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The Nature of Space and Time

ISBN: 0 691 03791 4 This book is almost unique in its category. Two world famous specialists are discussing in it one of the most fascinating problems of physics and philosophy, exchanging their views, criticising each other when necessary and leaving the reader to be a judge of their arguments. The book originated from a series of lectures given alternately by the two authors at the Newton Institute for Mathematical Sciences in Cambridge and it might serve as an example for other two-voiced works of this kind. The level is often far from elementary. We are told by Stephen Hawking at the beginning of his first lecture that this exchange will be technical, so that a basic knowledge of general relativity and quantum field theory is assumed of the reader. He is surely referring to the basic knowledge in Cambridge because I felt that what is required in general relativity would be called an advanced knowledge elsewhere. Roger Penrose is however less demanding and, in any case, not-so-professional readers will certainly be able to pick up here and there on the many beautiful ideas, deep results and fascinating questions. There are rather clear syntheses on various subjects: singularities in general relativity; cosmic censorship; namely how these singularities are kept out of sight of an external observer; entropy of black holes, showing them to be a source of basic randomness in our world different from the one in quantum mechanics; quantum radiation of black holes, which relates these two kinds of randomness; twistors: a mathematical representation of space-time where light rays become points and ordinary space-time points become Riemann spheres. One also learns about the `no-boundary condition', which could give uniquely specified initial conditions for the history of the universe. There is no doubt that these topics are very important and they are presented in a masterful way. They are restricted, however, to the contributions of the authors to the subject, either by one or the other or by both together. Perhaps this can only be the rule in this kind of dialogue, but other approaches are slighted or simply missing: string theory is mentioned in various places with somewhat disparaging remarks and non-commutative geometry is not mentioned. One can find a compensation, however, for this clearly personal approach when perceiving the active presence of a creative thought in both men so that even some one-sidedness can be seen as a condition for keeping concentration and unity in the pursuit of research. To speak of research is certainly more appropriate to the book than speaking of established science. This is due to the subject itself, which remains inevitably somewhat elusive and partly speculative because of the difficulties in getting down to predictions. Either they are not specific enough, or performing the necessary observations is still to difficult. Our fascination for the questions raised by space and time may be partly due to this lack of a definitive answer and one is not too surprised not to have received one when closing the present book. This reader feels enriched however in having his or her questions made sharper, more refined, with the possibility of dreaming (or even thinking) about the landmarks and the new avenues that have been found. The jacket of the book and the foreword by Michael Atiyah would let us expect even more. We are told that the present dialogue is a renewal of the classical one between Bohr and Einstein about realism. Admittedly, Penrose defines himself as a realist and Hawking as a positivist who asks only of science an account of observed facts. Whereas Einstein was a realist, Bohr would not accept being called a positivist and the analogy does not go in any case very far since the two present authors are willing to accept the intrinsic probabilism of quantum mechanics. Though there is some discussion of wave function reduction in the book, it is certainly not the best part of it if only because Penrose's proposals are still too premature for offering a sufficiently firm basis for a discussion. One would do better to wait. I enjoyed the book and more of its kind would be welcome.