Computing with Quantum Cats (18 page)

No concealed parameters can be introduced with the help of which the indeterministic description [of quantum physics] could be transformed into a deterministic one. Hence if a future theory should be deterministic, it cannot be a modification of the present one but must be essentially different. How this could be possible without sacrificing a whole treasury of well-established results I leave to the determinists to worry about.

Bell would have liked to make a career in research, and his professor at Queen's, Peter Paul Ewald (one of the many scientists to have fled Nazi persecution in the 1930s), suggested that he should join Rudolf Peierls' group in Birmingham as a PhD student. This was Bell's dream; but by 1949, at the age of twenty-one, he was feeling guilty about having lived off his parents for so long, and knew that he would need help to follow up this opportunity. He felt it his duty to get a job, and found one with the UK Atomic Energy Research Establishment at Harwell, in Oxfordshire, soon moving to join the AERE's particle accelerator design team based at Malvern, Worcestershire, where his practical background and deep understanding of physics were put to good use.

At Malvern, Bell met a young Scottish physicist, Mary Ross, from Glasgow. She came from a slightly more affluent family than the Bells, and had had the good fortune of attending a co-educational school which covered both the “primary” and “secondary” years. Because there were boys as well as girls at the school, there was a physics course; at that time it would have been most unlikely for a girls-only school to teach physics. Mary did well at school, especially in physics, and in 1941 went on to the University of Glasgow. Her
education was interrupted by compulsory war work in the radar lab at Malvern, which she hated. But after the war she completed her studies and returned to Malvern in a much more congenial role as a member of the accelerator design group. John and Mary married in 1954, and stayed happily together until his death.

In 1952, Bell became a consultant with the British team contributing to the design of what would become the first particle accelerator at the new European research center in Switzerland, CERN. The machine, which started operating in 1959, was a proton synchrotron which, at the time, was the world's highest-energy particle accelerator. But something else, far more significant, also happened in 1952. Bell was chosen by AERE to become (in 1953) one of the beneficiaries of a scheme whereby some of their young scientists were given leave to spend a year at university carrying out research. It wasn't something you applied for, and Bell always expressed astonishment that he had been selected, as he saw it, out of the blue. It must rank as one of the most important decisions in the history of science. He went to Birmingham, and “there I became a quantum field theorist.”

Rudolf Peierls suggested an area of research for Bell to work in, and this led to his developing an important piece of quantum field theory known as the CPT theorem. Unfortunately for Bell, while he was writing up this work for publication he found that Gerhard Lüders, based at the University of Göttingen, had just published a paper announcing the same discovery. His own work was, nevertheless, a significant piece of research, and combined with another completed after he returned to Harwell it formed the basis of a thesis for which Bell was awarded a PhD in 1956.

It was also in 1952 that Bell “saw the impossible done,” as he put it in his address to the de Broglie 90th birthday symposium thirty years later. David Bohm showed how “the indeterministic description [of quantum mechanics] could be transformed into a deterministic one.” This set questions buzzing in Bell's brain: “But why then had Born not told me of this ‘pilot wave'? If only to point out what was wrong with it? Why did von Neumann not consider it?…Why is the pilot wave picture ignored in text books?” Bell saw that von Neumann must have been wrong, and discussed the puzzle with a German colleague, Franz Mandl, who was able to give him the gist of von Neumann's argument. As Bell told Bernstein, “I already felt that I saw what von Neumann's unreasonable axiom was.” He also commented: “I hesitated to think [quantum mechanics] might be wrong, but I
knew
that it was rotten.” Even so, a full-scale assault on the puzzle would have to wait, since Bell had returned to Harwell to join a new group, the Theoretical Physics Division, carrying out fundamental research in areas related to particle physics.

Bell had a tenured post at Harwell—a job until he retired and a pension afterwards—but both he and Mary became increasingly unhappy there in the late 1950s. Harwell had been set up to develop peaceful uses of nuclear energy, and by then the first nuclear power stations had been built and future developments were more in the realm of industrial applications than fundamental science. So in 1960 they gave up the security of Harwell and moved to CERN—the ideal place to combine Mary's interest in accelerator design with John's interest in fundamental physics, but with no promise of long-term security. The practice at CERN was to offer a
three-year contract, on the understanding that in normal circumstances a second three-year contract would follow; and during those six years, a lucky few would be offered tenured posts. The point was to give as many people as possible a chance to spend some time at the multinational research center. The Bells would be among the lucky (or rather, talented) few who got the offer of tenure, and stayed there for the rest of their careers.

Although Bell carried out a great deal of research during his time at CERN, and published many important papers, he will be remembered above all for two pieces of work completed while he was in the United States in the mid-1960s. But although this burst of creative activity came to fruition in America, it was undoubtedly stimulated in CERN, in 1963, when a visitor from the nearby University of Geneva, Josef-Maria Jauch, gave a seminar in which he claimed to have “strengthened” von Neumann's impossibility theorem. Since Bell had already seen the impossible done, this was like the proverbial red rag to a bull, and he determined to resolve the issue once and for all. He was helped by two factors: von Neumann's book was now available in English, so he could examine the “proof” at first hand; and he and Mary were planning a sabbatical in the United States, where they would visit the Stanford Linear Accelerator Center in California (arriving in November 1963, just after the assassination of John F. Kennedy), Brandeis University in Massachusetts and the University of Wisconsin-Madison. Freed from his regular routine at CERN, Bell had time both to think and to put his thoughts down on paper.

VON NEUMANN'S SILLY MISTAKE AND BELL'S INEQUALITY

Among the great virtues of the two scientific papers that emerged from Bell's trip to the United States were their clarity and simplicity, related to the fact that with his practical experience in particle physics Bell was able to spell out the kinds of experiments that could, in principle, be carried out to test the ideas—not that he expected, at the time, to see such experiments carried out. The first of the two papers that he wrote (but not the first to be published, as we shall see) was “On the Problem of Hidden Variables in Quantum Mechanics,” in which he analyzed the flaws in von Neumann's argument, in the “refinement” proposed by Jauch, and in a third variation on the theme. At the time, he was quite unaware of Grete Hermann's earlier work. Bell went further than Hermann, though, in not just finding the flaw in von Neumann's argument, but also (actually, at the beginning of his paper) presenting his own version of a hidden variables theory, much simpler than Bohm's model but demonstrating with equal force that the “impossible” could be done. He also made clear that non-locality (“spooky action at a distance”) was an integral part both of Bohm's model and of his own. As Bell commented in the paper, this means that these hidden variables theories (and, he suspected,
all
such theories) resolve the EPR puzzle in exactly the way Einstein would have liked least!

Bell completed “On the Problem of Hidden Variables in Quantum Mechanics” while at Stanford (although he mentions in the acknowledgments that “the first ideas of this paper were conceived in 1952”), and sent it off to the journal
Reviews of Modern Physics
in 1964. As usual, the editor of the
journal sent the paper to an expert referee to assess its suitability for publication. The referee was sympathetic (it is widely thought that it was Bohm), but suggested some improvements be made before it was accepted for publication. Bell, as authors often do, made the bare minimum of changes to meet the referee's demands, and sent the paper back to the journal. Unfortunately, the revised paper was misfiled, and sometime later, thinking it had not come back, the editor wrote to Bell asking where it was. The letter went to Stanford, but by then Bell was back in England. By the time the confusion was sorted out, more than a year had passed and the paper was eventually published in 1966, after the second of Bell's great papers, the one which
proved
that all hidden variables theories must be non-local.

Although there is no need here to go into the details of Bell's refutation of von Neumann's argument, which is essentially the same as Hermann's, it does seem worth reiterating in Bell's own words (from an interview published in the science and science fiction magazine
Omni
in May 1988) how bizarre it is that people ever took it seriously: “The von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is
nothing
to it. It's not just flawed, it's
silly
!…You may quote me on that: The proof of von Neumann is not merely false but
foolish
!” Indeed, David Mermin, of Cornell University, commented in
Reviews of Modern Physics
itself, in 1993, that the argument is so silly that “one is led to wonder whether the proof was ever studied by either the students or those who appealed to it to rescue them from speculative adventures [in the realms of quantum interpretation].” Bell's second great paper was scarcely speculative, but it was certainly adventurous.

That second paper was entitled “On the Einstein-Podolsky-Rosen Paradox,” and begins by noting that the EPR argument was advanced in support of the idea that “quantum mechanics could not be a complete theory but should be supplemented by additional variables. These additional variables were to restore to the theory causality and locality.” He goes on to say: “in this note that idea will be formulated mathematically and shown to be incompatible with the statistical predictions of quantum mechanics.
It is the requirement of locality, or more precisely that the result of a measurement on one system be unaffected by operations on a distant system with which it has interacted in the past, that creates the essential difficulty
.”
¹³
In other words, if there is a real world out there independent of our observations (if the Moon is there when nobody is looking at it), then the world is non-local. Equally, though, if you insist on locality, then you have to give up the idea of reality and accept the literal truth of the “collapse of the wave function” as envisaged by the Copenhagen Interpretation. But you cannot have both—you cannot have local reality.

But the most dramatic feature of Bell's discovery is often overlooked, even today. This is not a result that applies only in the context of quantum mechanics, or a particular version of quantum mechanics, such as the Copenhagen Interpretation or the Many Worlds Interpretation. It applies to the Universe independently of the theory being used to describe the Universe. It is a fundamental property of the Universe not to exhibit local reality.

I do not intend to go into the details of Bell's calculation, which can be found in a thorough but accessible presentation by David Mermin in his book
Boojums All the Way Through
.
¹⁴
It happens that Mermin presents these ideas within the framework of the Copenhagen Interpretation, accepting locality but denying a reality independent of the observer; my own preference is to accept reality and live with non-locality, but this just emphasizes the point that whichever interpretation you use, Bell's result still stands. The crucial point is this: Bell found that if a series of measurements of the spins of particles in a Bohm-type version of the EPR experiment is carried out, with various orientations of the detectors used to measure the spin, then if the world is both real and local the results of one set of measurements will be larger than the results of another set of measurements. This is Bell's inequality. If Bell's inequality is violated, if the results of the second set of measurements are larger than those of the first, it proves that the world does not obey local reality. He then showed that the equations of quantum mechanics tell us that the inequality must indeed be violated. Since then, other similar inequalities have been discovered; all are known as Bell inequalities, even though he did not discover them all himself. The whole package of ideas is known as Bell's theorem.

Bell's conclusion is worth quoting:

In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously.

It's noteworthy that Bell did not expect to reach such a conclusion when he started out down this path. His instinct
was to side with Einstein and assert that local reality must be the basis on which the world works. As he later wrote to the American physicist Nick Herbert:

I was deeply impressed by Einstein's reservations about quantum mechanics and his views of it as an incomplete theory. For several reasons the time was ripe for me to tackle the problem head on. The result was the reverse of what I had hoped. But I was delighted—in a region of wooliness and obscurity to have come upon something hard and clear.

In the words that Arthur Conan Doyle put into the mouth of Sherlock Holmes in
The Sign of Four
, Bell had eliminated the impossible—local reality—and so what was left, however improbable, had to be the truth.