Foundations of Physics, Vol. 24, No. I1. 1994
Book Review Quantum Theory: Concepts and Methods. By Asher Peres. Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, xiv+446 pp., $129.00 (hardback); special price for course adoption (6 copies or more): $59.00. Imagine an oral comprehensive exam for admission into a physics Ph.D. program. The examinee jumps through hoops labeled "applications of quantum mechanics"--atomic and molecular spectroscopy, radiativetransition rates, scattering cross sections, specific heats of solids. Each examiner, unbeknownst to the examinee, is fervently thankful that he or she need not ever perform at such a ritual again. There is an uncomfortable lull in the questioning. Suddenly, one of the examiners pipes up, "What are the implications of the Bell inequalities? How have they been tested?" The examinee is struck dumb; none of his courses acquainted him with Bell inequalities. The other examiners, initially nonplussed, regroup after a hurried conference, their leader announcing, "Quantum mechanics works. Who cares about the foundations? A Ph.D. student needs to know how to u s e quantum mechanics. Nobody really knows what it means anyway." The exam ends in disarray as the student is excused from discussion of Bell inequalities. They're right, of course. The primary task of a physics Ph.D. student is to master the techniques for applying quantum theory to real-world problems. These techniques belong in the toolkit of every working physicist; their success teaches the astonishing power of the theory. Mastery of the techniques and experience of the theory's power often numb sensitivity to the genuine conundrums that lie at the foundations. Yet, some physicists remain curious, or even genuinely disturbed, about the conceptual foundations. For the advanced graduate student, familiar with quantum theory but not yet numbed by experience, who persists in asking foundational questions, for the working physicist who has a genuine interest in the meaning of quantum theory, for the odd course on foundations--for all these, Asher Peres's new book is made to order. 1583 0015-9018/94/1100.1583507.0o/o9 1994 Plenum Publishing Corporation
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A revolution, beginning in the 1960's, has occurred in thinking about the foundations of quantum theory. Moreover, recent developments in quantum information theory, quantum cryptography, and quantum computation hint that fundamental questions about quantum theory might turn out to be of practical importance. Peres surveys topics at the foundations of quantum theory. As one would expect from his papers, Peres's presentations are thorough, lucid, always scrupulously honest, and often provocative. In a field where the point of a theorem is to focus attention on the assumptions, Peres spells out assumptions carefully and explores their meaning and implications. The survey brings one up nearly to the present and leaves one with the sense of an active field where progress continues. Part I introduces the mathematical objects of quantum theory at a pedestrian level, but readers should not be misled. The intent is to stress the physical significance of abstract quantum concepts; the remainder of the book assumes considerably greater mathematical sophistication. Part II is the heart of the book. There Peres introduces the central conundrum: quantum theory is inconsistent with any "reasonable" realistic view of the world. He devotes one chapter to Bell inequalities and one chapter to contextuality and the Kochen-Specker theorem. In both cases he outlines carefully the role played by counterfactual reasoning--reasoning that uses the results of unperfomed experiments just as though they had been performed. Combining counterfactual reasoning with locality leads to Bell inequalities, which quantum theory violates. Combining counterfactual reasoning with the assumption that measurements are not contextual--i.e., that the answer to any yes-no question is independent of what other questions are asked along with it--leads to the Kochen-Specker theorem, which establishes that these assumptions are inconsistent with the Hilbertspace structure of quantum theory. In discussing counterfactual reasoning, Peres stresses its dependence on the assumption that we are free to perform any experiment we wish on a quantum system. Part III deals with a selection of topics: spacetime symmetries, information and thermodynamics, semiclassical methods, chaos and irreversibility, and the measuring process. Readers will find much of interest here, but I confine myself to mentioning just two topics. Peres develops the formalism needed to describe the most general measurements permitted by quantum theory; the necessary mathematical objects go by the unwieldy appellation of "positive-operator-valued measures." If you believe that all quantum measurements can be described by orthogonal projection operators or that there is no quantum description of simultaneous measurments of position and momentum, you're in the dark ages; Peres's treatment provides a path to the present. Peres's discussion of chaos and
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irreversibility is a g e m - - n o t because it solves the puzzle of irreversibility, but because Peres consistently refuses to take the easy way out. I was particularly impressed by his insistence that it won't do just to whine that it's difficult to reverse a system; one must find a way to quantify how difficult it is. This book provides a marvelous introduction to conceptual issues at the foundations of quantum theory. It is to be hoped that many physicists are able to take advantage of the opportunity. Carlton M. Caves
Department of Physics and Astronomy University of New Mexico Albuquerque, New Mexico 87131-1156
