Relativity and Geometry (eBook)

Front Cover 1
Relativity and Geometry 4
Copyright Page 5
Table of Contents 10
Preface 8
Introduction 14
Chapter 1. Newtonian Principles 21
1.1. The Task of Natural Philosophy 21
1.2. Absolute Space 22
1.3. Absolute Time 24
1.4. Rigid Frames and Coordinates 27
1.5. Inertial Frames and Newtonian Relativity 28
1.6. Newtonian Spacetime 33
1.7. Gravitation 44
Chapter 2. Electrodynamics and the Aether 48
2.1. Nineteenth-Century Views on Electromagnetic Action 48
2.2. The Relative Motion of the Earth and the Aether 51
Chapter 3. Einstein's 'Electrodynamics of Moving Bodies' 61
3.1. Motivation 61
3.2. The Definition of Time in an Inertial Frame 63
3.3. The Principles of Special Relativity 67
3.4. The Lorentz Transformation. Einstein's Derivation of 1905 69
3.5. The Lorentz Transformation. Some Corollaries and Applications 79
3.6. The Lorentz Transformation. Linearity 84
3.7. The Lorentz Transformation. Ignatowsky's Approach 89
3.8. The "Relativity Theory of Poincaré and Lorentz" 96
Chapter 4. Minkowski Spacetime 101
4.1. The Geometry of the Lorentz Group 101
4.2. Minkowski Spacetime as an Affine Metric Space and as a Riemannian Manifold 104
4.3. Geometrical Objects 111
4.4. Concept Mutation at the Birth of Relativistic Dynamics 120
4.5. A Glance at Spacetime Physics 127
4.6. The Causal Structure of Minkowski Spacetime 134
Chapter 5. Einstein's Quest for a Theory of Gravity 143
5.1. Gravitation and Relativity 143
5.2. The Principle of Equivalence 146
5.3. Gravitation and Geometry circa 1912 150
5.4. Departure from Flatness 156
5.5. General Covariance and the Einstein-Grossmann Theory 165
5.6. Einstein's Arguments against General Covariance: 1913-14 175
5.7. Einstein's Papers of November 1915 181
5.8. Einstein's Field Equations and the Geodesic Law of Motion 189
Chapter 6. Gravitational Geometry 199
6.1. Structures of Spacetime 199
6.2. Mach's Principle and the Advent of Relativistic Cosmology 207
6.3. The Friedmann Worlds 215
6.4. Singularities. 223
Chapter 7. Disputed Questions 233
7.1. The Concept of Simultaneity 233
7.2. Geometric Conventionalism 243
7.3. Remarks on Time and Causality 260
Appendix 270
A: Differentiable Manifolds. 270
B: Fibre Bundles 276
C: Linear Connections 278
D: Useful Formulae. 294
Notes 296
References 364
Index 394