This classic work offers a concise and comprehensive review of the literature on relativity as of 1921, along with the author's insightful update of later developments in relativity theory and coverage of subsequent controversies. Special attention is given to unified field theories. 1958 edition.

Table of Contents for Theory of Relativity

Preface by W. Pauli; Preface by A. Sommerfeld; Bibliography
Part I. The foundations of the special 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 special 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. Special 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 special cases
a. Integration of the equations for the potential
b. The field of a uniformly moving point charge
c. The field for hyperbolic motion
d. Invariance of the light phase. Reflection at a moving mirror. Radiation pressure
e. The radiation field of a moving dipole
f. Radiation reaction
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
a. The experiments of Rowland, Röntgen, Eichenwald and W
b. Resistance and induction in moving conductors
c. Propagation of light in moving media. The drag coefficient. Airy's experiment
d. Signal velocity and phase velocity in dispersive media
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 special 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. Special cases
a. Black-body radiation in a moving cavity
b. The ideal gas
Part IV. General theory of relativity
50. Historical review, up to Einstein's paper of 1916
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
a. The equations of motion of a point-mass for small velocities and weak gravitational fields
b. The red shift of spectral lines
c. Fermat's principle of least time in static gravitational fields
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
a. Newtonian theory as a first approximation
b. Rigorous solution for the gravitational field of a point-mass
c. Perihelion precession of Mercury and the bending of light rays
59. Other special, rigorous, solutions for the statical case
60. Einstein's general approximative solution and its applications
61. The energy of the gravitational field
62. Modifications of the field equations. Relativity of inertia and the space-bounded universe
a. The Mach principle
b. Remarks on the statistical equilibrium of the system of fixed stars. The lambda-term
c. The energy of the finite universe
Part V. Theories on the nature of charged elementary particles
63. The electron and the special theory of relativity
64. Mie's theory
65. Weyl's theory
a. Pure infinitesimal geometry. Gauge invar
b. Electromagnetic field and world metric
c. The tensor calculus in Weyl's geometry
d. Field equations and action principle. Physical deductions
66. Einstein's theory
67. General remarks on the present state of the problem of matter
Supplementary notes; Author index; Subject index

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