## Relativity: the special theoryNorth-Holland Pub. Co.; [sole distributors for U.S.A.: Interscience Publishers, New York,], 1965 - Science - 459 pages |

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### Contents

Preface vI
I Chapter I THE SPACETIME CONTINUUM AND THE SEPARATION BETWEEN EVENTS 1 Concepts | 1 |

Events and particles | 5 |

Spacetime | 6 |

The assignment of spacetime coordinates | 7 |

Notation | 8 |

World lines and spacetime diagrams | 9 |

The motion of a material particle | 10 |

Past present and future | 11 |

The triangle inequality in spacetime | 176 |

Masscentre reference system Release of energy in disintegration | 179 |

Some numerical values | 181 |

Inelastic collision of two particles | 182 |

Disintegration of one particle into two | 184 |

Emission of a photon from an atom | 186 |

The sameness of photons | 188 |

The emission and absorption of a photon | 190 |

Standard clocks | 14 |

The separation between events | 15 |

The fundamental quadratic form | 16 |

Finsler spacetime and Hamiltonian methods | 19 |

Spacetime as a Riemannian space | 22 |

Measurement of spacelike separation | 24 |

The physical meaning of orthogonality | 26 |

Distance between particles | 29 |

Rigid rods | 30 |

The world lines of free particles | 32 |

The special and general theories of relativity | 34 |

Rigid motions | 36 |

INTRODUCTION TO THE SPECIAL THEORY 1 Basis of the special theory of relativity | 38 |

Finite separations | 39 |

How to draw a straight line in spacetime | 42 |

Pairs of straight lines in spacetime parallel and skew | 44 |

The physical meaning of the special coordinates | 47 |

Splitting spacetime into space and time | 49 |

Galileian frames of reference | 52 |

Proper time and the speed of light | 54 |

Minkowskian coordinates | 56 |

SPACETIME DIAGRAMS 1 Some elements of the geometry of flat spacetime | 59 |

Orthogonal projections | 61 |

Spacetime diagrams | 63 |

Spacetime diagram of the null cone | 64 |

Mgeometry and geometry | 65 |

Pseudospheres | 67 |

General remarks | 68 |

THE LORENTZ TRANSFORMATION 1 The general Lorentz transformation | 69 |

Restrictions on Lorentz transformations | 73 |

The two ways of interpreting transformations | 75 |

Geometrical meaning of the Lorentz transformation | 76 |

Eulerian angles and pseudoangles | 79 |

Lorentz transformations regarded as rigid body dis placements | 84 |

Infinitesimal Lorentz transformations | 85 |

The Lorentz 4screw | 89 |

Correspondence between triads of null rays and unit orthogonal tetrads | 94 |

Lorentz transformations represented by arbitrary transformations of triads of null rays | 98 |

Spinors | 102 |

The two spin transformations corresponding to a given Lorentz transformation | 107 |

The simple Lorentz transformation between two frames of reference | 110 |

Lorentz transformations with Hermitian or sym metric matrix | 114 |

APPLICATIONS OF THE LORENTZ TRANS FORMATION 1 Apparent contraction of a moving body and apparent retardation of a moving clock | 117 |

Snapshots | 119 |

Spacetime diagrams of contraction and retardation | 121 |

Composition of velocities | 125 |

The velocity 4vector and the acceleration 4vector | 129 |

Transformation of a wave motion | 132 |

Reflection at moving mirrors | 137 |

Fresnels convection coefficient 14 1 | 141 |

Aberration | 145 |

The expanding universe in special relativity | 149 |

The redshift | 151 |

Luminosity and distance | 152 |

The dependence of redshift on apparent distance and the age of the universe | 155 |

The MichelsonMorley experiment | 157 |

The apparent shape of a moving sphere | 161 |

MECHANICS OF A PARTICLE AND COL LISION PROBLEMS 1 Force Action and reaction A philosophical digression | 162 |

Particles and mass | 164 |

Equations of motion | 165 |

Is proper mass constant? | 166 |

Interpretation of the equations of motion | 167 |

Motion under a constant relative force and in a constant magnetic field | 170 |

Momentum 4vector for a photon | 171 |

Collision and disintegration problems | 172 |

Spacetime diagrams of collisions | 175 |

The Compton effect | 192 |

The annihilation and creation of matter | 198 |

Elastic collisions | 204 |

MECHANICS OF A DISCRETE SYSTEM 1 Discrete and continuous systems | 207 |

Impulses and continuous forces | 208 |

Internal impulses | 209 |

The conservation of 4momentum for a system | 212 |

Angular momentum and its conservation | 215 |

The masscentre of a system | 217 |

Intrinsic angular momentum of a particle | 219 |

The geometrical representation of a skewsymmetric tensor | 222 |

Elastic collisions with unchanged intrinsic angular momentum invariants The case of identical material particles | 226 |

Example of an elastic collision with intrinsic angular momentum invariants unchanged | 234 |

General treatment of elastic collision with intrinsic angular momentum | 236 |

Summary of procedure for solving a collision problem | 245 |

Particular cases of collisions | 247 |

External impulses and impulsive torques acting on a system | 250 |

The twobody problem | 253 |

MECHANICS OF A CONTINUUM 1 Density | 260 |

Fundamental laws of relative momentum and relative energy for a system | 262 |

Impact of a stream of particles on a target | 264 |

Pressure in a relativistic gas | 266 |

Pressure due to the impact of photons | 268 |

World tubes and their crosssections | 271 |

Greens theorem and the expansion of world tubes | 275 |

The energy tensor of a continuous medium | 280 |

The physical meaning of the energy tensor | 284 |

The energy tensor for an incoherent stream of material particles | 287 |

Eigen values of the energy tensor | 289 |

Mean density mean velocity and stress | 295 |

Equations of motion of a continuous medium | 299 |

The perfect fluid in relativity | 301 |

Incompressible fluids | 305 |

Isolated systems and the energy tensor | 308 |

THE ELECTROMAGNETIC FIELD IN VACUO 1 The electromagnetic tensor Fr | 316 |

Lorentz transformations of the electric and magnetic 3vectors | 319 |

The energy tensor | 321 |

Eigen values and principal directions for the electro magnetic energy tensor | 324 |

The canonical forms for an electromagnetic field at an event | 330 |

Eigen properties of the tensors Fr and F | 335 |

The tensors F and F expressed in terms of invariants and principal null vectors | 338 |

The 4potential | 344 |

Plane electromagnetic waves | 349 |

Some special systems of plane waves | 353 |

Reduction of a pair of sinusoidal plane wave systems Interference | 355 |

Some scalar wave functions | 358 |

Generation of a Maxwellian field from a scalar wave function | 362 |

An electromagnetic model of a material particle | 365 |

Superposition of elementary wave functions | 371 |

A nearly static electromagnetic particle 3 large 373 | 373 |

Model of a photon with ? 0 | 374 |

Model of a photon with p small | 378 |

Null 3spaces and Greens theorem | 382 |

Electromagnetic shock waves | 384 |

FIELDS AND CHARGES 1 The discrete and continuous methods | 386 |

The Coulomb field of an electric charge | 387 |

The field of an accelerated charge | 390 |

The ponderomotive force | 393 |

Maxwells equations derived from a variational | 412 |

APPENDIX | 418 |

Scattering and capture by a fixed nucleus | 425 |

E Calculations for retarded potential | 431 |

G Rigid motions | 438 |

References | 444 |

Copyright | |