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Introduction: From Newton and Poincare to Einstein | 1 | |
Curiosity about Einstein's Theories | 1 | |
Geometry a Physical Science | 4 | |
Invariable Bodies and Various Scales | 6 | |
Geometry inseparable from Optics | 10 | |
Difficulties due to Motion | 11 | |
Scientific Importance of an Extra Decimal | 14 | |
Time a Measurable Quantity | 16 | |
Analogy between the Measurement of Time and the Measurement of Length | 17 | |
Artificial Clocks and the Clocks of Astronomers | 19 | |
The Influence of Gravitation upon Clocks | 21 | |
The Slowing Down of Clocks in Accelerated Motion | 25 | |
The Timing of Clocks | 27 | |
The Necessity of Successive Approximations | 27 | |
The Origin of Newton's Law | 28 | |
The Experiments of Cavendish | 31 | |
Gravitation an Isolated Phenomenon | 32 | |
Centrifugal Force and Force of Inertia | 34 | |
Gravitation a Force of Inertia | 35 | |
Chapter I | Geometry and the Shape of the Earth | |
1. | Origin of Geometry--Invariable Bodies | 38 |
2. | Geometry of Position, and Metric Geometry | 39 |
3. | Solid Bodies | 40 |
4. | Cartesian Co-ordinates | 41 |
5. | The Postulates of Euclid | 42 |
6. | Analytical Geometry and M. Jourdain's Prose | 44 |
7. | Analytical Geometry--Space on the Human Scale | 45 |
8. | Number knows no Limitations | 46 |
9. | Preservation of Landmarks | 47 |
10. | Geographical Co-ordinates | 47 |
11. | Geodetic Measurements | 49 |
12. | The Unit of Length and Richer's Pendulum | 51 |
13. | The Metric System and International Standards | 54 |
14. | The Metre in Terms of Wave-lengths | 55 |
15. | The Figure of the Earth | 56 |
16. | The Earth regarded as a Level Surface | 58 |
17. | Variation of the Poles--Tides in the Earth's Crust | 60 |
18. | The Scientific Value of Exact Measurements | 64 |
Chapter II | Space and Time in Astronomy | |
19. | Modern Astronomy is not Geocentric | 66 |
20. | The Distances of the Planets are deduced from Newton's Laws | 66 |
21. | The Absolute Value of the Dimensions of the Solar System | 68 |
22. | Galilean Axes | 70 |
23. | The Sidereal Day | 71 |
24. | The Time of Astronomers | 72 |
25. | Privileged Axes and Privileged Chronology | 74 |
26. | Are the Privileged Axes and Chronology Independent of the Earth? | 76 |
27. | Introduction of the Velocity of Light Necessary | 77 |
28. | Approximate Results retain Scientific Value | 78 |
29. | What do we know of Interstellar Space? | 80 |
Chapter III | Abstract Geometry and Geographical Maps | |
30. | The Abstract Conception of Geometry | 82 |
31. | A few Remarks on Mathematics | 83 |
32. | Analytical Geometry a Means of Defining Geometrical Conceptions | 84 |
33. | The Notion of Senes--It is incommunicable | 85 |
34. | The Notion of Sense | 87 |
35. | The Euclidean Schema | 89 |
36. | Example of a Schema of Imaginary Geometrical Elements | 90 |
37. | The Schema of Spherical Geometry--Riemann | 92 |
38. | Plane Schema for Any Geometry | 93 |
39. | Well-known Examples of a Schema | 94 |
40. | Mercator's Projection | 94 |
41. | Applicable Surfaces and Parallelism | 96 |
42. | Geodesic Lines and the Invariance of Direction | 99 |
43. | Utilization of the Linear Element | 100 |
Chapter IV | Continuity and Topology | |
44. | The Very Small More Difficult to Reach than the Very Great | 102 |
45. | Geometrical Intuition at Fault in the Infinitely Small | 104 |
46. | The Sub-atomic Scale | 106 |
47. | The Postulate of the Ellipsoid | 107 |
48. | Geometry and the Quantum Theory | 108 |
49. | Maps and the India-rubber Metre | 109 |
50. | Discontinuity Inevitable in a Plane Map of a Sphere | 110 |
51. | A Sphere has no Boundary | 113 |
52. | Topology of the Anchor-ring | 113 |
53. | Local Knowledge cannot give Knowledge of the Universe | 114 |
54. | The Plane Topological Representation of a Sphere | 116 |
55. | Topological Representation of a Hypersphere | 118 |
56. | A Finite but Unbounded Universe | 119 |
57. | The Ring and a Plane Network of Rectangles | 120 |
58. | The Hypertore and a Periodic Image of the Universe | 122 |
Chapter V | The Propagation of Light | |
59. | Fresnel's Theory and the Sinusoid | 124 |
60. | Wave-length and Difference of Phase | 126 |
61. | Measurement of Wave-lengths in Metric Units | 127 |
62. | Measurement of the Velocity of Light | 129 |
63. | Measurement of Very Short Intervals of Time | 131 |
64. | X-rays and Crystal Structure | 132 |
65. | Michelson and Morley's Experiment | 133 |
66. | Michelson and Morley's Experiment | 133 |
67. | Aberration of the Fixed Stars | 136 |
68. | The Doppler-Fizeau Effect | 137 |
69. | Fizeau's Experiment on Running Liquid | 139 |
70. | Phenomena shown by Double Stars | 140 |
Chapter VI | The Special Theory of Relativity | |
71. | What the Special or Restricted Theory of Relativity is | 143 |
72. | Acoustic Signals and the Wind | 144 |
73. | The Timing of Clocks by Means of Acoustic Signals | 146 |
74. | The Specification of Motion by Means of Acoustic Signals | 147 |
75. | Luminous Signals, and Intuitive Kinematics | 151 |
76. | We must escape the Contradiction | 154 |
77. | The Independence of Space and Time | 154 |
78. | The Special Theory a Logical Consequence of the above Premises | 155 |
79. | Examination of an Objection | 156 |
80. | The Possibility of Continual Increase of a Velocity does not Involve the Conclusion that the Velocity may Increase Indefinitely | 157 |
81. | Instantaneous Propagation has as Little Plausibility as a Velocity that cannot be Exceeded | 158 |
82. | Spatial Measurement of Time: Einstein's Interval | 161 |
83. | The Principle of Causality is not at Stake | 163 |
84. | Restricted Relativity concerns only Translations | 165 |
Chapter VII | The General Theory of Relativity | |
85. | The General Theory of Relativity is above all a Mathematical Theory | 167 |
86. | Euclidean Geometry and Curvilinear Co-ordinates on Surfaces | 167 |
87. | The Interval generalized by Means of the Quadratic Form in Four Variables | 169 |
88. | Change of Variables in Mathematical Theories | 172 |
89. | Can a Few Equations contain the Geometrical Universe? | 173 |
90. | Is the World Simple? | 175 |
91. | The Virtuoso and the Phonograph | 176 |
92. | Mechanical Representations | 178 |
93. | Einstein's Purely Geometrical Representation | 180 |
94. | The Gaps: Statistical Theories and Discontinuities: the Theory of Quanta | 182 |
Chapter VIII | Recent Theoretical and Experimental Researches | |
95. | The Equations of Electromagnetism | 183 |
96. | The New Mathematical Theories | 184 |
97. | Their Physical Significance still to be Found | 185 |
98. | Miller's Experiments | 185 |
99. | Miller's Experiments and other Phenomena | 188 |
100. | Michelson and Gale's Experiment | 190 |
101. | The Detractors of the Theory of Relativity | 193 |
102. | The Misconceptions of the Philosophers | 194 |
103. | It is now the Turn of Experiment | 195 |
104. | Supplementary Note | 196 |
Note I | The Kinematics of the Special Theory of Relativity | 197 |
Note II | On the Fundamental Hypotheses of Physics and of Geometry | 202 |
Note III | The Mathematical Continuum and the Physical Continuum | |
1. | The Scale of Rational Numbers | 205 |
2. | The Measurement of Magnitudes | 207 |
3. | Irrational Numbers | 210 |
4. | The Mathematical Continuum | 212 |
5. | The Practical Value of the Continuum | 214 |
6. | Numerical Approximations | 217 |
7. | The Physical Continuum | 218 |
8. | The Relations between the Two Continua | 220 |
Note IV | The Universe--Is It Infinite? | |
1. | A Finite Universe is Possible | 222 |
2. | The Mean Density and the Curvature of the Universe | 223 |
3. | The Hypothesis of an Infinitely Small Mean Density | 225 |
4. | Of what Use are these Cosmological Speculations? | 227 |
Index of Names | 229 | |
General Index | 231 |
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