Table of Contents
1 Old Physics 1
1 Motion of a Particle, The Inverse Square Law 1
2 Two Pictures of Matter 6
3 Vectors, Tensors, Operations 10
4 Maxwell's Equations 13
5 The Stress-Energy Tensor 20
6 General Equations of Motion. The Complete Tensor 23
2 New Geometry 26
7 Analytic Geometry of Four Dimensions 26
8 Transformation of Coordinates 32
9 Postulates for Four-Dimensional Geometry 38
10 Tensor Analysis 39
11 Complications Resulting from Imaginary Coordinate 51
12 Are the Equations of Physics Invariant? 64
13 Curves in the New Geometry 66
3 Special Relativity 70
14 Equations of Motion 70
15 Lorentz Transformations 76
16 Addition of Velocities 80
17 Light Corpuscles, or Photons 82
18 Electricity and Magnetism in Special Relativity 88
19 The Complete Tensor 90
4 Curved Space 99
20 Curvature of Curves and Surfaces 101
21 Generalizations 106
22 The Riemann Tensor 109
23 Points and Vectors in General Coordinates 113
24 Tensors in General Coordinates 116
25 Differentiation in General Coordinates 121
26 General Coordinates in Curved Spaces 127
27 Riemann Tensor in General Coordinates 133
28 Geodesies 137
29 Equations of Physics in General Coordinates 141
5 General Relativity 145
30 The Law of Geodesies 146
31 Solar System. Symmetry Conditions 148
32 Solution of the Field Equations 152
33 Equations of Geodesies 155
34 Newtonian Motion of a Planet 156
35 Relativity Motion of a Planet 159
36 Deflection of Light 162
37 Shift of Spectral Lines 164
Conclusion 169
Index 171
