Richard Feynman has had a somewhat complicated relationship with Bell's Theorem; in 1964, Bell1 had shown that no local theory of classical (or realist) type could give the same results as quantum theory. It was in 1981 that Feynman wrote an extremely influential paper2 on the relationship between quantum theory and computation. One of the questions he asked was, “Can quantum systems be simulated probabilistically by a classical computer with local connections?”
Feynman's answer was in the negative, and he explained this answer by analyzing what he called the two-photon correlation experiment, which was designed to check the possibility of using hidden variables to produce the quantum mechanical results for an entangled system. Feynman explains the crucial element of his analysis that causes it to fail: it requires some probabilities to be negative. He emphasizes that the experiment has been performed and that the results agree with the quantum predictions.
What Feynman constructs is undoubtedly just Bell's Theorem. In the collection that he has edited on Feynman's work on computation,3 which includes Feynman's influential paper,4 Hey comments5 that “Only Feynman could discuss ‘hidden variables,’ the Einstein-Podolsky-Rosen paradox and produce a proof of Bell's Theorem, without mentioning John Bell.” Hey assumes that Feynman had read or heard of Bell's work, almost certainly just the barest bones of it, but had not picked up or remembered his name. Feynman must also, of course, have known that the experiments had been performed.
Hey6 remarks that Feynman “had no problem about the fact that he was sometimes recreating things that other people already knew—in fact I don't think he could learn a subject any other way than by finding out for himself.” On the other hand, Mermin7 feels sure that Feynman produced the analysis off his own bat, though he must surely have been made aware of the experiments, particularly those of Clauser.8
In any case, since what Feynman describes is indeed Bell's Theorem, it is extremely interesting that he adds that he often entertained himself by squeezing the difficulty of quantum mechanics into a smaller and smaller place, and he finds this place precisely in this analysis. Thus, Feynman's view is apparently clear—the content of Bell's Theorem is the crucial point that distinguishes classical and quantum physics.
A different point of view comes from a set of lectures9 that Feynman recorded a couple of years later, in 1983. Having explained some fundamental aspects of quantum theory, he remarks, “Bell's Theorem is a contribution to [that set of ideas], which is to point out mathematically that it has to happen. People knew it had to happen before; all he did was to demonstrate it. It is not a theorem that anybody thinks is of any particular importance. We who use quantum mechanics have been using it all the time. It is not an important theorem. It is simply a statement of something we know is true—a mathematical proof of it.”
It is interesting to consider why Feynman's views on the significance of the type of argument involved in Bell's Theorem varied so much over such a short period of time. Along these lines, it is useful to discuss Feynman's response12 to a paper of Mermin,13 which provides an extremely simple explanation of why hidden variables are not forbidden in quantum theory, but also how no-hidden-variable proofs may be constructed for systems with more than two observables, and with joint distributions.
While Mermin's efforts in this paper are mainly directed at the simplicity of the proof, he also draws attention to the theorem of Bell,1 and that of Kochen and Specker.14 (Bell himself had previously proved a result very similar to the latter.15) Mermin stresses that these theorems have additional features; in particular, Bell's Theorem “proves the nonexistence of a joint distribution for a set of observables required to have one by a common-sense notion of physical locality.”
However, Feynman's response12 focuses entirely on the simplicity of the main argument, which he welcomes in much the same terms as those of Ref. 2, and he clearly regards Mermin's paper as in the same spirit as his own previous attempts, and moving further in the same direction. In this letter, he does not refer to the work of Bell.
One will clearly recognize, along with Feynman, that from the earliest days of quantum theory the mismatch between classical and quantum theory was apparent and was much discussed. It is also almost certainly the case that, whether or not Feynman had heard a mention of the result of Bell's Theorem, he developed his own proof entirely independently.
Nevertheless, it may seem rather disappointing that Feynman apparently did not feel it necessary to acknowledge Bell's attempt at exploring the mismatch in the same terms as his own and that of Mermin. It might even be said that since Bell had recently demonstrated,15 contrary to the proof of John von Neumann16 and the general belief of the community of physicists, that hidden variables were not ruled out of quantum theory (in a paper written before Ref. 1 but unfortunately not published until two years after it), it was particularly appropriate for him to study the limitations of the use of hidden variables in Ref. 1.
I would like to thank David Mermin and an anonymous referee for helpful comments on a previous version of this letter.