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CHAPTERⅠ．THE SPACE-TIME CONTINUUM AND THE SEPARATION BETWEEN EVENTS1

1．Concepts1

2．Events and particles5

3．Space-time6

4．The assignment of space-time coordinates7

5．Notation8

6．World lines and space-time diagrams9

7．The motion of a material particle10

8．Past，present and future11

9．Standard clocks14

10．The separation between events15

11．The fundamental quadratic form16

12．Finsler space-time and Hamiltonian methods19

13．Space-time as a Riemannian space22

14．Measurement of spacelike separation24

15．The physical meaning of orthogonality26

16．Distance between particles29

17．Rigid rods30

18．The world lines of free particles32

19．The special and general theories of relativity34

20．Rigid motions36

CHAPTER Ⅱ．INTRODUCTION TO THE SPECIAL THEORY38

1．Basis of the special theory of relativity38

2．Finite separations39

3．How to draw a straight line in space-time42

4．Pairs of straight lines in space-time，parallel and skew44

5．The physical meaning of the special coordinates47

6．Splitting space-time into space and time49

7．Galileian frames of reference52

8．Proper time and the speed of light54

9．Minkowskian coordinates56

CHAPTER Ⅲ．SPACE-TIME DIAGRAMS59

1．Some elements of the geometry of flat space-time59

2．Orthogonal projections61

3．space-time diagrams63

4．Space-time diagram of the null cone64

5．M-geometry and E-geometry65

6．Pseudospheres67

CHAPTER Ⅳ．THE LORENTZ TRANSFORMATION69

1．The general Lorentz transformation69

2．Restrictions on Lorentz transformations73

3．The two ways of interpreting transformations75

4．Geometrical meaning of the Lorentz transformation76

5．Eulerian angles and pseudoangles79

6．Lorentz transformations regarded as rigid body displacements84

7．The Lorentz 4-screw86

8．Reduction of any Lorentz transformation to a 4-screw90

9．Correspondence between triads of null rays and unit orthogonal tetrads94

10．Lorentz transformations represented by arbitrary transformations of triads of null rays98

11．Spinors103

12．The two spin transformations corresponding to a given Lorentz transformation107

13．The simple Lorentz transformation between two frames of reference110

14．Lorentz transformations with Hermitian (or symmetric) matrix114

CHAPTER Ⅴ．APPLICATIONS OF THE LORENTZ TRANSFORMATION118

1．Aparent contraction of a moving body and apparent retardation of a moving clock118

2．Snapshots120

3．Space-time diagrams of contraction and retardation122

4．Composition of velocities126

5．The velocity 4-vector and the acceleration 4-vector130

6．Transformation of a wave motion133

7．Reflection at moving mirrors138

8．Fresnel＇s convection coefficient142

9．Aberration146

10．Teh expanding universe in special relativity150

11．The red-shift152

12．Luminosity and distance153

13．The dependence of red-shift on apparent distance and the age of the universe156

14．The Michelson-Morley experiment158

CHAPTER Ⅵ．MECHANICS OF A PARTICLE AND COLLISION PROBLEMS163

1．Force．Action and reaction A philosophical digression163

2．Particles and mass165

3．Equations of motion166

4．Is proper mass constant?167

5．Interpretation of the equations of motion168

6．Motion under a constant relative force and in a constant magnetic field171

7．Momentum 4-vector for a photon172

8．Collisio and disintegration problems173

9．Space-time diagrams of collisions176

10．The triangle inequality in space-time177

11．Mass-centre reference system．Release of energy in disintegration180

12．Some numerical values182

13．Inelastic collision of two particles183

14．Disintegration of one particle into two185

15．Emission of a photon from an atom187

16．The sameness of photons189

17．The emission and absorption of a photon191

18．The Compton effect193

19．The annihilation and creation of matter199

20．Elastic collisions205

CHAPTER Ⅶ．MECHANICS OF A DISCRETE SYSTEM208

1．Discrete and continuous systems208

2．Impulses and continuous forces209

3．Internal impulses210

4．The conservation of 4-momentum for a system213

5．Angular momentum and its conservation216

6．The mass-centre of a system218

7．Intrinsic angular momentum of a particle220

8．The geometrical representation of a skew-symmetric tensor223

9．Elastic collisions with unchanged intrinsic angular momentum invariants．The case of identical material particles227

10．Example of an elastic collision with intrinsic angular momentum invariants unchanged235

11．General treatment of elastic collision with intrinsic angular momentum237

12．Summary of procedure for solving a collision problem246

13．Particular cases of collisions248

14．External impulses and impulsive torques acting on a system251

15．The two-body problem254

CHAPTER Ⅷ．MECHANICS OF A CONTINUUM261

1．Density261

2．Fundamental laws of relative momentum and relative energy for a system263

3．Impact of a stream of particles on a target265

4．Pressure in a relativistic gas267

5．Pressure due to the impact of photons269

6．World tubes and their cross-sections272

7．Green＇s theorem and the expansion of world tubes276

8．The energy tensor of a continuous medium281

9．The physical meaning of the energy tensor285

10．The energy tensor for an incoherent stream of material particles288

11．Eigen values of the energy tensor290

12．Mean density，mean velocity and stress296

13．Equations of motion of a continuous medium300

14．The perfect fluid in relativity302

15．Incompressible fluids306

16．Isolated systems and the energy tensor309

CHAPTER Ⅸ．THE ELECTROMAGNETIC FIELD IN CACUO317

1．The electromagnetic tensor Frs317

2．Lorentz transformations of the electric and magnetic 3-vectors320

3．The energy tensor322

4．Eigen values and principal directions for the electromagnetic energy tensor325

5．The canonical forms for an electromagnetic field at an event331

6．Eigen properties of the tensors Frs and F＊rs336

7．The tensors Frs and F＊rs expressed in terms of invariants and principal null vectors339

8．The 4-potential345

9．Plane electromagnetic waves350

10．Some special systems of plane waves354

11．Reduction of a pair of sinusoidal plane wave systems Interference356

12．Some scalar wave functions359

13．Generation of a Maxwellian field from a scalar wave function363

14．An electromagnetic model of a material particle366

15．Superposition of elementary wave functions372

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

17．Model of a photon with β=O375

18．Model of a photon with β small379

19．Null 3-spaces and Green＇s theorem383

20．Electromagnetic shock waves385

CHAPTER Ⅹ．FIELDS AND CHARGES387

1．The discrete and continuous methods387

2．The Coulomb field of an electric charge388

3．The field of an accelerated charge391

4．The ponderomotive force394

5．The electromagnetic Kepler problem396

6．Radiation of energy and third-order equations of motion399

7．Maxwell＇s equations with current403

8．Explicit formula for the 4-potential405

9．The energy tensor of a field with current410

10．Maxwell＇s equations derived from a variational principle413

11．Maxwell＇s equations in moving matter415

APPENDIX419

A．3-waves and 2-waves419

B．Radiation of energy from an accelerated charge422

C．Scattering and capture by a fixed nucleus426

D．The absolute 2-content of a 3-cell on a null cone430

E．Calculations for retarded potential432

References425

Index439