Relativity Thermodynamics and CosmologyPDF电子书下载

Ⅰ．INTRODUCTION 1

1．The Subject-Matter 1

2．The Method of Presentation 7

3．The Point of View 9

Ⅱ．THE SPECIAL THEORY OF RELATIVITY 12

Part Ⅰ．THE TWO POSTULATES AND THE LORENTZ TRANSFORMATION 12

4．Introduction 12

5．The First Postulate of Relativity 12

6．The Second Postulate of Relativity 15

7．Necessity for Modifying Older Ideas as to Space and Time 17

8．The Lorentz Transformation Equations 18

9．Transformation Equations for Spatial and Temporal Intervals Lorentz Contraction and Time Dilation 22

10．Transformation Equations for Velocity 25

11．Transformation Equation for the Lorentz Contraction Factor 27

12．Transformation Equations for Acceleration 27

Part Ⅱ．TREATMENT OF SPECIAL RELATIVITY WITH THE HELP OF A FOUR-DIMENSIONAL GEOMETRY 28

13．The Space-Time Continuum 28

14．The Three Plus One Dimensions of Space-Time 29

15．The Geometry Corresponding to Space-Time 30

16．The Signature of the Line Element and the Three Kinds of Interval 31

17．The Lorentz Rotation of Axes 32

18．The Transformation to Proper Coordinates 33

19．Use of Tensor Analysis in the Theory of Relativity 34

20．Simplification of Tensor Analysis in the Case of Special Relativity Galilean Coordinates 37

21．Correspondence of Four-Dimensional Treatment with the Postulates of Special Relativity 39

Ⅲ．SPECIAL RELATIVITY AND MECHANICS 42

Part Ⅰ．THE DYNAMICS OF A PARTICLE 42

22．The Principles of the Conservation of Mass and Momentum 42

23．The Mass of a Moving Particle 43

24．The Transformation Equations for Mass 45

25．The Definition and Transformation Equations for Force 45

26．Work and Kinetic Energy 47

27．The Relations between Mass，Energy，and Momentum 48

28．Four-Dimensional Expression of the Mechanics of a Particle 50

29．Applications of the Dynamics of a Particle 53

(a) The Mass of High-Velocity Electrons 53

(b) The Relation between Force and Acceleration 54

(c) Applications in Electromagnetic Theory 55

(d) Tests of the Interrelation of Mass，Energy，and Momentum 57

Part Ⅱ．THE DYNAMICS OF A CONTINUOUS MECHANICAL MEDIUM 59

30．The Principles Postulated 59

31．The Conservation of Momentum and the Components of Stress tij 60

32．The Equations of Motion in Terms of the Stresses tij 60

33．The Equation of Continuity 62

34．The Transformation Equations for the Stresses tij 62

35．The Transformation Equations for the Densities of Mass and Momentum 65

36．Restatement of Results in Terms of the (Absolute) Stresses pij 69

37．Four-Dimensional Expression of the Mechanics of a Continuous Medium 70

38．Applications of the Mechanics of a Continuous Medium 73

(a) The Mass and Momentum of a Finite System 74

(b) The Angular Momentum of a Finite System 77

(c) The Right-Angled Lever as an Example 79

(d) The Complete Static System 80

Ⅳ．SPECIAL RELATIVITY AND ELECTRODYNAMICS 84

Part Ⅰ．ELECTRON THEORY 84

39．The Maxwell-Lorentz Field Equations 84

40．The Transformation Equations for E，H，and ρ 86

41．The Force on a Moving Charge 88

42．The Energy and Momentum of the Electromagnetic Field 89

43．The Electromagnetic Stresses 91

44．Transformation Equations for Electromagnetic Densities and Stresses 92

45．Combined Result of Mechanical and Electromagnetic Actions 93

46．Four-Dimensional Expression of the Electron Theory 95

(a) The Field Equations 95

(b) Four-Dimensional Expression of Force on Moving Charge 98

(c) Four-Dimensional Expression of Electromagnetic Energy-Momentum Tensor 99

47．Applications of the Electron Theory 99

Part Ⅱ．MACROSCOPIC THEORY 101

48．The Field Equations for Stationary Matter 101

49．The Constitutive Equations for Stationary Matter 102

50．The Field Equations in Four-Dimensional Language 102

51．The Constitutive Equations in Four-Dimensional Language 104

52．The Field Equations for Moving Matter in Ordinary Vector Language 105

53．The Constitutive Equations for Moving Matter in Ordinary Vector Language 108

54．Applications of the Macroscopic Theory 109

(a) The Conservation of Electric Charge 109

(b) Boundary Conditions 110

(c) The Joule Heating Effect 112

(d) Electromagnetic Energy and Momentum 113

(e) The Energy-Momentum Tensor 115

(f) Applications to Experimental Observations 116

Ⅴ．SPECIAL RELATIVITY AND THERMODYNAMICS 118

Part Ⅰ．THE THERMODYNAMICS OF STATIONARY SYSTEMS 118

55．Introduction 118

56．The First Law of Thermodynamics and the Zero Point of Energy Content 120

57．The Second Law of Thermodynamics and the Starting-Point for Entropy Content 121

58．Heat Content，Free Energy，and Thermodynamic Potential 123

59．General Conditions for Thermodynamic Change and Equilibrium 125

60．Conditions for Change and Equilibrium in Homogeneous Systems 127

61．Uniformity of Temperature at Thermal Equilibrium 130

62．Irreversibility and Rate of Change 132

63．Final State of an Isolated System 134

64．Energy and Entropy of a Perfect Monatomic Gas 136

65．Energy and Entropy of Black-Body Radiation 139

66．The Equilibrium between Hydrogen and Helium 140

67．The Equilibrium between Matter and Radiation 146

Part Ⅱ．THE THERMODYNAMICS OF MOVING SYSTEMS 152

68．The Two Laws of Thermodynamics for a Moving System 152

69．The Lorentz Transformation for Thermodynamic Quantities 153

(a) Volume and Pressure 153

(b) Energy 154

(c) Work 156

(d) Heat 156

(e) Entropy 157

(f) Temperature 158

70．Thermodynamic Applications 159

(a) Carnot Cycle Involving Change in Velocity 159

(b) The Dynamics of Thermal Radiation 161

71．Use of Four-Dimensional Language in Thermodynamics 162

Ⅵ．THE GENERAL THEORY OF RELATIVITY 165

Part Ⅰ．THE FUNDAMENTAL PRINCIPLES OF GENERAL RELATIVITY 165

72．Introduction 165

73．The Principle of Covariance 166

(a) Justification for the Principle of Covariance 166

(b) Consequences of the Principle of Covariance 167

(c) Method of Obtaining Covariant Expressions 168

(d) Covariant Expression for Interval 169

(e) Covariant Expression for the Trajectories of Free Particles and Light Rays 171

74．The Principle of Equivalence 174

(a) Formulation of the Principle of Equivalence．Metric and Gravitation 174

(b) Principle of Equivalence and Relativity of Motion 176

(c) Justification for the Principle of Equivalence 179

(d) Use of the Principle of Equivalence in Generalizing the Principles of Special Relativity．Natural and Proper Coordinates 180

(e) Interval and Trajectory in the Presence of Gravitational Fields 181

75．The Dependence of Gravitational Field and Metric on the Distribution of Matter and Energy．Principle of Mach 184

76．The Field Corresponding to the Special Theory of Relativity．The Riemann-Christoffel Tensor 185

77．The Gravitational Field in Empty Space．The Contracted Riemann-Christoffel Tensor 187

78．The Gravitational Field in the Presence of Matter and Energy 188

Part Ⅱ．ELEMENTARY APPLICATIONS OF GENERAL RELATIVITY 192

79．Simple Consequences of the Principle of Equivalence 192

(a) The Proportionality of Weight and Mass 192

(b) Effect of Gravitational Potential on the Rate of a Clock 192

(c) The Clock Paradox 194

80．Newton＇s Theory as a First Approximation 198

(a) Motion of Free Particle in a Weak Gravitational Field 198

(b) Poisson＇s Equation as an Approximation for Einstein＇s Field Equations 199

81．Units to be Used in Relativistic Calculations 201

82．The Schwarzschild Line Element 202

83．The Three Crucial Tests of Relativity 205

(a) The Advance of Perihelion 208

(b) The Gravitational Deflexion of Light 209

(c) Gravitational Shift in Spectral Lines 211

Ⅶ．RELATIVISTIC MECHANICS 214

Part Ⅰ．SOME GENERAL MECHANICAL PRINCIPLES 214

84．The Fundamental Equations of Relativistic Mechanics 214

85．The Nature of the Energy-Momentum Tensor．General Expression in the Case of a Perfect Fluid 215

86．The Mechanical Behaviour of a Perfect Fluid 218

87．Re-expression of the Equations of Mechanics in the Form of an Ordinary Divergence 222

88．The Energy-Momentum Principle for Finite Systems 225

89．The Densities of Energy and Momentum Expressed as Divergences 229

90．Limiting Values for Certain Quantities at a Large Distance from an Isolated System 230

91．The Mass，Energy and Momentum of an Isolated System 232

92．The Energy of a Quasi-Static Isolated System Expressed by an Integral Extending Only Over the Occupied Space 234

Part Ⅱ．SOLUTIONS OF THE FIELD EQUATIONS 236

93．Einstein＇s General Solution of the Field Equations in the Case of Weak Fields 236

94．Line Elements for Systems with Spherical Symmetry 239

95．Static Line Element with Spherical Symmetry 241

96．Schwarzschild＇s Exterior and Interior Solutions 245

97．The Energy of a Sphere of Perfect Fluid 247

98．Non-Static Line Elements with Spherical Symmetry 250

99．Birkhoff＇s Theorem 252

100．A More General Line Element 253

Ⅷ．RELATIVISTIC ELECTRODYNAMICS 258

Part Ⅰ．THE COVARIANT GENERALIZATION OF ELECTRICAL THEORY 258

101．Introduction 258

102．The Generalized Lorentz Electron Theory．The Field Equations 258

103．The Motion of a Charged Particle 259

104．The Energy-Momentum Tensor 261

105．The Generalized Macroscopic Theory 261

Part Ⅱ．SOME APPLICATIONS OF RELATIVISTIC ELECTRODYNAMICS 264

106．The Conservation of Electric Charge 264

107．The Gravitational Field of a Charged Particle 265

108．The Propagation of Electromagnetic Waves 267

109．The Energy-Momentum Tensor for Disordered Radiation 269

110．The Gravitational Mass of Disordered Radiation 271

111．The Energy-Momentum Tensor Corresponding to a Directed Flow of Radiation 272

112．The Gravitational Field Corresponding to a Directed Flow of Radiation 273

113．The Gravitational Action of a Pencil of Light 274

(a) The Line Element in the Neighbourhood of a Limited Pencil of Light 274

(b) Velocity of a Test Ray of Light in the Neighbourhood of the Pencil 275

(c) Acceleration of a Test Particle in the Neighbourhood of the Pencil 277

114．The Gravitational Action of a Pulse of Light 279

(a) The Line Element in the Neighbourhood of the Limited Track of a Pulse of Light 279

(b) Velocity of a Test Ray of Light in the Neighbourhood of the Pulse 281

(c) Acceleration of a Test Particle in the Neighbourhood of the Pulse 282

115．Discussion of the Gravitational Interaction of Light Rays and Particles 285

116．The Ceneralized Doppler Effect 288

Ⅸ．RELATIVISTIC THERMODYNAMICS 291

Part Ⅰ．THE EXTENSION OF THERMODYNAMICS TO GENERAL RELATIVITY 291

117．Introduction 291

118．The Relativistic Analogue of the First Law of Thermodynamics 292

119．The Relativistic Analogue of the Second Law of Thermodynamics 293

120．On the Interpretation of the Relativistic Second Law of Thermodynamics 296

121．On the Interpretation of Heat in Relativistic Thermodynamics 297

122．On the Use of Co-Moving Coordinates in Thermodynamic Considerations 301

Part Ⅱ．APPLICATIONS OF RELATIVISTIC THERMODYNAMICS 304

123．Application of the First Law to Changes in the Static State of a System 304

124．Application of the Second Law to Changes in the Static State of a System 306

125．The Conditions for Static Thermodynamic Equilibrium 307

126．Static Equilibrium in the Case of a Spherical Distribution of Fluid 308

127．Chemical Equilibrium in a Gravitating Sphere of Fluid 311

128．Thermal Equilibrium in a Gravitating Sphere of Fluid 312

129．Thermal Equilibrium in a General Static Field 315

130．On the Increased Possibility in Relativistic Thermodynamics for Reversible Processes at a Finite Rate 319

131．On the Possibility for Irreversible Processes without Reaching a Final State of Maximum Entropy 326

132．Conclusion 330

Ⅹ．APPLICATIONS TO COSMOLOGY 331

Part Ⅰ．STATIC COSMOLOGICAL MODELS 331

133．Introduction 331

134．The Three Possibilities for a Homogeneous Static Universe 333

135．The Einstein Line Element 335

136．The de Sitter Line Element 335

137．The Special Relativity Line Element 336

138．The Geometry of the Einstein Universe 337

139．Density and Pressure of Material in the Einstein Universe 339

140．Behaviour of Particles and Light Rays in the Einstein Universe 341

141．Comparison of Einstein Model with Actual Universe 344

142．The Geometry of the de Sitter Universe 346

143．Absence of Matter and Radiation from the de Sitter Universe 348

144．Behaviour of Test Particles and Light Rays in the de Sitter Universe 349

(a) The Geodesic Equations 349

(b) Orbits of Particles 351

(c) Behaviour of Light Rays in the de Sitter Universe 353

(d) Doppler Effect in the de Sitter Universe 354

145．Comparison of de Sitter Model with Actual Universe 359

Part Ⅱ．THE APPLICATION OF RELATIVISTIC MECHANICS TO NON-STATIC HOMOGENEOUS COSMOLOGICAL MODELS 361

146．Reasons for Changing to Non-Static Models 361

147．Assumption Employed in Deriving Non-Static Line Element 362

148．Derivation of Line Element from Assumption of Spatial Isotropy 364

149．General Properties of the Line Element 370

(a) Different Forms of Expression for the Line Element 370

(b) Geometry Corresponding to Line Element 371

(c) Result of Transfer of Origin of Coordinates 372

(d) Physical Interpretation of Line Element 375

150．Density and Pressure in Non-Static Universe 376

151．Change in Energy with Time 379

152．Change in Matter with Time 381

153．Behaviour of Particles in the MOdel 383

154．Behaviour of Light Rays in the Model 387

155．The Doppler Effect in the Model 389

156．Change in Doppler Effect with Distance 392

157．General Discussion of Dependence on Time for Closed Models 394

(a) General Features of Time Dependence，R real，ρ00 ？ 0，p0 ？ 0 395

(b) Curve for the Critical Function of R 396

(c) Monotonic Universes of Type M1，for ？ > ？E 399

(d) Asymptotic Universes of Types A1 and A2，for ？ = ？E 400

(e) Monotonic Universes of Type M2 and Oscillating Universes of Types O1 and O2，for 0 < ？ < ？E 401

(f) Oscillating Universes of Type O1，for ？ 0 402

158．General Discussion of Dependence on Time for Open Models 403

159．On the Instability of the Einstein Static Universe 405

160．Models in Which the Amount of Matter is Constant 407

161．Models Which Expand from an Original Static State 409

162．Ever Expanding Models Which do not Start from a Static State 412

163．Oscillating Models (？ = 0) 412

164．The Open Model of Einstein and de Sitter (？ = 0，R0 = ？) 415

165．Discussion of Factors which were Neglected in Studying Special Models 416

Part Ⅲ．THE APPLICATION OF RELATIVISTIC THERMODYNAMICS TO NON-STATIC HOMOGENEOUS COSMOLOGICAL MODELS 420

166．Application of the Relativistic First Law 420

167．Application of the Relativistic Second Law 421

168．The Conditions for Thermodynamic Equilibrium in a Static Einstein Universe 423

169．The Conditions for Reversible and Irreversible Changes in Non-Static Models 424

170．Model Filled with Incoherent Matter Exerting No Pressure as an Example of Reversible Behaviour 426

171．Model Filled with Black-Body Radiation as an Example of Reversible Behaviour 427

172．Discussion of Failure to Obtain Periodic Motions without Singular States 429

173．Interpretation of Reversible Expansions by an Ordinary Observer 432

174．Analytical Treatment of a Succession of Expansions and Contractions for a Closed Model with ？ = 0 435

(a) The Upper Boundary of Expansion 436

(b) Time Necessary to Reach Maximum 436

(c) Time Necessary to Complete Contraction 437

(d) Behaviour at Lower Limit of Contraction 438

175．Application of Thermodynamics to a Succession of Irreversible Expansions and Contractions 439

Part Ⅳ．CORRELATION OF PHENOMENA IN THE ACTUAL UNIVERSE WITH THE HELP OF NON-STATIC HOMOGENEOUS MODELS 445

176．Introduction 445

177．The Observational Data 446

(a) The Absolute Magnitudes of the Nearer Nebulae 446

(b) The Corrected Apparent Magnitudes for more Distant Nebulae 448

(c) Nebular Distances Calculated from Apparent Magnitudes 453

(d) Relation of Observed Red-Shift to Magnitude and Distance 454

(e) Relation of Apparent Diameter to Magnitude and Distance 457

(f) Actual Diameters and Masses of Nebulae 458

(g) Distribution of Nebulae in Space 459

(h) Density of Matter in Space 461

178．The Relation between Coordinate Position and Luminosity 462

179．The Relation between Coordinate Position and Astronomically Determined Distance 465

180．The Relation between Coordinate Position and Apparent Diameter 467

181．The Relation between Coordinate Position and Counts of Nebular Distribution 468

182．The Relation between Coordinate Position and Red-shift 469

183．The Relation of Density to Spatial Curvature and Cosmological Constant 473

184．The Relation between Red-shift and Rate of Disappearance of Matter 475

185．Summary of Correspondences between Model and Actual Universe 478

186．Some General Remarks Concerning Cosmological Models 482

(a) Homogeneity 482

(b) Spatial Curvature 483

(c) Temporal Behaviour 484

187．Our Neighbourhood as a Sample of the Universe as a Whole 486

Appendix Ⅰ．SYMBOLS FOR QUANTITIES 489

Scalar Quantities 489

Vector Quantities 490

Tensors 490

Tensor Densities 491

Appendix Ⅱ．SOME FORMULAE OF VECTOR ANALYSIS 491

Appendix Ⅲ．SOME FORMULAE OF TENSOR ANALYSIS 493

(a) General Notation 493

(b) The Fundamental Metrical Tensor and its Properties 494

(c) Tensor Manipulations 495

(d) Miscellaneous Formulae 496

(e) Formulae Involving Tensor Densities 496

(f) Four-Dimensional Volume．Proper Spatial Volume 496

Appendix Ⅳ．USEFUL CONSTANTS 497

Subject Index 499

Name Index 502