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Preface by W. Pauli
Preface by A. Sommerfeld
Bibliography
Part Ⅰ. The Foundations of the Spe Theory of Relativity
1.Historical Background (Lorentz, Poincaré, Einstein)
2.The Postulate of Relativity
3.The Postulate of the Constancy of the Velocity of Light. Ritz's and Related Theories
4.The Relativity of Simultaneity. Derivation of the Lorentz Transformation from the Two Postulates. Axiomatic Nature of the Lorentz
Transformation
5.Lorentz Contraction and Time Dilatation
6.Einstein's Addition Theorem for Velocities and Its Application to Aberration and the Drag Coefficient. The Doppler Effect
Part Ⅱ. Mathematical Tools
7.The Four-Dimensional Space-Time World (Minkowski)
8.More General Transformation Groups
9.Tensor Calculus for Affine Transformations
10.Geometrical Meaning of the Contravariant and Covariant Components of a Vector
11."Surface" and "Volume" Tensors. Four-Dimensional Volumes
12.Dual Tensors
13.Transition to Riemannian Geometry
14.Parallel Displacement of a Vector
15.Geodesic Lines
16.Space Curvature
17.Riemannian Coordinates and Their Applications
18.The Spe Cases of Euclidean Geometry and of Constant Curvature
19.The Integral Theorems of Gauss and Stokes in a Four-Dimensional Riemannian Manifold
20.Derivation of Invariant Differential Operations, Using Geodesic Components
21.Affine Tensors and Free Vectors
22.Reality Relations
23.Infinitesimal Coordinate Transformations and Variational Theorems
Part Ⅲ. Spe Theory of Relativity. Further Elaborations
(a) Kinematics
24.Four-Dimensional Representation of the Lorentz Transformation
25.The Addition Theorem for Velocities
26.Transformation Law for Acceleration. Hyperbolic Motion
(b)Electrodynamics
27.Conservation of Charge. Four-Current Density
28.Covariance of the Basic Equations of Electron Theory
29.Ponderomotive Forces. Dynamics of the Electron
30.Momentum and Energy of the Electromagnetic Field. Differential and Integral Forms of the Conservation Laws
31.The Invariant Action Principle of Electrodynamics
32.Applications to Spe Cases
33.Minkowski's Phenomenological Electrodynamics of Moving Bodies
34.Electron-Theoretical Derivations
35.Energy-Momentum Tensor and Ponderomotive Force in Phenomenological Electrodynamics. Joule Heat
36.Applications of the Theory
(C)Mechanics and General Dynamics
37.Equation of Motion. Momentum and Kinetic Energy
38.Relativistic Mechanics on a Basis Independent of Electrodynamics
39.Hamilton's Principle in Relativistic Mechanics
40.Generalized Coordinates. Canonical Form of the Equations of Motion
41.The Inertia of Energy
42.General Dynamics
43.Transformation of Energy and Momentum of a System in the Presence of External Forces
44.Applications to Spe Cases. Trouton and Noble's Experiments
45.Hydrodynamics and Theory of Elasticity
(d)Thermodynamics and Statistical Mechanics
46.Behaviour of the Thermodynamical Quantities Under a Lorentz Transformation
47.The Principle of Least Action
48.The Application of Relativity to Statistical Mechanics
49.Spe Cases
Part Ⅳ. General Theory of Relativity
50.Historical Review, Up to Einstein's Paper of
51.General Formulation of the Principle of Equivalence. Connection Between Gravitation and Metric
52.The Postulate of the General Covariance of the Physical Laws
53.Simple Deductions from the Principle of Equivalence
54.Influence of the Gravitational Field on Material Phenomena
55.The Action Principles for Material Processes in the Presence of Gravitational Fields
56.The Field Equations of Gravitation
57.Derivation of the Gravitational Equations from a Variational Principle
58.Comparison with Experiment
59.Other Spe, Rigorous, Solutions for the Statical Case
60.Einstein's General Approximative Solution and Its Applications
61.The Energy of the Gravitational Field
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