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1．Relativity in Classical Mechanics 1

1.1 Frames of Reference 1

1.2 Relativity 2

1.3 Frames of Reference 4

1.4 Newton's Laws 5

1.5 Galilean Transformations 8

1.6 Mass,Energy,and Momentum 10

1.7 Space-time 12

1.8 *Galilean Symmetries 16

1.9 Historical Note 17

2．Maxwell's Theory 21

2.1 Introduction 21

2.2 The Unification of Electricity and Magnetism 22

2.3 Charges,Fields,and the Lorentz Force Law 23

2.4 Stationary Distributions of Charge 25

2.5 The Divergence of the Magnetic Field 27

2.6 Inconsistency with Galilean Relativity 28

2.7 The Limits of Galilean Invariance 29

2.8 Faraday's Law of Induction 30

2.9 The Field of Charges in Uniform Motion 32

2.10 Maxwell's Equations 33

2.11 The Continuity Equation 34

2.12 Conservation of Charge 34

2.13 Historical Note 36

3．The Propagation of Light 39

3.1 The Displacement Current 39

3.2 The Source-free Equations 41

3.3 The Wave Equation 42

3.4 Monochromatic Plane Waves 43

3.5 Polarization 44

3.6 Potentials 45

3.7 Gauge Transformations 48

3.8 Photons 49

3.9 Relativity and the Propagation of Light 50

3.10 The Michelson-Morley Experiment 51

4．Einstein's Special Theory of Relativity 57

4.1 Lorentz's Contraction 57

4.2 Operational Definitions of Distance and Time 58

4.3 The Relativity of Simultaneity 60

4.4 Bondi's k-Factor 63

4.5 Time Dilation 64

4.6 The Two-dimensional Lorentz Transformation 65

4.7 Transformation of Velocity 68

4.8 The Lorentz Contraction 69

4.9 Composition of Lorentz Transformations 69

4.10 Rapidity 71

4.11 *The Lorentz and PoincaréGroups 71

5．Lorentz Transformations in Four Dimensions 75

5.1 Coordinates in Four Dimensions 75

5.2 Four-dimensional Coordinate Transformations 76

5.3 The Lorentz Transformation in Four Dimensions 79

5.4 The Standard Lorentz Transformation 81

5.5 The General Lorentz Transformation 82

5.6 Euclidean Space and Minkowski Space 84

5.7 Four-vectors 84

5.8 Temporal and Spatial Parts 87

5.9 The Inner Product 87

5.10 Classification of Four-vectors 90

5.11 Causal Structure of Minkowski Space 92

5.12 Invariant Operators 93

5.13 The Frequency Four-vector 97

5.14 *Affine Spaces and Covectors 98

6．Relative Motion 103

6.1 Transformations Between Frames 103

6.2 Proper Time 104

6.3 Four-velocity 105

6.4 Four-acceleration 110

6.5 Constant Acceleration 113

6.6 Continuous Distributions 116

6.7 *Rigid Body Motion 117

6.8 Visual Observation 120

7．Relativistic Collisions 125

7.1 The Operational Definition of Mass 126

7.2 Conservation of Four-momentum 127

7.3 Equivalence of Mass and Energy 128

8．Relativistic Electrodynamics 133

8.1 Lorentz Transformations of E and B 133

8.2 The Four-Current and the Four-potential 136

8.3 Transformations of E and B 139

8.4 Linearly Polarized Plane Waves 141

8.5 Electromagnetic Energy 143

8.6 The Four-momentum of a Photon 144

8.7 *Advanced and Retarded Solutions 146

9．*Tensors and Isometries 151

9.1 Affine Space 152

9.2 The Lorentz Group 152

9.3 Tensors 154

9.4 The Tensor Product 155

9.5 Tensors in Minkowski Space 158

9.6 Tensor Components 159

9.7 Examples of Tensors 161

9.8 One-parameter Subgroups 165

9.9 Isometries 168

9.10 The Riemann Sphere and Spinors 169

Notes on Exercises 173

Vector Calculus 183

Bibliography 187

Index 189