Essential Relativity

1 The Rise and Fall of Absolute Space.- 1.1 Definition of Relativity.- 1.2 Newton’s Laws.- 1.3 The Galilean Transformation.- 1.4 The Set of All Inertial Frames.- 1.5 Newtonian Relativity.- 1.6 Newton’s Absolute Space.- 1.7 Objections to Newton’s Absolute Space.- 1.8 Maxwell’s Ether.- 1.9 Where is Maxwell’s Ether?.- 1.10 Lorentz’s Ether Theory.- 1.11 The Relativity Principle.- 1.12 Arguments for the Relativity Principle.- 1.13 Maxwellian Relativity.- 1.14 Origins of General Relativity.- 1.15 Mach’s Principle.- 1.16 Consequences of Mach’s Principle.- 1.17 Cosmology.- 1.18 Inertial and Gravitational Mass.- 1.19 The Equivalence Principle.- 1.20 The Semistrong Equivalence Principle.- 1.21 Consequences of the Equivalence Principle.- 2 Einsteinian Kinematics.- 2.1 Basic Features of Special Relativity.- 2.2 On the Nature of Physical Laws.- 2.3 An Archetypal Relativistic Argument.- 2.4 The Relativity of Simultaneity.- 2.5 The Coordinate Lattice.- 2.6 The Lorentz Transformation.- 2.7 Properties of the Lorentz Transformation.- 2.8 Hyperbolic Forms of the Lorentz Transformation.- 2.9 Graphical Representation of the Lorentz Transformation.- 2.10 World-picture and World-map.- 2.11 Length Contraction.- 2.12 Length Contraction Paradoxes.- 2.13 Time Dilation.- 2.14 The Twin Paradox.- 2.15 Velocity Transformation.- 2.16 Proper Acceleration.- 2.17 Special Relativity without the Second Postulate.- 3 Einsteinian Optics.- 3.1 The Drag Effect.- 3.2 The Doppler Effect.- 3.3 Aberration and the Visual Appearance of Moving Objects.- 4 Spacetime and Four-Vectors.- 4.1 Spacetime.- 4.2 Three-Vectors.- 4.3 Four-Vectors.- 4.4 Four-Tensors.- 4.5 The Three-Dimensional Minkowski Diagram.- 4.6 Wave Motion.- 5 Relativistic Particle Mechanics.- 5.1 Domain of Sufficient Validity of Newton’s Laws.- 5.2 Why Gravity Does not Fit Naturally into Special Relativity.- 5.3 Relativistic Inertial Mass.- 5.4 Four-Vector Formulation of Relativistic Mechanics.- 5.5 A Note on Galilean Four-Vectors.- 5.6 Equivalence of Mass and Energy.- 5.7 The Center of Momentum Frame.- 5.8 Relativistic Billiards.- 5.9 Threshold Energies.- 5.10 Three-Force and Four-Force.- 5.11 De Broglie Waves.- 5.12 Photons. The Compton Effect.- 5.13 The Energy Tensor of Dust.- 6 Relativity and Electrodynamics.- 6.1 Transformation of the Field Vectors.- 6.2 Magnetic Deflection of Charged Particles.- 6.3 The Field of a Uniformly Moving Charge.- 6.4 The Field of an Infinite Straight Current.- 7 Basic Ideas of General Relativity.- 7.1 Curved Surfaces.- 7.2 Curved Spaces of Higher Dimensions.- 7.3 Riemannian Spaces.- 7.4 A Plan for General Relativity.- 7.5 The Gravitational Doppler Effect.- 7.6 Metric of Static Fields.- 7.7 Geodesics in Static Fields.- 8 Formal Development of General Relativity.- 8.1 Tensors in General Relativity.- 8.2 The Vacuum Field Equations of General Relativity.- 8.3 The Schwarzschild Solution.- 8.4 Rays and Orbits in Schwarzschild Space.- 8.5 The Schwarzschild Horizon, Gravitational Collapse, and Black Holes.- 8.6 Kruskal Space and the Uniform Acceleration Field.- 8.7 A General-Relativistic 'Proof' of E = mc2.- 8.8 A Plane-Fronted Gravity Wave.- 8.9 The Laws of Physics in Curved Spacetime.- 8.10 The Field Equations in the Presence of Matter.- 8.11 From Modified Schwarzschild to de Sitter Space.- 8.12 The Linear Approximation to GR.- 9 Cosmology.- 9.1 The Basic Facts.- 9.2 Apparent Difficulties of Prerelativistic Cosmology.- 9.3 Cosmological Relativity: The Cosmological Principle.- 9.4 Milne’s Model.- 9.5 The Robertson-Walker Metric.- 9.6 Rubber Models, Red Shifts, and Horizons.- 9.7 Comparison with Observation.- 9.8 Cosmic Dynamics According to Pseudo-Newtonian Theory.- 9.9 Cosmic Dynamics According to General Relativity.- 9.10 The Friedmann Models.- 9.11 Once Again, Comparison with Observation.- 9.12 Mach’s Principle Reexamined.- Appendices.- Appendix I: Curvature Tensor Components for the Diagonal Metric.- Appendix II: How to 'Invent' Maxwell’s Theory.- Exercises.