Quantum theory is more than 100 years old and works exceedingly well in practice, but the arguments about its meaning, and what it implies for our picture of the physical universe, rumble on. After the Bohr-Einstein debate of the 1920s and 1930s, when the philosophical realism of Einstein was opposed by the subtle and elusive "complementarity" of Bohr's Copenhagen interpretation, it was accepted for some decades that Bohr had been triumphant. However, John Bell's work in the 1960s was a successful call for further investigation. Bell, though known as "the man who proved Einstein wrong", described himself as a follower of Einstein, and was central in questioning Copenhagen and encouraging the creation of novel interpretations.

Bell hoped that these interpretations would be based on good physics rather than on media-friendly but superficial or unconvincing speculation. At the Nobel Symposium in 1986, he contrasted three "romantic" quantum worlds with three "unromantic" but physically based worlds that he endorsed. He preferred an unapologetic pragmatism to the pretentiousness of Copenhagen, and was attracted to the hidden variable model of Louis de Broglie and David Bohm, rather than the "romantic" many-worlds interpretations of Hugh Everett and Bryce de Witt.

The last of the worlds he disliked was that of Eugene Wigner, for whom the change from the linear and fully deterministic evolution of the wave function in the absence of measurement, to the collapse to a single result at measurement, was caused by the consciousness of the observer. Bell hoped the result could be accomplished within orthodox physics by adding to the Schrödinger equation an extra term introducing non-linearity and perhaps a statistical element. He reported that there had been pioneering efforts but no breakthrough.

Later that year, there was a breakthrough in the work of Giancarlo Ghirardi and his colleagues, Alberto Rimini and Tullio Weber, who produced the now famous GRW approach to quantum theory. Bell gave this work tremendous publicity at the Schrodinger centenary conference at Imperial College London in 1987, and the GRW approach has since been continuously developed by the original workers, and Philip Pearle and Renata Grassi in particular, as have other interpretations, assessed positively or negatively by Bell, and further interpretations such as the consistent histories interpretation.

In this book, Ghirardi gives an account of all these events, and his opinions on all the matters of dispute. He covers the conceptual difficulties of quantum theory: quantisation, wave-particle dualism, indeterminism, superposition, the uncertainty principle and the problem of measurement. He describes complementarity and gives a full account of the famous Bohr-Einstein debate. He discusses the Einstein-Podolsky-Rosen thought experiment, Einstein's last attempt to demonstrate the inadequacy of Copenhagen. This leads to Ghirardi's account of hidden variables, one way of dealing with the EPR problem, and he includes a neat example of their contextuality, the fact that the result obtained when we measure a particular hidden variable may depend on which other measurements we make simultaneously.

Hidden variables take us on to Bell's proof that, contrary to Copenhagen and to John von Neumann's famous theorem, hidden variable theories, where lack of determinism is removed by the addition of variables not present in the Schrodinger equation, are possible but must be non-local. EPR and Bell's work were the main stimulants for today's hot topic of quantum information theory, and Ghirardi gives a brief account of this subject.

The final section of the book consists of an open-minded assessment of quantum theory's major difficulty, the measurement problem, and particularly its prediction of superpositions of macroscopic states, which are never found in practice. The possible ways of overcoming this difficulty - for example hidden variables, many worlds or many minds, and consistent histories - are discussed even-handedly, though it is clear that Ghirardi retains a special enthusiasm for his own creation, the GRW theory and its descendants.

In GRW theory, a stochastic (statistical) localisation term is added to the Schrodinger equation; it leaves the wave functions of microscopic systems practically untouched, but, as required, removes superpositions of wave functions for macroscopic objects almost instantaneously. Thus it satisfies Bell's demand for a physically based theory agreeing with orthodox quantum theory where the latter is successful, but also solving the measurement problem. As Ghirardi admits, though, like the de Broglie-Bohm hidden variable theory, there has been no satisfactory relativistic generalisation.

Ghirardi's approach in this book is almost entirely theoretical, the only experiments described being Alain Aspect's investigations of the Bell inequalities. He aims to avoid mathematics as much as possible but is only partially successful. In many sections of the book, his approach is tutorial in nature, and he admits that, though the book is for non-experts, it is by no means an easy read.

Two last points: first, though the English edition has just been published, it is largely a straight translation of the 1997 Italian edition. It is called a revised edition, but the only items added to the bibliography are by Ghirardi and his collaborators - there has been little general updating.

This matters little for the quantum theory itself, but quantum information theory, where events are moving fast, has suffered: the Shor algorithm of 1995 is spoken of as a "scoop", and the Grover algorithm of 1996 is not mentioned at all. Second, at £22.95 for a hardback of more than 500 pages, this book is exceptionally good value.

Andrew Whitaker is professor of physics, Queen's University, Belfast.

## Sneaking a Look at God's Cards: Unraveling the Mysteries of Quantum Mechanics

Author - Giancarlo Ghirardi

Publisher - Princeton University Press

Pages - 488

Price - £22.95

ISBN - 0 691 12139 7

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