by John Gribbin
Hermann's discovery of the failure of von Neumann's “proof” was published in 1935, but only in German and in a journal devoted more to philosophy than to physics, which physicists did not read. That also partly explains why it faded into obscurity.5 But Heisenberg knew of it, directly from Hermann, and it is a mystery that will now never be resolved why he did not at least draw it to the attention of a wider circle of quantum physicists. Hermann herself was never in a position to promote her finding, even if she had wanted to, because of the dramatic changes in her life and career brought about by the political developments in Germany; in any case, though, she does not seem to have been particularly enamored of hidden variables theories, and had simply been concerned as a mathematician with setting the record straight about von Neumann's claim. To all intents and purposes, in the quantum physics community it was as if Hermann had not existed, and from 1932 onwards “everybody knew” that hidden variables theories would not work, because Johnny von Neumann said so. Even people who never read his book believed this, because they had been told it was so. But while hidden variables theories languished, Einstein, along with a couple of colleagues, pointed out another problem with the Copenhagen Interpretation—in fact, an aspect of the “problem” with de Broglie's pilot wave pointed out by Pauli.
SPOOKY ACTION AT A DISTANCE
Einstein first expressed the idea behind what became known as the “EPR paradox,” although I prefer the term “puzzle,” in 1933, at another Solvay Congress. Leon Rosenfeld, one of Niels Bohr's collaborators, recalled that after a lecture by Bohr Einstein pointed out to Rosenfeld that if two particles interacted with one another and then flew apart,
an observer who gets hold of one of the particles, far away from the region of interaction, and measures its momentum…[will] from the conditions of the experiment,…obviously be able to deduce the momentum of the other particle. If, however, he chooses to measure the position of the first particle, he will be able to tell where the other particle is…is it not paradoxical? How can the final state of the second particle be influenced by a measurement performed on the first, after all physical connection has ceased between them?6
His point is that, according to the Copenhagen Interpretation, neither particle has a definite position or momentum until it is measured. So if measuring one particle immediately determines the state of the other particle, the particles seem to be connected by what he later called “spooky action at a distance,”7 as in my “thought experiment” involving the two cats. Rosenfeld said later that at the time he didn't realize that Einstein saw this as anything more than an illustration of the unfamiliar features of quantum phenomena, and that two years later, when Einstein presented a more complete version of the puzzle in a paper co-authored with Boris Podolsky and Nathan Rosen (hence EPR), it came to Bohr's group “as a bolt from the blue.”8
Shortly after the 1933 Solvay Congress, Einstein, like Hermann and so many other scientists a refugee from Nazi persecution, settled in what became his final academic home, the Institute for Advanced Study in Princeton. He was assigned Nathan Rosen, then aged twenty-four, as his assistant, and he already knew Boris Podolsky, a Russian-born American physicist who had moved to the United States with his family in 1913, when he was seventeen. The basic idea of the EPR paper was, of course, Einstein's; Rosen helped as a good assistant should, and Podolsky was recruited not only as a sounding board but to write the paper, since at that time Einstein's English was rather limited. Indeed, Podolsky's English wasn't perfect, as the missing “the” in the title of the paper, “Can Quantum-Mechanical Description of Physical Reality be Considered Complete?” suggests. More seriously, though, Einstein was never happy with the published version of the paper, feeling that Podolsky had obscured his fundamental point by elaborating the argument along philosophical lines. That need not bother us, since the essence is what Einstein said to Rosenfeld in 1933. But a couple of quotes from the EPR paper are apposite. First, a definition of an “element of physical reality,” with their emphasis: “If, without in any way disturbing a system, we can predict with certainty (i.e., with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity.” In other words, particles do have real positions and momenta, even when we are not observing them.9 Secondly, the paper points out that the Copenhagen Interpretation “makes the reality of P and Q [momentum and position for the second particle] depend on the process of measurement carried out on the first system, which does not disturb the second system in any way. No reasonable definition of reality could be expected to permit this.” So: “We are thus forced to the conclusion that the quantum-mechanical description of physical reality given by the wave function is not complete.” As we shall see, Einstein was right on this point; but, ironically, he was (probably) wrong about spooky action at a distance, and the “reasonableness” of reality.
Schrödinger responded enthusiastically to the paper, writing to Einstein that “my interpretation is that we do not have a q.m. that is consistent with relativity theory, i.e., with a finite transmission speed of all influences.” But he, too, was right for the wrong reason.
The most important point is made right at the end of the paper: “While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible.” Not only was it possible—de Broglie had already found it! But de Broglie's description of reality also includes the spooky action at a distance that Einstein abhorred: for the model that de Broglie had found, when applied to two or more particles, also requires that they influence one another in this way. This property is known more formally, as I have already noted in passing, as non-locality.10 In 1935, though, nobody worried about that. After all, von Neumann had “proved” that hidden variables theories were impossible. Instead, the EPR paper provoked a frantic burst of work by Bohr and his colleagues, culminating in a paper claiming to refute the argument. Bohr's counter-argument is itself rather woolly and “philosophical” in the sense Einstein disliked, and didn't really resolve the debate, so I shall not go into it here. A few people puzzled about the meaning of the EPR paper and the nature of reality, but most physicists were happy to accept the Copenhagen Interpretation FAPP, and very soon the outbreak of the Second World War gave them much more immediate problems to tackle. It was not until things settled down after the war that somebody did what was thought by all those who trusted von Neumann to be impossible and, without knowing about de Broglie's work, came up with a working hidden variables theory.
BOHM DOES THE IMPOSSIBLE
David Bohm didn't start out trying to upset the quantum mechanical applecart. He had been born in 1917 in the relative backwater of Wilkes-Barre, Pennsylvania, where his early interest in science was stirred by reading science fiction. He graduated from Pennsylvania State University in 1939, and moved on to Caltech and then to the University of California, Berkeley, to work for a PhD under Robert Oppenheimer. As a student, he was active in left-wing politics and a member of the Young Communist League. When Oppenheimer was given responsibility for the scientific side of the Manhattan Project to develop a nuclear bomb, he wanted Bohm to come with him to the new secret research laboratory at Los Alamos, but the military authorities vetoed this because of Bohm's political affiliations. So Bohm stayed in Berkeley, but worked on a problem involving interactions between protons and neutrons that was relevant to the Manhattan Project, reporting his results to Oppenheimer. Because of the secrecy surrounding this project, when he completed this work in 1943 he was not even allowed to write up a formal PhD thesis, let alone explain his work to the examiners, who awarded the degree solely on Oppenheimer's word that the work merited it. He continued to do theoretical work relevant to the development of the nuclear bomb until the end of the war, then moved to Princeton University.
At Princeton, after teaching a cou
rse on quantum mechanics Bohm wrote a textbook on the subject (entitled simply Quantum Theory) that was published in 1951 and became an instant classic. He wrote it “primarily in order to obtain a better understanding of the subject.” It set out clearly the standard Copenhagen Interpretation, and led to discussions with Einstein, who had seen an early version, and who said that while Bohm had “explained Bohr's point of view as well as could probably be done,” that didn't mean Bohr was right. Bohm himself reflected: “After the work was finished, I looked back over what I had done and still felt somewhat dissatisfied.”11 But in the book, as well as explaining Bohr's version of quantum mechanics better than Bohr did himself, Bohm also explains the EPR puzzle better than Podolsky had done in the EPR paper itself, using the example of particle spin rather than position and momentum. This is the way the puzzle has usually been described since that time, and the way the predictions were tested in experiments, so it is worth elaborating a little.
In this version of the experiment (still purely hypothetical in 1951), two particles interact and fly off in different directions as before. But the important characteristic of the particles now is that they must have opposite spins to one another. “Roughly speaking,” said Bohm, “this means that the spin of each particle points in a direction exactly opposite to that of the other, insofar as the spin may be said to have any definite direction at all.” But, according to the Copenhagen Interpretation, the direction of spin is not definite—it is not an “element of physical reality”—until it is measured. It could be up, down, sideways, or at any angle in between. And a spin at any angle can be specified in terms of a combination of a certain amount of “up” spin and a certain amount of “sideways” spin (these are known as the spin components). In the experiment imagined by Bohm, an experimenter can choose which direction of spin (which component) to measure after the two particles have interacted. Whichever component is measured, the equivalent component of the other particle must have the opposite spin. How is this possible unless the spins were indeed “elements of physical reality” (hidden variables) all along?
Having presented this clear explanation of the EPR puzzle, Bohm proceeded to knock it down! He claimed that Einstein and his colleagues had made an invalid assumption (since he was wrong, I won't go into details) and concluded that “no theory of mechanically determined hidden variables can lead to all of the results of the quantum theory [by which he means the Copenhagen Interpretation].” He acknowledged that it might in principle be possible to test this assertion by experiment, and that although “unfortunately, such an experiment is still far beyond present techniques…it is quite possible that it could someday be carried out. Until and unless some such disagreement between quantum theory and experiment is found however, it seems wisest to assume that quantum theory is substantially correct.”
But even while the book was going through the publishing process, Bohm changed his mind, partly as a result of discussions with Einstein. He found an “impossible” hidden variables theory that worked (essentially, a rediscovery in more fully worked out form of de Broglie's pilot wave), and published a pair of papers on the subject in the prestigious Physical Review in 1952. But by then Bohm's life was in turmoil, and he was in no position to promote the idea effectively.
At the end of the 1940s there was a growing paranoia in America about the “communist threat,” and as the Cold War began Congress set up the now notorious House Un-American Activities Committee, chaired by Senator Joseph McCarthy, to seek out communist sympathizers in positions of influence or responsibility. The nature of their investigations is neatly summed up by the present-day definition of “McCarthyism” in Wikipedia: the practice of making accusations of disloyalty, subversion or treason without proper regard for evidence. As somebody who had worked, if only peripherally, on the Manhattan Project, and had once been a member of a communist organization, Bohm was an early target of the committee; he was called before it in the spring of 1949, but refused to testify. As a result, he was charged with contempt of Congress, and suspended by Princeton University. Even though he was acquitted in 1951, and according to legend Einstein asked for Bohm to return as his assistant, Princeton refused to renew his contract. With no prospect of continuing his career in the United States, Bohm moved to Brazil, and was based at the University of São Paulo when his two-part paper on “A Suggested Interpretation of the Quantum Theory in terms of ‘Hidden’ Variables” appeared in the Physical Review in 1952. Never happy in Brazil, Bohm moved to Israel in 1957, then to England, eventually (in 1961) settling at Birkbeck College in London. He died in 1992.
Bohm's big idea met with an unenthusiastic response. The old guard of quantum physicists—people like Heisenberg and Pauli—were too set in their ways and dismissed it out of hand. The younger generation, raised on the Copenhagen Interpretation and happy that it worked FAPP, could not be bothered with a new idea that “only,” as far as they could see, reproduced all the results of the Copenhagen Interpretation. To such people, Bohm's papers did not seem to contain any new physics. Just two people were impressed: Louis de Broglie, who happily took up this revival of the pilot wave idea; and a young physicist working at the UK Atomic Energy Research Establishment, who knew about de Broglie's work and von Neumann's “proof,” and was astonished “to see the impossible done.” His name was John Bell, and he would be responsible for the most profound re-interpretation of quantum mechanics since its inception.
FROM BELFAST TO BOHM, AND BEYOND
John Stewart Bell was born in Belfast on July 28, 1928—the year after de Broglie presented his pilot wave idea to an unimpressed Solvay Congress. Bell's father was also named John, so “our” John Bell was known as Stewart to his family. In an interview with Jeremy Bernstein, Bell described his family as “poor but honest,” traditional working-class people typical of Northern Ireland at the time.12 His father had worked as a horse dealer, village blacksmith, and self-taught electrician; with an older daughter, Ruby, and two younger sons, David and Robert, to support as well as John, the family finances were stretched to the limit, and the usual expectation in families such as these was the children would leave school at about the age of fourteen and begin working. But, like many other working-class mothers, John senior's wife, Annie, saw education as the only way out of poverty. John Stewart was a bright child with an early interest in books and science, and did very well at his first schools, Ulsterville Avenue and Fane Street. When he was eleven he easily passed the examination allowing him to move on to secondary school; but secondary education in the UK was not free at the time, so the only hope was for the boy to pass more examinations which would be rewarded with scholarships. Annie encouraged his ambition to move on to secondary school, and although “I sat many examinations for the more prestigious secondary schools, hoping for scholarships, but I didn't win any,” she found funding from somewhere—John never knew where—for him to attend Belfast Technical High School, the least expensive option, where alongside the usual academic courses he was taught bricklaying, carpentry and book-keeping.
Bell did not, though, confine himself to the curriculum. Although he had been confirmed in the Protestant Church of Ireland, like many adolescents he began to question the teaching of the Church, and to doubt the existence of God. Unlike many adolescents, he sought answers to these questions by reading “thick books on Greek philosophy,” but soon became disillusioned with philosophy as well, and turned to physics. “Although physics does not address itself to the ‘biggest’ questions, still it does try to find out what the world is like. And it progresses. One generation builds on the work of another.” Bell's own progress then took a providential detour. At the age of sixteen, he graduated from the High School and qualified academically to move on to university. The only financially viable option was for him to carry on living with his parents and attend Queen's University in Belfast. This was (and is) an excellent university, but would not admit anyone younger than seventeen. In order to fill in the year he would have to wait, Bel
l applied unsuccessfully for many jobs before ending up as a laboratory assistant at the university itself. It was the best thing that could have happened. He met his future professors, who took a keen interest in this highly motivated young man, lent him books and gave him advice. In effect, “I did the first year of my college physics when I was cleaning out the lab and setting out wires for the students.” With this flying start, when Bell finally began his undergraduate studies in 1945 he sailed through the course, graduating with first class honors in experimental physics in 1948. By then, he had become intrigued by quantum physics (indeed, he had read popular books on quantum mechanics when he was still at the High School), and was able to stay on for a year, earning a first class degree in mathematical physics in 1949. He had also read Max Born's book Natural Philosophy of Cause and Chance, and accepted at face value Born's assertion that von Neumann had proven hidden variables theories to be impossible. Referring to von Neumann's “brilliant book,” Born said:
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.
