## Think Nonlocally

*Entanglement: The Greatest Mystery in Physics*. Amir D. Aczel. xviii + 284 pp. Four Walls Eight Windows, 2002. $25.

After the publication of so many popular books on quantum mechanics, it must now be common knowledge that the physics of the very small is strange and that even the greatest scientific minds of the last century have had trouble adapting to its implications. Going beyond the atomic scale, one can bring the strangeness of quantum physics into the realm of everyday objects by looking at systems that are correlated in a quantum mechanical way over macroscopic distances. This is what entanglement is about.

In *Entanglement: The Greatest Mystery in Physics*, Amir Aczel describes the history of this topic. After providing a standard story of the old quantum mechanics of Einstein and Bohr in the first part of the book, he chronicles the period that was ushered in by John Bell's 1966 locality theorem and is currently characterized by a flurry of work on topics such as quantum teleportation and quantum cryptography.

Bell's theorem tells us, in short, that the correlations between quantum mechanical systems cannot be explained by classical probability theory unless one accepts the existence of a nonlocal interaction that acts faster than the speed of light. This result has the form of a set of statistical inequalities—Bell's inequalities—that give limits on the experimental outcomes that can be explained with a classical, local theory. Quantum mechanics violates these inequalities and is thus intrinsically a nonlocal theory. More important, though, is the fact that one can experimentally verify these violations of locality, without having to assume that our current theory of quantum mechanics is absolutely correct. Such experiments have been done over the past 30 years with ever-increasing levels of thoroughness, and their outcomes tell us that not only quantum physics as we know it but also future, improved theories of nature will have to be nonlocal if they are to account for these observations.

The potential beauty of a popular book on entanglement lies in the fact that the conundrum this phenomenon poses can be explained to anyone with a basic understanding of statistics and the way physical theories are supposed to work. This is quite unlike the more common situation of the reader having to accept on good faith that it is really remarkable that, say, energy is quantized, that mathematics cannot be axiomatized or that pi is transcendental.

However, if entanglement is explained improperly (if it is "dumbed down" too much, for example), it will not seem different from traditional probability theory, and the attentive reader will wonder what all the fuss is about. One common, incorrect, explanation goes as follows: "It is possible to have two quantum mechanical particles whose properties are unknown. If, however, we measure the characteristics of the first particle, then by the laws of quantum physics we immediately know the characteristics of the second one as well. This happens without any interaction with the latter particle, and Einstein therefore called it 'spooky action at a distance.'" This fictional account, impressive as it may look on first sight, describes nothing more than a traditionally correlated system of two particles: When we choose between two closed hands, one of which holds a small prize, we face the same situation. The revelation that the hand we selected is empty tells us immediately that the other hand contains the prize, and vice versa. Clearly this does not qualify as "the greatest mystery in physics."

Although Aczel does not make the above mistake, he does not convey very well what is so mysterious about entanglement. In the first part of the book, he puts a lot of emphasis on merely the probabilistic nature of quantum mechanics, and he appears not to be particularly eager to tell readers how Bell's theorem led to the far-reaching conclusions that have been drawn from it. It is almost as an afterthought that Aczel tries to show how the outcomes of a relatively simple experiment force us to accept that nature does indeed work in a nonlocal way that defies common sense. And when he finally does so, late in the book, the essentials get buried under information about "half-silvered mirrors" and other experimental issues that, as previous popular texts have proved, are unnecessary for a proper understanding of the central idea.

Nevertheless, two groups of readers will likely enjoy this book. Those primarily interested in the dynamics of modern-day physics and its participants, rather than the science itself, will find much to their liking. There are many new stories in the post-Bell part of the book, where Aczel paints a lively picture of students, their ever-traveling professors and the reluctance of many to take the time to write up their research. This will no doubt sound familiar to the second audience for *Entanglement*: researchers who already know the physics involved. For these connoisseurs, the joy of this book will lie in reading about the history and background of the famous theorems and experiments they have studied. Where else can one learn that the experimental physicist Alain Aspect became interested in the foundations of quantum mechanics while doing social service in Cameroon in the 1970s?

But, as I've noted, for readers who want to learn about entanglement, nonlocality and Bell's inequality, this book falls short. They would be better off reading David Mermin's *Boojums All the Way Through* (Cambridge University Press, 1990), in which the mysteries of entanglement are explained with the clarity of thought they require and deserve.

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