Nothing in the world is easier than traveling in time. Just wait five minutes, and you will have moved that far into the future. It is even possible to get there faster; according to special relativity, observers undergoing acceleration experience the passage of less time between two events than do observers in free fall.

Time Travel in Einstein's Universe: The Physical Possibilities of Travel through TimeJ. Richard Gott IIIHoughton Mifflin, New York, 2001. $25.00 (291 pp.). ISBN 0-395-95563-7(This review appeared in the July, 2002 issue ofPhysics Today.)

The true excitement arises, however, with the possibility of traveling backward in time, a staple of science fiction. It is worth asking if such a journey is consistent with the laws of physics. In the absolute space-time of Newtonian mechanics, the answer is a definitive "No." Newtonian time marches relentlessly forward.

In special relativity, however, the notion of time is somewhat more flexible; clocks carried along different paths can measure different elapsed time intervals. Even in such circumstances, however, travelers are still moving locally more slowly than light, and consequently moving inevitably into the future.

General relativity preserves this feature--local movement at speeds below that of light--as observers move along timelike paths. The curvature of space-time, however, introduces the possibility of deforming the global geometry to allow what are called "closed timelike curves," paths that intersect themselves in the past. It is straightforward to find solutions to Einstein's equations that contain closed timelike curves. As a simple example, take empty Minkowski space and identify all spatial points at time *t*_{1} with the corresponding points at time *t*_{2}, to produce a cylindrical space-time in which particles at rest move on timelike loops.

The notion of closed timelike curves in the real world is hard to reconcile with our intuitive understanding of causality. Perhaps one can find global solutions to general relativity incorporating closed timelike curves. These, in effect, would be time machines. But it may be impossible to construct such a system in a local region of space. Theorems along these lines were proved by Frank Tipler in the 1970s. Tipler assumed that the energy density was never negative and showed that closed timelike curves could never arise in a local region without also creating a singularity. This was reassuring, as we could hope that both the singularity and the closed timelike curves were hidden behind an event horizon (although this was not part of the proof).

Interest in time travel was reinvigorated a little over a decade ago by the discovery of new space-times containing closed timelike curves: a wormhole solution discovered by Michael Morris, Kip Thorne, and Ulvi Yurtsever, and a solution with two parallel cosmic strings discovered by J. Richard Gott. The wormhole space-time requires negative energy densities, while the closed timelike curves in the cosmic string space-time do not originate in a local region. Both solutions are therefore consistent with Tipler's results, and these models spurred research into the possibility of time travel under more general conditions.

Gott's new book, *Time Travel in Einstein's Universe*, covers all this material in a readable way and at a popular level. As in recent books by Stephen Hawking, *A Brief History of Time* (Bantam Doubleday, 1988), Kip S. Thorne, *Black Holes and Time Warps* (W. W. Norton, 1994), Alan Guth, *The Inflationary Universe* (Perseus, 1997), and Brian Greene (*The Elegant Universe*, W. W. Norton, 1999), Gott personalizes the narrative by combining scientific exposition with the story of his own research. This approach can (and does) result in an idiosyncratic survey of the material. But it seems perfectly appropriate for a book aimed at general readers, who will gain more from such an honest account of the workings of science than they might from a strictly objective recitation of the facts.

After two introductory sections, Gott devotes three sizable chapters to topics loosely connected by the theme of time travel: 1) the creation of closed timelike curves in general relativity, 2) the possibility that the universe might originate in closed timelike curves, and 3) prediction of the future through application of the Copernican principle ("We are not special") to our relationship to the universe's current conditions.

The second of these topics, describing work in cosmology that Gott carried out with Li-Xin Li, is an interesting take on the problem of the universe's initial conditions, although their scenario is hard to evaluate without better knowledge of the early universe than we have. A third section describes an attempt to estimate the likely future duration of current conditions by presuming that we are observing them at a typical moment--neither in the first nor the last 2.5% of their lifetimes. As an example, the fact that the Internet is 33 years old leads us to predict, with 95% confidence, that it will last between another 10 months and another 1320 years. Such a level of precision is of little help to investors and planners; the method does, however, serve as a reality check against the temptation to extrapolate our current situation naively forward in time.

The test of a popular-level book is whether it will excite and educate the lay reader. The ideas discussed in this book are undoubtedly exciting and should appeal to a wide audience. The educational mission is less obviously fulfilled; Gott puts an effort into careful exposition, but he spends a great deal of time on issues unlikely to be of great public interest, such as the nature of various quantum vacuum states. I worry also that the initial explanation of the nature of space-time in special and general relativity was given short shrift; if readers do not fully follow the way time works in well-established contexts, it would be hard for them to understand the more exotic space-times.

Meanwhile, the question of what role closed timelike curves might play in the real universe remains embarassingly unclear. Very likely it will remain so until we achieve a fuller understanding of quantum gravity--or are visited by tourists from the future.

© 2002 American Institute of Physics