Physics in Space and Time

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1 Spacetime Fundamentals

1.1 What is an Inertial Coordinate System?

1.2 Space-Time Coordinates and Frames

1.3 Systems of Reference in Classical Dynamics

1.4 Fields and Coordinates

1.5 A Primer on Special Relativity

1.6 Linear Fractional Space-Time Transformations

1.7 Laminar Transformations

1.8 General Transformations and Relative Rotation

1.9 Boosts and Rotations

1.10 Preserving the Intervals

1.11 Spacetime Inversion

1.12 Symmetries and Persistent Identities

1.13 A Mass and Spring System in Motion

1.14 Path Lengths and Coordinates

1.15 Frequency and Energy

1.16 Resonance and Motion

2 Foundations of Special Relativity

2.1 The Center of Energy

2.2 Conditions for Relativity

2.3 Rational and Empirical Origins of Special Relativity

2.4 Passive and Active Transformations

2.5 Are Relativistic Effects Kinematic?

2.6 Dynamics and Kinematics of Special Relativity

2.7 Testing Lorentz Invariance

2.8 Stochastic Sprinkles

2.9 Newtonian and Relativistic Conservation Laws

2.10 Does Relativistic Mass Imply Special Relativity?

2.11 Lorentz’s Scale Factor

2.12 Different Wavelengths

2.13 Teaching Special Relativity

2.14 Absolute Rest

3 Topics in Special Relativity

3.1 Sagnac and Fizeau

3.2 The Doppler Effect

3.3 Integrating Polygonal Sagnac Paths

3.4 Doppler Effect for Arbitrary Motion

3.5 Round Trips and One-Way Speeds

3.6 Twin Times

3.7 Ballistic Sagnac

3.8 A Rotating Disk in Translation

3.9 Trouton-Noble and the Right-Angle Lever

3.10 Born Rigidity, Acceleration, and Inertia

3.11 The Phase Effect of Acceleration

3.12 Rigidly Re-Orienting An Extended Body

3.13 Another Derivation of Mass-Energy Equivalence

3.14 Hero and Fermat on Moving Mirrors

3.15 Classical Electrons and Spacetime Volume

3.16 The Aarau Question and the Light Complex

3.17 Velocity Compositions and Rapidity

3.18 Anisotropic Coordinates

3.29 Superluminal or Not

3.20 Disappearing Sun

4 Foundations of General Relativity

4.1 Accelerating in Place

4.2 Curved Coordinate Systems and Fictitious Forces

4.3 Gravitational Redshift and the Equivalence Principle

4.4 General Relativity and the Principle of Inertia

4.5 Controversies Over the Equivalence Principle

4.6 On The Many Principles of Equivalence

4.7 Gravity, Entropy, and Coherence

4.8 Acoustic Metrics and the Vacuum

4.9 Newtonian Gravity In Closed or Curved Space

4.10 The No-Curvature Interpretation

4.11 Gravity as Expansion and Many Worlds

4.12 The Spacetime Hole and the EPR Arguments

5 Topics in General Relativity

5.1 Light Deflection in Isotropic Coordinates

5.2 Shapiro Time Delay

5.3 Measuring the Speed of Gravity

5.4 The 3m Halo

5.5 Black Holes, Event Horizons, and the Universe

5.6 An Infinite Wall

5.7 From the Field Equations to the Kruskal Metric

5.8 Ricci Tensor in Riemann Normal Coordinates

5.9 Schwarzschild Coordinate Time

5.10 On Relativistic Precession

5.11 Series Solution for Relativistic Orbits

5.12 Geodesics by Differentiation

5.13 Derivations of Light Deflection

5.14 Celestial Deflection

5.15 Cosmological Horizons

6 History

6.1 Guillaume, Guillaume, and Einstein

6.2 The Moszkowski Affair

6.3 Whittaker and the Aether

6.4 Why Was Michelson Surprised?

6.5 Did Einstein Misunderstand Aberration?

6.6 Maxwell’s Displacement and Einstein’s Trace

6.7 Why Maxwell Couldn’t Explain Gravity

6.8 Soldner’s Deflections

6.9 Gerber’s Gravity

6.10 Gerber’s Light Deflection

6.11 What Happened to Dingle?

6.12 Timely Confessions

6.13 Gravitational and Inertial Mass in Newton’s Principia

6.14 Refraction Revisited and Newton’s Gespensterfeld

6.15 Fresnel’s Drag and Dispersion

6.16 Laplace on the Speed of Gravity

6.17 From Schwarzschild to Droste

6.18 Stokes’ Mistake

6.19 Einstein on the Inertia of Energy

6.20 The Emission Theory of Walter Ritz

6.21 The Step and the Footnote

6.22 Transverse Mass in Einstein’s Electrodynamics

6.23 Kinetic Pressure and Tetrode’s Star

6.24 Poincare Contemplates Copernicus

6.25 No One Will Believe You

6.26 Continuity and the Void