Theory of Relativity Based on Physical Reality

Title ......Page 1
Copyright ......Page 3
Contents ......Page 5
INTRODUCTION ......Page 13
A. The critical velocity ......Page 19
1. A general remark ......Page 21
a. Observations of Romer ......Page 22
b. The aberration of light ......Page 23
b. The experiments of Fizeau and Foucault ......Page 24
a. The refractive index ......Page 26
b. The determination of the velocity of light in a refracting medium ......Page 27
1. The Michelson interferometer ......Page 28
2. Measurement of the phase velocity of light ......Page 31
3. The experiment of Fizeau ......Page 32
D. The Doppler effect ......Page 33
1. Moving source ......Page 34
2. Observation of the Doppler effect ......Page 36
1. Experimental observations ......Page 37
2. Physical interpretation of the perpendicular Doppler effect ......Page 38
a. The question of the moving observer ......Page 40
b. Acoustical and electromagnetic Doppler effects ......Page 41
1. Variation of decay time with velocity ......Page 43
2. Change of mass with velocity ......Page 44
3. Remark on the methods of measuring the mass velocity relation ......Page 45
A. The question of the ether ......Page 48
2. The Sagnac experiment ......Page 50
C. Translational motion relative to the ether ......Page 53
1. Propagation of a spherical signal ......Page 56
2. Propagation of light relative to a moving system of reference ......Page 57
3. The Michelson-Morley experiment ......Page 59
4. The interpretation of the negative result of the Michelson-Morley experiment ......Page 60
5. Considerations concerning the contraction hypothesis ......Page 64
1. The Trouton-Noble experiment ......Page 65
2. The experiment of Isaak and co-workers ......Page 66
E. General remarks concerning the series of negative results ......Page 69
1. Generalization of negative experiences ......Page 71
1. Representations ......Page 72
2. An example: the measure of electric charge ......Page 73
3. Distinguished representations ......Page 76
4. Measures of lengths ......Page 77
1. Determination of coordinate vectors ......Page 79
2. Explicit determination of coordinate measures ......Page 81
4. Various representations ......Page 83
2. Coordinate transformations and deformations ......Page 86
a. Definitions ......Page 89
b. Group character of orthogonal matrices ......Page 90
4. Rigid bodies ......Page 92
1. General remarks ......Page 94
2. Atomic time scale ......Page 97
3. Systems of reference constructed with the help of light signals ......Page 98
B. The Lorentz transformation as coordinate transformation ......Page 100
1. The explicit form of the Lorentz transformation ......Page 102
2. The physical significance of the parameters of the Lorentz matrices ......Page 104
1. The concept ......Page 106
2. Test for homogeneous propagation of light ......Page 107
3. Connection between various representations ......Page 108
a. Transformations of the propagation tensor ......Page 109
D. The relation of systems of references obtained with light signals and with solids ......Page 110
1. Deformation operators ......Page 114
2. Lorentz deformations ......Page 116
3. Particular types of Lorentz deformations ......Page 117
1. Interpretation of the negative results of ether drift experiments in terms of the Lorentz principle ......Page 120
2. Non-orthogonal representations ......Page 123
3. General remarks on the Lorentz principle ......Page 124
C. The dynamical principle ......Page 125
a. Relaxation processes ......Page 127
c. Deformations of unconnected systems ......Page 128
d. Length contraction of non-connected systems ......Page 130
2. Significance of subgroups of the Lorentz group ......Page 131
1. Addition of velocities ......Page 133
2. Addition formula and Lorentz deformations ......Page 136
B. Considerations about contraction of solids and the slowing down of clocks ......Page 137
1. The clock "paradox" ......Page 142
2. The "paradox of the twins" ......Page 146
1. Newton's first law ......Page 148
2. Elastic collisions ......Page 149
3. Inelastic collisions ......Page 153
B. Equivalence of mass and energy ......Page 154
C. Distant collisions ......Page 155
D. Mechanical laws in terms of four-vectors and tensors ......Page 157
1. Newton's laws ......Page 159
2. The energy-momentum tensor ......Page 160
A. Maxwell's equations ......Page 162
1. Another formulation ......Page 163
B. Solutions of Maxwell's equations ......Page 165
1. Gauge transformation ......Page 167
2. Retarded potentials ......Page 168
3. Advanced potentials ......Page 169
4. Wandering waves ......Page 171
C. Maxwell's equations in terms of four-tensors ......Page 172
1. Retarded four-potential ......Page 174
2. The motion of light signals in terms of Maxwell's equations ......Page 177
D. Maxwell's equations and the Lorentz principle ......Page 179
1. The field of a point charge ......Page 181
1. Effective field strengths ......Page 183
2. The field of dipoles ......Page 184
B. Transformation properties of four-currents ......Page 186
1. The electric field of a moving current ......Page 187
1. Doppler effect and aberration ......Page 189
2. Frequencies of the Doppler effect ......Page 190
3. Effect of aberration ......Page 191
4. Intensities in the Doppler effect ......Page 192
5. Observation of the effect of aberration of star light ......Page 193
6. Propagation of light in a refracting medium ......Page 195
a. Dispersion ......Page 197
7. The experiment of Fizeau ......Page 199
1. Action of a charge upon itself ......Page 202
2. Mass defect ......Page 205
1. Interpretation of the Trouton-Noble experiment ......Page 206
F. Transient phenomena ......Page 207
A. Observational facts ......Page 211
B. Statement of the problem of the theory of gravitation ......Page 212
2. Experimental criteria for homogeneous regions ......Page 214
3. Construction of straight systems of references ......Page 216
a. Locally homogeneous regions ......Page 217
b. Criteria for homogeneous regions ......Page 218
4. Almost straight system of reference ......Page 222
5. Similar regions ......Page 225
C. The generalized Lorentz principle ......Page 226
1. The Lorentz principle formulated in terms of curved coordinates ......Page 227
a. A physical example ......Page 228
a. First approximation ......Page 230
b. A second approximation ......Page 231
4. The ambiguity in the formulation of the Lorentz principle ......Page 233
1. Definition ......Page 235
2. Lorentz invariance of geodetic orbits ......Page 236
B. Equation of motion in a gravitational field ......Page 237
1. Variational principles ......Page 238
2. The physical contents of the variational principle ......Page 239
1. The equations of motions in a gravitational field ......Page 242
2. Integrals of the equations of motions ......Page 244
a. Perihelion motion ......Page 245
b. The deflection of light in the vicinity of the Sun ......Page 246
c. The red shift of spectral lines ......Page 247
D. Connection between the sources of gravitation and the propagation tensor g ......Page 249
1. Einstein's equations of gravitation ......Page 250
2. Energy momentum considerations ......Page 251
3. The Schwarzschild solution of the gravitational equations ......Page 253
a. The planetary motion ......Page 255
E. Electromagnetic field and gravitation ......Page 256
1. An invariant formulation ......Page 257
3. Remark on the consistency of the generalized theory of electromagnetic fields ......Page 258
1. The gravitational force ......Page 260
2. Another aspect of the gravitational equations ......Page 261
3. The mechanism of the gravitational force ......Page 262
A. The physical significance of invariant formulation of physical laws ......Page 264
1. Tensors and distinguished measures ......Page 265
2. The physical significance of the tensor g ......Page 266
3. A normal form of the propagation tensor ......Page 267
1. Stationary representations ......Page 270
2. The energy momentum distribution ......Page 271
1. The results of astronomical observations ......Page 272
2. The solution of Friedmann ......Page 273
a. The measures of intergalactical distances ......Page 276
b. Doppler effect ......Page 278
E. Mach's principle ......Page 279
a. The Thirring effect ......Page 280
1. The Lorentz system ......Page 282
3. Propagation tensor g ......Page 283
4. Lorentz transformation ......Page 284
5. Standard form of linear coordinate transformations ......Page 285
B. Vectors and tensors ......Page 286
1. Two-dimensional tensors ......Page 287
a. Invariant products ......Page 288
C. Fields ......Page 289
a. The Grad operator ......Page 291
b. Further operations ......Page 292
1. k-dimensional measures ......Page 293
2. Multiplication of more-dimensional quantities ......Page 294
B. Permutation operators ......Page 295
1. Cyclic permutations ......Page 297
2. The transposition of a matrix ......Page 298
C. The R operator in curved representations ......Page 299
1. Tensor of several dimensions ......Page 300
2. Symmetry properties ......Page 301
3. The antisymmetric tensor E(4) ......Page 302
D. Tensor fields ......Page 303
1. The Christoffel bracket symbols ......Page 305
2. The covariant differentiation ......Page 306
E. Criteria for homogeneous regions ......Page 308
1. Almost straight representations ......Page 310
2. Tensor character of the Riemann-Christoffel tensor ......Page 312
3. Symmetries of the R(4) tensor ......Page 314
4. The reduced form of the R(4) tensor ......Page 316