[In the review below, Preskill describes The Nature of Space and Time as "a succinct and clear technical account of the penetrating work and thought of two of our most brilliant and eloquent scientists."]

The clash between Niels Bohr and Albert Einstein over the meaning of quantum theory greatly clarified some fundamental issues, but to this day it is widely felt that their differences have never been satisfactorily resolved. It seems most appropriate, then, for two leading physicists of the current era to carry on the debate, and who could be better qualified than Stephen Hawking and Roger Penrose? Arguably, the two most profound developments in general relativity since Einstein were the introduction of the global analysis of causal structure by Penrose an the discovery of black-hole radiance by Hawking. Furthermore, both men are justly admired for their lucidity of their writings and lectures, and they disagree sharply on some fundamental questions.

The Nature of Space and Time is based on a Hawking-Penrose debate that took place in England, at the University of Cambridge, in the spring of 1994; the "debate" consisted of alternating lectures (three by each author) followed by a final joint discussion. The lectures revealed that there is much on which Hawking and Penrose agree. Both believe that black holes destroy information and hence undermine the foundations of quantum theory. Both argue that the origin of the second law of thermodynamics can be traced back to the extremely homogeneous conditions that reigned in the very early universe and that it is ultimately the task of quantum gravity to explain these initial conditions. They also seem to agree that general relativity, a beautiful and highly successful fundamental theory, sometimes fails to get the respect it deserves from the particle physicists.

Various points of disagreement are mentioned at least in passing. Hawking advocated the Euclidean path-integral approach to the fundamental issues of quantum gravity; Penrose is skeptical. Hawking offers the "no boundary proposal" (rooted in the Euclidean formalism to account for the initial conditions in the Big Bang; Penrose prefers the more phenomenological Weyl-curvature hypothesis. Hawking believes that the universe must be closed (as seems to be required by the no-boundary proposal); Penrose favors an open universe (which meshes more easily with his idea that quantum gravity should be formulated in terms of "twistors"). Hawking is an enthusiast of the inflationary-universe; Penrose is not.

There are two important issues over which the disagreements are more profound and more interesting. First, there is disagreement about the time-reversal invariance (or more precisely, CPT invariance) of the microscopic laws of nature. Hawking has a strong conviction that CPT is an inviolable symmetry. But Penrose believes that the quantum behavior of black holes shows otherwise; he argues that the laws of quantum gravity must make a fundamental distinction between past and future singularities. Further, they disagree about the measurement problem of quantum theory; Penrose insists that there must be a genuine physical mechanism underlying the "reduction of the state vector" in the measurement process, and he further proposes that quantum gravity plays an essential role in this reduction; Hawking rejects these ideas.

These are certainly fascinating questions, so it is rather disappointing that the authors do not flesh out their positions more fully. To understand Penrose's views clearly, I needed to reread his previous books, especially chapters 6-8 of The Emperor's New Mind and chapter 6 of Shadows of the Mind. The key problem repeatedly stressed by Penrose in The Nature of Space and Time is that we never perceive macroscopic superpositions—the famous conundrum of Schrodinger's cat. This emphasis surprises me. While the modern theory of decoherence is surely incomplete—it is largely based on heuristic arguments and oversimplified models—I think that there is a plausible explanation, within conventional quantum theory, for the fact that superpositions of macroscopically distinct states decohere very rapidly. Penrose thinks otherwise. There may be other more serious objections to the foundations of quantum theory, some of which are mentioned in Penrose's other books, but these receive scant attention here. Hawking, for his part, defends the status quo, but in so sketchy a manner as to provide little guidance for the perplexed.

I should not give the impression that this is a book about the measurement problem in quantum theory; the lectures largely address other issues: Hawking's three lectures concern global methods and singularity theorems; quantum black holes and information loss; and quantum cosmology, inflation and the origin of the anisotropy of the cosmic background radiation. These lectures are unapologetically mathematical, at an appropriate level for a graduate student in theoretical physics but quite beyond the grasp of the typical lay reader. Penrose's lectures on cosmic censorship, the measurement problem and twistors are less demanding than Hawking's (and about half as long), but they are also intended for a mathematically sophisticated audience. Advanced students and even some experts will appreciate, for example, Hawking's succinct summary of the ideas underlying the singularity theorems or Penrose's overview of the ideas motivating the twistor program.

There is much to savor in this slim volume, but as a dialogue on fundamental issues in quantum theory, it falls well short of expectations. A reader seeking an exposition of Penrose's unconventional views will do better to read his other books. For a well-presented defense of the conventional wisdom, I would recommend The Interpretation of Quantum Mechanics by Roland Omnes. Still, we should appreciate this little book for what it is—a succinct and clear technical account of the penetrating work and thought of two of our most brilliant and eloquent scientists.