The mathematical theory of relativity

Title ......Page 3
Copyright ......Page 4
Preface ......Page 6
Contents ......Page 8
INTRODUCTION ......Page 12
1. Indeterminateness of the space-time frame ......Page 19
2. The fundamental quadratic form ......Page 21
3. Measurement of intervals ......Page 22
4. Rectangular coordinates and time ......Page 24
5. The Lorentz transformation ......Page 28
6. The velocity of light ......Page 29
7. Timelike and spacelike intervals ......Page 33
8. Immediate consciousness of time ......Page 34
10. The FitzGerald contraction ......Page 36
11. Simultaneity at different places ......Page 38
12. Momentum and Mass ......Page 40
13. Energy ......Page 43
14. Density and temperature ......Page 44
15. General transformations of coordinates ......Page 45
16. Fields of force ......Page 48
17. The Principle of Equivalence ......Page 50
18. Retrospect ......Page 52
19. Contra variant and covariant vectors ......Page 54
20. The mathematical notion of a vector ......Page 55
21. The physical notion of a vector ......Page 58
22. The summation convention ......Page 61
23. Tensors ......Page 62
24. Inner multiplication and contraction. The quotient law ......Page 63
25. The fundamental tensors ......Page 66
26. Associated tensors ......Page 67
27. Christoffel's 3-index symbols ......Page 69
28. Equations of a geodesic ......Page 70
29. Covariant derivative of a vector ......Page 71
30. Covariant derivative of a tensor ......Page 73
31. Alternative discussion of the covariant derivative ......Page 76
32. Surface-elements and Stokes's theorem ......Page 77
33. Significance of covariant differentiation ......Page 79
34. The Riemann-Christoffel tensor ......Page 82
35. Miscellaneous formulae ......Page 85
36. The condition for flat space-time. Natural coordinates ......Page 87
37. Einstein's law of gravitation ......Page 92
38. The gravitational field of an isolated particle ......Page 93
39. Planetary orbits ......Page 96
40. The advance of perihelion ......Page 99
41. The deflection of light ......Page 101
42. Displacement of the Fraunhofer lines ......Page 102
43. Isotropic coordinates ......Page 104
44. Problem of two bodies—Motion of the moon ......Page 106
45. Solution for a particle in a curved world ......Page 111
46. Transition to continuous matter ......Page 112
47. Experiment and deductive theory ......Page 115
48. The antisymmetrical tensor of the fourth rank ......Page 118
49. Element of volume. Tensor-density ......Page 120
50. The problem of the rotating disc ......Page 123
51. The divergence of a tensor ......Page 124
52. The four identities ......Page 126
53. The material energy-tensor ......Page 127
54. New derivation of Einstein's law of gravitation ......Page 130
55. The force ......Page 133
56. Dynamics of a particle ......Page 136
57. Equality of gravitational and inertial mass. Gravitational waves ......Page 139
58. Lagrangian form of the gravitational equations ......Page 142
59. Pseudo-energy-tensor of the gravitational field ......Page 145
60. Action ......Page 148
61. A property of invariants ......Page 151
62. Alternative energy-tensors ......Page 152
63. Gravitational flux from a particle ......Page 155
64. Retrospect ......Page 157
65. Curvature of a four-dimensional manifold ......Page 160
66. Interpretation of Einstein's law of gravitation ......Page 163
67. Cylindrical and spherical space-time ......Page 166
68. Elliptical space ......Page 168
69. Law of gravitation for curved space-time ......Page 170
70. Properties of de Sitter's spherical world ......Page 172
71. Properties of Einstein's cylindrical world ......Page 177
72. The problem of the homogeneous sphere ......Page 179
73. The electromagnetic equations ......Page 182
74. Electromagnetic waves ......Page 186
75. The Lorentz transformation of electromagnetic force ......Page 190
76. Mechanical effects of the electromagnetic field ......Page 191
77. The electromagnetic energy-tensor ......Page 193
78. The gravitational field of an electron ......Page 196
79. Electromagnetic action ......Page 198
80. Explanation of the mechanical force ......Page 200
81. Electromagnetic volume ......Page 204
82. Macroscopic equations ......Page 205
83. Natural geometry and world geometry ......Page 207
84. Non-integrability of length ......Page 209
85. Transformation of gauge-systems ......Page 211
86. Gauge-invariance ......Page 213
87. The generalised Riemann-Christoffel tensor ......Page 215
88. The in-invariants of a region ......Page 216
89. The natural gauge ......Page 217
90. Weyl's action-principle ......Page 220
91. Parallel displacement ......Page 224
92. Displacement round an infinitesimal circuit ......Page 225
93. Introduction of a metric ......Page 227
94. Evaluation of the fundamental in-tensors ......Page 229
95. The natural gauge of the world ......Page 230
96. The principle of identification ......Page 233
97. The bifurcation of geometry and electrodynamics ......Page 234
98. General relation-structure ......Page 235
99. The tensor *B ......Page 237
100. Dynamical consequences of the general properties of world-invariants ......Page 239
101. The generalised volume ......Page 243
102. Numerical values ......Page 246
103. Conclusion ......Page 248
Supplementary Notes ......Page 252
Bibliography ......Page 275
Index ......Page 278