Essential Relativity: Special, General, and Cosmological

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.