If quantum theory has you baffled, you're in good company, says Tony Hey.

Richard Feynman once memorably said: "I think I can safely say that nobody understands quantum mechanics." Albert Einstein to the end of his life refused to believe that quantum theory, with its intrinsic uncertainties and probabilities, was the last word on the structure of matter, and summed up his feelings in the much-quoted aphorism: "God does not play dice." Even Schrödinger, inventor of the equation that is to quantum mechanics what Newton's laws of motion are to classical mechanics, was so troubled by the implications of his own equation that he is quoted as saying: "If we are still going to have to put up with these damn quantum jumps, I am sorry that I ever had anything to do with quantum theory."

So, why did three of the smartest physicists of the 20th century, who certainly understood the mathematics of quantum mechanics, all have problems in coming to terms with the theory? The conceptual challenge posed by quantum theory is the subject of Amir Aczel's new book * Entanglement: The Greatest Mystery in Physics * .

For non-physicist readers, let me attempt to give some idea of the nature of quantum entanglement, which Schrodinger called "the characteristic trait of quantum mechanics". His equation described the evolution of a quantum wave, similar in form to the classical equation that describes how a water wave spreads out across a pond. But the new twist was that the quantum wave of an electron does not represent something tangible such as the height of a water wave, instead it gives a measure of the * probability * of finding an electron at any given point.

Many physicists are troubled by the inability of quantum mechanics, unlike Newtonian mechanics, to predict with certainty the trajectory of something as apparently particulate as an electron (a directed stream that bombards your television screen creating the moving image). Einstein and others preferred to think that there were some "hidden variables", that is an X-factor, for the electron such that, if we knew what they were, we could predict its trajectory with certainty and dispense with probabilistic "nonsense".

Quantum entanglement comes about as follows. In the famous double-slit interference experiment, a water wave passing through two slits in a barrier produces two waves X and Y on the other side that "interfere" with each other and produce patterns depending on whether the waves reinforce (constructive interference) or cancel each other out (destructive interference). Using the property of "superposition", the observed amplitude in the pattern is just (X+Y).

This same superposition holds true for quantum waves. But what happens when we regard the waves as particles? Particle one can be in state A or B, and particle two can be in state C or D. Using superposition, we can create entangled quantum states of the form (AC+BD). According to orthodox quantum mechanics, if we now make a measurement of the state of particle one, it must be either A or B. The remarkable property of entangled states is that if we find particle one in state A, we then know with certainty that particle two must be in state C, without making any measurement on particle two. Since particle two may be very distant from particle one, knowledge appears to have been transferred from one place to another instantaneously, faster than the speed of light. In the experiment of Nicholas Gisin, using entangled photon states separated by 10km of optical fibre under Lake Geneva, a signal from one end of the cable to the other, telling the as-yet-unmeasured photon two in what state photon one had been found, would have had to travel at 10 million times the speed of light!

Einstein called this conclusion "spooky action at a distance" and was the first to identify quantum entanglement as posing the most serious challenge to any "commonsense" view of the microscopic world. He preferred to believe that the photon states in this case were pre-determined "elements of reality", just as in our classical experience. To explain the quantum mechanical predictions for entangled states requires either information to travel between two separated quantum objects instantaneously or the existence of some "hidden variables" not yet taken into account by conventional quantum theory, which would remove the uncertainty from quantum mechanics and restore classical predictability.

This book is about the quest to devise experiments to distinguish between these two possibilities. The experiments were inspired by the Irish physicist (and something of a genius) John Bell, who in 1964 discovered an inequality that allowed such an experiment, at least in principle. As Aczel recounts, most of the physicists who pioneered laboratory tests of Bell's inequality were graduate students. In those days, research on the foundations of quantum mechanics was deeply unfashionable. When the French physicist Alain Aspect and Bell discussed possible experimental tests of his inequality, Bell asked Aspect if he had a tenured position, and Aspect replied that he was only a graduate student, to which Bell responded: "You must be a very courageous graduate student."

There can therefore be no question that the subject matter of this book is important, deep and challenging. Unfortunately, the book itself is something of a missed opportunity. There is no real attempt to give the reader any insight into Bell's inequality, the central pillar of the discussion. This omission is further compounded by an extraordinary absence of figure captions or explanations of the symbols used in the figures throughout.

Another irritation is the promise that "the ideas and concepts discussed are constantly being explained and re-explained in various forms". In my view, these repeated "explanations" are more like examples of sloppy copy-editing than illuminating writing.

Their level is also remarkably uneven. Key concepts such as causality and hidden variables are skipped over, while peripheral ones such as Hilbert space are defined obscurely twice in one page: "A Hilbert space is a linear vector space with a norm (a measure of distance) and the property of completeness", then a paragraph later: "A Hilbert space, denoted by H, is a complete linear vector space (where complete means the sequences of elements in this space converges to elements of the space)." There are also several incomprehensible statements such as "The noncommutativity of the multiplication on matrices has important consequences in quantum mechanics, which go beyond the work of Heisenberg", and a claim that one of Heisenberg's important contributions was "the concept of potentiality within quantum systems", which does not accord with my edition of Dirac's classic * Quantum Mechanics * .

Aczel's brief biographies of the major historical figures are both interesting and frustrating. Among several curiosities, there is the bizarre renaming of Ernest Rutherford as James. A throwaway remark claims that "the probabilistic interpretation of quantum mechanics was suggested by Max Born, although Einstein knew it first". Since Born was awarded the Nobel prize for his suggestion, this remark surely merits justification.

And to describe Bell as "quiet, polite and introspective" completely misses the passionate Celtic side of his nature: when confronted with superficial or woolly thinking, Bell could display something like the wrath of an Old Testament prophet.

The strongest feature of the book is undoubtedly the prominence given to the pioneering spirits who set out to test Bell's inequality: Aspect and Gisin, John Clauser, Michael Horne, Abner Shimony, Richard Holt and Stuart Freedman, and Daniel Greenberger and Anton Zeilinger. But surely, to quibble, Charles Bennett and his colleagues deserve a fuller treatment, along with the fields of quantum cryptography and quantum teleportation that they discovered? Also lacking is any discussion of the philosophical implications of the violation of Bell's inequality and of the triumph of quantum mechanics over hidden variables.

Quantum entanglement is a fascinating subject that deserves a full and careful treatment accessible to the general reader. Regrettably, this book does not measure up to the task.

Tony Hey is professor of computation, University of Southampton.

## Entanglement: The Greatest Mystery in Physics

Author - Amir D. Aczel

ISBN - 0 470 85046 9

Publisher - Wiley

Price - £16.99

Pages - 284

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