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

by John Earman

Overview

Almost from its inception, Einstein's general theory of relativity was known to sanction spacetime models harboring singularities. Until the 1960s, however, spacetime singularities were thought to be artifacts of the idealizations of the models. This attitude evaporated in the face of a series of theorems, due largely to Stephen Hawking and Roger Penrose, which 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 adopted the attitude 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 a number of foundational problems for physics and have profound implications for the philosophy of space and time. However, philosophers of science have been slow to awaken to the significance of these developments. Indeed, this is the first serious book-length study of the subject by a philosopher of science. 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.

Product Details

ISBN-13:	9780195095913
Publisher:	Oxford University Press
Publication date:	11/02/1995
Edition description:	New Edition
Pages:	272
Product dimensions:	6.50(w) x 9.50(h) x 1.13(d)

About the Author

University of Pittsburgh

Table of Contents

1.	Introducing Spacetime Singularities and Acausalities	3
1.1	Introduction	3
1.2	Spacetime singularities: In the beginning	5
1.3	Einstein's intolerance of singularities	11
1.4	Acausality and time travel	21
1.5	Singularities and acausalities together	22
2.	Defining, Characterizing, and Proving the Existence of Spacetime Singularities	27
2.1	Introduction	27
2.2	What is a spacetime singularity?	28
2.3	Extensions of Spacetimes	31
2.4	The received definition of singularities	33
2.5	The missing missing points	40
2.6	Naked singularities	44
2.7	What is a spacetime singularity (again)?	46
2.8	Singularity theorems	50
2.9	Singularities and quantum effects	56
2.10	Conclusion	58
2.	Cosmic Censorship	64
3.1	Introduction	64
3.2	Cozying up to singularities	65
3.3	Naked singularities and cosmic censorship	67
3.4	The cosmic censorship hypothesis	80
3.5	Is the cosmic censorship hypothesis true?	86
3.6	Black hole evaporation	90
3.7	What if cosmic censorship should fail?	92
3.8	A dirty open secret	97
3.9	Conclusion	98
4.	Supertasks	103
4.1	Introduction	103
4.2	Pitowsky spacetimes	105
4.3	Malament-Hogarth spacetimes	107
4.4	Paradoxes regained?	108
4.5	Characterization of Malament-Hogarth spacetimes	110
4.6	Supertasks in Malament-Hogarth spacetimes	114
4.7	Malament-Hogarth spacetimes and unresolved mathematical conjectures	116
4.8	Can [gamma subscript 1] carry out the assigned task?	119
4.9	Conclusion	119
Appendix	Proofs of Lemma 4.2 and Equation 4.4	120
5.	The Big Bang and the Horizon Problem	124
5.1	Introduction	124
5.2	Observability and light cones	125
5.3	What can we predict about the future?	128
5.4	Event and particle horizons	130
5.5	What is the horizon problem?	134
5.6	Reichenbach's principle of common cause	135
5.7	Particle horizons and common causes	137
5.8	Diagnosing the bellyache: Electromagnetism	140
5.9	Diagnosing the bellyache: Cosmic background radiation	142
5.10	Strategies for solving the horizon problem	147
5.11	Horizons in standard and inflationary models	150
5.12	Does inflation solve the horizon problem?	152
5.13	Conclusion	155
6.	Time Travel	160
6.1	Introduction	160
6.2	Types of time travel; backward causation	161
6.3	The causal structure of relativistic spacetimes	164
6.4	Why take Godelian time travel seriously?	167
6.5	The paradoxes of time travel	170
6.6	Consistency constraints	173
6.7	Therapies for time travel malaise	175
6.8	Non self-interacting test fields	179
6.9	Self-interacting test fields	183
6.10	Can we build and operate a time machine?	188
6.11	Conclusion	193
Appendix	Godel on the ideality of time	194
7.	Eternal Recurrence, Cyclic Time, and All That	203
7.1	Introduction	203
7.2	Tolman on eternal recurrence	204
7.3	Extending through the big bang and the big crunch	205
7.4	Finding God in the big bang	207
7.5	No recurrence theorems	210
7.6	Cyclic time	213
7.7	Conclusion	218
8.	Afterword	223
	References	228
	Index	247

Editorial Reviews

"...I enthusiastically recommend this important work to anyone, philosopher or scientist, interested in the foundations of spacetime. Not only does the book include discussions of fascinating topics previously neglected by philosophers, but it is also chock full of original arguments in both physics and philosophy."—The Philosophical Review

"This book should provide students of general relativity with a useful companion to the texts of Hawking and Ellis, Joshi and Clarke; professionals will also be interested in the different perspective it offers on work in global structure, and in its emphasis on points which can sometimes be lost in the detailed study of the mathematical structures involved." —Mathematical Reviews

"A worthwhile and recommended addition to collections on the philosophy of science."—Choice

"It is greatly to be hoped that this book, by setting out and elucidating the main problems, will stimulate more work in this area, so important for the understanding of the foundations of physics. Earman has shown in a most impressive way that the philosophy of science can develop only if it keeps closely in touch with the latest scientific advances."—International Philosophical Quarterly

From the Publisher