*Elegance and Enigma* explores the foundations of quantum mechanics through interviews with experts. The interviewer poses seventeen questions throughout the book. Each chapter consists of the responses of all seventeen experts to one of the questions. The experts are physicists, mathematicians, and philosophers — all of them with significant expertise and published work in quantum mechanics.

Over most of the past eighty years, the abiding paradigm of quantum mechanics for the practitioner has been, in David Mermin’s phrase, “shut up and calculate”. Quantum mechanics as an operational theory has been so successful that few have felt the need to probe its foundations. And those foundations — well, they do seem kind of dicey. The majority view among physicists is probably “Who cares about foundations?” Richard Feynman took a more nuanced perspective: “We have always had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do …. Okay, I still get nervous with it … I cannot define the real problem, therefore I suspect there’s no real problem, but I’m not sure there’s no real problem.”

Since Niels Bohr’s formulation of the so-called Copenhagen interpretation, discussion of the foundations of quantum mechanics has been sporadic and limited to a small set of physicists, mathematicians and philosophers. Late in the twentieth century a few things happened that provoked a wider interest. For one thing, there were experimental tests of a thought experiment originally due to David Bohm, cleverly reformulated by John Bell (leading to Bell’s theorem and inequality). These provided apparent confirmation that nonlocality — “spooky action-at-a-distance” — is not only inherent in quantum mechanics but is experimentally true. (For a mathematician’s perspective, “Bell’s Theorem and the Demise of Local Reality” by Stephen McAdam in the November 2003 *American Mathematical Monthly* is highly recommended.) Einstein (whose paper with Podolsky and Rosen triggered Bell’s work) was never comfortable with quantum mechanics, but he came to be regarded as just another old guy who couldn’t give up his old-fashioned ideas. Today there are several outspoken younger physicists who agree that the theory is at best incomplete.

At first glance the chapters in this book appear to be accessible to anyone who knows a bit about quantum mechanics. There are, after all, no equations and not too much specialized language. On closer reading, at least a few of the chapters read like shop-talk among people who know the subject so well that they feel no need to fill in the background. The editor-interviewer does provide good introductions to each of the chapters, but non-expert readers may still feel that they are missing something in the interviewees’ responses.

The chapter on the “measurement problem” has this feel to it. There are two distinct points of view about measurement in quantum mechanics. The doctrine of quantum theory says the after-measurement state of a physical system is an eigenstate of the operator corresponding to the measured observable, and the outcome of the measurement is represented by the corresponding eigenvalue. However, when measurement is considered as an interaction between a physical system and a measurement apparatus, one ends up with an entangled state consisting of system plus apparatus. What a measurement means in this context is not clear at all. These two perspectives seem to be inconsistent, and neither by itself is fully satisfactory.

The chapter on quantum states takes up another apparently irresolvable question: are quantum states real or purely mathematical entities? Does it matter? Similarly with quantum probabilities: do they reside in the world, in some sense, or are they merely a measure of the completeness of our information?

This book is best suited for those with some level of experience in quantum mechanics, especially from a physicist’s perspective. For those with less background, it is fruitful ground for dabbling. The editor-interviewer’s comments are accessible and insightful. I’d also recommend a few other chapters: one where the experts describe how they became involved with quantum mechanics and its deep questions, their description of the “big issues”, of how beliefs and values influence their approach to foundational questions, and of the role of philosophy.

Bill Satzer (wjsatzer@mmm.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.