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Theory of Relativity


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Preface by W. Pauli; Preface by A. Sommerfeld; Bibliography Part I. The foundations of the special theory of relativity 1. Historical background (Lorentz, Poincare, 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, Rontgen, Eichenwald and Wilson 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 invariance 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

About the Author

Wolfgang Pauli: The Young Genius Wolfgang Pauli (1900-1958), Austrian by birth, was one of the most influential physicists of the twentieth century and winner of the 1945 Nobel Prize in Physics for the discovery of the Pauli exclusion principle in quantum mechanics. His classic work on relativity was first published in Germany in 1921, when Pauli was twenty-one years old. The physicist A. Sommerfeld wrote this in his Preface to the 1921 German edition of Pauli's work: "In view of the apparently insatiable demand, especially in Germany, for accounts of the Theory of Relativity, both of a popular and of a highly specialized kind, I felt I ought to advise the publishers to arrange for a separate edition of the excellent article by Herr W. Pauli, Jr., which appeared in the Encyklopadie der mathematischen Wissenschaften, Vol. V. Although Herr Pauli was still a student at the time he was not only familiar with the most subtle arguments in the Theory of Relativity through his own research work, but was also fully conversant with the literature of the subject." First translated and published in English in 1958, and reprinted by Dover in 1981, Pauli's Theory of Relativity continues to find readers another fifty years later. In 2000, Dover reprinted the six volumes of Pauli's collected lectures on physics which had first been published by MIT: Electrodynamics (Volume 1), Optics and the Theory of Electrons (Volume 2), Thermodynamics and the Kinetic Theory of Gases (Volume 3), Statistical Mechanics (Volume 4), Wave Mechanics (Volume 5), and Selected Topics in Field Quantization (Volume 6). In 1928, Pauli, not yet thirty years old, was appointed Professor of Theoretical Physics at ETH Zurich where he did much of his most important work. Following Germany's takeover of Austria in 1938, and the outbreak of World War II in 1939, Pauli emigrated to the United States where he was Professor of Theoretical Physics at Princeton. In 1946, he became a naturalized American citizen before returning to Zurich, where he mostly lived for the last decade of his life.

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