Principles of relativity physics

Cover......Page 1
Title page......Page 3
Copyright page......Page 4
Dedication......Page 5
Preface......Page 7
Notation......Page 11
Contents......Page 13
Part I. Geometrical foundations for space-time theories......Page 19
1. Geometrical structures......Page 21
1.1. The space-time manifold......Page 22
1.2. Coordinates and coordinate coverings......Page 23
1.3. Space-time mappings......Page 24
1.4. Groups of mappings......Page 25
1.5. Geometrical objects......Page 32
1.6. Tensors......Page 34
1.7. Tensor densities......Page 41
1.8. Tensor fields......Page 44
1.9. Integrals and Stokes' theorem......Page 46
1.10. Geometrical interpretation of tensors......Page 49
1.11. Internal transformations......Page 53
2.1. Parallel transport and the coderivative......Page 56
2.2. The coderivative for internal groups......Page 62
2.3. Affine geodesics......Page 65
2.4. Distant parallelism and affine flatness......Page 67
3.1. The metric tensor......Page 73
3.2. Metric geodesics and the metric affinity......Page 75
3.3. Metric flatness......Page 78
3.4. The Riemann-Christoffel tensor......Page 79
3.5. Algebraic classification of the Weyl tensor......Page 83
3.6. Geometry of subspaces......Page 85
3.7. Characteristic surfaces......Page 88
4. Structure of space-time theories......Page 91
4.1. The elements of a physical theory......Page 92
4.2. Covariance properties of physical theories......Page 93
4.3. Absolute and dynamical objects in physical theories......Page 101
4.4. Symmetry groups......Page 102
4.5. Variational principles and conservation laws......Page 106
4.6. Gauge groups......Page 113
4.7. The initial value problem......Page 116
Part II. Absolute space-time theories......Page 121
5. Newtonian mechanics......Page 123
5.1. Newtonian space-time......Page 124
5.2. Newton's laws of motion......Page 128
5.3. The law of universal gravitation and action-at-a-distance......Page 135
5.4. Galilean relativity and absolute motion......Page 138
5.5. Maxwell's electrodynamics and the Galilean symmetries; the aether......Page 142
6. Special relativity......Page 145
6.1. The search for absolute velocity......Page 146
6.2. The development of special relativity......Page 154
6.3. Relation between theory and experiment......Page 155
6.4. Symmetries of special relativistic systems: absolute space-time......Page 158
6.5. The Poincaré group......Page 159
6.6. Geometry of Minkowski space......Page 169
6.7. Light signals......Page 175
6.8. Free particles in special relativity......Page 176
6.9. A light clock......Page 177
6.10. Measurements of space and time intervals with light clocks; inertial frames......Page 180
6.12. Comparison of clock rates, time dilation, length contraction......Page 182
6.13. Other clocks and measuring rods......Page 189
6.14. The twin paradox......Page 192
6.15. Relation between space-time measurements in different inertial frames......Page 197
6.16. Noninertial reference systems......Page 199
6.17. Derivation of the Poincaré mappings......Page 202
6.18. The einstein addition theorem for velocities; the fresnel coefficient......Page 205
6.19. Causality......Page 208
7. Relativistic particle dynamics......Page 210
7.1. The dynamics of a free particle......Page 211
7.2. Conservation laws for a free particle......Page 214
7.3. Relativistic force......Page 215
7.4. Relativistic systems of particles......Page 219
7.5. Conservation laws for relativistic systems of particles......Page 222
7.6. Elastic scattering......Page 226
7.7. Inelastic scattering......Page 229
7.8. Relativistic statistical mechanics......Page 233
7.9. Action-at-a-distance electrodynamics......Page 235
7.10. The relativistic two-body problem......Page 241
7.11. Slow-motion approximation to electrodynamics......Page 243
7.12. The motion of charges in fields......Page 245
7.14. Conservation laws for particles in fields......Page 249
7.15. Motion of a charged particle in a constant uniform electric field......Page 254
7.16. Motion of a charged particle in a constant uniform magnetic field......Page 256
7.17. Radiation damping......Page 258
7.18. Radiation reaction and pre-acceleration......Page 260
7.19. The uniformly accelerated charge; energy balance......Page 263
7.20. Motion of spinning particles in fields......Page 266
7.21. Gravidynamics......Page 271
8. Relativistic continuum mechanics; microscopic theory......Page 274
8.1. The electromagnetic field, Maxwell-Lorentz equations......Page 275
8.2. Transformation properties of the Maxwell field......Page 280
8.3. Solutions of Maxwell's equations......Page 283
8.4. Continuity equations and conservation laws......Page 290
8.5. The Minkowski tensor......Page 299
8.6. Classical electron theory......Page 301
8.7. Structure of the electromagnetic equations and the initial value program......Page 305
8.8. The Klein-Gordon equation......Page 306
8.9. The Dirac equation......Page 312
8.10. The gravitational field in special relativity......Page 315
9. Relativistic continuum mechanics; macroscopic theory......Page 325
9.1. Matter in bulk......Page 326
9.2. The perfect fluid, relativistic thermodynamics......Page 331
9.3. Kinematics of velocity fields......Page 335
9.4. Electrodynamics in matter......Page 340
Part III. Dynamical space-time theories......Page 345
10. Foundations of general relativity......Page 347
10.1. Mach's principle......Page 348
10.2. The principle of equivalence......Page 352
10.3. The principle of general invariance......Page 356
10.4. The Einstein field equations......Page 361
10.5. Stationary and static gravitational fields......Page 366
10.6. Interaction of physical systems with the gravitational field......Page 370
10.7. Newtonian limit of the Einstein equations......Page 378
10.8. Structure of the Einstein equations......Page 380
10.9. The initial value problem for the Einstein equations......Page 381
10.10. The linearized Einstein equations......Page 386
11. Solutions of the Einstein equations......Page 390
11.1. Solutions of the linearized Einstein equations......Page 391
11.2. Uniqueness of the flat-space solution......Page 397
11.3. Spherically symmetric exact solutions......Page 399
11.4. The Schwarzschild "singularity"; the topology of the Schwarzschild field......Page 404
11.5. Cylindrically symmetric fields......Page 410
11.6. Null gravitational fields......Page 413
11.7. Solutions with sources......Page 415
12. Experimental tests for general relativity......Page 421
12.1. Motion of test bodies in a Schwarzschild field and the advance of planetary perihelia......Page 422
12.2. Bending of light in a Schwarzschild field......Page 428
12.3. Gravitational red shift......Page 432
12.4. Other tests......Page 437
13. Further consequences of general relativity......Page 440
13.1. Conservation laws in general relativity......Page 441
13.2. Gravitational radiation......Page 448
13.3. Direct-particle equations of motion in general relativity......Page 455
14. Cosmology......Page 462
14.1. Homogeneous, isotropic cosmologies......Page 464
14.2. Structure of homogeneous, isotropic spaces......Page 470
14.3. Observational consequences......Page 473
14.4. The static Einstein model......Page 476
14.5. The de Sitter models and the steady-state cosmology......Page 477
14.6. The Friedmann models......Page 480
14.7. The Gödel model......Page 483
14.8. Further developments......Page 484
Appendix: the Dirac delta function......Page 487
Author index......Page 491
Subject index......Page 494