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Relativity: Special, General, and Cosmological / Edition 2 - Paperback | Diverse Reads

Relativity: Special, General, and Cosmological / Edition 2

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A modern thinking person's guide to all of Einstein's relativity. Full of mathematical rigor, but stressing physical insight, motivation, and clarity of concepts and logic, rather than mere formalism or experimental detail. Over 300 thought-provoking problems.

ISBN-13: 9780198567325

Media Type: Paperback

Publisher: Oxford University Press

Publication Date: 06-01-2006

Pages: 448

Product Dimensions: 9.20(w) x 6.28(h) x 0.97(d)

Professor Wolfgang Rindler Department of Physics The University of Texas at Dallas Richardson, TX 75083-0688 USA

Table of Contents

Introduction 1
1 From absolute space and time to influenceable spacetime: an overview 3
1.1 Definition of relativity 3
1.2 Newton's laws and intertial frames 4
1.3 The Galilean transformation 5
1.4 Newtonian relativity 6
1.5 Objections to absolute space; Mach's principle 7
1.6 The ether 9
1.7 Michelson and Morley's search for the ether 9
1.8 Lorentz's ether theory 10
1.9 Origins of special relativity 12
1.10 Further arguments for Einstein's two postulates 14
1.11 Cosmology and first doubts about inertial frames 15
1.12 Inertial and gravitational mass 16
1.13 Einstein's equivalence principle 18
1.14 Preview of general relativity 20
1.15 Caveats on the equivalence principle 22
1.16 Gravitational frequency shift and light bending 24
Exercises 1 27
I Special Relativity 31
2 Foundations of special relativity; The Lorentz transformation 33
2.1 On the nature of physical theories 33
2.2 Basic features of special relativity 34
2.3 Relativistic problem solving 36
2.4 Relativity of simultaneity, time-dilation and length-contraction: a preview 38
2.5 The relativity principle and the homogeneity and isotropy of inertial frames 39
2.6 The coordinate lattice; Definitions of simultaneity 41
2.7 Derivation of the Lorentz transformation 43
2.8 Properties of the Lorentz transformation 47
2.9 Graphical representation of the Lorentz transformation 49
2.10 The relativistic speed limit 54
2.11 Which transformations are allowed by the relativity principle? 57
Exercises 2 58
3 Relativistic kinematics 61
3.1 Introduction 61
3.2 World-picture and world-map 61
3.3 Length contraction 62
3.4 Length contraction paradox 63
3.5 Time dilation; The twin paradox 64
3.6 Velocity transformation; Relative and mutual velocity 68
3.7 Acceleration transformation; Hyperbolic motion 70
3.8 Rigid motion and the uniformly accelerated rod 71
Exercises 3 73
4 Relativistic optics 77
4.1 Introduction 77
4.2 The drag effect 77
4.3 The Doppler effect 78
4.4 Aberration 81
4.5 The visual appearance of moving objects 82
Exercises 4 85
5 Spacetime and four-vectors 89
5.1 The discovery of Minkowski space 89
5.2 Three-dimensional Minkowski diagrams 90
5.3 Light cones and intervals 91
5.4 Three-vectors 94
5.5 Four-vectors 97
5.6 The geometry of four-vectors 101
5.7 Plane waves 103
Exercises 5 105
6 Relativistic particle mechanics 108
6.1 Domain of sufficient validity of Newtonian mechanics 108
6.2 The axioms of the new mechanics 109
6.3 The equivalence of mass and energy 111
6.4 Four-momentum identities 114
6.5 Relativistic billiards 115
6.6 The zero-momentum frame 117
6.7 Threshold energies 118
6.8 Light quanta and de Broglie waves 119
6.9 The Compton effect 121
6.10 Four-force and three-force 123
Exercises 6 126
7 Four-tensors; Electromagnetism in vacuum 130
7.1 Tensors: Preliminary ideas and notations 130
7.2 Tensors: Definition and properties 132
7.3 Maxwell's equations in tensor form 139
7.4 The four-potential 143
7.5 Transformation of e and b; The dual field 146
7.6 The field of a uniformly moving point charge 148
7.7 The field of an infinite straight current 150
7.8 The energy tensor of the electromagnetic field 151
7.9 From the mechanics of the field to the mechanics of material continua 154
Exercises 7 157
II General Relativity 163
8 Curved spaces and the basic ideas of general relativity 165
8.1 Curved surfaces 165
8.2 Curved spaces of higher dimensions 169
8.3 Riemannian spaces 172
8.4 A plan for general relativity 177
Exercises 8 180
9 Static and stationary spacetimes 183
9.1 The coordinate lattice 183
9.2 Synchronization of clocks 184
9.3 First standard form of the metric 186
9.4 Newtonian support for the geodesic law of motion 188
9.5 Symmetries and the geometric characterization of static and stationary spacetimes 191
9.6 Canonical metric and relativistic potentials 195
9.7 The uniformly rotating lattice in Minkowski space 198
Exercises 9 200
10 Geodesics, curvature tensor and vacuum field equations 203
10.1 Tensors for general relativity 203
10.2 Geodesics 204
10.3 Geodesic coordinates 208
10.4 Covariant and absolute differentiation 210
10.5 The Riemann curvature tensor 217
10.6 Einstein's vacuum field equations 221
Exercises 10 224
11 The Schwarzschild metric 228
11.1 Derivation of the metric 228
11.2 Properties of the metric 230
11.3 The geometry of the Schwarzschild lattice 231
11.4 Contributions of the spatial curvature to post-Newtonian effects 233
11.5 Coordinates and measurements 235
11.6 The gravitational frequency shift 236
11.7 Isotropic metric and Shapiro time delay 237
11.8 Particle orbits in Schwarzschild space 238
11.9 The precession of Mercury's orbit 241
11.10 Photon orbits 245
11.11 Deflection of light by a spherical mass 248
11.12 Gravitational lenses 250
11.13 de Sitter precession via rotating coordinates 252
Exercises 11 254
12 Black holes and Kruskal space 258
12.1 Schwarzschild black holes 258
12.2 Potential energy; A general-relativistic 'proof' of E = mc[superscript 2] 263
12.3 The extendibility of Schwarzschild spacetime 265
12.4 The uniformly accelerated lattice 267
12.5 Kruskal space 272
12.6 Black-hole thermodynamics and related topics 279
Exercises 12 281
13 An exact plane gravitational wave 284
13.1 Introduction 284
13.2 The plane-wave metric 284
13.3 When wave meets dust 287
13.4 Inertial coordinates behind the wave 288
13.5 When wave meets light 290
13.6 The Penrose topology 291
13.7 Solving the field equation 293
Exercises 13 295
14 The full field equations; de Sitter space 296
14.1 The laws of physics in curved spacetime 296
14.2 At last, the full field equations 299
14.3 The cosmological constant 303
14.4 Modified Schwarzschild space 304
14.5 de Sitter space 306
14.6 Anti-de Sitter space 312
Exercises 14 314
15 Linearized general relativity 318
15.1 The basic equations 318
15.2 Gravitational waves. The TT gauge 323
15.3 Some physics of plane waves 325
15.4 Generation and detection of gravitational waves 330
15.5 The electromagnetic analogy in linearized GR 335
Exercises 15 341
III Cosmology 345
16 Cosmological spacetimes 347
16.1 The basic facts 347
16.2 Beginning to construct the model 358
16.3 Milne's model 360
16.4 The Friedman-Robertson-Walker metric 363
16.5 Robertson and Walker's theorem 368
Exercises 16 369
17 Light propagation in FRW universes 373
17.1 Representation of FRW universes by subuniverses 373
17.2 The cosmological frequency shift 374
17.3 Cosmological horizons 376
17.4 The apparent horizon 382
17.5 Observables 384
Exercises 17 388
18 Dynamics of FRW universes 391
18.1 Applying the field equations 391
18.2 What the field equations tell us 393
18.3 The Friedman models 396
18.4 Once again, comparison with observation 405
18.5 Inflation 409
18.6 The anthropic principle 413
Exercises 18 415
Appendix Curvature tensor components for the diagonal metric 417
Index 421