Ontology of Spacetime (eBook)

Cover 1
Contents 6
List of Contributors 8
Introduction 10
References 19
Part I: The Ontology of Spacetime 20
The Implications of General Covariance for the Ontology and Ideology of Spacetime 22
Introduction 22
Two concepts of general covariance 23
Gauge symmetries 25
Implications of substantive general covariance: classical spacetime14 theories 31
The implications of substantive general covariance: quantum spacetime theories 38
Conclusion 40
References 41
The Disappearance of Space and Time 44
The ontology of spacetime after relativity 44
Space 47
Time 51
References 54
Spacetime Structuralism 56
Introduction 56
Manifolds and manifold substantivalism 56
Manifolds vs. twistors 58
The twistor correspondence and the Penrose transformation 60
Interpretation 66
Manifolds vs. Einstein algebras 69
Einstein algebras and their generalizations 69
Interpretation 72
Manifolds vs. geometric algebra 73
Geometric algebra 74
Interpretation 79
Spacetime as structure 80
Against fundamentalism 80
For structuralism 82
References 83
Minkowski Space-Time: A Glorious Non-Entity 86
Einstein and the space-time explanation of inertia 86
The nature of absolute space-time 89
The principle versus constructive theory distinction 92
The explanation of length contraction 97
Minkowski space-time: the cart or the horse? 102
Acknowledgments 105
References 106
Further Reading 108
Part II: Time, Becoming and Relativity: Compatibilist Positions 110
The Irrelevance of the Presentist/Eternalist Debate for the Ontology of Minkowski Spacetime 112
The presentism/eternalism Debate and its Ramifications in Current Philosophy of Time 112
The lack of contrast class for the expression ‘‘the reality of the future (past)’’4 114
Occasionalism to the rescue? 117
A second blow at the debate: the pluralistic nature of existence 118
A debate on which of the two senses of existence is more fundamental? 119
Platonism and presentism 122
Tensed existence and nested quantifiers 123
Consequences for the philosophy of time and the ontology of Minkowski spacetime 126
Acknowledgments 128
References 128
Presentism and Eternalism in Perspective 130
Presentism or eternalism? 131
Quantifiers or tense operators? 135
Presentism and eternalism 141
Acknowledgments 146
Minkowski Spacetime and the Dimensions of the Present 148
The problem of the present 149
The manifold, reality and becoming present 150
The relativized present 157
The punctual present 162
The extended present 165
Conclusion 170
Acknowledgments 172
References 172
Becoming, Relativity and Locality 176
Simultaneity and the now 176
Rotating frames 179
Non-rotating universes 182
The block universe and becoming 187
Conclusion: local becoming 191
References 194
How to Square A Non-localized Present with Special Relativity 196
1. 196
2. 201
3. 207
References 209
Philosophical Consequences of the Twins Paradox 210
The paradox 211
Three dimensions or four? 212
The metrization of spacetime using 3D elements 214
3D/4D equivalence 217
The ontology of spacetime 218
The nature of time 219
Acknowledgement 222
References 222
Part III: Time, Becoming and Relativity: Incompatibilist Voices 224
Is There an Alternative to the Block Universe View? 226
Introduction 226
Has Stein disproved the Rietdijk-Putnam argument? 230
Only the four-dimensionalist view is compatible with special relativity 233
Different descriptions versus different ontologies 244
Conclusions 245
Acknowledgments 246
References 246
Special Relativity, Time, Probabilism and Ultimate Reality 248
Eventism versus objectism 249
Special and general relativity, eventism and objectism 251
The true theory of everything and aim-oriented empiricism 253
Time and probabilism 255
In defence of objectism 258
Probabilistic dynamic geometry 259
Acknowledgements 260
Appendix: Fundamentally probabilistic quantum theory (PQT) 260
References 263
Temporal Presentness and the Dynamics of Spacetime1 266
Probabilism and spacetime structure 267
Generalizing simultaneity 270
Telepathic twins? 270
Invariant simultaneity as equality of action 271
Conflicts with relativity? 272
Covariant state reduction based on phase invariance 275
Quantum mechanics and the ontology of the future 277
Acknowledgements 278
References 278
Presentism and Quantum Gravity 282
Introduction 282
Fixed foliation quantum gravity 284
Presentism and relativity theory 285
Belot and Earman’s objection 288
Callender’s objection 291
Gödel’s modal argument 293
The future of presentism 295
Acknowledgments 297
References 297
Author Index 300
Subject Index 304