Reflections on Relativity
Contents Preface 1 1. First Principles 1.1 Experience and Spacetime 3 1.2 Systems of Reference 9 1.3 Inertia and Relativity 14 1.4 The Dilemma of Light 20 1.5 Corresponding States 29 1.6 A More Practical Arrangement 38 1.7 Staircase Wit 45 1.8 Another Symmetry 52 1.9 Generalized Lorentz Transformations 60 1.10 Null Coordinates 65 2. A Complex of Phenomena 2.1 The Spacetime Interval 74 2.2 Force Laws and Maxwell's Equations 81 2.3 The Inertia of Energy 91 2.4 Doppler Shift for Sound and Light 98 2.5 Stellar Aberration 103 2.6 Mobius Transformations of the Night Sky 110 2.7 The Sagnac Effect 119 2.8 Refraction Between Moving Media 127 2.9 Accelerated Travels 135 2.10 The Starry Messenger 148 2.11 Thomas Precession 158 3. Several Valuable Suggestions 3.1 Postulates and Principles 167 3.2 Natural and Violent Motions 175 3.3 De Mora Luminis 179 3.4 Stationary Paths 188 3.5 A Quintessence of So Subtle a Nature 194 3.6 The End of My Latin 202 3.7 Zeno and the Paradox of Motion 205 3.8 A Very Beautiful Day 212 3.9 Menelaus and Ceva 217 4. Weighty Arguments 4.1 Immovable Spacetime 228 4.2 Inertial and Gravitational Separations 237 4.3 Free-Fall Equations 242 4.4 Force, Curvature, and Uncertainty 246 4.5 Conventional Wisdom 252 4.6 The Field of All Fields 263 4.7 The Inertia of Twins 268 4.8 The Breakdown of Simultaneity 272 5. Extending the Principle 5.1 Absorbing Acceleration 279 5.2 Tensors, Contravariant and Covariant 284 5.3 Curvature, Intrinsic and Extrinsic 296 5.4 Relatively Straight 313 5.5 Schwarzschild Metric from Kepler's 3rd Law 321 5.6 Curved Coordinates and Acceleration 326 5.7 Riemannian Geometry 331 5.8 The Field Equations 342 6. Ist Das Wirklich So? 6.1 An Exact Solution 353 6.2 Anomalous Precession 360 6.3 Bending Light 370 6.4 Radial Paths in a Spherically Symmetrical Field 377 6.5 Proper Time in Circular Orbits 382 6.6 Flying Clocks 388 6.7 Acceleration in Schwarzschild Coordinates 394 6.8 Sources in Motion 398 7. Cosmology 7.1 Is the Universe Closed? 403 7.2 The Formation and Growth of Black Holes 414 7.3 Falling Into and Hovering Near A Black Hole 424 7.4 Curled-Up Dimensions 434 7.5 Packing Universes In Spacetime 438 7.6 Multiple Hubble Constants? 444 7.7 Boundaries and Symmetries 446 7.8 Global Interpretations of Local Experience 453 8. The Secret Confidence of Nature 8.1 Kepler, Napier, and the Third Law 464 8.2 Newton's Cosmological Queries 469 8.3 The Helen of Geometers 477 8.4 Refractions On Relativity 480 8.5 Scholium 490 8.6 On Gauss' Mountains 495 8.7 Strange Meeting 499 8.8 Who Invented Relativity? 506 8.9 Paths Not Taken 516 9. The Relativistic Topology 9.1 In The Neighborhood 524 9.2 Up To Diffeomorphism 533 9.3 Higher-Order Metrics 536 9.4 Spin and Polarization 541 9.5 Entangled Events 544 9.6 Von Neumann's Fifth Postulate 549 9.7 Bell's Freedom 553 9.8 The Gestalt of Determinism 556 9.9 Imaginary Explanations 559 9.10 Locality and Temporal Asymmetry 562 9.11 Spacetime Mediation of Quantum Interactions 566 Conclusion 573 Appendix: Mathematical Miscellany 575 Bibliography 586