,
0.03952596336603165,
-0.00006180649506859481,
-0.032422225922346115,
0.04917147383093834,
0.0989367812871933,
-0.04889127239584923,
0.031483184546232224,
-0.03335824981331825,
-0.022368937730789185,
0.036670245230197906,
0.018290752544999123,
-0.056861016899347305,
-0.08012737333774567,
-0.06205931678414345,
0.0072951349429786205,
-0.03364504501223564,
0.052048660814762115,
0.04141182824969292,
-0.013418257236480713,
-0.004760971758514643,
0.00720980204641819,
-0.03442881628870964,
-0.005929851438850164,
0.012299198657274246,
0.03760310634970665,
-0.032493334263563156,
0.014369623735547066,
-0.03762958571314812,
-0.03461503982543945,
-0.05572453886270523,
0.0016170855378732085,
0.009872321039438248,
-0.004773976281285286,
-0.025820231065154076,
0.01903355121612549,
0.02923867106437683,
-0.055122602730989456,
0.05443954840302467,
-0.018254587426781654,
-0.022752484306693077,
0.08841679245233536,
-0.028526315465569496,
0.003478625789284706,
0.005628935527056456,
-0.0002726186066865921,
-0.06311709433794022,
-0.0004995427443645895,
0.007257391698658466,
0.00833535473793745,
0.04756814241409302,
-0.013319849036633968,
0.006764761172235012,
-0.04281199350953102,
0.01335806306451559,
-0.019475750625133514,
0.07809341698884964,
-0.014768031425774097,
0.011277424171566963,
0.027756990864872932,
-0.0002570438664406538,
0.05173981934785843,
-0.03154400363564491,
0.02388826198875904,
0.0673905536532402,
0.032432641834020615,
0.0225888192653656,
-0.005017295014113188,
0.0640004575252533,
0.025616485625505447,
0.002573471050709486,
-0.027594758197665215,
-0.009576758369803429,
0.03992532938718796,
0.038713399320840836,
0.053686778992414474,
-0.03838525339961052,
-0.006344323046505451,
0.053001902997493744,
0.00505003472790122,
-0.02850515954196453,
0.0003820065758191049,
0.02424299716949463,
-0.0135544678196311,
-0.07436720281839371,
-0.002772972919046879,
-0.04238273948431015,
0.019840974360704422,
-0.023293597623705864,
0.045620620250701904,
-0.016279436647892,
-0.02191965840756893,
0.036084581166505814,
0.003752463962882757,
-0.03429199382662773,
-0.03007604368031025,
-0.046704307198524475,
-0.02509292960166931,
-0.0010613566264510155,
-0.017886314541101456,
-0.08049309998750687,
0.03895054757595062,
0.008742261677980423,
-0.04642431437969208,
-0.0008440802339464426,
-0.00384811544790864,
-0.00954096857458353,
-0.00016911413695197552,
0.02063635177910328,
-0.021330367773771286,
0.0007547484710812569,
0.01615775004029274,
-0.015507126227021217,
-0.0007087343255989254,
-0.043136097490787506,
0.017729829996824265,
-0.010774258524179459,
0.048953671008348465,
0.04856295511126518,
-0.03402175381779671,
-0.02586415968835354,
-0.007145688869059086,
-0.035580042749643326,
0.007583445869386196,
0.048019811511039734,
-0.0714975968003273,
-0.011011909693479538,
-0.010977939702570438,
-0.03818678483366966,
-0.025887148454785347,
-0.10384667664766312,
0.052255019545555115,
0.013177836313843727,
0.05253826454281807,
-0.023662833496928215,
0.011447290889918804,
0.027263950556516647,
-0.09538581967353821,
-0.035444583743810654,
0.07529164850711823,
0.01553995069116354,
-0.04458737000823021,
0.012961762957274914,
-0.033484894782304764,
-0.012639445252716541,
0.0014445841079577804,
0.04024139791727066,
-0.05930809676647186,
0.01138297002762556,
-0.009665451943874359,
-0.03526827320456505,
0.05353089049458504,
-0.03792145475745201,
0.058685366064310074,
0.021439531818032265,
-0.03239003196358681,
-0.0058823092840611935,
-0.0016566398553550243,
-0.020012103021144867,
-0.014991501346230507,
-0.055928103625774384,
-0.0027977798599749804,
0.011150304228067398,
-0.021887533366680145,
0.0018684674287214875,
-0.020333413034677505,
0.011379976756870747,
-0.011690356768667698,
-0.01877155527472496,
0.019866999238729477,
-0.022426141425967216,
0.02350284345448017,
0.002733658766373992,
-0.01429116539657116,
-0.013797353021800518,
0.02992033213376999,
0.009645875543355942,
-0.005468872841447592,
-0.015376233495771885,
-0.02799731306731701,
-0.029355987906455994,
-0.05849306657910347,
-0.033586759120225906,
0.05562863498926163,
0.012449068017303944,
-0.10283102095127106,
0.010930115357041359,
0.0027950983494520187,
0.009238030761480331,
-0.03141630068421364,
0.037097617983818054,
-0.01984550803899765,
-0.028004838153719902,
0.0198681578040123,
0.038923732936382294,
0.01790391281247139,
0.023361284285783768,
0.029494676738977432,
0.01053853053599596,
0.018133407458662987,
-0.019722916185855865,
-0.027291765436530113,
-0.017911052331328392,
0.044155750423669815
] |
<p>Google has not been very useful in this regard. It seems no one has clearly defined terms and Kittel has too little on this. </p> | g6600 | [
0.014386100694537163,
0.0834764689207077,
0.0063358452171087265,
-0.011292628012597561,
0.004009667783975601,
-0.010120381601154804,
-0.02789306454360485,
-0.001429345109499991,
-0.012647275812923908,
-0.053677499294281006,
-0.05507182702422142,
-0.020685382187366486,
0.05409455671906471,
0.05732707306742668,
0.013704484328627586,
-0.02820206619799137,
0.036050520837306976,
0.02210616134107113,
0.046516042202711105,
0.0457996241748333,
0.011139066889882088,
0.046967145055532455,
-0.07095924764871597,
-0.023197680711746216,
-0.07458373159170151,
-0.08823981881141663,
0.01908872090280056,
0.016757186502218246,
-0.08040867745876312,
-0.008548470214009285,
-0.004045644775032997,
-0.04208999127149582,
-0.0019418520387262106,
-0.038105908781290054,
-0.07409247010946274,
-0.008526151068508625,
0.02696957252919674,
0.02356201596558094,
-0.0219903364777565,
-0.030519111081957817,
0.05083361640572548,
0.008760858327150345,
0.057896167039871216,
0.05436284840106964,
-0.016136668622493744,
-0.012166121043264866,
-0.0385950542986393,
-0.019784774631261826,
0.05371834710240364,
-0.037593089044094086,
0.0031543567311018705,
-0.022774752229452133,
0.016983753070235252,
0.003467724658548832,
0.06167882680892944,
-0.015998562797904015,
0.04675569385290146,
0.014888261444866657,
0.0004157833172939718,
-0.02435251511633396,
0.008040214888751507,
-0.022937925532460213,
0.004602500237524509,
0.04856747388839722,
0.020411845296621323,
0.0508718304336071,
0.024316541850566864,
-0.0007085904944688082,
0.07145106047391891,
-0.044216904789209366,
0.013891752809286118,
-0.03430119529366493,
0.0029866108670830727,
0.006469940301030874,
-0.02659914456307888,
0.005200408864766359,
-0.04397495836019516,
0.0041543603874742985,
0.02547767572104931,
0.051185719668865204,
0.0019217360531911254,
0.0030211943667382,
-0.05311046168208122,
-0.020751530304551125,
0.05763299763202667,
0.022188208997249603,
0.012526108883321285,
0.002360397018492222,
0.0391000472009182,
-0.002231006510555744,
0.05756121501326561,
0.012824675999581814,
0.031944744288921356,
0.008466693572700024,
-0.012442117556929588,
0.00872985552996397,
0.001476982026360929,
-0.01769784837961197,
0.07047554850578308,
-0.05192689970135689,
-0.06930834800004959,
0.0219187643378973,
0.0006974206771701574,
-0.026473667472600937,
-0.05886351317167282,
0.059730447828769684,
0.052366871386766434,
-0.024023810401558876,
0.05629696324467659,
-0.021900026127696037,
-0.0026651902589946985,
0.013314089737832546,
-0.051801614463329315,
0.03174779564142227,
0.016436155885457993,
-0.04345172643661499,
0.04077630490064621,
-0.006782379932701588,
0.00971873477101326,
0.001665809890255332,
0.02694462239742279,
-0.04172967001795769,
0.04232264682650566,
0.006836343090981245,
-0.02617802284657955,
0.015108173713088036,
-0.018827341496944427,
0.017415905371308327,
-0.03865104168653488,
-0.017813773825764656,
-0.01974525675177574,
-0.02896696701645851,
0.06036096438765526,
-0.029236026108264923,
-0.013583436608314514,
-0.0013363639591261744,
0.008350235410034657,
-0.056144580245018005,
-0.04078718274831772,
0.013648404739797115,
0.028321994468569756,
0.004169875290244818,
-0.035109419375658035,
0.024825407192111015,
0.06592254340648651,
-0.015327708795666695,
0.011144124902784824,
0.035391028970479965,
0.013055232353508472,
-0.009973062202334404,
0.02519974112510681,
-0.002365740481764078,
-0.04644184187054634,
-0.0035574212670326233,
0.023115189746022224,
-0.028448108583688736,
-0.031130526214838028,
0.06108725070953369,
0.04949643835425377,
0.01740768365561962,
0.0007404868374578655,
-0.021374430507421494,
-0.029719743877649307,
-0.011021528393030167,
-0.07626620680093765,
-0.03507440909743309,
-0.023020507767796516,
0.048896241933107376,
-0.05820321664214134,
-0.005444676615297794,
0.027838172391057014,
-0.003226693719625473,
0.02036658488214016,
0.06202549859881401,
0.07988280057907104,
0.0517241507768631,
0.020043879747390747,
0.008227898739278316,
0.001634070766158402,
-0.010330506600439548,
-0.0426471084356308,
-0.05060083046555519,
-0.010124950669705868,
0.052005063742399216,
-0.03922882303595543,
-0.01468292623758316,
0.016741277649998665,
-0.04169538989663124,
-0.021417856216430664,
0.0001461554493289441,
-0.006445132661610842,
-0.09133557230234146,
0.05459199845790863,
-0.02252276986837387,
-0.02204819768667221,
-0.00804080069065094,
0.005771977826952934,
-0.012788493186235428,
0.0011789893032982945,
-0.07324063777923584,
0.03366989642381668,
-0.030688468366861343,
-0.04327474907040596,
-0.005176053382456303,
-0.05666700378060341,
-0.005126187577843666,
0.005822007078677416,
0.02524019218981266,
0.05333907902240753,
-0.006329340860247612,
0.031283311545848846,
-0.05465264245867729,
-0.007988423109054565,
0.033677082508802414,
-0.010852486826479435,
-0.059907130897045135,
-0.02400672435760498,
0.06220513582229614,
-0.005038381088525057,
-0.04558302089571953,
-0.03532889485359192,
-0.01283561997115612,
-0.004145234357565641,
-0.034787122160196304,
-0.012797312811017036,
-0.058007363229990005,
0.07152829319238663,
0.01603017933666706,
-0.018915578722953796,
0.0450604148209095,
-0.059640415012836456,
-0.030221236869692802,
-0.03634060546755791,
-0.04032079875469208,
0.011282982304692268,
0.10959530621767044,
0.09692081063985825,
-0.0001477995829191059,
-0.021556220948696136,
0.033260926604270935,
-0.022480906918644905,
0.0020451496820896864,
-0.03449518606066704,
0.03283167630434036,
-0.07339005917310715,
0.04114087298512459,
0.06141321733593941,
0.01926221325993538,
0.0022113421000540257,
0.030918719246983528,
-0.032743413001298904,
0.04305736720561981,
0.015258615836501122,
-0.03495372086763382,
-0.004434545058757067,
-0.011725641787052155,
0.007147261407226324,
0.04310820251703262,
-0.04862973839044571,
0.056279078125953674,
0.021169906482100487,
-0.0822107344865799,
0.03857024759054184,
0.010617474094033241,
0.023290256038308144,
-0.05790448561310768,
-0.011726529337465763,
0.00022649265883956105,
0.0614623986184597,
0.014002280309796333,
-0.03694866597652435,
0.05401594191789627,
0.03696621209383011,
-0.033087100833654404,
0.013909564353525639,
-0.042775142937898636,
-0.04335698112845421,
-0.0492553673684597,
0.0006112369592301548,
-0.03262034058570862,
0.036860622465610504,
-0.04509161040186882,
0.006573561578989029,
0.027349961921572685,
-0.03410680964589119,
0.036763373762369156,
0.05541612580418587,
0.08824066072702408,
-0.039989542216062546,
0.01135167945176363,
-0.038379549980163574,
-0.018458882346749306,
0.027447903528809547,
-0.006396259646862745,
-0.0065793488174676895,
-0.01833988167345524,
0.013779825530946255,
0.04375359043478966,
0.06421131640672684,
-0.007826169021427631,
0.08254668861627579,
-0.046265967190265656,
-0.011666083708405495,
-0.036715395748615265,
0.024564597755670547,
0.002988974330946803,
0.012492097914218903,
-0.07871628552675247,
0.04955407977104187,
-0.018850404769182205,
-0.025156386196613312,
0.007285526022315025,
-0.009352883324027061,
0.020940590649843216,
-0.0475681908428669,
0.05814443901181221,
0.027203528210520744,
0.002088929759338498,
-0.010042019188404083,
0.04906650260090828,
-0.011194632388651371,
-0.005919417832046747,
0.001652050414122641,
0.03222281485795975,
0.033580441027879715,
0.09860970824956894,
-0.018977737054228783,
0.030557138845324516,
0.0381229929625988,
0.003889314364641905,
-0.02030404470860958,
0.044780973345041275,
0.020362308248877525,
-0.047614868730306625,
-0.02907295897603035,
0.008878770284354687,
-0.05857216939330101,
0.004292621742933989,
0.006774163339287043,
-0.006840735208243132,
0.020312918350100517,
0.02290084771811962,
0.012290578335523605,
-0.023766687139868736,
-0.0382857471704483,
0.033151403069496155,
-0.011828739196062088,
-0.006691679824143648,
0.026913989335298538,
-0.04125945270061493,
-0.022027138620615005,
-0.02631460130214691,
0.045654140412807465,
-0.022565506398677826,
-0.05291649326682091,
0.028532540425658226,
-0.0063703288324177265,
-0.02903791330754757,
0.009021006524562836,
0.04908027499914169,
0.021776575595140457,
0.03544295206665993,
-0.003760738531127572,
-0.013346179388463497,
0.06346779316663742,
0.033652763813734055,
0.049541231244802475,
0.04912842810153961,
-0.07848647236824036,
-0.014273937791585922,
0.002244561677798629,
0.0801086351275444,
-0.001271805725991726,
0.03240443766117096,
0.054136283695697784,
0.04395464062690735,
-0.038024768233299255,
-0.02180374786257744,
-0.051814403384923935,
0.03518136590719223,
0.012945826165378094,
0.013441978953778744,
0.026460042223334312,
0.011865787208080292,
-0.0010278631234541535,
-0.0356299914419651,
-0.04431312531232834,
0.00005871427492820658,
0.013272236101329327,
0.04224758222699165,
-0.0069331335835158825,
-0.0458902008831501,
-0.04713102802634239,
-0.016048215329647064,
0.009568046778440475,
-0.02988489344716072,
-0.005377049092203379,
-0.00019542814698070288,
0.023651935160160065,
0.03209921345114708,
0.02357766404747963,
0.018317166715860367,
0.04372604563832283,
0.015159353613853455,
-0.027734657749533653,
-0.011718250811100006,
0.018114620819687843,
-0.007921122014522552,
-0.001823939266614616,
-0.030883098021149635,
-0.03520738333463669,
0.017384402453899384,
0.002219089539721608,
-0.009898809716105461,
0.04909471422433853,
0.043638717383146286,
0.025861084461212158,
-0.030885791406035423,
0.05033095180988312,
0.024548102170228958,
-0.005202658008784056,
-0.001797789940610528,
-0.02128640003502369,
-0.04110805317759514,
0.023205310106277466,
0.04650482162833214,
0.06035929173231125,
0.03151985630393028,
0.0055868057534098625,
-0.06324182450771332,
0.008261437527835369,
-0.061208534985780716,
-0.008388351649045944,
0.06424040347337723,
-0.023547634482383728,
0.00904998742043972,
-0.016354097053408623,
0.012974359095096588,
-0.05492076277732849,
-0.0005791457952000201,
0.025709785521030426,
-0.048861805349588394,
-0.030388034880161285,
0.007082683499902487,
0.026909224689006805,
0.07384195178747177,
0.06211856007575989,
-0.022396065294742584,
-0.011304538697004318,
0.039455611258745193,
-0.056638095527887344,
0.015536687336862087,
-0.02346091717481613,
0.01303156279027462,
0.022129369899630547,
0.0072421482764184475,
0.009337576106190681,
-0.06640326231718063,
0.018376335501670837,
-0.038935769349336624,
-0.04538295790553093,
-0.03894827887415886,
0.026919061318039894,
0.01869533769786358,
0.0012339394306764007,
0.005943813361227512,
-0.03389821946620941,
-0.02319498173892498,
0.003017525188624859,
0.07070532441139221,
0.011493915691971779,
0.019424045458436012,
0.011157597415149212,
0.02111033909022808,
-0.03284168988466263,
0.022122031077742577,
0.021378079429268837,
-0.02026919648051262,
-0.06248288229107857,
-0.038105618208646774,
-0.015311571769416332,
-0.020962083712220192,
-0.037589676678180695,
-0.001169552095234394,
-0.016433753073215485,
0.017664669081568718,
0.0651806890964508,
-0.026261674240231514,
0.018705695867538452,
-0.04595768824219704,
0.060427308082580566,
0.03439275920391083,
0.02430347353219986,
0.008522299118340015,
-0.03708983212709427,
0.0071292053908109665,
-0.0106660770252347,
0.0916987955570221,
0.02496395632624626,
0.061618685722351074,
0.018724020570516586,
-0.023403367027640343,
-0.008581634610891342,
0.06520349532365799,
0.03704080730676651,
0.0354544073343277,
0.006940022576600313,
0.004879910498857498,
-0.034822236746549606,
0.028910856693983078,
-0.004365263041108847,
-0.026743358001112938,
-0.06250407546758652,
0.0005441468092612922,
-0.0024587896186858416,
0.001698023290373385,
-0.002568183932453394,
0.02088368870317936,
-0.019995540380477905,
-0.010437609627842903,
-0.0034365709871053696,
-0.024040881544351578,
-0.030253639444708824,
0.07660570740699768,
-0.021777676418423653,
-0.052424948662519455,
-0.03605189174413681,
-0.06330090761184692,
0.04570939019322395,
-0.09039467573165894,
0.046226564794778824,
0.03554762154817581,
0.04196615144610405,
-0.020014610141515732,
0.02820625901222229,
0.004139295779168606,
-0.02571973204612732,
0.03114708699285984,
-0.0016134480247274041,
-0.02899341471493244,
-0.06813443452119827,
-0.003019989002496004,
-0.013653473928570747,
0.007362789940088987,
-0.008846914395689964,
-0.05220424383878708,
0.039455607533454895,
0.03118973784148693,
-0.014173741452395916,
-0.04918069392442703,
0.0018578567542135715,
-0.07727500051259995,
0.024499228224158287,
-0.036946117877960205,
0.012836646288633347,
-0.04606116935610771,
0.0005569892236962914,
0.003293218556791544,
-0.05021313205361366,
-0.004692356567829847,
-0.018782690167427063,
0.03970479965209961,
0.06428667902946472,
0.058279071003198624,
0.022984914481639862,
-0.0191904716193676,
-0.038566574454307556,
-0.008843304589390755,
-0.006074466276913881,
-0.022366302087903023,
-0.025183705613017082,
-0.002608055714517832,
-0.024762775748968124,
-0.021527037024497986,
-0.053887709975242615,
-0.009510883130133152,
-0.01130493450909853,
0.02187383733689785,
0.025982219725847244,
0.06947427988052368,
-0.011858820915222168,
-0.02981499582529068,
-0.00013806586503051221,
-0.00498075969517231,
-0.07413668185472488,
-0.023331915959715843,
0.060207776725292206,
0.052297066897153854,
-0.008689753711223602,
0.01186971366405487,
0.03281219303607941,
0.015500635839998722,
-0.034191492944955826,
-0.03335542231798172,
0.037165071815252304,
0.06616219133138657,
-0.04651957377791405,
0.0842001736164093,
0.04292105510830879,
-0.008774465881288052,
-0.02838313579559326,
0.033428702503442764,
-0.0034639197401702404,
-0.0229170098900795,
0.025157302618026733,
0.07621654123067856,
0.02464362606406212,
0.05260208249092102,
0.02579563856124878,
0.008004993200302124,
-0.00876525416970253,
0.038396961987018585,
-0.026625581085681915,
-0.017747724428772926,
-0.013712041079998016,
-0.025731127709150314,
-0.08157360553741455,
-0.03524982929229736,
-0.02127327397465706,
-0.01137800607830286,
0.01486685685813427,
-0.0394064225256443,
0.05502358078956604,
0.07643366605043411,
-0.049936793744564056,
0.04912428557872772,
-0.0080678416416049,
-0.020093441009521484,
-0.018189992755651474,
-0.003938308916985989,
-0.014765731990337372,
0.0312659852206707,
-0.05686112120747566,
-0.03604903072118759,
-0.029280779883265495,
0.036305226385593414,
-0.040317993611097336,
-0.02481922321021557,
0.0018450487405061722,
0.004985431209206581,
0.01796114630997181,
0.0313863642513752,
-0.02768600545823574,
0.05359766259789467,
0.05544764921069145,
-0.006362064275890589,
0.029750024899840355,
-0.04512456804513931,
0.07029103487730026,
-0.014795491471886635,
-0.021835515275597572,
-0.0758742019534111,
-0.048982858657836914,
-0.01528704073280096,
-0.0003700941160786897,
-0.04277390241622925,
0.004653655458241701,
0.018740564584732056,
-0.020678235217928886,
-0.06002608314156532,
0.004627498798072338,
0.04333505779504776,
-0.0026756953448057175,
-0.004524642135947943,
-0.04098575934767723,
-0.016988281160593033,
0.007342025637626648,
-0.04785522073507309,
-0.0352642796933651,
-0.0010162327671423554,
0.009339334443211555,
0.007335354574024677,
0.021461233496665955,
0.00031034694984555244,
0.003967607393860817,
-0.037613194435834885,
-0.0020126886665821075,
0.007983154617249966,
-0.013557115569710732,
-0.004051525611430407,
0.02520369179546833,
0.0004914514720439911,
0.02602897584438324,
-0.0465162955224514,
0.0434110164642334,
-0.006294732913374901,
0.027365656569600105,
-0.028099384158849716,
0.09110130369663239,
-0.016430703923106194,
-0.01261513028293848,
0.032101329416036606,
-0.0012188449036329985,
-0.010385196655988693,
0.011896603740751743,
-0.018420575186610222,
-0.02506282553076744,
-0.0023326741065829992,
-0.020855003967881203,
0.006375032942742109,
0.006234381813555956,
0.044669341295957565,
-0.01774457097053528,
0.011871379800140858,
0.026765190064907074,
-0.027096396312117577,
0.01847940869629383,
0.006039964035153389,
-0.05776175856590271,
-0.002236774889752269,
0.007671996019780636,
-0.030787723138928413,
0.02374890446662903,
0.08211808651685715,
-0.05511161684989929,
-0.015875406563282013,
-0.010319766588509083,
0.03161371499300003,
0.04107113927602768,
-0.009795435704290867,
0.04481619596481323,
-0.06879962235689163,
0.0421522818505764,
-0.02569730579853058,
-0.05131024494767189,
0.005260738078504801,
-0.004265971947461367,
-0.02925581857562065,
-0.018713166937232018,
-0.04395250603556633,
-0.0587150901556015,
0.010953412391245365,
0.007593235466629267,
0.051817700266838074,
-0.07109871506690979,
0.022582968696951866,
-0.022836431860923767,
-0.040332477539777756,
-0.030486522242426872,
0.05996248498558998,
-0.051558345556259155,
-0.03419870883226395,
0.0062101781368255615,
-0.038974303752183914,
0.003482196945697069,
0.0156314168125391,
0.027569333091378212,
0.009921866469085217,
0.016658339649438858,
-0.02686295099556446,
0.048967037349939346,
0.04050404205918312,
-0.008098919875919819,
0.01828150264918804,
0.012054034508764744,
0.050287775695323944,
-0.06843475252389908,
0.012800357304513454,
-0.04688771814107895,
-0.01790771074593067,
-0.07087713479995728,
-0.025736812502145767,
-0.06826524436473846,
-0.06616243720054626,
0.056230299174785614,
-0.00558741670101881,
-0.01114957220852375,
-0.03477242961525917
] |
<p>Hey guys I really need help on this problem.</p>
<blockquote>
<p>A ceramic slab of dimentions 5cm x 10 cm x .25 cm has to be heated to $177\,^{\circ}{\rm C}$. The ceramic slab travels on a conveyor belt traveling at $.1 \frac{m}{s}$. The slab is initially at a temperature of $18\,^{\circ}{\rm C}$ when it enters a radiant heater on the conveyor belt. The heater surrounds the whole slab and emits heat as a black body at $1000\,^{\circ}{\rm C}$. Since the heat surrounds the slab, all the energy that leaves the heater is absorbed by the slab. The slab has an emissivity of .85. Find the amount of time it takes to heat the slab to $177\,^{\circ}{\rm C}$. The slab has properties $c_{p}=1500\frac{J}{Kg K}$ and $\rho=900\frac{kg}{m^{3}}$ and $k=1 \frac{W}{mK}$</p>
</blockquote>
<p>I started off by creating an energy balance on the slab as it's in the heater. I assumed convection that is caused by the conveyor belt traveling at such a slow speed to be insignificant to all calculations.
$$\dot{E}_{in}- \dot{E}_{out}+\dot{E}_{g}=\dot{E}_{st}$$
$$A\alpha\sigma T^{4}_{heater}-A\epsilon\sigma T^{4}=\rho c_{p}V\frac{dT}{dt}$$
$$A\sigma(T^{4}_{heater}-\epsilon T^{4})=\rho c_{p}V \frac{dT}{dt}$$</p>
<p>I then plugged in the values and got:
$$44.185-1.428x10^{-11} T^{4}=\frac{dT}{dt}$$</p>
<p>I realized that this comes out to be a VERY nasty integral so I tried to use matlab and numerically integrate it using Euler's method. My graph for that came out to be linear which I knew was not right and I came here straight away to figure out what I was doing wrong</p> | g6601 | [
0.06010657921433449,
0.07616796344518661,
0.012125416658818722,
-0.023468080908060074,
0.03863311558961868,
-0.0428815558552742,
0.052857644855976105,
0.012194096110761166,
-0.07930802553892136,
0.04063906520605087,
-0.06900890916585922,
0.07920035719871521,
0.025654027238488197,
0.03397586941719055,
0.045781273394823074,
-0.016108714044094086,
0.05261962115764618,
0.019328705966472626,
0.008174278773367405,
0.07413025200366974,
0.015904612839221954,
0.00003503758125589229,
-0.002641805913299322,
-0.08483567833900452,
0.03319503739476204,
-0.007100317161530256,
0.0025389923248440027,
0.018170978873968124,
-0.006490885280072689,
0.019359618425369263,
-0.02332391031086445,
0.04980025812983513,
0.010338926687836647,
-0.01013621874153614,
-0.07520212978124619,
-0.00612495094537735,
0.024137722328305244,
0.004300800152122974,
0.005369042512029409,
-0.03290293365716934,
-0.02049826830625534,
-0.033015668392181396,
0.02330872043967247,
0.06386607885360718,
0.037837352603673935,
0.024194350466132164,
-0.02185162715613842,
0.006089686881750822,
-0.04629804939031601,
0.027001122012734413,
-0.02873692288994789,
-0.013868758454918861,
0.07995093613862991,
-0.01042797788977623,
-0.027557045221328735,
0.04234999418258667,
-0.03171120584011078,
-0.05176800116896629,
0.017857594415545464,
0.032804884016513824,
-0.008613839745521545,
-0.026372285559773445,
-0.0325886607170105,
-0.03797148913145065,
0.011147445067763329,
-0.003288229228928685,
-0.029262447729706764,
-0.007933376356959343,
0.028537653386592865,
-0.004587825387716293,
0.03674958646297455,
0.008891196921467781,
0.03753677010536194,
-0.03388933464884758,
-0.04466618597507477,
-0.01222281251102686,
-0.008230465464293957,
-0.03315451368689537,
0.039034824818372726,
-0.005680319387465715,
-0.07573831081390381,
0.00644470751285553,
-0.005843851715326309,
0.06568184494972229,
-0.028038686141371727,
0.009218894876539707,
-0.03443961217999458,
-0.014637516811490059,
-0.08169831335544586,
-0.03801361098885536,
-0.005371733568608761,
-0.039943501353263855,
-0.013156875036656857,
0.04129460081458092,
0.027407269924879074,
0.008295352570712566,
-0.060392607003450394,
0.05253987014293671,
-0.01467812992632389,
-0.0536554716527462,
0.054645851254463196,
0.001129397191107273,
-0.00526511762291193,
0.001140673877671361,
-0.03425661101937294,
0.017776668071746826,
0.005792075768113136,
-0.009878488257527351,
-0.0058017512783408165,
0.012284721247851849,
0.06471680849790573,
-0.11676796525716782,
-0.044456589967012405,
-0.09428912401199341,
0.004359637852758169,
0.018823515623807907,
0.007735783234238625,
-0.032891299575567245,
-0.010403771884739399,
0.024624982848763466,
0.005246342159807682,
0.047275714576244354,
0.03305418789386749,
-0.0118438471108675,
0.02716263383626938,
-0.02350347489118576,
0.027832694351673126,
-0.01771194115281105,
0.03466292843222618,
-0.004258938133716583,
-0.01728985086083412,
0.014630855061113834,
0.01987195387482643,
0.04083127900958061,
-0.0222440417855978,
0.057245537638664246,
-0.02367100492119789,
0.04950716346502304,
-0.01696051098406315,
-0.001368233934044838,
0.009499671868979931,
-0.0634298175573349,
0.029592188075184822,
-0.002441499847918749,
-0.017209526151418686,
0.05949355661869049,
-0.06693275272846222,
-0.07188335806131363,
0.0847918912768364,
-0.04031083360314369,
-0.002227499382570386,
0.08944538235664368,
-0.008879401721060276,
0.01255644578486681,
0.026749474927783012,
0.02742936462163925,
0.06426388770341873,
0.00868984404951334,
0.02626180835068226,
-0.052071407437324524,
0.0354364737868309,
0.045328665524721146,
0.036695387214422226,
-0.02297668345272541,
-0.031585827469825745,
0.022745080292224884,
-0.01473737321794033,
-0.051362045109272,
0.017042377963662148,
-0.031785748898983,
-0.006888692267239094,
-0.05726495385169983,
0.019800201058387756,
0.022104008123278618,
-0.04056878387928009,
0.01971380226314068,
0.06494247168302536,
0.0498470813035965,
0.020456887781620026,
0.004655321594327688,
0.052618835121393204,
-0.019624430686235428,
0.024573925882577896,
-0.007065369747579098,
0.022330954670906067,
-0.005145907402038574,
0.01546237338334322,
0.011560735292732716,
-0.01026518177241087,
-0.020938215777277946,
0.010417585261166096,
0.0019863934721797705,
0.011480099521577358,
0.06977059692144394,
-0.01611221954226494,
-0.02822166681289673,
0.03288847580552101,
-0.047010548412799835,
-0.06945224851369858,
-0.09253976494073868,
0.07335710525512695,
0.03783884271979332,
0.10661879926919937,
0.03416777774691582,
0.039830274879932404,
-0.03919961676001549,
-0.00487464340403676,
-0.00022665690630674362,
-0.01679513044655323,
0.036846693605184555,
-0.01471039280295372,
-0.026298845186829567,
-0.031186405569314957,
0.050790902227163315,
0.0374370813369751,
-0.016608187928795815,
-0.015773015096783638,
0.01816701702773571,
0.024276647716760635,
-0.0064898026175796986,
-0.021079519763588905,
0.010091191157698631,
0.019989896565675735,
-0.01637425646185875,
-0.028154602274298668,
-0.00008517793321516365,
-0.024163302034139633,
-0.035925380885601044,
-0.03381611406803131,
0.014177362434566021,
-0.08412584662437439,
0.04020432382822037,
0.02774707041680813,
-0.05515958368778229,
0.03122456558048725,
-0.048937540501356125,
-0.014282789081335068,
0.023062990978360176,
-0.007673040498048067,
0.01740996539592743,
0.01473408006131649,
0.01623520255088806,
-0.027197351679205894,
-0.07265141606330872,
0.0043304357677698135,
-0.005694493651390076,
0.049552954733371735,
0.0076341209933161736,
0.01569126546382904,
-0.013414888642728329,
-0.012367142364382744,
-0.020012425258755684,
-0.047552019357681274,
0.007780320011079311,
0.028922542929649353,
0.005419174209237099,
-0.05422687530517578,
-0.01554570160806179,
0.000001275825979973888,
-0.007750357501208782,
-0.04557851701974869,
-0.05531084164977074,
0.011909067630767822,
-0.007807809393852949,
-0.04151077941060066,
0.02899736724793911,
-0.04825340211391449,
-0.05962926149368286,
0.013114606030285358,
0.012679863721132278,
0.0301213301718235,
0.027265548706054688,
0.053515076637268066,
0.013490592129528522,
0.041215937584638596,
0.026963988319039345,
0.04450196772813797,
-0.018802324309945107,
-0.04710124805569649,
-0.0093311732634902,
0.0535820871591568,
-0.04368334263563156,
-0.025662291795015335,
-0.029024789109826088,
0.014871662482619286,
-0.055793389678001404,
-0.005869852378964424,
0.012651520781219006,
-0.01724705658853054,
-0.02512022852897644,
-0.006393431685864925,
-0.018228106200695038,
-0.024247193709015846,
0.041561227291822433,
0.0006480849115177989,
0.022473178803920746,
0.06045880168676376,
-0.02925722301006317,
-0.004678879864513874,
-0.028713691979646683,
0.05236959084868431,
-0.025090446695685387,
-0.06047746539115906,
-0.01242807973176241,
-0.042169298976659775,
-0.005350994411855936,
0.004528595134615898,
-0.08760412782430649,
0.02076965756714344,
-0.003217324148863554,
0.026903145015239716,
-0.03071833960711956,
-0.01952829770743847,
-0.045850805938243866,
-0.00880521535873413,
0.002830595476552844,
-0.013681466691195965,
0.007752136792987585,
0.038918182253837585,
0.003270896151661873,
0.0145052345469594,
-0.009830431081354618,
-0.008367088623344898,
-0.0291628185659647,
-0.016005394980311394,
-0.003926924895495176,
0.012152566574513912,
-0.020122742280364037,
-0.017096037045121193,
-0.02313569374382496,
-0.06337238103151321,
0.010792192071676254,
0.013802943751215935,
-0.04542681947350502,
-0.07052582502365112,
-0.04399118199944496,
-0.03479352220892906,
0.03543704375624657,
0.014355739578604698,
0.043282244354486465,
-0.08980834484100342,
-0.03527085855603218,
-0.031896594911813736,
-0.011666135862469673,
0.026476260274648666,
-0.014910165220499039,
-0.018501870334148407,
-0.016125474125146866,
-0.0030746161937713623,
0.02815374918282032,
0.0603519082069397,
0.011710246093571186,
-0.0050878445617854595,
-0.01738494262099266,
-0.009654298424720764,
0.03261744976043701,
0.04191698506474495,
0.05038034915924072,
0.015438804402947426,
-0.005613239016383886,
0.004215870518237352,
0.03031770884990692,
0.05090169236063957,
0.003936318214982748,
0.001737439539283514,
0.022531120106577873,
-0.030020590871572495,
0.021113399416208267,
0.015006677247583866,
0.03900214284658432,
-0.024449214339256287,
-0.030504951253533363,
-0.028553972020745277,
0.03327621519565582,
0.03250477463006973,
-0.005568316671997309,
-0.026876457035541534,
0.02563684619963169,
0.0012128803646191955,
0.02600293979048729,
-0.05079721659421921,
0.0025124105159193277,
-0.02166999690234661,
-0.02270301803946495,
0.021506574004888535,
0.07749118655920029,
0.022606922313570976,
0.0009878871496766806,
0.024539822712540627,
-0.06264519691467285,
0.0640818178653717,
-0.026510639116168022,
-0.04456513375043869,
-0.013856791891157627,
0.04110468551516533,
-0.0359809473156929,
0.05836549773812294,
0.032787468284368515,
-0.025827575474977493,
0.016419721767306328,
0.058311887085437775,
-0.020353946834802628,
0.050158388912677765,
0.012255185283720493,
-0.059992432594299316,
-0.02609987184405327,
0.0291764996945858,
-0.013014387339353561,
0.06627418845891953,
-0.0031335295643657446,
-0.07869850099086761,
-0.027572117745876312,
0.007587766740471125,
-0.031062396243214607,
0.09606894850730896,
-0.05399702861905098,
0.019581913948059082,
0.009718136861920357,
0.01722368225455284,
-0.029923202469944954,
-0.054573122411966324,
0.02961188554763794,
-0.05595625191926956,
-0.006781386211514473,
0.050519295036792755,
0.01328093558549881,
0.05288218334317207,
-0.033682819455862045,
-0.004284883849322796,
0.037936531007289886,
-0.039478376507759094,
0.0054704840295016766,
-0.06425777822732925,
0.041086722165346146,
-0.059961624443531036,
0.05003206431865692,
0.02895577996969223,
-0.014978391118347645,
0.01451610866934061,
0.07272685319185257,
-0.03551759570837021,
-0.06211724132299423,
-0.03148644044995308,
-0.0008093048818409443,
0.028469307348132133,
0.016110319644212723,
-0.05302850157022476,
-0.13897539675235748,
-0.0006571693229489028,
0.0038351230323314667,
0.052834633737802505,
0.007535383105278015,
-0.019102632999420166,
0.02018354833126068,
0.005967221222817898,
0.012996695935726166,
-0.029874609783291817,
0.016560811549425125,
0.10379137098789215,
0.04263785853981972,
0.03497622534632683,
0.055351704359054565,
-0.01703159138560295,
-0.00694021163508296,
-0.030444178730249405,
-0.04089374840259552,
0.014452017843723297,
0.10109559446573257,
0.02436675876379013,
-0.02286895550787449,
0.004014627542346716,
0.026665573939681053,
-0.0029248162172734737,
0.04162674769759178,
-0.011414877139031887,
-0.012811725027859211,
-0.012378615327179432,
-0.0053816381841897964,
0.02607535757124424,
-0.019796481356024742,
-0.0023564505390822887,
-0.0003398476110305637,
0.041315708309412,
0.050626564770936966,
0.031101083382964134,
0.017825014889240265,
-0.04562040790915489,
0.03103698045015335,
0.04241166263818741,
-0.00030276618781499565,
0.006860402412712574,
0.009444786235690117,
-0.03989341855049133,
-0.04969511926174164,
-0.016933005303144455,
-0.0071488660760223866,
0.04020779952406883,
-0.010870018042623997,
-0.013347525149583817,
0.014085466973483562,
0.00048225861974060535,
0.022447913885116577,
-0.04327870532870293,
0.008339998312294483,
-0.008435217663645744,
0.03699179366230965,
0.06565133482217789,
0.04797070100903511,
-0.0005496796220541,
0.0509282723069191,
-0.04083333909511566,
0.04141415283083916,
0.045707572251558304,
-0.08181807398796082,
-0.04431336000561714,
-0.055222369730472565,
0.01065238006412983,
-0.06541656702756882,
-0.02333918958902359,
-0.04283616319298744,
0.025647182017564774,
0.030467398464679718,
-0.006861700210720301,
0.007028429303318262,
0.05570462718605995,
-0.004598561674356461,
-0.04640758037567139,
-0.035116057842969894,
-0.012503506615757942,
0.015325367450714111,
0.0031886163633316755,
-0.03206123411655426,
-0.07160414755344391,
0.020082717761397362,
-0.04339005798101425,
0.02331705391407013,
-0.006478681694716215,
-0.015079574659466743,
0.025997508317232132,
-0.050701405853033066,
0.024438362568616867,
-0.04520406946539879,
-0.010817783884704113,
0.0011227732757106423,
-0.01296162698417902,
-0.026809921488165855,
-0.030079500749707222,
-0.008303362876176834,
0.025600941851735115,
0.010019523091614246,
0.03815116733312607,
0.0033241529017686844,
0.02790883742272854,
-0.020540790632367134,
0.04529671370983124,
0.003830777248367667,
0.013680115342140198,
-0.00775781087577343,
-0.00855598971247673,
-0.009382032789289951,
0.030147477984428406,
0.013216729275882244,
-0.012388166040182114,
0.0026768003590404987,
-0.0033635743893682957,
-0.006679078098386526,
-0.042315587401390076,
-0.013517441228032112,
0.023643553256988525,
-0.010910764336585999,
0.043895117938518524,
-0.02960147149860859,
0.0035470356233417988,
0.020903974771499634,
0.048554595559835434,
0.07291904836893082,
-0.03374132141470909,
-0.025523176416754723,
-0.034734323620796204,
0.018838869407773018,
-0.0021596974693238735,
0.03904671221971512,
-0.013650137931108475,
0.04870087280869484,
0.019186604768037796,
-0.007327658124268055,
-0.06378535181283951,
0.00658572930842638,
-0.04470103234052658,
0.010888497345149517,
-0.026944763958454132,
0.03740797936916351,
-0.03194153681397438,
0.021947944536805153,
-0.023883787915110588,
-0.0411301851272583,
-0.0817171260714531,
-0.004782755393534899,
0.005389946047216654,
0.03741302713751793,
-0.02212676592171192,
-0.022085966542363167,
-0.028551828116178513,
-0.022933505475521088,
0.006913560908287764,
-0.03942865505814552,
-0.01059374213218689,
0.01054013054817915,
0.0007314824615605175,
0.039954934269189835,
0.0566832534968853,
0.05918791890144348,
0.06406251341104507,
-0.010264230892062187,
0.005683470517396927,
0.00103034358471632,
0.05101839825510979,
0.058068644255399704,
0.03443742170929909,
-0.07291071116924286,
0.04072192311286926,
0.03881964087486267,
-0.0004919696366414428,
-0.040102388709783554,
0.051003701984882355,
-0.011818901635706425,
-0.08163797855377197,
0.0067862775176763535,
0.07761267572641373,
0.005418762564659119,
0.024738667532801628,
-0.04118293151259422,
0.009583734907209873,
-0.039675820618867874,
0.04077276960015297,
-0.005793704651296139,
-0.04083707928657532,
0.014656910672783852,
-0.03073500283062458,
0.056435685604810715,
-0.03223298862576485,
-0.006860540248453617,
-0.006467857863754034,
0.01976630836725235,
-0.037437111139297485,
0.03658817335963249,
0.008541624993085861,
0.010726174339652061,
-0.03307536616921425,
-0.0025428161025047302,
0.030711451545357704,
0.0260926466435194,
-0.022043367847800255,
0.009192134253680706,
-0.05145353078842163,
-0.06227893754839897,
0.04778679832816124,
-0.009485521353781223,
0.0038563418202102184,
0.0068739959970116615,
0.012538731098175049,
-0.08684571087360382,
-0.02008218504488468,
0.027111314237117767,
0.04455850273370743,
0.03473212942481041,
0.01574304699897766,
-0.0236371960490942,
0.011193218640983105,
-0.08441516757011414,
-0.0403747521340847,
-0.015502702444791794,
-0.055149637162685394,
0.035232800990343094,
-0.002010645344853401,
-0.010488765314221382,
0.042530614882707596,
0.005913637112826109,
-0.005533332005143166,
-0.017269257456064224,
-0.052725907415151596,
-0.009725382551550865,
-0.005179110448807478,
0.024795176461338997,
0.056217506527900696,
0.008732030168175697,
-0.01607116125524044,
-0.07523947209119797,
0.040584102272987366,
0.043355148285627365,
-0.006021806504577398,
0.041948165744543076,
0.02431071363389492,
-0.03844552859663963,
0.02828982286155224,
0.03447885811328888,
-0.04703529551625252,
-0.02034224011003971,
0.014531455002725124,
-0.007849594578146935,
0.004774956963956356,
0.004372659604996443,
0.039713870733976364,
0.0030794646590948105,
-0.025353506207466125,
0.02267349697649479,
0.013013106770813465,
0.017471803352236748,
-0.002777062589302659,
0.016145486384630203,
0.045860473066568375,
0.012333015911281109,
-0.027181297540664673,
-0.002294400008395314,
0.003134685568511486,
0.015019954182207584,
-0.04875006526708603,
0.013548069633543491,
0.03125922381877899,
-0.01763538457453251,
-0.028246968984603882,
0.012377155013382435,
-0.027491571381688118,
-0.07346998900175095,
0.04918042942881584,
-0.035338420420885086,
-0.05442246049642563,
-0.01295615453273058,
0.04022330790758133,
0.03500847890973091,
0.013895070180296898,
0.050166722387075424,
-0.03686915338039398,
-0.011630689725279808,
-0.025147704407572746,
0.030880166217684746,
0.03807539865374565,
-0.01342590618878603,
0.07045239210128784,
0.02967114932835102,
0.011764814145863056,
-0.028971964493393898,
-0.03248732537031174,
0.03616628795862198,
-0.02965291403234005,
-0.013830003328621387,
-0.08324073255062103,
0.01000283844769001,
0.024542242288589478,
-0.010640890337526798,
0.029286624863743782,
-0.03683382272720337,
-0.06479010730981827,
-0.04742765426635742,
-0.014787280932068825,
-0.004818664398044348,
-0.021553080528974533,
-0.020098969340324402,
0.01907321624457836,
-0.0074054161086678505,
-0.013545648194849491,
-0.02075311355292797,
-0.02931777387857437,
0.017939886078238487,
0.08131315559148788,
0.019606923684477806,
0.048628054559230804,
-0.06517548114061356
] |
<p>Reading about plasmonic nanoparticles I faced the term "localised light".</p>
<p>How can one localise light? What are applications of it?</p> | g6602 | [
0.0552387461066246,
-0.011279604397714138,
0.0009552729316055775,
-0.049712494015693665,
0.017715727910399437,
0.035821910947561264,
0.010698208585381508,
0.013055150397121906,
0.024102086201310158,
-0.011028088629245758,
0.024361371994018555,
0.002297478262335062,
0.03018847480416298,
-0.00637641828507185,
-0.07577428966760635,
0.004803491290658712,
0.09695557504892349,
0.05611910670995712,
0.05681316554546356,
0.0006242684903554618,
-0.005736179184168577,
-0.007063813973218203,
0.021566860377788544,
-0.03299339488148689,
-0.062184982001781464,
0.022999053820967674,
-0.02761959098279476,
-0.016970882192254066,
-0.003301285207271576,
-0.03363441303372383,
0.04650292545557022,
-0.08251640945672989,
0.022325729951262474,
-0.05054958909749985,
0.03836739435791969,
-0.034573666751384735,
-0.01978708617389202,
0.013673857785761356,
-0.03028721548616886,
0.06132517382502556,
0.00887375045567751,
0.017408113926649094,
-0.0037039197050035,
0.000056624248827574775,
-0.0026856500189751387,
0.019662603735923767,
-0.011914994567632675,
-0.0368194542825222,
-0.014363930560648441,
-0.07123853266239166,
0.03315215930342674,
-0.010255546309053898,
0.047983285039663315,
0.02973397821187973,
0.11551813036203384,
-0.03120080940425396,
0.017365923151373863,
-0.032696761190891266,
0.08062387257814407,
-0.0007661252748221159,
0.08554769307374954,
0.026084868237376213,
0.016745731234550476,
0.030854040756821632,
-0.0010985697153955698,
-0.06316683441400528,
0.00010938546620309353,
0.010907698422670364,
0.03985285386443138,
-0.038927119225263596,
0.006656347308307886,
-0.029022997245192528,
0.007085732650011778,
-0.01941836252808571,
-0.03265393152832985,
-0.030664604157209396,
-0.005669090896844864,
0.03623506799340248,
-0.030482841655611992,
0.002199000446125865,
-0.0035737312864512205,
-0.01815073750913143,
-0.03094562143087387,
-0.03129647299647331,
0.03138142079114914,
0.010493953712284565,
-0.04706104099750519,
-0.04636865854263306,
0.01940036006271839,
-0.031331416219472885,
0.05306296795606613,
0.04515784606337547,
0.05734524875879288,
-0.0028285402804613113,
-0.01909351348876953,
-0.03601120039820671,
0.04305190220475197,
-0.018484361469745636,
-0.026531053707003593,
-0.01931760646402836,
-0.05133576691150665,
0.0006257024360820651,
-0.030469294637441635,
0.0191657692193985,
0.007591043133288622,
0.03628108650445938,
0.024944525212049484,
0.0008991278009489179,
0.007027999963611364,
-0.012842901982367039,
0.01694095879793167,
-0.061999425292015076,
-0.04743830859661102,
-0.03164564073085785,
-0.0707152783870697,
-0.005437618121504784,
0.07137398421764374,
-0.020725684240460396,
0.022178729996085167,
0.046300556510686874,
0.06597785651683807,
0.06643452495336533,
0.05286285653710365,
0.026391014456748962,
0.009517168626189232,
-0.03028913401067257,
-0.016512632369995117,
-0.020586185157299042,
-0.04069496691226959,
-0.05781705304980278,
0.01958787441253662,
-0.0002146062470274046,
-0.04887216165661812,
-0.023004349321126938,
-0.028638390824198723,
0.05184779316186905,
0.0560617633163929,
-0.05749601870775223,
0.02122475765645504,
0.030587101355195045,
0.027755029499530792,
-0.04458046704530716,
0.02024400606751442,
-0.0073359874077141285,
-0.014169889502227306,
-0.001692329184152186,
-0.035050828009843826,
0.029236719012260437,
0.009216686710715294,
0.031906433403491974,
0.021497558802366257,
0.0521591454744339,
-0.0004820187168661505,
-0.08306001871824265,
0.04878859221935272,
-0.03228039667010307,
0.06485164165496826,
-0.0044627259485423565,
-0.009015644900500774,
0.016383890062570572,
0.03988988324999809,
-0.018179049715399742,
-0.04234853759407997,
0.003914593253284693,
-0.04309249669313431,
0.0031657216604799032,
0.03547956421971321,
-0.06798020750284195,
0.002096418756991625,
-0.09016851335763931,
0.01708921231329441,
0.02397504448890686,
-0.07264388352632523,
0.009970363229513168,
0.012397321872413158,
0.04048359766602516,
0.0016769551439210773,
-0.03928326815366745,
-0.044266000390052795,
-0.007959879003465176,
0.0027231338899582624,
-0.08531318604946136,
-0.015990063548088074,
0.011776929721236229,
-0.039936941117048264,
0.011086168698966503,
-0.005563055630773306,
-0.042655784636735916,
0.053140003234148026,
0.02300138585269451,
-0.08283314108848572,
0.020348496735095978,
0.04547728970646858,
-0.012549239210784435,
-0.027074817568063736,
-0.04118071869015694,
-0.026138154789805412,
-0.0741565153002739,
-0.009003465063869953,
0.05099048838019371,
-0.036203257739543915,
0.04862580820918083,
0.006086430512368679,
0.028016844764351845,
0.09024115651845932,
-0.04599165916442871,
-0.019287051633000374,
-0.04795585200190544,
0.0280682984739542,
0.02937059849500656,
0.05456213653087616,
-0.031393539160490036,
0.041314538568258286,
0.01425275020301342,
-0.022446950897574425,
0.014461832121014595,
-0.014223896898329258,
-0.00521007040515542,
0.031779274344444275,
-0.01654193177819252,
-0.0003365726734045893,
0.04391651973128319,
0.00015763765259180218,
-0.006189997773617506,
0.004883367568254471,
0.05807633325457573,
-0.044525615870952606,
0.04206621274352074,
0.02414042130112648,
0.042326074093580246,
-0.040730785578489304,
-0.07109847664833069,
0.0025478582829236984,
-0.013033073395490646,
0.04625313729047775,
0.008701765909790993,
-0.04845152050256729,
-0.025942163541913033,
-0.036845430731773376,
0.06971874833106995,
0.01775011420249939,
0.005897079594433308,
0.02011917345225811,
-0.004528334829956293,
-0.0400761179625988,
0.0012940731830894947,
0.05516476556658745,
-0.03244705870747566,
-0.05454631894826889,
0.0737975463271141,
0.05851981043815613,
-0.033019058406353,
0.06424428522586823,
-0.005419921595603228,
0.02627726085484028,
-0.025251593440771103,
0.0014046545838937163,
0.07448049634695053,
0.022554127499461174,
0.007494345773011446,
0.03893599286675453,
-0.004603667184710503,
-0.04586899280548096,
-0.012907705269753933,
0.029823170974850655,
0.0061009544879198074,
-0.006739395204931498,
0.04854962229728699,
0.0009173998259939253,
0.006153724156320095,
-0.0034880463499575853,
0.029407180845737457,
-0.0025692435447126627,
-0.03739519417285919,
0.055758826434612274,
0.006066861562430859,
0.01819552481174469,
0.029208816587924957,
0.04830819368362427,
0.006452468689531088,
0.04525398835539818,
0.051515355706214905,
-0.058696992695331573,
-0.08271421492099762,
0.016937335953116417,
-0.04476768150925636,
-0.01573253981769085,
0.020099906250834465,
0.046896565705537796,
-0.08426142483949661,
-0.003508199704810977,
-0.044073671102523804,
0.02729247882962227,
-0.038196317851543427,
0.016235526651144028,
-0.025248559191823006,
0.04773249104619026,
0.03176487982273102,
0.03697836771607399,
0.06183497980237007,
0.01973290927708149,
-0.00014128508337307721,
0.025370720773935318,
-0.0015699604991823435,
0.026872985064983368,
0.02789444290101528,
-0.03055253066122532,
-0.008699370548129082,
0.0075835054740309715,
0.008325193077325821,
0.04906557500362396,
0.029795901849865913,
-0.0060905106365680695,
0.022666100412607193,
-0.001719595747999847,
0.0016214223578572273,
0.014945358969271183,
0.01507885567843914,
0.05994759872555733,
0.012272215448319912,
0.017194686457514763,
-0.031235547736287117,
0.017179176211357117,
-0.01304787490516901,
0.055554214864969254,
-0.04012564942240715,
0.02348228171467781,
0.0009616676834411919,
-0.002137821866199374,
-0.009685236029326916,
0.007316600531339645,
-0.005455577280372381,
-0.04841219633817673,
-0.06222079321742058,
-0.025440016761422157,
-0.07516247779130936,
-0.01701284572482109,
0.05593924969434738,
0.037599168717861176,
-0.023675335571169853,
0.039836518466472626,
-0.007425953634083271,
-0.03473842144012451,
-0.0030086322221904993,
0.02715217135846615,
0.0031963454093784094,
-0.03411852568387985,
0.00485950568690896,
-0.02264864556491375,
0.01892692781984806,
-0.0035159538965672255,
0.04010508954524994,
-0.018721401691436768,
-0.04951228201389313,
0.0014552605571225286,
0.002688594162464142,
0.015495959669351578,
0.036851685494184494,
0.08079609274864197,
-0.0626540258526802,
-0.00825986173003912,
-0.0036888804752379656,
0.03499865531921387,
-0.03641698881983757,
-0.020117059350013733,
-0.020529311150312424,
0.05495026335120201,
-0.000755766814108938,
-0.015625936910510063,
-0.03190646693110466,
-0.018198465928435326,
-0.026571108028292656,
-0.03478879854083061,
-0.02427123486995697,
-0.01856152154505253,
-0.012451800517737865,
-0.061384957283735275,
-0.04185747355222702,
-0.05040723457932472,
-0.005664040334522724,
-0.09332402795553207,
0.03255348652601242,
0.026130329817533493,
0.0032813793513923883,
0.01965855248272419,
0.034354839473962784,
-0.0019266682211309671,
-0.012421236373484135,
0.016151875257492065,
-0.019349168986082077,
-0.02826368808746338,
-0.028450103476643562,
-0.010058406740427017,
-0.04906684532761574,
-0.052363086491823196,
-0.016544010490179062,
-0.01669461652636528,
0.025599028915166855,
0.036295417696237564,
0.017687367275357246,
-0.010787950828671455,
-0.046992409974336624,
0.02255457080900669,
-0.030205976217985153,
-0.01775514706969261,
-0.06422966718673706,
0.01640934683382511,
-0.02509656362235546,
0.013997805304825306,
-0.005026561673730612,
0.019246770069003105,
0.023032646626234055,
0.06921415776014328,
-0.011406050063669682,
0.04916229844093323,
0.013215168379247189,
0.029727542772889137,
-0.04032257944345474,
-0.05115823820233345,
0.037416037172079086,
-0.008064504712820053,
0.06223822385072708,
0.0031845038756728172,
-0.0021794906351715326,
-0.03366968035697937,
0.0725645199418068,
-0.030338682234287262,
0.036378346383571625,
0.04391355440020561,
-0.018583165481686592,
-0.01845642179250717,
-0.007457824423909187,
0.06810353696346283,
0.02946668677031994,
-0.018757261335849762,
-0.03088855743408203,
0.058174923062324524,
-0.04405491054058075,
0.03189420700073242,
0.024688979610800743,
0.031632401049137115,
0.025316912680864334,
-0.0312114916741848,
0.029449015855789185,
-0.012664973735809326,
0.05484412983059883,
-0.028659237548708916,
0.05641033872961998,
0.006375467404723167,
0.009743282571434975,
0.02428363636136055,
-0.0387125127017498,
-0.047270625829696655,
-0.020967574790120125,
0.04594608023762703,
-0.018317997455596924,
-0.021725185215473175,
0.002815914573147893,
0.04564841836690903,
-0.04179465398192406,
-0.0569271445274353,
-0.012830921448767185,
-0.03622652590274811,
-0.014997215010225773,
0.05600982531905174,
0.03570842370390892,
-0.0352945439517498,
-0.0035858331248164177,
0.0011383112287148833,
-0.09990435093641281,
-0.0517338402569294,
-0.027801085263490677,
0.0296725332736969,
-0.01850617118179798,
0.03119250014424324,
0.005744481459259987,
0.048826735466718674,
-0.01892959140241146,
0.027857812121510506,
-0.02744802087545395,
0.01666182652115822,
0.023316431790590286,
0.02622881904244423,
-0.09261330217123032,
-0.07420890033245087,
-0.02944646216928959,
-0.0037029015365988016,
0.023166928440332413,
-0.0015709946164861321,
-0.07076700776815414,
-0.014938637614250183,
-0.051628414541482925,
-0.01787436753511429,
-0.004049775190651417,
-0.01267411932349205,
-0.006381932646036148,
0.0023026037961244583,
0.06002005562186241,
0.010006564669311047,
0.012117047794163227,
0.007258584722876549,
0.021523386240005493,
-0.030797403305768967,
0.015158011578023434,
0.015207844786345959,
-0.0030655208975076675,
0.040114425122737885,
-0.043469540774822235,
-0.0003526774817146361,
0.01116699818521738,
0.02844468131661415,
-0.0035022327210754156,
-0.062191691249608994,
0.055970169603824615,
-0.0254945307970047,
-0.022929592058062553,
-0.020771952345967293,
0.05479690060019493,
-0.014450587332248688,
-0.01484000589698553,
-0.09506212919950485,
-0.010852910578250885,
-0.0023998827673494816,
-0.009072587825357914,
-0.0008046019938774407,
0.005196072161197662,
-0.04060978814959526,
0.005472536198794842,
0.03706226125359535,
-0.057209987193346024,
-0.02045280858874321,
0.017645858228206635,
0.033338762819767,
-0.0562567412853241,
-0.021295737475156784,
-0.005241486243903637,
-0.013848301023244858,
0.02120017632842064,
0.012441112659871578,
0.024412598460912704,
-0.030269624665379524,
-0.07619417458772659,
-0.022579606622457504,
0.013461672700941563,
0.018888400867581367,
-0.008104407228529453,
0.018223710358142853,
0.028041861951351166,
0.03743387758731842,
-0.013493319042026997,
0.052877772599458694,
-0.00037823247839696705,
0.029369177296757698,
-0.0043779113329946995,
0.011274476535618305,
0.010814305394887924,
-0.03997040167450905,
-0.030545955523848534,
0.0013500534696504474,
-0.0019941667560487986,
0.057634737342596054,
0.06748443841934204,
-0.028837069869041443,
-0.049783382564783096,
0.033954013139009476,
-0.0027237660251557827,
0.0074758329428732395,
0.02313617430627346,
0.04971041902899742,
0.06416445225477219,
-0.04639757052063942,
0.009813717566430569,
0.028036611154675484,
0.011758933775126934,
0.04183650761842728,
0.007930610328912735,
0.04112734645605087,
0.04204083979129791,
-0.08209489285945892,
0.019301647320389748,
-0.0005222109030000865,
0.05293431133031845,
0.006399441044777632,
-0.0007365208002738655,
-0.05102603882551193,
0.004237147513777018,
0.0019208723679184914,
-0.0478130467236042,
0.05749675631523132,
-0.06546387821435928,
0.03967107832431793,
0.0053848158568143845,
-0.03066103346645832,
0.0179947130382061,
-0.04901601001620293,
-0.06843242794275284,
0.010050644166767597,
0.06020694598555565,
-0.02891596220433712,
0.05739545449614525,
-0.06038970500230789,
-0.042576905339956284,
0.03925095126032829,
0.0324995219707489,
0.03990098834037781,
0.023083550855517387,
0.0003460881707724184,
0.008853873237967491,
0.056193992495536804,
-0.015248897485435009,
-0.01295006275177002,
0.0033622505143284798,
-0.05671515315771103,
-0.008668984286487103,
-0.01320517435669899,
-0.050043463706970215,
-0.05425696074962616,
-0.046263113617897034,
0.038363419473171234,
-0.04659908264875412,
-0.0254571121186018,
0.01059548556804657,
-0.022570397704839706,
0.0036799958907067776,
-0.03563770651817322,
0.046163372695446014,
-0.0421859435737133,
0.039092909544706345,
-0.03189771622419357,
0.03256617486476898,
-0.01684611290693283,
0.014234126545488834,
0.005289182532578707,
0.027753446251153946,
0.014166236855089664,
0.012333963997662067,
0.014504768885672092,
-0.03390417620539665,
0.035750072449445724,
-0.04950103163719177,
-0.05869452655315399,
0.01955822855234146,
0.009668557904660702,
0.0030660824850201607,
0.0177740678191185,
0.050466958433389664,
0.003974206745624542,
0.06184903159737587,
0.027328327298164368,
-0.02034274861216545,
0.006346080452203751,
-0.03393065929412842,
-0.04160844534635544,
0.03246036544442177,
0.006832414772361517,
0.0447099506855011,
-0.04664942994713783,
-0.02393975481390953,
-0.011972806416451931,
-0.02933492511510849,
-0.027420826256275177,
0.019084841012954712,
-0.030629314482212067,
-0.015173511579632759,
-0.005999977700412273,
0.04448605328798294,
-0.016421446576714516,
-0.02857016585767269,
-0.049750782549381256,
-0.03439023345708847,
0.013480021618306637,
-0.030404042452573776,
-0.04134016111493111,
-0.06669285893440247,
-0.0386262908577919,
0.06887832283973694,
-0.01636412926018238,
0.08407628536224365,
-0.03324359282851219,
-0.028320124372839928,
-0.006734509486705065,
-0.010764814913272858,
-0.012742249295115471,
-0.05686355382204056,
-0.018426701426506042,
-0.025487497448921204,
-0.041300445795059204,
-0.020290952175855637,
0.04939332976937294,
-0.0572967529296875,
0.010111038573086262,
-0.0008486421429552138,
0.017045535147190094,
-0.06411595642566681,
0.0570681206882,
-0.031037069857120514,
0.05908321216702461,
0.03845783695578575,
0.006480436306446791,
0.0063773575238883495,
-0.0018159240717068315,
-0.023722531273961067,
0.027867324650287628,
0.011272601783275604,
0.00134326855186373,
-0.030479123815894127,
0.0017000050283968449,
0.04317793250083923,
-0.05234593152999878,
0.003208084963262081,
0.05881461501121521,
0.05896918103098869,
-0.0013731825165450573,
0.09812936931848526,
0.0447368249297142,
0.04693245515227318,
0.018858427181839943,
0.0408807098865509,
-0.0097851837053895,
0.04284762963652611,
0.024939386174082756,
0.0077630034647881985,
0.01759793795645237,
-0.03850724548101425,
-0.0067512826062738895,
-0.0005797294434159994,
0.06480693072080612,
0.011000819504261017,
-0.006571141071617603,
-0.020356083288788795,
0.014613403007388115,
0.055490847676992416,
-0.050331197679042816,
-0.003768367925658822,
-0.07500121742486954,
0.01427818089723587,
0.007607366424053907,
-0.04517446830868721,
-0.02749144285917282,
-0.0012054945109412074,
-0.0049958135932683945,
-0.027466390281915665,
0.025807935744524002,
0.014485885389149189,
0.028582969680428505,
-0.012165513820946217,
-0.00030460761627182364,
-0.03408745676279068,
-0.03218298405408859,
-0.027504295110702515,
0.02761685848236084,
0.0543847382068634,
-0.03420660272240639,
-0.002210376551374793,
0.04101358726620674,
-0.07894734293222427,
0.049753107130527496,
0.013091448694467545,
0.0016975003527477384,
0.0012785475701093674,
-0.02196471020579338,
0.02740633673965931,
0.012403225526213646,
0.016461487859487534,
-0.02387860044836998,
0.010954983532428741,
-0.03731689602136612,
0.012533011846244335
] |
<p>How to calculate the area / volume of a black hole?
Is there a corresponding mathematical function such as rotating $1/x$ around the $x$-axis or likewise to find the volume? </p> | g6603 | [
-0.0027690010610967875,
-0.0106113376095891,
-0.0029842876829206944,
-0.01864062249660492,
-0.029319697991013527,
-0.031604256480932236,
0.06194841489195824,
-0.023337071761488914,
-0.016354765743017197,
-0.005006841383874416,
0.02925335057079792,
0.03388339653611183,
0.06495536118745804,
0.015130365267395973,
0.0627870112657547,
-0.037460602819919586,
-0.05986568331718445,
0.007211575284600258,
-0.03029240295290947,
-0.023565765470266342,
0.035965438932180405,
-0.035527754575014114,
0.03620479255914688,
-0.016517503187060356,
-0.026008710265159607,
0.000720761832781136,
0.027889784425497055,
0.026142967864871025,
-0.04234333708882332,
0.02972497045993805,
0.004832753911614418,
0.03496340662240982,
-0.011864736676216125,
0.005312392488121986,
-0.015521727502346039,
-0.00046679546358063817,
-0.03818078339099884,
-0.016155509278178215,
0.04469688609242439,
0.03811013698577881,
0.021070100367069244,
-0.0793161615729332,
-0.0059960451908409595,
-0.0017283093184232712,
-0.007084621582180262,
-0.0010578400688245893,
-0.011438930407166481,
0.026752091944217682,
0.004917576909065247,
-0.019921543076634407,
0.008380701765418053,
0.011923420242965221,
0.12552018463611603,
-0.0051875547505915165,
0.004296445287764072,
0.04793883115053177,
0.035304754972457886,
-0.012742376886308193,
-0.03810825198888779,
0.04568930342793465,
-0.034673988819122314,
-0.015135610476136208,
-0.007960297167301178,
-0.014181959442794323,
0.0746176615357399,
-0.015851203352212906,
-0.032674871385097504,
-0.008960193954408169,
-0.0725289061665535,
0.0164018701761961,
0.028859935700893402,
0.01978621631860733,
0.07237810641527176,
0.011218818835914135,
-0.056998178362846375,
0.042376063764095306,
0.04057395085692406,
0.03720344603061676,
0.005386879201978445,
-0.03319096565246582,
-0.033419691026210785,
-0.02826959267258644,
0.08154000341892242,
-0.053549326956272125,
0.06569570302963257,
-0.00501199159771204,
0.036311469972133636,
-0.03251069411635399,
-0.027724450454115868,
0.042662061750888824,
-0.01361666340380907,
0.040048856288194656,
0.04949229583144188,
0.01061898935586214,
0.019186463207006454,
0.018372125923633575,
-0.000877783284522593,
0.031226299703121185,
-0.001508033717982471,
0.05365416407585144,
-0.008044969290494919,
0.023168668150901794,
-0.003619944676756859,
-0.01635507307946682,
0.02291657216846943,
0.028414152562618256,
-0.05844910070300102,
0.03095015324652195,
-0.027795707806944847,
0.007323544938117266,
-0.0378323569893837,
-0.08550108224153519,
0.015019236132502556,
-0.02479635551571846,
-0.019883329048752785,
-0.02438887394964695,
0.06628187745809555,
-0.006519948597997427,
0.028188707306981087,
0.09279865026473999,
-0.030991753563284874,
0.014947427436709404,
0.03649349883198738,
-0.007212942931801081,
0.03347800672054291,
-0.00800764374434948,
-0.018880140036344528,
-0.009140009060502052,
-0.003665186231955886,
0.03319960832595825,
0.010015754960477352,
-0.002638960024341941,
-0.0009055165573954582,
0.03791744261980057,
0.005783595144748688,
0.03605923801660538,
0.014896746724843979,
0.002513130195438862,
-0.03583725914359093,
0.006135210394859314,
-0.019029200077056885,
-0.03111177869141102,
-0.0039040790870785713,
0.05891202390193939,
0.012229369953274727,
0.017512628808617592,
-0.04787924140691757,
-0.08217906206846237,
-0.024413438513875008,
-0.011783733032643795,
-0.011846747249364853,
0.12079207599163055,
-0.012539426796138287,
-0.039498720318078995,
0.01771838590502739,
-0.018382862210273743,
0.06411119550466537,
0.0573369562625885,
-0.015757055953145027,
-0.011311789974570274,
0.04419733211398125,
0.019250398501753807,
-0.014590426348149776,
0.029455581679940224,
-0.018715152516961098,
-0.03199956566095352,
-0.044759415090084076,
-0.02170555479824543,
-0.03375794738531113,
-0.031622499227523804,
0.006760882679373026,
0.009357785806059837,
-0.0006767807644791901,
-0.007186384871602058,
0.02936924621462822,
0.018790585920214653,
-0.01634671352803707,
0.03531825169920921,
0.008320379070937634,
0.03132886812090874,
0.06955546885728836,
0.0223233662545681,
0.027916835620999336,
0.03775014728307724,
0.020949028432369232,
0.003103055292740464,
0.014580913819372654,
-0.012127405032515526,
-0.014490059576928616,
0.012043159455060959,
-0.013325156643986702,
0.029130922630429268,
0.07180359214544296,
0.014209010638296604,
-0.008987221866846085,
0.07259850203990936,
0.04534480348229408,
-0.04303006827831268,
-0.029960867017507553,
0.05932731181383133,
-0.027749383822083473,
-0.017387332394719124,
0.07652803510427475,
0.031393855810165405,
0.032602451741695404,
-0.005952021107077599,
-0.0233253613114357,
0.035198770463466644,
0.04725568741559982,
0.049773260951042175,
0.014112875796854496,
-0.03935355320572853,
0.01668149046599865,
-0.01864708587527275,
-0.0245067086070776,
0.043213434517383575,
-0.06398042291402817,
0.015500213950872421,
-0.017740299925208092,
0.0067364792339503765,
0.0035464817192405462,
-0.007215128745883703,
-0.029213543981313705,
-0.0030238700564950705,
-0.028355317190289497,
0.032497428357601166,
0.03302793949842453,
-0.035568904131650925,
-0.009409231133759022,
0.02506270632147789,
-0.10052686184644699,
-0.00897608045488596,
0.015870723873376846,
0.02977885492146015,
0.0166181493550539,
0.004169842693954706,
-0.01215599849820137,
0.06322431564331055,
0.014493677765130997,
0.03262120485305786,
0.047267038375139236,
0.062008339911699295,
-0.011412096209824085,
0.031367797404527664,
0.041427820920944214,
0.04118160158395767,
0.0053468425758183,
0.011854542419314384,
0.006894453428685665,
-0.014161650091409683,
-0.022758908569812775,
-0.028110748156905174,
-0.02932213619351387,
-0.00012283782416488975,
-0.00662414263933897,
-0.012101350352168083,
-0.024836065247654915,
-0.01864566281437874,
-0.011133415624499321,
-0.03427906706929207,
0.029993174597620964,
0.034006014466285706,
0.03729751706123352,
0.013626827858388424,
-0.031639907509088516,
-0.00822853296995163,
-0.09560314565896988,
-0.005885463673621416,
0.032832223922014236,
0.06824003905057907,
0.018620112910866737,
-0.0005831142188981175,
0.06845301389694214,
0.03627926483750343,
0.021616417914628983,
-0.06309634447097778,
-0.0397215336561203,
0.030236762017011642,
0.05521957948803902,
-0.02599329501390457,
0.01778739131987095,
-0.008572150953114033,
-0.06118983030319214,
0.03078448213636875,
-0.006810352206230164,
-0.024457640945911407,
0.050158072263002396,
0.012890887446701527,
-0.05713870748877525,
-0.05668613314628601,
0.028746360912919044,
-0.002926297951489687,
-0.04551473632454872,
0.03714079409837723,
0.02207927033305168,
0.03210186958312988,
0.04996231943368912,
0.008615173399448395,
0.046034522354602814,
0.014502860605716705,
0.025556454434990883,
-0.041123826056718826,
-0.001006013830192387,
-0.039773520082235336,
-0.04323754459619522,
0.04297145828604698,
-0.0017284833593294024,
-0.05560210719704628,
-0.02243642322719097,
0.026836073026061058,
0.008305296301841736,
-0.013584454543888569,
0.012156039476394653,
-0.03286081179976463,
-0.012238391675055027,
-0.023830575868487358,
0.002148199826478958,
-0.03325321897864342,
-0.006439280696213245,
0.017252527177333832,
-0.06547576189041138,
-0.021809745579957962,
-0.014952667988836765,
0.006553166545927525,
0.016811978071928024,
-0.006793603301048279,
-0.06424794346094131,
-0.008330758661031723,
0.00006200459756655619,
-0.007848440669476986,
-0.04758378118276596,
0.012116318568587303,
-0.0315215140581131,
0.03598172962665558,
-0.018520815297961235,
-0.002823450369760394,
0.000404631340643391,
-0.03152298554778099,
0.04156879708170891,
-0.006547155324369669,
0.011463858187198639,
-0.05242979899048805,
0.017936553806066513,
0.010082394815981388,
-0.012814652174711227,
-0.026050088927149773,
-0.07429549098014832,
-0.023393161594867706,
0.036666471511125565,
0.005891159176826477,
-0.03384840115904808,
-0.07316886633634567,
0.04984993115067482,
-0.037435587495565414,
0.09782934188842773,
-0.005486118141561747,
0.03874659910798073,
-0.008609860204160213,
-0.039334867149591446,
0.003786821383982897,
-0.020776310935616493,
-0.08672762662172318,
-0.029041115194559097,
0.0010819582967087626,
-0.02314121462404728,
-0.039127517491579056,
0.05739804729819298,
-0.00878943968564272,
-0.0903923362493515,
-0.021658429875969887,
0.01579689234495163,
-0.007119154091924429,
0.04338960722088814,
-0.0028421541210263968,
-0.030495954677462578,
-0.08789857476949692,
0.007203199435025454,
-0.03313199803233147,
-0.022871214896440506,
-0.01624414138495922,
0.016642296686768532,
-0.0401691272854805,
0.020526554435491562,
-0.019007986411452293,
-0.09194586426019669,
0.023851851001381874,
-0.03972237557172775,
-0.04302049055695534,
0.06816793233156204,
-0.04790147393941879,
0.01107533648610115,
-0.009763524867594242,
-0.02540576085448265,
-0.07741127908229828,
0.052892137318849564,
-0.005033145193010569,
-0.02699853852391243,
-0.023534320294857025,
-0.06781797111034393,
-0.02032812125980854,
0.04151085019111633,
-0.020607827231287956,
0.022117555141448975,
0.013314456678926945,
0.04714585468173027,
0.015720287337899208,
0.053882189095020294,
-0.0033966018818318844,
0.006371135823428631,
0.025502027943730354,
0.04428553208708763,
-0.01735888235270977,
0.023782234638929367,
-0.012267310172319412,
0.05386078357696533,
-0.028204403817653656,
-0.005829818081110716,
-0.012088547460734844,
0.029394129291176796,
-0.03760989382863045,
0.0026798867620527744,
-0.06230385601520538,
-0.015630295500159264,
0.014203867875039577,
-0.08858350664377213,
-0.033331699669361115,
0.016482576727867126,
0.0061096316203475,
0.008824307471513748,
0.0012576015433296561,
0.024841176345944405,
0.04235222935676575,
0.005009880289435387,
0.01242916565388441,
-0.05461800470948219,
-0.003043057629838586,
0.008601305074989796,
0.018193406984210014,
0.012640239670872688,
0.00026701821479946375,
-0.01214352436363697,
0.022996995598077774,
-0.0658368393778801,
-0.03495036065578461,
-0.03997363522648811,
0.012662981636822224,
0.03393300995230675,
-0.024147655814886093,
-0.04756259545683861,
-0.02650185115635395,
-0.03784311190247536,
-0.011374016292393208,
-0.023457510396838188,
-0.0690213143825531,
-0.011865803971886635,
0.00705892825499177,
-0.032563716173172,
0.04770650342106819,
0.057077210396528244,
0.00934265460819006,
-0.03705989196896553,
-0.0350557342171669,
-0.06389148533344269,
0.052705276757478714,
-0.01850675232708454,
-0.01944717764854431,
-0.05447106808423996,
-0.009384498931467533,
0.00211198884062469,
0.012359087355434895,
-0.030866075307130814,
0.03810390830039978,
-0.018379658460617065,
0.017580879852175713,
-0.04878722503781319,
0.07525163888931274,
-0.004276928957551718,
-0.012268904596567154,
-0.03514929488301277,
-0.04041994735598564,
-0.01729581318795681,
-0.01571805402636528,
0.039274487644433975,
0.029308820143342018,
0.03935077786445618,
0.03709206357598305,
-0.01606408692896366,
-0.004962206818163395,
0.02303619496524334,
0.047666244208812714,
0.003117666346952319,
0.017356179654598236,
0.08522927761077881,
-0.0466046966612339,
-0.008834975771605968,
-0.08448023349046707,
-0.029150599613785744,
-0.08769973367452621,
0.0321846567094326,
0.08712584525346756,
0.013432782143354416,
0.034348029643297195,
0.026006683707237244,
-0.015867944806814194,
-0.01596156135201454,
0.003285628277808428,
-0.015831945464015007,
0.047330956906080246,
-0.009491953067481518,
0.053739503026008606,
0.047572750598192215,
-0.006443863734602928,
0.019419223070144653,
0.041450124233961105,
0.022020358592271805,
-0.07689663767814636,
0.004598054103553295,
0.047622330486774445,
-0.0038751557003706694,
0.0384223647415638,
0.029485251754522324,
0.004987293854355812,
0.024158190935850143,
0.024814547970891,
0.008228342980146408,
-0.000758941809181124,
-0.06099358946084976,
-0.033635132014751434,
0.01810009777545929,
0.021357838064432144,
-0.03043282963335514,
-0.041921086609363556,
-0.024328559637069702,
-0.005500180646777153,
-0.0334608219563961,
0.005924216005951166,
-0.023008624091744423,
-0.01703152433037758,
0.10099461674690247,
-0.029030831530690193,
0.02670038491487503,
0.007932224310934544,
-0.010734864510595798,
0.007234241813421249,
-0.006646085996180773,
0.008214508183300495,
-0.053410887718200684,
-0.004648277070373297,
0.031692638993263245,
-0.027921821922063828,
-0.01289308164268732,
0.017935823649168015,
-0.001305767334997654,
-0.03385902941226959,
-0.018764588981866837,
0.0038775287102907896,
-0.027219008654356003,
-0.060211144387722015,
-0.01579313538968563,
-0.001067941077053547,
0.03597807139158249,
-0.06308663636445999,
0.004218770191073418,
-0.00801660306751728,
-0.03761373087763786,
0.015320190228521824,
0.029744723811745644,
-0.03258978947997093,
-0.01570191979408264,
0.015959689393639565,
-0.07582391053438187,
-0.01867733895778656,
-0.01983276568353176,
-0.01949767768383026,
0.0336131788790226,
0.05802258476614952,
-0.006282604765146971,
-0.006192707922309637,
-0.004953788127750158,
-0.00021192015265114605,
0.009696466848254204,
-0.006220351904630661,
0.05011976510286331,
-0.036024291068315506,
-0.006521755829453468,
-0.006338127888739109,
0.017273763194680214,
0.019166046753525734,
-0.01441904902458191,
-0.01110891904681921,
-0.02544528618454933,
-0.006296742707490921,
0.008242092095315456,
-0.059752751141786575,
-0.045828402042388916,
-0.005358085967600346,
-0.015494200401008129,
0.007977882400155067,
0.05619603022933006,
-0.05673613399267197,
-0.012783853337168694,
0.048443298786878586,
-0.02086135558784008,
-0.01268833689391613,
-0.0010702137369662523,
-0.05853412300348282,
-0.07472232729196548,
-0.027051052078604698,
0.0008389879949390888,
-0.03638254478573799,
0.009754800237715244,
0.03263934329152107,
0.009020566008985043,
0.029255423694849014,
0.011105033569037914,
0.005640619434416294,
0.029478667303919792,
0.0058974833227694035,
0.06493103504180908,
-0.04794640094041824,
0.015483847819268703,
0.01936735399067402,
-0.04394064098596573,
-0.04573405161499977,
0.04503604397177696,
0.012830602005124092,
-0.028769822791218758,
0.010706769302487373,
0.036826808005571365,
-0.013192735612392426,
0.09624162316322327,
0.0768899917602539,
-0.0217316634953022,
0.04306881129741669,
0.01750156469643116,
0.00995761901140213,
-0.06079612299799919,
0.03084346279501915,
0.0021217053290456533,
0.035430967807769775,
-0.04550893232226372,
-0.03691655397415161,
0.0439017228782177,
0.021153807640075684,
-0.058772049844264984,
-0.047914277762174606,
-0.05435916781425476,
0.028188269585371017,
-0.026219939813017845,
0.07159166783094406,
0.04326089844107628,
-0.06637674570083618,
-0.023611463606357574,
0.006718060467392206,
-0.07093743234872818,
-0.04152701795101166,
0.025628777220845222,
-0.06694167852401733,
0.002584553323686123,
-0.034761060029268265,
0.002746570622548461,
-0.05080639198422432,
-0.03698446974158287,
0.026914559304714203,
0.014960026368498802,
0.04827263206243515,
0.03820072486996651,
0.06908480077981949,
0.06587835401296616,
-0.050494808703660965,
-0.010752653703093529,
-0.0038458050694316626,
-0.07497572153806686,
0.03797908499836922,
-0.1078469455242157,
-0.016584264114499092,
0.0033832176122814417,
0.02400399185717106,
-0.030539875850081444,
0.040138378739356995,
0.006283591501414776,
0.037032149732112885,
-0.07007744163274765,
0.032560113817453384,
-0.014075776562094688,
-0.0384499691426754,
-0.04414932802319527,
0.00020574154041241854,
0.04013613983988762,
0.1047961637377739,
-0.008035385049879551,
-0.026763416826725006,
-0.02544235624372959,
-0.018932275474071503,
-0.027365390211343765,
0.005176491104066372,
0.02831406705081463,
0.022601528093218803,
0.0008159297285601497,
0.016549287363886833,
0.022810662165284157,
-0.03822696954011917,
0.034456148743629456,
-0.036597948521375656,
0.047583337873220444,
-0.007138925138860941,
0.005536078009754419,
0.029803600162267685,
-0.029479222372174263,
0.012506765313446522,
0.07383572310209274,
0.012415420264005661,
-0.00865956861525774,
-0.02634148672223091,
-0.008218671195209026,
0.0135641572996974,
0.01715611107647419,
-0.003457688959315419,
0.004912730306386948,
-0.07003522664308548,
-0.04400504752993584,
0.02930312417447567,
0.022866107523441315,
-0.07272984832525253,
0.011867687106132507,
-0.030084019526839256,
-0.0265236496925354,
-0.018646836280822754,
-0.007475436199456453,
0.026071272790431976,
-0.02423958107829094,
0.042335912585258484,
-0.026389624923467636,
0.03042927011847496,
0.015717383474111557,
-0.011320782825350761,
0.012992758303880692,
-0.008996857330203056,
0.034442123025655746,
0.07252511382102966,
0.019790062680840492,
-0.06533984839916229,
0.026127679273486137,
0.006070585921406746,
0.026377787813544273,
0.01656912826001644,
0.023757368326187134,
0.06029062718153,
0.03870680555701256,
-0.042734574526548386,
-0.02927759476006031,
0.04924511909484863,
-0.0039300802163779736,
0.00810453575104475,
0.026858489960432053,
-0.044749461114406586,
0.008619497530162334,
-0.04716133698821068,
-0.0734710544347763,
-0.000828991353046149,
0.01751384697854519,
0.030554499477148056,
0.035117145627737045,
-0.010988579131662846,
0.020356763154268265,
-0.02923249639570713,
0.03319743648171425,
0.034902408719062805
] |
<p>For a simulation, I want to compute the path that light follows near a black hole.</p>
<p>Non-relativistically, a massive point particle in a central newtonian gravitational field follows either an ellipse, a parabola, or a hyperbola. Is the same true relativistically for light around a black hole? A problem I see with this, is that while particles gain velocity when approaching a black hole, a photon gains energy instead. So do photons behave differently?</p> | g6604 | [
0.009113886393606663,
0.009012333117425442,
0.015452327206730843,
0.02883477509021759,
0.035764411091804504,
0.004021177999675274,
0.04054071381688118,
0.004817625042051077,
-0.03367689624428749,
0.004515461623668671,
0.032021623104810715,
0.016764087602496147,
0.03957255557179451,
-0.019474465399980545,
-0.03748718276619911,
-0.026948802173137665,
0.07946861535310745,
0.006925342138856649,
0.040814101696014404,
-0.009422973729670048,
-0.02263258583843708,
0.019669605419039726,
0.028589559718966484,
-0.029635459184646606,
-0.02352641150355339,
0.018387578427791595,
0.061572156846523285,
-0.03963903710246086,
-0.07922931760549545,
-0.007213506381958723,
0.06205523759126663,
-0.04508287087082863,
0.0656595528125763,
-0.026366278529167175,
0.023559695109725,
0.019732851535081863,
0.024096578359603882,
0.01271666307002306,
-0.016319040209054947,
-0.000039610971725778654,
0.03656682372093201,
-0.034631047397851944,
-0.007929881103336811,
-0.009494985453784466,
0.020713066682219505,
-0.05994020402431488,
0.043072693049907684,
-0.0016413844423368573,
0.016101451590657234,
0.0017794531304389238,
-0.0017989681800827384,
0.0024251791182905436,
-0.01735732890665531,
0.012644797563552856,
0.024046452715992928,
0.07361577451229095,
0.007450757082551718,
-0.002926895394921303,
0.040591590106487274,
0.05712733417749405,
-0.009008309803903103,
-0.015046444721519947,
-0.00353030301630497,
-0.01576215960085392,
-0.00153378548566252,
0.014651212841272354,
-0.03465479612350464,
-0.027941932901740074,
-0.10464229434728622,
0.0009143980569206178,
0.006029724143445492,
0.007407227531075478,
-0.024436885491013527,
-0.06368780881166458,
-0.01580685004591942,
0.02317025512456894,
-0.04333443194627762,
0.019686194136738777,
-0.01482333056628704,
0.004055427853018045,
0.007243347819894552,
0.020226264372467995,
0.04465356841683388,
-0.014078804291784763,
0.07317358255386353,
-0.008518975228071213,
-0.024857966229319572,
-0.01869610883295536,
-0.036806732416152954,
0.004392507951706648,
0.05839007720351219,
0.02532147616147995,
0.07966569811105728,
0.03727184608578682,
-0.040420643985271454,
0.009728767909109592,
-0.04777555540204048,
0.04470397159457207,
0.03856330364942551,
0.010384959168732166,
-0.015958910807967186,
0.005859507247805595,
0.005126905627548695,
0.03193208575248718,
0.018784036859869957,
-0.0033046065364032984,
-0.004997176118195057,
0.05271688848733902,
-0.003761403961107135,
0.0265958309173584,
-0.02839820086956024,
-0.11043848842382431,
-0.003010118380188942,
-0.09825655817985535,
-0.0878218337893486,
0.008550310507416725,
0.08430793881416321,
-0.04346168786287308,
0.027353515848517418,
0.12364405393600464,
0.019197413697838783,
0.011096959933638573,
0.031118858605623245,
0.10861803591251373,
0.018457069993019104,
0.018093155696988106,
-0.008864928968250751,
0.021093541756272316,
0.027539275586605072,
0.028276024386286736,
0.01740189827978611,
-0.019515102729201317,
-0.05332230404019356,
0.05273967608809471,
-0.03530789911746979,
-0.005421461071819067,
0.04310620576143265,
0.003506304929032922,
-0.042588572949171066,
-0.009683012031018734,
-0.0029461835511028767,
-0.04320499673485756,
-0.003948119468986988,
-0.03126906231045723,
-0.04872426390647888,
0.00993743259459734,
0.004428140819072723,
-0.023037148639559746,
0.03906863182783127,
0.008094629272818565,
0.027675002813339233,
0.11380635201931,
-0.00530534703284502,
0.007531875744462013,
-0.01069923210889101,
0.029864728450775146,
0.0214283037930727,
0.017654607072472572,
-0.06524956226348877,
-0.00909157283604145,
0.026642819866538048,
0.004896821454167366,
0.06494967639446259,
0.004203803837299347,
0.004410985391587019,
-0.0031417105346918106,
0.03630642220377922,
-0.047713395208120346,
0.03834913671016693,
-0.024506712332367897,
-0.02083870954811573,
-0.0033658910542726517,
-0.00923396460711956,
0.06263882666826248,
-0.0018300729570910335,
0.025296257808804512,
0.016270453110337257,
-0.00620436342433095,
-0.02168525941669941,
-0.015507584437727928,
-0.0064698196947574615,
-0.006458378862589598,
0.037043843418359756,
0.028339309617877007,
-0.001847420702688396,
0.0017857380444183946,
-0.01529688574373722,
0.0007643664721399546,
-0.052764423191547394,
-0.010002481751143932,
-0.045060619711875916,
-0.018652772530913353,
0.00834567192941904,
0.01535127591341734,
-0.004686689469963312,
0.05032409355044365,
0.013480023480951786,
-0.023126037791371346,
-0.01814397983253002,
0.06423114985227585,
-0.004855367820709944,
0.03608197346329689,
-0.04243838042020798,
0.026247724890708923,
0.031085263937711716,
-0.01965518295764923,
-0.037631090730428696,
-0.011685450561344624,
-0.018961744382977486,
0.02022632211446762,
0.03361295163631439,
0.0114476028829813,
0.05165993049740791,
0.00535618094727397,
-0.04608967527747154,
0.022730927914381027,
-0.10119873285293579,
0.010306614451110363,
0.008893544785678387,
0.05984864756464958,
-0.028618570417165756,
-0.051149021834135056,
0.013017871417105198,
-0.04819820448756218,
0.010855195112526417,
0.003025750396773219,
-0.0679679736495018,
-0.039301563054323196,
0.020023547112941742,
0.03507526218891144,
-0.06236927583813667,
0.029177991673350334,
-0.0026090554893016815,
-0.01442798599600792,
0.08863137662410736,
-0.04628211259841919,
-0.038330256938934326,
-0.0001910443970700726,
0.049420978873968124,
-0.013291174545884132,
0.003661447437480092,
-0.010802955366671085,
-0.02297528274357319,
-0.004340578801929951,
0.01550467312335968,
-0.009568637236952782,
0.037894412875175476,
0.005725827068090439,
-0.06277064979076385,
0.0018102115718647838,
0.05115083232522011,
-0.02198152430355549,
0.005032876040786505,
0.034241579473018646,
0.02303338795900345,
-0.0039982870221138,
-0.017147943377494812,
0.0140693886205554,
-0.06973434239625931,
-0.01362193375825882,
-0.02049224078655243,
-0.01573469676077366,
-0.03136421740055084,
0.00318464869633317,
-0.013782412745058537,
0.025893162935972214,
0.005807959008961916,
-0.017383480444550514,
0.027310030534863472,
0.03927001357078552,
-0.032002732157707214,
0.038307636976242065,
0.06611184030771255,
0.022299474105238914,
-0.002145954640582204,
-0.0023496549110859632,
-0.011205805465579033,
0.014706740155816078,
0.01504895742982626,
-0.0032881656661629677,
0.007392896339297295,
-0.04622979462146759,
-0.020242324098944664,
0.028762830421328545,
0.03918364271521568,
-0.11003150045871735,
0.007568312343209982,
-0.019209690392017365,
-0.06102166697382927,
-0.04630747437477112,
0.017950110137462616,
0.04552781581878662,
-0.00194668082986027,
0.06961642950773239,
0.01145952194929123,
-0.010796461254358292,
0.03319232910871506,
-0.014421077445149422,
-0.02004249207675457,
0.029685506597161293,
-0.031936995685100555,
-0.022423261776566505,
-0.030629092827439308,
0.011173175647854805,
-0.0018874111119657755,
0.035985711961984634,
-0.05948884040117264,
-0.06844137609004974,
0.05531331151723862,
0.016530239954590797,
0.01791701838374138,
0.03365263342857361,
-0.018011150881648064,
0.04221966490149498,
0.02443535067141056,
-0.016279559582471848,
0.008058549836277962,
0.03718046844005585,
0.014338801614940166,
0.05795999988913536,
0.002202268224209547,
0.016725415363907814,
-0.050869088619947433,
0.015491664409637451,
0.05533605441451073,
0.044397879391908646,
0.012278718873858452,
0.0019174396293237805,
-0.01416144147515297,
-0.0325903594493866,
0.010423922911286354,
-0.04095986858010292,
-0.01877034641802311,
0.06432376801967621,
0.035646095871925354,
-0.031928326934576035,
0.016094787046313286,
-0.028112350031733513,
0.0840969905257225,
-0.03663713485002518,
0.029096052050590515,
-0.04269558936357498,
0.010306647047400475,
0.0026975260116159916,
-0.012671548873186111,
-0.030024919658899307,
0.0395759642124176,
-0.013074223883450031,
-0.014357045292854309,
-0.024367885664105415,
0.011109191924333572,
-0.08569832891225815,
-0.013638114556670189,
-0.02816731110215187,
-0.00021487391495611519,
-0.00963673647493124,
-0.00732786487787962,
0.0003342202689964324,
0.026145823299884796,
0.018504075706005096,
-0.06405998021364212,
-0.031046276912093163,
-0.014947360381484032,
0.03373550996184349,
-0.007853299379348755,
-0.000987174455076456,
0.05381280183792114,
-0.03436479717493057,
0.0018042424926534295,
-0.016998644918203354,
-0.013714968226850033,
0.009858189150691032,
0.014087263494729996,
-0.004843450617045164,
0.0016036267625167966,
-0.0156463123857975,
0.0361156240105629,
-0.05227796733379364,
0.0036522201262414455,
-0.025745676830410957,
-0.0011629716027528048,
0.02066061832010746,
0.0016320523573085666,
-0.002030330477282405,
0.0020784351509064436,
0.05576813593506813,
-0.026730850338935852,
-0.04086786508560181,
0.0565948411822319,
-0.007327912840992212,
0.013848393224179745,
-0.06758628785610199,
-0.023121338337659836,
-0.048838645219802856,
0.01004072930663824,
-0.023868700489401817,
-0.013652483932673931,
0.004768596962094307,
0.013238130137324333,
-0.03138430044054985,
0.07672711461782455,
0.02321271412074566,
0.013841059058904648,
0.06632794439792633,
0.02619694359600544,
-0.03876321762800217,
0.010446104221045971,
-0.04608415439724922,
-0.04496857523918152,
0.00025436535361222923,
0.07127274572849274,
-0.02794327773153782,
0.015542126260697842,
-0.07929708063602448,
0.011599983088672161,
-0.03320945054292679,
0.018296534195542336,
0.0192363653331995,
-0.016728365793824196,
0.01059685181826353,
0.014975662343204021,
0.004252662416547537,
0.030761094763875008,
-0.025303589180111885,
-0.02631296217441559,
0.06623943150043488,
0.034036390483379364,
-0.012336505576968193,
-0.01939709670841694,
0.011995349079370499,
0.010579608380794525,
0.036734797060489655,
0.011978373862802982,
0.0034895772114396095,
-0.05569014698266983,
0.043751638382673264,
-0.012775328010320663,
-0.001461439998820424,
0.07180565595626831,
-0.024451827630400658,
0.0066873482428491116,
0.05465595796704292,
0.025323130190372467,
-0.07661077380180359,
0.018880145624279976,
0.0444847010076046,
-0.02244017831981182,
0.014272228814661503,
-0.05043096840381622,
-0.012256632559001446,
0.02633323334157467,
0.0188274048268795,
-0.04471590742468834,
-0.01853696070611477,
-0.014985576272010803,
-0.016264084726572037,
-0.014809513464570045,
0.04650457948446274,
-0.007385086268186569,
-0.007295542396605015,
-0.050380807369947433,
-0.014486793428659439,
0.043980248272418976,
0.009626484476029873,
-0.009202716872096062,
-0.02726517617702484,
-0.10117734968662262,
-0.018413808196783066,
-0.020525500178337097,
0.01283229049295187,
-0.07010499387979507,
0.01874653622508049,
0.003915649373084307,
0.014590849168598652,
-0.014550291001796722,
-0.012493611313402653,
-0.030313599854707718,
0.010451476089656353,
0.0019621325191110373,
-0.041824549436569214,
-0.012739147059619427,
-0.03070809319615364,
0.029243193566799164,
0.016272995620965958,
-0.0057172817178070545,
0.034997813403606415,
-0.0366416797041893,
0.04593104496598244,
-0.001410208409652114,
-0.007828841917216778,
0.0013640867546200752,
-0.0758664533495903,
-0.0277104489505291,
-0.04322989657521248,
0.003780738916248083,
-0.031157111749053,
0.014450805261731148,
0.015095748007297516,
0.045862384140491486,
-0.012487035244703293,
-0.0958697572350502,
0.03869660198688507,
0.02945483662188053,
-0.006449722684919834,
-0.014114568009972572,
0.05334240198135376,
0.06099452078342438,
0.00926736555993557,
-0.04532410949468613,
0.0451803095638752,
-0.035863254219293594,
-0.002579831052571535,
-0.010273969732224941,
0.0008276486187241971,
-0.00211000326089561,
-0.013819706626236439,
0.012345436029136181,
0.021172702312469482,
-0.037674836814403534,
-0.03112235851585865,
0.034627992659807205,
0.018544869497418404,
0.013526479713618755,
0.0218124371021986,
0.08822153508663177,
-0.005858711898326874,
-0.0025599421933293343,
-0.00863885972648859,
0.03558547794818878,
-0.013358836062252522,
0.027699559926986694,
-0.025353290140628815,
0.05525849014520645,
0.02200254797935486,
-0.04122936725616455,
-0.06474009901285172,
0.022625472396612167,
-0.016603393480181694,
0.05688345059752464,
-0.035678278654813766,
-0.006404274143278599,
-0.0005870094173587859,
0.011712226085364819,
0.04468783736228943,
-0.01636666990816593,
0.041576873511075974,
-0.017030412331223488,
0.04601167142391205,
0.005938342772424221,
-0.06936806440353394,
-0.0028968516271561384,
0.00854058563709259,
0.031534671783447266,
0.015671169385313988,
-0.03324901685118675,
0.023877033963799477,
-0.007885785773396492,
-0.045043814927339554,
-0.013480402529239655,
-0.036125004291534424,
0.006353674456477165,
-0.08347316831350327,
0.027770645916461945,
-0.03525911271572113,
-0.003416344290599227,
-0.05506886914372444,
-0.054125163704156876,
-0.06869803369045258,
0.04458007588982582,
0.032217636704444885,
-0.021782150492072105,
-0.016469042748212814,
-0.02448585070669651,
0.059713561087846756,
0.0049089896492660046,
0.02585124783217907,
0.00600785855203867,
-0.012327345088124275,
-0.03312817960977554,
-0.028452739119529724,
0.0021688633132725954,
0.017960961908102036,
0.04240676760673523,
-0.037563540041446686,
0.002579072490334511,
-0.003147043054923415,
0.008485356345772743,
0.11415465921163559,
0.022362159565091133,
0.015683908015489578,
-0.020482279360294342,
-0.03582434728741646,
0.018271885812282562,
-0.04779750853776932,
-0.08171799778938293,
-0.012670082040131092,
0.014799182303249836,
-0.01176487561315298,
0.00656163552775979,
-0.00254261726513505,
-0.038024842739105225,
0.045067764818668365,
0.017207160592079163,
-0.05497252568602562,
0.012328499928116798,
0.02109777368605137,
-0.06362079828977585,
-0.038321226835250854,
0.058276645839214325,
-0.03764772787690163,
0.06500118970870972,
0.043926600366830826,
-0.011360091157257557,
0.03074321337044239,
-0.021394146606326103,
-0.01870414800941944,
-0.019000018015503883,
0.01847587525844574,
0.07497982680797577,
-0.03144686669111252,
-0.007661622017621994,
-0.02719077654182911,
-0.0308796726167202,
-0.038599029183387756,
0.05331419035792351,
0.03445962443947792,
-0.07195938378572464,
0.08734362572431564,
0.025167861953377724,
0.0075052231550216675,
0.0464298352599144,
-0.0015761905815452337,
-0.04442266374826431,
0.05676655098795891,
0.06877395510673523,
0.0009219066123478115,
-0.06520483642816544,
0.03985438868403435,
0.0036835139617323875,
0.03496613726019859,
0.04056992381811142,
-0.048866890370845795,
0.022008821368217468,
0.02104794979095459,
-0.06387685984373093,
0.006003649439662695,
-0.013727745972573757,
0.028055984526872635,
-0.018252424895763397,
0.025983408093452454,
-0.0268547385931015,
-0.05575808510184288,
-0.02498863823711872,
0.012355729006230831,
-0.01754850335419178,
-0.017533747479319572,
-0.053754039108753204,
0.01390045415610075,
-0.0312928669154644,
-0.08367793262004852,
-0.021459579467773438,
-0.01846286468207836,
-0.061576999723911285,
-0.02804451249539852,
0.026965251192450523,
-0.00004079730570083484,
0.003057391382753849,
0.032380398362874985,
-0.06517238914966583,
0.016492703929543495,
-0.009485175833106041,
-0.04259650781750679,
-0.05953802913427353,
0.10448689013719559,
-0.0442388691008091,
-0.06331238150596619,
-0.048036713153123856,
0.05103089287877083,
-0.04425628483295441,
-0.005681407172232866,
0.07485293596982956,
0.05801260471343994,
0.0031741573475301266,
0.03312622383236885,
0.003591058077290654,
-0.014248853549361229,
-0.07133599370718002,
-0.010897469706833363,
-0.023968109861016273,
-0.00837504118680954,
-0.037665996700525284,
0.027720361948013306,
-0.01946692354977131,
-0.0553106963634491,
0.01890823245048523,
0.02680603228509426,
0.06087441369891167,
0.02104400284588337,
0.015220340341329575,
-0.01892819069325924,
-0.032215047627687454,
0.005579649470746517,
-0.017065158113837242,
-0.033087342977523804,
0.0005651854444295168,
0.012794858776032925,
-0.025300541892647743,
-0.01817171461880207,
-0.036403506994247437,
0.06717663258314133,
0.05192074924707413,
0.03537076339125633,
-0.02465083636343479,
-0.00568052614107728,
-0.0014650261728093028,
-0.006636802572757006,
0.017451418563723564,
0.04287589341402054,
-0.015012655407190323,
-0.039755694568157196,
-0.02970232255756855,
0.014180942438542843,
-0.054325371980667114,
-0.005447284318506718,
0.0022131726145744324,
-0.049297209829092026,
0.007935903035104275,
0.01583855226635933,
-0.021932095289230347,
-0.07307311147451401,
-0.020336806774139404,
0.021171029657125473,
-0.04018072038888931,
0.0030645050574094057,
0.0015937117859721184,
0.02177722565829754,
-0.06084504723548889,
-0.0006521473405882716,
0.02898186445236206,
-0.017436593770980835,
0.012899859808385372,
-0.13287127017974854,
0.06483864784240723,
-0.011540606617927551,
0.02592368982732296,
0.01449317205697298,
0.04535087198019028,
0.003350114682689309,
0.05498407781124115,
0.0316295325756073,
0.013021205551922321,
0.058931589126586914,
-0.015032644383609295,
0.051283881068229675,
0.027351684868335724,
-0.04167041555047035,
0.024124234914779663,
-0.04919687658548355,
-0.0244149137288332,
-0.029150471091270447,
0.000044533378968480974,
-0.024810858070850372,
0.004474131856113672,
-0.019093375653028488,
0.011225951835513115,
0.00260770320892334,
-0.016203783452510834,
0.04580770060420036
] |
<p>I know there may be missing information, but my question is really simple and yet I haven't found an answer to it. To make things easy, let's assume we have a $40×40×40$ cm oven that we want to keep its temperature at $200$ degrees Celsius using natural gas. How much energy per second is consumed to achieve this?</p> | g6605 | [
0.059209421277046204,
0.034295178949832916,
0.035851459950208664,
0.0478171706199646,
-0.06676128506660461,
-0.1051853746175766,
0.016286058351397514,
0.06241915002465248,
-0.07580402493476868,
0.017218466848134995,
-0.02768127992749214,
0.03237996622920036,
-0.021829793229699135,
0.023408856242895126,
0.013414724729955196,
0.001742515480145812,
0.005199011880904436,
-0.0017402124358341098,
0.08141680806875229,
0.0844925045967102,
-0.04440900310873985,
-0.07348020374774933,
0.0073357135988771915,
-0.04775280877947807,
-0.04920065775513649,
-0.017532039433717728,
0.000453010608907789,
0.010382069274783134,
-0.053569450974464417,
-0.004383379593491554,
-0.04200301319360733,
0.05148419737815857,
-0.01091942097991705,
-0.029928656294941902,
-0.07164088636636734,
-0.04102204740047455,
0.018819715827703476,
-0.011139943264424801,
0.01122993417084217,
-0.05303319916129112,
-0.010275091044604778,
0.017153840512037277,
0.00937908235937357,
0.019470371305942535,
0.03197271376848221,
0.05834859609603882,
0.021872172132134438,
-0.01809602417051792,
-0.012700927443802357,
-0.039493121206760406,
-0.028700053691864014,
0.006777903530746698,
0.013664080761373043,
-0.04045729339122772,
-0.02171829529106617,
-0.049223393201828,
-0.03091379813849926,
0.00034603587118908763,
0.04160212352871895,
0.036646269261837006,
0.021420614793896675,
-0.06344577670097351,
0.0046867444179952145,
-0.009533530101180077,
-0.012106760405004025,
-0.012268696911633015,
-0.027056047692894936,
0.007486357353627682,
0.06990517675876617,
0.04425537958741188,
-0.015801098197698593,
0.014780848287045956,
-0.04038352519273758,
-0.04871482402086258,
-0.018876710906624794,
-0.039444196969270706,
-0.001834746217355132,
-0.059167325496673584,
-0.012518215924501419,
0.0410614013671875,
-0.044458650052547455,
-0.03090856224298477,
-0.0015219127526506782,
0.00004589470336213708,
-0.03879324719309807,
-0.03775008022785187,
-0.005143657326698303,
0.027111709117889404,
-0.05928456410765648,
0.03937169909477234,
0.026638830080628395,
-0.008813493885099888,
0.10273509472608566,
0.0006714132032357156,
0.0481254868209362,
-0.014803478494286537,
-0.03970740735530853,
0.038335464894771576,
0.033387817442417145,
0.016425257548689842,
-0.005441186483949423,
-0.07520386576652527,
0.01618519425392151,
-0.05230465903878212,
-0.025388451293110847,
0.013707765378057957,
0.005609100218862295,
0.03136322647333145,
-0.042010944336652756,
0.0040514711290597916,
0.05409583821892738,
-0.03980129584670067,
-0.027862543240189552,
-0.008176296018064022,
-0.04992412030696869,
-0.018464986234903336,
0.04044842720031738,
0.0054931845515966415,
0.042066790163517,
0.03766932711005211,
0.014420670457184315,
0.07326903939247131,
-0.03980035334825516,
-0.0051725166849792,
-0.07783831655979156,
-0.008759663440287113,
-0.01607818715274334,
0.007604639977216721,
0.027838008478283882,
0.007911862805485725,
-0.06749401241540909,
0.013985793106257915,
-0.0025426747743040323,
0.018718816339969635,
0.025945967063307762,
0.01585577428340912,
-0.03769368678331375,
0.017013689503073692,
-0.027311231940984726,
-0.0032989669125527143,
-0.0034692473709583282,
0.013162483461201191,
0.041225917637348175,
-0.00438607856631279,
-0.027874285355210304,
0.037213560193777084,
-0.05287997052073479,
0.017613576725125313,
0.028293069452047348,
0.04172559827566147,
0.02146647684276104,
0.0010747136548161507,
0.049169350415468216,
-0.040029529482126236,
0.03608112409710884,
-0.03025958500802517,
-0.0198355745524168,
0.00741425110027194,
0.06093287840485573,
0.025656230747699738,
0.06683844327926636,
-0.0057374839670956135,
0.08390530943870544,
-0.014462697319686413,
-0.08885503560304642,
0.005759594962000847,
0.046691350638866425,
-0.018987298011779785,
0.01647961512207985,
-0.021981414407491684,
-0.043157223612070084,
-0.019421033561229706,
-0.028663484379649162,
0.0523395836353302,
-0.0553162656724453,
-0.00019287019676994532,
0.052471358329057693,
0.01572471484541893,
-0.01634455844759941,
0.0094304159283638,
-0.007938835769891739,
0.006276222411543131,
0.04729920253157616,
-0.025637054815888405,
-0.022376857697963715,
0.06910078227519989,
0.00991285964846611,
-0.028754843398928642,
-0.00901731476187706,
0.0025389669463038445,
0.01617581583559513,
0.026529598981142044,
0.003974508959800005,
-0.004368146415799856,
0.0017055569915100932,
0.025236403569579124,
0.01608501933515072,
-0.043197229504585266,
-0.052374888211488724,
-0.013110579922795296,
0.03511356934905052,
-0.023677105084061623,
0.0315638929605484,
0.02348487079143524,
0.022740574553608894,
0.023083357140421867,
-0.002825346775352955,
0.021383047103881836,
-0.013788683339953423,
-0.002309145638719201,
-0.012523307465016842,
0.03916407749056816,
0.002243981696665287,
0.0339631512761116,
0.07697849720716476,
0.03583335503935814,
-0.01799282431602478,
0.0008024142007343471,
-0.0067813280038535595,
0.0035536305513232946,
0.003937416709959507,
0.02187373675405979,
0.05468707159161568,
-0.010716846212744713,
-0.014701338484883308,
-0.07987701147794724,
-0.0018890087958425283,
-0.026435839012265205,
0.004227183759212494,
0.047140732407569885,
-0.01826033554971218,
0.029257597401738167,
-0.0020488854497671127,
-0.04721451178193092,
0.024564020335674286,
0.059430867433547974,
-0.01647949032485485,
0.05187731981277466,
0.009160343557596207,
0.0022733095102012157,
0.00993767473846674,
-0.019955338910222054,
0.019968288019299507,
0.05930592119693756,
-0.03378794342279434,
0.004985671956092119,
0.050937097519636154,
-0.024355625733733177,
-0.0016373669495806098,
-0.008860998786985874,
-0.00839765090495348,
-0.009697029367089272,
-0.032235972583293915,
0.013344533741474152,
-0.009986142627894878,
-0.010341983288526535,
-0.05813088268041611,
0.025868171826004982,
-0.005203541833907366,
-0.047984134405851364,
-0.015232987701892853,
-0.07471243292093277,
0.04932243004441261,
0.0016512596048414707,
0.04961393028497696,
-0.07856181263923645,
-0.017377464100718498,
-0.047668155282735825,
0.016587087884545326,
0.019055569544434547,
0.014507070183753967,
0.033450379967689514,
-0.030883368104696274,
0.018459588289260864,
0.001448635826818645,
-0.04358045384287834,
0.07730220258235931,
-0.04429280012845993,
0.04475756362080574,
0.00323595036752522,
0.017042217776179314,
-0.03577422350645065,
-0.06588934361934662,
0.0633450448513031,
0.0011428478173911572,
-0.0598301887512207,
-0.015949366614222527,
0.04795752838253975,
0.0044408636167645454,
-0.039258867502212524,
-0.020140355452895164,
0.027504919096827507,
-0.02730976603925228,
-0.008380657061934471,
-0.024248814210295677,
0.014021444134414196,
0.032029978930950165,
0.00505567342042923,
0.013310843147337437,
-0.03579743206501007,
0.017344743013381958,
-0.04776079207658768,
-0.04615702107548714,
0.045360267162323,
-0.07548671215772629,
-0.04267910495400429,
-0.10942032188177109,
-0.027135441079735756,
0.026569344103336334,
-0.04829736426472664,
-0.010547380894422531,
0.020994270220398903,
-0.04377548396587372,
0.05783933401107788,
-0.06532919406890869,
-0.05248195677995682,
-0.01638394221663475,
0.0075441147200763226,
0.037368010729551315,
-0.0046943058259785175,
-0.015975918620824814,
-0.05670461803674698,
0.021769804880023003,
-0.0116758793592453,
0.005088698118925095,
0.010747895576059818,
-0.012413379736244678,
-0.06187780573964119,
0.016541318967938423,
-0.03295298293232918,
-0.006080468650907278,
0.011571980081498623,
-0.07371022552251816,
-0.016044018790125847,
0.02497924119234085,
0.00008028766751522198,
0.013371954672038555,
-0.04759091138839722,
-0.011972058564424515,
0.06929154694080353,
-0.022552939131855965,
-0.024686286225914955,
-0.01637825183570385,
-0.011233128607273102,
0.0607064813375473,
-0.0026795112062245607,
-0.009861938655376434,
-0.022276876494288445,
-0.032566189765930176,
0.0003031066444236785,
0.07139961421489716,
-0.05885816738009453,
0.016655322164297104,
-0.026841972023248672,
-0.035345304757356644,
0.02321431040763855,
-0.0075529166497290134,
0.016968047246336937,
-0.045069269835948944,
0.004351125098764896,
-0.007475307211279869,
-0.0008845214615575969,
0.015168432146310806,
0.05768159031867981,
-0.014718363992869854,
-0.025120358914136887,
-0.05990974232554436,
0.005763978231698275,
0.017538513988256454,
0.01209384948015213,
-0.048039618879556656,
0.004473020322620869,
-0.0344427190721035,
0.009149108082056046,
0.06160682439804077,
0.04421072453260422,
0.03343009203672409,
0.025127409026026726,
0.010174108669161797,
0.04517760127782822,
-0.01661352440714836,
-0.015110941603779793,
-0.008220570161938667,
0.0007686577155254781,
-0.05889936536550522,
-0.019344979897141457,
-0.030779559165239334,
0.04577483981847763,
0.044536102563142776,
-0.06701789051294327,
-0.01674736477434635,
-0.043040383607149124,
-0.01284193154424429,
0.0023050156887620687,
0.01895315945148468,
-0.055834975093603134,
0.029181160032749176,
-0.044445816427469254,
-0.03955543041229248,
0.027897482737898827,
0.03713380545377731,
0.014705303125083447,
0.02499285154044628,
-0.048614926636219025,
-0.014747136272490025,
0.026608383283019066,
0.059984371066093445,
-0.015641113743185997,
-0.005212981719523668,
0.009089005179703236,
-0.008783726021647453,
0.03213951364159584,
-0.010498096235096455,
0.001036701025441289,
0.0885281190276146,
-0.05465276166796684,
-0.02159341238439083,
0.015576799400150776,
0.04717309772968292,
-0.03202507272362709,
-0.07953453063964844,
0.006545874290168285,
-0.027586570009589195,
-0.02927066572010517,
0.046553321182727814,
0.04733803868293762,
0.004154026508331299,
0.01668601669371128,
-0.006526466459035873,
-0.030068431049585342,
0.03412104770541191,
-0.016941262409090996,
-0.04305678978562355,
0.031462956219911575,
0.027974141761660576,
0.008996181190013885,
0.016653090715408325,
-0.014119970612227917,
0.05537520721554756,
0.0493563637137413,
0.006262620911002159,
-0.0026334149297326803,
0.06832264363765717,
0.0010089449351653457,
-0.012280136346817017,
-0.02192838490009308,
-0.017190642654895782,
-0.01035297755151987,
-0.009459618479013443,
-0.048296090215444565,
0.04778427258133888,
0.012906934134662151,
-0.024876927956938744,
-0.01640729047358036,
-0.02298020012676716,
0.0235732551664114,
0.030411621555685997,
0.008377437479794025,
0.03714818134903908,
0.08043024688959122,
-0.05803976580500603,
-0.005663057789206505,
0.029585883021354675,
0.0438440702855587,
-0.007787496317178011,
0.009791096672415733,
0.02984916791319847,
-0.003881375305354595,
-0.0015805780421942472,
0.02581796422600746,
0.026798082515597343,
-0.0179470032453537,
-0.004002880305051804,
0.04168161377310753,
0.015466051176190376,
-0.006427186541259289,
0.021216876804828644,
-0.0023406047839671373,
0.06427530199289322,
0.007585405837744474,
-0.04045531898736954,
0.009078078903257847,
0.034753113985061646,
0.03786584734916687,
0.03637560084462166,
-0.05511687695980072,
-0.06082337349653244,
-0.038613464683294296,
0.04771285504102707,
-0.011336488649249077,
-0.06119733676314354,
0.0549476332962513,
0.019162574782967567,
-0.004596341866999865,
0.008432439528405666,
0.007183136884123087,
0.0684126764535904,
-0.03995063900947571,
0.010613134130835533,
-0.004086293280124664,
-0.012139925733208656,
0.027425581589341164,
-0.04395824298262596,
-0.025947364047169685,
-0.023413656279444695,
0.03880327567458153,
0.036153364926576614,
0.04021010175347328,
-0.02786029689013958,
0.04466650262475014,
0.028772486373782158,
0.03784748911857605,
0.020888425409793854,
-0.08365172147750854,
0.022305235266685486,
-0.07036847621202469,
-0.019411703571677208,
-0.03025582805275917,
-0.03384160250425339,
0.01066386979073286,
0.04234463348984718,
-0.020540712401270866,
0.04136347770690918,
-0.01410937961190939,
0.002386491745710373,
0.008933180943131447,
-0.09606465697288513,
0.016558606177568436,
0.036399632692337036,
0.04058818146586418,
0.03691132739186287,
-0.009447859600186348,
-0.03304753452539444,
-0.04678383469581604,
-0.020261511206626892,
0.022622019052505493,
0.028581926599144936,
-0.01571822166442871,
0.03837896138429642,
-0.0010478933108970523,
-0.029169756919145584,
0.05341508612036705,
0.04877791926264763,
0.036486346274614334,
0.017448710277676582,
-0.053871139883995056,
0.013135092332959175,
0.02290262095630169,
0.008181481622159481,
0.013338335789740086,
0.003966260701417923,
-0.005357763729989529,
0.08029905706644058,
-0.0310857854783535,
0.09143298119306564,
0.03965381905436516,
0.06539556384086609,
0.010663146153092384,
0.03392237424850464,
-0.03818940743803978,
0.015886716544628143,
-0.010674804449081421,
0.06309287995100021,
0.037683382630348206,
0.04002128913998604,
-0.052462976425886154,
-0.033846378326416016,
-0.01798485778272152,
0.011904665268957615,
0.06999986618757248,
0.07986272871494293,
-0.04069457948207855,
-0.008015655912458897,
-0.0352686382830143,
0.02019503526389599,
0.023997632786631584,
-0.04889310523867607,
-0.021412866190075874,
-0.026584699749946594,
-0.0407903715968132,
0.02603830210864544,
-0.05601571500301361,
-0.002470294013619423,
-0.011716167442500591,
0.057475022971630096,
0.06578592211008072,
0.01841365359723568,
0.03126552328467369,
-0.03946324437856674,
-0.0007485253736376762,
0.04142485186457634,
-0.03465856611728668,
-0.012817424722015858,
0.007335174363106489,
0.03697590157389641,
-0.073379747569561,
-0.058213405311107635,
-0.03053409978747368,
-0.0331149585545063,
0.04119085147976875,
0.009146401658654213,
0.019736336544156075,
-0.024487469345331192,
-0.047432154417037964,
0.014725014567375183,
0.044351883232593536,
0.011209866032004356,
0.04481370374560356,
-0.007616123184561729,
-0.027164673432707787,
-0.0670870989561081,
0.011140049435198307,
0.08440171927213669,
-0.017314918339252472,
0.01384002435952425,
-0.020187310874462128,
-0.006830309517681599,
0.018223613500595093,
0.059728194028139114,
0.028528187423944473,
0.008985460735857487,
-0.03487318381667137,
0.024148616939783096,
-0.0019303119042888284,
0.07011348009109497,
0.005420409142971039,
-0.01974717155098915,
0.07361611723899841,
0.07574857026338577,
-0.047744881361722946,
-0.01510477066040039,
0.01646706834435463,
-0.01958320289850235,
0.008361672051250935,
0.02077510394155979,
0.0032638171687722206,
-0.09507138282060623,
-0.022117430344223976,
-0.02913064695894718,
0.04013962298631668,
-0.0062935734167695045,
-0.017487898468971252,
0.008484240621328354,
0.03450969234108925,
-0.028669744729995728,
0.016556669026613235,
-0.005663228686898947,
-0.049211740493774414,
0.010144339874386787,
-0.003360435599461198,
-0.05932796373963356,
-0.037494707852602005,
-0.04565806686878204,
0.010594232939183712,
-0.031188450753688812,
0.0005006772698834538,
-0.00903510581701994,
0.018190795555710793,
0.015491139143705368,
-0.03585164621472359,
0.022287802770733833,
-0.05646837130188942,
0.02562817744910717,
0.018291154876351357,
0.04147431626915932,
-0.002937434706836939,
0.001125793787650764,
-0.0017105662263929844,
0.03235899657011032,
-0.07878565043210983,
-0.03870663419365883,
-0.04205808788537979,
-0.06810116767883301,
-0.029104918241500854,
-0.049257371574640274,
-0.024071913212537766,
-0.003964140545576811,
-0.012327614240348339,
0.043252427130937576,
-0.02159428410232067,
0.034787617623806,
-0.029670853167772293,
-0.007529648020863533,
-0.009374317713081837,
0.027362830936908722,
0.006534605752676725,
0.005847204010933638,
0.025532489642500877,
0.017706476151943207,
-0.0033832727931439877,
-0.0031364543829113245,
0.007260843180119991,
0.053225427865982056,
0.007694551721215248,
-0.023441316559910774,
0.05157218500971794,
0.011867170222103596,
-0.054637305438518524,
0.0281123835593462,
-0.0288857314735651,
0.005412171594798565,
0.04017484188079834,
0.010049332864582539,
0.024461112916469574,
0.01742679253220558,
0.03764285892248154,
0.00615757517516613,
-0.04769006371498108,
-0.03506851568818092,
0.02637016773223877,
0.0020983335562050343,
-0.004835141357034445,
0.04964005574584007,
0.027266765013337135,
0.09394184499979019,
0.015331241302192211,
-0.054083481431007385,
-0.021747000515460968,
0.03057565540075302,
0.03197188675403595,
0.003549374407157302,
-0.005140580236911774,
-0.0033683963119983673,
0.033244937658309937,
-0.03918670862913132,
-0.0013482521753758192,
-0.023068420588970184,
-0.05670269578695297,
0.03379940986633301,
-0.022939305752515793,
0.015513928607106209,
0.07909494638442993,
-0.00996033102273941,
0.02745911478996277,
0.03173890337347984,
-0.0053481487557291985,
0.03385695815086365,
0.020382845774292946,
0.028027087450027466,
0.029609236866235733,
0.012891083024442196,
0.022546421736478806,
-0.0007530333823524415,
-0.024166004732251167,
0.012981105595827103,
-0.03411015495657921,
-0.06561361253261566,
0.02268698439002037,
0.051442742347717285,
0.018892910331487656,
0.005314364563673735,
-0.10790091753005981,
-0.023462461307644844,
-0.04166402295231819,
-0.011956221424043179,
-0.05230621621012688,
-0.007823257707059383,
0.014471200294792652,
-0.04892311990261078,
0.0034586333204060793,
-0.014580314978957176,
0.039792269468307495,
-0.001018369453959167,
-0.051894400268793106,
0.019514046609401703,
-0.06671443581581116,
0.010646023787558079,
-0.05480226129293442
] |
<p>Imagine two laser beams A and B are released at the same moment to bounce between two mirrors, A was moving and B was at rest, doing the calculations I found that for a person at rest B would reach the upper mirror before A because in his frame of reference A travels less distance. but for another person in the same reference frame of A, A would reach the upper mirror first.
Is that OK in relativity!<img src="http://i.stack.imgur.com/MJn2B.jpg" alt="the upper is moving and the lower is constant"></p> | g6606 | [
0.02181377075612545,
-0.008677463047206402,
0.010266163386404514,
0.008814582601189613,
-0.03161649778485298,
0.056360673159360886,
0.0572727806866169,
0.042063698172569275,
-0.031769949942827225,
-0.013141375035047531,
0.008496562018990517,
0.028236132115125656,
0.004069095943123102,
-0.04608527198433876,
0.018477313220500946,
-0.0020821592770516872,
0.09428688883781433,
-0.04494059830904007,
-0.002780314302071929,
0.01534752082079649,
-0.047847457230091095,
0.020766397938132286,
-0.03239988908171654,
-0.043135955929756165,
-0.005175401922315359,
-0.0007985663251020014,
0.01693662814795971,
0.00024163037596736103,
-0.059140533208847046,
-0.01137241069227457,
0.05678736791014671,
-0.0076811243779957294,
0.010683608241379261,
-0.09360738843679428,
0.006623584311455488,
-0.04431542754173279,
0.023976357653737068,
0.03172128275036812,
-0.005398005712777376,
0.005874555092304945,
0.05628166347742081,
0.019414477050304413,
-0.02649555169045925,
-0.018750272691249847,
0.06498976796865463,
0.01293919701129198,
0.037682775408029556,
-0.02350383624434471,
-0.012641623616218567,
-0.005550159141421318,
-0.029512567445635796,
0.06696081161499023,
-0.034643229097127914,
0.0008103158324956894,
0.06689818203449249,
0.026310663670301437,
-0.021854950115084648,
-0.02547963336110115,
0.04681461676955223,
0.0070455786772072315,
0.03682207316160202,
-0.04385102167725563,
0.006385899614542723,
0.0016405335627496243,
0.06448892503976822,
0.06065867468714714,
-0.06670117378234863,
-0.0169768538326025,
0.015658175572752953,
-0.0566207692027092,
-0.019998058676719666,
-0.01562649942934513,
-0.058626700192689896,
-0.0024704081006348133,
-0.06472308188676834,
0.023825570940971375,
0.059484656900167465,
-0.03162846714258194,
-0.034812986850738525,
0.03529461845755577,
-0.0841890275478363,
-0.012647448107600212,
0.05453457683324814,
0.03790152072906494,
0.06072789803147316,
0.01727883704006672,
-0.0326572060585022,
0.08927204459905624,
-0.00423812959343195,
0.0020354371517896652,
0.030738554894924164,
-0.015123634599149227,
0.10305193811655045,
0.06057514250278473,
-0.0548861064016819,
-0.003904887707903981,
-0.04227079823613167,
0.021425681188702583,
0.02905256114900112,
0.008397894911468029,
-0.08796728402376175,
0.03366962820291519,
0.0040648328140378,
0.03393486142158508,
0.021264348179101944,
-0.04308755695819855,
0.024419832974672318,
0.0015441963914781809,
-0.08145095407962799,
-0.03481573611497879,
-0.03202517703175545,
-0.07491826266050339,
-0.0029035680927336216,
0.014193789102137089,
-0.07714670896530151,
-0.03762780874967575,
0.11020828038454056,
-0.0251707024872303,
-0.019042519852519035,
-0.012095537036657333,
0.04154841974377632,
-0.021930351853370667,
-0.006706383544951677,
0.07767355442047119,
-0.026233762502670288,
0.02382637932896614,
-0.025019539520144463,
-0.01982863061130047,
0.027916481718420982,
0.04290411248803139,
-0.033738717436790466,
0.030914895236492157,
0.031183885410428047,
0.040424227714538574,
-0.01132199540734291,
0.0031211739405989647,
0.059808600693941116,
-0.03906262293457985,
0.00476166233420372,
0.0236856359988451,
0.03359511122107506,
0.0009437004919163883,
0.005120088346302509,
-0.0724022164940834,
-0.048002663999795914,
0.03181567043066025,
-0.021121375262737274,
0.015194736421108246,
0.02754397504031658,
0.06264420598745346,
0.0010934940073639154,
0.05675709620118141,
-0.022710446268320084,
-0.018673000857234,
0.025506772100925446,
-0.031247559934854507,
0.045235734432935715,
0.008326769806444645,
0.007393528241664171,
0.020977579057216644,
0.06973934173583984,
-0.03489615023136139,
-0.004258485045284033,
-0.028955936431884766,
-0.05235305801033974,
0.025213435292243958,
0.018670588731765747,
-0.05800776183605194,
0.021163206547498703,
-0.027332210913300514,
-0.053965695202350616,
-0.028944173827767372,
-0.00772760808467865,
-0.00403461791574955,
0.04791627824306488,
0.04442866891622543,
0.015517991967499256,
-0.029176894575357437,
-0.013897234573960304,
0.024214863777160645,
-0.03879847377538681,
-0.045555438846349716,
-0.027755631133913994,
-0.017744187265634537,
-0.00724882772192359,
-0.004262432921677828,
-0.020969456061720848,
-0.04212607815861702,
-0.06896759569644928,
0.008034461177885532,
-0.013837695121765137,
-0.04213897883892059,
-0.01323208399116993,
-0.006295326631516218,
-0.06760820001363754,
-0.0052808611653745174,
0.046618878841400146,
0.018997399136424065,
-0.06159811466932297,
0.08922872692346573,
-0.02625151164829731,
0.031252436339855194,
0.017240559682250023,
-0.014102970249950886,
-0.0020459219813346863,
0.08143656700849533,
0.021188639104366302,
0.0099727101624012,
-0.013925782404839993,
-0.025619378313422203,
-0.019158296287059784,
0.003318697912618518,
0.04737954959273338,
0.006572169717401266,
0.031685326248407364,
0.0036211805418133736,
-0.008393018506467342,
-0.0010689902119338512,
-0.04433337226510048,
0.056450121104717255,
-0.014001172967255116,
0.029407726600766182,
0.03290557116270065,
-0.03894232586026192,
0.027349138632416725,
-0.037597931921482086,
-0.041695691645145416,
-0.024074725806713104,
-0.0027310028672218323,
0.016975514590740204,
-0.02772659622132778,
0.040307383984327316,
-0.015522447414696217,
-0.004456300754100084,
0.05127904564142227,
-0.002687969012185931,
0.03553406894207001,
0.03993964567780495,
0.0373397022485733,
0.046665262430906296,
0.023569392040371895,
-0.01371785718947649,
-0.01577373407781124,
0.02083343267440796,
-0.00404736353084445,
0.0004972800379619002,
-0.007849584333598614,
-0.02300775609910488,
-0.02172231115400791,
0.0028700544498860836,
0.019508980214595795,
-0.03874699026346207,
-0.0552491657435894,
-0.05234554409980774,
-0.04360080882906914,
-0.0060917893424630165,
-0.023768866434693336,
0.0003739234816748649,
-0.08312732726335526,
-0.0662693977355957,
0.019817613065242767,
-0.048212628811597824,
0.024496670812368393,
-0.05690820887684822,
-0.05844806134700775,
-0.004807634279131889,
0.007494771853089333,
0.029542645439505577,
-0.007074529770761728,
-0.019949723035097122,
0.00031591817969456315,
0.08429691195487976,
0.032135237008333206,
0.02136888913810253,
-0.023983687162399292,
-0.005751236341893673,
-0.0005929329781793058,
-0.05002012848854065,
-0.032008297741413116,
0.024001803249120712,
-0.0631147250533104,
0.05697039142251015,
-0.03270244598388672,
-0.035522401332855225,
0.036567170172929764,
-0.04493067041039467,
-0.0012459747958928347,
0.005537078250199556,
0.00008047866867855191,
0.020995646715164185,
-0.029357297345995903,
0.06463959068059921,
0.05578826740384102,
0.05172181501984596,
0.013363848440349102,
0.06826107949018478,
0.051253341138362885,
-0.033616360276937485,
-0.024853244423866272,
0.04568498954176903,
-0.024338489398360252,
-0.06572453677654266,
0.023243200033903122,
-0.030773937702178955,
-0.0018482718151062727,
-0.026660006493330002,
-0.02314477041363716,
-0.0134429344907403,
0.01347238291054964,
0.019008830189704895,
-0.0023306410294026136,
0.06912443041801453,
0.019519580528140068,
-0.00156108767259866,
-0.04222794622182846,
-0.010608496144413948,
0.018486132845282555,
-0.013674207963049412,
0.002570793265476823,
0.031471364200115204,
-0.010100431740283966,
0.0001350604579783976,
-0.057182494550943375,
-0.039541926234960556,
0.03846578672528267,
0.05048849433660507,
-0.009100127033889294,
0.02037808857858181,
-0.031756553798913956,
0.018666859716176987,
0.01160957757383585,
0.017057884484529495,
0.007801587227731943,
-0.010131323710083961,
0.024861352518200874,
-0.013946618884801865,
-0.03627253696322441,
0.01283384207636118,
0.03761261701583862,
0.015117506496608257,
0.0059297229163348675,
0.047599032521247864,
-0.03275572136044502,
0.00004106889900867827,
0.05450383946299553,
0.03232625871896744,
0.01025003008544445,
0.015726033598184586,
-0.030839018523693085,
-0.011377966962754726,
-0.026845457032322884,
-0.04041716083884239,
-0.003005107631906867,
-0.007133759092539549,
-0.04836229979991913,
0.026353731751441956,
0.01681435853242874,
0.042989056557416916,
-0.021159933879971504,
-0.011242100968956947,
0.008393977768719196,
-0.0003220939834136516,
0.01391385868191719,
0.015579549595713615,
-0.02071012556552887,
-0.04718790948390961,
-0.06019578129053116,
0.03297628462314606,
0.02152865380048752,
0.028366198763251305,
0.011497152037918568,
-0.06198754534125328,
-0.01525974553078413,
-0.05798831954598427,
0.034994833171367645,
-0.005476226564496756,
0.13211797177791595,
-0.021626237779855728,
-0.054047755897045135,
0.025469768792390823,
0.031560949981212616,
0.03559829294681549,
0.012459473684430122,
0.01710169017314911,
0.026089468970894814,
0.030744250863790512,
-0.01891861855983734,
-0.03549103066325188,
0.01990010216832161,
-0.03758814558386803,
0.02817225456237793,
-0.02570437639951706,
-0.0016040815971791744,
-0.00475357286632061,
0.04118887335062027,
0.04798172041773796,
0.032180044800043106,
0.01809646002948284,
0.016992200165987015,
-0.016965487971901894,
0.010192397981882095,
0.051256000995635986,
-0.039064373821020126,
-0.006159854121506214,
-0.06860390305519104,
0.009422571398317814,
0.04629474878311157,
0.03579239919781685,
0.014626824297010899,
0.03557272255420685,
-0.045887358486652374,
0.013333845883607864,
-0.01790424808859825,
-0.05862122029066086,
0.03522650524973869,
0.03819194808602333,
-0.004506939090788364,
-0.013983878307044506,
0.007711810525506735,
0.04914885014295578,
0.012218410149216652,
0.0982360690832138,
0.10249657928943634,
0.003021474229171872,
0.04583907872438431,
0.06821015477180481,
0.04724908992648125,
-0.017702346667647362,
0.009594699367880821,
-0.049264561384916306,
0.031598906964063644,
0.075993113219738,
-0.0028463981579989195,
0.028015462681651115,
-0.041525937616825104,
0.04372454062104225,
0.03574681282043457,
0.015363838523626328,
0.023637782782316208,
0.038726553320884705,
0.037439629435539246,
-0.000958409917075187,
0.00613064831122756,
-0.026465006172657013,
-0.033386632800102234,
0.07297930121421814,
-0.04498552531003952,
-0.09606672823429108,
0.02704962156713009,
-0.06610442698001862,
-0.041987452656030655,
0.01982741244137287,
-0.011678939685225487,
-0.01052871160209179,
-0.01903260499238968,
-0.03237897902727127,
0.013359606266021729,
0.025421304628252983,
0.019969578832387924,
0.004102564416825771,
0.019455373287200928,
0.03953434154391289,
0.006690225098282099,
-0.06368689239025116,
0.026872633025050163,
-0.025307556614279747,
-0.035455748438835144,
-0.0374341756105423,
-0.0668628066778183,
0.027970116585493088,
0.01749078929424286,
0.019310705363750458,
-0.008037066087126732,
0.033897899091243744,
-0.02301030047237873,
0.007428184151649475,
0.03010513074696064,
0.01229016575962305,
0.010929289273917675,
-0.005845107138156891,
-0.03258273005485535,
0.021640300750732422,
0.05023902654647827,
-0.027058951556682587,
0.0041935327462852,
0.009299558587372303,
-0.005818681791424751,
-0.017713692039251328,
0.02872968278825283,
-0.01602618396282196,
-0.00783506128937006,
-0.049164384603500366,
-0.00699643837288022,
-0.00008050046017160639,
-0.028000418096780777,
0.04959503933787346,
-0.035464655607938766,
-0.029112068936228752,
-0.03197639063000679,
-0.00292701437138021,
-0.03983859345316887,
0.06225060671567917,
0.02903597429394722,
-0.03629697114229202,
-0.03551485389471054,
0.023602981120347977,
-0.005712601821869612,
0.014748930931091309,
-0.027466610074043274,
0.018186673521995544,
0.021325064823031425,
0.015574071556329727,
-0.03152632713317871,
0.03512578830122948,
-0.0033917019609361887,
-0.02822236716747284,
0.06396639347076416,
0.032488737255334854,
-0.010524788871407509,
-0.0109639847651124,
0.037762172520160675,
0.0292124692350626,
0.016395023092627525,
-0.00023246217460837215,
-0.03925412520766258,
0.023894188925623894,
-0.012063666246831417,
0.015078126452863216,
-0.037878602743148804,
0.03438907489180565,
0.0007116292254067957,
-0.024772511795163155,
0.03061600774526596,
-0.02214929834008217,
0.04478670284152031,
-0.027541089802980423,
-0.017094384878873825,
-0.008497706614434719,
0.011701938696205616,
-0.03867417946457863,
-0.0614040270447731,
0.004530836828052998,
0.019686024636030197,
0.07462510466575623,
0.01797659508883953,
-0.04117465391755104,
-0.030742254108190536,
-0.017327578738331795,
0.09724417328834534,
-0.04505627229809761,
-0.007976007647812366,
0.03581830486655235,
-0.00586207490414381,
0.052682001143693924,
-0.007446323521435261,
0.04546009749174118,
0.0070517477579414845,
0.005035187117755413,
0.01941385306417942,
0.008110066875815392,
0.03058476373553276,
-0.01675543002784252,
0.04796670004725456,
-0.02272510714828968,
-0.028857555240392685,
-0.06157904490828514,
-0.006726976018399,
0.02260322868824005,
0.02185213565826416,
-0.01396831963211298,
0.014349906705319881,
-0.007588260807096958,
-0.05294567719101906,
0.020710261538624763,
0.00015184222138486803,
0.06536366045475006,
-0.07778856158256531,
-0.04154336452484131,
-0.05273077264428139,
0.02644972689449787,
-0.007920010946691036,
-0.016531219705939293,
0.004315667320042849,
-0.003993540536612272,
-0.04335765913128853,
0.01601855456829071,
-0.031283967196941376,
-0.023378072306513786,
0.01715892367064953,
-0.048301033675670624,
-0.06339164078235626,
-0.05207895115017891,
0.0029650740325450897,
-0.011520870961248875,
-0.05020708218216896,
-0.023522265255451202,
0.002908297348767519,
-0.013274493627250195,
-0.07406437397003174,
0.07851310074329376,
0.025232970714569092,
0.002079193713143468,
0.08077608048915863,
0.025883866474032402,
-0.0502021498978138,
0.04817942529916763,
-0.042724449187517166,
0.003009106032550335,
0.038167569786310196,
0.035718657076358795,
0.03929750621318817,
0.012055566534399986,
0.03379032015800476,
0.036248691380023956,
-0.028678376227617264,
-0.0024509464856237173,
-0.038609277456998825,
0.007858618162572384,
-0.020632479339838028,
0.0020114537328481674,
0.014340749010443687,
-0.06412648409605026,
-0.009585625492036343,
-0.03269054368138313,
0.004146462306380272,
0.015029476024210453,
-0.04356955364346504,
0.009953970089554787,
-0.0001170045870821923,
0.059642475098371506,
-0.0022262255661189556,
-0.043679606169462204,
-0.03647830709815025,
0.046372219920158386,
0.018914910033345222,
0.036587778478860855,
-0.08933326601982117,
0.04543044790625572,
0.006441000383347273,
-0.0020160486456006765,
0.018185235559940338,
-0.005710096098482609,
-0.007545731030404568,
0.03411238268017769,
-0.011274583637714386,
-0.01454856712371111,
0.04285532608628273,
-0.005935228429734707,
-0.08257271349430084,
0.031585801392793655,
-0.007493044249713421,
-0.03766849264502525,
-0.02124159224331379,
0.021535776555538177,
-0.0601051039993763,
-0.0073528410866856575,
-0.012847136706113815,
0.019054211676120758,
-0.023997295647859573,
-0.0411018431186676,
0.010205594822764397,
-0.005246298853307962,
-0.015988340601325035,
0.0182502381503582,
-0.06381908059120178,
-0.042172063142061234,
-0.00987941212952137,
-0.034556325525045395,
0.0037729383911937475,
-0.01959831267595291,
0.003024202771484852,
-0.04073294624686241,
-0.05357404053211212,
0.002069717040285468,
-0.019856998696923256,
0.04895295575261116,
-0.028100397437810898,
-0.03888050466775894,
-0.016412392258644104,
-0.013801670633256435,
-0.006742184050381184,
-0.005672668572515249,
0.01600521057844162,
-0.00019454544235486537,
-0.08705968409776688,
0.09542074799537659,
0.005742858164012432,
-0.034003984183073044,
0.019580073654651642,
-0.04895922541618347,
-0.049665145576000214,
0.02379167079925537,
0.010288376361131668,
-0.03241026774048805,
-0.03321180120110512,
0.018174609169363976,
0.03931330516934395,
0.03311935067176819,
0.0055965520441532135,
-0.04227786138653755,
-0.039140485227108,
0.005873819347470999,
0.03478474169969559,
0.03218284621834755,
-0.01353976409882307,
0.0481937974691391,
-0.00869505200535059,
-0.020362919196486473,
0.02242967113852501,
-0.040680892765522,
0.02545098587870598,
0.05314791947603226,
0.024103200063109398,
0.03174711391329765,
-0.042271532118320465,
-0.00990668497979641,
0.009622614830732346,
0.019641317427158356,
0.017842058092355728,
-0.021537788212299347,
0.017480874434113503,
0.003612843342125416,
-0.004871048498898745,
-0.08180078119039536,
-0.04199718311429024,
0.01460601482540369,
0.016172412782907486,
-0.03451170399785042,
-0.06528837978839874,
-0.036065977066755295,
0.0011269082315266132,
0.0011176187545061111,
-0.08812418580055237,
0.03853735327720642,
0.008471977896988392,
0.06209815666079521,
-0.03894931450486183,
-0.02193104662001133,
-0.005780258681625128,
0.016585569828748703,
-0.013184159062802792,
-0.06037730351090431,
0.024584053084254265,
-0.020405901595950127,
0.005198670085519552,
-0.004729005973786116,
0.043102141469717026,
0.01844559796154499,
0.0018542094621807337,
-0.03197738528251648,
-0.03386147320270538,
0.045675624161958694,
-0.006592568475753069,
0.048784397542476654,
0.10663634538650513,
-0.03922325000166893,
-0.007330814376473427,
-0.015523852780461311,
0.0090021388605237,
0.004471734166145325,
-0.03446412831544876,
-0.009717978537082672,
-0.000782203336711973,
-0.012912895530462265,
-0.00673486664891243,
-0.0050708153285086155,
-0.026739465072751045,
0.016896696761250496
] |
<p>The <a href="http://en.wikipedia.org/wiki/Vis-viva_equation" rel="nofollow">proof</a> of the vis-viva equation of orbital mechanics found on wikipedia looks, in my opinion, somewhat convoluted and unenlightening. Considering the simplicity and importance of the vis-viva equation, is there a shorter or more insightful derivation?</p>
<p>The vis-viva equation states that for a Kepler orbit of a mass around a central mass $M$, the magnitude of the velocity at any distance $r$ from the center obeys $v^2 = GM(\frac{2}{r}-\frac{1}{a})$, where $a$ is the semi-major axis of the orbit.
It is equivalent to saying that the energy of a Kepler orbit with semi-major axis $a$ is $-\frac{GM}{2a}$.
This is a very natural generalization of the 'circular' case where the total energy is $-\frac{GM}{2r}$.</p>
<p>Because of the simplicity of the result, I guessed that there could be a relatively straightforward derivation. The derivation on wikipedia involves quite some algebra and, importantly, only holds for elliptical orbits.</p> | g6607 | [
0.038941722363233566,
0.01838459074497223,
0.002125899773091078,
-0.012153361923992634,
-0.05247882753610611,
-0.019359009340405464,
0.06597879528999329,
0.003965941723436117,
0.011935451067984104,
0.05609515681862831,
0.01275421492755413,
0.03829992935061455,
-0.01738055981695652,
0.011486245319247246,
0.05149572342634201,
-0.06569625437259674,
0.00848233513534069,
-0.0032405778765678406,
0.03571346774697304,
0.09726692736148834,
0.015079930424690247,
-0.037167251110076904,
-0.013032974675297737,
0.0103989839553833,
0.05274723842740059,
0.014804903417825699,
0.012970414943993092,
0.035259731113910675,
-0.012590872123837471,
0.01141798123717308,
0.06292089074850082,
-0.02857433818280697,
0.11102863401174545,
-0.0615924708545208,
0.002062288811430335,
0.09770193696022034,
-0.01769448257982731,
-0.02251076139509678,
-0.009394912049174309,
0.003511040238663554,
-0.033754900097846985,
-0.018037846311926842,
0.006828096229583025,
0.03529111295938492,
0.006721221376210451,
-0.012063327245414257,
-0.03889885172247887,
0.0022804788313806057,
-0.042348939925432205,
-0.028100987896323204,
-0.007868698798120022,
0.05192827060818672,
0.09352105110883713,
0.0036703080404549837,
-0.05624677613377571,
0.030685914680361748,
0.07177563011646271,
-0.04681405797600746,
-0.006399785168468952,
0.06579310446977615,
0.05376110598444939,
-0.020284634083509445,
-0.028473446145653725,
0.01608116552233696,
0.007037770468741655,
-0.02071414329111576,
-0.030800873413681984,
0.04139900580048561,
0.004105474334210157,
0.01835046149790287,
0.026559321209788322,
0.0033821784891188145,
-0.03101866878569126,
-0.042013198137283325,
-0.03589148446917534,
-0.007161060348153114,
0.021084362640976906,
-0.01690840534865856,
0.04579722881317139,
-0.0307757705450058,
0.013947311788797379,
0.011883229948580265,
0.02406240813434124,
0.015209956094622612,
0.08241488039493561,
-0.07185916602611542,
0.026692697778344154,
0.008928202092647552,
-0.030063612386584282,
-0.007448282092809677,
0.013286692090332508,
-0.004660292528569698,
0.06588225811719894,
-0.024263961240649223,
-0.031649742275476456,
-0.038843441754579544,
-0.03102349117398262,
0.053929418325424194,
-0.04223600775003433,
0.026778694242239,
0.022627398371696472,
0.0077025615610182285,
-0.0003494984994176775,
-0.03561234846711159,
0.051532965153455734,
-0.00011645806807791814,
0.0032615435775369406,
0.04424702003598213,
0.01102416217327118,
-0.006637714337557554,
-0.014004289172589779,
-0.07044949382543564,
-0.020141316577792168,
-0.0033614165149629116,
-0.05042567476630211,
-0.03423222154378891,
0.0701456367969513,
-0.030746852979063988,
-0.02689715474843979,
0.03535488247871399,
-0.007536780089139938,
0.044441770762205124,
-0.01382117997854948,
0.09954139590263367,
0.004114989656955004,
0.0017532632919028401,
-0.0008860991219989955,
-0.013651391491293907,
0.008478295989334583,
0.024664251133799553,
0.0068956962786614895,
-0.04406056925654411,
0.024227727204561234,
-0.01194673404097557,
0.029471654444932938,
0.024686340242624283,
-0.05193158984184265,
0.010832034982740879,
-0.07083892077207565,
-0.02369779348373413,
0.01653868518769741,
-0.03922446444630623,
0.013392782770097256,
-0.017756657674908638,
-0.07067467272281647,
0.052744559943675995,
-0.031303439289331436,
0.010149156674742699,
0.09262716770172119,
-0.014541110023856163,
-0.01861872896552086,
0.03640669211745262,
0.026561811566352844,
-0.07723090797662735,
0.008896763436496258,
-0.0377764068543911,
-0.020096305757761,
-0.013047019019722939,
-0.04008681699633598,
0.006745037157088518,
0.055475156754255295,
-0.0018387557938694954,
0.06895485520362854,
-0.02511262707412243,
-0.05244945362210274,
0.061056457459926605,
0.002040153369307518,
-0.046220771968364716,
0.00606138538569212,
-0.018155904486775398,
-0.03251498192548752,
-0.027935707941651344,
0.02902047336101532,
-0.020176032558083534,
-0.07499141991138458,
0.01585419476032257,
0.015108398161828518,
-0.01871166005730629,
-0.008824777789413929,
0.03614140301942825,
0.008222666569054127,
0.024673011153936386,
0.0159753430634737,
-0.05995113030076027,
0.026117147877812386,
-0.00710410438477993,
0.03702264279127121,
0.05272413417696953,
-0.03999455273151398,
0.014483895152807236,
0.01646607741713524,
-0.0325574167072773,
0.04902011528611183,
0.06628492474555969,
-0.011189587414264679,
0.0019031284609809518,
-0.003902818774804473,
-0.0670308917760849,
-0.05118698999285698,
0.04008413851261139,
0.010781274177134037,
-0.03339657187461853,
0.002483821241185069,
0.013682638294994831,
0.031195683404803276,
0.008487657643854618,
-0.012341623194515705,
-0.0009780260734260082,
0.07774030417203903,
-0.007384194992482662,
-0.01044622901827097,
-0.04102049022912979,
-0.0035265563055872917,
0.0157957561314106,
-0.017218492925167084,
-0.017174504697322845,
0.015689721331000328,
0.020882200449705124,
-0.03245476633310318,
0.049128878861665726,
0.02751990593969822,
-0.04782935976982117,
0.00954501610249281,
0.0035617605317384005,
0.007245154585689306,
0.019573047757148743,
-0.03204984962940216,
-0.02094048075377941,
-0.02158728428184986,
0.012248012237250805,
-0.0383327379822731,
-0.012248185463249683,
-0.01575106754899025,
0.0498996339738369,
0.048760510981082916,
0.03167099878191948,
-0.01905633509159088,
0.006364582106471062,
0.029600661247968674,
0.017590876668691635,
0.03557958826422691,
-0.03332773223519325,
-0.010857361368834972,
-0.041553888469934464,
0.03486919030547142,
-0.04309948906302452,
0.0667281225323677,
0.030011940747499466,
0.05123816803097725,
-0.025536291301250458,
-0.03584159165620804,
-0.06416404992341995,
-0.028624841943383217,
-0.03347380831837654,
0.0409267321228981,
-0.009593917988240719,
-0.05006151646375656,
0.03611238673329353,
-0.045617230236530304,
0.02182743325829506,
-0.015383505262434483,
-0.021872112527489662,
0.03300223499536514,
0.04399183765053749,
0.001033422420732677,
-0.0037134855519980192,
-0.0015231679426506162,
-0.008360123261809349,
-0.025167223066091537,
0.012586936354637146,
-0.006501947063952684,
0.07928704470396042,
-0.03442861884832382,
0.03869331628084183,
-0.04764751344919205,
-0.044493094086647034,
-0.03750476986169815,
-0.010963023640215397,
0.033741794526576996,
0.003827219596132636,
-0.03186338022351265,
-0.05040917545557022,
0.0043834904208779335,
0.03652850538492203,
0.030091822147369385,
-0.027680063620209694,
0.006616729777306318,
0.06321161240339279,
0.035625748336315155,
-0.058552149683237076,
0.046841222792863846,
0.04993578791618347,
-0.016311584040522575,
0.0008269732934422791,
-0.02353682555258274,
0.0498349703848362,
0.05313679203391075,
-0.01595275290310383,
0.02642831951379776,
-0.003113617654889822,
-0.014970619231462479,
-0.04220009595155716,
-0.029092110693454742,
0.021746132522821426,
-0.047239091247320175,
0.0219427477568388,
0.03383909538388252,
-0.06213736906647682,
0.01250634528696537,
-0.012148420326411724,
0.03554653003811836,
-0.036973368376493454,
0.005234839394688606,
-0.010038482025265694,
-0.009691230021417141,
0.02207256108522415,
0.007923540659248829,
0.0018291572341695428,
0.01434445008635521,
0.02550429478287697,
-0.08653795719146729,
-0.03076547384262085,
0.0034029283560812473,
0.03517701476812363,
0.03377244248986244,
-0.041571326553821564,
-0.029834548011422157,
-0.03215987607836723,
0.0037230257876217365,
-0.02073250338435173,
0.005915654823184013,
0.02592051401734352,
-0.0398898608982563,
0.021739859133958817,
0.008883452974259853,
-0.03298942744731903,
0.01065059844404459,
0.041103098541498184,
0.028735121712088585,
0.014055422507226467,
-0.007972877472639084,
-0.02480951137840748,
-0.041419535875320435,
0.03949093818664551,
-0.011596303433179855,
-0.0007299222052097321,
-0.05293526127934456,
0.019820231944322586,
0.030390482395887375,
-0.056077174842357635,
0.004012518096715212,
-0.01838037371635437,
0.026253648102283478,
-0.01986350491642952,
-0.03138533979654312,
0.05825736001133919,
0.034594789147377014,
-0.013067618012428284,
0.01989963836967945,
0.023400263860821724,
-0.0005966089083813131,
-0.019130805507302284,
0.008150717243552208,
0.020794162526726723,
0.046989087015390396,
-0.017819538712501526,
-0.03874213621020317,
0.01381071750074625,
-0.0027045549359172583,
-0.04427072033286095,
-0.0175506342202425,
-0.07494231313467026,
0.05847030505537987,
-0.033911097794771194,
0.05405205115675926,
-0.018999453634023666,
0.004236545413732529,
0.03132975846529007,
-0.044520098716020584,
0.0016274044755846262,
0.0767340213060379,
-0.021949054673314095,
0.04513942077755928,
0.07926027476787567,
-0.0035570317413657904,
-0.022355372086167336,
-0.08476186543703079,
0.03432691469788551,
0.06178480014204979,
-0.03473320230841637,
0.0300961434841156,
0.004265843890607357,
0.04372585564851761,
0.0051255603320896626,
0.07380643486976624,
-0.02277541160583496,
0.0024866857565939426,
-0.022002289071679115,
-0.0413626991212368,
0.04195080325007439,
0.02138330414891243,
-0.025595540180802345,
-0.005448548123240471,
0.045578472316265106,
0.006955574732273817,
0.04465648531913757,
-0.011082516983151436,
-0.010566268116235733,
-0.02507052570581436,
-0.02950921095907688,
0.031393058598041534,
-0.022818421944975853,
0.07024948298931122,
-0.016289304941892624,
0.00644313357770443,
0.012005426920950413,
-0.02257402427494526,
-0.020508233457803726,
0.06955858319997787,
0.05885099619626999,
-0.0311701949685812,
0.03425320237874985,
0.023300262168049812,
-0.0542767196893692,
0.016159484162926674,
0.0706627145409584,
0.024160616099834442,
-0.018895134329795837,
0.0035121417604386806,
-0.012296538800001144,
0.02976163662970066,
0.026258694007992744,
0.005478931590914726,
0.05343632027506828,
-0.04612717032432556,
0.033620890229940414,
-0.023578280583024025,
0.051714152097702026,
0.026788709685206413,
-0.03495962172746658,
-0.0028942818753421307,
0.03975344076752663,
-0.006575725506991148,
0.02550734579563141,
-0.05924340337514877,
-0.0044885980896651745,
0.05039669945836067,
-0.023547763004899025,
-0.02817418798804283,
-0.06722278892993927,
-0.032368406653404236,
0.020774440839886665,
0.015673255547881126,
0.013394249603152275,
-0.002067810855805874,
-0.03801378607749939,
-0.03657803684473038,
0.019251251593232155,
0.0037442364264279604,
-0.054399922490119934,
-0.05547710135579109,
-0.023688895627856255,
0.03176001086831093,
0.0541948527097702,
0.14071568846702576,
-0.01519734412431717,
-0.0021940707229077816,
0.025102758780121803,
-0.021351508796215057,
0.005406406242400408,
-0.010438334196805954,
-0.0018307807622477412,
-0.01624380424618721,
-0.04034499078989029,
-0.0024466689210385084,
0.00585966557264328,
-0.003826685016974807,
-0.03585748001933098,
-0.01909921132028103,
-0.04359016194939613,
-0.0447547547519207,
0.03392234817147255,
0.022833827883005142,
0.030218053609132767,
0.035598620772361755,
0.0543987937271595,
-0.033300358802080154,
-0.0207967609167099,
0.002391982590779662,
0.02353236824274063,
0.01653898134827614,
0.008070316165685654,
-0.04255761206150055,
-0.026752127334475517,
0.05910511314868927,
0.005946107674390078,
0.011918219737708569,
-0.06819160282611847,
0.03260422125458717,
-0.018908720463514328,
-0.09325604140758514,
0.03582380712032318,
-0.0407821349799633,
-0.02138606645166874,
-0.026777442544698715,
-0.011903056874871254,
0.0224942397326231,
-0.008495111018419266,
-0.05360369011759758,
0.03008679673075676,
-0.004710859153419733,
-0.07251951843500137,
-0.03850860148668289,
0.02414310723543167,
0.0084266671910882,
-0.036320846527814865,
0.02426835149526596,
0.03503976762294769,
0.03324558958411217,
-0.025996102020144463,
0.04936929792165756,
-0.002378293080255389,
0.04728023335337639,
-0.015411960892379284,
0.019169650971889496,
0.005461095832288265,
-0.03591901436448097,
-0.062185585498809814,
0.007864084094762802,
0.015113088302314281,
-0.056931670755147934,
-0.04862634092569351,
-0.017121993005275726,
-0.004321529064327478,
-0.04561441391706467,
-0.004523854237049818,
-0.05274060368537903,
0.03211776912212372,
0.01837138459086418,
-0.01865626871585846,
0.0019701963756233454,
-0.013350390829145908,
0.001188906840980053,
0.05188847333192825,
-0.03480589762330055,
0.019276177510619164,
-0.0416528657078743,
-0.03462119400501251,
0.04376187548041344,
-0.04957278445363045,
-0.05812806263566017,
-0.01402609795331955,
-0.000927580171264708,
-0.004703938495367765,
-0.005698123015463352,
0.04915544018149376,
-0.01504303514957428,
-0.002480175578966737,
-0.02919439785182476,
-0.012149101123213768,
0.04300890490412712,
-0.02041669376194477,
0.02689875289797783,
0.05914635211229324,
-0.007394320331513882,
-0.03812979534268379,
0.010241426527500153,
-0.03841124475002289,
0.06562665849924088,
0.023399559780955315,
-0.03170783817768097,
0.03442956879734993,
-0.013558450154960155,
-0.001246064086444676,
0.06132505461573601,
0.022152990102767944,
0.02193806692957878,
-0.0735754519701004,
-0.06180880218744278,
-0.025014538317918777,
0.003054517088457942,
-0.060249026864767075,
0.010668731294572353,
0.010637243278324604,
-0.012303918600082397,
0.02786221168935299,
-0.04785570129752159,
-0.009159225970506668,
-0.06337323784828186,
-0.03787213936448097,
0.012094386853277683,
0.006330845411866903,
-0.05793996527791023,
-0.032870400696992874,
0.003971974831074476,
-0.027210725471377373,
0.03024279698729515,
0.010371094569563866,
0.0000644691608613357,
0.032839491963386536,
-0.009798594750463963,
0.009538456797599792,
-0.005577061325311661,
-0.0180986151099205,
0.06174984201788902,
0.003814038820564747,
0.012819555588066578,
-0.004958644974976778,
-0.011035075411200523,
-0.009443053044378757,
-0.0024465618189424276,
0.07915544509887695,
0.03162291273474693,
0.027727989479899406,
0.009633307345211506,
0.021298592910170555,
-0.007437389809638262,
0.0504777655005455,
0.06862016022205353,
-0.012949135154485703,
-0.03102429024875164,
0.008101454004645348,
0.015215489082038403,
0.001450863666832447,
0.050766367465257645,
0.0064869532361626625,
-0.04130478948354721,
0.009602338075637817,
0.09865174442529678,
0.0030468411277979612,
0.017981451004743576,
-0.049493953585624695,
-0.04810504615306854,
0.024542024359107018,
0.054605502635240555,
0.03203359991312027,
-0.06551876664161682,
-0.0009098703158088028,
0.000651579990517348,
-0.0003465477202553302,
-0.029676703736186028,
-0.04606943577528,
0.008731053210794926,
-0.01854865625500679,
-0.04744713753461838,
-0.05298592522740364,
0.006763538345694542,
0.027565883472561836,
-0.04909462109208107,
-0.011897656135261059,
0.031169835478067398,
-0.018042705953121185,
-0.023236893117427826,
-0.0019054566510021687,
-0.03559449687600136,
-0.02957168035209179,
-0.028276152908802032,
-0.023697348311543465,
0.0533595010638237,
-0.03319700434803963,
0.005942516960203648,
0.024201225489377975,
0.0005011619068682194,
-0.008806006982922554,
0.008720087818801403,
0.004025101661682129,
-0.0042771827429533005,
-0.048365313559770584,
0.004419660661369562,
-0.05841078236699104,
0.017401104792952538,
0.017625337466597557,
-0.030526112765073776,
-0.034668974578380585,
-0.056286539882421494,
0.030677318572998047,
-0.020620839670300484,
-0.037543412297964096,
-0.033525314182043076,
0.01768043078482151,
-0.04588638246059418,
-0.005228483583778143,
0.04188057407736778,
0.03389784321188927,
-0.042525362223386765,
-0.012443098239600658,
-0.006574075669050217,
-0.014313901774585247,
-0.008253023028373718,
0.028808269649744034,
-0.0018288283608853817,
0.031760137528181076,
0.054699160158634186,
-0.01616273634135723,
-0.015021908096969128,
0.016723619773983955,
0.029340730980038643,
0.07475216686725616,
0.037736956030130386,
0.007014730013906956,
0.04013520106673241,
-0.006302980240434408,
0.017311355099081993,
0.03269673511385918,
0.05321675166487694,
0.07952257990837097,
0.024175496771931648,
0.011475817300379276,
-0.05386384204030037,
-0.03801373764872551,
0.017171060666441917,
-0.01469434518367052,
-0.011992285959422588,
-0.029088234528899193,
0.008468931540846825,
-0.00897893961519003,
-0.018036969006061554,
0.08273446559906006,
-0.029691198840737343,
-0.021796060726046562,
-0.004884897265583277,
-0.04618826508522034,
0.006617517676204443,
-0.08106596767902374,
0.027923347428441048,
0.017052896320819855,
0.016882581636309624,
-0.10426678508520126,
0.023902274668216705,
-0.08024588227272034,
-0.010331539437174797,
-0.015171335078775883,
-0.013760500587522984,
0.05203478783369064,
-0.039620351046323776,
-0.008915109559893608,
0.009630040265619755,
-0.061035383492708206,
0.01463035587221384,
-0.006267774384468794,
-0.018671128898859024,
-0.11382389068603516,
0.015110911801457405,
-0.04419751092791557,
-0.02444666251540184,
0.023337477818131447,
-0.00814367737621069,
0.024965886026620865,
0.021392781287431717,
-0.062362004071474075,
0.06097016856074333,
-0.002012416487559676,
-0.045569006353616714,
-0.01999186910688877,
0.06847801804542542,
-0.03687548637390137,
-0.003005693666636944,
-0.06401179730892181,
-0.020932737737894058,
0.043393924832344055,
-0.04982161894440651,
-0.0028472135309129953,
0.01575830578804016,
-0.003052885178476572,
0.006861743051558733,
-0.08875461667776108,
-0.01756044290959835,
0.06308021396398544
] |
<p>Lately I'm reading about surface enhanced fluorescence. In many articles I can see that <a href="http://en.wikipedia.org/wiki/Fluorophore" rel="nofollow">fluorophores</a> are called "dipoles". Is it because that they can be modelled by a vibrating electric dipole? Or maybe they are all chemical dipoles?</p> | g6608 | [
0.0037829559296369553,
0.02598509006202221,
-0.007738992106169462,
0.020215744152665138,
0.06331121921539307,
-0.011963516473770142,
0.0008764528320170939,
-0.011904960498213768,
0.014948609285056591,
-0.03508121892809868,
-0.056798774749040604,
-0.03256211057305336,
0.0397040955722332,
-0.019805176183581352,
-0.010645387694239616,
-0.016907919198274612,
0.012018628418445587,
-0.00032082773395814,
0.05356653779745102,
0.010426240973174572,
0.02569308504462242,
-0.004828457720577717,
-0.056632254272699356,
-0.0313890315592289,
-0.04476405680179596,
0.025432292371988297,
-0.029433881863951683,
-0.026064738631248474,
-0.015332072041928768,
-0.039689190685749054,
-0.03629516065120697,
-0.043870456516742706,
0.03179222345352173,
0.04309578984975815,
0.0764356479048729,
-0.05748404562473297,
-0.04305548220872879,
0.04690719023346901,
0.01247324701398611,
0.026573047041893005,
0.03077169694006443,
0.05075247958302498,
0.029482360929250717,
-0.007691843435168266,
-0.00845859944820404,
-0.02659459225833416,
-0.005342901684343815,
-0.03601430356502533,
0.01858619600534439,
0.006989220157265663,
0.031048009172081947,
0.0006537188892252743,
0.010445174761116505,
0.006944046355783939,
0.04009237512946129,
-0.028796859085559845,
0.018453804776072502,
0.0335145927965641,
0.0019529364071786404,
0.040434081107378006,
-0.038246557116508484,
0.07159047573804855,
0.009470995515584946,
0.005471772514283657,
0.029153166338801384,
-0.022205309942364693,
-0.010080913081765175,
-0.09402220696210861,
0.05957767739892006,
-0.024008404463529587,
-0.007964449003338814,
0.04147884622216225,
-0.07592739909887314,
-0.010995902121067047,
-0.007123319432139397,
0.06552191823720932,
-0.03192480280995369,
0.002434111898764968,
0.0214379969984293,
-0.022240279242396355,
-0.018307341262698174,
0.0015784390270709991,
-0.03260029852390289,
-0.007576585281640291,
0.08055420219898224,
0.026120688766241074,
-0.08443485200405121,
0.003042179625481367,
0.02359081618487835,
-0.03396470099687576,
0.01135147362947464,
-0.03270889073610306,
0.04752974584698677,
-0.023680003359913826,
-0.05968688055872917,
-0.020842408761382103,
-0.008776812814176083,
0.041666340082883835,
-0.012783577665686607,
-0.05677146092057228,
-0.06561891734600067,
0.017488732933998108,
0.06753380596637726,
-0.016886724159121513,
0.011320865713059902,
0.011504756286740303,
0.0022124843671917915,
-0.07127002626657486,
0.00911136344075203,
0.034833647310733795,
-0.02782084047794342,
0.016834694892168045,
-0.00796311441808939,
-0.004775636363774538,
0.00970317143946886,
-0.02102907933294773,
0.03689424693584442,
-0.011921346187591553,
-0.006647386122494936,
0.05702348053455353,
0.03342919424176216,
0.03243290260434151,
0.001886174432002008,
0.0003610800486057997,
-0.023515839129686356,
0.04900343343615532,
0.05856892839074135,
0.016236646100878716,
0.02267523668706417,
-0.05074182152748108,
0.02910510264337063,
-0.007203199435025454,
-0.04587126895785332,
0.005435553845018148,
0.06412064284086227,
0.010009423829615116,
0.014084454625844955,
-0.04232362285256386,
-0.018834611400961876,
0.04290667921304703,
0.06193167343735695,
-0.02118007466197014,
0.02192540280520916,
-0.04093077778816223,
-0.0039451839402318,
-0.006787542253732681,
-0.026952018961310387,
0.031164109706878662,
0.0657576248049736,
0.020932065322995186,
-0.013642226345837116,
0.07417027652263641,
0.04315004497766495,
-0.07897309213876724,
-0.012786146253347397,
-0.07334434986114502,
0.03372601047158241,
0.02589436061680317,
0.006360890809446573,
0.017598042264580727,
0.017111701890826225,
-0.027582291513681412,
-0.024286171421408653,
-0.025288211181759834,
-0.05493833124637604,
-0.035565316677093506,
0.03178972005844116,
-0.06747990846633911,
-0.040189243853092194,
-0.015314080752432346,
-0.01492090243846178,
0.031022831797599792,
0.026709437370300293,
0.026434263214468956,
0.02061302401125431,
0.02110270969569683,
-0.04229030758142471,
-0.010835884138941765,
-0.006747619714587927,
0.014399048872292042,
-0.07681164890527725,
0.004522486589848995,
-0.006127760745584965,
0.015798553824424744,
0.020366180688142776,
0.017993902787566185,
-0.03546448051929474,
-0.03847465291619301,
-0.041539981961250305,
0.04167333245277405,
-0.023316092789173126,
-0.010656949132680893,
0.07488391548395157,
-0.02575528435409069,
-0.015843601897358894,
0.002605603775009513,
-0.015425672754645348,
-0.052069466561079025,
0.01222250983119011,
0.0009439805871807039,
0.003921348601579666,
0.003113384358584881,
0.010728511959314346,
-0.018217364326119423,
-0.028834398835897446,
0.011977650225162506,
0.0006812714273110032,
-0.04102350398898125,
0.024300511926412582,
-0.0059322514571249485,
0.033704690635204315,
-0.01899036578834057,
-0.012283234857022762,
0.01834929920732975,
-0.019185282289981842,
-0.02450086735188961,
-0.03383563086390495,
0.0204648207873106,
-0.002087334170937538,
0.008424554951488972,
-0.011307699605822563,
-0.015087448991835117,
0.06170212849974632,
0.05306928977370262,
0.022557292133569717,
0.00601983442902565,
0.011201679706573486,
0.00868633296340704,
0.010848663747310638,
0.060461197048425674,
-0.0458526648581028,
-0.07128388434648514,
0.01024243887513876,
-0.010531594976782799,
0.028373321518301964,
0.017925914376974106,
-0.05298979952931404,
0.02249147929251194,
-0.06703683733940125,
0.006993025541305542,
0.0332980640232563,
-0.028475457802414894,
0.011287009343504906,
0.024480126798152924,
-0.0703425258398056,
-0.004946645349264145,
-0.013076256029307842,
0.016598496586084366,
0.014306719414889812,
0.0441349633038044,
0.07373179495334625,
-0.03535613790154457,
0.021446766331791878,
0.06314847618341446,
-0.00223681447096169,
0.007726711221039295,
-0.011482523754239082,
0.0344175286591053,
-0.004921811632812023,
-0.002518868073821068,
0.0033259261399507523,
0.0010134016629308462,
-0.0011841986561194062,
-0.0010621591936796904,
-0.017648939043283463,
0.017314080148935318,
-0.015685569494962692,
0.01070950273424387,
-0.047251611948013306,
0.03537905588746071,
-0.040298428386449814,
0.03241821005940437,
-0.029520457610487938,
-0.06688033044338226,
0.010633078403770924,
0.0213017575442791,
0.0409446656703949,
0.054733436554670334,
0.04325152933597565,
-0.0070978798903524876,
0.056444041430950165,
0.022258227691054344,
-0.008881612680852413,
-0.02009088546037674,
-0.046255722641944885,
-0.000630101072601974,
0.03620022162795067,
-0.01975305937230587,
-0.047828879207372665,
-0.06356541812419891,
-0.007827318273484707,
-0.04055800661444664,
0.027300212532281876,
-0.03567645698785782,
-0.09055210649967194,
0.009639390744268894,
0.025422725826501846,
-0.01252452377229929,
-0.028473129495978355,
0.1257845014333725,
0.03394605591893196,
0.02314901165664196,
-0.005967267788946629,
0.028248416259884834,
0.00260357279330492,
0.0500992089509964,
-0.001144600915722549,
-0.04035768285393715,
-0.012977082282304764,
0.018994182348251343,
-0.0019066083477810025,
0.06856545060873032,
-0.005248982924968004,
0.06281740218400955,
-0.009780092164874077,
-0.0035869551356881857,
-0.027647262439131737,
-0.020472699776291847,
0.06893914937973022,
-0.010850601829588413,
-0.04239974543452263,
-0.0028277658857405186,
-0.060535166412591934,
-0.00036714482121169567,
0.06012154743075371,
0.002993715228512883,
-0.044345930218696594,
-0.002955222735181451,
-0.034523848444223404,
-0.06962230056524277,
0.056739259511232376,
-0.0069539411924779415,
-0.0811815857887268,
-0.05325606092810631,
0.010131056420505047,
-0.08010400086641312,
-0.057462502270936966,
0.0680830180644989,
0.02872401848435402,
-0.012022227048873901,
0.027837051078677177,
0.005220192484557629,
-0.03284977376461029,
-0.026555834338068962,
-0.04771541804075241,
0.0814656987786293,
-0.035535696893930435,
0.0026412452571094036,
-0.00044095134944655,
-0.05016377195715904,
0.03338487073779106,
0.07843155413866043,
0.020196327939629555,
0.026975423097610474,
-0.011504295282065868,
-0.06982266157865524,
0.0419650599360466,
-0.0323861762881279,
0.0019183249678462744,
-0.02187490090727806,
0.07520180940628052,
0.03854461386799812,
0.022009072825312614,
-0.01734628714621067,
-0.002652037190273404,
-0.0339137464761734,
-0.010029521770775318,
0.05649262294173241,
0.0018702332163229585,
-0.07907173037528992,
-0.02014726772904396,
0.03506524860858917,
-0.03214442729949951,
-0.009770398028194904,
0.013143370859324932,
0.021423855796456337,
-0.010994039475917816,
-0.01784597896039486,
-0.09829778969287872,
-0.017290230840444565,
-0.007612144108861685,
0.0589645579457283,
0.05236022546887398,
0.03210895135998726,
0.009839149191975594,
-0.013228127732872963,
-0.028966130688786507,
0.017744189128279686,
0.010063864290714264,
-0.016889629885554314,
-0.012268801219761372,
0.01255671214312315,
0.03277793899178505,
-0.033450573682785034,
-0.007100328803062439,
-0.06315878033638,
0.026446308940649033,
-0.06662031263113022,
0.025830453261733055,
0.04341943562030792,
0.059821419417858124,
-0.023156525567173958,
0.011860690079629421,
0.0007847115630283952,
0.030196404084563255,
-0.004811235703527927,
-0.0007799836457706988,
-0.03770378977060318,
-0.009451061487197876,
-0.005839311517775059,
-0.06130434572696686,
0.029150325804948807,
0.003634409513324499,
-0.009613689966499805,
-0.0027110627852380276,
0.08355136960744858,
-0.003304488258436322,
-0.06328567117452621,
-0.0367928072810173,
0.02548707090318203,
0.006410600617527962,
0.04479411616921425,
0.019106358289718628,
0.003198920050635934,
0.009853359311819077,
0.002694726223126054,
0.007910773158073425,
0.02492992766201496,
-0.024568965658545494,
-0.08690007030963898,
-0.01824728585779667,
-0.037051789462566376,
0.020208677276968956,
0.0003745074209291488,
-0.04893814027309418,
0.015109796077013016,
-0.030206333845853806,
0.008882974274456501,
0.04807552322745323,
0.08046533167362213,
0.06844130158424377,
0.0074942344799637794,
0.001275204005651176,
0.02804916352033615,
0.034992434084415436,
0.04356915503740311,
-0.02235015295445919,
-0.004256764426827431,
-0.04041149467229843,
0.008771823719143867,
-0.09415490180253983,
0.02234267070889473,
-0.07402694225311279,
-0.022291896864771843,
0.029224781319499016,
-0.03183802589774132,
-0.06341421604156494,
-0.025534290820360184,
-0.009043829515576363,
0.02943282760679722,
-0.015138785354793072,
-0.011029081419110298,
0.015949012711644173,
-0.0561598502099514,
0.02768334560096264,
0.02525273896753788,
-0.0017559746047481894,
-0.06845401227474213,
-0.08124591410160065,
-0.055319320410490036,
-0.050196025520563126,
0.010145191103219986,
0.03127146139740944,
0.027430368587374687,
0.026260625571012497,
-0.029403099790215492,
0.05890382453799248,
-0.001639183727093041,
-0.017540017142891884,
-0.07901574671268463,
0.015194532461464405,
-0.003899817820638418,
0.045296233147382736,
-0.007493554148823023,
0.026994381099939346,
-0.011590249836444855,
0.02856249175965786,
0.03284591808915138,
-0.04383400082588196,
0.0018561023753136396,
-0.00019807732314802706,
-0.02745869569480419,
-0.044264908879995346,
-0.02428758144378662,
-0.031906720250844955,
-0.043425120413303375,
-0.020790789276361465,
0.01356783602386713,
0.02248760312795639,
0.0010891662677749991,
-0.03355376422405243,
0.017241746187210083,
0.033553265035152435,
0.013732727617025375,
0.036685772240161896,
0.04819582775235176,
0.017274007201194763,
-0.07798558473587036,
0.02365703135728836,
0.011679047718644142,
-0.02429514192044735,
-0.041900474578142166,
-0.013357170857489109,
0.040112875401973724,
0.028639961034059525,
-0.017038023099303246,
-0.01816965825855732,
0.06428580731153488,
-0.03642326965928078,
0.010640685446560383,
-0.0015991086838766932,
-0.06872197985649109,
-0.001962082926183939,
-0.028815748170018196,
-0.016877038404345512,
0.00021562115580309182,
-0.01555752195417881,
-0.0003570617700461298,
0.08822029829025269,
0.060817163437604904,
0.032375674694776535,
0.031078524887561798,
0.020663436502218246,
0.06956914067268372,
0.037760015577077866,
-0.03148934990167618,
0.02014303393661976,
0.012225369922816753,
-0.0013366873608902097,
0.0519464910030365,
-0.01716582104563713,
0.025741565972566605,
0.049651145935058594,
0.039554156363010406,
0.03362356498837471,
-0.0005344655364751816,
0.07132332026958466,
-0.0025518008042126894,
0.011844576336443424,
0.015561860054731369,
-0.01543337944895029,
-0.011211633682250977,
0.03542187437415123,
0.020370040088891983,
0.0036167690996080637,
0.0035001998767256737,
0.0015646808315068483,
0.002254984574392438,
0.028054680675268173,
-0.08142866939306259,
-0.005374821834266186,
0.05297021195292473,
0.013184040784835815,
-0.017465734854340553,
0.02161264419555664,
0.021392762660980225,
-0.03261023759841919,
0.006876888684928417,
0.010242351330816746,
0.009356589987874031,
-0.02051462046802044,
-0.01873200573027134,
-0.038203686475753784,
0.02208358235657215,
-0.037143055349588394,
-0.014351685531437397,
0.032498035579919815,
0.008298522792756557,
-0.043347541242837906,
0.04449706897139549,
-0.012983324006199837,
-0.04086383059620857,
-0.012497102841734886,
-0.04883098974823952,
0.005508639384061098,
-0.005535533186048269,
-0.026079855859279633,
-0.008616868406534195,
0.04030106961727142,
-0.028644397854804993,
-0.023098058998584747,
-0.04601171985268593,
-0.04530492424964905,
-0.03263173624873161,
-0.01786007359623909,
-0.0341777466237545,
-0.034329045563936234,
0.03511140123009682,
0.026506397873163223,
0.05426992103457451,
0.0378408282995224,
-0.010456726886332035,
-0.0029403797816485167,
-0.005846838001161814,
0.0772305503487587,
-0.003880404867231846,
0.01143404096364975,
0.03344034403562546,
0.005943709053099155,
-0.044508520513772964,
0.009849381633102894,
0.012376982718706131,
-0.04706040397286415,
-0.07043670117855072,
-0.01960906572639942,
-0.07372285425662994,
-0.06404602527618408,
-0.02526162564754486,
0.00919809378683567,
0.019561534747481346,
-0.0461495965719223,
-0.06200781837105751,
0.03626413270831108,
0.001626819372177124,
-0.014697303995490074,
0.024151982739567757,
-0.0539933405816555,
0.05647161975502968,
0.025437379255890846,
0.010172929614782333,
0.01601131446659565,
0.05479227006435394,
0.01409195177257061,
0.05050121620297432,
0.020832275971770287,
0.02065780572593212,
-0.04910412058234215,
-0.0018547708168625832,
0.04111278057098389,
0.019902890548110008,
-0.04789227992296219,
0.03905809670686722,
0.07285533100366592,
0.05505950376391411,
0.024890845641493797,
0.018114883452653885,
-0.017329847440123558,
-0.009280539117753506,
0.03882382810115814,
0.011411377228796482,
-0.010269710794091225,
-0.0791577398777008,
-0.05864189565181732,
0.0857151597738266,
0.004591172095388174,
0.030217088758945465,
0.028617870062589645,
-0.0021241039503365755,
-0.006632505916059017,
0.04333878308534622,
-0.04459051415324211,
-0.05650896579027176,
0.012187642976641655,
-0.06586775928735733,
0.0491417795419693,
0.060940325260162354,
0.015121720731258392,
-0.011798548512160778,
-0.024000106379389763,
0.02143160253763199,
-0.003970046993345022,
-0.018579084426164627,
0.03176366165280342,
-0.05929349362850189,
-0.017759134992957115,
0.03434505686163902,
-0.024325747042894363,
0.031130574643611908,
0.02689124271273613,
-0.05524720624089241,
-0.005952191539108753,
0.028279148042201996,
0.06695795059204102,
-0.08701980859041214,
-0.057605162262916565,
-0.02095065265893936,
-0.009787227027118206,
0.02098138816654682,
0.0022922521457076073,
-0.04470687359571457,
0.03653504326939583,
-0.003501236904412508,
-0.060387395322322845,
0.02198662795126438,
-0.01758919656276703,
-0.031620681285858154,
-0.00023970774782355875,
0.001199629856273532,
0.03618301823735237,
-0.03792358189821243,
-0.016174903139472008,
-0.0066135902889072895,
-0.008350993506610394,
0.011166197247803211,
-0.009461767971515656,
-0.03111433982849121,
-0.029163595288991928,
-0.014557743445038795,
0.0028609491419047117,
0.0332033596932888,
-0.030636413022875786,
0.05482158809900284,
0.019286727532744408,
0.036967769265174866,
-0.004510136786848307,
0.015361901372671127,
-0.011922172270715237,
0.029165053740143776,
-0.058513712137937546,
-0.013601607643067837,
0.014866742305457592,
0.008109736256301403,
-0.01695656031370163,
0.014336920343339443,
-0.0025659119710326195,
0.042160484939813614,
0.014725559391081333,
0.023413371294736862,
0.04208769649267197,
0.01233291532844305,
-0.017318248748779297,
-0.00006399888661690056,
-0.026160024106502533,
0.04729336500167847,
-0.07680180668830872,
0.04689192399382591,
0.07858417183160782,
0.012950530275702477,
-0.046455852687358856,
0.033353593200445175,
0.02569090574979782,
-0.0565585121512413,
0.04534019157290459,
-0.01283628772944212,
-0.05116413161158562,
-0.008758717216551304,
-0.011103831231594086,
-0.0045568253844976425,
-0.0037110347766429186,
0.06380753219127655,
-0.05821426957845688,
0.014099855907261372,
0.04392939433455467,
0.012252794578671455,
0.03648272529244423,
-0.027405904605984688,
-0.01160606648772955,
0.06571294367313385,
0.04731735959649086,
-0.008942020125687122,
-0.05209203064441681,
0.04850073531270027,
0.028537482023239136,
-0.0015764404088258743,
-0.03664879873394966,
-0.024288905784487724,
-0.025015514343976974,
0.021928761154413223
] |
<p>I saw the following way of derivation of Maxwell equations: author starts from Lorentz transformations for the 3-vector of force, then he applies them for the Coulomb law, after that gets the Lorentz force law with expressions for $\mathbf E $ and for $\mathbf B$ fields, then he takes curl and divergence and, finally, he derives the Maxwell equation for the field of charge moving with constant speed. </p>
<p>After that he uses a few axioms: superposition principle and independence of equations on acceleration, and generalizes equations on all electrodynamical processes.</p>
<p>But I have some doubts about this method. The most problematic question is followIng: there are EM fields of electric and magnetic type. For the first one $\mathbf E^{2} - \mathbf B^{2} > 0$, for the second one - $\mathbf E^{2} - \mathbf B^{2} < 0$. But the author have started from the electric type, so he can't generalize final result on all EM processes. </p>
<p>The question: can we violate this argument against this methot of derivation by introducing some other argument?</p> | g6609 | [
0.06578338891267776,
0.02566925808787346,
-0.007657061330974102,
0.028762424364686012,
0.09093473106622696,
0.02829000912606716,
0.09306734055280685,
0.002412329660728574,
-0.014346102252602577,
0.03227051720023155,
-0.018437154591083527,
-0.01167666632682085,
-0.007936883717775345,
0.024675505235791206,
-0.030839456245303154,
-0.05840473994612694,
0.06294789165258408,
-0.04967629909515381,
0.008120379410684109,
0.031734514981508255,
0.010684658773243427,
0.04736777022480965,
-0.018263233825564384,
-0.055500905960798264,
0.002790718572214246,
-0.04812713339924812,
0.058570269495248795,
-0.05668342486023903,
-0.021668419241905212,
-0.06956863403320312,
-0.006175206042826176,
0.01773579977452755,
0.039132010191679,
-0.06731420010328293,
0.0014256596332415938,
-0.04355385899543762,
0.042122598737478256,
0.0018208222463726997,
0.005367593374103308,
0.027275357395410538,
0.030552491545677185,
-0.012652777135372162,
0.04310234263539314,
0.005827305372804403,
0.015901442617177963,
-0.03161832317709923,
-0.022345175966620445,
-0.0006422497099265456,
-0.05819873511791229,
-0.014533178880810738,
0.0064178393222391605,
0.008268141187727451,
0.06421488523483276,
-0.06045851856470108,
-0.03235138580203056,
0.029888756573200226,
0.03557325154542923,
-0.035107892006635666,
0.008737755008041859,
0.008860676549375057,
-0.04427552968263626,
-0.06384968757629395,
0.053859103471040726,
0.03398386389017105,
0.022220440208911896,
0.000964659615419805,
-0.030656585469841957,
0.0031702578999102116,
0.00388951413333416,
0.02094622328877449,
0.022257447242736816,
-0.057651422917842865,
0.012150092981755733,
-0.018552593886852264,
-0.04525759443640709,
-0.018472595140337944,
0.024967696517705917,
-0.01682935282588005,
0.011266140267252922,
-0.009895090945065022,
-0.03703703358769417,
0.04109107330441475,
0.016051707789301872,
0.0026451179292052984,
0.05903451889753342,
0.008004896342754364,
0.022951442748308182,
0.0181158185005188,
0.03371764346957207,
-0.02224547415971756,
-0.019847499206662178,
-0.031058190390467644,
0.046698134392499924,
0.040684085339307785,
-0.03698917105793953,
-0.011908648535609245,
0.004810050129890442,
0.05635027959942818,
0.02189844287931919,
-0.060117222368717194,
-0.031077271327376366,
0.013506042771041393,
-0.011853931471705437,
0.010470916517078876,
0.009767758660018444,
-0.02785332500934601,
-0.025164572522044182,
0.04296015575528145,
0.01697925291955471,
-0.00806920975446701,
-0.04635144770145416,
-0.022720862179994583,
-0.03731311112642288,
0.014217649586498737,
-0.04578321799635887,
-0.026818780228495598,
-0.0046620131470263,
0.015168868936598301,
-0.015971792861819267,
0.05294742435216904,
0.04785711690783501,
-0.001574288704432547,
-0.0009581746417097747,
0.022708507254719734,
-0.03834937512874603,
-0.03052610717713833,
-0.05829374119639397,
-0.0007810810930095613,
0.019698815420269966,
-0.034884706139564514,
0.024477027356624603,
-0.012559640221297741,
0.09070250391960144,
0.009663610719144344,
-0.02192578837275505,
0.042739201337099075,
-0.01906372234225273,
-0.000059354453696869314,
-0.032859865576028824,
-0.04346933215856552,
0.04397391900420189,
-0.059491727501153946,
0.04643696919083595,
-0.02898879162967205,
-0.04277702793478966,
0.04716629907488823,
-0.012387748807668686,
-0.013281640596687794,
0.055762674659490585,
0.07289983332157135,
-0.009828498587012291,
0.06638812273740768,
-0.006272472906857729,
0.01166943833231926,
0.05134843662381172,
0.02365889959037304,
0.012295417487621307,
-0.012189664877951145,
-0.011338970623910427,
0.0395001657307148,
0.04966358467936516,
-0.05305495858192444,
0.029446916654706,
0.03759089857339859,
0.006797286681830883,
0.013948985375463963,
-0.016582775861024857,
-0.02140691876411438,
-0.024426233023405075,
-0.06313659250736237,
-0.03806259110569954,
0.0059395139105618,
0.026005884632468224,
-0.007603244855999947,
-0.0015820334665477276,
0.01774597354233265,
-0.013791289180517197,
-0.05602962151169777,
-0.04018392413854599,
-0.025564629584550858,
-0.09747034311294556,
0.0035840924829244614,
0.0273554939776659,
-0.0013528808485716581,
0.013536026701331139,
0.0003038315335288644,
-0.02816300094127655,
0.05376961827278137,
-0.03369831293821335,
-0.003753348020836711,
-0.012509340420365334,
0.03175538033246994,
-0.048632796853780746,
0.048879917711019516,
-0.03840499371290207,
0.041285548359155655,
0.014974556863307953,
-0.0223374180495739,
0.02441023662686348,
0.0330190509557724,
0.011467553675174713,
0.10731226205825806,
0.015572297386825085,
-0.0114158159121871,
0.016450949013233185,
-0.003899983363226056,
-0.028829505667090416,
-0.018412215635180473,
0.01787259429693222,
0.010289479047060013,
0.05973992124199867,
-0.0007841480546630919,
-0.0324694998562336,
0.0019216669024899602,
-0.010233079083263874,
-0.048081912100315094,
-0.011532352305948734,
0.009127872064709663,
-0.05682693421840668,
0.029759811237454414,
-0.09852287173271179,
-0.04847671836614609,
0.02748231776058674,
0.013587282970547676,
-0.04621446505188942,
-0.008801286108791828,
-0.0012293189065530896,
-0.03725928068161011,
0.0022680971305817366,
-0.014251119457185268,
-0.05519138276576996,
0.004447458311915398,
-0.027942828834056854,
-0.05200740322470665,
0.07516756653785706,
0.01815262995660305,
-0.00198067887686193,
0.014265051111578941,
0.03722050413489342,
0.046925682574510574,
0.03412641957402229,
0.0043509602546691895,
0.07861807942390442,
-0.04690191522240639,
-0.005199220031499863,
-0.07716897875070572,
0.10695294290781021,
-0.018111862242221832,
0.021902715787291527,
-0.03776697814464569,
0.01760018616914749,
-0.05165902525186539,
0.01719268597662449,
0.016838911920785904,
0.011618208140134811,
-0.02910124510526657,
-0.007226251065731049,
0.06229514256119728,
-0.002502841642126441,
0.03138403594493866,
0.002459739102050662,
0.025393323972821236,
0.024566615000367165,
0.0709308460354805,
-0.06506925821304321,
0.0034890100359916687,
-0.052426788955926895,
0.02038564719259739,
0.005889125168323517,
-0.0014945943839848042,
-0.09442585706710815,
0.041281357407569885,
-0.056023284792900085,
0.030481845140457153,
-0.02301529049873352,
-0.03347494825720787,
0.01003951020538807,
-0.05197976902127266,
0.06436195969581604,
0.007538718171417713,
-0.044118449091911316,
-0.05156440660357475,
0.009885400533676147,
0.013661563396453857,
0.02984495833516121,
-0.02415987104177475,
-0.04817494750022888,
-0.04800627380609512,
-0.023917343467473984,
0.006690491922199726,
-0.02421249821782112,
-0.017939060926437378,
0.03805918246507645,
-0.04690372571349144,
-0.03399128466844559,
0.03154267370700836,
-0.009448178112506866,
-0.10889871418476105,
-0.02404208667576313,
0.0013883166247978806,
0.02008768543601036,
-0.0011472278274595737,
0.013563660904765129,
0.007908089086413383,
0.07957777380943298,
0.053478192538022995,
-0.05410115048289299,
-0.05297352373600006,
0.059248458594083786,
-0.010552183724939823,
-0.022154588252305984,
0.004883396439254284,
0.02540968917310238,
0.030742255970835686,
-0.009800786152482033,
0.0061531332321465015,
0.031392309814691544,
-0.03637039661407471,
0.072353295981884,
0.0159431342035532,
-0.08653577417135239,
-0.06311659514904022,
0.030946392565965652,
-0.02085341140627861,
0.04050496593117714,
0.018604233860969543,
-0.01321800984442234,
0.01170816645026207,
-0.003598095616325736,
0.014890365302562714,
0.002732943743467331,
0.03420078381896019,
0.019573908299207687,
0.016292760148644447,
-0.00537201389670372,
-0.003943572286516428,
-0.006844197865575552,
0.058595407754182816,
0.014334974810481071,
-0.05651050806045532,
0.019700465723872185,
-0.06382544338703156,
-0.0854506641626358,
0.017747962847352028,
-0.037458695471286774,
0.015265116468071938,
-0.013561531901359558,
-0.03553237393498421,
0.0407799556851387,
-0.008254249580204487,
0.0043633971363306046,
-0.03481560945510864,
0.03148884326219559,
0.04447543993592262,
-0.05257623642683029,
-0.007893561385571957,
0.016059085726737976,
0.02440846897661686,
0.010843043215572834,
0.02975825034081936,
0.023310178890824318,
0.00030116495327092707,
0.015574432909488678,
0.010357819497585297,
-0.01258711889386177,
0.012693505734205246,
-0.018669046461582184,
0.08007942140102386,
-0.038328371942043304,
-0.03872879222035408,
-0.00041546791908331215,
-0.07069722563028336,
0.014652034267783165,
-0.017338931560516357,
0.026300717145204544,
-0.03485662490129471,
0.03847602754831314,
0.06371860206127167,
-0.04550093412399292,
0.016411390155553818,
0.061650510877370834,
0.0692148432135582,
0.006218515336513519,
0.06324826925992966,
0.007864166051149368,
0.04965660721063614,
-0.0012965155765414238,
0.056177109479904175,
-0.0021622919011861086,
-0.009524557739496231,
0.0461614690721035,
0.015316636301577091,
-0.006255395710468292,
0.010760693810880184,
-0.01386096142232418,
-0.039321206510066986,
-0.0020727580413222313,
-0.030195027589797974,
0.03188897296786308,
0.005311230663210154,
-0.004548683762550354,
-0.017704375088214874,
0.013761185109615326,
0.02503732219338417,
-0.062048085033893585,
0.001537369447760284,
0.04127361252903938,
-0.0404423289000988,
0.06670556217432022,
-0.0025549631100147963,
0.0058798762038350105,
-0.03836950659751892,
0.030204912647604942,
-0.015765614807605743,
0.04672093689441681,
-0.021293433383107185,
0.016464963555336,
-0.003221869235858321,
-0.01711087115108967,
-0.010314743965864182,
0.05542914569377899,
0.010301749221980572,
0.022030241787433624,
-0.05301368236541748,
-0.0010716901160776615,
0.07590167969465256,
0.07652120292186737,
-0.005667827557772398,
-0.006504126358777285,
0.005021215416491032,
-0.016321102157235146,
0.007646727841347456,
-0.0193523857742548,
0.03226056322455406,
-0.07070281356573105,
-0.0024673868902027607,
-0.03689867630600929,
0.07175905257463455,
0.024106575176119804,
0.07553043961524963,
0.08626776933670044,
0.02759900875389576,
0.06136222183704376,
-0.024780580773949623,
0.025752555578947067,
0.05892443656921387,
-0.025056077167391777,
-0.04067884385585785,
0.017345139756798744,
-0.021108495071530342,
-0.016482386738061905,
0.050552014261484146,
-0.0379374660551548,
0.045828063040971756,
-0.02884983830153942,
0.012414788827300072,
-0.008150167763233185,
-0.009160812012851238,
0.006909539923071861,
0.043661799281835556,
-0.008816559799015522,
0.0043883901089429855,
0.00622308487072587,
0.025129634886980057,
0.09834016859531403,
0.028949270024895668,
-0.05896003916859627,
-0.0016003455966711044,
-0.05476745590567589,
-0.020643597468733788,
0.03407352417707443,
0.01075640320777893,
-0.009206347167491913,
-0.05135282501578331,
-0.0019065720262005925,
0.0034829177893698215,
-0.033138908445835114,
0.013858258724212646,
-0.09261003136634827,
0.010824328288435936,
-0.03303772583603859,
-0.07003985345363617,
0.013862746767699718,
-0.02006097137928009,
-0.027935396879911423,
0.038388196378946304,
0.0005693744751624763,
0.03386745601892471,
-0.03533228114247322,
-0.014527147635817528,
-0.003965475130826235,
0.03350352123379707,
0.004339015576988459,
-0.02538718283176422,
-0.00909479707479477,
0.05966542288661003,
0.015040485188364983,
-0.029485667124390602,
-0.03382714092731476,
-0.0029949983581900597,
-0.10388492792844772,
-0.019862988963723183,
-0.045838866382837296,
0.009898648597300053,
0.01131818164139986,
0.04054221510887146,
0.05670096352696419,
0.056263457983732224,
-0.03706977143883705,
-0.05081090331077576,
0.002450618427246809,
0.006275632884353399,
0.010349711403250694,
-0.002885964000597596,
0.01087295450270176,
0.01322902087122202,
-0.010927332565188408,
0.03166749328374863,
0.029003361240029335,
-0.03986078128218651,
0.05498230829834938,
0.0408845990896225,
0.08299039304256439,
-0.06681141257286072,
-0.02176698110997677,
0.05374325066804886,
-0.05085618048906326,
-0.010386602021753788,
0.023332536220550537,
0.0016335169784724712,
-0.02731216512620449,
0.0017733739223331213,
0.03336680680513382,
-0.02006634511053562,
0.026923982426524162,
-0.08577365428209305,
0.040517598390579224,
-0.01859891414642334,
-0.02315337583422661,
-0.02748228795826435,
-0.012820987030863762,
-0.05399693548679352,
0.03114205040037632,
0.016386447474360466,
-0.0660722553730011,
0.04249919205904007,
-0.023863699287176132,
0.016987107694149017,
0.07370488345623016,
-0.05958028882741928,
-0.017942242324352264,
-0.018255403265357018,
-0.003253050846979022,
-0.014438939280807972,
-0.03614862263202667,
0.04550745710730553,
-0.06533470004796982,
-0.010687929578125477,
-0.059339702129364014,
0.03252626210451126,
-0.002714683534577489,
-0.018697578459978104,
0.005429047625511885,
0.00008685448119649664,
-0.0026050719898194075,
-0.0379481241106987,
0.023157978430390358,
0.026233503594994545,
0.000424140045652166,
0.053704604506492615,
0.002877064049243927,
0.0628482848405838,
-0.0494573600590229,
-0.010094101540744305,
-0.00341258873231709,
-0.0344185009598732,
0.04773755371570587,
-0.022641899064183235,
-0.05898614600300789,
0.020611876621842384,
0.015967179089784622,
0.0037665609270334244,
0.00890699028968811,
-0.03451749309897423,
-0.026471199467778206,
0.01741277426481247,
-0.05604223534464836,
0.024117309600114822,
0.03862135112285614,
-0.05258050188422203,
0.004493046551942825,
-0.021893931552767754,
0.008300550282001495,
-0.01871470734477043,
-0.004304622765630484,
-0.02516491338610649,
0.018589792773127556,
-0.03810317441821098,
0.0429220050573349,
0.03999445587396622,
0.034924764186143875,
-0.028494013473391533,
-0.026509754359722137,
-0.04838201776146889,
0.04255043715238571,
-0.006803740747272968,
-0.08831335604190826,
0.01146148145198822,
0.007641342934221029,
-0.055790603160858154,
-0.02183975651860237,
-0.039495281875133514,
-0.08093520253896713,
-0.021817756816744804,
0.025387724861502647,
0.021944595500826836,
-0.041637249290943146,
0.011042223311960697,
0.0275247935205698,
-0.004980898462235928,
0.026552913710474968,
-0.008105813525617123,
0.008728892542421818,
0.04348638281226158,
-0.009954048320651054,
0.05959620699286461,
-0.010437344200909138,
0.06031026318669319,
0.04314342141151428,
0.0049279797822237015,
0.03333515301346779,
-0.031104251742362976,
-0.04026976600289345,
0.013277550227940083,
-0.008997485041618347,
0.03113933652639389,
0.06209208443760872,
0.011428502388298512,
-0.014577111229300499,
0.03446006402373314,
-0.05050325766205788,
0.03593607619404793,
0.06481865793466568,
-0.011249922215938568,
-0.027516160160303116,
-0.006147540174424648,
0.019387871026992798,
0.01629207655787468,
-0.06484688073396683,
0.009912657551467419,
-0.014853991568088531,
-0.024004902690649033,
-0.02176414430141449,
0.01958882436156273,
-0.009005631320178509,
0.014518597163259983,
-0.008536339737474918,
0.02076127752661705,
-0.021292397752404213,
-0.04974355921149254,
0.004013076424598694,
-0.03689737617969513,
-0.001591086620464921,
-0.026744533330202103,
0.006008998490869999,
0.008354372344911098,
-0.0031070506665855646,
-0.04362349957227707,
0.03212275728583336,
0.019029635936021805,
-0.017324818298220634,
-0.06374572962522507,
0.02254888415336609,
0.028342776000499725,
-0.021856164559721947,
-0.04018622636795044,
-0.004421355668455362,
0.035185981541872025,
-0.05268532410264015,
-0.01598006673157215,
-0.06996830552816391,
0.03642994910478592,
0.0002498731773812324,
0.002338172635063529,
-0.03333055227994919,
0.022008933126926422,
-0.008589562959969044,
-0.0018333435291424394,
0.02041301690042019,
-0.029350196942687035,
-0.002180010313168168,
-0.009845065884292126,
0.048755452036857605,
0.005277167074382305,
-0.02691689506173134,
0.006408801767975092,
0.0012999196769669652,
0.03217595815658569,
0.022745084017515182,
0.02508586458861828,
0.002732098801061511,
-0.018088066950440407,
-0.037568382918834686,
0.017127342522144318,
-0.029690749943256378,
0.045934047549963,
-0.04194331169128418,
-0.007237471640110016,
-0.005976868327707052,
-0.009097515605390072,
0.011757195927202702,
0.0033731884323060513,
-0.011112557724118233,
0.024803612381219864,
0.03935302421450615,
0.04875267669558525,
0.009649613872170448,
0.026716364547610283,
-0.0015766556607559323,
0.010837625712156296,
0.0013556344201788306,
0.03486457094550133,
-0.010423450730741024,
-0.07526114583015442,
0.03497225046157837,
-0.017610201612114906,
-0.02637820690870285,
-0.011714351363480091,
-0.04885885864496231,
-0.043491192162036896,
-0.0009485912160016596,
-0.033087458461523056,
-0.026150235906243324,
0.04452734440565109,
0.004996117204427719,
0.0027859786059707403,
0.0035607663448899984,
-0.035318102687597275,
0.03227610141038895,
-0.03603774681687355,
0.012586602941155434,
-0.019656239077448845,
-0.034417107701301575,
-0.01671876199543476,
-0.018319912254810333,
0.007185665424913168,
-0.037232182919979095,
0.01636648178100586,
-0.02221163734793663,
0.005806352011859417,
0.010186363942921162,
0.02646167390048504,
-0.06661535799503326,
0.06302600353956223,
0.030665889382362366,
-0.04975108429789543,
-0.0021766212303191423,
-0.012333803810179234,
0.08137957006692886,
0.08206816017627716,
-0.0226135291159153,
-0.03996846079826355,
0.03746366500854492,
-0.030448371544480324,
-0.017328305169939995,
-0.029889089986681938,
-0.012987017631530762,
0.0599968321621418
] |
<p>I am studying the Fujikawa method of determining the chiral anomalies in a $U(1)$ theory. As we know the basis vectors selected are the eigenstates of the Dirac operator. One of the reasons given is that the eigenstates diagonalize the action which is needed for determining an exact quantity such as Ward-Takahashi identities. Anyone care to explain? I am referring to <em>Path Integrals and Quantum Anomalies</em> by Kazuo Fujikawa and Hiroshi Suzuki.</p> | g6610 | [
0.033072322607040405,
0.021744657307863235,
0.00612630695104599,
0.02247125282883644,
0.05636140704154968,
0.0028397648129612207,
0.0820031389594078,
0.05183812230825424,
0.012046800926327705,
-0.022517014294862747,
-0.04837975651025772,
-0.058777108788490295,
0.024110134690999985,
0.04471646994352341,
-0.008722378872334957,
-0.005554711911827326,
-0.022476742044091225,
0.011448940262198448,
0.03031260333955288,
-0.045286960899829865,
-0.029743917286396027,
0.029239753261208534,
0.01705755479633808,
-0.00863805040717125,
0.09884883463382721,
-0.05968816950917244,
0.0395282581448555,
0.025763479992747307,
-0.044052500277757645,
-0.0038600610569119453,
0.004482980351895094,
0.0033895389642566442,
0.055233169347047806,
0.003942975774407387,
-0.05608152225613594,
0.00028965031378902495,
0.10444309562444687,
0.03734423592686653,
0.03243027999997139,
-0.02450699731707573,
0.005553933791816235,
-0.043586112558841705,
-0.01515783742070198,
-0.030621515586972237,
-0.03117149882018566,
-0.035931166261434555,
-0.013126647099852562,
-0.005409160163253546,
-0.008183041587471962,
0.0645100325345993,
-0.017347924411296844,
0.013602503575384617,
0.05700157955288887,
-0.023325296118855476,
-0.019336538389325142,
0.05393156036734581,
0.0008302730857394636,
-0.03856699913740158,
0.04483411833643913,
0.039689790457487106,
0.016588112339377403,
-0.02677149698138237,
0.07295885682106018,
-0.011823456734418869,
0.06053142249584198,
-0.029617086052894592,
-0.009053892455995083,
0.005048895254731178,
-0.05939405411481857,
-0.04202335327863693,
-0.03175509721040726,
-0.027247674763202667,
0.023274576291441917,
-0.003750333795323968,
0.027268266305327415,
-0.018548445776104927,
0.012381378561258316,
0.014230819419026375,
0.003412374760955572,
-0.021957198157906532,
-0.030801156535744667,
-0.08752410113811493,
0.04305705055594444,
-0.003007770050317049,
0.04790636524558067,
0.023326287046074867,
0.04563622921705246,
0.0075262379832565784,
0.01623496599495411,
-0.00290321814827621,
-0.05068443343043327,
0.002578690880909562,
0.02323741279542446,
0.0012950693489983678,
-0.020435987040400505,
0.00316240475513041,
-0.029526207596063614,
0.05249142646789551,
0.024532390758395195,
-0.004751675296574831,
-0.01857445389032364,
0.0661652684211731,
-0.005788583308458328,
-0.017311442643404007,
-0.033467039465904236,
-0.012436940334737301,
0.011634941212832928,
-0.018035316839814186,
0.03865437209606171,
0.027423450723290443,
-0.03166113793849945,
0.027347536757588387,
-0.028193561360239983,
-0.004215691238641739,
0.011102097108960152,
0.036044515669345856,
0.04510580003261566,
-0.025080019608139992,
-0.020607778802514076,
0.018006568774580956,
0.02029256522655487,
0.027384450659155846,
-0.015268501825630665,
0.013261290267109871,
0.053060226142406464,
0.03459735959768295,
-0.02861965075135231,
0.042373403906822205,
0.0027279367204755545,
0.00016718407277949154,
0.05827545374631882,
0.011860298924148083,
0.02923678047955036,
0.06227923184633255,
0.022382713854312897,
-0.05350635573267937,
0.04885571822524071,
0.09275735169649124,
-0.0073903524316847324,
-0.015823282301425934,
0.0002951927308458835,
-0.01526856143027544,
-0.019379783421754837,
0.022593583911657333,
0.0203536506742239,
-0.026414206251502037,
0.01999523676931858,
-0.027216458693146706,
0.013230116106569767,
-0.016124479472637177,
0.030132077634334564,
0.026899276301264763,
0.003542969236150384,
-0.006398003548383713,
0.01356441993266344,
-0.002867513569071889,
-0.01984645240008831,
-0.04738520830869675,
-0.06051016226410866,
-0.029922116547822952,
0.056964874267578125,
0.03086566925048828,
0.021949203684926033,
0.03219471871852875,
-0.03999054431915283,
0.006684555672109127,
0.09291212260723114,
-0.03881793096661568,
0.03143139183521271,
-0.021168602630496025,
-0.01874270848929882,
0.0360838919878006,
-0.009418715722858906,
0.043427541851997375,
0.022099705412983894,
0.06537923216819763,
-0.08535923063755035,
-0.03041294403374195,
0.04984903708100319,
-0.03822537511587143,
-0.00883508287370205,
0.016689101234078407,
0.006657728925347328,
0.0009657554910518229,
-0.0624866783618927,
-0.05044003576040268,
0.012349224649369717,
-0.011865867301821709,
-0.02040184661746025,
0.015490232035517693,
0.06175677850842476,
-0.06892803311347961,
0.004586144350469112,
-0.01178425457328558,
0.030301343649625778,
-0.03056759014725685,
0.002742024604231119,
-0.03404322266578674,
-0.06770150363445282,
0.020934268832206726,
-0.01167456153780222,
-0.021123874932527542,
-0.0353291891515255,
-0.026552246883511543,
-0.012211172841489315,
-0.004831488244235516,
0.050472766160964966,
-0.06371351331472397,
0.0028219770174473524,
-0.04977961257100105,
-0.03872448205947876,
-0.03793781250715256,
0.03474834933876991,
0.05939600244164467,
0.032139141112565994,
-0.012700056657195091,
0.05852418392896652,
-0.07585496455430984,
0.0011520397383719683,
-0.04307336360216141,
-0.02373793162405491,
-0.01910858415067196,
0.06472575664520264,
0.04569298028945923,
0.025081414729356766,
0.06251995265483856,
-0.03407637029886246,
0.026413962244987488,
0.0011820782674476504,
-0.020311156287789345,
-0.06315590441226959,
0.025400180369615555,
0.015725674107670784,
-0.026047280058264732,
0.033788956701755524,
-0.002311397809535265,
-0.05486230179667473,
-0.0008172595407813787,
0.04220806062221527,
0.043733324855566025,
-0.014148388057947159,
-0.0028425275813788176,
-0.09560687094926834,
0.03538990020751953,
-0.011814639903604984,
0.04413633421063423,
0.03396777808666229,
0.019292667508125305,
-0.04936150088906288,
0.04338078573346138,
-0.00793930422514677,
0.007371638901531696,
-0.01699286885559559,
0.01159752532839775,
-0.003408299293369055,
-0.023478979244828224,
0.0009672889718785882,
0.029202906414866447,
-0.04129882529377937,
-0.050291117280721664,
0.04394698515534401,
-0.010264681652188301,
-0.0030375223141163588,
0.01676560752093792,
-0.044280458241701126,
0.029639296233654022,
0.006897323299199343,
-0.017252609133720398,
-0.04169198498129845,
-0.031609270721673965,
-0.01577390357851982,
0.051888611167669296,
-0.029978232458233833,
0.04209042713046074,
-0.0005079781985841691,
-0.029615657404065132,
-0.004729837644845247,
-0.011821082793176174,
0.04004285857081413,
0.005967873148620129,
-0.027490073814988136,
0.004116499796509743,
-0.030518973246216774,
0.03247195854783058,
0.0407685711979866,
0.0061998749151825905,
0.015926076099276543,
0.019412169232964516,
-0.010480963625013828,
-0.0556907020509243,
0.018277207389473915,
-0.02138405852019787,
0.028746383264660835,
0.011990890838205814,
0.012059936299920082,
-0.030062299221754074,
0.03715498372912407,
-0.03771983087062836,
0.013332771137356758,
0.06262694299221039,
0.0175949614495039,
0.010365116409957409,
-0.02465672604739666,
-0.028477150946855545,
0.010523298755288124,
0.019584177061915398,
0.002036817604675889,
-0.041106998920440674,
-0.02304467372596264,
0.0020469939336180687,
-0.03583020716905594,
0.006511421874165535,
-0.012592424638569355,
0.0017628888599574566,
0.03974076360464096,
-0.008316603489220142,
-0.03052811324596405,
-0.0014385824324563146,
-0.025593606755137444,
0.019813410937786102,
-0.04813115671277046,
-0.02532382309436798,
0.026313645765185356,
0.031759195029735565,
0.049409374594688416,
0.018026133999228477,
-0.07018294930458069,
0.03343562036752701,
-0.010324330069124699,
-0.09725893288850784,
-0.019533095881342888,
-0.048020049929618835,
0.0020567532628774643,
0.015859408304095268,
-0.05158744752407074,
-0.05039864778518677,
-0.045723896473646164,
-0.030014052987098694,
0.0008366756374016404,
-0.007373461499810219,
-0.0654461532831192,
-0.053650710731744766,
0.006948358379304409,
-0.005932897794991732,
0.00792551226913929,
-0.011453126557171345,
0.003941600676625967,
0.02991575002670288,
0.006370265502482653,
0.07230987399816513,
-0.030915552750229836,
0.013836168684065342,
0.00031523380312137306,
0.011804846115410328,
-0.005961035843938589,
-0.055606041103601456,
0.03628832846879959,
0.05141614004969597,
0.048379480838775635,
0.022737795487046242,
0.020424971356987953,
0.020431265234947205,
0.0021260587964206934,
-0.02843451499938965,
-0.0023790367413312197,
-0.029274657368659973,
-0.04497644677758217,
-0.0029922358226031065,
0.07407991588115692,
0.03316269442439079,
0.028264667838811874,
-0.02557951956987381,
0.0022081949282437563,
-0.03237870708107948,
-0.03275182843208313,
-0.03461841493844986,
0.03871871158480644,
0.010483388788998127,
0.01635126769542694,
0.002845627022907138,
0.013054745271801949,
0.05562916398048401,
0.02434159442782402,
0.010067849420011044,
-0.0116445766761899,
0.011664963327348232,
-0.04641382396221161,
-0.02555013634264469,
0.004860568325966597,
-0.06759195029735565,
-0.006829594261944294,
-0.05954276770353317,
-0.004268934950232506,
-0.004635772202163935,
0.012806045822799206,
-0.03010149858891964,
-0.028502020984888077,
0.007976477034389973,
-0.016454322263598442,
0.04316529259085655,
-0.01856183260679245,
-0.03742507845163345,
-0.05248221009969711,
0.02145676501095295,
-0.009346048347651958,
0.03130410611629486,
0.0026282190810889006,
-0.05635477229952812,
0.06135429069399834,
0.021029647439718246,
0.0060287960804998875,
0.010973403230309486,
0.03143111243844032,
-0.04563639685511589,
0.030755801126360893,
0.023778224363923073,
0.002539979526773095,
-0.049119606614112854,
0.0017786453245207667,
-0.033470652997493744,
0.059578198939561844,
0.019222954288125038,
-0.025618350133299828,
-0.005350491963326931,
-0.02049139142036438,
0.07447247952222824,
0.013270700350403786,
0.0103165153414011,
0.018087539821863174,
-0.01266422402113676,
-0.018434740602970123,
0.05122145265340805,
-0.06697149574756622,
0.023741481825709343,
-0.05661419406533241,
0.06376666575670242,
-0.02878132462501526,
0.03499548137187958,
0.0027248160913586617,
0.04638451710343361,
0.04128091782331467,
0.07258809357881546,
-0.11949921399354935,
0.0024373542983084917,
-0.013834577985107899,
-0.011212943121790886,
-0.02926516719162464,
-0.047220807522535324,
-0.005767075810581446,
-0.02977578155696392,
0.0019651700276881456,
0.022799545899033546,
-0.010691741481423378,
-0.07229187339544296,
0.0338529571890831,
-0.055947549641132355,
-0.06941332668066025,
0.0351155623793602,
0.016183873638510704,
0.053310226649045944,
-0.048933517187833786,
-0.1024002730846405,
0.002697017975151539,
0.05615362152457237,
-0.0055742450058460236,
-0.06776149570941925,
-0.03066553920507431,
0.054361727088689804,
-0.07689667493104935,
-0.015721917152404785,
0.03262333199381828,
-0.0015725045232102275,
0.011963693425059319,
-0.05706601217389107,
-0.020981591194868088,
-0.036117516458034515,
-0.027206171303987503,
-0.010871903039515018,
-0.03167687729001045,
-0.00513721676543355,
-0.035995002835989,
-0.012550024315714836,
0.032543860375881195,
0.033587295562028885,
0.01766819693148136,
-0.004757852293550968,
0.009928802959620953,
-0.0016087834956124425,
0.016722099855542183,
0.025840383023023605,
0.037140142172575,
0.0281946063041687,
0.05002585053443909,
-0.02518778294324875,
0.030249198898673058,
0.021992692723870277,
-0.016761185601353645,
0.04832242429256439,
-0.034482989460229874,
-0.03388739749789238,
0.020089996978640556,
0.024837477132678032,
-0.005620175041258335,
-0.008047865703701973,
0.030613407492637634,
-0.007827120833098888,
0.11225805431604385,
0.01420082338154316,
0.006329680792987347,
-0.10953536629676819,
-0.033165283501148224,
-0.0011601001024246216,
0.0137445367872715,
0.026810992509126663,
0.0018945689080283046,
0.005391101818531752,
-0.0163726806640625,
0.004120721016079187,
-0.020160473883152008,
0.0026031082961708307,
-0.01949002407491207,
0.018355894833803177,
-0.02508724480867386,
-0.04944100230932236,
0.016611535102128983,
-0.024376796558499336,
-0.04216637834906578,
-0.02104676328599453,
0.02017674222588539,
0.015342403203248978,
-0.004633627831935883,
0.013767078518867493,
0.00667150504887104,
0.022662874311208725,
0.06583355367183685,
-0.01926708221435547,
0.02038525976240635,
-0.00706039322540164,
0.02787483111023903,
-0.004620008636265993,
0.014833568595349789,
-0.012932389043271542,
0.00016426396905444562,
-0.02205815352499485,
-0.07258781790733337,
-0.02135600335896015,
-0.006682730279862881,
-0.012305290438234806,
0.006290691439062357,
-0.09197074919939041,
-0.0748143196105957,
0.04796532541513443,
-0.03568052873015404,
-0.05147537216544151,
-0.030014779418706894,
0.016021011397242546,
-0.028400558978319168,
0.026514802128076553,
0.007352902553975582,
0.00634742621332407,
0.018584460020065308,
0.017043031752109528,
0.040896136313676834,
-0.017501436173915863,
0.0010110738221555948,
-0.0006549643585458398,
-0.02222757413983345,
-0.03986131772398949,
0.0006421239813789725,
-0.03243042528629303,
-0.026135820895433426,
0.013230431824922562,
-0.026819530874490738,
0.011264597997069359,
-0.018261803314089775,
0.015164894983172417,
0.00854969210922718,
-0.02188037522137165,
-0.0372016504406929,
-0.0278642438352108,
0.013864497654139996,
0.025826748460531235,
0.023650025948882103,
-0.023301655426621437,
-0.008845685049891472,
0.020087357610464096,
-0.09687475115060806,
-0.01414560992270708,
0.034437768161296844,
0.07371299713850021,
-0.07535962760448456,
0.025980820879340172,
-0.08236070722341537,
0.038203995674848557,
-0.026730583980679512,
0.008405416272580624,
-0.029633278027176857,
0.006281341891735792,
0.013363128527998924,
0.023418003693223,
0.05601257085800171,
0.02034376561641693,
0.054740458726882935,
0.04545734077692032,
-0.011177055537700653,
0.014238120056688786,
0.006592942401766777,
-0.0011048418236896396,
-0.015783488750457764,
-0.005589333828538656,
0.0633682906627655,
-0.0034659358207136393,
-0.03541551157832146,
-0.006385717540979385,
-0.027478354051709175,
-0.09192859381437302,
-0.009122848510742188,
0.004592988174408674,
0.017001809552311897,
0.04082692787051201,
0.05808382108807564,
-0.004371694289147854,
0.004275412764400244,
-0.011780528351664543,
0.004807879216969013,
0.04156280308961868,
-0.033141858875751495,
-0.05106910690665245,
0.037991590797901154,
0.03437701612710953,
0.022437166422605515,
-0.025296619161963463,
0.02373562939465046,
0.0249614417552948,
-0.03544800728559494,
0.050879865884780884,
-0.039229683578014374,
0.06581353396177292,
-0.011820968240499496,
0.020424844697117805,
-0.020352080464363098,
0.012699740007519722,
0.07269848138093948,
-0.050844572484493256,
-0.007704585790634155,
0.018950508907437325,
0.03480001166462898,
0.03398405387997627,
-0.0759657472372055,
-0.037906598299741745,
0.07069458812475204,
0.051579851657152176,
-0.010029993019998074,
-0.023592384532094002,
0.017719771713018417,
-0.047991614788770676,
0.015044464729726315,
0.0107466671615839,
-0.020395103842020035,
-0.0305186677724123,
0.016040895134210587,
0.007971706800162792,
-0.015154724009335041,
-0.002961347810924053,
0.04161154106259346,
0.03797878697514534,
0.03844181075692177,
-0.05666430667042732,
0.02465103380382061,
0.05428072065114975,
-0.04159056022763252,
0.013923929072916508,
-0.008585215546190739,
-0.016373559832572937,
0.031070472672581673,
-0.021077342331409454,
0.0065059601329267025,
0.05569641664624214,
-0.05452544614672661,
0.02613854967057705,
0.020356567576527596,
0.021354537457227707,
-0.001368459314107895,
-0.0908752977848053,
-0.026309648528695107,
0.056157540529966354,
0.013903218321502209,
-0.034204307943582535,
-0.08219842612743378,
0.015711143612861633,
0.046692393720149994,
0.005864412989467382,
-0.043982334434986115,
-0.023824982345104218,
0.0037945397198200226,
-0.016082415357232094,
-0.021712636575102806,
0.0496353842318058,
0.052232351154088974,
-0.02239163964986801,
0.04012047499418259,
-0.04266886040568352,
0.012905953451991081,
0.03402639552950859,
0.0009239668142981827,
-0.09035144001245499,
-0.0018803199054673314,
-0.006646218243986368,
0.022993657737970352,
0.05429605394601822,
0.022734059020876884,
-0.0008943978464230895,
0.04614294692873955,
0.0318211130797863,
-0.019003698602318764,
0.003882824443280697,
-0.01467239111661911,
0.04158882051706314,
0.017227653414011,
-0.004623967222869396,
-0.00936497189104557,
0.011499293148517609,
-0.036831166595220566,
0.022154539823532104,
-0.07225880771875381,
-0.0637332871556282,
-0.011867654509842396,
0.04399394616484642,
0.06078227609395981,
0.0036259235348552465,
0.012235904112458229,
0.007478814106434584,
-0.0725921243429184,
0.03545761480927467,
-0.08824307471513748,
0.024022895842790604,
-0.04861278086900711,
-0.09493714570999146,
0.016197700053453445,
-0.02292797528207302,
0.04007531329989433,
-0.04393376410007477,
0.03473936393857002,
-0.02839517965912819,
-0.02781398966908455,
-0.03125930577516556,
-0.0010453573195263743,
-0.01981368474662304,
0.06636419892311096,
-0.01123715192079544,
-0.047441914677619934,
0.018950005993247032,
-0.016244711354374886,
0.08633885532617569,
0.03723839297890663,
0.08660484850406647,
0.0062652165070176125,
-0.03671615943312645,
-0.015538704581558704,
0.06401246041059494,
-0.0005725811934098601,
0.01013103500008583,
0.007480582222342491,
-0.0005618841387331486,
0.038334015756845474,
-0.020910460501909256,
0.00957976933568716,
-0.04038906469941139
] |
<p>Through what I learned from school, frequency $f=\frac1T$ while $T$ is the period. However, things get harder in college where there are non-periodic signal. That means they have no period or their period is extended to infinity but they still have frequency. How can they have frequencies even there is no period to apply the formula $f=\frac1T$? Is there any definition of frequency in those cases.</p> | g6611 | [
0.0014978033723309636,
-0.00024680880596861243,
0.005094306077808142,
-0.014777975156903267,
0.04830949380993843,
0.007183881010860205,
0.03737125173211098,
0.005510326474905014,
-0.0315508134663105,
-0.04072253033518791,
-0.019440947100520134,
0.003949363715946674,
0.0387267991900444,
0.045817781239748,
-0.051832061260938644,
0.05544814467430115,
0.008566325530409813,
0.07129903137683868,
0.0011137075489386916,
0.032900068908929825,
-0.016275126487016678,
0.03765992447733879,
-0.0393042229115963,
-0.022699499502778053,
-0.02833307348191738,
0.0188287403434515,
0.025390243157744408,
0.011966879479587078,
-0.05040121078491211,
-0.04623604938387871,
0.03251825273036957,
-0.015886787325143814,
0.03915321081876755,
0.01832112856209278,
0.05340396985411644,
-0.03256118670105934,
-0.04294893890619278,
-0.008720768615603447,
0.00855210330337286,
0.007303058635443449,
-0.013349677436053753,
0.017828747630119324,
-0.01592126674950123,
-0.02799193188548088,
-0.09391213953495026,
0.018256237730383873,
-0.05000170320272446,
-0.022655922919511795,
-0.026893479749560356,
-0.02180449478328228,
0.01892639324069023,
-0.02271837741136551,
0.05713207647204399,
-0.007394574582576752,
-0.01333249919116497,
0.03904702141880989,
0.008167028427124023,
0.04434197023510933,
0.047697097063064575,
0.05533186346292496,
0.02764245867729187,
-0.005827412940561771,
-0.008157407864928246,
0.03432636708021164,
0.013346669264137745,
0.008659605868160725,
0.06420809030532837,
-0.02315293624997139,
-0.015877990052103996,
-0.014228531159460545,
-0.023046696558594704,
-0.012171505950391293,
-0.02294064499437809,
0.00567020196467638,
-0.014976606704294682,
0.029866259545087814,
0.003756525693461299,
-0.03736726939678192,
0.012041178531944752,
0.00910020712763071,
-0.013298680074512959,
0.048573050647974014,
0.02169692888855934,
0.01480849925428629,
0.052710793912410736,
0.04609246551990509,
0.00799648743122816,
0.01075950637459755,
0.061978671699762344,
0.06064995750784874,
-0.012976291589438915,
-0.037966206669807434,
0.016959937289357185,
-0.04333140328526497,
0.01792590506374836,
-0.010193977504968643,
-0.006729658227413893,
0.06486248224973679,
-0.042525213211774826,
0.0022854474373161793,
0.015612141229212284,
0.03889160603284836,
0.04256734251976013,
0.01232131477445364,
-0.006535184103995562,
-0.02354431338608265,
0.033537957817316055,
-0.04185947775840759,
-0.024639645591378212,
-0.004375755786895752,
-0.027180887758731842,
0.032018568366765976,
-0.029702387750148773,
-0.06690526008605957,
0.030856125056743622,
0.0291904266923666,
0.024781180545687675,
0.003942658193409443,
0.019851455464959145,
0.016060784459114075,
0.03274669870734215,
-0.024665260687470436,
0.0113211739808321,
0.08182334154844284,
-0.08387336134910583,
0.04937663674354553,
0.08057676255702972,
0.04565627872943878,
0.0323384627699852,
-0.031405478715896606,
-0.035177264362573624,
0.004845189396291971,
0.043639134615659714,
-0.009420761838555336,
0.021765220910310745,
0.08437502384185791,
0.02612846903502941,
-0.023533713072538376,
0.004314308054745197,
0.05480705201625824,
-0.0023360943887382746,
-0.06851877272129059,
0.029365118592977524,
-0.06859384477138519,
-0.04842553660273552,
0.04972675070166588,
-0.07965376228094101,
-0.07163900882005692,
0.016081390902400017,
0.031816039234399796,
0.03442474082112312,
0.09497711807489395,
0.028281336650252342,
-0.05676920339465141,
0.010785842314362526,
-0.0008698623860254884,
0.0363713875412941,
0.024149123579263687,
-0.04227922111749649,
0.026292383670806885,
0.03924856707453728,
0.0113188112154603,
0.009582484140992165,
0.029297593981027603,
-0.0747920498251915,
0.016023164615035057,
-0.08495271950960159,
-0.01729194074869156,
-0.026804326102137566,
-0.014314454980194569,
-0.06050603464245796,
0.03160596266388893,
0.02775174006819725,
0.028609061613678932,
0.027022289112210274,
0.03914879262447357,
0.010753415524959564,
-0.010885569266974926,
0.057989150285720825,
-0.008995052427053452,
-0.03536541387438774,
-0.026351237669587135,
-0.021713338792324066,
-0.017342563718557358,
0.007289852946996689,
0.023359987884759903,
-0.01574518531560898,
0.02006557025015354,
-0.07167010009288788,
0.040810901671648026,
-0.014117438346147537,
-0.032386548817157745,
-0.009940960444509983,
0.020068790763616562,
-0.07402240484952927,
-0.00828239694237709,
-0.06475894153118134,
-0.021390734240412712,
-0.0023640329018235207,
0.020739926025271416,
0.01858745887875557,
-0.03476157411932945,
0.01882600411772728,
-0.011242740787565708,
0.044682011008262634,
0.003170834155753255,
-0.01844928227365017,
-0.04759050905704498,
-0.020660944283008575,
0.013968118466436863,
-0.05573061853647232,
-0.06802517175674438,
-0.032765861600637436,
0.0626324713230133,
-0.01608274318277836,
-0.02361871674656868,
-0.03859470412135124,
-0.004343210719525814,
0.005624481476843357,
0.05223996937274933,
0.01949554681777954,
-0.0016668644966557622,
0.018866287544369698,
-0.010488301515579224,
-0.022070474922657013,
-0.013199491426348686,
0.01952841691672802,
-0.010045060887932777,
-0.044510096311569214,
0.03280000016093254,
-0.0021356316283345222,
-0.013145931996405125,
-0.038178831338882446,
-0.02618551254272461,
0.01597643457353115,
0.05113533139228821,
0.0063956561498343945,
0.003649380523711443,
0.003257214557379484,
0.0031861423049122095,
-0.038125306367874146,
-0.023916101083159447,
0.020046349614858627,
-0.030514398589730263,
-0.019187506288290024,
-0.04540470987558365,
-0.0002712027635425329,
-0.005323885008692741,
0.025940600782632828,
0.002114182570949197,
0.0334513783454895,
-0.00981680117547512,
0.0027758467476814985,
0.03179736062884331,
-0.015103351324796677,
0.009625264443457127,
0.014925741590559483,
-0.007426518946886063,
-0.07754049450159073,
-0.06107787787914276,
0.06004994735121727,
-0.006093153264373541,
0.06103792041540146,
0.02177737094461918,
-0.03683815896511078,
-0.013779493048787117,
-0.011968834325671196,
0.051461778581142426,
-0.06220059469342232,
0.012159212492406368,
0.002510306891053915,
0.02075284719467163,
0.08647190034389496,
0.006220124661922455,
-0.02865542843937874,
-0.012693246826529503,
-0.007222296204417944,
-0.012502244673669338,
-0.015162386931478977,
0.010795659385621548,
0.005358306225389242,
-0.01694083772599697,
0.007565631065517664,
0.005995083134621382,
-0.010960138402879238,
-0.04409712553024292,
0.08723592013120651,
0.06702514737844467,
-0.05442202836275101,
0.015450905077159405,
-0.04025258496403694,
-0.06261106580495834,
0.023426054045557976,
0.012598286382853985,
-0.010170100256800652,
0.049090247601270676,
0.05656599625945091,
-0.022961169481277466,
0.03692864626646042,
0.06215088441967964,
0.06180310249328613,
0.038461752235889435,
0.000469025457277894,
-0.01830180175602436,
-0.01654406450688839,
-0.033021051436662674,
-0.0020947568118572235,
-0.060635071247816086,
-0.04665397107601166,
-0.014126394875347614,
0.010313027538359165,
0.02341691218316555,
0.06214407458901405,
0.0034909015521407127,
-0.024771997705101967,
0.05344117060303688,
0.004227864556014538,
0.018774161115288734,
0.007012930698692799,
0.023021310567855835,
0.001225467654876411,
-0.012870479375123978,
0.0464865081012249,
-0.04317409172654152,
0.010707530193030834,
0.010755816474556923,
-0.00803079828619957,
-0.017679007723927498,
-0.05902816727757454,
-0.025712203234434128,
0.028796419501304626,
-0.02930588833987713,
-0.02536730095744133,
-0.06419580429792404,
0.016879472881555557,
-0.03716229274868965,
0.012122801505029202,
0.0706995353102684,
0.040114764124155045,
0.03479383885860443,
-0.004090244881808758,
0.009474653750658035,
0.0007642214186489582,
-0.017513316124677658,
-0.03010038658976555,
0.013710279017686844,
-0.01834963820874691,
0.04327834025025368,
0.0052339923568069935,
-0.017863618209958076,
0.014627260155975819,
-0.027868103235960007,
-0.0339166484773159,
-0.01076818723231554,
0.01252788957208395,
0.029764793813228607,
0.0555960014462471,
0.04734126105904579,
-0.012884275056421757,
0.0030167957302182913,
0.03231391683220863,
-0.03853267431259155,
0.04594377800822258,
0.09419775009155273,
-0.013628266751766205,
0.016135362908244133,
0.03572250157594681,
0.1406002640724182,
0.02465962991118431,
0.00924233254045248,
0.0018051326042041183,
-0.010548497550189495,
0.06855536997318268,
0.03658025711774826,
-0.009443752467632294,
-0.023963939398527145,
-0.03944956138730049,
-0.016756294295191765,
-0.03081427328288555,
0.037934157997369766,
-0.01988954283297062,
-0.061515241861343384,
0.01111728884279728,
-0.05808556452393532,
0.003671457292512059,
-0.0011841908562928438,
0.010089386254549026,
0.010401630774140358,
0.0010566076962277293,
-0.02976076677441597,
0.03780323639512062,
-0.031624890863895416,
-0.005835790187120438,
0.05041906610131264,
0.04110115021467209,
-0.0664503276348114,
0.011220893822610378,
-0.008752130903303623,
0.017345547676086426,
0.016237277537584305,
0.03819010406732559,
0.003586637321859598,
-0.06974867731332779,
0.030185086652636528,
-0.030187703669071198,
0.09898687899112701,
0.008732553571462631,
-0.04889165610074997,
-0.025524385273456573,
-0.03403085097670555,
-0.05062803253531456,
-0.027837397530674934,
-0.01622987538576126,
-0.05676427111029625,
-0.0012180022895336151,
0.033236391842365265,
0.10962076485157013,
-0.0199353639036417,
0.03417443856596947,
0.025565708056092262,
-0.042885199189186096,
0.009236965328454971,
0.023286450654268265,
0.011136705055832863,
0.016367269679903984,
0.0177492443472147,
0.0018569001695141196,
-0.011784622445702553,
-0.030760152265429497,
-0.0018167878733947873,
-0.02463398687541485,
-0.01791626773774624,
0.0038728739600628614,
-0.02863418497145176,
0.0023645302280783653,
0.01624586619436741,
-0.05109933018684387,
0.04184257611632347,
0.026288287714123726,
-0.0007819116581231356,
0.006678372621536255,
-0.015143446624279022,
-0.05957282334566116,
0.001693215686827898,
-0.002833488630130887,
0.04362517595291138,
-0.04327674210071564,
-0.02609746716916561,
0.025777967646718025,
0.01855316013097763,
-0.03271661698818207,
0.07738031446933746,
-0.04784470424056053,
-0.01836196705698967,
0.0035849432460963726,
-0.039597101509571075,
-0.04038695991039276,
0.0030452825594693422,
-0.007371161598712206,
0.017114276066422462,
-0.028259778395295143,
0.006513878703117371,
-0.002716341521590948,
-0.02839597873389721,
-0.006115827243775129,
0.03827011585235596,
0.048516422510147095,
-0.09380441159009933,
-0.014571580104529858,
-0.005311673507094383,
0.006109780166298151,
-0.029858281835913658,
0.06050097197294235,
0.03665103018283844,
0.03713122755289078,
-0.028290588408708572,
0.036703839898109436,
-0.012681822292506695,
-0.01703663170337677,
-0.05484364926815033,
0.04148653522133827,
-0.06436757743358612,
0.03842921182513237,
0.0021005377639085054,
-0.02539324015378952,
0.038115035742521286,
0.005263787228614092,
0.016649622470140457,
0.023726386949419975,
-0.03479509428143501,
0.01293173898011446,
0.028230709955096245,
0.0028853677213191986,
0.009511992335319519,
0.004248008597642183,
-0.06943859905004501,
0.06055241823196411,
0.0057909018360078335,
0.03228660300374031,
-0.10459374636411667,
-0.04070189595222473,
0.04898299649357796,
-0.038813669234514236,
0.04529283940792084,
0.012636466883122921,
0.06874668598175049,
0.0074042389169335365,
-0.03805955499410629,
-0.04411930963397026,
0.050434600561857224,
0.004586046561598778,
0.006235502194613218,
0.01943996176123619,
0.03807090222835541,
0.031272754073143005,
-0.0060775550082325935,
-0.07294508069753647,
-0.053869783878326416,
-0.047754138708114624,
-0.008343611843883991,
-0.00620125001296401,
0.04396414756774902,
0.03627379983663559,
0.000654884148389101,
0.02364514209330082,
-0.034350618720054626,
-0.038349878042936325,
-0.11691900342702866,
0.001721331151202321,
-0.0027545022312551737,
0.009420117363333702,
0.01094113290309906,
-0.016419004648923874,
0.006694089155644178,
0.01972632110118866,
0.015550834126770496,
0.006313418969511986,
-0.029322046786546707,
-0.012596995569765568,
0.026067130267620087,
-0.01786022074520588,
0.02149241231381893,
0.023728158324956894,
-0.013015186414122581,
-0.012342923320829868,
-0.012025617994368076,
-0.010964864864945412,
-0.00991749856621027,
-0.0004717437259387225,
-0.024530986323952675,
-0.03172561526298523,
0.015996230766177177,
0.01185679156333208,
-0.01853092387318611,
0.00318133388645947,
0.04807212948799133,
-0.0023512032348662615,
-0.03006497025489807,
-0.046958647668361664,
-0.021288244053721428,
-0.02869783155620098,
0.01832498610019684,
0.027990473434329033,
0.00877709686756134,
0.018766801804304123,
-0.008622444234788418,
0.03224174678325653,
0.021872548386454582,
0.050179608166217804,
0.019551532343029976,
0.017689060419797897,
0.024491267278790474,
-0.01034622360020876,
-0.013600670732557774,
0.011233705095946789,
0.013622545637190342,
0.011338971555233002,
-0.040832456201314926,
0.03644382953643799,
-0.058521270751953125,
-0.018318211659789085,
0.003275818657130003,
0.011425620876252651,
0.017355628311634064,
-0.019460076466202736,
-0.011272656731307507,
0.036185529083013535,
-0.040698692202568054,
0.04525265842676163,
0.0016085132956504822,
-0.026933208107948303,
-0.039851829409599304,
-0.0036335166078060865,
0.06650158017873764,
-0.005696870386600494,
-0.005060577765107155,
-0.03642599657177925,
0.046622104942798615,
0.024632155895233154,
-0.039601389318704605,
-0.0076032765209674835,
0.036888349801301956,
0.03787485882639885,
0.017869219183921814,
-0.02059975266456604,
0.029764704406261444,
0.02386338636279106,
-0.021323222666978836,
-0.013403336517512798,
0.03290056809782982,
-0.04860827326774597,
0.09080995619297028,
0.042446333914995193,
-0.00036744173849001527,
-0.06425192952156067,
-0.05483761057257652,
-0.05150563269853592,
0.030367039144039154,
0.0008689243695698678,
0.0053124804981052876,
0.06340370327234268,
-0.06754014641046524,
0.01634136214852333,
-0.04482901096343994,
0.019451498985290527,
0.0654122605919838,
-0.03913431614637375,
0.024153433740139008,
0.04218548536300659,
-0.04930141940712929,
0.01930788904428482,
-0.03069913201034069,
-0.02876734733581543,
0.009548161178827286,
-0.039010751992464066,
0.04864228144288063,
-0.08367741852998734,
0.039283860474824905,
0.055122293531894684,
-0.01598254404962063,
0.004292318597435951,
0.024472882971167564,
0.04009409621357918,
-0.012630926445126534,
-0.010098719038069248,
0.029565399512648582,
0.027974803000688553,
-0.020576344802975655,
-0.03525755554437637,
-0.005444200709462166,
0.030276281759142876,
-0.06952033936977386,
-0.0007957331836223602,
0.05740498751401901,
0.003869552630931139,
-0.004528749268501997,
0.012127770110964775,
-0.024895360693335533,
0.003227542620152235,
-0.012878073379397392,
-0.01602092944085598,
-0.017752522602677345,
0.020988833159208298,
0.047309547662734985,
0.014281165786087513,
0.04542310908436775,
0.06521911919116974,
-0.040066909044981,
-0.02501976117491722,
-0.07303648442029953,
0.023484447970986366,
-0.044083841145038605,
-0.025405235588550568,
-0.013793508522212505,
0.008459885604679585,
-0.009361142292618752,
-0.04761643335223198,
0.03689006343483925,
-0.034354500472545624,
-0.042519498616456985,
-0.03697032853960991,
-0.03190094605088234,
0.0032785197254270315,
-0.03110053762793541,
0.01200204249471426,
0.07550143450498581,
-0.05243042856454849,
0.0073562911711633205,
0.03840462863445282,
0.0022112708538770676,
0.010312328115105629,
0.02171831764280796,
0.02191394753754139,
-0.012256389483809471,
0.014575635083019733,
-0.08355779200792313,
0.011880327947437763,
-0.011346901766955853,
-0.01643238216638565,
-0.013012498617172241,
0.058712493628263474,
-0.019314808771014214,
-0.03404586389660835,
-0.002810913138091564,
0.03704888001084328,
0.02586481347680092,
-0.05199051275849342,
-0.008450386114418507,
0.01186741515994072,
-0.033370763063430786,
0.004267702344805002,
0.038269270211458206,
0.01099683903157711,
0.009113564155995846,
-0.013814116828143597,
-0.010131911374628544,
-0.04611007124185562,
-0.012092006392776966,
-0.0403592474758625,
-0.030808592215180397,
-0.05009692907333374,
-0.1308450996875763,
-0.033156074583530426,
-0.07669033110141754,
-0.03310224786400795,
0.023860860615968704,
-0.03995903953909874,
-0.0689476951956749,
-0.015317372046411037,
-0.057368285953998566,
-0.04365267604589462,
0.0039065927267074585,
0.004666301887482405,
0.028745537623763084,
-0.0652637779712677,
0.027029823511838913,
0.05027374252676964,
0.03103598766028881,
-0.009172460064291954,
0.028900466859340668,
-0.01921437680721283,
0.04763396829366684,
0.004594672005623579,
-0.0015978120500221848,
0.017273318022489548,
0.049651216715574265,
-0.06390241533517838,
-0.012868733145296574,
0.05701540410518646,
-0.03382069244980812,
-0.10516511648893356,
0.058455199003219604,
-0.043558720499277115,
0.019460756331682205,
0.06913959980010986,
-0.04632427915930748,
0.0008055853541009128,
-0.005493290722370148,
0.047525804489851,
-0.022997012361884117,
-0.025519195944070816,
0.026754111051559448,
-0.013005456887185574,
0.029335660859942436,
0.019974878057837486,
-0.0576203316450119,
0.014630709774792194,
0.002812754362821579
] |
<p>This theory has bugged me ever since my first physics class on the subject. If this (<a href="http://en.wikipedia.org/wiki/Kinetic_theory" rel="nofollow">http://en.wikipedia.org/wiki/Kinetic_theory</a>) is true, it leads me to a few weird conclusions.</p>
<p>Opening the rear window in a pickup truck at 10 m/s doesn't empty the cabin of all its air. This means that gas molecules can catch up with us from behind so we can conclude that gases move much faster than 10 m/s at normal temperatures.</p>
<p>Then, shouldn't gases mix almost instantaneously? For example, shouldn't a fart's smell reach us faster than a car on an highway and then dissapear almost immediately into such a large area that the concentration is too low for our noses to detect?</p> | g6612 | [
0.04210115969181061,
-0.0035742949694395065,
-0.0035182947758585215,
0.010045425035059452,
0.0030576889403164387,
-0.0031717955134809017,
0.04566245526075363,
0.037174854427576065,
-0.062278784811496735,
-0.02022245153784752,
0.061140190809965134,
-0.013193272985517979,
0.020633749663829803,
0.015471111983060837,
-0.020299917086958885,
-0.02249298244714737,
0.06489922106266022,
-0.034680500626564026,
0.006693627219647169,
0.058639176189899445,
-0.02530289813876152,
-0.013090119697153568,
0.00019667850574478507,
-0.07438591867685318,
-0.0659516230225563,
0.029575474560260773,
0.022434134036302567,
-0.0032778484746813774,
-0.017423633486032486,
-0.0250172708183527,
0.03927090764045715,
0.0007897003670223057,
-0.07338128238916397,
-0.07286533713340759,
-0.058829206973314285,
-0.05787133798003197,
0.012191208079457283,
-0.033306099474430084,
-0.02873927168548107,
-0.03538252040743828,
0.0024505499750375748,
-0.04391227290034294,
0.047043364495038986,
-0.006046996917575598,
-0.046408478170633316,
0.0577835850417614,
0.013442178256809711,
0.021155547350645065,
0.016115795820951462,
-0.0005416455096565187,
-0.05234396085143089,
0.0022919976618140936,
-0.042754460126161575,
0.01723855547606945,
0.024616671726107597,
0.02770148776471615,
0.037601809948682785,
-0.014673549681901932,
0.01763535663485527,
-0.03354713320732117,
0.00047710337094031274,
0.03305833041667938,
0.04206589609384537,
0.03947947919368744,
0.03935542330145836,
-0.03493481129407883,
-0.04877032712101936,
0.048728421330451965,
0.025334347039461136,
-0.04335219785571098,
0.023231809958815575,
-0.03703608736395836,
-0.047140609472990036,
-0.020951474085450172,
0.024250557646155357,
0.03764757141470909,
-0.018936166539788246,
-0.008573638275265694,
0.05690358579158783,
0.002127281855791807,
-0.02013377659022808,
0.0025296586100012064,
-0.04493843764066696,
-0.0053863017819821835,
0.0033278712071478367,
-0.01218667533248663,
-0.0361565537750721,
0.005440264940261841,
-0.0002820505469571799,
0.005044890101999044,
0.02641814760863781,
-0.03062320314347744,
0.05432553216814995,
0.029178455471992493,
-0.026709910482168198,
0.0014949002070352435,
-0.010387376882135868,
0.0545320063829422,
-0.04345899820327759,
-0.046233270317316055,
-0.0829547867178917,
-0.012804463505744934,
0.008560243993997574,
0.02751789428293705,
0.00337718753144145,
0.01048976555466652,
-0.029840199276804924,
0.013820048421621323,
-0.01923021487891674,
-0.0101695004850626,
-0.04598680138587952,
0.006456781644374132,
-0.038326896727085114,
-0.03608647361397743,
-0.005375329405069351,
0.009493336081504822,
0.019695259630680084,
-0.019795939326286316,
0.03627170994877815,
-0.003998768050223589,
-0.006966765969991684,
0.08111469447612762,
-0.03987538069486618,
-0.01771508902311325,
-0.024620400741696358,
-0.02670750394463539,
-0.022949164733290672,
-0.021010739728808403,
-0.033530544489622116,
-0.012697392143309116,
-0.005691117141395807,
0.00023855238396208733,
-0.01658894680440426,
0.07361509650945663,
0.00040058305603452027,
0.0023986580781638622,
-0.02626155875623226,
0.02833729051053524,
0.007977953180670738,
0.04946719855070114,
-0.010515774600207806,
0.03982970118522644,
0.03021259605884552,
-0.01738300919532776,
-0.059605326503515244,
0.002281756838783622,
-0.04740550369024277,
0.02808500826358795,
-0.02035566046833992,
-0.02262105420231819,
-0.0359000563621521,
-0.015749994665384293,
0.029738958925008774,
0.038384851068258286,
-0.004945558961480856,
-0.011701731011271477,
0.039200473576784134,
0.027582351118326187,
0.026414476335048676,
0.002858412219211459,
0.05252841114997864,
-0.004512200132012367,
0.0013583592372015119,
0.009778442792594433,
-0.10346435010433197,
-0.011892912909388542,
-0.024616925045847893,
-0.008873780257999897,
0.028821038082242012,
0.003918022848665714,
-0.10455876588821411,
0.024383695796132088,
-0.004106038250029087,
0.027563923969864845,
-0.049453601241111755,
0.05162582919001579,
0.05963629111647606,
-0.007973683066666126,
-0.07549186050891876,
-0.034014832228422165,
0.011339600197970867,
-0.03133677691221237,
-0.02233811840415001,
-0.08005517721176147,
0.0214677844196558,
-0.03127651289105415,
-0.02836710214614868,
0.056609559804201126,
-0.11248217523097992,
-0.022352855652570724,
0.02506568282842636,
-0.02638382278382778,
0.00016054141451604664,
0.02494146302342415,
-0.05986962467432022,
-0.006009632255882025,
-0.011896017007529736,
-0.016306810081005096,
-0.00017995394591707736,
-0.01832074671983719,
-0.06213965266942978,
0.008286266587674618,
0.018472475931048393,
-0.017886778339743614,
0.014648105949163437,
-0.012980087660253048,
-0.030870260670781136,
-0.0015109266387298703,
0.036098841577768326,
0.010139490477740765,
0.007453458849340677,
0.0170910507440567,
0.02738644927740097,
0.022848717868328094,
0.018330061808228493,
0.012617978267371655,
-0.028243903070688248,
0.004040404222905636,
0.003429906675592065,
0.012612995691597462,
0.0225725919008255,
0.0010994928888976574,
-0.014004486612975597,
-0.04380005598068237,
0.007358862552791834,
-0.06967736780643463,
-0.004154058173298836,
-0.09615100175142288,
-0.01349245011806488,
0.05598263069987297,
0.03466349467635155,
0.03550950437784195,
-0.039230119436979294,
0.01422597374767065,
0.0384298600256443,
0.029842237010598183,
0.019255228340625763,
0.015211429446935654,
0.03825795277953148,
0.02173783630132675,
0.024507004767656326,
-0.04738275334239006,
-0.08954250067472458,
0.07131196558475494,
-0.013539128005504608,
-0.045434676110744476,
-0.017253445461392403,
-0.045052941888570786,
-0.015342273749411106,
0.03728637844324112,
-0.02930019237101078,
0.03955062851309776,
-0.011937455274164677,
-0.02410697378218174,
-0.000533316982910037,
-0.008200119249522686,
-0.01597643457353115,
0.014409441500902176,
-0.026724128052592278,
-0.0978427454829216,
-0.029694560915231705,
-0.0020952741615474224,
0.02751277945935726,
-0.06229936331510544,
-0.06284858286380768,
-0.0316273458302021,
-0.04288198798894882,
0.04517234489321709,
-0.014827204868197441,
-0.06427837163209915,
0.010848524048924446,
0.03528861328959465,
0.00802201684564352,
0.0032683033496141434,
0.0004994962946511805,
0.05856647714972496,
0.029921570792794228,
-0.03178563714027405,
0.0634196475148201,
-0.021851839497685432,
-0.08701404929161072,
0.015563267283141613,
-0.02385793626308441,
-0.027310175821185112,
0.04571622982621193,
-0.028961556032299995,
0.01930691860616207,
0.08479286730289459,
0.05975063145160675,
-0.016545254737138748,
0.061159539967775345,
0.019092421978712082,
0.050969984382390976,
0.09591837972402573,
0.006065107882022858,
0.06950746476650238,
0.047602392733097076,
-0.06612294912338257,
-0.005698681343346834,
-0.05403229221701622,
0.04710763692855835,
-0.04034337401390076,
0.013469270430505276,
-0.011811119504272938,
-0.03400224819779396,
0.0075844028033316135,
-0.05855429172515869,
-0.05468025058507919,
-0.005331859923899174,
-0.011471717618405819,
0.06842855364084244,
0.028870098292827606,
-0.02693459764122963,
0.044459983706474304,
-0.0293880645185709,
0.00992555171251297,
-0.0077746049501001835,
0.008897615596652031,
0.06483054906129837,
0.02790665812790394,
0.029626822099089622,
-0.019495591521263123,
-0.0786181092262268,
-0.025742903351783752,
0.0323038212954998,
-0.018135635182261467,
0.02393433451652527,
-0.04364442080259323,
-0.041114840656518936,
0.0075947605073452,
0.04243107885122299,
0.011256872676312923,
-0.010056661441922188,
-0.019405007362365723,
-0.025189854204654694,
-0.029677361249923706,
-0.00875483825802803,
0.07910396158695221,
0.019064243882894516,
-0.005199610721319914,
0.013622529804706573,
0.001069138408638537,
-0.012278420850634575,
-0.00877421349287033,
-0.008301391266286373,
0.02624920941889286,
0.03350228816270828,
0.05108538642525673,
-0.025914324447512627,
-0.03608741611242294,
0.053196754306554794,
0.04994598776102066,
-0.024351803585886955,
-0.04268147423863411,
-0.06282931566238403,
0.03965398296713829,
0.03917375206947327,
-0.016216009855270386,
0.012341012246906757,
0.009250173345208168,
0.00792080257087946,
0.028603021055459976,
0.016283255070447922,
0.05678781494498253,
-0.009140091016888618,
-0.009964721277356148,
-0.05709696188569069,
0.07127423584461212,
0.10585024952888489,
0.006363545544445515,
-0.08563166111707687,
0.0031137950718402863,
-0.06885191798210144,
0.06682086735963821,
0.10127244889736176,
-0.016335131600499153,
0.0966549664735794,
0.025131646543741226,
-0.015210354700684547,
0.03931491822004318,
0.03619048371911049,
0.03959369286894798,
-0.034346550703048706,
0.009845263324677944,
0.03177713230252266,
-0.031251296401023865,
-0.05620122328400612,
-0.01395378541201353,
-0.00833224505186081,
-0.004704372491687536,
-0.024365991353988647,
0.020498136058449745,
-0.019093478098511696,
-0.060315996408462524,
-0.0011582744773477316,
-0.014116810634732246,
0.029881222173571587,
0.009664822369813919,
0.009325218386948109,
0.033315278589725494,
0.04372773319482803,
0.02098853513598442,
-0.01279766857624054,
-0.006875861901789904,
0.008569831028580666,
0.007705364841967821,
0.010571427643299103,
-0.004311710130423307,
0.0017559746047481894,
-0.06416380405426025,
-0.03275164216756821,
0.00174437474925071,
-0.04356946051120758,
-0.029116123914718628,
0.04021725058555603,
0.06270261108875275,
-0.016436029225587845,
0.0182656142860651,
-0.002883761888369918,
0.03030041977763176,
-0.013660330325365067,
0.0658024325966835,
-0.006557900458574295,
-0.005943313241004944,
-0.0020078010857105255,
0.02063324861228466,
0.05637776106595993,
0.04254445433616638,
-0.00981612503528595,
-0.026401827111840248,
-0.006445758976042271,
-0.023586859926581383,
-0.024792160838842392,
0.032124727964401245,
-0.017936211079359055,
0.047145649790763855,
-0.02110270969569683,
0.07227024435997009,
0.05125775188207626,
0.08955741673707962,
0.017360351979732513,
0.029614154249429703,
-0.00048738770419731736,
0.017056908458471298,
-0.02210661582648754,
0.009329422377049923,
0.017081398516893387,
-0.02548053115606308,
0.027229519560933113,
-0.027752477675676346,
-0.030807940289378166,
0.07581515610218048,
-0.017647145316004753,
0.03427018225193024,
-0.03180209919810295,
0.00047232856741175056,
-0.04901780188083649,
0.03614659234881401,
0.012123394757509232,
-0.0005100444541312754,
-0.024488277733325958,
0.0943073034286499,
0.046942517161369324,
0.02061728574335575,
0.014309372752904892,
-0.00884617492556572,
0.02339359186589718,
0.007354523055255413,
-0.034719645977020264,
-0.016367938369512558,
-0.028514521196484566,
0.03261188045144081,
0.010781905613839626,
0.06012320891022682,
0.024908000603318214,
0.023891370743513107,
0.038117289543151855,
0.007880544289946556,
0.016028573736548424,
-0.054259803146123886,
0.026573628187179565,
0.039764877408742905,
0.021493103355169296,
0.03353752940893173,
0.03741968050599098,
0.005156242288649082,
-0.0734630823135376,
0.022318685427308083,
-0.03396201133728027,
-0.07257180660963058,
0.04539799690246582,
0.04307711869478226,
-0.05053362995386124,
0.002236147178336978,
-0.013874075375497341,
0.005319269839674234,
0.047907065600156784,
-0.03674371540546417,
-0.05044949799776077,
-0.028363045305013657,
-0.08898665755987167,
-0.0003637027111835778,
-0.038397010415792465,
-0.004866014700382948,
0.03688078746199608,
0.021335037425160408,
0.03497050702571869,
-0.015612557530403137,
-0.01906319335103035,
0.03956031799316406,
0.03346873074769974,
0.08261355012655258,
-0.0233109463006258,
0.015612580813467503,
0.009784541092813015,
-0.03743375465273857,
-0.014972330071032047,
-0.06257567554712296,
-0.016462821513414383,
-0.022130170837044716,
0.0266061220318079,
0.0001765829074429348,
0.01294526644051075,
-0.0018929354846477509,
-0.042788028717041016,
0.02773437090218067,
-0.025683118030428886,
-0.0076314727775752544,
-0.02848592959344387,
0.047836728394031525,
-0.00802625622600317,
-0.05217903479933739,
0.05668241158127785,
0.023514365777373314,
0.0326249934732914,
0.034635450690984726,
0.019325323402881622,
-0.0023957029916346073,
0.04517518728971481,
0.004180261865258217,
0.0006305408314801753,
0.010728023014962673,
-0.04350646957755089,
0.058126624673604965,
0.03677845746278763,
0.015625931322574615,
-0.02778267301619053,
0.014043872244656086,
0.06676531583070755,
-0.011624273844063282,
0.04359070211648941,
0.022747425362467766,
-0.05799909308552742,
-0.027126556262373924,
-0.00927803386002779,
0.011187100782990456,
0.018334485590457916,
0.030398191884160042,
-0.044572144746780396,
-0.026578111574053764,
0.05766695737838745,
0.05783207714557648,
0.09806621819734573,
0.004011469427496195,
0.05824817344546318,
-0.01677718199789524,
-0.004987320862710476,
0.0777575820684433,
0.04809023067355156,
0.002008673269301653,
0.03981819376349449,
0.003504483262076974,
0.03829112648963928,
-0.019887354224920273,
0.009653172455728054,
-0.029070883989334106,
0.02111227624118328,
-0.020633652806282043,
0.00919845700263977,
-0.01885959319770336,
0.024139637127518654,
-0.05648934096097946,
-0.00029323683702386916,
-0.019128456711769104,
-0.02102862298488617,
-0.010806749574840069,
0.0032427904661744833,
0.0019582086242735386,
0.05160309746861458,
0.030603814870119095,
-0.011563858017325401,
-0.046319130808115005,
-0.04502643272280693,
-0.05220794677734375,
-0.03280234709382057,
-0.1216534823179245,
-0.0055169169791042805,
-0.010194262489676476,
-0.004772499203681946,
0.06344101577997208,
0.0142816212028265,
0.014556564390659332,
0.007287222426384687,
-0.020318957045674324,
-0.040437135845422745,
0.014076112769544125,
0.035080183297395706,
0.02691945806145668,
-0.03537894785404205,
0.015731384977698326,
-0.003095431951805949,
0.02120991051197052,
0.04184550791978836,
0.009376890026032925,
-0.011866878718137741,
-0.0519038625061512,
-0.00818074680864811,
0.02774580754339695,
0.017982251942157745,
0.0020651016384363174,
-0.01687329262495041,
0.025944653898477554,
0.04523460566997528,
-0.020069457590579987,
0.04255388677120209,
-0.009685266762971878,
-0.035322822630405426,
-0.046077754348516464,
0.05411229282617569,
0.027596257627010345,
0.052212752401828766,
-0.05771063640713692,
0.004537364933639765,
-0.0021353275515139103,
-0.022141272202134132,
-0.05763963982462883,
-0.008148480206727982,
-0.007898302748799324,
0.02714042365550995,
0.005572120193392038,
-0.01795163005590439,
-0.051306985318660736,
-0.0013595422497019172,
0.03164088726043701,
0.008719922974705696,
-0.03229854255914688,
-0.00863516516983509,
0.023011336103081703,
-0.01602337136864662,
-0.055205006152391434,
-0.030195124447345734,
-0.05461271107196808,
-0.01630856841802597,
0.03523184359073639,
-0.0403623953461647,
-0.00422604801133275,
-0.010913750156760216,
0.03506745770573616,
0.034828174859285355,
-0.051582273095846176,
-0.031451888382434845,
-0.003135029226541519,
0.02620784565806389,
0.0456438809633255,
-0.012952165678143501,
0.025860676541924477,
-0.0038599453400820494,
-0.07145514339208603,
-0.0045423381961882114,
-0.041002582758665085,
0.02564355544745922,
-0.031399812549352646,
-0.025821363553404808,
-0.02795645035803318,
-0.009509180672466755,
0.05170291289687157,
-0.029392747208476067,
-0.012814179994165897,
0.0215940922498703,
0.0042722467333078384,
0.020812582224607468,
-0.0076858485117554665,
0.011210360564291477,
-0.004989870358258486,
-0.05034444481134415,
0.0521567240357399,
-0.012467274442315102,
-0.001923013012856245,
-0.017212288454174995,
-0.030331414192914963,
0.03011561743915081,
-0.00005233778938418254,
0.04267085716128349,
0.027949463576078415,
-0.027153272181749344,
-0.02922615222632885,
0.06423045694828033,
-0.04889332130551338,
-0.02275938354432583,
0.0043768067844212055,
-0.01483824010938406,
-0.006008805241435766,
-0.006812079343944788,
0.002227461664006114,
0.0158089529722929,
0.011792651377618313,
0.060113102197647095,
-0.019736867398023605,
-0.05655761808156967,
0.04995866119861603,
0.0005040405667386949,
0.06892690807580948,
0.004847124684602022,
0.07439656555652618,
-0.0029491265304386616,
-0.08461418002843857,
-0.0006977266748435795,
-0.052817054092884064,
0.02577969804406166,
0.0034099812619388103,
-0.023392297327518463,
-0.011412468738853931,
0.032969389110803604,
-0.012666798196732998,
-0.028014857321977615,
0.015697689726948738,
0.005504258908331394,
0.012761734426021576,
-0.0072941854596138,
-0.02095257304608822,
0.024863459169864655,
0.011337979696691036,
0.0022653795313090086,
-0.05230904743075371,
-0.02809816412627697,
-0.00252898340113461,
0.006854221690446138,
-0.024265902116894722,
-0.006309424061328173,
0.006862746085971594,
-0.012166228145360947,
-0.035537563264369965,
0.03870679438114166,
-0.015645772218704224,
0.008309274911880493,
-0.09448084980249405,
-0.0043839095160365105,
0.03384840860962868,
0.042731355875730515,
-0.008218377828598022,
0.031027989462018013,
-0.04790240153670311,
-0.04759381711483002,
0.014712671749293804,
0.024531353265047073,
-0.013128824532032013,
0.024276714771986008,
0.04517597705125809,
-0.014154837466776371,
-0.023588141426444054,
-0.005821529310196638,
-0.002195044420659542,
-0.035488877445459366,
-0.06305989623069763,
0.025121456012129784,
-0.02086067758500576,
-0.010376968421041965,
-0.044824521988630295
] |
<p><strong>If any equations are there ,for split the light particle, means
that i have a 1m length of light just consider that in that who can i
split the light particle into 1/2 m length Pls tell</strong> </p> | g6613 | [
0.008809944614768028,
0.03234610706567764,
-0.0029986160807311535,
-0.0063290074467659,
0.02388668805360794,
-0.02975541353225708,
-0.024128692224621773,
0.0009605145896784961,
0.03501228615641594,
-0.014410842210054398,
-0.00423715403303504,
0.003804980544373393,
-0.06017950177192688,
-0.007503341417759657,
0.00369343557395041,
-0.02305402047932148,
0.07883558422327042,
-0.05278795212507248,
0.020986242219805717,
0.03372323885560036,
-0.04858950525522232,
0.0025874332059174776,
0.0002503292926121503,
-0.0842568427324295,
0.0037049369420856237,
-0.036696985363960266,
0.037036631256341934,
0.006394180003553629,
-0.06678061187267303,
0.03254837915301323,
0.04405594617128372,
-0.01401430368423462,
0.0448453351855278,
-0.03026210330426693,
-0.04140055924654007,
-0.052273672074079514,
0.05438855662941933,
-0.02407883107662201,
0.014745170250535011,
0.026653572916984558,
0.02487361803650856,
-0.02395697310566902,
0.023667415603995323,
-0.04288431629538536,
0.031688813120126724,
-0.001383457682095468,
-0.004456010647118092,
0.02863325923681259,
-0.01250483188778162,
-0.09137865155935287,
-0.008347772061824799,
0.007623753510415554,
-0.02600673772394657,
0.013512801378965378,
0.018600542098283768,
0.03660503774881363,
-0.00308660208247602,
-0.05573815479874611,
0.06231939420104027,
0.02114729955792427,
0.008064983412623405,
-0.05999273061752319,
0.017637819051742554,
0.020201776176691055,
0.03805660828948021,
0.0036557589191943407,
-0.024181900545954704,
-0.07502482086420059,
-0.01866927556693554,
0.0030758981592953205,
0.025814665481448174,
-0.020162880420684814,
0.030070703476667404,
-0.05009875074028969,
-0.030719870701432228,
-0.0488470084965229,
0.0033312449231743813,
0.05793379247188568,
-0.0024775592610239983,
0.03688483685255051,
0.0074156043119728565,
-0.020771563053131104,
-0.022604892030358315,
0.022289790213108063,
0.0010073371231555939,
0.006252852734178305,
0.03251635655760765,
-0.030130799859762192,
-0.009309157729148865,
0.00693102739751339,
-0.020490873605012894,
-0.06220194324851036,
0.03247750923037529,
-0.0026268784422427416,
-0.006292527541518211,
-0.014429336413741112,
0.03903280571103096,
0.03371473774313927,
-0.029813092201948166,
-0.002271966775879264,
-0.0259584691375494,
0.01321231760084629,
-0.024490518495440483,
-0.00035110715543851256,
0.0378926582634449,
0.011799517087638378,
0.015030158683657646,
0.002726802369579673,
0.008989563211798668,
-0.00348004512488842,
0.012397252023220062,
-0.04492213577032089,
-0.08688739687204361,
0.009636472910642624,
-0.01173205766826868,
-0.05368747562170029,
0.08708995580673218,
-0.05895749107003212,
-0.020010925829410553,
0.026211990043520927,
0.0314534455537796,
-0.04839286953210831,
0.03919234499335289,
0.04688343033194542,
-0.010207561776041985,
-0.009568209759891033,
0.05094973370432854,
0.045831773430109024,
0.014292886480689049,
-0.029204120859503746,
0.016704149544239044,
-0.01337892934679985,
0.016109274700284004,
0.03257995843887329,
-0.05733034387230873,
0.06457240134477615,
0.07384926080703735,
-0.0032652902882546186,
0.008602926507592201,
0.007413126528263092,
-0.02684623934328556,
-0.01914733275771141,
0.01848687417805195,
0.007486459333449602,
-0.037060681730508804,
0.02230430208146572,
0.012472327798604965,
0.005100110545754433,
-0.019960980862379074,
0.0541682094335556,
-0.0007095457403920591,
0.055298540741205215,
-0.037231527268886566,
0.024899648502469063,
-0.015316436998546124,
-0.04782348498702049,
-0.009528973139822483,
-0.013482972979545593,
-0.027644570916891098,
-0.01304816547781229,
0.030135322362184525,
0.0653034895658493,
-0.05721953138709068,
-0.013591596856713295,
-0.1287352591753006,
0.03244408592581749,
-0.028903720900416374,
-0.043800950050354004,
-0.0111243249848485,
-0.0963967889547348,
-0.05687791481614113,
0.06623336672782898,
0.07460248470306396,
-0.027215519919991493,
0.029895147308707237,
0.018619436770677567,
-0.03182835504412651,
0.017834404483437538,
-0.012310046702623367,
0.06084132194519043,
-0.02937040477991104,
0.021757299080491066,
0.034349165856838226,
-0.02449236623942852,
-0.024678312242031097,
-0.032058436423540115,
-0.040687043219804764,
-0.03152688220143318,
-0.014921868219971657,
-0.029856521636247635,
0.005663187708705664,
0.04706630855798721,
-0.0009028769563883543,
0.021631108596920967,
-0.007927223108708858,
-0.032683584839105606,
0.007961422204971313,
0.015051268972456455,
-0.038374073803424835,
0.019368911162018776,
0.024801313877105713,
0.06585898250341415,
0.0073029357008636,
0.03655674681067467,
0.05668584257364273,
-0.05787672474980354,
-0.0018312743632122874,
-0.003180445171892643,
0.024473516270518303,
0.006084311753511429,
0.0468270368874073,
-0.024798288941383362,
0.01379158440977335,
0.008734040893614292,
-0.05155494809150696,
-0.0647689551115036,
-0.006995198782533407,
-0.000239901986788027,
0.011781774461269379,
-0.020507151260972023,
0.010370273143053055,
0.043355755507946014,
0.06223919987678528,
-0.025007760152220726,
0.0013551710871979594,
0.019682815298438072,
-0.003304692218080163,
-0.015087290666997433,
0.026729928329586983,
0.029789090156555176,
-0.03377583622932434,
0.026899952441453934,
0.018519723787903786,
-0.006837294436991215,
0.042895086109638214,
0.0010660119587555528,
-0.07389196753501892,
0.025002693757414818,
-0.00714271143078804,
0.00850710179656744,
0.008855056948959827,
-0.022106757387518883,
-0.003845229046419263,
0.006676706485450268,
-0.008267122320830822,
0.026599163189530373,
0.012522506527602673,
-0.025671809911727905,
-0.04649633541703224,
-0.03498663753271103,
0.005782025866210461,
-0.007448095362633467,
-0.031413108110427856,
0.029468141496181488,
-0.03820512816309929,
-0.07871027290821075,
-0.017316563054919243,
0.060507066547870636,
-0.10341386497020721,
-0.031539447605609894,
-0.0019453266868367791,
0.030589720234274864,
0.0005787981790490448,
-0.0007927383994683623,
-0.05539685860276222,
-0.02403545193374157,
-0.0017468467121943831,
0.04119015857577324,
0.04225142300128937,
-0.0019182795658707619,
-0.011920711025595665,
0.04288443922996521,
0.017305517569184303,
0.01056792214512825,
-0.05184146761894226,
0.00878725852817297,
-0.014536400325596333,
-0.032873477786779404,
0.029835281893610954,
-0.026548102498054504,
0.00007279690908035263,
0.006087622605264187,
-0.05059771239757538,
0.017293494194746017,
0.046187885105609894,
-0.07103496044874191,
-0.012390600517392159,
-0.008261640556156635,
-0.02890390157699585,
0.026610177010297775,
-0.037923648953437805,
0.007307861000299454,
0.04252133145928383,
-0.03395973518490791,
-0.012813159264624119,
-0.009955658577382565,
0.019041916355490685,
0.01196043100208044,
-0.019245600327849388,
-0.05051551014184952,
0.0037234663031995296,
-0.0023308603558689356,
-0.010685528628528118,
0.03819470480084419,
0.049198735505342484,
0.0356488898396492,
0.011347471736371517,
-0.004786030855029821,
0.05316240340471268,
0.0014531955821439624,
0.017241835594177246,
0.07562679052352905,
0.08942326158285141,
-0.026657061651349068,
-0.04489721730351448,
-0.042880717664957047,
-0.06190551817417145,
-0.03205212578177452,
-0.030093681067228317,
-0.0050192940980196,
0.040271539241075516,
-0.07228580862283707,
-0.020760223269462585,
-0.027980631217360497,
-0.030859149992465973,
-0.06250375509262085,
0.005677917506545782,
-0.005641002673655748,
-0.03813894838094711,
0.03298509120941162,
-0.05817165970802307,
-0.05057211592793465,
-0.005645722150802612,
-0.004937125835567713,
-0.0003900952578987926,
-0.021365264430642128,
0.021045871078968048,
-0.03416670113801956,
0.04232776165008545,
-0.07159032672643661,
-0.024011077359318733,
0.00338254333473742,
-0.08270703256130219,
0.057289257645606995,
-0.013283705338835716,
-0.011342054232954979,
-0.0214524082839489,
0.03026120737195015,
0.06556125730276108,
-0.030042069032788277,
-0.0018297376809641719,
0.025198061019182205,
-0.023402119055390358,
-0.07748272269964218,
0.0210577305406332,
-0.004543299321085215,
0.05429304018616676,
0.07119667530059814,
0.019056906923651695,
-0.012869144789874554,
0.03067578375339508,
0.022850871086120605,
0.05296020582318306,
0.023218734189867973,
-0.03532986715435982,
0.022592181339859962,
-0.0006532445549964905,
0.04937402904033661,
-0.004919958300888538,
0.007280793506652117,
0.026885146275162697,
-0.033151961863040924,
0.012719382531940937,
0.04814878851175308,
-0.017071478068828583,
-0.001261006691493094,
0.04249780625104904,
-0.02929338440299034,
0.03393450379371643,
0.01269487850368023,
0.0338040329515934,
0.04415447264909744,
0.01679288037121296,
0.04962576553225517,
-0.0016258730320259929,
0.001008909777738154,
-0.026566676795482635,
-0.011969302780926228,
-0.0019380308222025633,
-0.00622697826474905,
0.06893216073513031,
-0.09157753735780716,
-0.04928918927907944,
0.009771664626896381,
-0.023248877376317978,
0.004569647368043661,
-0.03200275078415871,
0.00953864585608244,
-0.06905490905046463,
-0.00720540527254343,
-0.04256201162934303,
0.003132687881588936,
0.011065494269132614,
-0.02567286789417267,
-0.007816562429070473,
0.016272038221359253,
-0.026978421956300735,
-0.06594433635473251,
0.012272818014025688,
0.03602002561092377,
0.03156478703022003,
-0.005806359462440014,
-0.012951940298080444,
-0.058864906430244446,
-0.028501367196440697,
-0.02511822059750557,
-0.023899201303720474,
0.009113956242799759,
0.020068097859621048,
0.0034614086616784334,
-0.0002493645588401705,
0.008168242871761322,
-0.02374342642724514,
0.017552262172102928,
-0.08182206004858017,
0.021695714443922043,
0.03357849270105362,
0.033669933676719666,
0.006505705416202545,
-0.02843031845986843,
-0.016303174197673798,
-0.02385588176548481,
-0.01333770714700222,
-0.058052267879247665,
0.0030303436797112226,
0.053867559880018234,
-0.00473722955211997,
-0.004155071452260017,
-0.03339114785194397,
0.03646857291460037,
0.0333516001701355,
-0.005901569966226816,
0.06169331446290016,
0.003015098161995411,
0.06008625403046608,
-0.04367293417453766,
0.0006483405013568699,
-0.03477868810296059,
-0.04443066939711571,
-0.03313305974006653,
0.01342792995274067,
0.012111752294003963,
-0.05347906053066254,
-0.043531496077775955,
-0.01153169572353363,
0.00770283117890358,
-0.02502436935901642,
-0.009499900974333286,
0.007227947004139423,
0.045124221593141556,
-0.01684695854783058,
-0.0425526462495327,
0.09439355134963989,
-0.028690608218312263,
-0.006439195945858955,
-0.0003028804494533688,
-0.08826802670955658,
0.027415135875344276,
0.009879772551357746,
0.011554940603673458,
-0.05909915268421173,
-0.0009399459231644869,
-0.01040488202124834,
-0.039086490869522095,
-0.008680474013090134,
-0.04174618795514107,
-0.06112522631883621,
-0.002738261828199029,
-0.013483863323926926,
0.001023232121951878,
0.013776049017906189,
-0.011456689797341824,
-0.010112036019563675,
-0.00602469639852643,
0.07497608661651611,
0.04025426134467125,
0.010445808991789818,
0.02482953853905201,
-0.003171484684571624,
-0.11327113956212997,
-0.009342964738607407,
0.06220490485429764,
-0.03576270863413811,
-0.006043475586920977,
-0.03403123840689659,
0.015569034032523632,
0.009947344660758972,
-0.04224727302789688,
0.03682701662182808,
0.04951101914048195,
0.001757943071424961,
-0.02559387870132923,
0.04366089031100273,
0.008360018022358418,
-0.03834552690386772,
0.012726033106446266,
-0.009186474606394768,
0.0062504480592906475,
-0.049136679619550705,
0.034462638199329376,
0.11904092133045197,
-0.042954664677381516,
0.06575385481119156,
0.021113432943820953,
-0.00007211721822386608,
-0.021057240664958954,
0.020342400297522545,
0.10513238608837128,
0.004824652802199125,
0.005091846454888582,
-0.0034934321884065866,
-0.053035080432891846,
0.08523021638393402,
-0.01400342583656311,
0.011539699509739876,
-0.05344250053167343,
-0.09836689382791519,
-0.01316033024340868,
0.04979986324906349,
0.0313439667224884,
0.021508662030100822,
0.03148868680000305,
-0.033809974789619446,
0.0066449581645429134,
0.01170854177325964,
-0.0636182650923729,
0.042294543236494064,
-0.015308920294046402,
-0.02072487771511078,
-0.049471303820610046,
0.0012474539689719677,
-0.013816985301673412,
-0.005867575760930777,
0.054496828466653824,
-0.01653168350458145,
-0.011027932167053223,
-0.03395526483654976,
-0.003324101446196437,
0.023445438593626022,
-0.029019832611083984,
0.07841723412275314,
0.01759609766304493,
0.003593775676563382,
-0.008127925917506218,
0.05489683896303177,
0.0257075484842062,
-0.021384643390774727,
-0.015408176928758621,
-0.001549220411106944,
0.035685282200574875,
-0.01966971904039383,
-0.015474542044103146,
0.028307948261499405,
-0.04782382771372795,
-0.02814732864499092,
-0.01880398578941822,
-0.0016417086590081453,
-0.05470661818981171,
-0.0006724241538904607,
0.04828551784157753,
0.021367469802498817,
0.011075091548264027,
0.012377593666315079,
-0.0005619129515253007,
0.019491884857416153,
-0.026401076465845108,
0.029789280146360397,
-0.02105504274368286,
-0.06368303298950195,
-0.013838517479598522,
-0.006431150250136852,
0.04882539436221123,
0.01267852634191513,
-0.016767382621765137,
-0.04678783938288689,
0.06878524273633957,
-0.020014839246869087,
0.026736542582511902,
0.05029233545064926,
-0.011451203376054764,
0.029438553377985954,
-0.026368020102381706,
-0.045650675892829895,
-0.062272120267152786,
-0.04275594651699066,
-0.016771715134382248,
0.03761174529790878,
-0.022752031683921814,
0.0183868445456028,
0.019691217690706253,
0.028954021632671356,
0.06656372547149658,
-0.025911826640367508,
0.012531975284218788,
0.03746237978339195,
-0.0018808591412380338,
-0.03874680772423744,
0.017238132655620575,
0.06466095894575119,
0.014330095611512661,
-0.005424927920103073,
0.016806792467832565,
-0.008983067236840725,
0.0018141631735488772,
-0.032664839178323746,
-0.03397364541888237,
0.00336338859051466,
-0.004910860676318407,
0.03289514780044556,
-0.007674399297684431,
-0.022680429741740227,
-0.031811751425266266,
-0.023584647104144096,
-0.06454755365848541,
0.05162922292947769,
0.11789047718048096,
-0.005401500966399908,
0.035893771797418594,
0.012370560318231583,
0.014494520612061024,
0.06689674407243729,
0.010502117685973644,
0.011648912914097309,
0.0037303308490663767,
0.029550207778811455,
0.03108813986182213,
-0.00966672319918871,
0.0029749118257313967,
-0.0058914716355502605,
0.11326602846384048,
0.046323634684085846,
0.03327799588441849,
0.03109363093972206,
0.020341554656624794,
-0.03667953237891197,
0.01536957360804081,
0.02412586100399494,
0.047991763800382614,
0.004868173506110907,
-0.028433717787265778,
-0.04464463144540787,
0.048846643418073654,
-0.04067124053835869,
0.03637075051665306,
0.030172379687428474,
-0.03339936584234238,
-0.03471149504184723,
-0.024739792570471764,
0.026487581431865692,
-0.04413105174899101,
0.003681376576423645,
-0.02755182422697544,
0.03681075572967529,
-0.07089850306510925,
0.0008492720080539584,
0.028887489810585976,
0.007095435634255409,
-0.02043348178267479,
-0.02196473255753517,
-0.02758052945137024,
-0.01601419970393181,
-0.0485554076731205,
-0.022738218307495117,
0.023759067058563232,
-0.03102591447532177,
0.01980181783437729,
-0.0015889956848695874,
0.040314026176929474,
0.02170741930603981,
-0.04733505845069885,
0.07167581468820572,
0.03687050938606262,
-0.031198957934975624,
-0.0008673352422192693,
0.014895268715918064,
-0.02440294623374939,
0.009425537660717964,
-0.031955163925886154,
0.07018774002790451,
0.01920800656080246,
-0.01608465611934662,
0.01849229820072651,
-0.00309633812867105,
-0.004067319445312023,
-0.0443129800260067,
-0.02585662715137005,
-0.00010805845522554591,
0.07922209054231644,
0.07257860153913498,
0.022539734840393066,
-0.01155238039791584,
-0.010515358299016953,
0.03586605191230774,
0.026121584698557854,
-0.01114126481115818,
-0.005635568872094154,
-0.01773533597588539,
0.010607769712805748,
0.0006506494246423244,
-0.03806658834218979,
-0.011728774756193161,
0.04193919897079468,
-0.015079171396791935,
0.035309694707393646,
0.01734633557498455,
0.012616113759577274,
0.013106072321534157,
0.049687910825014114,
0.09433571249246597,
0.006561491172760725,
0.008026588708162308,
-0.061730850487947464,
-0.019528469070792198,
-0.01704452373087406,
-0.007075236178934574,
-0.007928548380732536,
0.04393325373530388,
0.001123911584727466,
-0.014639308676123619,
0.03168296813964844,
0.09543102979660034,
0.02058178186416626,
-0.0032597738318145275,
-0.03077189438045025,
-0.01938355714082718,
0.0021368816960603,
-0.017791444435715675,
0.027106430381536484,
0.00401823315769434,
0.048134706914424896,
-0.009803405031561852,
-0.0774914100766182,
-0.04984922334551811,
-0.006241677328944206,
0.011742337606847286,
-0.024700528010725975,
-0.06254570186138153,
0.026401350274682045,
0.05432320386171341,
0.012573645450174809,
0.004302150569856167,
0.03583182021975517,
0.002072704490274191,
0.06326421350240707,
0.04976995661854744,
-0.0973975732922554,
0.01006518118083477,
0.01629512570798397,
-0.042399343103170395,
-0.00914961937814951,
0.003213695017620921,
-0.019727760925889015,
0.05491822212934494,
0.05054822564125061,
0.044897742569446564,
0.03339701518416405,
-0.005860649514943361,
-0.004111462272703648
] |
<p>While watching a <a href="http://en.wikipedia.org/wiki/Schlieren_photography" rel="nofollow">Schlieren</a> video of a <a href="https://www.youtube.com/watch?v=4CR22kpG3ig" rel="nofollow">hand clapping</a>, I noted a very distinct difference between a sound wave and a puff of air, which were both created by a hand clapping. What is the difference between a puff of air and a sound wave regarding creation and propagation?</p>
<p>In the video, it appears that some of the energy goes into the sound wave and some of the energy goes into the puff. Is there a principle that governs the distribution of impact energy between oscillation (sound) and pushing (puff?) </p> | g6614 | [
0.08384833484888077,
0.073977991938591,
-0.006369912065565586,
0.013381336815655231,
-0.010485394857823849,
0.07869991660118103,
0.04811746999621391,
0.08355558663606644,
0.0005751876742579043,
-0.06131456419825554,
-0.016468416899442673,
-0.019904348999261856,
-0.013665001839399338,
0.0450914092361927,
0.08835349977016449,
-0.02511064149439335,
0.06035479158163071,
-0.04272361844778061,
0.010289349593222141,
0.07585598528385162,
-0.018350351601839066,
-0.004585402086377144,
-0.045863520354032516,
-0.06827966123819351,
0.010753914713859558,
-0.023226451128721237,
-0.012861919589340687,
-0.0600050650537014,
-0.03184530511498451,
-0.07790631800889969,
0.009901560842990875,
0.04771178588271141,
0.07913520932197571,
-0.008925927802920341,
-0.037034906446933746,
0.011387346312403679,
0.0339181050658226,
-0.06403252482414246,
-0.004839964676648378,
0.006077186204493046,
0.0013869075337424874,
-0.02260078676044941,
0.015699751675128937,
-0.02733941189944744,
-0.008936001919209957,
0.027850143611431122,
-0.016840560361742973,
0.03049486130475998,
0.012159446254372597,
-0.027688145637512207,
-0.012177192606031895,
-0.04954086244106293,
-0.035333894193172455,
0.014535259455442429,
0.02335837110877037,
-0.01234493125230074,
0.038640379905700684,
-0.02585803158581257,
0.0656011700630188,
-0.008867952041327953,
-0.03838595002889633,
0.05811396241188049,
0.02134229987859726,
0.02088073082268238,
0.027282094582915306,
-0.010969760827720165,
-0.027611229568719864,
-0.018879162147641182,
0.061674561351537704,
0.015467624180018902,
0.04736122488975525,
-0.04553814232349396,
0.00561571167781949,
0.02233475260436535,
0.007937743328511715,
0.012846535071730614,
0.010421019978821278,
-0.020194299519062042,
-0.007050875574350357,
0.04742363095283508,
0.043649058789014816,
0.01540882047265768,
0.059397537261247635,
-0.011513526551425457,
0.08638425916433334,
-0.01893373765051365,
-0.02682610973715782,
0.017765291035175323,
-0.019748913124203682,
0.01537372823804617,
-0.01256510429084301,
-0.014408084563910961,
0.0925910472869873,
0.0367000587284565,
-0.05326593667268753,
-0.036991480737924576,
-0.051514238119125366,
0.10645856708288193,
0.04241056740283966,
-0.00282437726855278,
-0.013972864486277103,
-0.02032341994345188,
0.025682510808110237,
0.0027834626380354166,
-0.025981426239013672,
-0.01999458111822605,
-0.01701486110687256,
-0.027333373203873634,
-0.02215416356921196,
-0.029757047072052956,
-0.026009606197476387,
-0.03720858693122864,
0.01901589147746563,
0.015005160123109818,
0.005615530535578728,
-0.023676998913288116,
-0.00513291172683239,
0.0482960045337677,
-0.003296816721558571,
0.05303812399506569,
0.029919642955064774,
-0.04620921239256859,
-0.04744157940149307,
0.016684824600815773,
-0.007077193818986416,
-0.003033439861610532,
-0.0025457649026066065,
-0.06107762083411217,
-0.002812459832057357,
0.029569296166300774,
0.03009008802473545,
-0.008371514268219471,
0.022456806153059006,
-0.03829387575387955,
0.039563123136758804,
-0.02007485367357731,
0.010590349324047565,
-0.004324091598391533,
0.03413708508014679,
-0.009349600411951542,
0.061727650463581085,
-0.019943904131650925,
0.025219950824975967,
-0.0404522642493248,
-0.028568310663104057,
0.013039302080869675,
0.017248768359422684,
0.011383640579879284,
0.02637370489537716,
0.02923007868230343,
-0.01405855268239975,
0.03717466816306114,
-0.04275260120630264,
-0.01933782920241356,
0.022469040006399155,
0.017153723165392876,
-0.023521803319454193,
0.031179610639810562,
-0.01351141557097435,
0.028465477749705315,
0.013449195772409439,
-0.04195312783122063,
0.054383523762226105,
-0.008223573677241802,
-0.005671943537890911,
0.003706826362758875,
0.012328645214438438,
-0.055622730404138565,
0.006657175254076719,
0.03941228985786438,
-0.038489144295454025,
-0.027874428778886795,
-0.045996859669685364,
0.025827178731560707,
-0.021723223850131035,
0.060944247990846634,
0.05860523134469986,
-0.03248254582285881,
0.04202664643526077,
-0.0516357384622097,
-0.036050304770469666,
-0.06076280400156975,
-0.044749315828084946,
-0.037579506635665894,
0.05372995138168335,
0.022623801603913307,
0.03096761368215084,
-0.04877403751015663,
-0.05408762767910957,
0.0029479253571480513,
-0.052537452429533005,
-0.04641705006361008,
-0.018454745411872864,
0.024051904678344727,
-0.052076686173677444,
0.01915387250483036,
0.032780058681964874,
-0.03680836036801338,
-0.03930423781275749,
0.02749246172606945,
-0.015990622341632843,
-0.014358592219650745,
0.055765338242053986,
-0.040737226605415344,
-0.019063811749219894,
0.09302707761526108,
-0.0028128258418291807,
0.021140804514288902,
0.004656090866774321,
-0.02754145860671997,
-0.034601591527462006,
-0.012051675468683243,
0.037571799010038376,
0.0033958510030061007,
0.028801461681723595,
0.041794389486312866,
0.014586969278752804,
-0.02899756468832493,
-0.0348815992474556,
-0.015555167570710182,
0.01848219893872738,
0.03012125752866268,
0.05926733464002609,
-0.052400875836610794,
0.02004721574485302,
-0.03312944620847702,
-0.0059404801577329636,
-0.03038218803703785,
-0.055997658520936966,
0.031538840383291245,
-0.03131323307752609,
-0.02430458553135395,
-0.020976461470127106,
0.014281155541539192,
0.004103609826415777,
0.01434223260730505,
-0.001139226951636374,
0.001576690236106515,
0.002203154843300581,
-0.03493284061551094,
-0.020699091255664825,
-0.07951148599386215,
0.012630196288228035,
-0.012256472371518612,
0.00960597675293684,
-0.04868682846426964,
0.02813594602048397,
-0.021053485572338104,
0.006562119349837303,
0.002197884488850832,
0.021615060046315193,
-0.005627811886370182,
-0.01401451788842678,
-0.014833169989287853,
0.008711667731404305,
-0.011799231171607971,
-0.01978415809571743,
0.006634152960032225,
-0.011684421449899673,
0.0015878260601311922,
-0.012794229201972485,
-0.017958560958504677,
0.010031272657215595,
0.03144363686442375,
-0.05668574199080467,
0.00691373972222209,
0.009584013372659683,
0.032321035861968994,
-0.0485045425593853,
-0.03754917159676552,
-0.03511255607008934,
0.05921198055148125,
-0.04051951318979263,
-0.006435925606638193,
-0.03882419317960739,
-0.009899893775582314,
0.041045427322387695,
0.011518442071974277,
0.010296178981661797,
-0.010854020714759827,
0.02251424826681614,
-0.008214768022298813,
-0.0141378128901124,
0.015326405875384808,
0.04106829687952995,
-0.07958751171827316,
-0.0001726553018670529,
-0.008361311629414558,
0.007881324738264084,
0.020883167162537575,
-0.008565954864025116,
0.01558519434183836,
-0.033387862145900726,
0.04109114035964012,
-0.037633348256349564,
0.05644175037741661,
-0.002435702597722411,
-0.045562565326690674,
-0.04602905362844467,
-0.007242216728627682,
-0.0035051291342824697,
-0.03522436320781708,
0.0037062542978674173,
0.004906851798295975,
-0.0012094768462702632,
0.04810883104801178,
-0.021013472229242325,
-0.04152160510420799,
-0.01482956949621439,
-0.003422816749662161,
0.010147321969270706,
0.03139404579997063,
-0.01659378781914711,
0.023425985127687454,
-0.011797788552939892,
-0.07666178047657013,
-0.0075177354738116264,
0.006812987383455038,
0.022645113989710808,
0.012735101394355297,
-0.05329670011997223,
-0.04257113113999367,
0.006953629199415445,
0.011285376735031605,
0.04558686912059784,
0.007518148981034756,
-0.0012838257243856788,
0.030378930270671844,
-0.025866933166980743,
-0.054183073341846466,
-0.045705996453762054,
-0.007386409677565098,
-0.06711982190608978,
-0.04769400879740715,
0.01254427433013916,
-0.047426700592041016,
-0.042388666421175,
0.008880937471985817,
0.03152596950531006,
0.08358874917030334,
0.06898816674947739,
0.06966989487409592,
0.01352511253207922,
-0.024449005722999573,
-0.01989389955997467,
0.01996249333024025,
0.006479065865278244,
0.008059551008045673,
0.036567967385053635,
-0.09055033326148987,
0.06507272273302078,
0.008433863520622253,
0.0013848489616066217,
-0.003631048835813999,
-0.0019256504019722342,
-0.027416447177529335,
0.027205727994441986,
0.008110343478620052,
0.01650388538837433,
-0.012684717774391174,
-0.004082908388227224,
0.005690267309546471,
-0.0022628356236964464,
-0.011083169840276241,
0.010023537091910839,
-0.05756698548793793,
0.018030589446425438,
0.001756363664753735,
-0.010210709646344185,
0.0009247525595128536,
-0.026632236316800117,
-0.03767881169915199,
-0.021176941692829132,
0.021108051761984825,
0.03665202111005783,
-0.05891125276684761,
0.006242608185857534,
0.01015913300216198,
-0.004896423779428005,
0.044035930186510086,
0.007783227134495974,
0.009012638591229916,
0.02050895430147648,
-0.037364259362220764,
0.057323772460222244,
-0.021956320852041245,
0.0022445914801210165,
0.0022633655462414026,
0.026036754250526428,
-0.0631653293967247,
-0.036556001752614975,
-0.0814824178814888,
-0.03352920711040497,
0.022064248099923134,
0.034596025943756104,
0.003321345429867506,
-0.030566522851586342,
0.018144546076655388,
0.0019324923632666469,
0.10287855565547943,
0.025513263419270515,
-0.0012941688764840364,
-0.007438212167471647,
-0.05764837563037872,
0.022081462666392326,
0.04112861678004265,
0.057402174919843674,
-0.03777052462100983,
-0.0076088751666247845,
-0.047704026103019714,
0.0304248183965683,
-0.010413055308163166,
-0.02495875582098961,
-0.08373972028493881,
0.016327429562807083,
-0.0315493680536747,
0.07024655491113663,
-0.010070140473544598,
0.03504340350627899,
0.05015227198600769,
0.004067030735313892,
0.041767802089452744,
0.03493673726916313,
0.0262486282736063,
-0.0010963005479425192,
0.08694955706596375,
0.04407254233956337,
-0.010696356184780598,
-0.03365880623459816,
-0.03444463014602661,
-0.011952759698033333,
-0.01035620179027319,
0.043922021985054016,
0.006544408854097128,
-0.027364924550056458,
0.039554279297590256,
-0.041953667998313904,
-0.02111782878637314,
0.052311550825834274,
0.0034742355346679688,
0.1241784393787384,
-0.002615207340568304,
-0.06415656954050064,
0.027512334287166595,
0.061054255813360214,
0.027569040656089783,
0.013029024004936218,
-0.05209629237651825,
-0.045950453728437424,
-0.008240440860390663,
-0.07182437181472778,
0.013235863298177719,
0.0282417181879282,
-0.04548398405313492,
0.010708863846957684,
0.0314345508813858,
-0.018514450639486313,
-0.05465303361415863,
-0.03488157317042351,
-0.014689482748508453,
-0.005584534257650375,
-0.0010650248732417822,
0.05486435815691948,
-0.037817128002643585,
0.08414716273546219,
-0.029126258566975594,
-0.02854260988533497,
-0.057026635855436325,
-0.01859148219227791,
0.013047050684690475,
0.0495610237121582,
0.0021564802154898643,
-0.047001298516988754,
0.04812879115343094,
0.017617253586649895,
-0.03636360168457031,
-0.04347806051373482,
0.0005957354442216456,
0.05408162623643875,
-0.07100892812013626,
0.05257340148091316,
-0.03779405355453491,
-0.0008579888963140547,
0.034356240183115005,
0.013990470208227634,
0.03223944827914238,
-0.018930500373244286,
0.058281801640987396,
0.031012237071990967,
0.02540724165737629,
0.07086306810379028,
0.01605067029595375,
0.0025269249454140663,
-0.03307246044278145,
-0.04089972749352455,
-0.006909458432346582,
0.052892085164785385,
0.0032525670249015093,
-0.007135722320526838,
-0.018780680373311043,
-0.026653971523046494,
-0.00784239824861288,
-0.028731873258948326,
-0.01284824963659048,
-0.020773734897375107,
0.009820165112614632,
0.05311452969908714,
-0.010015340521931648,
-0.008058443665504456,
0.04378250241279602,
-0.013957662507891655,
-0.010854355059564114,
-0.0329887755215168,
0.019272999837994576,
0.013817149214446545,
0.020308079198002815,
-0.026678478345274925,
0.012730683200061321,
-0.017538199201226234,
-0.02655957080423832,
0.03919454663991928,
-0.028741003945469856,
0.023365451022982597,
-0.01831425540149212,
0.01587717793881893,
-0.026518693193793297,
-0.0392090305685997,
-0.04386306554079056,
0.054003290832042694,
0.0632624700665474,
-0.009230200201272964,
-0.007116042077541351,
0.059338804334402084,
0.005176869686692953,
0.028616786003112793,
-0.03804038465023041,
0.03558489307761192,
0.06501331180334091,
0.008039462380111217,
-0.018474292010068893,
-0.026577508077025414,
-0.01826193556189537,
-0.02226310968399048,
0.07194140553474426,
0.022214245051145554,
0.03282909095287323,
-0.008448432199656963,
0.05936991795897484,
0.0028175986371934414,
0.012219146825373173,
-0.032039713114500046,
0.03151853382587433,
0.061905309557914734,
0.06194230914115906,
0.014719570055603981,
-0.004275747109204531,
0.009379136376082897,
-0.05657663941383362,
-0.02290840819478035,
-0.034949056804180145,
0.04330058768391609,
0.0642893984913826,
0.024521097540855408,
-0.03534463793039322,
0.03220117464661598,
-0.023747285827994347,
-0.005641566589474678,
-0.055609770119190216,
0.04338708519935608,
0.04759029299020767,
0.0015739307273179293,
0.0284310020506382,
0.029761960729956627,
-0.022540388628840446,
-0.013241891749203205,
0.030220679938793182,
-0.010309685952961445,
-0.06081931293010712,
-0.02622200921177864,
0.012456412427127361,
0.01060551404953003,
0.018569279462099075,
0.05578719079494476,
-0.020304106175899506,
0.0056455680169165134,
-0.00538884149864316,
-0.011555164121091366,
-0.00656386511400342,
0.078624427318573,
0.025769643485546112,
0.034286245703697205,
-0.06729013472795486,
0.0014456628123298287,
-0.0624544695019722,
-0.005110317375510931,
-0.0574125237762928,
-0.011975414119660854,
-0.01087929867208004,
-0.004086502827703953,
0.0026448906864970922,
0.02980981208384037,
0.03129051998257637,
0.022896872833371162,
-0.009619687683880329,
-0.016344521194696426,
0.028061959892511368,
0.01584019884467125,
-0.01612487994134426,
0.01750355027616024,
0.012384540401399136,
-0.08363326638936996,
0.054552819579839706,
0.006825636141002178,
-0.03328132629394531,
0.028087031096220016,
-0.0182198379188776,
-0.03774665296077728,
-0.044188469648361206,
0.04640116170048714,
-0.007042976561933756,
0.00532380398362875,
-0.011142617091536522,
0.03433354198932648,
-0.0012750298483297229,
0.0414559468626976,
-0.014125922694802284,
-0.04936409369111061,
0.013272267766296864,
-0.0022303638979792595,
-0.035852059721946716,
-0.004266188479959965,
-0.01859046332538128,
-0.029250456020236015,
0.11653934419155121,
-0.04471305012702942,
0.02928108163177967,
-0.010765005834400654,
-0.001144228270277381,
-0.02456912025809288,
-0.023989038541913033,
-0.003286405699327588,
0.042749736458063126,
0.08690250664949417,
0.08036265522241592,
-0.03823476657271385,
0.015738731250166893,
0.0004504066309891641,
-0.011827844195067883,
-0.00437921704724431,
-0.06041434034705162,
-0.1229189932346344,
-0.03827083855867386,
-0.024441001936793327,
-0.014249080792069435,
-0.046621356159448624,
0.04900388419628143,
-0.021395429968833923,
0.003316617337986827,
0.012325221672654152,
-0.05291358381509781,
-0.043677918612957,
-0.09004135429859161,
-0.027638500556349754,
0.06150897592306137,
-0.009730669669806957,
0.031195301562547684,
0.017807940021157265,
0.010124375112354755,
0.01743893325328827,
0.01161176711320877,
0.07569380104541779,
-0.04791189357638359,
-0.02681262046098709,
-0.0328504741191864,
-0.019470680505037308,
-0.015335474163293839,
0.008610685355961323,
0.01992914453148842,
0.0158793106675148,
-0.06521837413311005,
0.02276606298983097,
-0.010302161797881126,
-0.01735963672399521,
-0.004304416477680206,
0.02370503358542919,
-0.01747613213956356,
-0.029607215896248817,
0.02914639189839363,
0.0016642825212329626,
-0.03489365056157112,
-0.001917422516271472,
0.0248983446508646,
0.005760928150266409,
0.0008241648320108652,
0.021180884912610054,
0.011773758567869663,
0.06177571043372154,
0.026429815217852592,
-0.0819801390171051,
0.027149569243192673,
0.01128390058875084,
0.015271667391061783,
0.03210771828889847,
-0.002888612449169159,
-0.009323963895440102,
0.030268454924225807,
0.013662737794220448,
-0.04874289408326149,
-0.043656185269355774,
-0.07052828371524811,
0.001493061543442309,
-0.04286181181669235,
-0.000452790962299332,
0.0000015380910554085858,
-0.049761828035116196,
0.06278067082166672,
-0.04299866035580635,
0.06295298039913177,
0.04412325844168663,
0.006785929668694735,
0.033711474388837814,
0.014514573849737644,
-0.016648003831505775,
-0.06131872907280922,
0.009025217033922672,
0.004316325299441814,
0.0604211688041687,
-0.011064641177654266,
-0.01161390170454979,
-0.0012741204118356109,
-0.040159814059734344,
-0.044808823615312576,
0.051826294511556625,
-0.023645732551813126,
-0.051193732768297195,
-0.012545171193778515,
0.03978027030825615,
0.025807438418269157,
0.0010945132235065103,
-0.057896409183740616,
0.06579017639160156,
-0.04418103024363518,
-0.020398365333676338,
0.011880872771143913,
-0.014286934398114681,
-0.06523474305868149,
-0.005983311682939529,
0.0735662505030632,
0.02229195274412632,
-0.03418070822954178,
0.02202046848833561,
-0.014757182449102402,
0.00959797389805317,
0.02352900803089142,
0.006692662835121155,
-0.03219721466302872,
-0.0059334211982786655,
0.025196924805641174,
0.02039468102157116,
-0.07367032021284103,
-0.014063666574656963,
0.006765598896890879,
0.0011613743845373392,
-0.03129918873310089,
-0.05523250997066498,
0.047217659652233124,
0.030393190681934357,
-0.0399845615029335
] |
<p>I am reading the original paper by Bondi, van der Berg and Metzner (<a href="http://rspa.royalsocietypublishing.org/content/269/1336/21" rel="nofollow">link</a>) regarding gravitational waves in asymptotically flat axisymmetric spacetimes. In the introduction, he makes the following comment - </p>
<blockquote>
<p>The conservation of mass effectively prohibits purely spherically symmetric waves and similarly, conservation of momentum prohibits waves of dipole symmetry. </p>
</blockquote>
<p>I know that Birkhoff's theorem tells us that spherically symmetric asymptotically flat solution to GR is necessarily static, and therefore contains a timelike Killing vector, which implies conservation of mass (energy). Bondi et. al. seem to be stating the converse of this theorem, whose validity I do not immediately see. How do we show this?</p>
<p>Also, what is the corresponding proof of the second statement made above?</p> | g6615 | [
0.031237509101629257,
-0.01979711279273033,
0.013877383433282375,
-0.00714497733861208,
0.056920867413282394,
0.01911979727447033,
0.025356004014611244,
-0.053620077669620514,
-0.07053400576114655,
0.022506577894091606,
0.004153742920607328,
-0.03331497311592102,
0.009635702706873417,
0.04200145602226257,
0.02247348427772522,
-0.05253342539072037,
0.0648723766207695,
0.0023704790510237217,
-0.05923978239297867,
0.031903523951768875,
0.010369056835770607,
-0.009779966436326504,
0.015371857210993767,
0.004221090115606785,
0.04151081293821335,
0.03665030375123024,
0.059383172541856766,
-0.008753265254199505,
-0.027178417891263962,
-0.03762452304363251,
0.06949781626462936,
0.045082319527864456,
0.014430810697376728,
-0.06739901006221771,
-0.005042156670242548,
0.0025222678668797016,
0.014998947270214558,
0.022267894819378853,
0.04455180838704109,
0.002814817475154996,
-0.005841264501214027,
-0.020358093082904816,
-0.03514397516846657,
0.020596353337168694,
0.0054839057847857475,
0.00645302701741457,
-0.062465302646160126,
-0.013984455727040768,
-0.023210469633340836,
-0.01816597953438759,
0.06000468134880066,
0.07668714225292206,
0.08330917358398438,
-0.06440743803977966,
-0.03323320299386978,
-0.02690097503364086,
0.006275222636759281,
-0.005192608572542667,
-0.030674079433083534,
0.03719751164317131,
-0.01986834779381752,
0.044860877096652985,
0.025737185031175613,
0.025807198137044907,
0.022868501022458076,
-0.03653870150446892,
-0.0409649983048439,
-0.027628030627965927,
-0.010044156573712826,
0.029642269015312195,
0.04696985334157944,
0.014396625570952892,
0.025491412729024887,
-0.08163022994995117,
-0.002357043558731675,
0.09273950010538101,
0.026619696989655495,
0.03397199138998985,
0.013657214120030403,
-0.03611262887716293,
-0.10177053511142731,
0.008943582884967327,
-0.003922844305634499,
0.058850228786468506,
0.08660943061113358,
-0.0328647717833519,
-0.047681257128715515,
-0.07845055311918259,
-0.010025178082287312,
0.023361295461654663,
0.012314309366047382,
-0.009562242776155472,
0.0336056724190712,
0.011236930266022682,
-0.004301193170249462,
0.028825754299759865,
-0.010452651418745518,
0.029396574944257736,
0.0009614977752789855,
0.009917499497532845,
-0.007903466001152992,
-0.0034616899210959673,
0.0076601458713412285,
0.011557785794138908,
0.07190775126218796,
-0.01947297714650631,
0.002178527181968093,
0.007856881245970726,
-0.02022438496351242,
0.0021003815345466137,
0.05671259015798569,
-0.06090928614139557,
-0.0296922717243433,
0.014235331676900387,
-0.07355421036481857,
-0.02801324613392353,
0.04524290934205055,
-0.05455867201089859,
0.01097559928894043,
0.06680652499198914,
-0.02706645429134369,
0.045392315834760666,
-0.00882713869214058,
0.06809438765048981,
0.038401443511247635,
-0.015037303790450096,
-0.018125442788004875,
-0.003979948814958334,
0.05119379982352257,
0.012928114272654057,
-0.02477186918258667,
-0.0021751257590949535,
0.002423371421173215,
0.018262455239892006,
-0.02121550589799881,
0.008395208977162838,
-0.0033052393700927496,
-0.0002287898096255958,
-0.022739669308066368,
-0.02826336771249771,
-0.08114814758300781,
-0.018635470420122147,
0.04650755971670151,
-0.0021953152026981115,
0.00913990754634142,
0.023924000561237335,
0.0007248620968312025,
0.0067733111791312695,
0.08453527092933655,
-0.01630992256104946,
-0.025389276444911957,
0.1014040857553482,
-0.0028331847861409187,
0.016233135014772415,
0.008404924534261227,
-0.008529636077582836,
-0.032035697251558304,
-0.01716017723083496,
0.02028362825512886,
0.02864350564777851,
0.06599836051464081,
0.006789727136492729,
-0.047564662992954254,
0.01986006088554859,
0.0006220114883035421,
0.021706558763980865,
-0.00016263945144601166,
-0.10041569173336029,
-0.00975874438881874,
-0.02922675386071205,
-0.059876326471567154,
0.022219467908143997,
0.009590787813067436,
0.10580137372016907,
-0.010433193296194077,
-0.014953801408410072,
-0.08056481927633286,
-0.04467303305864334,
-0.04000379145145416,
-0.03853333741426468,
-0.01978919841349125,
-0.06530478596687317,
0.012140889652073383,
-0.0015351253096014261,
0.014548011124134064,
0.0505763441324234,
-0.009160864166915417,
0.004185117781162262,
-0.08261720091104507,
-0.010545439086854458,
-0.009126793593168259,
0.046451136469841,
-0.000724641780834645,
0.09217506647109985,
0.04286634176969528,
0.055352918803691864,
0.06972856819629669,
-0.025033310055732727,
-0.039596907794475555,
0.06170271709561348,
-0.03603597730398178,
-0.013910144567489624,
0.0031011428218334913,
0.009043940342962742,
0.022091014310717583,
0.019410137087106705,
0.013379614800214767,
0.010637455619871616,
0.02944478765130043,
-0.028027892112731934,
-0.00012384458386804909,
0.01385254692286253,
0.020532209426164627,
-0.002746803453192115,
0.027157025411725044,
0.005642320029437542,
-0.04319591447710991,
0.06014930084347725,
-0.03440403565764427,
-0.028852250427007675,
-0.02989075891673565,
0.016729554161429405,
-0.0031472088303416967,
0.037055522203445435,
0.01248567271977663,
-0.027413103729486465,
-0.043882373720407486,
-0.03462964668869972,
-0.0025630949530750513,
-0.05099707841873169,
0.03333975374698639,
-0.0017281199106946588,
0.057171303778886795,
-0.03584284707903862,
0.09648153185844421,
-0.005499133840203285,
0.003463882952928543,
0.022733284160494804,
0.03941692039370537,
0.03174757957458496,
0.0073946756310760975,
0.022337760776281357,
-0.030604543164372444,
-0.039811111986637115,
0.03125862032175064,
0.013673988170921803,
0.04295174404978752,
0.0008266416843980551,
0.024057844653725624,
0.012243717908859253,
0.01953803189098835,
-0.02026669681072235,
-0.021548498421907425,
-0.015625273808836937,
0.02822960540652275,
-0.00568025466054678,
-0.0183227751404047,
0.029185974970459938,
-0.03215726464986801,
0.015118942596018314,
0.0035594068467617035,
-0.02043701894581318,
0.030409617349505424,
-0.026487277820706367,
-0.0561075396835804,
-0.008560288697481155,
0.006843199487775564,
0.019506679847836494,
-0.02393982745707035,
0.00725758820772171,
-0.021951919421553612,
0.06533323228359222,
-0.0024889004416763783,
0.14081938564777374,
-0.038845743983983994,
-0.003132973099127412,
0.03770997002720833,
-0.02023128606379032,
-0.03491585701704025,
0.005680204834789038,
-0.05073889344930649,
0.01106962189078331,
-0.034488286823034286,
0.012108861468732357,
0.022988211363554,
-0.011648821644484997,
-0.0029476513154804707,
0.007014173083007336,
0.015124120749533176,
0.009159481152892113,
-0.034874748438596725,
0.04303450882434845,
0.021422432735562325,
0.01738971844315529,
-0.00884352345019579,
0.07604242861270905,
-0.022610940039157867,
-0.08399824798107147,
0.005151629913598299,
-0.000369474058970809,
0.018625257536768913,
-0.015907466411590576,
-0.004752709064632654,
0.02919110469520092,
0.021240191534161568,
0.037522632628679276,
-0.05295306816697121,
-0.03497478738427162,
-0.03175823390483856,
0.0006204982637427747,
0.05345278978347778,
0.03436112776398659,
-0.013652446679770947,
-0.018105434253811836,
-0.02634633332490921,
-0.009059927426278591,
-0.034170445054769516,
-0.054258011281490326,
-0.015923384577035904,
-0.03405078500509262,
-0.05516078695654869,
0.03396822139620781,
0.00023175994283519685,
0.027978790923953056,
0.000640290614683181,
-0.003491723444312811,
-0.038398344069719315,
0.03538970276713371,
-0.05254639312624931,
-0.003954531159251928,
-0.021877992898225784,
-0.010572251863777637,
0.03569768741726875,
-0.022320957854390144,
-0.033436600118875504,
-0.0833396315574646,
0.04981112852692604,
0.017778025940060616,
0.0037808858323842287,
0.057635348290205,
0.0430942066013813,
-0.005956562235951424,
-0.044003427028656006,
-0.01652694121003151,
-0.04899704456329346,
0.02677534893155098,
-0.047322407364845276,
-0.014568339101970196,
-0.024864252656698227,
0.03729761764407158,
-0.001555957947857678,
0.0211026631295681,
0.01304690446704626,
-0.036963921040296555,
-0.0311251413077116,
0.018616097047924995,
0.027668679133057594,
0.038648299872875214,
-0.004723954014480114,
-0.011028946377336979,
0.010178475640714169,
-0.000659405835904181,
0.08061175793409348,
-0.002591080963611603,
0.027594996616244316,
-0.018774036318063736,
-0.014580138958990574,
-0.04431435838341713,
-0.015025005675852299,
-0.039888449013233185,
0.04595065861940384,
-0.04941385239362717,
-0.016346214339137077,
0.018031729385256767,
0.04952773079276085,
-0.0603783018887043,
0.018934041261672974,
0.015026789158582687,
-0.04608828201889992,
-0.015886837616562843,
0.017368465662002563,
-0.036573562771081924,
0.021077368408441544,
0.02062639407813549,
-0.01720350608229637,
0.014416511170566082,
-0.0653509646654129,
0.028159067034721375,
0.013864153996109962,
-0.030733177438378334,
0.02477956935763359,
-0.008833800442516804,
0.03547472506761551,
-0.0389733649790287,
-0.008832830004394054,
-0.019398843869566917,
0.01700589433312416,
-0.017147278413176537,
-0.010122344829142094,
0.06171353906393051,
0.02023358829319477,
0.015856025740504265,
-0.030175702646374702,
-0.03442114219069481,
0.05497537553310394,
0.023236919194459915,
-0.006623351946473122,
-0.006031005643308163,
-0.022889044135808945,
-0.0018660826608538628,
0.03964647278189659,
0.022924557328224182,
0.02742127701640129,
-0.04741598665714264,
0.07026226073503494,
-0.0035712863318622112,
-0.023652900010347366,
-0.048596519976854324,
0.06097540259361267,
0.01873732917010784,
-0.0021198317408561707,
0.02330414019525051,
-0.05305236205458641,
-0.017131594941020012,
-0.013410589657723904,
0.05331927537918091,
0.07711003720760345,
-0.02727149985730648,
-0.048281390219926834,
-0.0018613964784890413,
0.027300527319312096,
-0.018921906128525734,
0.019341468811035156,
0.03842395916581154,
-0.04181806370615959,
0.010090570896863937,
-0.05444229766726494,
0.03128325566649437,
0.020440783351659775,
0.0005492432392202318,
0.0815383791923523,
0.008634133264422417,
0.01763448305428028,
0.0019017751328647137,
0.01850690133869648,
0.03747889772057533,
0.02644811011850834,
-0.0454583615064621,
0.014353014528751373,
-0.013537285849452019,
-0.020651156082749367,
0.011060025542974472,
0.03906174749135971,
-0.05218224599957466,
-0.03410912677645683,
0.03076157346367836,
-0.018755769357085228,
0.05387982353568077,
0.06557394564151764,
0.008470824919641018,
-0.03867819160223007,
-0.03608943149447441,
0.07521060109138489,
-0.00379965896718204,
0.06477660685777664,
0.025275075808167458,
0.0027685160748660564,
-0.006260235793888569,
-0.040666013956069946,
-0.06202317774295807,
0.002138508716598153,
0.03339738771319389,
-0.018728161230683327,
-0.025821730494499207,
-0.07022988796234131,
0.04629213735461235,
0.006618625950068235,
-0.017694734036922455,
0.03785819560289383,
-0.014013184234499931,
-0.05242748185992241,
-0.019751334562897682,
0.05707581713795662,
0.03494827449321747,
0.054241400212049484,
0.05352691560983658,
-0.02349216490983963,
0.04270582273602486,
-0.0020805050153285265,
-0.08743554353713989,
0.015241163782775402,
-0.029925324022769928,
-0.022415967658162117,
0.07199861109256744,
0.010693221352994442,
0.05701243132352829,
0.015132905915379524,
-0.06745470315217972,
-0.042361781001091,
-0.0026584630832076073,
-0.05262840911746025,
-0.04716603085398674,
0.022785192355513573,
-0.0196994636207819,
-0.017462437972426414,
0.05672673135995865,
0.05636737123131752,
0.03431839123368263,
-0.023688044399023056,
0.055367011576890945,
-0.02895406074821949,
-0.007463290821760893,
0.02668253518640995,
0.021441694349050522,
0.03326251730322838,
-0.05576615408062935,
-0.029275281354784966,
0.034907229244709015,
-0.03590969368815422,
0.02603626251220703,
0.004535319283604622,
0.012416547164320946,
0.030317110940814018,
-0.002478399546816945,
0.036531418561935425,
0.02729824185371399,
-0.0831853598356247,
-0.025764821097254753,
-0.039580244570970535,
0.027667108923196793,
-0.022032754495739937,
-0.030288798734545708,
0.04350021108984947,
-0.01652766577899456,
0.044595617800951004,
-0.03208216279745102,
0.03152049332857132,
0.05628259479999542,
0.025079457089304924,
0.00012602627975866199,
-0.05198859050869942,
0.008872900158166885,
0.02001367136836052,
0.021494105458259583,
0.0007494205492548645,
0.029583953320980072,
-0.03500334918498993,
-0.028859248384833336,
0.010934303514659405,
-0.08649992197751999,
-0.04591915383934975,
-0.015485999174416065,
-0.06566575914621353,
-0.04433123767375946,
0.008265113458037376,
-0.009651224128901958,
-0.021371252834796906,
-0.019464001059532166,
-0.04551621526479721,
-0.021674219518899918,
-0.022263387218117714,
0.01590871438384056,
-0.018311770632863045,
-0.042456503957509995,
0.023589186370372772,
-0.03628451004624367,
-0.05673399940133095,
-0.04275249317288399,
0.02905779331922531,
-0.008612273260951042,
-0.06957497447729111,
0.018216390162706375,
-0.03682222589850426,
0.04977823793888092,
0.010347680188715458,
-0.02931121736764908,
0.009137438610196114,
-0.049491457641124725,
-0.04261563718318939,
-0.021391533315181732,
-0.071823850274086,
-0.050396036356687546,
0.0388542078435421,
-0.09042424708604813,
-0.03463995084166527,
-0.014798919670283794,
-0.03225446119904518,
0.020702872425317764,
0.0070524816401302814,
-0.0070425281301140785,
-0.03925342112779617,
-0.012991644442081451,
-0.032522767782211304,
0.000667352054733783,
-0.01483495719730854,
0.026134122163057327,
0.012032066471874714,
0.013715512119233608,
-0.08987940102815628,
-0.028217565268278122,
-0.009234650060534477,
-0.000050795053539332,
0.03130084276199341,
0.020362474024295807,
0.02769222855567932,
0.018962299451231956,
-0.00024193325953092426,
0.008834617212414742,
0.009543444029986858,
-0.015800731256604195,
-0.03683352470397949,
0.023145904764533043,
0.007149792741984129,
-0.01687663234770298,
0.0024778253864496946,
-0.0416579395532608,
0.0011259648017585278,
-0.013135412707924843,
0.016271434724330902,
-0.047751426696777344,
0.020762426778674126,
-0.01179247535765171,
0.010796191170811653,
-0.009745080024003983,
0.08438889682292938,
-0.009478368796408176,
-0.02488795854151249,
-0.014259285293519497,
0.004779220558702946,
0.028127485886216164,
-0.01589946262538433,
0.051703501492738724,
-0.034825440496206284,
0.00350671517662704,
0.03837165981531143,
0.009341041557490826,
0.0118781803175807,
-0.012782693840563297,
0.05884426459670067,
-0.03462856635451317,
-0.043530818074941635,
0.07314925640821457,
0.038691941648721695,
0.017044877633452415,
-0.12212124466896057,
0.03950684890151024,
0.0564558319747448,
-0.024886509403586388,
-0.02281826362013817,
0.019628390669822693,
0.036688029766082764,
-0.046775832772254944,
-0.015143261291086674,
-0.02017972618341446,
-0.03801519423723221,
-0.017171362414956093,
-0.03308321163058281,
-0.01108506042510271,
0.0521453320980072,
-0.056689705699682236,
0.03454003483057022,
-0.020174337550997734,
0.033234596252441406,
-0.011477172374725342,
-0.03173017129302025,
0.011465657502412796,
0.0030099027790129185,
0.02066224068403244,
0.06174197047948837,
-0.011147900484502316,
-0.019864941015839577,
0.01111646555364132,
-0.006792977452278137,
-0.04657179117202759,
-0.004052533768117428,
0.013704334385693073,
-0.027486613020300865,
0.0185310710221529,
0.014102891087532043,
0.010457216762006283,
-0.004566999152302742,
0.036816783249378204,
-0.056481584906578064,
0.04206803813576698,
0.011090314015746117,
-0.024724207818508148,
-0.046514078974723816,
-0.0017599613638594747,
-0.030560310930013657,
0.034811872988939285,
-0.017078766599297523,
0.03668210655450821,
0.0008833226747810841,
-0.015111531130969524,
0.03793306276202202,
-0.041050080209970474,
0.03728662058711052,
0.0853082612156868,
-0.02325415052473545,
-0.0022548912093043327,
-0.01656133122742176,
0.011443126015365124,
-0.007478462066501379,
0.03275156766176224,
0.03722197562456131,
-0.01192890852689743,
0.008411621674895287,
-0.06006389483809471,
0.027826933190226555,
0.03863914683461189,
0.00014309689868241549,
-0.0008173368987627327,
-0.05476713180541992,
-0.01812911592423916,
0.060670483857393265,
0.009038279764354229,
-0.02809922769665718,
-0.03102053515613079,
0.014655801467597485,
-0.05037989839911461,
0.01475953683257103,
-0.0023975244257599115,
-0.014538517221808434,
-0.07976637780666351,
-0.01703815720975399,
-0.0006025678012520075,
0.03239411860704422,
-0.010713672265410423,
0.03136543929576874,
0.002933985088020563,
-0.03463129326701164,
-0.04691033065319061,
-0.01720939762890339,
0.061764612793922424,
0.06797350943088531,
0.01917824149131775,
0.020144658163189888,
-0.03177377209067345,
0.00806893315166235,
-0.008810746483504772,
0.010965012013912201,
-0.04997987672686577,
0.012114403769373894,
-0.021045347675681114,
-0.02801155112683773,
0.02803967334330082,
-0.012682116590440273,
0.017347605898976326,
-0.004950283095240593,
-0.019350530579686165,
0.01653234474360943,
0.01786041632294655,
-0.06280136108398438,
0.004887855611741543,
0.002906262408941984,
-0.04318469762802124,
0.08417278528213501,
-0.05579250678420067,
0.06971831619739532,
-0.018679821863770485,
-0.002089804271236062,
0.012661454267799854,
-0.007531123701483011,
0.021925250068306923,
-0.01772019825875759,
-0.033681031316518784,
0.02447541244328022,
-0.019350755959749222
] |
<p>Suppose we have a material point. If it is moving from position $X_0$ with initial velocity $V_0$ and constant acceleration $A$, then from elementary physics course I remember that its movement is described by the equation</p>
<p>$$X(t) = X_0 + V_0t + At^2/2.$$</p>
<p>Now, my question is, what is the equation of the movement of the material point if its acceleration is an arbitrary function of $t$: $A(t)$. Is it simply:</p>
<p>$$X(t) = X_0 + V_0t + A(t)t^2/2,$$</p>
<p>or is it more complicated than that? From the looks of $At^2/2$ I have a suspicion that integrals may be involved. </p> | g228 | [
0.05854259431362152,
0.008873787708580494,
-0.021314270794391632,
0.03423384949564934,
0.03970173001289368,
0.0007781264139339328,
0.01260349154472351,
-0.01704808697104454,
-0.06813469529151917,
0.007730579935014248,
-0.04339650273323059,
0.027913128957152367,
0.057830560952425,
-0.01906886324286461,
-0.004787621088325977,
-0.059139568358659744,
0.025953521952033043,
-0.006015252787619829,
-0.012157159857451916,
0.021553149446845055,
0.056974753737449646,
0.036448683589696884,
0.028829989954829216,
-0.0393502451479435,
0.04565475881099701,
0.0018538587028160691,
0.006397627294063568,
-0.020541153848171234,
-0.05942421779036522,
-0.011190522462129593,
0.03905859217047691,
-0.017198210582137108,
0.029021579772233963,
-0.02705356478691101,
-0.027490967884659767,
-0.060606371611356735,
0.06201764941215515,
0.0055984691716730595,
0.04638484865427017,
-0.013585712760686874,
-0.02122415415942669,
-0.04767899587750435,
0.001016866648569703,
0.03241648152470589,
0.05291875824332237,
0.021992458030581474,
-0.03318192437291145,
-0.046816978603601456,
-0.06236075982451439,
0.03398176655173302,
-0.05803048238158226,
0.03772592172026634,
0.0009832317009568214,
-0.0033814478665590286,
-0.03517702594399452,
0.026850873604416847,
0.023827221244573593,
-0.04681863263249397,
0.06672674417495728,
0.04539014399051666,
0.003054398577660322,
-0.008867538534104824,
0.034684836864471436,
-0.05602560192346573,
0.09829329699277878,
-0.04804935306310654,
-0.037077371031045914,
0.00506331492215395,
-0.0018606034573167562,
0.011559669859707355,
0.054744575172662735,
-0.03382499888539314,
-0.014059755019843578,
-0.0780331939458847,
-0.051053766161203384,
-0.010457316413521767,
0.01559631247073412,
-0.028913423418998718,
-0.0018764202250167727,
0.02248121239244938,
-0.06514270603656769,
0.05112466961145401,
0.061474088579416275,
-0.006812938954681158,
0.005109828896820545,
-0.024576429277658463,
0.0446007065474987,
0.04163091257214546,
-0.06266343593597412,
0.023419784381985664,
0.006356322672218084,
0.03933553025126457,
0.011377213522791862,
-0.03284651041030884,
-0.019880881533026695,
-0.049648988991975784,
-0.045006006956100464,
0.061502695083618164,
-0.012384481728076935,
0.017523450776934624,
-0.02735084295272827,
-0.027363473549485207,
0.04430200532078743,
0.01031425315886736,
0.06862745434045792,
-0.043424684554338455,
0.04018179699778557,
-0.013642317615449429,
0.006075256038457155,
-0.01404075138270855,
0.0640270784497261,
-0.01915123127400875,
-0.007101112976670265,
-0.0476234033703804,
-0.04995119571685791,
-0.007341527380049229,
-0.025173740461468697,
0.020898234099149704,
0.02372492104768753,
0.06695070117712021,
-0.0006959376041777432,
0.013992560096085072,
0.005728035233914852,
0.06494388729333878,
0.013221072033047676,
-0.017526879906654358,
-0.017316149547696114,
-0.01751161739230156,
-0.02212625741958618,
-0.0019239233806729317,
0.03311704471707344,
-0.01288523431867361,
0.05337189882993698,
-0.029721131548285484,
-0.010979789309203625,
0.02831900306046009,
-0.0007807222427800298,
0.037412986159324646,
0.013529336079955101,
0.039924051612615585,
-0.01502794586122036,
-0.04516949877142906,
-0.04387228563427925,
-0.016785554587841034,
-0.07290206104516983,
0.05008630454540253,
0.017853502184152603,
-0.061361245810985565,
0.014855618588626385,
-0.0039501492865383625,
-0.006273596081882715,
0.08846314996480942,
-0.02341306023299694,
-0.016074521467089653,
0.0419558510184288,
-0.031072011217474937,
0.03664625063538551,
0.012109044007956982,
0.02004186064004898,
-0.023641102015972137,
0.062162525951862335,
-0.010740455240011215,
0.03265420347452164,
0.02517949789762497,
-0.0746019259095192,
0.014186255633831024,
-0.014727737754583359,
-0.016005156561732292,
0.004962661769241095,
-0.005011840723454952,
0.01405294518917799,
0.025266334414482117,
0.0307694673538208,
0.07152200490236282,
-0.03491481766104698,
-0.016922859475016594,
0.04217065870761871,
-0.024060754105448723,
0.015979180112481117,
-0.02539878711104393,
0.00934230349957943,
-0.053492944687604904,
0.020593173801898956,
-0.037166863679885864,
-0.043974701315164566,
0.022313272580504417,
-0.02272128313779831,
0.058506280183792114,
-0.058561962097883224,
-0.0022506671957671642,
0.010492527857422829,
-0.024920761585235596,
-0.012356378138065338,
0.02954792231321335,
-0.07426971942186356,
0.008408219553530216,
-0.006159869953989983,
0.008906778879463673,
0.013446204364299774,
-0.02883727103471756,
0.07656741887331009,
0.07664860785007477,
0.046914782375097275,
-0.0016577214701101184,
0.06708283722400665,
-0.019990038126707077,
-0.021378744393587112,
-0.005461707711219788,
-0.016842857003211975,
0.05010724812746048,
0.035844676196575165,
0.01419746596366167,
-0.007219066843390465,
0.08831825107336044,
-0.012766650877892971,
-0.059545475989580154,
0.005392255261540413,
-0.021447448059916496,
-0.004420071374624968,
-0.02198040299117565,
-0.08531137555837631,
-0.026409901678562164,
-0.022685062140226364,
0.08226609975099564,
-0.049126505851745605,
-0.010742872022092342,
0.03552542254328728,
-0.04503607004880905,
0.013675428926944733,
-0.0003771954798139632,
-0.02440783567726612,
0.03472786024212837,
0.015051957219839096,
-0.05081724002957344,
0.046270858496427536,
-0.0063985539600253105,
-0.06234383583068848,
0.024178029969334602,
0.04667731374502182,
0.02939547598361969,
0.0063325827941298485,
0.018091337755322456,
0.011232082732021809,
-0.05752689018845558,
0.0011063688434660435,
-0.08623484522104263,
0.07425860315561295,
-0.015792734920978546,
0.012353789061307907,
-0.00870291143655777,
0.01366997417062521,
-0.04966234788298607,
-0.030882790684700012,
0.010246628895401955,
0.029840311035513878,
0.00931531097739935,
-0.0135441729798913,
0.011418006382882595,
-0.028706228360533714,
-0.012344707734882832,
-0.00417699059471488,
-0.004217471461743116,
0.029475945979356766,
-0.004526800941675901,
-0.04887210577726364,
0.032593585550785065,
-0.04130358248949051,
0.0008008585427887738,
0.012794284150004387,
-0.006219983100891113,
0.013576637022197247,
0.05756526067852974,
-0.01739671640098095,
0.03792779892683029,
0.011417413130402565,
-0.06794606894254684,
0.0175753366202116,
-0.043321892619132996,
0.008766368962824345,
0.004426393657922745,
-0.007308647967875004,
-0.04725957661867142,
-0.05149869993329048,
0.004670209717005491,
0.001301199896261096,
-0.008694588206708431,
0.05207386612892151,
0.036776117980480194,
-0.03182237967848778,
-0.03108314611017704,
-0.0009928704239428043,
0.017544995993375778,
0.02087095007300377,
-0.031115960329771042,
-0.005985327996313572,
0.05988512188196182,
0.0047133550979197025,
-0.025418568402528763,
-0.0006177655886858702,
0.06289269030094147,
-0.010645195841789246,
-0.03758011758327484,
-0.022942401468753815,
-0.0038287858478724957,
0.030942806974053383,
0.015502152033150196,
-0.0009156183805316687,
-0.07739918678998947,
0.02023211307823658,
0.021200889721512794,
0.01796928606927395,
0.06442244350910187,
0.009054259397089481,
0.01219787448644638,
-0.010950765572488308,
-0.00677536753937602,
0.008590101264417171,
-0.011924752034246922,
0.03200245648622513,
0.022751260548830032,
-0.02887267991900444,
-0.09467700123786926,
-0.02003033459186554,
0.012410485185682774,
0.0509672574698925,
-0.009421817027032375,
0.0048602609895169735,
0.007872527465224266,
-0.03442837670445442,
-0.040438275784254074,
0.0027867525350302458,
0.0066777849569916725,
-0.014380349777638912,
-0.011169195175170898,
-0.009184220805764198,
-0.05381616950035095,
-0.016938921064138412,
0.026900315657258034,
0.06499668210744858,
-0.0072682262398302555,
0.020185686647892,
-0.000628257286734879,
-0.06817744672298431,
0.03219278156757355,
0.005300997756421566,
-0.05644842982292175,
0.05287093296647072,
0.020695123821496964,
0.021526210010051727,
-0.0059189521707594395,
0.059577953070402145,
-0.01882989890873432,
0.0011328001273795962,
-0.011339301243424416,
-0.039856843650341034,
0.019656354561448097,
0.07897049933671951,
0.004881601780653,
-0.03438892588019371,
-0.00697682099416852,
-0.023804159834980965,
-0.057165034115314484,
0.0056421770714223385,
0.021473510190844536,
0.026601683348417282,
-0.0523734986782074,
-0.018861953169107437,
0.035201482474803925,
-0.01996724307537079,
-0.017690012231469154,
0.021180616691708565,
-0.0651332437992096,
0.008599120192229748,
-0.008199194446206093,
-0.0029469402506947517,
-0.022965218871831894,
-0.007579871919006109,
-0.002473440021276474,
-0.07828628271818161,
0.06402995437383652,
0.04303815960884094,
0.016835717484354973,
0.0350373238325119,
0.04961511865258217,
-0.020940160378813744,
0.022452132776379585,
-0.07708120346069336,
-0.017886899411678314,
0.06260852515697479,
-0.05053079500794411,
0.06731598824262619,
-0.024541592225432396,
-0.037069957703351974,
-0.025525817647576332,
0.03890132158994675,
-0.03366978093981743,
-0.020892709493637085,
0.006379462778568268,
-0.018761107698082924,
0.014269868843257427,
0.0036463045980781317,
-0.015822771936655045,
-0.001430604257620871,
-0.017332768067717552,
-0.012170878238976002,
0.06570275872945786,
0.061097558587789536,
-0.024376798421144485,
0.048677679151296616,
-0.027262387797236443,
0.009663992561399937,
-0.03939832001924515,
-0.008411694318056107,
0.001503191888332367,
0.0006607907707802951,
-0.023449581116437912,
0.008660824038088322,
0.01269627921283245,
-0.04544336721301079,
-0.035614315420389175,
0.01163497008383274,
0.04200730845332146,
0.05418045446276665,
0.016432851552963257,
-0.025503667071461678,
0.057125914841890335,
0.07451068609952927,
0.04349319636821747,
0.0016449274262413383,
-0.017281528562307358,
-0.06881450116634369,
0.036922335624694824,
0.046982474625110626,
0.08221156895160675,
0.00841632392257452,
0.09256430715322495,
0.02388678677380085,
0.07364284992218018,
0.023266298696398735,
0.009682944044470787,
0.05502147972583771,
0.01666414365172386,
0.007679673843085766,
0.0055311634205281734,
-0.0038070804439485073,
0.017752662301063538,
-0.0015162170166149735,
-0.00604666443541646,
-0.008251967839896679,
-0.022677818313241005,
-0.006644608452916145,
0.03434700146317482,
-0.020586853846907616,
-0.020550377666950226,
-0.021255802363157272,
0.04679049551486969,
-0.02289610169827938,
-0.0296055655926466,
0.030170828104019165,
0.005505020264536142,
0.002849102718755603,
-0.029586996883153915,
-0.014463139697909355,
0.00013728783233091235,
0.0207062978297472,
-0.02901574969291687,
-0.03865223005414009,
0.017524151131510735,
-0.04318152740597725,
0.030698703601956367,
0.04760698974132538,
-0.001147706527262926,
0.014040102250874043,
0.013422773219645023,
-0.008594045415520668,
0.005441225599497557,
-0.03288261219859123,
0.023563936352729797,
-0.015968598425388336,
-0.06756039708852768,
0.0017286252696067095,
0.0066225589253008366,
0.021948648616671562,
-0.06869914382696152,
-0.011576870456337929,
-0.015157083980739117,
-0.09500984847545624,
-0.004621271509677172,
0.010370027273893356,
0.006190807092934847,
0.052988603711128235,
-0.03025696612894535,
-0.009487711824476719,
-0.03540201112627983,
-0.02960074692964554,
-0.05714894086122513,
-0.03621220216155052,
-0.013366316445171833,
0.011041802354156971,
0.017726128920912743,
-0.07403706014156342,
0.012255033478140831,
-0.010734017938375473,
0.03317622095346451,
0.005733982659876347,
0.047070831060409546,
0.009809243492782116,
0.002957392716780305,
-0.00010742265294538811,
0.032925333827733994,
0.11123449355363846,
0.0876716896891594,
0.01138615794479847,
-0.05246511101722717,
-0.05933782085776329,
0.031071625649929047,
-0.03622822090983391,
-0.06658615171909332,
-0.05695483833551407,
0.011117961257696152,
0.04103126749396324,
0.03301691636443138,
0.00187852350063622,
-0.02120121195912361,
0.07203315943479538,
0.017337920144200325,
-0.05622286722064018,
0.015437759459018707,
-0.02935553900897503,
0.06984995305538177,
-0.009079680778086185,
-0.04330551624298096,
0.046110328286886215,
-0.027642395347356796,
-0.009705482982099056,
0.033190108835697174,
0.026308191940188408,
-0.04128727316856384,
0.04286239296197891,
0.0011224846821278334,
-0.08704902976751328,
0.014267575927078724,
-0.0074121770448982716,
0.052268169820308685,
-0.008547656238079071,
0.05985228344798088,
-0.06459558010101318,
0.03177166357636452,
0.042161278426647186,
-0.10536719113588333,
-0.022451801225543022,
0.01925978995859623,
0.02101907506585121,
-0.049660585820674896,
-0.02443533018231392,
0.01574130170047283,
-0.023210205137729645,
-0.00491274893283844,
-0.024111781269311905,
-0.04432779923081398,
0.010853687301278114,
-0.03110920824110508,
0.06779123842716217,
-0.027440475299954414,
0.00771247548982501,
-0.0784720703959465,
0.07399170100688934,
-0.0228585097938776,
0.032732971012592316,
0.0034261432010680437,
-0.02059163711965084,
0.0238984115421772,
-0.014041837304830551,
0.03247958421707153,
-0.01489790715277195,
0.017564596608281136,
-0.06378750503063202,
-0.008676165714859962,
-0.09006846696138382,
0.016025414690375328,
-0.023069387301802635,
0.02458682470023632,
-0.02857663482427597,
-0.06097226217389107,
-0.052160970866680145,
0.0011199829168617725,
-0.050334710627794266,
-0.07834910601377487,
0.06001897156238556,
-0.013356322422623634,
-0.015486530028283596,
0.015790002420544624,
-0.047967687249183655,
-0.02485165372490883,
-0.015523108653724194,
-0.016361266374588013,
0.020937344059348106,
-0.053399547934532166,
0.01127245370298624,
0.054368313401937485,
0.05381465330719948,
0.022655528038740158,
-0.013336105272173882,
-0.016821857541799545,
0.028906002640724182,
-0.05568770691752434,
0.0053764465264976025,
0.022961780428886414,
0.018762290477752686,
-0.03517843410372734,
-0.020462624728679657,
0.04010046645998955,
-0.0017269502859562635,
0.024798423051834106,
0.0301809124648571,
0.008082510903477669,
-0.03124348819255829,
0.029536345973610878,
0.018101003021001816,
-0.07483533769845963,
0.01225398387759924,
0.0035219022538512945,
-0.004326743073761463,
0.003897135378792882,
0.04060959815979004,
-0.04120778664946556,
-0.023399414494633675,
0.06233404576778412,
0.026581209152936935,
-0.05716539919376373,
-0.003296758746728301,
-0.019311748445034027,
-0.006759967189282179,
0.05590682104229927,
-0.011229168623685837,
0.0407387837767601,
-0.012032969854772091,
0.03499816358089447,
-0.020007941871881485,
0.05027775466442108,
-0.01912088692188263,
0.00020329969993326813,
0.01829092763364315,
0.024037117138504982,
-0.07856118679046631,
-0.006880452390760183,
-0.041194427758455276,
-0.023953190073370934,
-0.0725722387433052,
0.0034565352834761143,
-0.028620662167668343,
-0.020679907873272896,
-0.029213234782218933,
0.014156457968056202,
-0.052932582795619965,
0.012481121346354485,
0.012705369852483273,
0.018417323008179665,
0.0134323975071311,
0.00718279043212533,
-0.0541076734662056,
-0.04249387979507446,
-0.002431978937238455,
-0.010474009439349174,
0.028287602588534355,
0.057860977947711945,
0.044254984706640244,
-0.045922014862298965,
-0.024746524170041084,
-0.005754956975579262,
0.039045561105012894,
0.003589075291529298,
-0.01306533720344305,
0.07182849943637848,
0.03660864010453224,
0.03941526636481285,
-0.03597576171159744,
-0.015389014035463333,
-0.005664191674441099,
-0.0006763956625945866,
0.028652753680944443,
0.03114602528512478,
-0.003394711297005415,
-0.0031641433015465736,
-0.026028454303741455,
0.060748059302568436,
-0.005555777810513973,
0.03983141481876373,
-0.0206336360424757,
-0.018360940739512444,
-0.022750020027160645,
-0.002671380527317524,
0.05313870683312416,
-0.04766788333654404,
0.03998564928770065,
0.008091813884675503,
-0.020746687427163124,
0.012368753552436829,
-0.03067704476416111,
0.04219634458422661,
0.04089513421058655,
-0.04840964078903198,
-0.009066129103302956,
0.018565664067864418,
-0.024924511089920998,
0.0056296298280358315,
0.034617096185684204,
-0.04255272075533867,
-0.013145980425179005,
0.009147979319095612,
0.010330740362405777,
0.02917889505624771,
0.05682305246591568,
0.021801941096782684,
-0.03520623967051506,
0.03061032108962536,
-0.01904965564608574,
-0.021641116589307785,
0.04152476787567139,
-0.00726598734036088,
-0.030905790627002716,
0.019414514303207397,
-0.018872538581490517,
-0.05627254769206047,
0.033957015722990036,
-0.0041604433208703995,
-0.0476059690117836,
-0.048764754086732864,
0.0082936342805624,
-0.03367028757929802,
0.0037989788688719273,
0.005788995418697596,
0.035602882504463196,
0.04857460781931877,
-0.018113376572728157,
-0.004273429978638887,
0.03875185176730156,
-0.04747811332345009,
0.00046352011850103736,
0.0056561012752354145,
-0.04876664653420448,
-0.04685754328966141,
-0.03576698526740074,
0.06082432344555855,
-0.016548071056604385,
-0.004068493843078613,
0.008493137545883656,
0.029540225863456726,
0.048800885677337646,
-0.01986944116652012,
0.0565360002219677,
0.019861873239278793,
-0.022567322477698326,
0.03954239934682846,
-0.011661192402243614,
-0.05580228194594383,
-0.015068289823830128,
0.02441217750310898,
-0.033244553953409195,
0.011437874287366867,
-0.03439567983150482,
0.01581816002726555,
0.0026984792202711105,
0.014250579290091991,
0.023416878655552864,
-0.040961429476737976,
-0.0373862124979496,
0.01681041345000267
] |
<p>The light traveling a 3 lake km/sec, but Pls tell me how can a control the speed of light, means can limit the speed like 2 lake km/sec are 1 lake km/sec </p>
<p>Pls tell me equation</p> | g6616 | [
-0.023947851732373238,
0.07588467001914978,
0.0010728135239332914,
0.03361589461565018,
0.030097637325525284,
-0.00021793255291413516,
0.05735895037651062,
-0.0008189197396859527,
-0.043109603226184845,
-0.02087804488837719,
-0.0051181139424443245,
0.015998762100934982,
0.06382087618112564,
0.04361213371157646,
-0.03277197480201721,
0.03893209993839264,
0.06217596307396889,
-0.005041681230068207,
0.02412690967321396,
0.010465177707374096,
-0.0006847767508588731,
0.018552478402853012,
-0.027254648506641388,
-0.035806696861982346,
-0.00680710282176733,
0.012107819318771362,
0.01942155510187149,
-0.06378119438886642,
-0.02407352440059185,
0.02037012204527855,
-0.012920104898512363,
-0.04742938652634621,
0.0065308427438139915,
-0.020556168630719185,
-0.013909803703427315,
-0.03435947000980377,
0.06737008690834045,
-0.012098059989511967,
-0.051317472010850906,
0.0647846981883049,
0.008537993766367435,
-0.01895921491086483,
-0.007555181626230478,
0.023362912237644196,
0.017018625512719154,
-0.006372318137437105,
0.007784551475197077,
-0.008754797279834747,
-0.07912829518318176,
-0.020917240530252457,
-0.02893114648759365,
0.03188116475939751,
-0.05786998197436333,
-0.01648801565170288,
-0.0057232617400586605,
0.02916991524398327,
-0.016661882400512695,
-0.06373957544565201,
0.008338753134012222,
0.02472798340022564,
-0.045756030827760696,
-0.0725727304816246,
0.025741027668118477,
-0.005590524990111589,
0.034251656383275986,
-0.020282940939068794,
-0.024206161499023438,
-0.03391091153025627,
0.027816584333777428,
0.05118301883339882,
0.0038685339968651533,
0.006768548861145973,
-0.04900515824556351,
-0.07258212566375732,
-0.010448764078319073,
-0.029790200293064117,
0.030431732535362244,
0.019383301958441734,
0.004152921959757805,
0.029081951826810837,
0.0048224846832454205,
0.00695571955293417,
-0.048421815037727356,
-0.03545704111456871,
-0.07188431918621063,
0.025314193218946457,
0.01627153344452381,
0.0021760694216936827,
-0.02658640407025814,
-0.03750665858387947,
-0.05043347552418709,
-0.02515139989554882,
0.07758022844791412,
0.012577125802636147,
-0.00801056157797575,
-0.0025926753878593445,
0.03256109356880188,
0.015942594036459923,
0.014103086665272713,
0.007864926941692829,
-0.052427444607019424,
-0.0124711524695158,
0.03335883095860481,
0.009544916450977325,
0.02006247453391552,
-0.03211472928524017,
-0.028554009273648262,
-0.0027995489072054625,
0.04731995612382889,
-0.05066139996051788,
0.009144606068730354,
-0.10219365358352661,
-0.030731363222002983,
-0.04997790977358818,
-0.037064291536808014,
-0.05683204531669617,
0.05898180976510048,
0.04367734491825104,
-0.01928705908358097,
-0.03984846919775009,
0.03954328969120979,
-0.0182627085596323,
-0.028347400948405266,
0.04001874476671219,
0.022776450961828232,
0.022559350356459618,
-0.0002488335594534874,
0.02728274278342724,
-0.012055615894496441,
0.004568547010421753,
-0.01842261478304863,
-0.008966232649981976,
-0.022202957421541214,
0.03043980710208416,
-0.06303015351295471,
-0.01947910524904728,
0.0032035314943641424,
0.03916475921869278,
0.031700681895017624,
-0.031768567860126495,
-0.027257919311523438,
-0.03028719685971737,
0.02652353048324585,
-0.021676961332559586,
-0.04132751375436783,
0.032853372395038605,
0.012796895578503609,
0.004169734660536051,
0.03426923602819443,
-0.05310216173529625,
0.05180396884679794,
0.07144010066986084,
-0.02949001081287861,
0.01491006463766098,
0.021482083946466446,
-0.007480548694729805,
0.04281289130449295,
0.022619731724262238,
-0.039365001022815704,
-0.032875653356313705,
0.024595756083726883,
0.05998328700661659,
-0.01654697209596634,
0.021930450573563576,
-0.10051680356264114,
0.07958443462848663,
0.05440406873822212,
0.07685332745313644,
-0.05960814282298088,
-0.06363365054130554,
-0.060505516827106476,
-0.0002433099434711039,
-0.031500887125730515,
0.016734836623072624,
0.00005945808516116813,
0.015423225238919258,
-0.00008156151307048276,
-0.017516551539301872,
-0.03816213831305504,
0.03171535208821297,
-0.09030980616807938,
-0.00007331507367780432,
-0.03077724762260914,
-0.02390286885201931,
0.006369678303599358,
0.014424425549805164,
-0.04372025653719902,
-0.017422538250684738,
-0.0833219364285469,
0.00045771527220495045,
0.026814637705683708,
-0.005787617061287165,
-0.0022921855561435223,
-0.023729978129267693,
-0.026707474142313004,
0.001222142018377781,
0.016007140278816223,
-0.047787025570869446,
0.02192038856446743,
0.003519820747897029,
0.0033600458409637213,
0.035972170531749725,
-0.013073013164103031,
-0.03063540905714035,
0.05836436524987221,
-0.03475317358970642,
0.026315458118915558,
-0.00018819229444488883,
0.022710898891091347,
0.028699494898319244,
0.01029801182448864,
0.010467559099197388,
-0.015213975682854652,
0.04468700662255287,
-0.020697511732578278,
0.013888457790017128,
0.013758650049567223,
0.012026824988424778,
0.03908180817961693,
-0.0363895557820797,
-0.022330746054649353,
0.030969763174653053,
0.036029066890478134,
-0.023342793807387352,
-0.10708873718976974,
-0.03083851747214794,
-0.013324359431862831,
-0.019236238673329353,
0.06315106153488159,
0.07302052527666092,
0.016482925042510033,
-0.008144949562847614,
-0.04036042094230652,
0.007285956759005785,
0.04836377128958702,
0.06303075700998306,
-0.01431762520223856,
0.0536365881562233,
-0.004087756387889385,
0.0034553934819996357,
-0.00423518056049943,
0.03892311453819275,
0.019876452162861824,
-0.004186712671071291,
-0.026409124955534935,
-0.008716076612472534,
0.010369769297540188,
-0.030688799917697906,
-0.027078600600361824,
0.05076085403561592,
0.032813265919685364,
0.019549624994397163,
-0.012067622505128384,
0.011335314251482487,
-0.006617691833525896,
-0.069981150329113,
-0.014246480539441109,
0.06629730761051178,
-0.09374748170375824,
0.006250995676964521,
-0.009502165019512177,
0.0147945461794734,
-0.0006244305404834449,
-0.06611927598714828,
-0.01442879531532526,
-0.04260176792740822,
-0.0226485263556242,
-0.011148273944854736,
0.041234567761421204,
0.04178173467516899,
-0.021372836083173752,
-0.002783052157610655,
0.01390292402356863,
0.024925386533141136,
-0.044162567704916,
-0.05651206895709038,
0.017324594780802727,
0.0021652819123119116,
0.037890102714300156,
0.0004340698360465467,
-0.020819300785660744,
-0.040637943893671036,
-0.0085611492395401,
0.0046744500286877155,
0.055633559823036194,
-0.05318080633878708,
0.09081701934337616,
0.06146401911973953,
-0.025800133123993874,
0.015674682334065437,
-0.0523756742477417,
0.02732764557003975,
0.022954363375902176,
0.03655300661921501,
0.013314391486346722,
0.033475253731012344,
0.0261082760989666,
-0.016411760821938515,
-0.007265138905495405,
0.04196614399552345,
0.06396351009607315,
0.012007523328065872,
-0.019272299483418465,
0.03710231930017471,
0.00021296968043316156,
0.04392797872424126,
-0.015487255528569221,
0.031108256429433823,
0.060154471546411514,
-0.009137898683547974,
-0.005649377126246691,
-0.020351547747850418,
-0.015114457346498966,
-0.006830520462244749,
-0.06081350892782211,
0.03411217778921127,
-0.001114161335863173,
-0.015831047669053078,
-0.0018440077546983957,
-0.011877945624291897,
0.03810500726103783,
-0.02977904863655567,
-0.013177602551877499,
0.02232038415968418,
-0.052972212433815,
0.026652591302990913,
0.012677161023020744,
-0.012968519702553749,
-0.03544251248240471,
0.020097699016332626,
-0.00016804455663077533,
0.04377836361527443,
-0.052855610847473145,
-0.02810629829764366,
-0.009311129339039326,
-0.008696729317307472,
0.049732644110918045,
0.060787491500377655,
0.0133181381970644,
-0.016724297776818275,
-0.021160053089261055,
0.003937446046620607,
-0.1065850481390953,
0.04828881472349167,
-0.013267450965940952,
-0.0016472558490931988,
-0.07090231031179428,
-0.018607784062623978,
-0.015241365879774094,
-0.009958868846297264,
0.015672847628593445,
0.04781220480799675,
-0.044055622071027756,
-0.07587765157222748,
0.019051797688007355,
0.04799441248178482,
-0.011853184551000595,
0.07514773309230804,
0.048656072467565536,
-0.018989939242601395,
-0.02321317419409752,
0.0171465165913105,
-0.022075900807976723,
0.04792153462767601,
-0.0174420028924942,
0.039693862199783325,
-0.0016776425763964653,
0.0603131465613842,
-0.06286083161830902,
0.0354088619351387,
-0.01665445975959301,
0.011670171283185482,
0.01292746514081955,
0.01664910465478897,
0.009787744842469692,
0.0000881068772287108,
0.0473412349820137,
0.044044945389032364,
-0.04478999972343445,
0.04438751935958862,
0.030390702188014984,
0.03234979882836342,
0.040864091366529465,
-0.032916340976953506,
-0.011003883555531502,
0.040708497166633606,
-0.01894262433052063,
-0.06824567914009094,
-0.01116868294775486,
-0.005536925047636032,
-0.0012191056739538908,
-0.07401134818792343,
-0.054451704025268555,
-0.04721381142735481,
-0.001937192166224122,
0.03707496076822281,
0.014678355306386948,
0.005817806348204613,
-0.07389316707849503,
-0.022940270602703094,
0.012460767291486263,
0.04326692223548889,
-0.025075457990169525,
0.016899384558200836,
-0.05325908213853836,
0.015913866460323334,
0.02306198887526989,
-0.003672598162665963,
0.04330875352025032,
0.0010995427146553993,
-0.04317077621817589,
0.02814842388033867,
-0.0031028324738144875,
-0.044174667447805405,
-0.0455022007226944,
0.012064121663570404,
0.018545012921094894,
-0.012108281254768372,
-0.0020638229325413704,
0.04743063449859619,
0.015277709811925888,
-0.00633211899548769,
0.010966944508254528,
0.007813218981027603,
-0.029831230640411377,
0.038066644221544266,
0.0025275626685470343,
-0.032609689980745316,
-0.0430515818297863,
-0.03271779045462608,
0.009255161508917809,
-0.013165823183953762,
0.03350769355893135,
0.02208090014755726,
0.0035250531509518623,
0.03075065091252327,
0.013221980072557926,
0.018094472587108612,
-0.037859268486499786,
0.01012191642075777,
0.024324100464582443,
0.013414901681244373,
0.002750771353021264,
0.021870700642466545,
-0.01920768991112709,
0.05107015743851662,
-0.02155940979719162,
-0.006978924851864576,
0.019408605992794037,
-0.043949030339717865,
-0.017614440992474556,
0.026532283052802086,
-0.049937792122364044,
-0.02644716389477253,
-0.0006040417356416583,
0.025922860950231552,
-0.05828021839261055,
0.06371040642261505,
0.033991508185863495,
0.021837996318936348,
-0.016235191375017166,
0.04851921647787094,
0.0015531486133113503,
-0.016013124957680702,
0.04459076747298241,
-0.004005813971161842,
0.0005215227720327675,
-0.020740216597914696,
-0.030153613537549973,
-0.021389083936810493,
0.03598642349243164,
0.019051898270845413,
0.002202301286160946,
0.058226078748703,
-0.008225958794355392,
-0.039591651409864426,
-0.025465674698352814,
0.036690592765808105,
-0.034225814044475555,
0.0021927852649241686,
0.014914278872311115,
0.00026260444428771734,
-0.02012346126139164,
0.0008882136316969991,
0.026813136413693428,
0.022222258150577545,
-0.03032200038433075,
0.025263076648116112,
-0.011972520500421524,
-0.07769936323165894,
-0.0032674912363290787,
0.02776327170431614,
0.003437593812122941,
0.01743025705218315,
-0.011539076454937458,
-0.0014160876162350178,
0.024895519018173218,
0.03449808061122894,
0.05005225911736488,
0.007863044738769531,
0.00020966603187844157,
-0.03792732208967209,
-0.02980729751288891,
0.010088255628943443,
-0.025843573734164238,
0.04607400670647621,
0.008806147612631321,
0.010622850619256496,
-0.010798378847539425,
0.022666851058602333,
0.04442065954208374,
0.0150468023493886,
0.04603312909603119,
0.02107223868370056,
0.025051353499293327,
-0.07732295989990234,
-0.004883262328803539,
0.057921119034290314,
0.05854098126292229,
-0.011670208536088467,
0.05578296259045601,
-0.04975153133273125,
0.01979413814842701,
0.00019389925000723451,
-0.027066553011536598,
-0.04767831787467003,
-0.08596845716238022,
-0.0040845712646842,
0.04616957902908325,
-0.0259576216340065,
-0.03341246768832207,
-0.02523866668343544,
-0.02145938202738762,
-0.060293473303318024,
-0.009919336065649986,
-0.03134584054350853,
0.10366363078355789,
-0.04340067133307457,
0.014392118901014328,
0.008383109234273434,
-0.006248405668884516,
-0.022764921188354492,
0.015906700864434242,
0.08697887510061264,
0.07356465607881546,
-0.02492971159517765,
-0.007465098053216934,
-0.015380318276584148,
0.0016487789107486606,
-0.03614683076739311,
0.03593588247895241,
-0.010712255723774433,
0.022340791299939156,
0.0020998793188482523,
0.03839559853076935,
0.00534633407369256,
-0.014602101407945156,
-0.00985681265592575,
-0.05052337050437927,
-0.015946028754115105,
0.02916192263364792,
0.010341905057430267,
0.02471163123846054,
-0.026145288720726967,
0.040162939578294754,
-0.08460089564323425,
-0.004921737592667341,
0.02216499112546444,
0.033777445554733276,
0.040029387921094894,
0.05867341160774231,
-0.02275759167969227,
-0.01753472164273262,
-0.02522219344973564,
0.030185014009475708,
0.023630820214748383,
0.02725958451628685,
-0.05364983156323433,
-0.041437458246946335,
-0.0342436321079731,
-0.02536601759493351,
0.0075613767839968204,
-0.017115775495767593,
-0.09295692294836044,
-0.045430801808834076,
-0.004331791307777166,
-0.004705351311713457,
0.04040302708745003,
0.01671930029988289,
-0.07381926476955414,
-0.006697516422718763,
0.03850797563791275,
-0.012338952161371708,
-0.016305342316627502,
0.03051820397377014,
-0.0612882524728775,
-0.0223177969455719,
0.029661906883120537,
0.005215964745730162,
0.015409466810524464,
-0.00510432431474328,
0.0018417882965877652,
0.039628490805625916,
0.0001931335573317483,
0.012807163409888744,
0.03200782090425491,
-0.01766495406627655,
-0.023078888654708862,
0.017439723014831543,
0.03586334362626076,
0.003657223889604211,
-0.00915435515344143,
0.0829748660326004,
0.03892543539404869,
-0.1028926745057106,
0.021794931963086128,
-0.03534763678908348,
-0.015365240164101124,
0.0015771174803376198,
-0.01609366200864315,
0.027272500097751617,
-0.04830538481473923,
0.020733626559376717,
-0.015916066244244576,
0.03834627941250801,
0.08246994018554688,
0.015568899922072887,
-0.013662606477737427,
-0.001323947450146079,
0.019682416692376137,
0.07205604761838913,
-0.013758786953985691,
-0.002156879287213087,
0.04326961562037468,
0.02033866196870804,
0.029606712982058525,
-0.018875667825341225,
0.037506647408008575,
0.07142385840415955,
0.034193117171525955,
0.036091022193431854,
0.04758945479989052,
0.019845884293317795,
0.04683545231819153,
-0.04333861172199249,
-0.017694367095828056,
-0.003766752779483795,
-0.07921335846185684,
-0.034129008650779724,
-0.022409340366721153,
-0.009774724021553993,
0.0071512977592647076,
-0.04929894953966141,
0.04779721796512604,
0.043399322777986526,
-0.029286859557032585,
0.0039002445992082357,
0.02687941864132881,
0.02910715341567993,
-0.06189718097448349,
-0.044974371790885925,
0.007973995991051197,
0.025447504594922066,
-0.02773476205766201,
0.014280767180025578,
0.09614640474319458,
-0.03462216258049011,
-0.05440238118171692,
-0.02635589987039566,
-0.027373451739549637,
-0.010683015920221806,
-0.0371757447719574,
0.025120409205555916,
-0.009062668308615685,
-0.04279756918549538,
0.04639328643679619,
-0.003795836353674531,
0.08820106089115143,
0.021824585273861885,
-0.013556702062487602,
0.03339600935578346,
0.017989637330174446,
-0.03406891971826553,
-0.05154770240187645,
-0.01744382455945015,
0.003778725629672408,
-0.015127364546060562,
-0.017323287203907967,
0.05320059135556221,
-0.0019912533462047577,
0.0023521475959569216,
0.038316886872053146,
0.008669476956129074,
-0.036003537476062775,
0.04242270812392235,
-0.0012680584331974387,
-0.011625723913311958,
0.025572730228304863,
0.02073242887854576,
-0.009641795419156551,
-0.020340634509921074,
-0.05672479793429375,
0.02939421497285366,
0.057022012770175934,
-0.0196538046002388,
-0.008329610340297222,
-0.029805509373545647,
-0.003561938414350152,
-0.012239671312272549,
-0.05273350328207016,
-0.09873290359973907,
0.02883181720972061,
-0.07458183914422989,
0.022538891062140465,
0.02286589704453945,
-0.00780436722561717,
0.03559491038322449,
0.018988709896802902,
-0.03141545131802559,
-0.013063524849712849,
-0.02333943545818329,
-0.027975060045719147,
-0.04417150840163231,
-0.05999736115336418,
-0.0036194822750985622,
-0.0357748419046402,
0.059415366500616074,
-0.027227073907852173,
-0.021506283432245255,
-0.024307435378432274,
0.008333100005984306,
-0.002216978231444955,
-0.06642395257949829,
-0.03230450674891472,
-0.06647388637065887,
0.07117842882871628,
-0.0282669048756361,
0.005959309637546539,
-0.0054974607191979885,
0.09695050120353699,
-0.03856273368000984,
0.01386930700391531,
-0.01174147892743349,
0.01938166283071041,
0.028143875300884247,
-0.018043672665953636,
0.03715112805366516,
0.01764075830578804,
0.03897275775671005,
-0.017729539424180984,
0.07956487685441971,
0.059363096952438354,
-0.029279660433530807,
0.002867079107090831,
0.10248970985412598,
-0.024756746366620064,
-0.03888693451881409,
-0.03828059881925583,
-0.035122521221637726,
0.005279623903334141,
-0.005686683114618063,
-0.04193175211548805,
0.038505759090185165,
0.06599659472703934,
-0.007990550249814987,
-0.03637811169028282,
-0.029659785330295563,
-0.014767221175134182
] |
<p>Given a black hole of some size, say $10^8$ solar masses, how can the size of its sphere of influence of light be calculated?</p>
<p>To clarify, ultimately I'd like to be able to calculate the apparent angle of a black hole's lensing effects, as viewed from some distance.</p>
<p>(I'm no physicist, so I might be making incorrect assumptions about gravitational lensing. If this is the case, sorry!)</p> | g6617 | [
-0.01054143812507391,
-0.003455492202192545,
0.023651335388422012,
-0.029962437227368355,
-0.01377317775040865,
-0.03639413043856621,
0.023269711062312126,
0.02167997695505619,
0.005832352209836245,
0.02075636386871338,
0.027408402413129807,
0.0432344526052475,
0.09395970404148102,
0.026186106726527214,
0.05784865468740463,
0.029734529554843903,
0.033895093947649,
-0.050531208515167236,
0.03476359695196152,
0.00015045030158944428,
0.048416439443826675,
-0.04228592291474342,
-0.016170721501111984,
-0.03896605595946312,
-0.04482833668589592,
0.07001835852861404,
0.03630242869257927,
0.04770009219646454,
-0.03755084425210953,
0.024487223476171494,
-0.056589651852846146,
-0.002333898562937975,
0.008436488918960094,
-0.006737059447914362,
-0.011582165025174618,
0.013076984323561192,
0.048879511654376984,
0.017726955935359,
0.03490371257066727,
-0.025454485788941383,
-0.0016880760667845607,
-0.056935641914606094,
0.01307631004601717,
0.04069938510656357,
-0.02088765799999237,
-0.023410256952047348,
0.03817199915647507,
0.05260780453681946,
0.03209739178419113,
-0.016061609610915184,
0.004919554106891155,
0.07145888358354568,
0.0636475533246994,
0.009891819208860397,
-0.026617711409926414,
0.06909795850515366,
-0.00803355686366558,
-0.021928058937191963,
0.03804190084338188,
0.06343004107475281,
-0.01964234560728073,
-0.009564178064465523,
-0.04764783754944801,
0.02053213305771351,
0.02536552958190441,
-0.020319420844316483,
-0.0901489183306694,
-0.03990095108747482,
-0.04837014898657799,
0.021398842334747314,
-0.010634460486471653,
0.0001772350660758093,
-0.003755891928449273,
-0.03902224823832512,
-0.06247276812791824,
0.015076062642037868,
-0.025664402171969414,
0.04971479997038841,
0.0018970239907503128,
0.021379902958869934,
0.004731458146125078,
-0.043990734964609146,
0.03637062385678291,
-0.029387393966317177,
0.06952251493930817,
0.006309450604021549,
0.03514289855957031,
-0.020892446860671043,
-0.04389882832765579,
0.0012857613619416952,
0.03793926164507866,
0.009510103613138199,
0.037287637591362,
0.055044613778591156,
0.04104665294289589,
0.02384079620242119,
0.0069050355814397335,
0.01170874759554863,
-0.004324923735111952,
0.037834398448467255,
-0.04517378285527229,
0.053731173276901245,
-0.029266543686389923,
0.01730825938284397,
0.020430099219083786,
0.003652602434158325,
-0.02629898302257061,
0.029127022251486778,
0.04267048463225365,
0.006424439139664173,
-0.051193878054618835,
-0.12005355209112167,
-0.022931639105081558,
-0.02859400399029255,
-0.11582955718040466,
-0.07041763514280319,
0.025788163766264915,
0.019093794748187065,
0.02513308636844158,
0.06050543859601021,
0.007751579396426678,
0.0219762921333313,
0.021087348461151123,
0.03326178714632988,
0.01299580279737711,
-0.04618310555815697,
-0.0462757907807827,
0.020991893485188484,
0.030508358031511307,
-0.02824423462152481,
0.000647478736937046,
-0.04452003538608551,
-0.012820283882319927,
0.01649966649711132,
0.013516911305487156,
0.09881202131509781,
-0.004585748538374901,
-0.041792307049036026,
-0.06753190606832504,
0.01354208029806614,
-0.01629934087395668,
0.022528279572725296,
0.034898415207862854,
0.008477123454213142,
-0.030759768560528755,
0.01551581546664238,
-0.010802848264575005,
-0.054671164602041245,
0.0473383404314518,
0.022887982428073883,
0.023698126897215843,
0.0807037428021431,
0.02823667600750923,
-0.002813989296555519,
-0.03205634281039238,
0.03401600569486618,
-0.01583161950111389,
0.010635544545948505,
-0.04311331734061241,
0.022110603749752045,
0.056623149663209915,
-0.04867773875594139,
-0.005381604190915823,
0.04162175953388214,
-0.058165788650512695,
0.028179865330457687,
0.016740301623940468,
-0.03288791701197624,
-0.02848186157643795,
-0.06693540513515472,
-0.02899581752717495,
0.02098783478140831,
0.05366604030132294,
-0.0037079784087836742,
-0.0062330844812095165,
0.025956381112337112,
0.02032947540283203,
-0.01281506847590208,
0.02687808871269226,
0.11202576011419296,
0.003181175095960498,
-0.030090613290667534,
-0.033474843949079514,
-0.0007089763530530035,
-0.021433431655168533,
-0.055201947689056396,
0.04521108418703079,
0.0045886836014688015,
0.04215874895453453,
0.047452714294195175,
-0.048251859843730927,
0.02820313349366188,
0.035390324890613556,
-0.013888251036405563,
0.014754879288375378,
0.0042953332886099815,
0.0634903684258461,
-0.02530769631266594,
0.00730746379122138,
0.07687896490097046,
-0.08663862198591232,
0.04679301381111145,
0.009707019664347172,
0.05545674264431,
0.06413185596466064,
0.010444866493344307,
0.044515833258628845,
0.009479725733399391,
-0.008830291219055653,
-0.005106670781970024,
0.023059718310832977,
-0.0585806779563427,
-0.017049606889486313,
-0.003391657490283251,
-0.03525620698928833,
0.10546219348907471,
-0.07964561134576797,
0.017680875957012177,
0.021888457238674164,
0.0028299279510974884,
-0.03947960212826729,
0.02975173108279705,
0.01301403995603323,
-0.0226120688021183,
-0.02381955273449421,
0.04699787497520447,
-0.04556800425052643,
0.0006005641771480441,
0.03295263275504112,
0.014312315732240677,
-0.09286922961473465,
-0.0037766462191939354,
-0.002256654901430011,
0.023626768961548805,
-0.01619410328567028,
0.0001608465245226398,
-0.03632953017950058,
-0.011270838789641857,
-0.0029790548142045736,
0.07305226475000381,
0.056093767285346985,
-0.00439319247379899,
-0.015801189467310905,
-0.03894706070423126,
-0.0004698116681538522,
0.0025546858087182045,
0.011265653185546398,
0.019298937171697617,
-0.031942784786224365,
0.014305880293250084,
0.00935124047100544,
0.03720533475279808,
0.043729018419981,
0.020231638103723526,
-0.004389993380755186,
0.015677301213145256,
-0.03650200739502907,
0.03452764078974724,
-0.07381564378738403,
0.025356682017445564,
-0.041122715920209885,
-0.011972388252615929,
0.03595716878771782,
0.01663777604699135,
-0.02540358155965805,
-0.04091596230864525,
-0.0407564640045166,
-0.011558561585843563,
0.0363912396132946,
0.04733670502901077,
0.0028133888263255358,
0.02649296261370182,
0.05276810750365257,
-0.0024584289640188217,
0.02160634472966194,
-0.019153660163283348,
-0.03382924571633339,
-0.008049552328884602,
0.03291088342666626,
0.010048260912299156,
-0.0018534036353230476,
0.02262037992477417,
-0.06997977942228317,
0.06828700751066208,
0.04477424919605255,
-0.05646570771932602,
0.038063790649175644,
0.024207886308431625,
-0.0005740758497267962,
-0.027902301400899887,
-0.016118060797452927,
0.05328487977385521,
-0.007685082498937845,
0.03175913169980049,
0.01055216696113348,
0.02375832013785839,
0.03678813949227333,
0.06578535586595535,
-0.026717206463217735,
0.007941847667098045,
0.011419972404837608,
-0.0018696858314797282,
-0.03173749893903732,
-0.026541339233517647,
-0.006617093924432993,
0.034951284527778625,
-0.04619988054037094,
-0.05137261748313904,
0.057893306016922,
-0.04199604690074921,
-0.025584109127521515,
0.0040385243482887745,
-0.0037157563492655754,
0.03524285927414894,
-0.07934049516916275,
-0.024825220927596092,
0.018387505784630775,
-0.0037657874636352062,
-0.0664893239736557,
0.0140862837433815,
0.01800426095724106,
-0.021429048851132393,
-0.02484123408794403,
0.002699580043554306,
0.019125832244753838,
0.008179700933396816,
0.007093657273799181,
-0.049140848219394684,
-0.01244356483221054,
-0.017405200749635696,
0.00945190992206335,
-0.005013155750930309,
-0.07179202884435654,
-0.010774586349725723,
-0.020261237397789955,
-0.03117147833108902,
-0.021994397044181824,
-0.017924858257174492,
0.039932992309331894,
-0.0062165642157197,
0.031890902668237686,
-0.03526251018047333,
-0.052123915404081345,
0.00785101018846035,
-0.03116001933813095,
0.00561655405908823,
-0.017034990713000298,
-0.1118156835436821,
-0.008274995721876621,
-0.03971448540687561,
0.031050128862261772,
-0.02084050513803959,
0.007696361746639013,
-0.035014357417821884,
0.10353963077068329,
0.018244311213493347,
-0.0011926147853955626,
0.04400515556335449,
0.03322892636060715,
-0.022960733622312546,
0.0193488672375679,
-0.020959416404366493,
-0.017402315512299538,
-0.014392780140042305,
0.014841048046946526,
-0.04883768409490585,
0.0358431302011013,
0.0026909795124083757,
0.011913917027413845,
-0.010758236050605774,
-0.01568576693534851,
0.032873839139938354,
-0.0414324514567852,
-0.006797417998313904,
-0.03015708364546299,
0.020618900656700134,
0.042286910116672516,
0.0435447096824646,
-0.0017189551144838333,
0.015067470259964466,
0.03898419812321663,
0.04059847816824913,
0.00993994902819395,
-0.02134835161268711,
-0.01763211190700531,
-0.034422241151332855,
-0.02842748910188675,
-0.046844933182001114,
0.03039906732738018,
-0.04762896150350571,
-0.009788969531655312,
-0.0942394882440567,
0.005105928517878056,
-0.0828385204076767,
0.023863110691308975,
0.004594639874994755,
0.03425384312868118,
-0.02286350540816784,
0.058486130088567734,
-0.02754782885313034,
0.060435108840465546,
0.022991105914115906,
0.06370101869106293,
0.01276226807385683,
0.019725868478417397,
0.02197261154651642,
0.03105221502482891,
0.012481640093028545,
-0.0038134006317704916,
-0.0037418778520077467,
0.030849363654851913,
-0.020799841731786728,
0.0023848945274949074,
-0.046671684831380844,
0.004143877886235714,
0.016661962494254112,
0.0014444231055676937,
-0.027346929535269737,
0.0038834973238408566,
-0.018995126709342003,
-0.03633703663945198,
-0.05603259429335594,
-0.010789184831082821,
0.007426572032272816,
-0.027025273069739342,
0.029958637431263924,
0.012036039493978024,
-0.044484466314315796,
0.004514805972576141,
0.0139859514310956,
0.006121098063886166,
0.012772159650921822,
-0.043253153562545776,
0.016739970073103905,
-0.06595508009195328,
0.050957486033439636,
0.013522975146770477,
0.06654129177331924,
-0.01847255975008011,
0.00028286047745496035,
0.023827919736504555,
0.028546670451760292,
-0.018958227708935738,
-0.03426198288798332,
0.02698523923754692,
-0.019999299198389053,
0.011602588929235935,
0.028870467096567154,
0.021467730402946472,
-0.013712766580283642,
-0.04640552029013634,
-0.08497787266969681,
-0.01738411746919155,
-0.05630554258823395,
-0.03510274738073349,
0.019122431054711342,
-0.054050151258707047,
0.04458106309175491,
0.05624287575483322,
-0.01693134754896164,
-0.02699625864624977,
-0.020060479640960693,
-0.010106886737048626,
0.05335727334022522,
0.0061872368678450584,
-0.018608560785651207,
-0.028449155390262604,
-0.028335554525256157,
-0.024183088913559914,
0.02175949700176716,
-0.0897991955280304,
0.04206349700689316,
0.014431128278374672,
-0.031176717951893806,
-0.07090675085783005,
-0.01832534931600094,
-0.061826106160879135,
-0.05335600674152374,
0.02007133699953556,
-0.006928289774805307,
-0.006365387234836817,
0.01023721694946289,
0.03742067888379097,
0.007927803322672844,
0.000905452820006758,
0.05242006108164787,
-0.003263085149228573,
0.03850856423377991,
0.03684814274311066,
0.04773080721497536,
-0.02527339942753315,
-0.011394510045647621,
-0.0145907923579216,
-0.023074666038155556,
-0.018697144463658333,
0.0005366393597796559,
0.02580489031970501,
0.01699085161089897,
0.06253524869680405,
0.052131060510873795,
0.011860599741339684,
0.013768146745860577,
0.043071307241916656,
-0.005686446093022823,
-0.007273436523973942,
0.012678014114499092,
0.04398117959499359,
-0.022343911230564117,
0.0523468479514122,
0.057503554970026016,
-0.012522331438958645,
0.04525759816169739,
0.013215212151408195,
0.06954748183488846,
0.037503212690353394,
-0.060883618891239166,
-0.034248583018779755,
0.02507687732577324,
0.02219473570585251,
0.04273984208703041,
0.04249858111143112,
-0.07144784182310104,
0.010653862729668617,
0.007927932776510715,
0.0438380129635334,
-0.009748570621013641,
-0.03786368668079376,
-0.0308797936886549,
0.0020152670331299305,
-0.025337520986795425,
-0.025333957746624947,
-0.016304651275277138,
-0.02481907792389393,
-0.01174583937972784,
0.03324883058667183,
-0.008053621277213097,
-0.01921173371374607,
-0.022729262709617615,
0.045600078999996185,
-0.04621698707342148,
-0.011255084536969662,
-0.011576858349144459,
0.02745421789586544,
0.010351826436817646,
0.03365302085876465,
-0.015332327224314213,
0.0158995334059,
0.02054796926677227,
0.017860276624560356,
0.029998116195201874,
-0.004951042588800192,
0.05657963827252388,
0.009106295183300972,
-0.0032747741788625717,
0.0067047541961073875,
0.016738951206207275,
0.0026529778260737658,
-0.050831254571676254,
0.008632613345980644,
-0.059124767780303955,
0.042461294680833817,
-0.032040826976299286,
-0.005774203222244978,
-0.03171056881546974,
-0.04763014614582062,
-0.05390944704413414,
0.0013839357998222113,
-0.024315593764185905,
0.04519902169704437,
0.029890315607190132,
-0.077660471200943,
0.007372272200882435,
-0.020339559763669968,
-0.04951004311442375,
0.04058333858847618,
0.019387556239962578,
0.0419326052069664,
0.023120619356632233,
-0.016808059066534042,
-0.020460832864046097,
0.005278443451970816,
0.03196348249912262,
0.05448402836918831,
-0.0665745735168457,
0.01095322985202074,
0.0028781017754226923,
-0.059508439153432846,
0.04145524650812149,
0.02173493057489395,
-0.0358477346599102,
-0.015723489224910736,
0.006444013677537441,
0.00032247655326500535,
-0.036497753113508224,
-0.04615642502903938,
-0.08454381674528122,
-0.03967853635549545,
0.03510504961013794,
0.012241637334227562,
0.012878959067165852,
0.024676000699400902,
0.06689932197332382,
-0.0031638205982744694,
0.010039268992841244,
-0.011983129195868969,
-0.012211778201162815,
-0.07591775059700012,
-0.0030785519629716873,
0.08197220414876938,
-0.004012578632682562,
0.004027833230793476,
0.05069075524806976,
0.011835182085633278,
0.030209418386220932,
-0.013612395152449608,
-0.019439540803432465,
-0.04783683642745018,
-0.08237430453300476,
-0.014541213400661945,
-0.07533629238605499,
-0.0013687440659850836,
-0.04624409228563309,
-0.022358078509569168,
-0.01981181465089321,
0.033552221953868866,
0.051009029150009155,
-0.044655706733465195,
0.01538380142301321,
-0.002959431614726782,
0.04039944335818291,
0.018572930246591568,
0.0009377249516546726,
0.011854151263833046,
0.05546940490603447,
0.06275591999292374,
0.06278621405363083,
-0.0643937885761261,
0.05404970049858093,
-0.018918754532933235,
0.03539539873600006,
-0.03761148452758789,
-0.037494052201509476,
-0.013732852414250374,
0.042219750583171844,
-0.04005272313952446,
-0.01335725374519825,
-0.013827326707541943,
0.03939863294363022,
-0.06436054408550262,
0.025134572759270668,
0.018442414700984955,
-0.03739578276872635,
-0.004481764044612646,
-0.01948278583586216,
-0.02813875488936901,
0.0017625748878344893,
-0.059563953429460526,
0.009269475005567074,
-0.018557706847786903,
-0.06238492950797081,
0.004058456514030695,
-0.003708898089826107,
-0.013060194440186024,
-0.01377293560653925,
0.010675301775336266,
0.025159111246466637,
0.016548210754990578,
-0.0060121892020106316,
0.007366718724370003,
0.02160242758691311,
-0.03881854563951492,
-0.028310319408774376,
-0.04509694501757622,
0.04086151719093323,
-0.04478181153535843,
-0.07651828974485397,
-0.003041408024728298,
0.02859742008149624,
-0.013574969954788685,
0.07125832140445709,
0.044420141726732254,
0.05377393588423729,
-0.01306264940649271,
0.007787585724145174,
-0.03204911947250366,
-0.02868219092488289,
-0.034472111612558365,
0.007324608508497477,
-0.0015518481377512217,
-0.008478804491460323,
-0.04481809586286545,
-0.016334015876054764,
-0.06128744035959244,
0.0173479076474905,
0.000490702164825052,
0.03934556990861893,
0.049908414483070374,
0.026908140629529953,
0.0012328127631917596,
0.0003781735140364617,
-0.05057426542043686,
-0.03105488047003746,
0.005704282782971859,
-0.06991855800151825,
0.04224874824285507,
0.0070978254079818726,
-0.046704381704330444,
-0.009211533702909946,
0.01343235932290554,
-0.012244787067174911,
0.03487451747059822,
-0.015883661806583405,
-0.00898904912173748,
0.019708994776010513,
0.01250999141484499,
-0.04156949743628502,
0.0249281395226717,
0.004843653179705143,
-0.040679413825273514,
-0.024093888700008392,
-0.04852406308054924,
0.017733359709382057,
0.04083491861820221,
-0.05515768751502037,
-0.009122258052229881,
-0.060691215097904205,
0.009405344724655151,
0.01799057237803936,
-0.0225877333432436,
-0.013128476217389107,
-0.011730660684406757,
-0.013441101647913456,
-0.034178540110588074,
-0.001943637733347714,
-0.008881931193172932,
0.014230320230126381,
-0.000700569071341306,
-0.04356936365365982,
-0.01724255457520485,
0.04475775361061096,
-0.0015800298424437642,
-0.030700117349624634,
0.02284136600792408,
-0.0300994161516428,
0.030570700764656067,
0.032586853951215744,
-0.021565845236182213,
0.030649593099951744,
0.057398442178964615,
0.005800114944577217,
-0.0057374462485313416,
0.03233274072408676,
0.06230037286877632,
-0.002702029189094901,
0.012906334362924099,
-0.004811383318156004,
-0.07078039646148682,
-0.0465279147028923,
-0.06590548157691956,
-0.039833229035139084,
-0.023446353152394295,
0.02126304619014263,
0.03508551046252251,
0.002856201957911253,
0.0501101128757,
-0.0522647500038147,
-0.007603331934660673,
0.008608299307525158
] |
<p>How would I figure the needed pressure differential to freeze water inside a cooler using ambient air? I am assuming that the combined gas law would apply here and that the formula P1•V1/T1=P2•V2/T2 would provide the answer. My understanding is that by lowering the pressure I could effectively lower the temp as well. By this calculation I would need to reduce the air pressure from 1 bar to 313 milibar. Does this seem right on the math side?
In an open system lowering the pressure should also lower the volume and therefore keep the temperature from dropping. Is this correct as well.</p>
<p>I would assume an ambient temp of 100 F. </p> | g6618 | [
0.024300366640090942,
-0.0397052988409996,
0.006112232804298401,
0.06720508635044098,
-0.028005165979266167,
0.06269122660160065,
0.05632159486413002,
0.03461526334285736,
-0.09401577711105347,
0.026701245456933975,
0.01083712000399828,
-0.00016187909932341427,
-0.009563564322888851,
0.006263320334255695,
-0.0030579320155084133,
0.02447943389415741,
-0.01840571127831936,
-0.007473621051758528,
0.005629273131489754,
-0.0014509836910292506,
-0.021917536854743958,
-0.012768552638590336,
0.01857731305062771,
-0.031156225129961967,
-0.003602022770792246,
-0.0271766297519207,
0.039338331669569016,
0.02173917554318905,
-0.09678877145051956,
0.0002527498872950673,
0.015459295362234116,
0.06437496840953827,
-0.0354556068778038,
-0.0008384421817027032,
-0.008879183791577816,
-0.02882014960050583,
0.06299727410078049,
0.06139162555336952,
-0.07057549804449081,
-0.05000653117895126,
0.009157058782875538,
0.03259396553039551,
0.02509332448244095,
-0.012056620791554451,
0.0005268402164801955,
-0.027429644018411636,
-0.01736985333263874,
-0.058413952589035034,
-0.08791647106409073,
-0.006257022265344858,
0.040770404040813446,
0.008187898434698582,
-0.03131192922592163,
-0.030054189264774323,
-0.026711732149124146,
-0.023682937026023865,
-0.0225352942943573,
-0.028060464188456535,
0.023750513792037964,
0.015200696885585785,
0.003951666411012411,
0.00027430380578152835,
0.006865457631647587,
0.001918550580739975,
0.028178930282592773,
0.010809794999659061,
-0.0113042201846838,
-0.05690303072333336,
0.04484252631664276,
0.01938694529235363,
0.014686571434140205,
-0.05928318202495575,
-0.03260425850749016,
-0.06278849393129349,
0.018758228048682213,
-0.01725645549595356,
-0.004730908665806055,
-0.05592814087867737,
0.0904126688838005,
-0.010354804806411266,
0.002635137876495719,
-0.03795947879552841,
0.07260194420814514,
0.0032499292865395546,
-0.007979417219758034,
-0.03417850658297539,
-0.0828830748796463,
-0.02657453715801239,
-0.033173490315675735,
0.007710421923547983,
-0.021268384531140327,
-0.005301667843014002,
0.05915622040629387,
-0.01742391102015972,
0.06538472324609756,
0.019558746367692947,
0.0033283201046288013,
0.017498688772320747,
0.004552504979074001,
0.06072714552283287,
0.0012478892458602786,
-0.08756549656391144,
0.015919428318738937,
-0.03752131760120392,
-0.04184339568018913,
0.021812601014971733,
0.04190941900014877,
-0.014290993101894855,
-0.046519529074430466,
0.05674416571855545,
0.020879773423075676,
-0.0736004188656807,
-0.05420413240790367,
0.0010506493272259831,
-0.03775500878691673,
-0.026612190529704094,
0.03141037002205849,
-0.004633051343262196,
0.011194977909326553,
0.04844937101006508,
0.05027032271027565,
0.048331569880247116,
0.00033907892066054046,
0.01781599037349224,
0.037016987800598145,
0.010931940749287605,
-0.03431067615747452,
-0.0073451632633805275,
0.027432702481746674,
-0.03425264358520508,
0.030485063791275024,
0.028804684057831764,
-0.03695077821612358,
0.0025859966408461332,
-0.045441046357154846,
0.024022547528147697,
-0.005279647186398506,
0.00978690106421709,
-0.03717915341258049,
-0.011120217852294445,
0.0495961494743824,
0.026337986811995506,
-0.014350679703056812,
0.044083092361688614,
-0.040500301867723465,
0.0015631136484444141,
-0.06627055257558823,
0.020251614972949028,
-0.0036250038538128138,
-0.007247421890497208,
0.02759074792265892,
0.03430074825882912,
0.05004841461777687,
0.03690889850258827,
0.03009103797376156,
-0.06434515863656998,
0.008078290149569511,
-0.04491877928376198,
0.04115558788180351,
0.02423659712076187,
0.016091452911496162,
0.011710288003087044,
0.0012667069677263498,
0.06252313405275345,
-0.08337574452161789,
0.022837040945887566,
-0.009199273772537708,
0.06682668626308441,
0.015258518047630787,
-0.04584868252277374,
-0.02280152402818203,
0.03872237727046013,
-0.06516540050506592,
-0.002525270450860262,
0.04415940120816231,
0.010154463350772858,
0.09586802870035172,
0.01137600652873516,
-0.04182356595993042,
0.019440269097685814,
0.019185345619916916,
0.05782634764909744,
0.029973210766911507,
-0.04732209071516991,
0.0029667688068002462,
0.08187349140644073,
0.0017353735165670514,
-0.03862825408577919,
0.006031128577888012,
0.0001961797388503328,
0.039548616856336594,
0.0171428881585598,
0.051405735313892365,
0.02442191168665886,
0.00017618756101001054,
-0.008668015711009502,
0.016172604635357857,
0.014634489081799984,
-0.032249920070171356,
0.08501280099153519,
-0.012927321717143059,
-0.01021837629377842,
0.04478789493441582,
0.025396812707185745,
0.04889838770031929,
0.05708015710115433,
-0.02378903143107891,
-0.004900907166302204,
0.028780579566955566,
0.02132786251604557,
-0.04948195070028305,
0.017383087426424026,
0.042803917080163956,
-0.011632092297077179,
0.012988755479454994,
0.05898291990160942,
0.012465894222259521,
-0.020054401829838753,
-0.042556628584861755,
0.009407739154994488,
0.018436046317219734,
0.06387428939342499,
-0.07118498533964157,
0.02634543552994728,
-0.054119452834129333,
-0.03176052123308182,
-0.02045520767569542,
-0.013688638806343079,
-0.018226366490125656,
-0.019282270222902298,
0.014545966871082783,
0.04396001249551773,
-0.0309425238519907,
-0.014558184891939163,
-0.00004646371598937549,
0.06720298528671265,
-0.02967972122132778,
0.0426698662340641,
0.074715256690979,
0.041436661034822464,
-0.046250443905591965,
0.02182377502322197,
-0.021393844857811928,
0.03779609501361847,
-0.018279805779457092,
-0.0006966544315218925,
-0.03722662106156349,
0.03454189747571945,
0.01826910302042961,
-0.03874024748802185,
-0.011408316902816296,
0.03979168459773064,
-0.0288093164563179,
-0.007226600311696529,
-0.045338571071624756,
0.01237295102328062,
-0.07784433662891388,
-0.011728961020708084,
0.048361364752054214,
-0.0580521859228611,
-0.009599138982594013,
-0.013428538106381893,
-0.014865884557366371,
0.01834867149591446,
-0.03240089491009712,
-0.027369271963834763,
-0.03160959109663963,
0.011868133209645748,
0.12314892560243607,
0.04154020547866821,
0.01984715461730957,
0.005244184751063585,
-0.06169579178094864,
-0.03553851321339607,
-0.012277834117412567,
-0.03223623335361481,
0.012889273464679718,
0.005777844227850437,
0.012745852582156658,
0.024043038487434387,
0.0005033315974287689,
-0.036310914903879166,
-0.0606074221432209,
0.0031761000864207745,
0.054383784532547,
-0.019994394853711128,
0.027411429211497307,
0.053820930421352386,
-0.00616066250950098,
-0.017224237322807312,
0.04985697567462921,
0.030893784016370773,
0.01300401147454977,
0.03657171502709389,
0.02815413847565651,
0.04279518127441406,
-0.02419411391019821,
0.036502592265605927,
0.039074286818504333,
0.010798769071698189,
-0.009700260125100613,
-0.04856133088469505,
0.0023320673499256372,
-0.0011628216598182917,
0.008651256561279297,
0.03238135948777199,
-0.03711104393005371,
-0.010271512903273106,
-0.028437407687306404,
0.017851170152425766,
-0.05570818856358528,
0.01639493554830551,
-0.005043804179877043,
-0.037525951862335205,
-0.01849380135536194,
-0.004943949170410633,
-0.005553075578063726,
0.0009958158480003476,
-0.031304288655519485,
0.017300110310316086,
-0.019485212862491608,
-0.008110953494906425,
0.011384380981326103,
0.027667995542287827,
0.0040415008552372456,
0.038359347730875015,
-0.04255923256278038,
0.017200954258441925,
0.0016126390546560287,
-0.01452180277556181,
-0.020296508446335793,
0.004507148638367653,
-0.014752891846001148,
0.004946691449731588,
-0.06395817548036575,
-0.015222098678350449,
0.047885049134492874,
-0.01388438418507576,
0.00020540098194032907,
-0.021902458742260933,
-0.002826703479513526,
-0.053915154188871384,
0.002066582441329956,
-0.02283940650522709,
-0.01528043020516634,
-0.0041391728445887566,
0.009982495568692684,
0.02232644148170948,
-0.03121897764503956,
0.028432026505470276,
0.04722260311245918,
-0.015954796224832535,
0.01917322538793087,
0.004133674316108227,
-0.02526002563536167,
-0.001539571792818606,
0.026495104655623436,
0.016347713768482208,
-0.028553884476423264,
0.01223746407777071,
0.04855366423726082,
-0.031165704131126404,
-0.011225511319935322,
0.07495343685150146,
-0.014563332311809063,
-0.015000088140368462,
0.0005954108783043921,
-0.01962146908044815,
-0.05602462589740753,
-0.056525349617004395,
0.019802333787083626,
0.02323201298713684,
-0.024297349154949188,
-0.028058182448148727,
0.042214520275592804,
-0.04035290330648422,
0.00032448358251713216,
0.008784517645835876,
-0.02847965992987156,
0.049465615302324295,
0.052898138761520386,
-0.013312295079231262,
-0.01633278653025627,
0.003072436200454831,
0.02179454080760479,
0.004812705796211958,
0.00570467347279191,
0.0255529023706913,
0.039444539695978165,
-0.013418142683804035,
-0.04597146064043045,
0.009848203510046005,
0.007992145605385303,
0.05767201632261276,
0.01733366958796978,
-0.009829355403780937,
-0.012222441844642162,
0.07266691327095032,
-0.07193691283464432,
-0.008922156877815723,
-0.013091783039271832,
0.001787777291610837,
0.07220540940761566,
-0.039415061473846436,
-0.021704165264964104,
-0.06106812134385109,
0.014648469164967537,
-0.025468727573752403,
0.04603693261742592,
-0.011272680014371872,
0.06466741114854813,
0.009162901900708675,
-0.03252153843641281,
0.01510675810277462,
0.009088574908673763,
-0.02601337432861328,
0.0231039859354496,
-0.00867537036538124,
0.03743628412485123,
0.03506817668676376,
-0.005816998891532421,
-0.036246638745069504,
-0.07211290299892426,
-0.03265073150396347,
-0.04621144384145737,
0.05362223461270332,
0.002170473337173462,
-0.012738915160298347,
-0.0017082234844565392,
-0.022184595465660095,
0.004925466142594814,
0.02247411012649536,
-0.06666649132966995,
0.00040562328649684787,
0.06171010062098503,
0.052820462733507156,
0.004217685200273991,
-0.030841505154967308,
0.05763174593448639,
0.0009512444958090782,
-0.01646050438284874,
0.003979520872235298,
-0.030651159584522247,
0.06393328309059143,
-0.02676681987941265,
0.05905614793300629,
-0.0014212368987500668,
-0.005428442731499672,
0.05150417611002922,
-0.030829140916466713,
-0.01322184968739748,
0.023156573995947838,
-0.04278682917356491,
0.02068076841533184,
-0.004907870665192604,
0.08088375627994537,
-0.029072975739836693,
0.05434940382838249,
-0.03801853209733963,
0.01665319874882698,
0.01660062000155449,
-0.029540162533521652,
-0.005812550894916058,
-0.0032771932892501354,
0.027769038453698158,
-0.01616925746202469,
0.006450190674513578,
0.01827101781964302,
-0.008050214499235153,
0.019349638372659683,
0.002898178994655609,
0.036030132323503494,
-0.02439556084573269,
0.055285170674324036,
-0.02023569494485855,
0.0637935996055603,
0.015856925398111343,
-0.03313629701733589,
0.04317422956228256,
-0.016760362312197685,
-0.009035547263920307,
0.04637826234102249,
0.0066799563355743885,
0.032515645027160645,
-0.011335461400449276,
-0.04285635054111481,
-0.054148364812135696,
0.0013140158262103796,
0.000963305588811636,
0.01314593106508255,
-0.01217662449926138,
0.07257518172264099,
0.044326990842819214,
-0.00522370170801878,
-0.04760083183646202,
-0.04058538004755974,
-0.0194398146122694,
-0.06836201250553131,
0.008608492091298103,
-0.015263205394148827,
-0.08589902520179749,
-0.030062835663557053,
0.01554960198700428,
-0.04029237851500511,
0.02181803062558174,
-0.00003112612466793507,
-0.004577459301799536,
0.0035355007275938988,
0.0037357285618782043,
0.04252452030777931,
0.03201332315802574,
0.02075156755745411,
0.02084748074412346,
0.048350073397159576,
0.07803279161453247,
-0.048831500113010406,
-0.05653534457087517,
-0.01322984043508768,
-0.023444004356861115,
-0.03235482797026634,
0.05762650817632675,
-0.012760994024574757,
0.027670040726661682,
-0.0031900755129754543,
-0.1150372326374054,
-0.018070749938488007,
-0.07417333871126175,
0.04053936526179314,
-0.024685421958565712,
-0.062267906963825226,
-0.034562841057777405,
-0.011240976862609386,
0.011837201192975044,
-0.0223526731133461,
0.009210314601659775,
-0.010954029858112335,
-0.015452373772859573,
0.027081409469246864,
0.06388898193836212,
-0.001985041191801429,
0.020651323720812798,
0.04244621843099594,
-0.025577852502465248,
0.018396316096186638,
0.04268237203359604,
-0.025131411850452423,
-0.035385169088840485,
-0.022493820637464523,
0.049144551157951355,
-0.018898623064160347,
-0.011941352859139442,
0.0013259591069072485,
-0.04012693464756012,
-0.05283786728978157,
0.03089572675526142,
-0.0173996239900589,
0.029616588726639748,
-0.008460690267384052,
0.01297762431204319,
0.03284540772438049,
0.013492844067513943,
-0.02187546156346798,
-0.014777157455682755,
0.01849060133099556,
0.03220633417367935,
-0.03630036488175392,
-0.042295653373003006,
0.05245354771614075,
0.02120257169008255,
0.012697231955826283,
0.057767271995544434,
-0.03209982439875603,
0.004044042434543371,
-0.04144594818353653,
0.01219449657946825,
0.04804578796029091,
-0.00047117911162786186,
0.03854912891983986,
0.02166702225804329,
0.010266171768307686,
0.04810190945863724,
0.003941676113754511,
-0.029600266367197037,
-0.043231647461652756,
0.009194614365696907,
0.011866495944559574,
-0.060241684317588806,
-0.021256159991025925,
-0.025076501071453094,
-0.025074902921915054,
0.0650775209069252,
-0.023485321551561356,
-0.044137436896562576,
-0.024866944178938866,
0.02575324848294258,
-0.020187437534332275,
0.05021519586443901,
0.04536987841129303,
0.0022310949862003326,
-0.03008151240646839,
-0.012523489072918892,
0.028298893943428993,
-0.011611171066761017,
-0.0678081139922142,
-0.016886897385120392,
0.03874978795647621,
-0.024088332429528236,
0.05588275566697121,
0.013021550141274929,
0.04514429345726967,
-0.03493725508451462,
0.012225315906107426,
0.1134348213672638,
-0.053238533437252045,
0.04098544642329216,
-0.020300112664699554,
-0.019503802061080933,
0.03409087285399437,
-0.02373724989593029,
0.00613999180495739,
-0.009684146381914616,
-0.02743856981396675,
0.01808198355138302,
-0.017948919907212257,
0.04427630081772804,
-0.01908169873058796,
-0.04561062529683113,
0.01490973774343729,
0.03908542916178703,
-0.004148548003286123,
0.006439205724745989,
-0.02042401023209095,
-0.02133428305387497,
-0.04155931621789932,
0.00003124481736449525,
0.02534063160419464,
0.0012205408420413733,
0.04398204758763313,
0.009276442229747772,
0.01589670218527317,
0.021464355289936066,
-0.0161861814558506,
-0.004126086365431547,
0.07001692801713943,
-0.012300722301006317,
0.010224025696516037,
-0.0033432303462177515,
-0.06220996379852295,
-0.031485415995121,
-0.0018464147578924894,
-0.025627896189689636,
-0.12200367450714111,
-0.047874338924884796,
0.05130714923143387,
-0.04275886341929436,
0.05165163800120354,
-0.0022325576283037663,
-0.05110698193311691,
0.0013232241617515683,
-0.001976510975509882,
0.019281573593616486,
-0.02549075335264206,
0.026505419984459877,
0.05720088630914688,
0.02735152654349804,
0.06032634526491165,
0.012582923285663128,
-0.02884114347398281,
0.056092169135808945,
-0.08114464581012726,
-0.054290659725666046,
-0.013916725292801857,
-0.03875307738780975,
-0.004326511174440384,
0.026271849870681763,
0.03728446736931801,
0.011556674726307392,
-0.02874385006725788,
0.002765259938314557,
-0.014683681540191174,
-0.011559510603547096,
-0.0017788432305678725,
-0.07604048401117325,
-0.05050713196396828,
0.004247840028256178,
0.05602720379829407,
-0.009655565954744816,
-0.004156356677412987,
0.013769056648015976,
-0.03547796607017517,
-0.036588773131370544,
-0.009988994337618351,
-0.0002665086940396577,
-0.004099773708730936,
-0.04675739258527756,
0.02861592546105385,
0.057260069996118546,
0.00028331473004072905,
-0.029418256133794785,
-0.04831987991929054,
0.07359551638364792,
-0.02768034301698208,
0.014314219355583191,
0.04072323068976402,
-0.019019903615117073,
-0.01442768145352602,
0.0045390380546450615,
0.021384980529546738,
0.05435590445995331,
0.007137272506952286,
0.008294395171105862,
0.01855078712105751,
0.004563296213746071,
-0.05991891771554947,
0.05052805319428444,
-0.039025016129016876,
-0.05963846296072006,
-0.03637993708252907,
-0.007631294429302216,
-0.005643489770591259,
-0.024292871356010437,
-0.0008388521964661777,
0.03034183941781521,
-0.048624325543642044,
-0.0005629821680486202,
-0.006023538298904896,
0.004702696576714516,
0.008809092454612255,
-0.03148898109793663,
-0.08042050153017044,
-0.05495753139257431,
0.06388115882873535,
-0.020020194351673126,
0.0054332842119038105,
0.004026493057608604,
-0.016147561371326447,
-0.0037577501498162746,
-0.016940996050834656,
0.027596116065979004,
0.05687931180000305,
0.023443739861249924,
0.06134076416492462,
-0.020884402096271515,
-0.08953934162855148,
0.047036878764629364,
-0.06478946655988693,
-0.03944620490074158,
0.027996573597192764,
0.05014295130968094,
-0.012355289421975613,
-0.0330628976225853,
-0.060907911509275436,
-0.06084360182285309,
-0.011038396507501602,
0.036649685353040695,
-0.05829223245382309,
-0.027756521478295326,
0.04516449198126793,
-0.07826119661331177,
-0.038521431386470795,
-0.019994892179965973,
0.0274452343583107,
0.022273844107985497,
0.049220241606235504,
0.015037189237773418,
0.003582300152629614,
-0.05398271977901459,
-0.054073743522167206
] |
<p>I have measured the total activity from a radioactive sample during an experiment by counting the number of decays happening in 3 seconds intervals. I got data as:</p>
<p>Time bin: 0 1 2 3 4 5 6 7 ... <br>
Count number: 307 294 257 246 250 216 186 169 ...</p>
<p>Now I want to curve fit an exponential $ae^{bt}$ to the data to determine $b$ as the decay constant. But since I have measured during intervals of 3 seconds, how should I convert/scale this data to get a proper estimate of the decay constant that has units s$^{-1}$?</p> | g6619 | [
0.024356111884117126,
-0.025211531668901443,
0.004960579331964254,
-0.039468489587306976,
0.053775086998939514,
0.03241823986172676,
0.022666359320282936,
0.05027302727103233,
-0.01449769176542759,
0.04557497426867485,
-0.006968919187784195,
0.057757847011089325,
0.012796344235539436,
0.001647113123908639,
0.024789603427052498,
0.0049638161435723305,
0.06811407208442688,
-0.06639798730611801,
0.016015952453017235,
-0.0062109180726110935,
0.04759499430656433,
-0.03503825142979622,
-0.026615368202328682,
-0.0335225872695446,
0.03173236921429634,
-0.06058010831475258,
0.05111986771225929,
0.07345782965421677,
-0.021846067160367966,
-0.018087880685925484,
-0.019674213603138924,
0.025227798148989677,
0.03533797711133957,
0.04704004153609276,
0.03422142565250397,
-0.009321533143520355,
-0.043099261820316315,
0.05070352554321289,
0.0466543547809124,
0.021560095250606537,
0.01054008211940527,
-0.033398352563381195,
0.006352230440825224,
0.09125860780477524,
0.014275970868766308,
-0.012389065697789192,
-0.023930111899971962,
-0.012882714159786701,
0.04803881421685219,
0.015596693381667137,
-0.013917301781475544,
0.024225324392318726,
-0.012469151988625526,
0.014364754781126976,
-0.04095437377691269,
0.06340238451957703,
-0.014094281010329723,
-0.004471426829695702,
-0.009365636855363846,
0.023951539769768715,
0.03963916003704071,
-0.07538080215454102,
-0.007931189611554146,
-0.02916850335896015,
0.06589436531066895,
0.07757139205932617,
0.026854857802391052,
-0.014158422127366066,
0.00921300332993269,
-0.012558240443468094,
-0.03087891824543476,
0.010056795552372932,
0.022800862789154053,
-0.011665414087474346,
-0.06459077447652817,
-0.008443296886980534,
0.008159562945365906,
-0.04283978417515755,
-0.005182553548365831,
0.04974818229675293,
-0.07110533118247986,
0.012053452432155609,
0.05319204926490784,
0.01781501993536949,
-0.005383663345128298,
0.002550408011302352,
-0.046506792306900024,
-0.02880222350358963,
-0.012196202762424946,
-0.033383551985025406,
-0.008279809728264809,
-0.03496333584189415,
0.04335170239210129,
0.0048074256628751755,
0.008927456103265285,
-0.06938067078590393,
-0.04048038646578789,
0.07144208997488022,
0.008789021521806717,
0.06267005205154419,
0.0021573808044195175,
-0.009751093573868275,
-0.026011371985077858,
-0.010960318148136139,
-0.06708420068025589,
-0.0608006976544857,
-0.007307914085686207,
-0.02119467966258526,
0.03176329657435417,
0.002490568207576871,
0.005815189331769943,
-0.04130604490637779,
0.009870666079223156,
-0.05606693774461746,
-0.0033589631784707308,
-0.0014400563668459654,
-0.006639425177127123,
-0.05550289899110794,
-0.03157370164990425,
-0.012425795197486877,
0.021280309185385704,
-0.09331795573234558,
0.02180624194443226,
0.025181543081998825,
-0.030544361099600792,
-0.014071960933506489,
-0.021386481821537018,
0.07529135793447495,
-0.023212825879454613,
0.00630771042779088,
-0.0015133346896618605,
0.004066885448992252,
-0.009715757332742214,
0.037571508437395096,
0.022037100046873093,
0.05626567453145981,
0.0052427505142986774,
-0.0032939082011580467,
-0.04268413037061691,
0.032641805708408356,
-0.021091409027576447,
-0.01460762694478035,
0.049039196223020554,
-0.004107223823666573,
-0.05463752895593643,
0.06533174216747284,
-0.029716458171606064,
-0.020556079223752022,
0.016002051532268524,
0.02134218066930771,
-0.01711530052125454,
0.03816722333431244,
-0.009528616443276405,
-0.0020793969742953777,
-0.051959630101919174,
-0.046197257936000824,
0.03288678452372551,
-0.0033318966161459684,
-0.059289999306201935,
-0.009658406488597393,
0.04778007045388222,
-0.021829314529895782,
-0.0459183044731617,
0.01949913240969181,
-0.005351061467081308,
0.0042678420431911945,
0.002589689800515771,
-0.05498725548386574,
-0.019059808924794197,
-0.016561323776841164,
-0.04262521117925644,
0.010112377814948559,
-0.015464148484170437,
-0.022144697606563568,
-0.031793706119060516,
0.06929337978363037,
0.04127530753612518,
0.0453505702316761,
0.05168690159916878,
-0.0023270363453775644,
0.06429640203714371,
0.053948789834976196,
0.06646230816841125,
-0.009702549315989017,
0.016863608732819557,
-0.028360987082123756,
0.01135931070894003,
-0.0009084664634428918,
-0.006521150935441256,
-0.00086433399701491,
0.014211846515536308,
-0.042678263038396835,
0.0002013757621170953,
-0.018792692571878433,
-0.043763525784015656,
0.0017366460524499416,
0.005740567110478878,
-0.09588199853897095,
0.033764876425266266,
-0.02091068960726261,
-0.005888475105166435,
0.008486621081829071,
0.019768748432397842,
-0.028257720172405243,
0.044873353093862534,
-0.009763315320014954,
-0.05643788352608681,
0.013456880114972591,
-0.028089206665754318,
0.00679885596036911,
0.04440084844827652,
0.019153330475091934,
-0.025218287482857704,
0.0010081829968839884,
-0.04983889311552048,
0.011669883504509926,
-0.015244144946336746,
0.030706753954291344,
0.027089785784482956,
0.06268902868032455,
-0.020370181649923325,
-0.007873381488025188,
0.04036083072423935,
-0.02912565879523754,
-0.002963721053674817,
-0.02346375584602356,
0.0017879342194646597,
0.03568887710571289,
0.02982494980096817,
-0.023098472505807877,
-0.07930149883031845,
0.04693792015314102,
-0.05278155580163002,
-0.01739894039928913,
0.011578190140426159,
0.028343331068754196,
-0.019614452496170998,
0.03449444845318794,
0.01838473044335842,
0.011891132220625877,
-0.009562305174767971,
-0.010934321209788322,
-0.033358894288539886,
-0.015600265935063362,
0.02832985296845436,
-0.023108193650841713,
-0.04452062398195267,
0.02139473706483841,
-0.012749570421874523,
0.012849445454776287,
-0.020223107188940048,
0.017297623679041862,
-0.0009442638256587088,
-0.008889943361282349,
0.001992475241422653,
-0.008199644275009632,
0.03221229463815689,
0.013041432946920395,
-0.012323732487857342,
-0.00971033051609993,
0.0026888574939221144,
-0.03922119364142418,
0.02781587280333042,
0.028349680826067924,
0.016059210523962975,
-0.1017187237739563,
-0.0375305600464344,
-0.056350383907556534,
0.015767613425850868,
0.0056696669198572636,
0.03543689101934433,
0.007768471725285053,
-0.017982538789510727,
0.030712764710187912,
0.0026350270491093397,
-0.01491275429725647,
0.05646360293030739,
-0.05801848694682121,
0.01164317224174738,
-0.04315844178199768,
-0.0014983428409323096,
-0.0026150888297706842,
-0.04538826644420624,
0.04160404950380325,
0.043218281120061874,
0.0011460947571322322,
-0.0013727691257372499,
-0.026104938238859177,
-0.0007447139360010624,
0.015106662176549435,
-0.04954272136092186,
-0.04407047852873802,
-0.019876157864928246,
0.01701321080327034,
0.004455280490219593,
0.013496840372681618,
0.07586309313774109,
-0.03039541095495224,
0.0816953256726265,
0.053429435938596725,
-0.036131277680397034,
-0.06422780454158783,
-0.04039213806390762,
-0.037608690559864044,
-0.021360324695706367,
-0.0012679853243753314,
-0.013403639197349548,
-0.00011700393952196464,
-0.007432357873767614,
0.01700570434331894,
-0.03414156660437584,
-0.04833362251520157,
0.03309312090277672,
-0.04286251589655876,
-0.008176906034350395,
-0.057574182748794556,
0.030484050512313843,
-0.00024756373022682965,
0.010561075992882252,
0.007590363267809153,
0.0572313629090786,
-0.0720122903585434,
0.02685071900486946,
0.03220098093152046,
-0.02069023624062538,
-0.015908537432551384,
-0.005154930520802736,
-0.008147581480443478,
-0.08540290594100952,
-0.015555809251964092,
-0.01609179936349392,
-0.008496575988829136,
0.018227582797408104,
-0.004734122194349766,
-0.0007643261342309415,
-0.00908712949603796,
0.0009727313881739974,
0.019349021837115288,
-0.0662311241030693,
-0.022381098940968513,
-0.06922604143619537,
0.03659357875585556,
-0.029163431376218796,
0.031356148421764374,
0.02873878926038742,
-0.022261375561356544,
-0.005865498911589384,
0.016248580068349838,
-0.017710058018565178,
-0.006381960120052099,
-0.003839417127892375,
0.015918154269456863,
-0.02606869675219059,
-0.018348265439271927,
0.00829825084656477,
0.03001318871974945,
-0.01182754896581173,
0.022677060216665268,
0.02236318401992321,
-0.06738243252038956,
0.011180231347680092,
-0.06907031685113907,
-0.013304058462381363,
0.0654289573431015,
-0.04894779995083809,
-0.03707389906048775,
-0.02525237761437893,
0.10240080207586288,
0.07863716036081314,
0.008251567371189594,
-0.0013121854281052947,
0.024651439860463142,
0.12056140601634979,
-0.003667161101475358,
0.0033898791298270226,
-0.03716893494129181,
0.018351629376411438,
0.023021843284368515,
-0.03615228459239006,
0.09074584394693375,
-0.007705229800194502,
0.02542874403297901,
0.008138401433825493,
-0.03778686374425888,
-0.020428137853741646,
-0.029791058972477913,
0.014030110090970993,
-0.023918163031339645,
-0.006091317627578974,
-0.08092479407787323,
0.017837796360254288,
-0.05322746932506561,
-0.006444654893130064,
-0.013457111082971096,
0.006035014986991882,
-0.11247983574867249,
0.052978165447711945,
0.04765157401561737,
-0.005386723205447197,
0.03060697391629219,
-0.020823759958148003,
0.009263564832508564,
0.008572223596274853,
0.04514463618397713,
-0.012268341146409512,
-0.02016201615333557,
0.020914986729621887,
-0.020022055134177208,
0.023637834936380386,
0.017147235572338104,
-0.04173414781689644,
-0.017026452347636223,
0.03872687742114067,
-0.03342586010694504,
-0.032339148223400116,
0.02365446463227272,
0.0432097353041172,
-0.01440043468028307,
0.028093580156564713,
0.023417159914970398,
0.0036857007071375847,
0.0029933254700154066,
-0.006832996848970652,
-0.044935427606105804,
-0.06691767275333405,
0.08755798637866974,
-0.00856525357812643,
-0.0004226206801831722,
0.009114669635891914,
-0.0029895431362092495,
0.003186834277585149,
0.04403284192085266,
0.02518143504858017,
0.04763346537947655,
-0.034721825271844864,
0.007538695819675922,
0.02713947743177414,
0.027690451592206955,
0.022889770567417145,
-0.0044663394801318645,
-0.018586788326501846,
-0.0002865018614102155,
-0.04603048413991928,
-0.01904563046991825,
-0.009824293665587902,
0.046755097806453705,
-0.04995490610599518,
-0.0830676481127739,
0.0739985778927803,
0.061418648809194565,
-0.019461901858448982,
0.03785833343863487,
-0.05130137503147125,
0.019474199041724205,
-0.0012434393865987659,
-0.047274962067604065,
0.00872049480676651,
0.04834122583270073,
0.015214363113045692,
0.045292794704437256,
-0.06666821241378784,
-0.01160832867026329,
-0.016559280455112457,
-0.01478651538491249,
0.015584384091198444,
-0.066605344414711,
-0.03660407289862633,
-0.03381161019206047,
0.01295184064656496,
-0.013589928857982159,
0.011692319996654987,
-0.02598894014954567,
0.05372356250882149,
-0.032068926841020584,
0.005612436216324568,
0.01609491929411888,
-0.06409069895744324,
0.04206749424338341,
-0.005000659730285406,
0.01745796948671341,
0.028931595385074615,
0.009252777323126793,
-0.020863302052021027,
0.018876761198043823,
-0.041681863367557526,
0.020415661856532097,
-0.041155919432640076,
-0.030862772837281227,
0.028102751821279526,
0.01617867313325405,
-0.019998544827103615,
0.054945867508649826,
0.1097743958234787,
-0.010850601829588413,
-0.0009724542615003884,
-0.05471325293183327,
0.040932923555374146,
0.019732201471924782,
-0.00669116759672761,
0.03295816853642464,
-0.02918875217437744,
0.029737427830696106,
-0.0322112962603569,
0.037778839468955994,
-0.017892107367515564,
0.06291335821151733,
-0.009679730050265789,
0.06736470758914948,
-0.011034305207431316,
0.06379248946905136,
-0.0015676585026085377,
-0.02406066097319126,
0.05431147664785385,
0.021145714446902275,
-0.013026709668338299,
0.02942962571978569,
0.049660973250865936,
0.0607435517013073,
-0.021849878132343292,
-0.05629158765077591,
0.030053921043872833,
0.01970827765762806,
0.03368566185235977,
-0.035503797233104706,
0.014216400682926178,
-0.059414222836494446,
-0.036413561552762985,
0.012875706888735294,
0.029656831175088882,
-0.01970445178449154,
0.041645072400569916,
-0.0282154381275177,
-0.07196391373872757,
-0.005882403813302517,
0.025552496314048767,
0.037124864757061005,
-0.0071674552746117115,
-0.004707287531346083,
-0.025671206414699554,
-0.005472993478178978,
-0.0574125237762928,
0.021231798455119133,
0.041343387216329575,
-0.029509160667657852,
-0.028790419921278954,
-0.005619559902697802,
-0.02685423567891121,
-0.03405936062335968,
0.008088545873761177,
-0.010743777267634869,
0.024965830147266388,
0.005232158116996288,
0.01668156497180462,
-0.06040479615330696,
-0.026491429656744003,
0.040968626737594604,
0.02682419866323471,
0.05626939237117767,
0.021137787029147148,
0.009501897729933262,
-0.03085886873304844,
0.01083478331565857,
0.010497009381651878,
0.04085558280348778,
-0.013654997572302818,
-0.08217964321374893,
0.020319746807217598,
0.03217559680342674,
-0.04046391323208809,
-0.006907807197421789,
0.022305777296423912,
-0.06480499356985092,
0.038112491369247437,
0.013617848046123981,
-0.02786412090063095,
0.045736923813819885,
-0.01085297204554081,
-0.028472356498241425,
0.012892315164208412,
0.006123493425548077,
-0.026143904775381088,
-0.0025209130253642797,
-0.024971172213554382,
-0.0000045706028686254285,
-0.06013437733054161,
0.025341007858514786,
-0.003991635050624609,
0.0012002693256363273,
0.000017423770259483717,
-0.03952302783727646,
-0.01572633907198906,
0.009475327096879482,
-0.030512483790516853,
-0.02402942255139351,
-0.02397312968969345,
-0.044175177812576294,
-0.02592262253165245,
-0.050687890499830246,
0.020509183406829834,
0.01778682880103588,
-0.03267034515738487,
0.020906826481223106,
0.019206760451197624,
-0.03135044127702713,
0.04063519462943077,
-0.003489595139399171,
0.008253821171820164,
0.00848537590354681,
0.062179986387491226,
-0.038926128298044205,
0.017069431021809578,
0.008082023821771145,
0.00699821300804615,
0.03671189770102501,
0.00042378815123811364,
-0.03918454796075821,
0.06260271370410919,
0.056779369711875916,
-0.06796637177467346,
0.02104514092206955,
0.019632957875728607,
0.00021261654910631478,
-0.008487649261951447,
-0.003655344480648637,
0.025868305936455727,
0.039984412491321564,
0.021755164489150047,
0.02847934700548649,
-0.010702717117965221,
-0.08063998073339462,
-0.046998534351587296,
0.026682360097765923,
-0.027771100401878357,
0.00897076353430748,
-0.0029841663781553507,
0.0744980201125145,
0.005434299819171429,
0.060910359025001526,
-0.013044878840446472,
0.05140891298651695,
0.014121376909315586,
0.0017751000123098493,
0.008691033348441124,
0.029404176399111748,
-0.07318286597728729,
0.002735929563641548,
0.023112518712878227,
0.0389077328145504,
0.009654312394559383,
0.039535317569971085,
0.053722016513347626,
-0.06293132156133652,
0.01830204948782921,
0.0011522320564836264,
0.04201267287135124,
-0.0020435303449630737,
0.021755171939730644,
0.02161102555692196,
0.0353667251765728,
0.0017866280395537615,
0.001330071478150785,
-0.09843584895133972,
0.03196752816438675,
-0.03762989491224289,
0.03751884400844574,
0.011026107706129551,
0.0052732182666659355,
-0.04085351899266243,
0.032282281666994095,
-0.12965264916419983,
-0.03347614407539368,
-0.04962893947958946,
0.019825292751193047,
0.029667964205145836,
0.02779778279364109,
0.031136417761445045,
0.0014193156966939569,
0.001262965495698154,
-0.008590142242610455,
-0.035190995782613754,
-0.004567198920994997,
-0.05599171295762062,
0.007249298971146345,
-0.02575830928981304,
-0.02677913010120392,
0.07296313345432281,
-0.05222739279270172,
-0.011020475067198277,
0.09344863891601562,
-0.003473052056506276,
-0.05659405514597893,
0.03342346101999283,
0.04148062318563461,
-0.014433002099394798,
0.006771576125174761,
-0.014221228659152985,
-0.0032157511450350285,
-0.06372253596782684,
0.0263166856020689,
0.022511783987283707,
0.05431875213980675,
-0.01857774145901203,
0.04625964164733887,
-0.03293817862868309,
0.012034272775053978,
0.029708387330174446,
-0.0016889260150492191,
-0.08149885386228561,
0.006738151889294386,
-0.022346172481775284,
-0.037323981523513794,
0.0030809352174401283,
-0.0056976377964019775,
-0.005402443930506706,
0.04533878713846207,
0.031227974221110344,
-0.06062117964029312,
-0.040444642305374146,
0.03211100772023201,
-0.020365770906209946,
-0.07499775290489197,
-0.026593688875436783,
-0.010549585334956646,
-0.004260065965354443,
0.02562383934855461,
-0.04550107941031456,
-0.05508320778608322,
0.0055562411434948444,
0.034798648208379745,
0.015174412168562412,
-0.03018243983387947,
-0.02043571136891842,
-0.03224055469036102,
0.024621479213237762,
-0.0030330787412822247,
0.024481741711497307,
0.04656215012073517,
0.03225548192858696,
-0.08969190716743469,
0.035120271146297455,
0.014559797011315823,
0.040878280997276306,
0.02400696650147438,
0.07216914743185043,
0.014958246611058712,
-0.05248855799436569,
-0.01907159760594368,
0.043372828513383865,
0.05082223564386368,
-0.030346037819981575,
-0.019561903551220894,
-0.003896490903571248,
0.03702038899064064,
0.050206512212753296,
-0.00795063842087984,
0.008364237844944,
0.019912585616111755,
0.007694924715906382,
0.023828336969017982,
0.00665742252022028,
-0.0896347388625145,
0.0010444681392982602,
-0.0404353104531765,
0.06001795455813408,
-0.028584839776158333,
-0.030556030571460724,
0.0286155566573143,
0.017385335639119148
] |
<p>I'm trying to calculate the initial velocity $v_0$ and angle $\theta$ for a given destination $(x, y)$ with a launch height of $y_0$. Obviously there will be a set of pairs of velocity and angle that will pass through the destination point. This set is given by
$$ \left\{(v_0,\theta) \middle|y = - \frac{g}{2 v_0^2 \cdot \cos^2(\theta)} \cdot x^2 + \tan(\theta) \cdot x +y_0 \right\} \ .$$</p>
<p>I have already looked at this questions:</p>
<p><a href="http://physics.stackexchange.com/questions/27992/solving-for-initial-velocity-required-to-launch-a-projectile-to-a-given-destinat">Solving for initial velocity required to launch a projectile to a given destination at a different height</a></p>
<p><a href="http://physics.stackexchange.com/questions/56265/how-to-get-the-angle-needed-for-a-projectile-to-pass-through-a-given-point-for-t">How to get the angle needed for a projectile to pass through a given point for trajectory plotting</a></p>
<p>So for example I could rewrite the set to
$$\left\{ (v_0,\theta) \middle| v_0 = \frac{1}{\cos(\theta)}\sqrt{\frac{\frac{1}{2} g x^2}{x \tan(\theta)+y_0}} \right\}\ .$$</p>
<p>Is there an easy way to compute this set for one given destination without iterating over all possible velocities or angles?</p> | g6620 | [
-0.02116360329091549,
0.00827487837523222,
-0.022109905257821083,
0.02299271710216999,
0.018664248287677765,
-0.031545817852020264,
0.03359300643205643,
-0.011329835280776024,
-0.07263092696666718,
0.014436503872275352,
-0.01982305943965912,
0.0762348622083664,
0.06241230294108391,
-0.0180913545191288,
0.006024669390171766,
-0.009330406785011292,
0.040321942418813705,
0.00396285904571414,
0.05683472007513046,
0.04279344901442528,
0.03189149871468544,
-0.059557121247053146,
0.003964546136558056,
-0.02129237912595272,
0.013382203876972198,
-0.03800201788544655,
-0.012535623274743557,
0.013560083694756031,
-0.09101595729589462,
0.06366444379091263,
0.004258205648511648,
-0.010723238810896873,
0.04272521659731865,
-0.040812842547893524,
-0.02045067586004734,
-0.01635267771780491,
-0.016382351517677307,
0.002431007567793131,
-0.04875792935490608,
-0.0784745067358017,
-0.002621161285787821,
-0.06909341365098953,
0.041170891374349594,
0.008594794198870659,
0.001978522166609764,
-0.0084706861525774,
-0.01606266386806965,
-0.017815761268138885,
-0.05745471268892288,
-0.02244322933256626,
-0.012427311390638351,
0.02774043381214142,
-0.011005764827132225,
-0.06950990110635757,
-0.06474590301513672,
0.04943028464913368,
0.004409248009324074,
-0.06442848592996597,
0.02678336203098297,
0.022448953241109848,
0.008293354883790016,
-0.018507909029722214,
-0.016469435766339302,
-0.00563026824966073,
0.024153124541044235,
-0.011400184594094753,
-0.004230073653161526,
-0.011258970014750957,
-0.006876675877720118,
-0.022909387946128845,
-0.010486100800335407,
-0.025710873305797577,
-0.0083943922072649,
-0.04371266812086105,
-0.0927928164601326,
0.019789930433034897,
0.025208977982401848,
-0.017745675519108772,
-0.034488122910261154,
0.007118788082152605,
-0.025833429768681526,
-0.020957667380571365,
0.01683119311928749,
-0.06922657042741776,
-0.021088896319270134,
-0.011569519527256489,
0.08039186149835587,
0.03064390830695629,
-0.020982889458537102,
-0.030251076444983482,
0.018857227638363838,
0.033616237342357635,
0.005371036473661661,
0.02669558860361576,
-0.009092051535844803,
0.022234199568629265,
-0.08103618025779724,
0.022611601278185844,
0.06302721053361893,
0.020874539390206337,
0.00789796095341444,
0.022616231814026833,
0.03704031929373741,
-0.042379509657621384,
0.010745474137365818,
-0.048487983644008636,
0.06949567794799805,
0.00039184759953059256,
0.023420993238687515,
-0.03068476729094982,
-0.022968478500843048,
-0.08221516013145447,
-0.028368888422846794,
-0.04556536674499512,
-0.022202687337994576,
-0.03203997761011124,
0.015292094089090824,
0.055769920349121094,
-0.026517240330576897,
0.02001596800982952,
-0.01607164554297924,
0.016318097710609436,
-0.01994885504245758,
0.029882848262786865,
-0.008386937901377678,
-0.001597182359546423,
-0.09503734111785889,
-0.05712563171982765,
0.013667547143995762,
-0.0026490739546716213,
-0.029134783893823624,
-0.02997024543583393,
0.04552839696407318,
0.04650023579597473,
-0.0036081215366721153,
-0.0006471475353464484,
0.020991791039705276,
-0.0031831127125769854,
0.015747196972370148,
0.016596876084804535,
-0.021369080990552902,
-0.010128508321940899,
-0.03442603349685669,
0.0025598981883376837,
-0.043672140687704086,
0.029192037880420685,
-0.00565457995980978,
-0.03017239272594452,
0.012932874262332916,
-0.0320676751434803,
0.003416879801079631,
0.06774073094129562,
-0.0028812908567488194,
0.05832400545477867,
-0.008771934546530247,
-0.05715155228972435,
0.024622729048132896,
0.01692657731473446,
0.017017241567373276,
-0.041430141776800156,
0.04887441173195839,
-0.0038906740956008434,
0.05875277519226074,
0.006047184579074383,
-0.04596969857811928,
0.021496769040822983,
-0.020548230037093163,
-0.0023761186748743057,
-0.06203238666057587,
-0.048219937831163406,
-0.009408287703990936,
0.01860005222260952,
0.05363909900188446,
0.032783392816782,
-0.011516747996211052,
-0.0054834154434502125,
-0.0022717625834047794,
0.011960815638303757,
-0.01718340814113617,
-0.003429278964176774,
0.013551546260714531,
-0.057459600269794464,
0.02634824626147747,
0.007058071903884411,
0.019567465409636497,
-0.013707789592444897,
0.003756557824090123,
0.008027028292417526,
0.00004050639472552575,
-0.009497502818703651,
0.050660692155361176,
0.004264888819307089,
-0.02114010602235794,
-0.02310159243643284,
-0.021798787638545036,
-0.018239403143525124,
0.056675415486097336,
0.01825377158820629,
-0.004353425465524197,
0.05514294281601906,
0.010607348755002022,
0.032336290925741196,
0.030493859201669693,
0.02163410186767578,
-0.04722650349140167,
0.04139043390750885,
0.035410650074481964,
-0.010894794017076492,
-0.013914515264332294,
0.06554678827524185,
-0.018620768561959267,
-0.053117360919713974,
-0.011023075319826603,
0.01849043183028698,
0.00861690565943718,
0.004369008354842663,
0.02836856059730053,
-0.006779915653169155,
-0.013025802560150623,
0.009067488834261894,
-0.027566539123654366,
0.0017687560757622123,
-0.013726175762712955,
-0.02290394902229309,
-0.01326177641749382,
0.05488862097263336,
0.008134179748594761,
-0.02485964633524418,
0.02143343724310398,
-0.015486180782318115,
0.037358541041612625,
0.04508017376065254,
-0.01790347509086132,
-0.05205367133021355,
0.0860774889588356,
-0.008513787761330605,
-0.004737963899970055,
-0.04229610413312912,
0.059064123779535294,
0.04056648537516594,
0.025974968448281288,
-0.05382673069834709,
0.030134277418255806,
-0.003790054004639387,
0.0657457560300827,
-0.06055612489581108,
-0.01772759109735489,
0.016863074153661728,
-0.011767768301069736,
-0.033730052411556244,
-0.04180889204144478,
0.009836947545409203,
-0.0627492368221283,
0.030419792979955673,
-0.03702107444405556,
-0.015184924006462097,
-0.033895280212163925,
0.009041553363204002,
-0.03296835348010063,
-0.052344754338264465,
-0.08095266669988632,
-0.014445050619542599,
-0.03440142795443535,
-0.010068400762975216,
-0.019973309710621834,
0.05537791550159454,
0.018244188278913498,
-0.05247507989406586,
-0.004346149042248726,
-0.03681183606386185,
-0.09723933786153793,
-0.010081898421049118,
0.07649429142475128,
0.030067363753914833,
-0.005199147388339043,
-0.04027214273810387,
0.003860853146761656,
0.012504462152719498,
-0.0386480949819088,
0.07679298520088196,
0.006398245692253113,
-0.04880955442786217,
-0.0025872287806123495,
0.0962316170334816,
0.03663673251867294,
-0.03172683343291283,
0.0709947943687439,
0.08892876654863358,
0.02486904338002205,
-0.04279201477766037,
0.036541081964969635,
0.033904071897268295,
0.031075984239578247,
-0.00903982575982809,
0.025949232280254364,
0.022626277059316635,
0.02744177356362343,
-0.007047588471323252,
0.01727334037423134,
-0.037686556577682495,
-0.030019044876098633,
-0.006107484456151724,
-0.021490223705768585,
-0.03437354043126106,
0.01497973408550024,
-0.01023014448583126,
0.021587751805782318,
-0.026166992262005806,
-0.008028380572795868,
-0.0019046204397454858,
0.059117596596479416,
0.0384182333946228,
-0.03252039849758148,
0.010468377731740475,
-0.01166960597038269,
-0.03498348221182823,
0.015638792887330055,
0.0022875620052218437,
-0.015965959057211876,
0.07126501947641373,
-0.013874398544430733,
-0.03032575361430645,
0.033907920122146606,
0.04154285043478012,
0.009543188847601414,
0.01738891936838627,
0.002275227103382349,
0.020201845094561577,
-0.017111700028181076,
-0.027823906391859055,
0.06058787927031517,
0.09413377940654755,
0.0437200590968132,
-0.006634347140789032,
-0.001360347610898316,
-0.06156236305832863,
0.007120721973478794,
0.027607720345258713,
0.060000497847795486,
0.006551850587129593,
-0.02300582267343998,
-0.00648996839299798,
-0.049906175583601,
-0.004743689671158791,
0.02069815620779991,
-0.03009330853819847,
0.03615039587020874,
0.020234614610671997,
0.017156977206468582,
-0.1075344830751419,
-0.008630813099443913,
-0.030327506363391876,
0.008209047839045525,
0.028350485488772392,
-0.025566691532731056,
0.05159278213977814,
0.07565362006425858,
-0.023828983306884766,
0.007102243136614561,
0.046423494815826416,
-0.012697141617536545,
0.015099719166755676,
-0.02197975292801857,
0.06103565916419029,
0.020755350589752197,
-0.043343715369701385,
-0.06917747110128403,
0.018512004986405373,
0.0075774784199893475,
0.0013544977409765124,
0.031107675284147263,
-0.0790005475282669,
0.02572724223136902,
-0.03958839550614357,
-0.025197694078087807,
0.0009476381819695234,
0.02633577212691307,
0.012248889543116093,
-0.03206638619303703,
0.06780955195426941,
0.0838688537478447,
0.006543691270053387,
-0.008424806408584118,
0.007100746035575867,
-0.010316666215658188,
0.06959541141986847,
-0.05277121439576149,
0.008261347189545631,
0.05546098202466965,
-0.004112886730581522,
-0.026263367384672165,
-0.028021616861224174,
-0.011772748082876205,
0.02113807201385498,
0.031377602368593216,
-0.007507281377911568,
0.01987863890826702,
0.00937692727893591,
-0.03159775212407112,
0.025224391371011734,
-0.03691459447145462,
-0.04476730152964592,
0.0016171075403690338,
-0.032577402889728546,
-0.0414646677672863,
-0.00901598110795021,
-0.018470725044608116,
0.014561411924660206,
-0.011777789331972599,
0.0005649371305480599,
-0.036676354706287384,
-0.03985465690493584,
0.03308430686593056,
0.0021943249739706516,
-0.01957179605960846,
-0.016295911744236946,
-0.02583649940788746,
-0.026022637262940407,
-0.04883045703172684,
-0.03380563110113144,
-0.0038570549804717302,
0.03628336265683174,
0.06326226145029068,
-0.07599160820245743,
0.07679466903209686,
0.0031628194265067577,
0.03918701410293579,
-0.019080758094787598,
0.055754031985998154,
0.0377754382789135,
0.0059362598694860935,
0.04363482818007469,
-0.013613421469926834,
0.019352898001670837,
-0.009553826414048672,
0.03362557291984558,
0.022908804938197136,
-0.008891758508980274,
0.03069736808538437,
-0.0250498466193676,
-0.010636639781296253,
0.0022230627946555614,
-0.025134773924946785,
-0.017054013907909393,
0.011889583431184292,
0.04690442606806755,
-0.013161041773855686,
0.016886811703443527,
0.024114197120070457,
-0.0029374794103205204,
0.0009871108923107386,
0.02513166517019272,
0.017292222008109093,
-0.004194101318717003,
-0.059466686099767685,
-0.04270010069012642,
0.006496243644505739,
0.00908885058015585,
-0.012536460533738136,
0.019801964983344078,
0.021699337288737297,
0.02572665549814701,
-0.02915126271545887,
-0.03414957970380783,
0.03260579705238342,
0.020848579704761505,
-0.00031561023206450045,
0.003936450462788343,
0.006836647167801857,
-0.021077953279018402,
0.00519930012524128,
0.01607532426714897,
0.0077714258804917336,
-0.007407782599329948,
-0.0489409975707531,
-0.02091645635664463,
0.0036385427229106426,
0.053274188190698624,
0.002592755714431405,
-0.02053896337747574,
-0.02484630048274994,
-0.030806371942162514,
-0.012543315067887306,
0.031807009130716324,
0.022170115262269974,
0.00005237826917436905,
-0.014820422977209091,
-0.06512658298015594,
0.014948728494346142,
-0.019755080342292786,
-0.04300794377923012,
-0.042556364089250565,
-0.02462012879550457,
0.049239013344049454,
0.008320322260260582,
-0.04537208378314972,
0.024580512195825577,
-0.01900908537209034,
0.011704972945153713,
-0.02030280977487564,
-0.037384454160928726,
-0.01373352576047182,
0.026644568890333176,
0.017394009977579117,
0.0036876723170280457,
0.003016845555976033,
0.04995248466730118,
0.01574091985821724,
-0.04926863685250282,
0.03271815553307533,
0.01976795867085457,
0.030842995271086693,
0.04681092128157616,
-0.005685518030077219,
0.01781311072409153,
0.0006600155611522496,
0.012448585592210293,
0.009650316089391708,
-0.012608152814209461,
-0.04333864897489548,
0.08098584413528442,
-0.054691389203071594,
-0.005024487618356943,
0.02383972331881523,
0.05272569879889488,
0.03477349877357483,
-0.06590753048658371,
-0.05474287271499634,
-0.064033642411232,
0.045099757611751556,
-0.04459003731608391,
-0.05197767913341522,
-0.08052914589643478,
-0.009614364244043827,
-0.0182971078902483,
-0.040019359439611435,
-0.06900805979967117,
-0.06894048303365707,
0.001222150633111596,
-0.038190651684999466,
-0.10367124527692795,
0.0003414618840906769,
0.008799797855317593,
0.03483610600233078,
-0.01927773840725422,
0.03528263047337532,
-0.052988164126873016,
-0.02813275158405304,
-0.0045651947148144245,
0.00009901825251290575,
-0.06421272456645966,
0.03726000338792801,
0.03362254053354263,
-0.09641032665967941,
-0.03922061622142792,
0.038098301738500595,
-0.051326584070920944,
0.06739839166402817,
-0.0032553940545767546,
-0.006937048863619566,
0.07833916693925858,
-0.05387531965970993,
0.042892035096883774,
0.11329922825098038,
-0.011232595890760422,
0.04549124836921692,
0.006400986108928919,
0.033607758581638336,
0.03234017640352249,
-0.04562082514166832,
0.003033928805962205,
0.01818924769759178,
-0.07651492208242416,
0.0031190726440399885,
0.04635332152247429,
0.06503302603960037,
-0.01692078448832035,
-0.044099897146224976,
-0.007765027694404125,
0.014072820544242859,
-0.0197829008102417,
0.054754145443439484,
0.025744706392288208,
0.01114258635789156,
-0.03571556508541107,
0.021007973700761795,
-0.0874917060136795,
-0.025237353518605232,
0.0014162086881697178,
-0.06523571908473969,
-0.001169639639556408,
0.035216402262449265,
-0.030066149309277534,
-0.059549059718847275,
-0.052770741283893585,
-0.03849794715642929,
0.022183477878570557,
0.034956324845552444,
-0.007025800179690123,
0.07316534221172333,
0.03464377671480179,
0.01644977740943432,
-0.018628710880875587,
-0.0012775035575032234,
0.009052565321326256,
0.03298645094037056,
0.03851545229554176,
-0.02289273589849472,
0.06300882250070572,
-0.052490703761577606,
0.019635867327451706,
0.07062888145446777,
0.059575460851192474,
0.0841016173362732,
-0.027730531990528107,
0.02722943387925625,
-0.038683537393808365,
-0.02960936166346073,
0.0242394357919693,
-0.015197284519672394,
0.06513772904872894,
-0.025622345507144928,
-0.03543510288000107,
0.038054730743169785,
0.021774770691990852,
0.0245782732963562,
0.06314022094011307,
0.030280333012342453,
0.021667052060365677,
0.01314206887036562,
0.04561552777886391,
0.0008396325865760446,
-0.022493427619338036,
0.006147066596895456,
0.016589200124144554,
0.009169216267764568,
0.026557229459285736,
0.08614631742238998,
-0.012673957273364067,
-0.002550416858866811,
0.060391709208488464,
0.018021659925580025,
-0.006417944096028805,
0.017193997278809547,
-0.017187878489494324,
0.004445655737072229,
-0.008294072933495045,
-0.04735220596194267,
-0.036062393337488174,
-0.010183693841099739,
0.0167767982929945,
-0.04899804666638374,
-0.02282804623246193,
0.029879525303840637,
-0.0026414135936647654,
-0.03750089183449745,
-0.02321746200323105,
0.03414032608270645,
-0.05589786916971207,
0.07394876331090927,
-0.007032678462564945,
0.00406158622354269,
0.027365801855921745,
0.012579850852489471,
0.015428495593369007,
0.03518291562795639,
0.007006193045526743,
0.014565086923539639,
0.005318598821759224,
-0.061804305762052536,
-0.04373788833618164,
0.0013226561713963747,
-0.03877139836549759,
0.03972756862640381,
-0.047355491667985916,
0.013912287540733814,
0.008647892624139786,
0.029639482498168945,
-0.010948234237730503,
-0.03995170444250107,
0.01679840125143528,
0.002620707731693983,
-0.03071717359125614,
-0.015788022428750992,
0.029077114537358284,
-0.005432455334812403,
0.013638772070407867,
-0.02580106072127819,
-0.011683857999742031,
-0.0003011315711773932,
-0.015396817587316036,
-0.030145009979605675,
0.030388280749320984,
0.030901869758963585,
0.02170700579881668,
-0.028067519888281822,
0.03533929958939552,
0.060466356575489044,
0.0362321212887764,
0.02326080948114395,
0.01700902171432972,
-0.012414554134011269,
0.060912732034921646,
0.026708504185080528,
-0.015082428231835365,
-0.018611852079629898,
0.017158348113298416,
0.019162990152835846,
-0.013509700074791908,
-0.0038675006944686174,
0.0009532316471450031,
0.05782828852534294,
-0.03165850043296814,
0.040423907339572906,
-0.02645917981863022,
0.02433653548359871,
-0.07117915898561478,
0.07916660606861115,
-0.006391060072928667,
-0.01710115745663643,
-0.022384921088814735,
-0.02548711746931076,
0.07041152566671371,
-0.03372741490602493,
0.02276589907705784,
-0.02401622384786606,
-0.01809948869049549,
0.012699807062745094,
-0.009526247158646584,
-0.02331223152577877,
0.015901925042271614,
-0.039879243820905685,
-0.030182434245944023,
0.08955778181552887,
-0.06288622319698334,
0.030998636037111282,
-0.02119145728647709,
-0.06356745213270187,
0.010085498914122581,
0.01573885604739189,
0.004264046438038349,
0.026104526594281197,
-0.03883981704711914,
-0.03860688954591751,
-0.0182508435100317,
0.043926969170570374,
0.03989819809794426,
0.03164482116699219,
0.028994936496019363,
-0.04674544185400009,
0.0847640410065651,
0.04663752764463425,
-0.029783135280013084,
0.0313984714448452,
-0.03854374960064888,
-0.029642462730407715,
0.009830916300415993,
0.03355328366160393,
0.024308379739522934,
-0.04009125381708145,
-0.049106959253549576,
-0.01513732224702835,
-0.009204273112118244,
-0.006760796066373587,
0.015258949249982834,
-0.02351279929280281,
-0.019303636625409126,
0.0031732029747217894
] |
<p>I was laying on my bed, reading a book when the sun shone through the windows on my left. I happened to look at the wall on my right and noticed this very strange effect. The shadow of my elbow, when near the pages of the book, joined up with the shadow of the book even though I wasn't physically touching it. </p>
<p>I have posted a video of the event <a href="http://tinypic.com/player.php?v=6xw7tc%3E&s=5#.UtqZmbRFCM8">here</a>. <em>(Note: the video seems to be wrong way up but you still get the idea of what is happening)</em></p>
<p>What is causing this? Some sort of optical illusion where the light get's bent?
Coincidentally, I have been wondering about a similar effect recently where if you focus your eye on a nearby object, say, your finger, objects behind it in the distance seem to get curved/distorted around the edge of your finger. It seems awfully related...</p>
<p><em><strong>EDIT:</em></strong> I could see the bulge with my bare eyes to the same extent as in the video! The room was well light and the wall was indeed quite bright.</p> | g6621 | [
0.028798775747418404,
-0.02142799273133278,
-0.006769026163965464,
0.012815400026738644,
0.006930546835064888,
0.0719638466835022,
0.023629089817404747,
0.07300284504890442,
0.01830402947962284,
-0.00958679523319006,
0.03857193887233734,
0.02995794266462326,
0.002190748928114772,
0.01871146447956562,
0.04694871976971626,
0.009966009296476841,
0.06429547816514969,
-0.022696174681186676,
0.007622253615409136,
0.0144930649548769,
-0.02459486573934555,
0.05235854908823967,
-0.044060636311769485,
-0.0017926858272403479,
-0.055001307278871536,
0.03537537157535553,
-0.02139204926788807,
-0.007977786473929882,
-0.023661239072680473,
-0.01861213892698288,
0.018482333049178123,
0.008012055419385433,
0.025538261979818344,
0.035437747836112976,
-0.005043335258960724,
-0.014682895503938198,
0.022838743403553963,
-0.008636043407022953,
0.030150212347507477,
0.01976723037660122,
-0.011997043155133724,
0.024676242843270302,
0.03107801079750061,
0.00859113223850727,
0.014306005090475082,
0.01730716973543167,
0.018990498036146164,
0.047856271266937256,
0.03856616094708443,
-0.020955011248588562,
-0.009980875998735428,
-0.04465305060148239,
0.007241477258503437,
0.00220281514339149,
0.07120134681463242,
0.013406259939074516,
-0.023195238783955574,
-0.007334747351706028,
0.05094245448708534,
0.04081285372376442,
0.04598236829042435,
0.0346904918551445,
0.05830686166882515,
0.013022588565945625,
0.027368666604161263,
0.021477803587913513,
-0.02913982793688774,
0.021507596597075462,
0.03270397335290909,
-0.048594050109386444,
-0.0017376068281009793,
0.023363398388028145,
-0.025014938786625862,
-0.020781217142939568,
-0.020992381498217583,
-0.02161041647195816,
0.02928905189037323,
-0.01018523145467043,
-0.013179445639252663,
0.05724480375647545,
-0.03881164640188217,
-0.044703785330057144,
-0.06364127993583679,
0.04648797586560249,
0.04479992389678955,
-0.024693699553608894,
-0.0024413035716861486,
-0.00679597957059741,
-0.03132690489292145,
-0.006053124088793993,
0.05349674075841904,
-0.014192547649145126,
0.027855398133397102,
-0.0011207772186025977,
-0.02259773574769497,
-0.021223159506917,
0.033877089619636536,
0.055784642696380615,
0.005186085123568773,
-0.01170111633837223,
-0.0938243418931961,
-0.019230591133236885,
-0.000041229137423215434,
0.02720956690609455,
-0.012875128537416458,
0.06957687437534332,
-0.01620892994105816,
0.007043821737170219,
-0.05178801715373993,
0.01281929574906826,
-0.057529937475919724,
-0.03153648227453232,
0.0010541371302679181,
-0.05165580287575722,
0.020098106935620308,
-0.05856953561306,
0.008151600137352943,
0.03718237951397896,
0.015065079554915428,
0.02511114440858364,
0.041933368891477585,
0.03334140405058861,
0.011793863028287888,
0.0364513136446476,
-0.011226354166865349,
-0.038082368671894073,
0.007956210523843765,
-0.06316616386175156,
0.009807691909372807,
-0.03110930137336254,
0.06140667945146561,
-0.00020810595015063882,
-0.027043743059039116,
0.0325872078537941,
0.010893648490309715,
0.007058112882077694,
0.030330205336213112,
-0.024807538837194443,
0.002756974659860134,
0.01186253223568201,
0.014159401878714561,
-0.023323671892285347,
0.027613017708063126,
-0.04863661900162697,
-0.0037576432805508375,
-0.00040663176332600415,
-0.027580352500081062,
0.010233053006231785,
0.042996011674404144,
-0.05454311892390251,
-0.04679684340953827,
-0.010376260615885258,
-0.03522103279829025,
-0.04908093437552452,
0.00900443084537983,
0.015972405672073364,
0.010777657851576805,
-0.041817326098680496,
-0.011938223615288734,
0.002370147965848446,
0.06840401142835617,
-0.029279675334692,
-0.025389034301042557,
-0.03497209772467613,
-0.01825963892042637,
-0.009467009454965591,
0.0007523405947722495,
-0.027729719877243042,
0.009776693768799305,
-0.04592007398605347,
-0.055724162608385086,
-0.006068455055356026,
-0.020202279090881348,
-0.036584626883268356,
-0.03087342157959938,
0.051435764878988266,
0.055608540773391724,
-0.027849966660141945,
0.05859905853867531,
0.00987690594047308,
-0.03794319927692413,
-0.0274598840624094,
-0.024313418194651604,
-0.04104432836174965,
0.021491946652531624,
-0.042130306363105774,
0.01782231405377388,
0.02332138642668724,
-0.021961843594908714,
0.011845894157886505,
-0.042878877371549606,
-0.06718698143959045,
-0.0074401539750397205,
0.0209119264036417,
-0.008798379451036453,
-0.010051365941762924,
0.0965471863746643,
-0.001469272654503584,
-0.037498973309993744,
0.0183020681142807,
-0.015400608070194721,
0.004654198419302702,
0.027758538722991943,
-0.010802811942994595,
-0.026008617132902145,
0.08073128759860992,
0.008039364591240883,
-0.006556476000696421,
-0.02455908991396427,
-0.008403515443205833,
-0.010801254771649837,
0.00827726162970066,
0.014898641966283321,
-0.027456894516944885,
-0.02297462522983551,
0.030717484652996063,
0.004026183858513832,
0.050106681883335114,
-0.06084715574979782,
0.060167890042066574,
0.07232633233070374,
0.07676766067743301,
0.027957966551184654,
-0.02923605404794216,
0.0402621254324913,
-0.008392227813601494,
-0.03137684985995293,
-0.014276172965765,
-0.004151610191911459,
0.0008226957870647311,
-0.09813694655895233,
-0.015072827227413654,
0.05161002278327942,
0.061305686831474304,
0.00607079453766346,
-0.029116634279489517,
-0.0030700890347361565,
0.010764580219984055,
-0.01123466994613409,
-0.039037641137838364,
0.048367977142333984,
-0.010220742784440517,
-0.04264669120311737,
-0.10473848134279251,
0.014723130501806736,
0.05577455088496208,
-0.006500603165477514,
0.02034035697579384,
0.01970088668167591,
-0.004959980491548777,
0.04761851951479912,
-0.0030222039204090834,
0.004759019240736961,
0.00993131473660469,
0.022922703996300697,
0.007082274649292231,
-0.05604051426053047,
0.013693198561668396,
-0.05016732215881348,
0.004631680436432362,
-0.04346417635679245,
-0.030536359176039696,
0.0149840684607625,
-0.005195403005927801,
-0.0143223712220788,
0.02498738281428814,
0.028103027492761612,
0.002588399685919285,
0.03385595977306366,
-0.004893885925412178,
-0.0017678870353847742,
0.06590356677770615,
-0.01814199611544609,
0.01711386814713478,
0.03210563212633133,
0.025689808651804924,
-0.02626774273812771,
-0.013669184409081936,
-0.0023254062980413437,
-0.004138332325965166,
-0.03403427451848984,
0.06352526694536209,
-0.025301093235611916,
0.04659649357199669,
0.014152965508401394,
-0.04498006030917168,
-0.07297048717737198,
0.009558508172631264,
0.0354488231241703,
-0.0059501430951058865,
-0.020604819059371948,
-0.003179173218086362,
-0.01563386432826519,
0.022481843829154968,
0.05579669401049614,
0.0635450929403305,
0.009418107569217682,
0.06434887647628784,
-0.0758705586194992,
0.0008491250919178128,
-0.04186666011810303,
-0.02385779842734337,
-0.011179829016327858,
0.06655748188495636,
-0.014603630639612675,
-0.03929596394300461,
0.009094059467315674,
-0.07285427302122116,
0.021818969398736954,
0.019901983439922333,
-0.024073075503110886,
-0.03162318468093872,
0.038011930882930756,
0.050568822771310806,
-0.004349544178694487,
0.019335048273205757,
-0.00102050241548568,
-0.012066727504134178,
-0.009066633880138397,
0.01860971748828888,
0.04102790355682373,
0.03260500356554985,
0.0066113220527768135,
0.012742310762405396,
0.05577448382973671,
-0.03967306390404701,
-0.000018029953935183585,
0.023416979238390923,
0.015636611729860306,
-0.010980004444718361,
-0.029169388115406036,
-0.04823891445994377,
-0.041243523359298706,
-0.016865134239196777,
-0.010718337260186672,
0.0254829078912735,
-0.05315125733613968,
0.01056104525923729,
0.046965859830379486,
-0.017492344602942467,
0.013273139484226704,
0.018414007499814034,
0.00904306024312973,
-0.05990075692534447,
0.06196923181414604,
0.016174854710698128,
-0.011180819012224674,
-0.042706962674856186,
0.004557441454380751,
0.020007044076919556,
0.06800568848848343,
0.004984654486179352,
-0.04073121398687363,
-0.09141095727682114,
0.014045444317162037,
0.05524909123778343,
-0.0317685529589653,
0.02646547555923462,
0.007715457584708929,
-0.07688354700803757,
0.008055002428591251,
-0.023484645411372185,
-0.008379749022424221,
-0.08316873759031296,
-0.06310902535915375,
0.011829862371087074,
0.015646863728761673,
0.033888719975948334,
0.0037887103389948606,
0.03947380557656288,
-0.04821157827973366,
-0.06822923570871353,
-0.03059564344584942,
-0.02619164064526558,
0.009084513410925865,
-0.04116048663854599,
0.05207797512412071,
0.0006038871360942721,
-0.017746400088071823,
0.02475654147565365,
0.011347975581884384,
0.01706053502857685,
0.03187790885567665,
0.04899601638317108,
0.037612129002809525,
-0.0007201418629847467,
-0.022116973996162415,
-0.02182035520672798,
0.07314261794090271,
-0.04253799095749855,
-0.021452128887176514,
-0.001119266264140606,
-0.006943417713046074,
-0.01909308135509491,
0.029904644936323166,
0.014130123890936375,
-0.020150423049926758,
0.014096824452280998,
-0.05697929486632347,
0.01219878625124693,
0.02188101038336754,
-0.0070714582689106464,
0.01994515024125576,
0.02560197375714779,
-0.07964693754911423,
0.005585600156337023,
0.02709333412349224,
0.03045502118766308,
-0.03308085724711418,
-0.01656918413937092,
0.03264400735497475,
0.020408660173416138,
-0.047358572483062744,
-0.06509855389595032,
0.011719243600964546,
0.0635276585817337,
0.0833057090640068,
0.059895023703575134,
-0.013515274971723557,
-0.0031259427778422832,
-0.02215142548084259,
0.07125311344861984,
-0.07071275264024734,
0.021898692473769188,
-0.03852018341422081,
0.044750895351171494,
0.0004290546348784119,
-0.035950686782598495,
0.0012268502032384276,
-0.0038313516415655613,
0.011595685966312885,
0.029472939670085907,
-0.06029362604022026,
-0.00127376988530159,
-0.014931837096810341,
0.035686034709215164,
-0.033045295625925064,
0.0394778810441494,
0.024018270894885063,
0.07154527306556702,
0.04220178350806236,
0.0070794071070849895,
0.05806374549865723,
-0.005407978314906359,
0.005194969475269318,
0.04758205637335777,
-0.052077628672122955,
-0.020876681432127953,
-0.021844644099473953,
-0.001548386295326054,
-0.06839986890554428,
0.00002972471156681422,
0.020552391186356544,
-0.0015257522463798523,
0.038619689643383026,
-0.04428872466087341,
-0.04545894265174866,
0.020779268816113472,
0.010064522735774517,
-0.02994714491069317,
-0.004382213111966848,
0.012915268540382385,
-0.0025215372443199158,
-0.009834816679358482,
0.017916999757289886,
-0.03666997700929642,
-0.054726745933294296,
-0.007210553158074617,
-0.01714906468987465,
0.011933304369449615,
-0.032507799565792084,
0.0471280962228775,
-0.018064778298139572,
-0.02322867140173912,
0.05863688141107559,
0.06692104786634445,
-0.06497291475534439,
0.03869560360908508,
-0.057693999260663986,
-0.05859072133898735,
-0.03558963164687157,
0.018391549587249756,
0.04860744625329971,
-0.0633799135684967,
0.002387135988101363,
-0.014243993908166885,
0.02645646221935749,
0.0849670022726059,
0.014187530614435673,
-0.0054662954062223434,
0.014756912365555763,
-0.039149027317762375,
-0.038326412439346313,
-0.006702804937958717,
-0.01448804885149002,
0.02224809303879738,
0.05405730381608009,
0.07122300565242767,
0.04122041165828705,
-0.009122571907937527,
-0.03224346786737442,
0.03843938931822777,
0.033092088997364044,
-0.024741416797041893,
0.0019721847493201494,
-0.01662999950349331,
-0.038587555289268494,
-0.02524527907371521,
0.06445992738008499,
0.06488484889268875,
-0.03509664908051491,
-0.027977950870990753,
-0.021576298400759697,
-0.017105191946029663,
0.026559390127658844,
-0.02957877330482006,
-0.033610325306653976,
0.01070267055183649,
0.015051783062517643,
-0.02170385979115963,
0.03344772756099701,
-0.025772036984562874,
-0.014220268465578556,
0.016377992928028107,
0.07085775583982468,
0.02416391856968403,
0.05303800106048584,
0.03570995107293129,
-0.019948383793234825,
0.03951277956366539,
-0.03145717829465866,
0.005072333849966526,
0.08658982813358307,
0.007723222486674786,
-0.004693131428211927,
-0.03130560368299484,
0.011138377711176872,
0.0015759438974782825,
0.010804074816405773,
0.02330068126320839,
-0.005379435606300831,
-0.029255656525492668,
0.016349785029888153,
0.04809200391173363,
-0.048128630965948105,
-0.014482101425528526,
-0.00195313966833055,
0.03142407536506653,
0.03269422426819801,
0.02904571406543255,
0.0682682916522026,
0.05304912477731705,
-0.05177599564194679,
0.08378392457962036,
0.024242127314209938,
-0.013338036835193634,
-0.002490004990249872,
-0.09929871559143066,
0.02525329403579235,
-0.06443813443183899,
0.06626325845718384,
0.0004218288231641054,
0.021716663613915443,
-0.02717471495270729,
0.026218319311738014,
0.005937209818512201,
0.01567760668694973,
-0.030268557369709015,
0.004959449637681246,
-0.007646711077541113,
0.03806433081626892,
-0.03958725556731224,
0.041030384600162506,
-0.010656640864908695,
-0.0004921292420476675,
0.02693249098956585,
0.008340959437191486,
-0.00189109961502254,
-0.01834290660917759,
0.0022435004357248545,
0.0016034082509577274,
0.010851164348423481,
0.020503297448158264,
-0.05584050342440605,
-0.018406342715024948,
-0.06309553980827332,
-0.007577354554086924,
0.0386962965130806,
0.10087287425994873,
-0.07084360718727112,
-0.08724437654018402,
0.008593952283263206,
-0.04271959513425827,
-0.02423287183046341,
-0.0009156459709629416,
-0.03215920180082321,
0.015553373843431473,
0.050739556550979614,
-0.09031432121992111,
0.002325560664758086,
-0.052525755017995834,
-0.029556384310126305,
0.04494414106011391,
0.006940584629774094,
0.0177780594676733,
-0.0193365216255188,
-0.022838395088911057,
-0.008380747400224209,
0.0036055089440196753,
0.0034428262151777744,
0.005566439125686884,
0.04805940389633179,
-0.010100145824253559,
-0.001632755040191114,
-0.05157233774662018,
-0.044836901128292084,
-0.033993519842624664,
-0.07569052278995514,
-0.047415778040885925,
-0.04746348038315773,
-0.007829035632312298,
0.0326961912214756,
0.017066072672605515,
-0.05149047449231148,
0.01497240737080574,
-0.004965002648532391,
-0.062151554971933365,
-0.04760228469967842,
-0.031536076217889786,
0.020650556311011314,
-0.050284817814826965,
-0.003551542293280363,
0.002032908843830228,
0.0437149703502655,
0.01263087335973978,
-0.0014326152158901095,
0.018464993685483932,
0.03713591396808624,
0.0080529460683465,
-0.0009652407607063651,
0.01646221987903118,
-0.07214681059122086,
0.0009024688042700291,
-0.050230685621500015,
-0.055030014365911484,
-0.04821506142616272,
-0.013138565234839916,
0.00731106149032712,
-0.0531613789498806,
-0.06106115132570267,
0.016482481732964516,
0.02142048068344593,
-0.0047564031556248665,
-0.030053140595555305,
-0.002765576122328639,
0.008427063934504986,
0.013177796266973019,
-0.037805262953042984,
0.005043934565037489,
-0.08316753059625626,
-0.09362240880727768,
-0.023307709023356438,
-0.02128102444112301,
0.01967567577958107,
-0.012320393696427345,
0.018398184329271317,
0.00499927019700408,
-0.01035438384860754,
-0.06517884880304337,
0.025798747316002846,
-0.00417066877707839,
-0.0012686372501775622,
0.00875002145767212,
-0.02795424871146679,
0.07602787762880325,
0.030406653881072998,
0.028615742921829224,
0.04859064519405365,
-0.011885055340826511,
-0.03673239424824715,
-0.04502302408218384,
0.04915913566946983,
0.047545526176691055,
-0.018341081216931343,
-0.06996512413024902,
0.0015969815431162715,
0.0280779916793108,
0.052689988166093826,
-0.03920198604464531,
-0.05765406787395477,
0.0032599312253296375,
0.004242787137627602,
-0.039000462740659714,
-0.005543089006096125,
0.07727649062871933,
-0.021940642967820168,
0.023761747404932976,
0.046995047479867935,
-0.006357893813401461,
0.022708792239427567,
-0.058231938630342484,
-0.016629308462142944,
-0.04706110060214996,
-0.018010495230555534,
0.03528657555580139,
0.0017858907813206315,
-0.06083594262599945,
0.03919163718819618,
0.02435966767370701,
-0.00036340116639621556,
0.09502886235713959,
-0.019899604842066765,
0.06989406049251556,
0.013221963308751583,
0.03725337237119675,
0.020984668284654617,
-0.011964973993599415,
0.04189811274409294,
-0.03758542239665985,
0.03749377653002739,
-0.02639049105346203,
-0.03538738936185837,
-0.028175566345453262,
-0.032391369342803955,
0.016197245568037033,
-0.04142604395747185,
0.03178427740931511,
0.011328925378620625,
0.020403064787387848,
0.028037631884217262,
0.02578469179570675,
-0.015370743349194527,
0.01295327115803957,
-0.06886845827102661,
-0.008516301400959492,
0.028994245454669,
-0.0008904133574105799,
-0.01046371553093195,
0.05675804987549782,
-0.06451315432786942,
0.05460533872246742,
-0.0016806377097964287,
0.0037839177530258894,
-0.01927793398499489,
0.03860064968466759,
-0.03454769402742386,
-0.0008278790046460927,
-0.005879395641386509,
-0.02894221618771553,
-0.00329654011875391,
-0.031451914459466934,
0.013188989832997322,
0.0001657791726756841,
0.014763123355805874,
0.07647224515676498,
0.015233691781759262,
-0.053120359778404236,
-0.03907058387994766,
0.0006264609983190894,
0.008037995547056198,
-0.06550369411706924,
-0.08286185562610626,
0.02104080840945244,
-0.04859650135040283,
-0.0028651743195950985,
-0.009170514531433582,
-0.015834102407097816,
0.047315411269664764
] |
<p>I am trying to prove that the momentum $p_x$ operator is Hermitian, my approach is the following</p>
<p>$$<p_x>~=~\int \Psi^*(\vec{r},t)[-ih\frac{\partial}{\partial x}]\Psi(\vec{r},t)\, d^3r.$$</p>
<p>I try to do integration by parts but I cannot resolve the differential, as the integration is in respect to $\vec{r}$ and the partial is in respect to $x$.</p> | g6622 | [
0.06699459999799728,
-0.013071822002530098,
-0.0351250097155571,
-0.0022750049829483032,
0.05474591255187988,
-0.0005893492489121854,
0.04709932208061218,
-0.009711296297609806,
-0.04237671196460724,
0.03180669620633125,
-0.014266664162278175,
-0.011868033558130264,
-0.09416745603084564,
0.01109224185347557,
0.031256940215826035,
-0.04922707751393318,
0.008557969704270363,
-0.010868998244404793,
0.0069131022319197655,
-0.019162898883223534,
-0.04236603155732155,
0.005907239392399788,
0.033185116946697235,
-0.02251283824443817,
0.04886982589960098,
-0.0411393828690052,
-0.014042087830603123,
-0.013882514089345932,
-0.007364213466644287,
0.003311365842819214,
0.010794291272759438,
0.007268256042152643,
0.022612448781728745,
0.025732623413205147,
-0.014659020118415356,
0.015010353177785873,
0.07983950525522232,
0.019422877579927444,
0.033904846757650375,
-0.02735799178481102,
0.010775207541882992,
-0.07044803351163864,
-0.017099924385547638,
0.0013056317111477256,
-0.004261136054992676,
-0.02725825272500515,
-0.0034180902875959873,
0.010217418894171715,
-0.04675322771072388,
0.07024995237588882,
-0.001097185304388404,
0.024611178785562515,
0.029748564586043358,
-0.021684926003217697,
-0.025482887402176857,
0.01909051649272442,
0.024341467767953873,
-0.023803306743502617,
0.03236572444438934,
0.009996846318244934,
0.016467144712805748,
-0.0723111480474472,
0.046162914484739304,
0.03738808259367943,
0.025312909856438637,
-0.012942458502948284,
-0.011424019932746887,
-0.019956480711698532,
0.03060251846909523,
-0.0449485220015049,
0.04310080409049988,
-0.02298840507864952,
0.07847800850868225,
0.044986095279455185,
-0.038009196519851685,
-0.021771637722849846,
0.00217609410174191,
-0.06581685692071915,
0.004303503315895796,
-0.01719023287296295,
0.033441636711359024,
-0.029229581356048584,
0.039744749665260315,
-0.021554309874773026,
-0.018860096111893654,
-0.05442852899432182,
0.007494943216443062,
-0.04315505549311638,
-0.06314465403556824,
0.033474065363407135,
0.003129031974822283,
0.03941773623228073,
0.015456056222319603,
0.024490341544151306,
-0.006081694271415472,
-0.05224601924419403,
-0.07362334430217743,
0.05853139981627464,
-0.014279620721936226,
-0.0016014258144423366,
0.002200876362621784,
0.03251635655760765,
0.007179049775004387,
-0.034410711377859116,
0.009990465827286243,
-0.009465841576457024,
-0.014299863949418068,
-0.0005892813787795603,
0.029301302507519722,
-0.03449944406747818,
0.012020893394947052,
0.007884836755692959,
-0.0204288512468338,
-0.015590904280543327,
0.02851409651339054,
-0.012490748427808285,
-0.0009400026756338775,
-0.035077184438705444,
-0.06938651204109192,
0.06674076616764069,
0.012888086959719658,
0.02450338751077652,
0.03866412863135338,
0.04595230892300606,
0.007994411513209343,
0.028533780947327614,
-0.0759376659989357,
0.01096777431666851,
0.07199369370937347,
-0.0026716510765254498,
0.02288801223039627,
0.03184737265110016,
-0.023483552038669586,
0.016281740739941597,
-0.005802453495562077,
-0.0018553296104073524,
-0.08321335911750793,
0.0021777120418846607,
-0.027621490880846977,
0.018035875633358955,
0.009211651980876923,
0.02135375142097473,
0.011579036712646484,
0.05008325353264809,
-0.02081095613539219,
-0.03542334958910942,
-0.03262445330619812,
-0.03294888883829117,
-0.03375814110040665,
0.024456443265080452,
0.03378778696060181,
0.08277022838592529,
0.0303016509860754,
0.02724630944430828,
0.012306378223001957,
0.018963156268000603,
0.04858236014842987,
-0.014578614383935928,
0.030007503926753998,
0.009975492022931576,
0.010252349078655243,
0.07514280080795288,
0.0216742604970932,
-0.000268058676738292,
0.025449758395552635,
-0.03323652222752571,
-0.001681806636042893,
-0.06148437038064003,
-0.033547233790159225,
-0.04202937334775925,
0.01447993516921997,
0.042275335639715195,
-0.014154248870909214,
0.002035961952060461,
0.017372649163007736,
0.03218253329396248,
-0.06022931635379791,
-0.0034772150684148073,
-0.00631676847115159,
0.08752721548080444,
0.01973816752433777,
-0.0265756044536829,
0.015645936131477356,
-0.08750392496585846,
0.041218966245651245,
0.0056244018487632275,
0.04201348498463631,
-0.0012737840879708529,
-0.0663267970085144,
-0.06439381837844849,
0.04189598560333252,
0.025336429476737976,
-0.0351981520652771,
0.02493920736014843,
0.015282999724149704,
-0.013806844130158424,
0.015462948009371758,
-0.06859755516052246,
0.0023249215446412563,
0.01766309328377247,
-0.02189442329108715,
0.019759882241487503,
0.08380778878927231,
0.045062173157930374,
0.050422608852386475,
0.018800033256411552,
0.03297753259539604,
-0.024117683991789818,
0.012866613455116749,
0.05168415233492851,
0.01943233609199524,
-0.08008365333080292,
0.007465670816600323,
0.038392528891563416,
-0.01197246927767992,
-0.04126432538032532,
0.057910870760679245,
0.021577803418040276,
-0.003522656625136733,
-0.025032682344317436,
-0.04559341073036194,
-0.006709032226353884,
-0.060030050575733185,
-0.002398787997663021,
-0.051788389682769775,
0.08641331642866135,
-0.028565699234604836,
0.04690403863787651,
-0.049375008791685104,
-0.008310390636324883,
0.007351793814450502,
0.018992533907294273,
-0.01874169148504734,
0.01288085151463747,
0.02970731072127819,
0.02987961657345295,
0.014856093563139439,
-0.015351245179772377,
-0.00022055320732761174,
0.04365646466612816,
0.02549760974943638,
0.0045639644376933575,
0.016298405826091766,
-0.03700452297925949,
0.057407446205616,
0.03754863515496254,
0.018137631937861443,
0.040383026003837585,
-0.032245781272649765,
-0.06408166140317917,
-0.010747411288321018,
0.055012837052345276,
-0.011389221996068954,
-0.02414540760219097,
-0.02675751969218254,
-0.006873232778161764,
0.004415880888700485,
0.030256569385528564,
0.011778493411839008,
-0.013788333162665367,
-0.03280039504170418,
-0.004044154193252325,
-0.03472296893596649,
0.0242503322660923,
-0.09228724241256714,
0.006165150087326765,
-0.006153718568384647,
0.003999273758381605,
0.034338075667619705,
-0.010523932985961437,
0.01012466661632061,
0.08197081834077835,
-0.00292127369903028,
0.02762593887746334,
-0.007646837271749973,
-0.0481887087225914,
0.04590011015534401,
-0.03287891671061516,
0.0024999340530484915,
-0.041199278086423874,
-0.010588577017188072,
0.033799897879362106,
-0.03855147957801819,
-0.003251046407967806,
0.04262382537126541,
-0.05401007458567619,
-0.003569431370124221,
0.029183221980929375,
0.01214088685810566,
0.016696717590093613,
0.030957194045186043,
-0.007154264021664858,
0.028218358755111694,
-0.00042841877439059317,
0.004376284312456846,
-0.012271794490516186,
0.06409241259098053,
-0.05611686035990715,
0.01452796719968319,
-0.01613244228065014,
0.03683116286993027,
0.03339524194598198,
-0.005054425448179245,
-0.0213395394384861,
0.03354108706116676,
-0.06724203377962112,
-0.02018889971077442,
0.04394053295254707,
-0.015946263447403908,
0.01087193377315998,
0.018616240471601486,
-0.016122067347168922,
-0.009109631180763245,
-0.011323720216751099,
-0.025961462408304214,
0.00444053765386343,
-0.044257987290620804,
-0.0256248340010643,
-0.02323412150144577,
0.0334618017077446,
-0.02846888266503811,
-0.012213352136313915,
0.05872612074017525,
0.02928009256720543,
0.03482717648148537,
0.015442482195794582,
-0.06099279224872589,
0.06652960181236267,
-0.0416904017329216,
-0.009097483940422535,
0.011669914238154888,
-0.006174331996589899,
0.028940901160240173,
0.015643678605556488,
-0.04666085168719292,
-0.011468417942523956,
-0.004406481981277466,
0.024109788239002228,
0.022005179896950722,
-0.038672976195812225,
0.0006966618821024895,
0.009669238701462746,
-0.0552372932434082,
0.00555967353284359,
-0.05813250318169594,
-0.06333811581134796,
0.002302769338712096,
0.06980430334806442,
0.023556802421808243,
0.013328890316188335,
-0.0386647954583168,
0.01596478931605816,
0.056494563817977905,
-0.014965486712753773,
-0.03527486324310303,
-0.0027023209258913994,
0.05696483701467514,
0.05429647117853165,
-0.0013683006400242448,
-0.02301030233502388,
0.008950034156441689,
-0.016941960901021957,
0.013719507493078709,
-0.023751448839902878,
0.010802163742482662,
-0.022888796404004097,
0.021787559613585472,
0.0219559483230114,
-0.016959842294454575,
0.00699534360319376,
-0.001750494004227221,
-0.024582119658589363,
0.02832539938390255,
0.04645586386322975,
-0.02184280939400196,
-0.0865052193403244,
-0.013838627375662327,
-0.015039373189210892,
0.01693323440849781,
0.05810565873980522,
0.0013371598906815052,
-0.002521590096876025,
-0.019180241972208023,
0.028983376920223236,
0.030691295862197876,
0.04481086507439613,
0.00381285697221756,
0.06621989607810974,
0.08087041974067688,
0.008568398654460907,
0.024851063266396523,
-0.03792152181267738,
-0.036867059767246246,
0.03739235922694206,
0.012358305044472218,
-0.032541003078222275,
0.011457085609436035,
-0.020480236038565636,
-0.05128776282072067,
0.018718445673584938,
-0.04323626682162285,
0.005426371935755014,
0.05922513082623482,
-0.01212488953024149,
0.023289578035473824,
0.054973747581243515,
-0.009659006260335445,
-0.022764867171645164,
-0.014340045861899853,
-0.009879866614937782,
-0.006006049923598766,
0.011701163835823536,
0.01694549433887005,
-0.0316394679248333,
-0.04042789340019226,
0.0003746037546079606,
0.00015894387615844607,
-0.062843918800354,
-0.018945857882499695,
0.02570069395005703,
0.015820704400539398,
0.011519979685544968,
0.05628165230154991,
-0.005844715517014265,
0.04462533816695213,
0.057953834533691406,
0.03327341005206108,
-0.01462563592940569,
-0.04438347369432449,
-0.00673644058406353,
-0.034887589514255524,
-0.02188303880393505,
-0.007534074131399393,
0.00841981079429388,
0.004727166146039963,
-0.027482159435749054,
-0.015943605452775955,
-0.03022279217839241,
-0.09429997205734253,
0.050683893263339996,
0.030339879915118217,
0.02975151687860489,
0.002114849165081978,
-0.02292811870574951,
-0.01695067808032036,
0.03259695693850517,
0.028991607949137688,
-0.04616415500640869,
0.04411252960562706,
0.007971830666065216,
-0.019323600456118584,
0.012441521510481834,
-0.015085671097040176,
-0.025271715596318245,
0.004116837400943041,
0.0397135354578495,
-0.059379205107688904,
0.022479141131043434,
-0.06803424656391144,
-0.04923582077026367,
-0.011312934570014477,
-0.0017174945678561926,
-0.00006523298361571506,
-0.0071792080998420715,
0.057881634682416916,
-0.030858207494020462,
-0.09133478999137878,
0.06546797603368759,
-0.0179463941603899,
-0.07270660251379013,
0.047142017632722855,
-0.05410508066415787,
-0.03393232449889183,
0.009686285629868507,
-0.015492892824113369,
0.012794802896678448,
0.03073343262076378,
0.018347840756177902,
0.005693802610039711,
-0.03290461003780365,
0.016510142013430595,
0.00950546469539404,
-0.03297146409749985,
0.023097291588783264,
-0.02889070473611355,
0.031320974230766296,
-0.05794232338666916,
-0.025290826335549355,
-0.0519934706389904,
-0.022369002923369408,
-0.02680366113781929,
0.09318171441555023,
0.04013210907578468,
-0.000261789740761742,
-0.014942768029868603,
0.05574723333120346,
0.0244273841381073,
-0.026337316259741783,
-0.015222195535898209,
0.027285393327474594,
-0.06055327504873276,
-0.04674334451556206,
0.008946524001657963,
-0.015416709706187248,
0.059003375470638275,
0.0043059466406702995,
0.05743502080440521,
-0.011068921536207199,
0.005906799342483282,
0.0578751303255558,
0.02707865461707115,
0.009507938288152218,
0.01853260211646557,
-0.03881508484482765,
-0.005192324053496122,
0.009557225741446018,
0.012015968561172485,
-0.015106565319001675,
-0.01764834299683571,
-0.10428678244352341,
0.09800323098897934,
-0.026840224862098694,
0.06108453869819641,
-0.04835859686136246,
0.006049658637493849,
0.02983037941157818,
-0.04557514935731888,
-0.07153941690921783,
-0.06325622648000717,
0.03254087641835213,
0.008609039708971977,
-0.06975296884775162,
0.04386566951870918,
-0.021777719259262085,
-0.05408422648906708,
-0.02441416308283806,
0.005545333493500948,
0.03550572693347931,
0.045833852142095566,
-0.02691100910305977,
-0.015597742982208729,
-0.05504431948065758,
-0.053573768585920334,
0.01922210492193699,
-0.06801013648509979,
0.01121978834271431,
0.04241087660193443,
-0.014837157912552357,
0.041837215423583984,
-0.06545247882604599,
-0.024912917986512184,
0.03686264902353287,
-0.11081434041261673,
-0.0417192205786705,
0.04322060942649841,
-0.0492982342839241,
0.02991010807454586,
-0.023213012143969536,
0.0016826910432428122,
0.017234448343515396,
0.043810028582811356,
-0.050944868475198746,
-0.0057141100987792015,
-0.00672163674607873,
0.009539955295622349,
0.0008480777614749968,
0.005751028191298246,
-0.0069823358207941055,
-0.03178657218813896,
0.024228708818554878,
-0.02629268355667591,
0.018743980675935745,
-0.0016452404670417309,
0.02045408822596073,
0.00817471370100975,
0.03611796349287033,
0.0008630467928014696,
-0.04582902416586876,
0.009593191556632519,
-0.01380881853401661,
-0.009485341608524323,
-0.008035661652684212,
0.010369883850216866,
-0.0016221447149291635,
0.00006487577047664672,
-0.01189463585615158,
-0.045235875993967056,
-0.04643416032195091,
0.05183575674891472,
0.09561172127723694,
-0.048966530710458755,
0.05926614999771118,
-0.0647098571062088,
-0.01102362759411335,
0.01736748032271862,
0.029394585639238358,
0.02864912711083889,
-0.012646717950701714,
0.022700097411870956,
0.042227279394865036,
0.006190019194036722,
-0.0196303129196167,
0.036264143884181976,
-0.01917143352329731,
-0.03809267655014992,
0.039047565311193466,
-0.0212058387696743,
-0.023717498406767845,
-0.02089209109544754,
0.07055789232254028,
-0.020876863971352577,
0.035074397921562195,
0.014217158779501915,
0.006049554329365492,
0.0246945358812809,
-0.0368194580078125,
-0.0031636084895581007,
0.07079334557056427,
0.01956506446003914,
-0.023253923282027245,
0.06870806217193604,
0.015666577965021133,
0.011930102482438087,
-0.009380446746945381,
0.017407460138201714,
-0.01637241430580616,
-0.008222285658121109,
0.02942332625389099,
-0.00283407187089324,
0.007110103033483028,
0.03247126191854477,
-0.012422436848282814,
-0.023617791011929512,
-0.04247207194566727,
-0.027537092566490173,
0.034626998007297516,
-0.03359239175915718,
0.05949736014008522,
0.04515894502401352,
0.03796663135290146,
0.033582959324121475,
0.03540866822004318,
-0.00430624233558774,
-0.018444709479808807,
-0.0642242580652237,
0.007900786586105824,
0.0013422737829387188,
-0.020260578021407127,
-0.10572244971990585,
0.01836303435266018,
0.08055725693702698,
0.04739462211728096,
0.027743281796574593,
0.005714585073292255,
-0.05080864951014519,
-0.001827529165893793,
0.035678062587976456,
-0.0010354063706472516,
0.010408075526356697,
-0.046167269349098206,
0.002626819768920541,
0.00947689637541771,
-0.017279639840126038,
-0.004728719592094421,
0.009950325824320316,
0.017788881435990334,
-0.03406423330307007,
-0.03931744396686554,
-0.0018882917938753963,
-0.03640463948249817,
-0.0029002518858760595,
-0.004249265417456627,
-0.07543422281742096,
0.0022104016970843077,
-0.05459616333246231,
0.011151579208672047,
0.03919240087270737,
0.03818534314632416,
-0.04976414889097214,
0.027147430926561356,
-0.008396944031119347,
0.06509178876876831,
-0.055631738156080246,
0.01624288409948349,
-0.017407353967428207,
-0.043418072164058685,
-0.032183729112148285,
-0.036500558257102966,
-0.013402407988905907,
0.08178646862506866,
-0.02786332555115223,
0.06379202753305435,
0.028278730809688568,
0.012624763883650303,
-0.03878263384103775,
0.0038284920156002045,
0.058867741376161575,
0.03966803103685379,
-0.0404512993991375,
0.028605369850993156,
0.026205047965049744,
-0.06124105304479599,
0.05842195823788643,
0.010941894724965096,
0.020531171932816505,
-0.013723696582019329,
-0.025385700166225433,
-0.004634670447558165,
0.012483596801757812,
0.011960482224822044,
0.06055415794253349,
-0.028521373867988586,
-0.029002616181969643,
-0.020039837807416916,
0.0345953106880188,
-0.019117916002869606,
-0.06378605216741562,
0.005981940310448408,
0.008728493936359882,
-0.06777481734752655,
0.027589404955506325,
0.01401566993445158,
-0.04680858179926872,
-0.07955128699541092,
-0.000515580817591399,
-0.018630312755703926,
-0.05645236745476723,
0.004405119456350803,
0.020237542688846588,
0.04399231821298599,
-0.011944427154958248,
-0.0006712759495712817,
-0.04895878955721855,
0.01607678085565567,
-0.018374230712652206,
0.0022060831543058157,
0.027195775881409645,
-0.03929315507411957,
0.0662505254149437,
0.017107129096984863,
-0.0014304162468761206,
-0.09694641083478928,
0.005769406445324421,
0.061021264642477036,
0.05930596590042114,
-0.04794006794691086,
-0.0016169490991160274,
0.06619922816753387,
0.0009240835788659751,
0.010042977519333363,
-0.02919067069888115,
0.059330862015485764,
-0.056756388396024704,
0.011978663504123688,
-0.03866958245635033,
-0.03246429190039635,
-0.020601220428943634,
0.0490792877972126,
-0.02498725615441799,
0.033895742148160934,
-0.02300841361284256,
-0.022410528734326363,
-0.037901248782873154,
-0.015900030732154846,
-0.02134430781006813,
-0.04731348156929016,
-0.016460848972201347,
-0.00736326863989234
] |
<p>Please bear with this experimentalist trying to understand the subtleties of TIs in what may well be imprecise language. I appreciate that one can deduce the topological trivial or non-trivial nature of a filled band for particular crystalline structures by virtue of $(-1)^{\nu_0} = \Pi \delta_i$ taken over the <a href="http://en.wikipedia.org/wiki/T-symmetry" rel="nofollow">TR</a> symmetry points of the <a href="http://en.wikipedia.org/wiki/Brillouin_zone" rel="nofollow">BZ</a>. I also appreciate that the gap must close at the interface between topologically distinct insulating phases. In my naive understanding, I would expect that the surface state must "fix" the overall parity difference between the valence bands of the TI and trivial insulator and believe that $N_k = \Delta \nu$ mod 2, where $N_k$ is the number of Kramers pair edge modes implies this fix. I would have expected however that their would be some implication about the parity of the edge mode itself (i.e. that is must be odd). Why is there no statement about the edge modes parity? </p> | g6623 | [
0.002431306056678295,
0.031243646517395973,
-0.016096986830234528,
0.0008301578927785158,
0.050820425152778625,
0.0054179769940674305,
0.04552817344665527,
0.06865342706441879,
0.003656350541859865,
-0.014109076000750065,
-0.002667797962203622,
-0.01799767091870308,
0.02842351794242859,
-0.061627086251974106,
0.00042077433317899704,
-0.012003210373222828,
0.010226028971374035,
0.07001902163028717,
0.04548073932528496,
-0.03369760140776634,
-0.026931850239634514,
0.00904738437384367,
-0.015750065445899963,
-0.03903067857027054,
0.00854360219091177,
0.023666005581617355,
0.00976751558482647,
-0.0491730272769928,
0.02411673776805401,
-0.04333343356847763,
0.0570843368768692,
0.004927944391965866,
0.05229099094867706,
-0.028689872473478317,
-0.04749564081430435,
0.015773484483361244,
0.040900133550167084,
0.005847444757819176,
0.03533954918384552,
-0.022404149174690247,
0.01368402037769556,
-0.0013642265694215894,
-0.02105940692126751,
-0.01007663644850254,
-0.008105004206299782,
-0.03930000588297844,
-0.02330283261835575,
0.0039964597672224045,
-0.037815503776073456,
-0.015553567558526993,
-0.012533319182693958,
0.04044389724731445,
0.07914097607135773,
0.021275898441672325,
-0.022766010835766792,
0.005163058638572693,
-0.013930144719779491,
0.01208267081528902,
0.07798752933740616,
0.07514756172895432,
-0.011697737500071526,
-0.0008947772439569235,
0.03278284892439842,
0.021690690889954567,
0.04951953515410423,
-0.004195813089609146,
0.006649576593190432,
0.010268653742969036,
0.04851744323968887,
-0.02281687594950199,
-0.005733747035264969,
-0.011429029516875744,
0.01369918417185545,
-0.03323690965771675,
-0.03428362309932709,
0.07867122441530228,
-0.0009789151372388005,
-0.0288856104016304,
-0.06283991038799286,
0.018556887283921242,
0.014242683537304401,
-0.043756887316703796,
-0.03376036509871483,
0.026953792199492455,
0.04351957142353058,
-0.027894407510757446,
-0.030055193230509758,
0.0008162495796568692,
-0.02559097297489643,
0.06668483465909958,
0.050131380558013916,
-0.016833262518048286,
0.05130178853869438,
-0.030645880848169327,
-0.0005717570311389863,
-0.019579697400331497,
0.016337649896740913,
0.02348039112985134,
0.01815045066177845,
-0.02253851853311062,
0.01300104521214962,
0.038953423500061035,
0.01086280308663845,
-0.031434252858161926,
0.019154293462634087,
0.0441337525844574,
-0.05248231813311577,
-0.007341050077229738,
-0.008638721890747547,
0.04467414692044258,
0.0033047052565962076,
-0.002124392194673419,
0.01312305685132742,
-0.023439055308699608,
-0.011000687256455421,
0.03916405886411667,
0.01929790899157524,
-0.02575107105076313,
-0.049825217574834824,
-0.006524040829390287,
0.026012182235717773,
-0.012878830544650555,
-0.015641210600733757,
0.04811063036322594,
-0.0008523925207555294,
-0.018856298178434372,
-0.008523681201040745,
-0.035747841000556946,
0.03569725155830383,
-0.004353546537458897,
-0.05359282344579697,
-0.005029542837291956,
-0.0016231294721364975,
0.015909135341644287,
0.035878993570804596,
-0.04183758795261383,
-0.020018769428133965,
-0.05452851951122284,
0.031696636229753494,
-0.03234761953353882,
-0.05831298232078552,
-0.01000469084829092,
-0.07687661796808243,
-0.05486680194735527,
0.01905086636543274,
-0.004467996768653393,
-0.08154497295618057,
-0.058727867901325226,
0.022615812718868256,
0.011591466143727303,
0.021933818235993385,
0.061660170555114746,
0.006174270063638687,
-0.044784240424633026,
-0.03809630125761032,
-0.009206228889524937,
0.12344636768102646,
0.00222056545317173,
0.03308877721428871,
0.008763845078647137,
-0.005866775754839182,
-0.020058980211615562,
0.014986083842813969,
0.05760794132947922,
-0.054681356996297836,
-0.03734751045703888,
0.043768785893917084,
-0.06313610076904297,
-0.006614642217755318,
-0.03873589634895325,
-0.031728487461805344,
0.02164159156382084,
-0.02800915203988552,
0.037627212703228,
-0.015335076488554478,
0.07422616332769394,
-0.05408626049757004,
-0.011230106465518475,
0.09197922796010971,
0.0036074984818696976,
0.007072282489389181,
0.016976824030280113,
-0.03005836345255375,
0.020384393632411957,
-0.01047390978783369,
-0.03675946220755577,
0.020060040056705475,
-0.0446329303085804,
-0.00035204397863708436,
0.08659777790307999,
0.03674476593732834,
0.003549169050529599,
0.018320009112358093,
0.015062949620187283,
0.044953085482120514,
0.00397393386811018,
0.06597401946783066,
-0.01390029862523079,
-0.07958772033452988,
0.005189287476241589,
-0.0764889195561409,
0.006736918352544308,
-0.011368876323103905,
-0.00961391907185316,
-0.046440720558166504,
0.014053620398044586,
0.021479802206158638,
0.012942515313625336,
0.030954837799072266,
0.0038712541572749615,
-0.044329650700092316,
0.02864489145576954,
-0.037490759044885635,
-0.001810701796784997,
-0.00010484526865184307,
0.00619493518024683,
0.04472322389483452,
-0.03274059668183327,
-0.00924028642475605,
-0.010478920303285122,
-0.08097567409276962,
-0.008599216118454933,
0.06976770609617233,
-0.002237572567537427,
-0.04121533781290054,
-0.022425850853323936,
0.027623331174254417,
0.0048097711987793446,
-0.061485450714826584,
0.05263330042362213,
-0.054393187165260315,
-0.011459482833743095,
-0.009614529088139534,
0.03748951107263565,
0.009680698625743389,
0.004550199024379253,
0.02695397473871708,
-0.0252907145768404,
0.03362101688981056,
-0.04702509194612503,
-0.0031619444489479065,
-0.005354427266865969,
-0.07742727547883987,
0.04155677556991577,
0.024053925648331642,
0.020792081952095032,
0.005156087223440409,
-0.024327393621206284,
-0.027300726622343063,
0.025458257645368576,
0.023604480549693108,
-0.021975068375468254,
-0.022584477439522743,
-0.001417877385392785,
0.023477628827095032,
-0.06863277405500412,
0.028286777436733246,
-0.025397516787052155,
0.036303095519542694,
-0.031119780614972115,
-0.01786566525697708,
-0.005482408218085766,
0.04770583659410477,
0.009743327274918556,
-0.03558160737156868,
0.0025715979281812906,
0.003129652002826333,
0.019443942233920097,
0.01301862858235836,
0.004640279803425074,
0.01455027423799038,
0.07887016981840134,
0.022754184901714325,
0.01246124878525734,
0.0024725906550884247,
-0.036668360233306885,
0.00803240854293108,
0.036323439329862595,
-0.0764138326048851,
-0.0567411445081234,
-0.02579890564084053,
0.03845996782183647,
-0.04236213117837906,
0.020919619128108025,
0.06031021103262901,
-0.08208514004945755,
0.03781504184007645,
0.008826988749206066,
-0.051404230296611786,
0.06040794774889946,
-0.010101905092597008,
0.0033325916156172752,
0.06160161271691322,
0.07388599216938019,
0.02251153439283371,
-0.044825345277786255,
-0.030361980199813843,
0.015982991084456444,
-0.05934314429759979,
0.08755488693714142,
-0.03619991987943649,
0.03982551395893097,
-0.0255599282681942,
0.035796813666820526,
-0.021706489846110344,
0.009004001505672932,
-0.0242608655244112,
-0.021817298606038094,
-0.013856662437319756,
-0.07047081738710403,
0.013268931768834591,
0.03428889065980911,
0.007907146587967873,
-0.033179622143507004,
0.017953956499695778,
0.0834687203168869,
-0.04599709436297417,
0.016077697277069092,
-0.0016274566296488047,
0.0412604957818985,
-0.0268885288387537,
0.08158507198095322,
0.03143811225891113,
0.046076949685811996,
-0.008064462803304195,
0.006595272570848465,
-0.08675301820039749,
0.0276804082095623,
-0.04626382514834404,
0.022716542705893517,
0.0351162888109684,
-0.0057136439718306065,
0.019369786605238914,
-0.031079493463039398,
-0.013073530979454517,
-0.04221409186720848,
-0.0023435361217707396,
0.07801714539527893,
0.07368496805429459,
-0.006002162117511034,
-0.08476754277944565,
-0.04304753243923187,
-0.008741224184632301,
0.042689450085163116,
0.028341401368379593,
-0.013548859395086765,
-0.07475455105304718,
-0.00241136085242033,
-0.018343811854720116,
-0.00968091655522585,
0.04919234290719032,
0.03831200674176216,
0.01776624470949173,
-0.007830454036593437,
-0.038696013391017914,
0.05858197063207626,
0.023729756474494934,
0.03553982824087143,
0.021221667528152466,
0.018950030207633972,
0.07413887977600098,
-0.07731135189533234,
-0.009768730029463768,
-0.08619953691959381,
-0.05262726545333862,
-0.004989649169147015,
0.00626435736194253,
0.032986026257276535,
0.027637183666229248,
-0.02227783016860485,
-0.029173433780670166,
-0.029635265469551086,
-0.0030888558831065893,
0.04198814556002617,
0.03336698189377785,
-0.027522113174200058,
-0.045770276337862015,
0.009013221599161625,
0.04430696368217468,
0.056333135813474655,
0.03266655653715134,
-0.0226215198636055,
0.03983541950583458,
-0.03287755325436592,
0.019600143656134605,
0.005852553527802229,
-0.0024737899657338858,
0.05820352956652641,
-0.015208670869469643,
-0.014246460050344467,
0.02178245596587658,
-0.020193476229906082,
0.02136617712676525,
-0.0038319905288517475,
-0.024131355807185173,
-0.04728935658931732,
-0.009517697617411613,
-0.011145083233714104,
-0.013262192718684673,
-0.005914743524044752,
0.028260884806513786,
-0.06325051188468933,
-0.016252774745225906,
-0.014488077722489834,
-0.012853975407779217,
0.004397462122142315,
0.03498794138431549,
0.039795514196157455,
0.014793626964092255,
-0.04058881476521492,
0.001137500279583037,
0.03408396989107132,
0.06776438653469086,
-0.031154492869973183,
0.033704690635204315,
0.03034937009215355,
0.01898382045328617,
-0.004136689472943544,
0.052901189774274826,
-0.046905338764190674,
-0.005999329965561628,
-0.004861182067543268,
0.00845250766724348,
-0.04168488457798958,
-0.0034020552411675453,
0.08816097676753998,
0.013534333556890488,
-0.04471756890416145,
-0.020870232954621315,
-0.038749467581510544,
-0.033562857657670975,
-0.031236398965120316,
-0.0253683403134346,
0.03476273640990257,
-0.03956236690282822,
-0.013299759477376938,
-0.08892083913087845,
0.04757734388113022,
-0.03958722576498985,
0.01931443065404892,
0.04380178451538086,
-0.029190247878432274,
-0.023290349170565605,
-0.048568740487098694,
-0.013612344861030579,
-0.03947969153523445,
-0.06395744532346725,
-0.01954011246562004,
-0.016407674178481102,
-0.01009372342377901,
-0.021655187010765076,
-0.003235073760151863,
0.0028686339501291513,
-0.023782772943377495,
-0.0018123987829312682,
-0.08257629722356796,
0.012089300900697708,
0.03352345526218414,
-0.01894097961485386,
0.020914187654852867,
-0.021399369463324547,
-0.02857704646885395,
-0.034732505679130554,
-0.0029307983350008726,
0.10356330126523972,
0.03845159336924553,
-0.021947676315903664,
0.010104629211127758,
-0.08110491931438446,
-0.009753754362463951,
0.04387030377984047,
0.04122700169682503,
0.04239024221897125,
0.01896696537733078,
0.011703959666192532,
-0.0076757012866437435,
-0.0096048004925251,
-0.008208922110497952,
-0.01396600715816021,
-0.02088969014585018,
-0.01350690983235836,
0.02732747793197632,
0.013190636411309242,
0.0757157951593399,
-0.023332420736551285,
0.024121342226862907,
-0.0968080535531044,
-0.029054371640086174,
-0.06561227887868881,
-0.01006130501627922,
0.07442066073417664,
0.033430445939302444,
0.048100795596838,
0.005708303768187761,
-0.03378933295607567,
-0.061165664345026016,
0.07032138109207153,
0.017681550234556198,
0.00436610309407115,
0.005293483380228281,
-0.028339918702840805,
-0.010129091329872608,
0.02929053083062172,
0.0306316539645195,
0.017603697255253792,
0.04284801334142685,
0.04805034026503563,
-0.03391110524535179,
0.04168834909796715,
0.001677977154031396,
0.018001966178417206,
0.022263431921601295,
-0.04077567532658577,
0.008443735539913177,
0.01220760028809309,
0.0038539329543709755,
-0.0016480126651003957,
0.011299408040940762,
0.009306316263973713,
-0.0112220523878932,
-0.027517516165971756,
0.03512532636523247,
-0.054077353328466415,
-0.01603844203054905,
-0.0025908690877258778,
0.005512093659490347,
-0.01914556697010994,
-0.07532978057861328,
0.0028960569761693478,
0.007613934576511383,
0.006669661030173302,
0.03826608881354332,
0.01662764884531498,
-0.00960406381636858,
0.03139349818229675,
0.029981477186083794,
-0.0025033005513250828,
-0.005410617683082819,
-0.011004157364368439,
0.041263360530138016,
0.01716144196689129,
0.002637638943269849,
0.034233931452035904,
0.03762612119317055,
0.06778029352426529,
-0.038101449608802795,
0.0056623429991304874,
0.055577535182237625,
0.020449206233024597,
-0.02581464871764183,
-0.04298284649848938,
-0.015810029581189156,
-0.01730768382549286,
-0.03493634983897209,
-0.0005865711136721075,
0.0011142591247335076,
-0.021938547492027283,
-0.0065168775618076324,
-0.04272156208753586,
-0.03965456783771515,
0.07057289034128189,
-0.012480012141168118,
-0.014522031880915165,
0.01104220561683178,
0.07501155138015747,
-0.03277139365673065,
-0.04113710671663284,
-0.007138761691749096,
0.02915278449654579,
-0.03082098253071308,
0.026494042947888374,
-0.01744314841926098,
0.03873256593942642,
0.004240887239575386,
-0.0326397567987442,
0.031126530840992928,
-0.010527932085096836,
0.016262104734778404,
-0.05029348284006119,
-0.05714165046811104,
0.01375157292932272,
-0.02855711057782173,
0.021518699824810028,
0.011383503675460815,
0.018100697547197342,
0.028654491528868675,
-0.0013838730519637465,
-0.08552257716655731,
0.03984181210398674,
0.04800475388765335,
-0.03527161478996277,
-0.07074175775051117,
-0.013012469746172428,
0.038970790803432465,
0.017680685967206955,
0.050314709544181824,
-0.029337966814637184,
0.00983221922069788,
-0.069563128054142,
0.045101914554834366,
0.04689130559563637,
-0.023695582523941994,
0.00561806233599782,
0.030165858566761017,
0.007642343640327454,
0.029877180233597755,
0.013595622032880783,
0.018308503553271294,
-0.09952107816934586,
0.015472285449504852,
-0.005693172570317984,
0.07901929318904877,
-0.03215450793504715,
-0.030604908242821693,
0.013969124294817448,
0.0154415313154459,
-0.03144218027591705,
-0.024791480973362923,
-0.024197259917855263,
0.01724299043416977,
0.02291116490960121,
-0.04099775105714798,
-0.01848587393760681,
0.00601746141910553,
0.051083337515592575,
-0.028042007237672806,
0.007553363684564829,
0.013148183934390545,
0.005167674273252487,
0.010316694155335426,
-0.011214652098715305,
0.010045703500509262,
0.005866320803761482,
0.034249503165483475,
-0.03608039394021034,
0.015248301438987255,
0.02198457345366478,
-0.03260837122797966,
-0.015544287860393524,
0.028517551720142365,
-0.026134410873055458,
0.03263411298394203,
0.08133324235677719,
-0.011442402377724648,
0.026671458035707474,
0.03410374000668526,
-0.05341576784849167,
0.0070680552162230015,
-0.007124981377273798,
-0.0233173631131649,
0.00932341255247593,
0.02821563556790352,
0.013406796380877495,
-0.004277059808373451,
0.025559453293681145,
-0.053446006029844284,
-0.012084629386663437,
-0.03565789386630058,
0.00793799851089716,
0.060304611921310425,
-0.07594514638185501,
0.014180399477481842,
0.03165721148252487,
-0.0010146736167371273,
0.022793034091591835,
0.03204895555973053,
0.006946846377104521,
-0.019630175083875656,
0.013445374555885792,
-0.04787500947713852,
0.001541400095447898,
-0.052703857421875,
-0.015457677654922009,
0.003574909409508109,
-0.047653477638959885,
0.02597750723361969,
-0.021285122260451317,
0.002623440930619836,
-0.029407843947410583,
0.015004847198724747,
-0.028395559638738632,
0.04905898869037628,
0.03133499622344971,
0.022488342598080635,
0.033091794699430466,
0.029461704194545746,
0.022141821682453156,
-0.01778138242661953,
-0.0274033322930336,
0.012703346088528633,
0.021179208531975746,
0.018579505383968353,
0.005600958596915007,
0.028725260868668556,
0.028500963002443314,
0.03441111370921135,
0.03812718391418457,
0.030064348131418228,
-0.016419265419244766,
0.01920628920197487,
-0.03747514635324478,
-0.014530457556247711,
-0.010587763041257858,
-0.07957568019628525,
0.06719458848237991,
0.01709890179336071,
0.02859104983508587,
-0.036380570381879807,
-0.019596142694354057,
0.02665705978870392,
-0.005465393420308828,
-0.011384334415197372,
-0.0015640530036762357,
0.0029453644528985023,
0.04684336856007576,
-0.10423289239406586,
-0.09287294000387192,
-0.021009815856814384,
0.005925922654569149,
-0.01446583028882742,
-0.03853241726756096,
-0.06473823636770248,
0.014882879331707954,
-0.006830071099102497,
-0.04864509031176567,
-0.02168119326233864,
0.03438222408294678,
0.006378998979926109,
0.03266467899084091,
0.0582907609641552,
-0.047392338514328,
-0.0007560633239336312,
0.013070151209831238,
-0.009025678038597107,
-0.06057283282279968,
0.08382052928209305,
0.0769587978720665,
-0.001226771273650229,
-0.002513093641027808,
0.01688127964735031,
-0.0044410862028598785,
-0.0231820996850729,
0.0633993074297905,
-0.023031828925013542,
-0.03912542015314102,
0.07838531583547592,
-0.008566509000957012,
-0.014591341838240623,
-0.032673195004463196,
-0.011554674245417118,
-0.021117258816957474,
-0.029682975262403488,
-0.028192363679409027,
-0.028832174837589264,
0.002866649068892002,
-0.019842665642499924,
-0.031550467014312744,
-0.02355991303920746,
0.06562032550573349,
-0.015341825783252716,
-0.03292734548449516,
0.013083774596452713,
-0.05023837834596634,
-0.01471619587391615,
-0.025980399921536446,
-0.02257312461733818,
-0.01613517664372921,
-0.04600420594215393
] |
<p>I want to know how a ceramic transparency is mostly affected by the pores, grain boundary, second phases etc. present inside of it, but the major contribution is due to the pores. </p>
<p>Let's consider the glass slab with an air gap between them. It is still transparent.</p>
<p>Hence: how can simple pores make ceramics opaque? I am after a theoretical description.</p> | g6624 | [
0.05431431159377098,
0.06147262826561928,
0.006259788293391466,
0.04846401512622833,
0.020054683089256287,
0.029747191816568375,
0.05911935865879059,
0.016285929828882217,
-0.007453508209437132,
-0.017756745219230652,
0.028195727616548538,
0.04039694741368294,
0.06278017908334732,
0.01745203137397766,
0.005561561789363623,
0.017332233488559723,
0.041292235255241394,
-0.033303212374448776,
0.007827852852642536,
0.036018356680870056,
-0.007362961303442717,
-0.041213005781173706,
0.023124825209379196,
-0.04080884903669357,
-0.10789860785007477,
0.03553295508027077,
0.017393019050359726,
-0.011428681202232838,
0.0536002479493618,
-0.019646545872092247,
0.04970107600092888,
-0.013837084174156189,
0.011032987385988235,
-0.013341393321752548,
0.009165726602077484,
0.0342300646007061,
-0.002566481474786997,
0.04582720622420311,
0.03115968592464924,
-0.03666184842586517,
0.005466397851705551,
0.0075353761203587055,
-0.003437475999817252,
0.007095338776707649,
-0.05507482588291168,
-0.016409171745181084,
-0.02972172573208809,
-0.011476846411824226,
-0.01372107770293951,
-0.0706162303686142,
-0.02027088962495327,
-0.00801403820514679,
0.004758514929562807,
0.013453037478029728,
-0.045729219913482666,
-0.021388232707977295,
0.019257673993706703,
-0.018237462267279625,
0.0731353908777237,
0.01294973585754633,
-0.029070593416690826,
-0.03397168219089508,
-0.004828090313822031,
0.06188053637742996,
0.02111344039440155,
-0.05443518981337547,
-0.08692684024572372,
0.02939716726541519,
0.06229732558131218,
-0.009525311179459095,
-0.0013797944411635399,
0.06951373815536499,
0.00018222037761006504,
-0.0726289302110672,
-0.07357747107744217,
0.0016740703722462058,
-0.008476579561829567,
0.025375457480549812,
0.08163198828697205,
-0.004343664739280939,
0.01976468227803707,
-0.005112071521580219,
-0.008715121075510979,
0.005551967304199934,
0.019296061247587204,
-0.011169222183525562,
0.06171809136867523,
-0.05705472081899643,
-0.05227218195796013,
-0.018331313505768776,
-0.010746215470135212,
-0.04514818638563156,
-0.003137137508019805,
0.06895309686660767,
0.011826055124402046,
0.05259944126009941,
-0.01810176484286785,
0.03517868369817734,
-0.01936967857182026,
0.03051540069282055,
0.04863618686795235,
-0.05298735201358795,
0.07389161735773087,
-0.01012257020920515,
-0.010269112884998322,
0.07333972305059433,
0.03765539079904556,
0.020136259496212006,
-0.023656493052840233,
0.05800359696149826,
-0.0022039897739887238,
0.01872345246374607,
-0.053651921451091766,
-0.027548357844352722,
0.03045954369008541,
-0.0032148438040167093,
0.08663484454154968,
-0.0026656314730644226,
0.03860241174697876,
0.01420698780566454,
0.0408683717250824,
0.0491693839430809,
0.03248602896928787,
-0.04128175228834152,
0.0037009010557085276,
-0.003430683398619294,
0.02335990034043789,
-0.027058042585849762,
0.02884003520011902,
-0.04780466854572296,
0.041291095316410065,
0.05817294865846634,
0.020194802433252335,
0.0016869611572474241,
0.03317124396562576,
-0.004550715908408165,
-0.012817056849598885,
0.0008257293375208974,
0.0016564639518037438,
-0.05090821534395218,
-0.05483752861618996,
0.007021928671747446,
-0.01211707852780819,
0.012424035929143429,
0.00735974358394742,
-0.0005901428521610796,
0.02076449804008007,
-0.014181891456246376,
0.018964305520057678,
-0.04511906951665878,
0.012163310311734676,
0.027259035035967827,
0.01328685600310564,
0.03755180537700653,
0.06820724159479141,
-0.025757890194654465,
0.0515388548374176,
-0.032829079777002335,
0.013771292753517628,
-0.008946879766881466,
0.06216643005609512,
0.013025009073317051,
-0.004694190341979265,
-0.0007212578784674406,
-0.11193370074033737,
-0.06218552961945534,
0.012184389866888523,
-0.04720151424407959,
0.006799245253205299,
-0.038818079978227615,
0.020482627674937248,
-0.008408579975366592,
0.06325584650039673,
0.08918330818414688,
0.0004632736381608993,
0.05481056123971939,
0.07895532995462418,
0.02686855010688305,
0.07847233861684799,
0.0497823990881443,
0.026669872924685478,
-0.004141092766076326,
-0.06178981438279152,
-0.04114599525928497,
0.043031979352235794,
-0.04179207608103752,
0.030194109305739403,
-0.028219833970069885,
-0.06267097592353821,
0.08136080205440521,
-0.012675318866968155,
-0.06540492922067642,
-0.010429183021187782,
0.001325444784015417,
-0.002630318282172084,
-0.026683606207370758,
0.08037696033716202,
-0.002356452401727438,
-0.024001261219382286,
-0.004115555435419083,
-0.026545729488134384,
0.010606479831039906,
0.029583631083369255,
0.02963116392493248,
0.05522654950618744,
0.01371744554489851,
-0.037732917815446854,
0.070072241127491,
-0.037994492799043655,
0.041211020201444626,
-0.07871237397193909,
0.0042859152890741825,
0.0452166311442852,
0.02171853557229042,
0.0039025458972901106,
0.02399003691971302,
-0.029334133490920067,
-0.002154128858819604,
-0.03168824315071106,
-0.05273626372218132,
0.02193949930369854,
-0.023872463032603264,
-0.04165618494153023,
0.00920017994940281,
-0.03461509197950363,
-0.022219624370336533,
0.03030397929251194,
0.04691816493868828,
0.003381092334166169,
0.050830598920583725,
-0.09369730949401855,
-0.02717597410082817,
-0.023550070822238922,
-0.025077953934669495,
-0.00341858621686697,
0.01741337776184082,
-0.050442807376384735,
0.014637655578553677,
0.012772401794791222,
-0.02276451885700226,
-0.001706314506009221,
-0.08294220268726349,
-0.03951273858547211,
-0.005509267095476389,
-0.01732262596487999,
-0.046076469123363495,
0.0028362059965729713,
0.016373274847865105,
-0.0033511498477309942,
0.015268007293343544,
-0.01999732293188572,
0.04492427036166191,
-0.02314012311398983,
-0.006583344656974077,
-0.04524746164679527,
-0.057575877755880356,
-0.03400979936122894,
0.010839915834367275,
0.003740218235179782,
-0.00977799016982317,
-0.01676795817911625,
-0.02949978969991207,
-0.003122730879113078,
-0.029556771740317345,
0.016468791291117668,
0.014881056733429432,
-0.009048204869031906,
0.028043944388628006,
-0.02742784284055233,
-0.03754528611898422,
0.023335272446274757,
0.08060035854578018,
0.056075569242239,
0.005627770442515612,
0.02607322484254837,
0.03474843502044678,
0.01454880926758051,
-0.07090894877910614,
-0.010970322415232658,
-0.04725524038076401,
-0.041350334882736206,
-0.012312488630414009,
-0.07425930351018906,
0.019992860034108162,
0.007703391835093498,
-0.052473269402980804,
0.03873832896351814,
0.02141583524644375,
0.012340656481683254,
0.03625987470149994,
-0.0032840524800121784,
0.012493814341723919,
0.010156105272471905,
0.01827443577349186,
0.00030153727857396007,
-0.03410720080137253,
0.03496819734573364,
-0.03698216751217842,
-0.05447584018111229,
0.020688381046056747,
-0.011384626850485802,
-0.009307264350354671,
-0.038143035024404526,
0.014178359881043434,
0.01669532246887684,
0.023259535431861877,
0.021149449050426483,
-0.07868675887584686,
-0.055154819041490555,
-0.008317268453538418,
0.008842876181006432,
-0.014003540389239788,
-0.01054319366812706,
0.008705192245543003,
-0.06675508618354797,
0.05820072814822197,
-0.01926770620048046,
0.02270374819636345,
-0.018404148519039154,
0.04458019882440567,
-0.034008145332336426,
0.02783842198550701,
0.0436372309923172,
-0.01699029467999935,
-0.028913402929902077,
-0.03102283552289009,
0.013396311551332474,
-0.042410023510456085,
-0.04302740469574928,
-0.0008238228620029986,
0.028043121099472046,
0.020759614184498787,
-0.02619142085313797,
-0.051282208412885666,
-0.0447206050157547,
0.011648694053292274,
-0.05115007981657982,
0.004725849721580744,
0.004890096373856068,
-0.02292337454855442,
0.03346451744437218,
-0.029590589925646782,
-0.03385147079825401,
0.012194477021694183,
-0.00308606238104403,
-0.03151906654238701,
0.022158917039632797,
-0.014628903940320015,
-0.001963152550160885,
-0.020475171506404877,
0.05347280576825142,
0.010052253492176533,
0.003999111242592335,
-0.054042279720306396,
-0.01422575581818819,
0.047067463397979736,
0.04350324347615242,
0.03450164198875427,
0.024611657485365868,
-0.013004190288484097,
0.04742289334535599,
-0.03680925816297531,
0.04408465698361397,
-0.052256014198064804,
-0.015817051753401756,
-0.0051979077979922295,
0.05286747217178345,
-0.009445622563362122,
0.02288799360394478,
0.029835423454642296,
-0.02688584104180336,
0.026388337835669518,
-0.017559347674250603,
0.09071337431669235,
0.009789476171135902,
-0.02242305874824524,
-0.035770170390605927,
0.04361801967024803,
0.01684643141925335,
0.017870986834168434,
0.0007431191625073552,
-0.028928332030773163,
0.023011241108179092,
-0.03111918643116951,
-0.003877960378304124,
0.03895217552781105,
-0.004229764454066753,
0.005658586509525776,
-0.048673100769519806,
-0.04689447954297066,
0.01346476748585701,
-0.023037418723106384,
-0.05023784190416336,
-0.040851328521966934,
-0.001093385391868651,
-0.08578712493181229,
-0.03407313674688339,
0.020935973152518272,
0.002514549531042576,
0.02154732495546341,
0.016192691400647163,
0.03415890783071518,
-0.025389641523361206,
-0.004960514605045319,
0.024620603770017624,
-0.00860469788312912,
0.008800451643764973,
-0.035606395453214645,
0.020394545048475266,
-0.011257682926952839,
-0.010274500586092472,
-0.002639945363625884,
-0.005103027913719416,
-0.01973043568432331,
0.053341273218393326,
-0.01977473683655262,
-0.010256010107696056,
0.0020533171482384205,
0.006770798936486244,
0.008767301216721535,
-0.030442435294389725,
0.009593113325536251,
-0.07390998303890228,
0.015220322646200657,
0.07720569521188736,
0.029179558157920837,
0.04204658418893814,
-0.07977063208818436,
0.01251841988414526,
0.003042754251509905,
0.007889355532824993,
0.038228828459978104,
0.0014937204541638494,
-0.006428062450140715,
-0.04149151220917702,
-0.008425683714449406,
-0.042734190821647644,
0.00450602313503623,
-0.0375724621117115,
-0.014344804920256138,
0.005794416181743145,
-0.025474248453974724,
-0.013433624058961868,
-0.0705583468079567,
0.008584124967455864,
-0.0355815626680851,
-0.02791747823357582,
0.006238299887627363,
0.01896769553422928,
-0.0264888908714056,
-0.023640576750040054,
0.009800272062420845,
-0.05466284230351448,
-0.018509436398744583,
-0.027098050341010094,
-0.0013444069772958755,
-0.009607077576220036,
-0.0067760394886136055,
0.0033081297297030687,
-0.029043374583125114,
-0.03456632047891617,
0.005658618174493313,
0.00810594204813242,
0.00883286353200674,
0.03102792240679264,
-0.0328095443546772,
0.02156100980937481,
0.027965668588876724,
-0.019584380090236664,
-0.007666795514523983,
0.036081988364458084,
0.06389445811510086,
-0.006028290838003159,
0.062368642538785934,
0.023944636806845665,
-0.024935686960816383,
-0.057056255638599396,
0.057691652327775955,
0.03813088312745094,
0.00441026920452714,
0.0009328193846158683,
0.04280742257833481,
0.14174410700798035,
0.030099859461188316,
-0.03185899928212166,
0.04219212010502815,
0.0021288625430315733,
0.007875310257077217,
-0.052577193826436996,
-0.03588765114545822,
0.01112352591007948,
0.0241991076618433,
-0.04424813762307167,
0.011374121531844139,
-0.027154946699738503,
-0.03723185881972313,
0.12394251674413681,
0.056249234825372696,
-0.03166899085044861,
0.027128875255584717,
-0.009215892292559147,
-0.05397499352693558,
0.03400568664073944,
0.03084261529147625,
0.038356173783540726,
0.05971058830618858,
0.052628692239522934,
-0.047070566564798355,
0.06119290739297867,
0.00457312585785985,
-0.013192282989621162,
-0.009198722429573536,
-0.07195808738470078,
0.004661632236093283,
0.03498892858624458,
0.001370078301988542,
-0.06537031382322311,
-0.04750126600265503,
0.0025065280497074127,
-0.02140994742512703,
-0.0041406420059502125,
0.0023468341678380966,
0.005169485695660114,
-0.012072846293449402,
-0.03337743878364563,
0.017679452896118164,
-0.014238073490560055,
-0.055750537663698196,
0.029446255415678024,
-0.038223136216402054,
-0.047787148505449295,
0.014632187783718109,
-0.02093888446688652,
0.00515341479331255,
-0.0012779298704117537,
-0.05253713205456734,
-0.01139734499156475,
0.005811321549117565,
0.028511330485343933,
-0.011753629893064499,
-0.00923445075750351,
0.058927491307258606,
0.007362165953963995,
0.0835188627243042,
0.05714229494333267,
-0.04972732812166214,
0.015734899789094925,
0.01671374775469303,
0.05152766406536102,
-0.01602315343916416,
0.04354986548423767,
-0.007521731313318014,
0.008846781216561794,
-0.0046213543973863125,
-0.00013520150969270617,
0.03882521390914917,
0.0077295247465372086,
-0.03916768729686737,
0.03400947153568268,
-0.028417468070983887,
0.08296194672584534,
0.051085248589515686,
-0.049106892198324203,
-0.022234966978430748,
-0.0056241219863295555,
-0.040413133800029755,
0.005331357475370169,
0.012423343025147915,
0.024164030328392982,
-0.002160043455660343,
0.01756155863404274,
-0.03669602796435356,
-0.005777424201369286,
-0.009003463201224804,
-0.056393101811409,
0.07829561829566956,
-0.05852202698588371,
0.013797047547996044,
-0.008674840442836285,
0.011920200660824776,
0.006537472363561392,
0.027542755007743835,
0.017277231439948082,
0.07065507024526596,
-0.01964263990521431,
0.02824229747056961,
-0.015042698010802269,
-0.02542242594063282,
-0.010452658869326115,
0.028240561485290527,
-0.034021344035863876,
-0.041015420109033585,
0.023157186806201935,
-0.06897067278623581,
0.038215089589357376,
-0.0014401976950466633,
-0.05008602514863014,
-0.007182959001511335,
0.010218612849712372,
0.06122340261936188,
-0.01665542460978031,
0.04020294174551964,
-0.009076436050236225,
0.012736978009343147,
-0.01978195831179619,
0.020744813606142998,
0.05151853710412979,
-0.02712610922753811,
0.00025840275338850915,
0.029889976605772972,
-0.016262806951999664,
0.0355105847120285,
0.003975508268922567,
-0.025037679821252823,
-0.0075438194908201694,
-0.051762904971838,
-0.05598028004169464,
0.005966904107481241,
-0.008432474918663502,
-0.03644110634922981,
0.017574338242411613,
-0.009761163033545017,
-0.0020538377575576305,
-0.02298239804804325,
0.06184348464012146,
-0.042092159390449524,
-0.026015469804406166,
0.01327014621347189,
0.024149633944034576,
0.0006519441958516836,
-0.02186417393386364,
-0.04888412728905678,
0.03273337334394455,
-0.044344086199998856,
0.014895247295498848,
0.03279289975762367,
-0.043480489403009415,
-0.017061425372958183,
-0.008266797289252281,
-0.08091586083173752,
0.05693547800183296,
0.006038888357579708,
0.05369805917143822,
0.11766236275434494,
0.02345575951039791,
-0.03331276774406433,
-0.03772642835974693,
-0.018486464396119118,
-0.037491898983716965,
0.009830296039581299,
0.000049066493374994025,
-0.003177097300067544,
-0.03626124933362007,
-0.023714635521173477,
-0.04313941299915314,
0.05641525983810425,
-0.055186521261930466,
0.012249604798853397,
0.04534732922911644,
-0.05468516796827316,
0.019477853551506996,
0.04910789802670479,
-0.009520422667264938,
0.045872658491134644,
0.005473144352436066,
0.044024787843227386,
0.08785846829414368,
-0.04485272988677025,
0.01604907214641571,
-0.018508877605199814,
0.0240703746676445,
-0.032068535685539246,
-0.004000527318567038,
0.014095203951001167,
-0.002241488080471754,
-0.01154090091586113,
-0.031915124505758286,
0.03940223902463913,
0.012226282618939877,
0.01567799039185047,
-0.001412339974194765,
0.041462674736976624,
0.041080866008996964,
-0.022277453914284706,
0.007934323512017727,
0.02480657771229744,
0.016859697178006172,
-0.012114085257053375,
-0.04066344350576401,
-0.014084894210100174,
-0.01446468010544777,
-0.061967745423316956,
0.0017879990627989173,
0.004979781806468964,
-0.03968419134616852,
-0.02720469795167446,
0.04504147171974182,
0.02309824526309967,
0.01574118807911873,
0.01290860679000616,
-0.022833416238427162,
-0.019741902127861977,
-0.019176216796040535,
-0.026134369894862175,
0.03562338277697563,
-0.02781253308057785,
-0.02708432264626026,
0.0005584299797192216,
-0.03251116722822189,
-0.04422438144683838,
0.048801522701978683,
0.020967533811926842,
0.048606470227241516,
-0.045274898409843445,
0.017866121605038643,
-0.03366710618138313,
-0.04577963054180145,
-0.017661908641457558,
-0.03720082715153694,
0.027696019038558006,
-0.03219955414533615,
-0.05586066469550133,
0.007031307555735111,
-0.013566882349550724,
-0.013279268518090248,
0.03739095479249954,
-0.01490594632923603,
-0.049446579068899155,
-0.027717387303709984,
0.03961275517940521,
0.017036376520991325,
0.033558979630470276,
0.028858140110969543,
0.027056485414505005,
-0.05356636643409729,
0.012233128771185875,
0.07894845306873322,
-0.030063951388001442,
0.04139401763677597,
0.01982337422668934,
0.021122245118021965,
-0.013269646093249321,
-0.024763189256191254,
-0.009332883171737194,
0.036752138286828995,
0.04073045775294304,
-0.05301446467638016,
-0.027413038536906242,
-0.022317565977573395,
0.03517048433423042,
-0.03861342743039131,
-0.03574255853891373,
0.022180970758199692,
-0.030783260241150856,
0.015105483122169971,
-0.0695294737815857,
-0.048697520047426224,
0.034174781292676926,
-0.015566865913569927,
-0.056338656693696976,
-0.045789722353219986,
0.010229397565126419,
-0.0196969173848629,
0.04952917620539665,
-0.03431571647524834,
-0.004645399283617735,
-0.018755780532956123,
-0.03824421390891075
] |
<p><strong>Edit 26/Sept/13: Fixed Typo in potential</strong></p>
<p>I'm solving the following (seemingly simple) quantum-mechanical problem in <em>four spatial dimensions</em>. In natural units ($\hbar^2/2m=1$), the Schrödinger equation reads:</p>
<p>$$
\Big[-\nabla^2-\frac{24 R^2}{(\mathbf{x}^2+R^2)^2}\Big]\psi(\mathbf{x})=E\,\psi(\mathbf{x})\,,
$$</p>
<p>where $R>0$ is a parameter simultaneously characterizing the depth and range of the potential.
The potential depends only on the distance away from the origin, so I can separate variables $\psi=R_{nl}(r)\,Y_l(\vec{\theta})$ and the radial equation then reads:</p>
<p>$$
\Big[-\frac{\partial^2}{\partial r^2}-\frac{3}{r}\frac{\partial}{\partial r}+\frac{l(l+2)}{r^2}-\frac{24 R^2}{(r^2+R^2)^2}\Big]\,R_{nl}(r)=E_{nl}\,R_{nl}(r)\,.
$$</p>
<p><strong>Problem:</strong> I seem to have found an <em>s</em>-wave ($l=0$) non-scattering state with zero energy $E_{nl}=0$ that appears to be localized:</p>
<p>$$R_{n,l=0}(r)=\mathcal{N}\frac{r^2-R^2}{(r^2+R^2)^2}\qquad E_{nl}=0.$$</p>
<p>But, I am unable to normalize this "bound" state since the integral $\int_0^\infty dr\, r^3 |R(r)|^2$ does not converge. What is the nature of this state? Or am I just totally screwing something up?</p> | g6625 | [
-0.010752318426966667,
0.017514124512672424,
-0.03402714058756828,
-0.020601855590939522,
-0.011233652010560036,
0.06333472579717636,
0.02623194456100464,
0.0050721121951937675,
-0.039858128875494,
-0.03831643611192703,
0.018401460722088814,
0.0010496595641598105,
-0.013125096447765827,
0.003922988194972277,
-0.015229962766170502,
-0.010003281757235527,
0.060626156628131866,
-0.028705434873700142,
0.01517521869391203,
-0.01140756905078888,
-0.061378758400678635,
0.03504842147231102,
-0.018805187195539474,
-0.03048577532172203,
0.0006947810179553926,
-0.006676953751593828,
0.027309458702802658,
-0.023647909983992577,
-0.012449711561203003,
-0.02569158934056759,
-0.015884241089224815,
-0.004592359997332096,
0.05242190882563591,
-0.07077359408140182,
-0.000027115444027003832,
0.04468836262822151,
0.054073844105005264,
0.012133248150348663,
-0.010115740820765495,
-0.013754796236753464,
-0.005449559073895216,
-0.07144426554441452,
-0.020635874941945076,
-0.039132148027420044,
0.0034432760439813137,
0.016757512465119362,
0.05389706790447235,
0.023498937487602234,
0.0516587533056736,
-0.0330943688750267,
0.008134516887366772,
0.041278161108493805,
0.030558515340089798,
-0.039581991732120514,
0.04166247323155403,
0.0316440649330616,
-0.03516533598303795,
0.035652704536914825,
0.05741479620337486,
0.016513116657733917,
0.06583718210458755,
-0.0197678841650486,
0.035250354558229446,
0.04479556903243065,
0.05305052921175957,
0.016602370887994766,
-0.051952093839645386,
0.01941678859293461,
-0.031092505902051926,
-0.03096667118370533,
0.006122729275375605,
-0.07284725457429886,
-0.026686344295740128,
-0.03306596726179123,
-0.0751240998506546,
0.016073428094387054,
-0.022820724174380302,
0.02924591489136219,
-0.008175584487617016,
0.01952909491956234,
-0.039751578122377396,
-0.020632313564419746,
-0.0004093546012882143,
-0.0336826927959919,
0.025178853422403336,
0.024394098669290543,
0.018979543820023537,
0.00935865007340908,
0.012065227143466473,
0.052475377917289734,
-0.0030837245285511017,
0.01617743819952011,
0.039461616426706314,
-0.026663556694984436,
0.07673466950654984,
0.013468904420733452,
-0.02425585314631462,
0.08245770633220673,
-0.005492246709764004,
-0.017507974058389664,
-0.026460621505975723,
-0.005615462549030781,
0.044964779168367386,
0.011811108328402042,
0.021285362541675568,
0.0012178990291431546,
0.023873155936598778,
0.023506484925746918,
0.034776750952005386,
-0.018402433022856712,
0.008104505017399788,
-0.009663420729339123,
-0.020538415759801865,
-0.07089120149612427,
-0.0729091539978981,
0.04022252932190895,
0.009854890406131744,
-0.001419035135768354,
-0.05032464116811752,
0.059060096740722656,
0.043036945164203644,
0.04284318536520004,
0.08114957809448242,
0.08707181364297867,
-0.013227461837232113,
0.03811585158109665,
-0.006510413717478514,
0.017690984532237053,
0.06863049417734146,
0.028895728290081024,
-0.050880368798971176,
0.003958902787417173,
0.005280597135424614,
-0.02171257883310318,
-0.025502296164631844,
0.04140753298997879,
-0.008557469584047794,
-0.05642053857445717,
-0.006846842356026173,
0.022913483902812004,
-0.06628848612308502,
-0.054973289370536804,
0.015352307818830013,
0.010087057948112488,
-0.06723518669605255,
-0.011617813259363174,
0.020750319585204124,
-0.06787259131669998,
-0.01305493526160717,
-0.016717035323381424,
0.002376542892307043,
0.02098825015127659,
-0.042038917541503906,
-0.02119959518313408,
-0.01286568958312273,
0.014783871360123158,
0.04185158386826515,
0.0031090734992176294,
0.04326638579368591,
0.009205544367432594,
0.019080638885498047,
0.050420839339494705,
-0.014567142352461815,
0.0007061751093715429,
-0.013314450159668922,
0.04690634459257126,
0.03419991955161095,
-0.03274957835674286,
0.019051343202590942,
-0.03320024907588959,
0.0008070493931882083,
-0.031007466837763786,
-0.006405537016689777,
-0.02080036699771881,
-0.05490618571639061,
0.07347480952739716,
0.02566186524927616,
-0.04443875700235367,
0.008343461900949478,
0.015570355579257011,
-0.04012094438076019,
-0.06360626220703125,
0.016500024124979973,
-0.046015236526727676,
0.011204118840396404,
0.01666419208049774,
0.0021645044907927513,
0.020481189712882042,
0.011803559958934784,
-0.08791917562484741,
-0.04422405734658241,
0.04977975785732269,
0.04544473811984062,
-0.003575998591259122,
-0.014806483872234821,
0.016800394281744957,
0.041998185217380524,
-0.07623245567083359,
-0.013337275944650173,
0.004829995799809694,
-0.017784297466278076,
0.08319158107042313,
0.0332302488386631,
0.029336530715227127,
0.051291778683662415,
-0.0033116338308900595,
0.01953194849193096,
0.02196153812110424,
-0.02007989212870598,
0.01499804388731718,
-0.033432140946388245,
-0.05067397654056549,
-0.03448385372757912,
0.0023596251849085093,
0.02952873520553112,
-0.07211627066135406,
0.0225138571113348,
0.009742007590830326,
-0.04307657480239868,
0.07547201961278915,
-0.05731829255819321,
-0.009535672143101692,
0.04625537246465683,
0.017719630151987076,
0.05742782726883888,
0.008636058308184147,
-0.03133852407336235,
0.03879017010331154,
-0.00313724298030138,
0.019655026495456696,
-0.06114739552140236,
0.02350040338933468,
0.04096776992082596,
0.01543927751481533,
0.050232432782649994,
0.04937407001852989,
-0.03022848255932331,
-0.031029414385557175,
-0.03094174712896347,
-0.036296822130680084,
0.032746247947216034,
-0.02537541091442108,
-0.046700332313776016,
0.023927053436636925,
0.060418013483285904,
0.024912362918257713,
-0.015727033838629723,
-0.014844098128378391,
-0.03229465335607529,
0.049644019454717636,
0.03826744481921196,
0.001720224041491747,
-0.012078886851668358,
0.04291774705052376,
-0.04313747584819794,
-0.020934177562594414,
0.0018933541141450405,
0.001027901773341,
-0.010668144561350346,
-0.04153885319828987,
-0.07589368522167206,
0.052666570991277695,
0.0564286969602108,
0.013933972455561161,
-0.03598649054765701,
0.034416209906339645,
-0.02247440628707409,
0.057032614946365356,
-0.011162555776536465,
-0.019993996247649193,
0.013205756433308125,
0.05837139114737511,
0.002668514149263501,
0.02526620775461197,
0.014521556906402111,
-0.014008675701916218,
-0.04410393908619881,
0.0014410382136702538,
0.05340782180428505,
0.016915909945964813,
-0.03830713406205177,
0.001318586291745305,
0.03810278698801994,
0.03302935138344765,
0.014427468180656433,
-0.07487960904836655,
0.035544898360967636,
0.05716049298644066,
0.006914662662893534,
0.010978295467793941,
0.017755646258592606,
0.00656924769282341,
0.028668498620390892,
0.03422147035598755,
-0.029017284512519836,
0.02160067670047283,
-0.005473525729030371,
-0.04232477769255638,
0.04056810587644577,
0.045300211757421494,
-0.004743751138448715,
-0.010931145399808884,
-0.02944023907184601,
-0.03116772696375847,
0.002946366323158145,
-0.02735547535121441,
-0.0359208881855011,
0.02508178912103176,
-0.017160724848508835,
-0.016365785151720047,
0.02347731962800026,
0.03580653294920921,
0.010214421898126602,
-0.013434232212603092,
0.003907374572008848,
0.034029170870780945,
0.002520227339118719,
0.010253850370645523,
-0.028675450012087822,
-0.011503375135362148,
0.0011517354287207127,
-0.0618370845913887,
0.015302739106118679,
0.031018612906336784,
0.0011962641729041934,
0.029062215238809586,
-0.04748281463980675,
0.005889832973480225,
-0.038372837007045746,
0.014471911825239658,
0.01681753806769848,
0.006288065109401941,
0.021573850885033607,
-0.03272651880979538,
-0.07060965895652771,
-0.058596085757017136,
-0.014643783681094646,
0.007438138592988253,
0.09113272279500961,
-0.00815632939338684,
-0.012032605707645416,
-0.07613220065832138,
0.017768707126379013,
0.005845008883625269,
0.035576120018959045,
-0.008444397710263729,
-0.08743482083082199,
0.054069533944129944,
-0.011879142373800278,
0.056550998240709305,
-0.02086765132844448,
0.009516830556094646,
-0.009869086556136608,
-0.007058193441480398,
-0.0594063475728035,
0.07719168812036514,
-0.013742544688284397,
-0.0017471995670348406,
-0.013995714485645294,
0.0037767565809190273,
0.015105288475751877,
-0.044843483716249466,
-0.0065453993156552315,
-0.010800011456012726,
0.012326731346547604,
0.008845466189086437,
0.042635902762413025,
0.004679120145738125,
0.019737644121050835,
-0.04272548109292984,
0.018737731501460075,
-0.021200397983193398,
0.01006851065903902,
0.04994409158825874,
0.018979357555508614,
-0.005025824997574091,
-0.04082159325480461,
-0.021048331633210182,
-0.0602586604654789,
0.03654008358716965,
0.02165685035288334,
0.01091054454445839,
-0.00447214487940073,
0.0026443018577992916,
0.039789021015167236,
0.028119320049881935,
-0.02280104160308838,
-0.03392999246716499,
0.002309688599780202,
0.024653326719999313,
-0.036229707300662994,
-0.045669883489608765,
-0.023501060903072357,
0.07076137512922287,
-0.020695360377430916,
0.014522206969559193,
0.036069147288799286,
-0.044840261340141296,
-0.07837893813848495,
0.06928733736276627,
-0.014768957160413265,
0.005372001323848963,
0.01809021830558777,
-0.03918635845184326,
-0.06051388382911682,
-0.07137555629014969,
0.03615555539727211,
0.04416661709547043,
-0.05014093220233917,
-0.00434987572953105,
0.01022059004753828,
0.00023257176508195698,
-0.03283271566033363,
-0.10031010955572128,
0.01922224462032318,
-0.06220404803752899,
0.027409672737121582,
-0.01739005371928215,
-0.0657130554318428,
0.027496805414557457,
0.02916780114173889,
0.046742603182792664,
0.02279307320713997,
0.009076756425201893,
0.03846738860011101,
0.002963475650176406,
-0.01348817441612482,
0.05539707839488983,
0.001229565590620041,
0.015187577344477177,
-0.004249327350407839,
0.02400679513812065,
-0.0070526874624192715,
0.07075345516204834,
-0.02745974250137806,
0.015619209967553616,
-0.08344841003417969,
-0.021652832627296448,
0.007911629043519497,
0.034454625099897385,
0.0020303374622017145,
0.021419404074549675,
-0.010996448807418346,
0.021581405773758888,
0.004420635290443897,
0.04507285729050636,
-0.0029351150151342154,
-0.010082906112074852,
0.01140751875936985,
-0.01442714687436819,
-0.028128404170274734,
-0.0008147372282110155,
0.02895953692495823,
-0.04912189021706581,
0.031854353845119476,
-0.02389691397547722,
-0.046171724796295166,
0.039729293435811996,
0.06902623921632767,
-0.028213147073984146,
0.03130672499537468,
-0.02788204699754715,
-0.0528283528983593,
-0.004476241301745176,
0.027735380455851555,
-0.05656147748231888,
-0.044521596282720566,
0.017042234539985657,
-0.06492672860622406,
-0.03407757356762886,
0.020699841901659966,
0.01840561255812645,
0.0597180612385273,
0.009990507736802101,
-0.02861320599913597,
0.03189953789114952,
-0.03882073611021042,
0.0011896839132532477,
-0.0008655350538901985,
-0.02216559648513794,
0.026477381587028503,
-0.04946030676364899,
-0.0030040929559618235,
0.0489797405898571,
0.018177039921283722,
0.07875770330429077,
-0.03724316880106926,
0.005304092075675726,
-0.020930083468556404,
-0.003818897530436516,
0.028760546818375587,
-0.011973872780799866,
-0.024806447327136993,
0.003759326646104455,
0.01983586885035038,
0.011027970351278782,
0.01843985728919506,
-0.015215789899230003,
0.00030872164643369615,
0.01842481642961502,
-0.04909209907054901,
0.01354034524410963,
0.02724062092602253,
0.026503371074795723,
-0.018918650224804878,
0.0692719966173172,
0.08434803783893585,
0.013806766830384731,
0.03190421313047409,
0.04902825877070427,
-0.028473986312747,
-0.03496824577450752,
0.00658848462626338,
-0.04204327613115311,
0.028062548488378525,
-0.08772637695074081,
-0.06116364151239395,
0.07007815688848495,
-0.05350847169756889,
-0.010823894292116165,
0.027742084115743637,
-0.014101176522672176,
0.026106109842658043,
-0.03529270738363266,
0.0192143265157938,
0.008252765983343124,
0.007987537421286106,
-0.019021285697817802,
-0.01897546835243702,
0.03371467813849449,
-0.003719168249517679,
0.009559130296111107,
0.013994570821523666,
0.008883961476385593,
0.04078829661011696,
-0.014266310259699821,
0.010262800380587578,
-0.01183213759213686,
-0.02652612328529358,
-0.017864268273115158,
0.03767872601747513,
-0.0581323467195034,
-0.04396890103816986,
0.042385172098875046,
-0.07372228056192398,
-0.014016778208315372,
-0.017399534583091736,
-0.059645283967256546,
0.030732491984963417,
0.011638314463198185,
-0.01572229526937008,
-0.05905721336603165,
-0.08345210552215576,
0.007749957498162985,
0.03333975002169609,
-0.02377372421324253,
0.01029106043279171,
0.0023860728833824396,
-0.08212674409151077,
-0.04186246171593666,
0.05504109710454941,
-0.050277650356292725,
0.02333046868443489,
0.03245198354125023,
0.011759250424802303,
-0.05494251102209091,
-0.028381530195474625,
-0.004221596289426088,
0.03612794354557991,
0.0037833251990377903,
-0.05458104982972145,
0.022629033774137497,
0.006261182948946953,
-0.01192803867161274,
0.03599844500422478,
-0.009174658916890621,
-0.02593528851866722,
-0.024823036044836044,
0.01045428216457367,
-0.0025992037262767553,
-0.04897093400359154,
0.026069926097989082,
0.062187083065509796,
-0.05130903422832489,
0.029304269701242447,
0.06409002840518951,
-0.02104371041059494,
-0.05712025985121727,
0.04736044257879257,
0.025071198120713234,
-0.024110501632094383,
0.02747015468776226,
-0.013019601814448833,
0.005935554392635822,
-0.0006345315487124026,
-0.060150206089019775,
0.05406038090586662,
-0.018241113051772118,
-0.1189364567399025,
0.009835940785706043,
0.032223351299762726,
-0.01126112136989832,
0.011512056924402714,
0.016294635832309723,
0.0036375431809574366,
0.03596009314060211,
-0.045351292937994,
-0.020648648962378502,
-0.01655391976237297,
0.06847495585680008,
-0.025099806487560272,
0.023691451177001,
0.012127150781452656,
0.0038714043330401182,
0.010122867301106453,
-0.08256738632917404,
0.08075519651174545,
0.025341838598251343,
-0.021496573463082314,
-0.0007569759036414325,
0.05826380103826523,
0.008761897683143616,
0.00395393930375576,
0.027918187901377678,
0.04612802714109421,
-0.0037227740976959467,
-0.05668127164244652,
-0.026011254638433456,
0.05317949131131172,
-0.005559240467846394,
0.020092379301786423,
0.0034151102881878614,
-0.043485116213560104,
0.05782227963209152,
-0.052327703684568405,
-0.004898651037365198,
-0.0525989830493927,
0.004854270257055759,
0.05255923420190811,
-0.038206446915864944,
-0.0454486645758152,
-0.01869611255824566,
0.03725259751081467,
-0.0588718056678772,
-0.017430445179343224,
-0.01677030324935913,
0.018672630190849304,
0.0014806858962401748,
-0.06353630870580673,
0.042178843170404434,
0.050685349851846695,
0.021810589358210564,
-0.02038159780204296,
0.017364341765642166,
-0.02215171605348587,
-0.003025510348379612,
-0.05180077254772186,
0.01804167404770851,
-0.02852855622768402,
-0.04084311053156853,
-0.012178709730505943,
-0.03528590500354767,
-0.051372770220041275,
0.012625981122255325,
-0.005844384431838989,
0.056691426783800125,
-0.010549123398959637,
-0.07506146281957626,
-0.03811006620526314,
-0.06665374338626862,
0.02933003380894661,
-0.0366707369685173,
-0.013286557979881763,
-0.002660637255758047,
0.014956473372876644,
0.024574870243668556,
0.050658777356147766,
0.022484473884105682,
-0.00014967925380915403,
-0.038985736668109894,
0.05714463070034981,
0.041710302233695984,
-0.022933300584554672,
0.04916640743613243,
-0.031309302896261215,
-0.005210586823523045,
-0.030700474977493286,
0.007477717939764261,
0.025982271879911423,
0.04810779541730881,
0.008497731760144234,
0.03795171156525612,
-0.021238472312688828,
0.01119003165513277,
0.013356813229620457,
-0.0083919707685709,
0.05061045289039612,
0.029747093096375465,
0.03670547530055046,
-0.022730471566319466,
-0.02671281062066555,
-0.028990130871534348,
0.010412433184683323,
0.011337327770888805,
0.025857383385300636,
-0.036384910345077515,
-0.00832592137157917,
-0.056636564433574677,
0.00683970469981432,
0.009068167768418789,
-0.0007584519917145371,
0.03888930007815361,
-0.0029351075645536184,
0.008581004105508327,
0.054095737636089325,
0.057533446699380875,
-0.010272372514009476,
0.05776612088084221,
0.04543337970972061,
-0.051698703318834305,
-0.04893561080098152,
0.0359322614967823,
0.01027158834040165,
-0.033133868128061295,
-0.0509771965444088,
-0.009078187867999077,
0.014281198382377625,
-0.007832138799130917,
0.025326626375317574,
0.02567865699529648,
-0.04943462088704109,
-0.02269596792757511,
-0.05103309452533722,
-0.01408536359667778,
0.00962898787111044,
-0.012035395950078964,
-0.04755409434437752,
0.026779696345329285,
0.05231664702296257,
-0.022457020357251167,
-0.030537419021129608,
-0.07716195285320282,
0.03321149945259094,
-0.021772876381874084,
0.017350638285279274,
-0.021406851708889008,
-0.013395926915109158,
0.04722396656870842,
0.03311943635344505,
-0.053381383419036865,
0.00982983224093914,
-0.04038922116160393,
-0.05124640837311745,
0.0601072683930397,
0.04818989709019661,
-0.06580661982297897,
0.04011267423629761,
-0.0214640274643898,
0.05247091129422188,
0.02334168553352356,
0.03500417619943619,
-0.0468648262321949,
-0.016636386513710022,
0.008378510363399982,
0.026959659531712532,
-0.06510543823242188,
-0.01421719416975975,
0.015840865671634674
] |
<p>I want to solve the TISE of a particle of charge $q$ and mass $m$ in a one dimensional triangular potential, with an infinitely high potential wall at $x = 0$, i.e.</p>
<p>$$\hat{H}=-\frac{\hbar^2}{2m}\frac{\partial^2}{\partial x^2}+V(x),$$
with</p>
<p>$$V\left(x\right)=\begin{cases}qEx&{\rm if}\,x>0 \\
\infty &{\rm if}\,x\leq0\end{cases}$$</p>
<p>For $x>0$, this gives the TISE
$$-\frac{\hbar^2}{2m}\frac{\partial^2\Psi_n}{\partial x^2}+qEx\cdot\Psi_n = E_n\Psi_n.$$
I know that the solutions of
$$\frac{d^2y}{dx^2} - xy = 0$$
are given by the Airy functions, however I don't know how I can transform the TISE to this form. I know it's possible, because I have the solution to the problem, but I don't know how I can myself come up with this, I don't see the aim which has to be reached in order for a substitution to be successful. Also, I don't know how the differential will transform under a substitution including $x$.
Any help?</p>
<p>The substitution used in the solution is
$$u=\left(\frac{2mqE}{\hbar^2}\right)^\frac{1}{3}\left(x-\frac{E_n}{qE}\right).$$</p> | g6626 | [
0.032329119741916656,
-0.016392681747674942,
-0.019404783844947815,
-0.028264285996556282,
0.07538879662752151,
0.02304951287806034,
0.03561263903975487,
0.01274141389876604,
-0.03287163004279137,
-0.018415100872516632,
-0.03451380133628845,
0.019914360716938972,
0.008008955046534538,
-0.007357101887464523,
0.043240007013082504,
0.009920146316289902,
0.0913306251168251,
0.049757570028305054,
-0.005513088312000036,
-0.008151336573064327,
-0.015189502388238907,
0.005243031308054924,
0.043236926198005676,
-0.03513412922620773,
-0.03737379238009453,
-0.0716644749045372,
-0.013514426536858082,
0.05745982751250267,
-0.016470035538077354,
0.03730328381061554,
-0.007879475131630898,
0.008703748695552349,
-0.013885864987969398,
0.04055078327655792,
0.018097708001732826,
0.023608362302184105,
0.08086781948804855,
0.005506827030330896,
0.016812553629279137,
-0.007293074391782284,
-0.008774037472903728,
-0.051402464509010315,
0.051308773458004,
0.017834827303886414,
-0.016087863594293594,
-0.007137447129935026,
-0.0021896513644605875,
0.024615738540887833,
-0.04282355681061745,
-0.0013368150684982538,
0.04412652179598808,
0.04181874915957451,
0.0016709028277546167,
-0.03879484906792641,
-0.019321899861097336,
0.010329230688512325,
0.0038399281911551952,
-0.03522546589374542,
0.024696556851267815,
0.08183786273002625,
-0.023627035319805145,
-0.05539770796895027,
0.007839023135602474,
0.016411593183875084,
0.053346846252679825,
-0.0027783315163105726,
-0.049119673669338226,
0.027605988085269928,
-0.020225895568728447,
-0.034330252557992935,
0.06080348417162895,
-0.03692607209086418,
0.04198165237903595,
-0.010633598081767559,
-0.0035486873239278793,
-0.019329000264406204,
0.011707206256687641,
-0.05047066509723663,
0.00037855171831324697,
-0.014954516664147377,
-0.032625049352645874,
-0.0014785524690523744,
0.031210454180836678,
-0.05061030387878418,
0.012802214361727238,
-0.06554736942052841,
0.04077932983636856,
-0.011784614063799381,
-0.004569659475237131,
-0.010872053913772106,
-0.03285631164908409,
0.003346157493069768,
0.06258808076381683,
0.014446905814111233,
-0.014901037327945232,
-0.025739477947354317,
0.009479164145886898,
0.020206261426210403,
0.01980574242770672,
-0.04181508347392082,
-0.016886992380023003,
-0.04030439630150795,
0.016484349966049194,
0.016835367307066917,
-0.03190073370933533,
0.00842488743364811,
0.020838575437664986,
-0.0012335542123764753,
0.03503437340259552,
-0.013423255644738674,
-0.032116226851940155,
-0.015610452741384506,
-0.004102468956261873,
-0.05425240099430084,
-0.011946510523557663,
0.014990244060754776,
-0.009853151626884937,
0.020226066932082176,
-0.05184409022331238,
0.06887906044721603,
0.020243769511580467,
0.006567444186657667,
0.0024269018322229385,
0.07433898001909256,
0.03405531123280525,
-0.03196297585964203,
-0.04929165542125702,
0.04079785197973251,
0.0014059903332963586,
-0.038455430418252945,
-0.01915784738957882,
0.03319542855024338,
0.030992239713668823,
-0.03608253225684166,
-0.010025108233094215,
0.02660336345434189,
-0.02895967848598957,
-0.018999813124537468,
-0.011394326575100422,
0.02157149650156498,
-0.02985829859972,
-0.019898878410458565,
0.009686087258160114,
0.07171116024255753,
-0.05123812332749367,
0.028551718220114708,
-0.007299437187612057,
-0.02439754456281662,
-0.0639348030090332,
-0.01160820759832859,
-0.04420943930745125,
0.042010221630334854,
0.053903911262750626,
0.05082324147224426,
0.058803144842386246,
-0.024774212390184402,
0.060646142810583115,
-0.0026697907596826553,
0.05681968480348587,
-0.03002479486167431,
0.0008788751438260078,
-0.0013999990187585354,
-0.0353325754404068,
-0.019862409681081772,
-0.02346237190067768,
0.0335424467921257,
0.019651338458061218,
0.012011156417429447,
-0.02623416855931282,
-0.09154747426509857,
-0.01365608163177967,
-0.008709847927093506,
0.025509925559163094,
0.054276976734399796,
0.01844853349030018,
0.020663805305957794,
-0.0719204694032669,
-0.02962682954967022,
0.019833270460367203,
0.024783577769994736,
-0.007158542051911354,
0.009792317636311054,
0.01554166804999113,
-0.014434318989515305,
0.008589377626776695,
0.016937123611569405,
0.029974717646837234,
0.055513665080070496,
-0.04704571142792702,
0.020724672824144363,
0.017827948555350304,
0.006335678044706583,
0.013457860797643661,
0.020940667018294334,
0.020681561902165413,
0.02762717567384243,
0.08211354166269302,
-0.0933331623673439,
-0.03394797444343567,
-0.01587555930018425,
-0.048944924026727676,
0.0722743347287178,
0.06865521520376205,
0.013173463754355907,
0.06019913777709007,
-0.007063894998282194,
-0.0071909744292497635,
-0.02914198860526085,
-0.014390948228538036,
0.00007455365266650915,
0.006504303775727749,
-0.02858126536011696,
-0.01293121837079525,
0.04710717499256134,
-0.009806407615542412,
-0.034983184188604355,
-0.043256208300590515,
0.04183927923440933,
-0.00743759423494339,
-0.01669882796704769,
-0.01760566420853138,
0.011920939199626446,
-0.021642711013555527,
0.016738375648856163,
-0.014001892879605293,
0.018470939248800278,
0.027154158800840378,
-0.008777297101914883,
-0.03749656677246094,
-0.01604524627327919,
0.011465856805443764,
0.015929579734802246,
0.02230556309223175,
-0.036461155861616135,
0.022326195612549782,
-0.007223712746053934,
-0.038034550845623016,
-0.0027817501686513424,
0.029396358877420425,
-0.00833605881780386,
0.011177548207342625,
-0.006630661431699991,
-0.010067432187497616,
-0.023102208971977234,
0.060909390449523926,
0.05282030254602432,
-0.02074653096497059,
0.03255259245634079,
0.045480724424123764,
0.005820655729621649,
-0.0040960488840937614,
-0.04330648109316826,
-0.06016049161553383,
-0.02335391193628311,
-0.04421733692288399,
-0.03886665031313896,
-0.014042140915989876,
-0.017790712416172028,
0.052414990961551666,
-0.04905815050005913,
-0.08315169811248779,
-0.002433094894513488,
-0.03825846686959267,
0.011822228319942951,
-0.09277967363595963,
0.02037145383656025,
-0.034456875175237656,
0.033910784870386124,
0.03916701301932335,
-0.005211766809225082,
0.0430128239095211,
0.04382462799549103,
0.028038617223501205,
0.024524947628378868,
-0.02126537263393402,
-0.06415163725614548,
-0.005754910409450531,
0.028242630884051323,
0.016787555068731308,
-0.021353455260396004,
0.035810425877571106,
0.018590914085507393,
-0.0011555771343410015,
0.07524678856134415,
0.01861041598021984,
-0.026016006246209145,
0.025661887601017952,
0.019436027854681015,
0.00850733369588852,
0.011530079878866673,
-0.05619043856859207,
-0.031533822417259216,
0.08158191293478012,
0.013053004629909992,
-0.015114622190594673,
-0.01278998889029026,
0.0009341079276055098,
-0.01799634099006653,
0.0057808817364275455,
-0.022895438596606255,
-0.07140441983938217,
0.03256082907319069,
-0.0009549235110171139,
0.03779701516032219,
0.05908266454935074,
-0.02225182205438614,
-0.03012934699654579,
-0.03366324305534363,
0.05187540128827095,
0.029630146920681,
0.03455381467938423,
0.013512331061065197,
-0.0023149859625846148,
0.02769060805439949,
-0.018036823719739914,
0.029382450506091118,
-0.029555518180131912,
-0.039648912847042084,
0.009567737579345703,
-0.00431823031976819,
0.006762154866009951,
-0.008142860606312752,
0.020018136128783226,
0.018100325018167496,
0.035002149641513824,
0.006921977736055851,
-0.027007706463336945,
0.03278334066271782,
-0.07015024870634079,
-0.007033409550786018,
0.026127811521291733,
0.03440089896321297,
0.055088385939598083,
-0.05803515017032623,
-0.0112153934314847,
-0.0013964163372293115,
0.01698657125234604,
0.023481613025069237,
0.04264546185731888,
-0.03308385610580444,
-0.049295369535684586,
0.012047667987644672,
-0.08268330991268158,
0.038458019495010376,
-0.005478156730532646,
-0.1037735790014267,
-0.01780608482658863,
0.029616400599479675,
0.010080025531351566,
-0.031235236674547195,
-0.01773008145391941,
0.0036515069659799337,
0.004442240111529827,
0.04455898329615593,
0.015960780903697014,
0.019037675112485886,
0.0506587028503418,
0.0434880368411541,
-0.03092781826853752,
0.0509367473423481,
0.0606875978410244,
-0.10823449492454529,
-0.017811324447393417,
0.04747893661260605,
-0.007014395669102669,
-0.003939816262573004,
0.003781914943829179,
-0.03324520215392113,
-0.011360131204128265,
-0.005186757538467646,
-0.015304503962397575,
0.009773483499884605,
0.009504854679107666,
0.06013474613428116,
-0.004304004833102226,
-0.062108878046274185,
-0.04249420762062073,
-0.01853792928159237,
-0.006549987010657787,
0.021119866520166397,
-0.00305566587485373,
-0.006183025427162647,
0.005772939417511225,
-0.029368244111537933,
0.08657281845808029,
0.011469087563455105,
-0.04449877887964249,
-0.014552636072039604,
0.017412792891263962,
0.0021631179843097925,
-0.00780884176492691,
-0.02455911785364151,
-0.00851205550134182,
0.03247782215476036,
0.014391118660569191,
-0.05990267172455788,
0.018194396048784256,
-0.038843605667352676,
-0.08803386241197586,
-0.016611862927675247,
-0.031721267849206924,
-0.037685807794332504,
-0.0037892155814915895,
-0.033129919320344925,
-0.03062357008457184,
-0.016984324902296066,
0.04159132391214371,
-0.06681031733751297,
0.022444672882556915,
-0.035640373826026917,
0.0037930416874587536,
-0.0066328346729278564,
0.04150128737092018,
-0.011094366200268269,
-0.053572628647089005,
-0.015934087336063385,
0.02800118550658226,
-0.025942794978618622,
-0.017577067017555237,
0.013819209299981594,
0.003094133222475648,
0.003969772253185511,
-0.04094843566417694,
0.037705279886722565,
0.044591255486011505,
0.042172424495220184,
0.05226024612784386,
-0.04242745786905289,
0.016378024592995644,
-0.004489087034016848,
-0.0247564148157835,
0.03749103099107742,
-0.012548611499369144,
0.013380835764110088,
-0.016878485679626465,
0.008731584995985031,
-0.034061506390571594,
-0.0929676741361618,
-0.004142803139984608,
0.02742840349674225,
0.05820289999246597,
0.028690902516245842,
-0.03646164759993553,
-0.023264912888407707,
0.012167399749159813,
0.03722177445888519,
-0.012892941012978554,
-0.05186938866972923,
0.05562905967235565,
0.019883334636688232,
0.0020536212250590324,
0.00132667925208807,
0.019848568364977837,
-0.011823492124676704,
0.0027197329327464104,
-0.008835649117827415,
-0.016790274530649185,
0.004736439790576696,
-0.04068990424275398,
-0.04019181802868843,
0.006625399924814701,
0.00899572018533945,
-0.03811732307076454,
0.0005868582520633936,
0.0421169139444828,
0.006126619875431061,
-0.07538297772407532,
0.050313808023929596,
-0.01885954663157463,
-0.12184233218431473,
-0.013577023521065712,
-0.0034563406370580196,
0.01587875559926033,
0.009222469292581081,
0.031150085851550102,
-0.05683625116944313,
-0.024944452568888664,
-0.058198679238557816,
-0.011119471862912178,
-0.025256814435124397,
-0.01126837357878685,
0.01343838032335043,
-0.015599903650581837,
0.03285088762640953,
-0.025117941200733185,
0.008000095374882221,
-0.04211696982383728,
0.028431493788957596,
-0.025004534050822258,
0.030386080965399742,
0.0002862806722987443,
0.0820106565952301,
-0.01246268954128027,
-0.046321697533130646,
0.041267529129981995,
0.0021949014626443386,
0.043721165508031845,
-0.003182938089594245,
0.022470081225037575,
0.05889607220888138,
-0.03917204588651657,
-0.06420136243104935,
0.0037226176355034113,
0.008616393432021141,
0.042277902364730835,
0.07830344140529633,
0.02102021314203739,
0.007445747498422861,
-0.023654820397496223,
0.027200942859053612,
-0.01793721131980419,
-0.05686477571725845,
0.06670050323009491,
-0.012383339926600456,
0.016740286722779274,
0.06046706438064575,
-0.04199155420064926,
0.007977528497576714,
-0.019950704649090767,
0.0008778165210969746,
0.08771421015262604,
-0.007161399815231562,
0.026655850932002068,
-0.022690296173095703,
0.04081282764673233,
0.013051468878984451,
-0.014966383576393127,
-0.07507006078958511,
-0.07495564222335815,
0.012129900977015495,
-0.019797515124082565,
-0.07658258825540543,
-0.04982396587729454,
0.005001815501600504,
-0.032130613923072815,
-0.04224161431193352,
-0.015850242227315903,
0.026144105941057205,
0.0243129413574934,
-0.03910191357135773,
0.027689160779118538,
-0.036656349897384644,
0.023131094872951508,
-0.030704297125339508,
-0.06987040489912033,
0.026665709912776947,
-0.06261055171489716,
0.061732176691293716,
-0.012923991307616234,
0.05393250286579132,
-0.013183455914258957,
-0.017193343490362167,
-0.044794853776693344,
-0.02228633314371109,
0.08634982258081436,
-0.01278337650001049,
0.03078017197549343,
-0.028426378965377808,
-0.007084606681019068,
-0.003979780711233616,
0.05802736058831215,
-0.04219900444149971,
0.05195410177111626,
-0.008970499970018864,
-0.06278499960899353,
-0.041944652795791626,
-0.010404638014733791,
0.04340621083974838,
0.05637982487678528,
0.01762956939637661,
-0.012868712656199932,
-0.02436210960149765,
0.048485781997442245,
-0.05469406396150589,
0.035967227071523666,
-0.01068444550037384,
0.0033818837255239487,
-0.05356720834970474,
0.0019760497380048037,
0.024389246478676796,
-0.0273195318877697,
0.04520086571574211,
0.006218673195689917,
-0.024166811257600784,
-0.024708615615963936,
-0.00006854134699096903,
0.003085063537582755,
-0.08877629786729813,
-0.0015944625483825803,
-0.009834486991167068,
-0.025049926713109016,
0.005449036601930857,
-0.028148602694272995,
-0.027189848944544792,
0.028711339458823204,
-0.004036999307572842,
0.04487793520092964,
-0.005077909678220749,
0.0002265923540107906,
0.0784057229757309,
0.0613628588616848,
-0.020658669993281364,
-0.018463682383298874,
0.0623258575797081,
0.02459060400724411,
-0.03234390541911125,
-0.040556665509939194,
0.009272083640098572,
-0.04352360591292381,
0.003041189629584551,
0.04221804812550545,
-0.0043167234398424625,
-0.0258809681981802,
-0.07595209777355194,
0.00009513198165223002,
-0.035335637629032135,
0.008420290425419807,
0.06602222472429276,
0.00914858840405941,
-0.03209839016199112,
0.04607614502310753,
0.00750315934419632,
0.019828541204333305,
-0.04604162275791168,
0.0669010654091835,
-0.0411967970430851,
0.03747321292757988,
0.06671000272035599,
0.023680156096816063,
-0.026510179042816162,
0.05677644535899162,
-0.00766735477373004,
-0.029093662276864052,
-0.017444154247641563,
-0.042737942188978195,
0.04509493336081505,
0.026238255202770233,
0.010526783764362335,
0.03544491529464722,
0.041290294378995895,
-0.041295476257801056,
0.04693305119872093,
-0.01624019630253315,
-0.020336490124464035,
-0.03949273005127907,
-0.03908270224928856,
0.0009839197155088186,
0.015362673439085484,
-0.06285469979047775,
0.05551193282008171,
0.06225445494055748,
0.010394570417702198,
-0.048367105424404144,
0.028885547071695328,
-0.03874935582280159,
-0.018170258030295372,
-0.012842785567045212,
0.0024990979582071304,
-0.01974697783589363,
-0.03780781850218773,
-0.043537817895412445,
-0.0034987989347428083,
0.01909123919904232,
0.01979243941605091,
-0.015180881135165691,
0.08111737668514252,
-0.002028184477239847,
-0.037680912762880325,
0.017358342185616493,
-0.07063905149698257,
0.023107530549168587,
-0.00022581653320230544,
-0.029558435082435608,
0.033849723637104034,
0.009026414714753628,
0.03368820622563362,
0.04316822066903114,
0.09134731441736221,
-0.051554638892412186,
0.001345709664747119,
0.010260281153023243,
-0.01890754885971546,
-0.024926021695137024,
0.0014216238632798195,
0.007205127738416195,
-0.0366823635995388,
0.003255631076171994,
0.04241438955068588,
0.015441671013832092,
0.08648991584777832,
-0.04859883710741997,
-0.029145462438464165,
-0.006660642102360725,
0.03994132950901985,
-0.013827556744217873,
0.02011445164680481,
-0.0065733217634260654,
0.01582418568432331,
-0.010219191201031208,
0.026494886726140976,
0.04274692386388779,
-0.03165023401379585,
0.023305360227823257,
-0.03453152999281883,
-0.07556767016649246,
-0.0176977701485157,
-0.03141706809401512,
0.0011557677062228322,
0.03646905720233917,
0.012788655236363411,
0.06874721497297287,
0.05652109533548355,
0.00022321731375996023,
-0.020358676090836525,
0.08300872147083282,
0.04049384966492653,
-0.021739540621638298,
0.08090554177761078,
0.017589325085282326,
-0.007791262120008469,
-0.038474779576063156,
0.01412123627960682,
-0.058234408497810364,
-0.044608455151319504,
0.03379892557859421,
-0.04025087133049965,
-0.054076265543699265,
0.0476544164121151,
-0.036170199513435364,
0.011171669699251652,
-0.046829063445329666,
0.05771619826555252,
0.0055787512101233006,
0.017726436257362366,
-0.005981029476970434,
-0.03230870142579079,
-0.019037391990423203,
-0.04263892024755478,
-0.02241198718547821,
0.03140052407979965,
0.010585902258753777,
-0.025979699566960335,
-0.003134089522063732,
-0.05507499724626541,
0.002583370078355074,
0.03550391271710396,
-0.00982310064136982,
0.017069639638066292,
0.01274384930729866,
-0.028323203325271606,
0.012553158216178417,
-0.03580830246210098,
-0.0273207426071167,
0.04822733253240585,
0.021236654371023178,
-0.047274377197027206,
0.020855773240327835,
0.07391592115163803,
-0.007192013319581747,
-0.0013153451727703214,
0.01705922558903694,
-0.033099930733442307,
-0.047918900847435,
0.05447753146290779,
0.004185870289802551,
-0.05122022703289986,
-0.005651545710861683,
0.06478749215602875
] |
<p>What I want:
I have a rubber rope which is $5m$ in length when not stressed and is able to stretch about $100\%$ (to $10m$ long). I want to accelerate a constant mass horizontally, which has negligible friction. I'd like to have a function that tells me the velocity of the mass dependent on time, so for instance velocity $1 s$ after releasing it.</p>
<p>What I did:
I've done some measurements of forces of the rope when pulling it to different lengths. Of course, when pulling $0cm$ (total length $5m$) I got a force of $0N$. Here is a graph of my results.</p>
<p><img src="http://i.stack.imgur.com/Mok8k.png" alt="http://i.imgur.com/vtEnACQ.png"></p>
<p>$x-axis$: displacement of one end of the rope</p>
<p>$y-axis$: measured force</p>
<p>I was also able to do a regression and found a function which describes how much force I get after I pull a given length.
I name this function $F(s)$ for Force dependent on displacement.
From this, it's easy to get the acceleration function, which is $a(s) = F(s)/m$ with $m = mass$ of the object I want to accelerate.
But now I'm stuck.
I somehow need to get $a(t)$ instead of $a(s)$, thus the acceleration by time, not by length, so I can then integrate that to get $v(t)$.</p>
<p>How do I convert the dependency of the function?</p> | g6627 | [
0.07304295152425766,
-0.02553195133805275,
0.004574873019009829,
-0.04652923345565796,
0.00923844426870346,
-0.017690487205982208,
0.04584794119000435,
-0.03234972059726715,
-0.043015770614147186,
-0.008220959454774857,
-0.021014388650655746,
-0.046052832156419754,
0.024760322645306587,
-0.015962211415171623,
0.05574975535273552,
0.006594739388674498,
0.07677333056926727,
-0.012188301421701908,
0.00041019011405296624,
-0.012721379287540913,
0.007019017823040485,
-0.007741084787994623,
-0.02386130765080452,
-0.038159679621458054,
0.0863710343837738,
-0.027119778096675873,
0.04803772643208504,
0.006032972130924463,
-0.05726107954978943,
0.03000340797007084,
0.005442796740680933,
-0.000011748632459784858,
0.01945149153470993,
-0.01115634385496378,
-0.0013649014290422201,
-0.005309425760060549,
0.026987237855792046,
-0.05758237838745117,
0.03725152835249901,
0.031157830730080605,
-0.02160670980811119,
0.005399853456765413,
0.03033767268061638,
0.0723762959241867,
0.04375186190009117,
-0.06999243795871735,
-0.005132394842803478,
0.014996935613453388,
-0.010982783511281013,
-0.00880272127687931,
-0.01607012003660202,
0.051201291382312775,
-0.02407538704574108,
-0.026492906734347343,
-0.007788999937474728,
0.0455840565264225,
0.04268554970622063,
0.04107923060655594,
-0.02205796353518963,
0.04589148983359337,
-0.02247922495007515,
-0.0872533768415451,
0.02845713309943676,
-0.04613819718360901,
0.0642690658569336,
-0.02526859939098358,
-0.0061368620954453945,
-0.027090447023510933,
-0.04823208227753639,
0.03792978823184967,
-0.006723359692841768,
-0.006299167405813932,
0.03938012570142746,
0.018074525520205498,
-0.040884267538785934,
-0.017646487802267075,
0.025896070525050163,
-0.04037756472826004,
-0.04451884329319,
0.026223106309771538,
0.00515311025083065,
0.09048271924257278,
0.025330999866127968,
0.018091753125190735,
-0.015847641974687576,
-0.04502763971686363,
-0.012336324900388718,
0.0014804970705881715,
-0.006270225625485182,
0.0015656669856980443,
0.03110392577946186,
0.015145995654165745,
0.05974533036351204,
0.07315318286418915,
0.016402041539549828,
-0.06909140944480896,
-0.03216170519590378,
0.06485698372125626,
0.06700944155454636,
0.014748086221516132,
-0.030398519709706306,
-0.004771335516124964,
-0.0007098644855432212,
-0.02694791741669178,
0.029018856585025787,
-0.012538455426692963,
0.01884285733103752,
-0.0006880268338136375,
-0.05144435167312622,
-0.06750410795211792,
0.016125954687595367,
0.013553451746702194,
-0.04704487696290016,
-0.06469231098890305,
-0.038513630628585815,
-0.1016964465379715,
-0.002599150175228715,
0.024534914642572403,
-0.03794369846582413,
0.004937843419611454,
-0.015425032004714012,
-0.0634051114320755,
0.022651419043540955,
0.05160826817154884,
-0.03882642090320587,
-0.06407946348190308,
-0.01623721979558468,
0.05231590196490288,
0.012697195634245872,
-0.032761916518211365,
0.0453326590359211,
-0.03535928949713707,
0.04328914359211922,
0.03656875342130661,
-0.03468003123998642,
0.05527346208691597,
-0.044016387313604355,
0.014550170861184597,
-0.01583130657672882,
0.07554282993078232,
-0.038990892469882965,
-0.02600414678454399,
-0.026251357048749924,
0.03169378265738487,
-0.04118841886520386,
0.0324271135032177,
-0.05008731782436371,
0.0006861492292955518,
0.02853287011384964,
0.007240195292979479,
0.017639035359025,
0.043025434017181396,
-0.07150793820619583,
0.014919635839760303,
0.03238101676106453,
-0.03420776128768921,
0.05368385463953018,
-0.010966891422867775,
-0.007597692776471376,
-0.017136646434664726,
0.025328056886792183,
-0.0010329346405342221,
0.009823407977819443,
-0.011333567090332508,
-0.06885386258363724,
0.03598242998123169,
-0.007150676101446152,
-0.030341070145368576,
-0.004222046118229628,
0.003775753080844879,
-0.01500585488975048,
0.014775899238884449,
0.03818865492939949,
-0.0397406667470932,
-0.025666585192084312,
0.0022532206494361162,
0.028284670785069466,
0.0030481850262731314,
0.007651893887668848,
-0.0051155961118638515,
0.03449162840843201,
-0.009528120048344135,
0.026324428617954254,
-0.025517288595438004,
-0.012945085763931274,
0.015216576866805553,
0.037154585123062134,
0.04468947649002075,
-0.06861874461174011,
-0.010728735476732254,
0.012024875730276108,
0.007088809739798307,
-0.0255444198846817,
-0.01371266320347786,
-0.07413199543952942,
-0.003018365940079093,
-0.0031348918564617634,
-0.07932116091251373,
0.027586814016103745,
0.02852623350918293,
0.011254362761974335,
0.05180716887116432,
0.03308088332414627,
0.04425148293375969,
0.04339984804391861,
-0.07611559331417084,
0.01291630044579506,
-0.04155445098876953,
-0.00005649979357258417,
-0.000018250246284878813,
0.05160576477646828,
0.03662751615047455,
-0.030814075842499733,
-0.015884369611740112,
0.014517570845782757,
-0.03753400593996048,
-0.011219128035008907,
0.05111793801188469,
0.011408847756683826,
-0.005828931927680969,
-0.004377031698822975,
0.01606180891394615,
0.07170127332210541,
0.014300276525318623,
-0.022678274661302567,
-0.027841717004776,
0.029402410611510277,
-0.025677263736724854,
-0.013099810108542442,
-0.029977573081851006,
-0.009578712284564972,
0.028839392587542534,
-0.036822862923145294,
0.025716988369822502,
0.04806290566921234,
0.016625212505459785,
0.00352111435495317,
0.021929800510406494,
0.011802867986261845,
0.03510081768035889,
0.020404502749443054,
-0.010178003460168839,
0.008236080408096313,
-0.06808168441057205,
0.002481152070686221,
-0.08769826591014862,
0.027322813868522644,
0.030735518783330917,
0.038506194949150085,
-0.01247238740324974,
-0.04357273876667023,
0.03595798835158348,
-0.01554696075618267,
0.01016922201961279,
0.021318411454558372,
-0.0015848323237150908,
-0.062471903860569,
0.001288460218347609,
-0.013282212428748608,
-0.05003252997994423,
-0.004455881658941507,
0.02336590550839901,
0.03701568767428398,
0.08046847581863403,
-0.03529050573706627,
0.014806274324655533,
-0.044811878353357315,
-0.05807413160800934,
0.024380294606089592,
-0.007893471047282219,
-0.018676288425922394,
0.010060392320156097,
-0.007562877144664526,
-0.009259017184376717,
-0.004740792326629162,
-0.036276206374168396,
0.0002326253306819126,
-0.002283821813762188,
0.029575685039162636,
0.00453233951702714,
0.03422186151146889,
-0.004468005150556564,
-0.019557679072022438,
0.05841181427240372,
-0.00221074977889657,
-0.02862783893942833,
0.015189369209110737,
0.012089446187019348,
-0.01708398386836052,
0.003217714373022318,
-0.02423446998000145,
0.05498092994093895,
-0.026471422985196114,
0.00029502061079256237,
0.017590831965208054,
0.03874180093407631,
-0.023130076006054878,
-0.011610381305217743,
0.009628567844629288,
-0.0032254871912300587,
-0.04592417925596237,
-0.04616524279117584,
0.016853515058755875,
0.06257139891386032,
-0.020249703899025917,
-0.03170613572001457,
-0.02572384849190712,
-0.06400774419307709,
0.024207837879657745,
0.00904412753880024,
-0.016429465264081955,
0.0235276035964489,
0.04566217213869095,
-0.005868222564458847,
-0.045338861644268036,
-0.04653758928179741,
0.03408512845635414,
-0.01708635315299034,
0.0092410733923316,
0.010337921790778637,
-0.02209531143307686,
-0.18120454251766205,
-0.00815011840313673,
0.015245199203491211,
-0.02142365463078022,
0.0005802235100418329,
0.0024561549071222544,
-0.019947292283177376,
0.0064318422228097916,
-0.014166067354381084,
-0.0035289835650473833,
0.0005903352866880596,
0.03716256842017174,
-0.038280390202999115,
-0.05037670210003853,
-0.012720827013254166,
0.0035793969873338938,
-0.0016144796973094344,
-0.03824485093355179,
-0.003106234362348914,
-0.05919446051120758,
-0.01148636918514967,
-0.05102682486176491,
0.0694996640086174,
-0.02606227435171604,
0.0201107170432806,
-0.021021220833063126,
0.0121286790817976,
0.07093489170074463,
-0.03231097757816315,
-0.013313248753547668,
-0.018621956929564476,
0.011105089448392391,
0.00011091689520981163,
0.03970915824174881,
0.03379131853580475,
0.09595916420221329,
0.002525798510760069,
-0.06398915499448776,
0.011823857203125954,
-0.000654948060400784,
-0.05080647021532059,
-0.009725414216518402,
0.02608778141438961,
0.0165073461830616,
0.005093742161989212,
0.026437899097800255,
0.06632232666015625,
-0.01776832900941372,
-0.006124850362539291,
0.003915122710168362,
-0.06655704975128174,
0.033290278166532516,
-0.030115406960248947,
-0.019808566197752953,
-0.05524759739637375,
0.05826708674430847,
0.025859326124191284,
0.0029407425317913294,
0.05770197883248329,
0.05335497483611107,
0.010830661281943321,
-0.08695577085018158,
0.07510076463222504,
0.020006921142339706,
0.003651822218671441,
-0.02831723727285862,
0.02580132707953453,
0.0306194219738245,
0.004997330717742443,
0.04221516475081444,
-0.02980855666100979,
-0.007888936437666416,
-0.008288711309432983,
0.03392301872372627,
-0.030800221487879753,
0.041281551122665405,
0.010060861706733704,
-0.030955104157328606,
0.01444244384765625,
-0.02989310584962368,
0.01316324807703495,
0.009203093126416206,
0.03450540080666542,
-0.051983047276735306,
0.0339277945458889,
0.02740064077079296,
-0.025389330461621284,
-0.015873393043875694,
0.00924859382212162,
0.0004941425868310034,
-0.051353901624679565,
0.02782421186566353,
-0.008743096143007278,
-0.019489720463752747,
0.00735779432579875,
0.062044087797403336,
-0.024117568507790565,
-0.04692412540316582,
-0.030082380399107933,
0.018747078254818916,
0.03360820189118385,
-0.020000508055090904,
-0.012035021558403969,
-0.006825741846114397,
0.03806658834218979,
0.03960192948579788,
0.013138624839484692,
0.04616531729698181,
-0.005835146643221378,
0.005801078397780657,
0.0738300085067749,
0.017126398161053658,
-0.018063867464661598,
-0.00916585698723793,
0.03182528540492058,
0.03271208330988884,
-0.017164036631584167,
0.05438057333230972,
0.03563409671187401,
0.007989028468728065,
0.06446432322263718,
-0.014483463950455189,
0.040436841547489166,
-0.038160745054483414,
0.023508084937930107,
-0.02198963053524494,
-0.04332737997174263,
-0.012463408522307873,
0.0233596321195364,
-0.07089401036500931,
0.0022918651811778545,
-0.020902900025248528,
-0.05190558359026909,
0.01944621279835701,
0.01251272577792406,
-0.005493997596204281,
-0.0007494104793295264,
0.031361278146505356,
-0.035066790878772736,
-0.04631447419524193,
-0.003833262948319316,
-0.07399445027112961,
-0.014355186372995377,
-0.00861557200551033,
-0.003447751048952341,
-0.022215858101844788,
0.0712525025010109,
0.03272618353366852,
0.03949391096830368,
0.021860478445887566,
-0.006350172217935324,
-0.007253069430589676,
-0.025119634345173836,
0.02278965711593628,
0.03168781101703644,
0.011750316247344017,
-0.006724115461111069,
0.06708546727895737,
-0.010148100554943085,
0.01959819346666336,
-0.014009447768330574,
0.004041192587465048,
-0.07176952809095383,
0.010759655386209488,
0.00034968997351825237,
0.026707356795668602,
-0.02159605547785759,
0.03618569299578667,
0.002200599294155836,
0.02699553593993187,
0.024577118456363678,
-0.025183243677020073,
-0.037850651890039444,
0.014826025813817978,
0.004322956316173077,
0.01301922369748354,
-0.044202715158462524,
0.051334448158741,
0.03300022333860397,
-0.06550045311450958,
0.008557385765016079,
-0.012169444933533669,
0.03945619985461235,
-0.029841555282473564,
0.031755801290273666,
0.04459843784570694,
0.037552230060100555,
-0.03719417005777359,
0.04752971604466438,
0.02056935429573059,
0.06032847613096237,
-0.006070647854357958,
-0.021167347207665443,
-0.051837850362062454,
0.029061920940876007,
0.019927816465497017,
0.02780098281800747,
0.003787905676290393,
0.03370320424437523,
0.053832024335861206,
-0.009994208812713623,
0.053172968327999115,
0.003782837651669979,
0.04578740894794464,
0.03473087400197983,
-0.00693410774692893,
0.0027288924902677536,
-0.05461537837982178,
-0.013258259743452072,
-0.056586381047964096,
-0.056631311774253845,
0.05051513388752937,
-0.044157419353723526,
-0.007580899633467197,
-0.01431252807378769,
0.0496736578643322,
-0.0004915018216706812,
-0.01479413639754057,
-0.06311967223882675,
-0.013891800306737423,
-0.026707323268055916,
0.021794667467474937,
-0.026010582223534584,
-0.0692233145236969,
0.03635093942284584,
0.014902947470545769,
-0.01589827984571457,
0.0011434719199314713,
-0.035203807055950165,
-0.014827102422714233,
0.015931494534015656,
0.0048559014685451984,
-0.04644598811864853,
-0.040539707988500595,
0.03529100492596626,
0.014354594983160496,
0.0004449401458259672,
-0.01983964443206787,
0.027038630098104477,
0.016503334045410156,
-0.041191089898347855,
0.025280745700001717,
0.01670149713754654,
-0.01823035441339016,
-0.05117879807949066,
0.049808599054813385,
0.026425974443554878,
0.009801646694540977,
0.00016678286192473024,
-0.01833239570260048,
0.012161321938037872,
-0.022248703986406326,
0.015428291633725166,
-0.008324963971972466,
0.017400091513991356,
-0.02220672369003296,
-0.03855372965335846,
-0.01040674652904272,
0.022034920752048492,
-0.029508057981729507,
-0.0800616592168808,
-0.00975821539759636,
-0.022631647065281868,
-0.057479195296764374,
-0.03111334703862667,
-0.00016046359087340534,
-0.06072745472192764,
-0.014379085041582584,
-0.0033685103990137577,
-0.06629116833209991,
0.020793665200471878,
-0.02458280883729458,
-0.029252737760543823,
-0.014201203361153603,
-0.056346382945775986,
-0.010537593625485897,
-0.03299686312675476,
0.03468696400523186,
0.03158973902463913,
0.028748681768774986,
0.007847229018807411,
0.08330533653497696,
-0.052516646683216095,
-0.005978004541248083,
-0.033565688878297806,
-0.01755889505147934,
-0.009341168217360973,
0.05791003629565239,
-0.0644046738743782,
-0.058429304510354996,
-0.015738673508167267,
0.01736629754304886,
0.015936624258756638,
0.007587846834212542,
0.03951718658208847,
0.0034833902027457952,
0.001414537662640214,
0.02199893817305565,
-0.015807662159204483,
-0.006134609691798687,
0.02765814960002899,
-0.0070632766000926495,
-0.019463324919342995,
0.03165537863969803,
-0.0022799929138273,
-0.035076893866062164,
0.010865160264074802,
0.04182397574186325,
-0.07767410576343536,
0.0018954755505546927,
0.03272193297743797,
-0.036200739443302155,
0.011732551269233227,
-0.025835607200860977,
0.11670134961605072,
0.0183760654181242,
0.07267610728740692,
0.044644806534051895,
0.04420635476708412,
0.0005232789553701878,
0.0011057087685912848,
-0.03878815099596977,
0.06295769661664963,
-0.06552045047283173,
-0.0315164215862751,
0.024491045624017715,
0.019218718633055687,
-0.04982609674334526,
0.07765673846006393,
0.024096375331282616,
-0.03450430557131767,
-0.016534434631466866,
0.009716803207993507,
-0.013132728636264801,
0.031089870259165764,
0.04016954079270363,
0.008232214488089085,
0.061373092234134674,
0.0029471702873706818,
-0.057090405374765396,
-0.08863063156604767,
0.01009880006313324,
0.036049652844667435,
-0.0021604590583592653,
0.05853942781686783,
0.00007153861952247098,
-0.02192828617990017,
0.042785100638866425,
-0.025557780638337135,
0.017037011682987213,
-0.012271489016711712,
0.0033884288277477026,
0.06397343426942825,
0.006829855497926474,
0.021229587495326996,
-0.018569480627775192,
-0.014796009287238121,
-0.05694829300045967,
0.05199476331472397,
-0.05959063023328781,
0.028547771275043488,
0.01897222362458706,
-0.025213496759533882,
-0.03276917338371277,
0.010598248802125454,
-0.017510835081338882,
-0.003816624404862523,
0.05582636594772339,
-0.018559858202934265,
-0.13898234069347382,
0.06483061611652374,
0.052533116191625595,
-0.012134760618209839,
0.023001356050372124,
-0.03732212260365486,
0.0036449905019253492,
0.007880471646785736,
0.025014681741595268,
0.017814606428146362,
0.047455668449401855,
-0.034224655479192734,
-0.010131261311471462,
-0.02829601615667343,
-0.034450713545084,
0.03692126274108887,
-0.06613854318857193,
-0.0336402952671051,
0.0021922090090811253,
0.019456781446933746,
-0.02803025208413601,
0.02054472267627716,
-0.05690578743815422,
-0.02868514508008957,
0.029762910678982735,
0.038966815918684006,
-0.009705323725938797,
0.008251244202256203,
0.026780782267451286,
-0.041985832154750824,
-0.011943813413381577,
-0.0007360469899140298,
0.02098659612238407,
-0.058380790054798126,
0.020969687029719353,
-0.034434184432029724,
-0.05935797467827797,
-0.03655117005109787,
-0.0528879351913929,
-0.028621407225728035,
0.015943635255098343,
-0.002407096093520522,
0.03805992379784584,
-0.0005419908557087183,
0.022281119599938393,
-0.01630932278931141,
0.004099026322364807,
0.060508452355861664,
-0.04687601327896118,
0.04235398396849632,
-0.052753422409296036,
-0.01746995933353901,
-0.08805818855762482,
0.05929436534643173,
0.05177148059010506,
-0.01698070950806141,
-0.013970466330647469,
0.07549627125263214,
0.03940229490399361,
-0.010000371374189854,
0.05266435444355011,
-0.004268244374543428,
-0.04260031878948212,
0.020285215228796005,
-0.021976668387651443,
-0.034068260341882706,
-0.041085872799158096,
0.05041198432445526,
0.0204205010086298,
0.0099317766726017,
-0.011921991594135761,
0.03785916045308113,
-0.048849917948246,
0.009138405323028564,
-0.0027911837678402662,
-0.025393541902303696,
0.002537332009524107,
0.05846516788005829
] |
<p>In light-front QFT, in the Minkowski space, we define a hypersurface, $\Sigma_+ : x^3+ x^0 = 0 $. How can I write its parametric equations? </p> | g6628 | [
0.00806262344121933,
-0.01589895412325859,
-0.02936309389770031,
-0.030348332598805428,
0.024173492565751076,
-0.020021839067339897,
0.06079036369919777,
-0.009500006213784218,
0.008456787094473839,
-0.07309563457965851,
-0.043167151510715485,
0.004318608902394772,
0.020661378279328346,
0.006655420642346144,
-0.045737430453300476,
0.014691151678562164,
0.07948463410139084,
0.0031997046899050474,
0.0386078841984272,
-0.029024695977568626,
0.0011926452862098813,
-0.0030711041763424873,
0.04027474299073219,
-0.0020001279190182686,
0.048532307147979736,
0.006398413795977831,
0.0118158720433712,
-0.032848816365003586,
0.013695350848138332,
-0.023154059424996376,
0.038001567125320435,
0.06302759051322937,
-0.024068307131528854,
0.024502675980329514,
0.05934722721576691,
-0.01943671517074108,
0.02321837842464447,
-0.0019219688838347793,
0.02393033728003502,
-0.032672490924596786,
-0.006953781004995108,
-0.018024535849690437,
0.03333752974867821,
0.019043752923607826,
0.05358131602406502,
-0.030519772320985794,
-0.026251984760165215,
0.04068991541862488,
0.006165241822600365,
0.011151614598929882,
0.0668507069349289,
0.0993892028927803,
0.034483663737773895,
-0.05089612677693367,
-0.0011110245250165462,
0.04039155691862106,
0.048680998384952545,
-0.06601276248693466,
0.06782619655132294,
0.026148362085223198,
-0.05079007148742676,
-0.0689716637134552,
-0.00898022297769785,
-0.0025673636700958014,
0.07114971429109573,
0.001299165771342814,
0.0006181494682095945,
-0.04017869383096695,
-0.07337283343076706,
0.04194657504558563,
-0.00717553123831749,
0.046746306121349335,
0.03325660899281502,
-0.019779585301876068,
-0.052860718220472336,
0.009340247139334679,
0.0027338259387761354,
0.03419894725084305,
0.03122968040406704,
-0.005509879440069199,
-0.029420940205454826,
0.01557855773717165,
0.018361445516347885,
0.0031526689417660236,
-0.006730864755809307,
-0.020274246111512184,
0.042637232691049576,
-0.025495586916804314,
-0.0015897653065621853,
-0.0561913326382637,
0.0011188380885869265,
0.05609511956572533,
-0.011068519204854965,
-0.021943220868706703,
-0.00111811060924083,
-0.011206884868443012,
0.03091346099972725,
0.00515708839520812,
-0.07402531057596207,
-0.026354679837822914,
-0.020222632214426994,
0.027059778571128845,
0.027805961668491364,
-0.0302924532443285,
-0.017917290329933167,
-0.032339729368686676,
0.022984791547060013,
0.06580476462841034,
0.02841864712536335,
-0.01001499779522419,
-0.04264688119292259,
0.03520844876766205,
-0.02591703087091446,
-0.04694078117609024,
-0.005939477123320103,
-0.010808492079377174,
0.004607573617249727,
-0.039608657360076904,
0.005630129482597113,
0.07409808784723282,
-0.030628537759184837,
-0.006794993299990892,
0.026746591553092003,
0.05269154533743858,
0.00030146545032039285,
0.020031694322824478,
-0.03505752235651016,
0.04200844466686249,
0.05033478885889053,
0.03320372477173805,
0.08539722859859467,
-0.030230209231376648,
0.0032124014105647802,
0.022939695045351982,
-0.015433700755238533,
0.06330537796020508,
-0.029175495728850365,
-0.010499680414795876,
-0.004220239352434874,
0.0502864308655262,
-0.0339764766395092,
-0.02265150286257267,
-0.0006554558640345931,
-0.01516543235629797,
0.031456541270017624,
-0.05521775782108307,
0.0153169771656394,
-0.049042485654354095,
-0.013294062577188015,
0.003161570057272911,
-0.006178415846079588,
0.09688982367515564,
-0.0007205678266473114,
0.03633493930101395,
-0.015037083998322487,
-0.036150459200143814,
0.027846919372677803,
-0.024191049858927727,
-0.058692000806331635,
-0.047221533954143524,
0.05273684486746788,
0.046116773039102554,
0.011902534402906895,
-0.010462755337357521,
-0.04320274293422699,
-0.03628654405474663,
-0.03399696201086044,
-0.016774194315075874,
0.007819379679858685,
-0.07688174396753311,
-0.0372958667576313,
0.024024270474910736,
0.04560646787285805,
0.031028099358081818,
-0.017513079568743706,
0.04412788525223732,
-0.0013790070079267025,
0.019772984087467194,
0.011651943437755108,
0.042629435658454895,
-0.05107331648468971,
-0.03699761629104614,
0.04042118415236473,
-0.031105026602745056,
-0.03678940609097481,
0.006827035918831825,
-0.016612863168120384,
0.031460732221603394,
-0.07205729931592941,
0.037556182593107224,
0.010273397900164127,
0.05472761020064354,
0.04842299222946167,
-0.0163620263338089,
0.05145099014043808,
0.04723072797060013,
0.009931040927767754,
-0.05767953768372536,
0.047633152455091476,
0.03304436430335045,
-0.05622035637497902,
0.032801736146211624,
0.0361456498503685,
-0.004346822388470173,
0.024139070883393288,
0.0020840081851929426,
-0.009282559156417847,
0.010068976320326328,
0.015771053731441498,
0.020652536302804947,
-0.029898228123784065,
-0.04098731651902199,
-0.012884312309324741,
-0.0036437103990465403,
-0.04284775257110596,
-0.004397585988044739,
-0.006729993969202042,
-0.03162249177694321,
-0.04013967514038086,
0.0602714829146862,
-0.02720719203352928,
-0.01661154069006443,
0.015561162494122982,
-0.0081136804074049,
-0.017287665978074074,
-0.0017818959895521402,
-0.006264058873057365,
-0.007128152996301651,
0.04889870434999466,
0.016238732263445854,
-0.04898614436388016,
-0.055017270147800446,
0.015828294679522514,
0.05375489965081215,
0.010071353055536747,
-0.0385872982442379,
-0.00019011822587344795,
0.022996576502919197,
0.03854161873459816,
0.08746128529310226,
0.01606840081512928,
0.03173767775297165,
-0.00311835203319788,
0.020512692630290985,
-0.03911826014518738,
-0.020553333684802055,
-0.047533467411994934,
-0.012087422423064709,
-0.016138100996613503,
0.03020372800529003,
0.05033965781331062,
-0.0368727445602417,
0.023911070078611374,
-0.001439619460143149,
-0.012907280586659908,
-0.0471634604036808,
-0.004510433878749609,
-0.036011721938848495,
-0.106822669506073,
-0.021044597029685974,
0.03003869578242302,
0.057186271995306015,
-0.057535938918590546,
-0.05108899623155594,
-0.027748582884669304,
0.009894625283777714,
0.007485512178391218,
0.004479957744479179,
-0.0031808356288820505,
0.06426872313022614,
0.026900803670287132,
0.04264814034104347,
0.013794055208563805,
0.06030117720365524,
-0.03224354609847069,
-0.04297482594847679,
0.005124712362885475,
-0.037002917379140854,
0.012895029038190842,
-0.007590718101710081,
0.0076059759594500065,
-0.03722278028726578,
-0.02998124249279499,
0.013274392113089561,
0.018087996169924736,
-0.07428694516420364,
0.033012691885232925,
0.06204952299594879,
0.037922680377960205,
-0.012861199676990509,
0.005928080528974533,
0.06220832094550133,
0.0039038704708218575,
0.01087124366313219,
-0.058608584105968475,
0.015532056801021099,
-0.01519683189690113,
-0.043299611657857895,
0.017510103061795235,
0.05395817384123802,
-0.0022228574380278587,
-0.0043482608161866665,
0.04516826570034027,
-0.0006505396449938416,
-0.04029753804206848,
-0.04203571006655693,
-0.0158891249448061,
-0.06964155286550522,
0.025409040972590446,
0.052162982523441315,
-0.026094874367117882,
-0.0029853263404220343,
-0.04256206005811691,
-0.017164601013064384,
0.00034186741686426103,
0.02393966354429722,
0.022397596389055252,
-0.057724595069885254,
0.010777747258543968,
-0.02874191850423813,
-0.04078512638807297,
-0.04123924672603607,
-0.009047252126038074,
0.006386909168213606,
-0.007424251642078161,
-0.021137019619345665,
0.027217227965593338,
0.05568096041679382,
-0.003947297111153603,
0.017021600157022476,
0.040126603096723557,
0.02639150433242321,
0.015421302057802677,
-0.015624462626874447,
0.07398080080747604,
0.08446262776851654,
0.022484809160232544,
0.025712642818689346,
0.018531832844018936,
-0.05044462904334068,
-0.017860224470496178,
-0.017316732555627823,
-0.06487409770488739,
-0.0035511262249201536,
-0.020890789106488228,
-0.06642251461744308,
0.03413153439760208,
0.017514867708086967,
0.0012077316641807556,
0.028453636914491653,
-0.0455826111137867,
0.03184328228235245,
-0.018624693155288696,
-0.05830657109618187,
0.025912510231137276,
0.02822628803551197,
0.00973169319331646,
0.009220000356435776,
0.05993134155869484,
-0.029812095686793327,
0.005788230337202549,
-0.06842014938592911,
-0.01255231723189354,
0.005180467385798693,
0.01784248650074005,
-0.05795075371861458,
0.016668379306793213,
0.005238477140665054,
-0.04895058646798134,
0.02324651926755905,
0.07519596070051193,
0.0007103159441612661,
0.054793622344732285,
0.03176112100481987,
-0.06208363547921181,
-0.10811875760555267,
-0.03050816059112549,
-0.082688108086586,
-0.03446933627128601,
-0.004321087151765823,
0.0516677126288414,
0.03459634259343147,
0.00894508883357048,
-0.0016778492135927081,
0.024341801181435585,
0.058132488280534744,
-0.06465666741132736,
-0.04394398629665375,
0.08305880427360535,
0.034508176147937775,
-0.022077323868870735,
0.03484170883893967,
-0.07032587379217148,
-0.04388072341680527,
-0.027091780677437782,
-0.017093785107135773,
0.052057813853025436,
-0.06902702897787094,
-0.06232745200395584,
0.03277188912034035,
0.022679785266518593,
0.038976479321718216,
0.07077671587467194,
0.015529602766036987,
-0.039297327399253845,
-0.0949254184961319,
-0.03882676735520363,
-0.04924767091870308,
-0.008844807744026184,
0.0015468396013602614,
0.05232110619544983,
-0.011418106965720654,
0.03446699678897858,
-0.03298176825046539,
0.03439752012491226,
0.019791841506958008,
0.021398140117526054,
-0.024414245039224625,
-0.011043279431760311,
-0.049960099160671234,
0.03421904519200325,
0.02437702566385269,
-0.0055367592722177505,
-0.017105506733059883,
0.05634644627571106,
0.006928696762770414,
0.07485820353031158,
-0.043233152478933334,
-0.0021116079296916723,
-0.014685030095279217,
0.008747304789721966,
0.020483290776610374,
0.027869289740920067,
0.09709015488624573,
0.012460571713745594,
-0.014924773015081882,
-0.07439552247524261,
-0.020293351262807846,
-0.008396477438509464,
0.022676818072795868,
0.0007785050547681749,
0.026122132316231728,
0.02914770320057869,
-0.06061593070626259,
-0.017112119123339653,
0.02715013548731804,
0.02844097651541233,
-0.04931142181158066,
0.016334302723407745,
-0.011460569687187672,
-0.00016392483667004853,
0.012385661713778973,
-0.03852067515254021,
-0.0015886790351942182,
-0.014693853445351124,
0.0477270632982254,
-0.07230746746063232,
-0.013251163065433502,
0.08181741833686829,
-0.020762771368026733,
0.00032428017584607005,
-0.06717357039451599,
0.07215180993080139,
0.005648770369589329,
0.04552750289440155,
0.006471122149378061,
-0.11215119808912277,
0.02858976274728775,
-0.01983823999762535,
0.004071212839335203,
0.04790692776441574,
0.018769660964608192,
-0.0026270542293787003,
-0.03660590946674347,
-0.08040619641542435,
0.042157020419836044,
0.01368745043873787,
-0.0022340393625199795,
-0.04735832288861275,
-0.022293314337730408,
0.03229924291372299,
0.044713012874126434,
-0.011935173533856869,
-0.03339782729744911,
-0.0007500117644667625,
-0.00922383926808834,
-0.009140641428530216,
-0.017704756930470467,
-0.0045621455647051334,
-0.04372905567288399,
-0.0354391373693943,
0.04839135706424713,
-0.017088379710912704,
0.02762329764664173,
-0.018033131957054138,
0.03417111933231354,
0.0368986576795578,
0.014124879613518715,
0.021799927577376366,
0.019639519974589348,
-0.03079627826809883,
0.034054696559906006,
0.08064405620098114,
-0.014686175622045994,
0.012135614641010761,
0.020156370475888252,
-0.002985498635098338,
0.010116745717823505,
0.014774217270314693,
0.05660475417971611,
0.045823488384485245,
-0.009617315605282784,
0.012255295179784298,
-0.001364204566925764,
0.012951396405696869,
0.022952266037464142,
-0.002577138366177678,
-0.026153117418289185,
-0.015621255151927471,
-0.026064597070217133,
0.049362678080797195,
-0.0034159848000854254,
-0.018553411588072777,
0.016343824565410614,
0.05359730124473572,
0.04230199009180069,
-0.057639818638563156,
-0.10262582451105118,
-0.0030440993141382933,
0.02047639526426792,
-0.037909675389528275,
0.02506462298333645,
0.037437766790390015,
-0.018147233873605728,
0.06411635130643845,
-0.0006734902272000909,
0.03281662240624428,
0.037634529173374176,
-0.004829321522265673,
0.0008913038764148951,
-0.06163204088807106,
-0.034215107560157776,
0.006138464901596308,
0.0635472983121872,
-0.0011027350556105375,
0.005834190174937248,
-0.023364229127764702,
0.06372560560703278,
-0.004473322536796331,
-0.04828547313809395,
0.014750339090824127,
0.0132112642750144,
-0.00789481122046709,
0.004959161393344402,
0.012712976895272732,
0.0045594885013997555,
-0.026577632874250412,
-0.06654960662126541,
-0.018391968682408333,
-0.06260069459676743,
0.00911040510982275,
-0.06939514726400375,
0.016750013455748558,
-0.046062957495450974,
-0.036523547023534775,
-0.04509812593460083,
-0.014548278413712978,
-0.0239349864423275,
0.01512649655342102,
-0.05731578916311264,
-0.037504978477954865,
-0.006830642465502024,
-0.016841068863868713,
0.014054808765649796,
-0.004416583105921745,
0.04511597380042076,
0.033790212124586105,
-0.015655599534511566,
-0.02261558175086975,
0.028815442696213722,
-0.04735390841960907,
0.04510548338294029,
-0.04243464395403862,
-0.044385623186826706,
-0.021885734051465988,
0.02222190797328949,
0.014112328179180622,
-0.001803751103579998,
0.016811290755867958,
-0.005719625391066074,
-0.009101798757910728,
0.016366569325327873,
-0.05055714398622513,
-0.010622922331094742,
0.03275328874588013,
0.04188816249370575,
0.04206434637308121,
0.05113593116402626,
-0.026534579694271088,
-0.04234962910413742,
-0.027021462097764015,
-0.0038567266892641783,
-0.02466275542974472,
-0.026969315484166145,
0.07231344282627106,
-0.020501427352428436,
-0.01947505958378315,
0.005354136694222689,
0.02615002542734146,
-0.03622324392199516,
-0.003590924432501197,
0.020705796778202057,
-0.017784956842660904,
0.03483276441693306,
-0.010434995405375957,
-0.01602366752922535,
0.03291471302509308,
0.03834180161356926,
0.017385907471179962,
-0.050104059278964996,
0.024137435480952263,
-0.01719793677330017,
0.029045619070529938,
-0.023002667352557182,
0.01625124365091324,
0.022875389084219933,
-0.008599812164902687,
0.022876325994729996,
-0.017435206100344658,
0.0026742529589682817,
0.04494982212781906,
-0.02709389291703701,
-0.05207474157214165,
-0.015047550201416016,
-0.00039461199776269495,
-0.02376856468617916,
-0.005625483114272356,
-0.00802688393741846,
-0.004111570306122303,
0.04766480252146721,
0.01876787282526493,
0.07267875969409943,
0.030244130641222,
-0.06801387667655945,
-0.013623080216348171,
-0.03579016402363777,
0.011812962591648102,
-0.01416870392858982,
-0.04538107290863991,
-0.001515703508630395,
0.03688156232237816,
-0.017969926819205284,
-0.012914026156067848,
0.00824452843517065,
-0.00034235461498610675,
0.044266022741794586,
-0.01624496467411518,
-0.023347128182649612,
-0.025752156972885132,
-0.05377866327762604,
0.021798748522996902,
0.019450560212135315,
0.006885741371661425,
-0.0060426052659749985,
-0.011363758705556393,
0.019353609532117844,
0.03215555474162102,
0.006342180538922548,
0.017063939943909645,
0.02446931041777134,
-0.04874884709715843,
-0.03478488698601723,
0.00036086104228161275,
0.07340483367443085,
-0.015626920387148857,
0.006779080722481012,
-0.02110418863594532,
0.12604370713233948,
0.010613544844090939,
-0.021915411576628685,
0.012002915143966675,
0.005309866741299629,
-0.0641796737909317,
-0.0625917837023735,
0.01708034798502922,
-0.03174728900194168,
0.010457595810294151,
-0.0011871680617332458,
0.016584821045398712,
0.027912957593798637,
0.01675304025411606,
0.0008522638236172497,
-0.017303774133324623,
-0.038657572120428085,
-0.0014485581777989864,
0.03141096234321594,
-0.023439927026629448,
0.03798118606209755,
-0.009545991197228432,
-0.0026233443059027195,
-0.017515283077955246,
-0.033412788063287735,
-0.0008679099264554679,
-0.006509173195809126,
0.0008466439903713763,
-0.022518273442983627,
-0.02137473039329052,
-0.0195666141808033,
-0.043199725449085236,
0.001563415164127946,
0.03483377769589424,
0.02746577374637127,
-0.010976514779031277,
0.00568312918767333,
0.07382592558860779,
-0.025876732543110847,
-0.038281455636024475,
0.01961815170943737,
-0.0039046392776072025,
-0.037789035588502884,
0.00491344602778554,
0.024111319333314896,
-0.03171321004629135,
-0.09588494896888733,
-0.006275085732340813,
-0.00923324003815651,
-0.03550112247467041,
-0.03758476674556732,
0.02642347663640976,
0.050402261316776276,
0.011863292194902897,
-0.009312854148447514,
-0.021202532574534416,
0.043560322374105453,
0.01084089931100607,
0.033272385597229004,
-0.055263400077819824,
-0.019571008160710335,
0.06991551071405411,
0.04008406400680542,
-0.04610472917556763,
-0.0740351602435112,
-0.002301363041624427,
-0.0200545284897089,
0.07050713896751404,
-0.017465269193053246,
0.03496449813246727,
-0.008421591483056545,
0.021887673065066338,
-0.024516796693205833,
0.02150237001478672,
0.016567254438996315,
-0.02716444805264473,
0.03223973512649536,
-0.011734655126929283,
-0.0027674150187522173,
0.01715359091758728,
-0.018810534849762917,
0.017510881647467613,
-0.05338887497782707,
-0.016475925222039223,
-0.03966163471341133,
0.01956961862742901,
0.027716293931007385,
-0.042539916932582855,
-0.05246580019593239,
-0.00860625971108675,
-0.002647851826623082
] |
<p>How much energy is derived from the full process from hydrogen-1 fused into helium-4? Including all the sub-reactions (H1 into Deuterium, etc).</p> | g6629 | [
0.017369426786899567,
0.008456752635538578,
0.0036709634587168694,
0.009727937169373035,
-0.04710770398378372,
-0.02370184287428856,
0.00773618184030056,
0.14033234119415283,
-0.036421287804841995,
-0.05493008717894554,
-0.0384180061519146,
-0.013021741062402725,
-0.03697224706411362,
0.02762019634246826,
0.01074194721877575,
-0.019634034484624863,
0.007877997122704983,
-0.03886905685067177,
-0.045973461121320724,
0.040199942886829376,
-0.04473291337490082,
-0.023908067494630814,
-0.046432774513959885,
-0.01972433738410473,
0.018827591091394424,
-0.040309131145477295,
0.006742250174283981,
-0.044869937002658844,
-0.0689464583992958,
-0.042667634785175323,
-0.029804032295942307,
0.012057559564709663,
0.0901976227760315,
-0.02868657559156418,
-0.05352618917822838,
0.035619866102933884,
0.038095466792583466,
-0.05362798273563385,
0.04391331225633621,
-0.03173883259296417,
-0.028500871732831,
0.014974774792790413,
-0.02173120528459549,
0.03202071413397789,
-0.019211435690522194,
0.013781149871647358,
0.03359666466712952,
-0.015162854455411434,
-0.0007408857927657664,
0.019093558192253113,
0.025941910222172737,
0.057703256607055664,
-0.01965772733092308,
0.007418008986860514,
0.02452908828854561,
0.03395663946866989,
-0.012611497193574905,
-0.0133829889819026,
0.04876689985394478,
0.04328031837940216,
0.02240077219903469,
-0.026738345623016357,
0.031550467014312744,
0.02838079072535038,
0.07798407226800919,
-0.0056827133521437645,
0.026206351816654205,
0.0003050594823434949,
0.03206838667392731,
0.031750425696372986,
0.002287744777277112,
-0.004848142620176077,
0.013952058739960194,
0.07647121697664261,
-0.05455414205789566,
-0.031950950622558594,
0.06041957065463066,
-0.015614709816873074,
-0.02214186079800129,
0.005847469437867403,
0.017570096999406815,
0.0067055136896669865,
0.021408744156360626,
0.011028781533241272,
0.05204027146100998,
-0.021804388612508774,
-0.0342618003487587,
0.0007740061264485121,
-0.08993788808584213,
0.0006905037444084883,
0.015317501500248909,
0.05438302084803581,
-0.002919647376984358,
-0.051861826330423355,
-0.02691354788839817,
0.002227444900199771,
-0.025166189298033714,
0.01811269298195839,
0.010870244354009628,
-0.05931098386645317,
0.015999330207705498,
-0.03042360208928585,
0.035920124500989914,
-0.0677461177110672,
0.021492788568139076,
0.022508280351758003,
-0.00911009032279253,
-0.054656170308589935,
0.023119846358895302,
0.026084866374731064,
0.022168627008795738,
0.006111700087785721,
-0.06006647273898125,
-0.00563359959051013,
0.00019248233002144843,
0.01274261437356472,
0.01587195321917534,
-0.0009887446649372578,
-0.032491087913513184,
0.02312290482223034,
0.0718354880809784,
0.031249912455677986,
0.009075077250599861,
-0.01055523008108139,
-0.049087490886449814,
-0.020867057144641876,
-0.08773493021726608,
0.05890003964304924,
-0.02322487346827984,
-0.021286850795149803,
-0.009863856248557568,
-0.06637495011091232,
0.020883655175566673,
-0.021643536165356636,
0.05156448483467102,
0.02049037627875805,
0.005864802747964859,
0.02091362327337265,
-0.01942252740263939,
-0.01822672411799431,
0.020332837477326393,
-0.0009154019644483924,
-0.007810573559254408,
-0.02930467016994953,
-0.03218616545200348,
0.010332486592233181,
-0.02056238241493702,
0.005742474924772978,
-0.028609195724129677,
0.03862978518009186,
-0.022863775491714478,
-0.0380646251142025,
0.053889766335487366,
-0.012744511477649212,
-0.0012940367450937629,
0.015215456485748291,
0.04514559730887413,
-0.05421283096075058,
-0.013975010253489017,
0.0663989931344986,
-0.006403232924640179,
0.004404224921017885,
0.04407934471964836,
-0.03297307714819908,
0.02660330943763256,
-0.0033855868969112635,
0.002660186728462577,
-0.04899593070149422,
0.01775524951517582,
-0.028321539983153343,
0.005876678973436356,
-0.027394209057092667,
0.03665606677532196,
-0.017799029126763344,
-0.05635921284556389,
0.024709494784474373,
0.07453672587871552,
-0.041617754846811295,
-0.043421708047389984,
0.029058480635285378,
0.06906270235776901,
-0.025663169100880623,
0.04580581560730934,
0.006098111625760794,
0.032948195934295654,
0.01672511361539364,
0.008417429402470589,
-0.011644423007965088,
-0.028440624475479126,
0.013078773394227028,
0.009924737736582756,
0.023078439757227898,
0.0061279600486159325,
-0.033602502197027206,
0.015326841734349728,
-0.012032154947519302,
-0.007975299842655659,
-0.028538933023810387,
-0.01924070715904236,
0.004584530834108591,
-0.017083358019590378,
0.0006345512811094522,
0.018000712618231773,
0.008648157119750977,
0.0734730139374733,
0.014996838755905628,
0.03473776951432228,
0.013494743034243584,
0.01865307427942753,
-0.002527476055547595,
-0.06328122317790985,
0.024159740656614304,
-0.004950712434947491,
-0.023698927834630013,
0.024280168116092682,
-0.011072231456637383,
0.01854821667075157,
0.011819504201412201,
0.02193645015358925,
0.01718277670443058,
-0.03893711045384407,
0.08017538487911224,
-0.01976003125309944,
-0.007877099327743053,
0.013182902708649635,
0.018887478858232498,
0.025209922343492508,
-0.01620110124349594,
-0.02859385311603546,
-0.03970595821738243,
0.006647969130426645,
0.07600270956754684,
-0.04172021523118019,
-0.033662211149930954,
-0.010062179528176785,
0.05545184761285782,
-0.010328018106520176,
-0.0384640209376812,
-0.006950729992240667,
0.0070006451569497585,
-0.008897879160940647,
-0.03404960036277771,
0.0054767015390098095,
-0.03676208481192589,
0.024291807785630226,
-0.09184147417545319,
0.024793153628706932,
-0.0009707014542073011,
-0.03203548118472099,
-0.048657841980457306,
-0.0008663049666211009,
0.005812378600239754,
-0.0020026525016874075,
0.028394505381584167,
-0.008777141571044922,
-0.01383030042052269,
-0.05000052973628044,
0.04149497300386429,
-0.005732596851885319,
-0.017904575914144516,
-0.0022690962068736553,
-0.06804414093494415,
0.0022510578855872154,
0.010283207520842552,
-0.0601138100028038,
-0.06369427591562271,
0.0008445233106613159,
-0.06671132147312164,
0.05003323778510094,
-0.0320778451859951,
-0.0674482211470604,
0.08594046533107758,
-0.015917547047138214,
0.040037982165813446,
-0.03432409092783928,
-0.021949756890535355,
0.02650400996208191,
-0.019003313034772873,
0.026061829179525375,
0.006374737713485956,
-0.005144455470144749,
0.010113908909261227,
-0.040341854095458984,
0.024499693885445595,
-0.012774988077580929,
-0.03461253643035889,
-0.016174614429473877,
0.02417539432644844,
0.009111572057008743,
0.03793610259890556,
-0.041685350239276886,
-0.061835892498493195,
0.019027872011065483,
-0.036242447793483734,
0.039579227566719055,
0.000566762057133019,
0.07654857635498047,
0.007664057891815901,
0.009010392241179943,
-0.045817725360393524,
-0.030308786779642105,
-0.03549377992749214,
-0.03589329496026039,
0.03066420927643776,
0.010000807233154774,
-0.018106941133737564,
-0.03139225021004677,
-0.05843496695160866,
0.004733541049063206,
-0.01385023444890976,
0.008124793879687786,
-0.004783398937433958,
0.07101468741893768,
0.04038012772798538,
-0.013363059610128403,
-0.04707818478345871,
0.05193457379937172,
0.012526948004961014,
0.059126269072294235,
-0.06390859186649323,
-0.013010633178055286,
-0.03026374988257885,
-0.029710158705711365,
-0.05323207005858421,
0.018623560667037964,
-0.003236817428842187,
0.026202013716101646,
-0.04030434414744377,
0.02253824658691883,
0.016793332993984222,
0.004460773430764675,
-0.014111427590250969,
-0.027938593178987503,
0.044593118131160736,
0.008216110058128834,
-0.050405967980623245,
-0.02472376637160778,
-0.04473981261253357,
0.04629073292016983,
0.043739207088947296,
-0.021467404440045357,
-0.006958942394703627,
0.05630524456501007,
0.0029230043292045593,
0.0996842160820961,
-0.06049886345863342,
-0.053786538541316986,
0.019888300448656082,
-0.009770819917321205,
0.0016903566429391503,
0.04146965593099594,
-0.015973500907421112,
-0.009621740318834782,
0.022912228479981422,
0.05164559185504913,
0.07036188244819641,
0.025377120822668076,
0.06040025129914284,
-0.016032328829169273,
0.039218414574861526,
-0.02065228298306465,
-0.04864460229873657,
0.031780343502759933,
-0.003469181712716818,
-0.05043798312544823,
-0.047229766845703125,
-0.03429437056183815,
0.0475601851940155,
-0.014876291155815125,
-0.005744043737649918,
-0.04820583015680313,
-0.0280899740755558,
0.034862156957387924,
-0.002120138378813863,
-0.046231865882873535,
0.024849507957696915,
0.007728101219981909,
0.005317118484526873,
-0.013771596364676952,
0.03758438304066658,
0.07351216673851013,
0.026912637054920197,
-0.011468681506812572,
0.03496706485748291,
-0.01635400578379631,
-0.03693670406937599,
-0.03611963987350464,
0.01734425500035286,
0.007251218426972628,
-0.026819081977009773,
0.025684090331196785,
-0.01319020614027977,
0.01491723395884037,
0.03388523310422897,
-0.04018843173980713,
-0.02797647938132286,
0.04820137098431587,
-0.05648166313767433,
-0.020424995571374893,
0.0015866924077272415,
-0.008901234716176987,
-0.04714740067720413,
0.04213637113571167,
-0.010428523644804955,
0.049536701291799545,
0.03690235689282417,
-0.013709789142012596,
-0.041202113032341,
0.06981759518384933,
0.008773978799581528,
0.07538390159606934,
0.042430054396390915,
-0.0018406682647764683,
0.028971843421459198,
0.03572172299027443,
-0.03908197209239006,
-0.00023853752645663917,
-0.03008202277123928,
0.03802623227238655,
-0.03300728648900986,
0.013219520449638367,
0.01631033606827259,
0.0223002377897501,
0.04946056380867958,
-0.009926523081958294,
-0.0022066812962293625,
0.04569929838180542,
0.001299712690524757,
-0.002400672994554043,
0.007749574258923531,
0.030379902571439743,
-0.011949634179472923,
0.03801727667450905,
-0.029607342556118965,
-0.05568888410925865,
0.040267761796712875,
0.07040323317050934,
0.060630131512880325,
-0.013936029747128487,
0.013525094836950302,
0.06867051124572754,
0.06792571395635605,
0.004336499609053135,
0.029087398201227188,
0.018453439697623253,
-0.02067878097295761,
-0.018903417512774467,
-0.06885246932506561,
-0.04074840992689133,
-0.0895945280790329,
-0.05797388032078743,
-0.004513447172939777,
-0.05368105694651604,
0.001795572112314403,
0.028214169666171074,
0.018729640170931816,
-0.049155041575431824,
0.027229053899645805,
-0.002256406005471945,
0.029152218252420425,
-0.04498511180281639,
-0.020012307912111282,
0.02561928704380989,
0.023874511942267418,
0.07659418135881424,
-0.015801891684532166,
-0.04254386946558952,
-0.0022464690264314413,
-0.005771744530647993,
0.09394626319408417,
0.032035741955041885,
-0.013131660409271717,
-0.018924124538898468,
-0.044120464473962784,
-0.022413451224565506,
0.05109803378582001,
-0.0307189729064703,
-0.01895930804312229,
0.019624490290880203,
-0.013188453391194344,
0.029109714552760124,
0.031507156789302826,
-0.011953240260481834,
0.0012585649965330958,
-0.02209801971912384,
0.052371036261320114,
-0.028557268902659416,
-0.039798617362976074,
-0.002470859559252858,
0.025093423202633858,
-0.08048497140407562,
0.03175079822540283,
0.03115164116024971,
-0.036887090653181076,
-0.002672400791198015,
0.04236971586942673,
0.008990439586341381,
-0.04721204563975334,
-0.013922099955379963,
0.08127512782812119,
-0.025483477860689163,
0.0031441275496035814,
-0.08392602205276489,
-0.024055734276771545,
0.0019792011007666588,
0.01989397592842579,
0.0379730723798275,
0.01392672024667263,
-0.010450351051986217,
-0.03452198952436447,
0.0134871331974864,
0.029910778626799583,
-0.026550646871328354,
0.0399300679564476,
0.0015520498855039477,
-0.011543593369424343,
-0.018089737743139267,
0.06185058504343033,
0.013839245773851871,
-0.004026231821626425,
0.06332888454198837,
-0.001711751101538539,
0.09491895884275436,
-0.019207924604415894,
0.007707878481596708,
0.009338990785181522,
-0.05180282145738602,
0.004153670743107796,
0.00011660849850159138,
0.036430198699235916,
0.06402336806058884,
0.008409354835748672,
0.006268423516303301,
0.0291594285517931,
0.012576252222061157,
0.03435315936803818,
-0.052705153822898865,
-0.01963319070637226,
0.036721937358379364,
0.01402098685503006,
0.016599079594016075,
0.026895079761743546,
-0.018964121118187904,
0.07667595893144608,
-0.08107013255357742,
-0.0033673064317554235,
-0.019127236679196358,
0.026582222431898117,
-0.04764534905552864,
0.001253961818292737,
0.022839557379484177,
-0.05717115104198456,
0.025552546605467796,
-0.04153142124414444,
0.0005642236210405827,
0.0504903681576252,
0.030559223145246506,
-0.0397331602871418,
-0.010224240832030773,
0.02301502600312233,
-0.0002982054720632732,
-0.02552109956741333,
0.003371104132384062,
0.07071436196565628,
0.01421944797039032,
-0.02709650993347168,
0.024543005973100662,
-0.09488722681999207,
-0.028189200907945633,
0.057573918253183365,
0.033036570996046066,
-0.06355959177017212,
-0.04056553542613983,
-0.06527568399906158,
-0.007888294756412506,
-0.025402268394827843,
0.05678217113018036,
-0.003372112289071083,
-0.059022098779678345,
0.005919961258769035,
0.023775683715939522,
-0.07797104865312576,
0.0260014608502388,
-0.005430278833955526,
-0.0360952727496624,
0.03415790572762489,
0.006031269673258066,
0.02344268187880516,
-0.03147100657224655,
0.03213037922978401,
-0.013573229312896729,
0.05230360105633736,
-0.013198236003518105,
-0.01118736807256937,
0.01742992363870144,
0.0008232223335653543,
0.02381463721394539,
-0.027747182175517082,
-0.05095912516117096,
-0.014078568667173386,
-0.025149259716272354,
-0.046958521008491516,
0.0051813796162605286,
-0.05032075569033623,
0.01790660433471203,
-0.019786255434155464,
0.02334975078701973,
0.01949816197156906,
-0.03621520847082138,
-0.006950067356228828,
0.020219916477799416,
-0.024286406114697456,
-0.028424080461263657,
-0.01275878306478262,
-0.040309637784957886,
-0.05606311559677124,
0.04499039426445961,
-0.016917474567890167,
0.04751044884324074,
-0.01111327763646841,
0.01757659763097763,
-0.06528868526220322,
0.05989859998226166,
-0.006353079341351986,
0.06256841123104095,
-0.0014092394849285483,
-0.0445978008210659,
0.04266249015927315,
0.02702517621219158,
0.02103092148900032,
-0.00824828166514635,
-0.022810354828834534,
-0.0038839727640151978,
0.0748218297958374,
0.015233046375215054,
0.03265035152435303,
0.004748528357595205,
-0.027941618114709854,
-0.029734397307038307,
0.039583008736371994,
0.016144679859280586,
-0.013288959860801697,
0.03473078832030296,
0.007188618648797274,
-0.042525097727775574,
-0.013445165008306503,
-0.009469729848206043,
-0.04321423918008804,
-0.016303610056638718,
-0.016450973227620125,
-0.06657276302576065,
-0.009525535628199577,
-0.009022128768265247,
0.01837410032749176,
-0.06810658425092697,
0.05339282006025314,
-0.0651063397526741,
0.019215404987335205,
-0.005198545753955841,
0.000012056798368575983,
0.04472614824771881,
0.00442133005708456,
-0.021158643066883087,
-0.017119279131293297,
0.034019507467746735,
-0.01550687849521637,
0.005682983435690403,
0.01243226695805788,
0.04431625455617905,
-0.03926114737987518,
0.02963990718126297,
0.021152369678020477,
-0.043082691729068756,
-0.00858462043106556,
-0.020806942135095596,
-0.0067704650573432446,
0.05744698643684387,
-0.001251278561539948,
0.0008118125260807574,
-0.028559666126966476,
-0.11021675914525986,
0.06355080008506775,
0.008036470040678978,
0.02918080985546112,
-0.036509234458208084,
-0.025843564420938492,
-0.045178864151239395,
-0.028523899614810944,
0.0350462906062603,
0.05648304149508476,
-0.04944106936454773,
0.020741509273648262,
0.03846634179353714,
-0.014171126298606396,
-0.0005952041829004884,
0.04315200820565224,
0.06170864403247833,
-0.04902103543281555,
-0.021583445370197296,
0.03224242478609085,
0.030939511954784393,
0.04885300248861313,
0.0013183996779844165,
-0.004001106135547161,
0.022998198866844177,
0.043333519250154495,
0.0534023642539978,
-0.00005900579708395526,
0.036878734827041626,
0.002463016426190734,
0.059217583388090134,
0.07397560030221939,
-0.029822710901498795,
-0.04582321271300316,
0.019649872556328773,
0.0008428452420048416,
-0.05177071690559387,
-0.034522030502557755,
0.047514062374830246,
0.043176084756851196,
0.07541880011558533,
-0.0079251229763031,
-0.03372678905725479,
-0.026103250682353973,
-0.009034295566380024,
-0.0016686591552570462,
-0.0008900851244106889,
-0.0456836111843586,
0.0018973553087562323,
-0.01087196171283722,
-0.01893959753215313,
-0.01171594113111496,
0.021434592083096504,
-0.018152233213186264,
-0.0031290159095078707,
-0.06677266210317612,
0.053425684571266174,
-0.03820287808775902,
0.014617614448070526,
-0.009256557561457157,
-0.04940987750887871,
-0.056623753160238266,
0.029482567682862282,
-0.016965016722679138,
0.013886176981031895,
-0.002803258830681443,
-0.037565283477306366,
0.06795292347669601,
0.0737515389919281,
-0.009162889793515205,
0.0148843452334404,
-0.036137718707323074,
0.04401939734816551,
-0.02568872831761837,
0.03910829871892929,
-0.08897001296281815,
-0.07460061460733414,
-0.0033034502994269133,
0.011717146262526512,
0.004045776091516018,
-0.0015534745762124658,
0.015091726556420326,
-0.005061287898570299,
-0.01826067827641964,
-0.024400047957897186,
-0.0012084243353456259,
0.00021599579486064613,
0.004269985016435385
] |
<p>In a typical photon experiment the photon is depicted as moving across the page, say from right to left.
Suppose we were actually able to witness such an experiment, from the side (to position of reader to a page).
If the photon is actually moving from left to right can I, standing at 90 degrees to the motion, see the photon? </p> | g6630 | [
-0.025103526189923286,
0.05731744319200516,
0.024611851200461388,
-0.00684794457629323,
0.02247682400047779,
0.0006682834937237203,
0.04745958000421524,
0.06501740217208862,
0.012828840874135494,
0.018441077321767807,
0.03980053588747978,
0.016896028071641922,
0.01887531951069832,
0.008291839621961117,
0.0024194070138037205,
-0.06016342714428902,
0.09007089585065842,
-0.03772246465086937,
-0.029828345403075218,
0.010039674118161201,
-0.03469851240515709,
0.061223383992910385,
-0.05810665339231491,
0.018530230969190598,
-0.024157004430890083,
-0.006590722594410181,
-0.04310169443488121,
-0.039232030510902405,
-0.05987995117902756,
-0.006956515833735466,
-0.019416680559515953,
-0.023534409701824188,
0.0029440713115036488,
0.026009652763605118,
0.013703815639019012,
-0.020612062886357307,
0.03148501366376877,
-0.0022467069793492556,
-0.0025618874933570623,
0.011368917301297188,
-0.016856081783771515,
0.0031930427066981792,
-0.011595233343541622,
-0.030109180137515068,
0.04450438171625137,
0.0393035002052784,
0.043659426271915436,
0.0347638800740242,
0.02269011177122593,
-0.025043785572052002,
-0.03219608590006828,
-0.014393344521522522,
-0.019252916797995567,
0.047592416405677795,
0.06417740136384964,
0.010661760345101357,
0.0042674909345805645,
-0.000893728865776211,
0.09710915386676788,
0.019477928057312965,
-0.0003373789368197322,
0.0004922744701616466,
-0.007663094438612461,
-0.05318044498562813,
0.057565271854400635,
0.01380984764546156,
-0.07901941239833832,
0.0030295327305793762,
-0.04482610151171684,
-0.015085212886333466,
0.02181030996143818,
0.06456352025270462,
-0.0561557412147522,
0.023086855188012123,
0.039347197860479355,
-0.010763694532215595,
0.0095731932669878,
-0.04771875962615013,
-0.016803303733468056,
0.039402883499860764,
-0.011763723567128181,
-0.0557950921356678,
-0.00205306732095778,
0.019745998084545135,
0.12131547182798386,
0.006146652158349752,
-0.029192950576543808,
-0.005924188997596502,
-0.02153564989566803,
-0.0013960166834294796,
0.05850335955619812,
-0.010780510492622852,
0.08791124075651169,
0.08214373886585236,
-0.0030472418293356895,
-0.035893455147743225,
-0.03426940739154816,
0.05897831916809082,
-0.012777958996593952,
0.006871515419334173,
-0.04964671656489372,
0.03718854486942291,
-0.004681704565882683,
0.044735655188560486,
-0.036784276366233826,
0.011449321173131466,
0.024365868419408798,
-0.042654506862163544,
-0.007465126924216747,
-0.0733032375574112,
-0.029882512986660004,
-0.04091477021574974,
-0.05508052930235863,
-0.03655559569597244,
-0.043236568570137024,
-0.03381282091140747,
0.06146315112709999,
0.03830813243985176,
0.012011563405394554,
0.07524317502975464,
0.04553935304284096,
0.06472744047641754,
-0.030331920832395554,
0.08786063641309738,
-0.01456771045923233,
0.02139095589518547,
-0.07033798098564148,
0.01737501285970211,
0.008512457832694054,
0.03430260717868805,
0.026078201830387115,
0.07918939739465714,
-0.04985743388533592,
0.04920164495706558,
0.024592028930783272,
0.018042638897895813,
0.045329730957746506,
0.03817489370703697,
0.009741989895701408,
0.016769705340266228,
0.048600949347019196,
-0.021188650280237198,
-0.025349419564008713,
0.0270485058426857,
-0.0039069764316082,
-0.0016174087068066,
0.0282205231487751,
0.03295617178082466,
0.005379287991672754,
0.04822423681616783,
-0.017577314749360085,
0.03703315183520317,
-0.0005550358910113573,
-0.022188328206539154,
0.06668049097061157,
-0.08556897193193436,
0.04366240277886391,
0.0021363974083215,
-0.016125934198498726,
0.04171114042401314,
0.04436064139008522,
0.010591698810458183,
-0.027000680565834045,
-0.04330172389745712,
-0.05135611817240715,
-0.03257054090499878,
-0.055075835436582565,
-0.009483828209340572,
-0.003433037782087922,
-0.06797771900892258,
-0.014758031815290451,
0.000054697371524525806,
-0.0011672533582895994,
0.009392503648996353,
-0.06963826715946198,
0.03995118662714958,
-0.02342979423701763,
0.008993564173579216,
0.02444034442305565,
0.022661102935671806,
-0.05496615543961525,
0.0239043477922678,
0.008242332376539707,
-0.07671687006950378,
0.010754100047051907,
-0.01951911672949791,
-0.03492176905274391,
0.037677980959415436,
-0.06696031987667084,
0.0007691275095567107,
-0.01830899901688099,
-0.07560829818248749,
-0.00593178067356348,
0.02986103482544422,
-0.06079023703932762,
-0.09375345706939697,
0.0024311039596796036,
-0.014689815230667591,
-0.01135410089045763,
0.0020555320661514997,
-0.015729669481515884,
0.047689780592918396,
-0.011526289395987988,
0.00866555143147707,
-0.02260054275393486,
-0.01957312971353531,
0.051021117717027664,
-0.022305546328425407,
-0.0009625715319998562,
-0.045547716319561005,
0.023652920499444008,
0.019080357626080513,
0.003706125309690833,
0.01586761698126793,
0.010228362865746021,
0.018489832058548927,
-0.01705627515912056,
-0.021487126126885414,
-0.007782681845128536,
0.040783196687698364,
0.00045418148511089385,
-0.03651275113224983,
0.001205124775879085,
-0.027071386575698853,
-0.022159727290272713,
0.007921218872070312,
-0.10855355113744736,
-0.05473651736974716,
0.0048031616024672985,
0.09709405153989792,
-0.06335451453924179,
0.02916872128844261,
0.04178730398416519,
0.02692641317844391,
0.020038077607750893,
0.03081771731376648,
-0.043941058218479156,
0.0485428050160408,
0.07034970819950104,
-0.05068432539701462,
-0.020409096032381058,
-0.031494736671447754,
-0.05954752862453461,
-0.0016613060142844915,
0.05476408451795578,
-0.00007011919660726562,
0.04582860320806503,
0.05965520441532135,
-0.009844725020229816,
0.031132908537983894,
0.06537405401468277,
-0.024742010980844498,
0.016367729753255844,
0.02874004654586315,
-0.022895868867635727,
0.03008611872792244,
-0.03388991951942444,
-0.0050864736549556255,
-0.01961875520646572,
-0.0008251877152360976,
-0.04818059131503105,
-0.08420766890048981,
-0.015316602773964405,
-0.000016357462300220504,
0.015384715981781483,
0.004279912915080786,
-0.006801912561058998,
0.007050907704979181,
0.009802456945180893,
0.01760362647473812,
0.03544946759939194,
0.024630500003695488,
0.08348429203033447,
0.024537568911910057,
-0.028182899579405785,
0.009122989140450954,
0.052825845777988434,
-0.0500761978328228,
-0.0451936200261116,
-0.0402287133038044,
-0.004095536656677723,
0.035814981907606125,
0.005835589487105608,
0.010515649802982807,
0.03255585953593254,
-0.03247095271945,
-0.0010547061683610082,
-0.038134362548589706,
-0.018039293587207794,
-0.03542548790574074,
-0.059985339641571045,
-0.015373741276562214,
0.023844735696911812,
0.03668029233813286,
-0.029720842838287354,
0.01694246008992195,
0.04000740125775337,
-0.0648445412516594,
-0.019908221438527107,
0.007766599301248789,
-0.0019111650763079524,
-0.0016246566083282232,
-0.03693397343158722,
0.035650305449962616,
0.036062657833099365,
0.036348018795251846,
-0.04299738258123398,
-0.028268679976463318,
0.04267854243516922,
-0.004859980195760727,
-0.04992932453751564,
0.03262781351804733,
-0.026198167353868484,
-0.031216315925121307,
0.002082517836242914,
-0.04685747250914574,
-0.03297162055969238,
0.03803705424070358,
-0.03421805426478386,
0.06788576394319534,
0.018777266144752502,
0.04140637442469597,
-0.03793617710471153,
-0.0030095549300312996,
0.1027747094631195,
0.0021814601495862007,
-0.020113473758101463,
0.006572364829480648,
-0.08978927880525589,
-0.01590423658490181,
0.018223026767373085,
0.027668656781315804,
-0.007845962420105934,
-0.014635455794632435,
0.06427973508834839,
0.03790070116519928,
0.013996995985507965,
0.011245757341384888,
0.019752489402890205,
-0.035120803862810135,
0.07256796211004257,
-0.028731832280755043,
-0.03493344783782959,
0.02521090768277645,
0.07258356362581253,
-0.025686129927635193,
-0.04306626319885254,
-0.009751247242093086,
0.010773234069347382,
-0.03978893160820007,
0.019434701651334763,
-0.016861477866768837,
-0.0331948958337307,
-0.069667749106884,
-0.014243297278881073,
0.029542025178670883,
0.01486755721271038,
0.023308780044317245,
-0.01511109434068203,
-0.018650570884346962,
-0.03793539106845856,
0.015069675631821156,
0.03872174024581909,
-0.06262753158807755,
-0.02164173685014248,
0.03886258229613304,
-0.049792658537626266,
0.053856655955314636,
0.0373123437166214,
0.010683784261345863,
-0.07344521582126617,
-0.08045733720064163,
-0.03118683211505413,
-0.02230510301887989,
-0.008867424912750721,
-0.020464489236474037,
0.004023105837404728,
-0.001617736998014152,
-0.013610035181045532,
0.037074778228998184,
-0.042296163737773895,
0.005256508477032185,
0.028718745335936546,
-0.0049827815964818,
0.04978419467806816,
0.052194830030202866,
-0.01943741738796234,
-0.018159780651330948,
0.03951152786612511,
0.016570502892136574,
0.06572660058736801,
-0.03771298751235008,
-0.012461329810321331,
-0.032842643558979034,
-0.022726139053702354,
0.03521004319190979,
0.0067161316983401775,
-0.04476100951433182,
0.0029677473939955235,
-0.037452634423971176,
0.05116445571184158,
0.01839362271130085,
0.009850197471678257,
0.029504744336009026,
-0.05206605792045593,
0.022372636944055557,
0.01959553360939026,
0.006961570121347904,
-0.05903676897287369,
0.01878109946846962,
-0.024273525923490524,
-0.024503784254193306,
-0.024699652567505836,
-0.019992731511592865,
0.025902658700942993,
0.054066479206085205,
-0.01120923925191164,
0.02815803326666355,
-0.015983005985617638,
0.013494262471795082,
-0.018794648349285126,
0.05142533406615257,
0.036910880357027054,
-0.012137875892221928,
-0.05012357607483864,
0.11768396943807602,
0.03094211407005787,
-0.006472837645560503,
-0.008004470728337765,
-0.008908817544579506,
0.03991379961371422,
0.010238302871584892,
-0.018857913091778755,
0.026158638298511505,
-0.0371730700135231,
0.027935298159718513,
0.003269053529947996,
0.028464147821068764,
0.06596095860004425,
0.06082873046398163,
0.03434930369257927,
0.013156075030565262,
0.030886465683579445,
-0.011667103506624699,
-0.035558801144361496,
0.07064628601074219,
0.022723518311977386,
-0.03164905682206154,
-0.03993745148181915,
-0.02745317481458187,
-0.049081332981586456,
-0.044864263385534286,
-0.07405833154916763,
0.0145349046215415,
0.009721087291836739,
-0.04038161784410477,
-0.0284144077450037,
0.018081024289131165,
-0.01584174484014511,
0.02451738715171814,
0.003057110123336315,
-0.04158558323979378,
0.03347539156675339,
0.004240481182932854,
0.03822759911417961,
0.03371284902095795,
-0.05064241960644722,
-0.015484885312616825,
-0.07449530065059662,
0.002979352604597807,
0.0025977501645684242,
0.016498617827892303,
0.01610313169658184,
0.03049122728407383,
-0.0271931029856205,
-0.010036887601017952,
-0.0295309666544199,
0.04831302538514137,
-0.000499040586873889,
-0.05198657140135765,
-0.035105057060718536,
0.01943369396030903,
0.05220938101410866,
-0.05371947959065437,
0.011312924325466156,
-0.03313824534416199,
-0.07146089524030685,
0.03805245831608772,
-0.006646582391113043,
-0.002797132357954979,
-0.004198997747153044,
-0.036698803305625916,
-0.001630825805477798,
-0.03448139503598213,
-0.0026825591921806335,
-0.012920812703669071,
0.005482284817844629,
-0.007624277379363775,
0.05893415957689285,
0.031476039439439774,
0.021565238013863564,
-0.0016534548485651612,
0.048339832574129105,
-0.0330476351082325,
-0.025312891229987144,
0.006942461710423231,
-0.016047624871134758,
-0.019984856247901917,
-0.02307891473174095,
0.02151385322213173,
-0.04924073442816734,
0.028361797332763672,
-0.06017352268099785,
-0.006409873254597187,
0.02719840034842491,
-0.03161359205842018,
-0.019335806369781494,
-0.004041698295623064,
0.00042505015153437853,
0.01703529804944992,
0.009719726629555225,
0.024403082206845284,
0.05475180596113205,
-0.03013480454683304,
0.0205344520509243,
-0.05239955708384514,
-0.07432620972394943,
0.03666873648762703,
0.02228025160729885,
-0.005338939838111401,
0.04340219125151634,
0.023409489542245865,
0.039209216833114624,
0.020478224381804466,
-0.016996245831251144,
-0.059079721570014954,
0.0360206700861454,
-0.037576284259557724,
0.041865184903144836,
0.0035505560226738453,
-0.07373598963022232,
-0.022092949599027634,
0.06605856120586395,
0.0662035122513771,
0.05760717764496803,
0.02180224284529686,
-0.011303763836622238,
-0.02499416284263134,
0.030371742323040962,
-0.013800961896777153,
0.004718750715255737,
0.05721093714237213,
-0.033693958073854446,
0.0051044742576777935,
-0.02441369742155075,
-0.020208820700645447,
-0.014719096943736076,
0.0008191345841623843,
-0.009881467558443546,
-0.011284729465842247,
0.08351708203554153,
0.013113866560161114,
0.0549197643995285,
0.005459317471832037,
-0.02299472503364086,
0.007791259326040745,
-0.0016295640962198377,
-0.03337915614247322,
0.016262678429484367,
0.0029241705778986216,
0.009004933759570122,
-0.012556234374642372,
-0.01160459965467453,
0.020473463460803032,
-0.004209264647215605,
-0.0001860731717897579,
0.011568430811166763,
0.031499240547418594,
-0.046650875359773636,
-0.011491145007312298,
-0.03069048933684826,
0.03694669157266617,
0.004579692613333464,
-0.021438518539071083,
0.014857642352581024,
0.003643831005319953,
-0.09751774370670319,
0.053373731672763824,
-0.007507015019655228,
-0.0024176512379199266,
-0.07877476513385773,
-0.019342603161931038,
-0.05305836349725723,
-0.02524506114423275,
-0.029614688828587532,
-0.03810019791126251,
-0.012519625015556812,
0.007510295137763023,
-0.03612324595451355,
0.08155422657728195,
0.027143068611621857,
-0.060407042503356934,
0.011292804032564163,
-0.05138128995895386,
-0.00046632287558168173,
-0.0008584921015426517,
-0.02657480351626873,
0.03128241002559662,
0.04782741889357567,
0.00837805587798357,
-0.018902437761425972,
-0.01563407853245735,
0.023514751344919205,
-0.03088943473994732,
-0.016314661130309105,
-0.04897623509168625,
-0.002928344067186117,
-0.02844824455678463,
0.00508134625852108,
-0.035956237465143204,
-0.03238717094063759,
-0.0008843985851854086,
0.028581244871020317,
0.012700718827545643,
0.008594220504164696,
0.06521348655223846,
-0.04765719175338745,
0.07389935851097107,
0.04110473766922951,
0.06501860916614532,
-0.030463172122836113,
0.02805762179195881,
0.012842277996242046,
0.029586514458060265,
0.0656830221414566,
-0.012276781722903252,
-0.06840282678604126,
-0.008811173029243946,
-0.005632209125906229,
0.04520487040281296,
0.018210474401712418,
0.02557278610765934,
0.02504166215658188,
-0.08256519585847855,
-0.005391761194914579,
0.037676747888326645,
0.001996708335354924,
0.007225734647363424,
-0.026759754866361618,
0.00461304048076272,
0.00493988860398531,
-0.008244195021688938,
-0.03377223759889603,
0.04273909330368042,
0.008976152166724205,
0.028569666668772697,
-0.0065996055491268635,
-0.011018695309758186,
-0.009483217261731625,
-0.057239364832639694,
-0.010272986255586147,
-0.07201938331127167,
-0.016818732023239136,
-0.02494380623102188,
-0.016829010099172592,
0.0039711506105959415,
0.022242678329348564,
-0.021505942568182945,
-0.0464521199464798,
-0.007159417495131493,
0.013473873026669025,
-0.04427611827850342,
-0.03254231810569763,
-0.005578814074397087,
-0.040544744580984116,
-0.012424701824784279,
0.022609826177358627,
0.04245421290397644,
-0.0484667532145977,
-0.025638017803430557,
-0.021838726475834846,
0.027405664324760437,
0.04035637900233269,
0.02978276088833809,
-0.04731934890151024,
-0.008659475483000278,
-0.024427147582173347,
-0.07071332633495331,
-0.003394674276933074,
-0.02398882433772087,
0.025192851200699806,
-0.025662805885076523,
0.021151134744286537,
-0.017284994944930077,
-0.015342107973992825,
-0.0004711211659014225,
0.05137074738740921,
0.0026047853752970695,
-0.009058116935193539,
0.0456995964050293,
0.010848977603018284,
-0.0007294787210412323,
-0.0260788444429636,
0.016579458490014076,
0.02025691233575344,
-0.014291108585894108,
-0.011983765289187431,
-0.019770320504903793,
-0.048368774354457855,
-0.061327386647462845,
0.049642715603113174,
0.05214167386293411,
-0.011886699125170708,
0.03693145141005516,
0.02427344210445881,
0.010587957687675953,
-0.03983468934893608,
0.039484698325395584,
0.07348929345607758,
0.006962263956665993,
-0.03528149425983429,
0.01979306899011135,
-0.05252595990896225,
0.008663258515298367,
-0.01659224182367325,
0.008455919101834297,
0.04083635285496712,
0.015543151646852493,
0.02407500520348549,
-0.00461924122646451,
0.04703756421804428,
0.025894997641444206,
-0.031280629336833954,
-0.006100178696215153,
-0.0071402378380298615,
0.0025845374912023544,
0.015654591843485832,
-0.05910424888134003,
-0.004091763403266668,
-0.013969890773296356,
0.011783121153712273,
-0.05597333982586861,
0.0194854736328125,
-0.008866841904819012,
0.0007151112076826394,
-0.0594601184129715,
0.02560635469853878,
-0.020024562254548073,
-0.00012778340897057205,
-0.000919485290069133,
0.019248662516474724,
0.056862179189920425,
-0.006956667173653841,
0.017770536243915558,
0.011513922363519669,
0.03687146306037903,
-0.0017555394442752004,
-0.02961263246834278,
-0.01428675651550293,
0.03316032886505127,
-0.0015125740319490433,
-0.03629373386502266,
-0.00862115528434515,
-0.051410872489213943,
-0.01399408932775259,
-0.006037629209458828,
0.0009615227463655174,
0.03505246713757515
] |
<p>What are the quantum mechanisms behind the emission and absorption of thermal radiation at and below room temperature? If the relevant quantum state transitions are molecular (stretching, flexing and spin changes) how come the thermal spectrum is continuous? What about substances (such as noble gases) which don't form molecules, how do they emit or absorb thermal radiation? Is there a semi-classical mechanism (with the EM field treated classically) and also a deeper explanation using the full apparatus of QFT?</p> | g6631 | [
0.01562088169157505,
-0.031026309356093407,
0.0019135111942887306,
0.02514065057039261,
0.0006137081072665751,
0.040670253336429596,
0.010169210843741894,
0.07362619042396545,
0.00616545882076025,
-0.04619579762220383,
-0.02421957440674305,
0.019829679280519485,
0.03367368131875992,
-0.0020804395899176598,
-0.010490473359823227,
-0.020776690915226936,
0.02065737172961235,
0.017072634771466255,
0.057691074907779694,
0.030423535034060478,
-0.09420481324195862,
-0.013554245233535767,
-0.010339666157960892,
-0.08123882114887238,
-0.08789441734552383,
0.01715783029794693,
-0.00119486334733665,
0.04866588115692139,
0.08422072976827621,
-0.049623940140008926,
-0.007617536932229996,
0.038707904517650604,
0.022789571434259415,
-0.010791691951453686,
0.08178853243589401,
-0.010681414976716042,
0.047786153852939606,
-0.005318383686244488,
-0.04549986869096756,
-0.03531975299119949,
-0.03324270248413086,
-0.03924020007252693,
0.02580728754401207,
0.018995601683855057,
0.03379139304161072,
0.05386532098054886,
-0.04610922560095787,
0.001364995609037578,
0.0006443258025683463,
0.04039207100868225,
0.003290865570306778,
-0.011240212246775627,
0.02202354557812214,
0.02117801643908024,
0.04382564127445221,
-0.0389304980635643,
-0.044578440487384796,
0.02539004571735859,
0.06662992388010025,
-0.05620381981134415,
0.04436379671096802,
0.008103931322693825,
0.009231941774487495,
-0.018722763285040855,
0.07793735712766647,
-0.026986435055732727,
-0.029117288067936897,
0.00887554232031107,
-0.024408642202615738,
0.004210931248962879,
0.006685568019747734,
-0.01909886673092842,
-0.07174025475978851,
0.0028623316902667284,
0.010750841349363327,
-0.01625533401966095,
-0.009724687784910202,
-0.012784244492650032,
-0.027848314493894577,
0.010240044444799423,
-0.03402411565184593,
-0.03540416061878204,
0.0036357783246785402,
-0.009760303422808647,
0.024403460323810577,
0.011561637744307518,
-0.011849273927509785,
0.03165779635310173,
0.0057740593329072,
0.0225993525236845,
0.016438089311122894,
0.012217352166771889,
0.06875859200954437,
0.013334285467863083,
0.013653899542987347,
-0.002355912933126092,
0.012156421318650246,
0.06137286499142647,
-0.004210442770272493,
-0.017705345526337624,
0.015200844965875149,
-0.01729651726782322,
0.016900034621357918,
0.010125957429409027,
0.01925421692430973,
-0.013537362217903137,
-0.010597825981676579,
0.008363056927919388,
-0.009952876716852188,
0.05649557709693909,
-0.06506114453077316,
0.00038690396468155086,
-0.0020342825446277857,
0.005186049733310938,
-0.01308613270521164,
0.019685138016939163,
0.0359024778008461,
-0.002495274180546403,
0.05015115812420845,
0.08295440673828125,
0.01679467223584652,
0.06681246310472488,
0.05935182049870491,
-0.01794765144586563,
-0.011403780430555344,
-0.044482603669166565,
-0.011088407598435879,
-0.01455506682395935,
-0.007488485425710678,
0.004875493235886097,
0.06482021510601044,
0.07448910176753998,
-0.0911421850323677,
0.05693819001317024,
0.023920617997646332,
0.04003004729747772,
-0.0026249291840940714,
-0.007787996903061867,
0.024968430399894714,
-0.005386741831898689,
0.0130881667137146,
-0.0066866204142570496,
-0.016754642128944397,
-0.035700298845767975,
-0.018277009949088097,
0.0035507928114384413,
-0.026195934042334557,
-0.019513219594955444,
-0.004376927390694618,
-0.00248732534237206,
0.0567450225353241,
0.04713863879442215,
0.06416439265012741,
-0.029090387746691704,
0.0488116629421711,
-0.04504157975316048,
0.022545434534549713,
-0.03477850928902626,
0.02574731595814228,
0.06666097044944763,
0.018569353967905045,
-0.010065728798508644,
-0.0696553960442543,
0.016385391354560852,
-0.034096233546733856,
-0.0010262159630656242,
-0.024126283824443817,
-0.05542540177702904,
0.04886803776025772,
-0.044171370565891266,
-0.047297846525907516,
0.016110070049762726,
-0.03937598690390587,
0.039021268486976624,
-0.049978941679000854,
0.054486922919750214,
0.050366438925266266,
-0.016170699149370193,
-0.0014453936601057649,
-0.03619864583015442,
-0.014347244054079056,
0.004710724111646414,
0.004541068337857723,
-0.035999562591314316,
0.01775062456727028,
0.03944150358438492,
-0.021898075938224792,
0.019136516377329826,
-0.07665466517210007,
0.018816448748111725,
-0.04463327303528786,
-0.07092776149511337,
0.021508129313588142,
0.002121805213391781,
-0.009923723526299,
-0.00411326065659523,
0.00786132737994194,
-0.03811837360262871,
-0.0472089983522892,
0.014362283051013947,
0.002570929704234004,
-0.00402282178401947,
-0.03175768628716469,
0.00865205843001604,
0.07479364424943924,
0.05645798146724701,
-0.005938869435340166,
-0.01026987750083208,
0.008953887037932873,
-0.05599229782819748,
-0.011148884892463684,
-0.007070932537317276,
0.03892577812075615,
-0.0028553418815135956,
-0.003921002149581909,
0.07438477873802185,
0.0006744781276211143,
-0.0374738946557045,
0.018351897597312927,
0.019914522767066956,
0.022119270637631416,
0.02527979388833046,
0.04240056872367859,
0.043673451989889145,
-0.01835005171597004,
-0.008627907373011112,
-0.08502598106861115,
0.018193652853369713,
-0.000990311847999692,
0.04428793117403984,
-0.1303817629814148,
0.045928049832582474,
0.009185784496366978,
0.0016390102682635188,
0.03900507092475891,
0.028297118842601776,
-0.030426662415266037,
-0.05445193126797676,
0.059444572776556015,
-0.016075406223535538,
-0.014612390659749508,
-0.01664847880601883,
-0.038791216909885406,
-0.006096449214965105,
-0.005137715954333544,
-0.02393771894276142,
-0.026458529755473137,
-0.0464872308075428,
0.007946801371872425,
-0.01859479583799839,
0.033141687512397766,
-0.013507700525224209,
-0.006369545590132475,
-0.008626852184534073,
-0.09209419786930084,
-0.0026665220502763987,
-0.07433272898197174,
0.05869356542825699,
-0.03445858880877495,
-0.07773643732070923,
-0.008964253589510918,
0.016868149861693382,
-0.03829490765929222,
0.013936459086835384,
0.01867217943072319,
0.008362327702343464,
-0.028569625690579414,
0.042251914739608765,
-0.05247243866324425,
-0.015180440619587898,
-0.02874828316271305,
0.07415933161973953,
-0.05925743654370308,
0.04127191752195358,
0.024550557136535645,
-0.00018707853450905532,
0.007752178702503443,
0.017383532598614693,
0.024189453572034836,
-0.03849494084715843,
-0.006086364388465881,
-0.02708611823618412,
-0.04484115540981293,
-0.01179394032806158,
0.035405974835157394,
-0.015161611139774323,
-0.011933068744838238,
0.0028275588992983103,
0.0026192357763648033,
-0.04711136221885681,
0.02416849508881569,
0.013993954285979271,
0.002183582866564393,
0.024379875510931015,
-0.1085968017578125,
0.0032087513245642185,
0.028352143242955208,
-0.022428365424275398,
-0.019723840057849884,
0.068998783826828,
0.03846321627497673,
-0.053347598761320114,
0.04056544974446297,
0.03177342936396599,
-0.0061370027251541615,
-0.020034311339259148,
-0.0345812663435936,
-0.060296740382909775,
0.014013233594596386,
0.028134658932685852,
-0.0257280170917511,
-0.022176643833518028,
-0.04658643901348114,
0.08082039654254913,
-0.011361805722117424,
-0.048917364329099655,
-0.03303998336195946,
0.017098497599363327,
0.06253726035356522,
-0.031077731400728226,
0.012422711588442326,
-0.028821535408496857,
0.003660846035927534,
-0.06343270093202591,
0.04988930746912956,
-0.009499958716332912,
0.01624459959566593,
-0.05504780262708664,
-0.016856292262673378,
-0.04869219288229942,
0.005681601352989674,
-0.007776487618684769,
-0.0025721334386616945,
-0.015810079872608185,
0.01085725985467434,
0.005335633642971516,
-0.09088923782110214,
0.007670914754271507,
0.0015552523545920849,
-0.016285080462694168,
0.05165552347898483,
-0.022001242265105247,
-0.03644122928380966,
0.03575839847326279,
0.03966888040304184,
-0.014653886668384075,
-0.013271257281303406,
-0.06159409135580063,
-0.0002634350676089525,
-0.003189890645444393,
-0.011013134382665157,
0.012491868808865547,
-0.019028212875127792,
0.018954936414957047,
-0.026303434744477272,
0.039829425513744354,
0.0014076679944992065,
0.08608090877532959,
0.050789251923561096,
0.006523543037474155,
-0.03176824003458023,
-0.051345840096473694,
0.07254081964492798,
0.03107837215065956,
-0.024701828137040138,
0.026395028457045555,
0.048601184040308,
0.02276180498301983,
0.07362842559814453,
0.03745444864034653,
-0.016426028683781624,
-0.0052126082591712475,
-0.05709930509328842,
-0.028755590319633484,
-0.017814388498663902,
0.053080763667821884,
0.043644823133945465,
0.004724327474832535,
-0.09388135373592377,
0.012513682246208191,
0.002701584715396166,
0.01396774873137474,
-0.010630397126078606,
0.03489994630217552,
0.04956183210015297,
0.04637869819998741,
-0.054866597056388855,
0.001969757955521345,
-0.038177378475666046,
-0.024866655468940735,
0.007013349793851376,
-0.06280326843261719,
-0.00331865600310266,
-0.027683144435286522,
0.030647587031126022,
-0.02082776091992855,
0.052988018840551376,
-0.013312365859746933,
0.0001840455224737525,
0.005643089767545462,
0.023253684863448143,
0.037028975784778595,
-0.04341530054807663,
-0.06585809588432312,
0.020289653912186623,
0.05999460443854332,
-0.02113702893257141,
-0.022482862696051598,
0.002351393224671483,
-0.014185723848640919,
0.020864233374595642,
0.06773670017719269,
-0.05315268412232399,
-0.022466516122221947,
0.005678071640431881,
0.001998109742999077,
0.015864599496126175,
-0.03354589641094208,
-0.04352070391178131,
-0.03878664970397949,
-0.0067152404226362705,
-0.002630068687722087,
-0.003958965186029673,
0.07134347409009933,
-0.004824730567634106,
0.05103546753525734,
0.04151756316423416,
-0.0030525478068739176,
0.016214920207858086,
-0.0034869126975536346,
-0.017024651169776917,
0.011441955342888832,
-0.0067537082359194756,
-0.002858435967937112,
-0.020061446353793144,
0.008611216209828854,
-0.0458061620593071,
-0.005858930293470621,
-0.0127600422129035,
0.002065334003418684,
0.15141676366329193,
-0.012129141949117184,
0.0013991734012961388,
0.025856366381049156,
-0.0330955944955349,
0.0034715256188064814,
-0.0175502710044384,
-0.017532717436552048,
-0.004503178410232067,
-0.05150976404547691,
-0.04277645796537399,
-0.005428812000900507,
-0.06103453412652016,
-0.007754739839583635,
-0.026437651365995407,
-0.04562199488282204,
-0.04931337758898735,
0.028839251026511192,
0.033277738839387894,
0.012104282155632973,
-0.07502884417772293,
0.0004310241201892495,
-0.020179573446512222,
-0.019946765154600143,
-0.012332791462540627,
-0.0038925844710320234,
-0.08007057011127472,
0.013047615066170692,
-0.030272124335169792,
0.013835560530424118,
0.006830114871263504,
0.017828339710831642,
0.03688409551978111,
0.019180903211236,
0.05227506905794144,
-0.0293867290019989,
0.02913898602128029,
-0.01721019670367241,
0.025380784645676613,
-0.06071767210960388,
0.06234416365623474,
0.02527938410639763,
0.0436614528298378,
0.01111249253153801,
0.00007496245962101966,
-0.003405240597203374,
-0.023814747110009193,
0.020089274272322655,
-0.004046483896672726,
-0.041722171008586884,
0.03204090893268585,
0.02934357337653637,
0.010246079415082932,
-0.00022624648408964276,
0.0009825777960941195,
0.02066449075937271,
0.0027558717411011457,
0.023313643410801888,
0.02525472082197666,
-0.023938195779919624,
-0.020508335903286934,
-0.02777733840048313,
-0.01899772696197033,
0.02923058159649372,
0.03499791771173477,
0.010341718792915344,
0.029526038095355034,
-0.0058133830316364765,
0.008942422457039356,
0.04640408977866173,
-0.04507700726389885,
0.010215387679636478,
-0.03493310511112213,
-0.013115956448018551,
0.044997699558734894,
-0.016842052340507507,
-0.022381553426384926,
-0.08109452575445175,
-0.029761910438537598,
-0.002137815812602639,
-0.06912412494421005,
-0.007135970052331686,
0.018013564869761467,
0.01333149429410696,
0.04430682957172394,
0.060077570378780365,
-0.009982053190469742,
0.04260045662522316,
0.021673740819096565,
0.046073731034994125,
0.016493387520313263,
0.013137034140527248,
0.00432739220559597,
0.04911445826292038,
0.0230901800096035,
0.031597305089235306,
-0.03694868087768555,
-0.033173568546772,
-0.0249063428491354,
0.09582037478685379,
-0.007960222661495209,
-0.051393162459135056,
0.010728491470217705,
0.033429134637117386,
0.05072677135467529,
-0.026583338156342506,
0.006107955705374479,
0.03698885813355446,
0.01619766652584076,
0.014063547365367413,
0.0386466309428215,
0.024318568408489227,
0.051848072558641434,
-0.0341896116733551,
0.02059035934507847,
-0.0026469682343304157,
-0.0062182885594666,
-0.028697572648525238,
0.02726532518863678,
0.015102881006896496,
0.0418015792965889,
0.029011812061071396,
0.06312800943851471,
-0.05001513287425041,
0.05393536388874054,
0.019296685233712196,
0.011446550488471985,
-0.03021244704723358,
0.06353449821472168,
0.01953226700425148,
0.0043597836047410965,
0.000921411148738116,
0.006003824528306723,
-0.04716344550251961,
-0.02237146534025669,
0.011878730729222298,
-0.002666550688445568,
-0.036449965089559555,
-0.05901237949728966,
-0.0189505685120821,
0.040513988584280014,
0.018185153603553772,
0.004911137744784355,
-0.03129757195711136,
-0.043559636920690536,
0.04197781905531883,
-0.002676913281902671,
-0.014194916002452374,
0.035084113478660583,
0.027554433792829514,
-0.04412737116217613,
-0.0462845154106617,
-0.04625996947288513,
0.014778721146285534,
0.008557443507015705,
0.002644856460392475,
-0.010967528447508812,
-0.04045348986983299,
-0.048852432519197464,
-0.04228167235851288,
-0.017606260254979134,
0.04023294150829315,
0.023166589438915253,
-0.0548148937523365,
0.061274848878383636,
-0.0107034370303154,
0.0022368920035660267,
-0.009722833521664143,
-0.00631807092577219,
0.03605848178267479,
-0.007107028737664223,
-0.030973423272371292,
-0.030989427119493484,
-0.009209089912474155,
-0.03452339395880699,
-0.018724314868450165,
-0.03217862546443939,
0.0662747323513031,
-0.006187800783663988,
-0.03644080460071564,
-0.02941693365573883,
-0.05763047933578491,
0.056629471480846405,
-0.028773581609129906,
0.045827776193618774,
0.036348551511764526,
-0.0682569071650505,
0.04596813768148422,
0.04072924703359604,
0.0076146842911839485,
-0.002433663932606578,
-0.01489591971039772,
0.01334279216825962,
0.002850121585652232,
-0.013684161007404327,
-0.02279752492904663,
0.015312179923057556,
-0.008083966560661793,
0.013436412438750267,
0.04069821164011955,
-0.01807655766606331,
-0.027152612805366516,
0.05908270552754402,
0.0012457841075956821,
-0.029802020639181137,
-0.01108590792864561,
-0.03785305097699165,
-0.024327443912625313,
-0.08398935943841934,
0.023454608395695686,
0.0011433286126703024,
-0.063820019364357,
-0.04834701865911484,
-0.0015836774837225676,
0.06322693079710007,
0.06017273664474487,
0.030926257371902466,
-0.012188343331217766,
-0.03140858933329582,
-0.06381037086248398,
0.006789681501686573,
-0.012884438969194889,
0.020034736022353172,
0.05808545649051666,
0.01171402633190155,
0.06984145939350128,
0.030330605804920197,
-0.035846561193466187,
0.019159767776727676,
-0.03649379685521126,
-0.01712005026638508,
-0.00431099021807313,
0.02374347299337387,
-0.039080556482076645,
-0.026545729488134384,
-0.021843789145350456,
-0.010799371637403965,
0.09387148916721344,
0.006674222182482481,
-0.04108015447854996,
-0.06238798424601555,
0.06742661446332932,
0.03389234095811844,
-0.0038097130600363016,
0.023408303037285805,
0.04170349985361099,
0.0047869374975562096,
0.05859674885869026,
-0.01232250314205885,
-0.034674741327762604,
-0.03890814632177353,
-0.043567266315221786,
-0.022979596629738808,
-0.012177671305835247,
0.04394715651869774,
0.012907166965305805,
0.013759179040789604,
-0.0713919997215271,
0.013120844028890133,
-0.030407048761844635,
0.01721876859664917,
-0.00308453431352973,
0.03670578449964523,
-0.008028878830373287,
0.03530643507838249,
0.015999892726540565,
0.02647916041314602,
0.014113586395978928,
0.0036634341813623905,
0.009891591966152191,
0.010965359397232533,
0.013635692186653614,
0.08018266409635544,
0.052590180188417435,
0.004999049939215183,
-0.03599517047405243,
-0.047325339168310165,
-0.004442358389496803,
0.015186617150902748,
-0.04334620386362076,
-0.04054791107773781,
0.016924824565649033,
-0.03205389529466629,
0.027679501101374626,
-0.0004662721767090261,
-0.03846389427781105,
-0.034952178597450256,
-0.02430419623851776,
0.03550191968679428,
-0.021364331245422363,
-0.012380409054458141,
0.07597381621599197,
-0.003508823225274682,
-0.046353988349437714,
-0.039827391505241394,
0.05468396097421646,
0.01134488359093666,
0.0013616315554827452,
0.04964404180645943,
0.003305035410448909,
-0.010824509896337986,
0.02078789286315441,
0.03227407857775688,
-0.009238667786121368,
-0.022401759400963783,
-0.08994244039058685,
-0.04025059565901756,
-0.011311940848827362,
0.029336044564843178,
0.0075743491761386395,
-0.040877100080251694,
-0.03741765394806862,
0.003844070713967085,
0.0258590467274189,
0.031238604336977005,
-0.06662260740995407,
-0.0370103120803833,
0.07190964370965958,
0.02305147424340248,
0.004846783820539713,
-0.06420116871595383,
0.0077580297365784645,
-0.0410289466381073,
-0.011235023848712444,
-0.015548588708043098,
0.008395034819841385,
-0.012960695661604404,
-0.024138011038303375
] |
<p><em>[insert obligatory statement of my lack of knowledge in physics]</em></p>
<p>Alright, so we have all seen the movies where someone gets blasted out of the airlock on their starship, or their suit decompresses while on a space walk. The poor schmoe usually either decompresses so violently that blood is oozing out of every orifice in their body, or they freeze instantly.</p>
<p>From this I have two questions:</p>
<ol>
<li><strong>Would the decompression really be that violent?</strong>
<ol>
<li>Clearly the drastic difference in pressure from a normal "earth" like environment to space would be bad, but would it be <em>that</em> devastating.</li>
<li>I vaguely remember that standard atmospheric pressure was something like 15 psi, which doesn't seem like enough to mess you up that bad.</li>
</ol></li>
<li><strong>Would you <em>actually</em> freeze instantly in space?</strong>
<ol>
<li>Heat, or lack thereof is a measure of internal energy, but in a vacuum there wouldn't be anything to have internal energy, so does space even have a temperature?</li>
<li>Wouldn't some form of matter have to be present in order to cool off? If there were no matter besides yourself and a few stray particles here and there, it seems like it would take a very long time to cool off.</li>
</ol></li>
</ol> | g6632 | [
0.04329506680369377,
0.04124606400728226,
-0.020321281626820564,
0.020844079554080963,
0.00785589125007391,
0.011136393994092941,
-0.060063865035772324,
0.0771104246377945,
-0.010187281295657158,
-0.007832055911421776,
-0.03691587597131729,
0.03741778805851936,
-0.014840591698884964,
-0.026998570188879967,
0.02023816667497158,
-0.04736565053462982,
0.06395857781171799,
-0.060085613280534744,
0.0011501050321385264,
-0.045897193253040314,
-0.03684987127780914,
-0.0643610954284668,
0.020070888102054596,
-0.022192154079675674,
-0.03085111826658249,
-0.015014143660664558,
0.03458600491285324,
0.0019713102374225855,
-0.059965964406728745,
0.012344611808657646,
-0.015617023222148418,
0.01495766919106245,
-0.04182625934481621,
-0.08949853479862213,
-0.037296704947948456,
-0.025494351983070374,
0.007744815666228533,
0.02171826735138893,
-0.029239213094115257,
-0.01984352618455887,
0.0031721077393740416,
-0.10995258390903473,
0.04447129741311073,
-0.024963924661278725,
-0.022611023858189583,
0.07760798186063766,
-0.042897894978523254,
-0.067288339138031,
-0.021740542724728584,
-0.013614760711789131,
-0.05324458330869675,
-0.01309348177164793,
0.008298657834529877,
0.0045150876976549625,
-0.00195335759781301,
-0.033523738384246826,
0.030354037880897522,
-0.023862004280090332,
0.029427802190184593,
-0.041895195841789246,
-0.051610298454761505,
-0.012023470364511013,
-0.0008498262614011765,
-0.04094414785504341,
-0.011445898562669754,
0.004766736179590225,
-0.0489274226129055,
0.010479799471795559,
0.06458357721567154,
-0.0008305946830660105,
0.06272772699594498,
-0.04929829761385918,
-0.0742875412106514,
-0.06299154460430145,
-0.025256333872675896,
0.04760884493589401,
-0.024671265855431557,
0.014097817242145538,
0.044963859021663666,
0.04910717159509659,
-0.04964366555213928,
0.014536120928823948,
0.015135113149881363,
-0.023804789409041405,
0.024459175765514374,
-0.032106153666973114,
-0.03558407723903656,
-0.048843275755643845,
0.020955506712198257,
0.051800861954689026,
-0.020689379423856735,
0.039959926158189774,
0.044704537838697433,
0.012442473322153091,
-0.02182709239423275,
0.028199993073940277,
0.01966949552297592,
0.08163957297801971,
-0.008280492387712002,
-0.028061863034963608,
-0.019100842997431755,
-0.04388312250375748,
-0.022750485688447952,
-0.010686635039746761,
-0.02871505543589592,
-0.039514295756816864,
0.03824126347899437,
0.013913977891206741,
0.0038590284530073404,
-0.032725103199481964,
0.0011204828042536974,
0.015114199370145798,
-0.048564862459897995,
-0.01822698302567005,
0.03858401998877525,
-0.009887966327369213,
0.04929294064640999,
-0.06410502642393112,
-0.011873424053192139,
0.03153418004512787,
0.019770290702581406,
0.04495267942547798,
0.0123817203566432,
0.00047079240903258324,
0.014761301688849926,
-0.004280903842300177,
0.03190126270055771,
0.002346461871638894,
0.029241980984807014,
-0.024691926315426826,
-0.03981836885213852,
0.008466914296150208,
-0.043364956974983215,
-0.0324302576482296,
-0.021091222763061523,
0.031187914311885834,
-0.0803234726190567,
0.01999541185796261,
-0.09903162717819214,
-0.01400975976139307,
0.06249169632792473,
0.008153215982019901,
0.022722851485013962,
0.056204505264759064,
-0.07467058300971985,
-0.031851913779973984,
-0.029115721583366394,
0.04987334832549095,
0.02285594493150711,
0.07134220749139786,
-0.013178879395127296,
0.040032483637332916,
0.01110555324703455,
-0.030100196599960327,
0.02932143211364746,
0.015199672430753708,
0.03350936248898506,
0.016672158613801003,
0.0501713752746582,
-0.017603322863578796,
0.05251654237508774,
0.008882805705070496,
0.05591587722301483,
0.0486464723944664,
-0.04789575934410095,
0.02701854333281517,
-0.06429015100002289,
0.02053518034517765,
0.04913762956857681,
0.007542913779616356,
-0.0490998774766922,
-0.04182848334312439,
0.04718678072094917,
0.05121355876326561,
0.006927527021616697,
0.010982632637023926,
0.059845931828022,
-0.014651413075625896,
-0.018754471093416214,
-0.05376414582133293,
0.030407438054680824,
0.050374630838632584,
-0.0034090587869286537,
-0.05767048895359039,
0.06345245987176895,
0.0049781156703829765,
0.010937903076410294,
0.019971046596765518,
0.000822357542347163,
-0.014850517734885216,
0.029302962124347687,
-0.041185490787029266,
-0.02961508184671402,
0.004755739122629166,
-0.003096126951277256,
-0.03532145172357559,
-0.02681386098265648,
0.0210852213203907,
-0.07996692508459091,
0.00625983951613307,
-0.005070607643574476,
-0.0003203070955350995,
0.030105434358119965,
0.027194872498512268,
0.012949174270033836,
0.017438232898712158,
-0.051979854702949524,
0.0006751759792678058,
0.000910692207980901,
-0.029914062470197678,
0.09924669563770294,
-0.012370985932648182,
0.03669458627700806,
0.02058192901313305,
0.011677801609039307,
-0.008796515874564648,
-0.048006948083639145,
0.016453875228762627,
-0.02962200902402401,
0.0014147298643365502,
0.007356890011578798,
0.028530655428767204,
0.03554769977927208,
-0.004234427586197853,
0.027319567278027534,
-0.06556737422943115,
-0.09965594857931137,
-0.0312669463455677,
0.015525235794484615,
-0.03651650622487068,
-0.07052093744277954,
0.03352329879999161,
0.0008497840026393533,
-0.05490700528025627,
-0.028424041345715523,
0.0520210862159729,
0.04329841211438179,
0.02193104848265648,
-0.00659993477165699,
0.03515215590596199,
0.029742559418082237,
-0.014550220221281052,
-0.04838952049612999,
0.0013781707966700196,
0.054008908569812775,
-0.03925468772649765,
-0.028257856145501137,
-0.001362259965389967,
0.016490943729877472,
-0.07694606482982635,
-0.06116316840052605,
0.027333112433552742,
-0.08731009066104889,
-0.017872022464871407,
-0.014028999954462051,
-0.028392869979143143,
-0.04256982356309891,
0.06926939636468887,
-0.03256547078490257,
0.011866535991430283,
-0.021996673196554184,
0.014470340684056282,
-0.0672542005777359,
-0.015539233572781086,
-0.07020793855190277,
0.03322107344865799,
0.019448427483439445,
0.06669320166110992,
0.025479357689619064,
0.007492329925298691,
0.008228342048823833,
0.016033781692385674,
-0.05831049382686615,
0.044344712048769,
0.030328765511512756,
-0.003226472996175289,
-0.019147271290421486,
-0.020551221445202827,
0.01947784051299095,
-0.05026732385158539,
0.010604463517665863,
0.02951771579682827,
-0.09133940935134888,
0.015115350484848022,
0.019051244482398033,
-0.04581524804234505,
0.01836365833878517,
0.051954761147499084,
-0.01000336091965437,
-0.049841638654470444,
-0.019951816648244858,
0.021662667393684387,
0.016155142337083817,
0.03497277572751045,
0.016661349684000015,
0.04314250871539116,
0.004747267812490463,
-0.017015503719449043,
-0.02890964411199093,
0.006601175293326378,
0.04660841450095177,
-0.0560254342854023,
0.016019651666283607,
0.05049401521682739,
-0.005527422297745943,
-0.010920303873717785,
-0.069285087287426,
0.006993464194238186,
-0.021928519010543823,
-0.037376631051301956,
0.011605562642216682,
0.06868456304073334,
0.08521655946969986,
0.02184055745601654,
-0.0013104366371408105,
-0.009820238687098026,
0.024840014055371284,
-0.046003036201000214,
0.00234140339307487,
-0.02566627785563469,
0.017732495442032814,
-0.013932691887021065,
-0.00737413065508008,
-0.03774699196219444,
0.05723707005381584,
0.01809246838092804,
-0.01526030246168375,
-0.037963587790727615,
-0.05189938843250275,
-0.019962843507528305,
-0.026521099731326103,
-0.0011360981734469533,
0.002409883076325059,
-0.04423096030950546,
-0.09263807535171509,
0.027202729135751724,
-0.027577245607972145,
-0.0019285879097878933,
0.017186131328344345,
-0.0001856287708505988,
0.030906639993190765,
-0.03876136615872383,
0.03261863812804222,
0.03308907151222229,
0.03893039748072624,
0.019619252532720566,
0.04604470357298851,
-0.048195697367191315,
-0.02639831230044365,
-0.01173324603587389,
0.06923753768205643,
-0.07588333636522293,
0.02011115290224552,
-0.02606768161058426,
-0.08235577493906021,
-0.03767605498433113,
0.02175091952085495,
0.01111458707600832,
-0.013344384729862213,
0.011323713697493076,
-0.04174114763736725,
0.010370982810854912,
-0.00541742192581296,
-0.020283058285713196,
-0.03412467613816261,
0.0012613151920959353,
0.015311368741095066,
0.02613736316561699,
-0.03701711446046829,
-0.03506995365023613,
0.03728213161230087,
0.03143542632460594,
-0.09586893022060394,
0.01998484879732132,
0.07381837069988251,
-0.01708264648914337,
0.024986648932099342,
0.001924957032315433,
0.008213935419917107,
-0.007808342110365629,
0.08539979159832001,
-0.00032161272247321904,
0.07520029693841934,
-0.0018408632604405284,
0.011243332177400589,
-0.015583752654492855,
-0.009452000260353088,
-0.0023427652195096016,
-0.012128438800573349,
-0.014406376518309116,
0.000562475819606334,
-0.06474597752094269,
0.015018930658698082,
0.06188712641596794,
0.010190824046730995,
0.007554356940090656,
0.04435684159398079,
0.015805598348379135,
-0.04412752762436867,
-0.0028332725632935762,
0.04524131119251251,
0.049961261451244354,
-0.009927400387823582,
0.006534956861287355,
0.014401200227439404,
0.002252132399007678,
-0.01329949963837862,
-0.018322933465242386,
-0.044942039996385574,
-0.006892087869346142,
0.04791030287742615,
-0.003777345409616828,
-0.021036744117736816,
-0.06160638481378555,
-0.015445181168615818,
0.00836738757789135,
-0.005300581920892,
0.024176383391022682,
0.04066137224435806,
0.018339375033974648,
-0.019989371299743652,
0.039119135588407516,
-0.03279145807027817,
-0.005198105238378048,
-0.05288618430495262,
0.06137556582689285,
0.036605700850486755,
-0.001659217057749629,
0.023972945287823677,
-0.016459722071886063,
0.05418248102068901,
-0.010469295084476471,
-0.005564965773373842,
0.09577494114637375,
0.019258635118603706,
0.01649247668683529,
0.014284445904195309,
-0.023541782051324844,
-0.014929902739822865,
0.06729208678007126,
0.011770689859986305,
-0.019092563539743423,
0.08117704093456268,
0.028362015262246132,
0.007770076859742403,
0.03693882003426552,
-0.00936851091682911,
-0.09110589325428009,
-0.031698085367679596,
0.010124348104000092,
-0.055818796157836914,
0.041966360062360764,
0.0009590588160790503,
0.010449327528476715,
0.02532212808728218,
-0.020438723266124725,
0.007067896891385317,
0.050126105546951294,
-0.038179825991392136,
0.04764263331890106,
0.004503421951085329,
0.03327147662639618,
0.018285268917679787,
0.023237600922584534,
0.014199434779584408,
-0.007805954664945602,
-0.003300912445411086,
0.002107333391904831,
-0.011606133542954922,
0.035368382930755615,
0.017997296527028084,
0.027022136375308037,
-0.0019127099076285958,
0.03544262424111366,
-0.010741099715232849,
0.030405191704630852,
-0.01613324135541916,
-0.05850300192832947,
-0.027124404907226562,
-0.002160673961043358,
0.028631772845983505,
0.03780417889356613,
0.021871346980333328,
0.0012694699689745903,
-0.012252085842192173,
0.006272332742810249,
-0.07249152660369873,
0.03196132183074951,
0.009430586360394955,
0.02892107330262661,
-0.038307517766952515,
0.06197534501552582,
-0.02316354028880596,
0.046795353293418884,
-0.02589985728263855,
0.0043328446336090565,
-0.015152853913605213,
-0.015811746940016747,
-0.05734463408589363,
0.015267658978700638,
-0.03658954054117203,
-0.01537236850708723,
0.020461928099393845,
-0.03623218834400177,
-0.035954054445028305,
-0.021970560774207115,
0.0038842863868921995,
-0.012562872841954231,
0.034601666033267975,
0.026656456291675568,
-0.019448747858405113,
0.06407155841588974,
0.03622102737426758,
0.018372489139437675,
0.05738861486315727,
-0.03703329339623451,
-0.03786810487508774,
0.009827835485339165,
0.029995763674378395,
-0.023110628128051758,
0.015878671780228615,
-0.0025023813359439373,
0.03016493283212185,
0.02064822055399418,
-0.010910045355558395,
0.012246008031070232,
-0.05698457732796669,
0.01024288684129715,
-0.07305728644132614,
0.05037127807736397,
-0.005237432662397623,
-0.058963365852832794,
-0.011042519472539425,
-0.002914606826379895,
-0.024923676624894142,
-0.039660658687353134,
-0.028403673321008682,
0.07619313895702362,
0.030863942578434944,
0.02297389693558216,
-0.04312559589743614,
-0.013050361536443233,
-0.023042334243655205,
0.05525092035531998,
-0.02734806202352047,
0.016394343227148056,
-0.002751080086454749,
0.004286748357117176,
0.022493047639727592,
0.000957752054091543,
-0.08047810196876526,
-0.016271322965621948,
0.004388167057186365,
-0.024054499343037605,
0.014902392402291298,
0.0075822994112968445,
0.01178324781358242,
-0.001871985848993063,
-0.016293426975607872,
-0.012420479208230972,
-0.0023792951833456755,
-0.041664447635412216,
0.0729028731584549,
0.05501880124211311,
0.026311272755265236,
-0.012368397787213326,
-0.0005164614995010197,
-0.044375743716955185,
0.04081520065665245,
0.048994217067956924,
0.016806865110993385,
-0.023917600512504578,
0.002377372467890382,
-0.05515294522047043,
-0.02109716087579727,
-0.03345019742846489,
0.006354409735649824,
0.04810282960534096,
-0.010825098492205143,
0.018022146075963974,
-0.005912971682846546,
0.027932599186897278,
0.046539828181266785,
-0.052021950483322144,
0.003912143409252167,
0.052846163511276245,
0.010228795930743217,
0.03198407590389252,
0.054393112659454346,
-0.015097204595804214,
0.027271434664726257,
-0.017833057790994644,
-0.032767631113529205,
-0.021485263481736183,
-0.046721700578927994,
0.003733907826244831,
0.03282005712389946,
-0.028814898803830147,
-0.013936271890997887,
0.055039189755916595,
0.04233606904745102,
0.04742901399731636,
0.013605223968625069,
-0.0041665262542665005,
-0.0007347279461100698,
0.03902224451303482,
0.0429612472653389,
0.06034732237458229,
0.03309774026274681,
0.02130705490708351,
-0.03712666779756546,
0.01188481692224741,
-0.011592810973525047,
-0.010862275958061218,
0.032827265560626984,
-0.003306033555418253,
0.019765814766287804,
0.003612245200201869,
0.01512824185192585,
0.014269156381487846,
-0.009102586656808853,
-0.049602556973695755,
-0.008999460376799107,
-0.0351942777633667,
0.047426488250494,
0.015635289251804352,
0.014538628049194813,
0.05727938190102577,
0.039400264620780945,
-0.03466789424419403,
0.02956637553870678,
-0.027598222717642784,
0.014653390273451805,
0.020854702219367027,
-0.032048068940639496,
0.05543132871389389,
0.0022779081482440233,
0.0131455659866333,
-0.0005747341201640666,
0.006704402156174183,
0.06322388350963593,
-0.03381397947669029,
-0.0024843087885528803,
-0.03474947437644005,
-0.048472195863723755,
0.04218732565641403,
0.04356846213340759,
-0.009562632068991661,
0.03452686965465546,
-0.042998384684324265,
-0.05488934367895126,
-0.04016260430216789,
-0.02626076713204384,
-0.0249846912920475,
0.015195564366877079,
0.06344719231128693,
-0.029010798782110214,
0.0010872099082916975,
-0.05334830284118652,
-0.07639167457818985,
0.026064343750476837,
-0.023748161271214485,
-0.05165635421872139,
0.012512910179793835,
0.007559408899396658,
0.0538378581404686,
0.041510775685310364,
-0.017658494412899017,
0.06880854070186615,
-0.022935057058930397,
0.038989488035440445,
0.03976517170667648,
-0.030426960438489914,
0.00868174433708191,
-0.008118724450469017,
0.018206322565674782,
0.023898763582110405,
-0.03892616182565689,
0.04291682317852974,
0.027872169390320778,
-0.022403312847018242,
-0.013455965556204319,
-0.029622193425893784,
0.018986977636814117,
-0.03603002801537514,
0.023903995752334595,
0.01189883891493082,
0.008623708039522171,
0.08063265681266785,
-0.015108712948858738,
-0.05164234712719917,
0.031137851998209953,
-0.017073120921850204,
-0.01256028562784195,
-0.023718638345599174,
0.015252839773893356,
0.028825121000409126,
0.06857138872146606,
0.03678812086582184,
-0.01987493224442005,
-0.011011159047484398,
0.021145857870578766,
-0.009268254041671753,
-0.012708654627203941,
-0.033322226256132126,
0.04453609511256218,
0.004200024995952845,
-0.013728184625506401,
-0.04361526668071747,
0.07229538261890411,
0.08150823414325714,
0.06237802281975746,
-0.006679821293801069,
-0.033647678792476654,
0.017567044124007225,
-0.013334646821022034,
0.004588935058563948,
-0.005342437420040369,
0.04431920126080513,
0.04852068051695824,
-0.016067003831267357,
-0.01088731549680233,
0.019542507827281952,
-0.007877830415964127,
0.07611414045095444,
0.026474960148334503,
0.0320134274661541,
-0.051197346299886703,
0.018126782029867172,
-0.05227702483534813,
-0.04693475365638733,
-0.010418549180030823,
0.037946559488773346,
-0.0009533556294627488,
-0.03260425105690956,
-0.0029679490253329277,
0.04761763662099838,
-0.040419407188892365,
-0.06346654891967773,
0.04511517658829689,
-0.03523555025458336,
0.020473673939704895,
-0.05229445919394493,
-0.023468831554055214,
0.05685795843601227,
0.025514114648103714,
-0.03916715830564499,
0.02097541280090809,
-0.015866609290242195,
-0.024270158261060715,
0.036383241415023804,
-0.0013687564060091972,
-0.025902768597006798,
-0.015245483256876469,
-0.024965092539787292,
-0.041784316301345825,
-0.058270931243896484,
-0.038051407784223557,
0.02103508822619915,
-0.027025295421481133,
-0.0008308264659717679,
-0.03377876430749893,
-0.01077784039080143,
-0.014119891449809074,
-0.00161369435954839,
-0.04501480981707573,
0.034578368067741394,
-0.011356060393154621
] |
<p>Given some observable $\mathcal O \in \mathcal H$ it is simple to construct a CP (completely positive) map $\Phi:\mathcal{H}\mapsto \mathcal{H}$ that conserves this quantity. All one has to observe is that
$$ \text{Tr}(\mathcal O \, \Phi[\rho]) = \text{Tr}(\Phi^*[\mathcal O] \rho).$$
Therefore, if we impose $\Phi^*[\mathcal O] = \mathcal O$, then $\text{Tr}(\mathcal O \, \Phi[\rho])=\text{Tr}(\mathcal O \rho), \; \forall \rho\in \mathcal H$. That amounts to impose that the Kraus operators of $\Phi^*$ should commute with $\mathcal O$.</p>
<p>I'd like, however, to construct a trace-preserving CP map for which the expectation value of $\mathcal O$ does not increase for any $\rho \in \mathcal H$. More explicitly, given $\mathcal O\in \mathcal H$, I want to construct $\Gamma:\mathcal H \mapsto \mathcal H$ such that
$$ \text{Tr}(\mathcal O\, \Gamma[\rho]) \le \text{Tr}(\mathcal O \rho), \; \forall \rho \in \mathcal H .$$</p>
<p>How would you go about that? Any ideas?</p> | g6633 | [
-0.0463545061647892,
-0.03593610227108002,
-0.020290065556764603,
-0.014598428271710873,
0.05574283003807068,
0.015966499224305153,
0.016926463693380356,
0.020368536934256554,
-0.03421960026025772,
-0.01709112711250782,
-0.0019916279707103968,
-0.004809324163943529,
0.022051770240068436,
0.03994215279817581,
-0.016707224771380424,
0.06118433550000191,
-0.00996400136500597,
0.004400775767862797,
-0.018874043598771095,
0.01460742112249136,
-0.0390341691672802,
-0.0013887598179280758,
0.04609113186597824,
0.001123229507356882,
0.05097733065485954,
-0.006938100792467594,
0.04770527780056,
0.017901824787259102,
0.008458451367914677,
-0.03131939843297005,
0.03209945559501648,
-0.008550796657800674,
0.013706986792385578,
-0.009789057075977325,
-0.047551557421684265,
0.014326394535601139,
0.04184681177139282,
0.06947380304336548,
0.038248155266046524,
0.00786143820732832,
0.036343153566122055,
-0.01957111433148384,
0.039472248405218124,
0.013774176128208637,
-0.010197022929787636,
-0.001497879857197404,
-0.0012036326806992292,
0.03479819372296333,
0.027746735140681267,
0.001136053237132728,
-0.015693126246333122,
0.027817843481898308,
0.01171023678034544,
-0.012133433483541012,
0.002933499636128545,
0.02380778267979622,
0.0006361700361594558,
-0.0645580068230629,
-0.01212812028825283,
-0.004313787445425987,
-0.007635803893208504,
-0.07837989181280136,
0.04923084378242493,
0.021446997299790382,
0.013745701871812344,
0.024579688906669617,
-0.030619004741311073,
0.012639946304261684,
-0.03742878884077072,
0.03036215342581272,
-0.02176346816122532,
0.0600176639854908,
0.018777206540107727,
-0.003199951956048608,
-0.053452782332897186,
0.04349832981824875,
-0.0023642675951123238,
0.01336135808378458,
0.04424944147467613,
-0.009002205915749073,
-0.03621259704232216,
0.009157177992165089,
0.07252877205610275,
0.05742306634783745,
-0.005154259502887726,
0.05826954543590546,
0.03387479484081268,
-0.02427259460091591,
-0.03528936579823494,
-0.005172667559236288,
0.009724079631268978,
-0.053904902189970016,
0.035353075712919235,
-0.0033914009109139442,
0.054818861186504364,
0.015548975206911564,
-0.005576504860073328,
0.01147354207932949,
0.04147084429860115,
-0.025375260040163994,
0.03658601641654968,
-0.008594289422035217,
0.03161325678229332,
-0.030957020819187164,
-0.01111580803990364,
-0.028010064736008644,
0.04523333162069321,
-0.023782595992088318,
-0.00492411432787776,
0.02187860943377018,
0.04365431144833565,
-0.017885297536849976,
-0.029241757467389107,
-0.050366077572107315,
-0.015881989151239395,
0.005228539928793907,
0.03992646560072899,
0.018942266702651978,
-0.015072178095579147,
0.02102554962038994,
-0.003242037957534194,
-0.012096705846488476,
0.007805502973496914,
0.028882352635264397,
0.015968019142746925,
0.05554413050413132,
-0.03852427005767822,
-0.002003749832510948,
0.07082872837781906,
-0.0016865675570443273,
0.00511731905862689,
0.026961499825119972,
-0.0014995213132351637,
0.033026114106178284,
-0.04168635234236717,
-0.019935976713895798,
-0.0475015826523304,
0.012821580283343792,
0.04515039548277855,
-0.051789551973342896,
-0.07666515558958054,
-0.011723808944225311,
-0.008259272202849388,
0.03604749217629433,
0.026323039084672928,
-0.06579285115003586,
0.022439394146203995,
-0.039510421454906464,
0.1023310124874115,
-0.020825650542974472,
-0.007064509205520153,
0.05701301991939545,
-0.04297996684908867,
0.05435064435005188,
0.00891746673732996,
0.006077669095247984,
0.037851423025131226,
-0.03003854490816593,
-0.046927936375141144,
0.003491699695587158,
-0.019534701481461525,
0.008758998475968838,
0.0031598203349858522,
-0.0220248531550169,
-0.02322029508650303,
-0.059045251458883286,
0.053582340478897095,
-0.06350147724151611,
-0.03038584068417549,
-0.014329330064356327,
-0.024179868400096893,
0.05133359506726265,
0.053145881742239,
-0.000627513334620744,
-0.03413321077823639,
-0.056143444031476974,
-0.06285372376441956,
0.012107468210160732,
0.010481237433850765,
0.001894516171887517,
-0.05413137748837471,
-0.05172491818666458,
-0.000343181483913213,
0.013330892659723759,
0.00036275730235502124,
-0.02166293002665043,
-0.07034824788570404,
-0.012428953312337399,
-0.07397769391536713,
0.015080547891557217,
0.01342836394906044,
-0.009620456956326962,
0.0001473135343985632,
0.052587997168302536,
-0.0008626988274045289,
0.0035921563394367695,
-0.011397657915949821,
-0.057240523397922516,
-0.01977686583995819,
0.032131511718034744,
0.029809923842549324,
-0.009360874071717262,
0.004656641744077206,
0.031093884259462357,
0.004295916296541691,
-0.009501320309937,
0.00656133983284235,
-0.05068756639957428,
0.020013729110360146,
-0.003044161479920149,
0.015094207599759102,
-0.08124859631061554,
0.0013459279434755445,
-0.018740670755505562,
0.008062539622187614,
-0.0603671669960022,
-0.018940772861242294,
0.013656348921358585,
0.011080797761678696,
-0.06714396178722382,
-0.015752339735627174,
-0.023172063753008842,
0.0966884195804596,
0.07044001668691635,
-0.08460187911987305,
0.04334164410829544,
0.00819172989577055,
0.01312434021383524,
-0.016768788918852806,
-0.004832219798117876,
-0.011413407512009144,
0.01949203573167324,
-0.05879319831728935,
-0.001992075936868787,
0.03919525071978569,
0.04473869875073433,
-0.050846848636865616,
0.07383663952350616,
-0.043523043394088745,
0.014703216962516308,
0.023806141689419746,
0.023533206433057785,
0.020886026322841644,
0.0363776795566082,
0.04545518755912781,
-0.04149574413895607,
0.05206730216741562,
0.0775216594338417,
-0.012034313753247261,
0.032517511397600174,
-0.05456569418311119,
0.026497434824705124,
0.03252110630273819,
-0.047596678137779236,
0.018249399960041046,
-0.023288168013095856,
0.011623878963291645,
-0.04498664662241936,
-0.01383946556597948,
0.00366421602666378,
-0.04156429320573807,
-0.036462027579545975,
-0.0195253174751997,
-0.024731451645493507,
-0.000705534010194242,
-0.006437093485146761,
-0.006282855290919542,
0.004453766625374556,
-0.0019686652813106775,
0.03345761075615883,
-0.02134772576391697,
0.01815136894583702,
0.022654030472040176,
0.08233091235160828,
-0.042151354253292084,
-0.05260506272315979,
-0.021172860637307167,
-0.0011935995426028967,
0.015379411168396473,
-0.0027714385651052,
0.05509527027606964,
-0.022723866626620293,
0.0007397879380732775,
0.012453729286789894,
-0.018150290474295616,
-0.07466291636228561,
-0.005361414980143309,
0.0005592532688751817,
0.042457472532987595,
0.05709698796272278,
-0.02615106664597988,
0.020464323461055756,
0.009849421679973602,
0.020152851939201355,
0.023866096511483192,
0.005290720146149397,
-0.021836601197719574,
0.002288177842274308,
0.0638013556599617,
-0.01789546199142933,
-0.0117284394800663,
0.011885834857821465,
0.03281603008508682,
0.019670885056257248,
0.052418727427721024,
0.020418260246515274,
-0.04900413379073143,
-0.0187798123806715,
0.009880832396447659,
0.001431447104550898,
0.003275218652561307,
-0.06570356339216232,
-0.0645880326628685,
-0.04967191815376282,
0.03134221211075783,
-0.019468260928988457,
-0.008752407506108284,
-0.025229426100850105,
-0.020470470190048218,
-0.03936068341135979,
0.010065258480608463,
-0.0417509526014328,
0.010788059793412685,
-0.011502006091177464,
0.022983135655522346,
0.034178297966718674,
-0.043672576546669006,
0.025938918814063072,
0.02293095365166664,
-0.02890692465007305,
0.02864302136003971,
0.023092731833457947,
0.04208509251475334,
-0.00458397576585412,
-0.020217780023813248,
-0.04346868395805359,
0.005243058316409588,
-0.0015145811485126615,
0.014271574094891548,
-0.03137408196926117,
0.003052202984690666,
-0.034975770860910416,
-0.054742760956287384,
-0.004470130894333124,
0.005100706126540899,
-0.036104317754507065,
0.011818013153970242,
-0.011941758915781975,
0.08377699553966522,
-0.06911769509315491,
0.003819570178166032,
-0.041545845568180084,
0.08105555176734924,
-0.02985934168100357,
0.012511814013123512,
0.030662978067994118,
0.01826043613255024,
0.03956916555762291,
0.043118298053741455,
0.007840480655431747,
-0.011652426794171333,
-0.03917673975229263,
-0.04306310415267944,
-0.002473750151693821,
-0.04227469488978386,
0.011630123481154442,
0.059539951384067535,
-0.01987098529934883,
0.015577636659145355,
0.023663882166147232,
0.030441300943493843,
0.02718193270266056,
0.008809366263449192,
-0.009583634324371815,
0.013701457530260086,
-0.054875850677490234,
0.02419397421181202,
0.0108128497377038,
0.000826752046123147,
0.0602370984852314,
-0.06175814941525459,
0.04044107720255852,
0.04236900806427002,
-0.02218429371714592,
0.029338721185922623,
-0.029623450711369514,
-0.00303148222155869,
0.002844860078766942,
-0.008918729610741138,
-0.02820710465312004,
-0.005456812679767609,
0.008913609199225903,
-0.0026162490248680115,
0.00017888452566694468,
0.04840478673577309,
-0.03663121163845062,
-0.00997205451130867,
-0.020298583433032036,
-0.007252700626850128,
0.031224332749843597,
0.00614508893340826,
-0.01367779541760683,
0.013308091089129448,
-0.04711700603365898,
-0.05059339478611946,
-0.06713451445102692,
0.10660809278488159,
0.07715961337089539,
0.001631382154300809,
-0.011036568321287632,
-0.03306591138243675,
-0.052719417959451675,
0.04266795516014099,
-0.01986994408071041,
0.049157049506902695,
0.024549361318349838,
0.005121659953147173,
-0.01714382879436016,
0.013686549849808216,
0.01505955122411251,
-0.05361536145210266,
0.018081214278936386,
-0.014323243871331215,
-0.018456749618053436,
0.026765547692775726,
0.04788434877991676,
0.007698428351432085,
0.01581702008843422,
-0.003481360152363777,
-0.004147957544773817,
-0.0034443484619259834,
0.0333203449845314,
0.019053371623158455,
0.027203667908906937,
-0.04812129959464073,
-0.007099401205778122,
-0.12401527911424637,
0.04427138715982437,
-0.09202836453914642,
0.0020482486579567194,
-0.019183587282896042,
-0.002440796233713627,
-0.04328560829162598,
-0.00619394239038229,
-0.03872097283601761,
0.020601851865649223,
0.0007026011007837951,
-0.0218493789434433,
-0.0213337279856205,
0.045988667756319046,
-0.05485035851597786,
0.03687693923711777,
0.009717602282762527,
0.011437472887337208,
0.03264262154698372,
-0.04081830754876137,
-0.014810249209403992,
-0.014985617250204086,
0.08615991473197937,
0.023258216679096222,
-0.04010792076587677,
-0.032666731625795364,
0.021272514015436172,
-0.010629327967762947,
0.07569169998168945,
0.011908654123544693,
-0.08984231948852539,
0.006639470811933279,
-0.043489888310432434,
-0.022534115239977837,
-0.017512129619717598,
0.08837573230266571,
0.03904100880026817,
-0.045012980699539185,
-0.042563438415527344,
0.07507909089326859,
-0.02190418913960457,
0.004045139066874981,
0.010065381415188313,
0.018327875062823296,
-0.06743641942739487,
0.017870446667075157,
0.01995149627327919,
0.013934536837041378,
0.02870939113199711,
0.053810521960258484,
-0.04051407426595688,
-0.04947032034397125,
-0.010647092945873737,
-0.013043002225458622,
0.033216509968042374,
0.041704628616571426,
0.06540685892105103,
0.05335767939686775,
-0.0023338235914707184,
-0.041586749255657196,
-0.011463794857263565,
0.009621698409318924,
0.004347218666225672,
-0.008618002757430077,
-0.04442044347524643,
-0.040215082466602325,
-0.032607946544885635,
0.009701544418931007,
0.01469505950808525,
0.026762016117572784,
0.03869253024458885,
0.04337453097105026,
0.011460237205028534,
0.011990280821919441,
-0.011816856451332569,
0.025954563170671463,
-0.010964767076075077,
0.006015580613166094,
-0.0318937674164772,
0.04648042097687721,
-0.04783187061548233,
-0.0004727527848444879,
-0.06481602787971497,
-0.1000719740986824,
0.057590287178754807,
-0.01678221859037876,
0.013019455596804619,
0.018024509772658348,
0.08008730411529541,
0.07195232063531876,
-0.022798752412199974,
-0.05956077575683594,
0.045122433453798294,
-0.027592696249485016,
0.037283800542354584,
-0.09335198253393173,
-0.0325547531247139,
-0.08022062480449677,
-0.009134355001151562,
-0.05628969520330429,
-0.01227666437625885,
0.0479600764811039,
0.02392447553575039,
0.008407220244407654,
-0.0490436926484108,
0.046924006193876266,
0.0165496114641428,
0.061356306076049805,
0.005941352806985378,
-0.03994840383529663,
-0.035092875361442566,
-0.015141488052904606,
-0.010547253303229809,
0.00628775916993618,
0.0014612057711929083,
-0.012799943797290325,
-0.0061596455052495,
-0.00493572186678648,
0.06757661700248718,
-0.001454037381336093,
0.017586370930075645,
-0.0016242775600403547,
-0.02167929708957672,
-0.0066025517880916595,
-0.014132853597402573,
-0.014112691394984722,
0.028203487396240234,
0.060179829597473145,
0.03385234624147415,
-0.009484559297561646,
0.001445333007723093,
-0.028402602300047874,
0.0706300288438797,
0.04098593816161156,
-0.013574767857789993,
0.025539297610521317,
-0.0011959712719544768,
0.012311034835875034,
-0.005235388409346342,
0.006970195099711418,
-0.026470854878425598,
-0.009294076822698116,
0.0458575077354908,
-0.01441638357937336,
0.0026940484531223774,
-0.034761857241392136,
0.0057588485069572926,
-0.06892403215169907,
-0.04675227403640747,
0.04154431074857712,
0.002651395509019494,
-0.009994695894420147,
0.061831388622522354,
0.05277718976140022,
0.01461088564246893,
0.04445669427514076,
-0.02438838593661785,
0.011902879923582077,
0.04464902728796005,
-0.029161011800169945,
-0.04663681611418724,
-0.00843653455376625,
-0.030782027170062065,
-0.05193887650966644,
0.024438604712486267,
0.010806816630065441,
0.0834498405456543,
-0.06838228553533554,
-0.01159269642084837,
0.012047256343066692,
-0.03618818148970604,
0.022251766175031662,
0.02278069593012333,
-0.01961812749505043,
-0.04198666289448738,
0.008932216092944145,
-0.03837299719452858,
-0.026384321972727776,
-0.0042589339427649975,
-0.02913593128323555,
0.04874042049050331,
0.06781435012817383,
-0.022570235654711723,
0.03457564488053322,
-0.040463417768478394,
0.01556306891143322,
0.0012410077033564448,
0.03211585804820061,
-0.019241061061620712,
-0.03284655138850212,
0.07555130869150162,
-0.013772435486316681,
0.030924247577786446,
0.00730855343863368,
-0.02323870174586773,
0.07031451165676117,
-0.02315625362098217,
-0.05657995492219925,
0.002012372948229313,
0.020621569827198982,
-0.04177144914865494,
0.024315761402249336,
0.01427350752055645,
0.010764236561954021,
0.011618106625974178,
0.0037003078032284975,
0.04083547741174698,
-0.030987540259957314,
-0.026620836928486824,
-0.04327531158924103,
0.03622567281126976,
-0.007317093666642904,
-0.06769106537103653,
0.010955573990941048,
0.08311440050601959,
0.02715974673628807,
-0.010651023127138615,
-0.0683659240603447,
-0.02011885493993759,
-0.003951107617467642,
0.058627888560295105,
0.041957370936870575,
0.05589045584201813,
-0.0028214072808623314,
0.0243461225181818,
-0.0795368030667305,
0.012928467243909836,
0.022078007459640503,
0.029024170711636543,
-0.0015452451771125197,
-0.057385869324207306,
-0.0065911561250686646,
0.0215334240347147,
-0.015709172934293747,
0.026425674557685852,
0.05302964895963669,
-0.008159837685525417,
0.019550157710909843,
0.035333339124917984,
-0.0005810914444737136,
0.03031572885811329,
0.054213106632232666,
-0.04290332645177841,
0.010924607515335083,
-0.03745512664318085,
-0.024834901094436646,
-0.002680027624592185,
-0.03436729684472084,
0.02365047112107277,
-0.01778990589082241,
-0.0705542266368866,
-0.02649286389350891,
0.00748396897688508,
-0.001992651494219899,
-0.01708958111703396,
-0.028083404526114464,
0.036145586520433426,
0.0022698005195707083,
0.025498967617750168,
0.04267304390668869,
-0.019956178963184357,
0.009894788265228271,
0.00450082216411829,
0.024601945653557777,
0.003148564137518406,
-0.020057352259755135,
0.02568860724568367,
-0.01750039868056774,
0.025119919329881668,
-0.029786890372633934,
-0.03200299292802811,
-0.09690862894058228,
-0.033951178193092346,
-0.020482221618294716,
-0.05577121302485466,
0.0013315394753590226,
-0.019657038152217865,
-0.011449357494711876,
0.09377753734588623,
-0.03148087486624718,
-0.011670957319438457,
-0.023353977128863335,
0.0883929505944252,
-0.04129461571574211,
-0.007266497705131769,
-0.03674152120947838,
-0.0098413722589612,
-0.03666268289089203,
-0.016630135476589203,
-0.05657817795872688,
-0.023318715393543243,
-0.011231360025703907,
-0.0015245237154886127,
0.048317402601242065,
-0.01111278124153614,
-0.06771713495254517,
-0.03558310493826866,
0.06254899501800537,
-0.0007887142128311098,
0.043775975704193115,
-0.01832784339785576,
0.009881734848022461,
-0.0019430036190897226,
-0.03635099157691002,
-0.06291035562753677,
-0.05589621886610985,
-0.0002644727355800569,
-0.021863697096705437,
0.0195908322930336,
0.05705060809850693,
0.02137768268585205,
-0.03900140896439552,
0.06840755045413971,
-0.05123795196413994,
-0.015190492384135723,
0.03234424069523811,
-0.014078565873205662,
-0.0017322424100711942,
-0.0015187151730060577,
-0.02785644680261612,
0.03640495613217354,
-0.030769865959882736,
0.037959273904561996,
0.020000265911221504,
0.05373430252075195,
-0.017083799466490746,
-0.052814073860645294,
0.0343858040869236,
-0.061041444540023804,
-0.037727925926446915,
0.07466711848974228,
-0.04598654434084892
] |
<p>I need to find the possible values of energies and impulses of virtual photon emitted by real electron. I don't understand how to compute it (look to the text below). </p>
<p>Let's introduce the free electron. Then let's use the frame in which it is at rest. </p>
<p>So the laws of energy-momentum conservation take the form
$$
E_{0} = E_{1} + E_{photon}, \quad 0 = p_{1} + p_{photon} .
$$
According to this, electron after photon emission must be virtual.
What to do after that? Formally I have only two equations for four unknown values. What to do next? To use energy-impulse relation $p_{\mu}p^{\mu} = m^2c^2$ for virtual particles?</p> | g6634 | [
0.022122198715806007,
-0.03383617848157883,
-0.010211775079369545,
-0.00836323481053114,
0.005989873316138983,
-0.018089473247528076,
0.0016359178116545081,
0.07748852670192719,
-0.032876405864953995,
0.014132913202047348,
-0.02462651953101158,
0.03675992414355278,
0.016582651063799858,
0.010322903282940388,
-0.00043542051571421325,
0.007425595074892044,
0.12196551263332367,
0.020006537437438965,
-0.0005244354251772165,
0.0037475954741239548,
-0.006630841176956892,
-0.019132662564516068,
-0.023568926379084587,
-0.05249559506773949,
0.005287772975862026,
0.013150759972631931,
0.009997650980949402,
0.03907677158713341,
-0.029118746519088745,
-0.028271827846765518,
-0.010478530079126358,
-0.011138688772916794,
0.061648525297641754,
0.005253027658909559,
-0.0027356345672160387,
-0.0007651867927052081,
0.08858942240476608,
-0.004487655591219664,
-0.001071658916771412,
-0.01753827929496765,
-0.023073792457580566,
-0.04537775367498398,
0.018114637583494186,
0.012072905898094177,
0.01443287543952465,
0.024916471913456917,
-0.0009631774155423045,
-0.012848773039877415,
0.015559643507003784,
-0.031601134687662125,
0.040197860449552536,
0.05772819370031357,
-0.00022645328135695308,
-0.0020817748736590147,
0.02925461158156395,
0.0015452464576810598,
0.024047406390309334,
-0.0027796169742941856,
0.07016520202159882,
0.023578127846121788,
0.02431711181998253,
-0.06051669269800186,
0.009405015036463737,
0.00921181496232748,
0.10335229337215424,
-0.01651736907660961,
-0.047420844435691833,
0.022216638550162315,
-0.03362080082297325,
-0.010935526341199875,
0.012560484930872917,
-0.027386998757719994,
-0.006631991360336542,
-0.030912388116121292,
0.012368266470730305,
-0.0399126298725605,
-0.030598705634474754,
-0.0430261492729187,
-0.017492834478616714,
0.036355264484882355,
-0.015319278463721275,
0.006939467042684555,
0.07503160089254379,
-0.017941614612936974,
0.01570536382496357,
-0.013109236024320126,
-0.03526390716433525,
-0.0009447582415305078,
-0.01956949755549431,
-0.06429688632488251,
0.04021007567644119,
-0.025666631758213043,
0.07025327533483505,
-0.01812121644616127,
0.021707884967327118,
0.0013436985900625587,
-0.0577697828412056,
0.060469165444374084,
0.0187155120074749,
-0.02695038728415966,
0.013178694061934948,
-0.05687138810753822,
0.009307446889579296,
-0.06233036890625954,
0.023788299411535263,
-0.04305442422628403,
-0.014794597402215004,
0.0021280318032950163,
0.031179916113615036,
0.0004017840838059783,
-0.04085918143391609,
-0.08970420062541962,
-0.03200014680624008,
-0.06790398061275482,
-0.04105140268802643,
-0.023944448679685593,
0.02661559171974659,
-0.04602072015404701,
-0.008306264877319336,
0.10242452472448349,
0.027981502935290337,
-0.01523937750607729,
0.0209937933832407,
0.05843242630362511,
0.036887433379888535,
-0.04089120030403137,
-0.0066842203959822655,
-0.007862482219934464,
0.01013996358960867,
-0.005386958830058575,
0.00571067351847887,
-0.032412897795438766,
0.009336075745522976,
0.040447745472192764,
0.018360339105129242,
0.010180076584219933,
0.045125238597393036,
0.016886482015252113,
0.027298806235194206,
-0.04075542464852333,
-0.005766131915152073,
-0.018897606059908867,
-0.010603716596961021,
-0.043845679610967636,
-0.07290560752153397,
-0.026806460693478584,
-0.012060901150107384,
-0.050980325788259506,
0.025650113821029663,
-0.006837224587798119,
0.05434832721948624,
0.06254949420690536,
-0.019745778292417526,
-0.02651044726371765,
0.03458642587065697,
-0.05256756395101547,
0.012868926860392094,
-0.025956472381949425,
-0.08523797988891602,
0.01622842252254486,
0.030873602256178856,
-0.022398239001631737,
0.019096486270427704,
0.0023652701638638973,
0.012854192405939102,
0.015535062178969383,
0.00129148259293288,
-0.07520359009504318,
-0.04213091358542442,
-0.049781810492277145,
-0.027146652340888977,
-0.0173760037869215,
0.01609310880303383,
0.011634409427642822,
-0.019830740988254547,
0.04284609481692314,
-0.008325130678713322,
-0.033773597329854965,
0.009469916112720966,
0.04091915115714073,
-0.013308743946254253,
-0.05480395257472992,
0.05018417537212372,
0.02797059156000614,
0.011223184876143932,
0.02372257597744465,
0.004983484745025635,
0.032655268907547,
0.0049177478067576885,
-0.02124808356165886,
-0.010665230453014374,
0.028895989060401917,
0.03300055116415024,
-0.02129165083169937,
-0.043154481798410416,
0.0016731125069782138,
0.009857461787760258,
-0.03169352188706398,
-0.037468671798706055,
0.027244633063673973,
-0.027153175324201584,
0.07900657504796982,
-0.016008738428354263,
0.01751951314508915,
0.004419159144163132,
-0.0025374034885317087,
0.03776589781045914,
-0.02458920143544674,
-0.021415814757347107,
-0.0031539828050881624,
0.047341488301754,
-0.045499227941036224,
0.017913656309247017,
0.03500693663954735,
0.010951134376227856,
-0.007988400757312775,
-0.007951137609779835,
-0.03280871361494064,
-0.02758888155221939,
0.01341198105365038,
-0.04202093929052353,
0.016777941957116127,
0.05260537937283516,
-0.019619332626461983,
-0.03174002841114998,
0.02072632499039173,
-0.0404001846909523,
-0.01779719814658165,
0.007833925075829029,
0.02046952210366726,
-0.005457252264022827,
0.042270202189683914,
-0.0041619762778282166,
-0.027662523090839386,
0.05149947106838226,
0.07383083552122116,
-0.048841726034879684,
0.034384287893772125,
0.030440164729952812,
-0.00013187942386139184,
0.064463771879673,
-0.015393955633044243,
0.06764468550682068,
-0.020413782447576523,
0.004703492857515812,
-0.03551322966814041,
0.07428158819675446,
0.02712482586503029,
-0.021782973781228065,
-0.022287385538220406,
-0.054214075207710266,
0.011431146413087845,
-0.007512653712183237,
0.08083619177341461,
-0.05262785777449608,
-0.029780542477965355,
-0.012418362312018871,
0.02020685374736786,
-0.09740503132343292,
-0.01901370659470558,
0.006019935477524996,
-0.029357170686125755,
-0.06905485689640045,
0.06855855882167816,
0.00044012037687934935,
0.004826460033655167,
0.023068564012646675,
0.013709943741559982,
-0.009485716931521893,
-0.011159214191138744,
-0.004094469361007214,
0.04153813421726227,
-0.045856721699237823,
-0.006727237720042467,
0.03274742513895035,
-0.020475367084145546,
0.05581328645348549,
0.0020005875267088413,
0.002746171085163951,
-0.04745887964963913,
-0.02393130585551262,
-0.029002051800489426,
-0.008120657876133919,
0.0029109951574355364,
0.02270076796412468,
-0.1414434164762497,
0.04441361501812935,
0.016356978565454483,
-0.01587997004389763,
-0.05404273420572281,
-0.0613553412258625,
0.030662810429930687,
-0.03514420613646507,
0.012903222814202309,
-0.059919361025094986,
0.02405400760471821,
0.06777006387710571,
0.03110348992049694,
-0.020081734284758568,
0.017453240230679512,
0.009793504141271114,
-0.01747375912964344,
-0.007763225585222244,
-0.03282700479030609,
0.025458892807364464,
0.02676239237189293,
-0.0704665556550026,
0.023354457691311836,
0.0338938944041729,
0.01812453381717205,
-0.017775803804397583,
0.033288829028606415,
0.0024325610138475895,
-0.06174618378281593,
-0.006960228551179171,
-0.008645097725093365,
0.031288374215364456,
-0.01080159842967987,
-0.04200907051563263,
0.0072546484880149364,
-0.06585177034139633,
-0.04280424863100052,
0.03294873237609863,
0.00043319573160260916,
0.03425245359539986,
0.042955122888088226,
-0.052649714052677155,
-0.011511360295116901,
-0.0037053250707685947,
0.0310768261551857,
0.012852621264755726,
0.007015963550657034,
0.012924487702548504,
0.0026634689420461655,
0.029079614207148552,
-0.04473303258419037,
-0.01322813332080841,
0.02534538134932518,
0.036069173365831375,
-0.06459987163543701,
0.0014529338805004954,
0.025769801810383797,
-0.0633307620882988,
0.013444600626826286,
0.04849257692694664,
-0.046667423099279404,
-0.05370178073644638,
0.04089833050966263,
-0.020577190443873405,
-0.08770500123500824,
0.006923421286046505,
-0.02570091001689434,
0.018922757357358932,
0.00914067029953003,
-0.008344287984073162,
0.06426853686571121,
0.010169652290642262,
0.027693284675478935,
0.02972721867263317,
-0.007872799411416054,
-0.05826808512210846,
-0.027809472754597664,
0.06691674888134003,
-0.017610281705856323,
-0.019208231940865517,
-0.04096322879195213,
-0.017687669023871422,
0.0032423639204353094,
0.01104048453271389,
-0.007649527862668037,
0.05775536969304085,
-0.02578035742044449,
-0.017048094421625137,
-0.0009636000031605363,
-0.07916262000799179,
-0.014741158112883568,
0.014300419948995113,
0.01495407149195671,
-0.02893303707242012,
0.02507486566901207,
0.014297395944595337,
0.005063161253929138,
0.07016943395137787,
0.038176264613866806,
0.04254883527755737,
0.04779372736811638,
-0.028941351920366287,
0.038363438099622726,
0.03392500802874565,
0.01937061734497547,
0.049759335815906525,
-0.06039327755570412,
-0.07005821913480759,
-0.01525053195655346,
-0.0036504450254142284,
-0.02043747901916504,
0.04484423249959946,
-0.07925871014595032,
-0.03700751066207886,
-0.0005255434662103653,
-0.005267843138426542,
0.05717695131897926,
0.042194467037916183,
0.010961441323161125,
0.013865700922906399,
0.05812409520149231,
0.0302484892308712,
0.000008780425559962168,
0.018850326538085938,
-0.019600413739681244,
-0.03551063686609268,
0.016163649037480354,
0.030491504818201065,
-0.04589458927512169,
-0.04601823911070824,
-0.028704017400741577,
0.002410290762782097,
-0.04339488223195076,
0.04309919849038124,
-0.012218519113957882,
0.018525371327996254,
-0.016337133944034576,
0.04756191372871399,
-0.061190370470285416,
-0.021022174507379532,
0.08401834964752197,
0.07451707124710083,
-0.03739793226122856,
0.00926977675408125,
-0.011396539397537708,
0.0316353365778923,
-0.01271421555429697,
0.010399945080280304,
0.026290226727724075,
-0.04133103787899017,
0.027286460623145103,
-0.061023078858852386,
0.02135051041841507,
-0.023929456248879433,
0.07230032235383987,
0.10319318622350693,
0.019635813310742378,
0.07014203816652298,
-0.008815169334411621,
0.01076155062764883,
0.051210369914770126,
-0.04050462320446968,
-0.03287394344806671,
0.032105568796396255,
-0.011305173859000206,
0.0826469212770462,
-0.03162309527397156,
-0.003840067656710744,
-0.036353982985019684,
0.014507207088172436,
-0.032573141157627106,
-0.019323932006955147,
-0.006527455057948828,
0.0389048270881176,
0.03315482661128044,
-0.019701343029737473,
-0.003120949724689126,
0.014598691835999489,
0.006596371065825224,
0.048344653099775314,
-0.003941453993320465,
-0.08532139658927917,
0.022225935012102127,
-0.027087388560175896,
-0.03228403627872467,
0.06662864983081818,
-0.006547538097947836,
-0.016337836161255836,
-0.04256009683012962,
0.004685089457780123,
-0.019263435155153275,
-0.05417339503765106,
0.010035140439867973,
-0.0028468724340200424,
0.0008597444393672049,
-0.007995509542524815,
-0.0064463065937161446,
0.008246159180998802,
0.022759808227419853,
-0.008172356523573399,
-0.015398044139146805,
-0.023131022229790688,
0.009233403950929642,
-0.01525248121470213,
-0.029590431600809097,
-0.011470256373286247,
0.04106241092085838,
-0.050389450043439865,
-0.0014227384235709906,
0.07652069628238678,
0.021209752187132835,
-0.005623131059110165,
0.03278637304902077,
-0.0031307300087064505,
0.007356664165854454,
-0.05092222988605499,
-0.017317993566393852,
-0.042690545320510864,
-0.01812257617712021,
0.0216506514698267,
0.018627161160111427,
0.04365244135260582,
-0.011853438802063465,
-0.012016755528748035,
-0.008339786902070045,
0.015553762204945087,
-0.030590049922466278,
0.017848920077085495,
-0.051048923283815384,
0.0021001624409109354,
0.0036177723668515682,
0.028344951570034027,
-0.010294223204255104,
-0.007198110222816467,
-0.01157298218458891,
0.09555863589048386,
0.005231753457337618,
0.08690577000379562,
-0.028655633330345154,
0.0036510443314909935,
-0.016063997521996498,
0.0035975580103695393,
-0.03705849498510361,
0.03493180125951767,
0.015240340493619442,
-0.0076984139159321785,
-0.05091528221964836,
-0.06208285689353943,
0.012020199559628963,
-0.027385447174310684,
0.019849015399813652,
-0.026989521458745003,
-0.01717614382505417,
0.005415512714534998,
0.011539104394614697,
-0.011409563012421131,
-0.008177953772246838,
0.00186153466347605,
0.027422942221164703,
0.01980910636484623,
-0.01664331741631031,
-0.0061873821541666985,
-0.0029388475231826305,
0.027171852067112923,
0.015604016371071339,
0.0031739973928779364,
-0.0030276011675596237,
0.020628033205866814,
-0.05261344835162163,
0.022828781977295876,
-0.008514335379004478,
0.04348661005496979,
0.020030273124575615,
-0.03435507044196129,
0.014113877899944782,
0.019984178245067596,
0.02455255389213562,
0.011971909552812576,
0.05319579690694809,
0.011926471255719662,
0.0509309321641922,
0.010928978212177753,
-0.06289467215538025,
-0.0412554033100605,
-0.028875205665826797,
-0.013164978474378586,
0.004831546917557716,
0.0017011883901432157,
-0.016832713037729263,
0.027423975989222527,
0.041908495128154755,
0.060999829322099686,
-0.005730749107897282,
-0.07698357105255127,
-0.012114107608795166,
0.0037097963504493237,
0.053244415670633316,
0.027422316372394562,
-0.0064612082205712795,
-0.010119414888322353,
0.03838683292269707,
-0.023987391963601112,
-0.026369865983724594,
0.03045508824288845,
-0.029905691742897034,
0.05742647126317024,
0.0014347319956868887,
-0.0577361099421978,
-0.020529979839920998,
-0.0359966978430748,
0.019527530297636986,
0.048151981085538864,
-0.07742299139499664,
-0.04799971356987953,
0.039865072816610336,
0.05776330828666687,
0.04691087454557419,
-0.03809129819273949,
-0.016131190583109856,
0.023903945460915565,
0.021067796275019646,
-0.01818791776895523,
0.03961601480841637,
-0.031547658145427704,
0.01605779118835926,
-0.050690799951553345,
0.009676385670900345,
0.01072672288864851,
0.002467980608344078,
0.002989367116242647,
-0.02931886911392212,
-0.007240956649184227,
0.0648496225476265,
0.014541545882821083,
-0.005836845841258764,
0.023899365216493607,
-0.049453891813755035,
-0.0010401791660115123,
0.00520152784883976,
0.08350448310375214,
0.0039293463341891766,
-0.02797766961157322,
0.029655858874320984,
0.09375264495611191,
0.004713563248515129,
-0.002021568128839135,
-0.03815663978457451,
0.02363838255405426,
0.058875031769275665,
0.03972085192799568,
0.05251492187380791,
-0.03187170624732971,
0.06768340617418289,
-0.020762739703059196,
0.04767397418618202,
0.009951883926987648,
-0.021903827786445618,
0.03494732826948166,
0.019071558490395546,
-0.056282807141542435,
-0.00390959158539772,
0.0018274409230798483,
-0.041560813784599304,
-0.015043582767248154,
0.016152942553162575,
-0.0019740008283406496,
-0.0014215100090950727,
0.04695834219455719,
0.03828714042901993,
-0.06222599744796753,
-0.01565958373248577,
-0.0020925540011376143,
-0.011129346676170826,
0.022823425009846687,
-0.04850809648633003,
-0.013040848076343536,
-0.08523614704608917,
0.0294962078332901,
0.001992426346987486,
0.053601861000061035,
0.00214563705958426,
-0.008025139570236206,
-0.054414331912994385,
0.011670942418277264,
-0.03589944541454315,
-0.017644770443439484,
-0.043710436671972275,
-0.07713209092617035,
-0.01958596520125866,
0.0002466272853780538,
0.0058565144427120686,
-0.012465585954487324,
0.09506049007177353,
-0.07451269775629044,
-0.004530498757958412,
-0.04256764426827431,
0.059766415506601334,
-0.06341991573572159,
0.0065464130602777,
-0.005036324728280306,
0.026328951120376587,
0.017714276909828186,
0.017573213204741478,
-0.010988876223564148,
0.027891743928194046,
-0.026309572160243988,
-0.003034924855455756,
0.04742198809981346,
-0.06327397376298904,
0.005733674857765436,
-0.007536624558269978,
0.011817220598459244,
-0.03748319298028946,
0.03391876444220543,
0.0009314838680438697,
0.017011627554893494,
-0.02793744206428528,
0.06356488913297653,
0.05004708468914032,
-0.04316489025950432,
0.003798567457124591,
0.009878904558718204,
-0.09253327548503876,
-0.01787268929183483,
0.009455590508878231,
-0.006024971138685942,
-0.04898285120725632,
0.012724760919809341,
0.022472769021987915,
0.026993338018655777,
-0.022994032129645348,
-0.020350730046629906,
0.0981953963637352,
0.03204500675201416,
0.01815744675695896,
-0.007527201436460018,
-0.0169194545596838,
-0.017903784289956093,
-0.006488972343504429,
0.028176860883831978,
-0.014090928249061108,
-0.0021754915360361338,
0.01257337350398302,
0.0018434333615005016,
-0.013011729344725609,
-0.05150473862886429,
-0.04574952274560928,
-0.030467543751001358,
0.016802702099084854,
0.04262230545282364,
0.011226806789636612,
0.022655973210930824,
0.008982725441455841,
0.021477585658431053,
0.03554235398769379,
0.011161407455801964,
-0.11395877599716187,
-0.014727378264069557,
-0.0156727135181427,
-0.007375455927103758,
-0.07532816380262375,
-0.024877864867448807,
-0.0011577816912904382,
0.057567447423934937,
0.007038157433271408,
-0.00013102177763357759,
-0.0027678452897816896,
-0.02924031764268875,
0.046515125781297684,
0.07460620254278183,
-0.08704342693090439,
-0.009447403252124786,
0.008455140516161919,
0.03711044043302536,
0.030358850955963135,
-0.018129484727978706,
0.01634235493838787,
-0.005174737423658371,
0.01670655980706215,
0.008795049041509628,
-0.08743573725223541,
-0.012707139365375042,
0.010844703763723373
] |
<p>Quantization of gravity (general relativity) seems to be impossible for spacetime dimension D >= 4. Instead, quantum gravity is described by string theory which is something more than quantization (for example it introduces an infinite number of fields). More direct approaches to quantization of gravity have failed (my opinion; not everyone would agree on this).</p>
<p>However, gravity in dimensions D < 4 is special, because it is topological (carries no dynamic degrees of freedom locally). It is possible to quantize gravity coupled to other fields at D = 2: in fact perturbative string theory is exactly that! What about D = 3? Are there approaches to quantization of gravity (coupled to other fields) which have been more successful at D = 3 than at D = 4?</p> | g6635 | [
0.04836403578519821,
0.04639919474720955,
0.002237471519038081,
-0.045342616736888885,
-0.009300848469138145,
0.056013114750385284,
0.0226230937987566,
-0.05022527649998665,
-0.07669596374034882,
-0.029176626354455948,
0.03936426341533661,
-0.024657245725393295,
0.0127084506675601,
-0.006568507757037878,
-0.017967768013477325,
0.0024522251915186644,
0.014387024566531181,
0.0337430015206337,
0.04699862748384476,
-0.0554727241396904,
0.023561138659715652,
-0.020684152841567993,
0.05379810556769371,
-0.041989438235759735,
-0.025914782658219337,
-0.030117211863398552,
0.026422036811709404,
-0.024710552766919136,
-0.008741949684917927,
-0.010517604649066925,
-0.030775997787714005,
-0.0024742642417550087,
0.018249662593007088,
0.029595712199807167,
-0.0007582546095363796,
-0.04940947890281677,
-0.002508187899366021,
0.027553893625736237,
-0.008454433642327785,
-0.06261114776134491,
-0.006997406017035246,
-0.0068379612639546394,
-0.027873879298567772,
0.01841813698410988,
-0.01774042285978794,
0.015560339204967022,
-0.001455472782254219,
0.017233580350875854,
0.04485685005784035,
-0.0008118526311591268,
0.0026890470180660486,
0.08606830984354019,
0.03803272172808647,
-0.03413434699177742,
0.053416237235069275,
0.011270283721387386,
0.01873217150568962,
0.01609034277498722,
0.0299547016620636,
0.055006325244903564,
-0.009914358146488667,
0.04159830883145332,
0.015922680497169495,
0.010345477610826492,
0.02644382230937481,
0.03530624136328697,
-0.03721123933792114,
-0.030498482286930084,
0.020470894873142242,
-0.06324180215597153,
0.03728247433900833,
-0.07129967212677002,
0.036200232803821564,
0.031836505979299545,
0.001225836924277246,
0.04383089765906334,
-0.026308514177799225,
0.009705285541713238,
-0.03943348303437233,
-0.010745923034846783,
-0.015660326927900314,
-0.00495596369728446,
-0.04356704279780388,
-0.04707081988453865,
0.058833684772253036,
-0.027537796646356583,
0.016729796305298805,
0.026305027306079865,
0.025944910943508148,
0.0399676077067852,
-0.011506878770887852,
0.0053285760805010796,
0.04239027202129364,
0.05030059069395065,
-0.03942158445715904,
0.0066440352238714695,
0.04797119274735451,
0.11686942726373672,
-0.02322731539607048,
-0.0419870987534523,
-0.021254926919937134,
0.05166160687804222,
0.029643651098012924,
0.01527989748865366,
0.004024064168334007,
-0.023939019069075584,
0.07554376125335693,
0.034865397959947586,
0.0624631904065609,
0.0016070569399744272,
-0.047916147857904434,
0.04007141664624214,
-0.012414978817105293,
0.00465846061706543,
-0.0694197490811348,
0.0186457596719265,
-0.007012238260358572,
-0.037799954414367676,
-0.05931691452860832,
0.02042289823293686,
0.011321833357214928,
0.041431013494729996,
0.022012151777744293,
0.027076682075858116,
-0.026910869404673576,
0.03231291472911835,
-0.06035465747117996,
-0.010925035923719406,
0.040562693029642105,
-0.00008734199946047738,
-0.0045953551307320595,
-0.03533416613936424,
0.0047022877261042595,
0.027536874637007713,
-0.011918674223124981,
0.024662073701620102,
-0.02260182425379753,
-0.009773507714271545,
-0.038744814693927765,
0.06310168653726578,
-0.03640418499708176,
-0.06201409548521042,
-0.004094368312507868,
0.01973867416381836,
-0.008810257539153099,
0.006732883397489786,
0.017075195908546448,
0.012496674433350563,
-0.00787370279431343,
0.008727556094527245,
0.03944697231054306,
0.050529345870018005,
0.05550793185830116,
-0.04822731018066406,
0.011749399825930595,
0.036555659025907516,
-0.014577721245586872,
0.0028984295204281807,
0.011187508702278137,
0.006985981948673725,
-0.00813011359423399,
0.032953664660453796,
-0.031871307641267776,
-0.06007647141814232,
0.04837606102228165,
0.0307049211114645,
0.06442267447710037,
-0.028099671006202698,
-0.012446374632418156,
-0.034427460283041,
-0.04319113492965698,
-0.003806181252002716,
0.022268271073698997,
0.026322484016418457,
-0.02956622838973999,
0.007519800215959549,
-0.06811197847127914,
0.008481744676828384,
-0.13300497829914093,
0.00830016192048788,
0.08824483305215836,
-0.022639427334070206,
-0.008753488771617413,
-0.06220315769314766,
0.0032586748711764812,
0.04757803678512573,
0.028719646856188774,
-0.026878399774432182,
0.01524004340171814,
0.018111905083060265,
-0.05066680163145065,
0.019016647711396217,
0.06355845183134079,
0.00727224163711071,
0.007584556937217712,
-0.013597645796835423,
0.0460960790514946,
-0.01729961484670639,
0.005996303167194128,
0.002734281588345766,
0.007834019139409065,
0.04776680842041969,
0.06133396923542023,
0.0036737381014972925,
0.06702814996242523,
0.005417016334831715,
-0.05373706296086311,
0.06373855471611023,
0.017138823866844177,
0.005724079441279173,
0.05142902210354805,
-0.01720556803047657,
0.03361840918660164,
-0.012781830504536629,
-0.026004130020737648,
0.020514989271759987,
0.008200835436582565,
0.031176621094346046,
-0.01748163066804409,
0.08077845722436905,
0.01591493748128414,
-0.00022190903837326914,
0.09566591680049896,
0.06483975052833557,
-0.039815183728933334,
-0.013169498182833195,
-0.05640658363699913,
0.01641264744102955,
-0.0002709509280975908,
-0.00022778984566684812,
-0.041480548679828644,
-0.03631583973765373,
-0.022682132199406624,
-0.02130313590168953,
-0.0013383427867665887,
0.029131906107068062,
-0.021118929609656334,
-0.09128188341856003,
0.022192930802702904,
0.019802870228886604,
0.05017276108264923,
0.025188015773892403,
-0.015594192780554295,
-0.05119987204670906,
0.04697701334953308,
-0.03589484468102455,
-0.023966288194060326,
0.028451375663280487,
-0.03008710965514183,
0.024183716624975204,
-0.0062055764719843864,
0.003525611711665988,
-0.02805478312075138,
-0.009154282510280609,
0.03565264120697975,
0.04504095017910004,
0.06203000992536545,
0.029670774936676025,
-0.05584334954619408,
-0.016248252242803574,
-0.0076897647231817245,
-0.039547890424728394,
0.04748310521245003,
0.00779788987711072,
-0.037685688585042953,
-0.019171861931681633,
-0.025904439389705658,
0.011330584064126015,
-0.01607789658010006,
0.018668828532099724,
-0.08431088924407959,
0.012529542669653893,
-0.003421878907829523,
0.023386836051940918,
0.0015987860970199108,
0.019461067393422127,
0.016683857887983322,
0.028567349538207054,
-0.014344636350870132,
-0.02721187099814415,
0.003735005622729659,
0.009395408444106579,
-0.023488739505410194,
-0.020383434370160103,
0.03407180309295654,
-0.028604883700609207,
-0.02014555223286152,
-0.02265860140323639,
-0.006834285333752632,
-0.001932348357513547,
0.04683854058384895,
0.005410900805145502,
-0.04805775731801987,
0.03368240222334862,
0.005256797652691603,
0.033925194293260574,
-0.06955987960100174,
-0.002396135590970516,
-0.006681548431515694,
0.013788643293082714,
0.022488972172141075,
0.004919647704809904,
0.021077895537018776,
0.02958398126065731,
0.038267869502305984,
-0.0574081651866436,
-0.059583019465208054,
-0.039907459169626236,
-0.023940425366163254,
-0.03815114498138428,
0.00603870814666152,
0.007693212479352951,
-0.007239201571792364,
0.017307814210653305,
-0.019976109266281128,
-0.00470660999417305,
0.06155332922935486,
-0.022624189034104347,
-0.011812363751232624,
-0.04157750681042671,
0.035579975694417953,
0.009464513510465622,
-0.0447382926940918,
-0.048814643174409866,
-0.011543993838131428,
0.07582435011863708,
-0.02504129521548748,
0.00864299014210701,
-0.032385580241680145,
0.03205617889761925,
0.03517080470919609,
-0.0115505987778306,
-0.0319301076233387,
0.024884629994630814,
-0.0464446134865284,
0.0003386420721653849,
-0.07559105008840561,
-0.015418085269629955,
0.06740225106477737,
-0.007336546201258898,
-0.007720813155174255,
-0.01501193642616272,
-0.051071297377347946,
-0.010469927452504635,
-0.0006103772320784628,
0.08864415436983109,
0.01560937613248825,
0.026853883638978004,
-0.002214273205026984,
0.029381200671195984,
-0.0069809104315936565,
-0.02208336628973484,
0.018905196338891983,
0.034939028322696686,
-0.004453952424228191,
0.07719230651855469,
0.022090652957558632,
0.08237557858228683,
-0.028936324641108513,
-0.04624709486961365,
0.0071131023578345776,
0.028101133182644844,
-0.006569047924131155,
0.012003447860479355,
-0.004626106005162001,
-0.03507830575108528,
0.04226578399538994,
-0.0473695732653141,
-0.0446859672665596,
0.015622524544596672,
0.048520948737859726,
-0.011841489002108574,
0.0030558244325220585,
-0.017096225172281265,
0.0858030840754509,
-0.06637337058782578,
-0.026272311806678772,
-0.03239112347364426,
-0.0030904822051525116,
0.0092649906873703,
0.0379142165184021,
0.0438753217458725,
0.02118692733347416,
-0.011834375560283661,
-0.014234015718102455,
-0.011183120310306549,
-0.036385755985975266,
-0.014095176011323929,
-0.05788775533437729,
-0.0033060803543776274,
-0.054671693593263626,
-0.014366392977535725,
-0.005108014214783907,
-0.023448342457413673,
-0.02180231176316738,
0.013844147324562073,
0.014095278456807137,
0.0021501651499420404,
0.008672746829688549,
-0.025112098082900047,
0.007879331707954407,
-0.010453070513904095,
0.010876152664422989,
-0.015808694064617157,
-0.054377324879169464,
-0.006777015049010515,
0.022992251440882683,
0.018839821219444275,
0.07735233008861542,
-0.004016509745270014,
0.023782728239893913,
0.021232984960079193,
0.015506835654377937,
-0.07751748710870743,
0.025613127276301384,
-0.0420391745865345,
-0.034710273146629333,
-0.03281150758266449,
0.016019346192479134,
0.03646044060587883,
0.03952416405081749,
0.08092017471790314,
-0.006764307618141174,
-0.01511557586491108,
0.035679012537002563,
0.07081708312034607,
-0.011913706548511982,
-0.004713319707661867,
-0.06000414863228798,
0.07932600378990173,
0.09255284070968628,
-0.026170333847403526,
-0.0043710689060389996,
0.04806015267968178,
-0.04573987051844597,
0.0076040239073336124,
-0.001977949868887663,
0.05228206142783165,
-0.02185879833996296,
-0.00910400040447712,
0.0745624378323555,
0.05030867084860802,
-0.014848818071186543,
-0.014314933679997921,
0.002433424349874258,
0.03847838565707207,
-0.03147738799452782,
0.011924095451831818,
-0.01252427976578474,
0.040800612419843674,
-0.006581588182598352,
0.010448092594742775,
-0.05953669920563698,
0.004865245893597603,
-0.02443629316985607,
-0.003598666051402688,
-0.03016490675508976,
0.036819543689489365,
-0.022868044674396515,
0.036824531853199005,
-0.11228334903717041,
0.008647514507174492,
-0.010300660505890846,
0.03560301661491394,
-0.023822572082281113,
-0.03918085992336273,
-0.07227419316768646,
-0.01172096561640501,
-0.0651736631989479,
-0.0005979918059892952,
0.012448396533727646,
0.002453584223985672,
-0.03403087705373764,
-0.005138548091053963,
-0.02837652899324894,
0.0360870286822319,
-0.01375574804842472,
-0.00451549282297492,
0.027839014306664467,
-0.09080885350704193,
0.061587993055582047,
-0.0569181852042675,
0.010919426567852497,
0.02875182032585144,
0.0009900325676426291,
0.023442968726158142,
-0.03267832100391388,
-0.013128183782100677,
-0.063868448138237,
-0.012911012396216393,
-0.007653382141143084,
-0.02790112979710102,
0.0018011975334957242,
-0.009807989932596684,
-0.0380382239818573,
0.020538443699479103,
-0.02360907383263111,
-0.0427175834774971,
-0.02713601663708687,
-0.025944149121642113,
-0.024437207728624344,
0.00725619588047266,
-0.010063385590910912,
-0.05567038804292679,
-0.045214276760816574,
-0.024224961176514626,
0.06304527074098587,
-0.026615366339683533,
-0.049736738204956055,
0.0768083706498146,
-0.04114445298910141,
0.03234817460179329,
-0.07486644387245178,
0.016685888171195984,
0.05071977898478508,
0.010941797867417336,
0.03722849488258362,
-0.0026808956172317266,
0.052457381039857864,
-0.04327831044793129,
-0.03323885798454285,
-0.003873374778777361,
-0.005233860109001398,
-0.032483190298080444,
0.10666122287511826,
0.03941794112324715,
-0.011097176931798458,
0.013437818735837936,
0.0033995804842561483,
-0.01898261345922947,
0.05510516092181206,
-0.019243530929088593,
0.026236511766910553,
0.011020494624972343,
-0.031501032412052155,
0.014023425057530403,
0.04583987593650818,
-0.028790315613150597,
0.0512656532227993,
0.027091067284345627,
-0.050706662237644196,
0.014653056859970093,
-0.036182429641485214,
0.06862188130617142,
0.01208219863474369,
-0.03621258959174156,
-0.02105174958705902,
0.010729730129241943,
0.0018608291866257787,
-0.021314533427357674,
-0.07543379068374634,
-0.04272790253162384,
-0.016104502603411674,
0.009739449247717857,
-0.015775853767991066,
-0.00892964843660593,
-0.0152589688077569,
-0.05259676277637482,
-0.001450550276786089,
-0.012224584817886353,
-0.006450737826526165,
0.03772479668259621,
0.020066015422344208,
-0.045504745095968246,
-0.07252980768680573,
-0.024182189255952835,
0.02341773733496666,
-0.02521156519651413,
0.011632701382040977,
0.006282075308263302,
-0.039193131029605865,
0.01104716770350933,
0.034452732652425766,
0.07391173392534256,
0.00790057796984911,
-0.0573880597949028,
0.06631496548652649,
-0.059960272163152695,
-0.041665900498628616,
-0.004687725566327572,
-0.012122875079512596,
0.015541881322860718,
0.05241086333990097,
-0.09190744906663895,
-0.08356153219938278,
0.07731065154075623,
-0.005561059340834618,
-0.028821585699915886,
-0.02841450832784176,
0.0009831805946305394,
-0.026519782841205597,
0.020862789824604988,
-0.036445021629333496,
0.015533220022916794,
-0.014082626439630985,
-0.02471105568110943,
0.042699605226516724,
0.00995643064379692,
-0.08656121045351028,
0.04818606376647949,
0.019744478166103363,
0.0028136055916547775,
0.05479355901479721,
-0.005442825146019459,
-0.0020331935957074165,
0.08367189019918442,
-0.05956456437706947,
-0.06738080829381943,
-0.005998768378049135,
0.03238710016012192,
0.058481670916080475,
0.0012877999106422067,
0.014078056439757347,
0.09884009510278702,
0.009140334092080593,
-0.0532282330095768,
0.02043168991804123,
-0.02146298997104168,
0.038746174424886703,
0.02417108602821827,
0.0380164235830307,
-0.054040487855672836,
0.03358568996191025,
-0.006259122397750616,
0.03253386169672012,
0.01911165378987789,
0.017885083332657814,
0.006415146868675947,
0.0057610091753304005,
-0.03467610478401184,
-0.03039572946727276,
-0.03250226005911827,
0.026328762993216515,
0.0169229656457901,
0.007713028695434332,
0.002059048041701317,
0.003224869491532445,
-0.02781645767390728,
-0.017493506893515587,
-0.0005683720810338855,
-0.03590446710586548,
-0.006196561735123396,
0.05269843339920044,
-0.0021035217214375734,
-0.0037561929784715176,
-0.03804850950837135,
0.0491289384663105,
0.004985260311514139,
-0.016084525734186172,
0.002639390993863344,
0.02867022342979908,
0.013665864244103432,
0.008845202624797821,
-0.037537433207035065,
-0.05373353511095047,
0.01069789007306099,
-0.027285080403089523,
0.02622867189347744,
0.02777991071343422,
-0.05329987034201622,
-0.03869377821683884,
0.011037737131118774,
-0.07862555980682373,
-0.030330656096339226,
-0.006574401166290045,
0.05117224529385567,
0.007628249004483223,
0.021415075287222862,
-0.015479318797588348,
-0.056820280849933624,
0.0011719631729647517,
0.022632773965597153,
-0.01656287908554077,
0.017962589859962463,
-0.008872153237462044,
-0.03009444661438465,
-0.018902605399489403,
0.07952806353569031,
0.03618668019771576,
0.007636458147317171,
0.008958698250353336,
0.03443975746631622,
0.009205475449562073,
0.0008280248730443418,
-0.015413695015013218,
0.02960520051419735,
0.028467925265431404,
-0.00770841259509325,
-0.04727395996451378,
0.032859642058610916,
0.027114644646644592,
-0.01284932903945446,
-0.017440559342503548,
-0.01798923872411251,
0.008112919516861439,
0.03801118955016136,
0.0030997171998023987,
-0.03620922565460205,
0.024661235511302948,
0.04720376431941986,
0.006163580808788538,
-0.0119670070707798,
-0.016726624220609665,
-0.041155438870191574,
0.024335848167538643,
-0.01953079178929329,
-0.007160933688282967,
-0.030161617323756218,
-0.053188592195510864,
0.04098151996731758,
-0.00614937674254179,
0.0417325533926487,
-0.03794407472014427,
0.006100452039390802,
-0.0039745597168803215,
-0.019144123420119286,
-0.05561206489801407,
-0.05198080092668533,
-0.020615175366401672,
-0.06651568412780762,
-0.0020813122391700745,
-0.016274597495794296,
-0.005698295310139656,
-0.03074839897453785,
-0.02356870286166668,
0.009745943360030651,
0.015349059365689754,
-0.07964567095041275,
0.04230543598532677,
-0.039648059755563736,
-0.025537334382534027,
0.009889106266200542,
-0.0222892165184021,
0.01627493090927601,
-0.06777457147836685,
0.09061665087938309,
-0.05945218726992607,
-0.016158124431967735,
0.01740163005888462,
0.001622162526473403,
-0.02234409563243389,
0.04967690259218216,
-0.030040012672543526,
0.0012355896178632975,
0.08167116343975067,
0.024961097165942192,
-0.004386947024613619,
0.008467459119856358,
0.033497437834739685,
-0.03150944039225578,
0.002584007801488042,
0.008068419061601162,
0.012204347178339958,
-0.005253613460808992,
0.015802159905433655,
-0.020593803375959396,
-0.01073373295366764,
-0.03363962098956108,
0.025580067187547684,
-0.029180627316236496,
-0.019211482256650925,
0.02249578945338726,
0.03535488620400429,
-0.011091278865933418,
-0.008459514006972313,
-0.012032766826450825,
0.01666942611336708,
0.04564506933093071
] |
<p>Does the PV regulator breaks SUSY? </p>
<p>Take for instance the 1-loop (top/stop loops) correction to the Higgs squared-mass parameter in the MSSM, and you'll get something like, </p>
<p>$$\delta m^2_{h_u} = - 3Y_u^2/(4 \pi^2) m_{\tilde{t}}^2 ln (\frac{\Lambda_{PV}^2}{m_{\tilde{t}}^2})$$ </p>
<p>Where, $\Lambda_{PV}$ is the PV regulator/cutoff, and $m_{\tilde{t}}$ is the stop-quark mass. </p>
<p>In my mind, as the calculation is performed before ElectroWeak Symmetry Breaking (EWSB) (i.e. no mass for the top), but at the same time it's considering softly broken susy (i.e. there is mass for the stop-quark), therefore we don't get perfect cancelation. But I heard someone saying that there's no perfect cancelation because PV regulator breaks SUSY!</p>
<p>I don't see where the PV breaking SUSY argument fits. Can anyone enlighten me?</p> | g6636 | [
-0.010307038202881813,
0.02602449059486389,
0.007846838794648647,
0.009065692313015461,
-0.00801057368516922,
-0.004481748212128878,
0.010809224098920822,
0.05477768927812576,
-0.04113864526152611,
0.06210522726178169,
-0.018684428185224533,
-0.002806193893775344,
-0.02219037152826786,
0.05060511827468872,
-0.01080423966050148,
0.06370768696069717,
0.03065173141658306,
0.025078853592276573,
0.049773745238780975,
-0.011823075823485851,
-0.08507389575242996,
-0.05433235689997673,
-0.03198616951704025,
-0.0383683517575264,
-0.029862070456147194,
0.00981774553656578,
0.018852796405553818,
0.04035573452711105,
-0.0009763878188095987,
0.04189411923289299,
0.0608593188226223,
0.033843256533145905,
0.047095853835344315,
-0.08255811035633087,
-0.06209369748830795,
-0.00868250709027052,
0.052571240812540054,
0.03915422409772873,
0.0009183078072965145,
-0.014515146613121033,
0.025711091235280037,
-0.06111517921090126,
0.0057326918467879295,
-0.042084719985723495,
-0.006120940204709768,
-0.015753820538520813,
-0.0008461858960799873,
-0.027295496314764023,
0.0002554296515882015,
0.017848528921604156,
0.023545444011688232,
0.0027105750050395727,
0.02755758911371231,
-0.025889132171869278,
-0.022852305322885513,
-0.0012471245136111975,
-0.03756968304514885,
0.011478765867650509,
0.006098488345742226,
0.03748072683811188,
-0.0073387762531638145,
-0.029023079201579094,
0.03542258217930794,
0.029277266934514046,
0.03447958081960678,
-0.009768703952431679,
-0.07847245037555695,
-0.026842255145311356,
-0.0007032696157693863,
0.04964689910411835,
0.009792227298021317,
-0.025966797024011612,
-0.02529888227581978,
-0.05431075766682625,
0.08025673776865005,
0.036181479692459106,
-0.022802095860242844,
-0.006725892424583435,
-0.02217107079923153,
-0.030921487137675285,
0.020085105672478676,
-0.0411258228123188,
-0.02056317776441574,
0.030275344848632812,
0.0245348047465086,
-0.058548543602228165,
-0.04525428265333176,
0.059216395020484924,
-0.055560123175382614,
0.018489288166165352,
-0.05437103286385536,
-0.015773393213748932,
-0.007042506244033575,
-0.04481621831655502,
0.0005970348138362169,
-0.008230207487940788,
0.04347033053636551,
-0.0008012694888748229,
-0.016026422381401062,
-0.01133832335472107,
-0.021991396322846413,
0.05720456689596176,
-0.004504446405917406,
0.009062455967068672,
-0.04577726870775223,
0.009073792956769466,
0.06535065919160843,
-0.044533129781484604,
-0.008282375521957874,
-0.017460200935602188,
0.0024285721592605114,
-0.015622193925082684,
-0.011959993280470371,
0.03047347255051136,
-0.06788399070501328,
-0.017153432592749596,
0.10555167496204376,
-0.013012496754527092,
-0.0029622556176036596,
-0.02200944721698761,
-0.010313684120774269,
0.012064443901181221,
0.007029355503618717,
0.06366077810525894,
-0.053259532898664474,
-0.01638062298297882,
0.006447863765060902,
0.060159191489219666,
-0.031593501567840576,
0.017155561596155167,
0.007607434876263142,
-0.011892518028616905,
-0.0226005706936121,
0.015070400200784206,
0.020968656986951828,
-0.011875546537339687,
0.04976119473576546,
-0.015058598481118679,
0.07559812068939209,
-0.08787450939416885,
-0.0658755749464035,
0.047956984490156174,
-0.025692326948046684,
-0.019985444843769073,
-0.046126823872327805,
-0.01507963240146637,
-0.0052914004772901535,
0.010553928092122078,
-0.022087575867772102,
0.00015373578935395926,
0.027644870802760124,
0.07716130465269089,
-0.023185331374406815,
-0.03181295841932297,
-0.03613462671637535,
-0.014502495527267456,
0.08092287182807922,
0.0457133986055851,
0.10409723967313766,
-0.00018318953516427428,
0.020826702937483788,
-0.0006972517003305256,
0.03644563630223274,
-0.020304445177316666,
-0.0872638151049614,
-0.015348277054727077,
-0.01449983473867178,
-0.005567390006035566,
-0.05302705988287926,
-0.03086751513183117,
-0.09680083394050598,
0.04597631096839905,
-0.0027192949783056974,
0.031996648758649826,
0.02226526476442814,
0.027048878371715546,
-0.009591317735612392,
-0.013197979889810085,
0.004143764264881611,
0.035963837057352066,
0.024044636636972427,
-0.008126482367515564,
0.016818255186080933,
-0.024259723722934723,
-0.003541802056133747,
0.018724314868450165,
-0.02156301587820053,
0.0024064737372100353,
0.061091288924217224,
0.02298109419643879,
-0.04286953806877136,
0.061782948672771454,
-0.0449826754629612,
-0.02206536941230297,
-0.035659100860357285,
0.01128388475626707,
-0.03520562872290611,
-0.037416279315948486,
-0.05269525200128555,
-0.024530695751309395,
-0.036795228719711304,
0.016015470027923584,
0.048654742538928986,
-0.04913424700498581,
-0.031735725700855255,
-0.03740663081407547,
-0.00016780402802396566,
0.029924316331744194,
-0.05265302583575249,
0.03588169068098068,
0.047511640936136246,
-0.03571557253599167,
0.024761423468589783,
-0.007188527379184961,
-0.0432768277823925,
-0.01980968751013279,
-0.008512897416949272,
0.037568576633930206,
0.01542892586439848,
-0.026827242225408554,
-0.06410057097673416,
-0.010295890271663666,
0.02896992117166519,
-0.04182843491435051,
-0.028217831626534462,
0.021967163309454918,
0.007926120422780514,
-0.03673874959349632,
0.012950499542057514,
-0.025980116799473763,
-0.03938458859920502,
0.013208786956965923,
-0.05743611231446266,
-0.03974162042140961,
0.016048412770032883,
0.028093263506889343,
-0.025158042088150978,
-0.007909776642918587,
0.0022701043635606766,
-0.03258740156888962,
0.07582729309797287,
0.016621967777609825,
0.011760435998439789,
0.05684661120176315,
0.06868216395378113,
0.02282363921403885,
0.06841456890106201,
0.009523235261440277,
-0.02440814860165119,
-0.007322990335524082,
0.04215109720826149,
0.014406825415790081,
-0.019258294254541397,
0.03954777866601944,
-0.004318118095397949,
-0.1039092019200325,
-0.01375278178602457,
0.03148622065782547,
-0.05790049582719803,
0.0168442539870739,
0.0481296069920063,
0.000638742174487561,
0.02126438543200493,
-0.0015993255656212568,
-0.011473406106233597,
0.03472557291388512,
-0.006765933241695166,
-0.013376283459365368,
0.04818671941757202,
-0.021811021491885185,
-0.004955630749464035,
0.020306354388594627,
-0.01049282681196928,
0.018001209944486618,
0.007814099080860615,
0.013095689937472343,
-0.01758936606347561,
0.02643194980919361,
0.06701656430959702,
-0.053841616958379745,
-0.039942823350429535,
0.05090498924255371,
-0.006850156933069229,
0.000750253617297858,
0.05542762950062752,
-0.01911124773323536,
-0.03620951995253563,
-0.034540798515081406,
-0.023777876049280167,
0.03020169772207737,
-0.05173225328326225,
-0.1005089282989502,
0.007259363308548927,
-0.0015948215732350945,
-0.028965448960661888,
0.03668737784028053,
0.003128959098830819,
0.0043793595395982265,
0.0029637387488037348,
0.022210918366909027,
-0.007469820324331522,
0.07723363488912582,
-0.026208922266960144,
0.013682973571121693,
-0.06193004921078682,
0.06874977797269821,
-0.011297157034277916,
0.05952350050210953,
0.02707732655107975,
-0.07005345076322556,
0.028373228386044502,
0.032095637172460556,
0.0388161726295948,
0.008165696635842323,
0.009958667680621147,
0.0017122639110311866,
0.01598432846367359,
-0.028393270447850227,
-0.04986147955060005,
-0.018764058127999306,
-0.11074908822774887,
0.06609096378087997,
0.035929955542087555,
0.008674194104969501,
-0.03977226838469505,
0.05864608287811279,
0.018099358305335045,
-0.020214857533574104,
-0.01847248710691929,
0.0031899549067020416,
-0.0008176215342245996,
0.035544253885746,
0.014131286181509495,
0.0728093609213829,
-0.027313265949487686,
-0.024102799594402313,
-0.018874960020184517,
0.022967059165239334,
0.016503900289535522,
-0.006319776643067598,
-0.0564795657992363,
0.048230525106191635,
0.016123343259096146,
0.024327389895915985,
0.02095078118145466,
0.03314505144953728,
0.002402115613222122,
-0.015261633321642876,
0.02477208711206913,
-0.03374619781970978,
0.06394624710083008,
0.024683455005288124,
-0.007965601980686188,
-0.03522910550236702,
0.014355474151670933,
0.0009978602174669504,
0.01912861503660679,
0.05751630291342735,
0.017004141584038734,
-0.03557832911610603,
0.05122532323002815,
0.02520315907895565,
0.0382104329764843,
-0.020146729424595833,
-0.04491868615150452,
0.01597500406205654,
-0.0047205714508891106,
0.012814055196940899,
-0.04891312122344971,
-0.05941672623157501,
0.007096365559846163,
-0.018311817198991776,
0.007375900633633137,
-0.014818633906543255,
-0.0380377396941185,
-0.022261247038841248,
0.012392131611704826,
0.03559080883860588,
0.03975678235292435,
0.03081274963915348,
0.013082055374979973,
0.02305394411087036,
0.003875523107126355,
-0.017958922311663628,
0.003946240060031414,
0.00966258067637682,
-0.016438977792859077,
-0.022332198917865753,
-0.07254228740930557,
-0.051605407148599625,
0.029808495193719864,
-0.009034335613250732,
-0.0017716488800942898,
-0.004607726354151964,
0.02322702296078205,
-0.008063453249633312,
0.012246964499354362,
0.015341157093644142,
-0.055198609828948975,
-0.015467831864953041,
-0.021072961390018463,
0.04698989912867546,
-0.0011704823700711131,
-0.047581687569618225,
0.03797857463359833,
-0.016143351793289185,
0.004599529784172773,
0.04181342571973801,
0.05528758466243744,
0.025364235043525696,
-0.01516338437795639,
0.027907341718673706,
-0.012736303731799126,
-0.07901188731193542,
-0.02928381785750389,
-0.009940276853740215,
-0.016946692019701004,
0.0014898123918101192,
0.05483848601579666,
-0.030905432999134064,
0.0074563114903867245,
-0.025774842128157616,
-0.03132234513759613,
-0.04912376403808594,
0.0018967732321470976,
0.009772738441824913,
0.024237528443336487,
0.004694943781942129,
0.030945077538490295,
-0.018396852537989616,
0.06939432770013809,
-0.0020667477510869503,
-0.04853544011712074,
0.02397834323346615,
-0.02242649532854557,
-0.0003989229444414377,
-0.0131171103566885,
-0.0010418263264000416,
-0.0619608573615551,
0.035839248448610306,
0.13108466565608978,
-0.07689131051301956,
-0.00436696782708168,
0.009748647920787334,
-0.014215050265192986,
-0.016050145030021667,
0.03806207329034805,
-0.03885417431592941,
0.020273709669709206,
0.010776236653327942,
-0.04716501757502556,
-0.011118829250335693,
0.004071125295013189,
-0.008725634776055813,
-0.029222754761576653,
-0.019586503505706787,
-0.025377420708537102,
0.017588559538125992,
0.023767618462443352,
0.030648626387119293,
-0.007625060621649027,
-0.046485915780067444,
0.0018462943844497204,
0.04345007613301277,
0.06757039576768875,
0.002231146674603224,
-0.06096304580569267,
-0.03530074283480644,
-0.005504177417606115,
0.036611177027225494,
-0.009759216569364071,
0.0500299371778965,
-0.008629794232547283,
0.07019126415252686,
0.064468152821064,
-0.03549730032682419,
-0.016153594478964806,
-0.040484149008989334,
0.012465843930840492,
-0.027302073314785957,
0.0318559966981411,
0.01039193756878376,
0.029196659103035927,
-0.04139157012104988,
0.007376087363809347,
-0.001978140790015459,
-0.04699078947305679,
-0.0783013328909874,
0.023746388033032417,
0.025356298312544823,
-0.01684006303548813,
0.10060573369264603,
0.003152135293930769,
-0.0920439213514328,
0.04000086337327957,
0.01748335361480713,
0.03680672124028206,
-0.033938929438591,
-0.05192235857248306,
-0.0013185651041567326,
-0.011105827987194061,
-0.00016775753465481102,
0.021686071529984474,
0.026703132316470146,
0.005036246497184038,
0.05534029379487038,
0.011826976202428341,
0.0064589218236505985,
0.0309272650629282,
-0.00871152151376009,
0.0172947458922863,
-0.0008578108390793204,
0.02648412436246872,
-0.0013173269107937813,
-0.009937587194144726,
-0.001919992733746767,
-0.016521736979484558,
0.010647309944033623,
-0.03516411781311035,
-0.05031117796897888,
0.012165536172688007,
-0.011783985421061516,
-0.053766243159770966,
-0.01197177916765213,
0.004838057328015566,
0.013279233127832413,
-0.08742556720972061,
-0.006335628218948841,
0.010898388922214508,
0.004913089796900749,
0.04226617515087128,
-0.009400085546076298,
0.04493247717618942,
0.05217180773615837,
0.04892219230532646,
-0.06621496379375458,
0.0012598700122907758,
-0.005928881466388702,
0.003148303832858801,
-0.004185448866337538,
-0.015029997564852238,
-0.018259387463331223,
-0.0016443372005596757,
-0.005978990346193314,
-0.0033814257476478815,
-0.0127011863514781,
-0.009117143228650093,
0.015166081488132477,
-0.01535720843821764,
-0.0008127878536470234,
-0.027716584503650665,
-0.06118280440568924,
0.018589312210679054,
0.0009619251359254122,
-0.03350285068154335,
0.03673485666513443,
-0.011939048767089844,
0.03137514367699623,
-0.04181993752717972,
-0.020882144570350647,
-0.051911354064941406,
0.04046223685145378,
-0.012780332937836647,
-0.0031623251270502806,
0.029979461804032326,
0.0023693640250712633,
-0.05211784690618515,
0.036438923329114914,
-0.016279254108667374,
0.006583354901522398,
0.05834490433335304,
0.023359494283795357,
0.04167989641427994,
0.03541107848286629,
-0.023651599884033203,
0.03329605981707573,
-0.053300172090530396,
0.0034232453908771276,
-0.02242698334157467,
-0.028084712103009224,
0.006184268277138472,
-0.02219419740140438,
-0.02716602385044098,
-0.0772477388381958,
0.02147965133190155,
-0.052698466926813126,
-0.03311435133218765,
-0.013877781108021736,
0.020320672541856766,
0.06136390194296837,
0.019127674400806427,
-0.010582294315099716,
-0.02452191896736622,
0.054854538291692734,
0.022128166630864143,
0.012431025505065918,
0.018681300804018974,
-0.003905493998900056,
-0.029595382511615753,
0.008121661841869354,
0.08179552108049393,
-0.062048450112342834,
-0.017916206270456314,
-0.020649369806051254,
0.002680852310732007,
0.067515067756176,
0.019815819337964058,
0.06988369673490524,
-0.06173134595155716,
-0.03388794884085655,
-0.038047391921281815,
0.04212334007024765,
0.021623611450195312,
-0.035370003432035446,
-0.006426890380680561,
-0.03815479576587677,
-0.05922141298651695,
0.05075877159833908,
-0.0462518185377121,
0.004849836230278015,
0.004439953248947859,
0.0412655770778656,
0.01794523559510708,
-0.06487896293401718,
0.03053715080022812,
0.0855032429099083,
0.11312980204820633,
-0.013922530226409435,
0.04646331071853638,
0.009118534624576569,
0.0006746617727912962,
-0.010371627286076546,
0.03798019140958786,
0.01234501600265503,
0.004363986663520336,
0.041941601783037186,
-0.0209538321942091,
0.032768819481134415,
-0.00441751116886735,
0.007004388142377138,
0.027108395472168922,
0.01764250546693802,
0.006168525665998459,
0.032061729580163956,
-0.017815282568335533,
0.001118966843932867,
0.0520012304186821,
0.007460214197635651,
-0.061728112399578094,
0.01184066291898489,
0.0025162266101688147,
0.006415938958525658,
-0.02022661082446575,
0.005107307806611061,
-0.025544149801135063,
0.02196681685745716,
-0.013718884438276291,
0.02675464190542698,
0.03777298703789711,
-0.04660111293196678,
0.0014489382738247514,
0.011891843751072884,
0.06177488714456558,
0.04533597081899643,
0.03624832257628441,
0.014446856454014778,
-0.06835723668336868,
-0.026394203305244446,
0.02803550846874714,
-0.06899211555719376,
-0.02758856676518917,
-0.026925038546323776,
-0.045350782573223114,
-0.020083483308553696,
0.06166256591677666,
-0.0014253623085096478,
-0.04496040940284729,
-0.010613078251481056,
-0.010960419662296772,
0.016741786152124405,
-0.002608366310596466,
-0.012328114360570908,
-0.032150592654943466,
0.001179142389446497,
-0.02259487472474575,
0.03300493583083153,
-0.04501207545399666,
0.018572207540273666,
-0.007024039980024099,
0.07150162011384964,
0.018606876954436302,
0.05326937511563301,
0.05275706201791763,
0.01359283085912466,
-0.057605985552072525,
-0.04040929302573204,
-0.006895594298839569,
0.025049669668078423,
-0.012576254084706306,
-0.017548151314258575,
0.015429403632879257,
-0.022208817303180695,
-0.004655752796679735,
0.008984039537608624,
0.0522615872323513,
0.0667816624045372,
-0.05379173532128334,
-0.010237942449748516,
-0.058142293244600296,
-0.0059007988311350346,
0.021226637065410614,
-0.0027000673580914736,
0.008732574991881847,
0.0007524057873524725,
0.07966243475675583,
-0.003808369394391775,
-0.03938550502061844,
0.00336147821508348,
0.05998971685767174,
-0.0045495787635445595,
-0.04632166028022766,
-0.0008099019178189337,
-0.020603280514478683,
-0.05981413647532463,
0.00797479972243309,
-0.010727953165769577,
0.0030324470717459917,
0.03060874342918396,
0.004407891072332859,
0.02624981850385666,
0.05693173408508301,
0.010305365547537804,
0.02075403369963169,
-0.05051316320896149,
-0.03736452758312225,
0.013725103810429573,
0.01617719791829586,
-0.002833282807841897,
-0.022508103400468826,
0.053532835096120834,
-0.04099030792713165,
-0.07147543132305145,
0.028745198622345924,
-0.03970867395401001,
0.020903419703245163,
0.01651395484805107,
-0.0163208469748497,
-0.027264611795544624,
-0.009406025521457195,
-0.08223024755716324,
0.03568645194172859,
-0.0033827240113168955,
-0.061705928295850754,
0.07271487265825272,
0.05764775723218918,
0.015102303586900234,
-0.00661048386245966,
-0.06734666973352432,
-0.05653144046664238,
0.033225372433662415,
0.02864287979900837,
-0.05269089713692665,
-0.0024788102600723505,
-0.011939394287765026,
0.01604042947292328,
-0.023731067776679993,
0.02108393795788288,
0.008577029220759869
] |
<p>The traditional (not taking into account phasor addition or complex addition) application of Kirchoff Voltage law, i.e. $\Sigma\Delta V=0$ along a loop, does not work for AC circuits. We can sum the voltage drops to zero if we take into account their phase differences. But at some particular time, no matter what the phase differences in the general equation for the voltages across various components, there will be only one numeric value of $\Delta V$. </p>
<blockquote>
<p><strong>Why doesn't this sum to zero over the loop in case of AC circuits with
non-zero <a href="http://en.wikipedia.org/wiki/Electrical_reactance" rel="nofollow">reactance</a>?</strong></p>
</blockquote>
<p>Is this because there is some contribution to the $\oint E.dl$ due to changing magnetic flux? If it is, even in absence of any inductance, the voltage drops still do not sum to zero. why? </p> | g6637 | [
0.0020187317859381437,
0.01135389693081379,
0.0023963828571140766,
0.01008893083781004,
0.07130923122167587,
-0.03783607482910156,
-0.0028097413014620543,
0.049306612461805344,
-0.015402321703732014,
-0.04419247433543205,
-0.06526520848274231,
0.023357121273875237,
0.029253866523504257,
0.06790079176425934,
-0.014012744650244713,
0.018055588006973267,
0.023622727021574974,
0.043595995754003525,
0.11065881699323654,
0.011905430816113949,
-0.0387866236269474,
-0.025111475959420204,
-0.040258754044771194,
-0.01770360767841339,
-0.015258871018886566,
-0.0003266554558649659,
0.03552383556962013,
-0.06211213022470474,
-0.0887312963604927,
0.013171074911952019,
0.01248752512037754,
0.019820155575871468,
0.003589390544220805,
-0.0011090392945334315,
0.0013567556161433458,
0.0007638809038326144,
0.022990360856056213,
0.020561128854751587,
0.04270254075527191,
-0.021217375993728638,
0.009596738032996655,
0.038448695093393326,
0.06719662249088287,
0.03128322586417198,
-0.02853846363723278,
-0.020654331892728806,
-0.04438493028283119,
0.021060636267066002,
-0.09046702086925507,
0.0053885383531451225,
-0.028396673500537872,
-0.0180507842451334,
0.028494514524936676,
0.011020183563232422,
0.0154540054500103,
-0.0421893484890461,
0.011246317997574806,
0.014245662838220596,
0.014742913655936718,
0.07679041475057602,
0.006768837105482817,
0.024016330018639565,
0.04436451569199562,
0.00018544885097071528,
0.03907015547156334,
-0.022986913099884987,
-0.013320814818143845,
-0.013784739188849926,
0.02369818277657032,
0.0802883431315422,
-0.020574813708662987,
-0.06640263646841049,
-0.01515222992748022,
-0.04229500889778137,
0.07646508514881134,
0.024179253727197647,
0.010056760162115097,
-0.031049098819494247,
0.0623021274805069,
-0.05836984142661095,
-0.07615760713815689,
-0.001152249169535935,
0.015199929475784302,
0.10757295787334442,
0.01658511534333229,
0.048431605100631714,
0.03843989968299866,
0.026069747284054756,
0.0011507124872878194,
0.027805399149656296,
0.0516568087041378,
-0.030220061540603638,
0.042660556733608246,
-0.035145003348588943,
-0.01967138610780239,
-0.05138854309916496,
0.019809840247035027,
0.05947525054216385,
0.0326695516705513,
-0.013224787078797817,
-0.048052359372377396,
0.050620999187231064,
0.015821462497115135,
-0.05241755396127701,
-0.03674456477165222,
0.017377479001879692,
0.004391881637275219,
-0.012272635474801064,
-0.00852134358137846,
0.014032602310180664,
-0.0632118359208107,
-0.06491735577583313,
-0.050834428519010544,
0.0014537337701767683,
0.0067574940621852875,
0.029334641993045807,
0.025809111073613167,
-0.009953848086297512,
0.015990925952792168,
-0.002490864833816886,
0.026817981153726578,
0.015225585550069809,
0.03499709069728851,
0.038136109709739685,
-0.016006601974368095,
0.010306021198630333,
0.04493407532572746,
0.07808548957109451,
0.04961489886045456,
-0.05877915397286415,
0.017124902456998825,
0.01885245181620121,
-0.04850255325436592,
0.024407360702753067,
0.043189357966184616,
-0.03660961985588074,
0.02595023438334465,
-0.05182074010372162,
-0.007443288806825876,
0.0012378799729049206,
0.004834107588976622,
0.018614603206515312,
-0.009042220190167427,
-0.022087758406996727,
-0.00018011595238931477,
0.043738991022109985,
-0.053532350808382034,
-0.006082497071474791,
0.022488730028271675,
-0.027111953124403954,
0.017484888434410095,
0.02974255383014679,
-0.03364875167608261,
0.011949880048632622,
-0.0020053894259035587,
-0.01446345541626215,
0.01228004228323698,
-0.01213244441896677,
-0.016903791576623917,
-0.02534635178744793,
-0.00670943409204483,
0.02055511251091957,
-0.05589231103658676,
-0.037983935326337814,
-0.054194167256355286,
-0.01862143725156784,
0.03580717369914055,
0.00214580399915576,
-0.016680622473359108,
-0.06610536575317383,
-0.04294724017381668,
-0.04707108810544014,
-0.004658638499677181,
0.029042674228549004,
0.04531431570649147,
0.024774348363280296,
0.04676613584160805,
0.014384221285581589,
0.05758289992809296,
-0.04646551236510277,
-0.059902504086494446,
0.04240738973021507,
0.005832131020724773,
0.003444350091740489,
0.02517586201429367,
0.01961679384112358,
-0.00625636475160718,
0.018782738596200943,
-0.09929793328046799,
-0.01624426618218422,
-0.04160206392407417,
0.01856835186481476,
0.02515791542828083,
0.05844953656196594,
-0.03794321417808533,
0.024728015065193176,
-0.007679899223148823,
-0.035083137452602386,
-0.05879552662372589,
0.06352178752422333,
0.048805199563503265,
-0.02341597154736519,
0.04617593064904213,
0.0028821344021707773,
-0.0034953870344907045,
0.041684992611408234,
0.0015440726419910789,
-0.026073217391967773,
0.030297791585326195,
-0.06297963112592697,
0.015128293074667454,
0.014375848695635796,
-0.04720913991332054,
0.03587603196501732,
0.017387568950653076,
-0.04166218638420105,
0.0013623121194541454,
-0.009279345162212849,
0.019368985667824745,
0.03997587040066719,
-0.039718303829431534,
-0.022849276661872864,
0.01715809665620327,
0.029164327308535576,
-0.06714257597923279,
-0.0036339450161904097,
-0.025539707392454147,
-0.0076641240157186985,
-0.024176854640245438,
-0.03348405286669731,
-0.031853705644607544,
0.00527842016890645,
-0.05422580987215042,
-0.02424447424709797,
0.017714036628603935,
0.019259760156273842,
0.02551613748073578,
0.003852528054267168,
0.009602432139217854,
0.0412156879901886,
0.017644086852669716,
-0.04221523553133011,
0.00461245235055685,
0.018805237486958504,
-0.0213173758238554,
-0.03299781307578087,
0.00037749181501567364,
0.03696587309241295,
-0.033590834587812424,
-0.04200959578156471,
-0.022057989612221718,
0.00472545949742198,
-0.010974924080073833,
-0.016230307519435883,
-0.04058615118265152,
-0.003993099555373192,
0.02694428525865078,
-0.0368632897734642,
-0.005768533330410719,
-0.03281199559569359,
-0.012998491525650024,
0.0357070118188858,
0.0068885856308043,
-0.0016125371912494302,
-0.0465213768184185,
0.07287969440221786,
-0.03484734520316124,
0.027873480692505836,
0.02154620923101902,
0.0008855066844262183,
-0.06720110028982162,
0.07264865934848785,
-0.02712702937424183,
0.003391571342945099,
-0.027695296332240105,
-0.0033064931631088257,
0.0291379876434803,
0.014012616127729416,
0.062178026884794235,
0.0355880931019783,
-0.030540211126208305,
-0.009371859021484852,
-0.06490994989871979,
-0.02714828960597515,
0.011205415241420269,
-0.059280652552843094,
0.04691436514258385,
0.010090518742799759,
-0.010369948111474514,
0.004069119691848755,
-0.028185267001390457,
0.010035742074251175,
-0.012457684613764286,
0.021369589492678642,
0.008909687399864197,
0.029576914384961128,
0.008289103396236897,
-0.03688330948352814,
-0.0373612605035305,
0.043293390423059464,
0.016509072855114937,
0.0009073446854017675,
-0.00760593032464385,
-0.011859267018735409,
0.022836958989501,
0.06675845384597778,
0.057357218116521835,
-0.03790179267525673,
-0.015001988038420677,
0.010377742350101471,
0.007243838626891375,
0.016285091638565063,
0.04627690836787224,
-0.05874165520071983,
-0.026041364297270775,
0.03303436562418938,
-0.03427942097187042,
0.012759285047650337,
-0.00623659323900938,
-0.02599158138036728,
-0.023236123844981194,
-0.012453087605535984,
-0.023606643080711365,
0.006823461037129164,
-0.015552064403891563,
0.0033417080994695425,
-0.04732513427734375,
0.06460705399513245,
-0.03252221271395683,
0.020182138308882713,
0.005082500632852316,
0.0189371295273304,
0.05590880662202835,
-0.03861330449581146,
-0.023686608299613,
-0.04434766247868538,
-0.018831046298146248,
0.004182853735983372,
-0.015362399630248547,
0.06282895058393478,
-0.05886630341410637,
0.007202738430351019,
-0.037089280784130096,
0.005089486949145794,
0.017860285937786102,
0.03181993216276169,
0.0004936392651870847,
0.01822974905371666,
-0.04062998294830322,
-0.011694530956447124,
0.054189588874578476,
0.03294346481561661,
0.029688198119401932,
0.019794151186943054,
0.015265381895005703,
0.003738947445526719,
-0.005743436980992556,
0.027063004672527313,
-0.005248197820037603,
0.021516922861337662,
0.03534991666674614,
-0.003548810025677085,
-0.016174623742699623,
-0.0058389692567288876,
0.04844524711370468,
0.03931078314781189,
0.027060149237513542,
0.036725182086229324,
-0.01925850287079811,
-0.055607929825782776,
0.02815108560025692,
0.009248904883861542,
-0.043038785457611084,
0.023251470178365707,
0.005311938468366861,
-0.04692362993955612,
-0.006217205431312323,
0.08138883858919144,
-0.021135129034519196,
0.028579620644450188,
0.015360267832875252,
0.008581229485571384,
0.015349763445556164,
-0.0014894417254254222,
-0.002818265464156866,
-0.04040190577507019,
-0.019377103075385094,
0.0384131520986557,
-0.03660339489579201,
-0.033167436718940735,
-0.0156601183116436,
0.03679654002189636,
0.05221511796116829,
0.036705005913972855,
-0.006089941598474979,
-0.02625907026231289,
0.029900364577770233,
-0.020756032317876816,
-0.0036693820729851723,
0.0016188659938052297,
-0.000876737292855978,
-0.004226795397698879,
0.021657830104231834,
-0.05533112585544586,
0.04801017418503761,
-0.02413531020283699,
0.05084342882037163,
-0.026593666523694992,
0.054099082946777344,
-0.04778946936130524,
-0.008487486280500889,
-0.04105551168322563,
-0.019041011109948158,
-0.07560412585735321,
0.03707338124513626,
0.022354423999786377,
0.03619380295276642,
-0.003688517725095153,
0.012009823694825172,
-0.06935174018144608,
-0.009528923779726028,
-0.018736062571406364,
-0.013905429281294346,
-0.014701761305332184,
-0.024127963930368423,
-0.007525190245360136,
-0.03207364305853844,
0.032762229442596436,
0.0499427504837513,
0.013671431690454483,
-0.052025340497493744,
0.03778371959924698,
-0.05558202043175697,
-0.011119399219751358,
-0.07842860370874405,
0.09147516638040543,
-0.028289873152971268,
0.020988916978240013,
-0.017511652782559395,
0.05638887360692024,
0.08244638890028,
0.024656997993588448,
0.007735205814242363,
0.04979797452688217,
-0.020780732855200768,
0.03752584382891655,
-0.04793495312333107,
-0.0396052822470665,
-0.011539285071194172,
-0.005985629744827747,
-0.038734108209609985,
0.03887214511632919,
0.0022404605988413095,
-0.0282440148293972,
0.002619443228468299,
0.007301618345081806,
-0.0016968499403446913,
-0.008463102392852306,
0.01587352715432644,
0.03777031973004341,
-0.015834661200642586,
-0.07608813792467117,
-0.03259940817952156,
-0.03331383690237999,
0.003732775105163455,
-0.010868489742279053,
0.022662164643406868,
-0.05115564540028572,
-0.10262793302536011,
-0.008301958441734314,
-0.003996505867689848,
0.04679384455084801,
-0.013021712191402912,
0.01769895851612091,
0.04934914782643318,
-0.02533680386841297,
0.05070599168539047,
-0.0044835759326815605,
-0.035791657865047455,
-0.047682877629995346,
-0.05645424500107765,
-0.04899858683347702,
-0.011915737763047218,
0.08700183033943176,
0.04728596657514572,
0.02252095565199852,
-0.054317545145750046,
-0.03417862206697464,
0.012437195517122746,
-0.07392751425504684,
0.05570847541093826,
0.08331232517957687,
0.0070660775527358055,
-0.04871513321995735,
0.009202784858644009,
0.0402984619140625,
-0.0377664752304554,
0.004013195168226957,
-0.05057545751333237,
-0.002280677203088999,
-0.07692541182041168,
0.020339258015155792,
-0.016338340938091278,
-0.007044665049761534,
-0.04441293329000473,
0.025496065616607666,
0.02477044239640236,
-0.009067123755812645,
0.05105370655655861,
0.001002551638521254,
0.0015145346987992525,
0.0007875474402680993,
0.06364858150482178,
0.06435715407133102,
0.04384678602218628,
0.05781443044543266,
-0.04589064046740532,
-0.04973766207695007,
-0.05696530267596245,
-0.022937975823879242,
0.028261525556445122,
0.04489376023411751,
-0.03597636893391609,
0.03760029748082161,
0.006648195441812277,
-0.004343188367784023,
-0.06869053840637207,
-0.06639120727777481,
0.002345333807170391,
0.003680228954181075,
0.01683112047612667,
0.02048276551067829,
0.009448510594666004,
-0.004957455210387707,
-0.01953130029141903,
-0.024635320529341698,
-0.006404049228876829,
0.012506588362157345,
-0.007014187518507242,
0.0642390325665474,
0.001960268709808588,
0.004530712496489286,
0.02182728238403797,
0.08885511755943298,
0.029861504212021828,
-0.04711143672466278,
-0.004880394320935011,
-0.06155543774366379,
0.014128759503364563,
-0.06026419624686241,
-0.07734351605176926,
0.030453477054834366,
-0.025145934894680977,
0.01017636526376009,
0.009455032646656036,
0.023566897958517075,
0.0018885649042204022,
0.019679199904203415,
-0.042959414422512054,
0.012503829784691334,
0.025294937193393707,
-0.005624231416732073,
-0.02122933231294155,
0.01821025460958481,
0.03559068962931633,
-0.0579107329249382,
-0.026867061853408813,
0.039090219885110855,
0.05005190894007683,
0.04432521387934685,
0.015341104008257389,
-0.026504941284656525,
0.010770373977720737,
-0.028941337019205093,
-0.008560823276638985,
0.021403446793556213,
-0.012877046130597591,
-0.07019615173339844,
0.01906088925898075,
-0.020815853029489517,
-0.032736919820308685,
0.01802084408700466,
0.04014318063855171,
-0.03864321485161781,
0.031976062804460526,
-0.06999564915895462,
-0.003116447478532791,
0.023814724758267403,
0.07232718169689178,
0.10093113034963608,
-0.03604019433259964,
-0.029054267331957817,
0.03869681805372238,
0.011097815819084644,
-0.0289783775806427,
-0.019740654155611992,
-0.00544716464355588,
0.023965565487742424,
0.028224749490618706,
-0.017551802098751068,
0.03029320016503334,
0.01451421994715929,
0.02524747885763645,
-0.011594472452998161,
-0.018512262031435966,
0.019891992211341858,
-0.04836612567305565,
0.01568026654422283,
-0.04653439298272133,
0.005802767816931009,
0.05261179059743881,
0.013417289592325687,
0.001005769707262516,
-0.0054509700275957584,
0.005401324480772018,
-0.05698155239224434,
-0.025563299655914307,
0.015708493068814278,
-0.035048626363277435,
0.007569253444671631,
-0.012836027890443802,
-0.013480440713465214,
-0.005742468871176243,
-0.006645526271313429,
0.022285468876361847,
0.05670938268303871,
-0.002117571420967579,
0.03398830443620682,
0.0647197738289833,
0.0638113021850586,
0.016512064263224602,
0.07614124566316605,
-0.08241957426071167,
0.02100237086415291,
0.024994906038045883,
0.05217394605278969,
-0.026841821148991585,
-0.0044882893562316895,
0.020499419420957565,
-0.008506039157509804,
-0.007077164947986603,
0.03310959041118622,
-0.008537359535694122,
0.033639054745435715,
-0.0337715744972229,
0.036288633942604065,
0.022346392273902893,
-0.025179220363497734,
-0.053348835557699203,
0.0017411753069609404,
0.07871054112911224,
0.026278315111994743,
0.007590625435113907,
0.01074456050992012,
-0.023322993889451027,
-0.03866395354270935,
0.03335883468389511,
0.02413330040872097,
0.031405046582221985,
-0.005852461326867342,
-0.048318423330783844,
-0.022096501663327217,
0.019715189933776855,
0.06692202389240265,
0.06690964102745056,
0.032840825617313385,
-0.02259199135005474,
-0.0473843477666378,
0.07106606662273407,
-0.01985079236328602,
0.018796756863594055,
-0.035647936165332794,
-0.026852020993828773,
0.006732690613716841,
0.016738286241889,
0.0006640337524004281,
0.009298535995185375,
-0.01719125173985958,
-0.007191171403974295,
0.043047089129686356,
0.029563384130597115,
-0.04898754507303238,
-0.0020368178375065327,
-0.06675133109092712,
-0.048180993646383286,
0.022499872371554375,
-0.03441474959254265,
0.030612105503678322,
-0.03530263155698776,
0.008754659444093704,
0.04651566222310066,
0.01761169359087944,
0.02239413559436798,
-0.029082706198096275,
0.011716768145561218,
0.049777694046497345,
0.033653125166893005,
-0.036773089319467545,
0.010936262086033821,
-0.05488014221191406,
0.10939367115497589,
-0.06127379462122917,
-0.03601165488362312,
-0.005639213137328625,
0.025481512770056725,
0.01983979158103466,
-0.003677751636132598,
-0.06491488218307495,
-0.00483417883515358,
0.06501079350709915,
0.026472115889191628,
0.050904303789138794,
-0.02892552688717842,
-0.006703634280711412,
0.014183895662426949,
-0.002487451070919633,
-0.006778663489967585,
0.012050548568367958,
-0.013077964074909687,
-0.0007749664946459234,
-0.013189125806093216,
-0.09128604829311371,
0.004492511041462421,
-0.08063481003046036,
-0.03284253180027008,
-0.013172918930649757,
0.011756159365177155,
-0.003593359375372529,
0.0227650236338377,
0.016943473368883133,
0.01239061914384365,
-0.013230827637016773,
-0.026474053040146828,
-0.015012810006737709,
-0.028210459277033806,
0.0398598313331604,
-0.0027114658150821924,
0.03420417755842209,
-0.008548406884074211,
0.0034794325474649668,
0.00005958178735454567,
-0.0455198734998703,
-0.025267915800213814,
-0.0382879301905632,
0.00019450958643574268,
-0.025391392409801483,
-0.04235564172267914,
0.03576602414250374,
0.0005932694766670465,
-0.019562089815735817,
-0.04715045914053917,
-0.008291758596897125,
-0.08354301005601883,
-0.023771919310092926,
0.04229108244180679,
0.021490786224603653,
-0.012771756388247013,
-0.032025597989559174,
0.010202974081039429,
-0.028077727183699608,
-0.062254898250103,
-0.016354087740182877,
-0.09081132709980011,
-0.00388540280982852,
0.04745222255587578,
-0.047946251928806305,
0.0019320037681609392,
-0.05754983797669411
] |
<p>I hope this is the right forum to ask this question. Is there a material (preferably thin, like a membrane) that changes its local conductivity (by that I mean the permeability for an electric field; I hope it's the right term) upon excitation with light or heat? I have no idea where to start my search for something like that. </p>
<p>Thanks a lot.</p> | g6638 | [
0.057145856320858,
0.026172442361712456,
0.017504161223769188,
-0.012199973687529564,
0.005529317073523998,
0.0198214128613472,
-0.06764878332614899,
0.01993352547287941,
0.005602739751338959,
0.03112521581351757,
-0.010138694196939468,
0.03867963328957558,
0.002691093599423766,
0.020131850615143776,
-0.042345479130744934,
-0.0470895878970623,
0.04357112944126129,
0.012370269745588303,
-0.0102439159527421,
0.036428507417440414,
-0.04865635558962822,
0.0039767432026565075,
0.05188274011015892,
-0.00939649622887373,
0.029792990535497665,
0.028632821515202522,
0.029245207086205482,
-0.036402080208063126,
0.034145258367061615,
-0.00448894128203392,
-0.032944560050964355,
-0.106554314494133,
0.02467857301235199,
-0.049100276082754135,
-0.040561240166425705,
-0.033223576843738556,
0.011955373920500278,
-0.010256379842758179,
0.0038577578961849213,
0.03825957328081131,
0.05944054573774338,
0.051758721470832825,
0.021317195147275925,
0.0007589203305542469,
0.07257629930973053,
-0.04536083713173866,
-0.021789375692605972,
0.017268052324652672,
-0.05173827335238457,
-0.007368532475084066,
-0.026641452684998512,
0.0024117438588291407,
0.019265642389655113,
0.0005869597080163658,
0.006441919133067131,
-0.04198284447193146,
-0.02355816587805748,
0.01794874668121338,
0.04415936768054962,
-0.003659419948235154,
-0.046167340129613876,
0.043307114392519,
0.012631027027964592,
-0.029546957463026047,
-0.016493704169988632,
0.012441440485417843,
-0.009709151461720467,
0.0019864330533891916,
-0.02046433463692665,
0.003953854087740183,
0.00811843667179346,
0.04214681312441826,
-0.05866448953747749,
-0.0024853781796991825,
0.034315019845962524,
0.0505220852792263,
0.030202198773622513,
0.0022286176681518555,
0.0064467815682291985,
-0.029505781829357147,
-0.07436206936836243,
-0.022148778662085533,
-0.05520404502749443,
-0.010112138465046883,
0.0337517149746418,
-0.056241609156131744,
0.01434365101158619,
0.030437029898166656,
0.03437938541173935,
-0.05621258541941643,
-0.038367267698049545,
0.019309628754854202,
0.08926911652088165,
-0.05725575238466263,
-0.023321999236941338,
0.04831346496939659,
0.018049374222755432,
0.000047134075430221856,
-0.0215535219758749,
-0.062063176184892654,
-0.005940424744039774,
-0.031056609004735947,
0.057850588113069534,
0.00729774683713913,
-0.050080105662345886,
0.02289307862520218,
0.021739456802606583,
-0.07114227861166,
-0.029394574463367462,
-0.003530737478286028,
0.038503360003232956,
-0.022596735507249832,
-0.03481801226735115,
-0.014925247058272362,
-0.007180166430771351,
0.011287313885986805,
0.034850943833589554,
-0.04267680272459984,
0.005529675632715225,
0.04077019914984703,
0.04731491208076477,
0.018125459551811218,
-0.012731559574604034,
0.06636388599872589,
-0.01115519180893898,
0.08980758488178253,
0.0044751898385584354,
0.03781907632946968,
-0.021405259147286415,
-0.004532081540673971,
0.026004236191511154,
0.01551496796309948,
-0.025275209918618202,
-0.007816750556230545,
-0.006264772731810808,
0.007779334671795368,
0.03827838599681854,
-0.00027023963048122823,
0.044961486011743546,
-0.008708292618393898,
0.009474193677306175,
-0.08349598944187164,
-0.011812853626906872,
0.013863544911146164,
0.017808396369218826,
-0.03291599452495575,
0.03501906245946884,
-0.0018762140534818172,
0.07357866317033768,
0.012416724115610123,
0.04065994173288345,
0.017684828490018845,
-0.019036466255784035,
-0.040029410272836685,
-0.016930921003222466,
-0.022931842133402824,
0.021769007667899132,
0.01079921331256628,
0.0779927596449852,
-0.06571868807077408,
-0.006119832396507263,
0.027394013479351997,
-0.010901326313614845,
-0.005009475164115429,
0.007661794777959585,
0.014230753295123577,
-0.02320794388651848,
-0.0023643707390874624,
-0.033539433032274246,
-0.01970485970377922,
-0.020158801227808,
-0.016020188108086586,
0.018909361213445663,
0.10175150632858276,
0.008252413012087345,
0.03500957041978836,
-0.0023501762188971043,
-0.0535496287047863,
-0.02383943274617195,
-0.03943701460957527,
-0.05141245201230049,
-0.014499913901090622,
0.02352711744606495,
-0.12402015179395676,
-0.011559512466192245,
0.025647738948464394,
-0.01142422016710043,
0.0075953747145831585,
-0.07519946247339249,
0.003900793381035328,
-0.05199515447020531,
-0.0075654867105185986,
0.006270201876759529,
-0.013146026991307735,
0.018802396953105927,
0.008871675468981266,
0.04968975484371185,
-0.03515254706144333,
-0.028409430757164955,
-0.05985349789261818,
0.024494128301739693,
0.03125690296292305,
0.05104810744524002,
0.035263482481241226,
0.013215659186244011,
0.022542959079146385,
-0.03525876998901367,
-0.046539269387722015,
0.024529000744223595,
0.005617949180305004,
0.02177892066538334,
-0.002070138929411769,
0.027712805196642876,
0.010308945551514626,
0.00034878196311183274,
-0.02904624491930008,
-0.04182504862546921,
-0.011547851376235485,
-0.014680140651762486,
-0.06636008620262146,
-0.014596077613532543,
0.046401362866163254,
0.015719499439001083,
-0.021876627579331398,
-0.05314389988780022,
-0.035119060426950455,
0.03959282487630844,
0.03249771147966385,
0.012494176626205444,
0.03593311086297035,
-0.07114768028259277,
-0.04201198369264603,
0.054990168660879135,
0.010705760680139065,
0.05567753687500954,
0.01820768602192402,
-0.07495398819446564,
-0.041064076125621796,
-0.03201251104474068,
-0.08742716163396835,
-0.015153340995311737,
-0.019735651090741158,
-0.06996350735425949,
0.007840408012270927,
-0.001200387952849269,
-0.02577725425362587,
-0.0448211245238781,
-0.007222009357064962,
0.05202150717377663,
-0.010988093912601471,
0.06426156312227249,
0.0014490013709291816,
-0.003618385409936309,
0.04842174053192139,
0.012383151799440384,
-0.021940059959888458,
0.005487335845828056,
0.05886705592274666,
-0.016190562397241592,
-0.024836340919137,
0.030768640339374542,
0.008082079701125622,
0.012459595687687397,
0.02999107725918293,
-0.01310588140040636,
-0.013694550842046738,
-0.025808289647102356,
0.03974269703030586,
-0.007621873635798693,
0.05032650753855705,
0.025907209143042564,
0.05351627245545387,
0.022688372060656548,
0.0006875856197439134,
0.06526132673025131,
-0.01418080274015665,
0.027742378413677216,
-0.07033894211053848,
0.05704981088638306,
-0.061086833477020264,
0.0353858508169651,
-0.044866736978292465,
-0.05090832710266113,
-0.0012977863661944866,
-0.00875114370137453,
-0.056359779089689255,
0.03073575720191002,
-0.0030926871113479137,
0.02454822137951851,
-0.04561396688222885,
-0.007501511834561825,
-0.004672701470553875,
-0.046738188713788986,
0.028281105682253838,
-0.023995371535420418,
0.0010970053263008595,
0.057390544563531876,
-0.008707741275429726,
0.02478650212287903,
0.027278879657387733,
0.012730118818581104,
-0.04205392301082611,
0.003890596330165863,
-0.004662184044718742,
0.05352802202105522,
-0.0027885264717042446,
-0.01536927092820406,
-0.07870103418827057,
0.054595645517110825,
-0.003820633515715599,
-0.023828810080885887,
-0.07407477498054504,
0.03338116407394409,
0.019276374951004982,
-0.010120181366801262,
0.002480874303728342,
-0.01291586086153984,
0.013059786520898342,
0.07062937319278717,
-0.07867871969938278,
0.02685350365936756,
0.01869042031466961,
0.02300902269780636,
-0.009113858453929424,
0.018570516258478165,
-0.0120201101526618,
-0.00808088667690754,
-0.006930414587259293,
-0.01759827323257923,
-0.041524488478899,
-0.002312413416802883,
0.01286004763096571,
-0.02365703321993351,
-0.060472384095191956,
-0.04553207382559776,
-0.0165970828384161,
-0.053095366805791855,
0.029387036338448524,
0.005381991155445576,
0.04436440020799637,
0.028475316241383553,
-0.03397485986351967,
-0.027522621676325798,
-0.009575514122843742,
-0.0272214412689209,
0.03312501311302185,
0.01828821748495102,
-0.05703303590416908,
-0.01489756628870964,
0.0006566998781636357,
0.034362610429525375,
0.004702966194599867,
0.04394040256738663,
-0.0014596657129004598,
-0.06925221532583237,
0.009807445108890533,
0.09508073329925537,
0.007726216688752174,
0.01396086160093546,
0.012123921886086464,
0.0006067308131605387,
-0.0972304418683052,
0.05770019069314003,
-0.03545474633574486,
-0.022376734763383865,
0.05743768811225891,
0.03746100887656212,
-0.028810789808630943,
-0.03996909782290459,
0.007436043117195368,
0.07066554576158524,
-0.01703723706305027,
-0.001865559839643538,
0.06954522430896759,
-0.002428248291835189,
-0.03430113568902016,
-0.031728047877550125,
-0.014519544318318367,
-0.042594775557518005,
-0.010872457176446915,
0.007969117723405361,
0.05711290240287781,
0.05900871753692627,
0.02560492977499962,
0.0319693498313427,
0.014229283668100834,
0.012291805818676949,
-0.007084887940436602,
-0.007935945875942707,
-0.0022930994164198637,
-0.06235671415925026,
0.017627259716391563,
-0.004121463745832443,
-0.013767112977802753,
-0.00544740492478013,
-0.024136461317539215,
0.0286802276968956,
-0.02116752415895462,
0.03430088981986046,
0.004448145627975464,
0.07886143773794174,
0.022532925009727478,
0.036492105573415756,
0.009186369366943836,
0.022954918444156647,
-0.0073645515367388725,
0.030510274693369865,
0.009863886050879955,
-0.017453230917453766,
-0.019171077758073807,
-0.026986412703990936,
-0.05469520762562752,
-0.02999618649482727,
-0.05397820845246315,
-0.04163992032408714,
0.0005396261112764478,
0.03135306015610695,
-0.036757487803697586,
0.06308188289403915,
-0.008313626982271671,
-0.011403697542846203,
0.008754896931350231,
0.007968368008732796,
0.008143024519085884,
0.04063359275460243,
0.07877400517463684,
0.07066366821527481,
-0.006180056370794773,
-0.01321761030703783,
-0.04807530343532562,
-0.02675931714475155,
-0.0023055728524923325,
-0.07460460066795349,
0.04521898180246353,
0.01333223283290863,
0.01940377801656723,
-0.07720883935689926,
-0.02153465710580349,
0.01570182479918003,
0.051966726779937744,
0.04461181163787842,
-0.018922701478004456,
0.004122121725231409,
-0.00939922221004963,
0.022830305621027946,
0.030213911086320877,
-0.025071915239095688,
0.03231484442949295,
-0.013693219050765038,
-0.001385206705890596,
-0.07361666858196259,
0.0025950679555535316,
-0.0006529315724037588,
-0.01081561204046011,
-0.06476445496082306,
-0.024324046447873116,
-0.03706808015704155,
-0.024917149916291237,
0.06243196129798889,
0.038988146930933,
-0.01620597578585148,
-0.03321095183491707,
-0.043115127831697464,
0.0550357848405838,
-0.0016945617971941829,
-0.003097702283412218,
-0.0017252721590921283,
-0.007473296485841274,
-0.005360414274036884,
0.002800233894959092,
0.03259257227182388,
0.06946618109941483,
0.013272399082779884,
0.039507247507572174,
0.027054140344262123,
0.014428946189582348,
-0.04650295898318291,
0.003197886049747467,
-0.06572463363409042,
-0.06731794029474258,
-0.008585115894675255,
0.02037971280515194,
0.04008480906486511,
0.014375098049640656,
0.0561247356235981,
0.023035703226923943,
-0.048701442778110504,
0.09132888913154602,
0.009806875139474869,
-0.09935358166694641,
0.00265158386901021,
-0.00015745509881526232,
0.007581488229334354,
0.04604329541325569,
-0.0296789463609457,
0.009841825813055038,
0.02520432323217392,
0.0030031127389520407,
-0.013101899065077305,
-0.0018654073355719447,
0.01866491138935089,
0.0462530218064785,
-0.005812627263367176,
-0.01672162115573883,
0.018442897126078606,
0.02359818108379841,
-0.03417099267244339,
0.003946084063500166,
0.0056405821815133095,
0.023930944502353668,
-0.05566143989562988,
-0.010974764823913574,
0.0030828313902020454,
-0.015469145029783249,
-0.0023090397007763386,
-0.0064926715567708015,
-0.08362405002117157,
0.004625051282346249,
-0.03910696133971214,
-0.05272574722766876,
-0.05955128371715546,
-0.065943643450737,
0.011812200769782066,
0.0017188148340210319,
0.0027966529596596956,
0.03105780854821205,
-0.029756968840956688,
0.015232571400702,
0.07021339982748032,
0.017267603427171707,
0.0583818145096302,
0.03327561169862747,
-0.03526165708899498,
-0.022731244564056396,
-0.0058952029794454575,
0.03352260962128639,
-0.0029182429425418377,
0.057222604751586914,
-0.0033595850691199303,
0.06802034378051758,
-0.016879161819815636,
-0.05277445539832115,
0.05791938677430153,
0.003924168646335602,
0.09125161916017532,
0.043620072305202484,
-0.02237544395029545,
0.009245127439498901,
0.024137109518051147,
0.014897583983838558,
0.03380622714757919,
-0.004957822151482105,
0.006762724835425615,
0.0363004170358181,
0.00439173448830843,
-0.03384888172149658,
-0.0133312176913023,
-0.011575555428862572,
0.012839997187256813,
0.029443856328725815,
0.06343533098697662,
0.003139093052595854,
0.03290928900241852,
-0.09400908648967743,
0.01706209033727646,
-0.04017113521695137,
0.006818066816776991,
-0.006115361582487822,
0.07447434961795807,
-0.01702040433883667,
-0.02768567204475403,
0.027107402682304382,
0.03869413956999779,
-0.0653252899646759,
-0.054348863661289215,
-0.02315661683678627,
-0.015717225149273872,
-0.05469389259815216,
-0.022482775151729584,
0.0007100154762156308,
-0.028096698224544525,
0.03277192264795303,
-0.02154706045985222,
-0.020562954246997833,
-0.013912105932831764,
0.01538576278835535,
0.03592189773917198,
-0.04671843349933624,
0.039349265396595,
-0.05309378728270531,
0.0017453496111556888,
-0.01059764251112938,
-0.04612341150641441,
0.021944524720311165,
0.004032788332551718,
0.015399874188005924,
-0.06821145862340927,
0.03738388791680336,
0.03506085276603699,
0.05013825744390488,
0.031783636659383774,
-0.06905229389667511,
0.003976874053478241,
-0.03553447872400284,
0.02585470862686634,
0.06690794974565506,
0.05638862028717995,
0.027463529258966446,
0.02977108582854271,
-0.028202906250953674,
-0.027489086613059044,
-0.057138316333293915,
-0.034815527498722076,
-0.0270379725843668,
-0.04205631837248802,
-0.01040146965533495,
-0.019411588087677956,
-0.028231382369995117,
0.031673505902290344,
-0.014868633821606636,
-0.05559367686510086,
-0.03204532340168953,
0.04938257485628128,
-0.0019503958756104112,
-0.03992342948913574,
0.028775623068213463,
-0.02606547251343727,
0.03526897355914116,
0.026437126100063324,
-0.014152402989566326,
-0.00813293643295765,
0.01176435500383377,
0.0226366575807333,
0.05018480122089386,
-0.016119539737701416,
-0.03949274122714996,
0.013707142323255539,
-0.061397913843393326,
0.02017258293926716,
0.002451792126521468,
0.0026669949293136597,
0.025181839242577553,
0.021765239536762238,
0.05173390731215477,
0.03264802321791649,
-0.02587546594440937,
-0.0165419839322567,
0.018685990944504738,
0.003312173066660762,
0.006400516256690025,
0.03128550574183464,
0.04214010387659073,
-0.045956019312143326,
-0.02843097411096096,
-0.005971607286483049,
0.018173107877373695,
-0.029190272092819214,
0.024911338463425636,
0.026575054973363876,
-0.022504456341266632,
-0.03588630259037018,
-0.02335176058113575,
-0.01202663779258728,
-0.015457995235919952,
0.009266546927392483,
0.0371369943022728,
-0.010496119037270546,
-0.04890236631035805,
-0.002220442984253168,
-0.010432717390358448,
0.0351836122572422,
-0.041976574808359146,
0.0068846228532493114,
-0.021120015531778336,
-0.027202041819691658,
-0.03997236490249634,
-0.009012113325297832,
0.10555774718523026,
0.022595174610614777,
-0.03600209951400757,
-0.000809424149338156,
0.010478992015123367,
0.06499651819467545,
-0.034825582057237625,
-0.004946602042764425,
0.005866880062967539,
-0.036277901381254196,
0.05207475274801254,
0.037635497748851776,
0.058570995926856995,
0.03082774020731449,
-0.007931920699775219,
0.03222660347819328,
-0.01928767003118992,
0.03411431610584259,
-0.033919356763362885,
0.027364518493413925,
0.0026111258193850517,
0.041554998606443405,
-0.03204687312245369,
-0.0486849844455719,
-0.001995476195588708,
-0.0007585271378047764,
-0.058631595224142075,
-0.0031902622431516647,
-0.031208638101816177,
-0.04151449352502823,
-0.054808661341667175,
-0.07875019311904907,
0.010824774391949177,
0.007742520421743393,
0.07857134193181992,
0.05226583406329155,
0.03509538993239403,
-0.0016445049550384283,
0.007839350029826164,
-0.037557195872068405,
0.07440702617168427,
-0.02669556438922882,
0.021130843088030815,
-0.05772015079855919,
0.00837499089539051,
-0.009327870793640614,
0.0031701119150966406,
-0.0006803765427321196,
-0.002006776863709092,
-0.01175603736191988,
0.018196623772382736,
0.06324836611747742,
0.02635577879846096,
0.0465359091758728,
-0.03912952169775963,
-0.005059929098933935,
-0.03287133201956749,
-0.07910352945327759,
-0.02299361675977707,
0.05537853017449379,
0.0018757618963718414,
0.06635067611932755,
-0.029430456459522247,
0.009787927381694317,
-0.029608575627207756,
-0.022352105006575584,
-0.02132255584001541,
0.009303211234509945,
0.010725721716880798,
0.0018626933451741934,
0.008230060338973999,
0.07185547798871994,
-0.040903523564338684,
-0.0535246916115284,
-0.004612677730619907,
0.00277357897721231,
0.010651208460330963,
-0.032630421221256256,
-0.0421128012239933,
0.007280729245394468,
0.003545660525560379,
-0.02893746830523014,
-0.039451729506254196,
0.010954039171338081,
-0.026655146852135658,
0.005224320571869612,
0.05055830627679825,
-0.005284145008772612,
0.010540231131017208,
0.057804930955171585,
0.011437805369496346
] |
<p>It seems as though I've come across a rather unusual conclusion that could either simply be a misinterpretation or a contradictory discovery. I seem to have found a way to utilize the Heisenberg Uncertainty Principle (HUP) to our benefit to communicate faster than the speed of light (FTL). I am aware of many proposals that try to utilize entangled spin particles and try to communicate, but this schemes fail because the measurement outcome can NOT be controlled. Therefore, even if two people share an entangled pair of particles, and Alice measures spin up, although she knows Bob has a spin down particle, Bob didn't measure yet and has no way of knowing that Alice has measured her particle. Hence, FTL is impossible based on the reason that the measurement outcome can not be controlled.</p>
<p>This leads to my proposal of using position and momentum entangled pairs. Consider <strong>Alice and Bob hold an ensemble of entangled particles in position and momenta</strong>, where each particle is trapped in a separate harmonic potential. At some specified time agreed upon in the future, Alice measures all of her particles' position to high precision. <strong>Alice and Bob have synchronized clocks</strong> and Bob measures all of his entangled particle's momentum to whatever accuracy he chooses. Alice can calculate the average value and also the standard deviation of position. The standard deviation of position would be extremely narrow, i.e, the spread of her measurements would be very small.</p>
<p>From the entanglement relation, <strong>x1 = x2 and p1 = -p2</strong>, we know that when Bob measures his particle's momentum, the spread of momentum will be very large. This must be true because position and momentum cannot be measured to arbitrary accuracy at the same time. This is very similar to Einstein's proposal to violate the HUP, however I am exploiting HUP.</p>
<p>What this all means is that the if Bob measures a very large momentum spread, it must mean that Alice has made her measurements. If Bob measures a relatively moderate momentum spread, then he knows Alice did not measure her particles. <strong>Since the position measurement can be made to arbitrary accuracy, we are "controlling the spread or the standard deviation as the means to communicate."</strong> (MAIN RATIONALE)</p>
<p>Say Alice and Bob have multiple ensembles of entangled particles. Alice can relay a message by simultaneously measuring her first ensemble, meaning its a "1" and not touch her second ensemble meaning its a "0", and perhaps she chose to measure the third ensemble, "1", etc. Hence generating the series 101..., where <strong>each ensemble of entangled particles represents one bit of information.</strong></p>
<p>What is flawed in this proposal? Entanglement in position and momenta is well established. We can also choose to measure the position of a particle to arbitrary precision. The HUP must hold for Bob and everyone involved.</p> | g6639 | [
0.004779121372848749,
0.04265236482024193,
-0.012958673760294914,
-0.03259092569351196,
0.04987020418047905,
0.005166764371097088,
0.059120528399944305,
0.010893522761762142,
-0.014159430749714375,
0.030057404190301895,
0.022417157888412476,
-0.02507779374718666,
-0.02288222685456276,
-0.01589748077094555,
-0.012728484347462654,
0.043046724051237106,
0.152746319770813,
0.020034823566675186,
0.018975352868437767,
0.005745709873735905,
0.03471788018941879,
0.02483193948864937,
-0.06484786421060562,
-0.04281998798251152,
-0.05725853890180588,
-0.023038366809487343,
-0.03273497521877289,
-0.05976879224181175,
-0.03145274147391319,
0.02071060985326767,
-0.02935301512479782,
-0.05768550559878349,
0.028627881780266762,
-0.03636045381426811,
0.02490408718585968,
-0.07996474206447601,
-0.004063581582158804,
-0.021999768912792206,
-0.012450417503714561,
0.03738444671034813,
-0.01035275124013424,
0.009142793715000153,
-0.02531476877629757,
-0.029119594022631645,
0.02798394486308098,
0.032488491386175156,
0.02225557528436184,
-0.02272189036011696,
0.01714993454515934,
-0.01838654838502407,
0.00914729107171297,
0.012815040536224842,
0.04716915637254715,
0.0464591421186924,
0.07440517842769623,
0.11519868671894073,
0.006426519248634577,
-0.02013608068227768,
0.03069990500807762,
0.0017578961560502648,
0.015004105865955353,
-0.006731315515935421,
0.014606039971113205,
0.04891534522175789,
0.02939065732061863,
0.06239274516701698,
-0.080436572432518,
0.03379024192690849,
-0.009359756484627724,
-0.01873195171356201,
-0.010373386554419994,
-0.06189693510532379,
-0.0008438630611635745,
-0.01991022750735283,
-0.03050685115158558,
0.057722050696611404,
-0.011170131154358387,
-0.04045189172029495,
-0.0018482115119695663,
0.051930587738752365,
-0.07705574482679367,
-0.034822460263967514,
0.005928352475166321,
-0.04900970682501793,
0.031647153198719025,
-0.03278447315096855,
-0.01864849030971527,
0.003102993592619896,
-0.0038213287480175495,
0.020856942981481552,
0.018675824627280235,
-0.05394745245575905,
0.05587230622768402,
-0.009046167135238647,
-0.04030471667647362,
-0.01306154578924179,
-0.039625994861125946,
-0.0084480419754982,
0.002273646416142583,
0.05385895073413849,
-0.06332559883594513,
0.05012954771518707,
-0.026276927441358566,
0.026762424036860466,
-0.022521143779158592,
-0.03275497257709503,
0.004203500226140022,
0.015243136323988438,
-0.007368106860667467,
-0.008123916573822498,
0.02216101810336113,
-0.021233852952718735,
-0.04160407930612564,
-0.05117132514715195,
-0.06058989092707634,
-0.0551108792424202,
0.07150977104902267,
0.014689148403704166,
-0.06853868812322617,
0.0024827569723129272,
0.03540107235312462,
0.02636374719440937,
0.0226286631077528,
0.10550267994403839,
-0.023943856358528137,
0.038081683218479156,
-0.02524278126657009,
0.034564532339572906,
0.02925959788262844,
0.0011495407670736313,
-0.049488987773656845,
-0.009588832966983318,
-0.03377099335193634,
0.05058857426047325,
-0.045901212841272354,
-0.024868423119187355,
0.03983837738633156,
0.03147747367620468,
0.03141435235738754,
0.008893760852515697,
-0.013660457916557789,
-0.01756587252020836,
0.02780146524310112,
-0.05537261441349983,
-0.012520751915872097,
0.02751922607421875,
-0.004129862878471613,
-0.027603454887866974,
0.03534764423966408,
0.03950340673327446,
0.00536614004522562,
0.09052444249391556,
-0.014357996173202991,
0.050229962915182114,
-0.011365961283445358,
0.02381565235555172,
0.04197172820568085,
0.031581904739141464,
0.024837227538228035,
0.04447036236524582,
0.06944151222705841,
0.003286791266873479,
-0.008066919632256031,
-0.06098233908414841,
0.015482679940760136,
0.0422510951757431,
0.04098377749323845,
0.008067445829510689,
-0.040778011083602905,
-0.03896193578839302,
-0.08722589910030365,
-0.0061394888907670975,
-0.003055717796087265,
0.00688586849719286,
0.04219313710927963,
0.0648394301533699,
-0.03499135375022888,
-0.07065369933843613,
-0.026221219450235367,
0.06155943125486374,
-0.007201863918453455,
0.022614706307649612,
-0.004486061632633209,
-0.015496845357120037,
-0.05531476438045502,
0.06764548271894455,
0.04355428367853165,
0.012911401689052582,
-0.014594613574445248,
-0.04934289678931236,
-0.03173324093222618,
-0.04159567877650261,
-0.024516727775335312,
0.009663446806371212,
-0.033061422407627106,
0.028891395777463913,
0.03302045539021492,
-0.009153853170573711,
-0.014415106736123562,
0.05986849591135979,
0.002616447862237692,
0.023702921345829964,
-0.02097037434577942,
-0.01432417519390583,
0.050366003066301346,
0.018053105100989342,
0.004144699312746525,
-0.007955973967909813,
0.031694136559963226,
-0.021568072959780693,
0.04651794210076332,
-0.016864625737071037,
-0.03385483846068382,
0.01262538693845272,
0.009547415189445019,
-0.06619416922330856,
0.01080274861305952,
-0.00936697144061327,
0.013658853247761726,
0.004486111458390951,
-0.02387131191790104,
-0.03157758340239525,
0.02791271172463894,
-0.024062206968665123,
-0.039376065135002136,
0.01203871425241232,
-0.04023996368050575,
-0.06689084321260452,
-0.08305788785219193,
0.05567061901092529,
-0.04696331545710564,
-0.00828714668750763,
-0.026707150042057037,
0.0069269523955881596,
0.06523717194795609,
0.02409319020807743,
-0.001534775597974658,
0.04091973975300789,
0.01896156556904316,
0.0524076446890831,
0.032132092863321304,
-0.062498655170202255,
-0.09976481646299362,
-0.012900127097964287,
0.0022180017549544573,
0.008330742828547955,
0.021053237840533257,
-0.07061415910720825,
0.0054582045413553715,
0.016490228474140167,
0.03354872390627861,
0.03134777396917343,
0.038757357746362686,
-0.09030821919441223,
0.001289257314056158,
0.001454461133107543,
0.012324754148721695,
0.04780503734946251,
-0.0980544164776802,
-0.04963948577642441,
-0.011010188609361649,
-0.012516850605607033,
-0.01659446768462658,
-0.0008462781552225351,
0.015908507630228996,
-0.00020707576186396182,
-0.025405608117580414,
0.04115176573395729,
-0.010085068643093109,
-0.0005944074946455657,
-0.027775965631008148,
-0.0021658821497112513,
0.009009843692183495,
0.009005164727568626,
-0.04483997821807861,
-0.060337238013744354,
0.006707294378429651,
-0.02868782915174961,
0.04974610358476639,
0.039594054222106934,
-0.07431914657354355,
0.05830354988574982,
-0.06568408012390137,
0.012851541861891747,
0.01825278252363205,
-0.0024520286824554205,
-0.02139454148709774,
0.015288992784917355,
0.03978506103157997,
0.022018464282155037,
0.033153679221868515,
0.012609248049557209,
0.052820026874542236,
0.001235397532582283,
-0.01351073943078518,
0.049437250941991806,
0.013728776015341282,
-0.03633362054824829,
-0.017480865120887756,
0.0018793079070746899,
0.006857965607196093,
0.06886749714612961,
0.00041531320312060416,
0.057823821902275085,
0.05907357111573219,
0.025676753371953964,
-0.04696148261427879,
0.010524974204599857,
-0.014635182917118073,
-0.01998397894203663,
-0.004739164840430021,
0.04935939982533455,
-0.02038700319826603,
-0.051163747906684875,
0.0004569707380142063,
-0.0257037915289402,
-0.0349898561835289,
0.02205931954085827,
0.014015043154358864,
-0.023461557924747467,
0.031989071518182755,
-0.017522409558296204,
0.0017613125964999199,
-0.03638071194291115,
0.07232129573822021,
0.028516484424471855,
-0.03373797982931137,
0.019091829657554626,
-0.06214047968387604,
-0.007760701701045036,
0.022327616810798645,
0.031978730112314224,
0.03529422730207443,
-0.0014489964814856648,
-0.014804038219153881,
-0.09057291597127914,
0.030362188816070557,
0.06511971354484558,
0.05013559013605118,
0.026776399463415146,
-0.035696983337402344,
-0.06403770297765732,
-0.055810391902923584,
0.05777498334646225,
0.003352018538862467,
-0.0006481771124526858,
-0.002866089344024658,
0.003769289469346404,
0.015079586766660213,
0.01683003641664982,
0.0034612189047038555,
0.06446844339370728,
0.022719746455550194,
-0.021555062383413315,
0.00912427343428135,
0.0349210761487484,
0.04791548103094101,
-0.013176994398236275,
0.004340306855738163,
0.00619897898286581,
0.03295177221298218,
0.014060446061193943,
0.029067493975162506,
0.002361259190365672,
-0.008496510796248913,
0.012716841883957386,
-0.033182740211486816,
0.01601896621286869,
0.0316094234585762,
-0.0010973234893754125,
-0.05525371804833412,
0.00024381848925258964,
-0.028029218316078186,
-0.0037301364354789257,
0.056720197200775146,
-0.047567445784807205,
0.0666629821062088,
-0.052475783973932266,
-0.011047356761991978,
-0.0075432173907756805,
0.016345413401722908,
0.07095932960510254,
0.002641953993588686,
0.020984264090657234,
0.021006081253290176,
0.0368303544819355,
-0.03820743039250374,
0.01619868166744709,
-0.04906313866376877,
0.0069487555883824825,
-0.01888229511678219,
-0.06881877034902573,
-0.021141590550541878,
-0.03950294479727745,
0.032357946038246155,
-0.012418046593666077,
0.020282717421650887,
-0.028062853962183,
0.03571053966879845,
-0.038966357707977295,
-0.0567285418510437,
-0.04653690755367279,
-0.02728225477039814,
-0.012288459576666355,
0.021862423047423363,
-0.003328048624098301,
0.013731472194194794,
-0.048617321997880936,
0.01622159034013748,
0.03042907454073429,
0.02096407301723957,
0.03369252383708954,
0.006019157357513905,
-0.01123371534049511,
0.03843269869685173,
-0.00436827726662159,
-0.02559443563222885,
-0.048640355467796326,
0.030291639268398285,
0.017223553732037544,
0.03163111209869385,
0.049538422375917435,
0.05662048980593681,
-0.021051691845059395,
-0.04178148880600929,
0.024977829307317734,
0.0031301481649279594,
0.010583835653960705,
0.0008011923055164516,
-0.042563918977975845,
0.02214142121374607,
-0.003218348603695631,
-0.017624331638216972,
0.0008658198057673872,
0.007443409878760576,
-0.0282462015748024,
0.0393015593290329,
-0.01407281868159771,
0.04871514067053795,
0.08273763209581375,
0.023336129263043404,
-0.023066775873303413,
-0.0018916117260232568,
-0.056075289845466614,
-0.00821780227124691,
0.08438292145729065,
-0.05560291185975075,
-0.004918853752315044,
-0.006181965582072735,
-0.013018024154007435,
0.02465103194117546,
0.021938607096672058,
-0.05767049640417099,
0.016533898189663887,
0.009027802385389805,
0.02270021289587021,
-0.03552563488483429,
0.03936445713043213,
0.08486942201852798,
0.006791363470256329,
-0.03960801288485527,
0.050860609859228134,
0.009403889067471027,
-0.009692894294857979,
-0.003107419004663825,
0.058532457798719406,
-0.07379002124071121,
-0.0352507084608078,
-0.056280869990587234,
-0.03385220468044281,
-0.01465301401913166,
-0.02580452524125576,
0.06828397512435913,
0.0595989003777504,
-0.03060568869113922,
-0.0007591306348331273,
0.013244583271443844,
0.009769285097718239,
-0.006723961792886257,
-0.04062377288937569,
-0.01632535085082054,
0.049991004168987274,
0.021977411583065987,
0.003492849413305521,
-0.03454441949725151,
0.014729767106473446,
-0.052801813930273056,
-0.009827898815274239,
0.006761873606592417,
-0.0007306173210963607,
0.049179185181856155,
-0.02615332417190075,
0.018081484362483025,
-0.009417245164513588,
-0.011679773218929768,
0.0169351976364851,
-0.006004213355481625,
0.01118193008005619,
-0.02773759700357914,
-0.027148278430104256,
-0.021257318556308746,
0.014353646896779537,
-0.009154336526989937,
0.02778494730591774,
-0.02682488039135933,
0.04883767291903496,
0.08359555155038834,
0.03750363364815712,
-0.03332072123885155,
-0.006833231076598167,
0.020008329302072525,
-0.0064933812245726585,
-0.016432104632258415,
-0.030730025842785835,
-0.018658161163330078,
-0.015580604784190655,
-0.012082806788384914,
-0.03874077647924423,
-0.007793846540153027,
0.0075172120705246925,
0.0005481706466525793,
0.0143720218911767,
0.03422102704644203,
-0.030673226341605186,
-0.04229648783802986,
-0.053861796855926514,
-0.06232481822371483,
0.07222495228052139,
-0.0019433344714343548,
0.040598638355731964,
0.05037675052881241,
0.012999975122511387,
0.03665538504719734,
-0.0750679224729538,
0.004786699544638395,
0.011674177832901478,
0.042388953268527985,
-0.04198465123772621,
0.008594093844294548,
0.02363632805645466,
0.0021447360049933195,
-0.027406128123402596,
0.013083807192742825,
0.06137924641370773,
-0.03334348648786545,
0.008851651102304459,
-0.022171037271618843,
-0.03487757220864296,
0.014595123007893562,
-0.03663768619298935,
0.012851654551923275,
-0.02750028669834137,
-0.03985246643424034,
-0.01077097188681364,
-0.019172074273228645,
0.03595855087041855,
-0.011989223770797253,
-0.04691482335329056,
-0.017846090719103813,
0.029392126947641373,
0.003665473312139511,
-0.020592764019966125,
0.04367474094033241,
-0.016495786607265472,
-0.0032856299076229334,
0.0005741027416661382,
0.009561676532030106,
0.012427911162376404,
-0.021301141008734703,
0.08075349032878876,
-0.019255533814430237,
0.038774263113737106,
-0.048580102622509,
0.0008679187740199268,
-0.01951601170003414,
0.021483398973941803,
-0.01269590761512518,
-0.005493485368788242,
-0.044175323098897934,
-0.0694856122136116,
-0.035782117396593094,
0.008550613187253475,
-0.010930893942713737,
-0.0012678271159529686,
0.01898283138871193,
0.008399357087910175,
-0.04407411068677902,
0.04652991518378258,
0.0313003771007061,
0.0005578591953963041,
-0.006413360591977835,
0.0013430260587483644,
-0.06080801039934158,
-0.054774876683950424,
-0.05840088799595833,
-0.04532443359494209,
0.010067641735076904,
-0.07410270720720291,
-0.07842089980840683,
0.0034117233008146286,
-0.02403542771935463,
-0.010202870704233646,
0.017219191417098045,
0.004964997060596943,
-0.025346316397190094,
0.04934284836053848,
0.0018966876668855548,
0.01051794458180666,
0.02078593708574772,
-0.022849498316645622,
0.010210556909441948,
0.02161294035613537,
0.030087294057011604,
0.01975889876484871,
-0.0022596505004912615,
0.03026708774268627,
0.025360245257616043,
-0.009823298081755638,
-0.06749440729618073,
0.03256191685795784,
0.06839409470558167,
0.020881954580545425,
0.019148657098412514,
-0.026819225400686264,
0.03216876462101936,
0.0319562666118145,
0.009478870779275894,
0.013398665003478527,
0.031141994521021843,
0.0567183755338192,
0.03979218751192093,
-0.009050692431628704,
0.054844073951244354,
0.03566393256187439,
-0.05175450071692467,
-0.008116835728287697,
-0.033971577882766724,
0.051619455218315125,
0.03914940357208252,
0.04447964206337929,
0.04653826728463173,
0.025391701608896255,
0.01874987594783306,
0.02783045917749405,
-0.05829237028956413,
0.01573711633682251,
0.051088057458400726,
0.006573187652975321,
-0.035181015729904175,
0.0000313522141368594,
-0.03491703048348427,
0.00032369588734582067,
-0.062078338116407394,
0.05526503175497055,
0.027617350220680237,
-0.015655936673283577,
-0.00639206962659955,
-0.006669018417596817,
0.041473012417554855,
-0.0555153489112854,
-0.046617768704891205,
-0.056888237595558167,
-0.01097462885081768,
-0.053101327270269394,
-0.025961976498365402,
-0.014941523782908916,
-0.0031228004954755306,
-0.0575777068734169,
-0.07111261039972305,
-0.02270139381289482,
0.04419761151075363,
-0.043922509998083115,
0.0009047329076565802,
-0.03712979331612587,
0.026369694620370865,
-0.02180762030184269,
-0.006893109530210495,
0.011859129182994366,
-0.08524654060602188,
0.0489877425134182,
-0.009631420485675335,
0.03184055536985397,
-0.020235896110534668,
0.022970376536250114,
-0.0030673311557620764,
0.05035153776407242,
-0.047480497509241104,
0.022515075281262398,
-0.01568513736128807,
-0.058831315487623215,
-0.010391270741820335,
0.0080783786252141,
0.007030968554317951,
-0.016262851655483246,
-0.02561306208372116,
0.04893223196268082,
0.04280366376042366,
0.030468996614217758,
-0.016613729298114777,
0.017768865451216698,
-0.048322632908821106,
-0.07309231907129288,
0.004588620271533728,
0.012605114839971066,
0.03993770480155945,
-0.02061154507100582,
0.024850893765687943,
0.010235308669507504,
-0.015279539860785007,
-0.03281840682029724,
0.014903889037668705,
0.03017125464975834,
-0.005448373034596443,
-0.02375692129135132,
-0.04699486494064331,
-0.017650026828050613,
-0.004898794926702976,
-0.02993084117770195,
0.019845599308609962,
0.007684247102588415,
0.029456807300448418,
-0.023177646100521088,
-0.02248290553689003,
0.01998625136911869,
-0.026481546461582184,
-0.04830159991979599,
0.04155363887548447,
0.058469079434871674,
0.011575441807508469,
-0.037597399204969406,
0.03961856663227081,
0.02268189750611782,
-0.03482494875788689,
-0.03883841261267662,
-0.01815180294215679,
0.05912128463387489,
-0.016060568392276764,
0.05160500109195709,
-0.034805525094270706,
0.01940714195370674,
-0.03829692304134369,
-0.052486274391412735,
0.02578877843916416,
0.015662437304854393,
-0.0019782069139182568,
-0.04270527511835098,
-0.05450032651424408,
0.02959006279706955,
-0.038161925971508026,
-0.035433508455753326,
-0.05301602929830551,
0.030524956062436104,
-0.03565182164311409,
0.02444125898182392,
0.04240699112415314,
-0.02010739967226982,
0.003755096811801195,
0.04177377372980118,
0.04121041297912598,
-0.027499886229634285,
-0.00017647798813413829,
-0.01967471092939377,
-0.026940271258354187,
0.02890414372086525,
-0.04554121941328049,
0.0031372469384223223,
0.02286078780889511,
0.06293299794197083
] |
<p><a href="http://www.google.com/search?q=haldane+conjecture">Haldane's conjecture</a> states that the integer spin antiferromagnetic Heisenberg chains have a gap in the excitation spectrum. However, the dispersion relation of the antiferromagnetic spin wave is $\omega_k\sim k$ in the long wave length limit, meaning that the excitation energy could be zero. What is the matter?</p> | g6640 | [
0.008988665416836739,
0.026123663410544395,
-0.012332845479249954,
-0.02446824498474598,
-0.014745712280273438,
0.03676227852702141,
-0.005953488405793905,
0.07927799969911575,
-0.022668754681944847,
-0.05872632935643196,
0.03887391462922096,
0.005971021018922329,
-0.023723939433693886,
-0.00283521949313581,
0.041256919503211975,
0.04103526845574379,
0.010402169078588486,
0.045141663402318954,
-0.005540994927287102,
-0.010276680812239647,
-0.04758009687066078,
-0.006394585594534874,
-0.044965341687202454,
-0.04282381758093834,
0.011243129149079323,
0.024543633684515953,
0.009810669347643852,
-0.08535408973693848,
-0.017621882259845734,
-0.013205201365053654,
0.0065393345430493355,
-0.007598553784191608,
0.03311403468251228,
-0.01342109777033329,
0.04885397106409073,
0.023508267477154732,
0.01663612760603428,
-0.0019682757556438446,
-0.05964941158890724,
-0.02115231566131115,
-0.03380758315324783,
0.023053845390677452,
0.029221463948488235,
0.009728283621370792,
-0.012920176610350609,
0.017208607867360115,
-0.007695105392485857,
0.05364353209733963,
0.010477033443748951,
0.012974470853805542,
-0.01003821287304163,
0.009929332882165909,
0.05927783250808716,
0.006420664023607969,
-0.017211226746439934,
0.07658354938030243,
-0.03106570802628994,
-0.03330368548631668,
0.006998388562351465,
0.050972986966371536,
0.017200207337737083,
-0.0070125386118888855,
-0.01661212556064129,
0.05138830840587616,
0.03123675473034382,
-0.001082873553968966,
-0.08054810762405396,
0.02862311340868473,
-0.0008214203990064561,
0.007510536350309849,
0.0240474846214056,
-0.02557423897087574,
-0.01009217556566,
-0.038284480571746826,
-0.039851732552051544,
0.0007057494367472827,
0.05322962999343872,
0.01861400157213211,
0.02188965119421482,
0.038629092276096344,
-0.052083518356084824,
0.04750807583332062,
-0.011633709073066711,
-0.05459893122315407,
0.046314630657434464,
-0.015794113278388977,
-0.03631037101149559,
0.025738419964909554,
0.02117050252854824,
0.10999977588653564,
0.00396436732262373,
0.01549815945327282,
0.021611783653497696,
-0.035018615424633026,
0.0021359883248806,
-0.03709564357995987,
0.0491001270711422,
0.034571029245853424,
-0.02996114082634449,
0.016201607882976532,
-0.02282807230949402,
0.046635981649160385,
0.0096511859446764,
-0.01988528110086918,
0.034894634038209915,
-0.006503894925117493,
-0.0029645415488630533,
-0.04925811290740967,
0.03249434754252434,
0.04266638308763504,
-0.012709620408713818,
0.020761603489518166,
-0.0703965499997139,
-0.024566199630498886,
-0.015140868723392487,
0.04106609895825386,
0.05863763019442558,
-0.027561990544199944,
-0.027740098536014557,
0.0075536794029176235,
0.016764283180236816,
0.013715834356844425,
-0.043395034968853,
0.11787614971399307,
0.006190564949065447,
0.004636468831449747,
0.0012483419850468636,
0.021433712914586067,
0.030659230425953865,
0.002266393043100834,
-0.006957231089472771,
0.007490926422178745,
-0.00875757820904255,
0.0023098792880773544,
0.019789371639490128,
0.003997527528554201,
0.020733611658215523,
0.036465905606746674,
-0.021127240732312202,
0.006392013281583786,
-0.017305029556155205,
-0.09187242388725281,
0.01902652531862259,
-0.030171560123562813,
-0.015729960054159164,
0.006672173738479614,
0.005228927358984947,
-0.038471072912216187,
0.004734414163976908,
0.002824280643835664,
0.009917891584336758,
0.07562840729951859,
-0.011828964576125145,
-0.07021584361791611,
0.007974544540047646,
0.030099904164671898,
0.0672372430562973,
0.0020698425360023975,
0.005618113558739424,
-0.000955990981310606,
-0.0051719113253057,
0.01334460824728012,
0.03004959225654602,
0.051407523453235626,
-0.06768914312124252,
-0.07116352021694183,
0.06869318336248398,
-0.015487066470086575,
-0.016639351844787598,
-0.02144235372543335,
-0.06787300109863281,
-0.0018255674513056874,
-0.01088473666459322,
-0.005423332564532757,
0.055319324135780334,
0.06547439098358154,
-0.057644665241241455,
-0.06082381308078766,
0.0027014226652681828,
-0.00917880330234766,
0.021792404353618622,
-0.011249951086938381,
0.015895159915089607,
0.018400510773062706,
-0.04538191109895706,
0.08049190044403076,
0.09761740267276764,
-0.04882765933871269,
0.026957442983984947,
-0.03545830771327019,
0.032721586525440216,
0.028825808316469193,
-0.03368685767054558,
-0.017539862543344498,
0.04677863419055939,
0.025643257424235344,
0.003052146639674902,
-0.047980133444070816,
-0.014650513418018818,
0.011525379493832588,
0.0525512658059597,
0.01230445597320795,
-0.04837701842188835,
0.006656534969806671,
0.02795041911303997,
0.012676510028541088,
0.007253770716488361,
-0.02962702512741089,
0.025066088885068893,
-0.06755302101373672,
0.020137500017881393,
-0.0023422474041581154,
-0.07284924387931824,
0.0056890700943768024,
0.01717577502131462,
0.01902809925377369,
0.010978790931403637,
-0.01911074109375477,
0.02285647951066494,
0.04239882156252861,
-0.0010627019219100475,
0.014385237358510494,
0.03631661832332611,
0.04760558530688286,
-0.02228359691798687,
-0.03136155381798744,
-0.07719089835882187,
-0.049126990139484406,
-0.06938102841377258,
0.014555482193827629,
-0.006737956311553717,
-0.07393676042556763,
0.03689444437623024,
0.002957595745101571,
0.016806870698928833,
-0.005005166865885258,
-0.01249291468411684,
-0.045960284769535065,
0.009288952685892582,
-0.014751722104847431,
-0.002096649492159486,
0.028253816068172455,
-0.060192544013261795,
0.005894476547837257,
0.04838870093226433,
-0.013731407932937145,
-0.01758662424981594,
-0.022642750293016434,
-0.016943883150815964,
-0.005722119938582182,
0.033466797322034836,
0.01669210009276867,
-0.0015629797708243132,
0.03733741492033005,
0.006203237920999527,
-0.039711326360702515,
-0.02888074517250061,
0.06506580859422684,
-0.02819347195327282,
-0.0628056600689888,
0.06364796310663223,
-0.0035954827908426523,
0.06834736466407776,
0.025437097996473312,
-0.04801982268691063,
-0.021975181996822357,
-0.0018463960150256753,
0.05112891271710396,
-0.041734881699085236,
-0.0601465217769146,
0.002585954964160919,
0.08855094015598297,
0.0005243102787062526,
0.003629835555329919,
-0.06007694825530052,
-0.020363280549645424,
-0.03102121688425541,
0.0020751217380166054,
0.012617039494216442,
-0.01608330011367798,
-0.04577767848968506,
0.03823074325919151,
0.011540837585926056,
0.0009301471873186529,
-0.016242608428001404,
-0.034030571579933167,
-0.0011222410248592496,
-0.0007375530549325049,
0.04130411148071289,
-0.029525088146328926,
-0.016039105132222176,
-0.0023687793873250484,
0.074832484126091,
0.004724488593637943,
-0.03550703078508377,
0.0666085034608841,
0.019854506477713585,
-0.006335557904094458,
0.007774462457746267,
0.020200183615088463,
-0.010661915875971317,
0.043408650904893875,
-0.04011541232466698,
0.011093816719949245,
0.04256061092019081,
0.01198611781001091,
-0.04213597998023033,
-0.03386242315173149,
-0.050428736954927444,
-0.006150409113615751,
-0.04018126428127289,
0.040844663977622986,
0.015131672844290733,
0.03539038076996803,
0.04141043499112129,
0.046444524079561234,
0.007128729484975338,
0.061651118099689484,
-0.00015644477389287204,
-0.027584202587604523,
-0.015606672503054142,
-0.03126826509833336,
0.014727940782904625,
-0.014101367443799973,
0.02320886217057705,
-0.019406281411647797,
-0.029952429234981537,
-0.0020337924361228943,
-0.08683416992425919,
0.019397681578993797,
-0.009082665666937828,
-0.0870424211025238,
-0.018065858632326126,
0.0010037687607109547,
-0.05900880694389343,
0.006781840696930885,
0.01105632446706295,
0.03874412178993225,
0.012049158103764057,
0.09810028225183487,
-0.09290911257266998,
0.01255156472325325,
-0.04981722682714462,
0.024905750527977943,
-0.006887497846037149,
0.06008697301149368,
-0.035189904272556305,
-0.007829990237951279,
-0.047411222010850906,
-0.017381390556693077,
-0.08066631108522415,
0.004042902495712042,
0.0028145534452050924,
-0.03994223475456238,
-0.0487387478351593,
0.010840150527656078,
0.01136280782520771,
0.02428092248737812,
0.03365756943821907,
-0.008385873399674892,
0.014023168943822384,
-0.0027602699119597673,
0.07289538532495499,
-0.02613990567624569,
-0.025530101731419563,
-0.020765462890267372,
-0.041821062564849854,
-0.01926497370004654,
0.05565757304430008,
-0.042328499257564545,
0.014587953686714172,
0.014480200596153736,
-0.001900744391605258,
-0.005938983056694269,
-0.006602533161640167,
-0.06501149386167526,
-0.031962085515260696,
0.01956229656934738,
-0.009120630100369453,
0.033223241567611694,
0.023498674854636192,
0.025274693965911865,
0.020004695281386375,
0.0308492761105299,
-0.008421882055699825,
-0.0021449404302984476,
-0.023938942700624466,
0.009423410519957542,
-0.05516965314745903,
-0.037652671337127686,
-0.018701117485761642,
-0.07948096841573715,
0.04645891860127449,
0.008452920243144035,
-0.05617212504148483,
-0.01900324411690235,
-0.012610959820449352,
-0.07548622786998749,
0.005263671278953552,
0.021500568836927414,
0.013456698507070541,
0.048164382576942444,
-0.044673752039670944,
-0.01621725596487522,
0.039196837693452835,
0.052158597856760025,
0.07390142232179642,
-0.01821601577103138,
0.02411184273660183,
0.029360337182879448,
-0.0084206722676754,
0.0009429972269572318,
-0.018369130790233612,
-0.05378128960728645,
-0.013952900655567646,
-0.014144676737487316,
0.027422301471233368,
-0.02301470935344696,
-0.010510256513953209,
-0.021532557904720306,
0.030691392719745636,
-0.0022719858679920435,
-0.020062793046236038,
0.047758523374795914,
-0.03890148177742958,
-0.009698254987597466,
0.0067403800785541534,
-0.008971184492111206,
-0.02238440327346325,
-0.017480041831731796,
-0.07220768928527832,
0.008071820251643658,
-0.008502677083015442,
0.027729187160730362,
-0.06169389188289642,
0.015397131443023682,
-0.008960784412920475,
0.0791233479976654,
0.037602949887514114,
0.027464071288704872,
0.016997192054986954,
0.03967660292983055,
0.07740828394889832,
0.03170739486813545,
0.03452720865607262,
0.04749979451298714,
-0.04331127181649208,
-0.021475303918123245,
-0.016164543107151985,
-0.031986989080905914,
0.04440038278698921,
-0.012328152544796467,
-0.050685714930295944,
-0.09204172343015671,
0.049865640699863434,
-0.028927091509103775,
-0.062347110360860825,
0.0065690320916473866,
0.0586102157831192,
0.05058690533041954,
-0.03224921226501465,
-0.030675308778882027,
-0.03823227062821388,
-0.015188144519925117,
0.02376498281955719,
0.00009211893484462053,
-0.03139512985944748,
-0.06524056941270828,
-0.08109112083911896,
0.036879442632198334,
0.042101699858903885,
0.00400701817125082,
-0.040920455008745193,
0.004831282421946526,
-0.027050048112869263,
-0.014258341863751411,
0.04217357560992241,
0.01616360805928707,
-0.047321002930402756,
-0.04573743790388107,
-0.008609018288552761,
0.012922714464366436,
0.0034858870785683393,
-0.014435747638344765,
0.023504555225372314,
0.01735183410346508,
-0.021014289930462837,
-0.01112973690032959,
-0.031016893684864044,
-0.07619882375001907,
0.08673688024282455,
0.017080333083868027,
-0.022674834355711937,
-0.01880338415503502,
0.04723956435918808,
-0.005738777108490467,
0.03022061102092266,
0.025935232639312744,
-0.013136845082044601,
0.008164369501173496,
0.008772947825491428,
-0.025329362601041794,
-0.0023785880766808987,
-0.01835084706544876,
-0.02334655076265335,
0.08724439144134521,
0.05292793735861778,
0.041285570710897446,
-0.009708854369819164,
0.006392957642674446,
-0.03198684751987457,
0.01025352906435728,
0.026690028607845306,
0.030619867146015167,
0.06063820421695709,
0.013937987387180328,
-0.028922714293003082,
-0.08722301572561264,
0.06599672883749008,
-0.002880824264138937,
-0.029715409502387047,
-0.04931727051734924,
0.009860469959676266,
-0.02524174004793167,
-0.009694445878267288,
-0.05047112703323364,
0.022499166429042816,
0.032476041465997696,
-0.015057219192385674,
0.0205918587744236,
0.04240939021110535,
0.02248242497444153,
-0.047294020652770996,
-0.03520768880844116,
0.02347453683614731,
0.024474887177348137,
0.017604079097509384,
0.03027847409248352,
-0.04786039888858795,
0.06344940513372421,
-0.022203700616955757,
-0.07507355511188507,
0.02989007532596588,
0.031383905559778214,
0.060890037566423416,
-0.019978439435362816,
-0.012589224614202976,
-0.03637968376278877,
0.016309427097439766,
-0.06117696315050125,
-0.040573377162218094,
0.0064558652229607105,
-0.004870302975177765,
-0.026248103007674217,
0.029695332050323486,
0.00015884972526691854,
0.012164964340627193,
-0.025816958397626877,
0.028682075440883636,
-0.03387802839279175,
0.011584257706999779,
0.03352629393339157,
0.010996950790286064,
-0.0017385657411068678,
0.001372201251797378,
0.03852758929133415,
-0.06911584734916687,
-0.06347176432609558,
-0.014171660877764225,
-0.038482099771499634,
-0.015246852301061153,
0.039245352149009705,
-0.015054672956466675,
0.020960554480552673,
0.0512213371694088,
0.001220401143655181,
0.0385751947760582,
-0.07848022878170013,
-0.02808113396167755,
-0.026002679020166397,
-0.060481708496809006,
0.020395776256918907,
0.000581811647862196,
0.009513475000858307,
0.01850220374763012,
-0.001418369123712182,
-0.01142230723053217,
-0.058500587940216064,
0.0678471252322197,
0.02710563689470291,
-0.0301379207521677,
-0.009529750794172287,
-0.033340491354465485,
-0.0032067354768514633,
0.030003253370523453,
-0.01993951015174389,
0.016546577215194702,
-0.023879501968622208,
-0.07457566261291504,
-0.04764356464147568,
0.010698425583541393,
-0.03821273148059845,
0.01818188838660717,
0.052356868982315063,
-0.07885242998600006,
0.00646683806553483,
-0.0022391341626644135,
-0.019464312121272087,
-0.02126610465347767,
0.03822138532996178,
-0.020326673984527588,
-0.014665406197309494,
0.05175581946969032,
0.016677534207701683,
0.050459496676921844,
-0.03318889066576958,
0.008350269868969917,
-0.005373791325837374,
0.011534717865288258,
0.03616616874933243,
0.023336073383688927,
-0.01706622540950775,
-0.04666145145893097,
-0.007181528490036726,
0.03377068042755127,
0.05004653334617615,
0.006022301968187094,
0.017194030806422234,
-0.007932611741125584,
-0.005190448369830847,
-0.014113010838627815,
0.011293979361653328,
-0.04050575569272041,
0.07047808170318604,
-0.03838283196091652,
0.009427061304450035,
-0.0581045001745224,
-0.04726121202111244,
0.02262972667813301,
0.03167605772614479,
-0.009628537110984325,
0.007179584354162216,
0.043236006051301956,
0.005990516394376755,
-0.025876887142658234,
-0.009636078961193562,
0.01464706938713789,
-0.030047746375203133,
0.016893496736884117,
-0.05399087443947792,
0.0009501728345640004,
-0.017576921731233597,
-0.05279893800616264,
0.06552647054195404,
-0.018058976158499718,
-0.06864867359399796,
-0.031367573887109756,
-0.04504597559571266,
0.039513200521469116,
0.0004267246404197067,
-0.0069486419670283794,
-0.011237633414566517,
-0.006710892077535391,
-0.0811440646648407,
-0.03836999461054802,
0.022794976830482483,
0.020227180793881416,
-0.0056466832756996155,
-0.002794967032968998,
0.0367581844329834,
0.01502195280045271,
-0.016115939244627953,
-0.017302649095654488,
-0.05611618235707283,
0.03235029801726341,
0.009532150812447071,
-0.04109220579266548,
-0.019321849569678307,
-0.005455670412629843,
0.007715458981692791,
0.018162112683057785,
0.05556883662939072,
-0.00026875498588196933,
0.0457945317029953,
0.011175047606229782,
0.038069985806941986,
-0.040681444108486176,
0.02689751610159874,
0.017137160524725914,
0.004161499440670013,
0.009214073419570923,
0.011671452783048153,
0.04415854066610336,
-0.011130592785775661,
0.03791000694036484,
0.03224407136440277,
-0.005571354646235704,
0.023195646703243256,
0.005098997615277767,
0.03441563621163368,
0.0676751583814621,
-0.005316723603755236,
-0.02197539433836937,
0.06310410797595978,
-0.010447494685649872,
-0.010544943623244762,
0.04678644612431526,
0.031245455145835876,
-0.03217603266239166,
-0.037148259580135345,
0.050109077244997025,
0.011773635633289814,
0.0017337239114567637,
-0.020990807563066483,
0.09329479932785034,
0.031001778319478035,
-0.049444299191236496,
0.02715623937547207,
0.015845071524381638,
-0.0452374704182148,
0.016881508752703667,
-0.005173829384148121,
0.04301862418651581,
0.014164574444293976,
-0.05670217424631119,
-0.013570466078817844,
0.002751615596935153,
0.011759787797927856,
0.056974951177835464,
0.0328977108001709,
-0.02528274618089199,
0.03036884404718876,
-0.043090347200632095,
-0.012025733478367329,
-0.059199653565883636,
-0.014113316312432289,
-0.047882407903671265,
0.010414449498057365,
0.041329193860292435,
-0.012810994870960712,
-0.0053551881574094296,
0.07692456990480423,
0.036350708454847336,
-0.03429562598466873,
-0.009672056883573532,
-0.009601716883480549,
-0.0040334295481443405,
-0.016608022153377533,
0.0012593342689797282,
0.015119798481464386,
-0.10863955318927765,
0.020421389490365982,
0.038072213530540466,
0.031214600428938866,
0.04035287722945213,
-0.04474731907248497,
0.01654350385069847,
0.05251893773674965,
0.03960367292165756,
-0.0402584969997406,
0.004570513963699341,
-0.03580386936664581,
0.00645240256562829,
0.0549180693924427,
0.0455084852874279,
-0.04587450250983238,
0.02699854038655758,
0.017490997910499573
] |
<p>Relativity of Simultaneity seems to be about OBSERVING two events simultaneously (please correct me if I am wrong). </p>
<p>However, as long as the two events are separated by a distance (any distance) then two observers (in the same frame) cannot agree that they happen simultaneously unless they are equidistant from the two events within the frame.</p>
<p>Consider the example of A and B at rest with respect to another observer C. A and B are stationary in space but separated by 1 light second of distance.</p>
<p>An event occurs simultaneously at A and B, the time should be the same since they are at rest with respect to each other. However, A will OBSERVE event at A and exactly after 1 second, the event at B. B will OBSERVE the event at B and exactly after 1 second, the event at A.</p>
<p>C may observe A first, B first or A and B simultaneously (which is fine).</p>
<p>My questions are:</p>
<ol>
<li>Are A and B in the same inertial frame? And if so, if simultaneity is about OBSERVING an event, then how do we account for the different observation times within the same frame? An event can never be simultaneous for A and B unless they are at the same location.</li>
<li>If A and B are not in the same frame, then they are not in inertial frames as there is no motion with respect to each other.</li>
<li>If simultaneity is not about OBSERVING two events, then how do we separate the visual aspect (time taken for light to travel) from the temporal aspects (time at which the two events actually occurred.</li>
</ol> | g6641 | [
0.03388296067714691,
0.006326586008071899,
0.02906462363898754,
-0.011673971079289913,
0.03441745042800903,
-0.018794942647218704,
0.0435754656791687,
0.07606346160173416,
-0.006865248084068298,
-0.0012892299564555287,
-0.014212274923920631,
-0.061292991042137146,
0.0009346013539470732,
0.011108767241239548,
0.005564126651734114,
-0.026310494169592857,
0.06987124681472778,
-0.06114688888192177,
-0.0163583867251873,
0.02120615914463997,
0.030230727046728134,
0.08368862420320511,
0.03399937227368355,
-0.012883211486041546,
-0.005324784200638533,
-0.004471728578209877,
0.03631377965211868,
-0.047134511172771454,
-0.027273381128907204,
-0.008548890240490437,
-0.01146771665662527,
-0.018849896267056465,
-0.0025676204822957516,
-0.03159503638744354,
0.05644938349723816,
-0.020408743992447853,
0.011309762485325336,
0.026601487770676613,
-0.036795731633901596,
0.018947076052427292,
0.030158597975969315,
0.02735055983066559,
0.028947819024324417,
-0.08532299846410751,
0.07205749303102493,
0.022971024736762047,
0.006704101804643869,
-0.0010280795395374298,
0.005503576714545488,
-0.04281889274716377,
-0.0009959707967936993,
0.07450348138809204,
-0.018350711092352867,
0.012761479243636131,
0.021892298012971878,
0.059335507452487946,
0.01884412206709385,
-0.015767866745591164,
0.07015015929937363,
0.024924132972955704,
0.054348353296518326,
-0.03952199965715408,
0.0014993727672845125,
0.04124448075890541,
0.02897193469107151,
-0.03580954670906067,
-0.034981101751327515,
0.013025959953665733,
0.0183868408203125,
-0.03850792720913887,
-0.0004283323069103062,
-0.016840077936649323,
-0.0262016411870718,
-0.034902069717645645,
-0.04595634713768959,
0.013337739743292332,
0.05778347700834274,
-0.0013532170560210943,
0.005877387244254351,
0.05036765709519386,
-0.06302576512098312,
-0.0241704098880291,
0.02581760659813881,
-0.004789270926266909,
0.03500790521502495,
-0.0319296158850193,
0.016201598569750786,
-0.007492385804653168,
-0.03691935911774635,
0.004764148034155369,
0.06055538356304169,
-0.027801338583230972,
0.07056628912687302,
0.054042696952819824,
-0.06458339840173721,
-0.011636518873274326,
-0.037839438766241074,
0.06679636985063553,
0.03361443057656288,
0.024286311119794846,
-0.029534736648201942,
0.04825398698449135,
-0.0091446153819561,
0.007555011659860611,
0.0361051969230175,
-0.07792668044567108,
-0.020153822377324104,
0.036628708243370056,
-0.0642523542046547,
-0.05313330888748169,
-0.037124019116163254,
-0.052673663944005966,
-0.03400202840566635,
-0.02628166973590851,
-0.0729554295539856,
-0.04040826857089996,
0.04571676626801491,
-0.01950649730861187,
-0.022944897413253784,
-0.011489459313452244,
-0.030955204740166664,
0.0445697158575058,
-0.035286739468574524,
0.039972566068172455,
-0.04752475768327713,
0.005810490343719721,
-0.01187201775610447,
0.009911044500768185,
0.04213543236255646,
0.004901933949440718,
0.038764581084251404,
0.008626958355307579,
0.04989367723464966,
0.01225409284234047,
-0.03617884963750839,
-0.01986568421125412,
0.03620128706097603,
-0.009604689665138721,
0.022576825693249702,
0.03278632089495659,
0.030060019344091415,
-0.0057578072883188725,
-0.02043754793703556,
-0.00550341559574008,
0.01807275414466858,
-0.008968481793999672,
-0.0511343814432621,
0.017880836501717567,
0.018849637359380722,
0.042722124606370926,
-0.05000612139701843,
0.06622689217329025,
0.005306701175868511,
-0.028465019538998604,
-0.012652786448597908,
-0.010805141180753708,
-0.03670898824930191,
-0.03430015593767166,
0.02346119098365307,
0.0198433306068182,
0.07763145118951797,
-0.02485453337430954,
0.005984045099467039,
-0.0386095866560936,
-0.02075861394405365,
0.01782158948481083,
-0.0121479956433177,
-0.039182692766189575,
0.025221101939678192,
-0.10617423057556152,
0.0002573981473688036,
-0.00726982019841671,
0.028822986409068108,
0.0018061435548588634,
0.02532973699271679,
0.03750285878777504,
-0.0008191427914425731,
0.003553692251443863,
-0.07362044602632523,
-0.012921744957566261,
-0.05266791954636574,
-0.017788199707865715,
-0.0410495363175869,
-0.06777498126029968,
-0.036141473799943924,
-0.08360093832015991,
0.02201305516064167,
-0.018589649349451065,
-0.05170855298638344,
0.048020292073488235,
-0.019897613674402237,
-0.03685326129198074,
-0.029728960245847702,
0.013083199970424175,
-0.047226935625076294,
-0.002272383775562048,
0.053470417857170105,
0.006742296740412712,
-0.029371878132224083,
0.01898031122982502,
-0.02888096496462822,
-0.002802637405693531,
-0.008298673667013645,
0.06447604298591614,
0.0065551032312214375,
0.027676472440361977,
0.006777560338377953,
-0.022599752992391586,
-0.008308645337820053,
0.0008324087248183787,
0.0035241972655057907,
-0.06462917476892471,
0.015961987897753716,
-0.031116735190153122,
-0.015822913497686386,
0.05477846413850784,
0.02754906751215458,
0.008797060698270798,
-0.026004042476415634,
-0.018653562292456627,
-0.027206744998693466,
-0.018523866310715675,
-0.006620908156037331,
-0.04723664000630379,
-0.05273567885160446,
-0.01738787814974785,
-0.02696159854531288,
0.05346043407917023,
0.061092402786016464,
0.03856130689382553,
-0.045246295630931854,
0.059007249772548676,
-0.042040836066007614,
0.0323326401412487,
0.015806077048182487,
0.03721421957015991,
0.008611060678958893,
0.02075337804853916,
0.02405664324760437,
0.004905065521597862,
0.04542671516537666,
0.011736923828721046,
-0.014303558506071568,
0.010046439245343208,
0.03531371057033539,
-0.02329128608107567,
0.09669937193393707,
-0.02482164278626442,
0.005634802859276533,
0.01384365651756525,
-0.03354572877287865,
-0.05656767636537552,
-0.05698340758681297,
-0.015416824258863926,
-0.031695228070020676,
-0.0669528916478157,
0.009977847337722778,
0.010527409613132477,
-0.10118340700864792,
-0.008257483132183552,
0.017808089032769203,
-0.045073945075273514,
0.0270280372351408,
0.0218916367739439,
-0.027703164145350456,
-0.02186018042266369,
0.009688426740467548,
0.016340211033821106,
-0.043208200484514236,
-0.014879644848406315,
0.006911073811352253,
0.006212130188941956,
0.018889833241701126,
0.06525057554244995,
-0.00039717555046081543,
0.014913504011929035,
-0.027536649256944656,
-0.010353777557611465,
0.015583411790430546,
0.01057878602296114,
-0.017802033573389053,
0.02531297691166401,
-0.06007501855492592,
-0.038623400032520294,
0.071605384349823,
-0.0337580069899559,
0.009216878563165665,
0.002769813407212496,
0.0363897867500782,
0.01936625875532627,
-0.06994406878948212,
0.04583305865526199,
0.010335937142372131,
0.01590903475880623,
-0.03995414450764656,
0.05958981439471245,
-0.06005379185080528,
-0.025716843083500862,
-0.023061972111463547,
0.025053061544895172,
-0.01402619294822216,
-0.010135194286704063,
0.029135687276721,
0.030029725283384323,
0.04990851506590843,
0.023440435528755188,
-0.04199409484863281,
-0.04643994942307472,
0.014377059414982796,
-0.0345349982380867,
-0.03881867602467537,
0.010255200788378716,
-0.00993443001061678,
-0.004739777185022831,
0.0011184263275936246,
0.05252673849463463,
-0.013276146724820137,
-0.018785709515213966,
-0.052821170538663864,
-0.005367261357605457,
-0.0018322091782465577,
0.030412422493100166,
-0.053205594420433044,
0.007221553940325975,
0.005840978119522333,
-0.015309958718717098,
0.0284531619399786,
-0.05657565966248512,
-0.03294261917471886,
0.018417324870824814,
-0.03633158653974533,
0.02865339256823063,
0.005616459995508194,
-0.012024608440697193,
0.04164986312389374,
0.04126676172018051,
-0.042557887732982635,
0.0016332784434780478,
0.05642135813832283,
0.03521174564957619,
0.045717496424913406,
0.04491610825061798,
-0.06995395570993423,
0.013369509018957615,
-0.01143606100231409,
0.031047770753502846,
-0.0016060664784163237,
0.022418614476919174,
0.007476448081433773,
-0.008371769450604916,
0.03813977912068367,
0.0033975783735513687,
-0.003598501905798912,
-0.05787452310323715,
0.007774203550070524,
0.04117437079548836,
0.03879807889461517,
0.02103741094470024,
-0.003492828458547592,
-0.009421356953680515,
0.028011033311486244,
0.020358329638838768,
0.0027984511107206345,
0.0061429524794220924,
0.01605834625661373,
-0.03200807422399521,
-0.005663529969751835,
-0.01868988387286663,
0.06122366711497307,
-0.00523749552667141,
0.013531887903809547,
0.05583905801177025,
-0.03693617880344391,
-0.05172518268227577,
0.07542143762111664,
-0.028392305597662926,
0.05146227777004242,
0.05223218351602554,
-0.005615410394966602,
0.026504019275307655,
0.02259971760213375,
0.00845902506262064,
-0.010663911700248718,
-0.004057640675455332,
0.09779737889766693,
0.0053375218994915485,
0.02815207839012146,
0.03010101057589054,
-0.014427012763917446,
-0.04088349640369415,
0.03317582234740257,
-0.07017119973897934,
-0.053227752447128296,
-0.0850539281964302,
0.03358261659741402,
0.02945404127240181,
0.03935308754444122,
0.004163100849837065,
0.006162288133054972,
0.01802799105644226,
0.005816277582198381,
0.020118163898587227,
0.012395473197102547,
-0.02926313504576683,
-0.05235225707292557,
0.042616382241249084,
0.006737823598086834,
-0.008807897567749023,
-0.019995002076029778,
0.06143622100353241,
0.051799874752759933,
0.019727317616343498,
-0.02938796952366829,
-0.04609007388353348,
0.016370797529816628,
0.0015575765864923596,
0.0293988436460495,
0.02692853845655918,
0.06968527287244797,
0.02605242282152176,
-0.010382731445133686,
0.04795876145362854,
0.037927914410829544,
-0.024438980966806412,
0.032221049070358276,
0.08923342078924179,
0.009017513133585453,
0.010298298671841621,
-0.049095191061496735,
-0.02191300503909588,
-0.017111780121922493,
0.004979285411536694,
0.02272825688123703,
0.02030179277062416,
-0.03943570330739021,
0.04445672407746315,
0.030294612050056458,
0.061114124953746796,
0.04833552613854408,
0.010719917714595795,
-0.004058322869241238,
-0.014753609895706177,
0.010494478046894073,
-0.029700811952352524,
0.004597689025104046,
0.032671187072992325,
-0.06009252741932869,
-0.06300429254770279,
-0.029992971569299698,
-0.04048699140548706,
-0.014395270496606827,
0.05276235565543175,
-0.031735021620988846,
-0.020597007125616074,
0.009354962036013603,
0.0014485872816294432,
-0.03965264558792114,
0.02687891758978367,
-0.017374934628605843,
-0.0009932961547747254,
0.021401461213827133,
-0.023266570642590523,
0.027579965069890022,
-0.02782224863767624,
-0.018148839473724365,
0.015554160811007023,
-0.04553866758942604,
-0.014628312550485134,
-0.04782146215438843,
-0.006490305531769991,
-0.030164800584316254,
-0.01271179597824812,
-0.016648564487695694,
-0.009811848402023315,
0.04160548374056816,
-0.03604671359062195,
0.0029845840763300657,
-0.01621006429195404,
-0.013476583175361156,
-0.03861387073993683,
-0.027225416153669357,
-0.052616529166698456,
-0.009329755790531635,
-0.03257131949067116,
0.043071623891592026,
-0.017572922632098198,
0.026990467682480812,
-0.017110632732510567,
0.05890117585659027,
0.0012769402237609029,
-0.005966118071228266,
0.04288201034069061,
0.01188600528985262,
0.00045806312118656933,
-0.011150562204420567,
0.007559910416603088,
0.038539156317710876,
0.03053608536720276,
-0.019666971638798714,
-0.0043612257577478886,
-0.05498943477869034,
0.036381326615810394,
0.0011559209087863564,
-0.045149579644203186,
-0.023703765124082565,
0.033919841051101685,
0.00000834296861285111,
-0.025279657915234566,
-0.059790242463350296,
0.04153009131550789,
0.00855250284075737,
0.051311805844306946,
-0.07694827020168304,
0.047442156821489334,
0.004353978205472231,
-0.07367399334907532,
0.09088007360696793,
-0.039366111159324646,
0.001042350078932941,
-0.05680171400308609,
0.00587817607447505,
0.02091943845152855,
0.00718538835644722,
-0.041313961148262024,
0.005693493876606226,
-0.04603029787540436,
-0.05524367094039917,
0.0353546179831028,
0.02256760187447071,
0.010858148336410522,
-0.003289995016530156,
0.010368689894676208,
-0.012105783447623253,
-0.02191983535885811,
-0.00796521082520485,
-0.0007647516904398799,
0.03481396660208702,
-0.05107662081718445,
0.01842541992664337,
0.02853291481733322,
-0.07713628560304642,
-0.03335018828511238,
-0.011320937424898148,
0.07653287053108215,
-0.06112661957740784,
-0.055983152240514755,
0.028360256925225258,
0.006894153542816639,
0.05164730176329613,
-0.021304940804839134,
-0.01452102791517973,
0.02592337504029274,
0.02946535125374794,
0.0277351476252079,
-0.005177414510399103,
0.059181928634643555,
-0.0019099069759249687,
-0.0039743282832205296,
-0.0039136228151619434,
-0.0451430082321167,
0.02068292908370495,
0.008795961737632751,
0.015939444303512573,
-0.035192735493183136,
-0.0006156240706332028,
-0.023163940757513046,
0.025207335129380226,
-0.03327902406454086,
0.03368943929672241,
-0.01614442467689514,
0.04161114990711212,
-0.03197869658470154,
-0.020608726888895035,
-0.043228015303611755,
-0.0024559476878494024,
0.0013326914049685001,
-0.012380401603877544,
0.01764453575015068,
-0.06759794056415558,
0.013288346119225025,
-0.02098812907934189,
-0.003206385299563408,
0.04675542563199997,
-0.001911198953166604,
-0.03295449540019035,
0.013241243548691273,
-0.019418446347117424,
-0.025843963027000427,
-0.038261134177446365,
-0.008137822151184082,
0.0048523773439228535,
-0.029191171750426292,
-0.060768384486436844,
-0.0285209808498621,
-0.049193281680345535,
-0.042098671197891235,
-0.006144129671156406,
0.02313801646232605,
-0.018430177122354507,
0.089580237865448,
-0.011466478928923607,
-0.04586358368396759,
0.01581287756562233,
-0.05847858637571335,
-0.01890769600868225,
0.05067843571305275,
-0.06109900772571564,
0.01649348996579647,
0.05260953679680824,
-0.017695358023047447,
-0.0024173292331397533,
-0.008902433328330517,
0.0044997925870120525,
0.059354592114686966,
-0.049746885895729065,
-0.009790081530809402,
-0.005844769533723593,
-0.019960030913352966,
-0.00813452247530222,
-0.024140911176800728,
0.05938392132520676,
-0.019380846992135048,
0.0001792604016372934,
0.017279889434576035,
0.012803052552044392,
0.056395430117845535,
-0.0387636199593544,
-0.020635029301047325,
0.0245364960283041,
0.07606461644172668,
0.018552547320723534,
0.002821022877469659,
-0.052062056958675385,
0.059623897075653076,
0.021384848281741142,
0.038296494632959366,
-0.027690807357430458,
0.02601328119635582,
0.004157920368015766,
0.01189005933701992,
0.05078572779893875,
0.044368427246809006,
0.03186798095703125,
0.038194891065359116,
-0.01675080880522728,
-0.051509372889995575,
0.03365205228328705,
-0.0315479077398777,
-0.03963371738791466,
-0.009468882344663143,
0.0022928393445909023,
-0.05703849345445633,
0.007748542353510857,
0.019306516274809837,
-0.08242692053318024,
-0.005234635900706053,
0.000823453301563859,
-0.021659132093191147,
0.009474175982177258,
-0.06885313987731934,
-0.04333077371120453,
0.028359021991491318,
-0.09355323761701584,
-0.02582830749452114,
-0.03428274020552635,
0.010635611601173878,
-0.001531996880657971,
-0.126581609249115,
0.0072199562564492226,
-0.0014719688333570957,
0.020181166008114815,
-0.015631064772605896,
-0.021064244210720062,
0.0162812452763319,
-0.04874606058001518,
-0.0008122339495457709,
-0.03208059072494507,
0.014027005061507225,
0.0037493386771529913,
-0.0065202293917536736,
-0.039457693696022034,
0.039383407682180405,
0.020794101059436798,
0.016597917303442955,
-0.01931399293243885,
0.05030319467186928,
0.06934758275747299,
-0.03927530720829964,
-0.014434035867452621,
-0.041175782680511475,
-0.04059338569641113,
0.034874655306339264,
0.00023038405925035477,
-0.016698893159627914,
-0.01878659427165985,
-0.016305014491081238,
0.07538865506649017,
0.018670611083507538,
-0.027597377076745033,
-0.0002900470863096416,
-0.05147057771682739,
-0.00681638577952981,
0.06475412100553513,
-0.018253883346915245,
0.045599762350320816,
-0.015441264025866985,
0.0008515233639627695,
-0.012114128097891808,
0.04745055362582207,
0.05567330867052078,
0.028843477368354797,
0.04668433219194412,
0.024272926151752472,
-0.0078179482370615,
-0.026263097301125526,
-0.08061132580041885,
-0.031110819429159164,
0.02619086764752865,
0.048537012189626694,
0.015990274026989937,
-0.005990341305732727,
-0.0449797622859478,
0.0014957134844735265,
-0.042935360223054886,
0.029149170964956284,
0.021830342710018158,
0.10918349772691727,
-0.05776171758770943,
-0.011514288373291492,
-0.03343307226896286,
0.025217514485120773,
0.038598574697971344,
-0.018911154940724373,
0.07157482951879501,
-0.005480180028825998,
0.06693509966135025,
0.058943524956703186,
-0.07577540725469589,
-0.02199573814868927,
0.014020177535712719,
0.03369813412427902,
-0.006325984839349985,
-0.03650113195180893,
0.01113571971654892,
0.01744023710489273,
0.04156642407178879,
0.025672651827335358,
0.022390197962522507,
0.024366185069084167,
0.03572829067707062,
-0.03382182493805885,
0.0949111208319664,
-0.04876236617565155,
0.01775725930929184,
0.06209760159254074,
0.0068069640547037125,
-0.03530165180563927,
-0.010453673079609871,
0.03849480673670769,
0.010935179889202118,
-0.028090395033359528,
0.014779924415051937,
-0.012818980030715466,
-0.019728755578398705,
-0.021134350448846817,
-0.024168772622942924,
-0.022385871037840843,
0.06169311702251434
] |
<p>The water-gas phase transition is said to be similar to the ferromagnetic-paramagnetic phase transition (same set of critical exponents = same universality class). In the former case the order parameter is the difference in the densities, while in the latter it is the magnetization density.</p>
<p>In the magnetic case the $O(N)$ symmetry is broken spontaneously - hence we talk about two distinct phases as suggested by Landau, i.e. the ferromagnetic phase (which has $O(N-1)$ symmetry) and the paramagnetic phase (which has the full $O(N)$ symmetry). Now for the water-gas case, what symmetry is spontaneously broken? Both liquid water and gaseous water have translational and rotational symmetry..</p>
<p>Also, sometimes it is suggested that water and liquid should not be considered as distinct phases, since one can join the two phases by an excursion in the parameter space which does not encounter any singularities in the free energy. If so, then shouldn't we consider the paramagnetic and ferromagnetic phase to be just one phase as well?</p>
<p>How do we reconcile the concept of phases being characterized by symmetry (and their breakings), or being characterized by excursions in the parameter space, since they seem to give contradictory results? Thanks.</p> | g6642 | [
-0.03929635137319565,
0.04353421926498413,
-0.0022248034365475178,
0.03304586187005043,
0.00421879580244422,
0.035443175584077835,
-0.00025577237829566,
0.04661151394248009,
-0.02173929288983345,
0.01659315824508667,
-0.0062997955828905106,
0.012566604651510715,
-0.03266053646802902,
0.006121492013335228,
-0.032765597105026245,
-0.011633066460490227,
-0.019211042672395706,
0.03099551796913147,
-0.009145240299403667,
0.021074259653687477,
-0.02340450882911682,
-0.002837836043909192,
-0.0009371294872835279,
-0.025341657921671867,
0.011638755910098553,
-0.004449950065463781,
0.03698478266596794,
-0.060062576085329056,
-0.006662928033620119,
-0.0020485708955675364,
0.024892527610063553,
0.052481509745121,
-0.00860700011253357,
-0.0690455213189125,
-0.027875395491719246,
-0.07489003986120224,
0.01615295745432377,
-0.006878410931676626,
0.019966185092926025,
-0.02706580050289631,
0.0020564221777021885,
0.07010339200496674,
0.015379493124783039,
0.004439039155840874,
0.0033209456596523523,
0.04755290970206261,
-0.025358548387885094,
-0.029749765992164612,
-0.07438793778419495,
0.019440216943621635,
0.07780518382787704,
0.09541039168834686,
0.03997187316417694,
0.012952746823430061,
-0.029220739379525185,
0.037215933203697205,
-0.04018815606832504,
0.04069993272423744,
0.0881781205534935,
0.015418585389852524,
-0.0006535890279337764,
0.057756975293159485,
0.0018913989188149571,
-0.008111821487545967,
0.09171873331069946,
-0.0504951998591423,
-0.050627451390028,
0.01656430773437023,
-0.0022594425827264786,
-0.03543921932578087,
-0.004592324141412973,
-0.04883808270096779,
0.0038085526321083307,
-0.020223567262291908,
-0.019071165472269058,
0.009247773326933384,
-0.0024507474154233932,
-0.007501598447561264,
0.021729465574026108,
-0.0677875429391861,
-0.00345189543440938,
0.02414257638156414,
0.0015382798155769706,
0.0346074216067791,
0.005931300111114979,
-0.026082325726747513,
-0.0026446781121194363,
-0.030584782361984253,
0.0067148590460419655,
0.0032574539072811604,
-0.018187733367085457,
-0.003691535908728838,
-0.010285099036991596,
0.046822577714920044,
0.0074225859716534615,
0.007513910997658968,
0.042501550167798996,
0.04728015884757042,
-0.020521705970168114,
0.015222717076539993,
-0.04590931162238121,
0.006681577768176794,
-0.003837008262053132,
-0.0395817868411541,
-0.006131459027528763,
-0.008942069485783577,
0.02332931011915207,
0.03459256514906883,
0.03942638263106346,
0.014337214641273022,
-0.017220189794898033,
0.03376356512308121,
-0.06050315871834755,
0.060248833149671555,
-0.023215536028146744,
0.024216987192630768,
0.09088419377803802,
-0.05037132650613785,
0.008406003005802631,
0.0033096959814429283,
-0.003764551132917404,
-0.006940694525837898,
0.0332314670085907,
0.11535625904798508,
-0.022617381066083908,
0.014780677855014801,
0.02494853176176548,
-0.017792047932744026,
-0.0009043518221005797,
0.0026266679633408785,
-0.04104861244559288,
-0.004240547306835651,
-0.026524338871240616,
0.0353100411593914,
0.0028199381195008755,
-0.027168309316039085,
0.03378830477595329,
0.08652424812316895,
0.009062392637133598,
-0.06031697243452072,
0.026323555037379265,
0.019293857738375664,
-0.044995471835136414,
-0.029755348339676857,
-0.04825149103999138,
-0.0393303781747818,
-0.009235134348273277,
-0.006101325154304504,
-0.00651959702372551,
0.04432806745171547,
0.04334696754813194,
0.010496364906430244,
-0.029457954689860344,
-0.008037630468606949,
-0.01712600328028202,
-0.002661369275301695,
-0.02343299612402916,
-0.04771312326192856,
0.051159173250198364,
-0.006033333484083414,
0.020861441269516945,
-0.012736155651509762,
0.037198878824710846,
0.05822999030351639,
-0.07384043186903,
-0.045413222163915634,
0.041504766792058945,
0.023388609290122986,
0.04486915469169617,
-0.03163312003016472,
0.002031573560088873,
-0.016849933192133904,
-0.016160013154149055,
0.08572550117969513,
0.02825411781668663,
0.050095535814762115,
0.007908635772764683,
-0.016703886911273003,
-0.00660844286903739,
0.03028145246207714,
0.0013268173206597567,
-0.016079092398285866,
-0.04272571578621864,
-0.033655401319265366,
0.004828437231481075,
0.022414574399590492,
0.010179354809224606,
0.01755227893590927,
-0.06701194494962692,
-0.03602911904454231,
0.009507082402706146,
0.03339361399412155,
-0.022112801671028137,
-0.008511449210345745,
0.03063911385834217,
-0.03712448477745056,
-0.028335949406027794,
0.05658815801143646,
-0.07643920928239822,
-0.03914782032370567,
-0.006142742466181517,
-0.005452085752040148,
-0.035202205181121826,
0.025044480338692665,
-0.007591188419610262,
0.027207311242818832,
-0.011645245365798473,
0.00023027189308777452,
0.012404167093336582,
0.019556924700737,
0.011590961366891861,
-0.01569913886487484,
0.006808388978242874,
-0.025258611887693405,
-0.015572689473628998,
0.06397393345832825,
-0.01191404927521944,
-0.0026941169053316116,
0.008084116503596306,
0.013683455996215343,
0.01589156873524189,
0.038400158286094666,
0.013162320479750633,
0.027986647561192513,
0.035102445632219315,
0.006882154382765293,
0.0006046537891961634,
-0.006903345230966806,
0.02812790870666504,
-0.06602813303470612,
-0.007812981493771076,
0.0006042419699952006,
-0.012292033061385155,
-0.02228359691798687,
0.007896192371845245,
0.02608048915863037,
-0.023586956784129143,
-0.0451359823346138,
0.02154487743973732,
-0.033320438116788864,
-0.0046094609424471855,
-0.02169395051896572,
-0.02917121909558773,
0.041128646582365036,
-0.0028789089992642403,
-0.02017543837428093,
0.01421317644417286,
-0.0032759823370724916,
0.05597136914730072,
-0.003302905708551407,
-0.010922849178314209,
-0.06586114317178726,
-0.046005137264728546,
0.00857063289731741,
-0.025218641385436058,
0.013910094276070595,
0.050389885902404785,
0.09427943825721741,
-0.0904657244682312,
0.03114939294755459,
-0.006235170178115368,
0.01097885612398386,
0.01013590581715107,
0.011003452353179455,
-0.060248780995607376,
-0.0020416025072336197,
-0.01909317634999752,
0.04521443322300911,
0.012015909887850285,
-0.013733395375311375,
0.0011827804846689105,
0.049683138728141785,
-0.004510337021201849,
0.036076322197914124,
-0.030475139617919922,
-0.010507686994969845,
0.002335907658562064,
-0.024834858253598213,
0.06555670499801636,
-0.02276875078678131,
-0.0824851393699646,
-0.047929950058460236,
-0.05572587996721268,
-0.027982043102383614,
0.04684942215681076,
-0.0321776382625103,
-0.01651717722415924,
0.04008902609348297,
-0.011589284986257553,
0.059764962643384933,
0.02462591603398323,
0.03340347483754158,
0.0316942073404789,
0.012172555550932884,
-0.0216414425522089,
0.0015368059976026416,
-0.0352528840303421,
0.0006501677562482655,
0.0008270661346614361,
-0.004499667324125767,
0.029439644888043404,
-0.022192854434251785,
0.022289114072918892,
0.027703456580638885,
0.012862978503108025,
-0.004501542076468468,
-0.025246068835258484,
-0.03481576591730118,
-0.01613765023648739,
-0.056898150593042374,
-0.09696783125400543,
0.03620770573616028,
-0.03099595010280609,
-0.02117163874208927,
0.0029873994644731283,
-0.0054328544065356255,
-0.009553348645567894,
0.031526077538728714,
0.061237022280693054,
-0.05423927307128906,
-0.08982279896736145,
-0.0028746044263243675,
0.022659635171294212,
-0.05506375804543495,
-0.035606712102890015,
-0.01630229875445366,
-0.04588869586586952,
0.002604371402412653,
-0.018348848447203636,
0.013047476299107075,
-0.04710903391242027,
-0.04606194794178009,
0.017115164548158646,
-0.08233314752578735,
-0.05580313503742218,
-0.0024881765712052584,
0.0032576206140220165,
0.011121760122478008,
-0.012326990254223347,
-0.0005146936164237559,
-0.00008733629510970786,
-0.02188410609960556,
0.03862611949443817,
0.031198490411043167,
0.010194937698543072,
0.0006293230107985437,
0.024398908019065857,
-0.008703676052391529,
0.0030878218822181225,
0.030599549412727356,
0.045707494020462036,
0.01338530145585537,
0.013821844011545181,
0.01406139601022005,
-0.07529785484075546,
0.018636412918567657,
0.04611135274171829,
-0.032218143343925476,
0.017932549118995667,
-0.0036639650352299213,
0.013513275422155857,
-0.030832242220640182,
0.01928587444126606,
0.02825584076344967,
-0.02733469195663929,
0.004041118081659079,
-0.01754705049097538,
0.045995671302080154,
0.027472253888845444,
-0.0797937884926796,
0.05038008838891983,
-0.03665994107723236,
0.03834200277924538,
-0.08827030658721924,
0.07434561103582382,
-0.025265203788876534,
-0.008157751522958279,
-0.035075947642326355,
-0.015293385833501816,
0.02642289362847805,
0.024507392197847366,
-0.053669337183237076,
0.015390311367809772,
0.0202811136841774,
0.019641300663352013,
0.00815313309431076,
-0.011385477147996426,
-0.008123255334794521,
-0.03680044785141945,
-0.08237617462873459,
0.03277343884110451,
0.029140643775463104,
-0.0004915853496640921,
-0.019722357392311096,
0.029859164729714394,
0.04654240235686302,
0.0029679040890187025,
0.043146051466464996,
-0.04396705701947212,
0.08905238658189774,
-0.043171487748622894,
-0.051026441156864166,
-0.01662561297416687,
-0.037187036126852036,
0.019916821271181107,
-0.07040584087371826,
0.025471748784184456,
-0.0344376415014267,
-0.018282247707247734,
0.002277249237522483,
0.01683434657752514,
-0.01749538443982601,
-0.04407985135912895,
-0.04031902924180031,
0.01754925586283207,
0.01383662223815918,
-0.00166614493355155,
-0.08051694184541702,
0.029471835121512413,
-0.029208600521087646,
-0.01440352015197277,
0.02625800296664238,
-0.08726969361305237,
-0.08075802773237228,
-0.02190369926393032,
0.04951656237244606,
0.055942416191101074,
-0.002623805543407798,
-0.0052763065323233604,
0.0045708660036325455,
-0.0038963868282735348,
0.016257507726550102,
0.005552720744162798,
0.006079715210944414,
-0.007126465439796448,
-0.025529352948069572,
-0.03867199644446373,
0.04912784695625305,
0.005234813317656517,
0.040250468999147415,
0.05470229685306549,
0.057037290185689926,
0.018614692613482475,
0.036359116435050964,
0.06837698072195053,
-0.021800540387630463,
0.06291566044092178,
-0.006968997418880463,
-0.022275259718298912,
0.017704088240861893,
-0.060890428721904755,
0.028397873044013977,
-0.01589084230363369,
-0.024995187297463417,
-0.03380889073014259,
-0.03516523167490959,
-0.04344955086708069,
0.03241635486483574,
-0.003853460540995002,
-0.00841586384922266,
0.010263447649776936,
-0.041187092661857605,
0.0014906551223248243,
0.023472731932997704,
-0.012987535446882248,
0.005696979351341724,
-0.0205950029194355,
-0.015002775005996227,
0.00953658577054739,
-0.002008673269301653,
0.022417526692152023,
0.0668753907084465,
0.03638678789138794,
0.011866630986332893,
0.09432745724916458,
0.04357610642910004,
0.05541583523154259,
-0.05493149906396866,
0.004111586604267359,
-0.05794057250022888,
-0.0028181306552141905,
-0.008530299179255962,
0.0708039179444313,
0.005743103101849556,
-0.06773606687784195,
0.004948718938976526,
0.008284803479909897,
-0.014332722872495651,
-0.018192151561379433,
0.02115662768483162,
0.01165247056633234,
0.06265857070684433,
0.0041822828352451324,
-0.05589160695672035,
0.03364614397287369,
-0.03451746329665184,
0.000043926280341111124,
-0.015014796517789364,
-0.03740249574184418,
-0.04074477776885033,
-0.025588935241103172,
0.0016634792555123568,
0.04191884770989418,
0.007101905532181263,
0.026130346581339836,
0.027314482256770134,
0.004855839069932699,
0.0023473254404962063,
-0.043153904378414154,
0.013096222653985023,
0.05128553509712219,
-0.058273300528526306,
-0.05026020109653473,
0.024247445166110992,
0.028268514201045036,
0.004536905791610479,
0.02838767319917679,
-0.010238377377390862,
-0.049727387726306915,
-0.06408064812421799,
0.012741915881633759,
-0.0008121184655465186,
0.04855833947658539,
-0.08333580940961838,
-0.01350120548158884,
-0.026910968124866486,
-0.06563440710306168,
-0.013992391526699066,
0.03552108630537987,
0.004133517853915691,
0.024945946410298347,
-0.011035350151360035,
0.04187331721186638,
-0.021991107612848282,
0.01975991576910019,
-0.09048453718423843,
-0.03865158185362816,
0.0047423336654901505,
0.0625176802277565,
0.03327416256070137,
-0.030839206650853157,
0.0221411045640707,
0.06541009247303009,
-0.038817111402750015,
0.017422372475266457,
0.013571745716035366,
-0.03542865067720413,
0.005018823780119419,
-0.040826216340065,
-0.009832058101892471,
-0.03282429277896881,
-0.008261633105576038,
-0.061171822249889374,
-0.014700116589665413,
0.030150532722473145,
0.06809370219707489,
-0.007306800689548254,
-0.017984583973884583,
-0.06566838920116425,
0.009607581421732903,
0.08442332595586777,
-0.011696330271661282,
0.03011501207947731,
-0.03897162526845932,
0.004401425831019878,
0.0032909137662500143,
-0.01027184072881937,
-0.034881919622421265,
-0.040135882794857025,
0.035294484347105026,
-0.007491920609027147,
0.05594703555107117,
0.02565586380660534,
-0.051189132034778595,
0.04096995294094086,
-0.016256388276815414,
0.004256132058799267,
-0.0018954912666231394,
0.01476565282791853,
0.021873481571674347,
-0.008661380037665367,
-0.009794430807232857,
0.03314423933625221,
0.004488688427954912,
-0.05254056677222252,
0.004460858181118965,
-0.06911898404359818,
-0.005061266478151083,
-0.0004874480946455151,
0.022307781502604485,
-0.04108797758817673,
-0.005359030794352293,
-0.046983636915683746,
-0.0063359737396240234,
0.06767160445451736,
0.03836681321263313,
-0.02380317822098732,
-0.06737951189279556,
-0.031691405922174454,
0.059391919523477554,
-0.014156630262732506,
0.008325599133968353,
0.02303669974207878,
0.032853156328201294,
-0.03153575584292412,
0.05392112955451012,
-0.033484674990177155,
0.07500452548265457,
-0.0007112363236956298,
0.0006044817855581641,
0.004530542064458132,
0.04230920225381851,
-0.006003311835229397,
0.007528279442340136,
-0.03748941421508789,
-0.014437857083976269,
-0.03313538432121277,
0.02087455615401268,
-0.01688680239021778,
0.046862006187438965,
-0.02447994239628315,
-0.032435331493616104,
-0.012303313240408897,
-0.046311669051647186,
0.009520039893686771,
0.04796256497502327,
-0.0183568112552166,
-0.0008673844276927412,
-0.01564432680606842,
0.009141550399363041,
0.030790340155363083,
-0.030957862734794617,
-0.013064329512417316,
0.004139618016779423,
0.027271108701825142,
-0.03037319891154766,
-0.07272840291261673,
0.0010327694471925497,
0.0641472339630127,
0.015580645762383938,
0.024170508608222008,
-0.017016392201185226,
0.010267933830618858,
-0.009025667794048786,
-0.015065751038491726,
0.037361156195402145,
0.022292597219347954,
-0.04212908446788788,
-0.03517967835068703,
0.04045531898736954,
0.005602787248790264,
-0.06476869434118271,
-0.024172572419047356,
-0.007165820803493261,
-0.0330236554145813,
0.07231190800666809,
0.04399031400680542,
0.003998271655291319,
0.037431444972753525,
0.0177688617259264,
-0.058282479643821716,
0.1151801347732544,
0.01952405832707882,
-0.029373854398727417,
-0.014961699955165386,
-0.007748682051897049,
-0.02940799482166767,
0.017460865899920464,
-0.0034428141079843044,
-0.029155902564525604,
-0.029822854325175285,
-0.011653388850390911,
-0.057122860103845596,
0.0353337787091732,
0.0317334346473217,
0.027094583958387375,
0.007372424006462097,
0.06177681311964989,
0.04205043986439705,
-0.034151703119277954,
0.004090241622179747,
0.0013710842467844486,
-0.007735871244221926,
-0.03809979930520058,
-0.01202966645359993,
0.01421345490962267,
-0.059316329658031464,
0.060001276433467865,
0.06319282203912735,
-0.011128525249660015,
0.017904730513691902,
0.01683996245265007,
0.06885693222284317,
-0.02135181613266468,
0.0027277444023638964,
0.027685197070240974,
0.03816138580441475,
-0.0034030992537736893,
0.036319486796855927,
0.002462511183694005,
0.08677053451538086,
0.009615280665457249,
-0.013678454793989658,
0.010816970840096474,
0.020308757200837135,
-0.00046008749632164836,
0.05463755875825882,
-0.05181412398815155,
0.018172500655055046,
-0.05408182367682457,
-0.09616190195083618,
0.09278815984725952,
0.009967966936528683,
-0.020226186141371727,
0.04502757638692856,
-0.04061119258403778,
-0.04825141653418541,
0.010566598735749722,
0.04623913764953613,
0.04558219015598297,
-0.041302844882011414,
-0.03712790086865425,
0.011198523454368114,
-0.05202706530690193,
-0.031199609860777855,
0.014453493990004063,
0.013516911305487156,
0.0296577587723732,
0.03948531672358513,
-0.012137243524193764,
-0.06539084762334824,
-0.023626063019037247,
-0.012737277895212173,
0.0361480750143528,
-0.006289168260991573,
0.017656950280070305,
0.005286083556711674,
-0.025125019252300262,
0.03755444288253784,
-0.043756674975156784,
0.026470709592103958,
0.06906065344810486,
0.06320412456989288,
0.002183754462748766,
-0.022130191326141357,
-0.04423623904585838,
-0.013465968891978264,
0.032875221222639084,
0.024155110120773315,
-0.0375613272190094,
-0.018254630267620087,
-0.05587818846106529,
0.03754615783691406,
0.0030038838740438223,
-0.018110880628228188,
-0.08315089344978333,
0.011510012671351433,
0.06203337386250496,
0.010045399889349937,
-0.001097799395211041,
-0.012773583643138409,
0.03025190159678459,
-0.014111407101154327,
0.028236495330929756,
-0.0700019896030426,
0.029222598299384117,
-0.01610260270535946,
0.07248752564191818
] |
<p>According to <a href="http://www.ted.com/talks/jeremy_kasdin_the_flower_shaped_starshade_that_might_help_us_detect_earth_like_planets" rel="nofollow">this TED talk by Jeremy Kasdin,</a> Nasa is planning to spend $1bn on a "Starshade" project, where a giant flower shaped metal eclipser 20 meters wide is placed 50k kilometers in front of a space telescope, to fit the telescope diameter.</p>
<p>The idea is to occlude a star and photograph it's exoplanets.</p>
<p>The above solution is surreal. Why can't they control the diffraction of the light around the occlusion circle with a refractive material, to direct it outwards?</p>
<p>I suggest that they can design a round black occluder with soft edges overlaid with a refractive material that deflects the light away from the centre, similar to a lense.</p>
<p>Why do the angles and shapes at the edge of the flower shaped occluder have to be very precise in order to control diffraction?</p> | g6643 | [
-0.013617859221994877,
0.06504971534013748,
-0.012536461465060711,
-0.012915550731122494,
-0.05248399078845978,
0.028437206521630287,
0.003876978997141123,
0.028319744393229485,
0.006620426662266254,
-0.041809625923633575,
0.08548030257225037,
0.03583647310733795,
0.09058975428342819,
0.004631610121577978,
0.07739116996526718,
0.06021399050951004,
0.02370862476527691,
-0.001593244494870305,
0.04841611161828041,
0.05199500173330307,
0.021183010190725327,
0.0033180154860019684,
-0.06228369474411011,
-0.0027145962230861187,
-0.04004766792058945,
0.027110056951642036,
0.032579295337200165,
-0.022115860134363174,
-0.02993900142610073,
0.0034268752206116915,
0.04743942990899086,
-0.00951910950243473,
0.0357428677380085,
-0.012003076262772083,
0.02394256182014942,
0.03545055165886879,
-0.023632602766156197,
-0.006631587166339159,
-0.01033503096550703,
-0.015516516752541065,
-0.037868060171604156,
0.016147997230291367,
-0.011280020698904991,
-0.02233787253499031,
0.00500693591311574,
-0.018311351537704468,
-0.028314027935266495,
0.010679585859179497,
0.051066555082798004,
-0.04884958639740944,
0.0040279715321958065,
0.03359517827630043,
0.004519645590335131,
-0.026249244809150696,
0.02251688949763775,
0.013080665841698647,
-0.02036866545677185,
0.0020591523498296738,
0.09994002431631088,
-0.046856798231601715,
-0.020229505375027657,
0.028955727815628052,
-0.03617769479751587,
0.07514206320047379,
0.004543194081634283,
-0.016908327117562294,
0.024981826543807983,
0.0020841388031840324,
0.06928860396146774,
0.013663168996572495,
-0.0009693413157947361,
0.007456108462065458,
0.01016797311604023,
-0.029554318636655807,
-0.054706599563360214,
0.013836725614964962,
-0.04091251641511917,
0.04179663211107254,
-0.005481553729623556,
0.039823953062295914,
0.00864045973867178,
-0.022367069497704506,
-0.0535602867603302,
-0.023331422358751297,
0.0753675103187561,
0.019991831853985786,
-0.01632731221616268,
-0.056875698268413544,
0.01634731888771057,
0.0184079110622406,
0.014073595404624939,
-0.017309240996837616,
0.02428789995610714,
-0.02469239942729473,
0.020530737936496735,
-0.026668518781661987,
-0.0010335850529372692,
-0.016026318073272705,
-0.05324018746614456,
0.016169164329767227,
-0.02785957045853138,
0.005509371403604746,
0.0054730745032429695,
0.05398303642868996,
0.02696308307349682,
-0.016265058889985085,
0.001620789640583098,
0.023119106888771057,
0.05289413034915924,
0.007073690649122,
-0.034715961664915085,
-0.042739029973745346,
-0.013289786875247955,
-0.03542289137840271,
-0.012459708377718925,
-0.018751565366983414,
0.06745974719524384,
-0.013996188528835773,
0.04833260551095009,
0.0639440044760704,
0.030234094709157944,
-0.043571580201387405,
0.024798747152090073,
0.07407771050930023,
0.009998149238526821,
-0.02381659671664238,
0.024472683668136597,
-0.02624194324016571,
0.041087325662374496,
-0.05347304418683052,
-0.05392530560493469,
-0.000023457514544134028,
-0.017174122855067253,
-0.009801463223993778,
0.00991052109748125,
0.013636411167681217,
-0.024056516587734222,
-0.01331323105841875,
-0.015009447000920773,
-0.029830945655703545,
-0.021704116836190224,
0.03733544796705246,
-0.0005884810816496611,
0.012439983896911144,
-0.09809788316488266,
0.007038874085992575,
0.0076822079718112946,
0.05193145573139191,
-0.024851618334650993,
-0.018349701538681984,
0.005255377385765314,
0.029202112928032875,
0.0164871234446764,
0.013856294564902782,
-0.05415351688861847,
-0.032541170716285706,
0.03883127123117447,
0.0426907017827034,
-0.018354507163167,
0.014578278176486492,
0.05200706422328949,
0.05630050227046013,
-0.05037618800997734,
0.0038446467369794846,
-0.0028605719562619925,
0.008255007676780224,
-0.009947977028787136,
-0.07112215459346771,
-0.05572135001420975,
-0.03308922052383423,
-0.019318154081702232,
0.028070086613297462,
-0.007403065450489521,
0.011621128767728806,
0.037689391523599625,
0.05219467356801033,
0.05241219699382782,
-0.04369749128818512,
0.025915447622537613,
0.0685616210103035,
-0.004079217556864023,
-0.04876038432121277,
-0.001184142311103642,
0.004872980993241072,
-0.013923383317887783,
-0.024167150259017944,
0.034634657204151154,
-0.038489602506160736,
0.01848823018372059,
0.008879365399479866,
0.06981157511472702,
0.004482008051127195,
0.007020897231996059,
0.009373076260089874,
0.007171047851443291,
-0.006708608474582434,
0.06237579882144928,
-0.027706580236554146,
-0.03599468246102333,
0.060914333909749985,
-0.02026396431028843,
0.046581584960222244,
0.010078683495521545,
0.030501844361424446,
0.006376826204359531,
-0.02216850221157074,
-0.043827515095472336,
0.06217458099126816,
0.0004414991126395762,
0.01470654271543026,
0.013841469772160053,
-0.0011250147363170981,
0.0009089999366551638,
0.001950525213032961,
0.0011252430267632008,
0.021690934896469116,
-0.016821684315800667,
-0.01565217599272728,
-0.028239434584975243,
-0.012314185500144958,
0.03431243821978569,
-0.0062828343361616135,
0.10138264298439026,
-0.03609057143330574,
-0.018245285376906395,
0.022562159225344658,
-0.06633036583662033,
-0.019394632428884506,
0.032960113137960434,
-0.008947400376200676,
0.006261872127652168,
-0.04461747780442238,
0.03429679200053215,
-0.0034414257388561964,
0.07324754446744919,
0.005024785175919533,
0.0007045655511319637,
0.021152546629309654,
-0.04785018041729927,
0.017501618713140488,
0.02840171754360199,
-0.03818783536553383,
-0.0346376895904541,
-0.07167918235063553,
-0.0013690697960555553,
-0.006104141939431429,
-0.03501679748296738,
-0.006966308690607548,
-0.07136465609073639,
0.0248089712113142,
0.04271438345313072,
0.026489244773983955,
0.015537161380052567,
-0.029240282252430916,
-0.05392345413565636,
-0.02448171004652977,
-0.05220445245504379,
0.023799221962690353,
-0.033513393253088,
-0.03235890716314316,
-0.02418816275894642,
-0.02007637359201908,
0.0019273237558081746,
-0.006059938110411167,
-0.03597330302000046,
0.021420029923319817,
-0.017310282215476036,
-0.0019880463369190693,
0.03876107186079025,
0.04136507958173752,
0.039565395563840866,
0.03881913796067238,
0.03453008458018303,
0.01123158261179924,
-0.028537744656205177,
0.059938736259937286,
-0.03878800570964813,
0.018618160858750343,
0.07708393037319183,
0.09401001036167145,
-0.01129496656358242,
0.040095485746860504,
-0.03224441036581993,
0.024496732279658318,
0.012736043892800808,
0.01161322370171547,
-0.0286082923412323,
0.005136010702699423,
0.003088301280513406,
-0.03541475161910057,
-0.027454564347863197,
0.043815597891807556,
-0.027204295620322227,
-0.03825998306274414,
0.02146194502711296,
0.0010470559354871511,
-0.00940679106861353,
0.07503567636013031,
-0.025616297498345375,
0.03272014111280441,
0.0016729490598663688,
0.04643339663743973,
0.003218302270397544,
0.051226597279310226,
-0.019953742623329163,
0.04225568845868111,
0.023669404909014702,
-0.027018235996365547,
0.017549794167280197,
0.00886351615190506,
0.0758323147892952,
-0.01804456301033497,
0.01930011250078678,
0.049361422657966614,
0.023637404665350914,
-0.020144466310739517,
-0.026560626924037933,
0.0025280937552452087,
-0.024627279490232468,
0.05196129530668259,
0.043425530195236206,
0.0754554271697998,
-0.045117322355508804,
-0.02554761804640293,
0.012149471789598465,
-0.005835383199155331,
0.011833012104034424,
-0.03619874641299248,
-0.031291041523218155,
-0.00944216363132,
0.05283576622605324,
0.0706239715218544,
-0.03669191151857376,
-0.045214198529720306,
-0.005651397164911032,
0.0649651288986206,
0.00765324616804719,
0.03575004264712334,
0.06794068962335587,
0.029277395457029343,
-0.04182907193899155,
0.009985942393541336,
-0.053529929369688034,
-0.027768278494477272,
0.0518239326775074,
0.009718972258269787,
0.03070887178182602,
-0.02487707883119583,
0.0025391329545527697,
-0.027235759422183037,
0.05596188083291054,
0.01203830260783434,
-0.004914677236229181,
-0.055172961205244064,
-0.027262182906270027,
0.03700465336441994,
0.04915301129221916,
0.002763223135843873,
0.028578732162714005,
-0.04754209518432617,
0.02800815925002098,
0.041314058005809784,
-0.01800207979977131,
-0.0469716340303421,
0.019812988117337227,
-0.00989922508597374,
0.060147177428007126,
0.051019709557294846,
-0.02451295219361782,
0.05184405669569969,
-0.018570391461253166,
-0.03330789878964424,
-0.04632384702563286,
-0.026647228747606277,
0.009085227735340595,
0.010959528386592865,
0.035908475518226624,
0.03803442046046257,
0.016775064170360565,
-0.0018773960182443261,
0.02232147566974163,
0.06343375891447067,
0.0012618873734027147,
-0.017288029193878174,
0.011739259585738182,
0.004685307387262583,
-0.00779078109189868,
-0.09439807385206223,
0.0047062975354492664,
-0.014236261136829853,
-0.0035252326633781195,
-0.06767845898866653,
0.06405004858970642,
-0.05731907859444618,
-0.00047702345182187855,
0.018364589661359787,
0.0012308413861319423,
-0.053461816161870956,
-0.05065587908029556,
-0.05660086125135422,
0.08470060676336288,
0.00534299248829484,
0.0097831254824996,
-0.009521585889160633,
-0.03260787948966026,
-0.08002380281686783,
-0.006715382914990187,
-0.052705343812704086,
-0.04778201878070831,
0.018311403691768646,
0.05946088954806328,
-0.005467362701892853,
-0.017416037619113922,
-0.014043264091014862,
0.0071590859442949295,
0.017092525959014893,
0.005817313212901354,
0.045709241181612015,
0.003038253867998719,
-0.024714788421988487,
-0.0036904553417116404,
0.09792165458202362,
0.0018745617708191276,
0.0030826914589852095,
0.051683761179447174,
0.0869104340672493,
-0.02805444225668907,
-0.05699117109179497,
0.03131953626871109,
-0.01524039264768362,
0.04154082015156746,
0.00477008568122983,
0.010246170684695244,
-0.010822802782058716,
-0.02738182805478573,
-0.013185781426727772,
-0.0016136823687702417,
-0.00777098536491394,
-0.02177181839942932,
-0.004167498089373112,
0.009748106822371483,
-0.06524796783924103,
-0.010713908821344376,
-0.050669919699430466,
0.02203623577952385,
0.045179519802331924,
-0.008858304470777512,
0.036030273884534836,
-0.022761572152376175,
0.01664571836590767,
-0.0038532742764800787,
-0.048253659158945084,
-0.023151064291596413,
0.004941555671393871,
-0.01836777664721012,
-0.03186739236116409,
-0.09116719663143158,
-0.008865813724696636,
0.007784713059663773,
0.037409503012895584,
0.0107108224183321,
-0.020929360762238503,
-0.0014839572831988335,
-0.007825808599591255,
0.07169938832521439,
0.04270567744970322,
-0.013056154362857342,
-0.062249165028333664,
0.013191794976592064,
-0.027391958981752396,
-0.0351581834256649,
0.07609978318214417,
0.0075912270694971085,
0.08509255200624466,
-0.0365334078669548,
-0.024600306525826454,
-0.03420913219451904,
-0.05945605784654617,
-0.02108573541045189,
-0.033494025468826294,
-0.021668605506420135,
0.012210103683173656,
0.0411062017083168,
-0.03071664273738861,
-0.011872736737132072,
0.018399160355329514,
-0.028071526437997818,
-0.035627078264951706,
-0.07059044390916824,
-0.014156599529087543,
-0.017221415415406227,
-0.0503963977098465,
0.003958116285502911,
-0.00237076822668314,
0.029416752979159355,
0.0067269569262862206,
0.038399308919906616,
0.026912054046988487,
0.06779946386814117,
-0.0071185799315571785,
0.0021071217488497496,
-0.01386351604014635,
-0.06694941967725754,
-0.007298566401004791,
-0.022581880912184715,
-0.017292018979787827,
0.0195208340883255,
-0.033042360097169876,
0.027411365881562233,
0.04434385150671005,
-0.029063798487186432,
-0.026517236605286598,
0.027108199894428253,
0.008118710480630398,
0.026852257549762726,
-0.021968873217701912,
-0.044305216521024704,
-0.058007918298244476,
-0.01668853498995304,
-0.005207267124205828,
0.03594940900802612,
0.017881184816360474,
-0.05372360348701477,
-0.009276431053876877,
0.024748442694544792,
0.024864288046956062,
-0.009675632230937481,
0.013075442984700203,
-0.03433927521109581,
-0.002972938120365143,
-0.03402416780591011,
0.02581632137298584,
-0.026467127725481987,
-0.0372825488448143,
-0.02190009318292141,
0.015968801453709602,
0.07608254253864288,
0.05533071979880333,
0.04010045900940895,
-0.04374958202242851,
-0.02743208035826683,
0.04311944916844368,
0.061287324875593185,
0.040760189294815063,
0.043913811445236206,
-0.037830740213394165,
0.02273201197385788,
0.052845776081085205,
0.007209674455225468,
-0.01848466694355011,
-0.0012426100438460708,
0.03872132673859596,
-0.0017911497270688415,
0.015921710059046745,
0.02331911027431488,
-0.007593956775963306,
-0.0804566815495491,
-0.0716552659869194,
-0.023916523903608322,
-0.05939215421676636,
0.009647371247410774,
-0.0009437656844966114,
0.01112072728574276,
0.02857079729437828,
0.002996566006913781,
-0.002073801588267088,
0.008951330557465553,
0.02619003877043724,
0.031551577150821686,
0.011393922381103039,
-0.0630178228020668,
-0.07146542519330978,
0.012358295731246471,
-0.013353347778320312,
0.0393490269780159,
0.0017399366479367018,
-0.004476458765566349,
-0.030567947775125504,
-0.04264695569872856,
0.010091021656990051,
0.026542291045188904,
0.017753256484866142,
-0.009461659938097,
-0.04158217832446098,
-0.00004663097934098914,
0.016012893989682198,
-0.05343157798051834,
0.041078031063079834,
0.06016632169485092,
-0.10604163259267807,
0.042194075882434845,
-0.07015698403120041,
0.008677292615175247,
0.006808374542742968,
-0.05965616926550865,
-0.020415307953953743,
0.007983414456248283,
0.06439127773046494,
-0.01596948131918907,
0.010905815288424492,
-0.009362276643514633,
-0.012371452525258064,
0.051248949021101,
0.04718444123864174,
0.000033306481782346964,
-0.02487241104245186,
-0.026555495336651802,
-0.013689389452338219,
0.07710610330104828,
-0.03154965490102768,
0.03376384079456329,
0.01290807593613863,
0.041881997138261795,
0.0008773807203397155,
-0.04284805804491043,
-0.015178854577243328,
-0.03894748166203499,
-0.0636725127696991,
-0.007250905968248844,
-0.026333484798669815,
0.011263707652688026,
-0.0005462705157697201,
-0.03830474987626076,
0.007907415740191936,
-0.004813524894416332,
0.015497579239308834,
-0.03170572593808174,
-0.03649881109595299,
0.022829566150903702,
0.03875143080949783,
-0.01093938760459423,
-0.014871008694171906,
0.029677610844373703,
0.03290093317627907,
-0.004652236122637987,
0.01803090050816536,
-0.06222572177648544,
0.06975392252206802,
0.028837792575359344,
0.052598316222429276,
-0.011703616939485073,
-0.003920146729797125,
0.014119991101324558,
0.07077214866876602,
-0.04159938544034958,
0.004271919373422861,
0.0077018048614263535,
0.003389563877135515,
-0.058655090630054474,
-0.010026907548308372,
-0.002927359426394105,
-0.04108297452330589,
-0.0338309146463871,
0.0017499102978035808,
0.005433409474790096,
0.008893703110516071,
-0.057816557586193085,
-0.017170721665024757,
-0.02465382032096386,
-0.08591113984584808,
-0.019667070358991623,
-0.017259255051612854,
-0.013018004596233368,
-0.010488562285900116,
-0.0024416858796030283,
-0.041835471987724304,
0.03791112080216408,
0.004137574229389429,
-0.09924019128084183,
0.0040775323286652565,
-0.03038155660033226,
-0.004534636624157429,
-0.04491381719708443,
-0.015066488645970821,
0.01458087470382452,
-0.04832039028406143,
0.019610334187746048,
0.019341476261615753,
-0.029220907017588615,
0.005702233873307705,
0.03867965564131737,
0.07746826857328415,
0.08191706240177155,
-0.014314649626612663,
-0.08983679115772247,
-0.03464648872613907,
-0.038237571716308594,
0.001091423095203936,
0.048847269266843796,
-0.038778241723775864,
-0.013269844464957714,
0.05769853666424751,
-0.02554113045334816,
0.016256999224424362,
0.02984151802957058,
0.016269266605377197,
0.04188442602753639,
0.020198959857225418,
-0.05082789435982704,
-0.04688394069671631,
-0.02292230911552906,
-0.00380457891151309,
0.010338133201003075,
0.01116181630641222,
0.07043484598398209,
0.009739920496940613,
-0.03886101394891739,
0.04156910255551338,
0.002033863216638565,
0.02232632040977478,
0.00992629211395979,
-0.012774252332746983,
-0.00845764484256506,
0.053155794739723206,
-0.022276829928159714,
0.010360251180827618,
-0.033465564250946045,
0.0162601750344038,
-0.033616308122873306,
0.0033187330700457096,
-0.047126684337854385,
-0.053961046040058136,
0.035301338881254196,
-0.062031492590904236,
0.014715726487338543,
-0.029873423278331757,
0.02780064381659031,
-0.030039342120289803,
-0.0000858598286868073,
-0.05169977992773056,
0.041972480714321136,
0.021361172199249268,
0.010704915970563889,
-0.0005535816308110952,
-0.02734965831041336,
-0.052038200199604034,
-0.03907021880149841,
-0.09332729876041412,
-0.047034718096256256,
-0.0037940777838230133,
0.0003465965564828366,
-0.07582402974367142,
-0.020402271300554276,
-0.05500943958759308,
-0.006769181694835424,
0.023973921313881874,
-0.022461600601673126,
0.0474882610142231,
-0.019971953704953194,
0.011160358786582947,
-0.025062790140509605,
0.0413038432598114,
-0.035388555377721786,
-0.0578877292573452,
0.05258140340447426,
-0.009604526683688164,
0.03292706608772278,
-0.027713727205991745,
0.02341209352016449,
0.022028174251317978,
0.047858644276857376,
-0.025581877678632736,
-0.05747022479772568,
-0.009722065180540085,
-0.0302390418946743,
0.01713927835226059,
0.0015304289991036057,
0.022287946194410324
] |
<p>I currently have a very limited knowledge of how radiation works etc, but while sat in class the other day, one question occurred to me that even my teacher could not answer.</p>
<p>We have been learning about alpha, beta and gamma radiation. I know that alpha is positive and that makes perfect sense. However, when the neutron is broken down to form a β particle and this particle is then sent out of the nucleus, why is this negatively charged β particle not attracted (presumably by electromagnetic force) back into the overall positive nucleus of the atom? To me, at least, it does not make sense that it would not be attracted back the nucleus.</p>
<p>Sorry if this is simple stuff but even after some furious googling I haven't been able to find an answer.</p> | g6644 | [
0.024008337408304214,
0.013104435987770557,
0.005203351844102144,
-0.053528089076280594,
0.08220955729484558,
0.03225436434149742,
0.002178701339289546,
0.03713184967637062,
-0.012504644691944122,
-0.04860677197575569,
0.016384193673729897,
0.0390351377427578,
-0.03740372881293297,
-0.0007375533459708095,
0.025300676003098488,
0.022249735891819,
0.07992994040250778,
0.002636966062709689,
0.027181534096598625,
0.03376111388206482,
0.026229720562696457,
0.033722855150699615,
-0.0015861892607063055,
-0.08599025011062622,
-0.023555783554911613,
0.01480264775454998,
0.01592269539833069,
-0.044380225241184235,
-0.009709008038043976,
-0.047539930790662766,
0.013196096755564213,
-0.01608046144247055,
0.029988043010234833,
0.004550194833427668,
-0.010513652116060257,
-0.045635975897312164,
-0.027131684124469757,
0.006673981435596943,
-0.031157152727246284,
0.012325192801654339,
0.007433324586600065,
0.004565738607198,
0.029932593926787376,
-0.01218253094702959,
0.04475054889917374,
0.06658322364091873,
0.020105253905057907,
-0.012505666352808475,
0.005861582234501839,
0.005941448267549276,
-0.011953008361160755,
-0.06801658123731613,
-0.03921535983681679,
0.04591453820466995,
0.005113149993121624,
-0.007570828776806593,
0.06823675334453583,
-0.02857235260307789,
0.05823609605431557,
0.008677699603140354,
-0.03213096037507057,
0.07262355089187622,
-0.009177197702229023,
-0.022545792162418365,
-0.008519860915839672,
-0.0534583255648613,
-0.06749644130468369,
0.043606992810964584,
0.007827619090676308,
0.04087134078145027,
-0.010678162798285484,
-0.030108634382486343,
-0.05518632009625435,
-0.001300169969908893,
0.04124215617775917,
-0.003973799757659435,
0.03128350153565407,
-0.04472209885716438,
-0.006164440885186195,
0.016752086579799652,
-0.032463472336530685,
-0.07300935685634613,
0.03710492327809334,
-0.0020754374563694,
0.08252081274986267,
0.036959078162908554,
-0.03593679890036583,
-0.009389572776854038,
-0.0032167346216738224,
-0.025759033858776093,
0.029964759945869446,
-0.04217880591750145,
0.04694414511322975,
0.028194459155201912,
-0.010586078278720379,
-0.06860880553722382,
0.006662388797849417,
0.03062525764107704,
-0.0492803156375885,
-0.003966463264077902,
0.038062237203121185,
-0.03527618944644928,
0.003946647979319096,
0.04368068277835846,
-0.02359722927212715,
0.005853528622537851,
0.0014246258651837707,
-0.02469157613813877,
0.009922667406499386,
0.0010898654581978917,
-0.06028526648879051,
-0.021036701276898384,
-0.0026932668406516314,
-0.04716429114341736,
0.007237538229674101,
0.0018596445443108678,
0.066513791680336,
-0.03881646692752838,
0.02417495846748352,
0.06706994771957397,
-0.00979013554751873,
0.06605706363916397,
-0.06457554548978806,
-0.037656333297491074,
-0.03637458756566048,
-0.01154681108891964,
0.0028777618426829576,
0.041369203478097916,
0.036960892379283905,
-0.010073859244585037,
0.03803354874253273,
0.004258362576365471,
-0.04510539397597313,
0.038257040083408356,
0.024606380611658096,
0.03647425398230553,
0.05172261968255043,
-0.03804304078221321,
0.03341378644108772,
-0.04460824280977249,
0.03785775601863861,
0.023357493802905083,
0.022206038236618042,
-0.011906581930816174,
-0.03596967086195946,
0.054659027606248856,
-0.02239908091723919,
0.012934240512549877,
0.026708686724305153,
0.05510854348540306,
0.010199070908129215,
0.023308873176574707,
0.05856743082404137,
-0.04089329391717911,
0.05657301843166351,
-0.05781913176178932,
0.0185447596013546,
0.0155800711363554,
-0.011980175971984863,
-0.014999225735664368,
0.11932379007339478,
0.012279496528208256,
-0.02658260427415371,
-0.04131532832980156,
-0.047943610697984695,
-0.0025827977806329727,
-0.020395515486598015,
-0.051687512546777725,
-0.04137426242232323,
-0.001620463328436017,
-0.05270455405116081,
0.02059837244451046,
0.03280344605445862,
-0.018964426591992378,
-0.0198370348662138,
0.016743039712309837,
0.0025643259286880493,
-0.021434329450130463,
0.012719676829874516,
-0.024911116808652878,
-0.08189425617456436,
0.02385142259299755,
0.05486496165394783,
-0.004707769025117159,
0.026324240490794182,
-0.04042007401585579,
-0.04653218761086464,
0.06303077191114426,
-0.022051485255360603,
0.0037054617423564196,
0.024924537166953087,
-0.010785982012748718,
-0.01581132411956787,
-0.029201123863458633,
0.0014537564711645246,
-0.06448669731616974,
0.007658961694687605,
-0.043525807559490204,
0.040438584983348846,
0.029319047927856445,
-0.06078903004527092,
0.009470688179135323,
0.011904066428542137,
0.009028492495417595,
0.06668001413345337,
-0.056755006313323975,
-0.00843418575823307,
0.07114797830581665,
0.06799673289060593,
0.003790526883676648,
-0.020976901054382324,
-0.03513554111123085,
0.012860799208283424,
-0.03221127763390541,
-0.01787118799984455,
-0.017809651792049408,
-0.03176768496632576,
0.043620169162750244,
-0.04783922806382179,
-0.028119711205363274,
-0.08079154789447784,
-0.00788796879351139,
0.01302406843751669,
-0.05136760696768761,
-0.03504627197980881,
0.05802728235721588,
-0.027364028617739677,
-0.01642524264752865,
-0.0063940719701349735,
0.04393840581178665,
-0.09648862481117249,
0.01505488995462656,
-0.11146394908428192,
-0.011369824409484863,
0.06223639100790024,
0.018214119598269463,
-0.011680670082569122,
0.04000990092754364,
-0.010215471498668194,
-0.09903072565793991,
-0.05565400794148445,
-0.049058347940444946,
-0.055002741515636444,
0.021006999537348747,
-0.006696353200823069,
-0.06416959315538406,
0.05198054015636444,
-0.03198239207267761,
-0.028649022802710533,
-0.04506491497159004,
0.035971708595752716,
0.004323019180446863,
-0.03720952570438385,
0.006356388330459595,
-0.006352782249450684,
-0.009832971729338169,
-0.03438153117895126,
0.044866789132356644,
-0.052710361778736115,
-0.05159865692257881,
-0.018079543486237526,
-0.08522658050060272,
-0.03591831028461456,
-0.012781777419149876,
-0.04791006073355675,
0.02743457816541195,
-0.050350721925497055,
-0.00892589520663023,
0.03640083596110344,
0.006439703982323408,
-0.03745906800031662,
0.07495267689228058,
0.03358636423945427,
-0.0009639313211664557,
-0.02186143770813942,
-0.0031380890868604183,
-0.02278119884431362,
0.00757890148088336,
0.03568378835916519,
-0.056130845099687576,
0.02270391955971718,
0.055499009788036346,
-0.045622389763593674,
-0.06692954897880554,
-0.008722427301108837,
-0.013788966462016106,
-0.011098324321210384,
-0.05174361169338226,
0.016592862084507942,
-0.009133884683251381,
-0.06819593906402588,
-0.008883056230843067,
0.06418554484844208,
-0.034488026052713394,
0.012146592140197754,
0.022192971780896187,
0.06602034717798233,
-0.0028488973621279,
-0.07565132528543472,
0.040926139801740646,
-0.012958812527358532,
-0.013746222481131554,
0.00017265736823901534,
-0.05935890972614288,
-0.006109361071139574,
0.02092129737138748,
-0.0763331949710846,
-0.015003949403762817,
-0.034325942397117615,
0.040512267500162125,
-0.10714663565158844,
0.04906326159834862,
-0.010473434813320637,
-0.0015837600221857429,
0.020766394212841988,
-0.010837838053703308,
-0.034884028136730194,
0.038063809275627136,
0.08016347885131836,
0.035176511853933334,
-0.04476333037018776,
-0.0076172081753611565,
0.034770406782627106,
-0.023589778691530228,
0.04655473306775093,
0.048292968422174454,
-0.007634319830685854,
-0.009946691803634167,
-0.02128951996564865,
-0.02257121540606022,
0.03899078816175461,
-0.04305754974484444,
0.012115230783820152,
0.04437435045838356,
-0.03293107450008392,
0.010670213960111141,
-0.05488073453307152,
0.018192918971180916,
-0.008496078662574291,
0.0282120518386364,
0.08122716844081879,
-0.03494789078831673,
-0.03796069324016571,
0.01610582508146763,
0.03977423906326294,
0.01841888017952442,
-0.02871103398501873,
-0.03509612753987312,
0.011291349306702614,
0.015182922594249249,
0.009097039699554443,
0.03912065178155899,
0.008985728025436401,
0.031704384833574295,
-0.043443866074085236,
-0.015309975482523441,
-0.005342015530914068,
0.02395355887711048,
-0.012103231623768806,
0.023312628269195557,
-0.00834363792091608,
-0.02692270837724209,
0.03521772846579552,
-0.0034732019994407892,
-0.05823604390025139,
0.028340741991996765,
-0.021489620208740234,
0.024618685245513916,
-0.0044670067727565765,
-0.015429383143782616,
0.015251915901899338,
0.005061228759586811,
-0.007071575615555048,
0.009091213345527649,
0.036523446440696716,
-0.021980328485369682,
0.040213800966739655,
0.05734353885054588,
-0.017961299046874046,
0.006425293628126383,
-0.011120130307972431,
-0.022580290213227272,
0.024395272135734558,
0.05394676327705383,
0.028625858947634697,
0.03078303672373295,
-0.007062160409986973,
-0.010940102860331535,
-0.05260468274354935,
-0.027434740215539932,
0.010173683054745197,
-0.007171657867729664,
-0.020839078351855278,
0.019063780084252357,
-0.002941218437626958,
-0.03886469453573227,
0.03388813138008118,
-0.013480727560818195,
0.017847903072834015,
0.015536894090473652,
-0.034110892564058304,
0.06006808578968048,
-0.012208400294184685,
-0.08006241172552109,
0.05494699999690056,
0.07102359086275101,
-0.014310114085674286,
-0.018523214384913445,
-0.022164588794112206,
-0.05471891909837723,
-0.0002275825827382505,
0.003947950899600983,
-0.005269313231110573,
-0.016433846205472946,
0.012335012666881084,
-0.023191725835204124,
0.013714032247662544,
0.052245113998651505,
0.009120741859078407,
0.0067535401321947575,
0.014283024705946445,
0.04216058924794197,
-0.007470922078937292,
0.0008636991842649877,
0.02203856222331524,
0.07448168843984604,
0.0763126015663147,
0.06240600347518921,
0.023898977786302567,
-0.016858994960784912,
0.04384475201368332,
0.04850734770298004,
0.005719411186873913,
0.02165745384991169,
-0.07026269286870956,
0.07082975655794144,
-0.07349307835102081,
0.04674805328249931,
0.016082776710391045,
0.013982289470732212,
0.10259625315666199,
-0.012123540975153446,
0.012167047709226608,
-0.013107881881296635,
0.009341711178421974,
0.04630301520228386,
-0.04454249143600464,
-0.04089805856347084,
-0.058856554329395294,
-0.02537338063120842,
-0.03447786346077919,
0.033479806035757065,
-0.08221606910228729,
-0.04454364255070686,
-0.01103514339774847,
0.007808181457221508,
-0.01317609939724207,
0.017782168462872505,
-0.03134036436676979,
0.05094905197620392,
-0.03574219346046448,
0.0016318553825840354,
0.08377016335725784,
0.030997753143310547,
-0.006486591883003712,
-0.016089705750346184,
0.023550264537334442,
0.014791514724493027,
-0.029337847605347633,
0.002745134988799691,
-0.009459028020501137,
0.057887446135282516,
0.02278796397149563,
-0.03222283720970154,
0.018348217010498047,
0.010363280773162842,
0.01312261912971735,
-0.0011226222850382328,
0.030299587175250053,
-0.002959260018542409,
-0.038406722247600555,
-0.03393549844622612,
-0.009494448080658913,
-0.020868368446826935,
-0.0217429231852293,
0.04468364641070366,
0.008715223520994186,
0.052366338670253754,
0.030535059049725533,
-0.045611001551151276,
0.0406990572810173,
-0.001848449232056737,
0.013389049097895622,
-0.060892559587955475,
0.020607590675354004,
-0.06770399212837219,
-0.03020750731229782,
0.022914379835128784,
-0.004981471691280603,
-0.020884785801172256,
-0.03436347469687462,
-0.06888731569051743,
-0.03229309991002083,
0.00017190611106343567,
-0.016718696802854538,
0.04944879561662674,
0.05075613409280777,
-0.05829655006527901,
-0.03543149307370186,
-0.0282397773116827,
-0.032116807997226715,
-0.0367506667971611,
0.016247626394033432,
-0.004040278494358063,
-0.0030471826903522015,
0.0008315090672113001,
-0.044764306396245956,
0.03152347356081009,
0.03104388527572155,
0.014656055718660355,
-0.03547373786568642,
0.04382555931806564,
0.028664221987128258,
-0.05606174096465111,
0.022395355626940727,
-0.009676077403128147,
-0.07360689342021942,
0.06000053137540817,
0.07290121167898178,
-0.013853057287633419,
0.04981537535786629,
-0.0001593426859471947,
0.04299171641469002,
0.04299129173159599,
-0.007558618206530809,
-0.0564851313829422,
-0.0011463494738563895,
0.0012836935929954052,
0.0352875292301178,
0.037040773779153824,
0.05171312764286995,
-0.007939034141600132,
0.04345688223838806,
0.021366385743021965,
-0.013018704019486904,
0.01684701442718506,
0.004993203561753035,
0.007241586688905954,
-0.01796887069940567,
0.028490647673606873,
-0.008965401910245419,
0.010696743614971638,
0.010824211873114109,
0.03404921293258667,
-0.008658863604068756,
0.001809529261663556,
0.033766139298677444,
-0.0047990866005420685,
0.011453681625425816,
-0.06542462110519409,
-0.01989665813744068,
-0.007969456724822521,
-0.02439797669649124,
0.0543917752802372,
0.03623871132731438,
-0.024231472983956337,
0.04175820201635361,
-0.024435047060251236,
-0.012614801526069641,
0.03058621659874916,
0.028443042188882828,
0.04572557657957077,
0.05747642368078232,
0.025429973378777504,
0.026666970923542976,
0.00831251684576273,
-0.02839074097573757,
-0.021859971806406975,
-0.021122515201568604,
0.018850259482860565,
0.06536190211772919,
0.04133354127407074,
0.030205778777599335,
-0.0371679924428463,
-0.026199568063020706,
0.023518217727541924,
-0.0012881850125268102,
-0.02529798448085785,
-0.009075951762497425,
-0.06786465644836426,
0.005253199953585863,
-0.02894006296992302,
0.023044655099511147,
-0.02098877727985382,
-0.05322481691837311,
-0.020359134301543236,
0.009265003725886345,
-0.051492948085069656,
-0.02446179836988449,
-0.0058364262804389,
0.015399886295199394,
0.01699930615723133,
-0.017300445586442947,
-0.004936514887958765,
0.030858218669891357,
-0.009822240099310875,
0.041700802743434906,
0.007526930887252092,
0.03474051505327225,
0.035487085580825806,
-0.04786737635731697,
0.019451675936579704,
-0.051232803612947464,
-0.013639037497341633,
-0.0021152286790311337,
-0.04856562241911888,
0.007587404455989599,
0.039192844182252884,
0.006704396568238735,
0.011772490106523037,
-0.003963933326303959,
0.012282779440283775,
0.04011773318052292,
-0.006938769016414881,
0.07628504931926727,
0.02577836997807026,
-0.008705666288733482,
0.015111436136066914,
0.03889397904276848,
0.06236952543258667,
-0.03365257382392883,
0.02887517213821411,
-0.03982142359018326,
0.012250701896846294,
-0.018739255145192146,
0.008483322337269783,
0.03985096141695976,
0.013224761933088303,
0.02615310810506344,
-0.006590492557734251,
-0.02273404225707054,
0.0616505891084671,
-0.007780627813190222,
0.014604340307414532,
-0.03573332726955414,
0.049433059990406036,
0.016795936971902847,
0.015544612891972065,
-0.09849315136671066,
0.02591557614505291,
0.039414841681718826,
0.0034325141459703445,
0.017308661714196205,
0.04206031933426857,
-0.07511650025844574,
0.02534538321197033,
0.0035258790012449026,
0.03678567707538605,
-0.00964437797665596,
-0.04585350677371025,
0.005571971647441387,
-0.02843708172440529,
-0.04083005338907242,
0.008907526731491089,
-0.006073298864066601,
-0.010094336234033108,
0.033471304923295975,
0.020240163430571556,
0.009392048232257366,
-0.015262461267411709,
0.005065002012997866,
-0.01441741082817316,
-0.024471184238791466,
-0.018428107723593712,
-0.012746669352054596,
0.002400614321231842,
0.020590174943208694,
0.01734563522040844,
0.01921400986611843,
0.0023156525567173958,
-0.015993166714906693,
-0.010305529460310936,
0.023030562326312065,
0.002401150530204177,
-0.03943723812699318,
0.05668448656797409,
-0.05250254273414612,
0.009500067681074142,
0.034136541187763214,
0.04918240010738373,
-0.020600249990820885,
0.04334097355604172,
0.03907141834497452,
-0.021889889612793922,
-0.05636664107441902,
0.0061730737797915936,
-0.011899064294993877,
0.07654765248298645,
0.024244900792837143,
-0.047730669379234314,
0.0002900279650930315,
-0.02891838736832142,
0.004623137414455414,
-0.03071674145758152,
0.02190426178276539,
0.0037668601144105196,
-0.02599795162677765,
-0.00018964662740472704,
-0.06231628358364105,
-0.0655316486954689,
-0.003818314289674163,
-0.0042290715500712395,
0.038578346371650696,
0.010197813622653484,
0.006608373019844294,
0.01996975764632225,
-0.04038846120238304,
-0.003640318289399147,
-0.026916582137346268,
-0.030833667144179344,
0.03486448526382446,
0.01396010909229517,
-0.04939447343349457,
-0.03048538602888584,
0.03762148320674896,
-0.04276926442980766,
-0.02173345908522606,
-0.049336157739162445,
0.03420514985918999,
0.027311544865369797,
-0.02991143986582756,
0.028163917362689972,
-0.01216072216629982,
-0.03450652211904526,
-0.016862543299794197,
0.005153050180524588,
0.051275163888931274,
-0.042827315628528595,
-0.01138138398528099,
0.008827990852296352,
0.03507039695978165,
-0.020392438396811485,
0.017465874552726746,
-0.029169298708438873,
-0.01313522644340992,
-0.052225589752197266,
-0.04203731194138527,
0.05613362044095993,
0.00003253899558330886,
-0.0028461602050811052,
-0.008793225511908531,
-0.001671862555667758,
0.008590484037995338,
0.08780514448881149,
0.0871891900897026,
-0.03655454143881798,
0.0035551053006201982,
0.022410385310649872,
-0.03909618407487869,
-0.0000199421319848625,
0.004578769207000732,
0.032618723809719086,
-0.0015884237363934517,
-0.012376928701996803,
-0.02862759865820408,
-0.026135612279176712,
-0.05739225819706917,
0.028470326215028763
] |
<p>If I knew the exact value of constant centripetal force and the <strong>average velocity</strong> of an object travelling around a circle for time $t$, would that be enough information to determine the final positon of an object? What I mean is what if I had another object, at the same initial position and with identical centripetal force applied to it, which would have a different velocity function $f(t)$, but identical average velocity - would it eventually be in the same place as the first object after time $t$?
Deriving a formula answering this question was beyond my skills.</p> | g6645 | [
0.04353971779346466,
-0.0266567412763834,
0.0009197763283737004,
0.0028293814975768328,
0.08210050314664841,
-0.033833302557468414,
0.054894447326660156,
-0.01454002782702446,
-0.08535398542881012,
0.009339424781501293,
-0.01195644959807396,
-0.05001015588641167,
-0.000647502311039716,
-0.04055473580956459,
0.019740840420126915,
-0.004924615379422903,
0.06514380872249603,
-0.06769785284996033,
0.046202417463064194,
0.04458828270435333,
0.011171135120093822,
0.010548685677349567,
0.021569959819316864,
-0.06584851443767548,
-0.008940332569181919,
-0.009721551090478897,
-0.046193927526474,
-0.03526166081428528,
-0.0788915753364563,
0.005608078092336655,
0.02909708395600319,
-0.012129191309213638,
0.03218824416399002,
-0.08303665369749069,
-0.03656738996505737,
-0.0021200363989919424,
0.045674946159124374,
0.02928503416478634,
-0.005845578853040934,
0.012348833493888378,
0.07309254258871078,
-0.004425890743732452,
0.005948483943939209,
0.007406247314065695,
0.014988220296800137,
-0.022067343816161156,
-0.0040277475491166115,
0.007694547064602375,
-0.004771776497364044,
-0.006320117507129908,
-0.045228321105241776,
0.042627934366464615,
0.041702184826135635,
-0.01353511307388544,
-0.02733514830470085,
0.08567172288894653,
0.1168610155582428,
-0.08065695315599442,
-0.05899495631456375,
0.0005857729120180011,
-0.0127163240686059,
0.014278331771492958,
-0.01564817503094673,
-0.023488789796829224,
0.04613432660698891,
-0.03308026120066643,
-0.012365484610199928,
0.025632916018366814,
-0.05768154561519623,
-0.010481095872819424,
-0.009632245637476444,
-0.02657717652618885,
0.03313445672392845,
-0.03677753731608391,
-0.07965671271085739,
0.018116919323801994,
0.032421231269836426,
-0.024295929819345474,
0.0529676154255867,
-0.023306572809815407,
0.005290166940540075,
0.0497729554772377,
0.006117481272667646,
0.04749318212270737,
0.04336445778608322,
-0.025699306279420853,
-0.010821087285876274,
-0.006104364525526762,
0.01822780817747116,
-0.014185721054673195,
0.04593803361058235,
-0.04687883332371712,
0.023288138210773468,
0.022422198206186295,
0.05946759879589081,
-0.06190218776464462,
-0.012161028571426868,
0.08891426026821136,
0.006302427034825087,
0.058539558202028275,
-0.028547171503305435,
-0.02077954076230526,
-0.03210775926709175,
0.0003232562739867717,
0.021860383450984955,
-0.028261760249733925,
0.059237655252218246,
0.001917438581585884,
-0.0461307056248188,
-0.013436878100037575,
0.0011948273750022054,
-0.04944697767496109,
-0.013777070678770542,
0.004577916581183672,
-0.025302710011601448,
-0.07917580008506775,
0.04613422229886055,
-0.000028596299671335146,
-0.016624823212623596,
0.0076682488434016705,
-0.013285009190440178,
0.0033232388086616993,
-0.017244745045900345,
0.10519175231456757,
0.003859111573547125,
-0.02595204859972,
0.0015048653585836291,
0.036482539027929306,
0.02157771959900856,
-0.025247057899832726,
0.024579249322414398,
-0.01785595715045929,
0.06613966077566147,
0.060096625238657,
-0.017658434808254242,
0.06251352280378342,
-0.03299852833151817,
0.04148395359516144,
-0.001741983462125063,
0.016322942450642586,
-0.03248244524002075,
-0.05234859511256218,
0.019726626574993134,
-0.008430412970483303,
-0.06463656574487686,
0.04871523380279541,
-0.03650376573204994,
-0.01957724802196026,
0.04920150339603424,
-0.012955179437994957,
0.04573509469628334,
0.08640392869710922,
-0.0020153201185166836,
-0.016160912811756134,
-0.05344155803322792,
-0.07298559695482254,
-0.0019332498777657747,
-0.0023772181011736393,
0.015865905210375786,
0.0037851978559046984,
0.07242216169834137,
-0.01598469354212284,
0.016612811014056206,
-0.004568103235214949,
-0.026700006797909737,
0.03276386111974716,
-0.012230511754751205,
-0.0218111053109169,
0.0038477247580885887,
-0.032989926636219025,
-0.06609262526035309,
0.016009768471121788,
0.04033169522881508,
-0.011132367886602879,
-0.019802842289209366,
-0.045960359275341034,
-0.014700503088533878,
-0.037378620356321335,
0.02692185528576374,
0.036418043076992035,
0.012213722802698612,
0.029895514249801636,
0.048458222299814224,
-0.003361618844792247,
-0.014029942452907562,
0.040074244141578674,
0.00247055827639997,
-0.0036704016383737326,
-0.05102788284420967,
0.03102257288992405,
-0.006265699863433838,
-0.031634777784347534,
-0.049735039472579956,
0.07359088957309723,
-0.03331486135721207,
0.004981496836990118,
0.026651514694094658,
-0.0044099013321101665,
-0.10830803960561752,
0.03016674891114235,
0.008074557408690453,
0.05025073513388634,
0.028512263670563698,
-0.014856936410069466,
-0.035634152591228485,
0.0016791182570159435,
0.017473658546805382,
-0.00770752876996994,
0.021607903763651848,
0.04116986691951752,
0.027997374534606934,
0.002565425354987383,
-0.03679139167070389,
0.0894477590918541,
-0.0713944211602211,
-0.0331033393740654,
0.052885886281728745,
0.059215933084487915,
-0.010715936310589314,
0.004318607971072197,
-0.023931490257382393,
-0.006696994416415691,
0.012987880036234856,
0.008809740655124187,
-0.07067835330963135,
-0.021108802407979965,
0.049234166741371155,
-0.01092806551605463,
-0.010623844340443611,
0.060013674199581146,
-0.006449488922953606,
0.01589787006378174,
0.00863347202539444,
0.04738617688417435,
0.060877200216054916,
0.03237117826938629,
0.015624083578586578,
-0.0018796502845361829,
0.039481405168771744,
0.022439010441303253,
0.015485040843486786,
-0.03139863163232803,
-0.01265066396445036,
-0.033475082367658615,
0.014177347533404827,
-0.05533915385603905,
0.0227633249014616,
-0.014380773529410362,
0.08179289102554321,
0.021805906668305397,
-0.01640700362622738,
-0.032654523849487305,
-0.039176419377326965,
0.026702074334025383,
0.016498515382409096,
0.008642693981528282,
-0.04269491508603096,
-0.00020915400818921626,
-0.07267433404922485,
-0.04947194829583168,
-0.028774462640285492,
0.022633880376815796,
0.03247150033712387,
0.03147243708372116,
-0.046758756041526794,
-0.0444650836288929,
-0.012744479812681675,
0.02499304711818695,
-0.026148824021220207,
0.009689802303910255,
-0.01403598953038454,
0.028782309964299202,
0.011899701319634914,
0.09095852822065353,
0.005737868137657642,
-0.0385388620197773,
0.0041525294072926044,
-0.018551655113697052,
-0.04321648180484772,
0.04676470533013344,
-0.04182302579283714,
0.004904879257082939,
-0.06857480853796005,
0.04152282327413559,
-0.045973870903253555,
-0.055469412356615067,
0.05478757247328758,
0.043049078434705734,
0.008448154665529728,
0.03505093604326248,
-0.0041018589399755,
0.06903377920389175,
0.029833072796463966,
-0.006620712578296661,
0.028906825929880142,
0.037702735513448715,
0.04039401561021805,
-0.028546923771500587,
0.05013590306043625,
-0.019915562123060226,
0.008365722373127937,
-0.05817157030105591,
-0.017160633578896523,
0.023464763537049294,
0.015606231987476349,
0.011671800166368484,
-0.002469174098223448,
-0.02991882897913456,
-0.003912950865924358,
0.05641259253025055,
-0.01448810938745737,
0.07610836625099182,
0.008412133902311325,
-0.01774751767516136,
-0.026599518954753876,
0.007608960382640362,
0.027124173939228058,
0.025486480444669724,
-0.0044585722498595715,
0.05358861759305,
0.028267089277505875,
-0.05060262978076935,
0.016421914100646973,
-0.004145995248109102,
0.08031170070171356,
0.028958642855286598,
-0.0888034999370575,
-0.00011600655125221238,
-0.02167220413684845,
0.002302467357367277,
-0.014184628613293171,
0.06083584576845169,
-0.002082463353872299,
0.01568872295320034,
-0.005282111931592226,
-0.002969548339024186,
0.036793824285268784,
-0.004623688291758299,
0.022846532985568047,
0.033306851983070374,
0.00386771559715271,
-0.04294869303703308,
-0.028760863468050957,
0.008598319254815578,
0.0241900235414505,
-0.008974021300673485,
0.026620950549840927,
-0.021769246086478233,
0.028569037094712257,
0.02645418979227543,
0.049466732889413834,
-0.02912069484591484,
-0.0004962672246620059,
-0.031679168343544006,
0.015079321339726448,
0.004431623499840498,
0.054523494094610214,
0.012450278736650944,
-0.05154172703623772,
-0.004214044194668531,
-0.0021256243344396353,
-0.042966872453689575,
0.014952307567000389,
0.025530459359288216,
0.009005827829241753,
0.011900014244019985,
-0.008030497469007969,
0.0636759102344513,
-0.0071565257385373116,
-0.011402352713048458,
0.02807270549237728,
0.006620288826525211,
0.00014989193005021662,
-0.011717651970684528,
0.03777997940778732,
-0.022367466241121292,
0.025658629834651947,
-0.020039210096001625,
-0.057364173233509064,
0.021308524534106255,
0.08599629998207092,
0.06401804834604263,
-0.024336611852049828,
0.033316511660814285,
-0.033742379397153854,
0.007646465674042702,
-0.07934503257274628,
-0.018456533551216125,
0.03835597634315491,
-0.05070723965764046,
0.0017221750458702445,
-0.006562143098562956,
0.0023093419149518013,
-0.0016575391637161374,
0.058637335896492004,
-0.029387054964900017,
-0.0039346059784293175,
-0.07323647290468216,
-0.005791193805634975,
-0.028235958889126778,
-0.03822639584541321,
0.0277464147657156,
-0.04521181434392929,
0.014742707833647728,
0.013424808159470558,
0.01335902139544487,
0.010665264911949635,
-0.012454980053007603,
-0.01719534583389759,
-0.0184109378606081,
-0.04823578521609306,
0.010531964711844921,
0.039651308208703995,
-0.06332626938819885,
0.023610716685652733,
0.026486601680517197,
0.02110188454389572,
-0.039427269250154495,
0.019131505861878395,
-0.057884056121110916,
0.02501833066344261,
0.06233109533786774,
0.02016938105225563,
-0.012840043753385544,
-0.04207323491573334,
0.0089748939499259,
0.054100267589092255,
0.035178642719984055,
-0.028449585661292076,
-0.05752323195338249,
-0.014776958152651787,
0.04996330291032791,
0.04082798585295677,
0.020175637677311897,
-0.03928351774811745,
0.022354470565915108,
0.004802272189408541,
0.034499358385801315,
0.0241878479719162,
0.031572144478559494,
-0.0325985886156559,
0.07456402480602264,
0.03830435499548912,
-0.052612483501434326,
-0.04640578851103783,
0.059460680931806564,
-0.049869269132614136,
-0.024189362302422523,
-0.006875297985970974,
-0.026709534227848053,
-0.06313461065292358,
-0.00456717424094677,
-0.01089085265994072,
-0.03351695463061333,
-0.03287277743220329,
0.018557382747530937,
-0.014347922056913376,
0.0018313664477318525,
-0.006949422415345907,
-0.007915099151432514,
-0.04645540565252304,
-0.007888195104897022,
-0.023881809785962105,
-0.025371471419930458,
0.04143191874027252,
-0.002057966310530901,
0.005313408561050892,
0.043802596628665924,
-0.02750062383711338,
0.02221202664077282,
-0.006355695892125368,
0.0164552703499794,
0.05890979617834091,
0.02854984439909458,
-0.05097438022494316,
0.008246892131865025,
0.025560462847352028,
0.009000035002827644,
0.04189364239573479,
-0.010921983048319817,
-0.04069259390234947,
0.015607777051627636,
0.024294927716255188,
-0.058489326387643814,
0.01204756274819374,
-0.035220637917518616,
-0.03879919275641441,
-0.011588993482291698,
-0.0009468371281400323,
-0.01009219978004694,
0.03386939689517021,
-0.00969797745347023,
0.05182052403688431,
-0.04085015133023262,
-0.019628729671239853,
-0.030477670952677727,
-0.002807521028444171,
-0.03740726038813591,
-0.0008189553045667708,
0.0292629674077034,
-0.08712983131408691,
0.021489253267645836,
-0.02519087865948677,
0.035048458725214005,
-0.03244360163807869,
0.029282694682478905,
0.02043808624148369,
-0.019122719764709473,
-0.023884255439043045,
0.053924817591905594,
0.012766746804118156,
0.041988421231508255,
-0.019283294677734375,
0.010395447723567486,
-0.05582490935921669,
0.028713567182421684,
-0.0201618243008852,
0.053765200078487396,
-0.01742606796324253,
0.002569229807704687,
0.06590594351291656,
0.10503962635993958,
0.04015880450606346,
-0.017014184966683388,
-0.02195023186504841,
-0.01741959899663925,
-0.005515672266483307,
0.047945309430360794,
0.02797725237905979,
0.021676724776625633,
0.027059340849518776,
0.028082968667149544,
-0.033413562923669815,
-0.03955802693963051,
-0.02038361132144928,
-0.03851611912250519,
0.017901232466101646,
-0.026388905942440033,
0.05641571059823036,
-0.020795321092009544,
-0.02892177179455757,
-0.0071141705848276615,
0.03626372292637825,
0.032568324357271194,
-0.031832125037908554,
0.0008218034054152668,
-0.031195268034934998,
-0.03132477030158043,
0.03575952351093292,
-0.03450005501508713,
-0.014481117017567158,
0.07274752855300903,
-0.0069069769233465195,
-0.01782308705151081,
-0.029558898881077766,
0.06023193523287773,
-0.006602788344025612,
-0.004468689672648907,
0.05839446559548378,
-0.05438148230314255,
0.040878310799598694,
-0.05505941063165665,
0.031122712418437004,
0.023215100169181824,
-0.010033657774329185,
-0.04473300650715828,
-0.013980009593069553,
0.0005453746998682618,
0.059164077043533325,
0.039100874215364456,
-0.004497114568948746,
0.018040750175714493,
-0.02345416136085987,
-0.03982875868678093,
0.039063453674316406,
0.017468249425292015,
-0.04963494464755058,
-0.005504811182618141,
-0.04480650648474693,
0.04478532448410988,
0.02062370441854,
-0.013159988448023796,
0.01638825424015522,
0.02737342193722725,
-0.0064310356974601746,
0.037415213882923126,
-0.05603202432394028,
-0.029673557728528976,
0.018707487732172012,
-0.0420290008187294,
0.011194782331585884,
-0.0460505373775959,
-0.038412779569625854,
-0.0284382626414299,
-0.03299683332443237,
-0.026634061709046364,
0.00772356241941452,
-0.019145585596561432,
-0.012126099318265915,
0.06509941816329956,
0.00009672233136370778,
-0.039441175758838654,
0.024670839309692383,
-0.00909749511629343,
0.015926627442240715,
-0.02053758129477501,
0.04497866332530975,
-0.04081827402114868,
0.017754001542925835,
-0.07038228213787079,
0.05383161082863808,
0.03441982343792915,
-0.016910776495933533,
0.05651599168777466,
-0.014073891565203667,
0.028065789490938187,
0.021669883280992508,
-0.034993015229701996,
-0.01457471214234829,
-0.06524727493524551,
0.04841654375195503,
0.014539213851094246,
0.005055748391896486,
0.00843723677098751,
0.05214846134185791,
0.02989771217107773,
-0.07107115536928177,
0.013277657330036163,
0.04065603390336037,
0.017636898905038834,
0.04207601398229599,
0.022176070138812065,
0.040241409093141556,
0.008017953485250473,
-0.01109718531370163,
0.04737778380513191,
-0.024201884865760803,
0.06546047329902649,
0.0002550850622355938,
-0.0013745902106165886,
0.02856431156396866,
0.02322228252887726,
0.03585885092616081,
-0.018088771030306816,
-0.08347517251968384,
-0.04618864879012108,
0.04819178953766823,
0.0031263113487511873,
-0.05883755162358284,
0.02246885374188423,
0.017727263271808624,
-0.04187296703457832,
0.005685168318450451,
0.012582900002598763,
-0.01766210049390793,
0.02231445536017418,
0.010391149669885635,
-0.0009390320628881454,
-0.009023378603160381,
-0.03425443172454834,
-0.004126960877329111,
-0.03473398834466934,
-0.039392195641994476,
-0.003773806383833289,
-0.06382817775011063,
0.02617296762764454,
-0.05345049127936363,
-0.03830334171652794,
-0.021403435617685318,
-0.04577986150979996,
0.05285055562853813,
0.015336866490542889,
-0.03224104270339012,
0.04035448282957077,
0.031038060784339905,
0.05733276158571243,
-0.024843033403158188,
-0.023470453917980194,
0.004109720233827829,
0.0008327236864715815,
-0.050829511135816574,
-0.03904261440038681,
0.0030629283282905817,
-0.003224763786420226,
-0.015202068723738194,
0.06581976264715195,
-0.03426060453057289,
-0.01871594972908497,
-0.025816908106207848,
-0.05332811921834946,
-0.03136298060417175,
0.008475434966385365,
0.02723543532192707,
-0.02834286540746689,
-0.024849779903888702,
-0.039094794541597366,
0.03524589166045189,
0.05395002290606499,
0.014221261255443096,
0.03050645813345909,
0.004838998429477215,
-0.016323380172252655,
-0.017303092405200005,
0.004208833444863558,
-0.022127635776996613,
0.020714614540338516,
-0.08040875941514969,
0.004270937293767929,
-0.04236910864710808,
0.047603290528059006,
0.04145584627985954,
0.04509939253330231,
-0.004822999704629183,
-0.058982379734516144,
-0.04544205218553543,
0.046258509159088135,
-0.05778017267584801,
-0.04017821326851845,
-0.0003293571644462645,
0.008527185767889023,
-0.05634346976876259,
0.007826164364814758,
-0.019431930035352707,
-0.08039932698011398,
-0.04711131379008293,
-0.010561845265328884,
-0.06924860179424286,
-0.06660446524620056,
-0.03238408640027046,
0.02595462277531624,
0.017255054786801338,
-0.01391313225030899,
-0.04153492674231529,
0.024254055693745613,
-0.04472942650318146,
0.041149117052555084,
-0.008182859048247337,
0.008619243279099464,
-0.039828523993492126,
0.011973167769610882,
-0.021695543080568314,
-0.0095602348446846,
-0.013930272310972214,
0.027833281084895134,
-0.02975505404174328,
0.013190541416406631,
-0.01677774265408516,
0.04869060218334198,
0.02947351150214672,
-0.0268220454454422,
-0.012844801880419254,
-0.005598758347332478,
-0.050605855882167816,
-0.022781280800700188,
0.013303562998771667,
-0.04638449102640152,
-0.030883364379405975,
-0.013164830394089222,
-0.047386977821588516,
-0.004937140736728907,
0.009066871367394924,
0.024686580523848534,
0.0083415936678648,
-0.0021794030908495188,
-0.023833079263567924,
-0.020908670499920845,
-0.021144261583685875,
0.05659044161438942
] |
<p>My professor said that the $k_BT$ displacement in the energy levels of the band electrons is due to the space-thermal displacement of the potential of the ion host. I think that this displacement is due to the thermal fluctuations of the electromagnetic field coupled to the electron charge.</p>
<p>Who is right?</p> | g6646 | [
0.03460930287837982,
0.047548532485961914,
-0.01796858198940754,
0.023692185059189796,
0.03999689221382141,
0.07774480432271957,
-0.03389572352170944,
0.03472660109400749,
0.02133367955684662,
0.039587490260601044,
0.013766037300229073,
0.05345182865858078,
0.0017046671127900481,
-0.0012800573604181409,
0.011388961225748062,
-0.0375053845345974,
0.048954810947179794,
0.06318743526935577,
-0.031127318739891052,
0.034684114158153534,
-0.02919880487024784,
0.01953607238829136,
-0.06735359132289886,
-0.07810233533382416,
0.03168107941746712,
0.000775331340264529,
-0.006333683617413044,
0.010306078009307384,
0.007708210032433271,
-0.0625397339463234,
0.015432697720825672,
0.0245395228266716,
0.0004630371113307774,
-0.043039336800575256,
-0.07025863230228424,
-0.037846874445676804,
0.0689743384718895,
0.014751560054719448,
-0.0035997903905808926,
0.0064277793280780315,
-0.030645929276943207,
-0.02250969409942627,
-0.007500307634472847,
0.02657463774085045,
0.010252850130200386,
-0.015048382803797722,
-0.013809570111334324,
0.01186484657227993,
-0.047370586544275284,
-0.02522866055369377,
-0.03650818392634392,
0.02487367019057274,
0.02082614041864872,
0.03937897831201553,
0.06417680531740189,
-0.01913321204483509,
-0.035044845193624496,
0.01409171987324953,
0.06601965427398682,
0.030117789283394814,
0.12835350632667542,
-0.00027368118753656745,
-0.013076297007501125,
0.012701566331088543,
0.03803957998752594,
-0.023893747478723526,
-0.05432488024234772,
0.041061196476221085,
-0.0006448783096857369,
-0.05603881925344467,
0.02629167027771473,
0.026897557079792023,
-0.039866406470537186,
0.04496817663311958,
-0.044270433485507965,
-0.03253331780433655,
-0.03610892593860626,
0.004522262141108513,
0.0163617804646492,
0.00636918842792511,
-0.06843217462301254,
-0.0005063213175162673,
0.02138701267540455,
0.014740088023245335,
0.04754723981022835,
-0.028340037912130356,
0.005054083652794361,
0.11513296514749527,
0.018793659284710884,
0.03065483085811138,
0.0035938743967562914,
-0.03963306546211243,
0.05256149172782898,
0.014318271540105343,
0.014527054503560066,
-0.019185218960046768,
-0.027348043397068977,
0.07108692824840546,
-0.006134359166026115,
-0.039233725517988205,
-0.025876980274915695,
-0.016024595126509666,
-0.030709730461239815,
0.03193247318267822,
-0.060515936464071274,
0.009489928372204304,
-0.03267798200249672,
-0.03638899326324463,
0.08246278017759323,
0.008633092977106571,
-0.03680470213294029,
-0.05399869754910469,
0.009149250574409962,
0.004893959499895573,
-0.017115026712417603,
-0.014389581978321075,
-0.027210796251893044,
-0.05251672863960266,
-0.021882226690649986,
0.05719629302620888,
-0.038222536444664,
-0.04677128791809082,
-0.019431615248322487,
0.02881510555744171,
0.019399341195821762,
-0.011215435341000557,
-0.03002765215933323,
-0.021512653678655624,
0.03482203930616379,
0.018267914652824402,
-0.030474474653601646,
0.022714106366038322,
-0.030886828899383545,
0.006036215461790562,
0.05622722953557968,
-0.03116004355251789,
0.014843433164060116,
0.002039730316027999,
-0.06162184849381447,
-0.014749862253665924,
0.016892269253730774,
-0.023856330662965775,
0.020889952778816223,
-0.07063499838113785,
-0.006458251737058163,
-0.011620745062828064,
-0.06741529703140259,
-0.025848813354969025,
0.03561482951045036,
0.030396167188882828,
0.03879428282380104,
0.017001619562506676,
0.005695968866348267,
-0.09324999898672104,
0.02711022086441517,
-0.05811365693807602,
0.06858289986848831,
0.03978115692734718,
-0.0026239128783345222,
0.044076915830373764,
0.0022626908030360937,
0.0029163570143282413,
0.013460504822432995,
0.007959598675370216,
0.05967746675014496,
-0.028285397216677666,
-0.03299392759799957,
-0.007494649849832058,
0.005675560794770718,
0.022586019709706306,
-0.020495830103754997,
-0.001650986378081143,
0.0022389679215848446,
0.02160254865884781,
-0.06321392208337784,
0.09161154925823212,
0.007803629618138075,
-0.03828783705830574,
0.057040128856897354,
-0.0385131761431694,
-0.01537037268280983,
0.014409205876290798,
0.05099198594689369,
-0.04457069933414459,
0.05017529055476189,
-0.024675220251083374,
-0.06539325416088104,
0.04607657343149185,
-0.016383809968829155,
-0.05288517847657204,
0.02613462507724762,
-0.036353498697280884,
0.026261407881975174,
-0.030309977009892464,
0.012015330605208874,
-0.005140268709510565,
0.03802276775240898,
0.005120570305734873,
-0.014008392579853535,
-0.005600152537226677,
-0.001738077844493091,
-0.013781430199742317,
0.019153229892253876,
-0.03821322321891785,
0.07674244046211243,
0.005228622350841761,
-0.06064101308584213,
0.00462711276486516,
-0.0033092277590185404,
-0.04723108187317848,
-0.015513637103140354,
-0.027133021503686905,
-0.08138324320316315,
0.05216922238469124,
0.015176059678196907,
-0.005338956601917744,
-0.023763395845890045,
-0.02255171537399292,
0.02760266698896885,
0.001123751513659954,
-0.03911709040403366,
-0.0041892207227647305,
0.0031671866308897734,
0.050156064331531525,
-0.015025852248072624,
-0.016032177954912186,
-0.0009512268588878214,
-0.044284798204898834,
-0.07775495946407318,
-0.02559652179479599,
-0.06725482642650604,
0.05307833105325699,
-0.01721886731684208,
0.009704502299427986,
0.06931191682815552,
0.09862516820430756,
-0.0046795569360256195,
-0.0007142131216824055,
0.0030204476788640022,
-0.051434457302093506,
-0.026164984330534935,
-0.011782663874328136,
-0.024851810187101364,
0.0059520769864320755,
0.016173765063285828,
0.030863218009471893,
0.016661599278450012,
-0.02987688221037388,
-0.05862674489617348,
-0.055093877017498016,
0.044850170612335205,
-0.05474163591861725,
0.024320287629961967,
-0.024903446435928345,
-0.0083766533061862,
-0.00811618659645319,
-0.00756290927529335,
0.0375283882021904,
-0.0025750796776264906,
-0.035273972898721695,
0.02099255658686161,
-0.018974797800183296,
0.012104709632694721,
-0.02234835736453533,
-0.03113715723156929,
-0.04869072511792183,
0.005327119491994381,
-0.06070958450436592,
0.021018335595726967,
-0.03513789176940918,
0.060097385197877884,
0.09756956249475479,
-0.004438301548361778,
0.03927411884069443,
0.04263913631439209,
-0.032391589134931564,
0.041448574513196945,
-0.003337305970489979,
0.0062842159532010555,
-0.062401965260505676,
-0.05447668954730034,
0.033889494836330414,
0.00044595569488592446,
-0.03985995054244995,
-0.019563188776373863,
0.020289916545152664,
-0.035534415394067764,
0.011483260430395603,
-0.012785953469574451,
0.00781413447111845,
-0.0027061232831329107,
-0.04155273735523224,
0.03872820362448692,
0.017611438408493996,
-0.052350208163261414,
0.03424913436174393,
0.06131976470351219,
-0.07222039252519608,
-0.044074781239032745,
0.06144101545214653,
0.02991194650530815,
0.015052549540996552,
-0.02230137214064598,
-0.001507361652329564,
0.01421307772397995,
0.019856994971632957,
0.010590873658657074,
-0.019581953063607216,
0.02769588492810726,
-0.023509105667471886,
-0.008339671418070793,
-0.016873536631464958,
0.015610210597515106,
0.02725042961537838,
-0.027807652950286865,
-0.01059703528881073,
-0.07666803151369095,
-0.008050207048654556,
0.08102953433990479,
0.019142091274261475,
-0.017550133168697357,
-0.021293768659234047,
-0.015541971661150455,
0.0016248931642621756,
0.03596174716949463,
-0.01921631023287773,
0.002158544957637787,
-0.027702588587999344,
-0.007171804551035166,
0.006073388736695051,
-0.043445687741041183,
-0.030261510983109474,
0.0014390544965863228,
-0.02529050037264824,
0.011377234943211079,
0.015258101746439934,
0.0336117148399353,
0.050691891461610794,
-0.033707212656736374,
0.02617291733622551,
-0.02978881448507309,
0.007049274630844593,
-0.038248300552368164,
-0.029107926413416862,
-0.008681501261889935,
0.023254437372088432,
-0.019955193623900414,
-0.06368767470121384,
-0.03937498852610588,
-0.005429940298199654,
0.02059348300099373,
0.02188509702682495,
0.011965828016400337,
0.004730653949081898,
-0.059375517070293427,
0.019076770171523094,
0.019828835502266884,
0.0066789546981453896,
-0.02964729815721512,
-0.019468843936920166,
0.039985038340091705,
-0.02038523741066456,
0.06794333457946777,
-0.008056835271418095,
-0.05585760623216629,
0.01582976058125496,
0.0019884409848600626,
0.06883123517036438,
0.018598316237330437,
-0.034553367644548416,
-0.07293552160263062,
-0.05577455088496208,
-0.033814139664173126,
0.0013509117998182774,
0.0663001537322998,
-0.0295051671564579,
0.008916264399886131,
0.020230459049344063,
-0.0030653986614197493,
0.01279172208160162,
-0.002333048963919282,
-0.026265041902661324,
0.03124990500509739,
0.02329016663134098,
0.051999643445014954,
0.0036709727719426155,
-0.03788355365395546,
0.054051823914051056,
-0.02080918289721012,
-0.0517348051071167,
-0.019535215571522713,
0.013108571991324425,
0.011838112026453018,
-0.029025152325630188,
0.05498230829834938,
-0.040109895169734955,
0.018023360520601273,
-0.011206626892089844,
0.06219162791967392,
0.06220325827598572,
0.07247669249773026,
-0.00969199649989605,
-0.002748957835137844,
-0.032612767070531845,
-0.020916201174259186,
0.038345564156770706,
0.07985375821590424,
-0.07418622821569443,
-0.06331761926412582,
-0.019507750868797302,
-0.06051773577928543,
0.02617683634161949,
0.013137749396264553,
-0.01959231309592724,
-0.006464075762778521,
-0.02119622752070427,
-0.0026430313009768724,
0.05650939792394638,
0.0587259866297245,
-0.009196655824780464,
0.006710915360599756,
0.01943144015967846,
0.01440845150500536,
-0.00374624109826982,
0.03127438202500343,
0.06307879090309143,
0.028641054406762123,
0.0021953475661575794,
0.005080417264252901,
0.0052850800566375256,
-0.02273689955472946,
0.016162453219294548,
-0.009412380866706371,
0.0006007853080518544,
-0.03510640934109688,
0.04106476157903671,
0.0025502177886664867,
0.02383374609053135,
-0.02363557554781437,
0.06712771952152252,
0.054520122706890106,
-0.032732971012592316,
-0.011568657122552395,
0.010824568569660187,
0.005954512394964695,
0.022580072283744812,
0.020682353526353836,
-0.0138260992243886,
-0.02532484196126461,
0.007960687391459942,
0.019140096381306648,
0.020474817603826523,
0.004905482288450003,
0.028643865138292313,
0.05917060747742653,
-0.03472605720162392,
-0.031738825142383575,
-0.007541889790445566,
0.02700759470462799,
0.016260264441370964,
-0.018944386392831802,
0.02917107380926609,
-0.020552702248096466,
0.03336592763662338,
0.04159305617213249,
-0.009983118623495102,
0.02293882519006729,
0.01704045757651329,
-0.04040051996707916,
-0.023956317454576492,
0.047230903059244156,
0.016168680042028427,
0.01816873997449875,
0.01153455302119255,
0.08237109333276749,
0.02767837792634964,
-0.01960301585495472,
-0.012823468074202538,
-0.030978895723819733,
-0.05389378219842911,
-0.02431502752006054,
0.007433013524860144,
0.028511526063084602,
0.02926289476454258,
-0.06251653283834457,
0.01599576510488987,
0.01917039230465889,
0.02697387896478176,
0.009836188517510891,
-0.029802056029438972,
0.061639826744794846,
-0.00519126933068037,
0.00018307010759599507,
-0.0003376675595063716,
0.0007467591785825789,
0.04864494130015373,
0.025258824229240417,
0.09129256755113602,
0.047403912991285324,
0.03787703812122345,
0.007026121485978365,
-0.00353047763928771,
0.038034114986658096,
0.0014289451064541936,
-0.008076532743871212,
0.00631379010155797,
-0.032973989844322205,
-0.021502867341041565,
0.003366178600117564,
-0.02520127408206463,
-0.027048330754041672,
0.07231318950653076,
0.034979067742824554,
0.010893560014665127,
0.032749470323324203,
-0.048716604709625244,
-0.030671512708067894,
-0.021985944360494614,
-0.04592634737491608,
-0.03156738728284836,
-0.00465557212010026,
0.007193485740572214,
0.03834811598062515,
-0.01935669407248497,
0.0380275659263134,
0.06631465256214142,
-0.006404994986951351,
-0.014006432145833969,
-0.01268637366592884,
0.00824923999607563,
0.005509025417268276,
0.039991021156311035,
0.02615775726735592,
0.030488381162285805,
-0.026082457974553108,
-0.016422834247350693,
0.05303814634680748,
0.020898018032312393,
0.00868554413318634,
0.018069561570882797,
0.04382321238517761,
0.03562904894351959,
0.007371301297098398,
0.03364647924900055,
-0.00637924624606967,
0.0026370242703706026,
-0.0435749813914299,
0.02511700429022312,
0.061318665742874146,
-0.08533487468957901,
-0.009212149307131767,
0.07313080877065659,
-0.012643503956496716,
-0.03190992400050163,
0.046127744019031525,
-0.052558787167072296,
0.02019830048084259,
-0.02546524815261364,
-0.05086119845509529,
-0.038640234619379044,
0.0037721614353358746,
0.07413173466920853,
0.03974973037838936,
0.016577549278736115,
0.06223538890480995,
-0.022988779470324516,
-0.01399378664791584,
0.011563453823328018,
0.06813229620456696,
0.010331668891012669,
-0.04561908543109894,
-0.024360505864024162,
-0.023109659552574158,
-0.04099331051111221,
0.007774297147989273,
0.04146431013941765,
-0.0024272555019706488,
-0.0032526555005460978,
-0.062262337654829025,
-0.04561515897512436,
0.003112140344455838,
0.005478855688124895,
-0.040248364210128784,
0.0006691617309115827,
-0.07952015101909637,
0.0014964727452024817,
-0.008558188565075397,
0.015562540851533413,
0.12783828377723694,
0.0010167992440983653,
-0.020815853029489517,
-0.012846243567764759,
0.020366616547107697,
0.020640281960368156,
-0.07329102605581284,
-0.016333425417542458,
-0.028490394353866577,
-0.010122151114046574,
-0.03170815855264664,
0.02536674402654171,
0.01192964892834425,
-0.030665120109915733,
-0.028955334797501564,
-0.024734407663345337,
0.015681924298405647,
-0.05846570432186127,
-0.01997389830648899,
0.029946310445666313,
-0.04944441840052605,
0.052839722484350204,
-0.008192424662411213,
-0.001687506097368896,
0.052609242498874664,
-0.04593354091048241,
-0.00765186594799161,
-0.0049271476455032825,
-0.01890779472887516,
0.06235095113515854,
-0.05452603101730347,
-0.0013353853719308972,
0.0006341035477817059,
0.018612803891301155,
-0.05333983525633812,
0.0019038388272747397,
0.002522937720641494,
0.017817460000514984,
0.009492242708802223,
0.0062307086773216724,
-0.012816289439797401,
-0.05722356587648392,
-0.0038818230386823416,
0.03965688869357109,
-0.0000012329539913480403,
-0.0011253093834966421,
-0.006539076566696167,
0.007687485311180353,
-0.007695392239838839,
0.01785784587264061,
-0.03554791957139969,
-0.016530334949493408,
-0.02539924532175064,
-0.03095374070107937,
0.06553617119789124,
0.01831338368356228,
0.022014470770955086,
-0.013522293418645859,
-0.018292849883437157,
0.0408112071454525,
-0.04074360802769661,
-0.038830723613500595,
0.007426835596561432,
-0.03565611690282822,
-0.0428837351500988,
0.005611916072666645,
0.03339622542262077,
0.0033018786925822496,
0.0028650867752730846,
0.009076130576431751,
0.059162240475416183,
-0.03446376323699951,
-0.07617288827896118,
-0.06700148433446884,
0.004414185415953398,
0.024968372657895088,
0.03907542675733566,
0.054401565343141556,
0.017885230481624603,
-0.03759991377592087,
-0.015149232931435108,
-0.034939173609018326,
0.0014270574320107698,
-0.03541399911046028,
0.05854225158691406,
0.035922564566135406,
-0.07603936642408371,
0.003419933607801795,
-0.045411672443151474,
0.02924981899559498,
-0.06298667937517166,
-0.0024189024697989225,
-0.03622573986649513,
-0.0017337746685370803,
0.07610733062028885,
-0.02939159795641899,
-0.014543630182743073,
-0.01511085219681263,
-0.0423135980963707,
0.011141203343868256,
0.019288986921310425,
0.0067709521390497684,
0.0022574784234166145,
0.005881755147129297,
-0.02555616945028305,
0.01856793835759163,
0.034429725259542465,
0.025415407493710518,
-0.007174644153565168,
-0.01552498247474432,
0.04533250257372856,
0.033545587211847305,
0.0028184056282043457,
0.01162804290652275,
0.0072598643600940704,
-0.00008274303399957716,
0.0599667988717556,
0.007807470392435789,
0.03648647665977478,
0.015005247667431831,
-0.052166957408189774,
-0.05631861835718155,
0.05969904363155365,
-0.03285617008805275,
-0.01421412080526352,
0.026032404974102974,
0.06120571866631508,
-0.031087974086403847,
0.005984306335449219,
0.0019019665196537971,
-0.056561343371868134,
-0.0235836710780859,
0.05226876214146614,
-0.003613716224208474,
0.03682003170251846,
-0.047303706407547,
0.0392644926905632,
-0.052873607724905014,
0.021896645426750183,
-0.03439214453101158,
0.029156621545553207,
-0.004957652650773525,
-0.034676581621170044,
-0.004092361778020859,
-0.058411795645952225,
-0.08872569352388382,
0.0047865561209619045,
0.02295106276869774,
-0.02498195692896843,
0.03578637167811394,
0.0570729523897171,
-0.010220769792795181,
-0.024299975484609604,
-0.011513818055391312,
0.029160311445593834,
0.009174766018986702,
-0.0793825089931488,
-0.0005373951280489564,
-0.06689851731061935,
-0.05217713862657547,
0.07938551157712936,
-0.00439412472769618,
0.01301709283143282,
-0.05631306767463684,
-0.08379704505205154,
0.03782051056623459,
0.021207449957728386,
-0.028404798358678818,
0.005319562740623951,
0.013915247283875942,
-0.006584205664694309,
0.04906393587589264,
-0.025228939950466156,
-0.03679696470499039,
-0.016408000141382217,
-0.005260862410068512,
0.02367708645761013,
-0.010688061825931072,
-0.008720108307898045,
0.01723296009004116
] |
<p>Is there any phenomenon where the 'wave description' of the electron's motion is not applicable?</p>
<p>The reason for this question is to find out if there are any situations were quantum wave theories fail. If not, it seems that the Everett's multiworld analysis as described by Coleman, <a href="http://media.physics.harvard.edu/video/index.php?id=SidneyColeman_QMIYF.flv" rel="nofollow">http://media.physics.harvard.edu/video/index.php?id=SidneyColeman_QMIYF.flv</a> works.</p> | g6647 | [
-0.0013621350517496467,
0.07000938802957535,
0.015017482452094555,
-0.013214039616286755,
0.04966193065047264,
0.015259429812431335,
-0.0015748055884614587,
-0.009824639186263084,
0.018493788316845894,
-0.04884197935461998,
0.02493792213499546,
-0.023272398859262466,
0.01738852821290493,
0.04036519676446915,
-0.06640604883432388,
-0.06057244539260864,
0.044967494904994965,
0.008780800737440586,
0.044503990560770035,
0.03008451499044895,
-0.024746593087911606,
0.0007296839030459523,
0.00032009329879656434,
0.026396483182907104,
-0.00913142692297697,
0.0029808832332491875,
-0.042813755571842194,
-0.05626661702990532,
0.028176242485642433,
-0.049088772386312485,
0.04707092046737671,
0.012492635287344456,
0.05527344346046448,
-0.07726645469665527,
-0.03408658877015114,
0.02166634239256382,
0.013694923371076584,
0.0354788713157177,
-0.025789985433220863,
0.015551924705505371,
-0.044109612703323364,
0.0011129964841529727,
-0.029496662318706512,
0.01723405160009861,
0.021655773743987083,
-0.01766136847436428,
0.04427702724933624,
0.0154911819845438,
-0.04223114252090454,
-0.005488433875143528,
-0.01627531461417675,
0.044435951858758926,
0.04980489984154701,
0.010105771943926811,
0.06922467797994614,
0.03569777309894562,
-0.003182807704433799,
0.04676533490419388,
0.08708616346120834,
0.005360639188438654,
0.01241656020283699,
0.020316408947110176,
0.024641267955303192,
0.02343756891787052,
0.04514094069600105,
-0.00863596610724926,
-0.04858306422829628,
-0.013094492256641388,
-0.008626675233244896,
-0.025904737412929535,
0.04551054909825325,
-0.09186400473117828,
-0.07341589033603668,
-0.006997805554419756,
0.026540113613009453,
0.07255496084690094,
-0.036177199333906174,
0.0004506851837504655,
0.004251823760569096,
0.006682919338345528,
-0.04640228673815727,
-0.02185666374862194,
0.02373826690018177,
0.025347312912344933,
0.06446725875139236,
-0.04943455010652542,
0.012081761844456196,
0.018070051446557045,
0.004279685206711292,
-0.008529270067811012,
0.01148125808686018,
0.005213269963860512,
0.06577228009700775,
0.035351116210222244,
-0.015468730591237545,
-0.06970727443695068,
-0.05154472589492798,
0.053379762917757034,
-0.029707230627536774,
0.03898127004504204,
-0.0743110403418541,
0.008718159049749374,
-0.008050740696489811,
0.005245953798294067,
0.04158202186226845,
-0.01363291684538126,
-0.02254394069314003,
-0.026605509221553802,
0.03768592327833176,
0.012874096632003784,
-0.051732663065195084,
-0.03939851000905037,
-0.004473347682505846,
-0.014490695670247078,
-0.037620510905981064,
-0.03141315281391144,
0.0444820299744606,
-0.044871892780065536,
-0.001967886695638299,
0.04829976335167885,
0.0019257866078987718,
0.0040015773847699165,
0.011360954493284225,
0.05916942283511162,
-0.027120845392346382,
0.01589670404791832,
-0.025342755019664764,
-0.02482105791568756,
0.037816811352968216,
0.03256549313664436,
0.06489987671375275,
0.05070199817419052,
0.023389747366309166,
0.07492849230766296,
0.005533550400286913,
0.020581522956490517,
0.02104341611266136,
0.04267806559801102,
-0.012208711355924606,
0.019321097061038017,
0.02649417705833912,
-0.06469271332025528,
-0.007708462420850992,
-0.05340429022908211,
-0.027149232104420662,
-0.03852051869034767,
0.0002600049483589828,
0.006648136302828789,
0.03226562216877937,
0.026214612647891045,
-0.01843060366809368,
0.04015115648508072,
0.018892617896199226,
0.03756916895508766,
0.023702984675765038,
0.001762037049047649,
0.07690735906362534,
0.039426788687705994,
-0.02012604847550392,
-0.01440003514289856,
0.01829744689166546,
-0.0189859289675951,
0.01106201484799385,
0.042978737503290176,
-0.004601727705448866,
-0.027736978605389595,
0.037385664880275726,
-0.0012115244753658772,
0.00899248756468296,
-0.025560712441802025,
-0.04082225635647774,
-0.027786988765001297,
0.014905395917594433,
0.059625983238220215,
0.020411154255270958,
0.08447287976741791,
-0.01428980939090252,
-0.05512324348092079,
-0.025735601782798767,
-0.01020266953855753,
-0.01637415960431099,
0.04008518159389496,
-0.041158173233270645,
-0.04450985789299011,
0.04382960870862007,
-0.011299444362521172,
0.00683435145765543,
0.029018959030508995,
-0.0213945209980011,
-0.04373162239789963,
-0.0245938953012228,
-0.04716760665178299,
0.009426716715097427,
0.009228760376572609,
-0.014366667717695236,
-0.019323725253343582,
0.0003428374184295535,
0.0047318171709775925,
-0.03803631290793419,
-0.031023165211081505,
0.042274829000234604,
0.08181273192167282,
0.014989826828241348,
-0.02418479137122631,
0.01735072210431099,
-0.02949557639658451,
-0.018165530636906624,
-0.0020047293510288,
0.04315716773271561,
-0.007921111769974232,
0.028842473402619362,
0.012579691596329212,
-0.02193387784063816,
0.0590193048119545,
-0.0658593699336052,
-0.046331167221069336,
-0.012084153480827808,
0.025985704734921455,
-0.004953691270202398,
-0.0056433710269629955,
-0.06717287003993988,
-0.0073949433863162994,
0.00024984730407595634,
0.003547836095094681,
0.018290704116225243,
0.013157902285456657,
-0.0509883277118206,
-0.05417074263095856,
-0.03601595759391785,
0.01828160136938095,
-0.0682612732052803,
0.01157111395150423,
0.0038303083274513483,
-0.05292419344186783,
0.04600299894809723,
0.03486189618706703,
-0.03956133872270584,
-0.06590832769870758,
0.04787002131342888,
0.011614929884672165,
0.01688925363123417,
-0.007013093680143356,
-0.0892418697476387,
-0.04569915309548378,
0.027776477858424187,
-0.021489333361387253,
0.011843012645840645,
0.03210316598415375,
0.009422854520380497,
0.013485579751431942,
-0.0009680688381195068,
-0.030397342517971992,
-0.06660091131925583,
0.007688258774578571,
0.038469430059194565,
-0.008785140700638294,
0.013318556360900402,
0.0377187542617321,
-0.053785666823387146,
0.022337771952152252,
0.008529509417712688,
-0.03298204019665718,
0.019145911559462547,
-0.013026649132370949,
0.0008231918909586966,
-0.05128883942961693,
0.05251692235469818,
0.05938331037759781,
-0.051021162420511246,
-0.0423738956451416,
-0.07582978159189224,
0.06453555077314377,
-0.020739350467920303,
0.004197648726403713,
-0.020819418132305145,
0.010998012498021126,
-0.027247078716754913,
0.008761615492403507,
0.01737871766090393,
-0.04450727254152298,
-0.0636528804898262,
-0.008311321027576923,
-0.004641886800527573,
0.007307419553399086,
0.046978987753391266,
-0.08166658878326416,
-0.0032731813844293356,
-0.0035451462026685476,
0.025051360949873924,
0.04481874406337738,
-0.02105058915913105,
-0.0048535605892539024,
0.026011601090431213,
0.0711006447672844,
-0.07507525384426117,
0.056467462331056595,
-0.006611973512917757,
-0.01999269612133503,
0.0040517766028642654,
0.007182684261351824,
-0.030121302232146263,
-0.019215622916817665,
-0.10480815917253494,
0.03601706400513649,
0.0697813332080841,
0.04875244200229645,
-0.001948743243701756,
-0.0283761415630579,
-0.024248570203781128,
-0.07525112479925156,
0.007024653255939484,
0.0825958177447319,
-0.06678859889507294,
-0.02595784328877926,
-0.010943040251731873,
0.029267648234963417,
0.002605560002848506,
0.055567435920238495,
0.06623080372810364,
0.0014845422701910138,
-0.06836842745542526,
-0.023209132254123688,
0.03913704305887222,
0.013103092089295387,
0.05133461579680443,
0.07877534627914429,
-0.008313283324241638,
-0.0008214960689656436,
-0.05236624553799629,
0.0001483952219132334,
-0.01573600433766842,
-0.05336512625217438,
-0.0015239116037264466,
-0.012718379497528076,
0.014035441912710667,
-0.03529058024287224,
0.01540267001837492,
0.025437988340854645,
0.019934508949518204,
0.02088947966694832,
-0.041206568479537964,
-0.03677470609545708,
-0.04453490674495697,
0.011185575276613235,
-0.00505985738709569,
0.007432349491864443,
-0.06695453822612762,
0.03782059997320175,
0.00821763463318348,
-0.030366022139787674,
0.018734050914645195,
0.029080169275403023,
-0.03131258860230446,
0.026814641430974007,
-0.05624052882194519,
0.012846040539443493,
0.06069802865386009,
0.018564684316515923,
0.017667869105935097,
0.0023860358633100986,
-0.04327226057648659,
0.024726906791329384,
-0.003552098758518696,
-0.043902527540922165,
0.0053265755996108055,
0.01443681214004755,
-0.013576002791523933,
0.025745896622538567,
0.05517176166176796,
-0.045422013849020004,
-0.00809895247220993,
-0.0076503269374370575,
0.028255002573132515,
0.02830343134701252,
0.03519440069794655,
-0.048885952681303024,
-0.023825395852327347,
0.0029849293641746044,
-0.08580655604600906,
0.050617847591638565,
0.05254814401268959,
0.025318969041109085,
0.026061950251460075,
0.020087646320462227,
0.0020920992828905582,
-0.012638612650334835,
-0.06419062614440918,
-0.0016477034660056233,
-0.0622868575155735,
0.03626440465450287,
-0.036485858261585236,
-0.0020171068608760834,
0.004557735286653042,
0.03208605572581291,
0.025445111095905304,
-0.03606528043746948,
0.04110177606344223,
-0.09673523157835007,
0.004101267550140619,
0.040395013988018036,
0.021353675052523613,
-0.022625457495450974,
0.01409773901104927,
0.009850895032286644,
-0.012101965956389904,
0.04880295321345329,
0.047504618763923645,
0.003946335054934025,
-0.016535473987460136,
-0.04368302598595619,
-0.03245019540190697,
0.0020950285252183676,
-0.00029870233265683055,
-0.04459727928042412,
-0.010350191034376621,
0.01658375933766365,
0.02140365168452263,
-0.013822990469634533,
-0.02063499018549919,
0.050870466977357864,
0.025511108338832855,
0.09270618855953217,
0.011736253276467323,
0.0006113110575824976,
-0.004083031322807074,
0.04369071498513222,
-0.0006766283186152577,
0.020088545978069305,
-0.014852814376354218,
-0.034263186156749725,
-0.0420982725918293,
0.0007514093886129558,
-0.009999526664614677,
0.05036822333931923,
-0.007708718068897724,
0.03570430725812912,
-0.013781964778900146,
0.05624852329492569,
0.05068529397249222,
-0.01884549856185913,
0.04493749514222145,
0.012397886253893375,
0.027021080255508423,
0.05164242908358574,
-0.02690262719988823,
0.05769345536828041,
-0.008884322829544544,
-0.01889467053115368,
-0.05543477088212967,
-0.042582571506500244,
-0.029994294047355652,
-0.0009804156143218279,
-0.06917886435985565,
0.03226910158991814,
-0.006048185750842094,
-0.01905536837875843,
-0.01678970828652382,
0.0044984412379562855,
-0.01625174470245838,
0.04331699758768082,
-0.07797148078680038,
-0.004620987921953201,
0.004765767138451338,
0.06777486950159073,
0.011739867739379406,
-0.043110303580760956,
-0.02511095441877842,
0.014624375849962234,
-0.09836134314537048,
-0.04035963490605354,
0.05360987037420273,
0.004812272265553474,
0.038704901933670044,
0.016422994434833527,
0.039303719997406006,
-0.03407217934727669,
-0.018831850960850716,
0.019502103328704834,
-0.0482562817633152,
-0.04881095513701439,
0.02227560430765152,
-0.0690062940120697,
0.02573814056813717,
0.031918153166770935,
-0.028418783098459244,
-0.0017003050306811929,
0.022062942385673523,
0.06964170187711716,
-0.023967385292053223,
-0.008707020431756973,
0.044620219618082047,
0.0240367092192173,
-0.01818910799920559,
-0.07308637350797653,
-0.02792356349527836,
-0.005278596188873053,
0.05134952813386917,
0.025297068059444427,
-0.019301360473036766,
0.025378184393048286,
-0.05606121942400932,
0.009566917084157467,
-0.015341520309448242,
-0.04273655265569687,
0.012851525098085403,
-0.008134735748171806,
0.06992929428815842,
-0.027560792863368988,
-0.027493838220834732,
-0.017323462292551994,
0.02129887044429779,
0.00012128321395721287,
-0.04008721187710762,
-0.01580309495329857,
0.05393628031015396,
-0.040200624614953995,
-0.019460143521428108,
-0.035213734954595566,
0.000004864543825533474,
-0.03362007439136505,
0.033820923417806625,
0.011820985935628414,
0.00782421138137579,
-0.03239954262971878,
0.037853118032217026,
-0.006411231122910976,
-0.057581011205911636,
-0.025080587714910507,
0.01960703171789646,
0.06074553728103638,
0.05821697786450386,
-0.01235116831958294,
0.05420771241188049,
0.04595578834414482,
0.023737598210573196,
-0.036690112203359604,
0.03536740690469742,
0.0407181940972805,
0.012101331725716591,
0.014653678052127361,
-0.021899567916989326,
-0.007604105398058891,
0.0053381165489554405,
0.0491664744913578,
0.03665461018681526,
0.016899473965168,
-0.03276988863945007,
0.032706573605537415,
0.04693489894270897,
-0.01426965557038784,
-0.03014177270233631,
0.024818038567900658,
-0.055953823029994965,
-0.025751303881406784,
0.0031778716947883368,
0.04850776121020317,
-0.03440186753869057,
-0.06062914803624153,
-0.04353945329785347,
-0.007753915153443813,
0.002272329991683364,
0.03442462533712387,
0.06625854969024658,
0.055762115865945816,
0.022087672725319862,
0.030401060357689857,
-0.025269076228141785,
0.003165997564792633,
0.02706257253885269,
0.04207702726125717,
-0.039500802755355835,
0.009389450773596764,
0.019090911373496056,
0.0019492305582389235,
0.014601231552660465,
-0.05356207117438316,
0.059737883508205414,
-0.038018714636564255,
-0.06626366078853607,
-0.0425979346036911,
0.0234806127846241,
-0.004251433070749044,
-0.026454197242856026,
-0.013560998253524303,
-0.0490713007748127,
0.03254944086074829,
-0.05273659527301788,
-0.005459349136799574,
0.04045800864696503,
0.029920728877186775,
-0.06738957017660141,
0.044999442994594574,
-0.003975720144808292,
0.001413852209225297,
0.0014210803201422095,
-0.034304168075323105,
-0.008799443021416664,
-0.025975756347179413,
-0.057728298008441925,
0.020443232730031013,
0.04214058071374893,
-0.01195781771093607,
-0.0012380055850371718,
0.05971033126115799,
0.05313916876912117,
0.08036191016435623,
-0.010716882534325123,
0.023937471210956573,
-0.04454779252409935,
-0.019809536635875702,
-0.0565624013543129,
0.052533455193042755,
0.06049513444304466,
-0.019263649359345436,
-0.036255497485399246,
-0.06946209818124771,
-0.007910673506557941,
0.006934745702892542,
-0.04217333346605301,
0.023018117994070053,
0.034350402653217316,
-0.05600305274128914,
-0.016964003443717957,
0.03156307712197304,
0.002898275852203369,
0.0626974031329155,
-0.051417455077171326,
-0.031189413741230965,
0.05554933473467827,
-0.035220447927713394,
0.03717447817325592,
0.009421469643712044,
0.01306093204766512,
0.043741267174482346,
-0.015479647554457188,
0.07524172961711884,
-0.028238413855433464,
-0.0046809762716293335,
0.014389397576451302,
0.006824050564318895,
-0.05450055003166199,
0.023809058591723442,
0.024949809536337852,
-0.033705174922943115,
-0.0608009435236454,
0.040921151638031006,
0.014437874779105186,
0.006346666254103184,
-0.07703562825918198,
-0.042768463492393494,
0.02910836599767208,
0.00047790436656214297,
-0.02198145166039467,
0.004082647152245045,
-0.009393740445375443,
-0.024744991213083267,
-0.013248834758996964,
-0.015240282751619816,
-0.01463159266859293,
-0.022907616570591927,
-0.015858659520745277,
-0.024549538269639015,
0.016587091609835625,
0.014082260429859161,
-0.012330309487879276,
0.01405903697013855,
-0.05225837230682373,
-0.06568673253059387,
-0.008027665317058563,
-0.02275742031633854,
0.037135180085897446,
-0.011685251258313656,
-0.02322130836546421,
0.011078685522079468,
-0.0005208863294683397,
-0.04588567465543747,
-0.03699810057878494,
0.034412141889333725,
-0.025960519909858704,
0.0015070806257426739,
-0.014024892821907997,
0.028237612918019295,
0.029779132455587387,
0.024688031524419785,
0.0065991682931780815,
-0.005583116784691811,
-0.004330586176365614,
-0.008636126294732094,
-0.029057057574391365,
-0.00989220105111599,
0.021521177142858505,
-0.031162137165665627,
0.032120492309331894,
-0.04927840456366539,
0.018201619386672974,
0.0414937287569046,
-0.05210643261671066,
0.037678062915802,
0.01630202867090702,
0.01536223292350769,
-0.0009229753632098436,
0.017976216971874237,
-0.0045513431541621685,
0.0027577958535403013,
0.03409680724143982,
-0.03738939017057419,
0.010983317159116268,
-0.05102169141173363,
-0.029830463230609894,
0.04364897310733795,
0.014774629846215248,
0.04449208453297615,
0.014999217353761196,
-0.010687166824936867,
0.053584519773721695,
-0.02412973903119564,
0.01479587983340025,
0.07727771252393723,
0.0318426676094532,
0.010045060887932777,
-0.003608312690630555,
0.027997398748993874,
-0.03784298524260521,
-0.0024967670906335115,
0.008579361252486706,
-0.01749097742140293,
0.025211051106452942,
0.002320587867870927,
-0.0003891638189088553,
-0.03311256319284439,
-0.038879092782735825,
0.010647540912032127,
-0.03082893043756485,
-0.004321170970797539,
-0.09687667340040207,
0.010794722475111485,
-0.0164787657558918,
-0.026188068091869354,
0.036685679107904434,
0.009644033387303352,
0.01537309866398573,
0.03355785086750984,
0.007180203218013048,
-0.05100046843290329,
-0.07712263613939285,
-0.024850979447364807,
0.006228949408978224,
-0.03188588097691536,
0.00995649490505457,
-0.022448450326919556,
-0.03543122857809067,
0.03629226237535477,
-0.03887753561139107,
0.017145894467830658,
0.032903384417295456,
0.028056252747774124,
0.0015785150462761521,
0.006616910453885794,
0.10164371132850647,
0.019413545727729797,
0.0018538812873885036,
-0.03338427469134331,
0.0316329300403595,
-0.02680218406021595,
-0.008160294964909554,
-0.0800933837890625,
-0.02723892591893673,
-0.014123520813882351
] |
<p><img src="http://i.stack.imgur.com/orT7X.png" alt="enter image description here"></p>
<p>In the left side example of cantilever brakes, how do I find the tension in strings DE and DC, in terms of T. According to me applying force balance equations, horizontal and vertical forces should be zero</p>
<p>i.e. $T_{DE} \cos(45) + T_{DE} \cos(45) = T$...</p>
<p>The answer given is $T/2$, which is against general understanding.</p>
<p><strong>SOURCE:- Mechanics of Materials by JM Gere Ed2009- Problem 1.2.3</strong></p> | g6648 | [
0.04999784007668495,
0.004906171932816505,
-0.01799197308719158,
0.014704706147313118,
0.07315494865179062,
0.03439902141690254,
0.05836116150021553,
0.0161586944013834,
-0.04169495776295662,
-0.028209730982780457,
-0.07054080069065094,
-0.036448393017053604,
-0.03536612167954445,
-0.008314262144267559,
0.08544694632291794,
0.06603771448135376,
0.008938221260905266,
-0.02544245310127735,
0.03160812705755234,
-0.004777961410582066,
-0.01099968608468771,
-0.009666850790381432,
-0.026722939684987068,
-0.047522448003292084,
0.061948541551828384,
0.03216458484530449,
-0.04346851631999016,
0.004864024464040995,
-0.03892233595252037,
0.0014197751879692078,
-0.002199504990130663,
0.029145853593945503,
0.025599950924515724,
-0.06331898272037506,
-0.05778880417346954,
-0.031250450760126114,
0.03319086879491806,
0.009540234692394733,
-0.011224744841456413,
-0.0009596096351742744,
0.012841925956308842,
-0.01398816704750061,
0.03177434578537941,
-0.02872365713119507,
-0.021280862390995026,
-0.07218897342681885,
-0.06938895583152771,
0.013282451778650284,
-0.03972756862640381,
0.0015415328089147806,
0.007749233394861221,
-0.011558793485164642,
0.04689273238182068,
-0.02488567866384983,
-0.017482709139585495,
0.024988502264022827,
0.07748167961835861,
-0.05510082095861435,
-0.011329399421811104,
0.00562133127823472,
-0.04998476058244705,
0.026523498818278313,
0.006493566557765007,
0.001796087482944131,
-0.0159181896597147,
-0.020315513014793396,
0.002195394830778241,
0.017840778455138206,
0.0753885805606842,
0.021213917061686516,
-0.030200103297829628,
-0.0040571726858615875,
-0.006911570206284523,
-0.05109798163175583,
-0.06723172217607498,
-0.030124759301543236,
0.019037824124097824,
0.0328846350312233,
-0.0174910519272089,
-0.02371012233197689,
0.003554112045094371,
0.05398225411772728,
-0.0016166639979928732,
0.00883957464247942,
0.03744510933756828,
-0.0004871421551797539,
0.009353317320346832,
0.031343523412942886,
-0.0041782609187066555,
0.05787516385316849,
0.01477271318435669,
0.008148805238306522,
0.03966160863637924,
0.010530417785048485,
0.020034529268741608,
-0.042554840445518494,
0.004391990602016449,
0.09025745093822479,
0.008359269239008427,
-0.06678604334592819,
-0.019949933513998985,
-0.002763067139312625,
-0.032697804272174835,
-0.030979836359620094,
-0.0059695676900446415,
0.010322760790586472,
0.05823188275098801,
0.012808435596525669,
-0.033764198422431946,
-0.057074081152677536,
-0.054413408041000366,
0.01775233820080757,
-0.041668739169836044,
-0.05878879502415657,
0.01644289493560791,
0.03490334376692772,
0.032334599643945694,
0.001172711723484099,
-0.009098942391574383,
0.028752047568559647,
0.031064681708812714,
-0.026655975729227066,
-0.005904292222112417,
0.06033826619386673,
-0.006290811114013195,
-0.02689533494412899,
-0.020584672689437866,
0.04353711009025574,
0.022401386871933937,
-0.0662844181060791,
0.002309543779119849,
-0.004917277488857508,
0.07008297741413116,
-0.03448961675167084,
0.022750673815608025,
0.07745806872844696,
-0.024962561205029488,
0.00004365333734313026,
0.012627918273210526,
-0.005809021648019552,
0.0043084449134767056,
0.011363000608980656,
-0.006711848545819521,
0.04527558386325836,
-0.009844654239714146,
-0.010776173323392868,
-0.041595280170440674,
0.039291445165872574,
0.02390526793897152,
-0.059749625623226166,
0.028378400951623917,
0.03439520671963692,
0.005212290678173304,
0.004377945326268673,
-0.024862922728061676,
-0.0011260168394073844,
0.06561378389596939,
-0.018289824947714806,
-0.005368316546082497,
0.04848664626479149,
0.015047232620418072,
-0.0005788501584902406,
0.03140246123075485,
-0.03226516395807266,
-0.06903141736984253,
0.025402026250958443,
-0.009611261077225208,
0.035151999443769455,
0.043044328689575195,
-0.0189723651856184,
-0.09868234395980835,
-0.01153076346963644,
0.02489691786468029,
-0.013304636813700199,
0.03351207822561264,
0.026015715673565865,
0.010298354551196098,
-0.05547920614480972,
0.0500749871134758,
0.006532460916787386,
0.04265446588397026,
-0.04096426069736481,
0.062252018600702286,
0.03825319930911064,
-0.015047676861286163,
-0.004575981758534908,
0.03197145834565163,
0.019973156973719597,
-0.04308971390128136,
0.012818398885428905,
-0.030172284692525864,
0.026705775409936905,
-0.03206660598516464,
-0.0252083633095026,
-0.05412137508392334,
-0.01863716170191765,
-0.02836044691503048,
-0.0646359920501709,
0.02598670683801174,
0.05423939600586891,
-0.00904853641986847,
0.04555780813097954,
0.020179925486445427,
-0.0020587146282196045,
-0.04053378105163574,
-0.006828693673014641,
0.019360123202204704,
-0.008782102726399899,
0.02387002296745777,
-0.004132390953600407,
-0.045307476073503494,
-0.013222905807197094,
0.007104736287146807,
0.0007634610519744456,
-0.05333137512207031,
-0.06699207425117493,
0.024183275178074837,
0.04756913334131241,
-0.04014844074845314,
0.0026083795819431543,
-0.05971373990178108,
-0.024492302909493446,
-0.0036475281231105328,
-0.00400205235928297,
-0.0633445680141449,
-0.03891604393720627,
-0.008934647776186466,
0.027698233723640442,
-0.022817309945821762,
-0.004147959873080254,
-0.020897842943668365,
-0.027470914646983147,
-0.039935555309057236,
0.03415288031101227,
0.07407563924789429,
0.059864312410354614,
0.027512501925230026,
0.020220013335347176,
-0.004972646478563547,
0.033666882663965225,
0.03561791032552719,
-0.0276041217148304,
0.034256067126989365,
0.007905524224042892,
0.04054718464612961,
0.03227551281452179,
0.0166550911962986,
0.049944259226322174,
-0.0036138847935944796,
0.000169296283274889,
0.034429218620061874,
-0.0700036808848381,
0.014944790862500668,
0.0775580033659935,
0.02499878592789173,
-0.03840286284685135,
-0.05826079100370407,
-0.01677403599023819,
-0.013148731552064419,
-0.027785183861851692,
-0.013973942957818508,
0.03906389698386192,
0.06154790148139,
0.0587177649140358,
-0.08558700233697891,
-0.03920060396194458,
-0.04499201476573944,
-0.12307928502559662,
0.06196334958076477,
-0.006676510442048311,
-0.0009049735381267965,
0.004503224045038223,
-0.057500362396240234,
0.021848265081644058,
-0.0052391537465155125,
-0.11365540325641632,
0.023652315139770508,
-0.008431198075413704,
-0.041110169142484665,
0.006494633387774229,
0.041819360107183456,
0.016396140679717064,
0.05536745488643646,
0.028425369411706924,
-0.002616016659885645,
0.021242182701826096,
-0.025778716430068016,
-0.018529772758483887,
-0.006303057074546814,
0.02210625261068344,
-0.046392206102609634,
0.07052052766084671,
0.05552826076745987,
-0.016878413036465645,
0.022069547325372696,
0.054020803421735764,
0.001108188764192164,
-0.037139348685741425,
-0.04567250981926918,
0.014088531024754047,
-0.039021339267492294,
0.007130054756999016,
0.0325716957449913,
0.008532574400305748,
-0.00977868027985096,
-0.056550558656454086,
0.0005556911928579211,
0.0014641981106251478,
0.06165879964828491,
0.020975010469555855,
-0.004312146455049515,
-0.0012384499423205853,
0.04954083636403084,
-0.07626377046108246,
-0.056042321026325226,
0.030139733105897903,
0.08071210980415344,
-0.04842266067862511,
-0.022238334640860558,
-0.042457301169633865,
-0.021026944741606712,
-0.08115669339895248,
0.06617017835378647,
0.020896777510643005,
-0.051681436598300934,
0.05882447957992554,
-0.029510580003261566,
0.010440535843372345,
-0.030494771897792816,
-0.021568330004811287,
0.0216305423527956,
-0.0024703452363610268,
0.05879690870642662,
-0.05130184441804886,
0.008776490576565266,
-0.03284502029418945,
0.024092799052596092,
-0.01771598681807518,
0.04453738033771515,
0.039850879460573196,
-0.03585470840334892,
-0.024103598669171333,
-0.011347954161465168,
0.01709434948861599,
-0.0027945174369961023,
-0.008468965999782085,
0.04570714011788368,
0.10769960284233093,
0.05663776025176048,
-0.04770255088806152,
0.008093205280601978,
-0.018652480095624924,
-0.00043117860332131386,
0.008740696124732494,
0.016547923907637596,
0.02201845869421959,
0.03908831626176834,
0.007584292907267809,
-0.04085593298077583,
0.01646718941628933,
0.023331530392169952,
0.0018610424594953656,
-0.07596409320831299,
0.009587411768734455,
0.026299109682440758,
-0.023933691903948784,
0.012197157368063927,
0.06244412809610367,
-0.02348286844789982,
-0.022517431527376175,
0.03372597321867943,
0.02396542578935623,
0.03938442841172218,
-0.009178733453154564,
0.047047361731529236,
-0.05259735509753227,
0.03849327936768532,
-0.03956529498100281,
0.014933518134057522,
0.033098023384809494,
0.03845193609595299,
0.023681873455643654,
0.02684278041124344,
0.011330349370837212,
0.023107565939426422,
-0.006336945574730635,
0.016694463789463043,
0.0347680039703846,
-0.015943991020321846,
-0.001906442572362721,
-0.0004194672219455242,
-0.021061621606349945,
-0.03357500210404396,
0.01422104611992836,
-0.02871564030647278,
0.014030646532773972,
0.039774052798748016,
0.03902466967701912,
-0.06554755568504333,
-0.020085198804736137,
0.012900195084512234,
0.02572455257177353,
0.002223030664026737,
-0.007576439063996077,
-0.011705405078828335,
0.05559831112623215,
0.003432230092585087,
-0.01831240952014923,
0.03675597161054611,
0.02353942021727562,
0.07377860695123672,
-0.08419721573591232,
0.0018554653506726027,
-0.020720167085528374,
0.05030885338783264,
0.006805162876844406,
0.05777037516236305,
0.058862797915935516,
0.04656638950109482,
-0.01506555825471878,
0.02792954631149769,
0.05817017704248428,
-0.018825901672244072,
-0.013234919868409634,
-0.02791823446750641,
0.05178775265812874,
-0.02193060703575611,
0.038312725722789764,
0.049811482429504395,
-0.00806669145822525,
-0.01704201102256775,
-0.02096528373658657,
0.021245455369353294,
0.013116412796080112,
-0.03556932881474495,
0.061763957142829895,
0.01117753703147173,
0.05372920632362366,
-0.021796438843011856,
0.04384922981262207,
0.01794729009270668,
0.03370042145252228,
0.000485809869132936,
-0.008286019787192345,
-0.06100023165345192,
0.03561782091856003,
-0.042060088366270065,
-0.044172756373882294,
0.002328588394448161,
-0.043923377990722656,
-0.04644528403878212,
-0.015996403992176056,
-0.02703973650932312,
-0.025469249114394188,
-0.014765091240406036,
-0.03842506557703018,
-0.004789098631590605,
0.018461838364601135,
-0.004033700097352266,
-0.010234125889837742,
0.02608310617506504,
-0.03478046879172325,
0.005294401198625565,
-0.0013164080446586013,
-0.0071031213738024235,
0.005769351962953806,
0.03675739839673042,
0.024328745901584625,
-0.03759549558162689,
0.01634599268436432,
-0.008319634012877941,
0.05348176509141922,
0.0078547652810812,
0.00400385819375515,
-0.007292375434190035,
-0.005435221362859011,
0.03996817767620087,
-0.013998816721141338,
0.08126211911439896,
-0.023156482726335526,
-0.01077476516366005,
0.02107621170580387,
-0.0238094050437212,
-0.021985039114952087,
0.005510121583938599,
-0.0532897487282753,
-0.0021710346918553114,
-0.03633880987763405,
0.009008696302771568,
0.0062871105037629604,
-0.012136729434132576,
0.04673205316066742,
-0.049207113683223724,
-0.0567808523774147,
-0.007851979695260525,
-0.0240041371434927,
-0.008331162855029106,
-0.04551553353667259,
-0.07201254367828369,
-0.029293198138475418,
-0.05978880077600479,
-0.0019437676528468728,
-0.0016801427118480206,
0.02909589558839798,
-0.039849791675806046,
0.029921291396021843,
0.003903847187757492,
0.020337846130132675,
0.00784569326788187,
-0.011058436706662178,
-0.0202036090195179,
0.006049788556993008,
0.018459802493453026,
0.03783411905169487,
-0.0017659926088526845,
0.011505521833896637,
0.05683065950870514,
0.007865151390433311,
-0.032711006700992584,
0.01189052127301693,
0.05823943018913269,
0.013808023184537888,
0.045886676758527756,
-0.024109812453389168,
-0.01671571284532547,
-0.03476395457983017,
-0.0008236009743995965,
-0.033301323652267456,
-0.022232474759221077,
-0.025997363030910492,
-0.05444057285785675,
-0.022982100024819374,
-0.002416834933683276,
-0.04852497577667236,
-0.0020097827073186636,
-0.02338540181517601,
-0.002173907123506069,
-0.0152857955545187,
-0.0349641889333725,
-0.013875449076294899,
0.01977667212486267,
0.006677404046058655,
0.008433595299720764,
0.03271499276161194,
-0.02282826229929924,
0.012225535698235035,
-0.03138110041618347,
-0.04574720188975334,
0.031671296805143356,
-0.01865757815539837,
-0.02917693741619587,
0.030484279617667198,
-0.045887771993875504,
0.007183191366493702,
0.005549621768295765,
0.029211871325969696,
-0.0108371302485466,
-0.06172119081020355,
-0.03345685079693794,
-0.0013005792861804366,
0.042671117931604385,
0.01608535833656788,
0.002455485286191106,
0.01684148982167244,
0.004729310050606728,
0.025359518826007843,
-0.042812950909137726,
0.03464442491531372,
0.050337981432676315,
0.03985666483640671,
0.07178337126970291,
0.005192285403609276,
0.0013832624536007643,
0.07873506098985672,
0.03560376912355423,
0.0156891830265522,
-0.06252804398536682,
-0.030900875106453896,
-0.04363445192575455,
0.026745958253741264,
-0.04498806595802307,
0.044439490884542465,
0.006549648474901915,
-0.0296440701931715,
-0.014533279463648796,
0.05831470713019371,
-0.036501433700323105,
-0.11488877981901169,
0.0350959450006485,
-0.03428255394101143,
0.020704109221696854,
0.010640619322657585,
-0.02441979944705963,
0.018778346478939056,
0.023685164749622345,
0.011165427044034004,
0.047569334506988525,
0.05232573300600052,
0.027881991118192673,
0.048950787633657455,
0.05484602600336075,
0.05227166786789894,
0.032416243106126785,
-0.00458566565066576,
0.052577905356884,
-0.0691794827580452,
0.03168904781341553,
0.018855439499020576,
-0.08784569799900055,
-0.011041009798645973,
0.015448855236172676,
-0.015600863844156265,
-0.019613010808825493,
0.02068556472659111,
0.011450564488768578,
0.0076192826963961124,
-0.0007305457256734371,
0.012143773026764393,
0.001108453026972711,
-0.028848525136709213,
-0.02750079147517681,
-0.044368211179971695,
0.04058079048991203,
0.008053958415985107,
0.007397419773042202,
-0.011108104139566422,
-0.09773913770914078,
0.0022666689474135637,
0.021552573889493942,
0.002976813353598118,
0.018773240968585014,
-0.005440154112875462,
0.0031196274794638157,
0.018120799213647842,
0.0027464109007269144,
0.10656715929508209,
-0.03539907932281494,
-0.021558934822678566,
0.04911345615983009,
0.04004532843828201,
-0.0029237098060548306,
-0.007861468009650707,
0.02496080845594406,
-0.052630990743637085,
0.02058524452149868,
0.004815967287868261,
0.01726037636399269,
-0.03852565959095955,
-0.020888572558760643,
0.05784231051802635,
0.006167768035084009,
0.0045203473418951035,
-0.018204933032393456,
0.01332128420472145,
-0.019337566569447517,
0.003885352285578847,
0.01691298559308052,
-0.05614442750811577,
0.04430687427520752,
-0.03576179966330528,
-0.035464394837617874,
0.029463835060596466,
0.05760597810149193,
0.005872953683137894,
-0.006117471028119326,
0.056309718638658524,
0.011690719053149223,
-0.005285147577524185,
-0.006222874391824007,
-0.000995161710307002,
-0.003993268124759197,
-0.03717305138707161,
0.007069431245326996,
-0.021557491272687912,
0.0407923087477684,
0.04204433411359787,
-0.035895127803087234,
0.01198728010058403,
0.028644373640418053,
-0.028189275413751602,
0.004448122810572386,
-0.0027789201121777296,
-0.08677983283996582,
0.0022294095251709223,
-0.04182993248105049,
0.05450769141316414,
0.011950727552175522,
-0.0037925560027360916,
-0.015420492738485336,
0.006068493705242872,
0.008148920722305775,
0.11653118580579758,
-0.0074395607225596905,
-0.028972255066037178,
-0.022602509707212448,
-0.040704768151044846,
0.03792557120323181,
0.06424904614686966,
0.008575881831347942,
-0.0116495406255126,
-0.00042464619036763906,
-0.025738397613167763,
-0.008151920512318611,
0.062061410397291183,
-0.033121176064014435,
-0.023159919306635857,
-0.053293369710445404,
-0.07709678262472153,
-0.055516358464956284,
-0.009105215780436993,
0.0001955949264811352,
0.0037521638441830873,
-0.06301090866327286,
0.03570296987891197,
0.038759712129831314,
-0.011435930617153645,
-0.020119622349739075,
-0.005401841830462217,
0.025801347568631172,
0.019627509638667107,
-0.04224126413464546,
-0.06297007203102112,
0.03860146924853325,
-0.08018387854099274,
-0.08190726488828659,
-0.004114795476198196,
-0.003732583485543728,
-0.018484635278582573,
-0.017258260399103165,
0.02186489850282669,
0.003193987999111414,
0.02041487768292427,
0.04821581766009331,
-0.02077571675181389,
-0.008029277436435223,
0.009390332736074924,
-0.002095441333949566,
-0.049708303064107895,
-0.03357324004173279,
-0.010408584028482437,
0.0034445011988282204,
-0.06711210310459137,
-0.03639889135956764,
-0.006023835856467485,
0.04061504825949669,
-0.018827252089977264,
-0.06099850311875343,
-0.00761778000742197,
0.021226173266768456,
-0.039328690618276596,
0.04008995369076729,
-0.048392537981271744,
0.02579939179122448,
0.006481945980340242,
-0.05586060509085655,
-0.06516627222299576,
0.01883358508348465,
-0.024833152070641518,
0.011311338283121586,
-0.0034621693193912506,
-0.004262613132596016,
0.04450298100709915,
-0.05082837492227554,
-0.03380909934639931,
0.02852005884051323,
-0.022753145545721054,
-0.03569376468658447,
0.029612433165311813
] |
<p>As any light reflected or emitted from objects inside a black hole (if it is possible to be there) does not leave the event horizon and comes back inside, would it be like seeing yourself?</p>
<p>What I mean is that would the light we might emit/reflect return to our eyes and make us sort of look at ourselves? </p> | g6649 | [
-0.0239707138389349,
0.0032647543121129274,
0.04332872852683067,
-0.001407713396474719,
-0.015380152501165867,
0.01624464988708496,
0.004733889829367399,
0.040875520557165146,
0.0015321398386731744,
-0.04215230792760849,
0.03587333485484123,
0.055541444569826126,
0.040914248675107956,
-0.024084821343421936,
-0.03684449940919876,
-0.043770551681518555,
0.03763732686638832,
-0.03876335546374321,
-0.019576579332351685,
-0.026350220665335655,
0.025998039171099663,
-0.0062496718019247055,
-0.00201324000954628,
-0.03202072158455849,
-0.07047664374113083,
0.03812223672866821,
0.014584087766706944,
-0.02227378822863102,
-0.017602451145648956,
-0.011030798777937889,
0.04898766800761223,
0.001236693817190826,
0.004953450057655573,
-0.019252123311161995,
0.03551958501338959,
0.0035574156790971756,
0.01786063425242901,
0.08790483325719833,
-0.008694222196936607,
0.012230230495333672,
-0.016597433015704155,
-0.01795043610036373,
-0.01729142852127552,
-0.024705499410629272,
0.018026070669293404,
0.023659585043787956,
0.04579602926969528,
0.011107861064374447,
0.06702660024166107,
-0.029739033430814743,
0.012898564338684082,
-0.023244401440024376,
0.02380642481148243,
0.04909372329711914,
0.06878966838121414,
0.010447710752487183,
-0.005074169021099806,
-0.0004946187837049365,
0.04536668583750725,
-0.019679494202136993,
-0.023017166182398796,
0.012101591564714909,
0.04487869516015053,
0.04222865775227547,
0.016339875757694244,
-0.014211219735443592,
-0.08652663975954056,
-0.00003978354288847186,
-0.033817358314991,
-0.0010558853391557932,
0.03602350503206253,
0.05303911119699478,
-0.06337326765060425,
-0.01234771404415369,
0.000023962649720488116,
0.04716923087835312,
0.018094653263688087,
0.02769232913851738,
0.0018091467209160328,
-0.009371763095259666,
-0.05105127766728401,
-0.059090789407491684,
-0.002388512948527932,
0.02170342393219471,
0.06469743698835373,
0.04163694009184837,
-0.013061627745628357,
-0.04579095169901848,
-0.0012142941122874618,
0.014972837641835213,
0.0862002745270729,
-0.03674960508942604,
0.028763528913259506,
0.03942003473639488,
-0.02082190476357937,
0.01589619368314743,
0.032535430043935776,
-0.006708693690598011,
0.001627687830477953,
0.06494680792093277,
-0.06201326847076416,
-0.009217885322868824,
-0.03574658930301666,
-0.01079491339623928,
0.01998264156281948,
-0.0496390201151371,
-0.02285890467464924,
0.011979966424405575,
-0.04640374705195427,
0.030239490792155266,
-0.02674916386604309,
-0.10108241438865662,
-0.03519180417060852,
-0.00013807885989081115,
-0.07060494273900986,
-0.015461176633834839,
0.05793042853474617,
-0.011858814395964146,
-0.01798936538398266,
0.09754712134599686,
0.026641540229320526,
-0.0001905107346829027,
-0.00030018165125511587,
0.020164595916867256,
0.04905395209789276,
0.01328070368617773,
-0.04003779590129852,
-0.0418085977435112,
0.024734782055020332,
-0.01977418176829815,
-0.014147316105663776,
0.014333928003907204,
-0.031603943556547165,
0.09328431636095047,
0.012136156670749187,
-0.01159617304801941,
0.03760356456041336,
-0.013308636844158173,
0.030961228534579277,
0.005101427435874939,
0.04354194551706314,
-0.014863855205476284,
-0.018141547217965126,
0.0026610626373440027,
-0.0026229757349938154,
-0.0008409183938056231,
-0.0018288494320586324,
-0.05628398433327675,
0.0008626916096545756,
0.05347742140293121,
-0.022694576531648636,
0.06508025527000427,
0.022687094286084175,
0.0032462060917168856,
-0.05441652610898018,
-0.03807413950562477,
0.01110078115016222,
0.04144173488020897,
-0.039757516235113144,
0.0073404270224273205,
0.08081933110952377,
-0.04019719362258911,
0.0011418333742767572,
0.027721788734197617,
-0.011401454918086529,
-0.06484542787075043,
-0.021960677579045296,
-0.029131194576621056,
0.04086105525493622,
-0.041500821709632874,
0.02073059231042862,
0.011548450216650963,
-0.0187512319535017,
0.03527770936489105,
0.031716883182525635,
-0.006181045435369015,
-0.01736462116241455,
0.03858686238527298,
-0.04349828511476517,
0.014643962495028973,
0.0021012581419199705,
-0.02344619296491146,
-0.06390256434679031,
-0.05469866469502449,
0.012780317105352879,
-0.05813799425959587,
0.02757805772125721,
0.04199376329779625,
0.04640983045101166,
0.014246570877730846,
0.011387228965759277,
-0.014062728732824326,
0.031298357993364334,
0.010421646758913994,
0.030006995424628258,
-0.03993695601820946,
-0.00815910380333662,
-0.011504272930324078,
0.05843228101730347,
0.0707998126745224,
0.041564375162124634,
0.019140416756272316,
0.014606551267206669,
-0.007444484159350395,
0.0057399095967411995,
-0.009851145558059216,
0.03326908499002457,
-0.038018736988306046,
-0.01741374097764492,
-0.07915918529033661,
0.03416988626122475,
-0.013710025697946548,
0.05228620395064354,
-0.021648604422807693,
-0.01788044162094593,
0.04736757650971413,
-0.04428466409444809,
0.038520697504282,
0.009726867079734802,
0.04173891991376877,
-0.02467615343630314,
0.026977742090821266,
-0.005516801495105028,
-0.03254934027791023,
-0.029037119820713997,
0.05363955721259117,
-0.08456685394048691,
-0.01691638119518757,
0.007634854409843683,
-0.0016870941035449505,
-0.05324805900454521,
-0.03190089017152786,
-0.012885505333542824,
0.015643354505300522,
0.032115742564201355,
-0.0011519237887114286,
-0.04353085532784462,
0.027548005804419518,
0.017101531848311424,
0.007455251645296812,
-0.008095575496554375,
-0.03625955805182457,
-0.06705880165100098,
-0.037000373005867004,
0.03143961355090141,
0.009284377098083496,
-0.01040107011795044,
0.04757583513855934,
0.048780884593725204,
0.018639253452420235,
0.018322838470339775,
0.008325062692165375,
-0.02124939300119877,
-0.04963197559118271,
0.009194828569889069,
-0.009533282369375229,
0.01886913552880287,
0.048248495906591415,
-0.04712880775332451,
0.0017456929199397564,
-0.018060091882944107,
-0.025749346241354942,
-0.029090560972690582,
0.045860908925533295,
-0.03358948603272438,
0.008116784505546093,
-0.009604323655366898,
-0.0029813593719154596,
0.013189288787543774,
0.06461294740438461,
-0.02060682699084282,
0.02762784995138645,
0.02415764145553112,
-0.005420529283583164,
0.02586408704519272,
0.010455065406858921,
-0.04170728474855423,
0.004589115735143423,
0.051489561796188354,
0.007655960042029619,
-0.0070896572433412075,
-0.03509347140789032,
-0.052128009498119354,
-0.0182332806289196,
-0.041511036455631256,
-0.06229383870959282,
0.0071602133102715015,
0.003564838320016861,
0.03294477239251137,
0.0270377267152071,
-0.018148714676499367,
0.02657158672809601,
-0.03215327858924866,
0.03222065418958664,
-0.012682048603892326,
0.01668095961213112,
0.03276851028203964,
0.03452331945300102,
0.003852325025945902,
0.02836637571454048,
0.009224984794855118,
0.0006652529700659215,
-0.010678875260055065,
0.016508817672729492,
-0.04261097311973572,
-0.013942183926701546,
-0.016815993934869766,
0.020264320075511932,
0.033474572002887726,
-0.000880238541867584,
-0.000448943639639765,
0.010342826135456562,
0.020861094817519188,
0.040096040815114975,
0.021285222843289375,
-0.00010536659829085693,
0.005599826108664274,
-0.004010195378214121,
-0.00452469801530242,
-0.03760111331939697,
-0.007261150050908327,
0.05356670916080475,
-0.005313768982887268,
0.006508509628474712,
0.03317932039499283,
0.022704821079969406,
0.006582960486412048,
-0.030939696356654167,
-0.054946914315223694,
-0.030138013884425163,
-0.027204889804124832,
0.027587469667196274,
-0.012348681688308716,
0.012384694069623947,
0.027949251234531403,
-0.02606513351202011,
-0.04743750020861626,
0.003713093465194106,
0.033125314861536026,
0.0391613245010376,
0.08477388322353363,
-0.0377812497317791,
-0.013155411928892136,
-0.02712298557162285,
0.03497333824634552,
-0.009189257398247719,
-0.03378636762499809,
-0.0367516428232193,
-0.018666474148631096,
-0.014860434457659721,
0.03744499012827873,
-0.014149541966617107,
0.023675573989748955,
-0.044106971472501755,
0.02882068045437336,
-0.037795159965753555,
0.0555194728076458,
0.04254120960831642,
0.03819999471306801,
-0.015953829512000084,
-0.017071688547730446,
-0.06306301057338715,
0.04331200569868088,
-0.08775829523801804,
0.017455117776989937,
-0.06506059318780899,
0.019137322902679443,
0.02717450074851513,
0.02779320813715458,
0.03028448112308979,
-0.009049288928508759,
0.01710972748696804,
-0.02422679401934147,
-0.01402701623737812,
-0.051170121878385544,
-0.06925322115421295,
0.04719525948166847,
0.0034469999372959137,
-0.004949145019054413,
-0.024945365265011787,
0.002180797280743718,
-0.013448049314320087,
0.00992597360163927,
0.0034755023662000895,
0.01515701599419117,
0.020800497382879257,
-0.004334277007728815,
-0.07213687151670456,
-0.0035199651028960943,
-0.010646309703588486,
-0.004438588861376047,
0.002244623377919197,
0.014590495266020298,
-0.09825334697961807,
-0.017736118286848068,
0.03520682454109192,
-0.0012649840209633112,
-0.044747259467840195,
0.01687721349298954,
-0.04562455415725708,
0.009867136366665363,
0.0211839210242033,
0.04117213562130928,
0.06361565738916397,
0.03197325021028519,
0.006651428062468767,
0.03678309544920921,
-0.03126157820224762,
-0.030146516859531403,
-0.048079054802656174,
-0.03403700143098831,
0.01910402439534664,
-0.03709689900279045,
0.015515363775193691,
0.00476679066196084,
-0.004480347037315369,
0.041330091655254364,
0.00992168951779604,
0.05474972724914551,
0.013134332373738289,
0.028566043823957443,
-0.02394186705350876,
0.0115354023873806,
0.07971753925085068,
-0.014551489613950253,
-0.011452481150627136,
-0.013035549782216549,
0.024240948259830475,
-0.04992343485355377,
-0.005157948937267065,
-0.0483776330947876,
-0.026844540610909462,
-0.015504928305745125,
0.017386993393301964,
-0.026751220226287842,
0.05257038027048111,
-0.04246596246957779,
0.004434899426996708,
0.016209889203310013,
-0.010521158576011658,
0.02568315528333187,
0.009961257688701153,
0.03383008763194084,
-0.0025231114123016596,
0.02149379625916481,
0.05473580211400986,
0.03357327729463577,
0.048047974705696106,
0.0358438603579998,
-0.017176732420921326,
-0.04718303680419922,
0.001099359360523522,
0.008411787450313568,
-0.07901518046855927,
-0.049897219985723495,
-0.0011903384001925588,
-0.0457737073302269,
0.0436798520386219,
-0.028994055464863777,
0.00316813588142395,
0.028924020007252693,
-0.03076784312725067,
0.04668217524886131,
0.03180750459432602,
0.010557224042713642,
-0.005115966312587261,
-0.07237789034843445,
-0.023783689364790916,
-0.016018729656934738,
-0.021210193634033203,
-0.08575363457202911,
0.05198289826512337,
0.008869706653058529,
0.011017690412700176,
-0.0330694317817688,
0.028813842684030533,
0.02117922715842724,
-0.0008556635002605617,
-0.010974349454045296,
-0.04644188657402992,
-0.02652103081345558,
-0.00023513143241871148,
0.04670273885130882,
-0.054203614592552185,
-0.028687505051493645,
0.04061764106154442,
-0.05403026193380356,
0.04362800717353821,
-0.04675044119358063,
-0.014836695976555347,
-0.029013285413384438,
-0.07191145420074463,
-0.027161937206983566,
-0.04498365893959999,
-0.04620438814163208,
-0.03200322762131691,
-0.010721931234002113,
-0.0005437556537799537,
0.018915066495537758,
0.015733366832137108,
-0.05611643195152283,
-0.02980717085301876,
-0.0012102389009669423,
0.006749883759766817,
-0.03405550494790077,
0.0034096878953278065,
-0.0026311606634408236,
-0.02858513779938221,
0.028382722288370132,
0.07620732486248016,
0.02144596353173256,
-0.023223653435707092,
-0.07389124482870102,
0.03223560377955437,
0.03335056081414223,
-0.04514742270112038,
-0.043928809463977814,
-0.004311276599764824,
0.04531830921769142,
-0.017109891399741173,
-0.04575334116816521,
-0.007817615754902363,
0.026808617636561394,
0.015820734202861786,
0.04576531797647476,
0.043863724917173386,
-0.03368600085377693,
0.02017023414373398,
0.04711698368191719,
-0.01780950091779232,
0.05208838731050491,
0.03727451339364052,
0.04593293368816376,
-0.028538094833493233,
0.04252297803759575,
-0.029239067807793617,
0.013954604975879192,
0.02622004598379135,
0.05291074514389038,
-0.01139377523213625,
-0.027998510748147964,
-0.00016365903138648719,
-0.02585960179567337,
0.019859740510582924,
0.0631944090127945,
-0.001051575061865151,
-0.009525268338620663,
0.01852433755993843,
-0.03709005191922188,
-0.016033511608839035,
-0.004427238833159208,
0.07134076207876205,
-0.044932059943675995,
0.060748495161533356,
0.00840143021196127,
0.008355864323675632,
0.00691392133012414,
0.008904213085770607,
-0.024635201320052147,
-0.06757088005542755,
0.031386133283376694,
-0.020021596923470497,
-0.03510207310318947,
-0.0751507431268692,
0.0022849170491099358,
0.003004113445058465,
0.039550259709358215,
0.03061133436858654,
0.010817205533385277,
-0.01659402996301651,
0.04090389981865883,
-0.047681812196969986,
0.02535712532699108,
-0.030674036592245102,
-0.036760132759809494,
0.03300650045275688,
0.05505189672112465,
0.006176677532494068,
-0.019490668550133705,
-0.045873917639255524,
0.028719047084450722,
-0.014239383861422539,
0.07830810546875,
-0.05277277156710625,
-0.004231204278767109,
-0.05227163806557655,
-0.00020361706265248358,
0.08197930455207825,
0.0341964066028595,
-0.0327436625957489,
-0.02697352133691311,
0.004262660164386034,
0.024867430329322815,
-0.07656098902225494,
-0.022761434316635132,
-0.03742307424545288,
-0.041066378355026245,
-0.041407261043787,
-0.008290383964776993,
-0.030735857784748077,
-0.045823995023965836,
0.03774604573845863,
-0.002952516544610262,
0.007998176850378513,
0.03404022380709648,
0.0568159818649292,
-0.04843507334589958,
0.01850091852247715,
0.06325185298919678,
0.024525314569473267,
0.059624478220939636,
-0.01584574021399021,
-0.02271120622754097,
0.04749515280127525,
-0.020570222288370132,
0.029424628242850304,
-0.032687243074178696,
-0.057670075446367264,
0.03648316115140915,
-0.046297114342451096,
-0.009200284257531166,
0.013613397255539894,
0.015952276065945625,
-0.00448211096227169,
-0.026249825954437256,
0.04066348448395729,
-0.08746810257434845,
0.026533136144280434,
0.030915692448616028,
0.08450420945882797,
0.02894119918346405,
-0.0057539925910532475,
0.018442092463374138,
0.05469096079468727,
0.047240544110536575,
0.03486327826976776,
0.023581309244036674,
-0.028088226914405823,
-0.058959949761629105,
-0.07190636545419693,
0.007025860249996185,
-0.008825143799185753,
-0.004599285777658224,
0.012216475792229176,
-0.08174740523099899,
0.07265741378068924,
0.025255758315324783,
-0.029819997027516365,
-0.05850615352392197,
0.01549422275274992,
0.014797864481806755,
-0.013387015089392662,
-0.011660978198051453,
-0.03054412640631199,
-0.03673529624938965,
-0.05912412703037262,
-0.03327217325568199,
0.054318636655807495,
-0.043668318539857864,
-0.07790165394544601,
0.0033454885706305504,
0.030505074188113213,
-0.1048455685377121,
-0.04455675929784775,
-0.007979877293109894,
0.011450029909610748,
0.012308647856116295,
-0.004852321930229664,
0.0012129426468163729,
0.059643831104040146,
-0.00599076971411705,
-0.0597536638379097,
-0.04677543789148331,
0.008783182129263878,
-0.06626202166080475,
-0.04967067763209343,
-0.018199484795331955,
0.1368422955274582,
0.022956399247050285,
0.04698098078370094,
0.01479820441454649,
0.017121488228440285,
0.006363051012158394,
0.07164762169122696,
-0.04024006798863411,
0.03481069207191467,
0.03917217627167702,
-0.042721670120954514,
-0.005741593427956104,
-0.007673954591155052,
-0.0730995163321495,
0.03784520551562309,
-0.017810095101594925,
-0.07655611634254456,
-0.011600266210734844,
-0.01318176556378603,
0.029869096353650093,
0.021249454468488693,
0.009850245900452137,
-0.008287206292152405,
-0.022699078544974327,
0.061313483864068985,
0.06418021768331528,
-0.04799606651067734,
-0.0012098689330741763,
-0.04683426395058632,
-0.02927444688975811,
-0.020919937640428543,
-0.00986680667847395,
-0.010459152981638908,
0.04589037969708443,
0.07343585789203644,
-0.04067784547805786,
0.04317011311650276,
-0.008988682180643082,
-0.03676416352391243,
-0.007551256101578474,
0.012146621011197567,
0.015226298943161964,
-0.034540969878435135,
-0.0018541284371167421,
0.032805997878313065,
-0.018850285559892654,
0.05604725331068039,
-0.008482161909341812,
0.023468894883990288,
0.005894903559237719,
-0.03941617161035538,
0.014865955337882042,
-0.03735315427184105,
0.05301298201084137,
0.06749029457569122,
-0.03607923910021782,
-0.021626342087984085,
0.023033656179904938,
0.011426803655922413,
0.009234733879566193,
0.02391386590898037,
-0.01577405072748661,
-0.027496393769979477,
0.007024792488664389,
-0.0006773851346224546,
0.03136590123176575,
-0.03312971815466881,
0.031216410920023918,
-0.021853718906641006,
0.021458284929394722,
-0.02917482703924179,
-0.013636201620101929,
0.01589258946478367,
0.024110324680805206,
-0.02367895096540451,
-0.02741927281022072,
0.022064805030822754,
0.0778345987200737,
-0.0063793533481657505,
-0.0457349494099617,
0.03401578962802887,
-0.0958515852689743,
0.018710745498538017,
-0.0470479354262352,
0.01986398920416832,
-0.04252918064594269,
0.009964946657419205,
0.04394473880529404,
-0.054685596376657486,
0.052415698766708374,
0.027916230261325836
] |
<p><a href="http://en.wikipedia.org/wiki/Turbulence" rel="nofollow">Wikipedia</a> states that </p>
<blockquote>
<p><em>Turbulent flow is chaotic. However, not all chaotic flows are turbulent.</em></p>
</blockquote>
<p>Someone give a picture for that?</p> | g6650 | [
0.027859004214406013,
0.07114582508802414,
0.016339782625436783,
0.02343682199716568,
0.07207565754652023,
-0.03500496596097946,
0.04430226981639862,
0.0075719296000897884,
0.017306188121438026,
-0.023703936487436295,
0.03248849883675575,
0.01715298555791378,
0.039821743965148926,
0.04089473560452461,
-0.013095922768115997,
0.015026197768747807,
-0.009124206379055977,
-0.015626464039087296,
0.0612904392182827,
0.02110333740711212,
-0.04953475296497345,
0.008368309587240219,
0.056147608906030655,
0.005035641603171825,
-0.02897855080664158,
0.006865441799163818,
-0.01325117889791727,
-0.10482358932495117,
-0.06547939777374268,
0.01193151529878378,
0.06014544889330864,
0.016729215160012245,
0.009707032702863216,
-0.02872699685394764,
-0.04197175055742264,
0.027664121240377426,
-0.03108047880232334,
-0.007650179322808981,
0.06328339129686356,
0.03367723897099495,
0.05531067028641701,
0.06620129942893982,
-0.04531367868185043,
-0.002170511521399021,
-0.07920066267251968,
0.024431852623820305,
-0.03599056228995323,
0.019683076068758965,
-0.08435934782028198,
0.006926180794835091,
0.026087503880262375,
0.017727253958582878,
0.03456303849816322,
0.03505045548081398,
0.04098192974925041,
0.043951041996479034,
0.029658500105142593,
0.04415101930499077,
0.026018602773547173,
-0.017297882586717606,
0.0019714159425348043,
-0.018039926886558533,
0.023204006254673004,
0.024170080199837685,
-0.01836741529405117,
0.023880554363131523,
-0.01929759979248047,
-0.07033424079418182,
0.07020339369773865,
0.0358496755361557,
0.01110452227294445,
-0.02118084765970707,
-0.010910114273428917,
0.01522983331233263,
-0.06050983816385269,
0.03478795662522316,
0.0030884083826094866,
-0.02802751213312149,
0.039391085505485535,
0.0020576179958879948,
0.018688788637518883,
0.0165676511824131,
-0.019768916070461273,
0.03093177266418934,
0.09124356508255005,
0.03726280853152275,
-0.02981109917163849,
-0.05424007400870323,
-0.019833168014883995,
-0.04801178351044655,
0.03277209401130676,
-0.029557453468441963,
0.015238556079566479,
0.02196572534739971,
0.0807529017329216,
0.02456175722181797,
-0.05873243883252144,
-0.00507791293784976,
-0.03669391945004463,
0.027947911992669106,
-0.057800501585006714,
0.021107442677021027,
0.03842946141958237,
-0.007363724056631327,
0.012299840338528156,
-0.0508306585252285,
-0.005996244959533215,
-0.03751713037490845,
-0.033517997711896896,
-0.03295193240046501,
-0.025734199211001396,
-0.02060089074075222,
-0.012820875272154808,
0.05324399098753929,
0.04088669642806053,
-0.014290557242929935,
0.07695279270410538,
-0.005836241878569126,
0.004490263294428587,
0.006016289349645376,
0.025647634640336037,
-0.054053083062171936,
0.021457351744174957,
0.018905026838183403,
0.0381617471575737,
0.04898502305150032,
0.045962922275066376,
-0.041748665273189545,
0.04072941839694977,
0.0031306392047554255,
0.02866080217063427,
0.02329288050532341,
-0.011563552543520927,
0.002056070137768984,
0.032871320843696594,
0.029254943132400513,
0.010090716183185577,
-0.029818544164299965,
-0.022056037560105324,
0.019248541444540024,
0.07885637134313583,
-0.03933459520339966,
0.001824633334763348,
-0.03804473206400871,
-0.04343662038445473,
-0.03697808459401131,
0.028649671003222466,
0.01564883254468441,
0.0032822219654917717,
-0.014660566113889217,
-0.048592459410429,
0.039689164608716965,
-0.023349285125732422,
0.034930191934108734,
-0.00884224008768797,
0.03669740632176399,
0.046319738030433655,
0.05445254221558571,
-0.042474906891584396,
0.05317104607820511,
-0.0407884456217289,
0.0354488380253315,
0.0553714893758297,
-0.03984430804848671,
-0.04979954659938812,
-0.07694195955991745,
-0.014677268452942371,
-0.05663269758224487,
-0.028862835839390755,
-0.007442896720021963,
-0.0007884556544013321,
0.006186733487993479,
0.007483945693820715,
0.011061514727771282,
0.04484202712774277,
-0.011236576363444328,
0.03236429765820503,
0.03277541697025299,
0.02572018653154373,
-0.03360769897699356,
-0.003035500645637512,
0.023875737562775612,
0.07625254988670349,
-0.1026107594370842,
0.01232729572802782,
0.03284035995602608,
-0.0035684281028807163,
0.034607041627168655,
-0.022619744762778282,
-0.023472260683774948,
0.03457413986325264,
-0.06842517107725143,
-0.003460348816588521,
0.016208728775382042,
0.01894773170351982,
-0.016106421127915382,
-0.0567326545715332,
-0.01548855286091566,
-0.032053496688604355,
-0.0030958112329244614,
0.048190392553806305,
0.021033260971307755,
0.04297330975532532,
0.004313704092055559,
-0.06285326182842255,
-0.0064221518114209175,
-0.04104098305106163,
0.02084294706583023,
-0.03053157962858677,
-0.031664423644542694,
0.02514142356812954,
-0.0653800368309021,
0.013995017856359482,
0.016023265197873116,
0.004564589820802212,
0.0021812596824020147,
0.035741183906793594,
-0.049135856330394745,
-0.007400549948215485,
0.006222862284630537,
0.005921903531998396,
-0.032291848212480545,
-0.03236250579357147,
-0.021489527076482773,
0.039847493171691895,
0.025315286591649055,
-0.007182449102401733,
-0.06670847535133362,
0.01398080587387085,
0.00835868064314127,
-0.005163013935089111,
-0.030162019655108452,
-0.028744002804160118,
0.011816335842013359,
0.00951203890144825,
0.02374928817152977,
0.04650082439184189,
0.0531388483941555,
-0.05441131815314293,
-0.021215250715613365,
0.013008831068873405,
-0.03678277134895325,
-0.008029146119952202,
-0.02958783321082592,
0.02195373736321926,
-0.03693301975727081,
0.008257114328444004,
-0.037976328283548355,
-0.015562132932245731,
0.018718361854553223,
0.05178198590874672,
-0.11236078292131424,
0.004772764164954424,
-0.01634244993329048,
0.024309933185577393,
-0.01706526055932045,
0.02990272082388401,
0.01816677115857601,
-0.01425292156636715,
0.056823886930942535,
-0.011234537698328495,
-0.015707744285464287,
0.0021840373519808054,
-0.0012030648067593575,
-0.0263510774821043,
-0.015722738578915596,
0.011419166810810566,
0.026884494349360466,
-0.025481397286057472,
0.0019343390595167875,
-0.008368014357984066,
-0.015936726704239845,
0.03442613035440445,
-0.053909771144390106,
-0.05381990224123001,
-0.016614794731140137,
-0.03207746148109436,
0.013714803382754326,
-0.07937082648277283,
-0.009070388972759247,
0.007695455104112625,
0.042205799371004105,
-0.0014693750999867916,
0.00032227474730461836,
-0.024447571486234665,
-0.029013928025960922,
-0.02181960642337799,
0.01974351331591606,
-0.030211716890335083,
-0.029628997668623924,
-0.03891186788678169,
-0.01528833992779255,
-0.007542503532022238,
0.022457698360085487,
-0.03515155240893364,
0.027066545560956,
0.039461683481931686,
-0.003863263875246048,
-0.028772130608558655,
-0.0023442180827260017,
-0.025390567258000374,
-0.006242353469133377,
0.0661473497748375,
0.04932670667767525,
0.025162287056446075,
0.004576727282255888,
0.023829957470297813,
-0.03471636027097702,
0.013571631163358688,
-0.006987296510487795,
0.025983743369579315,
0.030071783810853958,
-0.053196728229522705,
0.09041216224431992,
0.014765404164791107,
0.06101126968860626,
-0.010965121909976006,
0.024834902957081795,
0.026167066767811775,
0.019739557057619095,
-0.03021189756691456,
-0.046750523149967194,
0.03263258934020996,
0.0036665061488747597,
-0.0030949425417929888,
-0.03145812824368477,
-0.0049153659492731094,
0.00005290106128086336,
-0.03359682485461235,
-0.017830749973654747,
-0.014477331191301346,
-0.020621445029973984,
0.0010187618900090456,
-0.01733710803091526,
0.0014983551809564233,
-0.02963765524327755,
0.03802584111690521,
0.024088652804493904,
0.03967462107539177,
0.0031013835687190294,
0.06764749437570572,
-0.02066522277891636,
-0.04076569899916649,
-0.016100412234663963,
-0.005363245494663715,
0.05553140491247177,
-0.009848909452557564,
-0.06627839803695679,
0.045880287885665894,
-0.04730425402522087,
0.015208776108920574,
-0.0041312058456242085,
0.009427232667803764,
-0.03455723077058792,
0.018592996522784233,
-0.014434858225286007,
0.01890607737004757,
-0.019061073660850525,
0.011885580606758595,
0.006684346590191126,
-0.005631421227008104,
-0.029990442097187042,
-0.01637328416109085,
-0.019494403153657913,
-0.006002705078572035,
0.06743646413087845,
0.0332159548997879,
0.04987838864326477,
-0.051753513514995575,
0.003822948085144162,
-0.04020208492875099,
-0.02577630989253521,
-0.009560585021972656,
-0.015666376799345016,
0.09206891804933548,
0.02391553670167923,
0.040172405540943146,
0.05217009410262108,
0.05814019590616226,
0.011140725575387478,
-0.00988035462796688,
-0.018640918657183647,
-0.002113253576681018,
-0.022377120330929756,
0.01204567588865757,
-0.03876013681292534,
-0.009167304262518883,
0.044937483966350555,
-0.02797478251159191,
-0.05455296114087105,
0.022218132391572,
0.01346875261515379,
-0.03924395889043808,
0.03551251068711281,
-0.026716817170381546,
0.02462633326649666,
0.06828620284795761,
0.014954489655792713,
-0.02028685435652733,
0.04598996043205261,
0.03250693529844284,
-0.022427430376410484,
-0.08252732455730438,
0.03784042224287987,
-0.00014732961426489055,
0.04412810504436493,
0.0011405987897887826,
-0.05088046193122864,
0.01917371153831482,
0.03842001035809517,
0.05380070582032204,
0.02373906970024109,
0.015933938324451447,
-0.020315121859312057,
-0.0022294751834124327,
0.011027132160961628,
0.0008129854686558247,
0.008882284164428711,
0.0082778949290514,
0.014886678196489811,
0.03385470062494278,
0.02994062937796116,
-0.008771544322371483,
-0.004097565542906523,
-0.012334853410720825,
-0.0037784690503031015,
0.0025592471938580275,
0.029312457889318466,
-0.021438850089907646,
0.05087171122431755,
0.01629268191754818,
-0.022092891857028008,
-0.08478477597236633,
0.014884797856211662,
-0.027624184265732765,
0.0002731596177909523,
0.06337447464466095,
0.004229038022458553,
0.05153858661651611,
0.008429141715168953,
-0.006974752526730299,
-0.019557489082217216,
0.039802707731723785,
-0.0015958414878696203,
-0.023008069023489952,
0.01266511995345354,
0.08105983585119247,
0.02937019243836403,
-0.03416489437222481,
0.059456389397382736,
-0.02947554551064968,
0.00785953737795353,
-0.017557667568325996,
0.0708574652671814,
0.008555748499929905,
-0.04204903542995453,
-0.01230843085795641,
0.0034860996529459953,
-0.032990142703056335,
0.015614691190421581,
-0.021028537303209305,
-0.007241738028824329,
0.038805779069662094,
0.04133859649300575,
-0.048633843660354614,
-0.009222433902323246,
-0.03760536387562752,
-0.05187788978219032,
0.0023171924985945225,
-0.01726364903151989,
0.01505843736231327,
-0.010122155770659447,
-0.04255657643079758,
0.026275936514139175,
0.02426164411008358,
-0.014654864557087421,
0.040636587888002396,
-0.04349411278963089,
0.05844860523939133,
-0.02074149064719677,
0.06001149117946625,
0.0193799939006567,
0.026302598416805267,
-0.0025972158182412386,
0.06819919496774673,
0.004396509844809771,
-0.013061195611953735,
0.0511469841003418,
0.0380752868950367,
0.036838967353105545,
-0.004383734427392483,
0.04649389535188675,
-0.10949645191431046,
-0.0424157939851284,
-0.014072167687118053,
-0.07667293399572372,
0.035264261066913605,
-0.05752519145607948,
0.009181453846395016,
-0.026128089055418968,
-0.07273674011230469,
-0.05752449110150337,
-0.01418119203299284,
0.018235646188259125,
-0.018530847504734993,
0.020374206826090813,
-0.07048515230417252,
-0.0007644129218533635,
-0.02927418425679207,
0.07107311487197876,
-0.03786903992295265,
-0.09168969839811325,
-0.07220610231161118,
0.013421889394521713,
-0.0024750379379838705,
-0.041818395256996155,
-0.008208787068724632,
-0.024483418092131615,
0.06489087641239166,
-0.003082213457673788,
0.004218581132590771,
-0.0023603986483067274,
0.01953056827187538,
0.003879155730828643,
-0.022629667073488235,
0.017267737537622452,
-0.004444533959031105,
-0.03270861878991127,
-0.006942568346858025,
0.010430664755403996,
-0.036739882081747055,
-0.017835021018981934,
0.048093829303979874,
-0.004579734522849321,
-0.010194110684096813,
-0.011097093112766743,
0.058726511895656586,
0.018236640840768814,
-0.01249244436621666,
0.057876329869031906,
0.0355258546769619,
0.046021122485399246,
-0.03536165505647659,
0.002698845462873578,
0.016137901693582535,
0.03483333811163902,
-0.00926624983549118,
0.01238342747092247,
0.030215119943022728,
-0.029341837391257286,
0.04167141020298004,
-0.034239135682582855,
-0.0033768832217901945,
-0.011666244827210903,
-0.04453614354133606,
-0.012286175042390823,
0.03503792732954025,
-0.01957876794040203,
-0.018282463774085045,
0.015505345538258553,
-0.01808200590312481,
-0.0077808392234146595,
0.01235367450863123,
-0.03564581274986267,
0.02296455204486847,
-0.03880895674228668,
-0.03663652017712593,
0.06249475106596947,
0.006416612770408392,
0.07677489519119263,
0.003841473488137126,
0.007072026375681162,
-0.010791006498038769,
0.01551817450672388,
0.049282755702733994,
-0.07753202319145203,
0.005193809513002634,
-0.03366565331816673,
-0.008915111422538757,
-0.015252522192895412,
-0.05172179266810417,
0.0002969339257106185,
0.09880650788545609,
-0.06314907968044281,
-0.009396258741617203,
-0.04299117252230644,
0.0022009043022990227,
0.05699918791651726,
-0.05604531243443489,
0.10554231703281403,
-0.06898388266563416,
0.01871330477297306,
-0.031658828258514404,
0.016607247292995453,
0.0336114764213562,
-0.00959803070873022,
-0.05664265528321266,
0.05134883522987366,
0.0019068861147388816,
0.0161306019872427,
-0.039712969213724136,
-0.012787766754627228,
0.03901445120573044,
-0.037645477801561356,
-0.03639901429414749,
0.015253636986017227,
0.05273818597197533,
-0.017956478521227837,
-0.07782566547393799,
0.08308488875627518,
0.007087985053658485,
0.019215762615203857,
0.06954886019229889,
-0.010341261513531208,
-0.05685615912079811,
-0.052166398614645004,
-0.0022040398325771093,
-0.005655866581946611,
-0.011857379227876663,
0.01767028123140335,
-0.0022915878798812628,
-0.050352029502391815,
0.0346999391913414,
-0.030702559277415276,
-0.0026143311988562346,
0.047593969851732254,
-0.052478887140750885,
0.03430873528122902,
-0.007380962371826172,
-0.03617379814386368,
0.0007854893337935209,
0.004149863496422768,
-0.017918981611728668,
0.04105885326862335,
-0.05938402935862541,
-0.03527594357728958,
-0.1067735031247139,
-0.01784013770520687,
0.06022278591990471,
0.061029233038425446,
0.03180660679936409,
0.06340749561786652,
0.023831715807318687,
0.005448182579129934,
-0.0012931199744343758,
-0.011917890049517155,
0.014120914973318577,
0.02772126905620098,
-0.02000139094889164,
-0.004976593889296055,
0.019495565444231033,
0.01358808297663927,
0.018949497491121292,
-0.017313798889517784,
-0.045646920800209045,
0.036704156547784805,
0.013557225465774536,
-0.004356517922133207,
-0.024909021332859993,
-0.06778304278850555,
0.026722174137830734,
0.02912464365363121,
-0.011907362379133701,
-0.017367271706461906,
0.0026611306238919497,
0.0011369772255420685,
0.024089708924293518,
0.0294755008071661,
-0.0037491596303880215,
-0.025467898696660995,
0.006273264996707439,
-0.04015868157148361,
0.009402522817254066,
0.006749319843947887,
-0.033781204372644424,
-0.030044734477996826,
-0.009928412735462189,
-0.006388651207089424,
0.08113981038331985,
-0.023113897070288658,
0.01630137488245964,
-0.012186550535261631,
0.02743096649646759,
-0.01109043974429369,
-0.02323911152780056,
0.04500935971736908,
-0.05218002572655678,
-0.02295476756989956,
-0.02795172482728958,
-0.05356095731258392,
-0.008304073475301266,
0.052684225142002106,
-0.010218443349003792,
-0.07493863254785538,
-0.06566377729177475,
0.01652689091861248,
0.011932571418583393,
-0.042405854910612106,
-0.013765738345682621,
-0.030269118025898933,
0.0077221631072461605,
-0.0003022924647666514,
-0.05549158900976181,
-0.005055303685367107,
0.004601724911481142,
-0.035433217883110046,
0.06262476742267609,
0.030162151902914047,
-0.07007554918527603,
-0.01826717145740986,
0.0015060289297252893,
-0.0013297871919348836,
-0.058114465326070786,
-0.05689931660890579,
-0.030193835496902466,
0.0048585389740765095,
0.04180833697319031,
-0.005375262815505266,
-0.02194703370332718,
0.01530943252146244,
0.015184485353529453,
-0.023725131526589394,
-0.09458635747432709,
-0.06600029021501541,
-0.010134241543710232,
0.0186853539198637,
0.02166038192808628,
-0.011924592778086662,
0.008493640460073948,
-0.03526679053902626,
-0.03435661643743515,
0.006667339242994785,
0.02091514877974987,
0.028850281611084938,
-0.012001512572169304,
0.027833860367536545,
0.021715112030506134,
0.038520101457834244,
0.04396650195121765,
-0.05138975381851196,
0.05781325325369835,
0.04101787135004997,
-0.034892600029706955,
0.0070027136243879795,
0.00857979990541935,
-0.0636693611741066,
-0.05812305584549904,
-0.0328044630587101,
-0.0382259301841259,
-0.060969460755586624,
0.050083670765161514,
0.0718788281083107,
0.007644055876880884,
-0.012050561606884003,
0.05575953423976898,
-0.0008517641690559685,
-0.05544539913535118,
0.048479024320840836,
0.0016656152438372374,
-0.025220947340130806,
0.007296327035874128,
-0.009808002039790154,
0.007291468791663647,
-0.002006121212616563,
-0.020076479762792587,
-0.025006048381328583,
-0.027938449755311012,
-0.0026304994244128466
] |
<p>Assuming you have container with heat insulation (something like boiler).<br>
You can store water at any temperature <strong>below 100°C</strong>. At these conditions, you can drill a hole into container and <strong>store water at air pressure</strong>.<br>
But when you heat water to tempertature <strong>over 100°C</strong>, it starts to boil, increasing pressure in contailner. If you drill a hole, water will start to evaporate and that'll cause temperature drop. If you try to maintain constant temperature, after some time <strong>all water will evaporate</strong>.<br>
<strong>Water with temperature over 100°C can be stored only at high pressure?</strong><br>
If so, it'll reach some pressure (depending on temperature) and stop boiling?<br>
Are there any other risks besides high pressure to be aware when trying to store water at these conditions?</p> | g6651 | [
0.02423362247645855,
0.02324635721743107,
0.009729226119816303,
0.05891000106930733,
-0.0010378170991316438,
-0.0013865010114386678,
-0.010411796160042286,
0.015104986727237701,
-0.03520512580871582,
0.00423286110162735,
-0.038787584751844406,
-0.0005913322675041854,
0.014410190284252167,
0.02858855202794075,
-0.0007283001905307174,
0.0011263287160545588,
0.015595623292028904,
-0.0020170039497315884,
0.014864008873701096,
0.0026148331817239523,
-0.02794823795557022,
-0.01232092920690775,
0.033080704510211945,
0.03366909921169281,
-0.07431778311729431,
-0.008004754781723022,
-0.013173160143196583,
0.003598253009840846,
-0.02733059599995613,
0.0020022413227707148,
-0.036334600299596786,
-0.0017973445355892181,
-0.03530963882803917,
0.02936716005206108,
-0.01866231858730316,
-0.11302143335342407,
0.03132276609539986,
0.010711262933909893,
-0.019433721899986267,
-0.05769116431474686,
0.015445074997842312,
-0.008472942747175694,
0.02025679126381874,
-0.01427252683788538,
-0.006950889714062214,
0.03835827112197876,
-0.008191482163965702,
-0.025061622262001038,
-0.02155155874788761,
0.0251711905002594,
0.05304021015763283,
-0.03263574093580246,
-0.005780862644314766,
-0.03776155412197113,
-0.01416193787008524,
-0.033280353993177414,
-0.0828574001789093,
0.022520629689097404,
0.01691252551972866,
-0.03346186503767967,
0.002045807195827365,
-0.03251475840806961,
0.011678828857839108,
-0.005370077211409807,
0.01593797281384468,
0.0465092733502388,
-0.09401921927928925,
0.013604652136564255,
0.023670390248298645,
0.06491358578205109,
0.053680334240198135,
0.01400713250041008,
-0.0725189745426178,
-0.05314277857542038,
-0.014860033988952637,
0.01814381219446659,
-0.004129674285650253,
0.0074553778395056725,
0.04084894061088562,
0.03578980639576912,
-0.009544127620756626,
0.038794003427028656,
0.043649815022945404,
0.012397020123898983,
-0.015773270279169083,
-0.008680579252541065,
0.008264428935945034,
0.01586207188665867,
0.04180959612131119,
0.031161390244960785,
-0.051017407327890396,
-0.04218578338623047,
0.0622207336127758,
0.08543483912944794,
0.07324203103780746,
0.05482322350144386,
0.04461539536714554,
0.009791496209800243,
0.003829371416941285,
0.009311361238360405,
0.06296242028474808,
-0.0528346449136734,
0.00499120494350791,
0.017023460939526558,
-0.08113093674182892,
0.011483482085168362,
0.06073052063584328,
0.007883085869252682,
-0.00864349864423275,
-0.03295101225376129,
0.05658535659313202,
0.011669730767607689,
-0.11494637280702591,
-0.04174436628818512,
-0.03879847750067711,
0.057132184505462646,
0.015122207812964916,
0.011234745383262634,
-0.002480450551956892,
-0.01979338750243187,
0.043544501066207886,
0.0523868128657341,
0.01126070786267519,
0.05633767694234848,
0.027752939611673355,
0.015834301710128784,
-0.03496994450688362,
-0.006827474571764469,
-0.021327638998627663,
0.02239006757736206,
-0.03351129963994026,
0.02165757678449154,
-0.07742089033126831,
0.0045288195833563805,
-0.00016660305846016854,
0.010993724688887596,
-0.017807113006711006,
0.03288140147924423,
-0.012531943619251251,
0.008341692388057709,
0.039034437388181686,
0.03176208958029747,
-0.010669588111341,
0.04508938267827034,
0.01101524755358696,
-0.050984106957912445,
-0.019328860566020012,
0.02616771310567856,
0.00014321260096039623,
0.007606051862239838,
-0.06179118528962135,
0.025057924911379814,
0.009704405441880226,
0.03177662938833237,
0.03837475925683975,
0.012526953592896461,
-0.005846142303198576,
-0.02520284615457058,
0.09409233182668686,
0.0663084164261818,
0.03812934458255768,
0.04736337438225746,
0.031987596303224564,
0.05661936476826668,
-0.07300593703985214,
-0.0050787609070539474,
-0.023164482787251472,
0.02874232642352581,
-0.002604336477816105,
-0.0361349992454052,
-0.05759790167212486,
0.05575491860508919,
-0.020818503573536873,
0.0025460764300078154,
0.022153647616505623,
-0.05402183532714844,
0.06800876557826996,
0.011481989175081253,
-0.0177301038056612,
-0.02107926830649376,
-0.03531821072101593,
0.030865630134940147,
-0.036126453429460526,
-0.03614521026611328,
-0.02416081167757511,
0.05481741949915886,
0.05653068423271179,
0.017134789377450943,
-0.03602168336510658,
0.010384623892605305,
0.003206714754924178,
-0.03508780151605606,
-0.009616010822355747,
0.058344461023807526,
0.043998561799526215,
-0.050240445882081985,
0.00967312790453434,
-0.022352144122123718,
-0.08253917843103409,
-0.02102609910070896,
-0.007587699219584465,
-0.036156196147203445,
0.010260422714054585,
0.034510206431150436,
-0.008673618547618389,
0.022227441892027855,
-0.0697162076830864,
0.01567300781607628,
-0.020998168736696243,
-0.04682547226548195,
0.02161075919866562,
0.005360657349228859,
-0.012858357280492783,
0.023581111803650856,
0.027506526559591293,
0.03539162874221802,
0.005416559986770153,
0.009484604932367802,
-0.027178671211004257,
0.014481281861662865,
-0.0012714428594335914,
0.0031133696902543306,
-0.035146500915288925,
0.009595888666808605,
-0.07962958514690399,
0.022873256355524063,
-0.0751391351222992,
0.012604652903974056,
0.007900986820459366,
0.007792606949806213,
-0.003376032691448927,
0.02384515106678009,
0.027953816577792168,
-0.015289600938558578,
-0.051459237933158875,
0.024816472083330154,
0.02597125619649887,
0.007418523542582989,
0.018571672961115837,
0.02071050927042961,
0.010925404727458954,
0.003096206346526742,
-0.04019380360841751,
0.00468492554500699,
0.01723875105381012,
-0.03269543871283531,
-0.007690201047807932,
-0.03233209252357483,
0.09373416006565094,
0.008906221948564053,
0.009637361392378807,
-0.012798897922039032,
0.007528143003582954,
0.01936963014304638,
-0.043295469135046005,
-0.010705813765525818,
0.003494181903079152,
0.018165946006774902,
-0.04699220880866051,
-0.05719245225191116,
0.03112008608877659,
-0.011243334040045738,
0.01235434040427208,
-0.006503434851765633,
0.038136135786771774,
0.028456123545765877,
-0.03416992351412773,
0.028779450803995132,
0.010823538526892662,
0.06629893183708191,
0.051830992102622986,
0.00369862443767488,
-0.05417128652334213,
0.06598731875419617,
-0.007065140176564455,
-0.0020096362568438053,
-0.02659740298986435,
0.004586962517350912,
0.043462373316287994,
-0.044048093259334564,
0.0011075244983658195,
-0.05101059377193451,
0.0022322337608784437,
-0.008152049034833908,
0.0006527910009026527,
-0.028156934306025505,
0.019020352512598038,
0.05190959572792053,
-0.00857371836900711,
-0.054707929491996765,
0.01869637332856655,
0.012408420443534851,
-0.02667885273694992,
0.03968745470046997,
0.0437062606215477,
0.009819401428103447,
-0.07684595137834549,
-0.009943450801074505,
-0.004478934686630964,
-0.03636300936341286,
0.0025242227129638195,
-0.018606653437018394,
-0.009260236285626888,
0.015080577693879604,
0.03924207389354706,
0.013175610452890396,
-0.014625110663473606,
0.005416059400886297,
0.004758534952998161,
-0.05985400453209877,
-0.04470513015985489,
-0.016360197216272354,
-0.017186319455504417,
0.016360415145754814,
-0.02611764892935753,
0.02428559586405754,
-0.017825422808527946,
0.0008190869702957571,
0.07629316300153732,
-0.09478097409009933,
0.009234289638698101,
0.002393563510850072,
0.0025042707566171885,
0.011674690991640091,
0.02959960699081421,
0.09165096282958984,
-0.03485674038529396,
0.007859215140342712,
-0.07847649604082108,
-0.03187065199017525,
0.01970706321299076,
-0.00775474077090621,
-0.010791785083711147,
0.02517106756567955,
0.031194085255265236,
-0.013378341682255268,
0.04623033478856087,
-0.025191480293869972,
-0.0025853607803583145,
0.0020641745068132877,
0.08343856036663055,
-0.020445549860596657,
0.0028297794051468372,
-0.01858530193567276,
0.017500806599855423,
-0.01428636908531189,
0.03782273083925247,
-0.0035298725124448538,
0.008258523419499397,
0.04417914152145386,
0.07022827863693237,
-0.05909671634435654,
0.037376295775175095,
-0.022943314164876938,
-0.0490880087018013,
0.013054690323770046,
0.017374422401189804,
0.02299770712852478,
-0.009009087458252907,
0.04530470073223114,
-0.019648315384984016,
0.002313639037311077,
0.035202909260988235,
-0.014660746790468693,
-0.013742751441895962,
0.03545486181974411,
0.018306303769350052,
0.02950317971408367,
-0.052289269864559174,
-0.03006390482187271,
-0.004784951917827129,
-0.032355498522520065,
-0.034007806330919266,
0.034573543816804886,
0.04068637266755104,
-0.01500240433961153,
0.03679930046200752,
-0.005245921667665243,
-0.011200028471648693,
0.041749268770217896,
0.03173191845417023,
-0.04130266234278679,
-0.017744362354278564,
-0.027657445520162582,
-0.01777227781713009,
-0.06150238588452339,
0.06465394794940948,
0.038483139127492905,
0.039972275495529175,
-0.029956171289086342,
0.04788679629564285,
-0.04064446687698364,
0.08589664101600647,
0.016625814139842987,
0.04333801567554474,
0.0017266510985791683,
-0.014162225648760796,
0.04114086553454399,
-0.02614136040210724,
-0.06304382532835007,
0.013083040714263916,
-0.0473259836435318,
0.06002877280116081,
-0.012854122556746006,
-0.030507197603583336,
-0.04020986706018448,
0.03533456474542618,
0.03335355594754219,
-0.02247072570025921,
-0.07248460501432419,
0.05961114913225174,
-0.0039723701775074005,
-0.060524001717567444,
0.040935371071100235,
-0.01453317329287529,
-0.07944277673959732,
0.013729846104979515,
0.04082765057682991,
0.023484613746404648,
-0.012837251648306847,
-0.011052356101572514,
0.013667131774127483,
-0.04956788197159767,
0.00024444778682664037,
0.06160994619131088,
-0.028353475034236908,
-0.0076449159532785416,
-0.05015285313129425,
0.013316232711076736,
0.018980789929628372,
-0.02787591703236103,
0.02919459529221058,
-0.03548466041684151,
-0.019178012385964394,
0.04107922688126564,
0.03551320359110832,
-0.025530466809868813,
-0.05023296922445297,
-0.046830713748931885,
-0.003841657191514969,
0.009558480232954025,
0.005742446053773165,
0.052077777683734894,
0.010631678625941277,
-0.03456522896885872,
0.08215419948101044,
0.007859032601118088,
-0.014306393451988697,
0.05264444649219513,
-0.04216925799846649,
-0.05027075484395027,
0.05660927668213844,
0.03802911937236786,
-0.03255461901426315,
-0.006701285019516945,
-0.01149918045848608,
0.025581443682312965,
0.012923878617584705,
-0.04465867206454277,
0.04844781383872032,
0.01703067123889923,
-0.025685949251055717,
-0.010782497934997082,
0.00278676045127213,
0.016652911901474,
-0.050058163702487946,
-0.016659045591950417,
-0.07341264933347702,
0.0011061688419431448,
-0.015218349173665047,
0.005254777614027262,
0.07894287258386612,
0.03507494926452637,
0.05596877261996269,
0.07451082020998001,
0.07007782906293869,
-0.03751548379659653,
-0.043021731078624725,
-0.05114273354411125,
-0.05112273246049881,
-0.010543199256062508,
0.013465330004692078,
-0.033521659672260284,
0.024874256923794746,
0.0073244948871433735,
-0.04377048835158348,
0.013566277921199799,
-0.0010783191537484527,
0.059041570872068405,
0.025240479037165642,
0.025717103853821754,
-0.0024729901924729347,
0.036053456366062164,
0.06203406676650047,
-0.004523129668086767,
-0.030167194083333015,
0.012130034156143665,
0.017329713329672813,
-0.0058727990835905075,
0.018593406304717064,
0.01320224441587925,
-0.03039940632879734,
-0.009526929818093777,
-0.01124329399317503,
-0.0014980070991441607,
0.008175423368811607,
-0.015292230062186718,
0.016033360734581947,
0.007511019241064787,
0.03188275545835495,
0.02609223686158657,
0.050804320722818375,
-0.028970956802368164,
-0.021358318626880646,
0.1163688376545906,
-0.010158935561776161,
-0.05192221328616142,
-0.007770488038659096,
-0.04975324869155884,
-0.026760444045066833,
-0.013663462363183498,
-0.005961814429610968,
0.0019171233288943768,
-0.01896330527961254,
-0.02396736666560173,
-0.008126812055706978,
-0.060634054243564606,
-0.04328714683651924,
0.028926465660333633,
0.020755695179104805,
0.09650171548128128,
0.04657290130853653,
0.038129959255456924,
-0.029444163665175438,
0.029110627248883247,
-0.01333942636847496,
-0.0650537833571434,
0.008074114099144936,
0.07012396305799484,
0.07327087223529816,
0.04332020506262779,
-0.008721916936337948,
-0.03629510477185249,
0.041518960148096085,
-0.03358820080757141,
-0.05030576139688492,
-0.06484133750200272,
-0.012758605182170868,
0.02366049215197563,
0.01645577698945999,
-0.007390379905700684,
0.04298153147101402,
-0.047033924609422684,
-0.02904999442398548,
0.043881140649318695,
-0.06747319549322128,
0.005111182574182749,
-0.02658209763467312,
-0.01483581867069006,
-0.0033102096058428288,
-0.01947249472141266,
0.02448560856282711,
0.027286464348435402,
0.01699952408671379,
-0.0015296988422051072,
-0.00802711583673954,
-0.04568187892436981,
-0.013553843833506107,
0.02179528772830963,
0.06232098862528801,
0.05249960720539093,
0.0017822764348238707,
0.026700805872678757,
-0.07160778343677521,
-0.04009602591395378,
-0.022310109809041023,
-0.06776005029678345,
0.037520892918109894,
0.04075060412287712,
-0.009481850080192089,
-0.05897558480501175,
-0.019391320645809174,
-0.06331311911344528,
0.021561186760663986,
-0.03532979637384415,
-0.007598415482789278,
-0.00854698196053505,
-0.010619071312248707,
0.031512558460235596,
0.01373361423611641,
-0.016156325116753578,
0.01101644802838564,
0.013000491075217724,
0.016322314739227295,
0.10712974518537521,
0.0026973385829478502,
-0.004847291391342878,
0.02269996702671051,
-0.03899557143449783,
-0.022010838612914085,
0.014930143021047115,
0.04306800290942192,
0.044108156114816666,
0.0135397519916296,
-0.04761591553688049,
0.024448368698358536,
0.0228760726749897,
0.060977451503276825,
0.021585581824183464,
0.02549656108021736,
0.004629957024008036,
-0.017761148512363434,
0.04343128949403763,
-0.011145949363708496,
-0.018093552440404892,
-0.082340769469738,
0.02472950518131256,
0.021136581897735596,
-0.02927350252866745,
-0.018426423892378807,
0.0428885817527771,
0.008979376405477524,
-0.020081644877791405,
-0.02401064708828926,
0.0002805162512231618,
0.005922493524849415,
-0.013029194436967373,
0.012407930567860603,
0.046457819640636444,
-0.06104087829589844,
0.013418988324701786,
-0.014537124894559383,
-0.026983199641108513,
-0.03462418541312218,
-0.05781342834234238,
-0.012265753000974655,
-0.056823790073394775,
0.04540606588125229,
0.007111736107617617,
0.0607987642288208,
0.02319011464715004,
-0.023580830544233322,
-0.008783528581261635,
0.007123890332877636,
-0.01931471936404705,
0.030833657830953598,
-0.023267490789294243,
-0.02614077366888523,
-0.05968986451625824,
-0.01617581956088543,
-0.013813412748277187,
-0.04370115324854851,
-0.06746447831392288,
-0.03147786483168602,
-0.019744114950299263,
0.027130872011184692,
0.019511962309479713,
-0.029545610770583153,
-0.033299483358860016,
0.013600443489849567,
0.012978645041584969,
0.001443567336536944,
0.021823257207870483,
0.025230126455426216,
-0.013979713432490826,
0.032662611454725266,
0.024282781407237053,
-0.0810462012887001,
0.028635818511247635,
-0.020069759339094162,
0.017398715019226074,
-0.01286348793655634,
0.015192762948572636,
-0.07788196951150894,
0.01894989050924778,
-0.007432455196976662,
0.0502353310585022,
0.04999668151140213,
-0.015624729916453362,
0.034096427261829376,
-0.06814906001091003,
-0.019546890631318092,
0.0025620583910495043,
-0.015314942225813866,
0.024206874892115593,
-0.006448097061365843,
-0.024255940690636635,
-0.02717779017984867,
0.044810980558395386,
-0.05910325050354004,
-0.04919305816292763,
0.00022146131959743798,
0.061564989387989044,
-0.006977428216487169,
-0.013480076566338539,
-0.0018795933574438095,
0.045408859848976135,
-0.020682021975517273,
0.0003057889989577234,
-0.0358671173453331,
-0.026484092697501183,
0.04125317186117172,
0.07566976547241211,
-0.03178922459483147,
0.023849692195653915,
0.04831951856613159,
-0.017592864111065865,
0.05159991234540939,
-0.04145491495728493,
0.02786407805979252,
0.05097295716404915,
0.04117929935455322,
0.040968962013721466,
-0.06837542355060577,
-0.02600165829062462,
-0.010173696093261242,
-0.05658843740820885,
-0.08737685531377792,
-0.022567816078662872,
-0.017578249797225,
-0.05805679038167,
-0.01958511397242546,
-0.025485243648290634,
0.010524147190153599,
0.030466344207525253,
0.016267333179712296,
0.005552561488002539,
-0.008456805720925331,
-0.05648847296833992,
-0.02441568858921528,
-0.03551023453474045,
-0.005899531301110983,
-0.05051156133413315,
0.03048378974199295,
0.02858228236436844,
-0.014314697124063969,
0.04905502125620842,
0.028985116630792618,
-0.020586920902132988,
0.012112978845834732,
0.0067055197432637215,
0.054370928555727005,
0.006922802422195673,
-0.013533871620893478,
0.021307969465851784,
-0.026039930060505867,
-0.011891062371432781,
-0.015176810324192047,
-0.013154062442481518,
0.002561017405241728,
-0.03205830231308937,
-0.02570350654423237,
-0.03609636798501015,
-0.013015108183026314,
-0.022520901635289192,
-0.05181402713060379,
-0.025422193109989166,
0.011589739471673965,
0.015645548701286316,
-0.06739791482686996,
-0.006367370951920748,
0.03213251754641533,
-0.038244593888521194,
-0.036305177956819534,
0.046324290335178375,
-0.009795185178518295,
-0.03851763904094696,
-0.05744398385286331
] |
<p>Need help in understanding the direction of magnetic force in the magnetic field!Totally confused by directions.</p>
<p>Why is it that magnetic force is perpendicular to the direction of magnetic field and velocity of charged particle.
Why is it(force) not in the same direction as the magnetuc field</p> | g6652 | [
0.014354052022099495,
0.027517113834619522,
-0.013795237988233566,
0.006213229149580002,
0.089993417263031,
0.04479372873902321,
0.002825644798576832,
0.029730597510933876,
-0.02601042203605175,
-0.04362841695547104,
0.016507940366864204,
0.02655922621488571,
-0.02573975920677185,
-0.021102100610733032,
0.012599700130522251,
0.04445575550198555,
0.060521624982357025,
0.012430809438228607,
0.020264966413378716,
0.02329053170979023,
-0.022990545257925987,
0.03774946555495262,
-0.0007416162407025695,
-0.007848531939089298,
0.034214086830616,
-0.04321770742535591,
-0.030814064666628838,
-0.079442098736763,
-0.004768475890159607,
-0.03696679696440697,
0.06771087646484375,
0.00761566823348403,
0.05886493995785713,
-0.08678814768791199,
-0.024272236973047256,
-0.03847610577940941,
0.04728361591696739,
0.056268975138664246,
0.02567506954073906,
0.008236750960350037,
0.0012219795025885105,
0.0015635995659977198,
0.043973058462142944,
-0.01880493201315403,
0.0037385961040854454,
0.019832776859402657,
-0.0729941576719284,
-0.033984530717134476,
-0.0584111250936985,
-0.016245895996689796,
-0.03333372622728348,
-0.02200334705412388,
0.029481174424290657,
0.020008528605103493,
-0.030589846894145012,
0.027200182899832726,
0.06914038956165314,
-0.03566516935825348,
0.04227829724550247,
0.03193163499236107,
0.03650444746017456,
0.07958833128213882,
-0.014404387213289738,
0.002132660709321499,
-0.016347993165254593,
-0.07061569392681122,
-0.017352566123008728,
0.04501723870635033,
-0.007830467075109482,
0.0019493559375405312,
-0.0053832740522921085,
-0.07604934275150299,
0.025307374075055122,
-0.05498490855097771,
-0.03632291778922081,
-0.050936926156282425,
0.05868292599916458,
-0.02671286277472973,
0.01948707364499569,
-0.04482472315430641,
0.009741811081767082,
-0.008672502823174,
0.02416257932782173,
-0.006017701234668493,
0.08400260657072067,
-0.07166695594787598,
0.010145356878638268,
0.03710753470659256,
0.03346696123480797,
-0.044502489268779755,
-0.04126150161027908,
0.010760234668850899,
0.048077795654535294,
0.05730670690536499,
-0.018145019188523293,
-0.06350113451480865,
-0.01187067199498415,
0.0616510845720768,
0.006232374347746372,
0.04002503678202629,
-0.005604507401585579,
0.013283169828355312,
-0.0037472746334969997,
0.01605825498700142,
0.009753381833434105,
-0.050261106342077255,
0.04110293835401535,
0.07211300730705261,
-0.00012616554158739746,
-0.03568795323371887,
-0.0548093318939209,
-0.005980517249554396,
-0.002054881304502487,
0.023713165894150734,
0.027074452489614487,
-0.029726002365350723,
0.02716253511607647,
-0.0279995147138834,
0.023054398596286774,
0.029728081077337265,
-0.01243661344051361,
0.0038220405112951994,
0.005436800420284271,
-0.0032040816731750965,
-0.027181340381503105,
-0.052584223449230194,
-0.022253038361668587,
0.024489156901836395,
-0.023863237351179123,
-0.07391621917486191,
0.04482570290565491,
-0.02405206859111786,
0.019887374714016914,
0.025409147143363953,
-0.02457876317203045,
0.003905927063897252,
0.005758898798376322,
0.057804469019174576,
0.04889264330267906,
-0.02832738496363163,
0.022911829873919487,
0.006689269095659256,
0.04458368942141533,
-0.013058346696197987,
-0.05803750827908516,
-0.013215100392699242,
0.011393586173653603,
-0.06264085322618484,
0.09174059331417084,
-0.024295510724186897,
0.046947088092565536,
0.037685707211494446,
-0.03254853934049606,
-0.0053520905785262585,
0.013829580508172512,
-0.03955443948507309,
0.05318208038806915,
0.03297189250588417,
0.0031926834490150213,
-0.022801440209150314,
0.0014953130157664418,
0.024647889658808708,
-0.007834713906049728,
0.004747758619487286,
-0.03140914440155029,
-0.011560549959540367,
0.05855480581521988,
-0.01629273220896721,
0.0028617680072784424,
0.01856350526213646,
-0.030003657564520836,
-0.004316007252782583,
-0.003996949177235365,
0.06940304487943649,
-0.0003812369250226766,
0.038720421493053436,
-0.04540760815143585,
-0.031109519302845,
-0.014998607337474823,
0.03543398156762123,
-0.003836067160591483,
0.010271945036947727,
0.05726490914821625,
-0.025705227628350258,
-0.02495921030640602,
-0.031146060675382614,
-0.025824714452028275,
0.07154371589422226,
0.0021775865461677313,
0.04564312845468521,
-0.04261630401015282,
0.02314622513949871,
-0.05214469134807587,
0.040526703000068665,
0.005372297018766403,
-0.033463288098573685,
-0.0014706089859828353,
0.010420102626085281,
-0.014968665316700935,
0.0037372438237071037,
-0.05714511126279831,
-0.0033934793900698423,
0.05208945646882057,
0.04057193174958229,
-0.000006320599823084194,
-0.026523642241954803,
0.025996556505560875,
0.028459545224905014,
0.0549452006816864,
0.03120049461722374,
0.013114961795508862,
-0.0021053061354905367,
0.026773586869239807,
-0.01608300767838955,
-0.01806253008544445,
-0.002697078278288245,
0.01618053764104843,
0.0009564705542288721,
-0.028995729982852936,
-0.02454206347465515,
-0.02652909606695175,
-0.03908015415072441,
0.06281132251024246,
-0.021761657670140266,
-0.06098020449280739,
-0.027482377365231514,
-0.0034062517806887627,
-0.018085621297359467,
-0.00808879267424345,
-0.016307638958096504,
-0.03687076270580292,
0.012146491557359695,
0.009391008876264095,
0.02684234268963337,
0.06757504492998123,
0.027019398286938667,
0.0032783562783151865,
0.011678779497742653,
-0.013634984381496906,
-0.058477647602558136,
-0.05697513744235039,
0.013305377215147018,
0.06082458421587944,
-0.0314168818295002,
-0.00009167360258288682,
0.005772556643933058,
0.0892781913280487,
-0.027274886146187782,
0.01485030073672533,
0.0034051642287522554,
0.028451036661863327,
-0.011535369791090488,
-0.004532074090093374,
0.00391777791082859,
0.03739066421985626,
0.0034786334726959467,
-0.06939589977264404,
0.01536629255861044,
-0.07171370089054108,
-0.0732511579990387,
-0.03784027695655823,
-0.045044783502817154,
0.06039689481258392,
0.08595868200063705,
-0.03125806525349617,
0.015910722315311432,
-0.012098596431314945,
0.05494332313537598,
0.09514274448156357,
-0.039514027535915375,
0.006737083662301302,
0.06444954127073288,
0.01833207532763481,
-0.021397821605205536,
0.025911033153533936,
-0.03146159648895264,
0.007327658124268055,
0.004862890113145113,
-0.005262627732008696,
-0.03582567349076271,
-0.0335598848760128,
0.03534817695617676,
0.015547562390565872,
-0.0300966314971447,
-0.01049825083464384,
0.008686551824212074,
-0.0033186848741024733,
-0.05367468670010567,
-0.01157717127352953,
-0.014474404975771904,
-0.05615350604057312,
-0.016258716583251953,
0.051589611917734146,
-0.0681706964969635,
-0.0004414677096065134,
-0.007836882956326008,
0.046568818390369415,
-0.0007413927232846618,
-0.06979720294475555,
0.04260222241282463,
0.0054514664225280285,
-0.0033622898627072573,
-0.020424509420990944,
0.014546718448400497,
0.027120215818285942,
-0.01010992843657732,
-0.01753777451813221,
-0.0852009728550911,
-0.036718692630529404,
0.05906409025192261,
-0.03481975570321083,
0.0519770085811615,
-0.003449300304055214,
0.004123310092836618,
-0.023550087586045265,
-0.023925045505166054,
-0.07092028856277466,
0.03711463883519173,
-0.013082877732813358,
0.013921619392931461,
-0.04746151342988014,
-0.05987900123000145,
-0.004615894518792629,
0.02973128668963909,
0.022484462708234787,
0.017688177525997162,
-0.03623334690928459,
-0.00795028917491436,
-0.032015781849622726,
-0.03269613906741142,
0.006972129922360182,
0.0009168102405965328,
0.038302160799503326,
-0.003218994941562414,
-0.08786480128765106,
0.021761104464530945,
0.004689205437898636,
-0.02416829951107502,
0.012033239006996155,
-0.000007504173026973149,
0.04563003033399582,
-0.051693473011255264,
-0.0346984937787056,
0.02584400214254856,
-0.021943144500255585,
0.03498387709259987,
0.05666583776473999,
-0.015333279967308044,
0.04485630616545677,
0.04161472246050835,
0.031958483159542084,
0.01050823274999857,
0.004506903700530529,
0.020907428115606308,
-0.012938489206135273,
-0.022036448121070862,
0.024317020550370216,
0.02906731702387333,
-0.048393528908491135,
0.032680775970220566,
0.02031378448009491,
0.004737926181405783,
-0.03759569302201271,
0.016992788761854172,
-0.03813527524471283,
0.026120809838175774,
0.043740883469581604,
-0.0041688913479447365,
-0.05837727710604668,
-0.019884632900357246,
-0.005788406357169151,
-0.055676452815532684,
0.00349604245275259,
-0.02539706602692604,
-0.04630381613969803,
-0.05733140558004379,
-0.0017634113319218159,
-0.03827811777591705,
0.010069714859127998,
-0.012233810499310493,
0.0014404802350327373,
-0.00849908497184515,
-0.0035520431119948626,
0.007644318044185638,
-0.005648882128298283,
0.04150386154651642,
-0.009090801700949669,
0.059418052434921265,
0.020733928307890892,
0.007716627325862646,
-0.012739033438265324,
-0.0056570968590676785,
-0.029210172593593597,
0.02265140414237976,
-0.00502495002001524,
-0.02746857888996601,
-0.04349402338266373,
0.015729349106550217,
-0.06138831004500389,
-0.030409902334213257,
0.012315886095166206,
-0.03491050377488136,
-0.034434571862220764,
-0.014427559450268745,
-0.01045203860849142,
0.0991392582654953,
-0.0013220316031947732,
-0.018277691677212715,
0.022553203627467155,
-0.03262060508131981,
0.060177989304065704,
-0.02660953626036644,
-0.020724939182400703,
-0.029683688655495644,
0.055716127157211304,
-0.011534983292222023,
-0.016959408298134804,
0.09003797918558121,
0.02053995430469513,
-0.038504939526319504,
0.07886950671672821,
0.01963588036596775,
0.018996387720108032,
-0.042131323367357254,
0.003403429174795747,
0.06078675016760826,
0.024619290605187416,
-0.0008932098862715065,
-0.011585798114538193,
0.008045135997235775,
-0.016247084364295006,
0.056510016322135925,
0.025210421532392502,
-0.009918482042849064,
-0.05816708877682686,
0.042141277343034744,
0.009200330823659897,
0.038900963962078094,
0.02193952538073063,
0.035273514688014984,
0.012215553782880306,
0.07077722996473312,
0.055775754153728485,
-0.04678205028176308,
-0.06208847463130951,
0.011962422169744968,
-0.02374396286904812,
-0.014736495912075043,
-0.01673746667802334,
-0.031600549817085266,
0.0019143930403515697,
0.04182817414402962,
-0.11629433929920197,
-0.01109961699694395,
-0.03151395171880722,
-0.0032144682481884956,
-0.00399125786498189,
-0.040538255125284195,
0.0018635679734870791,
0.0011357334442436695,
-0.03234296664595604,
0.004539181012660265,
-0.011188148520886898,
0.011454838328063488,
-0.032817427068948746,
-0.006560957990586758,
0.008304321207106113,
-0.01565883308649063,
-0.04688739404082298,
0.06447318196296692,
0.005304322112351656,
0.017175469547510147,
-0.0030355583876371384,
-0.025175413116812706,
0.05446489155292511,
0.014246055856347084,
0.006293074693530798,
-0.013214911334216595,
0.0004515083855949342,
0.007419583387672901,
-0.0142684830352664,
-0.03876885399222374,
0.069343701004982,
-0.005021483171731234,
-0.02477453090250492,
-0.02436053566634655,
0.017184758558869362,
0.05139809474349022,
0.034654438495635986,
-0.05120326206088066,
-0.012209540233016014,
0.0427202545106411,
-0.04883558303117752,
-0.018877265974879265,
0.01838664337992668,
-0.007103923242539167,
-0.06942560523748398,
0.021759362891316414,
0.012901602312922478,
-0.04216114059090614,
-0.02723785489797592,
-0.06552896648645401,
-0.004427958745509386,
0.007719587069004774,
-0.02504492923617363,
0.0542914979159832,
0.06374889612197876,
-0.0076008946634829044,
0.00252058869227767,
-0.012852064333856106,
0.00990210846066475,
0.020721346139907837,
0.06265252828598022,
-0.04514317214488983,
0.003955371677875519,
0.008213396184146404,
0.036274127662181854,
0.061944760382175446,
0.052583277225494385,
0.008708965964615345,
0.030393052846193314,
0.026909688487648964,
0.007594936527311802,
-0.030497970059514046,
0.011009312234818935,
-0.03477730602025986,
-0.028913529589772224,
0.042927682399749756,
0.05035622790455818,
0.012635333463549614,
-0.02273300662636757,
0.02513492852449417,
0.05817147344350815,
-0.012334064580500126,
-0.05108063295483589,
-0.07483576238155365,
0.07308407127857208,
-0.09731883555650711,
0.015141691081225872,
-0.012773394584655762,
0.00408434122800827,
-0.024989807978272438,
0.017636330798268318,
-0.0044372715055942535,
-0.07432565838098526,
0.05285362899303436,
-0.007000181823968887,
-0.03097730129957199,
0.03823255002498627,
-0.0790223702788353,
-0.041304100304841995,
0.0337090827524662,
-0.003651420818641782,
-0.037234481424093246,
0.011540377512574196,
-0.039037566632032394,
-0.007695751264691353,
-0.030491573736071587,
0.0033440550323575735,
-0.014957226812839508,
0.060371872037649155,
-0.06745550036430359,
-0.016411131247878075,
0.012548045255243778,
0.024061139672994614,
0.008212228305637836,
-0.01790076121687889,
-0.013698765076696873,
0.05211891606450081,
0.02753746695816517,
-0.025270264595746994,
-0.02370707504451275,
-0.05419037863612175,
0.06395018100738525,
0.09279163181781769,
0.045469433069229126,
0.014300057664513588,
-0.019493279978632927,
-0.0758560448884964,
0.034038033336400986,
0.07835206389427185,
0.021976163610816002,
0.004111345391720533,
-0.013574027456343174,
0.001282283803448081,
0.07078805565834045,
-0.0484396331012249,
0.047665636986494064,
0.06835397332906723,
-0.054767463356256485,
0.001741182990372181,
0.010402399115264416,
0.014440384693443775,
-0.004651047755032778,
-0.07571949064731598,
0.011846291832625866,
-0.005724411923438311,
0.02180420234799385,
0.0030687961261719465,
0.03170725330710411,
-0.06042858958244324,
-0.0013633152702823281,
-0.09594954550266266,
0.018372809514403343,
0.0368560366332531,
-0.00545220822095871,
0.01069777924567461,
0.016453124582767487,
-0.05418914183974266,
-0.014146139845252037,
-0.025371870025992393,
0.00494268536567688,
-0.04794231057167053,
-0.007409923244267702,
0.03563105687499046,
-0.004112219903618097,
-0.02539394237101078,
-0.04362916201353073,
-0.023793574422597885,
0.02551109343767166,
0.0029372056014835835,
-0.005496799014508724,
-0.007175202015787363,
-0.01575019583106041,
0.03564805909991264,
0.00709370244294405,
-0.026972219347953796,
0.03762191906571388,
0.024931568652391434,
-0.00339300069026649,
0.02513018622994423,
-0.01684415712952614,
0.0019080584170296788,
0.027609942480921745,
0.06474968045949936,
0.0014532277127727866,
0.011964072473347187,
0.002757695969194174,
0.005186048336327076,
0.06457779556512833,
-0.007442719303071499,
0.006673616357147694,
-0.0038111500907689333,
-0.03770165517926216,
-0.021075958386063576,
-0.0021343862172216177,
-0.01370785292237997,
0.03922412917017937,
-0.032996442168951035,
0.019553881138563156,
-0.06936653703451157,
0.03143274039030075,
0.052944380789995193,
-0.0025741129647940397,
0.00823222380131483,
0.027792630717158318,
0.03272673487663269,
0.004339282400906086,
-0.004561918321996927,
-0.0541827529668808,
-0.029239626601338387,
0.02537132240831852,
-0.03825732320547104,
0.004289598204195499,
-0.02507402002811432,
0.02127332054078579,
-0.03830147534608841,
0.02166222408413887,
0.03256857395172119,
-0.055403709411621094,
-0.013675183057785034,
-0.012247749604284763,
-0.01126887183636427,
-0.02709922008216381,
-0.034154195338487625,
0.023220879957079887,
-0.04396677762269974,
0.05792829394340515,
0.002982750767841935,
-0.025928771123290062,
-0.02543981745839119,
0.05314578860998154,
-0.0032205332536250353,
-0.033254560083150864,
0.012512889690697193,
-0.06408771872520447,
0.028789576143026352,
-0.0019928414840251207,
0.007956248708069324,
-0.017905045300722122,
-0.00012723184772767127,
0.020915845409035683,
0.060193922370672226,
-0.0014059528475627303,
-0.01945733278989792,
0.004180495161563158,
0.0007463741931132972,
0.05721981078386307,
0.04447281360626221,
0.01532236859202385,
-0.014449362643063068,
-0.0427262969315052,
0.01664835773408413,
0.0008637438295409083,
-0.007306645158678293,
-0.006751710083335638,
0.008831602521240711,
0.06905947625637054,
-0.049618493765592575,
-0.02941828966140747,
-0.025083184242248535,
0.0057310424745082855,
0.013272560201585293,
-0.007251111324876547,
0.023763181641697884,
0.01151452399790287,
-0.018496548756957054,
0.06814165413379669,
-0.017399286851286888,
-0.052516110241413116,
0.029226941987872124,
-0.016648391261696815,
0.005340774077922106,
-0.03519602119922638,
-0.05726286768913269,
-0.021182728931307793,
-0.00367446755990386,
0.037974707782268524,
0.012754330411553383,
-0.028511052951216698,
0.0165717676281929,
0.04455362260341644,
-0.030884526669979095,
-0.0488012433052063,
-0.021805696189403534,
0.03807364031672478,
0.005575858056545258,
-0.06010103225708008,
0.04598382115364075,
-0.05205731838941574,
0.06128089874982834,
-0.01944253034889698,
-0.03384256362915039,
-0.025286303833127022,
-0.07186610996723175,
-0.021443713456392288,
-0.06430558115243912,
0.022464102134108543,
0.008393400348722935,
0.008518505841493607,
0.05317072942852974,
0.033114612102508545,
0.01817028969526291,
0.01490041520446539,
0.000327732355799526,
-0.056595202535390854,
0.04637138172984123,
0.07495900988578796,
0.004395592957735062,
-0.041448235511779785,
-0.00904888566583395,
0.0017539623659104109,
0.03681841492652893,
-0.0022588386200368404,
0.04388086870312691,
0.024660397320985794,
-0.09416119009256363,
-0.008829199708998203
] |
<p>I know that if two air bubbles which are formed inside a liquid are somehow joined using something (say a small tube), then, as the bubble with the larger radius has less pressure and the one with the smaller radius has more air pressure, air will flow to the larger bubble from the smaller bubble as the excess pressure inside the smaller bubble is greater.</p>
<p>But will we be able to quantitatively calculate the time taken for this to happen?</p>
<p>If so then what is the relation connecting time and every other variable?</p> | g6653 | [
0.05291192606091499,
-0.00036051389179192483,
-0.004223006311804056,
0.028457337990403175,
-0.00848881620913744,
0.08019773662090302,
0.016047921031713486,
0.007433564402163029,
-0.06299249827861786,
-0.02475038915872574,
-0.05014685168862343,
-0.00043360484414733946,
-0.028333498165011406,
0.001975847175344825,
0.004042487591505051,
-0.02871454320847988,
0.039741162210702896,
0.010502811521291733,
-0.04400395601987839,
0.00882717128843069,
0.014652810990810394,
-0.005003285128623247,
0.018988775089383125,
-0.03357740119099617,
-0.07404188066720963,
-0.05524028092622757,
0.011451161466538906,
0.013434560969471931,
-0.05929978936910629,
0.01247584167867899,
0.014347121119499207,
0.044620972126722336,
0.03485693782567978,
-0.05337826535105705,
-0.017504030838608742,
-0.03816020116209984,
-0.04715506732463837,
0.01691974326968193,
-0.0009700463269837201,
-0.0007768390350975096,
0.027185361832380295,
0.05417827144265175,
-0.009925245307385921,
0.01275279838591814,
-0.050747163593769073,
-0.004319646395742893,
0.008417281322181225,
0.040626410394907,
0.00539037212729454,
-0.03429841250181198,
-0.015884196385741234,
0.05176901817321777,
-0.03647991642355919,
0.03917370364069939,
0.011641782708466053,
0.04193456470966339,
0.07291301339864731,
-0.035985223948955536,
0.04132765159010887,
0.06262023001909256,
-0.02622193470597267,
-0.02680765464901924,
-0.004013724159449339,
0.05321625992655754,
0.04612041264772415,
0.04374277591705322,
-0.03684600070118904,
-0.06277011334896088,
0.061663709580898285,
0.021949877962470055,
-0.05630936846137047,
-0.050824761390686035,
0.005072483327239752,
-0.0634084939956665,
-0.049993470311164856,
0.020548345521092415,
0.011788050644099712,
-0.01382732018828392,
-0.004754603374749422,
0.0007568751461803913,
0.04297995567321777,
0.008900856599211693,
0.002285178517922759,
0.056522950530052185,
0.05640510469675064,
-0.013413089327514172,
-0.007317651994526386,
-0.02411572076380253,
-0.03561163321137428,
0.025586742907762527,
0.019857486709952354,
-0.03608536720275879,
0.06819616258144379,
0.0033035920932888985,
-0.007471892982721329,
-0.019818555563688278,
-0.0417100191116333,
0.01710488833487034,
-0.02906091883778572,
-0.00627564312890172,
-0.0007493874290958047,
0.005246223881840706,
0.009725560434162617,
0.007303421385586262,
-0.08640200644731522,
-0.002273903926834464,
0.01887211576104164,
0.002687020692974329,
-0.03141370788216591,
0.004789118189364672,
-0.039147987961769104,
-0.010216085240244865,
-0.04366229474544525,
0.047923799604177475,
0.007976521737873554,
-0.0218502264469862,
-0.020217567682266235,
-0.04615982621908188,
-0.01027186680585146,
0.01657205820083618,
0.007552814204245806,
0.02159951813519001,
0.004383330699056387,
0.028441255912184715,
-0.0033253722358494997,
-0.006559772416949272,
-0.004978245589882135,
0.08840028196573257,
0.03183583915233612,
0.0420856811106205,
0.03520793095231056,
-0.02722328156232834,
0.03129873797297478,
-0.017847940325737,
-0.04386548697948456,
0.024398498237133026,
-0.052959755063056946,
0.0036115194670856,
-0.02893056720495224,
-0.004118236713111401,
-0.024355405941605568,
-0.024144405499100685,
0.007991272024810314,
0.01581559330224991,
-0.0754871666431427,
0.03861352801322937,
-0.013874168507754803,
-0.004644016269594431,
-0.02913922630250454,
-0.0007533961324952543,
-0.0056977239437401295,
0.0029428075067698956,
0.010078709572553635,
-0.006157419178634882,
0.03086821548640728,
0.061692290008068085,
-0.030103549361228943,
-0.049083054065704346,
0.04055667668581009,
0.000564179674256593,
0.021070081740617752,
-0.024711446836590767,
0.0466294139623642,
-0.016305191442370415,
-0.0733635276556015,
0.027755621820688248,
0.05359803885221481,
-0.03202899545431137,
0.006104279309511185,
-0.054502420127391815,
-0.010767652653157711,
-0.06953876465559006,
-0.012538043782114983,
0.019345907494425774,
0.042314715683460236,
0.06419298052787781,
0.05274537578225136,
-0.024503318592905998,
-0.03144882991909981,
0.01602192409336567,
0.006645594257861376,
0.015855200588703156,
0.004099498502910137,
-0.04447215050458908,
-0.007932687178254128,
0.028756624087691307,
0.019905241206288338,
-0.04509354382753372,
-0.07256605476140976,
-0.03165363147854805,
-0.038987088948488235,
-0.009144962765276432,
0.04123171046376228,
0.05202987790107727,
-0.04088776931166649,
0.0020991256460547447,
0.06662849336862564,
-0.029057303443551064,
-0.06006753444671631,
0.03362308442592621,
-0.04931197315454483,
0.04156521335244179,
0.04898867383599281,
0.000719048548489809,
0.063560351729393,
0.061029233038425446,
-0.01423674263060093,
0.015578905120491982,
0.003316726768389344,
0.07172752916812897,
0.016574088484048843,
0.028264617547392845,
0.004064652603119612,
0.007521939929574728,
-0.010019625537097454,
-0.034046296030282974,
-0.027278145775198936,
-0.026946790516376495,
0.005927844438701868,
0.03292073309421539,
-0.008960962295532227,
0.003585915779694915,
0.017319269478321075,
-0.03957124054431915,
0.01865139603614807,
-0.04343768209218979,
0.008498548530042171,
-0.033410631120204926,
-0.0065338509157299995,
-0.025567159056663513,
-0.03512134775519371,
0.03084622137248516,
0.010467111133038998,
-0.026680536568164825,
-0.0563727468252182,
0.07499255985021591,
0.04034668579697609,
0.06464377045631409,
-0.016891740262508392,
0.027169641107320786,
0.03241357579827309,
-0.04696245118975639,
-0.03469756990671158,
0.09318994730710983,
-0.001002162811346352,
0.03495194762945175,
0.02510266751050949,
-0.04241470620036125,
-0.030922474339604378,
0.08632483333349228,
-0.053947269916534424,
0.04029277339577675,
-0.0426359660923481,
-0.01728234812617302,
-0.017621764913201332,
-0.004300146829336882,
0.029723182320594788,
0.040981877595186234,
-0.038603924214839935,
-0.03106553666293621,
0.0012650109129026532,
-0.0019310333300381899,
-0.0020008038263767958,
-0.030442358925938606,
-0.07289743423461914,
0.0012082192115485668,
0.016143284738063812,
0.009422323666512966,
-0.01689690165221691,
-0.00396526837721467,
-0.012951971031725407,
0.010686121881008148,
-0.027406666427850723,
0.003405851311981678,
0.029845552518963814,
-0.04955010116100311,
-0.0015942761674523354,
-0.02839607372879982,
-0.018264491111040115,
-0.01625894196331501,
-0.030861251056194305,
-0.042757466435432434,
-0.09976650774478912,
0.01053330022841692,
0.0035783604253083467,
-0.05389266461133957,
0.03720076382160187,
0.07240357995033264,
0.02984800562262535,
0.0059867072850465775,
0.018884852528572083,
0.0036950912326574326,
0.00944356620311737,
0.013801591470837593,
0.05410172417759895,
0.08080510795116425,
0.059600524604320526,
0.028760045766830444,
0.0037755435332655907,
-0.047234270721673965,
-0.057231172919273376,
-0.012426118366420269,
0.008350237272679806,
0.0170893594622612,
0.018616795539855957,
-0.004844880662858486,
-0.05547114834189415,
-0.012035921216011047,
-0.03281751275062561,
-0.0021571002434939146,
0.04566212370991707,
0.03085457906126976,
-0.00731866667047143,
0.002603760687634349,
-0.022579066455364227,
-0.03293626755475998,
0.010662935674190521,
0.060542091727256775,
-0.0005727636744268239,
0.018589889630675316,
-0.009299315512180328,
-0.057369690388441086,
-0.005841018632054329,
-0.03071223385632038,
0.03735385462641716,
-0.04719087854027748,
-0.03786666318774223,
0.022497396916151047,
-0.06736081093549728,
0.010694161988794804,
-0.0317285880446434,
-0.013176080770790577,
-0.02086004614830017,
-0.011357870884239674,
-0.029028886929154396,
0.0029216224793344736,
-0.003263175254687667,
-0.006099015939980745,
-0.0005612043896690011,
0.025116657838225365,
0.017513088881969452,
-0.011408444494009018,
-0.02302924357354641,
0.012519989162683487,
0.004323160741478205,
0.028570979833602905,
0.01142210140824318,
0.044224321842193604,
0.03430378809571266,
-0.0014785077655687928,
0.025073189288377762,
0.002396530006080866,
0.004451428540050983,
-0.06726394593715668,
0.014989051036536694,
0.03812194988131523,
0.032514650374650955,
0.012503212317824364,
0.028224991634488106,
-0.066848024725914,
0.0220616664737463,
-0.03010481223464012,
0.01074634213000536,
0.07800114899873734,
-0.06565432995557785,
-0.050638843327760696,
0.028527338057756424,
0.023975059390068054,
-0.016455262899398804,
-0.03481640666723251,
-0.042136356234550476,
0.031018704175949097,
-0.018824458122253418,
-0.0006588195101357996,
0.035611849278211594,
-0.04611861705780029,
0.061667315661907196,
-0.040169838815927505,
0.011498413980007172,
0.030267488211393356,
0.05839269980788231,
0.05706923454999924,
-0.006248271558433771,
-0.0014113489305600524,
0.03606375306844711,
-0.03480330482125282,
-0.05228172615170479,
0.004131294321268797,
0.01256717462092638,
-0.10749725997447968,
-0.016952725127339363,
-0.05030505731701851,
-0.041391558945178986,
-0.0032135110814124346,
-0.00458489079028368,
-0.009520306251943111,
0.014921926893293858,
0.028166579082608223,
-0.00024283028324134648,
-0.01839587651193142,
-0.035625409334897995,
-0.04637554660439491,
-0.03982250764966011,
0.0347873717546463,
-0.012195906601846218,
0.026266619563102722,
0.050554998219013214,
-0.0017660033190622926,
-0.028376998379826546,
-0.008903414011001587,
0.017939891666173935,
-0.04364514350891113,
0.04197853058576584,
-0.04323486238718033,
0.018927985802292824,
-0.02752373367547989,
-0.013861196115612984,
-0.027209172025322914,
0.0047356183640658855,
0.016375472769141197,
0.00752910366281867,
-0.011424252763390541,
0.04667830467224121,
-0.02103562280535698,
0.00635620066896081,
0.02686285972595215,
0.03784344345331192,
0.02083420567214489,
-0.012268017046153545,
-0.030559005215764046,
-0.04421757906675339,
0.03914358839392662,
-0.060297273099422455,
0.0054656872525811195,
-0.023205868899822235,
0.009374505840241909,
-0.011035491712391376,
0.05421553924679756,
0.04151077941060066,
0.003934135194867849,
0.028398094698786736,
-0.011304153129458427,
0.01077120378613472,
-0.004798769950866699,
0.059956036508083344,
0.056442759931087494,
-0.014585692435503006,
-0.050371259450912476,
-0.026341766119003296,
-0.06407288461923599,
0.005308622494339943,
0.04668896645307541,
0.02348426729440689,
-0.02332659251987934,
-0.02588888257741928,
-0.0045839776284992695,
0.0015097821597009897,
0.039055462926626205,
0.009307147935032845,
0.014295181259512901,
-0.057492636144161224,
0.05392804369330406,
0.02340591885149479,
0.03369664400815964,
0.011587720364332199,
-0.09666363149881363,
0.014678205363452435,
-0.034187451004981995,
-0.07386516034603119,
0.05338180810213089,
0.004049889277666807,
0.03386237844824791,
0.01272420771420002,
0.09565966576337814,
0.028224727138876915,
0.0067940750159323215,
-0.037326350808143616,
0.019672948867082596,
0.09427181631326675,
-0.06575046479701996,
-0.0017085239524021745,
0.014472674578428268,
-0.009500941261649132,
0.009149639867246151,
0.036037199199199677,
0.002670848509296775,
-0.0534246452152729,
-0.007163798902183771,
0.044746410101652145,
0.021570054814219475,
0.012517809867858887,
0.015503674745559692,
0.05774068087339401,
0.024051159620285034,
-0.06567935645580292,
-0.015069611370563507,
-0.023846542462706566,
-0.020706290379166603,
0.017881980165839195,
-0.01724795624613762,
-0.026694752275943756,
0.06665702909231186,
0.0295161884278059,
-0.0022436981089413166,
0.00048275766312144697,
0.0477072149515152,
-0.015005411580204964,
0.029255883768200874,
-0.04172927886247635,
0.07485909759998322,
-0.019185425713658333,
0.016803592443466187,
-0.031126726418733597,
0.012708602473139763,
-0.02399872988462448,
-0.01437817420810461,
-0.030714120715856552,
-0.016381725668907166,
-0.029524900019168854,
-0.03097769431769848,
0.07654251903295517,
-0.0028932136483490467,
0.008651519194245338,
-0.011594509705901146,
-0.025693243369460106,
-0.002082153921946883,
-0.03817678615450859,
0.004271872341632843,
0.03528914228081703,
-0.04520643875002861,
-0.03297927603125572,
-0.033959560096263885,
-0.0012624847004190087,
0.021017318591475487,
-0.00003271522291470319,
-0.011097063310444355,
0.019271252676844597,
-0.004670056980103254,
0.05356211960315704,
-0.004371627699583769,
-0.06040449067950249,
0.006159151438623667,
-0.02181319147348404,
0.07403264194726944,
0.016643555834889412,
-0.023120557889342308,
-0.007221599575132132,
0.0338108204305172,
0.022667773067951202,
0.013251724652945995,
0.008165277540683746,
-0.0381016843020916,
-0.0053405496291816235,
0.05078813061118126,
0.020020002499222755,
-0.007638188544660807,
0.03570707142353058,
-0.013705894351005554,
0.0002841506211552769,
0.012080362997949123,
0.026484087109565735,
-0.013860585168004036,
0.006516503635793924,
0.011561066843569279,
-0.03746051713824272,
-0.04127032682299614,
-0.0019807976204901934,
0.0155174620449543,
-0.003988747484982014,
0.05635847523808479,
0.030131468549370766,
-0.09562540054321289,
0.036282528191804886,
-0.04189145937561989,
0.03290772810578346,
-0.003335186280310154,
0.03509877249598503,
-0.012886155396699905,
-0.0026059316005557775,
0.011868540197610855,
0.004972963128238916,
-0.029930463060736656,
-0.024982856586575508,
-0.015851521864533424,
-0.002554244827479124,
0.03309095650911331,
-0.004232244566082954,
0.0005792572046630085,
0.006769038271158934,
-0.0220344178378582,
-0.041681934148073196,
-0.026008347049355507,
-0.06206429377198219,
-0.041000381112098694,
-0.014259968884289265,
-0.003918585833162069,
0.025268372148275375,
-0.007763662841171026,
0.0033724401146173477,
0.016726680099964142,
-0.046376608312129974,
0.02670094184577465,
0.09090904146432877,
-0.03289191797375679,
-0.048456307500600815,
-0.005252680741250515,
-0.005577104166150093,
0.02049955353140831,
0.020486872643232346,
0.026068316772580147,
-0.009548849426209927,
0.030784599483013153,
0.09103930741548538,
0.019589262083172798,
0.02213614247739315,
-0.05148524418473244,
0.03127763420343399,
-0.024081256240606308,
0.016464876011013985,
-0.029842238873243332,
0.02741044946014881,
-0.016614707186818123,
0.01928938925266266,
-0.024621693417429924,
0.04500165581703186,
0.035185545682907104,
-0.0538487434387207,
-0.028490161523222923,
-0.08591766655445099,
-0.03331708535552025,
0.05042006075382233,
-0.028147753328084946,
-0.010494573041796684,
-0.017435580492019653,
0.012458447366952896,
0.04316435754299164,
-0.043863337486982346,
0.01647765375673771,
0.019107185304164886,
0.045826505869627,
0.030295170843601227,
0.03244924172759056,
0.02345644123852253,
0.08652559667825699,
0.015178157947957516,
-0.025908833369612694,
0.08918513357639313,
0.005274937022477388,
-0.07404632866382599,
-0.03828173875808716,
-0.029829736799001694,
0.009478605352342129,
-0.029432186856865883,
0.05973059684038162,
-0.07429526001214981,
-0.019197607412934303,
-0.038040369749069214,
-0.004396253731101751,
0.010675126686692238,
0.011152835562825203,
-0.02192549966275692,
-0.006601386237889528,
-0.028537556529045105,
0.0254436656832695,
0.020655978471040726,
0.037059370428323746,
0.026610875502228737,
-0.0427800714969635,
0.02623678371310234,
-0.055354248732328415,
0.04529095068573952,
0.020708654075860977,
-0.007711335550993681,
-0.05953394994139671,
-0.0065315100364387035,
0.009974130429327488,
0.025910470634698868,
0.022177230566740036,
0.04956921562552452,
0.003310210071504116,
-0.033835358917713165,
0.03780356049537659,
-0.0338703878223896,
0.04747700318694115,
-0.07073770463466644,
0.06444865465164185,
-0.0011156578548252583,
-0.03915438801050186,
-0.016686158254742622,
-0.02372715063393116,
-0.029766470193862915,
-0.0035368921235203743,
0.013705862686038017,
0.008820881135761738,
0.0008342951186932623,
0.024264633655548096,
0.07991877943277359,
-0.008594613522291183,
0.013833768665790558,
0.041226599365472794,
0.02147963084280491,
0.02312205545604229,
-0.027898326516151428,
-0.06320178508758545,
0.027335723862051964,
0.011999672278761864,
0.0012207786785438657,
-0.00028553063748404384,
-0.048303667455911636,
0.008934415876865387,
0.058694664388895035,
0.0631880834698677,
-0.009768969379365444,
-0.024280663579702377,
0.01587783172726631,
-0.07543819397687912,
-0.05638543888926506,
0.039872244000434875,
0.02783402055501938,
0.04544797167181969,
-0.030698416754603386,
-0.08475412428379059,
-0.027731433510780334,
-0.05163290351629257,
-0.011129898019134998,
-0.016749773174524307,
-0.01471636164933443,
-0.013692766427993774,
-0.05815006047487259,
0.0032426947727799416,
-0.033588215708732605,
-0.014626597054302692,
0.03278575465083122,
0.06137029454112053,
0.002596390899270773,
-0.025523405522108078,
0.023069532588124275,
0.05378137528896332,
-0.07066118717193604,
0.006965606007725,
-0.04185185208916664,
0.007942047901451588,
0.04853424057364464,
-0.019426528364419937,
0.011849706061184406,
-0.0801534652709961,
-0.0041917539201676846,
0.07157611101865768,
0.05816994607448578,
-0.030936909839510918,
-0.010255751200020313,
0.05002354830503464,
0.015910208225250244,
0.020752299576997757,
0.09233952313661575,
-0.04123612865805626,
-0.0877939909696579,
0.03188418224453926,
-0.04702235013246536,
-0.035081010311841965,
-0.011390507221221924,
0.07689737528562546,
-0.07437758147716522,
-0.021234747022390366,
0.034132447093725204,
0.003588547697290778,
-0.010001814924180508,
0.06761743128299713
] |
<p>I do not have much experience on this but if an atom has some electrons around nucleus and the atom itself it is moving at some speed does that affect the distribution of electrons around?</p>
<p>I am presuming that the interaction between the nucleus and electrons has a constant speed $c$. Anything I found so far is a calculation for interactions that presume an infinite speed. </p>
<p>As an argument I am thinking of relativistic Doppler effect that does not change proportional with $v/c$. So I am thinking that maybe the speed does affect the distribution and so that is why the difference in the emission energy.</p> | g6654 | [
0.048009179532527924,
0.03378889709711075,
0.018799996003508568,
0.027472540736198425,
0.04513786733150482,
0.006622040178626776,
-0.008254799991846085,
0.07440896332263947,
-0.028358913958072662,
-0.0166776180267334,
0.030557435005903244,
0.02470303885638714,
0.00046062315232120454,
0.0304719265550375,
-0.005039358511567116,
0.009942373260855675,
0.05099909380078316,
-0.04009988531470299,
0.01498967781662941,
0.07433230429887772,
0.003033527173101902,
-0.021755840629339218,
-0.021616939455270767,
-0.020085524767637253,
0.002711279783397913,
0.005989363417029381,
0.004110068082809448,
-0.05460376292467117,
-0.04474084824323654,
0.0011784539092332125,
-0.004877518396824598,
-0.0049287304282188416,
0.0046027665957808495,
-0.013058740645647049,
-0.04764952138066292,
-0.05679307132959366,
0.03586357831954956,
0.027366647496819496,
0.03411474451422691,
0.0159311480820179,
-0.016085254028439522,
0.020032141357660294,
0.0322849303483963,
-0.02870219200849533,
0.0019386926433071494,
0.010790172964334488,
0.01369027141481638,
0.014385647140443325,
-0.059447064995765686,
0.014841903932392597,
-0.05801619589328766,
-0.0051167188212275505,
-0.021921096369624138,
0.05174285173416138,
0.020967813208699226,
-0.016613861545920372,
-0.004264076240360737,
-0.007448376156389713,
0.03008997067809105,
0.02308681607246399,
0.01921420730650425,
0.003406043630093336,
0.020547280088067055,
-0.014376518316566944,
0.04480884596705437,
0.0009760981774888933,
-0.025806043297052383,
0.03371269255876541,
0.0230917539447546,
0.016171514987945557,
-0.008733836933970451,
-0.025597183033823967,
-0.07729333639144897,
-0.04106459021568298,
0.005354158580303192,
-0.022684792056679726,
0.0027429957408457994,
-0.08184424042701721,
0.009878196753561497,
0.026630720123648643,
-0.07042267173528671,
-0.03182927519083023,
0.05351515859365463,
0.0028401543386280537,
0.03508361056447029,
0.01040763221681118,
0.034690938889980316,
-0.0024848810862749815,
-0.0007144584669731557,
-0.04512651637196541,
0.021782973781228065,
-0.05847258120775223,
-0.009164606221020222,
-0.020860547199845314,
-0.025692714378237724,
-0.053045764565467834,
-0.022279078140854836,
0.07850520312786102,
-0.05592610314488411,
-0.026156682521104813,
-0.021480634808540344,
0.0017114531947299838,
0.015194764360785484,
0.010937646962702274,
-0.04325491935014725,
-0.027530914172530174,
-0.05903639644384384,
-0.01722422055900097,
0.019944975152611732,
0.0074263159185647964,
-0.009303407743573189,
-0.1515662670135498,
0.026774773374199867,
-0.01249829400330782,
-0.02023899555206299,
-0.032100215554237366,
0.01129396352916956,
-0.044779643416404724,
-0.023209301754832268,
0.04702817276120186,
-0.006572707090526819,
0.05132802203297615,
-0.04102401062846184,
0.0186240803450346,
-0.01570815034210682,
0.010453051887452602,
-0.0116362189874053,
-0.008331955410540104,
0.00038305038469843566,
-0.02182937040925026,
0.02561161108314991,
0.005463102832436562,
0.013460418209433556,
0.04759541526436806,
-0.03376040607690811,
0.0006361613632179797,
0.0018006647005677223,
0.020477939397096634,
-0.04401961341500282,
-0.02668776549398899,
0.06778732687234879,
0.02674449421465397,
0.05191199108958244,
-0.018645519390702248,
-0.02798163890838623,
0.015728680416941643,
-0.010691840201616287,
-0.015329299494624138,
0.018313782289624214,
-0.06662831455469131,
0.017883913591504097,
0.006376019679009914,
0.0011332754511386156,
-0.041001420468091965,
-0.054091595113277435,
0.0179289560765028,
-0.017528245225548744,
0.020510684698820114,
-0.062477707862854004,
0.05526680499315262,
0.02207317017018795,
-0.02434714138507843,
-0.03663002699613571,
-0.02459818683564663,
-0.038643158972263336,
0.030620679259300232,
0.04555526748299599,
0.0076849861070513725,
0.03702050447463989,
-0.04207734391093254,
0.019253864884376526,
0.032051973044872284,
-0.027917008846998215,
0.02139611355960369,
0.00013979982759337872,
-0.019255632534623146,
0.051913194358348846,
0.012924298644065857,
0.0017959533724933863,
0.010051875375211239,
-0.01958898827433586,
-0.009061465039849281,
0.03429873660206795,
-0.024890322238206863,
0.03256038576364517,
0.009970652870833874,
-0.025975605472922325,
-0.0002281040360685438,
-0.08038904517889023,
-0.003540788544341922,
-0.0011801562504842877,
-0.046222563832998276,
0.0034935942385345697,
-0.01251496747136116,
-0.038714054971933365,
0.007092752493917942,
0.0064163594506680965,
-0.020413387566804886,
-0.005127776879817247,
-0.04082126170396805,
0.010890720412135124,
0.029641127213835716,
-0.014771691523492336,
0.01743404194712639,
0.1097811609506607,
-0.02939332090318203,
0.00311743700876832,
-0.00863890815526247,
0.038363102823495865,
-0.010371586307883263,
0.06389803439378738,
-0.006828645709902048,
-0.06092936918139458,
0.07163424044847488,
0.06676054000854492,
0.025847529992461205,
-0.04399087280035019,
0.007973936386406422,
-0.009688974358141422,
0.04165186360478401,
-0.03347396478056908,
-0.036803219467401505,
-0.023424062877893448,
-0.030882354825735092,
-0.03893638029694557,
-0.05031266435980797,
0.012979745864868164,
-0.04456314072012901,
0.014079216867685318,
0.08961878716945648,
-0.03624188154935837,
0.05999042093753815,
-0.043181437999010086,
-0.0017810070421546698,
-0.008584156632423401,
0.02865223027765751,
-0.013349955901503563,
-0.010608007200062275,
-0.02903173677623272,
0.006213774438947439,
0.002066938439384103,
-0.023647375404834747,
-0.04925135150551796,
-0.009738310240209103,
0.030660182237625122,
-0.038193754851818085,
0.043212562799453735,
-0.0402316115796566,
0.013595297001302242,
-0.04964964836835861,
0.04295244812965393,
-0.01718209683895111,
-0.06943701207637787,
-0.00685862684622407,
0.008913223631680012,
-0.008073616772890091,
-0.05157248675823212,
0.05227644369006157,
-0.045531224459409714,
-0.042146068066358566,
-0.03774530813097954,
-0.010425613261759281,
-0.0001700754655757919,
0.030237438157200813,
0.0018888968043029308,
-0.0045665958896279335,
-0.00946616381406784,
-0.0021009566262364388,
-0.027022330090403557,
0.004412517417222261,
-0.005779891274869442,
0.05179595574736595,
-0.044502872973680496,
0.033230219036340714,
-0.013549836352467537,
-0.017820186913013458,
0.0009159618057310581,
-0.04418756812810898,
-0.024707837030291557,
0.008127374574542046,
-0.013865579850971699,
-0.04504001885652542,
-0.02205144613981247,
-0.03332291916012764,
0.05935799330472946,
-0.03995605185627937,
0.01612289622426033,
-0.03055521287024021,
0.016255071386694908,
-0.03298313543200493,
0.013736770488321781,
0.02874629572033882,
0.01970364712178707,
0.005582625512033701,
0.028174199163913727,
0.054598722606897354,
0.09580107033252716,
-0.044604238122701645,
-0.03151104226708412,
0.05012963339686394,
0.012900427915155888,
-0.050470318645238876,
-0.0366055853664875,
0.03855862468481064,
0.023152342066168785,
0.005183980334550142,
-0.07956677675247192,
-0.016279255971312523,
0.008228998631238937,
-0.005822184029966593,
-0.024456879124045372,
0.01495390385389328,
0.011274286545813084,
0.004915801342576742,
-0.025988170877099037,
-0.004238571971654892,
-0.016986843198537827,
0.026529312133789062,
0.022381383925676346,
-0.004120506811887026,
0.04755350574851036,
0.01889554224908352,
-0.02318638004362583,
-0.0032986835576593876,
0.017297325655817986,
0.05601539462804794,
0.003423150861635804,
0.02393473871052265,
-0.007278289645910263,
-0.0008339608320966363,
-0.009897963143885136,
0.013305590488016605,
-0.0009785187430679798,
-0.00905364565551281,
-0.06916318088769913,
-0.03225817531347275,
0.03633550554513931,
0.03914811089634895,
0.003598393639549613,
0.04248181730508804,
0.06787983328104019,
-0.0011616110568866134,
-0.0805734395980835,
0.029139943420886993,
0.003953315317630768,
0.008791749365627766,
0.007038187235593796,
0.010055836290121078,
-0.06482386589050293,
-0.013733835890889168,
0.061131369322538376,
0.007514940574765205,
-0.029502324759960175,
-0.030458837747573853,
0.022391173988580704,
-0.01166046503931284,
0.0015815277583897114,
-0.005986676085740328,
-0.026818066835403442,
0.008242379873991013,
-0.03998352214694023,
-0.03651636466383934,
0.012918500229716301,
0.017285943031311035,
-0.0636216253042221,
0.0034236283972859383,
-0.03705830127000809,
0.019678179174661636,
0.06409274786710739,
-0.006018731743097305,
-0.06452446430921555,
0.03418266400694847,
-0.013836086727678776,
0.01769532449543476,
0.014662003144621849,
0.016576839610934258,
0.03701023757457733,
0.055069297552108765,
-0.05845554545521736,
0.019071875140070915,
-0.017603300511837006,
0.022055942565202713,
-0.00545019144192338,
0.026465637609362602,
0.007746540941298008,
-0.035542599856853485,
-0.03599679470062256,
-0.030605528503656387,
0.005927532445639372,
-0.045670442283153534,
-0.01934673637151718,
-0.015229769982397556,
-0.010558721609413624,
0.03945538401603699,
0.015803314745426178,
-0.00751987099647522,
0.031063389033079147,
-0.004033308010548353,
0.05970858410000801,
0.034325599670410156,
-0.029370969161391258,
-0.026729414239525795,
-0.01207639928907156,
-0.04233746603131294,
0.031446099281311035,
0.014675432816147804,
0.03052341565489769,
-0.022469887509942055,
-0.04924628883600235,
-0.035759277641773224,
-0.05093199759721756,
0.04170622304081917,
-0.052156366407871246,
0.026179485023021698,
-0.024024005979299545,
0.02523011714220047,
-0.014973893761634827,
0.03126411885023117,
-0.02910776436328888,
-0.007384985685348511,
-0.04203274846076965,
0.05133649334311485,
0.06439100950956345,
0.030377373099327087,
-0.016907019540667534,
0.06554247438907623,
0.07428470253944397,
-0.004459386225789785,
-0.005714762955904007,
-0.018077727407217026,
-0.0019825384952127934,
0.02841765619814396,
0.03566506877541542,
0.01360805332660675,
-0.07739348709583282,
0.07828320562839508,
-0.0251946859061718,
0.019115669652819633,
0.045403581112623215,
-0.0016359704313799739,
0.06241225078701973,
0.036608096212148666,
0.04256755858659744,
0.04972637817263603,
-0.046681832522153854,
0.09208911657333374,
-0.08619894087314606,
-0.048841606825590134,
-0.07008206099271774,
-0.04345402494072914,
-0.0021741841919720173,
0.020274877548217773,
-0.03159955143928528,
-0.0019610710442066193,
0.023993022739887238,
-0.01116917748004198,
-0.08565085381269455,
0.0026983662974089384,
0.08251947909593582,
0.00605913856998086,
-0.08828935027122498,
0.0419219471514225,
0.050027087330818176,
0.050516169518232346,
-0.028824351727962494,
-0.000987290171906352,
-0.008811579085886478,
-0.010612836107611656,
-0.0826459750533104,
-0.009264384396374226,
0.023793430998921394,
-0.03428531065583229,
0.02486802078783512,
0.016871942207217216,
0.015455225482583046,
-0.0356101393699646,
0.03954237699508667,
-0.05563497915863991,
-0.00015408893523272127,
-0.03915669023990631,
-0.04372518137097359,
-0.0729018971323967,
0.03611311689019203,
0.027348270639777184,
-0.0024035486858338118,
0.020608793944120407,
-0.0325334332883358,
0.06469127535820007,
0.053730301558971405,
-0.08977539837360382,
0.04600505530834198,
0.01022669579833746,
-0.02566119097173214,
-0.04317481070756912,
0.05072863772511482,
0.011807174421846867,
0.07004077732563019,
-0.007034470792859793,
-0.011877373792231083,
0.009441526606678963,
-0.0368431881070137,
0.069581039249897,
-0.03164716064929962,
0.0009595583542250097,
-0.006793367676436901,
0.06108340993523598,
0.07582369446754456,
-0.009983422234654427,
-0.031343813985586166,
0.013744979165494442,
-0.053853292018175125,
0.027259791269898415,
0.03243619576096535,
0.00539342500269413,
-0.051050543785095215,
0.023668481037020683,
-0.017294788733124733,
-0.012570816092193127,
-0.014410538598895073,
-0.028004098683595657,
0.06351886689662933,
0.016332069411873817,
0.003639979287981987,
-0.00880371406674385,
0.026397021487355232,
-0.04478352889418602,
-0.019939756020903587,
0.029609685763716698,
0.02561989426612854,
0.05774649605154991,
0.05928651615977287,
0.0013692877255380154,
-0.0013291279319673777,
0.039839766919612885,
-0.0034872356336563826,
-0.013162430375814438,
-0.004339046310633421,
0.000021748563085566275,
0.01786145195364952,
0.008765647187829018,
0.055099643766880035,
-0.023816129192709923,
0.010276807472109795,
0.08202313631772995,
-0.0362204909324646,
-0.013847769238054752,
-0.05929316580295563,
-0.0035967768635600805,
0.018378524109721184,
0.005829867906868458,
0.03655394911766052,
0.04447128623723984,
0.0002767450059764087,
0.027014585211873055,
0.021000955253839493,
0.022876501083374023,
0.05056328698992729,
-0.005102957133203745,
0.017109276726841927,
-0.009277800098061562,
0.0313473604619503,
0.03491713106632233,
0.07433334738016129,
0.03657342493534088,
0.02460390143096447,
-0.016980493441224098,
-0.009864674881100655,
-0.048555538058280945,
0.027207301929593086,
0.05078810080885887,
0.011671343818306923,
0.003578126896172762,
-0.033813998103141785,
-0.032838962972164154,
0.050571344792842865,
0.023448340594768524,
-0.024043964222073555,
-0.0403204970061779,
-0.061180245131254196,
0.014288684353232384,
0.06740937381982803,
0.012346744537353516,
-0.06054449453949928,
-0.05988204479217529,
0.010946705937385559,
-0.0325939804315567,
0.03938177973031998,
0.046616703271865845,
0.07673797011375427,
-0.03229227289557457,
0.004622017033398151,
-0.056901488453149796,
0.021427759900689125,
-0.032456688582897186,
-0.04836197942495346,
-0.040734339505434036,
-0.02532038278877735,
-0.10167164355516434,
-0.033350132405757904,
0.0724826231598854,
0.043091826140880585,
-0.034133292734622955,
0.022134093567728996,
0.010881547816097736,
0.005714064463973045,
-0.0017409243155270815,
-0.028956597670912743,
0.033380087465047836,
-0.0020875718910247087,
0.03822153061628342,
-0.02786492556333542,
0.046672847121953964,
0.04025402292609215,
-0.03255749121308327,
-0.00514841778203845,
-0.04140634089708328,
-0.03072584606707096,
0.013235361315310001,
0.0354759506881237,
-0.004145987797528505,
0.009434498846530914,
-0.023696355521678925,
-0.03222072497010231,
-0.03155065327882767,
0.05759480968117714,
0.04961361363530159,
-0.05022922903299332,
0.030274948105216026,
0.015323055908083916,
-0.025954077020287514,
0.05843166634440422,
0.010666358284652233,
-0.03394347056746483,
0.053358450531959534,
0.0012634850572794676,
0.055005840957164764,
0.0026889846194535494,
-0.028161797672510147,
0.04015154018998146,
0.0347461923956871,
0.019221464172005653,
-0.014860117807984352,
0.030486363917589188,
0.03229710832238197,
-0.02585453912615776,
-0.04174058139324188,
0.04504593089222908,
0.04113992303609848,
-0.026984291151165962,
-0.00982234999537468,
-0.012872990220785141,
-0.045725855976343155,
-0.015673227608203888,
0.07689446955919266,
-0.013925883919000626,
-0.036686014384031296,
-0.016993772238492966,
-0.03567500412464142,
-0.011523234657943249,
-0.07060734182596207,
-0.047445736825466156,
-0.0683782771229744,
-0.005533864721655846,
-0.01021422166377306,
0.013919712975621223,
0.012613768689334393,
0.012788818217813969,
-0.03889736533164978,
-0.06629180163145065,
0.01320914551615715,
-0.022641688585281372,
-0.07688559591770172,
-0.010700320824980736,
0.05398782715201378,
0.06701838970184326,
0.009621103294193745,
-0.002064254367724061,
-0.013276580721139908,
-0.019314667209982872,
-0.05530676990747452,
0.04827811196446419,
0.027027597650885582,
0.0010635207872837782,
-0.00012250083091203123,
-0.03890656679868698,
0.05453380569815636,
-0.05661335587501526,
-0.0318303257226944,
-0.008877811953425407,
-0.02668418549001217,
0.02053006738424301,
-0.056858208030462265,
-0.022513961419463158,
-0.008722417987883091,
-0.03356198966503143,
0.04109059274196625,
-0.028588738292455673,
0.036048609763383865,
-0.004626499488949776,
0.028852108865976334,
-0.0038964594714343548,
-0.034086719155311584,
0.05667196959257126,
0.037412796169519424,
0.05422502011060715,
0.019203033298254013,
0.029904978349804878,
0.048240624368190765,
-0.008882707916200161,
0.02440185286104679,
0.06648987531661987,
-0.04761407896876335,
0.10202106088399887,
-0.02813401073217392,
-0.036763131618499756,
-0.04152948781847954,
0.0003026828053407371,
0.028078746050596237,
0.0123522337526083,
0.03339940682053566,
-0.022685106843709946,
-0.0050488547421991825,
-0.008262081071734428,
-0.024696901440620422,
0.010251500643789768,
-0.037577565759420395,
-0.007735682651400566,
-0.0016999533399939537,
0.05014289170503616,
0.018141571432352066,
-0.007356452289968729,
0.033973079174757004,
-0.03868852183222771,
-0.01547261606901884,
-0.06674911826848984,
-0.0009346549049951136,
0.06755805760622025,
-0.04231848195195198,
0.0003698507498484105,
0.022689249366521835,
-0.0044649140909314156,
-0.060648199170827866,
0.041547320783138275,
0.045493148267269135,
-0.024039505049586296,
-0.06784824281930923,
0.01583082415163517,
0.004210211802273989,
0.008439244702458382,
0.03843230754137039,
-0.012789457105100155,
0.005528615787625313,
-0.06616277247667313,
0.06857732683420181,
0.03930037096142769,
0.020206891000270844,
0.0034682198893278837,
0.0061630988493561745,
-0.02340654283761978,
0.01168078277260065,
-0.007488748524338007,
-0.027660099789500237,
0.021818777546286583,
0.005531261209398508,
0.028881283476948738,
-0.027065645903348923,
0.004418287891894579,
-0.028499579057097435
] |
<p>Is the classical doopler effect for light shift equal to $1-v/c$ exact or an approximation of a classical formula? I know that it is an approximation of the relativistic formula, but what was the corresponding classical formula? I ask this because in Einstein's On the Electrodynamics of moving bodies he derives $\sqrt\frac{1-v/c}{1+v/c}$ and notes that it is different from the classical case. I'm not exactly sure what formula he is comparing it to. </p> | g6655 | [
-0.015626616775989532,
0.0022808092180639505,
-0.007539005018770695,
0.009474537335336208,
0.030035270377993584,
0.012674909085035324,
0.07102043181657791,
-0.030297495424747467,
-0.019603868946433067,
0.010208811610937119,
-0.029798241332173347,
0.030163664370775223,
0.009804647415876389,
0.03922615945339203,
-0.03203315660357475,
-0.004896062891930342,
0.04924827441573143,
-0.012320649810135365,
0.054563652724027634,
-0.04112367331981659,
0.018544843420386314,
-0.0007734078099019825,
-0.042225491255521774,
-0.04969145730137825,
0.013236486352980137,
-0.004405772779136896,
0.003295435104519129,
0.007431844249367714,
-0.026263391599059105,
0.004034930374473333,
0.01237572357058525,
0.048737943172454834,
0.015388469211757183,
0.003258625278249383,
0.04773953929543495,
-0.0552721805870533,
0.014677280560135841,
0.03127675876021385,
0.03525802120566368,
0.020283395424485207,
-0.047052185982465744,
0.01494350004941225,
0.03741057217121124,
0.008789819665253162,
0.016547109931707382,
-0.00263024284504354,
-0.009046203456819057,
0.0006247534183785319,
-0.035581644624471664,
-0.02112078107893467,
-0.045705750584602356,
0.022563567385077477,
0.029226865619421005,
0.04511604085564613,
-0.03586534038186073,
0.005705224350094795,
-0.006502749864012003,
-0.04095792397856712,
0.04746130108833313,
0.04941757768392563,
-0.007395220920443535,
-0.02504023350775242,
0.018236201256513596,
-0.02956170216202736,
0.028618425130844116,
-0.01832663267850876,
0.0015051077352836728,
-0.039960239082574844,
0.024861691519618034,
-0.010721515864133835,
-0.012205350212752819,
-0.08157899975776672,
-0.015629971399903297,
-0.02573402412235737,
-0.029183652251958847,
-0.036240361630916595,
-0.011397771537303925,
-0.045265574008226395,
0.023892562836408615,
-0.05848511680960655,
0.0028667456936091185,
-0.04626946896314621,
0.03408926725387573,
0.050567030906677246,
0.06387095153331757,
-0.0058167921379208565,
0.03758300840854645,
0.0640595555305481,
0.0038019195199012756,
-0.030995363369584084,
0.02688005566596985,
-0.051400016993284225,
0.010517685674130917,
-0.022004704922437668,
0.006223409436643124,
-0.05217021331191063,
-0.008036830462515354,
0.04154123365879059,
-0.024152882397174835,
-0.0304148830473423,
-0.03089084103703499,
-0.04223811626434326,
0.009219804778695107,
0.0348246768116951,
-0.020487219095230103,
-0.030336519703269005,
0.037740543484687805,
-0.019649337977170944,
0.005091092083603144,
-0.013230605982244015,
-0.09508559107780457,
-0.1076526865363121,
0.03269099071621895,
-0.07819537073373795,
-0.051121897995471954,
-0.03629574179649353,
0.0329289436340332,
-0.04809502139687538,
0.024747449904680252,
0.024647939950227737,
0.021603913977742195,
0.03112826868891716,
0.04467129707336426,
0.06782110035419464,
0.025124935433268547,
-0.027231406420469284,
-0.013023891486227512,
-0.004137316253036261,
0.014141076244413853,
0.026474758982658386,
0.011083764024078846,
-0.009439130313694477,
0.004209313075989485,
0.008891772478818893,
-0.04793648049235344,
0.05234391987323761,
0.09302625805139542,
-0.00978008285164833,
0.06337954103946686,
-0.012722951360046864,
0.06666149199008942,
-0.0038419514894485474,
-0.017826812341809273,
-0.016857976093888283,
-0.06985890120267868,
0.0340566411614418,
-0.027905534952878952,
-0.025008616968989372,
0.04976482689380646,
-0.018511727452278137,
0.07176285982131958,
0.005504312925040722,
0.04865841194987297,
-0.011446143500506878,
-0.003526862245053053,
0.012205805629491806,
0.018454495817422867,
0.04598783701658249,
-0.03881121426820755,
0.07151561975479126,
0.012118814513087273,
-0.01684555597603321,
-0.02046467736363411,
-0.0066778818145394325,
-0.006907177157700062,
0.002366642700508237,
-0.005060720723122358,
-0.030985001474618912,
0.005541848950088024,
-0.10515926778316498,
-0.02542768232524395,
0.018721062690019608,
0.027719693258404732,
-0.00030471134232357144,
0.008632679469883442,
0.031161794438958168,
0.020176295191049576,
0.009312277659773827,
-0.002344020875170827,
0.046129871159791946,
-0.05783768370747566,
-0.0353519506752491,
-0.005316445603966713,
0.007379458285868168,
-0.05115893855690956,
-0.055345457047224045,
-0.021099556237459183,
-0.017292290925979614,
-0.04047374054789543,
-0.016653867438435555,
-0.04754684120416641,
-0.014983762055635452,
0.010354338213801384,
0.04111819714307785,
-0.08141225576400757,
0.027015196159482002,
-0.010668870061635971,
-0.018969310447573662,
-0.012633257545530796,
0.037622980773448944,
0.012382132932543755,
0.02703983150422573,
0.03174320235848427,
-0.03697085753083229,
0.025385817512869835,
0.0028890520334243774,
-0.01950933039188385,
-0.048951681703329086,
0.10036483407020569,
0.006084609776735306,
0.06779082119464874,
-0.022734008729457855,
0.040264662355184555,
0.05041706562042236,
-0.029026154428720474,
-0.029307281598448753,
-0.055163074284791946,
-0.009573707357048988,
0.002924968721345067,
0.04940386116504669,
-0.04710753262042999,
-0.007410296238958836,
0.011341225355863571,
0.04527369886636734,
0.017440075054764748,
-0.008448266424238682,
0.006947332993149757,
-0.01899847574532032,
0.08137574791908264,
0.023107513785362244,
-0.050101254135370255,
0.043072815984487534,
-0.05338551476597786,
0.04005055874586105,
0.02790774218738079,
0.05641718581318855,
-0.06874087452888489,
-0.015855712816119194,
0.04148370772600174,
0.024415897205471992,
0.04772373288869858,
-0.03397157043218613,
-0.03804673254489899,
-0.0059316628612577915,
-0.014936063438653946,
0.042898740619421005,
0.094915971159935,
0.00020554174261633307,
-0.02473454736173153,
-0.05280382186174393,
-0.020658668130636215,
0.011992122046649456,
-0.05368763953447342,
0.006123456638306379,
0.011323487386107445,
-0.04445461556315422,
-0.04662143439054489,
0.06510202586650848,
-0.047876209020614624,
-0.002176599809899926,
-0.04586631804704666,
-0.005412972066551447,
0.01855570822954178,
-0.002545316470786929,
-0.003963455557823181,
0.016087155789136887,
0.002404238563030958,
0.006637379061430693,
0.04338444769382477,
-0.020456798374652863,
0.012441441416740417,
0.02292000874876976,
-0.03806499019265175,
0.035834506154060364,
-0.022951874881982803,
-0.03193133696913719,
0.012574578635394573,
-0.04865972325205803,
0.04260902479290962,
-0.04143749177455902,
-0.013979931361973286,
-0.0027712553273886442,
-0.03951055556535721,
-0.01661692000925541,
0.021723952144384384,
-0.07627490162849426,
0.003884869394823909,
-0.024395490065217018,
-0.03913476690649986,
0.014778858982026577,
-0.06078990176320076,
0.02802429534494877,
0.0032421823125332594,
0.0030226081144064665,
0.022346362471580505,
0.052765313535928726,
0.058946575969457626,
0.03801332414150238,
-0.03898930922150612,
0.09756898134946823,
0.016332000494003296,
-0.018886437639594078,
-0.03262617439031601,
0.004854556638747454,
0.009294582530856133,
0.008640208281576633,
-0.01151889469474554,
-0.07214029133319855,
0.09705831110477448,
0.07856032997369766,
-0.011497316882014275,
0.07667440921068192,
0.007062940392643213,
-0.0006276261992752552,
-0.06594720482826233,
-0.02045777626335621,
0.04454711824655533,
-0.02084271050989628,
0.014364269562065601,
-0.004900261294096708,
0.010066735558211803,
-0.038288265466690063,
-0.026109695434570312,
0.010406763292849064,
0.02943824976682663,
0.042947035282850266,
-0.04812593758106232,
0.02701793983578682,
-0.015660323202610016,
-0.00572211341932416,
0.01894356682896614,
-0.020556937903165817,
-0.030508849769830704,
-0.03905252739787102,
-0.025189366191625595,
-0.015741553157567978,
-0.07082119584083557,
0.06515497714281082,
0.009838924743235111,
0.004668170586228371,
-0.02552853897213936,
0.028366899117827415,
-0.10148033499717712,
0.04323562607169151,
0.034413959830999374,
0.013575728982686996,
0.02951861545443535,
0.006408335641026497,
-0.007977757602930069,
0.015253635123372078,
0.018942752853035927,
-0.004249344114214182,
-0.032558318227529526,
0.017951471731066704,
-0.04749992862343788,
-0.0014353051083162427,
0.011978461407124996,
0.039191655814647675,
0.03323153778910637,
0.009375940077006817,
0.01072264090180397,
-0.0155080771073699,
-0.050844334065914154,
0.03336426243185997,
0.018696404993534088,
-0.04720146209001541,
0.0029437385965138674,
0.04877697676420212,
-0.010813646949827671,
-0.021348964422941208,
-0.010826303623616695,
-0.008962390013039112,
0.022931864485144615,
0.08162157982587814,
-0.005061354022473097,
-0.0325319766998291,
0.0007533460156992078,
0.04972895607352257,
-0.06962757557630539,
0.016602886840701103,
0.035744909197092056,
0.04400409758090973,
-0.03548337146639824,
0.022893939167261124,
-0.028976839035749435,
-0.06647871434688568,
-0.045553576201200485,
-0.041146643459796906,
0.04919159784913063,
0.004204663913697004,
0.024754159152507782,
-0.050536442548036575,
0.003819243749603629,
0.02820623479783535,
0.029426436871290207,
0.002136226510629058,
0.008830014616250992,
0.00583312613889575,
-0.07176202535629272,
-0.0031052331905812025,
0.011581439524888992,
0.0069349342957139015,
0.057114869356155396,
-0.011721285991370678,
-0.021923402324318886,
-0.02571006305515766,
0.02830454520881176,
-0.06453336775302887,
0.006194959860295057,
0.034428875893354416,
-0.02626839466392994,
-0.019257700070738792,
-0.05695696547627449,
-0.03642994537949562,
0.04786420240998268,
0.015767060220241547,
0.05825083330273628,
-0.036677442491054535,
0.03815830126404762,
0.009105360135436058,
0.010034369304776192,
0.009293703362345695,
0.002460115822032094,
0.0035917460918426514,
-0.06273160129785538,
0.013338676653802395,
0.012574438005685806,
0.004859566688537598,
0.047566067427396774,
-0.025465484708547592,
0.018446609377861023,
0.003943024668842554,
-0.0035387431271374226,
0.07172109186649323,
-0.006715315859764814,
0.07417071610689163,
0.01107680331915617,
0.08623112738132477,
-0.04546743631362915,
0.003126532770693302,
0.036757439374923706,
0.016362229362130165,
0.06763394176959991,
-0.02707991562783718,
-0.02092711441218853,
0.06099701300263405,
-0.03676356002688408,
-0.04011526703834534,
0.027807287871837616,
-0.02050931751728058,
-0.0014000277733430266,
0.0684170350432396,
0.03900633379817009,
0.015644880011677742,
0.01135456096380949,
-0.0020744893699884415,
-0.017291098833084106,
-0.00531914783641696,
0.008201230317354202,
-0.0014385636895895004,
-0.03000381961464882,
0.03465331718325615,
0.023365234956145287,
-0.002566492883488536,
0.058455146849155426,
0.028538625687360764,
-0.06394651532173157,
-0.017931215465068817,
-0.06988893449306488,
-0.027244070544838905,
-0.02676169015467167,
-0.008402137085795403,
-0.01055123284459114,
-0.04663654416799545,
0.005270105320960283,
-0.0028451804537326097,
0.03215590491890907,
0.0020091538317501545,
-0.07336102426052094,
-0.02698659338057041,
-0.057601988315582275,
-0.02610790729522705,
-0.011300098150968552,
-0.03282107785344124,
-0.043751854449510574,
0.005459798965603113,
0.032104019075632095,
0.02686716429889202,
-0.021191053092479706,
-0.06243768706917763,
0.031349360942840576,
0.03599585220217705,
-0.0037336796522140503,
-0.036425601691007614,
0.03591296821832657,
0.01986830309033394,
-0.00609580148011446,
0.034021709114313126,
-0.027277139946818352,
0.07853256911039352,
-0.07720806449651718,
0.0824228972196579,
0.017188958823680878,
0.031479764729738235,
-0.008755944669246674,
0.05294700339436531,
0.0036186848301440477,
-0.005677683744579554,
-0.038797780871391296,
0.015076732262969017,
0.016532540321350098,
0.01622970961034298,
-0.0009898539865389466,
0.07748502492904663,
0.027699388563632965,
0.010441453196108341,
-0.019971774891018867,
-0.02171284705400467,
0.00961487926542759,
-0.042942389845848083,
-0.017516572028398514,
0.003117222571745515,
-0.014290520921349525,
0.05833560228347778,
0.014880925416946411,
0.0035297684371471405,
-0.04266941174864769,
-0.011790220625698566,
0.004214041400700808,
-0.014135966077446938,
0.009850161150097847,
0.021275749430060387,
0.01067341398447752,
-0.012137120589613914,
-0.011481614783406258,
0.009479972533881664,
0.0057514021173119545,
-0.009185045957565308,
0.012640983797609806,
0.004600127227604389,
-0.04087897017598152,
-0.014871044084429741,
-0.0015429112827405334,
0.06009253114461899,
0.010262244381010532,
0.016174346208572388,
-0.09303728491067886,
0.010477304458618164,
0.025740627199411392,
-0.023459535092115402,
-0.004124837461858988,
-0.0005966501776129007,
-0.004520396236330271,
0.044517580419778824,
0.050898563116788864,
0.002892149845138192,
0.01859208010137081,
-0.06897764652967453,
-0.0011580891441553831,
0.004937749356031418,
0.02813507616519928,
-0.0010319227585569024,
0.026504328474402428,
-0.05161742866039276,
0.012339308857917786,
-0.04372883588075638,
0.06645925343036652,
-0.027501247823238373,
0.07320711761713028,
-0.010632924735546112,
0.0026305534411221743,
-0.021408187225461006,
-0.01597069576382637,
-0.03302759677171707,
0.004167531616985798,
0.06359338760375977,
-0.016009701415896416,
-0.06523417681455612,
-0.07064007222652435,
0.02655266597867012,
0.009465005248785019,
0.02137599140405655,
0.01708551123738289,
-0.04553917050361633,
-0.07873788475990295,
0.04130885750055313,
-0.03820408508181572,
0.026558713987469673,
0.0340166911482811,
0.012492566369473934,
-0.04130689799785614,
0.0228594820946455,
-0.04997764900326729,
-0.003944505006074905,
-0.029934721067547798,
-0.0031133743468672037,
-0.003329283557832241,
0.021463066339492798,
0.015296103432774544,
0.04285714775323868,
0.004951562266796827,
0.020897405222058296,
0.043697092682123184,
0.007930864579975605,
0.025955021381378174,
-0.003438614308834076,
-0.06417842954397202,
-0.005975633859634399,
-0.0008421734673902392,
0.010603846982121468,
0.008464266546070576,
0.025620659813284874,
-0.03556219860911369,
-0.06698955595493317,
-0.029066476970911026,
-0.018258031457662582,
-0.013044881634414196,
0.03210804983973503,
0.03557628393173218,
-0.026030901819467545,
-0.03393813222646713,
-0.05263863131403923,
0.02794589474797249,
-0.04576737433671951,
-0.019091947004199028,
0.05524001270532608,
-0.06610801815986633,
-0.018890392035245895,
-0.006899764761328697,
0.018585072830319405,
0.03921111300587654,
-0.032207388430833817,
-0.031461987644433975,
0.030029213055968285,
0.06735535711050034,
0.04772938787937164,
-0.04009336978197098,
0.029116623103618622,
-0.010189114138484001,
0.03770698606967926,
-0.013574620708823204,
0.018147267401218414,
0.033765945583581924,
-0.007037260569632053,
-0.0837387815117836,
-0.005320834461599588,
0.010267367586493492,
0.016824111342430115,
-0.04671398922801018,
0.008827805519104004,
0.03416912630200386,
-0.0593811497092247,
0.009797045961022377,
0.05140494555234909,
-0.011768280528485775,
-0.029418645426630974,
0.010709871537983418,
0.01784708723425865,
-0.02610512264072895,
-0.09213877469301224,
-0.02046571858227253,
-0.02285899594426155,
0.0053976671770215034,
0.030937401577830315,
-0.007210811134427786,
0.020756326615810394,
0.026665711775422096,
-0.07065630704164505,
-0.0010129412403330207,
0.02402419224381447,
0.056509144604206085,
-0.012525453232228756,
-0.01971045508980751,
0.044858165085315704,
0.0281747505068779,
-0.02849787473678589,
-0.057304322719573975,
0.032855622470378876,
-0.027163848280906677,
-0.007499809376895428,
-0.02845054306089878,
0.06104610487818718,
-0.0004086627159267664,
-0.011608988046646118,
-0.058588869869709015,
0.041454996913671494,
-0.03192389756441116,
-0.050397202372550964,
0.01893266662955284,
0.03839770331978798,
-0.0007107707788236439,
-0.03210625424981117,
-0.06660228967666626,
-0.02709071710705757,
0.0065661207772791386,
0.006205464713275433,
0.057596661150455475,
0.06168632209300995,
0.05009671300649643,
0.01717039942741394,
-0.03245553374290466,
-0.060947928577661514,
-0.014021310023963451,
0.009293453767895699,
0.018696378916502,
0.004826740827411413,
-0.04259565472602844,
-0.020933037623763084,
-0.009268484078347683,
0.0008395957993343472,
0.08920136839151382,
0.03450383245944977,
0.08119707554578781,
-0.022178947925567627,
0.03432142734527588,
0.035906124860048294,
-0.014795270748436451,
0.009624593891203403,
0.02069329470396042,
0.04242818057537079,
-0.013825672678649426,
-0.03363534063100815,
-0.021265313029289246,
-0.04842601716518402,
0.000542005873285234,
-0.018579840660095215,
-0.014590886421501637,
-0.04706433042883873,
0.05253973230719566,
0.001904331729747355,
0.0341363325715065,
0.009953576140105724,
-0.01961648277938366,
-0.03545680269598961,
-0.057562489062547684,
0.01734689064323902,
0.002769030863419175,
0.03857601061463356,
0.05626445636153221,
0.03721921518445015,
-0.050139378756284714,
-0.04406126216053963,
0.026168638840317726,
-0.010590104386210442,
-0.002944723702967167,
0.012762363068759441,
0.00982585921883583,
0.0014273474225774407,
0.017718706279993057,
-0.02387184277176857,
-0.051290303468704224,
0.006343240849673748,
-0.013504840433597565,
-0.004696964751929045,
0.11327365040779114,
-0.018637247383594513,
-0.03712743893265724,
-0.05246720835566521,
-0.026918485760688782,
0.03131740540266037,
-0.05646705999970436,
-0.028548864647746086,
0.005231549963355064,
0.012288481928408146,
-0.01055698562413454,
0.004353044088929892,
-0.013215682469308376,
0.034717656672000885
] |
<p>It's easy for me to imagine that if we brake the front wheel then there is a chance that I'll flip.</p>
<p>On the other hand if I brake the back wheel, there is no way it'll happen no matter how fast I brake.</p>
<p>But whether I brake the front wheel or back wheel, the force I've added is a backward force at the bottom of the wheel.</p>
<p>So why the different outcome?</p> | g6656 | [
0.006249392870813608,
0.04578869417309761,
0.019698109477758408,
0.0665786862373352,
0.05725788697600365,
-0.009193730540573597,
0.07072439789772034,
0.02551305666565895,
-0.05320252478122711,
-0.10357079654932022,
0.04017137736082077,
-0.015269159339368343,
0.007788257207721472,
0.028158649802207947,
0.04582811892032623,
0.04968714341521263,
0.024999039247632027,
-0.0032704125624150038,
-0.001301003503613174,
-0.006236828397959471,
-0.058584850281476974,
0.047348830848932266,
-0.09193043410778046,
0.00174474879167974,
-0.10415389388799667,
-0.02771509438753128,
0.006404741667211056,
-0.003977152984589338,
0.01854977197945118,
0.002255754778161645,
0.026272853836417198,
0.05842796713113785,
0.023106774315238,
-0.017441097646951675,
-0.004043392837047577,
-0.032714083790779114,
-0.012114823795855045,
-0.00801118090748787,
-0.004115517251193523,
-0.03844441846013069,
0.018365727737545967,
0.02393362857401371,
0.011139752343297005,
-0.004921303130686283,
0.02809964306652546,
-0.016167091205716133,
-0.022749805822968483,
0.018779801204800606,
0.036026109009981155,
0.039162538945674896,
0.009488997049629688,
-0.02088679000735283,
-0.0304420068860054,
0.015957526862621307,
0.0272416602820158,
-0.004601547960191965,
-0.009475051425397396,
0.039378419518470764,
-0.03735976293683052,
-0.016760800033807755,
-0.10016632080078125,
0.029850902035832405,
0.01757770963013172,
0.024340862408280373,
0.011120728217065334,
-0.017824923619627953,
0.0007328384672291577,
0.015240529552102089,
0.05362960696220398,
0.04220130667090416,
-0.020032504573464394,
0.020060401409864426,
0.007830032147467136,
-0.02699185349047184,
-0.003241222584620118,
0.03224596381187439,
0.06354529410600662,
0.0003243524697609246,
0.007164319511502981,
0.006763744633644819,
-0.027059733867645264,
-0.01928689330816269,
0.006016076076775789,
0.04941802844405174,
0.05644097179174423,
-0.0006088881054893136,
-0.014569654129445553,
0.006455046124756336,
-0.054235320538282394,
0.04190540686249733,
0.02197386510670185,
-0.04712331295013428,
0.04009556397795677,
0.030686719343066216,
-0.07370534539222717,
-0.07510874420404434,
-0.047586992383003235,
0.06050292029976845,
-0.037873655557632446,
0.009776998311281204,
-0.052612628787755966,
0.022224346175789833,
0.051175713539123535,
0.023151004686951637,
-0.001559039345011115,
-0.08518879115581512,
0.016767311841249466,
-0.0008205152116715908,
-0.021229760721325874,
-0.058769818395376205,
-0.015758905559778214,
-0.006898854393512011,
-0.02201312780380249,
-0.02570517733693123,
0.003527988912537694,
0.006130249239504337,
0.004960750229656696,
0.024783195927739143,
0.041369225829839706,
0.0015191107522696257,
0.0032822692301124334,
0.014280377887189388,
-0.06844247132539749,
0.03731098771095276,
-0.018095847219228745,
-0.0721009224653244,
0.01610707677900791,
-0.018857011571526527,
0.07779748737812042,
-0.007847968488931656,
0.029216116294264793,
-0.013199973851442337,
0.020514942705631256,
-0.002187053207308054,
0.06137198582291603,
0.05757027864456177,
0.017706165090203285,
0.05844223499298096,
0.049322739243507385,
0.024099912494421005,
-0.017872711643576622,
0.047169893980026245,
0.05259665474295616,
0.0036680155899375677,
-0.05023818463087082,
0.004118210636079311,
-0.03982000797986984,
0.04848581552505493,
-0.017171699553728104,
0.04017737880349159,
-0.01097404956817627,
0.013193443417549133,
-0.009885531850159168,
-0.00917037669569254,
0.03460703417658806,
0.011217220686376095,
0.06441419571638107,
0.06739208847284317,
-0.0009658081689849496,
0.015089566819369793,
0.08649777621030807,
-0.039620738476514816,
-0.04569481313228607,
0.04428288713097572,
-0.0893024131655693,
0.0003987907839473337,
-0.07077019661664963,
-0.02912275865674019,
-0.019339734688401222,
0.03531971573829651,
-0.02871975302696228,
0.007009136024862528,
0.021250328049063683,
0.031063398346304893,
0.07791098207235336,
0.028995566070079803,
-0.016537271440029144,
0.010783669538795948,
0.011450573801994324,
0.05424414575099945,
0.011157373897731304,
0.015778174623847008,
-0.04506557434797287,
0.01168027799576521,
0.020442049950361252,
-0.05675510689616203,
-0.04884077608585358,
0.0625072792172432,
-0.03580716997385025,
0.015891754999756813,
0.04454701766371727,
-0.032590415328741074,
-0.03777151182293892,
0.019367240369319916,
-0.03657011315226555,
-0.04579411447048187,
-0.04590018838644028,
0.0016794884577393532,
0.026208218187093735,
0.02097329869866371,
-0.0278493519872427,
0.025284353643655777,
0.03412807732820511,
0.014139831997454166,
-0.07584617286920547,
-0.02331850491464138,
-0.026597240939736366,
0.028399139642715454,
0.030111899599432945,
-0.08100082725286484,
-0.04297226294875145,
0.05382636561989784,
0.01828310638666153,
-0.0096138846129179,
-0.044860489666461945,
0.026121972128748894,
0.006178174167871475,
0.03571513295173645,
-0.0008289034012705088,
0.01775941252708435,
0.051369037479162216,
-0.048809416592121124,
0.0012843901058658957,
-0.026864193379878998,
-0.03942064940929413,
-0.01703117974102497,
0.0054001277312636375,
0.009655306115746498,
0.012876957654953003,
0.04498891532421112,
0.0023509436286985874,
-0.02271745726466179,
-0.01426638849079609,
0.011643514968454838,
0.032203949987888336,
0.02273416519165039,
0.06760138273239136,
0.002737967995926738,
0.038167983293533325,
-0.008373004384338856,
0.0207507461309433,
-0.030688451603055,
-0.025676874443888664,
0.030032433569431305,
0.018933413550257683,
-0.0398649238049984,
0.015865178778767586,
-0.08515362441539764,
0.004696998745203018,
0.02735680527985096,
0.0029673930257558823,
-0.008201994933187962,
-0.023170843720436096,
0.015748748555779457,
-0.02320345863699913,
-0.02229980193078518,
-0.04967706277966499,
0.010698411613702774,
-0.0614234134554863,
0.007469042204320431,
0.005586240906268358,
0.020601151511073112,
0.006626702379435301,
-0.008938368409872055,
-0.06992070376873016,
-0.02477562613785267,
-0.010432487353682518,
-0.0067176553420722485,
-0.019018301740288734,
0.018355295062065125,
-0.020328911021351814,
0.037335824221372604,
-0.030012628063559532,
-0.018953319638967514,
0.001040066359564662,
0.002244379837065935,
-0.01016187109053135,
-0.04003441333770752,
-0.010658856481313705,
-0.004250854253768921,
-0.0352904386818409,
0.04574322700500488,
0.039495453238487244,
0.009707977995276451,
-0.013502022251486778,
0.0012089986121281981,
0.003403270151466131,
-0.038320377469062805,
-0.022998543456196785,
0.00622107507660985,
-0.11207671463489532,
0.04887150228023529,
0.10698498040437698,
-0.026823945343494415,
0.06893368810415268,
0.06732557713985443,
0.03855128213763237,
-0.02248445339500904,
-0.061193883419036865,
-0.0012224201345816255,
-0.029373034834861755,
-0.002392652677372098,
-0.001487288624048233,
-0.004464054945856333,
-0.026769492775201797,
0.027606742456555367,
-0.017459610477089882,
-0.0038593634963035583,
-0.030416959896683693,
0.014844376593828201,
-0.031008290126919746,
-0.009292514994740486,
-0.04592099413275719,
-0.0064620948396623135,
-0.06332700699567795,
-0.01863490231335163,
-0.04669084772467613,
0.02031833492219448,
-0.015468795783817768,
-0.04386691376566887,
-0.04523077234625816,
-0.01636182889342308,
-0.016968853771686554,
-0.015510727651417255,
-0.009394114837050438,
0.06468520313501358,
-0.09760450571775436,
-0.011593291535973549,
0.04742218554019928,
-0.03953242674469948,
0.05276774242520332,
0.02511410601437092,
-0.029268046841025352,
-0.016709357500076294,
-0.03728785365819931,
0.06063920632004738,
0.05685364827513695,
0.06517788767814636,
0.015052189119160175,
0.018308743834495544,
0.021113401278853416,
-0.009636232629418373,
-0.053478486835956573,
-0.024167293682694435,
0.000047165500291157514,
0.052042700350284576,
0.022161206230521202,
0.0038120774552226067,
0.028114618733525276,
-0.007214436307549477,
-0.011865333653986454,
-0.029711082577705383,
0.033595409244298935,
-0.009169225580990314,
0.0502023920416832,
0.010049923323094845,
-0.03203664720058441,
-0.0012456623371690512,
0.03081698901951313,
0.015748130157589912,
0.048290252685546875,
0.04120558872818947,
-0.044465694576501846,
-0.007878700271248817,
-0.011964811012148857,
-0.005554727278649807,
-0.08519787341356277,
0.008154772222042084,
-0.05329758673906326,
-0.0026019772049039602,
0.019415386021137238,
0.023577818647027016,
0.021013781428337097,
0.06031264364719391,
0.05650770291686058,
-0.03288291022181511,
0.04382580146193504,
-0.0024424311704933643,
0.0411112979054451,
-0.05063599720597267,
0.07358796149492264,
0.09516022354364395,
0.073414146900177,
-0.011866549029946327,
-0.011695642955601215,
0.005172015633434057,
-0.03338467329740524,
-0.06815598160028458,
0.00468283798545599,
0.03386470675468445,
-0.03603759780526161,
0.007269761525094509,
0.03843742981553078,
-0.04161371663212776,
0.000041683488234411925,
0.04000331461429596,
0.0024145643692463636,
-0.04546664282679558,
0.021533865481615067,
0.034594543278217316,
-0.057344406843185425,
0.08140196651220322,
-0.011954572051763535,
0.009296131320297718,
-0.025256458669900894,
-0.003047060687094927,
0.02805577963590622,
0.007584171835333109,
-0.018284611403942108,
0.023468082770705223,
0.020300090312957764,
0.012996632605791092,
-0.01336209662258625,
-0.015749085694551468,
0.0624377615749836,
-0.01668676733970642,
0.05059979483485222,
0.05875574052333832,
0.0335550382733345,
-0.052335385233163834,
0.017142733559012413,
0.03369210287928581,
-0.009545105509459972,
-0.0053433883003890514,
-0.029447028413414955,
0.04857867583632469,
-0.02509983256459236,
-0.038288362324237823,
-0.022011198103427887,
0.01632172055542469,
0.010936791077256203,
0.025425050407648087,
-0.024833351373672485,
-0.030298026278614998,
0.005221288185566664,
-0.020987985655665398,
-0.0065958513878285885,
0.02845522202551365,
0.023681242018938065,
0.014938745647668839,
0.027895966544747353,
0.03248213604092598,
-0.02668141759932041,
-0.005759075749665499,
-0.02310531958937645,
-0.02532101422548294,
-0.03569263592362404,
-0.017448751255869865,
0.022443637251853943,
-0.03246309608221054,
-0.0537298284471035,
0.02934086136519909,
-0.010675042867660522,
-0.04542529955506325,
0.022178463637828827,
-0.0199009720236063,
-0.03165123611688614,
-0.01829708181321621,
-0.026836689561605453,
0.04960181936621666,
-0.04854743555188179,
-0.03798013925552368,
0.03462094068527222,
0.00671661039814353,
-0.0398646742105484,
0.03178032487630844,
0.0201282761991024,
-0.017263449728488922,
-0.01363372802734375,
0.05366535484790802,
-0.016152746975421906,
-0.026299098506569862,
-0.005478902719914913,
0.0763145461678505,
0.043424464762210846,
0.022597551345825195,
0.023820601403713226,
0.007659277878701687,
0.036386504769325256,
-0.04088659584522247,
-0.06494755297899246,
0.023138469085097313,
0.05134052783250809,
-0.06640022248029709,
-0.042454663664102554,
0.024128105491399765,
-0.05724173039197922,
-0.03031250648200512,
0.011743367649614811,
-0.012229806743562222,
0.03878806158900261,
0.0629877820611,
-0.007265590131282806,
-0.051580388098955154,
-0.014692540280520916,
0.04574273154139519,
-0.007064292207360268,
-0.0024736300110816956,
-0.07442107796669006,
0.029257791116833687,
-0.07565227895975113,
0.017814064398407936,
0.0150374174118042,
-0.03331945464015007,
0.03095768392086029,
0.0928395688533783,
0.035385578870773315,
-0.0505608506500721,
-0.01232203096151352,
0.03349755331873894,
-0.027137786149978638,
-0.01488465629518032,
-0.04788130894303322,
0.0515141636133194,
0.0042325956746935844,
-0.00024575780844315886,
-0.020956702530384064,
-0.008083459921181202,
0.024609167128801346,
-0.06695427745580673,
-0.038865458220243454,
-0.03347516059875488,
-0.001611686428077519,
-0.057524118572473526,
-0.04704387113451958,
-0.05567808449268341,
-0.015212757512927055,
-0.04011651873588562,
-0.03646127134561539,
-0.012612714432179928,
-0.00410059466958046,
0.06440524756908417,
0.10478335618972778,
0.0561947263777256,
-0.023122092708945274,
-0.0321129634976387,
0.08901476114988327,
-0.053247831761837006,
0.03751416876912117,
-0.04063206538558006,
0.051600925624370575,
0.0460984893143177,
-0.020668765529990196,
0.04560081660747528,
-0.05705811083316803,
-0.014870342798531055,
-0.05730384215712547,
0.03603498637676239,
-0.007346741855144501,
-0.0412420891225338,
0.011361289769411087,
0.04193751513957977,
-0.04020237550139427,
-0.03582165017724037,
-0.06318321079015732,
0.07320290803909302,
-0.04838055372238159,
-0.025837505236268044,
-0.003296319395303726,
-0.06909811496734619,
-0.008671076036989689,
-0.008800704032182693,
0.0065209041349589825,
-0.0014036872889846563,
0.014444690197706223,
-0.04589544236660004,
-0.021192898973822594,
-0.005127254407852888,
0.00918115209788084,
-0.018506130203604698,
0.03779803588986397,
0.005449108313769102,
-0.06401902437210083,
0.034792494028806686,
-0.010757914744317532,
0.008807959966361523,
0.016542136669158936,
-0.008932081051170826,
-0.013271963223814964,
-0.03115678019821644,
-0.017492128536105156,
-0.021374506875872612,
0.03344147279858589,
0.012636984698474407,
-0.00035225696046836674,
0.0013738442212343216,
-0.1025756448507309,
-0.0057035828940570354,
0.028713783249258995,
-0.052766188979148865,
-0.006072354037314653,
0.00777187617495656,
0.04001171886920929,
-0.00003224071770091541,
-0.025865335017442703,
-0.007209185976535082,
0.0006552883423864841,
-0.00978511106222868,
-0.04274201765656471,
-0.03179516643285751,
0.02852185256779194,
0.04636048525571823,
0.07950783520936966,
0.005245145410299301,
0.04142790287733078,
0.020959140732884407,
0.027774153277277946,
0.004086748696863651,
0.05161790922284126,
0.044868990778923035,
0.02293296344578266,
0.017418337985873222,
0.015951821580529213,
0.03327307105064392,
-0.0482809841632843,
0.03496347367763519,
-0.015319611877202988,
-0.02404852770268917,
0.011792383156716824,
0.01189067680388689,
0.010562053881585598,
-0.009376810863614082,
0.023174451664090157,
-0.0034901818726211786,
0.01724294014275074,
0.001068971469067037,
-0.03725232928991318,
0.0362069234251976,
0.049483876675367355,
0.03366644307971001,
0.0447191447019577,
-0.027544280514121056,
-0.08024511486291885,
0.07655828446149826,
-0.00757242739200592,
0.027254397049546242,
-0.04097921401262283,
-0.013972285203635693,
-0.007229135371744633,
0.015239682979881763,
-0.002140713855624199,
0.09165605157613754,
0.0013694713125005364,
0.01828007958829403,
-0.03628532215952873,
0.013354028575122356,
0.007053551729768515,
-0.01638953387737274,
0.018366526812314987,
0.0320945642888546,
-0.02266610413789749,
-0.0003134776488877833,
-0.023453164845705032,
-0.01759326457977295,
-0.038950156420469284,
0.01390641275793314,
0.06257840991020203,
0.015066898427903652,
0.01520628947764635,
0.014371571131050587,
0.03753145784139633,
-0.005392427556216717,
-0.017539232969284058,
0.027183324098587036,
-0.029316969215869904,
-0.0007733228267170489,
0.01124764047563076,
-0.023796673864126205,
0.03590350225567818,
0.02847174182534218,
0.017212046310305595,
-0.043936945497989655,
-0.05290614813566208,
-0.01863698661327362,
0.026879174634814262,
0.008749880827963352,
-0.026369597762823105,
-0.035211801528930664,
0.051671382039785385,
0.024604137986898422,
0.051067762076854706,
0.010806690901517868,
-0.011349612846970558,
0.052587322890758514,
-0.01912868767976761,
0.04277690127491951,
0.01877721957862377,
0.05668744817376137,
0.010217361152172089,
-0.037425532937049866,
0.039595115929841995,
-0.02634856291115284,
-0.0015876076649874449,
0.022392310202121735,
-0.06284863501787186,
-0.04402392357587814,
-0.053981713950634,
0.005086091347038746,
0.0029133413918316364,
-0.018488867208361626,
-0.0044981385581195354,
0.01450517401099205,
0.03879006579518318,
-0.010555491782724857,
0.006984459701925516,
-0.023656722158193588,
-0.034389838576316833,
0.024255098775029182,
-0.028051408007740974,
-0.051755014806985855,
0.04396471381187439,
0.02016463130712509,
-0.019470954313874245,
0.009428104385733604,
0.006664067506790161,
0.013313173316419125,
0.027496181428432465,
0.012856798246502876,
-0.01344930287450552,
0.007203623186796904,
-0.01795397512614727,
-0.03682642802596092,
0.0003299155505374074,
-0.040155503898859024,
-0.03036498837172985,
-0.040343835949897766,
0.05580131337046623,
-0.01485668309032917,
-0.011470481753349304,
0.030643930658698082,
-0.011641192249953747,
-0.002528828103095293,
0.02184806391596794,
-0.030647970736026764,
-0.030931614339351654,
0.03424759954214096,
-0.021743761375546455,
-0.024526264518499374,
-0.08058831840753555,
-0.0051688337698578835,
-0.04453444108366966,
-0.013637821190059185,
-0.009438755922019482,
-0.036382053047418594,
-0.026095477864146233,
0.013069521635770798,
0.010151245631277561,
0.018012760207057,
0.024664347991347313,
0.028272487223148346,
-0.00842487346380949,
-0.0459025613963604,
-0.03589210286736488,
0.02397165261209011,
0.0456504188477993,
0.033721376210451126,
-0.06429331749677658,
-0.008422085084021091,
0.020799292251467705,
-0.013327069580554962,
-0.016211630776524544,
-0.010396637953817844,
-0.028774479404091835,
-0.06007775664329529,
0.00005820317528559826,
-0.020393088459968567,
-0.060337699949741364,
0.015029017813503742
] |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.