Reflections on Relativity

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Preface

1. First Principles

1.1 From Experience to Spacetime

1.2 Systems of Reference

1.3 Inertia and Relativity

1.4 The Relativity of Light

1.5 Corresponding States

1.6 A More Practical Arrangement

1.7 Staircase Wit

1.8 More Symmetry

1.9 Null Coordinates

2. A Complex of Phenomena

2.1 The Spacetime Interval

2.2 Force Laws and Maxwell's Equations

2.3 The Inertia of Energy

2.4 Doppler Shift for Sound and Light

2.5 Stellar Aberration

2.6 Mobius Transformations of the Night Sky

2.7 The Sagnac Effect

2.8 Refraction Between Moving Media

2.9 Accelerated Travels

2.10 The Starry Messenger

2.11 Thomas Precession

3. Several Valuable Suggestions

3.1 Postulates and Principles

3.2 Natural and Violent Motions

3.3 De Mora Luminis

3.4 Stationary Paths

3.5 A Quintessence of So Subtle a Nature

3.6 The End of My Latin

3.7 Zeno and the Paradox of Motion

3.8 A Very Beautiful Day

3.9 Constructing the Principles

4. Weighty Arguments

4.1 Immovable Spacetime

4.2 Inertial and Gravitational Separations

4.3 Free-Fall Equations

4.4 Force, Curvature, and Uncertainty

4.5 Conventional Wisdom

4.6 The Field of All Fields

4.7 The Inertia of Twins

4.8 The Breakdown of Simultaneity

5. Extending the Principle

5.1 Vis Inertiae

5.2 Tensors, Contravariant and Covariant

5.3 Curvature, Intrinsic and Extrinsic

5.4 Relatively Straight

5.5 Schwarzschild Metric from Kepler's 3rd Law

5.6 The Equivalence Principle

5.7 Riemannian Geometry

5.8 The Field Equations

6. Ist Das Wirklich So?

6.1 An Exact Solution

6.2 Anomalous Precession

6.3 Bending Light

6.4 Radial Paths in a Spherically Symmetrical Field

6.5 Intersecting Orbits

6.6 Ideal Clocks in Arbitrary Motion

6.7 Acceleration in Schwarzschild Coordinates

6.8 Moving Sources and Gravitational Waves

7. Cosmology

7.1 Is the Universe Closed?

7.2 The Formation and Growth of Black Holes

7.3 Falling Into and Hovering Near A Black Hole

7.4 Curled-Up Dimensions

7.5 Packing Universes In Spacetime

7.6 Cosmological Coherence

7.7 Boundaries and Symmetries

7.8 Global Interpretations of Local Experience

8. The Secret Confidence of Nature

8.1 Kepler, Napier, and the Third Law

8.2 Newton's Cosmological Queries

8.3 The Helen of Geometers

8.4 Refractions On Relativity

8.5 Scholium

8.6 On Gauss' Mountains

8.7 Strange Meeting

8.8 Who Invented Relativity?

8.9 Doubling the Deflection

8.10 Conquering the Perihelion

8.11 Paths Not Taken

9. The Relativistic Topology

9.1 In The Neighborhood

9.2 Up To Diffeomorphism

9.3 Higher-Order Metrics

9.4 Polarization and Spin

9.5 Entangled Events

9.6 Von Neumann's Postulate and Bell's Freedom

9.7 Angels and Archetypes

9.8 Quaedam Tertia Natura Abscondita

9.9 Locality and Temporal Asymmetry

9.10 Spacetime Mediation of Quantum Interactions

Conclusion

Appendices

1. Vector Products

2. Total Derivatives

3. Differential Operators

4. Tensor Differentiation

5. Variational Principle for the Gravitational Field

6. Geodesic Redundancy

7. Independent Components of the Curvature Tensor

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