Quantum
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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 similar 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 mechanics.
Bell was able to calculate the limits on the degree of spin correlation between pa
irs 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 coefficients, 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 200 hours 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.