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CHAPTERⅠ．THE SPACE-TIME CONTINUUM AND THE SEPARATION BETWEEN EVENTS 1

1．Concepts 1

2．Events and particles 5

3．Space-time 6

4．The assignment of space-time coordinates 7

5．Notation 8

6．World lines and space-time diagrams 9

7．The motion of a material particle 10

8．Past，present and future 11

9．Standard clocks 14

10．The separation between events 15

11．The fundamental quadratic form 16

12．Finsler space-time and Hamiltonian methods 19

13．Space-time as a Riemannian space 22

14．Measurement of spacelike separation 24

15．The physical meaning of orthogonality 26

16．Distance between particles 29

17．Rigid rods 30

18．The world lines of free particles 32

19．The special and general theories of relativity 34

20．Rigid motions 36

CHAPTER Ⅱ．INTRODUCTION TO THE SPECIAL THEORY 38

1．Basis of the special theory of relativity 38

2．Finite separations 39

3．How to draw a straight line in space-time 42

4．Pairs of straight lines in space-time，parallel and skew 44

5．The physical meaning of the special coordinates 47

6．Splitting space-time into space and time 49

7．Galileian frames of reference 52

8．Proper time and the speed of light 54

9．Minkowskian coordinates 56

CHAPTER Ⅲ．SPACE-TIME DIAGRAMS 59

1．Some elements of the geometry of flat space-time 59

2．Orthogonal projections 61

3．space-time diagrams 63

4．Space-time diagram of the null cone 64

5．M-geometry and E-geometry 65

6．Pseudospheres 67

CHAPTER Ⅳ．THE LORENTZ TRANSFORMATION 69

1．The general Lorentz transformation 69

2．Restrictions on Lorentz transformations 73

3．The two ways of interpreting transformations 75

4．Geometrical meaning of the Lorentz transformation 76

5．Eulerian angles and pseudoangles 79

6．Lorentz transformations regarded as rigid body displacements 84

7．The Lorentz 4-screw 86

8．Reduction of any Lorentz transformation to a 4-screw 90

9．Correspondence between triads of null rays and unit orthogonal tetrads 94

10．Lorentz transformations represented by arbitrary transformations of triads of null rays 98

11．Spinors 103

12．The two spin transformations corresponding to a given Lorentz transformation 107

13．The simple Lorentz transformation between two frames of reference 110

14．Lorentz transformations with Hermitian (or symmetric) matrix 114

CHAPTER Ⅴ．APPLICATIONS OF THE LORENTZ TRANSFORMATION 118

1．Aparent contraction of a moving body and apparent retardation of a moving clock 118

2．Snapshots 120

3．Space-time diagrams of contraction and retardation 122

4．Composition of velocities 126

5．The velocity 4-vector and the acceleration 4-vector 130

6．Transformation of a wave motion 133

7．Reflection at moving mirrors 138

8．Fresnel＇s convection coefficient 142

9．Aberration 146

10．Teh expanding universe in special relativity 150

11．The red-shift 152

12．Luminosity and distance 153

13．The dependence of red-shift on apparent distance and the age of the universe 156

14．The Michelson-Morley experiment 158

CHAPTER Ⅵ．MECHANICS OF A PARTICLE AND COLLISION PROBLEMS 163

1．Force．Action and reaction A philosophical digression 163

2．Particles and mass 165

3．Equations of motion 166

4．Is proper mass constant? 167

5．Interpretation of the equations of motion 168

6．Motion under a constant relative force and in a constant magnetic field 171

7．Momentum 4-vector for a photon 172

8．Collisio and disintegration problems 173

9．Space-time diagrams of collisions 176

10．The triangle inequality in space-time 177

11．Mass-centre reference system．Release of energy in disintegration 180

12．Some numerical values 182

13．Inelastic collision of two particles 183

14．Disintegration of one particle into two 185

15．Emission of a photon from an atom 187

16．The sameness of photons 189

17．The emission and absorption of a photon 191

18．The Compton effect 193

19．The annihilation and creation of matter 199

20．Elastic collisions 205

CHAPTER Ⅶ．MECHANICS OF A DISCRETE SYSTEM 208

1．Discrete and continuous systems 208

2．Impulses and continuous forces 209

3．Internal impulses 210

4．The conservation of 4-momentum for a system 213

5．Angular momentum and its conservation 216

6．The mass-centre of a system 218

7．Intrinsic angular momentum of a particle 220

8．The geometrical representation of a skew-symmetric tensor 223

9．Elastic collisions with unchanged intrinsic angular momentum invariants．The case of identical material particles 227

10．Example of an elastic collision with intrinsic angular momentum invariants unchanged 235

11．General treatment of elastic collision with intrinsic angular momentum 237

12．Summary of procedure for solving a collision problem 246

13．Particular cases of collisions 248

14．External impulses and impulsive torques acting on a system 251

15．The two-body problem 254

CHAPTER Ⅷ．MECHANICS OF A CONTINUUM 261

1．Density 261

2．Fundamental laws of relative momentum and relative energy for a system 263

3．Impact of a stream of particles on a target 265

4．Pressure in a relativistic gas 267

5．Pressure due to the impact of photons 269

6．World tubes and their cross-sections 272

7．Green＇s theorem and the expansion of world tubes 276

8．The energy tensor of a continuous medium 281

9．The physical meaning of the energy tensor 285

10．The energy tensor for an incoherent stream of material particles 288

11．Eigen values of the energy tensor 290

12．Mean density，mean velocity and stress 296

13．Equations of motion of a continuous medium 300

14．The perfect fluid in relativity 302

15．Incompressible fluids 306

16．Isolated systems and the energy tensor 309

CHAPTER Ⅸ．THE ELECTROMAGNETIC FIELD IN CACUO 317

1．The electromagnetic tensor Frs 317

2．Lorentz transformations of the electric and magnetic 3-vectors 320

3．The energy tensor 322

4．Eigen values and principal directions for the electromagnetic energy tensor 325

5．The canonical forms for an electromagnetic field at an event 331

6．Eigen properties of the tensors Frs and F＊rs 336

7．The tensors Frs and F＊rs expressed in terms of invariants and principal null vectors 339

8．The 4-potential 345

9．Plane electromagnetic waves 350

10．Some special systems of plane waves 354

11．Reduction of a pair of sinusoidal plane wave systems Interference 356

12．Some scalar wave functions 359

13．Generation of a Maxwellian field from a scalar wave function 363

14．An electromagnetic model of a material particle 366

15．Superposition of elementary wave functions 372

16．A nearly static electromagnetic particle (β large) 374

17．Model of a photon with β=O 375

18．Model of a photon with β small 379

19．Null 3-spaces and Green＇s theorem 383

20．Electromagnetic shock waves 385

CHAPTER Ⅹ．FIELDS AND CHARGES 387

1．The discrete and continuous methods 387

2．The Coulomb field of an electric charge 388

3．The field of an accelerated charge 391

4．The ponderomotive force 394

5．The electromagnetic Kepler problem 396

6．Radiation of energy and third-order equations of motion 399

7．Maxwell＇s equations with current 403

8．Explicit formula for the 4-potential 405

9．The energy tensor of a field with current 410

10．Maxwell＇s equations derived from a variational principle 413

11．Maxwell＇s equations in moving matter 415

APPENDIX 419

A．3-waves and 2-waves 419

B．Radiation of energy from an accelerated charge 422

C．Scattering and capture by a fixed nucleus 426

D．The absolute 2-content of a 3-cell on a null cone 430

E．Calculations for retarded potential 432

References 425

Index 439