Computing with Quantum Cats by John Gribbin

Author:John Gribbin
Language: eng
Format: epub, azw3
Publisher: Prometheus Books
Published: 2014-01-26T16:00:00+00:00

VON NEUMANN'S SILLY MISTAKE AND BELL'S INEQUALITY

Among the great virtues of the two scientific papers that emerged from Bell's trip to the United States were their clarity and simplicity, related to the fact that with his practical experience in particle physics Bell was able to spell out the kinds of experiments that could, in principle, be carried out to test the ideas—not that he expected, at the time, to see such experiments carried out. The first of the two papers that he wrote (but not the first to be published, as we shall see) was “On the Problem of Hidden Variables in Quantum Mechanics,” in which he analyzed the flaws in von Neumann's argument, in the “refinement” proposed by Jauch, and in a third variation on the theme. At the time, he was quite unaware of Grete Hermann's earlier work. Bell went further than Hermann, though, in not just finding the flaw in von Neumann's argument, but also (actually, at the beginning of his paper) presenting his own version of a hidden variables theory, much simpler than Bohm's model but demonstrating with equal force that the “impossible” could be done. He also made clear that non-locality (“spooky action at a distance”) was an integral part both of Bohm's model and of his own. As Bell commented in the paper, this means that these hidden variables theories (and, he suspected, all such theories) resolve the EPR puzzle in exactly the way Einstein would have liked least!

Bell completed “On the Problem of Hidden Variables in Quantum Mechanics” while at Stanford (although he mentions in the acknowledgments that “the first ideas of this paper were conceived in 1952”), and sent it off to the journal Reviews of Modern Physics in 1964. As usual, the editor of the journal sent the paper to an expert referee to assess its suitability for publication. The referee was sympathetic (it is widely thought that it was Bohm), but suggested some improvements be made before it was accepted for publication. Bell, as authors often do, made the bare minimum of changes to meet the referee's demands, and sent the paper back to the journal. Unfortunately, the revised paper was misfiled, and sometime later, thinking it had not come back, the editor wrote to Bell asking where it was. The letter went to Stanford, but by then Bell was back in England. By the time the confusion was sorted out, more than a year had passed and the paper was eventually published in 1966, after the second of Bell's great papers, the one which proved that all hidden variables theories must be non-local.

Although there is no need here to go into the details of Bell's refutation of von Neumann's argument, which is essentially the same as Hermann's, it does seem worth reiterating in Bell's own words (from an interview published in the science and science fiction magazine Omni in May 1988) how bizarre it is that people ever took it seriously: “The von Neumann proof, if you actually come to grips with it, falls apart in your hands! There is nothing to it.

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