Spooky Action at a Distance and the Bell Inequality
It is 50 years since John Bell published a paper on the nature of reality which is often quoted but also often misunderstood. This may clear up some of the confusion.
The paper was titled “On the Einstein-Podolsky-Rosen Paradox”, and begins by noting that the so-called 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.” Bell says that “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.” 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 World 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 detailed but accessible presentation by David Mermin in his book Boojums All The Way Through. 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 emphasises the point that whichever interpretation you use Bell’s result still stands. The crucial point is that Bell found that if a series of measurements of the spins of particles in a 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 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; they are all 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 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 unto the mouth of Sherlock Holmes, in The Sign of Four, Bell had eliminated the impossible — local reality. What was left, however improbable, had to be the truth.
But it is one thing to prove mathematically that the world is either unreal or non-local, and quite another to prove it by experiment. Bell realised this; at the end of his paper he said “The example considered above has the advantage that it requires little imagination to envisage the measurements involved actually being made.” Little imagination, but a great deal of experimental skill. Astonishingly it was less than ten years before the first such experiments were carried out by a team headed by Alain Aspect.
The essence of the experiments to test Bell’s theorem is that photons from a single source fly off in opposite directions, and that their polarizations at various angles across the line of sight are measured at detectors as far away as possible from the source. The angle of polarization being measured can be chosen by setting one detector — a polarizing filter — at a particular angle, and the number of photons passing through the filter (let’s call it filter A) can be compared with the number of photons passing through a filter set at another, carefully chosen, angle on the other wing of the experiment (let’s call it filter B). The results of first-generation experiments, notably those of John Clauser, showed that the setting of filter A affected the number of photons passing through filter B. Somehow, the photons arriving at B “knew” the setting of A, and adjusted their behaviour accordingly. This is startling enough, but it does not yet prove that the communication between A and B is happening faster than light (non-locally), because the whole experimental setup is determined before the photons leave the source. Conceivably, some signal could be travelling between A and B at less than the speed of light, so that they are in some sense coordinated, before the photons reach them. This would still be pretty spooky, bit it would not be non-local.
John Bell expressed this clearly, in a paper first published in 1981. After commenting that “those of us who are inspired by Einstein” would be happy to discover that quantum mechanics may be wrong, and that “perhaps Nature is not as queer as quantum mechanics”, he went on:
But the experimental situation is not very encouraging from this point of view. It is true that practical experiments fall far short of the ideal, because of counter inefficiencies, or analyzer inefficiencies, [or other practical difficulties]. Although there is an escape route there, it is hard for me to believe that quantum mechanics works so nicely for inefficient practical set-ups and yet is going to fail badly when sufficient refinements are made. Of more importance, in my opinion, is the complete absence of the vital time factor in existing experiments. The analyzers are not rotated during the flight of the particles. Even if one is obliged to admit some long range influence, it need not travel faster than light — and so would be much less indigestible. For me, then, it is of capital importance that Aspect is engaged in an experiment in which the time factor is introduced.
That experiment bore fruit soon after Bell highlighted its significance. But it had been a long time in the making.
Alain Aspect was born in 1947, which makes him the first significant person in this story to be younger than me (just by a year). He was brought up in the southwest of France, near Bordeaux, and had a childhood interest in physics, astronomy and science fiction. After completing high school, he studied at the École Normale Supérieure de Chachan, near Paris, and went on to the University of Orsay, completing his first postgraduate degree, roughly equivalent to an MPhil in the English-speaking world and sometimes known in France as the “little doctorate”, in 1971. Aspect then spent three years doing national service, working as a teacher in the former French colony of Cameroon. This gave him plenty of time to read and think, and most of his reading and thinking concerned quantum physics. The courses he had taken as a student in France had covered quantum mechanics from a mathematical perspective, concentrating on the equations rather than the fundamental physics, and scarcely discussing the conceptual foundations at all. But it was the physics that fascinated Aspect, and it was while in Cameroon that he read the EPR paper and realised that it contained a fundamental insight into the nature of the world. This highlights Aspect’s approach — he always went back to the sources wherever possible, studying Schrödinger’s, or Einstein’s, or Bohm’s original publications, not secondhand interpretations of what they had said. It was, however, not until he returned to France, late in 1974, that he read Bell’s paper on the implications of the EPR idea; it was, he has said “love at first sight”. Eager to make a contribution, and disappointed to find that Clauser had already carried out a test of Bell’s theorem, he resolved to tackle the locality loophole as the topic for his “big doctorate”.
Under the French system at the time, this could be a large, long-term project provided he could find a supervisor and a base from which to work. Christian Imbert and the Institute of Physics at the University of Paris-South, located at Orsay, agreed to take him on, and as a first step he visited Bell in Geneva early in 1975 to discuss the idea. Bell was enthusiastic, but warned Aspect that it would be a long job, and if things went wrong it could blight his career. In fact, it took four years to obtain funding and build the experiment, two more years to start to get meaningful results, and Aspect did not receive his big doctorate (“doctorat d’état”) until 1983. But it was worth it.
Such an epic achievement could not be carried out alone, and Aspect led a team that included Philippe Grangier, Gérard Roger and Jean Dalibard. The key improvement over earlier tests of Bell’s theorem was to find, and apply, a technique for switching the polarizing filters while the photons were in flight, so that there was no way that relevant information could be conveyed between A and B at less than light speed. To do this, they didn’t actually rotate the filters while the photons were flying through the apparatus, but switched rapidly between two different polarizers oriented at different angles, using an ingenious optical-acoustic liquid mirror.
The photons set out on their way towards the polarizing filters in the usual way, but part of the way along their journey they encounter the liquid mirror. This is simply a tank of water, into which two beams of ultrasonic sound waves can be propagated. If the sound is turned off, the photons go straight through the water and arrive at a polarizing filter set at a certain angle. If the sound is turned on, the two acoustic beams interact to create a standing wave in the water, which deflects the photons towards a second polarizing filter set at a different angle. On the other side of the experiment, the second beam of photons is subjected to similar switching, and both beams are monitored; the polarization of large numbers of photons is automatically compared with the settings of the polarizers on the other side. It is relatively simple to envisage such an experiment, but immensely difficult to put it into practice, matching up the beams and polarizers, and recording all the data automatically — which is why the first results were not obtained until 1981, and more meaningful data in 1982. But what matters is that the acoustic switching (carried out automatically, of course) occurred every 10 nanoseconds (1 ns is one billionth of a second), and it occurred after the photons had left their source. But the time taken for light to get from one side of the experiment to the other (a distance of nearly 13 metres) was 40 ns. There is no way that a message could travel from A to B quickly enough to “tell” the photons on one side of the apparatus what was happening to their partners on the other side of the apparatus, unless that information travelled faster than light. Aspect and his colleagues discovered that even under these conditions Bell’s inequality is violated. Local realism is not a good description of how the Universe works.
Adapted from my book Computing with Quantum Cats.