Table of Contents

Publisher's Note vii

Introduction Roger Penrose ix

Special Preface xvii

Feynman's Preface xxiii

1 Vectors 1

1-1 Symmetry in physics 1

1-2 Translations 2

1-3 Rotations 5

1-4 Vectors 9

1-5 Vector algebra 12

1-6 Newton's laws in vector notation 15

1-7 Scalar product of vectors 18

2 Symmetry in Physical Laws 23

2-1 Symmetry operations 23

2-2 Symmetry in space and time 24

2-3 Symmetry and conservation laws 29

2-4 Mirror reflections 30

2-5 Polar and axial vectors 35

2-6 Which hand is right? 38

2-7 Parity is not conserved! 40

2-8 Antimatter 43

2-9 Broken symmetries 46

3 The Special Theory of Relativity 49

3-1 The principle of relativity 49

3-2 The Lorentz transformation 53

3-3 The Michelson-Morley experiment 54

3-4 Transformation of time 59

3-5 The Lorentz contraction 63

3-6 Simultaneity 63

3-7 Four-vectors 65

3-8 Relativistic dynamics 66

3-9 Equivalence of mass and energy 68

4 Relativistic Energy and Momentum 73

4-1 Relativity and the philosophers 73

4-2 The twin paradox 77

4-3 Transformation of velocities 79

4-4 Relativistic mass 83

4-5 Relativistic energy 88

5 Space-Time 93

5-1 The geometry of space-time 93

5-2 Space-time intervals 97

5-3 Past, present, and future 99

5-4 More about four-vectors 102

5-5 Four-vector algebra 106

6 Curved Space 111

6-1 Curved spaces with two dimensions 111

6-2 Curvature in three-dimensional space 123

6-3 Our space is curved 125

6-4 Geometry in space-time 128

6-5 Gravity and the principle of equivalence 129

6-6 The speed of clocks in a gravitational field 131

6-7 The curvature of space-time 137

6-8 Motion in curved space-time 137

6-9 Einstein's theory of gravitation 141

Index 145

About Richard Feynman 153