The Mathematical Theory of Relativity

Description

Title Page Contents Editor's Foreword Preface Introduction I. Elementary Principles 1. Indeterminateness of the space-time frame 2. The fundamental quadratic form 3. Measurement of intervals 4. Rectangular coordinates and time 5. The Lorentz transformation 6. The velocity of light 7. Timelike and spacelike intervals 8. Immediate consciousness of time 9. The ``3 + 1 dimensional'' world 10. The FitzGerald contraction 11. Simultaneity at different places 12. Momentum and mass 13. Energy 14. Density and temperature 15. General transformations of coordinates 16. Fields of force 17. The Principle of Equivalence 18. Retrospect II. The Tensor Calculus 19. Contravariant and covariant vectors 20. The mathematical notion of a vector 21. The physical notion of a vector 22. The summation convention 23. Tensors 24. Inner multiplication and contraction. The quotient law 25. The fundamental tensors 26. Associated tensors 27. Christoffel's 3-index symbols 28. Equations of a geodesic 29. Covariant derivative of a vector 30. Covariant derivative of a tensor 31. Alternative discussion of the covariant derivative 32. Surface-elements and Stokes's theorem 33. Significance of covariant differentiation 34. The Riemann-Christoffel tensor 35. Miscellaneous formulae III. The Law of Gravitation 36. The condition for flat space-time. Natural coordinates 37. Einstein's law of gravitation 38. The gravitational field of an isolated particle 39. Planetary orbits 40. The advance of perihelion 41. The deflection of light 42. Displacement of the Fraunhofer lines 43. Isotropic coordinates 44. Problem of two bodies—Motion of the moon 45. Solution for a particle in a curved world 46. Transition to continuous matter 47. Experiment and deductive theory IV. Relativity Mechanics 48. The antisymmetrical tensor of the fourth rank 49. Element of volume. Tensor-density 50. The problem of the rotating disc 51. The divergence of a tensor 52. The four identities 53. The material energy-tensor 54. New derivation of Einstein's law of gravitation 55. The force 56. Dynamics of a particle 57. Equality of gravitational and inertial mass. Gravitational waves 58. Lagrangian form of the gravitational equations 59. Pseudo-energy-tensor of the gravitational field 60. Action 61. A property of invariants 62. Alternative energy-tensors 63. Gravitational flux from a particle 64. Retrospect V. Curvature of Space and Time 65. Curvature of a four-dimensional manifold 66. Interpretation of Einstein's law of gravitation 67. Cylindrical and spherical space-time 68. Elliptical space 69. Law of gravitation for curved space-time 70. Properties of de Sitter's spherical world 71. Properties of Einstein's cylindrical world 72. The problem of the homogeneous sphere VI. Electricity 73. The electromagnetic equations 74. Electromagnetic waves 75. The Lorentz transformation of electromagnetic force 76. Mechanical effects of the electromagnetic field 77. The electromagnetic energy-tensor 78. The gravitational field of an electron 79. Electromagnetic action 80. Explanation of the mechanical force 81. Electromagnetic volume 82. Macroscopic equations VII. World Geometry 83. Natural geometry and world geometry 84. Non-integrability of length 85. Transformation of gauge-systems 86. Gauge-invariance 87. The generalised Riemann-Christoffel tensor 88. The in-invariants of a region 89. The natural gauge 90. Weyl's action-principle 91. Parallel displacement 92. Displacement round an infinitesimal circuit 93. Introduction of a metric 94. Evaluation of the fundamental in-tensors 95. The natural gauge of the world 96. The principle of identification 97. The bifurcation of geometry and electrodynamics 98. General relation-structure 99. The tensor B 100. Dynamical consequences of the general properties of world-invariants 101. The generalised volume 102. Numerical values 103. Conclusion Bibliography Index