Bibliography

1. H. Weyl, A. Einstein, H. A. Lorentz, and H. Minkowski. The Principle of Relativity. Dover, New York, 1924. 2. J. Aharoni. The Special Theory of Relativity. Oxford at the Clarendon Press, Oxford, 1965. 3. A. Das. The Special Theory of Relativity: A Mathematical Exposition. Springer, New York, 1996. 4. W. C. Dixon. : The Foundation of Macroscopic Physics. Cambridge Univer- sity Press, Cambridge, 1978. 5. A. P. Lightman et al. Problem Book in Relativity and Gravitation. Princeton University Press, Princeton, 1975. 6. V. V. Batygin et al. Problems in Electrodynamics. Academic Press, New York, 1978. 7. A. P. French. Special Relativity. M.I.T. Introductory Physics Series, Massachusetts, 1968. 8. R. Hagedorn. Relativistic Kinematics. W. A. Bemjamen INC., New York, 1964. 9. J. D. Jackson. Classical Electrodynamics. John Wiley and Sons, New York, 1998. 10. D. F. Lawden. An Introduction to Tensor Calculus and Relativity Third Edition. John Wiley and Sons, New York, 1982. 11. H. Muirhead. The Special Theory of Relativity. The MacMillen Press Ltd., London, 1973. 12. R. Resnick. Introduction to Special Relativity. John Wiley and Sons, New York, 1968. 13. W. Rindler. Essential Relativity Special, General, and Cosmological Revised Second Edition. Springer -Verlag, New York, 1969. 14. W. Rindler. Introduction to Special Relativity. Oxford University Press, Oxford, 1982. 15. R. D. Sard. Relativistic Mechanics Special Relativity and Classical Particle Dynamics. Springer, New York, 1970. 16. J. L. Synge. Relativity: The Special Theory. North Holland Publishing Company, Amsterdam, 1965. 17. V. A. Ugarov. Special Theory of Relativity. MIR Publishers, Moscow, 1979. 18. J. VanBladel. Relativity and Engineering. W. A. Benjamin, New York, 1984.

M. Tsamparlis, Special Relativity, DOI 10.1007/978-3-642-03837-2, 589 C Springer-Verlag Berlin Heidelberg 2010

Index

A Clock, 72 Abberation, 143 Closed system, 84 time dilatation, 209 Comoving observers, 133 Action integral, 344 Composite vector, 540 Active transformation, 6 Composition law Affine parametrization, 99 Newtonian vectors, 82 Affine space, 95 Composition rule for 3-vectors Algebraic method, 146 Newtonian, 160 Arrow of time, 103 relativistic, 161 Axiom Composition Rule of four-vectors, 540 realtivistic inertia, 103 Conduction current, 406, 449, 456 Conduction four-current, 406 B Conformal, 242 Basic sensors, 56 Conformally flat, 242 Basis Conservation g-Cartesian, 7 of angular momentum, 502 g-orthonormal, 7 mechanical energy, 330 Biot-Savart, 482 Constancy of c, 315 Bivector, 495 Constitutive relations, 398, 459 simple, 447, 495 Constraint equations, 449, 454 dual, 447, 495 Continuity equation, 397, 449 Boosts, 20, 28, 31, 35 Contravariant indices, 4 Born acceleration, 207 Convection current, 449, 456 Born rigid motion, 206, 207 Coordinate functions, 2 Born rigidity, 206 Coulomb gauge, 402 Bradyons, 98 Covariance Principle, 63 Galileo, 79–81 C Lorentz, 108, 109 Canonical form, 7, 48 Covariant indices, 4 Cartesian coordinate system, 63 , 252 Cartesian frames a curve, 366 Euclidean, 9 worldline, 157 Lorentz, 9 Cyclotronic frequency, 435, 516 Center of momentum particle, 287, 563 Center System, 52 D Character of inner product, 7 D’Alembert operator, 401, 403 Characteristic quantity of a theory, 59 Decomposition 1+3, 561 Chronometry, 92, 103, 104 Dielectric constant, 398 of two events, 118 Dielectric permittivity constant, 459

591 592 Index

Dual space, 5 Four-velocity, 156 Dummy index, 4 Frame E center of momentum, 291 ECF, 9, 14 laboratory, 291 Elastic collision, 284 target, 291 Electric conductivity, 455, 460, 465 Frame Frenet-Serret, 363 tensor, 455 Free fall, 247 Electric part, 496 Frenet-Serret frame, 363 Electric susceptibility, 460 Fundamental equation of isometry, 10 Electromagnetic field tensor, 414, 445 Future, 103 Electromagnetic four-potential, 412 Future directed, 48 Electromagnetic waves, 421 G Energy G-basis, 11 internal, 268 G-factor, 514 total , 268 G-isometries, 9 EOT, 14 G-orthogonal transformations, 9 Equation of continuity, 405 Gauge Lorentz, 401 electormagetism, 406 Gauge transformation, 400 Ether, 88 General linear group, 6 Euclidean inner product, 7, 8 Generalized Lorentz transformation, 239 Euler angles, 16 Generalized Ohm Law, 467 Event, 94 Generic reaction, 293 Event horizon, 97 Geometric description of collissions F Newtonian, 556 Fine structure constant, 354 Gravitational red-shift, 215, 250 Focussing of beams of particles, 272 Gravitational time dilation, 251 Foliation, 95 Gyromagnetic ratio, 514 Force H Lorentz force, 428 Hall current, 465 Four-acceleration, 157, 186 Hamilton formalism, 343 Four-electric field, 442 Heron, 565 Four-force Holonomic basis, 2 Bonnor, 375 Homogeneous and isotropic material, 460 definition, 325 Homopolar induction, 462 generic, 372 Hyperbolic motion, 197, 335 inertial, 327 Lorentz-Dirac, 373 I Newtonian, 373 Image of physical phenomenon, 57 pure, 327 Index of refraction, 459 thermal, 327 Induction field tensor, 445 Four-force on a charge, 427 Inelastic collision, 284 Four-magnetic induction, 442 Inertial motion, 76 Four-momentum, 267 Inner product, 6 photon, 276 character, 7 Four-vectors, 17 Euclidean, 7, 8 center of momentum, 563 Lorentz, 8 future directed, 26 non-degenerate, 7 null, 17 representation, 7 past directed, 26 Instantaneous inertial direction, 76 spacelike, 17 Internal energy, 268 timelike, 17 International System of Units (SI), 278 future directed, 96 Intrinsic angular momentum, 508 past directed, 96 Isotropic group, 551 Index 593

L Minkowski, 93 Laboratory System, 570 , 8 Lagrange formalism, 343 Lagrangian N relativistic, 344 Net angular momentum, 502, 503 Laue, 139 Net moment, 501 Law Net torque, 501 conservation of four-momentum, 287 NIO, 78 conservation of linear momentum, 84 Normal LCF, 9, 104 first, second, third, 366 , 46, 127 Normal component, 380 Levi Civita tensor density, 440 Null cone, 18 Lienard´ - Wiechert potentials, 479 Null curves, 98 Light aberration formula, 277 Null electromagnetic fields, 421 Null vectors, 96 Light cone, 96 future, 96 O past, 96 Observation, 59 Linear transformations, 5 Observers, 59 Little group, 551 inetrial, 63 Local Relativistic Inertial Observer, 188 Newtonian, 63 Lorentz Newtonian inertial, 103 gauge, 401, 412 Newtonian observers, 75 vector form, 26 relativistic , 63 Lorentz Cartesian Frame, 104 relativistic accelerated, 103 Lorentz force, 428 relativistic inertial, 103 Lorentz inner product, 8 Optical image, 135 Lorentz transformation Orbital angular momentum, 506 boost, 35 Orbital magnetic dipole moment, 508 Luxons, 275 Oscillator, 195

P M Paradox, 118, 253 Magnetic dipole, 508 Parallel component, 380 Magnetic dipole moment, 486, 507 Particle abberation formula, 272 Magnetic moment anomaly, 515 Particle four-vector, 50, 278 Magnetic part, 496 Particle reactions, 283 Magnetic permeability, 398 Passive transformation, 6 Magnetic permeability constant, 459 Past, 103 Magnetization four-vector, 448 Past directed, 48 Magnetization Vector, 398 Photongun, 102 Mass, 266 Physical quantity, 61 inertial, 83 Newtonian, 81 photon, 276 Poincare´ transformations, 99 Maxwell equations, 412 Poisson equation, 402 Ampere´ Law, 397 Polarization four-vector, 448 Faraday Law, 397 Polarization Vector, 398 Gauss Law, 397 Position four-vector, 107 Newtonian form, 397 Position vector, 59 Measuring sensors, 56 Potential Metric electric, 399 Euclidean, 9 magnetic, 399 Lorentz, 9 Newtonian Physical quantity, 81, 84 space, 7 relativistic physical quantity, 110 594 Index

Poynting vector, 464 Relativistic mass, 266 Prediction, 66 Relativistic mass point (ReMaP), 155, 157 Principle Relativistic measurement Covariance, 63, 64 spatial distance, 120 Inertia, 64 temporal difference, 120 of Inertia, 63 Relativistically parallel axes, 41 Principle of Communication ReMaP, 155 of Einstein , 107 Rest frame, 49 Principle of Least Action, 248 Rest length Principle of Relativity, 62 , 132 Galileo, 79, 84 Retarding point, 484 Projection tensor, 562 motion, 212 Propagation equations, 449, 454 Rigid motion, 207 Proper Rigid rod, 132 clock, 102 characteristic observers, 133 Proper frame, 48, 101 relativistic length, 133 instantaneous, 100 rest length, 132 Proper length, 207 rest observer, 134 Proper mass loss, 308 Rigid rotation, 219 Proper space, 101 Rocket motion, 355 Proper time, 100, 155 Proper transformation S Lorentz, 20 Sandeh D, 317 Scattering, 283 Compton, 320, 583 R elastic, 317 Rapidity, 20, 38, 43, 101, 122, 197 Screen projection operator, 393 Reactions Space, 69 excitation reactions, 308 homogeneity, 71 radiative transitions, 308 isotropy, 71 Reality of a physical theory, 61 Spacelike curves, 98 Reciprocity of motion, 114 , 8, 59, 93 Reciprocity principle, 524 reflections, 528 Redshift Speed of light, 92 acceleration, 215 Spin angular momentum, 508 Reduced form, 48 Spin of a particle, 511 Relative 3-velocity, 169 Spin vector, 511 Relative four-acceleration, 167 Standard configuration, 25 Relative four-vector, 167 State transition, 283 Relative four-velocity, 167 Straight line of time, 72 Relative position vector, 166 Synchronization, 74, 102, 204 Relativistic Einstein, 205 Light Frame, 104 of LRIO, 208 observation, 92 Synchronization of chronometry, 209 observers, 92 System of Natural Units, 278 physical quantity, 110 Relativistic angular momentum, 503 T Relativistic composition rule Tachyons, 98 3-velocities, 161 Tangent basis of a curve, 369 Relativistic electric field, 442 Target system, 570 Relativistic inertial directions, 103 Tensorial transformation, 9 Relativistic inertial motion, 95 Tensors, 11 Relativistic Inertial Observers, 99 Euclidean, 12 Relativistic magnetic field, 442 Lorentz, 12, 265 Index 595

Theorem of the zeroth component, 290 Transformation matrix, 3 Thomas phenomenon, 177 Transformations Thomas precession, 177 improper g-orthogonal, 10 Threshold, 297, 567 proper g-orthogonal, 10 Threshold energy, 299 Transverse conductivity, 465 Time, 71 Triangle function, 295 “arrow” of time, 73 Time dilation, 46, 123 V Torque tensor, 504 Vector four-potential , 340 Total energy, 268 3-Velocity space, 174 Transformation 3-Velocity triangle, 175 coordinates, 1 Galileo, 160 Vorticity vector, 451 Lorentz generalized, 240 W of fields E, B, 415 Wigner angle, 170 similarity, 7 , 97