The main focus of this volume is the question: is spacetime nothing more than a mathematical space (which describes the evolution in time of the ordinary three-dimensional world) or is it a mathematical model of a real four-dimensional world with time entirely given as the fourth dimension? The book contains fourteen invited papers which either directly address the main question of the nature of spacetime or explore issues related to it.
Author(s): Vesselin Petkov
Edition: 1
Year: 2007
Language: English
Pages: 292
Contents......Page 10
Preface......Page 6
1.1 Introduction......Page 17
1.2 Dimensions and Fundamental Constants......Page 18
1.3 Eddington and His Legacy......Page 21
1.4 Campbell and His Theorem......Page 23
1.5 Summary......Page 26
2.1 Introduction......Page 28
2.2 Geometry......Page 29
2.3 Classical Mechanics......Page 31
2.4 Special Relativity......Page 36
2.5 The 4D Formulation of Special Relativity......Page 38
3.1 Introduction......Page 45
3.2 Mathematical Space-Time......Page 48
3.3 Physical Space-Time......Page 52
3.4 Concluding Remarks......Page 58
4.1 The Block Universe......Page 62
4.2 The Unfolding of Time......Page 64
4.2.1 A Broken Wine Glass, Coarse-graining......Page 66
4.2.2 Friction, Coarse-graining......Page 68
4.2.3 Quantum Uncertainty......Page 70
4.2.4 Space-Time Curvature: Time-dependent Equations of State......Page 71
4.2.5 Emergent Complexity and Human Intentions......Page 73
4.2.6 Overall: A Lack of Predictability in the Real Universe......Page 76
4.3 A Realistic Space-Time Picture......Page 77
4.3.1 The Newtonian Case......Page 78
4.3.3 General Relativity......Page 79
4.4.1 Classical Cases......Page 83
4.4.2 Quantum Indeterminism......Page 84
4.4.4 The Far Future Universe......Page 85
4.5 Overall: AMore Realistic View......Page 86
4.5.1 Determinism and Becoming......Page 87
4.5.3 The Chronology Protection Conjecture......Page 88
4.5.5 Issues of Ontology......Page 89
5.1 Introduction......Page 93
5.2 The Space-Time of Relativistic Physics......Page 95
5.3 The 3D World vs. the 4D World......Page 102
5.4 The Observable World......Page 110
6.1 Introduction......Page 113
6.2 Reality of a Mirror Reflecting My Light Signal Now at a Distance......Page 114
6.3 Further Verification of the Above Thought Experiment......Page 116
6.4 As Influences from the Future Sometimes Appear (Retroaction), the Future Itself has to Exist......Page 118
6.5 A Thought Experiment Showing Here and Now that the Future Elsewhere Exists......Page 119
6.6 EPR is Highly Relevant to the Problems of Reality at a Distance and Determinism......Page 121
6.7 The Clock Paradox too Demonstrates that Physical Processes at a Distance Realistically Behave According to "merely metrical" Relativistic Relations......Page 122
6.8 Comments on Ohanian's Criticism......Page 124
7.1 Introduction......Page 126
7.2 Special Relativity is Impossible in a Three-dimensional World......Page 127
7.2.1 Relativity of Simultaneity is Impossible in a Three-dimensional World......Page 128
7.2.2 Conventionality of Simultaneity is Impossible in a Three-dimensional World......Page 134
7.2.3 The Existence of Accelerated Observers in Special Relativity is Impossible in a Three-dimensional World......Page 136
7.3.1 Length Contraction Would be Impossible if the Contracting Meter Stick were a Three-dimensional Object......Page 138
7.3.2 The Twin Paradox Would be Impossible if the Twins Were Three-dimensional Bodies......Page 142
8.1 Introduction......Page 147
8.2 Canonical Relativity......Page 150
8.2.1 ADM Formulation......Page 151
8.2.2 Relational Observables......Page 153
8.2.3 Recovering the Minkowski Background......Page 155
8.3.1 Singularities......Page 158
8.3.3 Resolutions......Page 159
8.4 Conclusions......Page 160
9. Relativity Theory Does Not Imply that the Future Already Exists: A Counterexample......Page 163
10.1 Introduction......Page 172
10.2 The Status of Becoming Within Special Relativity......Page 175
10.3 A Purely Heraclitean Generalization of Relativity......Page 180
10.3.1 Fresh Look at the Proper Duration in Special Relativity......Page 181
10.3.2 Physical Implications of the Generalized Theory of Relativity......Page 188
10.3.3 The Raison D'être of Time: Causal Inevitability of Becoming......Page 192
10.4 Prospects for the Experimental Metaphysics of Time......Page 196
10.4.1 Testing Heraclitean Relativity Using Cosmic Neutrinos......Page 197
10.4.2 Testing Heraclitean Relativity Using γ-ray Binary Pulsars......Page 198
10.5 Concluding Remarks......Page 202
11.1 Introduction......Page 205
11.2 Motivating the Geometric Interpretation: STR versus NRQM on the Dimensionality of the World......Page 206
11.3 The Relativity of Simultaneity and Nonrelativistic Quantum Mechanics......Page 209
11.3.1 NRQM: Space-Time Structure for Commutation Relations......Page 211
11.3.2 Heterodoxy: NRQM Does not Live in Galilean Space-Time......Page 213
11.3.3 Philosophical Significance......Page 214
11.4.1 Formalism......Page 215
11.4.2 Philosophical Significance......Page 217
11.5 Geometric Interpretation of NRQM......Page 218
11.5.1 Interpretive Consequences of Our Geometrical NRQM......Page 220
11.6 Conclusion: NRQM Resides in a 4D Block World......Page 223
12.1 Introduction......Page 225
12.2.1 The Kerr–Newman Metric......Page 226
12.2.2 The Hawking–Ellis Extended Interpretation......Page 227
12.2.3 Causality Versus Singularity......Page 228
12.3.1 Preliminaries......Page 229
12.3.3 Topological Structure......Page 231
12.3.4 Existence of Space-time Spinorial Structures......Page 232
12.4 Concluding Remarks......Page 233
13.1 Introduction......Page 236
13.2 Newton's Absolute Distant–Simultaneity......Page 242
13.3 Special Relativity: Conventional Distant Simultaneity......Page 244
13.4 General Relativity: Dynamically Determined Distant Simultaneity......Page 248
13.5 Conclusions......Page 260
14.1 Introduction......Page 268
14.2 Analogue Models of General Relativity......Page 269
14.3 A Simple Parabolic Model......Page 271
14.4 A Simple Elliptic Model......Page 273
14.5 Characteristic Surfaces......Page 274
14.6 Discussion......Page 275
