Bangs, Crunches, Whimpers, and Shrieks: Singularities and Acausality in Relativistic Spacetimes

John Earman019509591X, 9780195095913, 9781423765233

Almost from its inception, Einstein’s general theory of relativity was known to sanction spacetime models harboring singularities, which involve a breakdown in the very fabric of space and time and, consequently, a failure of the known laws of physics. Until the 1960s, however, spacetime singularities were thought to be artifacts of idealizations of the models. This attitude evaporated in the face of work by Stephen Hawking and Roger Penrose, whose theorems showed that Einstein’s general theory implies that singularities can be expected to occur in a wide variety of conditions in both gravitational collapse and in cosmology. In the light of these results, some physicists began to believe that, since spacetime singularities are intolerable, general relativity contains within itself the seeds of its own destruction. Others hoped that peaceful coexistence with singularities could be achieved by proving a form of Roger Penrose’s “cosmic censorship” hypothesis, which would place singularities safely inside black holes. Whatever the attitude one adopts toward spacetime singularities, it is evident that they raise foundational problems for physics and have profound implications for the philosophy of space and time. However, philosophers have been slow to awaken to the significance of these developments. Now John Earman, the noted philosopher of science, offers for the first time a book-length study of the subject. It features an overview of the literature on singularities, as well as an analytic commentary on their significance to a number of scientific and philosophical issues.

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Table of contents :
Contents……Page 10
1.1 Introduction……Page 16
1.2 Spacetime singularities: In the beginning……Page 18
1.3 Einstein’s intolerance of singularities……Page 24
1.4 Acausality and time travel……Page 34
1.5 Singularities and acausalities together……Page 35
2.1 Introduction……Page 40
2.2 What is a spacetime singularity?……Page 41
2.3 Extensions of spacetimes……Page 44
2.4 The received definition of singularities……Page 46
2.5 The missing missing points……Page 53
2.6 Naked singularities……Page 57
2.7 What is a spacetime singularity (again)?……Page 59
2.8 Singularity theorems……Page 63
2.9 Singularities and quantum effects……Page 69
2.10 Conclusion……Page 71
3.1 Introduction……Page 77
3.2 Cozying up to singularities……Page 78
3.3 Naked singularities and cosmic censorship……Page 80
3.4 The cosmic censorship hypothesis……Page 93
3.5 Is the cosmic censorship hypothesis true?……Page 99
3.6 Black hole evaporation……Page 103
3.7 What if cosmic censorship should fail?……Page 105
3.8 A dirty open secret……Page 110
3.9 Conclusion……Page 111
4.1 Introduction……Page 116
4.2 Pitowsky spacetimes……Page 118
4.3 Malament–Hogarth spacetimes……Page 120
4.4 Paradoxes regained?……Page 121
4.5 Characterization of Malament–Hogarth spacetimes……Page 123
4.6 Supertasks in Malament–Hogarth spacetimes……Page 127
4.7 Malament–Hogarth spacetimes and unresolved mathematical conjectures……Page 129
4.9 Conclusion……Page 132
Appendix: Proofs of Lemma 4.2 and Equation 4.4……Page 133
5.1 Introduction……Page 137
5.2 Observability and light cones……Page 138
5.3 What can we predict about the future?……Page 141
5.4 Event and particle horizons……Page 143
5.5 What is the horizon problem?……Page 147
5.6 Reichenbach’s principle of common cause……Page 148
5.7 Particle horizons and common causes……Page 150
5.8 Diagnosing the bellyache: Electromagnetism……Page 153
5.9 Diagnosing the bellyache: Cosmic background radiation……Page 155
5.10 Strategies for solving the horizon problem……Page 160
5.11 Horizons in standard and inflationary models……Page 163
5.12 Does inflation solve the horizon problem?……Page 165
5.13 Conclusion……Page 168
6.1 Introduction……Page 173
6.2 Types of time travel; backward causation……Page 174
6.3 The causal structure of relativistic spacetimes……Page 177
6.4 Why take Gödelian time travel seriously?……Page 180
6.5 The paradoxes of time travel……Page 183
6.6 Consistency constraints……Page 186
6.7 Therapies for time travel malaise……Page 188
6.8 Non self-interacting test fields……Page 192
6.9 Self-interacting test fields……Page 196
6.10 Can we build and operate a time machine?……Page 201
6.11 Conclusion……Page 206
Appendix: Gödel on the ideality of time……Page 207
7.1 Introduction……Page 216
7.2 Tolman on eternal recurrence……Page 217
7.3 Extending through the big bang and the big crunch……Page 218
7.4 Finding God in the big bang……Page 220
7.5 No recurrence theorems……Page 223
7.6 Cyclic time……Page 226
7.7 Conclusion……Page 231
8. Afterword……Page 235
References……Page 241
C……Page 260
E……Page 262
G……Page 263
H……Page 264
L……Page 265
P……Page 266
S……Page 267
W……Page 269
Z……Page 270