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Reflections on Relativity

Preface 1 1. First Principles 1.1 From Experience to Spacetime 5 1.2 Systems of Reference 12 1.3 Inertia and Relativity 19 1.4 The Relativity of Light 26 1.5 Corresponding States 36 1.6 A More Practical Arrangement 47 1.7 Staircase Wit 61 1.8 Another Symmetry 73 1.9 Null Coordinates 81 2. A Complex of Phenomena 2.1 The Spacetime Interval 90 2.2 Force Laws and Maxwell's Equations 97 2.3 The Inertia of Energy 108 2.4 Doppler Shift for Sound and Light 121 2.5 Stellar Aberration 130 2.6 Mobius Transformations of the Night Sky 144 2.7 The Sagnac Effect 152 2.8 Refraction Between Moving Media 163 2.9 Accelerated Travels 171 2.10 The Starry Messenger 186 2.11 Thomas Precession 197 3. Several Valuable Suggestions 3.1 Postulates and Principles 206 3.2 Natural and Violent Motions 216 3.3 De Mora Luminis 223 3.4 Stationary Paths 232 3.5 A Quintessence of So Subtle a Nature 238 3.6 The End of My Latin 244 3.7 Zeno and the Paradox of Motion 252 3.8 A Very Beautiful Day 259 3.9 Constructing the Principles 266 4. Weighty Arguments 4.1 Immovable Spacetime 272 4.2 Inertial and Gravitational Separations 283 4.3 Free-Fall Equations 288 4.4 Force, Curvature, and Uncertainty 292 4.5 Conventional Wisdom 298 4.6 The Field of All Fields 310 4.7 The Inertia of Twins 316 4.8 The Breakdown of Simultaneity 322 5. Extending the Principle 5.1 Vis Inertiae 330 5.2 Tensors, Contravariant and Covariant 338 5.3 Curvature, Intrinsic and Extrinsic 348 5.4 Relatively Straight 366 5.5 Schwarzschild Metric from Kepler's 3rd Law 375 5.6 The Equivalence Principle 382 5.7 Riemannian Geometry 389 5.8 The Field Equations 401 6. Ist Das Wirklich So? 6.1 An Exact Solution 413 6.2 Anomalous Precession 421 6.3 Bending Light 432 6.4 Radial Paths in a Spherically Symmetrical Field 442 6.5 Intersecting Orbits 454 6.6 Ideal Clocks in Arbitrary Motion 462 6.7 Acceleration in Schwarzschild Coordinates 470 6.8 Sources in Motion 477 7. Cosmology 7.1 Is the Universe Closed? 484 7.2 The Formation and Growth of Black Holes 495 7.3 Falling Into and Hovering Near A Black Hole 504 7.4 Curled-Up Dimensions 516 7.5 Packing Universes In Spacetime 521 7.6 Cosmological Coherence 527 7.7 Boundaries and Symmetries 535 7.8 Global Interpretations of Local Experience 542 8. The Secret Confidence of Nature 8.1 Kepler, Napier, and the Third Law 554 8.2 Newton's Cosmological Queries 559 8.3 The Helen of Geometers 567 8.4 Refractions On Relativity 573 8.5 Scholium 584 8.6 On Gauss' Mountains 589 8.7 Strange Meeting 594 8.8 Who Invented Relativity? 601 8.9 Paths Not Taken 614 9. The Relativistic Topology 9.1 In The Neighborhood 622 9.2 Up To Diffeomorphism 631 9.3 Higher-Order Metrics 637 9.4 Polarization and Spin 643 9.5 Entangled Events 652 9.6 Von Neumann's Postulate and Bell's Freedom 658 9.7 Angels and Archetypes 665 9.8 Quaedam Tertia Natura Abscondita 671 9.9 Locality and Temporal Asymmetry 675 9.10 Spacetime Mediation of Quantum Interactions 682 Conclusion 697 Appendix: Mathematical Miscellany 699