Table Of ContentThe Historical Development
of
Quantum Theory
Jagdish Mehra
Helmut Rechenberg
The Historical Development
of
Quantum Theory
VOLUME 6
The Completion of Quantum Mechanics
1926–1941
Part 2
The Conceptual Completion and the Extensions
of Quantum Mechanics
1932–1941
Epilogue: Aspects of the Further Development
of Quantum Theory
1942–1999
Subject Index: Volumes 1 to 6
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Mehra,Jagdish.
Thecompletionofquantummechanics,1926–1941/JagdishMehra,HelmutRechenberg.
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Contents—Part 2
Chapter IV The Conceptual Completion and theExtensions of
Quantum Mechanics (1932–1941)
671
Introduction 671
IV.1 The Causality Debate(1929–1935) 678
(a) Introduction:ThePrincipleofCausalityinQuantumTheory 678
(b) Heisenberg’sDiscussionsConcerningthePositivismofthe‘Vienna
Circle’(1929–1932) 683
(c) TheIndeterminacyRelationsforRelativisticQuantumFields
(1929–1933) 692
(d) TheContinuationoftheDebateonCausalitywiththeBerlin
Physicists(1929–1935) 703
IV.2 The Debateon the Completeness of Quantum Mechanicsand Its
Description of Reality (1931–1936) 713
(a) Introduction 713
(b) FromInconsistencytoIncompletenessofQuantumMechanics:
TheEPRParadox(1931–1935) 717
(c) TheResponseoftheQuantumPhysicists,Notably,Bohrand
HeisenbergtoEPR(1935) 725
(d) ErwinSchro¨dingerJoinsAlbertEinstein:TheCatParadox(1935–
1936) 738
(e) RealityandtheQuantum-MechanicalDescription(1935–1936) 747
IV.3 New Elementary Particles in Nuclear and Cosmic-Ray Physics
(1929–1937) 759
(a) Introduction:‘PureTheory’Versus‘ExperimentandTheory’ 759
(b) TheTheoreticalPredictionofDirac’s‘Holes’and‘Monopoles’
(1928–1931) 772
(c) TheDiscoveryofNewElementaryParticlesofMatterand
Antimatter(1930–1933) 785
(d) QuantumMechanicsoftheAtomicNucleusandBeta-Decay
(1931–1934) 801
(e) UniversalNuclearForcesandYukawa’sNewIntermediateMass
Particle(1933–1937) 822
IV.4 Solid-State,Low-Temperature, and RelativisticHigh-Density
Physics (1930–1941) 837
(a) Introduction 837
(b) NewAmericanandEuropeanSchoolsofSolid-StatePhysics
(1933–1937) 840
vi Contents
(c) Low-TemperaturePhysicsandQuantumDegeneracy(1928–1941) 857
(d) TowardAstrophysics:MatterUnderHighPressuresandHigh
Temperatures(1926–1939) 877
IV.5 High-EnergyPhysics:Elementary Particles and Nuclear
Reactions (1932–1942) 898
(a) Introduction 898
(b) BetweenHopeandDespair:ProgressinQuantum
Electrodynamics(1930–1938) 902
(c) NewFieldsDescribingElementaryParticles,TheirProperties,and
Interactions(1934–1941) 935
(d) NuclearForcesandReactions:Transmutation,Fusion,and
FissionofNuclei(1934–1942) 964
Epilogue:Aspects ofthe Further Developmentof QuantumTheory
(1942–1999) 1015
1. The ElementaryConstitution of Matter: Subnuclear Particles and
Fundamental Interactions 1020
1.1 SomeProgress in Relativistic QuantumField Theory and the
Formulation of the Alternative S-Matrix Theory (1941–1947) 1024
(a) E.C.G.Stueckelberg:‘NewMechanics(1941)’ 1024
(b) ThePrincipleofLeastActioninQuantumMechanics(Feynman
andTomonaga,1942–1943) 1024
(c) Heisenberg’sS-Matrix(1942–1947) 1030
1.2 The Renormalized Quantum Electrodynamics (1946–1950) 1033
(a) TheShelterIslandConference(1947) 1033
(b) HansBetheandtheInitialCalculationoftheLambShift(1947) 1038
(c) TheAnomalousMagneticMomentoftheElectron(1947) 1043
(d) ThePoconoConference(1948) 1051
(e) VacuumPolarization(1948) 1057
(f) TheMichiganSummerSchool:FreemanDysonatJulian
Schwinger’sLectures(1948) 1059
(g) TheImmediateImpactofSchwinger’sLectures(1948) 1062
(h) Schwinger’sCovariantApproach(1948–1949) 1064
(i) GaugeInvarianceandVacuumPolarization(1950) 1074
(j) TheQuantumActionPrinciple(1951) 1081
(k) TomonagaWritestoOppenheimer(April1948) 1085
(l) Tomonaga’sPapers(1946–1948) 1086
(m) Feynman’sPreparationsupto1947 1088
(n) RichardFeynmanaftertheShelterIslandConference(1947–
1950) 1091
(o) FreemanDysonandtheEquivalenceoftheRadiationTheories
ofSchwinger,Tomonaga,andFeynman(1949–1952) 1099
(p) TheImpactofDyson’sWork 1104
(q) FeynmanandSchwinger:CrossFertilization 1106
1.3 New Elementary Particles and TheirInteractions (1947–1964) 1107
1.4 The Problems of Strong-InteractionTheory: Fields, S-Matrix,
Currents, and the Quark Model (1952–1969) 1118
Contents vii
1.5 The ‘Standard Model’ and Beyond(1964–1999) 1125
(a) The‘ElectroweakTheory’(1964–1983) 1126
(a1) The‘IntermediateWeakBoson’ 1126
(a2) SpontaneousSymmetry-BreakingandtheHiggsMechanism 1127
(a3) TheWeinberg–SalamModelandItsRenormalization 1127
(a4) NeutralCurrentsandtheDiscoveryoftheWeakBosons 1128
(b) QuantumChromodynamics(QCD)(1965–1995) 1130
(b1) TheDiscoveryofPhysicalQuarks 1130
(b2) AsymptoticFreedomofStrongInteractionForces 1131
(b3) QuantumChromodynamics 1132
(b4) TheCompletionofQCD 1133
(c) BeyondtheStandardModel(1970–1999) 1134
2. Quantum E¤ects in the PhysicalLaboratory and in theUniverse 1138
2.1 The Industrialand Celestial Laboratories (1947–1957) 1139
(a) TheTransistorintheIndustrialLaboratory(1947–1952) 1139
(b) TheCelestialLaboratory(1946–1957) 1143
2.2 The Application of Known QuantumE¤ects (1947–1995) 1145
(a) TheCasimirE¤ectandItsApplications(1947–1978) 1145
(b) TheMaserandtheLaser(1955–1961) 1153
(c) TheBose-EinsteinCondensation(1980–1995) 1156
2.3 Superfluidity, Superconductivity,andFurther Progress in
Condensed Matter Physics (1947–1974) 1159
(a) RotonsandOtherQuasi-Particles(1947–1957) 1159
(b) TheSolutionoftheRiddleofSuperconductivity(1950–1959) 1163
(c) CriticalPhenomenaandtheRenormalizationGroup(1966–1974) 1170
2.4 New Quantum E¤ects in Condensed Matter Physics (1958–1986) 1173
(a) TheMo¨ssbauerE¤ect(1958) 1173
(b) ExperimentalProofofMagneticFluxQuantization(1961) 1175
(c) TheJosephsonE¤ect(1962) 1176
(d) SuperfluidHeliumIII:PredictionandVerification(1961–1972) 1177
(e) TheQuantumHallE¤ectandLowerDimensionalQuantization
(1980) 1179
(f) High-TemperatureSuperconductors(1986) 1181
2.5 Stellar Evolution, the NeutrinoCrisis, and 3 K Radiation (1957–
1999) 1183
(a) StellarEvolutionandNewTypesofStars(1957–1971) 1185
(b) TheSolarNeutrinoProblemandtheNeutrinoMass(1964–1999) 1187
(c) 3KRadiationandtheEarlyUniverse(1965–1990) 1190
3. New Aspectsof the Interpretationof Quantum Mechanics 1193
3.1 The Copenhagen InterpretationRevisitedand Extended (1948–
1966) 1197
3.2 Causality, Hidden Variables, and Locality (1952–1968) 1208
(a) TheHiddenVariablesandvonNeumann’sMathematical
DisproofRevisited(1952–1963) 1212
viii Contents
(b) TheEPRParadoxRevisited,Bell’sInequalities,andAnother
ReturntoHiddenVariables(1957–1968) 1216
(c) TheAharonov–BohmE¤ect(1959–1963) 1222
3.3 Further Interpretationsand Experimental Confirmation of the
Standard QuantumMechanics (1957–1999) 1224
(a) TheMany-WorldInterpretationandOtherProposals(1957–1973) 1224
(b) TestsofEPR-TypeGedankenexperiments:HiddenVariablesor
Nonlocality(1972–1986) 1229
(c) TheProcessofDisentanglementofStatesandSchro¨dinger’sCat:
AnExperimentalDemonstration(1981–1999) 1235
Conclusion: Four Generations of QuantumPhysicists 1244
References 1255
AuthorIndex 1441
Subject Index for Volumes 1to 6 1469
Chapter IV
The Conceptual Completion and the Extensions of
Quantum Mechanics (1932–1941)
Introduction
The invention of quantum and wave mechanics and the great, if not complete,
progress achieved by these theories in describing atomic, molecular, solid-state
and—to some extent—nuclear phenomena, established a domain of microphysics
in addition to the previously existing macrophysics. To the latter domain of clas-
sicaltheoriescreatedsincethe17thcenturyapplied—principally,themechanicsof
Newton and his successors, and the electrodynamics of Maxwell, Hertz, Lorentz,
and Einstein. The statistical mechanics of Maxwell, Boltzmann, Gibbs, Einstein,
and others indicated a transition to microphysics; when applied to explain the
behaviour of atomic and molecular ensembles, it exhibited serious limitations of
theclassicalapproach.Classicaltheorieswerecloselyconnectedwithacontinuous
description of matter and the local causality of physical processes. The micro-
scopic phenomena exhibited discontinuities, ‘quantum’ features, which demanded
changes fromthe classical description. In the standard scheme of quantum theory
that emerged between 1926 and 1928, notably in Go¨ttingen, Cambridge, and
Copenhagen,thefollowing descriptionarose:
(i) Microscopicnaturalphenomenacouldbetreatedonthebasisofthetheoriesof
matrix and wave mechanics, i.e., formally di¤erent but mathematically equiva-
lentalgebraicandoperatorformulations.
(ii) Thequantum-mechanicaltheoriessatisfiedtheknownconservationprinciplesof
energy,momentum,angularmomentum,electricchargeandcurrent,etc.
(iii) Thevisualizable(anschauliche)particleandwavepicturesoftheclassicaltheories
had to be replaced by ‘dualistic’ or ‘complementary’ aspects of microscopic
objectswhichexhibitedsimultaneousparticleandwavefeatures.
(iv) The causal structure known from the classical laws—i.e., the di¤erential equa-
tions—remained valid for the quantum-mechanical laws, but the behaviour of
quantum-mechanicalobjectsdeviatedfromthoseofclassicalones.
(v) BasedonBorn’sstatisticalinterpretationofthewavefunctionandHeisenberg’s
uncertainty (or indeterminacy) relations, Bohr (on the physical side) and von
Neumann (on the mathematical side) proposed a subtle formalism that ac-
counted for the measurement of microscopic properties by macroscopic instru-
ments (and observers), in which the classical subject–object relation introduced
300yearsearlierbyRene´ Descarteswasreplacedbyadi¤erentone.
The completed physical theory of microscopic phenomena that thus arose,and
wassooncharacterizedasthe‘Copenhageninterpretationofquantummechanics,’
