Modern classical physics: optics, fluids, plasmas, elasticity, relativity, and statistical physics

1552 Pages·2017·11.69 MB·English

by  Roger D.

Modern Classical Physics

Modern Classical Physics
Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics
KIPS.THORNE and ROGERD.BLANDFORD
PRINCETONUNIVERSITYPRESS
PrincetonandOxford
Copyright©2017byPrincetonUniversityPress
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LibraryofCongressCataloging-in-PublicationData
Names:Thorne,KipS.,author.|Blandford,RogerD.,author.
Title:Modernclassicalphysics:optics,fluids,plasmas,elasticity,
relativity,andstatisticalphysics/KipS.ThorneandRogerD.Blandford.
Description:Princeton:PrincetonUniversityPress,2017.|Includes
bibliographicalreferencesandindex.
Identifiers:LCCN2014028150|ISBN9780691159027(hardcover:alk.paper)|
ISBN0691159025(hardcover:alk.paper)
Subjects:LCSH:Physics.
Classification:LCCQC21.3.T462015|DDC530—dc23
LCrecordavailableathttps://lccn.loc.gov/2014028150
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CONTENTS
ListofBoxes xxvii
Preface xxxi
Acknowledgments xxxix
PARTI FOUNDATIONS 1
1 NewtonianPhysics:GeometricViewpoint 5
1.1 Introduction 5
1.1.1 TheGeometricViewpointontheLawsofPhysics 5
1.1.2 PurposesofThisChapter 7
1.1.3 OverviewofThisChapter 7
1.2 FoundationalConcepts 8
1.3 TensorAlgebrawithoutaCoordinateSystem 10
1.4 ParticleKineticsandLorentzForceinGeometricLanguage 13
1.5 ComponentRepresentationofTensorAlgebra 16
1.5.1 Slot-NamingIndexNotation 17
1.5.2 ParticleKineticsinIndexNotation 19
1.6 OrthogonalTransformationsofBases 20
1.7 DifferentiationofScalars,Vectors,andTensors;CrossProductandCurl 22
1.8 Volumes,Integration,andIntegralConservationLaws 26
1.8.1 Gauss’sandStokes’Theorems 27
1.9 TheStressTensorandMomentumConservation 29
1.9.1 Examples:ElectromagneticFieldandPerfectFluid 30
1.9.2 ConservationofMomentum 31
1.10 GeometrizedUnitsandRelativisticParticlesforNewtonianReaders 33
1.10.1 GeometrizedUnits 33
1.10.2 EnergyandMomentumofaMovingParticle 34
BibliographicNote 35
TrackTwo;seepagexxxiv
Nonrelativistic(Newtonian)kinetictheory;seepage96
Relativistictheory;seepage96
vii
2 SpecialRelativity:GeometricViewpoint 37
2.1 Overview 37
2.2 FoundationalConcepts 38
2.2.1 InertialFrames,InertialCoordinates,Events,Vectors,andSpacetimeDiagrams 38
2.2.2 ThePrincipleofRelativityandConstancyofLightSpeed 42
2.2.3 TheIntervalandItsInvariance 45
2.3 TensorAlgebrawithoutaCoordinateSystem 48
2.4 ParticleKineticsandLorentzForcewithoutaReferenceFrame 49
2.4.1 RelativisticParticleKinetics:WorldLines,4-Velocity,4-Momentumand
ItsConservation,4-Force 49
2.4.2 GeometricDerivationoftheLorentzForceLaw 52
2.5 ComponentRepresentationofTensorAlgebra 54
2.5.1 LorentzCoordinates 54
2.5.2 IndexGymnastics 54
2.5.3 Slot-NamingNotation 56
2.6 ParticleKineticsinIndexNotationandinaLorentzFrame 57
2.7 LorentzTransformations 63
2.8 SpacetimeDiagramsforBoosts 65
2.9 TimeTravel 67
2.9.1 MeasurementofTime;TwinsParadox 67
2.9.2 Wormholes 68
2.9.3 WormholeasTimeMachine 69
2.10 DirectionalDerivatives,Gradients,andtheLevi-CivitaTensor 70
2.11 NatureofElectricandMagneticFields;Maxwell’sEquations 71
2.12 Volumes,Integration,andConservationLaws 75
2.12.1 SpacetimeVolumesandIntegration 75
2.12.2 ConservationofChargeinSpacetime 78
2.12.3 ConservationofParticles,BaryonNumber,andRestMass 79
2.13 Stress-EnergyTensorandConservationof4-Momentum 82
2.13.1 Stress-EnergyTensor 82
2.13.2 4-MomentumConservation 84
2.13.3 Stress-EnergyTensorsforPerfectFluidsandElectromagneticFields 85
BibliographicNote 88
PARTII STATISTICALPHYSICS 91
3 KineticTheory 95
3.1 Overview 95
3.2 PhaseSpaceandDistributionFunction 97
3.2.1 NewtonianNumberDensityinPhaseSpace,N 97
3.2.2 RelativisticNumberDensityinPhaseSpace,N 99
viii Contents
3.2.3 DistributionFunctionf(x,v,t)forParticlesinaPlasma 105
3.2.4 DistributionFunctionI /ν3forPhotons 106
ν
3.2.5 MeanOccupationNumberη 108
3.3 Thermal-EquilibriumDistributionFunctions 111
3.4 MacroscopicPropertiesofMatterasIntegralsoverMomentumSpace 117
3.4.1 ParticleDensityn,FluxS,andStressTensorT 117
(cid:2)
3.4.2 RelativisticNumber-Flux4-VectorSandStress-EnergyTensorTTT 118
3.5 IsotropicDistributionFunctionsandEquationsofState 120
3.5.1 NewtonianDensity,Pressure,EnergyDensity,andEquationofState 120
3.5.2 EquationsofStateforaNonrelativisticHydrogenGas 122
3.5.3 RelativisticDensity,Pressure,EnergyDensity,andEquationofState 125
3.5.4 EquationofStateforaRelativisticDegenerateHydrogenGas 126
3.5.5 EquationofStateforRadiation 128
3.6 EvolutionoftheDistributionFunction:Liouville’sTheorem,theCollisionless
BoltzmannEquation,andtheBoltzmannTransportEquation 132
3.7 TransportCoefficients 139
3.7.1 DiffusiveHeatConductioninsideaStar 142
3.7.2 Order-of-MagnitudeAnalysis 143
3.7.3 AnalysisUsingtheBoltzmannTransportEquation 144
BibliographicNote 153
4 StatisticalMechanics 155
4.1 Overview 155
4.2 Systems,Ensembles,andDistributionFunctions 157
4.2.1 Systems 157
4.2.2 Ensembles 160
4.2.3 DistributionFunction 161
4.3 Liouville’sTheoremandtheEvolutionoftheDistributionFunction 166
4.4 StatisticalEquilibrium 168
4.4.1 CanonicalEnsembleandDistribution 169
4.4.2 GeneralEquilibriumEnsembleandDistribution;GibbsEnsemble;
GrandCanonicalEnsemble 172
4.4.3 Fermi-DiracandBose-EinsteinDistributions 174
4.4.4 EquipartitionTheoremforQuadratic,ClassicalDegreesofFreedom 177
4.5 TheMicrocanonicalEnsemble 178
4.6 TheErgodicHypothesis 180
4.7 EntropyandEvolutiontowardStatisticalEquilibrium 181
4.7.1 EntropyandtheSecondLawofThermodynamics 181
4.7.2 WhatCausestheEntropytoIncrease? 183
4.8 EntropyperParticle 191
4.9 Bose-EinsteinCondensate 193
Contents ix