1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Part I From Galileo to Minkowski
Part I Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 On the Impossibility of Detecting Uniform Motion . . 13
2.1 Aristotle's View on Motion . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Copernicus and Ptolemy's Arguments Against the Earth's Motion . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Galileo's Disproof of Aristotle's View on Motion . . . . . 17
2.4 Galileo's Principle of Relativity . . . . . . . . . . . . . . . . . . . . 25
3 Exploring the Internal Logic of Galileo's Principle of Relativity . . . . . . . . . . . . . . . . . . 29
3.1 On the Physical Meaning of Galileo's Principle of Relativity . . . . . . . . . . . . . . . . . . 30
3.2 On the Two Postulates of Special Relativity . . . . . . . . . 48
3.3 A Lesson from a Delayed Discovery . . . . . . . . . . . . . . . . . 51
3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4 Relativity in Euclidean Space and in Spacetime . . . . . 55
4.1 Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.2 Derivation of the Lorentz Transformations . . . . . . . . . . . 70
4.3 Four-Dimensional Distance and Three Kinds of Length 78
4.4 Y `Dilation' in Euclidean Space and Time Dilation in Spacetime . . . . . . . . . . . . . . . . . . . . 84
4.5 Length Contraction in Euclidean Space and in Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.6 The Twin Paradox in Euclidean Space and in Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.7 Addition of Velocities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.8 The Metric of Spacetime . . . . . . . . . . . . . . . . . . . . . . . . . . 106
4.9 On Proper and Coordinate Time . . . . . . . . . . . . . . . . . . . 107
4.10 Four-Velocity, Four-Momentum, and Relativistic Mass... 111
4.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Part II On the Nature of Spacetime: Conceptual and Philosophical Issues
Part II Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5 Relativity and the Dimensionality of the World: Spacetime Is Real . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.1 Has Special Relativity Posed the Greatest Intellectual Challenge to Humankind? . . . 122
5.2 Relativity and Dimensionality of the World . . . . . . . . . . 123
5.3 Length Contraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.4 Time Dilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.5 Relativization of Existence and the Twin Paradox . . . . 142
5.6 Why Is the Issue of the Nature of Spacetime So Important? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
5.6.1 Conventionality of Simultaneity . . . . . . . . . . . . . . 146
5.6.2 Temporal Becoming. . . . . . . . . . . . . . . . . . . . . . . . . 147
5.6.3 Flow of Time and Consciousness . . . . . . . . . . . . . 148
5.6.4 Free Will . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
6 Quantum Mechanics and the Nature of Spacetime . . 155
6.1 Quantum Mechanical Arguments Against the Reality of Spacetime . . . . . . . . . . . . . . . . . . . 157
6.2 Is Quantum Mechanical Probability Objective? . . . . . . 158
6.3 The Nature of the Quantum Object and the Nature of Spacetime. . . . . . . . . . . . . . . . . . . . . . . 160
6.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168
7 The Nature of Spacetime and Validity of Scientific Theories . . . . . . . . . . . . . . . . . . . 171
7.1 Reliability of Knowledge: Induction as Hidden Deduction . . . . . . . . . . . . . . . . . . . . 172
7.2 Correspondence Principle and Growth of Scientific Knowledge . . . . . . . . . . . . . . . . 177
7.3 Can an Accepted Scientific Theory Be Refuted? . . . . . . 180
7.4 Is a Final Scientific Theory Possible? . . . . . . . . . . . . . . . 182
7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
Part III Spacetime, Non-Inertial Reference Frames, and Inertia
Part III Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
8 Propagation of Light in Non-Inertial Reference Frames . . . . . . . . . . . . . . . . . . . 191
8.1 Acceleration Is Absolute in Special and General Relativity . . . . . . . . . . . . . . . . . . . 191
8.2 The Need for Two Average Velocities of Light in Non-Inertial Reference Frames . . . . . . . . . . . . . . . . . . . 193
8.3 Average Coordinate Velocity of Light . . . . . . . . . . . . . . . 197
8.4 Average Proper Velocity of Light . . . . . . . . . . . . . . . . . . . 201
8.5 Shapiro Time Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211
8.6 On the Gravitational Redshift . . . . . . . . . . . . . . . . . . . . . 213
8.7 The Sagnac Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
8.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
9 Calculating the Electric Field of a Charge in a Non-Inertial Reference Frame . . . . . . . . . . . . . . . . . . 225
9.1 Calculating the Potential of a Charge in a Non-Inertial Reference Frame . . . . . . . . . . . . . . . . . . 225
9.2 Common Physical Origin of the Liénard-Wiechert Potentials and the Potentials of a Charge in a Non-Inertial Reference Frame . . . . . . . . . . . . . . . . . . 229
9.3 Calculating the Electric Field of a Charge in a Non-Inertial Reference Frame . . . . . . . . . . . . . . . . . . 237
9.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
10 Inertia as a Manifestation of the Reality of Spacetime . . . . . . 243
10.1 Are Inertial Forces Real? . . . . . . . . . . . . . . . . . . . . . . . . . . 244
10.2 Inertial Forces Originate from a Four-Dimensional Stress Arising in the Deformed Worldtubes of Non-Inertial Bodies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246
10.3 Electromagnetic Mass and Inertia of the Classical Electron . . . . . . . . . . . . . . . . . . . . . . . . . . 252
10.4 The Standard Model and Inertia . . . . . . . . . . . . . . . . . . . 262
10.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
A Classical Electromagnetic Mass Theory and the Arguments Against It . . . . . . . . . . . . . . . . . . . . . . 273
B Calculation of the Self-Force . . . . . . . . . . . . . . . . . . . . . . . . 277
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287