Gott's proposal is hardly a practical one, and encounters a number of objections on physical grounds, e.g. infinitely long straight strings do not exist, while finite string loops threaten to collapse into black holes before they can be turned into time machines. But it establishes that time travel is a generic feature of Einstein's theory of relativity and not just a quirk of one scenario.
Gott has become so enthusiastic about time machines he even goes so far as to suggest the entire cosmos may be one, pointing out that the universe would then be able to create itself. Just as a time traveller could, in principle, go back and become his own father (or her own mother), so the universe could loop back in time and bring itself into existence in a big bang without the need for a mysterious origin from nothing. In that way the universe will in some sense always have existed, even though time itself remains finite in the past.
This survey by no means exhausts the different designs of time machine on offer. Most proposals involve some sort of ‘cutting-and-pasting’ job on spacetime, as if a superbeing wielding vast scissors hacks holes out of space, yanks and twists the exposed edges around and then glues them together again in a different pattern. Although these schemes are very artificial, they all describe possible spacetimes, and they serve as test beds for exploring the amazing physical consequences of time travel.
Reversing time
Time travel must not be confused with the equally fascinating (and equally speculative) topic of time reversal. Since at least the time of Plato, philosophers and scientists have mused about the idea of time ‘running backwards’. Actually this is a misnomer, since time itself doesn't run anywhere. It is more accurate to talk of physical systems running backwards in time, like a movie played in reverse. Could this happen? Could water flow uphill or broken eggs reassemble themselves?
To get some idea of what is involved, imagine a rigid box confining a dozen molecules of gas rushing about chaotically, colliding with each other and the walls of the box. Suppose at a certain moment all the molecules were crowded together in one corner. This arrangement wouldn't last long, as the speeding molecules bounced and scattered each other across the available space. The transition from ‘crowded’ to ‘distributed’ provides an ‘arrow of time’ that serves to distinguish past from future. The existence of many such transitions in the world about us gives the impression that time has a definite direction associated with it. Time reversal would then involve such things as widely distributed molecules of gas rushing into one corner of the box together. Is such a thing credible? It certainly is. One would expect that after a long enough duration, a dozen randomly moving molecules might find themselves revisiting one corner of the box together, purely by chance. In fact, it can be proved mathematically that such occurrences must happen repeatedly.
Of course, it's one thing for a handful of molecules to ‘go backwards’, quite another for the entire universe to reverse its normal behaviour. The wait needed for things to get back to their starting arrangement grows rapidly with each extra particle involved. A typical room contains more than a trillion trillion molecules of air, which would take vastly longer than the age of the universe to congregate spontaneously in one corner, so there is no need to worry about suddenly being left gasping for breath. What this means is that whilst in principle the world could return to the state it had in, say, 1900, it is exceedingly unlikely to do so in our lifetime unless there's some inbuilt cosmic conspiracy among the countless constituent particles.
Some physicists have conjectured that there may be just such a conspiracy programmed into the initial conditions of the universe, which would compel the entire cosmos to eventually revisit its starting condition in the big bang. We probably wouldn't know if all the particles in the universe had been cleverly programmed to find their way back one day, thereby re-creating a past state. If this bizarre reversal were to happen, it would differ from time travel of the sort I have been discussing in this book in a fundamental way. Time reversal means re-creating the past, not visiting it. If the universe did run backwards, so too would human brain activity. We wouldn't see the great cosmic movie going in reverse, with stars sucking in light and black holes spewing out gas, because our minds and senses would be in reverse gear too. In short, living in a universe in which ‘time runs backwards’ would be no different from living in the one we now observe.
Epilogue
Why study time travel? The subject has provided fertile soil for novelists over the last century, cropping up repeatedly in both mainstream and science fiction. It has also provoked an extended (and rather confused) debate among philosophers about the nature of time and the logical contradictions that seem to occur when travel into the past is considered. Mostly, however, professional scientists have given the subject a wide berth – until recently. Now, research into time travel has become something of a cottage industry in the theoretical physics community. Some people find this surprising. We have seen how it still seems rather fanciful, drawing upon extremely speculative ideas of wormholes, cosmic engineering and exotic forms of matter. How can professional scientists justify spending valuable time and research funds on such a frivolous topic?
Of course, there is no denying it is fun, and that some scientists treat the subject as an intellectual game. But there is a serious side to it, too. The ‘thought experiment’ is a time-honoured part of the scientific process. It works by the scientist dreaming up a scenario, which may appear at the time to be fantastical, in order to push current theories to their outer limits. The purpose in so doing is to expose any logical flaws or inconsistencies in the theory. Thought experiments enabled Galileo to deduce the law of falling bodies by pure reasoning alone. They also led Einstein to correctly predict the time dilation effect. In the 1930s, thought experiments such as the one associated with the famous Schrödinger cat paradox played an important role in clarifying the meaning of quantum mechanics. Significantly, advances in technology have enabled many thought experiments to now be performed as real experiments.
Just because time travel seems doubtful, or even impossible, to us today, doesn't mean we can ignore its implications. It may be that easier ways to build a time machine will be discovered, ways that would not require the resources of a supercivilization. But the very possibility of visiting or signalling the past presents a serious challenge to our understanding of physics, regardless of whether or not time travel ever becomes a practical proposition. Researchers agree that any attempt to make a time machine would almost certainly generate dramatic quantum vacuum effects, the consequences of which cannot be fully explored without a tractable and reliable theory of quantum gravity. Since achieving such a theory is currently a major priority among theoretical physicists, the study of time loops and the resulting illumination of the deep causal structure of the universe is very timely, so to speak.
Part of the fascination of time travel concerns the stark paradoxes that threaten as soon as travel into the past is considered. The purpose of science is to provide a consistent picture of reality, so if a scientific theory produces genuinely paradoxical (rather than merely weird or counter-intuitive) predictions, that is a very good reason for rejecting the theory. As we have seen, time travel is replete with paradoxes. At the moment, opinions differ markedly on how to deal with them. Perhaps causal loops can be made self-consistent. Perhaps reality consists of multiple universes. Or maybe our description of nature must be radically revised altogether. On the other hand, there may be no way to evade the paradoxical nature of time travel, and we shall be obliged to invoke Hawking's chronology protection conjecture (see p. 124) and discard all theories that permit travel into the past.
Most recent attempts to provide a quantum description of gravity are formulated within the broader context of a completely unified theory of physics, in which all the particles and forces of nature, along with space and time, are amalgamated in a common mathematical scheme. Fashionable among these ‘theories of everything’ are superstrings, and the more comprehensive sch
eme known cryptically as M-theory.
It is fascinating to speculate that chronology protection could be a global principle of nature on a par with, say, the second law of thermodynamics. We might even compile a list of cosmic taboos:
No time machines!
No perpetual motion machines!
No naked singularities!
etc.
and use this list as a filter for physical theories. Any theory that did not respect all the taboos on the list should be rejected. That would be an excellent way of culling contender theories. If the list is long enough, it may happen that only one ‘theory of everything’ would pass through the filter. We would then know the answer to the ultimate scientific question: Why this universe rather than some other?
Bibliography
Non-fiction
Al-Khalali, Jim. Black Holes, Wormholes & Time Machines, Institute of Physics Publishing, Bristol, 1999. A good, clear introduction to relativity, cosmology and gravitation, with a large section on time travel.
Berry, Adrian. The Iron Sun, Jonathan Cape, 1977. An early speculation about crossing the universe using a black hole/wormhole.
Davies, Paul. About Time, Penguin, London, 1995. An in-depth survey of the subject of time in its many aspects.
Deutsch, David. The Fabric of Reality, Penguin, London, 1997. An exposition of the many-universes interpretation of quantum mechanics, including its relevance for time travel.
Gott III, J. Richard. Time Travel in Einstein's Universe, Houghton Mifflin, Boston, 2001. A good technical summary of time travel, with special emphasis on the cosmic strings model.
Greene, Brian. The Elegant Universe, Norton, New York, 1999. A lucid account of recent attempts to unify the fundamental forces and particles of nature.
Novikov, Igor D. The River of Time, Cambridge University Press, Cambridge, 1998. A very readable account of relativity. Includes a section on time travel.
Nahin, Paul J. Time Machines, AIP Press, New York, 1993. A fascinating survey of time travel in fiction and non-fiction. Many references.
Pickover, Clifford. Time: a traveller's guide, Oxford University Press, Oxford, 1999. A readable survey.
Thorne, Kip S. Black Holes & Timewarps, Norton, New York, 1994. An extensive, detailed account of the general theory of relativity, black holes and wormholes by one of the key players. Many references to the original literature.
Wheeler, John A. A Journey into Gravity and Spacetime, Scientific American Library, New York, 1990. From the man who coined the terms ‘black hole‘, ‘wormhole‘, ‘spacetime foam’ and much else.
Will, Clifford. Was Einstein Right?, Basic Books, New York, 1986. An excellent introduction to the theory of relativity and experimental tests thereof.
Fiction
Benford, Gregory. Timescape, Spectra, New York, 1996, reissue. Written by a professional physicist, this award-winning science-fiction story includes this author as a character!
Benford, Gregory. Cosm, Orbit, London, 1998. A hard sci-fi story about the creation of a baby universe in the laboratory, initiated by a heavy-ion collision at the Brookhaven National Laboratory.
Bradbury, Ray. ‘A sound of thunder’, in: The Stories of Ray Bradbury, Alfred A. Knopf, New York, 1980. Short story illustrating how the future depends delicately on small details of past states.
Crichton, Michael. Timeline, Random House, New York, 1999. Drawing upon ideas of quantum wormholes, Crichton weaves an action-packed time travel drama, with an attempt at a self-consistent history.
Sagan, Carl. Contact, Simon & Schuster, New York, 1985. The novel that launched time travel as a serious topic.
Wells, H. G. The Time Machine and Other Stories, Penguin, London, 1946. The classic, founding story by the master himself.
Technical
Gödel, K. ‘An example of a new type of cosmological solution of Einstein's field equations of gravitation’, Reviews of Modern Physics, 21 (1949), 447.
Morris, M. S. and Thorne, K. S. ‘Wormholes in spacetime and their use for interstellar travel: a tool for teaching general relativity’, American Journal of Physics, 56 (1988), 395.
Roman, T. A. ‘Inflating Lorentzian wormholes’, Physical Review D, 47, (1993) 1370.
Tipler, F.J. ‘Rotating cylinders and the possibility of global causality violation’, Physical Review D, 9 (1974), 2203.
Visser, Matt. Lorentzian Wormholes from Einstein to Hawking, AIP Press, New York, 1995.
Index
Figures in italics indicate illustrations.
Amis, Kingsley 1
antigravity x, 68, 70–71, 72, 88, 124, 127
antimatter 3
Aquila constellation 23
‘arrow of time’ 131
‘atom smashers’ 15
atomic clocks 10, 12
atomic orbits 85
Back to the Future (film) xi, 3, 106
big bang 36, 77, 85, 126, 132
billiards 110–11, 116–17
black holes x, 3, 38, 132
blackness of 43–4
and cosmic strings 129
emptiness of 41–3
how to make a black hole 39, 41–5
and light 68
and negative energy 95, 96
and singularities 54, 55, 62–3, 68
size of 39, 41
spacewarp 49, 52
spaghettification 60, 61
spinning xi, 58, 62, 63, 65
Bradbury, Ray: ‘A Sound of Thunder’ 107
Brookhaven National Laboratory, Long Island, New York 85
Casimir, Hendrik 89, 90
Casimir effect xi, 85, 89, 91–2
causal loops 106–8, 111, 114, 116, 119, 123–4, 125, 135
causality 31, 33, 38, 116
centrifugal force 58, 62
changing the past 105–11
chronology horizon 125
chronology protection hypothesis xi, 123–6, 135, 136
clocks
atomic 10, 12
and elastic time 9–10
and gravity 18
hydrogen maser 18
on a neutron star 23
purpose of 4
and slowing up time 23–4
and wormholes 100–101
collider 77, 80–86
conservation laws 113
Contact (film) 65, 72
cosmic censorship hypothesis 63, 65, 116
cosmic rays 15
cosmic repulsion force x, 70
cosmic string time machine xi, 126–7
cosmic strings 126
crab nebula 20, 25
Crichton, Michael: Timeline xi
crystals 94
Cygnus X-1 xi
Deutsch, David 114, 116, 121, 123
differentiator 77, 99–100
double images 127, 128
Dr Who (BBC television series) xi, 3
duplicating entities 111, 112, 113
E=mc2 equation 24, 26, 27–8, 71
Earth
geometry on a curved surface 46, 47
gravitational field of 95
gravity diminishes with height 60
Mercator's projection 74
Einstein, Albert 8
concept of time x, 4–5, 7
E=mc2 equation 24, 26, 27–8
and Gödel's rotating universe model 36, 38
time dilation 12, 15, 134
see also under relativity
Einstein rings 49 50
Einstein-Rosen bridge x, 51, 53
electrons
collision with protons 117, 119–20
and virtual photons 85
and wormholes 99
Eliot, T. S. 104
energy
borrowed 82, 91
kinetic 27
and mass 24, 25, 26
mass as a form of energy 27
negative 71–2, 89, 91–5, 93, 96, 98,124
posi
tive 71, 72, 94
radiated 96
zero 71, 91
entropy 114
Equator 46, 47
Euclid 45–6
Everett, Hugh, III xi
falling bodies, law of 134
field excitations 89
Flamm, Ludwig x, 51
Foster, Jodie 65, 67–8
fourth dimension 28
free will 108
Fulling, Stephen 92, 96
galaxies
and black holes 41
Einstein rings 49
spinning 36
Galileo Galilei 24, 57, 134
general theory of relativity x, 17–18, 23, 35, 36, 38, 65, 67, 70, 71, 126
geometry, rules of 45–6
gluons 85
Gödel, Kurt xi, 36, 37,126
Gott, J. Richard, III xi, 126, 129
gravitational fields 42, 43, 49, 51, 57, 72, 95, 98, 100, 125, 126
gravity
and antigravity 70
black hole 49
and centrifugal force 58
and clocks 18
effect on time x, 17–18, 20, 21, 23,43
and falling bodies 55, 57
and pressure 126, 127
quantum 125–6
at surface of object 20, 42
and space 45, 72
Hafele, Joe 10, 12