Relativity and Geometry (Foundations and Philosophy of Science and Technology Series)

Title. In the SerIes......Page 1
Title: Relativity and Geometry......Page 2
ISBN 0-08-026773-4......Page 3
Dedicated to Christian......Page 5
Preface......Page 7
Contents......Page 9
Introduction......Page 13
1.1 The Task of Natural Philosophy......Page 20
1.2. Absolute Space......Page 21
1.3. Absolute Time......Page 23
1.4. Rigid Frames and Coordinates.......Page 26
1.5. Inertial Frames and Newtonian Relativity.......Page 27
1.6 Newtonian Spacetime......Page 32
1.7 Gravitation......Page 43
2.1 Nineteenth-Century Views on Electromagnetic Action......Page 47
2.2 The Relathe Motion of the Earth and the Aether......Page 50
3.1 Motiwation......Page 60
3.2 The Definition of Time in an Inertial Frame......Page 62
3.3. The Principles of Special Relativity......Page 66
3.4 The Lorentz Transformation. Einstein\'s Derivation of 1905......Page 68
3.5 The Lorentz Transformation. Some Corollaries and Applications......Page 78
3.6 The Lorentz Transformation. Linearity......Page 83
3.7 The Lorentz Transformation. Ignatowsky\'s Approach......Page 88
3.8. The \"Relativity Theory of Poincaré and Lorentz\"......Page 95
4.1 The Geometry of the Lorentz Group......Page 100
4.2 Minkowski Spacetime as an Affine Metric Space and as a Riemannian Manifold......Page 103
4.3 Geometrical Objects......Page 110
4.4 Concept Mutation at the Birth of Relativistic Dynamics......Page 119
4.5 A Glance at Spacetime Physics1......Page 126
4.6 The Causal Structure of Minkowski Spacetime......Page 133
5.1 Gravitation and Relativity......Page 142
5.2 The Principle of Equivalence......Page 145
5.3 Gravitation and Geometry, circa 1912......Page 149
5.4 Departure from Flatness......Page 155
5.5 General Covariance and the Einstein-Grossmann Theory.......Page 164
5.6 Einstein\'s Arguments against General Covariance: 1913-14\'......Page 174
5.7 Einstein\'s Papers of November 1915......Page 180
5.8 Einstein\'s Field Equations and the Geodesic Law of Motion.......Page 188
6.1 Structures of Spacetime......Page 198
6.2 Mach\'s Principle and the Advent of Relativistic Cosmology......Page 206
6.3 The Friedmann Worlds......Page 214
6.4 Singularities......Page 222
7.1 The Concept of Simultaneity......Page 232
7.2 Geometric Conventionalism.......Page 242
7.3 Remarks on Time and Causality......Page 259
A Differentiable Manifolds......Page 269
B Fibre Bundles......Page 275
C Linear Connections......Page 277
1. Vector-valued Differential Forms......Page 278
2. The Lie Algebra of a Lie Group......Page 280
3. Connections in a Principal Fibre Bundle......Page 281
4. Linear Connections......Page 284
5. Covariant DWerentiation......Page 286
6. The Torsion and Curvature of a Linear Connection......Page 287
7. Geodesics......Page 289
8. Metric Connections in Riemannian Manifolds......Page 291
D Useful Formulae......Page 293
Introduction......Page 295
Section 1.1......Page 296
Section 1.2......Page 297
Section 1.5......Page 298
Section 1.6......Page 299
Section 1.7......Page 300
Section 2.1......Page 301
Section 2.2......Page 302
Section 3.1......Page 304
Section 3.2......Page 305
Section 3.4......Page 306
Section 3.6......Page 308
Section 3.7......Page 310
Section 3.8......Page 312
Section 4.1......Page 314
Section 4.2......Page 315
Section 4.3......Page 316
Section 4.4......Page 318
Section 4.5......Page 319
Section 4.6......Page 320
Section 5.1......Page 321
Section 5.2......Page 322
Section 5.3......Page 323
Section 5.4......Page 325
Section 5.5......Page 328
Section 5.6......Page 331
Section 5.7......Page 333
Section 5.8......Page 335
Section 6.1......Page 337
Section 6.2......Page 340
Section 6.3......Page 344
Section 6.4......Page 346
Section 7.1......Page 350
Section 7.2......Page 352
Section 7.3......Page 358
A. Differntiable Manifolds......Page 359
B. Fibre Bundles......Page 360
C. Linear Connections......Page 361
References......Page 363
Index......Page 393