Relativity: the special theory

Front Cover
North-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
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