The subtitle of this book is "From Bell to Quantum Information" and it is the published record of a conference held in Vienna in November 2000 to commemorate the tenth anniversary of the death of the Irish physicist John Bell. There are no posthumous Nobel prizes but if there were, it is clear that Bell would top the shortlist for many physicists. Almost single-handedly, he made reexamination of the foundations of quantum mechanics a respectable occupation for physicists. He dared to question the assumptions of the founding fathers of quantum mechanics - Bohr, Einstein and Von Neumann. With the now-famous Bell inequalities, he dragged the debate between Einstein and Bohr back from seemingly one about mere philosophy to a sharply defined question capable of experimental test. The subsequent experiments confirming the quantum predictions also highlighted the bizarre properties of "entangled" quantum states. A new generation of quantum physicists is now using quantum entanglement to create the new science of quantum information and to explore such things as quantum cryptography and quantum teleportation. This book is a record of developments in these areas by the community of physicists that Bell's own efforts did so much to create.

The Bell inequalities were a vital contribution towards the resolution of the debate between Einstein and Bohr, two of the early pioneers of quantum theory. As is well known, Einstein was unhappy with the probabilistic nature of quantum mechanics. With two colleagues (Podolsky and Rosen), he devised a "thought experiment" to demonstrate that a quantum system must contain "elements of reality" that are pre-determined before any measurements.

In its modern guise, the so-called "EPR" thought experiment concerns measurements of a two-particle quantum state in which the two particles can become very distant from each other. In the initial quantum state, the properties of the two particles are "entangled" so that although we do not know with certainty what is the state of each particle, measurement of the state of one of the particles automatically determines the state of the second. Thus, when the two particles have been allowed to separate, measurement of one particle immediately gives us information about the other. Orthodox quantum theory therefore appears to involve what Einstein called "spooky action at a distance" - some sort of signal travelling faster than light. Unsurprisingly, Einstein preferred an explanation in which the results were somehow already pre-determined by some unknown "hidden variables". Bohr's response to Einstein's challenge was summarised by Bell as the following advice: "By resisting the impulse to analyze and localize, mental discomfort can be avoided."

This volume contains articles by the modern-day quantum pioneers who were inspired by Bell to make Einstein's thought experiment a reality. Bell's inequalities enabled them to demonstrate that, in the words of Anton Zeilinger, "any local realistic view of the world is incompatible with quantum mechanics".

Besides his contribution to the Bohr-Einstein debate, Bell also took issue with Bohr's "Copenhagen" interpretation of quantum mechanics at a very fundamental level. This approach divides up the world into a "quantum system" made up of atoms and electrons obeying the Schrödinger wave equation - and a "classical" measuring apparatus with switches, dials and pointers. This "shifty split" between the quantum world and the classical world was at the heart of Bell's objections; after all, he argued, any "classical" measuring apparatus is also made up of atoms and electrons and must be describable by quantum mechanics. The problem for Bell was that conventional quantum theory gives no precise formulation of what actually happens during a measurement, when fuzzy quantum probabilities "collapse" to yield precise information about the properties of a quantum object.

Although Bell recognised that quantum mechanics worked "For All Practical Purposes" - "FAPP" as he used to say - he was sufficiently unhappy about the ambiguities in its formulation as a theory to declare that while he "hesitated to think that it might be wrong, (he) knew that it was rotten!" It was for these reasons that Bell was willing to champion exploration of unfashionable and unconventional approaches to quantum mechanics such as the De Broglie-Bohm hidden variable theory and the GRW modification of the Schrodinger equation, described by GianCarlo Ghirardi in this collection.

Before reviewing the book's articles in more detail it would be wise to explain some terminology, not least the title of the book. What are "quantum unspeakables"? In contrast to Einstein's wish for some non-probabilistic "elements of reality" to describe quantum systems, Bohr was reported as saying: "There is no quantum world. There is only an abstract quantum mechanical description." In Bell's terminology, these are the quantum "unspeakables" that Bohr forbids us to talk about. Instead, according to Bohr, we are allowed to talk only about the classical "speakables" of the measuring apparatus. Bell made a similar distinction between the quantum "observ-ables" - defined very precisely in quantum theory - and the classical "be-ables", such as "the settings of switches and knobs on experimental equipment, the currents in coils and the readings of instruments".

The collection begins with some reminiscences about Bell himself including a short note by his wife, Mary. An article by Reinhold Bertlmann, one of the editors, describes his interactions with Bell and how he became a victim of John's quiet wit. Bertlmann was collaborating with Bell on a paper that had nothing to do with the fundamentals of quantum mechanics and he was unaware that Bell had noticed his habit of wearing socks of different colours. He was therefore taken by surprise by the appearance of a paper by Bell on the EPR paradox titled "Bertlmann's socks and the nature of reality". Bertlmann also recounts how Bell asked him to write the first draft of their joint paper. When Bell returned his draft he was shocked to find there was not one word left in the place where he had put it. I myself had a similar lesson from Bell in the art of writing scientific papers.

Whereas my first draft set out our new result in a grandiose context, John's version was much truncated and pragmatically retitled as "A theoretical argument for something like the second Melosh transformation".

The next section discusses the history and current state of experimental tests of Bell's inequalities and the contributor list reads like a "Who's Who" of the field. This leads on to a section on the burgeoning field of quantum information. After discursions into quantum cryptography and teleportation, the section concludes with a paper by Zeilinger, co-editor of this volume, who puts forward the view that "information might be at the root of the interpretation of quantum mechanics". He concludes that although this "explanation" would be unlikely to have satisfied Bell, he surely would have been impressed by the recent developments stressing the role of quantum entanglement.

The remaining sections cover a number of different topics in quantum mechanics, field theory and particle physics. These contain many other interesting and thought-provoking contributions. As an example, David Mermin's "Whose knowledge?" is a technical critique of an attempt by the late Rudolf Peierls to address Bell's concerns about quantum mechanics.

Peierls did not agree with Bell that the problems were very difficult and said: "I think it is easy to give an acceptable account." Stating that he has recently fallen into bad company and "started hanging out with the quantum computation crowd, for many of whom quantum mechanics is self-evidently and unproblematically all about information", Mermin demonstrates that one apparently innocent assumption in Peierls'

"acceptable account" is incorrect. (Reading this article reminded me that, in 1977, I initiated a three-way correspondence with Peierls and Bell concerning their views on quantum mechanics. In a letter to me, Bell summarised their positions by saying that he and Peierls agreed on the need for "something outside quantum mechanics, whether 'measuring apparatus' or 'observers'". And he speculated about making a model "of one or more 'consciousnesses' at work reducing the wavepacket", concluding that problems with relativity "may lead us to contemplate 'point consciousnesses' - a funny thought!") Two other highlights are the paper by Gerard 't Hooft titled "How does God play dice?", in which 't Hooft imagines the existence of a classical deterministic theory for physics at the incredibly small distances governed by the Planck scale. He speculates that quantum mechanics may simply be our attempt to handle at our length scales the underlying fluctuating dynamics down at the Planck scale. Clearly there are still many unanswered questions for such an approach.

The second highlight is Franco Selleri on "Bell's spaceships and special relativity" that refers to Bell's pedagogically controversial paper "How to teach special relativity".

To quantum physicists, it will be obvious that this collection covers a lot of ground and contains contributions from most of the established authorities on quantum mechanics and quantum information. The book is a fitting tribute to Bell and to his efforts to clarify some of the obscurities bequeathed by Bohr and his colleagues. It will be a worthy addition to the bookshelf of all quantum physicists who think they understand quantum mechanics.

Tony Hey is professor of computation, University of Southampton.

## Quantum (Un)speakables: From Bell to Quantum Information

Editor - R. A. Bertlmann and A. Zeilinger

ISBN - 3 540 456 2

Publisher - Springer

Price - £56.00

Pages - 483

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