Fock The Theory of Space, Time and Gravitation

2. Auflage 2015
ISBN: 978-1-4831-8490-6
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 460 Seiten, Web PDF

The Theory of Space, Time, and Gravitation, 2nd Revised Edition focuses on Relativity Theory and Einstein's Theory of Gravitation and correction of the misinterpretation of the Einsteinian Gravitation Theory. The book first offers information on the theory of relativity and the theory of relativity in tensor form. Discussions focus on comparison of distances and lengths in moving reference frames; comparison of time differences in moving reference frames; position of a body in space at a given instant in a fixed reference frame; and proof of the linearity of the transformation linking two inertial frames. The text then ponders on general tensor analysis, including permissible transformations for space and time coordinates, parallel transport of a vector, covariant differentiation, and basic properties of the curvature tensor. The publication examines the formulation of relativity theory in arbitrary coordinates and principles of the theory of gravitation. Topics include equations of mathematical physics in arbitrary coordinates; integral form of the conservation laws in arbitrary coordinates; variational principle and the energy tensor; and comparison with the statement of the problem in Newtonian theory. The manuscript is a dependable reference for readers interested in the theory of space, time, and gravitation.

Autoren/Hrsg.

Fock, V.

Inhaltsverzeichnis

1;Front Cover
;1
2;The Theory of Space, Time and Gravitation;4
3;Copyright Page;5
4;Table of Contents;6
5;TRANSLATOR'S PREFACE;10
6;TRANSLATOR'S PREFACE TO SECOND EDITION;11
7;PREFACE;12
8;PREFACE TO SECOND EDITION;12
9;INTRODUCTION;14
10;CHAPTER I. THE THEORY OF RELATIVITY;22
10.1;1. Coordinates of Space and Time;22
10.2;2. The Position of a Body in Space at a given Instant, in a Fixed Reference Frame;22
10.3;3. The Law of Propagation of an Electromagnetic Wave Front;24
10.4;4. Equations for Rays;27
10.5;5. Inertial Frames of Reference;28
10.6;6. The Basic Postulates of the Theory of Relativity;29
10.7;7. The Galileo Transformations and the Need to Generalize Them;32
10.8;8. Proof of the Linearity of the Transformation Linking Two Inertial Frames;33
10.9;9. Determination of the Coefficients of the Linear Transformations and of a Scale Factor;37
10.10;10. Lorentz Transformations;39
10.11;11. Determination of Distances and Synchronization of Clocks within One Inertial Reference Frame;43
10.12;12. Time Sequence of Events in Different Reference Frames;46
10.13;13. Comparison of Time Differences in Moving Reference Frames. The Doppler Effect;50
10.14;14. Comparison of Clock Readings in Moving Reference Frames;53
10.15;15. Comparison of Distances and Lengths in Moving Reference Frames;57
10.16;16. Relative Velocity;58
10.17;17. The Lobachevsky-Einstein Velocity Space;61
11;CHAPTER II. THE THEORY OF RELATIVITY IN TENSOR FORM;67
11.1;18. Some Remarks on the Covariance of Equations;67
11.2;19. Definition of a Tensor in Three Dimensions and some Remarks on Covariant Quantities;68
11.3;20. Definition of a Four-Dimensional Vector;72
11.4;21. Four-Dimensional Tensors;74
11.5;22. Pseudo-Tensors;77
11.6;23. Infinitesimal Lorentz Transformations;78
11.7;24. The Transformation Laws for the Electromagnetic Field and the Covariance of Maxwell's Equations;80
11.8;25. The Motion of a Charged Mass-Point in a given External Field;86
11.9;26. Approximate Description of a System of Moving Point Charges;90
11.10;27. Derivation of the Conservation Laws in the Mechanics of Point Systems;96
11.11;28. The Tensor Character of the Integrals of Motion;99
11.12;29. A Remark on the Conventional Formulation of the Conservation Laws;102
11.13;30. The Vector of Energy Current (Umov's Vector).;104
11.14;31. The Mass Tensor;107
11.15;32. Examples of the Mass Tensor;114
11.16;33. The Energy Tensor of the Electromagnetic Field;119
11.17;34. Mass and Energy;123
12;CHAPTER III: GENERAL TENSOR ANALYSIS;127
12.1;35. Permissible Transformations for Space and Time Coordinates;127
12.2;36. General Tensor Analysis and Generalized Geometry;132
12.3;37. The Definitions of a Vector and of a Tensor. Tensor Algebra;135
12.4;38. The Equation of a Geodesic;142
12.5;39. Parallel Transport of a Vector;148
12.6;40. Covariant Differentiation;152
12.7;41. Examples of Covariant Differentiation;155
12.8;42. The Transformation Law for Christoffel Symbols and the Locally Geodesic Coordinate System. Conditions for transforming ds2 to a Form with Constant Coefficients;159
12.9;43. The Curvature Tensor;163
12.10;44. The Basic Properties of the Curvature Tensor;166
13;CHAPTER IV: A FORMULATION OF RELATIVITY THEORY IN ARBITRARY COORDINATES;171
13.1;45. Properties of Space-Time and Choice of Coordinates;171
13.2;46. The Equations of Mathematical Physics in Arbitrary Coordinates;174
13.3;47. A Variational Principle for the Maxwell-Lorentz System of Equations;178
13.4;48. The Variational Principle and the Energy Tensor;183
13.5;49. The Integral Form of the Conservation Laws in Arbitrary Coordinates;188
14;CHAPTER V. THE PRINCIPLES OF THE THEORY OF GRAVITATION;196
14.1;50. The Generalization of Galileo's Law;196
14.2;51. The Square of the Interval in Newtonian Approximation;197
14.3;52. Einstein's Gravitational Equations;202
14.4;53. The Characteristics of Einstein's Equations. The Speed of Propagation of Gravitation;205
14.5;54. A Comparison with the Statement of the Problem in Newtonian Theory. Boundary Conditions;207
14.6;55. Solution of Einstein's Gravitational Equations in First Approximation and Determination of the Constant;210
14.7;56. The Gravitational Equations in the Static Case and Conformal Space;216
14.8;57. Rigorous Solution of the Gravitational Equations for a Single Concentrated Mass;222
14.9;58. The Motion of the Perihelion of a Planet;228
14.10;59. The Deflection of a Light Ray Passing Near the Sun;234
14.11;60. A Variational Principle for the Equations of Gravitation;237
14.12;61. On the Local Equivalence of Fields of Acceleration and of Gravitation;241
14.13;62. On the Clock Paradox;247
15;CHAPTER VI. THE LAW OF GRAVITATION AND THE LAWS OF MOTION;251
15.1;63. The Equations of Free Motion for a Mass Point and their Connection with the Gravitational Equations;251
15.2;64. General Statement of the Problem of the Motion of a System of Masses;254
15.3;65. The Divergence of the Mass Tensor in Second Approximation;257
15.4;66. The Approximate Form of the Mass Tensor for an Elastic Solid with Inclusion of the Gravitational Field;260
15.5;67. Approximate Expressions for the Christoffel Svmbols and Some Other Quantities;262
15.6;68. Approximate Form of the Gravitational Equations;267
15.7;69. The Connection Between the Divergence of the Mass Tensor and the Quantities;272
15.8;70. The Equations of Motion and the Harmonic Conditions;276
15.9;71. The Internal and the External Problems in the Mechanics of Systems of Bodies. Newton's Equations for Translational Motion;280
15.10;72. Newton's Equations for Rotational Motion;285
15.11;73. The Internal Structure of a Body. Liapunov's Equation;290
15.12;74. Evaluation of Some Integrals that Characterize the Internal Structure of a Body;293
15.13;75. Transformation of the Integral Form of the Equations of Motion;296
15.14;76. Evaluation of the Momentum in Second Approximation;300
15.15;77. Evaluation of the Force;304
15.16;78. The Equations of Translational Motion in Lagrangian Form;310
15.17;7 9 . The Integrals of the Equations of Motion for Systems of Bodies;313
15.18;80. Additional Remarks on the Problem of the Motion of a System of Bodies. The Explicit Form of the Integrals of Motion for the Case of Non-Rotating Masses;320
16;CHAPTER VII. APPROXIMATE SOLUTIONS, CONSERVATION LAWS AND SOME QUESTIONS OF PRINCIPLE;331
16.1;82. The Gravitational Potentials for Non-Rotating Bodies (Spatial Components);331
16.2;83. The Gravitational Potentials for Non-Rotating Bodies (Mixed and Temporal Components);337
16.3;84. Gravitational Potentials at Large Distances from a System of Bodies (Spatial Components);343
16.4;85. Gravitational Potentials at Large Distances from a System of Bodies (Mixed and Temporal Components);347
16.5;86. Solution of the Wave Equation in the Wave Zone;353
16.6;87. The Gravitational Potentials in the Wave Zone;355
16.7;88. Some General Remarks on the Conservation Laws;362
16.8;89. Formulation of the Conservation Laws;363
16.9;90. The Emission of Gravitational Waves and its Role in the Energy Balance;370
16.10;91. The Connection between the Conservation Laws for the Field and the Integrals of Mechanics;373
16.11;92. The Uniqueness Theorem for the Wave Equation;378
16.12;9 3 . On the Uniqueness of the Harmonic Coordinate System;382
16.13;94. Friedmann-Lobachevsky Space;388
16.14;9 5 . Theory of the Red Shift;396
16.15;96. The Development of the Theory of Gravitation and of the Motion of Masses (A Critical Survey);405
17;CONCLUSION;413
18;APPENDIX A: ON THE DERIVATION OF THE LORENTZ TRANSFORMATIONS;416
19;APPENDIX B: PROOF OF THE UNIQUENESS OF THE ENERGY MOMENTUM TENSOR OF THE ELECTROMAGNETIC FIELD;424
20;APPENDIX C: PROOF OF THE UNIQUENESS OF THE HYDRODYNAMIC MASS TENSOR;430
21;APPENDIX D: THE TRANSFORMATION OF THE EINSTEIN TENSOR;435
22;APPENDIX E: THE CHARACTERISTICS OF THE GENERALIZED D'ALEMBERT EQUATION;444
23;APPENDIX F: INTEGRATION OF THE WAVE FRONT EQUATION;447
24;APPENDIX G: NECESSARY AND SUFFICIENT CONDITIONS FOR THE EUCLIDEAN CHARACTER OF THREE-DIMENSIONAL SPACE;451
25;REFERENCES;454
26;INDEX;456