The Book of Nothing
Page 35
33. The recently discovered microwave background radiation was sufficient to meet this requirement.
34. It is known that incomplete histories occur which are not accompanied by infinities of physical quantities, like density or temperature. However, whilst it is suspected that these examples are in some way atypical of solutions to Einstein’s equations, this has not been proven in general. The original theorem of Penrose was proved for the situation of a collapsing cloud of matter (like the expanding universe in reverse). Subsequently, Hawking and Penrose proved a version of the theorem which applies specifically to cosmologies. For a detailed survey, see S.W. Hawking & G.F.R. Ellis, The Large Scale Structure of Space-time, Cambridge University Press (1973).
35. J. Earman, Bangs, Crunches, Whimpers, and Shrieks: singularities and acausalities in relativistic spacetimes, Oxford University Press (1995).
36. If one interprets the lambda force as a vacuum energy in Einstein’s equations then it behaves like a form of matter that exhibits gravitational repulsion because its pressure p and density ρ satisfy the relationship p = −ρc2. Gravitational repulsion arises whenever matter satisfies the weaker condition 3p < −ρc2. The singularity theorems assume that 3p > –ρc2.
37. M. Eliade, The Myth of the Eternal Return; see also J.D. Barrow & F.J. Tipler, The Anthropic Cosmological Principle, Oxford University Press (1986).
38. It is very likely that these two singularities would be very different in structure. Irregularities tend to grow during the evolution of the Universe in its expanding phase. These irregularities will be amplified even further during the contraction phase and the final singularity should be extremely irregular.
39. The big assumption here is that nothing counter to the second law of thermodynamics occurs at the moments when the Universe bounces (or indeed, that any such ‘law’ is applicable).
40. This was first pointed out by R.C. Tolman in two articles, ‘On the problem of the entropy of the universe as a whole’, Physical Review, 37, pp. 1639–1771 (1931), and ‘On the theoretical requirements for a periodic behaviour of the universe’, Physical Review, 38, p. 1758 (1931). Recently, a detailed reanalysis was given by J.D. Barrow and M. Dbrowski, ‘Oscillating Universes’, Mon. Not. Roy. Astron. Soc., 275, pp. 850–62 (1995).
41. See, for example, E.R. Harrison, Cosmology: the science of the universe, Cambridge University Press (1981), pp. 299–300.
42. A. Swinburne, ‘The Garden of Proserpine’, Collected Poetical Works, p. 83.
43. F. Dyson, ‘Life in an open universe’, Reviews of Modern Physics, 51, p. 447 (1979).
44. J.D. Barrow & F.J. Tipler, The Anthropic Cosmological Principle, Oxford University Press (1986), chap. 10.
45. The absolute minimum amount of energy required to process a given amount of information is determined by the second law of thermodynamics. If ∆I is the number of bits of information processed, the second law requires ∆I ≤ ∆E/kTln2 = ∆E/T(ergs/K)(1.05×1016), where T is the temperature in degrees Kelvin, k is Boltzmann’s constant and ∆E is the amount of free energy expended. If the temperature operates at a temperature above absolute zero (T > 0, asrequired by the third law of thermodynamics), there is a minimum amount of energy that must be expended to process a single bit of information. This inequality is due to Brillouin.
46. See S.R.L. Clark, How to Live Forever, Routledge (1995).
47. See The Anthropic Cosmological Principle, op.cit., p. 668.
48. The current observations are indicating that this is not the case in our Universe. It appears to be destined to keep expanding for ever, locally, and if the eternal inflation scenario is true it will continue expanding globally as well. Recently, João Magueijo, Rachel Bean and I (‘Can the Universe escape eternal inflation?’, Mon. Not. Roy. Astron. Soc., 316, L41–44 [2000]) have found a way for the Universe to escape from accelerating expansion. If it contains a scalar field, which is falling in a potential energy landscape which descends steeply but has a small U-shaped crevice on it, with a local minimum, then the scalar field can pass through along this valley and produce a short period of inflation. It carries on up the slope and then continues to fall down the slope again. When this happens the expansion stops accelerating and reverts to the usual decelerated expansion that it experiences for most of its history. Potential landscapes with this shape have been identified in string theories at high energy. They were suggested for cosmological applications by A. Albrecht and C. Skordis, Phys. Rev. Lett., 84, pp. 2076–9 (2000), but they envisaged that they would lead to a state of never-ending inflation.
49. This must lie at least about thirty billion years in the future. It should be noted that it is possible for us to encounter a singularity in the future without this lambda energy decay, even if the expansion appears to be going to carry on for ever. There could be a gravitational shock-wave travelling towards us at the speed of light that hits us without warning.
Copyright © 2000 by John D. Barrow
All rights reserved under International and Pan-American Copyright Conventions. Published in the United States by Vintage Books, a division of Random House, Inc., New York.
Vintage and colophon are registered trademarks of Random House, Inc.
The Library of Congress has cataloged the Pantheon edition as follows: Barrow, John D., 1952–
The book of nothing: vacuums, voids, and the latest ideas about the origins of the
universe / John D. Barrow.
p. cm.
eISBN: 978-0-307-55481-9
1. Zero (The Number) 2. Vacuum. 3. Nothing (Philosophy) I. Title.
QA141.B36 2001 111′.5—dc21 00-058894
Author photograph © J. Pembrey
www.vintagebooks.com
v3.0_r2