상대성이론의 수학적이론. The Book of The Mathematical Theory of Relativity, by Arthur Stanley
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상대성이론의 수학적이론. The Book of The Mathematical Theory of Relativity, by Arthur Stanley
상대성원리의 물리적 개념에 수학의 공식을 적용해서 설명한 책으로 영국의 캠브리지 대학교의 교수가 기술한 책.
과거에는 철학에 수학 천문학 물리학등이 포함됨.
THE MATHEMATICAL THEORY
OF
RELATIVITY
BY
A. S. EDDINGTON, M.A., M.Sc., F.R.S.
PLUMIAN PROFESSOR OF ASTRONOMY AND EXPERIMENTAL
PHILOSOPHY IN THE UNIVERSITY OF CAMBRIDGE
CAMBRIDGE
AT THE UNIVERSITY PRESS
1923
목차연속 3.
CHAPTER V
CURVATURE OF SPACE AND TIME
SECTION PAGE
65. Curvature of a four-dimensional manifold . . . . . . . . . . . . . . . . . . . . . . 251
66. Interpretation of Einstein’s law of gravitation . . . . . . . . . . . . . . . . . . 257
67. Cylindrical and spherical space-time . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
68. Elliptical space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
69. Law of gravitation for curved space-time . . . . . . . . . . . . . . . . . . . . . . . 268
70. Properties of de Sitter’s spherical world . . . . . . . . . . . . . . . . . . . . . . . . 271
71. Properties of Einstein’s cylindrical world . . . . . . . . . . . . . . . . . . . . . . . 280
72. The problem of the homogeneous sphere . . . . . . . . . . . . . . . . . . . . . . . 284
CHAPTER VI
ELECTRICITY
73. The electromagnetic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
74. Electromagnetic waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
75. The Lorentz transformation of electromagnetic force . . . . . . . . . . . 304
76. Mechanical effects of the electromagnetic field. . . . . . . . . . . . . . . . . . 305
77. The electromagnetic energy-tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
78. The gravitational field of an electron. . . . . . . . . . . . . . . . . . . . . . . . . . . 313
79. Electromagnetic action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
80. Explanation of the mechanical force. . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
81. Electromagnetic volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
SECTION PAGE
82. Macroscopic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
상대성원리의 물리적 개념에 수학의 공식을 적용해서 설명한 책으로 영국의 캠브리지 대학교의 교수가 기술한 책.
과거에는 철학에 수학 천문학 물리학등이 포함됨.
THE MATHEMATICAL THEORY
OF
RELATIVITY
BY
A. S. EDDINGTON, M.A., M.Sc., F.R.S.
PLUMIAN PROFESSOR OF ASTRONOMY AND EXPERIMENTAL
PHILOSOPHY IN THE UNIVERSITY OF CAMBRIDGE
CAMBRIDGE
AT THE UNIVERSITY PRESS
1923
목차연속 3.
CHAPTER V
CURVATURE OF SPACE AND TIME
SECTION PAGE
65. Curvature of a four-dimensional manifold . . . . . . . . . . . . . . . . . . . . . . 251
66. Interpretation of Einstein’s law of gravitation . . . . . . . . . . . . . . . . . . 257
67. Cylindrical and spherical space-time . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
68. Elliptical space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
69. Law of gravitation for curved space-time . . . . . . . . . . . . . . . . . . . . . . . 268
70. Properties of de Sitter’s spherical world . . . . . . . . . . . . . . . . . . . . . . . . 271
71. Properties of Einstein’s cylindrical world . . . . . . . . . . . . . . . . . . . . . . . 280
72. The problem of the homogeneous sphere . . . . . . . . . . . . . . . . . . . . . . . 284
CHAPTER VI
ELECTRICITY
73. The electromagnetic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
74. Electromagnetic waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
75. The Lorentz transformation of electromagnetic force . . . . . . . . . . . 304
76. Mechanical effects of the electromagnetic field. . . . . . . . . . . . . . . . . . 305
77. The electromagnetic energy-tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
78. The gravitational field of an electron. . . . . . . . . . . . . . . . . . . . . . . . . . . 313
79. Electromagnetic action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317
80. Explanation of the mechanical force. . . . . . . . . . . . . . . . . . . . . . . . . . . . 320
81. Electromagnetic volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328
SECTION PAGE
82. Macroscopic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 330
상대성이론의 수학적이론. The Book of The Mathematical Theory of Relativity, by Arthur Stanley
CONTENTS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
CHAPTER I
ELEMENTARY PRINCIPLES
SECTION PAGE
1. Indeterminateness of the space-time frame . . . . . . . . . . . . . . . . . . . . . 11
2. The fundamental quadratic form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3. Measurement of intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4. Rectangular coordinates and time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5. The Lorentz transformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6. The velocity of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
7. Timelike and spacelike intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
8. Immediate consciousness of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
9. The “3 + 1 dimensional” world. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
10. The FitzGerald contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
SECTION PAGE
11. Simultaneity at different places . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
12. Momentum and mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
13. Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
14. Density and temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
15. General transformations of coordinates. . . . . . . . . . . . . . . . . . . . . . . . . 55
16. Fields of force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
17. The Principle of Equivalence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
18. Retrospect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
CHAPTER II
THE TENSOR CALCULUS
19. Contravariant and covariant vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
20. The mathematical notion of a vector. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
21. The physical notion of a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
22. The summation convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
23. Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
24. Inner multiplication and contraction. The quotient law . . . . . . . . 85
25. The fundamental tensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
26. Associated tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
27. Christoffel’s 3-index symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
28. Equations of a geodesic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
29. Covariant derivative of a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
30. Covariant derivative of a tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
CONTENTS
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
CHAPTER I
ELEMENTARY PRINCIPLES
SECTION PAGE
1. Indeterminateness of the space-time frame . . . . . . . . . . . . . . . . . . . . . 11
2. The fundamental quadratic form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3. Measurement of intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4. Rectangular coordinates and time. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
5. The Lorentz transformation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
6. The velocity of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
7. Timelike and spacelike intervals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
8. Immediate consciousness of time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
9. The “3 + 1 dimensional” world. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
10. The FitzGerald contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
SECTION PAGE
11. Simultaneity at different places . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
12. Momentum and mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
13. Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
14. Density and temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
15. General transformations of coordinates. . . . . . . . . . . . . . . . . . . . . . . . . 55
16. Fields of force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
17. The Principle of Equivalence. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
18. Retrospect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
CHAPTER II
THE TENSOR CALCULUS
19. Contravariant and covariant vectors. . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
20. The mathematical notion of a vector. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
21. The physical notion of a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
22. The summation convention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
23. Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
24. Inner multiplication and contraction. The quotient law . . . . . . . . 85
25. The fundamental tensors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
26. Associated tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
27. Christoffel’s 3-index symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
28. Equations of a geodesic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
29. Covariant derivative of a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
30. Covariant derivative of a tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
목차연속 2 .
SECTION PAGE
31. Alternative discussion of the covariant derivative . . . . . . . . . . . . . . . 106
32. Surface-elements and Stokes’s theorem . . . . . . . . . . . . . . . . . . . . . . . . . 109
33. Significance of covariant differentiation. . . . . . . . . . . . . . . . . . . . . . . . . 112
34. The Riemann-Christoffel tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
35. Miscellaneous formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
CHAPTER III
THE LAW OF GRAVITATION
36. The condition for flat space-time. Natural coordinates . . . . . . . . . 127
37. Einstein’s law of gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
38. The gravitational field of an isolated particle . . . . . . . . . . . . . . . . . . . 138
39. Planetary orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
40. The advance of perihelion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
41. The deflection of light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
42. Displacement of the Fraunhofer lines. . . . . . . . . . . . . . . . . . . . . . . . . . . 154
43. Isotropic coordinates. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
44. Problem of two bodies―Motion of the moon . . . . . . . . . . . . . . . . . . . 160
45. Solution for a particle in a curved world . . . . . . . . . . . . . . . . . . . . . . . 168
46. Transition to continuous matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
47. Experiment and deductive theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
CHAPTER IV
RELATIVITY MECHANICS
SECTION PAGE
48. The antisymmetrical tensor of the fourth rank . . . . . . . . . . . . . . . . . 181
49. Element of volume. Tensor-density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
50. The problem of the rotating disc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
51. The divergence of a tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192
52. The four identities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 195
53. The material energy-tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
54. New derivation of Einstein’s law of gravitation . . . . . . . . . . . . . . . . . 201
55. The force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
56. Dynamics of a particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
57. Equality of gravitational and inertial mass. Gravitational waves 216
58. Lagrangian form of the gravitational equations. . . . . . . . . . . . . . . . . 222
59. Pseudo-energy-tensor of the gravitational field . . . . . . . . . . . . . . . . . 227
60. Action. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
61. A property of invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
62. Alternative energy-tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239
63. Gravitational flux from a particle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
64. Retrospect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
작가정보
저자(글) Arthur Stanley
상대성이론의 수학적이론. The Book of The Mathematical Theory of Relativity, by Arthur Stanley
영국 캠브리지 대학교의 교수.
THE MATHEMATICAL THEORY
OF
RELATIVITY
BY
A. S. EDDINGTON, M.A., M.Sc., F.R.S.
PLUMIAN PROFESSOR OF ASTRONOMY AND EXPERIMENTAL
PHILOSOPHY IN THE UNIVERSITY OF CAMBRIDGE
CAMBRIDGE
AT THE UNIVERSITY PRESS
1923
목차 4.
Part II. Generalised Theory
91. Parallel displacement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
92. Displacement round an infinitesimal circuit . . . . . . . . . . . . . . . . . . . . 363
93. Introduction of a metric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
94. Evaluation of the fundamental in-tensors. . . . . . . . . . . . . . . . . . . . . . . 370
95. The natural gauge of the world . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372
96. The principle of identification. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 376
97. The bifurcation of geometry and electrodynamics . . . . . . . . . . . . . . 379
SECTION PAGE
98. General relation-structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380
99. The tensor ？B
？νσ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384
100. Dynamical consequences of the general properties of world invariants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
101. The generalised volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393
102. Numerical values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398
103. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 402
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413
이 상품의 총서
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2. 운영 원칙 안내
Klover리뷰를 통한 리뷰를 작성해 주셔서 감사합니다. 자유로운 의사 표현의 공간인 만큼 타인에 대한 배려를 부탁합니다. 일부 타인의 권리를 침해하거나 불편을 끼치는 것을 방지하기 위해 아래에 해당하는 Klover 리뷰는 별도의 통보 없이 삭제될 수 있습니다.
- 도서나 타인에 대해 근거 없이 비방을 하거나 타인의 명예를 훼손할 수 있는 리뷰
- 도서와 무관한 내용의 리뷰
- 인신공격이나 욕설, 비속어, 혐오 발언이 개재된 리뷰
- 의성어나 의태어 등 내용의 의미가 없는 리뷰
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문장수집
문장수집 안내
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리워드 안내
- 구매 후 90일 이내에 문장 수집 등록 시 e교환권 100원을 적립해 드립니다.
- e교환권은 적립일로부터 180일 동안 사용 가능합니다.
- 리워드는 5,000원 이상 eBook에 한해 다운로드 완료 후 문장수집 등록 시 제공됩니다. (2024년 9월 30일부터 적용)
- 리워드는 한 상품에 최초 1회만 제공됩니다.
- sam 이용권 구매 상품 / 선물받은 eBook / 오디오북·동영상 상품/주문취소/환불 시 리워드 대상에서 제외됩니다.
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