Table Of ContentEinstein’s Struggles with
Quantum Theory
Einstein’s Struggles with
Quantum Theory
A Reappraisal
Dipankar Home
Bose Institute, Kolkata
and
Andrew Whitaker
Queen’s University Belfast
DipankarHome AndrewWhitaker
BoseInstitute Queen’sUniversityBelfast
Kolkata
LibraryofCongressControlNumber:2006931196
ISBN-13:978-0-387-71519-3 e-ISBN-13:978-0-387-71520-9
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©2007SpringerScience+BusinessMedia,LLC
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9 8 7 6 5 4 3 2 1
springer.com
Theauthorsrespectfullydedicatethisbooktothememoryof
DavidBohm
and
JohnStewartBell
whosepioneeringworkdidsomuchtodemonstratethe
importanceofEinstein’sviewsandargumentson
quantumtheory.
Contents
ForewordbySirRogerPenrose xiii
Preface xvii
PartA SettingtheScene 1
1. ThePhilosophicalBackground:EinsteinandMach 3
Introduction 3
PositivismandErnstMach 4
Mach’sCritiqueofNewton 6
EinsteinandMach—Part1 8
EinsteinandMach—Part2 12
EinsteinandMach—theDenouement 16
References 17
2. EinsteinandQuantumTheory:TheEarlyYears 21
EinsteinandtheDevelopmentofQuantumTheory 21
ThePhotonandSpecificHeats 23
SpontaneousandStimulatedEmission;Probability
andStatistics 26
ThePathtotheNewQuantumTheory 29
TheNewQuantumTheory:BohrandHeisenberg 30
TheNewQuantumTheory:Einstein’sContributions 32
References 36
3. QuantumMechanicsandItsFundamentalIssues 39
Introduction 39
SomePreliminaries 40
TheUncertaintyPrinciple 44
‘Time-EnergyUncertaintyPrinciple’ 45
PureandMixedStates 46
StatisticalPropertiesofPureStates 47
StatisticalPropertiesofMixedStates 48
ObservableDistinctionBetweenaPureandaMixedState 48
vii
viii Contents
ClassicalRealismorMacrorealism 50
QuantumRealism 50
TheQuantumMeasurementProblem 51
TheClassicalLimitProblemofQuantumMechanics 53
TheLimitProblem:WaveandRayOptics 54
TheLimitProblem:SpecialRelativityand
NewtonianMechanics 54
TheClassicalLimitProbleminStandard
QuantumMechanics 55
Wave-ParticleDuality 56
References 57
4. TheStandardInterpretationofQuantumMechanics 59
Introduction 59
TheBohr–HeisenbergVersion 61
TheEnsembleInterpretation 64
SingleSystemvis-à-visEnsembleInterpretation 65
TheBohr–Heisenberg‘Solution’totheQuantum
MeasurementProblem 67
Position-MomentumComplementarity 68
Wave-ParticleComplementarity 70
Bohrandthe‘DisturbanceInterpretation’ 72
vonNeumannandtheProjectionPostulate 73
vonNeumann’sImpossibility‘Proof’ 76
References 77
Interlude 81
PartB EinsteinConfrontingQuantumTheoryfrom1925 83
5. Einstein’sApproachestoQuantumTheory1925–1935 85
InitialImpressions 85
Einstein’sUnpublishedPaperonHiddenVariables 89
TheSolvayConference1927—MainProceedingsand
Einstein–BohrPartI 91
TheSolvayConference1930—Einstein–BohrPartII 96
Einstein–Bohr:ArgumentandConceptsinthe
EarlyPartsoftheDebate 97
Einstein’sBoxes 103
References 105
6. EPRanditsAftermath 107
Introduction 107
EinsteinLocalityandBellLocality 110
Entanglement 111
Einstein’sVersionoftheEPRArgument 113
Einstein’sVersionoftheEPRArgument:FurtherConsideration 115
Contents ix
TheBohmVersionofEPR 119
TheOriginalEPRArgumentof1935 121
Bohr’sResponsetoEPR35 126
EPR—WhatDidItMean? 132
EinsteinandSchrödinger:The1935Correspondence 136
References 138
7. EinsteinandtheMacroscopicLimit
ofQuantumMechanics 141
Introduction 141
Macrorealism:Examples 142
Macrorealism:Discussion 143
ParticleinaBox 145
DephasingoftheWave-Packet 149
LocalisationoftheWave-Packet 150
Conclusions 151
References 152
8. SummaryofEinstein’sViews 155
DidEinstein‘Reject’QuantumTheory? 155
Einstein’sPhilosophicalPosition—GeneralRemarks 159
Einstein’sApproachtotheCopenhagenInterpretation 163
EinsteinonDeterminism 168
EinsteinonRealism 172
RealismasaProgramme 177
EinsteinonLocality 182
Einstein’sVisionforPhysics—theUnifiedFieldTheory 185
EinsteinandEnsembles 189
EinsteinandtheBohmTheory 196
Realism,Determinism,Locality 199
References 202
Interlude 207
PartC Denouement 209
9. Bell’sContributionsandQuantumNon-locality 211
Introduction 211
LimitationtovonNeumann’sTheoremandPrelude
toBell’sTheorem 213
Bell’sTheorem 215
Bell’sTheoremUsingStochasticHiddenVariables 220
Contextuality 222
SignalLocality,andParameterandOutcomeIndependence 223
GeneralRemarksonLocalRealismandEntanglement 226
Bell-typeArgumentsWithoutInequalities:
Greenberger–Horne–Zeilinger 227
x Contents
Bell-typeArgumentsWithoutInequalities:Hardy’sArgument 229
ExperimentalTestsofBell-typeInequalities 231
ExperimentalTestsofQuantumNon-locality
WithoutInequalities 236
QuantumTeleportation 236
BellandEinstein 239
References 241
10. Non-standardQuantumInterpretations 247
Introduction 247
Many-WorldsInterpretation 248
Bohm’sModel:TheOntologicalInterpretation 250
Bohm’sModel:ASimpleIllustrativeExample 254
Bohm’sModel:ApproachtotheMeasurementProblem 255
DynamicalModelsofSpontaneousWave-FunctionCollapse 256
ConsistentHistoriesandDecoherentHistories 259
KnowledgeandInformationInterpretations 261
StochasticInterpretations 262
TheQuantumStateDiffusionModel 263
ManyHilbertSpaceApproach 264
GravitationallyInducedWave-FunctionCollapseApproach 265
Wave-FunctionCollapseModelsBasedonIrreversibility 267
Conclusions 268
References 268
11. EinsteinandQuantumInformationTheory 273
TheRiseofQuantumInformationTheory 273
EinsteinandQuantumInformationTheory 276
ASketchoftheTheoryofQuantumComputation 279
TheDeutschAlgorithm 284
OtherTopicsinQuantumComputation 287
EinsteinandQuantumComputation 288
QuantumCryptography 290
References 294
12. BridgingtheQuantum-ClassicalDivide 299
Introduction 299
Environment-inducedDecoherenceSchemes:BasicIdeas 299
CollisionwithExternalEnvironmentParticles:Photons,
GasMolecules,etc. 303
OscillatorModeloftheEnvironment 306
AssessmentoftheDecoherenceProgramme 307
OtherApproachestotheClassicalLimit 309
Theh→0Limit 309
TheN →∞Limit 312
Ehrenfest’sTheorem 313
Contents xi
TheQuantumTheoryofMacroscopicSystems 314
Conclusions 315
References 315
Interlude 319
PartD LookingForward 321
13. QuantumFoundations:GeneralOutlook 323
Introduction 323
MacrorealisminRelationtoQuantumMechanics 324
TheLeggett–GargInequality 326
OtherExamplesTestingQuantumSuperpositions
forMacrosystems 329
TheQuantumZenoEffect 331
TheQuantumZenoEffect:ExperimentalTest 334
TheQuantumZenoEffect:RecentWork 335
TimeinQuantumMechanics 335
References 339
14. AssessmentofEinstein’sViewsandContributions 345
HowWouldEinsteinhaveReactedto
thePresentSituation? 345
SummaryandAssessmentofEinstein’sContributions 349
AThoughtConcerningEinstein’sPossibleChoice
ofInterpretation 353
References 353
Epilogue 355
NameIndex 357
SubjectIndex 365
Description:This book presents an account of all aspects of Einstein’s achievements in quantum theory, his own views, and the progress his work has stimulated since his death. While some chapters use mathematics at an undergraduate physics level, a path is provided for the reader more concerned with ideas tha
