Table Of ContentQuantum 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
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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
