Quantum: Einstein, Bohr and the Great Debate About the Nature of Reality - Manjit Kumar (2009)

Part IV. DOES GOD PLAY DICE?

'I want to know how God created this world. I am not interested in this or that phenomenon, in the spectrum of this or that element. I want to know His thoughts, the rest are details.'

—ALBERT EINSTEIN

Chapter 14. FOR WHOM BELL'S THEOREM TOLLS

'You believe in the God who plays dice, and I in complete law and order in a world which objectively exists, and which I, in a wildly speculative way, am trying to capture', Einstein wrote to Born in 1944.¹ 'I firmly believe, but I hope that someone will discover a more realistic way, or rather a more tangible basis than it has been my lot to find. Even the great initial success of quantum theory does not make me believe in the fundamental dice game, although I am well aware that our younger colleagues interpret this as a consequence of senility. No doubt the day will come when we shall see whose instinctive attitude was the correct one.' Twenty years passed before a discovery brought that day of judgement closer.

In 1964 the radio astronomers Arno Penzias and Robert Woodrow detected the echo of the big bang; the evolutionary biologist Bill Hamilton published his theory of the genetic evolution of social behaviour; and the theoretical physicist Murray Gell-Mann predicted the existence of a new family of fundamental particles called quarks. These were just three of the landmark scientific breakthroughs that year. Yet according to the physicist and historian of science Henry Stapp, none rivalled Bell's theorem, 'the most profound discovery of science'.² It was ignored.

Most physicists were too busy using quantum mechanics as it continued to notch up one success after another to be bothered about the subtleties of the arguments between Einstein and Bohr over its meaning and interpretation. It was little wonder they failed to recognise that a 34-year-old Irish physicist, John Stewart Bell, had discovered what Einstein and Bohr could not: a mathematical theorem that could decide between their two opposing philosophical worldviews. For Bohr there was 'no quantum world', only 'an abstract quantum mechanical description'.³ Einstein believed in a reality independent of perception. The debate between Einstein and Bohr was as much about the kind of physics that was acceptable as a meaningful theoretical description of reality as it was about the nature of reality itself.

Einstein was convinced that Bohr and the supporters of the Copenhagen interpretation were playing a 'risky game' with reality.⁴ John Bell was sympathetic to Einstein's position, but part of the inspiration behind his ground-breaking theorem lay in the work done in the early 1950s by an American physicist forced into exile.

David Bohm was a talented PhD student of Robert Oppenheimer's at the University of California at Berkeley. Born in Wilkes-Barre, Pennsylvania in December 1917, Bohm was prevented from joining the top-secret research facility in Los Alamos, New Mexico to work on the development of the atomic bomb in 1943 after Oppenheimer was appointed its director. The authorities cited Bohm's many relatives in Europe, nineteen of whom were to die in Nazi concentration camps, as the reason they considered him to be a security risk. In truth, having been questioned by US army intelligence, and attempting to secure his position as the scientific leader of the Manhattan Project, Oppenheimer had named Bohm as a possible member of the American Communist party.

Four years later, in 1947, the self-confessed 'shatterer of worlds' took charge of the 'madhouse', as Oppenheimer once called the Institute for Advanced Study in Princeton.⁵ Maybe in an attempt to atone for his earlier naming of Bohm, of which his protégé was unaware, Oppenheimer helped him obtain an assistant professorship at Princeton University. Amid the anti-Communist paranoia sweeping the United States after the Second World War, Oppenheimer was soon under suspicion because of his earlier left-wing political views. Having watched him closely for some years, the FBI had compiled a large dossier on the man who knew America's atomic secrets.

In an attempt to smear Oppenheimer, some of his friends and colleagues were investigated by the House Un-American Activities Committee and forced to appear before it. In 1948 Bohm, who had joined the American Communist party in 1942 but left after only nine months, invoked the Fifth Amendment that protected him against self-incrimination. Within a year he was subpoenaed to appear before a grand jury, and once again pleaded the Fifth. In November 1949 Bohm was arrested, charged with contempt of court and briefly imprisoned before being released on bail. Princeton University, worried about losing wealthy donors, suspended him. Although he was acquitted when his case came to trial in June 1950, the university chose to pay off the remaining year of Bohm's contract, provided he did not set foot on campus. Bohm was blacklisted and unable to find another academic post in the United States, and Einstein seriously considered appointing him as his research assistant. Oppenheimer opposed the idea and was among those who advised his former student to leave the country. In October 1951, Bohm left for Brazil and the University of São Paulo.

He had been in Brazil only a matter of weeks when the American embassy, fearing that his final destination might be the Soviet Union, confiscated Bohm's passport and reissued it as valid only for travel to the United States. Worried that his South American exile would cut him off from the international physics community, Bohm acquired Brazilian nationality to circumvent the travel ban imposed by the Americans. Back in the United States, Oppenheimer faced a hearing. Pressure on him intensified the moment it emerged that Klaus Fuchs, a physicist he had selected to work on the atomic bomb, was a Soviet spy. Einstein advised Oppenheimer to turn up, tell the committee they were fools, and return home. He did no such thing, but another hearing in the spring of 1954 revoked Oppenheimer's security clearance.

Bohm left Brazil in 1955 and spent two years at the Technion Institute in Haifa, Israel before moving to England. After four years at Bristol University, in 1961 Bohm settled once and for all in London after being appointed professor of theoretical physics at Birkbeck College. During his troubled time in Princeton, Bohm had largely devoted himself to studying the structure and interpretation of quantum mechanics. In February 1951 he published Quantum Theory, one of the first textbooks to examine in some detail the interpretation of the theory and the EPR thought experiment.

Einstein, Podolsky and Rosen had conjured up an imaginary experiment that involved a pair of correlated particles, A and B, so far apart that it should be impossible for them to physically interact with one another. EPR argued that a measurement carried out on particle A could not physically disturb particle B. Since any measurement is performed on only one of the particles, EPR believed they could cut off Bohr's counter-attack - an act of measurement causes a 'physical disturbance'. Since the properties of the two particles are correlated, they argued that by measuring a property of particle A, such as its position, it is possible to know the corresponding property of B without disturbing it. EPR's aim was to demonstrate that particle B possessed the property independently of being measured, and since this was something that quantum mechanics failed to describe, it was therefore incomplete. Bohr countered, never so succinctly, that the pair of particles were entangled and formed a single system no matter how far apart they were. Therefore, if you measured one, then you also measured the other.

'If their [EPR] contention could be proved,' wrote Bohm, 'then one would be led to search for a more complete theory, perhaps containing something like hidden variables, in terms of which the present quantum theory would be a limiting case.'⁶ But he concluded 'that quantum theory is inconsistent with the assumption of hidden causal variables'.⁷ Bohm looked at quantum theory from the prevailing Copenhagen viewpoint. However, in the process of writing his book he became dissatisfied with Bohr's interpretation, even as he agreed with the dismissal by others of the EPR argument as 'unjustified, and based on assumptions concerning the nature of matter which implicitly contradict the quantum theory at the outset'.⁸

It was the subtlety of the EPR thought experiment, and what he came to regard as the reasonable assumptions on which it was constructed, that led Bohm to question the Copenhagen interpretation. It was a brave step for a young physicist whose contemporaries were busy using quantum theory to make their reputations rather than risking career suicide by raking over the embers of a dying fire. But Bohm was already a marked man after his appearance before the House Un-American Activities Committee, and, suspended by Princeton, he had little left to lose.

Bohm presented Einstein with a copy of Quantum Theory and discussed his reservations with Princeton's most famous resident. Encouraged to examine the Copenhagen interpretation more closely, Bohm produced two papers that appeared in January 1952. In the first of these he publicly thanked Einstein 'for several interesting and stimulating discussions'.⁹ By then Bohm was in Brazil, but the papers had been written and sent to the Physical Review in July 1951, just four months after the publication of his book. Bohm appeared to have had a Paul-like conversion on the road not to Damascus, but Copenhagen.

In his papers Bohm outlined an alternative interpretation of quantum theory and argued that 'the mere possibility of such an interpretation proves that it is not necessary for us to give up a precise, rational, and objective description of individual systems at a quantum level of accuracy'.¹⁰ Reproducing the predictions of quantum mechanics, it was a mathematically more sophisticated and coherent version of Louis de Broglie's pilot wave model, which the French prince had abandoned after it was severely criticised at the 1927 Solvay conference.

Whereas the wave function in quantum mechanics is an abstract wave of probability, in the pilot wave theory it is a real, physical wave that guides particles. Just as an ocean current carries along a swimmer or a ship, the pilot wave produces a current that is responsible for the motion of a particle. The particle has a well-defined trajectory determined by the precise values of position and velocity that it possesses at any given time but which the uncertainty principle 'hides' by preventing an experimenter from measuring them.

On reading Bohm's two papers, Bell said that he 'saw the impossible done'.¹¹ Like almost everyone else, he thought that Bohm's alternative to the Copenhagen interpretation had been ruled out as impossible. He asked why no one had told him about the pilot wave theory: 'Why is the pilot wave picture ignored in textbooks? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?'¹² A part of the answer was the legendary Hungarian-born mathematician John von Neumann.

The eldest of three brothers, the Jewish banker's son was a mathematical prodigy. When his first paper was published at eighteen, von Neumann was a student at Budapest University but spent most of his time in Germany at the universities of Berlin and Göttingen, returning only to take his exams. In 1923 he enrolled at the ETH in Zurich to study chemical engineering after his father insisted that he have something more practical to fall back on than mathematics. After graduating from the ETH and gaining a doctorate from Budapest in double-quick time, von Neumann became at 23 the youngest-ever privatdozent appointed by Berlin University in 1927. Three years later he began teaching at Princeton University and in 1933 joined Einstein as a professor at the Institute for Advanced Study, remaining there for the rest of his life.

A year earlier, in 1932, the then 28-year-old von Neumann wrote a book that became the quantum physicist's bible, Mathematical Foundations of Quantum Mechanics.¹³ In it he asked whether quantum mechanics could be reformulated as a deterministic theory by the introduction of hidden variables, which, unlike ordinary variables, are inaccessible to measurement and therefore not subject to the restrictions imposed by the uncertainty principle. Von Neumann argued that 'the present system of quantum mechanics would have to be objectively false in order that another description of the elementary processes than the statistical one may be possible'.¹⁴ In other words, the answer was 'No', and he offered a mathematical proof that outlawed the 'hidden variables' approach that Bohm would adopt twenty years later.

It was an approach with a history. Ever since the seventeenth century, men like Robert Boyle had studied the various properties of gases as their pressure, volume and temperature were varied, and had discovered the gas laws. Boyle found the law describing the relationship between the volume of a gas and its pressure. He established that if a certain quantity of a gas was kept at a fixed temperature and its pressure was doubled, its volume was halved. If the pressure was increased threefold, then its volume was reduced to a third. At constant temperature, the volume of a gas is inversely proportional to the pressure.

The correct physical explanation of the gas laws had to wait until Ludwig Boltzmann and James Clerk Maxwell developed the kinetic theory of gases in the nineteenth century. 'So many of the properties of matter, especially when in gaseous form, can be deduced from the hypothesis that their minute parts are in rapid motion, the velocity increasing with temperature,' wrote Maxwell in 1860, 'that the precise nature of this motion becomes the subject of rational curiosity.'¹⁵ It led him to conclude that 'the relations between pressure, temperature, and density in a perfect gas can be explained by supposing the particles to move with uniform velocity in straight lines, striking against the sides of the containing vessel and thus producing pressure'.¹⁶ Molecules in a continual state of motion, haphazardly colliding into one another and the walls of the container holding the gas, produced the relationships between pressure, temperature and volume expressed in the gas laws. Molecules could be regarded as the unobserved microscopic 'hidden variable' that explained the observed macroscopic properties of gases.

Einstein's explanation of Brownian motion in 1905 is an example where the 'hidden variable' is the molecules of the fluid in which the pollen grains are suspended. The reason behind the erratic movement of the grains that had so perplexed everyone was suddenly clear after Einstein pointed out that it was due to the bombardment by invisible, but very real, molecules.

The appeal of hidden variables in quantum mechanics had its roots in Einstein's claim that the theory is incomplete. Maybe that incompleteness was due to the failure to capture the existence of an underlying layer of reality. This untapped seam in the form of hidden variables - possibly hidden particles, forces, or something completely new - would restore an independent, objective reality. Phenomena that at one level appear probabilistic would with the help of hidden variables be revealed as deterministic, and particles would possess a definite velocity and position at all times.

As von Neumann was acknowledged as one of the great mathematicians of the day, most physicists simply accepted, without bothering to check, that he had proscribed hidden variables when it came to quantum mechanics. For them the mere mention of 'von Neumann' and 'proof' was enough. However, von Neumann admitted that there remained the possibility, though small, that quantum mechanics might be wrong. 'In spite of the fact that quantum mechanics agrees well with experiment, and that it has opened up for us a qualitatively new side of the world, one can never say of the theory that it has been proved by experience, but only that it is the best known summarization of experience',¹⁷ he wrote. Yet despite these words of caution, von Neumann's proof was held to be sacrosanct. Virtually everyone misinterpreted it as proving that no theory of hidden variables could reproduce the same experimental results as quantum mechanics.

When he analysed von Neumann's argument, Bohm believed that it was wrong but could not clearly pinpoint the weakness. Nevertheless, encouraged by his discussions with Einstein, Bohm attempted to construct the hidden variables theory that was deemed to be impossible. It would be Bell who demonstrated that one of the assumptions used by von Neumann was unwarranted, and therefore that his 'impossibility' proof was incorrect.

Born in July 1928 in Belfast, John Stewart Bell was descended from a family of carpenters, blacksmiths, farm workers, labourers and horse dealers. 'My parents were poor but honest', he once said.¹⁸ 'Both of them came from large families of eight or nine that were traditional of the working class people of Ireland at that time.' With a father who was in and out of work, Bell's childhood was far removed from the comfortable middle-class upbringing of the quantum pioneers. Nevertheless, before he reached his teens, the bookish Bell had earned the nickname 'The Prof', even before he told his family that he wanted to become a scientist.

There was an older sister and two younger brothers, and though their mother believed that a good education was the route to future prosperity for her children, John was the only one who went on to secondary school aged eleven. It was not a lack of ability that denied his siblings the same opportunity, only a shortage of money for a family always struggling to make ends meet. Luckily the family came into a small sum of money that enabled Bell to enrol at the Belfast Technical High School. Not as prestigious as some of the other schools in the city, it offered a curriculum that combined the academic and the practical that suited him. In 1944, aged sixteen, Bell gained the qualifications necessary to study at Queen's University in his home town.

With seventeen the minimum age for admission and his parents unable to finance his university studies, Bell looked for work and fortuitously found it as an assistant technician in the laboratory of the physics department at Queen's University. Before long, the two senior physicists recognised Bell's abilities and allowed him to attend the first-year lectures whenever his duties permitted. His enthusiasm and obvious talent were rewarded with a small scholarship, and this, together with the money he was able to set aside, meant that he returned after his year as a technician as a fully-fledged physics student. With the sacrifices that he and his parents had made, Bell was focused and driven. He proved to be an exceptional student and in 1948 obtained a degree in experimental physics. A year later he gained another in mathematical physics.

Bell admitted that he 'had a very bad conscience about having lived off my parents for so long, and thought I should get a job'.¹⁹ With his two degrees and glowing references, he went to England to work for the United Kingdom Atomic Energy Research Establishment. In 1954 Bell married a fellow physicist, Mary Ross. In 1960, having gained a PhD from Birmingham University, he and his wife moved to CERN, the Conseil Européen pour la Recherche Nucléaire, near Geneva, Switzerland. For a man who would make his name as a quantum theorist, Bell's job was designing particle accelerators. He was proud to call himself a quantum engineer.

Bell first came across von Neumann's proof in 1949, his last year as a student in Belfast, when he read Max Born's new book, Natural Philosophy of Cause and Chance. 'I was very impressed that somebody - von Neumann - had actually proved that you couldn't interpret quantum mechanics as some sort of statistical mechanics', he later recalled.²⁰ But Bell did not read von Neumann's book as it was written in German and he did not know the language. Instead he accepted Born's word for the soundness of von Neumann's proof. According to Born, von Neumann had put quantum mechanics on an axiomatic basis by deriving it from a few postulates of a 'very plausible and general character', such that the 'formalism of quantum mechanics is uniquely determined by these axioms'.²¹ In particular, Born said, it meant that 'no concealed parameters can be introduced with the help of which the indeterministic description could be transformed into a deterministic one'.²² Implicitly, Born was arguing in favour of the Copenhagen interpretation, because 'if a future theory should be deterministic, it cannot be a modification of the present one but must be essentially different'.²³ Born's message was that quantum mechanics is complete, therefore it cannot be modified.

It was 1955 before von Neumann's book was published in English, but by then Bell had read Bohm's papers on hidden variables. 'I saw that von Neumann must have been just wrong', he said later.²⁴ Yet Pauli and Heisenberg branded Bohm's hidden variables alternative as 'metaphysical' and 'ideological'.²⁵ The ready acceptance of von Neumann's impossibility proof proved only one thing to Bell, a 'lack of imagination'.²⁶ Nevertheless, it had allowed Bohr and the advocates of the Copenhagen interpretation to consolidate their position even while some of them suspected that vonNeumann might be wrong. Even though he later dismissed Bohm's work, Pauli in his published lectures on wave mechanics wrote that 'no proof of the impossibility of extending [i.e. completing quantum theory by hidden variables] has been given'.²⁷

For 25 years, hidden variable theories had been ruled impossible by the authority of von Neumann. However, if such a theory could be constructed to yield the same predictions as quantum mechanics, then there would be no reason for physicists to simply accept the Copenhagen interpretation. When Bohm demonstrated that such an alternative was possible, the Copenhagen interpretation was so well entrenched as the only interpretation of quantum mechanics that he was either ignored or attacked. Einstein, who had initially encouraged him, dismissed Bohm's hidden variables as 'too cheap'.²⁸

'I think he was looking for a much more profound rediscovery of quantum phenomena', Bell said as he tried to understand Einstein's reaction.²⁹ 'The idea that you could just add a few variables and the whole thing would remain unchanged apart from the interpretation, which was a kind of trivial addition to ordinary quantum mechanics, must have been a disappointment to him.' Bell was convinced that Einstein wanted to see some grand new principle emerge on a par with the conservation of energy. Instead, what Bohm offered Einstein was an interpretation that was 'non-local', requiring the instantaneous transmission of so-called 'quantum mechanical forces'. There were other horrors lurking in Bohm's alternative. 'For example,' clarified Bell, 'the trajectories that were assigned to the elementary particles were instantaneously changed when anyone moved a magnet anywhere in the universe.'³⁰

It was in 1964, during a year-long sabbatical from CERN and his day job designing particle accelerators, that Bell found the time to enter the Einstein-Bohr debate. Bell decided to find out if non-locality was a peculiar feature of Bohm's model or if it was a characteristic of any hidden variable theory that aimed to reproduce the results of quantum mechanics. 'I knew, of course, that the Einstein-Podolsky-Rosen setup was the critical one, because it led to distant correlations', he explained. 'They ended their paper by stating that if you somehow completed the quantum mechanical description, non-locality would only be apparent. The underlying theory would be local.'³¹

Bell started out trying to preserve locality by attempting to construct a 'local' hidden variable theory in which if one event caused another, then there had to be enough time between the two to allow a signal travelling at the speed of light to pass between them. 'Everything I tried didn't work', he said later.³² 'I began to feel that it very likely couldn't be done.' In his attempt to eliminate what Einstein decried as 'spooky actions at a distance', non-local influences that were transmitted instantly between one place and another, Bell derived his celebrated theorem.³³

He began by looking at a version of the EPR thought experiment first devised by Bohm in 1951 that was simpler than the original. Whereas Einstein, Podolsky and Rosen had used two properties of a particle, position and momentum, Bohm used only one, quantum spin. First proposed in 1925 by the young Dutch physicists George Uhlenbeck and Samuel Goudsmit, the quantum spin of a particle had no analogue in classical physics. An electron had just two possible spin states, 'spin-up' and 'spin-down'. Bohm's adaptation of EPR involved a spin-zero particle that disintegrates and in the process produces two electrons, A and B. Since their combined spin must remain zero, one electron must have spin-up and the other spin-down.³⁴ Flying off in opposite directions until they are far enough apart to rule out any physical interaction between them, the quantum spin of each electron is measured at exactly the same time by a spin detector. Bell was interested in the correlations that could exist between the results of these simultaneous measurements carried out on pairs of such electrons.

The quantum spin of an electron can be measured independently in any one of three directions at right angles to each other, labelled x, y, and z.³⁵ These directions are just the normal three dimensions of the everyday world in which everything moves - left and right (x-direction), up and down (y-direction), and back and forth (z-direction). When the spin of electron A is measured along the x-direction by a spin-detector placed in its path, it will be either 'spin-up' or 'spin-down'. The odds are 50-50, the same as those for flipping a coin to see whether it lands heads or tails. In both cases, whether it is one or the other is pure chance. But as with flipping a coin repeatedly, if the experiment is done again and again, then electron A will be found to have spin-up in half the measurements and spin-down in the rest.

Unlike two coins that are flipped at the same time, each of which can be heads or tails, as soon as the spin of electron A is measured as spin-up, then a simultaneous measurement of the spin of electron B along the same direction will reveal it to be spin-down. There is a perfect correlation between the results of the two spin measurements. Bell later attempted to demonstrate that there was nothing strange about the nature of these correlations: 'The philosopher in the street, who has not suffered a course in quantum mechanics, is quite unimpressed by Einstein-Podolsky-Rosen correlations. He can point to many examples of similar correlations in everyday life. The case of Bertlemann's socks is often cited. Dr Bertlemann likes to wear two socks of different colours. Which colour he will have on a given foot on a given day is quite unpredictable. But when you see that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience of Bertlemann, gives immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is not the EPR business the same?'³⁶ As with the colour of Bertlemann's socks, given that the spin of the parent particle is zero, it is no surprise that once the spin of electron A along any direction is measured as spin-up, the spin of electron B in the same direction is confirmed as spin-down.

According to Bohr, until a measurement is made, neither electron A nor electron B has a pre-existing spin in any direction. 'It is as if we had come to deny the reality of Bertlemann's socks,' said Bell, 'or at least of their colours, when not looked at.'³⁷ Instead, before they are observed, the electrons exist in a ghostly superposition of states so that they are spin-up and spin-down at the same time. Since the two electrons are entangled, the information concerning their spin states is given by a wave function simi-lar to = (A spin-up and B spin-down)+(A spin-down and B spin-up). Electron A has no x-component of spin until a measurement to determine it causes the wave function of the system, A and B, to collapse, and then it is either spin-up or spin-down. At that very moment, its entangled partner B acquires the opposite spin in the same direction, even if it is on the other side of the universe. Bohr's Copenhagen interpretation is non-local.

Einstein would explain the correlations by arguing that both electrons possess definite values of quantum spin in each of the three directions x, y, and z whether they are measured or not. For Einstein, said Bell, 'these correlations simply showed that the quantum theorists had been hasty in dismissing the reality of the microscopic world'.³⁸ Since the pre-existing spin states of the electron pair cannot be accommodated by quantum mechanics, this led Einstein to conclude that the theory was incomplete. He did not dispute the correctness of the theory, only that it was not a complete picture of physical reality at the quantum level.

Einstein believed in 'local realism': that a particle cannot be instantly influenced by a distant event and that its properties exist independently of any measurement. Unfortunately, Bohm's clever reworking of the original EPR experiment could not distinguish between the positions of Einstein and Bohr. Both men could account for the results of such an experiment. Bell's stroke of genius was to discover a way out of the impasse by changing the relative orientation of the two spin detectors.

If the spin detectors measuring electrons A and B are aligned so that they are parallel, then there is a 100 per cent correlation between the two sets of measurements - whenever spin-up is measured by one detector, spin-down is recorded by the other and vice versa. If one of the detectors is rotated slightly, then they are no longer perfectly aligned. Now if the spin states of many pairs of entangled electrons are measured, when A is found to be spin-up, the corresponding measurement of its partner B will sometimes also be spin-up. Increasing the angle of orientation between the detectors results in a reduction in the degree of correlation. If the detectors are at 90 degrees to each other and the experiment is once again repeated many times, when A is measured along the x-direction as spin-up, only in half of these instances will B be detected as spin-down. If the detectors are orientated at 180 degrees to one another, then the pair of electrons will be completely anti-correlated. If A's spin state is measured as spin-up, then B's will also be spin-up.

Although a thought experiment, it was possible to calculate the exact degree of spin correlation for a given orientation of the detectors predicted by quantum mechanics. However, it was not possible to do a similar calculation using an archetypal hidden variables theory that preserved locality. The only thing that such a theory would predict was a less than perfect match between spin states of A and B. This was not enough to decide between quantum mechanics and a local hidden variables theory.

Bell knew that any actual experiment that found spin correlations in line with the predictions of quantum mechanics could easily be disputed. After all, it was possible that in the future someone might develop a hidden variables theory that also exactly predicted the spin correlations for different orientations of the detectors. Bell then made an astonishing discovery. It was possible to decide between the predictions of quantum mechanics and any local hidden variables theory by measuring the correlations of pairs of electrons for a given setting of the spin detectors and then repeating the experiment with a different orientation.

This enabled Bell to calculate the total correlation for both sets of orientations in terms of the individual results predicted by any local hidden variables theory. Since in any such theory the outcome of a measurement at one detector cannot be affected by what is measured at the other, it is possible to distinguish between hidden variables and quantum mechanic.

Bell was able to calculate the limits on the degree of spin correlation between pairs of entangled electrons in a Bohm-modified EPR experiment. He found that in the ethereal realm of the quantum there is a greater level of correlation if quantum mechanics reigns supreme than in any world that depends on hidden variables and locality. Bell's theorem said that no local hidden variables theory could reproduce the same set of correlations as quantum mechanics. Any local hidden variables theory would lead to spin correlations that generated numbers, called the correlation coefficient, between -2 and +2. However, for certain orientations of the spin detectors, quantum mechanics predicted correlation coefficients that lay outside of the range known as 'Bell's inequality' that ran from -2 to +2.³⁹

Although Bell, with his red hair and pointed beard, was difficult to miss, his extraordinary theorem was ignored. This was hardly surprising, since in 1964 the journal to get noticed in was the Physical Review, published by the American Physical Society. The problem for Bell was that the Physical Review charged, and it was your university that usually paid the bill once your paper was accepted. As a guest at Stanford University in California at the time, Bell did not want to abuse the hospitality he had been shown by asking the university to pay. Instead, his six-page paper, 'On the Einstein Podolsky Rosen Paradox', was published in the third issue of Physics, a little-read, short-lived journal that actually paid its contributors.⁴⁰

In fact this was the second paper that Bell wrote during his sabbatical year. The first reconsidered the verdict of von Neumann and others that 'quantum mechanics does not permit a hidden variable interpretation'.⁴¹ Unfortunately, mis-filed by the Review of Modern Physics, with a letter from the editor going astray causing a further delay, the paper was not published until July 1966. It was, wrote Bell, aimed at those 'who believe that "the question concerning the existence of such hidden variables received an early and rather decisive answer in the form of von Neumann's proof on the mathematical impossibility of such variables in quantum theory"'.⁴² He went on to show, once and for all, that von Neumann had been wrong.

A scientific theory that does not agree with experimental facts will either be modified or discarded. Quantum mechanics, however, had passed every test it had been subjected to. There was no conflict between theory and experiment. For the vast majority of Bell's colleagues, young and old alike, the dispute between Einstein and Bohr over the correct interpretation of quantum mechanics was more philosophy than physics. They shared Pauli's view, expressed in a letter to Born in 1954, that 'one should no more rack one's brain about the problem of whether something one cannot know anything about exists all the same, than about the ancient question of how many angels are able to sit on the point of a needle'.⁴³ To Pauli it seemed 'that Einstein's questions are ultimately always of this kind' in his critique of the Copenhagen interpretation.⁴⁴

Bell's theorem changed that. It allowed the local reality advocated by Einstein, that the quantum world exists independently of observation and that physical effects cannot be transmitted faster than the speed of light, to be tested against Bohr's Copenhagen interpretation. Bell had brought the Einstein-Bohr debate into a new arena, experimental philosophy. If Bell's inequality held, then Einstein's contention that quantum mechanics was incomplete would be right. However, should the inequality be violated, then Bohr would emerge the victor. No more thought experiments; it was Einstein vs. Bohr in the laboratory.

It was Bell who first challenged the experimentalists to put his inequality to the test when he wrote in 1964 that 'it requires little imagination to envisage the measurements involved actually being made'.⁴⁵ But like Gustav Kirchhoff and his imaginary blackbody a century earlier, it is easier for a theorist to 'envisage' an experiment than for his colleagues to realise it in practice. Five years passed before Bell received a letter in 1969 from a young physicist at Berkeley in California. John Clauser, then 26, explained that he and others had devised an experiment to test the inequality.

Two years earlier, Clauser had been a doctoral student at New York's Columbia University when he first came across Bell's inequality. Convinced that it was worth testing, Clauser went to see his professor and was bluntly told that 'no decent experimentalist would ever go to the effort of actually trying to measure it'.⁴⁶ It was a reaction in keeping with the near 'universal acceptance of quantum theory and its Copenhagen interpretation as gospel', Clauser wrote later, 'along with a total unwillingness to even mildly question the theory's foundations'.⁴⁷ Nevertheless, by the summer of 1969 Clauser had devised an experiment with the help of Michael Horne, Abner Shimony and Richard Holt. It required the quartet to fine-tune Bell's inequality so that it could be tested in a real laboratory rather than in the imaginary laboratory of the mind equipped with perfect instruments.

Clauser's search for a postdoctoral position took him to the University of California at Berkeley, where he had to settle for a job doing radio astronomy. Luckily, when Clauser explained to his new boss the experiment he really wanted to perform, he was allowed to devote half of his time to it. Clauser found a willing graduate student, Stuart Freedman, to help. Instead of electrons, Clauser and Freedman used pairs of correlated photons in their experiment. The switch was possible because photons have a property called polarisation that for the purposes of the test played the role of quantum spin. Although a simplification, a photon can be regarded as being polarised either 'up' or 'down'. Just like electrons and spin, if the polarisation of one photon along the x-direction is measured as 'up', then the other will be measured as 'down', since the combined polarisations of both photons must be zero.

The reason for employing photons rather than electrons is that they are easier to produce in the laboratory, especially since the experiment would involve numerous pairs of particles being measured. It was 1972 before Clauser and Freedman were ready to put Bell's inequality to the test. They heated calcium atoms until they acquired enough energy for an electron to jump from the ground state to a higher energy level. As the electron fell back down to the ground state, it did so in two stages and emitted a pair of entangled photons, one green and the other blue. The photons were sent in opposite directions until detectors simultaneously measured their polarisations. The two detectors were initially oriented at 22.5 degrees relative to each other for the first set of measurements, and then realigned at 67.5 degrees for the second set. Clauser and Freedman found, after 200hours of measurements, that the level of photon correlations violated Bell's inequality.

It was a result in favour of Bohr's non-local Copenhagen interpretation of quantum mechanics with its 'spooky action at a distance', and against the local reality backed by Einstein. But there were serious reservations as to the validity of the outcome. Between 1972 and 1977 different teams of experimenters conducted nine separate tests of Bell's inequality. It was violated in only seven.⁴⁸ Given these mixed results, there were misgivings concerning the accuracy of the experiments. One problem was the inefficiency of the detectors that resulted in only a small fraction of the total number of pairs generated being measured. No one knew precisely what effect this had on the level of correlations. There were other loopholes that needed to be closed before it could be conclusively shown for whom Bell's theorem tolled.

As Clauser and others were busy planning and executing their experiments, a French physics graduate was doing voluntary work in Africa and spending his spare time reading up on quantum mechanics. It was while working his way through an influential French textbook on the subject that Alain Aspect first became fascinated by the EPR thought experiment. After reading Bell's seminal papers, he began thinking about subjecting Bell's inequality to a rigorous test. In 1974, after three years in Cameroon, Aspect returned to France.

The 27-year-old set about making his African dream come true in a basement laboratory at the Institut d'Optique Théoretique et Appliquée, Université Paris-Sud in Orsay. 'Do you have a permanent position?' Bell asked, when Aspect went to see him in Geneva.⁴⁹ Aspect explained that he was just a graduate student aiming for a doctorate. 'You must be a very courageous graduate student', replied Bell.⁵⁰ He was concerned that the young Frenchman could be damaging his future prospects by attempting to conduct such a difficult experiment.

It took longer than he imagined at the outset, but in 1981 and 1982 Aspect and his collaborators used the latest technological innovations, including lasers and computers, to perform not one but three delicate experiments to test Bell's inequality. Like Clauser, Aspect measured the correlation of the polarisation of entangled pairs of photons moving in opposite directions after being simultaneously emitted from individual calcium atoms. However, the rate at which photon pairs were created and measured was many times higher. His experiments revealed, said Aspect, 'the strongest violation of Bell's inequalities ever achieved, and excellent agreement with quantum mechanics'.⁵¹

Bell was one of the examiners when Aspect received his doctorate in 1983, but some doubts remained concerning the results. Since the nature of quantum reality hung in the balance, every possible loophole, however improbable, had to be considered. For example, the possibility that the detectors might somehow be signalling to each other was later eliminated by the random switching of their orientation while the photons were in mid-flight. Although it fell short of being the definitive experiment, further refinements and other investigations in the years since have led to Aspect's original results being confirmed. Although no experiment has been conducted in which every possible loophole is closed, most physicists accept that Bell's inequality has been violated.

Bell derived the inequality from just two assumptions. First, there exists an observer-independent reality. This translates into a particle having a well-defined property such as spin before it is measured. Second, locality is preserved. There is no faster-than-light influence, so that what happens here cannot possibly instantaneously affect what happens way over there. Aspect's results mean that one of these two assumptions has to be given up, but which one? Bell was prepared to give up locality. 'One wants to be able to take a realistic view of the world, to talk about the world as if it is really there, even when it is not being observed', he said.⁵²

Bell, who died in October 1990 at the age of 62 from a brain haemorrhage, was convinced that 'quantum theory is only a temporary expedient' that would eventually be replaced by a better theory.⁵³ Nevertheless, he conceded that experiments had shown that 'Einstein's world view is not tenable'.⁵⁴ Bell's theorem tolled for Einstein and local reality.