Space, Time, and Spacetime (eBook)

Vesselin Petkov received a graduate degree in physics from Sofia University, a doctorate in philosophy from the Institute for Philosophical Research of the Bulgarian Academy of Sciences, and a doctorate in physics from Concordia University. He taught at Sofia University and is currently teaching at Concordia University. He wrote the book "Relativity and the Nature of Spacetime" (Springer 2005) and edited the books "Relativity and the Dimensionality of the World" (Springer 2007), and "Minkowski Spacetime: A Hundred Years Later" (Springer, forthcoming). He is a member of the Governing Board of the International Society for the Advanced Study of Spacetime

Space, Time, and Spacetime 3
Preface 5
Contents 9
Contributors 11
Part I Minkowski's Representation of Special Relativity – Examples of Its Impact on the Twentieth Century Physics 13
The Minkowskian Background of Whitehead's Theory of Gravitation 14
1 Introduction 14
2 Why Whitehead Was Interested in Special Relativity 15
3 Cunningham 17
4 Silberstein and the Aristotelian Society 18
5 Minkowski's 1908 Papers 19
6 The Search for a Relativistic Theory of Gravitation 20
7 Eddington and de Sitter 23
8 Whitehead's Enquiry 26
9 Silberstein's 1918 Paper 28
10 The 1919 Solar Eclipse 29
11 Whitehead's Alternative Theory of Gravitation 31
References 33
The Experimental Verdict on Spacetime from Gravity Probe B 36
1 Space and Time Before Minkowski 36
2 Spacetime After Minkowski 41
3 Minkowski's Legacy in Higher Dimensions 44
4 Experimental Tests: An Unfinished Job 48
5 The Geodetic and Frame-Dragging Effects 54
6 Gravity Probe B 61
7 Summary 67
References 68
Rigidity and the Ruler Hypothesis 71
1 Rigid Rods and Rigid Spheres 71
1.1 A Toy Electron 71
1.2 A Rigid Rod 74
1.3 Equation of Motion for Points on the Rod 76
1.4 A Frame for an Accelerating Observer 76
1.5 Lengths Measured by the Rigid Rod 81
1.6 Properties of a Semi-Euclidean Frame 82
1.7 Behaviour of a Rigid Rod 83
1.8 Rigid Spheres and Instantaneous Transmission of Motion 86
1.9 Rigid Electrons and Rigid Atoms 90
1.10 A Note on the Pound–Rebka Experiment 92
2 Rigid Motion 97
2.1 General Motion of a Continuous Medium 98
2.2 Rigid Motion of a Continuous Medium 99
2.3 Rate of Strain Tensor 100
2.4 Examples of Rigid Motion 103
2.5 Rigid Motion Without Rotation 105
2.6 Rigid Rotation 108
2.7 Rigid Motion in Schwarzschild Spacetime 111
3 Conclusion 114
References 115
Minkowski Space and Quantum Mechanics 117
1 Introduction 117
2 Metrics and the Dirac Equation 118
2.1 General Formalism 119
2.2 A Gauge Approach to Mass 121
2.3 A Theorem 122
2.4 Covariance 123
3 Quantum and Classical Mechanics 124
3.1 Wave Equation of a Massless Particle 125
3.2 Quantum Mechanics and Hilbert Space 127
3.3 Classical Mechanics 129
4 Non-Geodesic Motion 131
4.1 Methodological Unification 132
4.2 The Hydrogen Atom 135
5 Conclusion 136
References 137
Relativity and Quantum Field Theory 138
1 Introduction 138
2 NQFTs and Particles 139
2.1 Classical Spacetimes vs. Minkowski Spacetime 139
2.2 Particle Interpretations 141
2.2.1 Particles in RQFTs? 142
2.2.2 Particles in NQFTs? 144
3 Newtonian Quantum Gravity 146
4 Intertheoretic Relations 149
5 Conclusion 154
References 154
Ether, the Theory of Relativity and Quantum Physics 156
1 Introduction 156
2 The Afshar Experiment 158
3 Consequences of the Afshar Experiment 160
4 Properties of the Wave Aspect of a Photon 161
5 Einstein's New Ether and Final Remarks 162
References 163
Part II Implications of Minkowski's Ideas for the Philosophy of Space and Time 165
Minkowski's Proper Time and the Status of the Clock Hypothesis 166
1 Proper Time, Local Time and Proper Length 167
2 Acceleration and Appeals to General Relativity 170
3 Acceleration and the Clock Hypothesis 172
4 Conclusion 184
References 185
Why Spacetime Is Not a Hidden Cause: A Realist Story 187
1 Introduction 187
2 Cause and Classical Inertial Motion 188
3 GR Space, Time and Spacetime 190
3.1 Free Fall in a Purely Gravitational Field 191
3.2 Light Bending 193
4 About Matter 193
5 A Parody of `Hidden Cause' 194
6 Conclusion 196
References 196
Structural Explanations in Minkowski Spacetime: Which Account of Models? 198
1 Introduction: Contractions, Dilation and Structural Explanations 198
2 The Debate on Models: The State of the Art 204
3 Minkowski's Model and Structural Explanations 207
4 Conclusion 210
References 211
Relativity of Simultaneity and Eternalism: In Defense of the Block Universe 213
1 Introduction 213
2 The Argument from the Relativity of Simultaneity 215
2.1 General Outline and Definition of Terms 215
2.2 
218 
3 Presentist Points of Contention 220
3.1 Deflationary Objections: No Presentist/Eternalist Distinction 220
3.2 Compatibilist and Incompatibilist Objections 221
4 Response to Objections 222
4.1 Defining Terms: Establishing a Presentist/Eternalist Distinction 222
4.2 The Transitivity of Reality 227
4.3 Against the Point Presentist 228
4.4 Preferred Foliations in Space-Time 231
4.5 The Spatial Presentist: Absurdity in Incompatibilist Presentism? 233
5 Conclusion 235
6 Appendix A: Against the Dynamical Interpretation of Special Relativity 235
7 Appendix B: Objection to RoS Argument by Meta-Time 237
8 Appendix C: A ``God's Eye'' View of Space-Time on Different Theories of Time 239
References 240
Minkowski Space-Time and Thermodynamics 242
1 Introduction: Geometric and Axiomatic Approaches 242
2 Axiomatic Approaches to Space-Time 243
2.1 Robb's Account 244
2.2 Carathéodory 246
3 Towards Dynamics 248
3.1 Dynamic Aspects 248
3.2 Provisos 248
3.3 Inferences to the Nature Space-Time 250
4 Irreversibility, Regularity and Invariance 251
4.1 Reichenbach & Grünbaum
4.2 Time & Invariance
5 Conclusion 256
References 258
No Presentism in Quantum Gravity 260
1 Introduction 260
2 Minkowski Spacetime and the Pressure from Special Relativity 262
3 Monton's Incompatibilist Defence of Presentism 268
4 The CMC Foliation Approach: A New Homefor Presentism? 273
5 Conclusion 278
References 280
Part III The Impact of Minkowski's Ideas Beyond the Philosophy of Space and Time 282
Space-Time, Phenomenology, and the Picture Theory of Language 283
References 292
The Fate of Mathematical Place: Objectivity and the Theory of Lived-Space from Husserl to Casey 293
1 Introduction 293
2 The Place Theory and the Subjective/Objective Dichotomy 294
2.1 Radical Spatial Subjectivism 294
2.2 Internal and External Constraints 296
2.3 Physical Space and Merleau-Ponty's Metric Conventionalism 296
3 The Place Theory and The Mathematization of Space 299
3.1 Husserl and the Early Phenomenological Influence 300
3.2 Contemporary Social Trends 302
4 Towards a Mathematical Conception of Subjective Space 304
4.1 Geometry and the Subjective 304
4.2 The Problem of Quantifying the Qualitative 307
5 A Concluding Case Study: Deleuze on Differential Geometry 310
References 312
Index 314