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Contents
List of Complementsxv
List of Biographiesxvii
1.Space and Time Before Einstein 1
1.1 Absolute Space and Time 1
1.2 Geometric Properties of the Space 2
1.3 Galileo and the Laws of Motion 4
1.4 Change of Coordinates Between Frames in Relative Motion 6
1.5 Principle of Inertia 8
1.6 Principle of Relativity 9
1.7 Physical Phenomena having a Privileged Reference System 11
1.8 Maxwell's Electromagnetism 13
2.In Search of the Ether 17
2.1 Two Models for the Light 17
2.2 First Determination of the Speed of Light 21
2.3 The Aberration of Light 23
2.4 First Terrestrial Method to Measure c 26
2.5 The Luminiferous Ether 27
2.6 Searching for the Absolute Terrestrial Motion: Dragging of Ether 29
2.7 Fizeau's Experiment 32
2.8 Hoek's Experiment 34
2.9 Airy's Experiment 36
2.10 Michelson-Morley Experiment 36
2.11 Fitz-Gerald-Lorentz Length Contraction 43
2.12 The Twilight of the Ether 44
3.Space and Time in Special Relativity 47
3.1 Postulates of Special Relativity 47
3.2 Length Contractions and Time Dilatations 49
3.3 The Muon Journey 52
3.4 Lengths Transversal to Motion 53
3.5 Composition of Motions 54
3.6 Interpretation of Fizeau's Experiment 57
3.7 Transversal Components of the Velocity 58
3.8 The Notion of Simultaneity 58
3.9 Events and World Lines 62
3.10 Coordinate Lines of S' in the Space-Time Diagram of 565
3.11 Lorentz Transformations 69
3.12 Comparing Clocks in Different Frames 74
3.13 Velocity and Acceleration Transformations 78
3.14"Paradoxes": Remnants of Classical Thought 81
3.15 Doppler Effect 86
3.16 Transformation of Light Rays 90
3.17 Transformation of a Plane Wave 92
3.18 Propagation of Light in Material Media 95
4.Geometric Structure of Space-Time 97
4.1 Interval 97
4.2 Calibration Hyperbola 98
4.3 Light Cone 100
4.4 Timelike-Separated Events 101
4.5 Twin Paradox 103
4.6 Spacelike-Separated Events 107
4.7 Velocity Parameter: Rapidity 109
4.8 Wigner Rotation 111
5.Transformation of the Electromagnetic Field 117
5.1 The Electromagnetic Plane Wave 117
5.2 Transformation of E and B 119
5.3 Charge and Current Transformations 122
5.4 Field of a Uniformly Moving Charge 126
5.5 Transformation of Potentials 127
5.6 Fields in Material Media 128
5.7 Moving Dipoles Fields 130
5.8 Lorentz Force Transformation 132
5.9 Electromagnetic Field Invariants 133
6.Energy and Momentum 135
6.1 Conservation Laws 135
6.2 Energy and Momentum of a Particle 137
6.3 Energy-Momentum Invariant. Force 141
6.4 Charge Movement in Uniform Fields 143
6.5 Center-of-Momentum Frame 146
6.6 Phenomena Derived from Mass-Energy equivalence 148
6.7 Center of Inertia 153
6.8 Elastic Collisions 155
6.9 Interaction Between Electromagnetic Radiation and Matter 163
7.Covariant Formulation 171
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Index
Aaberration of light, 22, 29, 31, 35, 42, 53, 91, 121
absolute motion, 207, 208, 215
absolute rotation, 208, 275, 284
absolute space, 1, 2, 9, 10, 23, 29, 43, 48, 105, 207, 208, 210
absolute time, 1, 45, 48
accelerationinvariance, 10
- relative between close orbits, 213, 224
accretion disk, 284, 286
action, 288
- Hilbert's, 291, 292, 293
- of a freely gravitating particle, 223
- of a particle in an electromagnetic field, 289
- of the electromagnetic field, 289, 292
action and reaction, Principle of, 135, 137
active galactic nucleus, 272, 286
adiabatic evolution, 267
affine connection, 229, 230, 232, 234, 236, 291
age of the universe, 265, 275, 278, 279
Airy, George Biddell experiment, 35, 96
Alcock, C, 286
ALLEGRO, 285
alpha decay, 151
angular momentum, 181
- conservation, 194, 295
- density, 194
- intrinsic, 114, 155, 183, 184, 203
anti-de Sitter universe, 274
Arago, Dominique François Jean, 20
experiment, 29, 30, 31, 35, 36, 96
Aristotle, 4
AURIGA, 285
automatic conservation, 240, 241, 273, 290, 293
autoparallel, 230, 232-236
axial vector, 119, 120
BBabacock, G.C., 44
Balbi, Amedeo, 277
Bartholin, Erasmus, 17
baryon number, 151
Beltran-Löpez, V., 209
Bennett, Charles, L., 278
Bergman, T.G., 44
Bertotti, Bruno, 283
Bessel, Friedrich Wilhelm, 24
beta decay, 151, 268
Bianchi identities, 234, 240, 241
- generalized, 240-241
Big-Bang model, 265, 268, 269, 278, 280-281
big-crunch, 270, 276
binary pulsar, 284-285
binding energy, 148-151
- per nucleon, 149, 151
Birkhoff, George, D., 244, 285
birefringence, 17, 44
black body radiation, 21, 267
black hole, 243, 245, 254, 255, 266, 284-286
Boltzmann constant, 169
Bondi, Hermann, 273
boost, 109
Brace, D.B., 44
Bradley, James, 22-26
Braginsky, Vladimir Borisovich, 282
Brans, Carl, H., 282
Brillouin, Léon, 93
Broglie, Louis Victor Pierre Raymond duc de, 95, 164
Bucherer, A.H., 145
Ccalculus of variations, 225, 227, 287-288
calibration hyperbolas, 99
Cannon, Russell, 259
Carter, W.E., 283
Cartesian coordinates, 3, 6, 7, 10
center of inertia, 153-155, 182-184
center of mass, 146, 147, 284
center-of-momentum frame, 146, 147, 151, 153, 154, 157, 158, 167, 168, 183
centrifugal force, 208, 211, 275
cepheid, 262
Chandrasekhar, Subrahmanyan limit, 286
charge local conservation, 175, 189, 293, 295
charge-current density, 177
Chen, Wan, 284
Christoffel symbols, 227, 228, 229, 230, 233, 234, 237, 264, 273, 290
Ciufolini, Ignazio, 284
Clarke, Samuel, 1
clocks synchronization, 61, 75, 77, 106
closed universe, 270, 271, 274, 277
COBE, 268
Colless, Matthew, 259
comoving frame, 195, 196, 260, 264
Compton effect, 165, 166, 167
Compton wavelength, 166
Compton, Arthur Holly, 164, 165, 167
conformai time, 278
conservation laws, 135, 136, 140, 152, 156, 157, 165, 166, 171, 173, 189, 235
contact interaction, 188
continuity equation, 12, 16, 123, 125, 126, 128, 175, 189, 198
continuous medium, 43, 128, 130, 188, 189, 192, 194
contravariant vector, 173, 176, 188, 221, 222
coordinate lines, 65, 66, 68, 71, 106, 187
Coriolis force, 210, 211
cosmic background radiation, 267, 268, 277, 278, 281, 282, 286
- fluctuations, 277, 278, 282
cosmological constant, 272, 273, 275, 276, 277, 291
cosmological principle, 259
cosmological redshift, 260, 286
Cottingham, E.T., 217
covariance of fundamental laws, 171
covariant derivative, 227, 229, 230, 233, 234
- of the metric tensor, 230
covariant vector, 174, 221, 222, 223, 229
covector, 222
Crommelin, Andrew, 217
Cui, Wei, 284
curvature scalar, 235
curve parametric equations, 221, 225, 232
- tangent vector, 221, 230, 232
curved space, 224
cyclotron, 144
Dd'Alembert, Jean Le Rond, 20
d'Alembertian, 198, 239
dark energy, 272, 277
dark matter, 266, 267, 269
Davidson, Charles, 217
de Bernardis, Paolo, 277
de Sitter effect, 283
de Sitter universe, 274
de Sitter, Willem, 274, 283
deceleration parameter, 263, 272, 275, 276, 277
decoupling of matter and radiation, 267
degrees of freedom in electromagnetism, 199
- in gravitation, 239, 273
Descartes, René, 21
determinant, 184-187
derivative of, 230
Dicke, Robert Henry, 211, 268, 282
differential geometry, 221
diffraction, 17, 20, 21
Dillinger, W.H., 283
directional derivative, 227
dispersion, 17, 20, 43
dispersion relation, 95, 165
dispersive material, 43, 57, 93
distance, 3, 220, 223
- invariance, 3, 7, 10 14, 31, 43, 44, 45, 47, 69, 71, 74, 97
divergence, 175, 231, 235
divergence theorem, 291, 294
- in 3 dimensions, 190
- in 4 dimensions, 192
Doppler effect, 86-89, 169, 216, 262
- relativistic for light in vacuum, 88
dust, 195, 196, 265, 267, 270, 273, 275, 276
Dyson, Frank Watson, 217
EEddington, Arthur Stanley, 217
Einstein convention, 172
Einstein equations, 234, 235, 237, 240, 243, 256, 265, 290, 294
- linearized, 237, 238
- without sources, 238, 243, 272
Einstein tensor, 235, 240, 241, 293
Einstein universe, 273, 274, 276
Einstein, Albert, 44, 47, 51, 148, 163, 164, 172, 208, 209, 210, 211, 212, 217, 219, ...
elastic collision, 155
- in the center-of-momentum frame, 158
electric charge
- invariance, 123
- local conservation, 16, 123, 126, 189, 295
- movement in a magnetostatic field, 143
- movement in an electrostatic field, 144
- movement in crossed fields, 146
- moving, field of, 126
electric dipole, 128, 130, 131
- moving, field of, 130, 131
electromagnetic energy density, 200
electromagnetic field tensor, 197
- dual, 198
electromagnetic momentum density, 201
electromagnetic potential, 127, 197, 237, 289
electromagnetism, 13, 45, 96, 197, 198, 210, 219, 239, 240, 241, 283, 285
electron-volt, 149
emission of photons, 168
emission theories, 44, 45
energy at rest, 139
- kinetic, 139
- relativistic, 139
energy density, 192, 195, 200, 235, 237, 260, 267
energy-momentum, 141, 152, 156, 157, 165, 166, 173, 174, 177, 182, 188, 189, 192-195,...
- conservation, 145, 189, 193, 226, 295
energy-momentum invariant, 141, 152, 156, 166, 177
energy-momentum tensor, 188, 192, 233, 235, 237, 291
- of a flux of free particles, 195
- of a perfect fluid, 196
- of pure radiation, 195
- of the electromagnetic field, 200, 291
envelope, 18, 20, 28
Eötvös, Lörand Baron von, 211
ESA-Planck, 278
ether, 14
electromagnetic, 27
- local, 29
- luminiferous, 27-28
- partial dragging, 30, 31, 35, 36, 40, 45, 57, 96
- universal, 29, 34
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