Quantum theory is the most successful scientific theory of all time. Many of the great names of physics are associated with quantum theory. Heisenberg and Schrödinger established the mathematical form of the theory, while Einstein and Bohr analysed many of its important features. However, it was John Bell who investigated quantum theory in the greatest depth and established what the theory can tell us about the fundamental nature of the physical world. **Andrew Whitaker** tells us more

Moreover, by stimulating experimental tests of the deepest and most profound aspects of quantum theory, Bell’s work led to the possibility of exploring seemingly philosophical questions, such as the nature of reality, directly through experiments. And this was just Bell’s “hobby”.

### Early life

John Stewart Bell was born in Belfast on 28 July 1928. The families of both his parents, Annie and John, had lived in the north of Ireland for several generations. Annie’s family had originally come from Scotland and John’s middle name, Stewart, was her family name. In fact, John was known as Stewart at home, only becoming John when he went to university.

John Stewart, his elder sister Ruby and his two younger brothers David and Robert were brought up as firm members of the (Anglican) Church of Ireland. There was no hint of prejudice in the family, and Annie Bell had many friends in the Catholic community.

Bell’s parents were known as intelligent lively people, and although the family was not well-off, love and care were never in short supply. In particular Annie Bell was keen to impress on the children that education was the key to a satisfying life in which “they could wear their Sunday suits all week”. Although only John was able to stay at school much beyond the age of 14, David studied in the evening to become a qualified electrical engineer, and now lectures at Lambton College in Canada, while Robert is a successful local businessman. Later in life they were all able to joke with their mother that they could indeed wear their Sunday suits all week, although John rarely did!

John showed exceptional promise at his first schools, Ulsterville Avenue and Fane Street, and also used the public library in Belfast voraciously. Indeed, he was known as “The Prof” at home because of his tendency to amass great quantities of information, on which he would then freely expound. At the age of 11 John announced to his mother that he wanted to be a scientist.

Although John did extremely well in his “qualifying examination” at 11, his family could not afford to send him to any of Belfast’s more prestigious schools. However, money was found for John to attend the Belfast Technical High School for four years. This was probably ideal for him, as practical courses, which he enjoyed, were mixed in with a full academic curriculum that allowed him to qualify for entrance to university.

At age 16, however, Bell was a year younger than the minimum age for admission to Queen’s, the local university. Instead in 1944 he entered the physics department at Queen’s as a technician in the teaching laboratory, where he greatly impressed the lecturing staff, Professor Karl Emeleus and Dr Robert Sloane. Indeed, Emeleus and Sloane lent John books and allowed him to attend the first-year lectures while still working as a technician. With savings from this year’s salary, and help from other sources, Bell was able to enter the university as a student in 1945. His performance was outstanding and he graduated with first-class honours in experimental physics in 1948.

Bell was especially interested in theoretical physics and a year later he was able to graduate for a second time, obtaining a first in mathematical physics in 1949. His teacher in this area was Peter Paul Ewald, famous as one of the founders of X-ray crystallography, who had been driven out of Germany by the Nazis and had been in Belfast since 1939. Bell enjoyed his contact with Ewald from an academic point of view and for its lack of formality.

Bell was less happy about the way Queen’s taught quantum theory, a subject in which he was already interested. Although there was a good course on the basics, later courses concentrated on applying quantum theory to atoms, whereas Bell wanted to study the more philosophical aspects of the theory as well. In particular he clashed with Sloane, whose account of the Heisenberg principle made it appear rather subjective in nature, which was not unusual in those days.

In retrospect Sloane should not feel guilty about not living up to Bell’s standards concerning quantum theory; over the next 40 years or so, many others would follow suit.

### Career: particles and accelerators

In 1949, after he graduated, Bell joined the UK Atomic Energy Research Establishment (AERE) at Harwell, although he soon moved to the accelerator design group in Malvern. After the financial stresses of student life, it must have been pleasant to have a tenured position and a steady, if modest, income. He bought a motorbike, though a nasty accident while riding this led to a deep cut around the mouth, and thus to the famous beard.

An important event in this period was meeting his future wife, Mary Ross, who had joined the accelerator design group with a degree in mathematics and physics from Glasgow. They married in 1954, and enjoyed a long and happy life together, even writing joint papers. When some of John’s papers were collected as *Speakable and Unspeakable in Quantum Mechanics* in 1987 (see further reading), he ended the preface with the following words: “I here renew very especially my warm thanks to Mary Bell. When I look through these papers again I see her everywhere.”

Bell’s work up to 1953 consisted of modelling the paths of charged particles through accelerators. Without the benefit of computers, the work required a thorough knowledge of physical principles, together with the skill to retain the important physics while making sufficient approximations to allow the problem to be solved on a mechanical calculator. Bell’s work, produced in a series of AERE reports (including one in collaboration with Mary), was excellent.

This was the period when the discovery of “strong focusing”, in which axial and radial focusing are applied separately to the beam being accelerated, led to the next generation of synchrotrons. Bell’s numerical calculations had shown signs of the strong focusing principle, and when it was established formally in 1952 he rapidly became an expert and acted as a consultant to the team designing the Proton Synchrotron at CERN in Geneva.

The accelerator design group moved from Malvern to Harwell in 1951. That same year Bell was delighted to be offered a year’s leave to work with Rudolf Peierls, professor of theoretical physics at Birmingham University. At Birmingham, Bell discovered the important CPT theorem of quantum field theory. The CPT theorem states that the combined operation of charge conjugation (in which a particle is replaced by its antiparticle), parity reversal (reflection in a mirror) and time reversal is a symmetry operation that leaves the system unchanged. This is a fundamental theorem which proves, for example, that particles and antiparticles must have equal masses. Unfortunately Gerhard Lüders and Wolfgang Pauli performed similar work at the same time and received all the credit for what is usually called the Lüders-Pauli theorem.

Bell, however, had built up his reputation where it counted, and on his return to Harwell in 1954 he joined a group being set up to work on elementary particle physics, obtaining his PhD in 1956. However, in the years that followed he and Mary became worried that Harwell was moving away from fundamental work, and in 1960 they moved to CERN, where they spent the rest of their careers.

Between 1955 and 1984, Bell published around 80 papers in the general area of high-energy physics and field theory, including nuclear physics and many-body physics. Some work was directly concerned with experiments at CERN; for example, Bell helped to analyse the first neutrino experiments performed there in 1963. Most of the work, however, tackled theoretical issues.

Bell’s most famous paper in this area – published with Roman Jackiw in *Il Nuovo Cimento* in 1969 and cited more than any other of his papers – was the discovery, clarified to some extent by Stephen Adler, of the Bell–Jackiw–Adler anomaly. At the time, theory predicted that the neutral pion could not decay into two photons, but this had been observed in experiments. Bell, Jackiw and Adler were able to explain the observed decays theoretically by adding an “anomalous” term resulting from the divergences of quantum field theory. A condition that the “anomaly” produced agreement with experiment was that the sum of the charges of the elementary fermions had to be zero. This provided support for the idea that quarks come in three colours, now part of the widely accepted Standard Model. (The first family of elementary fermions consists of the electron, which has charge –1; the neutrino, which has no charge; and the three colours of up- and down-quarks, which have charges 2/3 and –1/3, respectively. If quarks came in only one colour, then the sum of the charges would be –2/3, not zero.)

Another crucial paper was Bell’s 1967 argument that weak interactions should be described using a gauge theory. (Gauge theories possess gauge symmetries: these symmetries are connected with the idea that quantities such as electric charge and quark colour are conserved *locally* as well as globally.) This suggestion was picked up by his collaborator, Martinus Veltman, whose research student, Gerard ‘t Hooft, later showed that the unwanted infinities in this gauge theory could be removed or “renormalized”. This in turn gave mass to the particles, now known as the W and Z bosons, that carried the weak nuclear force. The Standard Model of particle physics is based on gauge theories.

In the 1980s Bell returned to accelerator design, writing papers with his wife on electron cooling, radiation damping and quantum bremsstrahlung, including a theoretical tour de force in which he related Hawking radiation to the heating of electrons in an accelerator beam.

### The quantum background

As a man of the highest principles, Bell gave every effort to his work on accelerator and particle physics, for which CERN paid him. Quantum theory, on the other hand, was his hobby, perhaps his obsession. And it was quantum theory that was to make him famous.

From his student days Bell had been fascinated by the theory and its implications for the nature of the physical universe. Many of these implications had been argued over by Bohr and Einstein in the 1920s and 1930s (see Whitaker in further reading). From the birth of the theory it was clear that if the only properties of the system that exist are those that are implicit in the wavefunction, then many properties with precise classical values just do not have quantum values at any particular time. The most famous example was the Heisenberg uncertainty principle: if a particle has a precise value of position, then its momentum cannot have a value. Similarly, if a spin-1/2 particle possesses a value of spin in the z-direction, *s _{z}*, then it does not have values of spin in either the x- or y-direction. This is a much stronger statement than saying that the particle may have such values but that we do not or cannot know them. Physicists often call this property a lack of realism, although philosophers may define the same word in a more general manner.

Furthermore, measurement has a very special role in quantum theory: if we measure, say, spin in the x-direction, *s _{x}*, then we must obtain a precise value for this quantity, even if a precise value did not exist beforehand. There are two possible results or “eigenvalues” for

*s*: +

_{x}*hw/2*, which is associated with a quantum “eigenstate” a

_{+}, and –

*hw/2*, which is associated with the eigenstate a

_{–}. We can predict the result of a measurement if the initial state vector describing the system, y

_{0}, is either a

_{+}or a

_{–}: if y

_{0}= a

_{+}the result will be +

*hw/2*, and if y

_{0}= a

_{–}the result will be –

*hw/2*.

In general, however, the state vector will be a linear combination of both eigenstates: y = *c*_{+}a_{+} + *c*_{–}a_{–}, where *c*_{+} and *c*_{–} are complex constants, and *c*_{+}^{2} + *c*_{–}^{2} = 1. In this case, we are still bound to get one or other of the eigenvalues, but it is not certain which one. Born’s postulate tells us that the probabilities of obtaining +*hw/2* and – *hw/2* are *c*_{+}^{2} and *c*_{–}^{2}, respectively. Therefore the long-cherished principle of *determinism*, according to which identical initial conditions (e.g. identical state vectors) must always evolve with time in exactly the same way, is no longer valid.

The most common approach to measurement is von Neumann’s collapse postulate: for example, if the result +*hw/2* is obtained in the measurement, then the state vector collapses at that instant to the corresponding eigenstate, a_{+}, and another measurement of the same quantity will again yield +*hw/2*. The scheme works well pragmatically but, as von Neumann admitted, the collapse process is mathematically distinct from the normal evolution of the state as described by the Schrödinger equation. However, as measurement is just a conventional physical process, it should be governed by the Schrödinger equation.

Moreover, to Einstein the collapse postulate was an even more pernicious retreat from realism than that described above: it implied that physical quantities usually have no values until they are observed, and therefore that the observer must be intrinsically involved in the physics being observed. This suggests that there might be no real world in the absence of an observer!

### Enter the hidden variables

One obvious way to reinstate realism and determinism was to add “hidden variables” to the wavefunction to provide the most complete description of the system possible. These hidden variables might, for example, provide values for all components of the spin at all times, and thus dictate whether the result +*hw/2* or –*hw/2* was obtained in a measurement. However, Bohr and Heisenberg were convinced that one could not supplement quantum theory with hidden variables. Therefore they were pleased when, in 1932, von Neumann claimed to have proved that the application of hidden variables to quantum theory was indeed impossible. This was to remain accepted wisdom for over 30 years.

A conceptual approach to the problems of quantum measurement was provided by Bohr in the 1920s. Bohr’s starting point was that the results of a measurement must be expressed classically; there must be a classical region of every experiment where physicists can set apparatus, read pointers and so on. And since (in the absence of hidden variables) there must also be a quantum region, then there must also be a “cut” between the two regions. The position of this cut will, to a considerable extent, be arbitrary.

The arbitrary position of the cut implies what Bohr called wholeness. The object being observed and the measuring apparatus cannot be regarded as separate – they are inextricably linked. Therefore measurement is *not* a passive registration by the apparatus of the value of a pre-existing property of the observed system. Rather measurement is a physical procedure involving the entire experimental set-up. So values of, say, *s _{z}* and

*s*cannot be combined in a simple way, because completely different experimental arrangements are required to measure these two quantities.

_{x}This led Bohr to his framework of *complementarity*, according to which the value of a particular quantity can only be discussed in the context of an apparatus for measuring that quantity being in place. Evidence obtained under different conditions cannot be comprehended within a simple picture but is *complementary*. Thus one may not discuss simultaneously values of *s _{x}* and

*s*, or

_{z}*x*and

*p*. Complementarity essentially forbids one to discuss the very situations that gave rise to conceptual problems; whether it actually explains anything is another question!

_{x}Bohr’s position was at least self-consistent, and quickly became regarded as “orthodox”. But it also contradicted many of science’s most cherished beliefs, such as realism, and, as is well known, Einstein had a long-standing debate with Bohr over what he perceived to be its inadequacies. The only aspect of Einstein’s criticisms that really struck home, and even then it took decades to do so, was his demonstration of entanglement via the famous Einstein-Podolsky-Rosen (EPR) thought experiment of 1935.

EPR argued that either there was a breakdown in locality, in the form of an instantaneous movement of information from one point to another (and obviously Einstein was appalled by this as it implied faster-than-light communication), or that the orthodox view of quantum theory was incomplete and there were elements of reality over and above those implicit in the wavefunction. EPR concluded that quantum theory was incomplete, but Bohr strongly disagreed with them. His response was to extend his definition of wholeness – both spins in the EPR set-up, although spatially separated, should be regarded as aspects of a single system. The scientific community almost unanimously sided with Bohr.

### Enter John Bell

When Bell became interested in these matters in the late 1940s, his position on the Bohr-Einstein debate was unambiguous. Years later he explained this to Jeremy Bernstein: “I felt that Einstein’s intellectual superiority over Bohr, in this instance, was enormous; a vast gulf between the man who saw clearly what was needed, and the obscurantist.” Bell later showed Einstein to be wrong on this question, but that was the opposite of what he intended.

Bell felt that the introduction of deterministic hidden variables was very natural for three reasons. First it might eliminate the need for the cut between the classical and quantum regions of a measuring apparatus. In the terms used above, it could restore realism. His second, less compelling, motivation was to restore determinism.

His third motivation was specifically connected with EPR. Bell regarded Einstein’s call for the completion of quantum theory as a simple call for the addition of hidden variables: if all components of each spin had precise values at all times, there could be no problems for locality. Bell may have actually misunderstood Einstein – who probably hoped for a theory on a much grander scale, rather like his general theory of relativity, that would almost incidentally solve all the problems of quantum theory – but much of Bell’s major work would stem from this approach to hidden variables.

Bell described himself as a follower of Einstein. As for Bohr, Bell practically regarded him as two separate people. Bell strongly supported his assertion that apparatus must be classical in nature and his concept of *wholeness* in an individual measurement. Moreover, Bohr’s idea that the measurement process was not a simple discovery of a pre-existing property was a major component of Bell’s most important work, and he gave Bohr great credit for this insight. But Bell was repelled by what he felt was the complete lack of clarity in Bohr’s complementarity, which he preferred to call *contradictoriness*. Bell regarded Bohr’s “solution” of the EPR problem as incoherent.

Bell’s enthusiasm for hidden variables had been tempered by reading about von Neumann’s “proof” of their impossibility in his student days.He was frustrated because von Neumann’s book was written in German and was not translated into English until 1955. However, in 1952 Bell “saw the impossible done”. David Bohm, largely repeating work done a quarter of a century earlier by Louis de Broglie, was able to add hidden variables, actually particle positions, to standard quantum theory, and to obtain a fully realist and deterministic version of the theory.

Bohm suffered the strange fate of being dismissed equally by Bohr and Einstein. Bell, however, was enthralled and for a long time was just about the only supporter of the de Broglie–Bohm theory, which is also known as the pilot wave theory or the causal interpretation of quantum theory.

In 1953 Rudolf Peierls, who was to be a life-long friend and supporter, asked Bell to give a short talk at Birmingham. Bell offered to talk about either accelerator design or the foundations of quantum theory. Peierls, however, was part of the generation who considered that all the problems of quantum theory had been solved by Bohr, so he asked Bell to talk about accelerators. In fact it was probably a good thing that Bell resisted the temptation to join the debate on quantum theory until he was more established. By 1963, however, he had reached the peak of his “daytime” profession of high-energy physics, and a year’s stay at the Stanford Linear Accelerator Center in California gave him time and space to think.

### John Bell and quantum theory

At last Bell was able to devote a fair proportion of his time to the questions that had interested him for so long. First he addressed von Neumann’s work on hidden variables in the light of Bohm’s theory. Bohm’s argument had been fairly complicated, and it was easy for those who did not welcome its conclusions to assume it was flawed. Bell started by producing a hidden-variable model of his own. It was fairly simple, covering just the measurement of any component of spin for a spin-1/2 particle. But the simplicity was really the point – it was too simple just to ignore.

Bell then turned his attention to von Neumann. Clearly both Bohm’s hidden-variable model and his own must violate one of the axioms of von Neumann’s proof, and Bell was soon able to trace this down. In quantum theory let us say we measure *s _{x}* and then

*s*on a particular spin. It is obviously wrong to say that, had we measured

_{y}*s*+

_{x}*s*, we would have obtained the sum of the two individual measurements. Bohr’s argument of

_{y}*wholeness*tells us that all three measurements require totally different arrangements of the apparatus, and that we cannot combine the results in a simple way.

However, if we calculate the “expectation value” of *s _{x}* +

*s*, which is essentially the value of

_{y}*s*+

_{x}*s*averaged over all possible states of the system, we find that it is equal to the sum of the expectation values of

_{y}*s*and

_{x}*s*. Although this is little more than a strange coincidence in quantum theory, von Neumann had used this result as an axiom for his hypothetical hidden-variable states. There was no justification for this axiom and it did not work for either Bohm’s or Bell’s hidden-variable models. And when it was removed, von Neumann’s theorem crashed. Thus Bell was able to remove a 30-year-long log-jam from the study of the fundamentals of quantum theory. There were other well known “impossibility theorems” and, in the same paper, Bell disposed of these as well. Although the paper was written in 1964 while Bell was at Stanford, it was not published in

_{y}*Reviews of Modern Physics*until 1966. (The journal had mis-filed Bell’s revised version of the paper, and by the time the editor had written to Bell to ask about the revisions, he had already returned to CERN and the letter was not forwarded.)

In the same paper, Bell also discussed two rather unwelcome properties of hidden-variables theories. The first was *contextuality*. This tells us that, except in trivial cases, any hidden-variable theory must be such that the result of measuring a particular observable will depend on which other observable(s) are measured simultaneously. The second was *non-locality*. All the hidden-variable models that Bell examined, including Bohm’s, had the unpleasant feature that the behaviour of a particular particle depended on the properties of all others, however far away they were. In the EPR case, the measurement result obtained on one particle would depend on what measurement is performed on the second. As Bell said, this was the resolution of the EPR problem that Einstein would have liked least, and it is in this sense that it may be said that Bell proved Einstein wrong.

These two features are actually related, for contextuality in a system with entanglement suggests that the results of a measurement on one particle may depend on measurements made simultaneously on a second particle, spatially separated from the first, with which the first has become entangled.

Suggestions of non-locality were one thing; Bell wished for a rigorous proof, and was able to provide one in his second great quantum paper, written and published in *Physics*, a now-defunct journal, in 1964. Bell wrote the first draft of the paper during a stay at Brandeis University in Massachusetts and completed it at the University of Wisconsin at Madison.

As he stressed later, Bell started from locality and, following EPR, argued for the existence of deterministic hidden variables. However, he also went beyond EPR and considered measurements of spin components along arbitrary directions in each wing of the experiment (rather than just *s _{z}* or

*s*as in EPR). Bell calculated what happened when the measurement direction was kept constant in one wing of the experiment and varied in the other. He was able to show that the behaviour predicted by quantum theory could not be duplicated by a hidden-variable theory if the hidden variables acted locally.

_{x}As subsequently shown by Bell and others, local realist theories (i.e. theories with hidden variables) satisfy a so-called Bell inequality. This is a constraint on the relationship between the joint probability densities of the signals recorded in the two wings of the apparatus; it involves the four distinct cases that may be obtained by having two settings in each wing. Quantum theory, on the other hand, does not obey the Bell inequality. In this way Bell had opened up the possibility of experimental philosophy, the study of what are normally thought of as philosophical issues in experiments. Not only do these experiments probe the deepest and most profound aspects of quantum theory, they also provide information on the fundamental nature of the universe. Henry Stapp of the Lawrence Berkeley National Laboratory in California was later to call Bell’s work on quantum theory “the most profound discovery of science”. Bell’s work in this area is also a major influence on the rapidly growing field of quantum information (see *Physics World* March 1998).

### After the inequality

A large number of Bell inequality experiments have been performed over the last 30 years or so, the most famous being those of Alain Aspect and co-workers at Orsay. In these experiments, pairs of photons are emitted in a cascade from an excited atomic state and their polarizations are measured along different axes. More recent experiments have used pairs of entangled photons emitted by nonlinear optical crystals. In these experiments the polarization of the photon plays the role of the spin in the EPR–Bohm–Bell set-up.

However, the low efficiency of the detectors used in the experiments means that additional assumptions (essentially that those photons detected are a fair sample of the total flux) have to be made to test the Bell inequality. If these assumptions are made, the results are found to rule out local realist theories, and to be in good agreement with the quantum predictions. Most physicists now accept that quantum theory is correct, and that local realism has to be abandoned.

However, other physicists, often known as the realists, strongly disagree. They question the additional assumptions in the experiments and insist on the “detection loophole” being taken seriously (see Selleri in further reading). Particles are easier to detect than photons and it will be possible to close the detection loophole with measurements of the kaons produced in f-meson decays. Such experiments are planned for the “f-factory” that was opened in Frascati, Italy, last year.

Bell himself was worried that, according to special relativity, the nonlocal (faster than light) influence demonstrated in the Aspect experiment could involve propagation backward in time in other inertial reference frames of equal status. What he called the “cheapest resolution” to this problem was to return to the Lorentz (i.e. pre-Einstein) approach to relativity in which an ether is retained. In other words, there is a preferred frame of reference in which a real causal sequence may be defined (see Bell’s contribution to *The Ghost in the Atom* in further reading). Propagation backward in time in other frames may then be dismissed as “unreal” or “apparent”. More generally, however, Bell hoped for better theories than the ones we have now, and insisted that our current version of quantum theory was no more than a temporary expedient.

In the 1980s Bell’s work on quantum theory was centred on criticisms of the orthodox view of quantum measurement and suggestions for its modification. At the 1987 Schrödinger conference, he famously championed the 1985 theory of Ghirardi, Rimini and Weber (GRW) in which the collapse of the wavefunction is not an arbitrary and artificial device but is represented by a precise, though probabilistic, term in a nonlinear modification of the standard Schrödinger equation. Collapse would occur very fast for systems of macroscopic size, but its speed would decrease with the size of the system, and become negligible on the atomic scale.

In 1990, in an aggressive article called “Against ‘measurement'” published in *Physics World* (August pp33–40), Bell severely criticized the von Neumann collapse procedure and the very idea of “measurement” as a “fundamental term”. He also dismissed other approaches that, although more sophisticated, were in Bell’s opinion no less contrived. Once again he advocated Bohm and the GRW theory.

### The man

John Bell was greatly respected by all who knew him as a man of total integrity and great generosity. He was modest and unassuming, with a delightfully puckish sense of humour – most notably exhibited in his “Bertlmann’s socks” paper in which the EPR problem was explained in analogy with the unmatched socks of one of his closest collaborators, Reinhold Bertlmann. Bell and his wife were both long-term vegetarians, and in his version of Schrödinger’s cat paradox, the two states of the cat are being hungry or not hungry, rather than being dead or alive.

Bell became a Fellow of the Royal Society in 1972, and although he received many awards, they did not come for many years, until the nature of his exceptional achievements became fully realized. Indeed, between 1987 and 1989 he was awarded the Hughes Medal of the Royal Society, the Dirac Medal of the Institute of Physics and the Heineman Prize of the American Physical Society. And in 1988 he received honorary degrees from both the Queen’s University of Belfast and Trinity College, Dublin. He was nominated for a Nobel prize and, had he lived longer, might well have received it.

In 1988 he made another visit to Belfast to lecture to the British Association. However, Bell remembered his early days in the teaching laboratory and spotting Reggie Scott, with whom he had worked as a technician over 40 years previously, left the assembled bigwigs to have a yarn about the old days when they were two young men making their way in the world.

Sadly it was much nearer the end than anyone would have hoped. On 1 October 1990 John Bell died suddenly of a stroke. This was of course a terrible tragedy for family and friends, but also a cause of great sadness to all those who knew him mainly from his work and his reputation. It may be a source of a little consolation that, over the last eight years, recognition has increased still further, and it is now unquestioned that he stands among the truly great scientists.

### Further reading

J S Bell 1987 *Speakable and Unspeakable in Quantum Mechanics* (Cambridge University Press). This book contains most of Bell’s quantum papers

J S Bell 1995 *Quantum Mechanics, High Energy Physics and Accelerators* (World Scientific, Singapore). This book, edited by M Bell, K Gottfried and M Veltman, contains many papers by Bell on these three topics

J Bernstein 1991 *Quantum Profiles* (Princeton University Press). Bernstein interviewed Bell extensively and his profile of Bell contains a lot of material on Bell’s early years

P C W Davies and J R Brown (ed) 1986 *The Ghost in the Atom* (Cambridge University Press)

F Selleri 1990 *Quantum Paradoxes and Physical Reality* (Kluwer, Dordrecht)

A Whitaker 1996 *Einstein, Bohr and the Quantum Dilemma* (Cambridge University Press)

Recent *Physics World* articles related to Bell’s work on quantum theory include: C Jack “Sherlock Holmes investigates the EPR paradox” April 1995 pp39-42; D Greenberger and A Zeilinger “Quantum theory: still crazy after all these years” September 1995 pp33-38; A Zeilinger “Fundamentals of quantum information” March 1998 pp35–40