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Quantum Physics Without Quantum Philosophy Detlef Dürr (cid:129) Sheldon Goldstein (cid:129) Nino Zanghì Quantum Physics Without Quantum Philosophy 2123 Authors Dr.DetlefDürr SheldonGoldstein MathematischesInstitut DepartmentofMathematics,Rutgers UniversitätMünchen StateUniversityofNewJersey München,Germany Piscataway NewJersey,USA NinoZanghì IstitutoNazionaleFisicaNucleare, SezionediGenova(INFN) UniversitàdiGenova, Genova,Italy ISBN978-3-642-30689-1 ISBN978-3-642-30690-7(eBook) DOI10.1007/978-3-642-30690-71 SpringerHeidelbergDordrechtLondonNewYork LibraryofCongressControlNumber:2012952411 © Springer-VerlagBerlinHeidelberg2013 Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialis concerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting, reproductiononmicrofilmorinanyotherway,andstorageindatabanks.Duplicationofthispublication orpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9, 1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.Violations areliabletoprosecutionundertheGermanCopyrightLaw. Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply, evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotectivelaws andregulationsandthereforefreeforgeneraluse. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Foreword Inanidealworld,thisbookwouldnotoccasionanycontroversy.Itprovidestheartic- ulationandanalysisofaphysicaltheory,presentedwithmoreclarityandprecision thanisusualinaworkofphysics.Areadermightstartoutpredisposedtowardsthe theory,orskeptical,orneutral,butshouldinanycasebeimpressedbythepellucid explication.Thetheory,invariousincarnations,postulatesexactphysicalhypotheses aboutwhatexistsintheworld,andprecise,universal,mathematicallydefinedlaws that determine how those physical entities behave. Large, visible objects (such as planets,orrocks,ormacroscopiclaboratoryequipment)arepostulatedtobecollec- tions of small objects (particles). Since the theory specifies how the small objects behave,itautomaticallyimplieshowthelarge,visibleobjectsbehave.Itisthenjust a matter of analysis to determine what the theory predicts about the outcomes of experimentsandothersortsofobservablephenomena,andtocomparethesepredic- tionswithempiricaldata.Solongasthosepredictionsproveaccurate(theydo),the theorymustberegardedasacandidateforthetruetheoryofthephysicaluniverse. Ithastofacecompetitionfromotherempiricallyaccuratetheories,andtheremight bedisputesoverwhichofthevariouscontendersisthemostpromising.Butafair competition requires that all the contestants be judged on their merits, which de- mandsthateachbeclearlyandsympatheticallypresented.Thisbooksuppliessuch apresentation. Unfortunately,wedonotliveinanidealworld.Oncertaintopics,coolrational judgmentishardtofind,andquantummechanicsisoneofthosetopics.Forreasons rootedinthetortuoushistoryofthetheory1,clearandstraightforwardphysicalthe- oriesthatcanaccountforthephenomenatreatedbyquantummechanicsareviewed withsuspicion,ifnotdownrighthostility.Thesephenomena,itissaid,admitofno clearor“classical”explanation,andanyonewhothinksthattheydohasnotappre- ciated the revolutionary character of the quantum world. In order to “understand” quantumphenomena,itissaid,wemustrenounceclassicallogic,oramendclassical probabilitytheory,oradmitaplethoraofinvisibleuniverses,orrecognizethecen- tralrolethatconsciousobserversplayinproductionofthephysicalworld.Lestthe 1AusefulaccountofthathistorymaybefoundinthebookofJamesCushing[1]. v vi Foreword readerthinkIamexaggerating,therearemanyclearexamplesofeachofthese.The ManyWorldsinterpretationpositsthatwheneverquantumtheoryseemstopresent a probability, there is in fact a multiplicity: Schrödinger’s cat splits into a myriad of cats in each experiment, some of which are alive and some dead. Defenders of the“consistenthistories”approachinsistthatclassicallogicmustbeabandoned:in somecases,theclaimPcanbetrueandtheclaimQcanbetruebuttheconjunction “PandQ”benotonlynottrue,butmeaningless.2DavidMermin,inafamousarticle onBell’stheorem[2],assertsthat“[w]enowknowthatthemoonisdemonstrably nottherewhennobodylooks.” Thesesortsofextraordinaryclaimsshouldnotbedismissedoutofhand.Perhaps theworldissostrangethat“classical”modesofthoughtareincapableofcompre- hending it. But extraordinary claims require extraordinary proof. And one would hopethatsuchextremepositionswouldonlybeadvocatedifonewerecertainthat nothing less radical could be correct. Surely, one imagines, these sorts of claims wouldnotbemadeifsomeclear,precisetheorythatusesclassicalprobabilitytheory andclassicallogic,atheorythatpostulatesonlyone,commonplaceworldinwhich observers are just complicated physical systems interacting by the same physical laws as govern everything else, actually existed. Surely, one imagines, respected physicistswouldnotbedriventotheseextrememeasuresunlessnoalternativewere available.Butsuchanalternativeisavailable,andhasbeenforalmostaslongasthe quantumtheoryitselfhasexisted.ItwasfirstdiscoveredbyLouisdeBroglie,and later rediscovered by David Bohm. It goes by the names “pilot wave theory” and “causalinterpretation”and“ontologicalinterpretation”and“Bohmianmechanics.” Itisthemainsubjectofthisbook. Howcouldthemostprominentphysicistsofthelastcenturyhavefailedtorec- ognizethesignificanceofBohmianmechanics?Thisisafascinatingquestion,but subsidiarytoourmaintask.Theimportantthingistobecomeconvincedthatthey didfailtorecognizeitssignificance.Consideroneexample. In his classic Lectures on Physics, Richard Feynman introduces his students to quantumtheorybymeansofanexperiment: In this chapter, we shall tackle immediately the mysterious behavior in its most strange form.Wechoosetoexamineaphenomenonwhichisimpossible,absolutelyimpossible,to explaininanyclassicalway,andwhichhasinittheheartofquantummechanics.Inreality, itcontainstheonlymystery.Wecannotexplainthemysteryinthesenseof“explaining”how itworks.Wewilltellyouhowitworks.Intellingyouhowitworkswewillhavetoldyou aboutthebasicpeculiaritiesofallquantummechanics.[3,p.37-2] TheexperimentFeynmandescribesisthetwo-slitinterferenceexperimentforelec- trons.Anelectronbeam,shotthroughabarrierwithtwoholesinit,formsinterference bandsonadistantscreen.Thebandsareformedbyindividualmarksonthescreen, oneforeachelectron.Theyformevenwhentheintensityofthebeamissolowthat onlyoneelectronatatimepassesthroughthedevice. WhatdoesFeynmanfindsomysteriousaboutthisphenomenon?Heconsidersthe moststraightforward,obviousattempttounderstandit:“Thefirstthingwewouldsay 2Cf.Omnes[4]orGriffiths[5]. Foreword vii isthatsincetheycomeinlumps,eachlump,whichwemayaswellcallanelectron, hascomeeitherthroughhole1orhole2.[3,p.37–6]”Thisleadshimtowhathe callsPropositionA: Eachelectroneithergoesthroughhole1oritgoesthroughhole2.[3,p.37-6] TheburdenofFeynman’sargumentisthentoshowthatPropositionAisfalse:itis notthecasethateachelectrongoesthroughexactlyoneofthetwoholes.Inorderto provethis,hesuggeststhatwe“checkthisideabyexperiment.”First,blockuphole 2andcountthenumberofelectronsthatarriveateachpartofthescreen,yielding a distribution P1. Then, block up hole 1 and count the arrival rates to get another distribution P2. Finally, note that the distribution of electrons on the screen when bothholesareopen,P12,isnotthesumofP1andP2.Thisisanempiricalresultthat cannotbedenied.Butwhat,exactly,doesitimply? Feynmanassertsthatthesephenomenasimplycannotbeexplainedifweaccept PropositionA: Itisallquitemysterious.Andthemoreyoulookatit,themoremysteriousitseems.Many ideashavebeenconcoctedtotrytoexplainthecurveforP12intermsofindividualelectrons goingaroundincomplicatedwaysthroughtheholes.Noneofthemhassucceeded.Noneof themcangettherightcurveforP12intermsofP1andP2.[3.p.37–6] Thereadershouldnowturntop.13oftheintroductionandstudythediagramtobe foundonthatpage.Thediagramdepictsthetrajectoriesofindividualelectronsinthe two-slitexperimentaccordingtoBohmianmechanics.Notethateachelectrondoes gothroughexactlyoneslit,validatingPropositionA.Notealsothatthetrajectories donotlookparticularly“complicated.”Andthevisualsimplicityofthediagramfails toconveythemathematicalsimplicityoftheexactequations:thetrajectoriesofthe electronsareguidedbythewavefunctioninthesimplest,moststraightforwardpossi- bleway.Feynman’sclaimabouttheimpossibilityofunderstandingthisexperiment consistent with electrons following continuous trajectories, and hence consistent withPropositionA,isflatlyfalse.Ithadbeenknowntobefalsesince1927,whende Brogliefirstpresentedthepilotwavetheory,anditsfalsitywasreinforcedin1952 whenBohmpublishedthetheoryagain. Andyet,accordingtoFeynman,thisexperimentpresentsthefundamentalmystery of quantum mechanics, a phenomenon that cannot possibly be understood in any “classical”way.Howdidhemanagetogetsoconfused? The argument Feynman gives above turns on a plausible idea that cannot be correct,namelythatifanelectrongoesthroughhole1,thenitslatertrajectorycannot be depend on whether hole 2 was open or closed. This is refuted directly by the experimentaldata:thereareplacesonthescreenwhereelectronsarrivewhenonly hole1isopenandelectronsarrivewhenonlyhole2isopen,butwherenoelectrons arrivewhenbothholesareopen.Hencethebehaviorofeverysingleelectrondepends upon whether only one hole is open or both are open. But once we accept this surprising fact, forced on us by experiment, we see that there is no reason at all to expect P12 to be any sort of function (much less a simple sum) of P1 and P2. Experiments done with only one hole open give us no guidance about what will happenwithbothholesopen,becausesomethinginthephysicalworldissensitive viii Foreword tothefactthatbothholesareopen.Itisthisthingthatgivesrisetotheinterference phenomenainthefirstplace. If we want to accept the obvious explanation of the fact that electrons “arrive in lumps,” namely that electrons are particles that follow continuous trajectories, thenweneedtopostulatesomethingelsethatissomehowsensitivetothefactthat bothholesareopen.Everyversionofquantummechanicspostulatessuchathing: the wave function. And every version of quantum mechanics postulates a linear dynamicsforthewavefunction,suchastheSchrödingerequation.Allthatisneeded is a “guidance equation” for the particles, which specifies how the particles move giventhewavefunction.Bohmianmechanicsprovidesjustsuchaguidanceequation, whichcompletesthetheory. Feynmanpassesontoothermysteries.Whathappensifwetrytoexperimentally determinewhichholeeachelectrongoesthroughbyconstructingsomesortofde- tectorattheholes?Ifthedetectorworks,theneachelectronisdetectedatonehole ortheother,buttheinterferencepatternalsodisappears.Apparently,thebehaviorof theelectronsischangedifwe“lookfor”them.Doesn’tthissomehowshowthatthe act of observation, and the existence of observers, plays a central role in quantum theorythatisabsententirelyfromclassicalphysics?CanMermin’sremarkaboutthe moonbefarbehind? Onceagain,Bohmianmechanicsprovidesaratherprosaicanswer.Inanyphysical theory,theoutcomeofanexperimentdependsonhowtheexperimentisconstructed. Whatonewantsisaphysicsthattreatsexperiments,andobservers,andobservations, injustthesamewayasittreatsallphysicalsystemsandinteractions.Placingdetectors intheexperimentalset-upchangesitsphysicalconstruction.Anyphysicaltheory— classical or otherwise—must take account of those changes when predicting the outcome. In Bohmian mechanics, the presence of detectors necessarily results in theentanglementofthewavefunctionoftheelectronwiththewavefunctionofthe detector:otherwisethedetectorcan’tdetectanythingabouttheelectron.Thissame entanglementsuppressestheformationofinterferencebandsatthescreenbymeans ofthesamephysicallawsthatcreatethebandsintheoriginalexperiment.Nomagic isinvolved,andnospecialstatusisascribedto“observation:”rather,itisallsimple physicalanalysisofthesituation. Insum,noneofthe“inexplicablemysteries”thatFeynmancitespresentanyprob- lemsatallforBohmianmechanics.Thephenomenafollowfromtheapplicationof precisedynamicallawstotheappropriatephysicalsystems.Nochangesinlogicor probabilitytheoryarerequired,nospecialstatusascribedtoobserversor“measure- ments,” worlds are not multiplied. The only mystery is how Feynman could have beensomystified,andwhyheinsistedthathisstudentsshouldbemystifiedaswell. IhavenotusedFeynmanasanexampleinordertoparticularlycriticizehim.His remarks are typical of even the most distinguished physicists. Since the inception ofquantumtheory,claimshavebeenmadethatthephenomenathemselvesadmitof nopossible“classical”explanation,andthatthemicroscopicdetailsofthephysical worldeitherdon’texistatalloraresomehowbeyondourgrasp.Bohmianmechanics serves as a counterexample to such claims. Mermin’s assertion that the moon is demonstrably not there when no one looks is itself demonstrably false: Bohmian