The New Quantum Age: From Bell’s Theorem to Quantum Computation and Teleportation,

Subtitles seem to be mandatory for popular science books, and the subtitle of *The New Quantum Age* tells us it covers topics “From Bell’s Theorem to Quantum Computation and Teleportation.” If I were in a position to suggest an edit to the subtitle, I would add “…but Mostly Bell’s Theorem.” The book provides a concise introduction to quantum mechanics and quantum information and gives an in-depth look at the history and science of the Bell inequalities. Author Andrew Whitaker shows his hand when he introduces John Bell as “undoubtedly the main hero of this book.” Although some other scientists appearing in the book are also labelled heroes, none gets quite as enthusiastic an endorsement, and none receives more than a fraction of the attention that Whitaker lavishes on Bell and his work.

*The New Quantum Age* is divided into three parts. Part 1, titled “The First Quantum Age,” gives a careful introduction to quantum mechanics as it was understood in the 1930s and culminates with a discussion of the famous 1935 Einstein-Podolsky-Rosen (EPR) paper. Part 3, “An Introduction to Quantum Information Theory,” gives a quick but dated overview of the basic results in the field of quantum information processing, including quantum computation. Sandwiched between the two and occupying more than half the book, part 2 is entitled “The Foundations of Quantum Theory,” but actually it is mostly about hidden variables and John Bell. Whitaker does offer a brief summary of non-hidden-variable approaches to quantum mechanics, but it is half-hearted. For instance, he devotes the same amount of space, roughly three pages, to the much more accepted many-worlds interpretation as he does to the fringe view that a local hidden-variable approach may still be possible.

The first two parts rise to a much higher standard of technical correctness than one normally finds in a popular book on quantum mechanics. Admittedly, that is not a high standard at all, but someone who thoroughly reads the first two parts of this book will have a pretty good lay understanding of the subject. Parts 1 and 2 have a number of typos and some statements I disagree with—inevitable, I think, in a book that talks seriously about interpretations of quantum mechanics—but I found nothing substantially incorrect.

The book’s accuracy comes with a price, as the technical parts can be tough going for a novice. The author eschews some of the usual tropes of popular science writing; in particular, his book is almost completely devoid of analogies. Personally, I am not that fond of analogies when explaining quantum mechanics, since they are invariably misleading in one way or another, but a few well-chosen ones can liven things up.

The author indulges in a good deal of philosophical hair-splitting. Some of it, such as the distinction between parameter independence and outcome independence, is helpful for understanding the material; some, such as the author’s insistence that the EPR paper was correct, is not. Also, the book is littered with formulas, mostly state vectors written as kets. Although perhaps sometimes abstract, none of the math in the book is in other respects more difficult than addition, but a reader unwilling or unable to parse statements containing mathematical symbols will not get far.

Unfortunately, part 3 is not as reliable as the first two parts. It contains several errors, mostly small but a few more significant. For instance, in the discussion on private-key cryptography, the author appears to confuse the one-time pad with DES, a now-retired private-key encryption protocol. The one-time pad is completely secure, independent of how much computer power the eavesdropper Eve can throw at the problem, so long as the sender Alice and the receiver Bob use a secret key that is as long as the message and is not reused. By contrast, DES can be broken with a concerted computational effort by Eve. Outdated portions in this section include the discussion of how to build a quantum computer.

*The New Quantum Age* fits into an unusual niche. It provides an exceptionally detailed look at the physics and the historical development of the notion that hidden classical variables underlie quantum indeterminacy, and it also carefully examines the major theoretical and experimental results bearing on it. And it does this at a level completely accessible to a layperson, albeit one who is willing to work to attain understanding. For someone interested in other interpretations of quantum mechanics or wishing to learn about quantum computation, this is not the place to go. But for those interested in hidden variable theories, *The New Quantum Age* provides an authoritative introduction.