H Dieter Zeh
Time Travel in Einstein's Universe: The Physical Possibility of
Travel Through Time
J Richard Gott
2001 Weidenfeld and Nicolson 302pp £18.99/$25.00hb
Science-fiction writers have long been fascinated by the idea of time travel. H G Wells, for example, wrote his classic story The Time Machine in 1895 -- well before Einstein's discovery of relativistic spacetime. Unfortunately for science-fiction writers, you cannot "move" in Newtonian absolute time for logical reasons, since motion is defined as change with time. Returning to the past would require time itself to be cyclic -- a concept that, according to Leibniz, would be appropriate if the whole universe returned exactly to a former state. This would in general be inconsistent with the laws of motion, and would violate the second law of thermodynamics.
However, the discovery of relativity -- with its concept of "proper times" -- opened up novel possibilities for time travel. Einstein's general theory of relativity allows spacetimes with "closed time-like curves", or CTCs. These are pathways through curved spacetime in which proper time loops back on itself into the past. While this situation still leads to consistency problems (with the dynamical laws) as far as the motion of matter is concerned, spacetime is dynamical, too, in Einstein's universe. It evolves in interaction with matter, controlled by a global time co-ordinate the progression of which may be locally chosen at will. In order to explain the second law and the causal appearance of the world, this evolution of the universe is assumed to have started with an initial condition of low entropy. But can such an evolution lead to spacetimes with CTCs, and how are their consistency problems then resolved?
This new book by Richard Gott -- a cosmologist at Princeton University in the US -- discusses the problem of time travel in Einstein's universe in a way that even the lay reader can understand. Gott, who is an expert in the field, begins his story by discussing ideas behind many well-known science-fiction stories and movies, which were often developed in co-operation with physicists. Many of these stories offer clever solutions to consistency problems, but, in doing so, are more like detective stories. They construct a logically consistent web based on those events that are explicitly mentioned, neglecting everything else that might be relevant in reality.
Some physicists play similar games, studying the possibility of recurrent states in closed deterministic systems, such as balls moving on an ideal billiard table. But are such systems closed in reality? What about tiny distortions, such as collisions of the balls with air molecules? Even more important is the environmental quantum effect of "decoherence". It would, for example, seriously affect objects that are assumed to exist solely on a closed time-like curve. As we need something that prevents a time traveller from committing suicide after saying hello to an older version of himself, would it not be more "physical" to conjecture that the second law must break down in the presence of CTCs? (This would prevent living systems from existing at all on such a curve.) In any case, this part of the book is thought provoking and fun to read!
After explaining, without the use of equations, the major topics of relativity (including the twin paradox), Gott comes to the central part of his book: time travel to the past in the context of general relativity. This calls for exotic spacetimes, which he manages to explain in an intuitive and non-mathematical way. Here you will learn about Gödel's universe, worm holes, and what a warpdrive really is. The rule of the game for Gott is always "in principle". Everything goes provided it is compatible with the laws of physics -- including the idea of super-civilizations that can accelerate a whole galaxy.
Gott's description of a time machine that operates by means of two cosmic strings is a masterpiece of how to present mind-boggling things in a simple way. He also mentions why such situations may have to remain hidden behind spacetime horizons in reality. This is one of several arguments that Stephen Hawking has used to conjecture that "chronology is protected". Nature's causal structure may be stronger than all super-civilizations. So I am tempted to compare the design of a time machine with that of a perpetual-motion machine: an instructive activity if done consistently. It's all great intellectual fun -- and there is much to be learned about non-trivial spacetime geometries.
Another problem with Gott's approach is that the fundamental laws are not completely known, and we are forced to enter the realm of hypothetical physics. Since the spacetime "stage" is only part of the game, we may also require matter to be exotic, which would involve negative energy, superstrings, M-theory and other strange things. These novel physical concepts are mathematically exciting, but none of them has yet been confirmed to apply to our empirical world. On the other hand, quantum concepts may become relevant on the cosmic scale.
Although a full theory of quantum gravity does not exist, some of its general consequences can well be taken into account. In particular, quantum gravity must postulate the existence of superpositions of different curvatures -- analogous to Schrödinger's superposition of a live and dead cat. While we may now understand why such "classical components" of a conceivable superposition appear as independent "worlds", they must be expected to act "coherently" under extreme conditions. David Deutsch even suggested that they might co-operate to resolve some consistency problems arising from CTCs. However, this suggestion is in no way supported by the theory, and thus appropriately listed in Gott's chapter on science fiction.
In quantum field theories that contain gravity, the universal superposition (or wave function) obeys a time-less Schrödinger equation. The concept of time can only "emerge" together with quasi-classical spacetimes, though obviously not as a process in time. Deep novel conceptual problems arise in this way. Thus, when cosmologists construct exotic classical spacetimes, such as closed time-like curves or Gott's self-creating universe, I am again reminded of those detective stories that simply neglect the "rest of reality": quantum theory in this case. So far, only der Herr Gott knows -- as Einstein would have put it -- how (or indeed whether) the universe began.
In spite of these general criticisms, I am sure that readers will not only enjoy this book, but also find it informative and a source of inspiration. My only advice would be to tell any non-physicists for whom you buy this book that Richard Gott is being a little too optimistic on some fronts. And you'd better not put any money on Gott's method of predicting the future, even though he correctly "foresaw" the fall of the Berlin wall!
H Dieter Zeh is now retired and was professor of theoretical physics
at the University of Heidelberg, Germany, www.zeh-hd.de